{"math": [{"id": "002dba45", "domain": "Algebra", "skill": "Linear equations in two variables", "difficulty": "M", "type": "spr", "stimulus": "", "stem": "

Line k\n is defined by y=-173x+5. Line j\n is perpendicular to line k\n in the xy-plane. What is the slope of line j\n?

", "choices": [], "answerId": ".1764", "acceptedAnswers": [".1764", ".1765", "3/17"], "rationale": "

The correct answer is \n\t3\n\t17\n\n. It’s given that line j\n is perpendicular to line k\n in the xy-plane. This means that the slope of line j\n is the negative reciprocal of the slope of line k\n. The equation of line k\n, y=-173x+5, is written in slope-intercept form \n\ty\n\t=\n\t\n\t\t\n\t\t\tm\n\t\t\tx\n\t\t\n\t\t+\n\t\tb\n\t\n\n, where m\n is the slope of the line and b\n is the y-coordinate of the y-intercept of the line. It follows that the slope of line k\n is \n\t-\n\t\n\t\t17\n\t\t3\n\t\n\n. The negative reciprocal of a number is -1\n divided by the number. Therefore, the negative reciprocal of \n\t-\n\t\n\t\t17\n\t\t3\n\t\n\n is -1-173, or \n\t3\n\t17\n\n. Thus, the slope of line j\n is \n\t3\n\t17\n\n. Note that 3/17, .1764, .1765, and 0.176 are examples of ways to enter a correct answer.

"}, {"id": "f224df07", "domain": "Algebra", "skill": "Linear inequalities in one or two variables", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

A cargo helicopter delivers only 100-pound packages and 120-pound packages. For each delivery trip, the helicopter must carry at least 10 packages, and the total weight of the packages can be at most 1,100 pounds. What is the maximum number of 120-pound packages that the helicopter can carry per trip?

\n", "choices": [{"id": "A", "text": "

2

\n"}, {"id": "B", "text": "

4

\n"}, {"id": "C", "text": "

5

\n"}, {"id": "D", "text": "

6

\n"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. Let a equal the number of 120-pound packages, and let b equal the number of 100-pound packages. It’s given that the total weight of the packages can be at most 1,100 pounds: the inequality 120 a, + 100 b, < or equal to 1,100 represents this situation. It’s also given that the helicopter must carry at least 10 packages: the inequality a, + b, > or equal to 10 represents this situation. Values of a and b that satisfy these two inequalities represent the allowable numbers of 120-pound packages and 100-pound packages the helicopter can transport. To maximize the number of 120-pound packages, a, in the helicopter, the number of 100-pound packages, b, in the helicopter needs to be minimized. Expressing b in terms of a in the second inequality yields b > or equal to, 10 \u2212 a, so the minimum value of b is equal to 10 \u2212 a. Substituting 10 \u2212 a for b in the first inequality results in 120 a, + 100, times, open parenthesis, 10 \u2212 a, close parenthesis, < or equal to 1,100. Using the distributive property to rewrite this inequality yields 120 a, + 1,000, \u2212 100 a, < or equal to 1,100, or 20 a, + 1,000, < or equal to 1,100. Subtracting 1,000 from both sides of this inequality yields 20 a, < or equal to 100. Dividing both sides of this inequality by 20 results in a, < or equal to 5. This means that the maximum number of 120-pound packages that the helicopter can carry per trip is 5.

Choices A, B, and D are incorrect and may result from incorrectly creating or solving the system of inequalities.

\n"}, {"id": "3008cfc3", "domain": "Algebra", "skill": "Linear equations in two variables", "difficulty": "H", "type": "spr", "stimulus": "", "stem": "
\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
x\ny\n
k\n13\n
\n\tk\n\t+\n\t7\n\n-15\n
\n

The table gives the coordinates of two points on a line in the xy-plane. The y-intercept of the line is k-5,b, where k\n and b\n are constants. What is the value of b\n?

", "choices": [], "answerId": "33", "acceptedAnswers": ["33"], "rationale": "

The correct answer is 33\n. It’s given in the table that the coordinates of two points on a line in the xy-plane are (k,13) and (k+7,-15). The y-intercept is another point on the line. The slope computed using any pair of points from the line will be the same. The slope of a line, m\n, between any two points, x1,y1 and x2,y2, on the line can be calculated using the slope formula, m=y2-y1x2-x1. It follows that the slope of the line with the given points from the table, (k,13) and (k+7,-15), is m=-15-13k+7-k, which is equivalent to m=-287, or m=-4. It's given that the y-intercept of the line is (k-5,b). Substituting -4\n for m\n and the coordinates of the points (k-5,b) and (k,13) into the slope formula yields -4=13-bk-k-5, which is equivalent to -4=13-bk-k+5, or -4=13-b5. Multiplying both sides of this equation by 5\n yields -20=13-b. Subtracting 13\n from both sides of this equation yields -33=-b. Dividing both sides of this equation by -1 yields b=33. Therefore, the value of b\n is 33\n.

"}, {"id": "cb8f449f", "domain": "Algebra", "skill": "Systems of two linear equations in two variables", "difficulty": "M", "type": "mc", "stimulus": "
\n\t\n\t\t\t\n\t\t\t
one half y = 4
x minus, one half y = 2
\n", "stem": "

The system of equations above has solution (x, y). What is the value of x ?

\n", "choices": [{"id": "A", "text": "

three

 

\n"}, {"id": "B", "text": "

(7)/(2)

 

\n"}, {"id": "C", "text": "

four

 

\n"}, {"id": "D", "text": "

six

 

\n"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. Adding the corresponding sides of the two equations eliminates y and yields x = 6, as shown.

The equation one half y = 4, added to the equation x \u2212 one half y = 2, gives the equation x + 0 = 6

If (x, y) is a solution to the system, then (x, y) satisfies both equations in the system and any equation derived from them. Therefore, x = 6.

Choices A, B, and C are incorrect and may be the result of errors when solving the system.

 

\n"}, {"id": "88e13c8c", "domain": "Algebra", "skill": "Linear functions", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

The total cost f(x), in dollars, to lease a car for 36\n months from a particular car dealership is given by f(x)=36x+1,000, where x\n is the monthly payment, in dollars. What is the total cost to lease a car when the monthly payment is $400?

", "choices": [{"id": "A", "text": "

$13,400\n

"}, {"id": "B", "text": "

$13,000\n

"}, {"id": "C", "text": "

$15,400\n

"}, {"id": "D", "text": "

$37,400

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. It's given that fx is the total cost, in dollars, to lease a car from this dealership with a monthly payment of x\n dollars. Therefore, the total cost, in dollars, to lease the car when the monthly payment is $400 is represented by the value of fx when x=400. Substituting 400\n for x\n in the equation fx=36x+1,000 yields  f400=36400+1,000, or f400=15,400. Thus, when the monthly payment is $400, the total cost to lease a car is $15,400. 

\n

Choice A is incorrect and may result from conceptual or calculation errors.

\n

Choice B is incorrect and may result from conceptual or calculation errors.

\n

Choice D is incorrect and may result from conceptual or calculation errors.

"}, {"id": "3cdbf026", "domain": "Algebra", "skill": "Linear equations in two variables", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

The graph of the equation a, x + k y = 6 is a line in the xy-plane, where a and k are constants. If the line contains the points \u22122, \u22126and 0, \u22123, what is the value of k ?

\n", "choices": [{"id": "A", "text": "\n \u22122\n \n"}, {"id": "B", "text": "\n \u22121\n \n"}, {"id": "C", "text": "2\n"}, {"id": "D", "text": "3\n"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. The value of k can be found using the slope-intercept form of a linear equation, y = m x + b, where m is the slope and b is the y-coordinate of the y-intercept. The equation a, x plus, k y = 6 can be rewritten in the form y = the \u2212of (a, x,)/(k, end fraction, plus, the fraction 6 over k). One of the given points, 0, \u22123, is the y-intercept. Thus, the y-coordinate of the y-intercept \u22123 must be equal to (6)/(k). Multiplying both sides by k gives \u22123 k = 6. Dividing both sides by \u22123 gives k = \u22122.

Choices B, C, and D are incorrect and may result from errors made rewriting the given equation.

\n"}, {"id": "ff501705", "domain": "Algebra", "skill": "Systems of two linear equations in two variables", "difficulty": "H", "type": "spr", "stimulus": "", "stem": "

32y-14x=23-32y

\n

12x+32=py+92

\n

In the given system of equations, p\n is a constant. If the system has no solution, what is the value of p\n?

", "choices": [], "answerId": "6", "acceptedAnswers": ["6"], "rationale": "

The correct answer is 6\n. A system of two linear equations in two variables, x\n and y\n, has no solution if the lines represented by the equations in the xy-plane are parallel and distinct. Lines represented by equations in standard form, Ax+By=C and Dx+Ey=F, are parallel if the coefficients for x\n and y\n in one equation are proportional to the corresponding coefficients in the other equation, meaning DA=EB; and the lines are distinct if the constants are not proportional, meaning FC is not equal to DA or EB. The first equation in the given system is 32y-14x=23-32y. Multiplying each side of this equation by 12\n yields 18y-3x=8-18y. Adding \n\t18\n\ty\n\n to each side of this equation yields 36y-3x=8, or -3x+36y=8. The second equation in the given system is 12x+32=py+92. Multiplying each side of this equation by 2\n yields x+3=2py+9. Subtracting \n\t2\n\tp\n\ty\n\n from each side of this equation yields x+3-2py=9. Subtracting 3\n from each side of this equation yields x-2py=6. Therefore, the two equations in the given system, written in standard form, are -3x+36y=8 and x-2py=6. As previously stated, if this system has no solution, the lines represented by the equations in the xy-plane are parallel and distinct, meaning the proportion 1-3=-2p36, or -13=-p18, is true and the proportion 68=1-3 is not true. The proportion 68=1-3 is not true. Multiplying each side of the true proportion, -13=-p18,  by -18\n yields 6=p. Therefore, if the system has no solution, then the value of p\n is 6\n. 

"}, {"id": "8c5e6702", "domain": "Algebra", "skill": "Linear functions", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

A window repair specialist charges $220 for the first two hours of repair plus an hourly fee for each additional hour. The total cost for 5\n hours of repair is $400. Which function f\n gives the total cost, in dollars, for x\n hours of repair, where x≥2?

", "choices": [{"id": "A", "text": "

f(x)=60x+100

"}, {"id": "B", "text": "

f(x)=60x+220

"}, {"id": "C", "text": "

f(x)=80x

"}, {"id": "D", "text": "

f(x)=80x+220

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. It’s given that the window repair specialist charges $220 for the first two hours of repair plus an hourly fee for each additional hour. Let n\n represent the hourly fee for each additional hour after the first two hours. Since it’s given that x\n is the number of hours of repair, it follows that the charge generated by the hourly fee after the first two hours can be represented by the expression \n\tn\n\t\n\t\t\n\t\t\tx\n\t\t\t-\n\t\t\t2\n\t\t\n\t\n\n. Therefore, the total cost, in dollars, for x\n hours of repair is  fx=220+nx-2. It’s given that the total cost for 5\n hours of repair is $400. Substituting 5\n for x\n and 400\n for fx into the equation  fx=220+nx-2 yields 400=220+n5-2, or 400=220+3n. Subtracting 220\n from both sides of this equation yields \n\t180\n\t=\n\t\n\t\t3\n\t\tn\n\t\n\n. Dividing both sides of this equation by 3\n yields \n\tn\n\t=\n\t60\n\n. Substituting 60\n for n\n in the equation  fx=220+nx-2 yields  fx=220+60x-2, which is equivalent to  fx=220+60x-120, or  fx=60x+100. Therefore, the total cost, in dollars, for x\n hours of repair is  fx=60x+100.

\n

Choice B is incorrect. This function represents the total cost, in dollars, for x\n hours of repair where the specialist charges $340, rather than $220, for the first two hours of repair.

\n

Choice C is incorrect. This function represents the total cost, in dollars, for x\n hours of repair where the specialist charges $160, rather than $220, for the first two hours of repair, and an hourly fee of $80, rather than $60, after the first two hours.

\n

Choice D is incorrect. This function represents the total cost, in dollars, for x\n hours of repair where the specialist charges $380, rather than $220, for the first two hours of repair, and an hourly fee of $80, rather than $60, after the first two hours.

"}, {"id": "2937ef4f", "domain": "Algebra", "skill": "Linear equations in one variable", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

Hector used a tool called an auger to remove corn from a storage bin at a constant rate. The bin contained 24,000 bushels of corn when Hector began to use the auger. After 5 hours of using the auger, 19,350 bushels of corn remained in the bin. If the auger continues to remove corn at this rate, what is the total number of hours Hector will have been using the auger when 12,840 bushels of corn remain in the bin?

\n", "choices": [{"id": "A", "text": "

  3

\n"}, {"id": "B", "text": "

  7

\n"}, {"id": "C", "text": "

  8

\n"}, {"id": "D", "text": "

12

\n"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. After using the auger for 5 hours, Hector had removed 24,000 – 19,350 = 4,650 bushels of corn from the storage bin. During the 5-hour period, the auger removed corn from the bin at a constant rate of (4,650)/(5 = 930) bushels per hour. Assuming the auger continues to remove corn at this rate, after x hours it will have removed 930x bushels of corn. Because the bin contained 24,000 bushels of corn when Hector started using the auger, the equation 24,000 – 930x = 12,840 can be used to find the number of hours, x, Hector will have been using the auger when 12,840 bushels of corn remain in the bin. Subtracting 12,840 from both sides of this equation and adding 930x to both sides of the equation yields 11,160 = 930x. Dividing both sides of this equation by 930 yields x = 12. Therefore, Hector will have been using the auger for 12 hours when 12,840 bushels of corn remain in the storage bin.

\n Choice A is incorrect. Three hours after Hector began using the auger, 24,000 – 3(930) = 21,210 bushels of corn remained, not 12,840. Choice B is incorrect. Seven hours after Hector began using the auger, 24,000 – 7(930) = 17,490 bushels of corn will remain, not 12,840. Choice C is incorrect. Eight hours after Hector began using the auger, 24,000 – 8(930) = 16,560 bushels of corn will remain, not 12,840.

\n"}, {"id": "548a4929", "domain": "Algebra", "skill": "Linear functions", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

The function h\n is defined by hx=4x+28. The graph of y=hx in the xy-plane has an x-intercept at a,0 and a y-intercept at 0,b, where a\n and b\n are constants. What is the value of \n\ta\n\t+\n\tb\n\n?

", "choices": [{"id": "A", "text": "

21\n

"}, {"id": "B", "text": "

28\n

"}, {"id": "C", "text": "

32\n

"}, {"id": "D", "text": "

35\n

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. The x-intercept of a graph in the xy-plane is the point on the graph where \n\ty\n\t=\n\t0\n\n. It's given that function h\n is defined by hx=4x+28. Therefore, the equation representing the graph of y=hx is \n\ty\n\t=\n\t\n\t\t\n\t\t\t4\n\t\t\tx\n\t\t\n\t\t+\n\t\t28\n\t\n\n. Substituting 0\n for y\n in the equation \n\ty\n\t=\n\t\n\t\t\n\t\t\t4\n\t\t\tx\n\t\t\n\t\t+\n\t\t28\n\t\n\n yields \n\t0\n\t=\n\t\n\t\t\n\t\t\t4\n\t\t\tx\n\t\t\n\t\t+\n\t\t28\n\t\n\n. Subtracting 28\n from both sides of this equation yields \n\t-28\n\t=\n\t\n\t\t4\n\t\tx\n\t\n\n. Dividing both sides of this equation by 4\n yields \n\t-7\n\t=\n\tx\n\n. Therefore, the x-intercept of the graph of y=hx in the xy-plane is -7,0. It's given that the x-intercept of the graph of y=hx is a,0. Therefore, \n\ta\n\t=\n\t-7\n\n. The y-intercept of a graph in the xy-plane is the point on the graph where \n\tx\n\t=\n\t0\n\n. Substituting 0\n for x\n in the equation \n\ty\n\t=\n\t\n\t\t\n\t\t\t4\n\t\t\tx\n\t\t\n\t\t+\n\t\t28\n\t\n\n yields y=40+28, or \n\ty\n\t=\n\t28\n\n. Therefore, the y-intercept of the graph of y=hx in the xy-plane is 0,28. It's given that the y-intercept of the graph of y=hx is 0,b. Therefore, \n\tb\n\t=\n\t28\n\n. If \n\ta\n\t=\n\t-7\n\n and \n\tb\n\t=\n\t28\n\n, then the value of \n\ta\n\t+\n\tb\n\n is -7+28, or 21\n.

\n

Choice B is incorrect. This is the value of b\n, not \n\ta\n\t+\n\tb\n\n.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

\n

Choice D is incorrect. This is the value of \n\t\n\t\t-\n\t\ta\n\t\n\t+\n\tb\n\n, not \n\ta\n\t+\n\tb\n\n.

"}, {"id": "9bbce683", "domain": "Algebra", "skill": "Linear equations in two variables", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "
\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
x\ny\n
18\n130\n
23\n160\n
26\n178\n
\n

For line h\n, the table shows three values of x\n and their corresponding values of y\n. Line k\n is the result of translating line h\n down 5\n units in the xy-plane. What is the x-intercept of line k\n?

", "choices": [{"id": "A", "text": "

-263,0

"}, {"id": "B", "text": "

-92,0

"}, {"id": "C", "text": "

-113,0

"}, {"id": "D", "text": "

-176,0

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. The equation of line h\n can be written in slope-intercept form \n\ty\n\t=\n\t\n\t\t\n\t\t\tm\n\t\t\tx\n\t\t\n\t\t+\n\t\tb\n\t\n\n, where m\n is the slope of the line and 0,b is the y-intercept of the line. It’s given that line h\n contains the points 18,130, 23,160, and 26,178. Therefore, its slope m\n can be found as 160-13023-18, or 6\n. Substituting 6\n for m\n in the equation \n\ty\n\t=\n\t\n\t\t\n\t\t\tm\n\t\t\tx\n\t\t\n\t\t+\n\t\tb\n\t\n\n yields \n\ty\n\t=\n\t\n\t\t\n\t\t\t6\n\t\t\tx\n\t\t\n\t\t+\n\t\tb\n\t\n\n. Substituting 130\n for y\n and 18\n for x\n in this equation yields 130=6(18)+b, or 130=108+b. Subtracting 108\n from both sides of this equation yields \n\t22\n\t=\n\tb\n\n. Substituting 22\n for b\n in \n\ty\n\t=\n\t\n\t\t\n\t\t\t6\n\t\t\tx\n\t\t\n\t\t+\n\t\tb\n\t\n\n yields \n\ty\n\t=\n\t\n\t\t\n\t\t\t6\n\t\t\tx\n\t\t\n\t\t+\n\t\t22\n\t\n\n. Since line k\n is the result of translating line h\n down 5\n units, an equation of line k\n is y=6x+22-5, or \n\ty\n\t=\n\t\n\t\t\n\t\t\t6\n\t\t\tx\n\t\t\n\t\t+\n\t\t17\n\t\n\n. Substituting 0\n for y\n in this equation yields \n\t0\n\t=\n\t\n\t\t\n\t\t\t6\n\t\t\tx\n\t\t\n\t\t+\n\t\t17\n\t\n\n. Solving this equation for x\n yields x=-176. Therefore, the x-intercept of line k\n is -176,0.

\n

Choice A is incorrect and may result from conceptual or calculation errors.

\n

Choice B is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

"}, {"id": "2b15d65f", "domain": "Algebra", "skill": "Linear functions", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

An economist modeled the demand Q for a certain product as a linear function of the selling price P. The demand was 20,000 units when the selling price was $40 per unit, and the demand was 15,000 units when the selling price was $60 per unit. Based on the model, what is the demand, in units, when the selling price is $55 per unit?

\n", "choices": [{"id": "A", "text": "

16,250

\n"}, {"id": "B", "text": "

16,500

\n"}, {"id": "C", "text": "

16,750

\n"}, {"id": "D", "text": "

17,500

\n"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. Let the economist’s model be the linear function Q = m P + b, where Q is the demand, P is the selling price, m is the slope of the line, and b is the y-coordinate of the y-intercept of the line in the xy-plane, where y = Q. Two pairs of the selling price P and the demand Q are given. Using the coordinate pairs P, Q, two points that satisfy the function are 40, 20,000 and 60, 15,000. The slope m of the function can be found using the formula m = (Q sub 2, \u2212 Q sub 1)/(P sub 2, \u2212 P sub 1, end fraction). Substituting the given values into this formula yields m = (15,000 \u2212 20,000)/(60 \u2212 40, end fraction), or  m = \u2212250. Therefore, Q = \u2212250 P + b. The value of b can be found by substituting one of the points into the function. Substituting the values of P and Q from the point 40, 20,000 yields 20,000 = \u2212250 \u00d7 40, + b, or 20,000 = \u221210,000 + b. Adding 10,000 to both sides of this equation yields b = 30,000. Therefore, the linear function the economist used as the model is Q = \u2212250 P + 30,000. Substituting 55 for P yields Q = \u2212250 \u00d7 55, + 30,000 = 16,250. It follows that when the selling price is $55 per unit, the demand is 16,250 units.

Choices B, C, and D are incorrect and may result from calculation or conceptual errors.

 

\n"}, {"id": "686b7244", "domain": "Algebra", "skill": "Linear equations in two variables", "difficulty": "H", "type": "spr", "stimulus": "", "stem": "

A certain apprentice has enrolled in 85\n hours of training courses. The equation \n\t\n\t\t\n\t\t\t10\n\t\t\tx\n\t\t\n\t\t+\n\t\t\n\t\t\t15\n\t\t\ty\n\t\t\n\t\n\t=\n\t85\n\n represents this situation, where x\n is the number of on-site training courses and y\n is the number of online training courses this apprentice has enrolled in. How many more hours does each online training course take than each on-site training course?

", "choices": [], "answerId": "5", "acceptedAnswers": ["5"], "rationale": "

The correct answer is 5\n. It's given that the equation \n\t\n\t\t\n\t\t\t10\n\t\t\tx\n\t\t\n\t\t+\n\t\t\n\t\t\t15\n\t\t\ty\n\t\t\n\t\n\t=\n\t85\n\n represents the situation, where x\n is the number of on-site training courses, y\n is the number of online training courses, and 85\n is the total number of hours of training courses the apprentice has enrolled in. Therefore, \n\t10\n\tx\n\n represents the number of hours the apprentice has enrolled in on-site training courses, and \n\t15\n\ty\n\n represents the number of hours the apprentice has enrolled in online training courses. Since x\n is the number of on-site training courses and y\n is the number of online training courses the apprentice has enrolled in, 10\n is the number of hours each on-site course takes and 15\n is the number of hours each online course takes. Subtracting these numbers gives 15-10, or 5\n more hours each online training course takes than each on-site training course.

"}, {"id": "b86123af", "domain": "Algebra", "skill": "Systems of two linear equations in two variables", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

Hiro and Sofia purchased shirts and pants from a store. The price of each shirt purchased was the same and the price of each pair of pants purchased was the same. Hiro purchased 4 shirts and 2 pairs of pants for $86, and Sofia purchased 3 shirts and 5 pairs of pants for $166. Which of the following systems of linear equations represents the situation, if x represents the price, in dollars, of each shirt and y represents the price, in dollars, of each pair of pants?

\n", "choices": [{"id": "A", "text": "

\n 4 x + 2 y = 86, ; 3 x + 5 y = 166\n

\n"}, {"id": "B", "text": "

\n 4 x + 3 y = 86, ; 2 x + 5 y = 166\n

\n"}, {"id": "C", "text": "

\n 4 x + 2 y = 166, ; 3 x + 5 y = 86\n

\n"}, {"id": "D", "text": "

\n 4 x + 3 y = 166, ; 2 x + 5 y = 86\n

\n"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. Hiro purchased 4 shirts and each shirt cost x dollars, so he spent a total of 4x dollars on shirts. Likewise, Hiro purchased 2 pairs of pants, and each pair of pants cost y dollars, so he spent a total of 2y dollars on pants. Therefore, the total amount that Hiro spent was 4x + 2y. Since Hiro spent $86 in total, this can be modeled by the equation 4x + 2y = 86. Using the same reasoning, Sofia bought 3 shirts at x dollars each and 5 pairs of pants at y dollars each, so she spent a total of 3x + 5y dollars on shirts and pants. Since Sofia spent $166 in total, this can be modeled by the equation 3x + 5y = 166.

Choice B is incorrect and may be the result of switching the number of shirts Sofia purchased with the number of pairs of pants Hiro purchased. Choice C is incorrect and may be the result of switching the total price each person paid. Choice D is incorrect and may be the result of switching the total price each person paid as well as switching the number of shirts Sofia purchased with the number of pairs of pants Hiro purchased.

\n"}, {"id": "ee846db7", "domain": "Algebra", "skill": "Linear equations in two variables", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

A store sells two different-sized containers of a certain Greek yogurt. The store’s sales of this Greek yogurt totaled 1,277.94\n dollars last month. The equation \n\t\n\t\t\n\t\t\t5.48\n\t\t\tx\n\t\t\n\t\t+\n\t\t\n\t\t\t7.30\n\t\t\ty\n\t\t\n\t\n\t=\n\t1,277.94\n\n represents this situation, where x\n is the number of smaller containers sold and y\n is the number of larger containers sold. According to the equation, which of the following represents the price, in dollars, of each smaller container?

", "choices": [{"id": "A", "text": "

5.48\n

"}, {"id": "B", "text": "

\n\t7.30\n\ty\n\n

"}, {"id": "C", "text": "

7.30\n

"}, {"id": "D", "text": "

\n\t5.48\n\tx\n\n

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. It's given that the store's sales of a certain Greek yogurt totaled 1,277.94\n dollars last month. It's also given that the equation 5.48x+7.30y=1,277.94 represents this situation, where x\n is the number of smaller containers sold and y\n is the number of larger containers sold. Since x\n represents the number of smaller containers of yogurt sold, the expression \n\t5.48\n\tx\n\n represents the total sales, in dollars, from smaller containers of yogurt. This means that x\n smaller containers of yogurt were sold at a price of 5.48\n dollars each. Therefore, according to the equation, 5.48\n represents the price, in dollars, of each smaller container.

\n

Choice B is incorrect. This expression represents the total sales, in dollars, from selling y\n larger containers of yogurt.

\n

Choice C is incorrect. This value represents the price, in dollars, of each larger container of yogurt.

\n

Choice D is incorrect. This expression represents the total sales, in dollars, from selling x\n smaller containers of yogurt.

"}, {"id": "5b8a8475", "domain": "Algebra", "skill": "Linear equations in two variables", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

Line k\n is defined by \n\ty\n\t=\n\t\n\t\t\n\t\t\t3\n\t\t\tx\n\t\t\n\t\t+\n\t\t15\n\t\n\n. Line j\n is perpendicular to line k\n in the xy-plane. What is the slope of line j\n?

", "choices": [{"id": "A", "text": "

\n\t-\n\t\n\t\t1\n\t\t3\n\t\n\n

"}, {"id": "B", "text": "

\n\t-\n\t\n\t\t1\n\t\t12\n\t\n\n

"}, {"id": "C", "text": "

\n\t-\n\t\n\t\t1\n\t\t18\n\t\n\n

"}, {"id": "D", "text": "

\n\t-\n\t\n\t\t1\n\t\t45\n\t\n\n

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. It's given that line j\n is perpendicular to line k\n in the xy-plane. It follows that the slope of line j\n is the opposite reciprocal of the slope of line k\n. The equation for line k\n is written in slope-intercept form \n\ty\n\t=\n\t\n\t\t\n\t\t\tm\n\t\t\tx\n\t\t\n\t\t+\n\t\tb\n\t\n\n, where m\n is the slope of the line and b\n is the y-coordinate of the y-intercept of the line. It follows that the slope of line k\n is 3\n. The opposite reciprocal of a number is -1\n divided by the number. Thus, the opposite reciprocal of 3\n is -13. Therefore, the slope of line j\n is \n\t-\n\t\n\t\t1\n\t\t3\n\t\n\n.

\n

Choice B is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

\n

Choice D is incorrect and may result from conceptual or calculation errors.

"}, {"id": "cfe67646", "domain": "Algebra", "skill": "Linear inequalities in one or two variables", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

The point (8,2) in the xy-plane is a solution to which of the following systems of inequalities?

", "choices": [{"id": "A", "text": "

x>0

\n

y>0

"}, {"id": "B", "text": "

x>0

\n

y<0

"}, {"id": "C", "text": "

x<0

\n

y>0

"}, {"id": "D", "text": "

x<0

\n

y<0

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. The given point, 8,2, is located in the first quadrant in the xy-plane. The system of inequalities in choice A represents all the points in the first quadrant in the xy-plane. Therefore, 8,2 is a solution to the system of inequalities in choice A.

\n

Alternate approach: Substituting 8\n for x\n in the first inequality in choice A, x>0, yields 8>0, which is true. Substituting 2\n for y\n in the second inequality in choice A, y>0, yields 2>0, which is true. Since the coordinates of the point 8,2 make the inequalities x>0 and y>0 true, the point 8,2 is a solution to the system of inequalities consisting of x>0 and y>0.

\n

Choice B is incorrect. This system of inequalities represents all the points in the fourth quadrant, not the first quadrant, in the xy-plane.

\n

Choice C is incorrect. This system of inequalities represents all the points in the second quadrant, not the first quadrant, in the xy-plane.

\n

Choice D is incorrect. This system of inequalities represents all the points in the third quadrant, not the first quadrant, in the xy-plane.

"}, {"id": "608eeb6e", "domain": "Algebra", "skill": "Systems of two linear equations in two variables", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

\n\t\n\t\t5\n\t\tx\n\t\n\t=\n\t15\n\n

\n

\n\t\n\t\t\n\t\t\t-\n\t\t\t4\n\t\t\tx\n\t\t\n\t\t+\n\t\ty\n\t\n\t=\n\t-2\n\n

\n

The solution to the given system of equations is x,y. What is the value of \n\tx\n\t+\n\ty\n\n?

", "choices": [{"id": "A", "text": "

-17\n

"}, {"id": "B", "text": "

-13\n

"}, {"id": "C", "text": "

13\n

"}, {"id": "D", "text": "

17\n

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. Adding the second equation of the given system to the first equation yields 5x+-4x+y=15+-2, which is equivalent to x+y=13. So the value of x+y is 13\n.

\n

Choice A is incorrect and may result from conceptual or calculation errors.

\n

Choice B is incorrect. This is the value of -(x+y).

\n

Choice D is incorrect and may result from conceptual or calculation errors.

"}, {"id": "be9cb6a2", "domain": "Algebra", "skill": "Linear functions", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

The cost of renting a backhoe for up to 10\n days is $270\n for the first day and $135\n for each additional day. Which of the following equations gives the cost y\n, in dollars, of renting the backhoe for x\n days, where x\n is a positive integer and x≤10?

", "choices": [{"id": "A", "text": "

\n\ty\n\t=\n\t\n\t\t\n\t\t\t270\n\t\t\tx\n\t\t\n\t\t-\n\t\t135\n\t\n\n

"}, {"id": "B", "text": "

\n\ty\n\t=\n\t\n\t\t\n\t\t\t270\n\t\t\tx\n\t\t\n\t\t+\n\t\t135\n\t\n\n

"}, {"id": "C", "text": "

\n\ty\n\t=\n\t\n\t\t\n\t\t\t135\n\t\t\tx\n\t\t\n\t\t+\n\t\t270\n\t\n\n

"}, {"id": "D", "text": "

\n\ty\n\t=\n\t\n\t\t\n\t\t\t135\n\t\t\tx\n\t\t\n\t\t+\n\t\t135\n\t\n\n

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. It's given that the cost of renting a backhoe for up to 10\n days is $270\n for the first day and $135\n for each additional day. Therefore, the cost y\n, in dollars, for x\n days, where x≤10, is the sum of the cost for the first day, $270\n, and the cost for the additional \n\tx\n\t-\n\t1\n\n days, $135x-1. It follows that y=270+135x-1, which is equivalent to y=270+135x-135, or y=135x+135.

\n

Choice A is incorrect. This equation represents a situation where the cost of renting a backhoe is $135\n for the first day and $270\n for each additional day.

\n

Choice B is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

"}, {"id": "097e10f5", "domain": "Algebra", "skill": "Linear equations in one variable", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

What value of p\n satisfies the equation \n\t\n\t\t\n\t\t\t5\n\t\t\tp\n\t\t\n\t\t+\n\t\t180\n\t\n\t=\n\t250\n\n?

", "choices": [{"id": "A", "text": "

14\n

"}, {"id": "B", "text": "

65\n

"}, {"id": "C", "text": "

86\n

"}, {"id": "D", "text": "

250\n

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. Subtracting 180\n from both sides of the given equation yields \n\t\n\t\t5\n\t\tp\n\t\n\t=\n\t70\n\n. Dividing both sides of this equation by 5\n yields \n\tp\n\t=\n\t14\n\n. Therefore, the value of p\n that satisfies the equation 5p+180=250 is 14\n.

\n

Choice B is incorrect. This value of p\n satisfies the equation 5p+180=505.

\n

Choice C is incorrect. This value of p\n satisfies the equation 5p+180=610.

\n

Choice D is incorrect. This value of p\n satisfies the equation 5p+180=1,430.

"}, {"id": "84664a7c", "domain": "Algebra", "skill": "Linear functions", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

The front of a roller-coaster car is at the bottom of a hill and is 15 feet above the ground. If the front of the roller-coaster car rises at a constant rate of 8 feet per second, which of the following equations gives the height h, in feet, of the front of the roller-coaster car s seconds after it starts up the hill?

\n", "choices": [{"id": "A", "text": "

\n h = 8 s, + 15\n

\n"}, {"id": "B", "text": "

\n h = 15 s, + (335)/(8)\n

\n"}, {"id": "C", "text": "

\n h = 8 s, + (335)/(15)\n

\n"}, {"id": "D", "text": "

\n h = 15 s, + 8\n

\n"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. It’s given that the front of the roller-coaster car starts rising when it’s 15 feet above the ground. This initial height of 15 feet can be represented by a constant term, 15, in an equation. Each second, the front of the roller-coaster car rises 8 feet, which can be represented by 8s. Thus, the equation h = 8 s + 15 gives the height, in feet, of the front of the roller-coaster car s seconds after it starts up the hill.

Choices B and C are incorrect and may result from conceptual errors in creating a linear equation. Choice D is incorrect and may result from switching the rate at which the roller-coaster car rises with its initial height.

\n"}, {"id": "b0fc3166", "domain": "Algebra", "skill": "Systems of two linear equations in two variables", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n

\n

The graph of a system of linear equations is shown. What is the solution x,y to the system?

", "choices": [{"id": "A", "text": "

0,3

"}, {"id": "B", "text": "

1,3

"}, {"id": "C", "text": "

2,3

"}, {"id": "D", "text": "

3,3

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. The solution to this system of linear equations is represented by the point that lies on both lines shown, or the point of intersection of the two lines. According to the graph, the point of intersection occurs when \n\tx\n\t=\n\t2\n\n and \n\ty\n\t=\n\t3\n\n, or at the point 2,3. Therefore, the solution x,y to the system is 2,3.

\n

Choice A is incorrect and may result from conceptual or calculation errors.

\n

Choice B is incorrect and may result from conceptual or calculation errors.

\n

Choice D is incorrect and may result from conceptual or calculation errors.

"}, {"id": "db422e7f", "domain": "Algebra", "skill": "Linear equations in two variables", "difficulty": "H", "type": "spr", "stimulus": "", "stem": "

Line p\n is defined by 4y+8x=6. Line r\n is perpendicular to line p\n in the xy-plane. What is the slope of line r\n?

", "choices": [], "answerId": ".5", "acceptedAnswers": [".5", "1/2"], "rationale": "

The correct answer is 12. For an equation in slope-intercept form y=mx+b, m\n represents the slope of the line in the xy-plane defined by this equation. It's given that line p\n is defined by 4y+8x=6. Subtracting 8x from both sides of this equation yields 4y=-8x+6. Dividing both sides of this equation by 4\n yields y=-84x+64, or y=-2x+32. Thus, the slope of line p\n is -2\n. If line r\n is perpendicular to line p\n, then the slope of line r\n is the negative reciprocal of the slope of line p\n. The negative reciprocal of -2\n is -1-2=12. Note that 1/2 and .5 are examples of ways to enter a correct answer.

"}, {"id": "01682aa5", "domain": "Algebra", "skill": "Linear equations in two variables", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

Line p\n is defined by 2y+18x=9. Line r\n is perpendicular to line p\n in the xy-plane. What is the slope of line r\n?

", "choices": [{"id": "A", "text": "

-9\n

"}, {"id": "B", "text": "

\n\t-\n\t\n\t\t1\n\t\t9\n\t\n\n

"}, {"id": "C", "text": "

\n\t1\n\t9\n\n

"}, {"id": "D", "text": "

9\n

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. It’s given that line r\n is perpendicular to line p\n in the xy-plane. This means that the slope of line r\n is the negative reciprocal of the slope of line p\n. If the equation for line p\n is rewritten in slope-intercept form \n\ty\n\t=\n\t\n\t\t\n\t\t\tm\n\t\t\tx\n\t\t\n\t\t+\n\t\tb\n\t\n\n, where m\n and b\n are constants, then m\n is the slope of the line and 0,b is its y-intercept. Subtracting \n\t18\n\tx\n\n from both sides of the equation 2y+18x=9 yields \n\t\n\t\t2\n\t\ty\n\t\n\t=\n\t\n\t\t\n\t\t\t-\n\t\t\t18\n\t\t\tx\n\t\t\n\t\t+\n\t\t9\n\t\n\n. Dividing both sides of this equation by 2\n yields \n\ty\n\t=\n\t\n\t\t\n\t\t\t-\n\t\t\t9\n\t\t\tx\n\t\t\n\t\t+\n\t\t\n\t\t\t9\n\t\t\t2\n\t\t\n\t\n\n. It follows that the slope of line p\n is -9\n. The negative reciprocal of a number is -1\n divided by the number. Therefore, the negative reciprocal of -9\n is -1-9, or \n\t1\n\t9\n\n. Thus, the slope of line r\n is \n\t1\n\t9\n\n.

\n

Choice A is incorrect. This is the slope of line p\n, not line r\n.

\n

Choice B is incorrect. This is the reciprocal, not the negative reciprocal, of the slope of line p\n.

\n

Choice D is incorrect. This is the negative, not the negative reciprocal, of the slope of line p\n.

"}, {"id": "45cfb9de", "domain": "Algebra", "skill": "Linear inequalities in one or two variables", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

Adam’s school is a 20-minute walk or a 5-minute bus ride away from his house. The bus runs once every 30 minutes, and the number of minutes, w, that Adam waits for the bus varies between 0 and 30. Which of the following inequalities gives the values of w for which it would be faster for Adam to walk to school?

\n", "choices": [{"id": "A", "text": "w \u2212 5, < 20\n"}, {"id": "B", "text": "w \u2212 5, > 20\n"}, {"id": "C", "text": "w + 5, < 20\n"}, {"id": "D", "text": "w + 5, > 20\n"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. It is given that w is the number of minutes that Adam waits for the bus. The total time it takes Adam to get to school on a day he takes the bus is the sum of the minutes, w, he waits for the bus and the 5 minutes the bus ride takes; thus, this time, in minutes, is w + 5. It is also given that the total amount of time it takes Adam to get to school on a day that he walks is 20 minutes. Therefore, w + 5 > 20 gives the values of w for which it would be faster for Adam to walk to school.

Choices A and B are incorrect because w – 5 is not the total length of time for Adam to wait for and then take the bus to school. Choice C is incorrect because the inequality should be true when walking 20 minutes is faster than the time it takes Adam to wait for and ride the bus, not less.

\n"}, {"id": "06fc1726", "domain": "Algebra", "skill": "Linear functions", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

If f is the function defined by f(x) = (2 x \u2212 1)/(3), what is the value of f(5) ?

\n", "choices": [{"id": "A", "text": "

\n 4 thirds\n

\n"}, {"id": "B", "text": "

\n 7 thirds\n

\n"}, {"id": "C", "text": "

3

\n"}, {"id": "D", "text": "

9

\n"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. If f(x) = (2 x \u2212 1)/(3), then f(5) = (2 \u00d7 5, \u2212 1)/(3, which = (with numerator 10 \u2212 1, and denominator 3, which = the fraction 9)/(3, which = 3)).

Choice A is incorrect and may result from not multiplying x by 2 in the numerator. Choice B is incorrect and may result from dividing 2x by 3 and then subtracting 1. Choice D is incorrect and may result from evaluating only the numerator 2x – 1.

\n"}, {"id": "6863c7ce", "domain": "Algebra", "skill": "Linear functions", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

\n\td\n\t=\n\t\n\t\t16\n\t\tt\n\t\n\n

\n

The given equation represents the distance d\n, in inches, where t\n represents the number of seconds since an object started moving. Which of the following is the best interpretation of 16\n in this context?

", "choices": [{"id": "A", "text": "

The object moved a total of 16\n inches.

"}, {"id": "B", "text": "

The object moved a total of \n\t16\n\tt\n\n inches.

"}, {"id": "C", "text": "

The object is moving at a rate of 16\n inches per second.

"}, {"id": "D", "text": "

The object is moving at a rate of \n\t1\n\t16\n\n inches per second.

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. It’s given that in the equation \n\td\n\t=\n\t\n\t\t16\n\t\tt\n\t\n\n, d\n represents the distance, in inches, and t\n represents the number of seconds since an object started moving. In this equation, t\n is being multiplied by 16\n. This means that the object’s distance increases by 16\n inches each second. Therefore, the best interpretation of 16\n in this context is that the object is moving at a rate of 16\n inches per second.

\n

Choice A is incorrect and may result from conceptual errors.

\n

Choice B is incorrect. This is the best interpretation of \n\t16\n\tt\n\n, rather than 16\n, in this context.

\n

Choice D is incorrect and may result from conceptual errors.

"}, {"id": "a5834ea4", "domain": "Algebra", "skill": "Linear functions", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

f(x)=39

\n

For the given linear function f\n, which table gives three values of x\n and their corresponding values of fx? 

", "choices": [{"id": "A", "text": "
\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
x\nfx
0\n0\n
1\n0\n
2\n0\n
"}, {"id": "B", "text": "
\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
x\nfx
0\n39\n
1\n39\n
2\n39\n
"}, {"id": "C", "text": "
\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
x\nfx
0\n0\n
1\n39\n
2\n78\n
"}, {"id": "D", "text": "
\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
x\nfx
0\n39\n
1\n0\n
2\n-39\n
"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. For the given linear function f\n, fx must equal 39\n for all values of x\n. Of the given choices, only choice B gives three values of x\n and their corresponding values of fx for the given linear function f\n.

\n

Choice A is incorrect and may result from conceptual errors.

\n

Choice C is incorrect and may result from conceptual errors.

\n

Choice D is incorrect and may result from conceptual errors.

"}, {"id": "0b332f00", "domain": "Algebra", "skill": "Linear functions", "difficulty": "E", "type": "spr", "stimulus": "", "stem": "

The function g\n is defined by gx=6x. For what value of x\n is g(x)=54\n?

", "choices": [], "answerId": "9", "acceptedAnswers": ["9"], "rationale": "

The correct answer is 9\n. It’s given that gx=6x. Substituting 54\n for gx in the given function yields \n\t54\n\t=\n\t\n\t\t6\n\t\tx\n\t\n\n. Dividing both sides of this equation by 6\n yields \n\tx\n\t=\n\t9\n\n. Therefore, the value of x\n when gx=54 is 9\n.

"}, {"id": "349a5bc1", "domain": "Algebra", "skill": "Linear equations in one variable", "difficulty": "E", "type": "spr", "stimulus": "", "stem": "

\n\t\n\t\t\n\t\t\t4\n\t\t\tx\n\t\t\n\t\t+\n\t\t5\n\t\n\t=\n\t165\n\n

\n

What is the solution to the given equation?

", "choices": [], "answerId": "40", "acceptedAnswers": ["40"], "rationale": "

The correct answer is 40\n. Subtracting 5\n from both sides of the given equation yields 4x=160. Dividing both sides of this equation by 4\n yields x=40. Therefore, the solution to the given equation is 40\n.

"}, {"id": "bf4a8b6a", "domain": "Algebra", "skill": "Systems of two linear equations in two variables", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

A company that provides whale-watching tours takes groups of 21\n people at a time. The company’s revenue is 80\n dollars per adult and 60\n dollars per child. If the company’s revenue for one group consisting of adults and children was 1,440\n dollars, how many people in the group were children?

", "choices": [{"id": "A", "text": "

3\n

"}, {"id": "B", "text": "

9\n

"}, {"id": "C", "text": "

12\n

"}, {"id": "D", "text": "

18\n

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. Let x\n represent the number of children in a whale-watching tour group. Let y\n represent the number of adults in this group. Because it's given that 21\n people are in a group and the group consists of adults and children, it must be true that x+y=21. Since the company's revenue is 60\n dollars per child, the total revenue from x\n children in this group was \n\t60\n\tx\n\n dollars. Since the company's revenue is 80\n dollars per adult, the total revenue from y\n adults in this group was \n\t80\n\ty\n\n dollars. Because it's given that the total revenue for this group was 1,440\n dollars, it must be true that 60x+80y=1,440. The equations x+y=21 and 60x+80y=1,440 form a linear system of equations that can be solved to find the value of x\n, which represents the number of children in the group, using the elimination method. Multiplying both sides of the equation x+y=21 by 80\n yields 80x+80y=1,680. Subtracting 60x+80y=1,440 from 80x+80y=1,680 yields (80x+80y)-(60x+80y)=1,680-1,440, which is equivalent to 80x-60x+80y-80y=240, or 20x=240. Dividing both sides of this equation by 20\n yields x=12. Therefore, 12\n people in the group were children.

\n

Choice A is incorrect and may result from conceptual or calculation errors.

\n

Choice B is incorrect. This is the number of adults in the group, not the number of children in the group.

\n

Choice D is incorrect and may result from conceptual or calculation errors.

"}, {"id": "7e3f8363", "domain": "Algebra", "skill": "Linear functions", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

In the xy-plane, the graph of the linear function f\n contains the points 0,3 and 7,31. Which equation defines f\n, where y=fx?

", "choices": [{"id": "A", "text": "

fx=28x+34

"}, {"id": "B", "text": "

fx=3x+38

"}, {"id": "C", "text": "

fx=4x+3

"}, {"id": "D", "text": "

fx=7x+3

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. In the xy-plane, an equation of the graph of a linear function can be written in the form fx=mx+b, where m\n represents the slope and 0,b represents the y-intercept of the graph of y=fx. It’s given that the graph of the linear function f\n, where y=fx, in the xy-plane contains the point 0,3. Thus, \n\tb\n\t=\n\t3\n\n. The slope of the graph of a line containing any two points x1,y1 and x2,y2 can be found using the slope formula, m=y2-y1x2-x1. Since it’s given that the graph of the linear function f\n contains the points 0,3 and 7,31, it follows that the slope of the graph of the line containing these points is m=31-37-0, or \n\tm\n\t=\n\t4\n\n. Substituting 4\n for m\n and 3\n for b\n in fx=mx+b yields fx=4x+3.

\n

Choice A is incorrect. This function represents a graph with a slope of 28\n and a y-intercept of 0,34.

\n

Choice B is incorrect. This function represents a graph with a slope of 3\n and a y-intercept of 0,38.

\n

Choice D is incorrect. This function represents a graph with a slope of 7\n and a y-intercept of 0,3.

"}, {"id": "0eae6be1", "domain": "Algebra", "skill": "Linear functions", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

The number y\n is 84\n less than the number x\n. Which equation represents the relationship between x\n and y\n?

", "choices": [{"id": "A", "text": "

\n\ty\n\t=\n\t\n\t\tx\n\t\t+\n\t\t84\n\t\n\n

"}, {"id": "B", "text": "

y=184x

"}, {"id": "C", "text": "

\n\ty\n\t=\n\t\n\t\t84\n\t\tx\n\t\n\n

"}, {"id": "D", "text": "

\n\ty\n\t=\n\t\n\t\tx\n\t\t-\n\t\t84\n\t\n\n

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. It’s given that the number y\n is 84\n less than the number x\n. A number that's 84\n less than the number x\n is equivalent to 84\n subtracted from the number x\n, or \n\tx\n\t-\n\t84\n\n. Therefore, the equation \n\ty\n\t=\n\t\n\t\tx\n\t\t-\n\t\t84\n\t\n\n represents the relationship between x\n and y\n.

\n

Choice A is incorrect and may result from conceptual errors.

\n

Choice B is incorrect and may result from conceptual errors.

\n

Choice C is incorrect and may result from conceptual errors.

"}, {"id": "447fa970", "domain": "Algebra", "skill": "Linear functions", "difficulty": "E", "type": "spr", "stimulus": "", "stem": "

The function f\n is defined by the equation fx=7x+2. What is the value of fx when \n\tx\n\t=\n\t4\n\n?

", "choices": [], "answerId": "30", "acceptedAnswers": ["30"], "rationale": "

The correct answer is 30\n. The value of fx when x=4 can be found by substituting 4\n for x\n in the given equation fx= 7x+2. This yields f4=74+2, or f4=30. Therefore, when x=4, the value of fx is 30\n.

"}, {"id": "0dd6227f", "domain": "Algebra", "skill": "Systems of two linear equations in two variables", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

At how many points do the graphs of the equations \n\ty\n\t=\n\t\n\t\tx\n\t\t+\n\t\t20\n\t\n\n and \n\ty\n\t=\n\t\n\t\t8\n\t\tx\n\t\n\n intersect in the xy-plane?

", "choices": [{"id": "A", "text": "

0\n

"}, {"id": "B", "text": "

1\n

"}, {"id": "C", "text": "

2\n

"}, {"id": "D", "text": "

8\n

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. Each given equation is written in slope-intercept form, \n\ty\n\t=\n\t\n\t\t\n\t\t\tm\n\t\t\tx\n\t\t\n\t\t+\n\t\tb\n\t\n\n, where m\n is the slope and 0,b is the y-intercept of the graph of the equation in the xy-plane. The graphs of two lines that have different slopes will intersect at exactly one point. The graph of the first equation is a line with slope 1\n. The graph of the second equation is a line with slope 8\n. Since the graphs are lines with different slopes, they will intersect at exactly one point.

\n

Choice A is incorrect because two graphs of linear equations have 0\n intersection points only if they are parallel and therefore have the same slope.

\n

Choice C is incorrect because two graphs of linear equations in the xy-plane can have only 0\n, 1\n, or infinitely many points of intersection.

\n

Choice D is incorrect because two graphs of linear equations in the xy-plane can have only 0\n, 1\n, or infinitely many points of intersection.

"}, {"id": "b1228811", "domain": "Algebra", "skill": "Linear inequalities in one or two variables", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

Marisa needs to hire at least 10 staff members for an upcoming project. The staff members will be made up of junior directors, who will be paid $640 per week, and senior directors, who will be paid $880 per week. Her budget for paying the staff members is no more than $9,700 per week. She must hire at least 3 junior directors and at least 1 senior director. Which of the following systems of inequalities represents the conditions described if x is the number of junior directors and y is the number of senior directors?

\n", "choices": [{"id": "A", "text": "640 x, + 880 y, > or equal to 9,700; x + y < or equal to 10; x > or equal to 3; y > or equal to 1\n"}, {"id": "B", "text": "640 x, + 880 y, < or equal to 9,700; x + y > or equal to 10; x > or equal to 3; y > or equal to 1\n"}, {"id": "C", "text": "640 x, + 880 y, > or equal to 9,700; x + y > or equal to 10; x < or equal to 3; y < or equal to 1\n"}, {"id": "D", "text": "640 x, + 880 y, < or equal to 9,700; x + y < or equal to 10; x < or equal to 3; y < or equal to 1\n"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. Marisa will hire x junior directors and y senior directors. Since she needs to hire at least 10 staff members, x + y, > or equal to 10. Each junior director will be paid $640 per week, and each senior director will be paid $880 per week. Marisa’s budget for paying the new staff is no more than $9,700 per week; in terms of x and y, this condition is 640 x + 880 y, < or equal to 9,700. Since Marisa must hire at least 3 junior directors and at least 1 senior director, it follows that x > or equal to 3 and y > or equal to 1. All four of these conditions are represented correctly in choice B.

Choices A and C are incorrect. For example, the first condition, 640 x + 880 y, > or equal to 9,700, in each of these options implies that Marisa can pay the new staff members more than her budget of $9,700. Choice D is incorrect because Marisa needs to hire at least 10 staff members, not at most 10 staff members, as the inequality x + y, < or equal to 10 implies.

\n"}, {"id": "6105234d", "domain": "Algebra", "skill": "Linear equations in one variable", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

John paid a total of $165\n for a microscope by making a down payment of $37\n plus p\n monthly payments of $16\n each. Which of the following equations represents this situation?

", "choices": [{"id": "A", "text": "

\n\t\n\t\t\n\t\t\t16\n\t\t\tp\n\t\t\n\t\t-\n\t\t37\n\t\n\t=\n\t165\n\n

"}, {"id": "B", "text": "

\n\t\n\t\t\n\t\t\t37\n\t\t\tp\n\t\t\n\t\t-\n\t\t16\n\t\n\t=\n\t165\n\n

"}, {"id": "C", "text": "

\n\t\n\t\t\n\t\t\t16\n\t\t\tp\n\t\t\n\t\t+\n\t\t37\n\t\n\t=\n\t165\n\n

"}, {"id": "D", "text": "

\n\t\n\t\t\n\t\t\t37\n\t\t\tp\n\t\t\n\t\t+\n\t\t16\n\t\n\t=\n\t165\n\n

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. It’s given that John made a $16 payment each month for p\n months. The total amount of these payments can be represented by the expression \n\t16\n\tp\n\n. The down payment can be added to that amount to find the total amount John paid, yielding the expression \n\t\n\t\t16\n\t\tp\n\t\n\t+\n\t37\n\n. It’s given that John paid a total of $165. Therefore, the expression for the total amount John paid can be set equal to that amount, yielding the equation \n\t\n\t\t\n\t\t\t16\n\t\t\tp\n\t\t\n\t\t+\n\t\t37\n\t\n\t=\n\t165\n\n.

\n

Choice A is incorrect and may result from conceptual or calculation errors.

\n

Choice B is incorrect and may result from conceptual or calculation errors.

\n

Choice D is incorrect and may result from conceptual or calculation errors.

"}, {"id": "7efe5495", "domain": "Algebra", "skill": "Systems of two linear equations in two variables", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

\n\ty\n\t=\n\t\n\t\t3\n\t\tx\n\t\n\n

\n

\n\t\n\t\t\n\t\t\t2\n\t\t\tx\n\t\t\n\t\t+\n\t\ty\n\t\n\t=\n\t12\n\n

\n

The solution to the given system of equations is x,y. What is the value of \n\t5\n\tx\n\n?

", "choices": [{"id": "A", "text": "

24\n

"}, {"id": "B", "text": "

15\n

"}, {"id": "C", "text": "

12\n

"}, {"id": "D", "text": "

5\n

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. It's given by the first equation in the system that y=3x. Substituting \n\t3\n\tx\n\n for y\n in the equation 2x+y=12 yields 2x+3x=12, or 5x=12. 

\n

Choice A is incorrect and may result from conceptual or calculation errors.

\n

Choice B is incorrect and may result from conceptual or calculation errors.

\n

Choice D is incorrect and may result from conceptual or calculation errors.

"}, {"id": "2c121b25", "domain": "Algebra", "skill": "Linear inequalities in one or two variables", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

Valentina bought two containers of beads. In the first container 30% of the beads are red, and in the second container 70% of the beads are red. Together, the containers have at least 400 red beads. Which inequality shows this relationship, where x is the total number of beads in the first container and y is the total number of beads in the second container?

\n", "choices": [{"id": "A", "text": "0 point 3 x, plus, 0 point 7 y, > or equal to, 400\n"}, {"id": "B", "text": "0 point 7 x, plus, 0 point 3 y, < or equal to, 400\n"}, {"id": "C", "text": "(x)/(3, end fraction, plus, the fraction y over 7, end fraction, < or equal to, 400)\n"}, {"id": "D", "text": "30 x, plus, 70 y, > or equal to, 400\n"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. It is given that x is the total number of beads in the first container and that 30% of those beads are red; therefore, the expression 0.3x represents the number of red beads in the first container. It is given that y is the total number of beads in the second container and that 70% of those beads are red; therefore, the expression 0.7y represents the number of red beads in the second container. It is also given that, together, the containers have at least 400 red beads, so the inequality that shows this relationship is 0.3x + 0.7y ≥ 400.

Choice B is incorrect because it represents the containers having a total of at most, rather than at least, 400 red beads. Choice C is incorrect and may be the result of misunderstanding how to represent a percentage of beads in each container. Also, the inequality shows the containers having a combined total of at most, rather than at least, 400 red beads. Choice D is incorrect because the percentages were not converted to decimals.

\n"}, {"id": "83f2c3bf", "domain": "Algebra", "skill": "Linear equations in two variables", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

\n\ty\n\t=\n\t\n\t\tx\n\t\t+\n\t\t4\n\t\n\n

\n

Which table gives three values of x\n and their corresponding values of y\n for the given equation?

", "choices": [{"id": "A", "text": "
\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
x\ny\n
0\n4\n
1\n5\n
2\n6\n
"}, {"id": "B", "text": "
\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
x\ny\n
0\n6\n
1\n5\n
2\n4\n
"}, {"id": "C", "text": "
\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
x\ny\n
0\n2\n
1\n1\n
2\n0\n
"}, {"id": "D", "text": "
\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
x\ny\n
0\n0\n
1\n1\n
2\n2\n
"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. Substituting 0\n for x\n into the given equation yields y=0+4, or \n\ty\n\t=\n\t4\n\n. Therefore, when \n\tx\n\t=\n\t0\n\n, the corresponding value of y\n for the given equation is 4\n. Substituting 1\n for x\n into the given equation yields y=1+4, or \n\ty\n\t=\n\t5\n\n. Therefore, when \n\tx\n\t=\n\t1\n\n, the corresponding value of y\n for the given equation is 5\n. Substituting 2\n for x\n into the given equation yields y=2+4, or \n\ty\n\t=\n\t6\n\n. Therefore, when \n\tx\n\t=\n\t2\n\n, the corresponding value of y\n for the given equation is 6\n. Of the choices given, only the table in choice A gives these three values of x\n and their corresponding values of y\n for the given equation.

\n

Choice B is incorrect. This table gives three values of x\n and their corresponding values of y\n for the equation \n\ty\n\t=\n\t\n\t\t\n\t\t\t-\n\t\t\tx\n\t\t\n\t\t+\n\t\t6\n\t\n\n.

\n

Choice C is incorrect. This table gives three values of x\n and their corresponding values of y\n for the equation \n\ty\n\t=\n\t\n\t\t\n\t\t\t-\n\t\t\tx\n\t\t\n\t\t+\n\t\t2\n\t\n\n.

\n

Choice D is incorrect. This table gives three values of x\n and their corresponding values of y\n for the equation \n\ty\n\t=\n\tx\n\n.

"}, {"id": "c50ede6d", "domain": "Algebra", "skill": "Linear inequalities in one or two variables", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

The total cost, in dollars, to rent a surfboard consists of a $25\n service fee and a $10\n per hour rental fee. A person rents a surfboard for t\n hours and intends to spend a maximum of $75\n to rent the surfboard. Which inequality represents this situation?

", "choices": [{"id": "A", "text": "

10t≤75

"}, {"id": "B", "text": "

10+25t≤75

"}, {"id": "C", "text": "

25t≤75

"}, {"id": "D", "text": "

25+10t≤75

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. The cost of the rental fee depends on the number of hours the surfboard is rented. Multiplying t\n hours by 10\n dollars per hour yields a rental fee of \n\t10\n\tt\n\n dollars. The total cost of the rental consists of the rental fee plus the 25\n dollar service fee, which yields a total cost of 25+10t dollars. Since the person intends to spend a maximum of 75\n dollars to rent the surfboard, the total cost must be at most 75\n dollars. Therefore, the inequality 25+10t\u226475 represents this situation.

\n

Choice A is incorrect. This represents a situation where the rental fee, not the total cost, is at most 75\n dollars.

\n

Choice B is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

"}, {"id": "c1bd5301", "domain": "Algebra", "skill": "Linear functions", "difficulty": "M", "type": "spr", "stimulus": "", "stem": "

A model predicts that a certain animal weighed 241\n pounds when it was born and that the animal gained 3\n pounds per day in its first year of life. This model is defined by an equation in the form fx=a+bx, where fx is the predicted weight, in pounds, of the animal x\n days after it was born, and a\n and b\n are constants. What is the value of a\n?

", "choices": [], "answerId": "241", "acceptedAnswers": ["241"], "rationale": "

The correct answer is 241\n. For a certain animal, it's given that a model predicts the animal weighed 241\n pounds when it was born and gained 3\n pounds per day in its first year of life. It's also given that this model is defined by an equation in the form fx=a+bx, where fx is the predicted weight, in pounds, of the animal x\n days after it was born, and a\n and b\n are constants. It follows that a\n represents the predicted weight, in pounds, of the animal when it was born and b\n represents the predicted rate of weight gain, in pounds per day, in its first year of life. Thus, the value of a\n is 241\n.

"}, {"id": "b23bba4c", "domain": "Algebra", "skill": "Linear equations in two variables", "difficulty": "E", "type": "mc", "stimulus": "
\n

\n 3 a + 4 b = 25\n

\n
\n", "stem": "

A shipping company charged a customer $25 to ship some small boxes and some large boxes. The equation above represents the relationship between a, the number of small boxes, and b, the number of large boxes, the customer had shipped. If the customer had 3 small boxes shipped, how many large boxes were shipped?

\n", "choices": [{"id": "A", "text": "

3

\n"}, {"id": "B", "text": "

4

\n"}, {"id": "C", "text": "

5

\n"}, {"id": "D", "text": "

6

\n"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. It’s given that a represents the number of small boxes and b represents the number of large boxes the customer had shipped. If the customer had 3 small boxes shipped, then a = 3. Substituting 3 for a in the equation 3 a, + 4 b = 25 yields 3 \u00d7 3, + 4 b = 25 or 9 + 4 b = 25. Subtracting 9 from both sides of the equation yields 4 b = 16. Dividing both sides of this equation by 4 yields b = 4. Therefore, the customer had 4 large boxes shipped.

Choices A, C, and D are incorrect. If the number of large boxes shipped is 3, then b = 3. Substituting 3 for b in the given equation yields 3 a, plus, 4 \u00d7 3 = 25 or 3 a, + 12 = 25. Subtracting 12 from both sides of the equation and then dividing by 3 yields a = thirteen thirds. However, it’s given that the number of small boxes shipped, a, is 3, not thirteen thirds, so b cannot equal 3. Similarly, if b = 5 or b = 6, then a = five thirds or a = one third, respectively, which is also not true.

\n"}, {"id": "24854644", "domain": "Algebra", "skill": "Linear equations in two variables", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

What is the equation of the line that passes through the point 0,5 and is parallel to the graph of \n\ty\n\t=\n\t\n\t\t\n\t\t\t7\n\t\t\tx\n\t\t\n\t\t+\n\t\t4\n\t\n\n in the xy-plane?

", "choices": [{"id": "A", "text": "

\n\ty\n\t=\n\t\n\t\t5\n\t\tx\n\t\n\n

"}, {"id": "B", "text": "

\n\ty\n\t=\n\t\n\t\t\n\t\t\t7\n\t\t\tx\n\t\t\n\t\t+\n\t\t5\n\t\n\n

"}, {"id": "C", "text": "

\n\ty\n\t=\n\t\n\t\t7\n\t\tx\n\t\n\n

"}, {"id": "D", "text": "

\n\ty\n\t=\n\t\n\t\t\n\t\t\t5\n\t\t\tx\n\t\t\n\t\t+\n\t\t7\n\t\n\n

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. The equation of a line in the xy-plane can be written in slope-intercept form \n\ty\n\t=\n\t\n\t\t\n\t\t\tm\n\t\t\tx\n\t\t\n\t\t+\n\t\tb\n\t\n\n, where m\n is the slope of the line and 0,b is its y-intercept. It’s given that the line passes through the point 0,5. Therefore, \n\tb\n\t=\n\t5\n\n. It’s also given that the line is parallel to the graph of \n\ty\n\t=\n\t\n\t\t\n\t\t\t7\n\t\t\tx\n\t\t\n\t\t+\n\t\t4\n\t\n\n, which means the line has the same slope as the graph of \n\ty\n\t=\n\t\n\t\t\n\t\t\t7\n\t\t\tx\n\t\t\n\t\t+\n\t\t4\n\t\n\n. The slope of the graph of \n\ty\n\t=\n\t\n\t\t\n\t\t\t7\n\t\t\tx\n\t\t\n\t\t+\n\t\t4\n\t\n\n is 7\n. Therefore, \n\tm\n\t=\n\t7\n\n. Substituting 7\n for m\n and 5\n for b\n in the equation \n\ty\n\t=\n\t\n\t\t\n\t\t\tm\n\t\t\tx\n\t\t\n\t\t+\n\t\tb\n\t\n\n yields \n\ty\n\t=\n\t\n\t\t\n\t\t\t7\n\t\t\tx\n\t\t\n\t\t+\n\t\t5\n\t\n\n.

\n

Choice A is incorrect. The graph of this equation passes through the point 0,0, not 0,5, and has a slope of 5\n, not 7\n.

\n

Choice C is incorrect. The graph of this equation passes through the point 0,0, not 0,5.

\n

Choice D is incorrect. The graph of this equation passes through the point 0,7, not 0,5, and has a slope of 5\n, not 7\n.

"}, {"id": "71189542", "domain": "Algebra", "skill": "Systems of two linear equations in two variables", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

A group of 202 people went on an overnight camping trip, taking 60 tents with them. Some of the tents held 2 people each, and the rest held 4 people each. Assuming all the tents were filled to capacity and every person got to sleep in a tent, exactly how many of the tents were 2-person tents?

\n", "choices": [{"id": "A", "text": "

30

\n"}, {"id": "B", "text": "

20

\n"}, {"id": "C", "text": "

19

\n"}, {"id": "D", "text": "

18

\n"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. Let x represent the number of 2-person tents and let y represent the number of 4-person tents. It is given that the total number of tents was 60 and the total number of people in the group was 202. This situation can be expressed as a system of two equations, x + y = 60 and 2 x + 4 y = 202. The first equation can be rewritten as y = \u2212x + 60. Substituting \u2212x + 60 for y in the equation 2 x + 4 y = 202 yields 2 x plus, 4 times, open parenthesis, \u2212x + 60, close parenthesis = 202. Distributing and combining like terms gives \u22122 x + 240 = 202. Subtracting 240 from both sides of \u22122 x + 240 = 202 and then dividing both sides by \u22122 gives x = 19. Therefore, the number of 2-person tents is 19.

Alternate approach: If each of the 60 tents held 4 people, the total number of people that could be accommodated in tents would be 240. However, the actual number of people who slept in tents was 202. The difference of 38 accounts for the 2-person tents. Since each of these tents holds 2 people fewer than a 4-person tent, thirty eight halves = 19 gives the number of 2-person tents.

Choice A is incorrect. This choice may result from assuming exactly half of the tents hold 2 people. If that were true, then the total number of people who slept in tents would be 2 \u00d7 30, plus, 4 \u00d7 30 = 180; however, the total number of people who slept in tents was 202, not 180. Choice B is incorrect. If 20 tents were 2-person tents, then the remaining 40 tents would be 4-person tents. Since all the tents were filled to capacity, the total number of people who slept in tents would be 2 \u00d7 20, plus, 4 \u00d7 40 = 40 + 160, which = 200; however, the total number of people who slept in tents was 202, not 200. Choice D is incorrect. If 18 tents were 2-person tents, then the remaining 42 tents would be 4-person tents. Since all the tents were filled to capacity, the total number of people who slept in tents would be 2 \u00d7 18, plus, 4 \u00d7 42 = 36 + 168, which = 204; however, the total number of people who slept in tents was 202, not 204.

\n"}, {"id": "dba8d38a", "domain": "Algebra", "skill": "Systems of two linear equations in two variables", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

A petting zoo sells two types of tickets. The standard ticket, for admission only, costs $5. The premium ticket, which includes admission and food to give to the animals, costs $12. One Saturday, the petting zoo sold a total of 250 tickets and collected a total of $2,300 from ticket sales. Which of the following systems of equations can be used to find the number of standard tickets, s, and premium tickets, p, sold on that Saturday?

\n", "choices": [{"id": "A", "text": "

\n Equation 1: s + p = 250. Equation 2: 5 s + 12 p = 2,300.\n

\n"}, {"id": "B", "text": "

\n Equation 1: s + p = 250. Equation 2: 12 s + 5 p = 2,300.\n

\n"}, {"id": "C", "text": "

\n Equation 1: 5 s + 12 p = 250. Equation 2: s + p = 2,300.\n

\n"}, {"id": "D", "text": "

\n Equation 1: 12 s + 5 p = 250. Equation 2: s + p = 2,300.\n

\n"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. It’s given that the petting zoo sells two types of tickets, standard and premium, and that s represents the number of standard tickets sold and p represents the number of premium tickets sold. It’s also given that the petting zoo sold 250 tickets on one Saturday; thus, s + p = 250. It’s also given that each standard ticket costs $5 and each premium ticket costs $12. Thus, the amount collected in ticket sales can be represented by 5 s for standard tickets and 12 p for premium tickets. On that Saturday the petting zoo collected a total of $2,300 from ticket sales; thus, 5 s + 12 p = 2,300. These two equations are correctly represented in choice A.

Choice B is incorrect. The second equation in the system represents the cost per standard ticket as $12, not $5, and the cost per premium ticket as $5, not $12. Choices C and D are incorrect. The equations represent the total collected from standard and premium ticket sales as $250, not $2,300, and the total number of standard and premium tickets sold as $2,300, not $250. Additionally, the first equation in choice D represents the cost per standard ticket as $12, not $5, and the cost per premium ticket as $5, not $12.

\n"}, {"id": "64c85440", "domain": "Algebra", "skill": "Linear inequalities in one or two variables", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

In North America, the standard width of a parking space is at least 7.5 feet and no more than 9.0 feet. A restaurant owner recently resurfaced the restaurant’s parking lot and wants to determine the number of parking spaces, n, in the parking lot that could be placed perpendicular to a curb that is 135 feet long, based on the standard width of a parking space. Which of the following describes all the possible values of n ?

\n", "choices": [{"id": "A", "text": "

\n 18 < or equal to n, which < or equal to 135\n

\n"}, {"id": "B", "text": "

\n 7 point 5 < or equal to n, which < or equal to 9\n

\n"}, {"id": "C", "text": "

\n 15 < or equal to n, which < or equal to 135\n

\n"}, {"id": "D", "text": "

\n 15 < or equal to n, which < or equal to 18\n

\n"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. Placing the parking spaces with the minimum width of 7.5 feet gives the maximum possible number of parking spaces. Thus, the maximum number that can be placed perpendicular to a 135-foot-long curb is 135 over 7 point 5 = 18. Placing the parking spaces with the maximum width of 9 feet gives the minimum number of parking spaces. Thus, the minimum number that can be placed perpendicular to a 135-foot-long curb is 135 over 9 = 15. Therefore, if n is the number of parking spaces in the lot, the range of possible values for n is 15 < or equal to n, which < or equal to 18.

Choices A and C are incorrect. These choices equate the length of the curb with the maximum possible number of parking spaces. Choice B is incorrect. This is the range of possible values for the width of a parking space instead of the range of possible values for the number of parking spaces.

\n"}, {"id": "87322577", "domain": "Algebra", "skill": "Linear equations in two variables", "difficulty": "E", "type": "mc", "stimulus": "
\n

\n x + y = 75\n

\n
\n", "stem": "

The equation above relates the number of minutes, x, Maria spends running each day and the number of minutes, y, she spends biking each day. In the equation, what does the number 75 represent?

\n", "choices": [{"id": "A", "text": "

The number of minutes spent running each day

\n"}, {"id": "B", "text": "

The number of minutes spent biking each day

\n"}, {"id": "C", "text": "

The total number of minutes spent running and biking each day

\n"}, {"id": "D", "text": "

The number of minutes spent biking for each minute spent running

\n"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. Maria spends x minutes running each day and y minutes biking each day. Therefore, x + y represents the total number of minutes Maria spent running and biking each day. Because x + y = 75, it follows that 75 is the total number of minutes that Maria spent running and biking each day.

Choices A and B are incorrect. The number of minutes Maria spent running each day is represented by x and need not be 75. Similarly, the number of minutes that Maria spends biking each day is represented by y and need not be 75. The number of minutes Maria spends running each day and biking each day may vary; however, the total number of minutes she spends each day on these activities is constant and equal to 75. Choice D is incorrect. The number of minutes Maria spent biking for each minute spent running cannot be determined from the information provided.

\n"}, {"id": "5c94e6fa", "domain": "Algebra", "skill": "Linear equations in one variable", "difficulty": "E", "type": "spr", "stimulus": "", "stem": "

3x+21=3x+k

\n

In the given equation, k\n is a constant. The equation has infinitely many solutions. What is the value of k\n?

", "choices": [], "answerId": "21", "acceptedAnswers": ["21"], "rationale": "

The correct answer is 21\n. It's given that the equation \n\t\n\t\t\n\t\t\t3\n\t\t\tx\n\t\t\n\t\t+\n\t\t21\n\t\n\t=\n\t\n\t\t\n\t\t\t3\n\t\t\tx\n\t\t\n\t\t+\n\t\tk\n\t\n\n has infinitely many solutions. If an equation in one variable has infinitely many solutions, then the equation is true for any value of the variable. Subtracting \n\t3\n\tx\n\n from both sides of the given equation yields \n\tk\n\t=\n\t21\n\n. Since this equation must be true for any value of x\n, the value of k\n is 21\n.

"}, {"id": "7a5a74a6", "domain": "Algebra", "skill": "Linear equations in one variable", "difficulty": "M", "type": "mc", "stimulus": "
\n

\n 3 times, open parenthesis, 2 x \u2212 6, close parenthesis, \u2212 11 = 4 times, open parenthesis, x \u2212 3, close parenthesis, + 6\n

\n
\n", "stem": "

If x is the solution to the equation above, what is the value of x \u2212 3 ?

\n", "choices": [{"id": "A", "text": "23 over 2\n"}, {"id": "B", "text": "17 over 2\n"}, {"id": "C", "text": "15 over 2\n"}, {"id": "D", "text": "negative, 15 over 2\n"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. Because 2 is a factor of both 2 x and 6, the expression 2 x \u2212 6 can be rewritten as 2 times, open parenthesis, x \u2212 3, close parenthesis. Substituting 2 times, open parenthesis, x \u2212 3, close parenthesis for 2 x \u2212 6 on the left-hand side of the given equation yields 3 \u00d7 2, times, open parenthesis, x \u2212 3, close parenthesis, \u2212 11 = 4 times, open parenthesis, x \u2212 3, close parenthesis, + 6, or 6 times, open parenthesis, x \u2212 3, close parenthesis, \u2212 11 = 4 times, open parenthesis, x \u2212 3, close parenthesis, + 6. Subtracting 4 times, open parenthesis, x \u2212 3, close parenthesis from both sides of this equation yields 2 times, open parenthesis, x \u2212 3, close parenthesis, \u2212 11 = 6. Adding 11 to both sides of this equation yields 2 times, open parenthesis, x \u2212 3, close parenthesis = 17. Dividing both sides of this equation by 2 yields x \u2212 3 = (17)/(2).

Alternate approach: Distributing 3 to the quantity 2 x \u2212 6 on the left-hand side of the given equation and distributing 4 to the quantity x \u2212 3 on the right-hand side yields 6 x \u2212 18, \u2212 11 = 4 x \u2212 12, + 6, or 6 x \u2212 29 = 4 x \u2212 6. Subtracting 4 x from both sides of this equation yields 2 x \u2212 29 = \u22126. Adding 29 to both sides of this equation yields 2 x = 23. Dividing both sides of this equation by 2 yields x = (23)/(2). Therefore, the value of x \u2212 3 is (23)/(2, end fraction, \u2212 3), or (17)/(2).

Choice A is incorrect. This is the value of x, not x \u2212 3. Choices C and D are incorrect. If the value of x \u2212 3 is (15)/(2) or \u2212of (15)/(2), it follows that the value of x is (21)/(2) or \u2212of (9)/(2), respectively. However, solving the given equation for x yields x = (23)/(2). Therefore, the value of x \u2212 3 can’t be (15)/(2) or \u2212of (15)/(2).

\n"}, {"id": "b7e6394d", "domain": "Algebra", "skill": "Linear equations in one variable", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

Alan drives an average of 100 miles each week. His car can travel an average of 25 miles per gallon of gasoline. Alan would like to reduce his weekly expenditure on gasoline by $5. Assuming gasoline costs $4 per gallon, which equation can Alan use to determine how many fewer average miles, m, he should drive each week?

\n", "choices": [{"id": "A", "text": "

(25)/(4, end fraction, \u00d7 m = 95)

\n"}, {"id": "B", "text": "

(25)/(4, end fraction, \u00d7 m = 5)

\n"}, {"id": "C", "text": "

(4)/(25, end fraction, \u00d7 m = 95)

\n"}, {"id": "D", "text": "

(4)/(25, end fraction, \u00d7 m = 5)

\n"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. Since gasoline costs $4 per gallon, and since Alan’s car travels an average of 25 miles per gallon, the expression 4 over 25 gives the cost, in dollars per mile, to drive the car. Multiplying 4 over 25 by m gives the cost for Alan to drive m miles in his car. Alan wants to reduce his weekly spending by $5, so setting 4 over 25m equal to 5 gives the number of miles, m, by which he must reduce his driving.

Choices A, B, and C are incorrect. Choices A and B transpose the numerator and the denominator in the fraction. The fraction 25 over 4 would result in the unit miles per dollar, but the question requires a unit of dollars per mile. Choices A and C set the expression equal to 95 instead of 5, a mistake that may result from a misconception that Alan wants to reduce his driving by 5 miles each week; instead, the question says he wants to reduce his weekly expenditure by $5.

 

\n"}, {"id": "95cad55f", "domain": "Algebra", "skill": "Linear inequalities in one or two variables", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

A laundry service is buying detergent and fabric softener from its supplier. The supplier will deliver no more than 300 pounds in a shipment. Each container of detergent weighs 7.35  pounds, and each container of fabric softener weighs 6.2 pounds. The service wants to buy at least twice as many containers of detergent as containers of fabric softener. Let d represent the number of containers of detergent, and let s represent the number of containers of fabric softener, where d and s are nonnegative integers. Which of the following systems of inequalities best represents this situation?

\n", "choices": [{"id": "A", "text": "7 point three five d, plus, 6 point 2 s, < or equal to 300; d > or equal to 2 s\n"}, {"id": "B", "text": "7 point three five d, plus, 6 point 2 s, < or equal to 300; 2 d > or equal to s\n"}, {"id": "C", "text": "14 point 7 d, plus, 6 point 2 s, < or equal to 300; d > or equal to 2 s\n"}, {"id": "D", "text": "14 point 7 d, plus, 6 point 2 s, < or equal to 300; 2 d > or equal to s\n"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

\n \n

Choice A is correct. The number of containers in a shipment must have a weight less than or equal to 300 pounds. The total weight, in pounds, of detergent and fabric softener that the supplier delivers can be expressed as the weight of each container multiplied by the number of each type of container, which is 7.35d for detergent and 6.2s for fabric softener. Since this total cannot exceed 300 pounds, it follows that 7 point 3 5 d, + 6 point 2 s, < or equal to 300. Also, since the laundry service wants to buy at least twice as many containers of detergent as containers of fabric softener, the number of containers of detergent should be greater than or equal to two times the number of containers of fabric softener. This can be expressed by the inequality d > or equal to 2 s.

Choice B is incorrect because it misrepresents the relationship between the numbers of each container that the laundry service wants to buy. Choice C is incorrect because the first inequality of the system incorrectly doubles the weight per container of detergent. The weight of each container of detergent is 7.35, not 14.7 pounds. Choice D is incorrect because it doubles the weight per container of detergent and transposes the relationship between the numbers of containers.

\n"}, {"id": "bf36c815", "domain": "Algebra", "skill": "Linear functions", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

The function g is defined by g(x) = \u2212x, + 8. What is the value of g(0)?

\n", "choices": [{"id": "A", "text": "

\n \u22128\n

\n"}, {"id": "B", "text": "

\n 0\n

\n"}, {"id": "C", "text": "

\n 4\n

\n"}, {"id": "D", "text": "

\n 8\n

\n"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. The value of g(0) is found by substituting 0 for x in the function g. This yields g(0) = \u22120, + 8, which can be rewritten as g(0) = 8.

Choice A is incorrect and may result from misinterpreting the equation as g(x) = x plus, \u22128 instead of g(x) = \u2212x plus, \u22128. Choice B is incorrect. This is the value of x, not g(x). Choice C is incorrect and may result from calculation errors.

\n"}, {"id": "968e9e51", "domain": "Algebra", "skill": "Linear inequalities in one or two variables", "difficulty": "M", "type": "mc", "stimulus": "
\n\t

Inequality 1: y < or equal to x.

\n\n\t

Inequality 2: y < or equal to \u2212x.

\n
\n", "stem": "

Which of the following ordered pairs x, y is a solution to the system of inequalities above?

\n", "choices": [{"id": "A", "text": "

1, 0

\n"}, {"id": "B", "text": "

\u22121, 0

\n"}, {"id": "C", "text": "

0, 1

\n"}, {"id": "D", "text": "

0, \u22121

\n"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. The solutions to the given system of inequalities is the set of all ordered pairs x, y that satisfy both inequalities in the system. For an ordered pair to satisfy the inequality y < or equal to x, the value of the ordered pair’s y-coordinate must be less than or equal to the value of the ordered pair’s x-coordinate. This is true of the ordered pair 0, \u22121, because \u22121 < or equal to 0. To satisfy the inequality y < or equal to \u2212x, the value of the ordered pair’s y-coordinate must be less than or equal to the value of the additive inverse of the ordered pair’s x-coordinate. This is also true of the ordered pair 0, \u22121. Because 0 is its own additive inverse, \u22121 < or equal to the negative(0) is the same as \u22121 < or equal to 0. Therefore, the ordered pair 0, \u22121 is a solution to the given system of inequalities.

Choice A is incorrect. This ordered pair satisfies only the inequality y < or equal to x in the given system, not both inequalities. Choice B incorrect. This ordered pair satisfies only the inequality y < or equal to \u2212x in the system, but not both inequalities. Choice C is incorrect. This ordered pair satisfies neither inequality.

 

\n"}, {"id": "9f3cb472", "domain": "Algebra", "skill": "Linear equations in two variables", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

Line t\n in the xy-plane has a slope of \n\t-\n\t\n\t\t1\n\t\t3\n\t\n\n and passes through the point 9,10. Which equation defines line t\n?

", "choices": [{"id": "A", "text": "

\n\ty\n\t=\n\t\n\t\t\n\t\t\t13\n\t\t\tx\n\t\t\n\t\t-\n\t\t\n\t\t\t1\n\t\t\t3\n\t\t\n\t\n\n

"}, {"id": "B", "text": "

\n\ty\n\t=\n\t\n\t\t\n\t\t\t9\n\t\t\tx\n\t\t\n\t\t+\n\t\t10\n\t\n\n

"}, {"id": "C", "text": "

\n\ty\n\t=\n\t\n\t\t\n\t\t\t-\n\t\t\t\n\t\t\t\tx\n\t\t\t\t3\n\t\t\t\n\t\t\n\t\t+\n\t\t10\n\t\n\n

"}, {"id": "D", "text": "

\n\ty\n\t=\n\t\n\t\t\n\t\t\t-\n\t\t\t\n\t\t\t\tx\n\t\t\t\t3\n\t\t\t\n\t\t\n\t\t+\n\t\t13\n\t\n\n

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. The equation that defines line t\n in the xy-plane can be written in slope-intercept form \n\ty\n\t=\n\t\n\t\t\n\t\t\tm\n\t\t\tx\n\t\t\n\t\t+\n\t\tb\n\t\n\n, where m\n is the slope of line t\n and 0,b is its y-intercept. It’s given that line t\n has a slope of \n\t-\n\t\n\t\t1\n\t\t3\n\t\n\n. Therefore, \n\tm\n\t=\n\t\n\t\t-\n\t\t\n\t\t\t1\n\t\t\t3\n\t\t\n\t\n\n. Substituting \n\t-\n\t\n\t\t1\n\t\t3\n\t\n\n for m\n in the equation \n\ty\n\t=\n\t\n\t\t\n\t\t\tm\n\t\t\tx\n\t\t\n\t\t+\n\t\tb\n\t\n\n yields y=-13x+b, or \n\ty\n\t=\n\t\n\t\t\n\t\t\t-\n\t\t\t\n\t\t\t\tx\n\t\t\t\t3\n\t\t\t\n\t\t\n\t\t+\n\t\tb\n\t\n\n. It’s also given that line t\n passes through the point 9,10. Substituting 9\n for x\n and 10\n for y\n in the equation \n\ty\n\t=\n\t\n\t\t\n\t\t\t-\n\t\t\t\n\t\t\t\tx\n\t\t\t\t3\n\t\t\t\n\t\t\n\t\t+\n\t\tb\n\t\n\n yields 10=-93+b, or 10=-3+b. Adding 3\n to both sides of this equation yields \n\t13\n\t=\n\tb\n\n. Substituting 13\n for b\n in the equation \n\ty\n\t=\n\t\n\t\t\n\t\t\t-\n\t\t\t\n\t\t\t\tx\n\t\t\t\t3\n\t\t\t\n\t\t\n\t\t+\n\t\tb\n\t\n\n yields \n\ty\n\t=\n\t\n\t\t\n\t\t\t-\n\t\t\t\n\t\t\t\tx\n\t\t\t\t3\n\t\t\t\n\t\t\n\t\t+\n\t\t13\n\t\n\n.

\n

Choice A is incorrect and may result from conceptual or calculation errors.

\n

Choice B is incorrect. This equation defines a line that has a slope of 9\n, not \n\t-\n\t\n\t\t1\n\t\t3\n\t\n\n, and passes through the point 0,10, not 9,10.

\n

Choice C is incorrect. This equation defines a line that passes through the point 0,10, not 9,10.

"}, {"id": "aa85b138", "domain": "Algebra", "skill": "Linear equations in one variable", "difficulty": "M", "type": "mc", "stimulus": "
\n\t

2 n + 6 = 14

\n
\n", "stem": "

A tree had a height of 6 feet when it was planted. The equation above can be used to find how many years n it took the tree to reach a height of 14 feet. Which of the following is the best interpretation of the number 2 in this context?

\n", "choices": [{"id": "A", "text": "

The number of years it took the tree to double its height

\n"}, {"id": "B", "text": "

The average number of feet that the tree grew per year

\n"}, {"id": "C", "text": "

The height, in feet, of the tree when the tree was 1 year old

\n"}, {"id": "D", "text": "

The average number of years it takes similar trees to grow 14 feet

\n"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. The height of the tree at a given time is equal to its height when it was planted plus the number of feet that the tree grew. In the given equation, 14 represents the height of the tree at the given time, and 6 represents the height of the tree when it was planted. It follows that 2 n represents the number of feet the tree grew from the time it was planted until the time it reached a height of 14 feet. Since n represents the number of years between the given time and the time the tree was planted, 2 must represent the average number of feet the tree grew each year.

Choice A is incorrect and may result from interpreting the coefficient 2 as doubling instead of as increasing by 2 each year. Choice C is incorrect. The height of the tree when it was 1 year old was 2 \u00d7 1, + 6 = 8 feet, not 2 feet. Choice D is incorrect. No information is given to connect the growth of one particular tree to the growth of similar trees.

 

\n"}, {"id": "15daa8d6", "domain": "Algebra", "skill": "Linear equations in one variable", "difficulty": "M", "type": "spr", "stimulus": "", "stem": "

2x+16=ax+8

\n

In the given equation, a\n is a constant. If the equation has infinitely many solutions, what is the value of a\n?

", "choices": [], "answerId": "2", "acceptedAnswers": ["2"], "rationale": "

The correct answer is 2\n. An equation with one variable, x\n, has infinitely many solutions only when both sides of the equation are equal for any defined value of x\n. It's given that 2x+16=ax+8, where a\n is a constant. This equation can be rewritten as 2x+8=ax+8. If this equation has infinitely many solutions, then both sides of this equation are equal for any defined value of x\n. Both sides of this equation are equal for any defined value of x\n when 2=a. Therefore, if the equation has infinitely many solutions, the value of a\n is 2\n.

\n

Alternate approach: If the given equation, 2x+16=ax+8, has infinitely many solutions, then both sides of this equation are equal for any value of x\n. If \n\tx\n\t=\n\t0\n\n, then substituting 0\n for x\n in 2x+16=ax+8 yields 20+16=a0+8, or 16=8a. Dividing both sides of this equation by 8\n yields 2=a.

"}, {"id": "2f0a43b2", "domain": "Algebra", "skill": "Linear equations in one variable", "difficulty": "E", "type": "spr", "stimulus": "", "stem": "

If \n\t\n\t\t\n\t\t\tx\n\t\t\t8\n\t\t\n\t\n\t=\n\t5\n\n, what is the value of \n\t\n\t\t8\n\t\tx\n\t\n\n?

", "choices": [], "answerId": ".2", "acceptedAnswers": [".2", "1/5"], "rationale": "

The correct answer is 15. Since the number 5\n can also be written as 51, the given equation can also be written as x8=51. This equation is equivalent to 8x=15. Therefore, the value of 8x is 15. Note that 1/5 and .2 are examples of ways to enter a correct answer.

\n

Alternate approach: Multiplying both sides of the equation x8=5 by 8\n yields x=40. Substituting 40\n for x\n into the expression 8x yields 840, or 15. 

"}, {"id": "ebf8d2b7", "domain": "Algebra", "skill": "Linear equations in two variables", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

A machine makes large boxes or small boxes, one at a time, for a total of 700\n minutes each day. It takes the machine 10\n minutes to make a large box or 5\n minutes to make a small box. Which equation represents the possible number of large boxes, x\n, and small boxes, y\n, the machine can make each day?

", "choices": [{"id": "A", "text": "

5x+10y=700

"}, {"id": "B", "text": "

10x+5y=700

"}, {"id": "C", "text": "

x+y10+5=700

"}, {"id": "D", "text": "

10+x5+y=700

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. It’s given that it takes the machine 10\n minutes to make a large box. It's also given that x\n represents the possible number of large boxes the machine can make each day. Multiplying 10\n by x\n gives \n\t10\n\tx\n\n, which represents the amount of time spent making large boxes. It’s given that it takes the machine 5\n minutes to make a small box. It's also given that y\n represents the possible number of small boxes the machine can make each day. Multiplying 5\n by y\n gives \n\t5\n\ty\n\n, which represents the amount of time spent making small boxes. Combining the amount of time spent making x\n large boxes and y\n small boxes yields \n\t\n\t\t10\n\t\tx\n\t\n\t+\n\t\n\t\t5\n\t\ty\n\t\n\n. It’s given that the machine makes boxes for a total of 700\n minutes each day. Therefore \n\t\n\t\t\n\t\t\t10\n\t\t\tx\n\t\t\n\t\t+\n\t\t\n\t\t\t5\n\t\t\ty\n\t\t\n\t\n\t=\n\t700\n\n represents the possible number of large boxes, x\n, and small boxes, y\n, the machine can make each day.

\n

Choice A is incorrect and may result from associating the time of 10\n minutes with small, rather than large, boxes and the time of 5\n minutes with large, rather than small, boxes.

\n

Choice C is incorrect and may result from conceptual errors.

\n

Choice D is incorrect and may result from conceptual errors.

"}, {"id": "997bec28", "domain": "Algebra", "skill": "Linear equations in one variable", "difficulty": "E", "type": "spr", "stimulus": "", "stem": "

The perimeter of an isosceles triangle is 83\n inches. Each of the two congruent sides of the triangle has a length of 24\n inches. What is the length, in inches, of the third side?

", "choices": [], "answerId": "35", "acceptedAnswers": ["35"], "rationale": "

The correct answer is 35\n. It’s given that the perimeter of an isosceles triangle is 83 inches and that each of the two congruent sides has a length of 24 inches. The perimeter of a triangle is the sum of the lengths of its three sides. The equation 24+24+x=83 can be used to represent this situation, where x\n is the length, in inches, of the third side. Combining like terms on the left-hand side of this equation yields 48+x=83. Subtracting 48\n from both sides of this equation yields \n\tx\n\t=\n\t35\n\n. Therefore, the length, in inches, of the third side is 35.

"}, {"id": "12ee1edc", "domain": "Algebra", "skill": "Linear equations in one variable", "difficulty": "M", "type": "mc", "stimulus": "
\n

\n open parenthesis, b \u2212 2, close parenthesis, \u00d7 x = 8\n

\n
\n", "stem": "

In the given equation, b is a constant. If the equation has no solution, what is the value of b ?

\n", "choices": [{"id": "A", "text": "

2

\n"}, {"id": "B", "text": "

4

\n"}, {"id": "C", "text": "

6

\n"}, {"id": "D", "text": "

10

\n"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. This equation has no solution when there is no value of x that produces a true statement. Solving the given equation for x by dividing both sides by open parenthesis, b \u2212 2, close parenthesis gives x = the fraction with numerator 8, and denominator, open parenthesis, b \u2212 2, close parenthesis. When open parenthesis, b \u2212 2, close parenthesis = 0, the right-hand side of this equation will be undefined, and the equation will have no solution. Therefore, when b = 2, there is no value of x that satisfies the given equation.

Choices B, C, and D are incorrect. Substituting 4, 6, and 10 for b in the given equation yields exactly one solution, rather than no solution, for x. For example, substituting 4 for b in the given equation yields open parenthesis, 4 \u2212 2, close parenthesis, \u00d7 x = 8, or 2 x = 8. Dividing both sides of 2 x = 8 by 2 yields x = 4. Similarly, if b = 6 or b = 10, x = 2 and x = 1, respectively.

\n"}, {"id": "c6b151d4", "domain": "Algebra", "skill": "Linear equations in two variables", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

A total of 364\n paper straws of equal length were used to construct two types of polygons: triangles and rectangles. The triangles and rectangles were constructed so that no two polygons had a common side. The equation \n\t\n\t\t\n\t\t\t3\n\t\t\tx\n\t\t\n\t\t+\n\t\t\n\t\t\t4\n\t\t\ty\n\t\t\n\t\n\t=\n\t364\n\n represents this situation, where x\n is the number of triangles constructed and y\n is the number of rectangles constructed. What is the best interpretation of x,y=24,73 in this context?

", "choices": [{"id": "A", "text": "

If 24\n triangles were constructed, then 73\n rectangles were constructed.

"}, {"id": "B", "text": "

If 24\n triangles were constructed, then 73\n paper straws were used.

"}, {"id": "C", "text": "

If 73\n triangles were constructed, then 24\n rectangles were constructed.

"}, {"id": "D", "text": "

If 73\n triangles were constructed, then 24\n paper straws were used.

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. It's given that 364\n paper straws of equal length were used to construct triangles and rectangles, where no two polygons had a common side. It's also given that the equation 3x+4y=364 represents this situation, where x\n is the number of triangles constructed and y\n is the number of rectangles constructed. The equation x,y=24,73 means that if x=24, then y=73. Substituting 24\n for x\n and 73\n for y\n in 3x+4y=364 yields 324+473=364, or 364=364, which is true. Therefore, in this context, the equation x,y=24,73 means that if 24\n triangles were constructed, then 73\n rectangles were constructed. 

\n

Choice B is incorrect and may result from conceptual errors.

\n

Choice C is incorrect and may result from conceptual errors.

\n

Choice D is incorrect and may result from conceptual errors.

"}, {"id": "0d391910", "domain": "Algebra", "skill": "Linear functions", "difficulty": "E", "type": "spr", "stimulus": "", "stem": "

The function f\n is defined by fx=4x. For what value of x\n does fx=8?

", "choices": [], "answerId": "2", "acceptedAnswers": ["2"], "rationale": "

The correct answer is 2\n. Substituting 8\n for fx in the given equation yields 8=4x. Dividing the left- and right-hand sides of this equation by 4\n yields x=2. Therefore, the value of x\n is 2\n when fx=8.

"}, {"id": "ee439cff", "domain": "Algebra", "skill": "Linear inequalities in one or two variables", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

On a car trip, Rhett and Jessica each drove for part of the trip, and the total distance they drove was under 220\n miles. Rhett drove at an average speed of 35 miles per hour mph, and Jessica drove at an average speed of 40 mph. Which of the following inequalities represents this situation, where r\n is the number of hours Rhett drove and j\n is the number of hours Jessica drove?

", "choices": [{"id": "A", "text": "

35r+40j>220

"}, {"id": "B", "text": "

35r+40j<220

"}, {"id": "C", "text": "

40r+35j>220

"}, {"id": "D", "text": "

40r+35j<220

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. It’s given that Rhett drove at an average speed of 35\n miles per hour and that he drove for r\n hours. Multiplying 35\n miles per hour by r\n hours yields \n\t35\n\tr\n\n miles, or the distance that Rhett drove. It’s also given that Jessica drove at an average speed of 40\n miles per hour and that she drove for j\n hours. Multiplying 40\n miles per hour by j\n hours yields 40j miles, or the distance that Jessica drove. The total distance, in miles, that Rhett and Jessica drove can be represented by the expression 35r+40j. It’s given that the total distance they drove was under 220\n miles. Therefore, the inequality 35r+40j<220 represents this situation.

\n

Choice A is incorrect. This inequality represents a situation in which the total distance Rhett and Jessica drove was over, rather than under, 220\n miles.

\n

Choice C is incorrect. This inequality represents a situation in which Rhett drove at an average speed of 40\n, rather than 35\n, miles per hour, Jessica drove at an average speed of 35\n, rather than 40\n, miles per hour, and the total distance they drove was over, rather than under, 220\n miles.

\n

Choice D is incorrect. This inequality represents a situation in which Rhett drove at an average speed of 40\n, rather than 35\n, miles per hour, and Jessica drove at an average speed of 35\n, rather than 40\n, miles per hour.

"}, {"id": "8c98c834", "domain": "Algebra", "skill": "Linear equations in two variables", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

The equation y = 0 point 1 x models the relationship between the number of different pieces of music a certain pianist practices, y, during an x-minute practice session. How many pieces did the pianist practice if the session lasted 30 minutes?

\n", "choices": [{"id": "A", "text": "

1

\n"}, {"id": "B", "text": "

3

\n"}, {"id": "C", "text": "

10

\n"}, {"id": "D", "text": "

30

\n"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. It’s given that the equation y = 0 point 1 x models the relationship between the number of different pieces of music a certain pianist practices, y, and the number of minutes in a practice session, x. Since it’s given that the session lasted 30 minutes, the number of pieces the pianist practiced can be found by substituting 30 for x in the given equation, which yields y = 0 point 1 \u00d7 30, or y = 3.

Choices A and C are incorrect and may result from misinterpreting the values in the equation. Choice D is incorrect. This is the given value of x, not the value of y.

\n"}, {"id": "563407e5", "domain": "Algebra", "skill": "Linear inequalities in one or two variables", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

A bakery sells trays of cookies. Each tray contains at least 50 cookies but no more than 60. Which of the following could be the total number of cookies on 4 trays of cookies?

\n", "choices": [{"id": "A", "text": "

165

\n"}, {"id": "B", "text": "

205

\n"}, {"id": "C", "text": "

245

\n"}, {"id": "D", "text": "

285

\n"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. If each tray contains the least number of cookies possible, 50 cookies, then the least number of cookies possible on 4 trays is 50 × 4 = 200 cookies. If each tray contains the greatest number of cookies possible, 60 cookies, then the greatest number of cookies possible on 4 trays is 60 × 4 = 240 cookies. If the least number of cookies on 4 trays is 200 and the greatest number of cookies is 240, then 205 could be the total number of cookies on these 4 trays of cookies because 200 < or equal to 205, which < or equal to 240..

Choices A, C, and D are incorrect. The least number of cookies on 4 trays is 200 cookies, and the greatest number of cookies on 4 trays is 240 cookies. The choices 165, 245, and 285 are each either less than 200 or greater than 240; therefore, they cannot represent the total number of cookies on 4 trays. 
\n 

\n"}, {"id": "25e1cfed", "domain": "Algebra", "skill": "Linear equations in one variable", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

How many solutions does the equation 1015x-9=-156-10x have?

", "choices": [{"id": "A", "text": "

Exactly one

"}, {"id": "B", "text": "

Exactly two

"}, {"id": "C", "text": "

Infinitely many

"}, {"id": "D", "text": "

Zero

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. Applying the distributive property to each side of the given equation yields 150x-90=-90+150x. Applying the commutative property of addition to the right-hand side of this equation yields 150x-90=150x-90. Since the two sides of the equation are equivalent, this equation is true for any value of x\n. Therefore, the given equation has infinitely many solutions.

\n

Choice A is incorrect and may result from conceptual or calculation errors.

\n

Choice B is incorrect and may result from conceptual or calculation errors.

\n

Choice D is incorrect and may result from conceptual or calculation errors.

"}, {"id": "317e80f9", "domain": "Algebra", "skill": "Systems of two linear equations in two variables", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

\n\t\n\t\tx\n\t\t+\n\t\ty\n\t\n\t=\n\t18\n\n

\n

\n\t\n\t\t5\n\t\ty\n\t\n\t=\n\tx\n\n

\n

What is the solution x,y to the given system of equations?

", "choices": [{"id": "A", "text": "

15,3

"}, {"id": "B", "text": "

16,2

"}, {"id": "C", "text": "

17,1

"}, {"id": "D", "text": "

18,0

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. The second equation in the given system defines the value of x\n as \n\t5\n\ty\n\n. Substituting \n\t5\n\ty\n\n for x\n into the first equation yields 5y+y=18 or 6y=18. Dividing each side of this equation by 6\n yields \n\ty\n\t=\n\t3\n\n. Substituting 3\n for y\n in the second equation yields 53=x or x=15. Therefore, the solution x,y to the given system of equations is 15,3. 

\n

Choice B is incorrect. Substituting 16\n for x\n and 2\n for y\n in the second equation yields 52=16, which is not true. Therefore, 16,2 is not a solution to the given system of equations.

\n

Choice C is incorrect. Substituting 17\n for x\n and 1\n for y\n in the second equation yields 51=17, which is not true. Therefore, 17,1 is not a solution to the given system of equations.

\n

Choice D is incorrect. Substituting 18\n for x\n and 0\n for y\n in the second equation yields 50=18, which is not true. Therefore, 18,0 is not a solution to the given system of equations.

"}, {"id": "3f5375d9", "domain": "Algebra", "skill": "Linear functions", "difficulty": "E", "type": "mc", "stimulus": "
\n
\n
\n

The line graphed in the xy-plane below models the total cost, in dollars, for a cab ride, y, in a certain city during nonpeak hours based on the number of miles traveled, x.

\n
\n \"The
\n
\n
\n
\n", "stem": "

According to the graph, what is the cost for each additional mile traveled, in dollars, of a cab ride?

\n", "choices": [{"id": "A", "text": "

$2.00

\n"}, {"id": "B", "text": "

$2.60

\n"}, {"id": "C", "text": "

$3.00

\n"}, {"id": "D", "text": "

$5.00

\n"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. The cost of each additional mile traveled is represented by the slope of the given line. The slope of the line can be calculated by identifying two points on the line and then calculating the ratio of the change in y to the change in x between the two points. Using the points 1, 5 and 2, 7, the slope is equal to (7 \u2212 5)/(2 \u2212 1, end fraction), or 2. Therefore, the cost for each additional mile traveled of the cab ride is $2.00.

Choice B is incorrect and may result from calculating the slope of the line that passes through the points 5, 13 and 0, 0. However, the point 0, 0 does not lie on the line shown. Choice C is incorrect. This is the y-coordinate of the y-intercept of the graph and represents the flat fee for a cab ride before the charge for any miles traveled is added. Choice D is incorrect. This value represents the total cost of a 1-mile cab ride.

\n"}, {"id": "541bef2f", "domain": "Algebra", "skill": "Linear inequalities in one or two variables", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

y≤x+7

\n

y≥-2x-1

\n

Which point x,y is a solution to the given system of inequalities in the xy-plane?

", "choices": [{"id": "A", "text": "

-14,0

"}, {"id": "B", "text": "

0,-14

"}, {"id": "C", "text": "

0,14

"}, {"id": "D", "text": "

14,0

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. A point x,y is a solution to a system of inequalities in the xy-plane if substituting the x-coordinate and the y-coordinate of the point for x\n and y\n, respectively, in each inequality makes both of the inequalities true. Substituting the x-coordinate and the y-coordinate of choice D, 14\n and 0\n, for x\n and y\n, respectively, in the first inequality in the given system, y\u2264x+7, yields 0\u226414+7, or 0\u226421, which is true. Substituting 14\n for x\n and 0\n for y\n in the second inequality in the given system, y\u2265-2x-1, yields 0\u2265-214-1, or 0\u2265-29, which is true. Therefore, the point 14,0 is a solution to the given system of inequalities in the xy-plane.

\n

Choice A is incorrect. Substituting -14\n for x\n and 0\n for y\n in the inequality y\u2264x+7 yields 0\u2264-14+7, or 0\u2264-7, which is not true.

\n

Choice B is incorrect. Substituting 0\n for x\n and -14\n for y\n in the inequality y\u2265-2x-1 yields -14\u2265-20-1, or -14\u2265-1, which is not true.

\n

Choice C is incorrect. Substituting 0\n for x\n and 14\n for y\n in the inequality y\u2264x+7 yields 14\u22640+7, or 14\u22647, which is not true.

"}, {"id": "620fe971", "domain": "Algebra", "skill": "Linear functions", "difficulty": "M", "type": "mc", "stimulus": "
\n
\n
\n

A team of workers has been moving cargo off of a ship. The equation below models the approximate number of tons of cargo, y, that remains to be moved x hours after the team started working.

\n

\n y = 120 \u2212 25 x\n

\n
\n
\n
\n", "stem": "

The graph of this equation in the xy-plane is a line. What is the best interpretation of the x-intercept in this context?

\n", "choices": [{"id": "A", "text": "

The team will have moved all the cargo in about 4.8 hours.

\n"}, {"id": "B", "text": "

The team has been moving about 4.8 tons of cargo per hour.

\n"}, {"id": "C", "text": "

The team has been moving about 25 tons of cargo per hour.

\n"}, {"id": "D", "text": "

The team started with 120 tons of cargo to move.

\n"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. The x-intercept of the line with equation y = 120 – 25x can be found by substituting 0 for y and finding the value of x. When y = 0, x = 4.8, so the x-intercept is at (4.8, 0). Since y represents the number of tons of cargo remaining to be moved x hours after the team started working, it follows that the x-intercept refers to the team having no cargo remaining to be moved after 4.8 hours. In other words, the team will have moved all of the cargo after about 4.8 hours.

Choice B is incorrect and may result from incorrectly interpreting the value 4.8. Choices C and D are incorrect and may result from misunderstanding the x-intercept. These statements are accurate but not directly relevant to the x-intercept.

\n"}, {"id": "6a87902f", "domain": "Algebra", "skill": "Systems of two linear equations in two variables", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

\n\ty\n\t=\n\t\n\t\t\n\t\t\t2\n\t\t\tx\n\t\t\n\t\t+\n\t\t10\n\t\n\n

\n

\n\ty\n\t=\n\t\n\t\t\n\t\t\t2\n\t\t\tx\n\t\t\n\t\t-\n\t\t1\n\t\n\n

\n

At how many points do the graphs of the given equations intersect in the xy-plane?

", "choices": [{"id": "A", "text": "

Zero

"}, {"id": "B", "text": "

Exactly one

"}, {"id": "C", "text": "

Exactly two

"}, {"id": "D", "text": "

Infinitely many

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. A system of two linear equations in two variables, x\n and y\n, has zero points of intersection if the lines represented by the equations in the xy-plane are distinct and parallel. The graphs of two lines in the xy-plane represented by equations in slope-intercept form, \n\ty\n\t=\n\t\n\t\t\n\t\t\tm\n\t\t\tx\n\t\t\n\t\t+\n\t\tb\n\t\n\n, are distinct if the y-coordinates of their y-intercepts, b\n, are different and are parallel if their slopes, m\n, are the same. For the two equations in the given system, \n\ty\n\t=\n\t\n\t\t\n\t\t\t2\n\t\t\tx\n\t\t\n\t\t+\n\t\t10\n\t\n\n and \n\ty\n\t=\n\t\n\t\t\n\t\t\t2\n\t\t\tx\n\t\t\n\t\t-\n\t\t1\n\t\n\n, the values of b\n are 10\n and -1\n, respectively, and the values of m\n are both 2\n. Since the values of b\n are different, the graphs of these lines have different y-coordinates of the y-intercept and are distinct. Since the values of m\n are the same, the graphs of these lines have the same slope and are parallel. Therefore, the graphs of the given equations are lines that intersect at zero points in the xy-plane.

\n

Choice B is incorrect. The graphs of a system of two linear equations have exactly one point of intersection if the lines represented by the equations have different slopes. Since the given equations represent lines with the same slope, there is not exactly one intersection point.

\n

Choice C is incorrect. The graphs of a system of two linear equations can never have exactly two intersection points.

\n

Choice D is incorrect. The graphs of a system of two linear equations have infinitely many intersection points when the lines represented by the equations have the same slope and the same y-coordinate of the y-intercept. Since the given equations represent lines with different y-coordinates of their y-intercepts, there are not infinitely many intersection points.

"}, {"id": "b2845d88", "domain": "Algebra", "skill": "Linear equations in two variables", "difficulty": "E", "type": "mc", "stimulus": "
\n
\n
\n
\n \"The
\n
\n
\n
\n", "stem": "

Which of the following is an equation of the graph shown in the xy-plane above?

\n", "choices": [{"id": "A", "text": "

\n y = \u2212one fourth x, \u2212 1\n

\n"}, {"id": "B", "text": "

\n y = \u2212x, \u2212 4\n

\n"}, {"id": "C", "text": "

\n y = \u2212x, \u2212 one fourth\n

\n"}, {"id": "D", "text": "

\n y = \u22124 x, \u2212 1\n

\n"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. The slope of the line can be found by choosing any two points on the line, such as (4, –2) and (0, –1). Subtracting the y-values results in –2 – (–1) = –1, the change in y. Subtracting the x-values results in 4 – 0 = 4, the change in x. Dividing the change in y by the change in x yields \u22121, divided by 4 = \u2212one fourth, the slope. The line intersects the y-axis at (0, –1), so –1 is the y-coordinate of the y-intercept. This information can be expressed in slope-intercept form as the equation y = \u2212one fourth, x, \u2212 1.

Choice B is incorrect and may result from incorrectly calculating the slope and then misidentifying the slope as the y-intercept. Choice C is incorrect and may result from misidentifying the slope as the y-intercept. Choice D is incorrect and may result from incorrectly calculating the slope.

\n"}, {"id": "f75bd744", "domain": "Algebra", "skill": "Systems of two linear equations in two variables", "difficulty": "H", "type": "spr", "stimulus": "", "stem": "

\n\t\n\t\t4\n\t\tx\n\t\n\t-\n\t\n\t\t6\n\t\ty\n\t\n\n=10y+2

\n

ty=12+2x

\n

In the given system of equations, t\n is a constant. If the system has no solution, what is the value of t\n?

", "choices": [], "answerId": "8", "acceptedAnswers": ["8"], "rationale": "

The correct answer is 8\n. The given system of equations can be solved using the elimination method. Multiplying both sides of the second equation in the given system by -2 yields -2ty=-1-4x, or -1-4x=-2ty. Adding this equation to the first equation in the given system, 4x-6y=10y+2, yields 4x-6y+-1-4x=10y+2+-2ty, or -1-6y=10y-2ty+2. Subtracting \n\t10\n\ty\n\n from both sides of this equation yields -1-6y-10y=10y-2ty+2-10y, or -1-16y=-2ty+2. If the given system has no solution, then the equation -1-16y=-2ty+2 has no solution. If this equation has no solution, the coefficients of y\n on each side of the equation, -16 and -2t, must be equal, which yields the equation -16=-2t. Dividing both sides of this equation by -2 yields 8=t. Thus, if the system has no solution, the value of t\n is 8\n.

\n

Alternate approach: A system of two linear equations in two variables, x\n and y\n, has no solution if the lines represented by the equations in the xy-plane are parallel and distinct. Lines represented by equations in the form Ax+By=C, where A\n, B\n, and C\n are constant terms, are parallel if the ratio of the x-coefficients is equal to the ratio of the y-coefficients, and distinct if the ratio of the x-coefficients are not equal to the ratio of the constant terms. Subtracting 10y from both sides of the first equation in the given system yields 4x-6y-10y=10y+2-10y, or 4x-16y=2. Subtracting 2x from both sides of the second equation in the given system yields ty-2x=12+2x-2x, or -2x+ty=12. The ratio of the x-coefficients for these equations is -24, or -12. The ratio of the y-coefficients for these equations is -t16. The ratio of the constant terms for these equations is 122, or 14. Since the ratio of the x-coefficients, -12, is not equal to the ratio of the constants, 14, the lines represented by the equations are distinct. Setting the ratio of the x-coefficients equal to the ratio of the y-coefficients yields -12=-t16. Multiplying both sides of this equation by -16 yields -12-16=-t16-16, or t=8. Therefore, when t=8, the lines represented by these equations are parallel. Thus, if the system has no solution, the value of t\n is 8\n.

"}, {"id": "b450ab03", "domain": "Algebra", "skill": "Linear equations in two variables", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

An employee at a restaurant prepares sandwiches and salads. It takes the employee 1.5\n minutes to prepare a sandwich and 1.9\n minutes to prepare a salad. The employee spends a total of 46.1\n minutes preparing x\n sandwiches and y\n salads. Which equation represents this situation?

", "choices": [{"id": "A", "text": "

1.9x+1.5y=46.1

"}, {"id": "B", "text": "

1.5x+1.9y=46.1

"}, {"id": "C", "text": "

x+y=46.1

"}, {"id": "D", "text": "

30.7x+24.3y=46.1

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. It’s given that the employee takes 1.5 minutes to prepare a sandwich. Multiplying 1.5 by the number of sandwiches, x, yields 1.5x, the amount of time the employee spends preparing x sandwiches. It’s also given that the employee takes 1.9 minutes to prepare a salad. Multiplying 1.9 by the number of salads, y, yields 1.9y, the amount of time the employee spends preparing y salads. It follows that the total amount of time, in minutes, the employee spends preparing x sandwiches and y salads is 1.5x+1.9y. It's given that the employee spends a total of 46.1 minutes preparing x sandwiches and y salads. Thus, the equation 1.5x+1.9y=46.1 represents this situation.

\n

Choice A is incorrect. This equation represents a situation where it takes the employee 1.9 minutes, rather than 1.5 minutes, to prepare a sandwich and 1.5 minutes, rather than 1.9 minutes, to prepare a salad.

\n

Choice C is incorrect. This equation represents a situation where it takes the employee 1 minute, rather than 1.5 minutes, to prepare a sandwich and 1 minute, rather than 1.9 minutes, to prepare a salad.

\n

Choice D is incorrect. This equation represents a situation where it takes the employee 30.7 minutes, rather than 1.5 minutes, to prepare a sandwich and 24.3 minutes, rather than 1.9 minutes, to prepare a salad.

"}, {"id": "b3abf40f", "domain": "Algebra", "skill": "Linear functions", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

Fx=95x-273.15+32

\n

The function F\n gives the temperature, in degrees Fahrenheit, that corresponds to a temperature of x\n kelvins. If a temperature increased by 9.10\n kelvins, by how much did the temperature increase, in degrees Fahrenheit?

", "choices": [{"id": "A", "text": "

16.38\n

"}, {"id": "B", "text": "

48.38\n

"}, {"id": "C", "text": "

475.29\n

"}, {"id": "D", "text": "

507.29\n

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. It’s given that the function Fx=95x-273.15+32 gives the temperature, in degrees Fahrenheit, that corresponds to a temperature of x\n kelvins. A temperature that increased by 9.10 kelvins means that the value of x\n increased by 9.10 kelvins. It follows that an increase in x\n by 9.10 increases F(x) by 959.10, or 16.38. Therefore, if a temperature increased by 9.10 kelvins, the temperature increased by 16.38 degrees Fahrenheit. 

\n

Choice B is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

\n

Choice D is incorrect and may result from conceptual or calculation errors.

"}, {"id": "6ac23de7", "domain": "Algebra", "skill": "Linear equations in one variable", "difficulty": "E", "type": "mc", "stimulus": "
\n

\n
\n", "stem": "

\n (4 x)/(5 = 20)

In the equation above, what is the value of x ?

\n", "choices": [{"id": "A", "text": "

25

\n"}, {"id": "B", "text": "

24

\n"}, {"id": "C", "text": "

16

\n"}, {"id": "D", "text": "

15

\n"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. Multiplying both sides of the equation by 5 results in 4 x = 100. Dividing both sides of the resulting equation by 4 results in x = 25.

Choice B is incorrect and may result from adding 20 and 4. Choice C is incorrect and may result from dividing 20 by 5 and then multiplying the result by 4. Choice D is incorrect and may result from subtracting 5 from 20.

\n"}, {"id": "6e6a3241", "domain": "Algebra", "skill": "Systems of two linear equations in two variables", "difficulty": "M", "type": "mc", "stimulus": "
\n

\n Equation 1: x + 5 y = 5. Equation 2: 2 x \u2212 y = \u22124\n

\n
\n", "stem": "

Which of the following graphs in the xy-plane could be used to solve the system of equations above?

\n", "choices": [{"id": "A", "text": "

\"The

\n"}, {"id": "B", "text": "

\"The

\n"}, {"id": "C", "text": "

\"The

\n"}, {"id": "D", "text": "

\"The

\n"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. The graph of a system of equations is the graph that shows the lines represented by each of the equations in the system. The x-intercept of the graph of each given equation can be found by substituting 0 for y in each equation: x plus, 5 \u00d7 0 = 5, or x = 5, and 2 x \u2212 0 = \u22124, or x = \u22122. The y-intercept of the graph of each equation can be found by substituting 0 for x in each equation: 0 + 5 y = 5, or y = 1, and 2 \u00d7 0, \u2212 y = \u22124 or y = 4. Using these x- and y- intercept values, the line that has equation x + 5 y = 5 passes through the points 0, 1 and 5, 0, and the line that has equation 2 x \u2212 y = \u22124 passes through the points 0, 4 and \u22122, 0. Only the lines in choice C pass through these points and can be used to solve the given system of equations.

Choices A, B, and D are incorrect. In choices A and B, neither line passes through the points 0, 1 and 5, 0 or the points 0, 4 and \u22122, 0. In choice D, although one line passes through the points 0, 4 and \u22122, 0 the other line doesn’t pass through the points 0, 1 and 5, 0.

\n"}, {"id": "e6cb2402", "domain": "Algebra", "skill": "Linear equations in one variable", "difficulty": "H", "type": "spr", "stimulus": "", "stem": "

3(kx+13)=\n\t48\n\t17\n\n\n\tx\n\t+\n\t36\n\n

\n

In the given equation, k\n is a constant. The equation has no solution. What is the value of k\n?

", "choices": [], "answerId": ".9411", "acceptedAnswers": [".9411", ".9412", "16/17"], "rationale": "

The correct answer is 1617. It's given that the equation 3kx+13=4817x+36 has no solution. A linear equation in the form ax+b=cx+d, where a\n, b\n, c\n, and d\n are constants, has no solution only when the coefficients of x\n on each side of the equation are equal and the constant terms aren't equal. Dividing both sides of the given equation by 3\n yields kx+13=4851x+363, or kx+13=1617x+12. Since the coefficients of x\n on each side of the equation must be equal, it follows that the value of k\n is \n\t16\n\t17\n\n. Note that 16/17, .9411, .9412, and 0.941 are examples of ways to enter a correct answer.

"}, {"id": "e470e19d", "domain": "Algebra", "skill": "Linear functions", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

The function f\n is defined by f(x)=7x-84. What is the x-intercept of the graph of y=f(x) in the xy-plane?

", "choices": [{"id": "A", "text": "

-12,0

"}, {"id": "B", "text": "

-7,0

"}, {"id": "C", "text": "

7,0

"}, {"id": "D", "text": "

12,0

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. The given function f is a linear function. Therefore, the graph of y=fx in the xy-plane has one x-intercept at the point k,0, where k\n is a constant. Substituting 0\n for fx and k\n for x\n in the given function yields 0=7k-84. Adding 84\n to both sides of this equation yields 84=7k. Dividing both sides of this equation by 7\n yields 12=k. Therefore, the x-intercept of the graph of y=fx in the xy-plane is 12,0.

\n

Choice A is incorrect and may result from conceptual or calculation errors.

\n

Choice B is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

"}, {"id": "f7e39fe9", "domain": "Algebra", "skill": "Linear functions", "difficulty": "M", "type": "spr", "stimulus": "", "stem": "\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
x\n10\n15\n20\n25\n
fx82\n137\n192\n247\n
\n

The table shows four values of x\n and their corresponding values of fx. There is a linear relationship between x\n and fx that is defined by the equation fx=mx-28, where m\n is a constant. What is the value of m\n?

", "choices": [], "answerId": "11", "acceptedAnswers": ["11"], "rationale": "

The correct answer is 11\n. It's given that fx is defined by the equation f(x)=mx-28, where m\n is a constant. It's also given in the table that when \n\tx\n\t=\n\t10\n\n, fx=82. Substituting 10\n for x\n and 82\n for fx in the equation fx=mx-28 yields, 82=m10-28. Adding 28\n to both sides of this equation yields \n\t110\n\t=\n\t\n\t\t10\n\t\tm\n\t\n\n. Dividing both sides of this equation by 10\n yields \n\t11\n\t=\n\tm\n\n. Therefore, the value of m\n is 11\n.

"}, {"id": "aff28230", "domain": "Algebra", "skill": "Systems of two linear equations in two variables", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

\n\tx\n\t=\n\t10\n\n

\n

\n\ty\n\t=\n\t\n\t\tx\n\t\t+\n\t\t21\n\t\n\n

\n

The solution to the given system of equations is x,y. What is the value of y\n?

", "choices": [{"id": "A", "text": "

2.1\n

"}, {"id": "B", "text": "

10\n

"}, {"id": "C", "text": "

21\n

"}, {"id": "D", "text": "

31\n

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. It's given by the first equation in the given system of equations that \n\tx\n\t=\n\t10\n\n. Substituting 10\n for x\n in the second equation in the given system yields y=10+21, or \n\ty\n\t=\n\t31\n\n. Therefore, the value of y\n is 31\n.

\n

Choice A is incorrect and may result from conceptual or calculation errors.

\n

Choice B is incorrect. This is the value of x\n, not the value of y\n.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

"}, {"id": "f5929f7a", "domain": "Algebra", "skill": "Systems of two linear equations in two variables", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

y=-19x

\n

y=12x

\n

The solution to the given system of equations is x,y. What is the value of x\n?

", "choices": [{"id": "A", "text": "

-9\n

"}, {"id": "B", "text": "

-7\n

"}, {"id": "C", "text": "

0\n

"}, {"id": "D", "text": "

2\n

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. It's given by the first equation in the system that y=-19x. Substituting -19x for y\n in the second equation in the system yields -19x=12x. Multiplying the left-hand side of this equation by 22 and the right-hand side by 99 yields -218x=918x. Adding 218x to both sides of this equation yields 0=1118x. Multiplying both sides of this equation by 1811 yields \n\tx\n\t=\n\t0\n\n.

\n

Choice A is incorrect and may result from conceptual or calculation errors. 

\n

Choice B is incorrect and may result from conceptual or calculation errors. 

\n

Choice D is incorrect and may result from conceptual or calculation errors. 

"}, {"id": "6c71f3ec", "domain": "Algebra", "skill": "Linear inequalities in one or two variables", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

A salesperson’s total earnings consist of a base salary of x\n dollars per year, plus commission earnings of 11\n% of the total sales the salesperson makes during the year. This year, the salesperson has a goal for the total earnings to be at least 3\n times and at most 4\n times the base salary. Which of the following inequalities represents all possible values of total sales s\n, in dollars, the salesperson can make this year in order to meet that goal? 

", "choices": [{"id": "A", "text": "

\n\t2\n\tx\n\n≤s≤\n\t3\n\tx\n\n

"}, {"id": "B", "text": "

20.11x≤s≤30.11x

"}, {"id": "C", "text": "

\n\t3\n\tx\n\n≤s≤\n\t4\n\tx\n\n

"}, {"id": "D", "text": "

30.11x≤s≤40.11x

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. It’s given that a salesperson's total earnings consist of a base salary of x\n dollars per year plus commission earnings of 11% of the total sales the salesperson makes during the year. If the salesperson makes s\n dollars in total sales this year, the salesperson’s total earnings can be represented by the expression x+0.11s. It’s also given that the salesperson has a goal for the total earnings to be at least 3\n times and at most 4\n times the base salary, which can be represented by the expressions \n\t3\n\tx\n\n and \n\t4\n\tx\n\n, respectively. Therefore, this situation can be represented by the inequality 3x≤x+0.11s≤4x. Subtracting x\n from each part of this inequality yields 2x≤0.11s≤3x. Dividing each part of this inequality by 0.11\n yields 20.11x≤s≤30.11x. Therefore, the inequality 20.11x≤s≤30.11x represents all possible values of total sales s\n, in dollars, the salesperson can make this year in order to meet their goal.

\n

Choice A is incorrect. This inequality represents a situation in which the total sales, rather than the total earnings, are at least 2\n times and at most 3\n times, rather than at least 3\n times and at most 4\n times, the base salary.

\n

Choice C is incorrect. This inequality represents a situation in which the total sales, rather than the total earnings, are at least 3\n times and at most 4\n times the base salary.

\n

Choice D is incorrect. This inequality represents a situation in which the total earnings are at least 4\n times and at most 5\n times, rather than at least 3\n times and at most 4\n times, the base salary.

"}, {"id": "7392dfc1", "domain": "Algebra", "skill": "Linear equations in one variable", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

Which of the following is equivalent to 4 x + 6 = 12 ?

\n", "choices": [{"id": "A", "text": "

\n 2 x + 4 = 6\n

\n"}, {"id": "B", "text": "

\n x + 3 = 3\n

\n"}, {"id": "C", "text": "

\n 3 x + 2 = 4\n

\n"}, {"id": "D", "text": "

\n 2 x + 3 = 6\n

\n"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. Dividing each side of the original equation by \"\" yields (4 x + 6)/(2 = twelve halves), which simplifies to 2 x + 3 = 6.

Choice A is incorrect. Dividing each side of the original equation by \"\" gives 2 x + 3 = 6, which is not equivalent to 2 x + 4 = 6. Choice B is incorrect. Dividing each side of the original equation by \"\" gives x + three halves = 3, which is not equivalent to x + 3 = 3. Choice C is incorrect. Dividing each side of the original equation by \"\" gives four thirds x, + 2 = 4, which is not equivalent to 3 x + 2 = 4. 

\n"}, {"id": "93954cfa", "domain": "Algebra", "skill": "Linear equations in one variable", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

One pound of grapes costs $2. At this rate, how many dollars will c pounds of grapes cost?

\n", "choices": [{"id": "A", "text": "2 c\n"}, {"id": "B", "text": "2 + c\n"}, {"id": "C", "text": "(2)/(c)\n"}, {"id": "D", "text": "(c)/(2)\n"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. If one pound of grapes costs $2, two pounds of grapes will cost 2 times $2, three pounds of grapes will cost 3 times $2, and so on. Therefore, c pounds of grapes will cost c times $2, which is 2c dollars.

Choice B is incorrect and may result from incorrectly adding instead of multiplying. Choice C is incorrect and may result from assuming that c pounds cost $2, and then finding the cost per pound. Choice D is incorrect and could result from incorrectly assuming that 2 pounds cost $c, and then finding the cost per pound.

\n"}, {"id": "5cf1bbc9", "domain": "Algebra", "skill": "Linear functions", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n

\n

The graph of the function f\n, where y=f(x), gives the total cost y\n, in dollars, for a certain video game system and x\n games. What is the best interpretation of the slope of the graph in this context?

", "choices": [{"id": "A", "text": "

Each game costs $25\n.

"}, {"id": "B", "text": "

The video game system costs $100\n.

"}, {"id": "C", "text": "

The video game system costs $25\n.

"}, {"id": "D", "text": "

Each game costs $100\n.

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. The given graph is a line, and the slope of a line is defined as the change in the value of y\n for each increase in the value of x\n by 1\n. It’s given that y\n represents the total cost, in dollars, and that x\n represents the number of games. Therefore, the change in the value of y\n for each increase in the value of x\n by 1\n represents the change in total cost, in dollars, for each increase in the number of games by 1\n. In other words, the slope represents the cost, in dollars, per game. The graph shows that when the value of x\n increases from 0\n to 1\n, the value of y\n increases from 100\n to 125\n. It follows that the slope is 25\n, or the cost per game is $25. Thus, the best interpretation of the slope of the graph is that each game costs $25.

\n

Choice B is incorrect. This is an interpretation of the y-intercept of the graph rather than the slope of the graph.

\n

Choice C is incorrect. The slope of the graph is the cost per game, not the cost of the video game system.

\n

Choice D is incorrect. Each game costs $25, not $100.

"}, {"id": "74c03c21", "domain": "Algebra", "skill": "Systems of two linear equations in two variables", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

A bus traveled on the highway and on local roads to complete a trip of 160 miles. The trip took 4 hours. The bus traveled at an average speed of 55 miles per hour mph on the highway and an average speed of 25 mph on local roads. If x\n is the time, in hours, the bus traveled on the highway and y\n is the time, in hours, it traveled on local roads, which system of equations represents this situation?

", "choices": [{"id": "A", "text": "

55x+25y=4
x+y=160

"}, {"id": "B", "text": "

55x+25y=160
x+y=4

"}, {"id": "C", "text": "

25x+55y=4
x+y=160

"}, {"id": "D", "text": "

25x+55y=160
x+y=4

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. If the bus traveled at an average speed of 55 miles per hour mph on the highway for x\n hours, then the bus traveled \n\t55\n\tx\n\n miles on the highway. If the bus traveled at an average speed of 25 mph on local roads for y\n hours, then the bus traveled \n\t25\n\ty\n\n miles on local roads. It's given that the trip was 160\n miles. This can be represented by the equation 55x+25y=160. It's also given that the trip took 4\n hours. This can be represented by the equation \n\t\n\t\tx\n\t\t+\n\t\ty\n\t\n\t=\n\t4\n\n. Therefore, the system consisting of the equations 55x+25y=160 and \n\t\n\t\tx\n\t\t+\n\t\ty\n\t\n\t=\n\t4\n\n represents this situation.

\n

Choice A is incorrect. This system of equations represents a situation where the trip was 4\n miles and took 160\n hours.

\n

Choice C is incorrect. This system of equations represents a situation where the trip was 4\n miles and took 160\n hours, and the bus traveled at an average speed of 25 mph on the highway and 55 mph on local roads.

\n

Choice D is incorrect. This system of equations represents a situation where the bus traveled at an average speed of 25 mph on the highway and 55 mph on local roads.

"}, {"id": "68f2cbaf", "domain": "Algebra", "skill": "Linear inequalities in one or two variables", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

Ty set a goal to walk at least 24\n kilometers every day to prepare for a multiday hike. On a certain day, Ty plans to walk at an average speed of 4\n kilometers per hour. What is the minimum number of hours Ty must walk on that day to fulfill the daily goal?

", "choices": [{"id": "A", "text": "

4\n

"}, {"id": "B", "text": "

6\n

"}, {"id": "C", "text": "

20\n

"}, {"id": "D", "text": "

24\n

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. It's given that Ty plans to walk at an average speed of 4\n kilometers per hour. The number of kilometers Ty will walk is determined by the expression \n\t4\n\ts\n\n, where s\n is the number of hours Ty walks. The given goal of at least 24\n kilometers means that the inequality 4s\u226524 represents the situation. Dividing both sides of this inequality by 4\n gives s\u22656 , which corresponds to a minimum of 6\n hours Ty must walk. 

\n

Choice A is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

\n

Choice D is incorrect and may result from conceptual or calculation errors.

"}, {"id": "8abed0fb", "domain": "Algebra", "skill": "Systems of two linear equations in two variables", "difficulty": "E", "type": "mc", "stimulus": "
\n

\n Equation 1: y = 2 x + 3. Equation 2: x = 1.\n

\n
\n", "stem": "

What is the solution x, y to the given system of equations?

\n", "choices": [{"id": "A", "text": "

\n 1, 2

\n"}, {"id": "B", "text": "

\n 1, 5

\n"}, {"id": "C", "text": "

\n 2, 3

\n"}, {"id": "D", "text": "

\n 2, 7

\n"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. Since it’s given that x = 1, substituting 1 for x in the first equation yields y = 2 \u00d7 1, + 3. Simplifying the right-hand side of this equation yields y = 2 + 3, or y = 5. Therefore, the ordered pair 1, 5 is a solution to the given system of equations.

Choice A is incorrect and may result from a calculation error when substituting 1 for x in the first equation. Choices C and D are incorrect. Because it’s given that x = 1, x cannot equal 2 as stated in these ordered pairs.

\n"}, {"id": "e1259a5a", "domain": "Algebra", "skill": "Systems of two linear equations in two variables", "difficulty": "E", "type": "mc", "stimulus": "
\n
\n
\n

A system of two linear equations is graphed in the xy-plane below.

\n
\n \"The
\n
\n
\n
\n", "stem": "

Which of the following points is the solution to the system of equations?

\n", "choices": [{"id": "A", "text": "

\n the point 3, 9

\n"}, {"id": "B", "text": "

\n the point 6, 15

\n"}, {"id": "C", "text": "

\n the point 8, 10

\n"}, {"id": "D", "text": "

\n the point 12, 18

\n"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. The solution to this system of linear equations is the point that lies on both lines graphed, or the point of intersection of the two lines. According to the graphs, the point of intersection occurs when x = 3 and y = 9, or at the point 3, 9.

Choices B and D are incorrect. Each of these points lies on one line, but not on both lines in the xy-plane. Choice C is incorrect. This point doesn’t lie on either of the lines graphed in the xy-plane.

\n"}, {"id": "b988eeec", "domain": "Algebra", "skill": "Linear functions", "difficulty": "H", "type": "spr", "stimulus": "", "stem": "

The functions f\n and g\n are defined as f(x)=\n\t1\n\t4\n\n\n\tx\n\t-\n\t9\n\n and g(x)=\n\t3\n\t4\n\n\n\tx\n\t+\n\t21\n\n. If the function h\n is defined as h(x)=f(x)+g(x), what is the x-coordinate of the x-intercept of the graph of y=hx in the xy-plane?

", "choices": [], "answerId": "-12", "acceptedAnswers": ["-12"], "rationale": "

The correct answer is -12\n. It's given that the functions f\n and g\n are defined as fx=14x-9 and gx=34x+21. If the function h\n is defined as hx=fx+gx, then substituting 14x-9 for fx and 34x+21 for gx in this function yields hx=14x-9+34x+21. This can be rewritten as hx=44x+12, or hx=x+12. The x-intercept of a graph in the xy-plane is the point on the graph where \n\ty\n\t=\n\t0\n\n. The equation representing the graph of y=hx is y=x+12. Substituting 0\n for y\n in this equation yields 0=x+12. Subtracting 12\n from both sides of this equation yields \n\t-12\n\t=\n\tx\n\n, or \n\tx\n\t=\n\t-12\n\n. Therefore, the x-coordinate of the x-intercept of the graph of y=hx in the xy-plane is -12\n.

"}, {"id": "3d04de9c", "domain": "Algebra", "skill": "Linear equations in one variable", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

A principal used a total of 25\n flags that were either blue or yellow for field day. The principal used 20\n blue flags. How many yellow flags were used?

", "choices": [{"id": "A", "text": "

5\n

"}, {"id": "B", "text": "

20\n

"}, {"id": "C", "text": "

25\n

"}, {"id": "D", "text": "

30\n

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. It's given that a principal used a total of 25\n blue flags and yellow flags. It's also given that of the 25\n flags used, 20\n flags were blue. Subtracting the number of blue flags used from the total number of flags used results in the number of yellow flags used. It follows that the number of yellow flags used is 25-20, or 5\n. 

\n

Choice B is incorrect. This is the number of blue flags used.

\n

Choice C is incorrect. This is the total number of flags used.

\n

Choice D is incorrect and may result from conceptual or calculation errors.

"}, {"id": "70feb725", "domain": "Algebra", "skill": "Systems of two linear equations in two variables", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

During a month, Morgan ran r miles at 5 miles per hour and biked b miles at 10 miles per hour. She ran and biked a total of 200 miles that month, and she biked for twice as many hours as she ran. What is the total number of miles that Morgan biked during the month?

\n", "choices": [{"id": "A", "text": "

80

\n"}, {"id": "B", "text": "

100

\n"}, {"id": "C", "text": "

120

\n"}, {"id": "D", "text": "

160

\n"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. The number of hours Morgan spent running or biking can be calculated by dividing the distance she traveled during that activity by her speed, in miles per hour, for that activity. So the number of hours she ran can be represented by the expression (r)/(5), and the number of hours she biked can be represented by the expression (b)/(10). It’s given that she biked for twice as many hours as she ran, so this can be represented by the equation (b)/(10, end fraction = 2 \u00d7 the fraction r over 5), which can be rewritten as b = 4 r. It’s also given that she ran r miles and biked b miles, and that she ran and biked a total of 200 miles. This can be represented by the equation r + b = 200. Substituting 4 r for b in this equation yields r + 4 r = 200, or 5 r = 200. Solving for r  yields r = 40. Determining the number of miles she biked, b, can be found by substituting 40 for r in r + b = 200, which yields 40 + b = 200. Solving for b yields b = 160.

Choices A, B, and C are incorrect because they don’t satisfy that Morgan biked for twice as many hours as she ran. In choice A, if she biked 80 miles, then she ran 120 miles, which means she biked for 8 hours and ran for 24 hours. In choice B, if she biked 100 miles, then she ran 100 miles, which means she biked for 10 hours and ran for 20 hours. In choice C, if she biked 120 miles, then she ran for 80 miles, which means she biked for 12 hours and ran for 16 hours.

 

\n"}, {"id": "8a87c2c8", "domain": "Algebra", "skill": "Systems of two linear equations in two variables", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

\n\t\n\t\tx\n\t\t+\n\t\t3\n\t\n\t=\n\t\n\t\t\n\t\t\t-\n\t\t\t2\n\t\t\ty\n\t\t\n\t\t+\n\t\t5\n\t\n\n

\n

\n\t\n\t\tx\n\t\t-\n\t\t3\n\t\n\t=\n\t\n\t\t\n\t\t\t2\n\t\t\ty\n\t\t\n\t\t+\n\t\t7\n\t\n\n

\n

The solution to the given system of equations is x,y. What is the value of \n\t2\n\tx\n\n?

", "choices": [{"id": "A", "text": "

-2\n

"}, {"id": "B", "text": "

6\n

"}, {"id": "C", "text": "

12\n

"}, {"id": "D", "text": "

24\n

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. Adding the second equation in the given system to the first equation in the given system yields x+3+x-3=-2y+5+2y+7. Adding like terms in this equation yields 2x=12. Thus, the value of \n\t2\n\tx\n\n is 12\n.

\n

Choice A is incorrect. This is the value of y\n, not \n\t2\n\tx\n\n.

\n

Choice B is incorrect. This is the value of x\n, not \n\t2\n\tx\n\n.

\n

Choice D is incorrect and may result from conceptual or calculation errors.

"}, {"id": "60f71697", "domain": "Algebra", "skill": "Linear equations in one variable", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

\n\t\n\t\t8\n\t\tx\n\t\n\t=\n\t88\n\n

\n

What value of x\n is the solution to the given equation?

", "choices": [{"id": "A", "text": "

11\n

"}, {"id": "B", "text": "

80\n

"}, {"id": "C", "text": "

96\n

"}, {"id": "D", "text": "

704\n

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. Dividing both sides of the given equation by 8\n yields \n\tx\n\t=\n\t11\n\n. Therefore, 11\n is the solution to the given equation.

\n

Choice B is incorrect. This is the solution to the equation \n\t\n\t\tx\n\t\t+\n\t\t8\n\t\n\t=\n\t88\n\n.

\n

Choice C is incorrect. This is the solution to the equation \n\t\n\t\tx\n\t\t-\n\t\t8\n\t\n\t=\n\t88\n\n.

\n

Choice D is incorrect. This is the solution to the equation x8=88.

"}, {"id": "13294295", "domain": "Algebra", "skill": "Linear functions", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

The graph shown models the number of candy bars a certain machine wraps with a label in x\n seconds.

\n

\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n\n

\n

According to the graph, what is the estimated number of candy bars the machine wraps with a label per second?

", "choices": [{"id": "A", "text": "

2\n

"}, {"id": "B", "text": "

40\n

"}, {"id": "C", "text": "

78\n

"}, {"id": "D", "text": "

80\n

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. For the graph shown, the x-axis represents time, in seconds, and the y-axis represents the number of candy bars wrapped. The slope of a line in the xy-plane is the change in y\n for each 1\n-unit increase in x\n. It follows that the slope of the graph shown represents the estimated number of candy bars the machine wraps with a label per second. The slope, m\n, of a line in the xy-plane can be found using any two points, x1,y1 and x2,y2, on the line and the slope formula m=y2-y1x2-x1. The graph shown passes through the points 0,0 and 2,80. Substituting these points for x1,y1 and x2,y2, respectively, in the slope formula yields m=80-02-0, which is equivalent to m=802, or \n\tm\n\t=\n\t40\n\n. Therefore, the estimated number of candy bars the machine wraps with a label per second is 40\n.

\n

Choice A is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

\n

Choice D is incorrect and may result from conceptual or calculation errors.

"}, {"id": "ed92fb68", "domain": "Algebra", "skill": "Systems of two linear equations in two variables", "difficulty": "M", "type": "mc", "stimulus": "
\n

\n 4 x + 5 y = 100, ; 5 x + 4 y = 62\n

\n
\n", "stem": "

If the system of equations above has solution x, y, what is the value of x + y ?

\n", "choices": [{"id": "A", "text": "

0

\n"}, {"id": "B", "text": "

9

\n"}, {"id": "C", "text": "

18

\n"}, {"id": "D", "text": "

38

\n"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. Adding the given equations yields 9x + 9y = 162. Dividing each side of the equation 9x + 9y = 162 by 9 gives x + y = 18.

Choice A is incorrect and may result from incorrectly adding the equations. Choice B is incorrect and may result from conceptual or computational errors. Choice D is incorrect. This value is equivalent to y – x.

\n"}, {"id": "1a621af4", "domain": "Algebra", "skill": "Linear inequalities in one or two variables", "difficulty": "H", "type": "spr", "stimulus": "", "stem": "

A number x\n is at most 2\n less than 3\n times the value of y\n. If the value of y\n is -4\n, what is the greatest possible value of x\n?

", "choices": [], "answerId": "-14", "acceptedAnswers": ["-14"], "rationale": "

The correct answer is -14\n. It's given that a number x\n is at most 2\n less than 3\n times the value of y\n. Therefore, x\n is less than or equal to 2\n less than 3\n times the value of y\n. The expression \n\t3\n\ty\n\n represents 3\n times the value of y\n. The expression \n\t\n\t\t3\n\t\ty\n\t\n\t-\n\t2\n\n represents 2\n less than 3\n times the value of y\n. Therefore, x\n is less than or equal to \n\t\n\t\t3\n\t\ty\n\t\n\t-\n\t2\n\n. This can be shown by the inequality x≤3y-2. Substituting -4\n for y\n in this inequality yields x≤3-4-2 or, x≤-14. Therefore, if the value of y\n is -4\n, the greatest possible value of x\n is -14\n.

"}, {"id": "3e9eaffc", "domain": "Algebra", "skill": "Linear functions", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

Caleb used juice to make popsicles. The function fx=-5x+30 approximates the volume, in fluid ounces, of juice Caleb had remaining after making x\n popsicles. Which statement is the best interpretation of the y-intercept of the graph of y=fx in the xy-plane in this context?

", "choices": [{"id": "A", "text": "

Caleb used approximately 5\n fluid ounces of juice for each popsicle.

"}, {"id": "B", "text": "

Caleb had approximately 5\n fluid ounces of juice when he began to make the popsicles.

"}, {"id": "C", "text": "

Caleb had approximately 30\n fluid ounces of juice when he began to make the popsicles.

"}, {"id": "D", "text": "

Caleb used approximately 30\n fluid ounces of juice for each popsicle.

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. An equation that defines a linear function f\n can be written in the form fx=mx+b, where m\n represents the slope and b\n represents the y-intercept, 0,b, of the line of y=fx in the xy-plane. The function fx=-5x+30 is linear. Therefore, the graph of the given function y=fx in the xy-plane has a y-intercept of 0,30. It’s given that fx gives the approximate volume, in fluid ounces, of juice Caleb had remaining after making x\n popsicles. It follows that the y-intercept of 0,30 means that Caleb had approximately 30\n fluid ounces of juice remaining after making 0\n popsicles. In other words, Caleb had approximately 30\n fluid ounces of juice when he began to make the popsicles.

\n

Choice A is incorrect. This is an interpretation of the slope, rather than the y-intercept, of the graph of y=fx in the xy-plane.

\n

Choice B is incorrect and may result from conceptual errors.

\n

Choice D is incorrect and may result from conceptual errors.

"}, {"id": "af2ba762", "domain": "Algebra", "skill": "Linear functions", "difficulty": "H", "type": "mc", "stimulus": "
\n\t
\n\t\t
\n\t\t\t

According to data provided by the US Department of Energy, the average price per gallon of regular gasoline in the United States from September 1, 2014, to December 1, 2014, is modeled by the function F defined below, where F(x) is the average price per gallon x months after September 1.

\n\t\t
\n\t
\n\n\t

\"\"

\n
\n", "stem": "

The constant 2.74 in this function estimates which of the following?

\n", "choices": [{"id": "A", "text": "

The average monthly decrease in the price per gallon

\n"}, {"id": "B", "text": "

The difference in the average price per gallon from September 1, 2014, to December 1, 2014

\n"}, {"id": "C", "text": "

The average price per gallon on September 1, 2014

\n"}, {"id": "D", "text": "

The average price per gallon on December 1, 2014

\n"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. Since 2.74 is a constant term, it represents an actual price of gas rather than a measure of change in gas price. To determine what gas price it represents, find x such that F(x) = 2.74, or 2.74 = 2.74 – 0.19(x – 3). Subtracting 2.74 from both sides gives 0 = –0.19(x – 3). Dividing both sides by –0.19 results in 0 = x – 3, or x = 3. Therefore, the average price of gas is $2.74 per gallon 3 months after September 1, 2014, which is December 1, 2014.

Choice A is incorrect. Since 2.74 is a constant, not a multiple of x, it cannot represent a rate of change in price. Choice B is incorrect. The difference in the average price from September 1, 2014, to December 1, 2014, is F(3) – F(0) = 2.74 – 0.19(3 – 3) – (2.74 – 0.19(0 – 3)) = 2.74 – (2.74 + 0.57) = –0.57, which is not 2.74. Choice C is incorrect. The average price per gallon on September 1, 2014, is F(0) = 2.74 – 0.19(0 – 3) = 2.74 + 0.57 = 3.31, which is not 2.74.

\n"}, {"id": "19fdf387", "domain": "Algebra", "skill": "Systems of two linear equations in two variables", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

In the xy-plane, the graph of y = x + 3 intersects the graph of y = 2 x \u2212 6 at the point a,, b. What is the value of a ?

\n", "choices": [{"id": "A", "text": "

3

\n"}, {"id": "B", "text": "

6

\n"}, {"id": "C", "text": "

9

\n"}, {"id": "D", "text": "

12

\n"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. Since the graph of y = x + 3 intersects the graph of y = 2 x \u2212 6 at the point a,, b, the ordered pair a,, b is the solution to the system of linear equations consisting of y = x + 3 and y = 2 x \u2212 6, and the value of a is the value of x in the solution of this system. Since both x + 3and 2 x \u2212 6 are equal to y, it follows that x + 3 = 2 x \u2212 6. Subtracting x from and adding 6 to both sides of the equation yields 9 = x. Therefore, the value of a is 9.

Choices A and B are incorrect and may result from a calculation or conceptual error in solving the system of equations consisting of y = x + 3 and y = 2 x \u2212 6. Choice D is incorrect. This is the value of b, not a.

\n"}, {"id": "a775af14", "domain": "Algebra", "skill": "Linear functions", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

In the xy-plane, the graph of the linear function f\n contains the points 0,2 and 8,34. Which equation defines f\n, where y=fx?

", "choices": [{"id": "A", "text": "

fx=2x+42

"}, {"id": "B", "text": "

fx=32x+36

"}, {"id": "C", "text": "

fx=4x+2

"}, {"id": "D", "text": "

fx=8x+2

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. In the xy-plane, the graph of a linear function can be written in the form fx=mx+b, where m\n represents the slope and 0,b represents the y-intercept of the graph of y=fx. It’s given that the graph of the linear function f\n, where y=fx, in the xy-plane contains the point 0,2. Thus, \n\tb\n\t=\n\t2\n\n. The slope of the graph of a line containing any two points x1,y1 and x2,y2 can be found using the slope formula, m=y2-y1x2-x1. Since it’s given that the graph of the linear function f\n contains the points 0,2 and 8,34, it follows that the slope of the graph of the line containing these points is m=34-28-0, or  \n\tm\n\t=\n\t4\n\n. Substituting 4\n for m\n and 2\n for b\n in fx=mx+b yields fx=4x+2.

\n

Choice A is incorrect. This function represents a graph with a slope of 2\n and a y-intercept of 0,42.

\n

Choice B is incorrect. This function represents a graph with a slope of 32\n and a y-intercept of 0,36.

\n

Choice D is incorrect. This function represents a graph with a slope of 8\n and a y-intercept of 0,2.

"}, {"id": "db0107df", "domain": "Algebra", "skill": "Linear equations in two variables", "difficulty": "E", "type": "spr", "stimulus": "", "stem": "

The y-intercept of the graph of \n\t\n\t\t\n\t\t\t12\n\t\t\tx\n\t\t\n\t\t+\n\t\t\n\t\t\t2\n\t\t\ty\n\t\t\n\t\n\t=\n\t18\n\n in the xy-plane is 0,y. What is the value of y\n?

", "choices": [], "answerId": "9", "acceptedAnswers": ["9"], "rationale": "

The correct answer is 9\n. It's given that the y-intercept of the graph of \n\t\n\t\t\n\t\t\t12\n\t\t\tx\n\t\t\n\t\t+\n\t\t\n\t\t\t2\n\t\t\ty\n\t\t\n\t\n\t=\n\t18\n\n in the xy-plane is 0,y. Substituting 0\n for x\n in the equation \n\t\n\t\t\n\t\t\t12\n\t\t\tx\n\t\t\n\t\t+\n\t\t\n\t\t\t2\n\t\t\ty\n\t\t\n\t\n\t=\n\t18\n\n yields 120+2y=18, or \n\t\n\t\t2\n\t\ty\n\t\n\t=\n\t18\n\n. Dividing both sides of this equation by 2\n yields \n\ty\n\t=\n\t9\n\n. Therefore, the value of y\n is 9\n.

"}, {"id": "b9835972", "domain": "Algebra", "skill": "Linear equations in two variables", "difficulty": "H", "type": "spr", "stimulus": "", "stem": "

In the xy-plane, line l passes through the point 0,0 and is parallel to the line represented by the equation \n\ty\n\t=\n\t\n\t\t\n\t\t\t8\n\t\t\tx\n\t\t\n\t\t+\n\t\t2\n\t\n\n. If line l also passes through the point 3,d, what is the value of d\n?

", "choices": [], "answerId": "24", "acceptedAnswers": ["24"], "rationale": "

The correct answer is 24\n. A line in the xy-plane can be defined by the equation \n\ty\n\t=\n\t\n\t\t\n\t\t\tm\n\t\t\tx\n\t\t\n\t\t+\n\t\tb\n\t\n\n, where m\n is the slope of the line and b\n is the y-coordinate of the y-intercept of the line. It's given that line l passes through the point 0,0. Therefore, the y-coordinate of the y-intercept of line l is 0\n. It's given that line l is parallel to the line represented by the equation y=8x+2. Since parallel lines have the same slope, it follows that the slope of line l is 8\n. Therefore, line l can be defined by an equation in the form \n\ty\n\t=\n\t\n\t\t\n\t\t\tm\n\t\t\tx\n\t\t\n\t\t+\n\t\tb\n\t\n\n, where \n\tm\n\t=\n\t8\n\n and \n\tb\n\t=\n\t0\n\n. Substituting 8\n for m\n and 0\n for b\n in \n\ty\n\t=\n\t\n\t\t\n\t\t\tm\n\t\t\tx\n\t\t\n\t\t+\n\t\tb\n\t\n\n yields the equation y=8x+0, or \n\ty\n\t=\n\t\n\t\t8\n\t\tx\n\t\n\n . If line l passes through the point 3,d, then when \n\tx\n\t=\n\t3\n\n, \n\ty\n\t=\n\td\n\n for the equation \n\ty\n\t=\n\t\n\t\t8\n\t\tx\n\t\n\n. Substituting 3\n for x\n and d\n for y\n in the equation \n\ty\n\t=\n\t\n\t\t8\n\t\tx\n\t\n\n yields d=83, or \n\td\n\t=\n\t24\n\n.

"}, {"id": "df32b09c", "domain": "Algebra", "skill": "Linear inequalities in one or two variables", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

Tom scored 85, 78, and 98 on his first three exams in history class. Solving which inequality gives the score, G, on Tom’s fourth exam that will result in a mean score on all four exams of at least 90 ?

\n", "choices": [{"id": "A", "text": "

\n 90 minus, open parenthesis, 85 + 78 + 98, close parenthesis, < or equal to 4 G\n

\n"}, {"id": "B", "text": "

\n 4 G, + 85, + 78, + 98, > or equal to 360\n

\n"}, {"id": "C", "text": "

\n the fraction with numerator, open parenthesis, G + 85 + 78 + 98, close parenthesis, and denominator 4, end fraction, > or equal to 90\n

\n"}, {"id": "D", "text": "

\n the fraction with numerator, open parenthesis, 85 + 78 + 98, close parenthesis, and denominator 4, end fraction, > or equal to 90 \u2212 4 G\n

\n"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. The mean of the four scores (G, 85, 78, and 98) can be expressed as  (G, + 85, + 78, + 98)/(4). The inequality that expresses the condition that the mean score is at least 90 can therefore be written as (G, + 85, + 78, + 98)/(4, > or equal to 90).

Choice A is incorrect. The sum of the scores (G, 85, 78, and 98) isn’t divided by 4 to express the mean. Choice B is incorrect and may be the result of an algebraic error when multiplying both sides of the inequality by 4. Choice D is incorrect because it doesn’t include G in the mean with the other three scores.

\n"}, {"id": "e1248a5c", "domain": "Algebra", "skill": "Systems of two linear equations in two variables", "difficulty": "H", "type": "mc", "stimulus": "
\n
\n
\n

\n
\n
\n
\n", "stem": "

In the system of equations below, a and c are constants.

\n Equation 1: one half x, + one third y = one sixth. Equation 2: a, x, + y = c\n

If the system of equations has an infinite number of solutions x, y, what is the value of a ?

\n", "choices": [{"id": "A", "text": "\n \u2212one half\n \n"}, {"id": "B", "text": "\n 0\n \n"}, {"id": "C", "text": "\n one half\n \n"}, {"id": "D", "text": "\n three halves\n \n"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. A system of two linear equations has infinitely many solutions if one equation is equivalent to the other. This means that when the two equations are written in the same form, each coefficient or constant in one equation is equal to the corresponding coefficient or constant in the other equation multiplied by the same number. The equations in the given system of equations are written in the same form, with x and y on the left-hand side and a constant on the right-hand side of the equation. The coefficient of y in the second equation is equal to the coefficient of y in the first equation multiplied by 3. Therefore, a, the coefficient of x in the second equation, must be equal to 3 times the coefficient of x in the first equation: a = one half \u00d7 3, or a = three halves.

Choices A, B, and C are incorrect. When a = \u2212one half, a = 0, or a = one half, the given system of equations has one solution.

\n"}, {"id": "b8cbe394", "domain": "Algebra", "skill": "Linear functions", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

Sean rents a tent at a cost of $11 per day plus a onetime insurance fee of $10. Which equation represents the total cost c\n, in dollars, to rent the tent with insurance for d\n days?

", "choices": [{"id": "A", "text": "

c=11d+10

"}, {"id": "B", "text": "

c=10d+11

"}, {"id": "C", "text": "

\n\tc\n\t=\n\t\n\t\t\n\t\t\t11\n\t\t\td\n\t\t\n\t\t+\n\t\t10\n\t\n\n

"}, {"id": "D", "text": "

\n\tc\n\t=\n\t\n\t\t\n\t\t\t10\n\t\t\td\n\t\t\n\t\t+\n\t\t11\n\t\n\n

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. It’s given that the cost of renting a tent is $11 per day for d\n days. Multiplying the rental cost by the number of days yields $11d, which represents the cost of renting the tent for d\n days before the insurance is added. Adding the onetime insurance fee of $10 to the rental cost of $11d gives the total cost c\n, in dollars, which can be represented by the equation c=11d+10.

\n

Choice A is incorrect. This equation represents the total cost to rent the tent if the insurance fee was charged every day.

\n

Choice B is incorrect. This equation represents the total cost to rent the tent if the daily fee was $d+11 for 10\n days.

\n

Choice D is incorrect. This equation represents the total cost to rent the tent if the daily fee was $10 and the onetime fee was $11.

"}, {"id": "05bb1af9", "domain": "Algebra", "skill": "Linear equations in two variables", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n\n

\n

The graph of y=fx+14 is shown. Which equation defines function f\n?

", "choices": [{"id": "A", "text": "

fx=\n\t-\n\t\n\t\t1\n\t\t4\n\t\n\n\n\tx\n\t-\n\t12\n\n

"}, {"id": "B", "text": "

fx=\n\t-\n\t\n\t\t1\n\t\t4\n\t\n\n\n\tx\n\t+\n\t16\n\n

"}, {"id": "C", "text": "

fx=\n\t-\n\t\n\t\t1\n\t\t4\n\t\n\n\n\tx\n\t+\n\t2\n\n

"}, {"id": "D", "text": "

fx=\n\t-\n\t\n\t\t1\n\t\t4\n\t\n\n\n\tx\n\t-\n\t14\n\n

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. An equation for the graph shown can be written in slope-intercept form \n\ty\n\t=\n\t\n\t\t\n\t\t\tm\n\t\t\tx\n\t\t\n\t\t+\n\t\tb\n\t\n\n, where m\n is the slope of the graph and its y-intercept is 0,b. Since the y-intercept of the graph shown is 0,2, the value of b\n is 2\n. Since the graph also passes through the point 4,1, the slope can be calculated as 1-24-0, or \n\t-\n\t\n\t\t1\n\t\t4\n\t\n\n. Therefore, the value of m\n is \n\t-\n\t\n\t\t1\n\t\t4\n\t\n\n. Substituting \n\t-\n\t\n\t\t1\n\t\t4\n\t\n\n for m\n and 2\n for b\n in the equation \n\ty\n\t=\n\t\n\t\t\n\t\t\tm\n\t\t\tx\n\t\t\n\t\t+\n\t\tb\n\t\n\n yields y=-14x+2. It’s given that an equation for the graph shown is y=fx+14. Substituting fx+14 for y\n in the equation y=-14x+2  yields fx+14=-14x+2. Subtracting 14\n from both sides of this equation yields fx=-14x-12.

\n

Choice B is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

\n

Choice D is incorrect and may result from conceptual or calculation errors.

"}, {"id": "cc7ffe02", "domain": "Algebra", "skill": "Linear equations in two variables", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

Keenan made 32\n cups of vegetable broth. Keenan then filled x\n small jars and y\n large jars with all the vegetable broth he made. The equation 3x+5y=32 represents this situation. Which is the best interpretation of \n\t5\n\ty\n\n in this context?

", "choices": [{"id": "A", "text": "

The number of large jars Keenan filled

"}, {"id": "B", "text": "

The number of small jars Keenan filled

"}, {"id": "C", "text": "

The total number of cups of vegetable broth in the large jars

"}, {"id": "D", "text": "

The total number of cups of vegetable broth in the small jars

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. It’s given that the equation \n\t\n\t\t\n\t\t\t3\n\t\t\tx\n\t\t\n\t\t+\n\t\t\n\t\t\t5\n\t\t\ty\n\t\t\n\t\n\t=\n\t32\n\n represents the situation where Keenan filled x\n small jars and y\n large jars with all the vegetable broth he made, which was 32\n cups. Therefore, \n\t3\n\tx\n\n represents the total number of cups of vegetable broth in the small jars and \n\t5\n\ty\n\n represents the total number of cups of vegetable broth in the large jars. 

\n

Choice A is incorrect. The number of large jars Keenan filled is represented by y\n, not \n\t5\n\ty\n\n.

\n

Choice B is incorrect. The number of small jars Keenan filled is represented by x\n, not \n\t5\n\ty\n\n.

\n

Choice D is incorrect. The total number of cups of vegetable broth in the small jars is represented by \n\t3\n\tx\n\n, not \n\t5\n\ty\n\n. 

"}, {"id": "dae126d7", "domain": "Algebra", "skill": "Linear functions", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

The boiling point of water at sea level is 212 degrees Fahrenheit degrees Fahrenheit. For every 550 feet above sea level, the boiling point of water is lowered by about 1 degree Fahrenheit. Which of the following equations can be used to find the boiling point B of water, in degrees Fahrenheit, x feet above sea level?

\n", "choices": [{"id": "A", "text": "

\n B = 550 plus, (x)/(212)\n

\n"}, {"id": "B", "text": "

\n B = 550 minus, (x)/(212)\n

\n"}, {"id": "C", "text": "

\n B = 212 plus, (x)/(550)\n

\n"}, {"id": "D", "text": "

\n B = 212 minus, (x)/(550)\n

\n"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. It’s given that the boiling point of water at sea level is 212°F and that for every 550 feet above sea level, the boiling point of water is lowered by about 1°F. Therefore, the change in the boiling point of water x feet above sea level is represented by the expression the \u2212of (x)/(550). Adding this expression to the boiling point of water at sea level gives the equation for the boiling point B of water, in °F, x feet above sea level: B = the \u2212of (x)/(550, end fraction, + 212), or B = 212 minus, (x)/(550).

Choices A and B are incorrect and may result from using the boiling point of water at sea level as the rate of change and the rate of change as the initial boiling point of water at sea level. Choice C is incorrect and may result from representing the change in the boiling point of water as an increase rather than a decrease.

\n"}, {"id": "bf5f80c6", "domain": "Algebra", "skill": "Linear inequalities in one or two variables", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

y<−4x+4

\n

Which point (x\n, y\n) is a solution to the given inequality in the \n\tx\n\ty\n\n-plane?

", "choices": [{"id": "A", "text": "

(-4\n, 0\n)

"}, {"id": "B", "text": "

(0\n, 5\n)

"}, {"id": "C", "text": "

(2\n, 1\n)

"}, {"id": "D", "text": "

(2\n, -1\n)

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice D is correct. For a point x,y to be a solution to the given inequality in the xy-plane, the value of the point’s y-coordinate must be less than the value of -4x+4, where x\n is the value of the x-coordinate of the point. This is true of the point -4,0 because 0<-4-4+4, or 0<20. Therefore, the point -4,0 is a solution to the given inequality.

\n


Choices A, B, and C are incorrect. None of these points are a solution to the given inequality because each point’s y-coordinate is greater than the value of -4x+4 for the point’s x-coordinate.

"}, {"id": "12983c1e", "domain": "Algebra", "skill": "Linear functions", "difficulty": "E", "type": "mc", "stimulus": "
\n\t
\n\t\t
\n\t\t\t
\"The
\n\t\t
\n\t
\n
\n", "stem": "

Some values of the linear function f are shown in the table above. Which of the following defines f ?

\n", "choices": [{"id": "A", "text": "

f(x) = 2 x + 3

\n"}, {"id": "B", "text": "

f(x) = 3 x + 2

\n"}, {"id": "C", "text": "

f(x) = 4 x + 1

\n"}, {"id": "D", "text": "

f(x) = 5 x

\n"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. Because f is a linear function of x, the equation f(x) = m x + b, where m and b are constants, can be used to define the relationship between x and f (x). In this equation, m represents the increase in the value of f (x) for every increase in the value of x by 1. From the table, it can be determined that the value of f (x) increases by 8 for every increase in the value of x by 2. In other words, for the function f the value of m is eight halves, or 4. The value of b can be found by substituting the values of x and f (x) from any row of the table and the value of m into the equation f(x) = m x + b and solving for b. For example, using x = 1, f(x) = 5, and m = 4 yields 5 = 4 \u00d7 1, + b. Solving for b yields b = 1. Therefore, the equation defining the function f can be written in the form f(x) = 4 x + 1.

Choices A, B, and D are incorrect. Any equation defining the linear function f must give values of f (x) for corresponding values of x, as shown in each row of the table. According to the table, if x = 3, f(x) = 13. However, substituting x = 3 into the equation given in choice A gives f(3) = 2 \u00d7 3, + 3, or f(3) = 9, not 13. Similarly, substituting x = 3 into the equation given in choice B gives f(3) = 3 \u00d7 3, + 2, or f(3) = 11, not 13.

Lastly, substituting x = 3 into the equation given in choice D gives f(3) = 5 \u00d7 3, or f(3) = 15, not 13. Therefore, the equations in choices A, B, and D cannot define f.

 

\n"}, {"id": "8368afd1", "domain": "Algebra", "skill": "Linear equations in two variables", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n\n

\n

The graph shows the possible combinations of the number of pounds of tangerines and lemons that could be purchased for $18 at a certain store. If Melvin purchased lemons and 4\n pounds of tangerines for a total of $18, how many pounds of lemons did he purchase?

", "choices": [{"id": "A", "text": "

7\n

"}, {"id": "B", "text": "

10\n

"}, {"id": "C", "text": "

14\n

"}, {"id": "D", "text": "

16\n

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. It's given that the graph shows the possible combinations of the number of pounds of tangerines, x, and the number of pounds of lemons, y, that could be purchased for $18 at a certain store. If Melvin purchased lemons and 4 pounds of tangerines for a total of $18, the number of pounds of lemons he purchased is represented by the y-coordinate of the point on the graph where x=4. For the graph shown, when x=4, y=10. Therefore, if Melvin purchased lemons and 4 pounds of tangerines for a total of $18, then he purchased 10 pounds of lemons.

\n

Choice A is incorrect. This is the number of pounds of tangerines Melvin purchased if he purchased tangerines and 4 pounds of lemons for a total of $18.

\n

Choice C is incorrect. This is the number of pounds of lemons Melvin purchased if he purchased lemons and 2 pounds of tangerines for a total of $18.

\n

Choice D is incorrect. This is the number of pounds of lemons Melvin purchased if he purchased lemons and 1 pound of tangerines for a total of $18.

"}, {"id": "ae2287e2", "domain": "Algebra", "skill": "Linear equations in one variable", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

A certain product costs a company $65 to make. The product is sold by a salesperson who earns a commission that is equal to 20% of the sales price of the product. The profit the company makes for each unit is equal to the sales price minus the combined cost of making the product and the commission. If the sales price of the product is $100, which of the following equations gives the number of units, u, of the product the company sold to make a profit of $6,840 ?

\n", "choices": [{"id": "A", "text": "

\"\"

\n"}, {"id": "B", "text": "

\"\"

\n"}, {"id": "C", "text": "

0 point 8 \u00d7 100, \u2212 65 u = 6,840

\n"}, {"id": "D", "text": "

\"\"

\n"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. The sales price of one unit of the product is given as $100. Because the salesperson is awarded a commission equal to 20% of the sales price, the expression 100(1 – 0.2) gives the sales price of one unit after the commission is deducted. It is also given that the profit is equal to the sales price minus the combined cost of making the product, or $65, and the commission: 100(1 – 0.2) – 65. Multiplying this expression by u gives the profit of u units: (100(1 – 0.2) – 65)u. Finally, it is given that the profit for u units is $6,840; therefore (100(1 – 0.2) – 65)u = $6,840.

Choice B is incorrect. In this equation, cost is subtracted before commission and the equation gives the commission, not what the company retains after commission. Choice C is incorrect because the number of units is multiplied only by the cost but not by the sale price. Choice D is incorrect because the value 0.2 shows the commission, not what the company retains after commission.

 

\n"}, {"id": "70d9516e", "domain": "Algebra", "skill": "Linear functions", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

A bus is traveling at a constant speed along a straight portion of road. The equation \n\td\n\t=\n\t\n\t\t30\n\t\tt\n\t\n\n gives the distance d\n, in feet from a road marker, that the bus will be t\n seconds after passing the marker. How many feet from the marker will the bus be 2\n seconds after passing the marker?

", "choices": [{"id": "A", "text": "

30\n

"}, {"id": "B", "text": "

32\n

"}, {"id": "C", "text": "

60\n

"}, {"id": "D", "text": "

90\n

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. It’s given that t\n represents the number of seconds after the bus passes the marker. Substituting 2\n for t\n in the given equation \n\td\n\t=\n\t\n\t\t30\n\t\tt\n\t\n\n yields d=302, or \n\td\n\t=\n\t60\n\n. Therefore, the bus will be 60\n feet from the marker 2\n seconds after passing it.

\n

Choice A is incorrect. This is the distance, in feet, the bus will be from the marker 1\n second, not 2\n seconds, after passing it.

\n

Choice B is incorrect and may result from conceptual or calculation errors.

\n

Choice D is incorrect. This is the distance, in feet, the bus will be from the marker 3\n seconds, not 2\n seconds, after passing it.

"}, {"id": "1362ccde", "domain": "Algebra", "skill": "Systems of two linear equations in two variables", "difficulty": "H", "type": "spr", "stimulus": "", "stem": "

\n\ty\n\t=\n\t\n\t\t\n\t\t\t4\n\t\t\tx\n\t\t\n\t\t+\n\t\t1\n\t\n\n
\n\t\n\t\t4\n\t\ty\n\t\n\t=\n\t\n\t\t\n\t\t\t15\n\t\t\tx\n\t\t\n\t\t-\n\t\t8\n\t\n\n

\n

The solution to the given system of equations is x,y. What is the value of x-y?

", "choices": [], "answerId": "35", "acceptedAnswers": ["35"], "rationale": "

The correct answer is 35\n. The first equation in the given system of equations defines y\n as 4x+1. Substituting 4x+1 for y\n in the second equation in the given system of equations yields 44x+1=15x-8. Applying the distributive property on the left-hand side of this equation yields 16x+4=15x-8. Subtracting \n\t15\n\tx\n\n from each side of this equation yields x+4=-8. Subtracting 4\n from each side of this equation yields x=-12. Substituting -12\n for x\n in the first equation of the given system of equations yields y=4-12+1, or y=-47. Substituting -12\n for x\n and -47\n for y\n into the expression x-y yields -12--47, or 35\n.

"}, {"id": "720e51ac", "domain": "Algebra", "skill": "Linear functions", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

The cost y\n, in dollars, for a manufacturer to make x\n rings is represented by the line shown.

\n

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n

\n

What is the cost, in dollars, for the manufacturer to make 60\n rings?

", "choices": [{"id": "A", "text": "

100\n

"}, {"id": "B", "text": "

125\n

"}, {"id": "C", "text": "

175\n

"}, {"id": "D", "text": "

225\n

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. The line shown represents the cost y\n, in dollars, for a manufacturer to make x\n rings. For the line shown, the x-axis represents the number of rings made by the manufacturer and the y-axis represents the cost, in dollars. Therefore, the cost, in dollars, for the manufacturer to make 60\n rings is represented by the y-coordinate of the point on the line that has an x-coordinate of 60\n. The point on the line with an x-coordinate of 60\n has a y-coordinate of 175\n. Therefore, the cost, in dollars, for the manufacturer to make 60\n rings is 175\n.

\n

Choice A is incorrect and may result from conceptual or calculation errors.

\n

Choice B is incorrect. This is the cost, in dollars, for the manufacturer to make 20\n rings.

\n

Choice D is incorrect. This is the cost, in dollars, for the manufacturer to make 100\n rings.

"}, {"id": "4de87c9a", "domain": "Algebra", "skill": "Linear equations in one variable", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

3\n more than 8\n times a number x\n is equal to 83. Which equation represents this situation?

", "choices": [{"id": "A", "text": "

(3)(8)x=83

"}, {"id": "B", "text": "

8x=83+3

"}, {"id": "C", "text": "

3x+8=83

"}, {"id": "D", "text": "

8x+3=83

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. The given phrase “8\n times a number x\n” can be represented by the expression \n\t8\n\tx\n\n. The given phrase “3\n more than” indicates an increase of 3\n to a quantity. Therefore “3\n more than 8\n times a number x\n” can be represented by the expression \n\t\n\t\t8\n\t\tx\n\t\n\t+\n\t3\n\n. Since it’s given that 3\n more than 8\n times a number x\n is equal to 83\n, it follows that \n\t\n\t\t8\n\t\tx\n\t\n\t+\n\t3\n\n is equal to 83\n, or \n\t\n\t\t\n\t\t\t8\n\t\t\tx\n\t\t\n\t\t+\n\t\t3\n\t\n\t=\n\t83\n\n. Therefore, the equation that represents this situation is \n\t\n\t\t\n\t\t\t8\n\t\t\tx\n\t\t\n\t\t+\n\t\t3\n\t\n\t=\n\t83\n\n.

\n

Choice A is incorrect. This equation represents 3\n times the quantity 8\n times a number x\n is equal to 83\n. 

\n

Choice B is incorrect. This equation represents 8\n times a number x\n is equal to 3\n more than 83\n.

\n

Choice C is incorrect. This equation represents 8\n more than 3\n times a number x\n is equal to 83\n.

"}, {"id": "52cb8ea4", "domain": "Algebra", "skill": "Systems of two linear equations in two variables", "difficulty": "H", "type": "mc", "stimulus": "
\n\t

Equation 1: 7 x \u2212 5 y = 4. Equation 2: 4 x \u2212 8 y = 9.

\n
\n", "stem": "

If x, y is the solution to the system of equations above, what is the value of 3 x + 3 y ?

\n", "choices": [{"id": "A", "text": "

\u221213

\n"}, {"id": "B", "text": "

\u22125

\n"}, {"id": "C", "text": "

5

\n"}, {"id": "D", "text": "

13

\n"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. Subtracting the second equation, 4 x \u2212 8 y = 9, from the first equation, 7 x \u2212 5 y = 4, results in open parenthesis, 7 x \u2212 5 y, close parenthesis, minus, open parenthesis, 4 x \u2212 8 y, close parenthesis = 4 \u2212 9, or 7 x \u2212 5 y, \u2212 4 x, + 8 y = 5. Combining like terms on the left-hand side of this equation yields 3 x + 3 y = \u22125.

Choice A is incorrect and may result from miscalculating 4 \u2212 9 as \u221213. Choice C is incorrect and may result from miscalculating 4 \u2212 9 as 5. Choice D is incorrect and may result from adding 9 to 4 instead of subtracting 9 from 4.

 

\n"}, {"id": "c307283c", "domain": "Algebra", "skill": "Linear equations in two variables", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n\n

\n

What is an equation of the graph shown?

", "choices": [{"id": "A", "text": "

\n\ty\n\t=\n\t\n\t\t\n\t\t\t-\n\t\t\t2\n\t\t\tx\n\t\t\n\t\t-\n\t\t8\n\t\n\n

"}, {"id": "B", "text": "

\n\ty\n\t=\n\t\n\t\tx\n\t\t-\n\t\t8\n\t\n\n

"}, {"id": "C", "text": "

\n\ty\n\t=\n\t\n\t\t\n\t\t\t-\n\t\t\tx\n\t\t\n\t\t-\n\t\t8\n\t\n\n

"}, {"id": "D", "text": "

\n\ty\n\t=\n\t\n\t\t\n\t\t\t2\n\t\t\tx\n\t\t\n\t\t-\n\t\t8\n\t\n\n

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. An equation of a line can be written in the form \n\ty\n\t=\n\t\n\t\t\n\t\t\tm\n\t\t\tx\n\t\t\n\t\t+\n\t\tb\n\t\n\n, where m\n is the slope of the line and 0,b is the y-intercept of the line. The line shown passes through the point 0,-8, so b=-8. The line shown also passes through the point -8,0. The slope, m\n, of a line passing through two points x1,y1 and x2,y2 can be calculated using the equation m=y2-y1x2-x1. For the points 0,-8 and -8,0, this gives m=-8-00--8, or m=-1. Substituting -8 for b\n and -1 for m\n in \n\ty\n\t=\n\t\n\t\t\n\t\t\tm\n\t\t\tx\n\t\t\n\t\t+\n\t\tb\n\t\n\n yields y=-1x+-8, or y=-x-8. Therefore, an equation of the graph shown is y=-x-8.

\n

Choice A is incorrect. This is an equation of a line with a slope of -2\n, not -1\n.

\n

Choice B is incorrect. This is an equation of a line with a slope of 1\n, not -1\n.

\n

Choice D is incorrect. This is an equation of a line with a slope of 2\n, not -1\n.

"}, {"id": "8adf1335", "domain": "Algebra", "skill": "Linear equations in two variables", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

A city’s total expense budget for one year was x million dollars. The city budgeted y million dollars for departmental expenses and 201 million dollars for all other expenses. Which of the following represents the relationship between x and y in this context?

\n", "choices": [{"id": "A", "text": "

\n x + y = 201\n

\n"}, {"id": "B", "text": "

\n x \u2212 y = 201\n

\n"}, {"id": "C", "text": "

\n 2 x \u2212 y = 201\n

\n"}, {"id": "D", "text": "

\n y \u2212 x = 201\n

\n"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. Of the city’s total expense budget for one year, the city budgeted y million dollars for departmental expenses and 201 million dollars for all other expenses. This means that the expression y + 201 represents the total expense budget, in millions of dollars, for one year. It’s given that the total expense budget for one year is x million dollars. It follows then that the expression y + 201 is equivalent to x, or y + 201 = x. Subtracting y from both sides of this equation yields 201 = x \u2212 y. By the symmetric property of equality, this is the same as x \u2212 y = 201.

Choices A and C are incorrect. Because it’s given that the total expense budget for one year, x million dollars, is comprised of the departmental expenses, y million dollars, and all other expenses, 201 million dollars, the expressions x + y and 2 x \u2212 y both must be equivalent to a value greater than 201 million dollars. Therefore, the equations x + y = 201and 2 x \u2212 y = 201aren’t true. Choice D is incorrect. The value of x must be greater than the value of y. Therefore, y \u2212 x = 201 can’t represent this relationship.

\n"}, {"id": "9db5b5c1", "domain": "Algebra", "skill": "Systems of two linear equations in two variables", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

\n\t\n\t\t4\n\t\tx\n\t\n\t=\n\t20\n\n

\n

\n\t\n\t\t\n\t\t\t-\n\t\t\t3\n\t\t\tx\n\t\t\n\t\t+\n\t\ty\n\t\n\t=\n\t-7\n\n

\n

The solution to the given system of equations is x,y. What is the value of \n\tx\n\t+\n\ty\n\n?

", "choices": [{"id": "A", "text": "

-27\n

"}, {"id": "B", "text": "

-13\n

"}, {"id": "C", "text": "

13\n

"}, {"id": "D", "text": "

27\n

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. It's given that \n\t\n\t\t4\n\t\tx\n\t\n\t=\n\t20\n\n and \n\t\n\t\t\n\t\t\t-\n\t\t\t3\n\t\t\tx\n\t\t\n\t\t+\n\t\ty\n\t\n\t=\n\t-7\n\n is a system of equations with a solution x,y. Adding the second equation in the given system to the first equation yields 4x+(-3x+y)=20+-7, which is equivalent to x+y=13. Thus, the value of x+y is 13\n. 

\n

Choice A is incorrect. This represents the value of -2x+y-1.

\n

Choice B is incorrect. This represents the value of -x+y.

\n

Choice D is incorrect. This represents the value of 2x+y+1.

"}, {"id": "80da233d", "domain": "Algebra", "skill": "Linear inequalities in one or two variables", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

A certain elephant weighs 200 pounds at birth and gains more than 2 but less than 3 pounds per day during its first year. Which of the following inequalities represents all possible weights w, in pounds, for the elephant 365 days after birth?

\n", "choices": [{"id": "A", "text": "

\n 400 < w, which < 600\n

\n"}, {"id": "B", "text": "

\n 565 < w, which < 930\n

\n"}, {"id": "C", "text": "

\n 730 < w, which < 1,095\n

\n"}, {"id": "D", "text": "

\n 930 < w, which < 1,295\n

\n"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. It’s given that the elephant weighs 200 pounds at birth and gains more than 2 pounds but less than 3 pounds per day during its first year. The inequality 200 + 2 d, < w, which < 200 + 3 d represents this situation, where d is the number of days after birth. Substituting 365 for d in the inequality gives 200 + 2, \u00d7 365, < w, which < 200 + 3, \u00d7 365, or 930 < w, which < 1,295.

Choice A is incorrect and may result from solving the inequality 200 \u00d7 2, < w, which < 200 \u00d7 3. Choice B is incorrect and may result from solving the inequality for a weight range of more than 1 pound but less than 2 pounds: 200 + 1, \u00d7 365, < w, which < 200 + 2, \u00d7 365. Choice C is incorrect and may result from calculating the possible weight gained by the elephant during the first year without adding the 200 pounds the elephant weighed at birth.

\n"}, {"id": "271f7e3f", "domain": "Algebra", "skill": "Linear functions", "difficulty": "M", "type": "mc", "stimulus": "
\n

\n f(x) = (x + 7)/(4)\n

\n
\n", "stem": "

For the function f defined above, what is the value of f(9), minus, f(1) ?

\n", "choices": [{"id": "A", "text": "

\n 1

\n"}, {"id": "B", "text": "

\n 2

\n"}, {"id": "C", "text": "

\n one fourth

\n"}, {"id": "D", "text": "

\n nine fourths

\n"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. The value of f(9) \u2212 f(1) can be calculated by finding the values of f(9) and f(1). The value of f(9) can be found by substituting 9 for x in the given function: f(9) = the fraction with numerator, open parenthesis, 9 + 7, close parenthesis, and denominator 4. This equation can be rewritten as f(9) = 16 over 4, or 4. Then, the value of f(1) can be found by substituting 1 for x in the given function: f(1) = the fraction with numerator, open parenthesis, 1 + 7, close parenthesis, and denominator 4. This equation can be rewritten as f(1) = 8 over 4, or 2. Therefore, f(9) \u2212 f(1) = 4 \u2212 2, which is equivalent to 2.

Choices A, C, and D are incorrect and may result from incorrectly substituting values of x in the given function or making computational errors.

\n"}, {"id": "70e29454", "domain": "Algebra", "skill": "Linear equations in one variable", "difficulty": "M", "type": "mc", "stimulus": "
\n\t

\"\"

\n
\n", "stem": "

In the equation above, a and b are constants. If the equation has infinitely many solutions, what are the values of a and b ?

\n", "choices": [{"id": "A", "text": "

a = 2 and b = 1

\n"}, {"id": "B", "text": "

a = 2 and b = 7

\n"}, {"id": "C", "text": "

a = \u22122 and b = 5

\n"}, {"id": "D", "text": "

a = \u22122 and b = \u22125

\n"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. Distributing the a on the left-hand side of the equation gives 3a – b – ax = –1 – 2x. Rearranging the terms in each side of the equation yields –ax + 3a – b = –2x –1. Since the equation has infinitely many solutions, it follows that the coefficients of x and the free terms on both sides must be equal. That is,  –a = –2, or a = 2, and 3a – b = –1. Substituting 2 for a in the equation 3a – b = –1 gives 3(2) – b = –1, so  b = 7.

Choice A is incorrect and may be the result of a conceptual error when finding the value of b. Choices C and D are incorrect and may result from making a sign error when simplifying.

\n"}, {"id": "e7b6f0d1", "domain": "Algebra", "skill": "Linear equations in one variable", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

\n\t\n\t\t\n\t\t\t4\n\t\t\tx\n\t\t\n\t\t+\n\t\t6\n\t\n\t=\n\t18\n\n

\n

Which equation has the same solution as the given equation?

", "choices": [{"id": "A", "text": "

\n\t\n\t\t4\n\t\tx\n\t\n\t=\n\t108\n\n

"}, {"id": "B", "text": "

\n\t\n\t\t4\n\t\tx\n\t\n\t=\n\t24\n\n

"}, {"id": "C", "text": "

\n\t\n\t\t4\n\t\tx\n\t\n\t=\n\t12\n\n

"}, {"id": "D", "text": "

\n\t\n\t\t4\n\t\tx\n\t\n\t=\n\t3\n\n

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. Subtracting 6\n from both sides of the given equation yields \n\t\n\t\t4\n\t\tx\n\t\n\t=\n\t12\n\n, which is the equation given in choice C. Since this equation is equivalent to the given equation, it has the same solution as the given equation.

\n

Choice A is incorrect and may result from conceptual or calculation errors.

\n

Choice B is incorrect and may result from conceptual or calculation errors.

\n

Choice D is incorrect and may result from conceptual or calculation errors.

"}, {"id": "0b46bad5", "domain": "Algebra", "skill": "Linear equations in two variables", "difficulty": "H", "type": "mc", "stimulus": "
\n

\n a, x, + b y = b\n

\n
\n", "stem": "

In the equation above, a and b are constants and 0 < a, which < b. Which of the following could represent the graph of the equation in the xy-plane?

\n", "choices": [{"id": "A", "text": "

\n \n \n

\n \"The

\n"}, {"id": "B", "text": "

\n \n \n

\n \"The

\n"}, {"id": "C", "text": "

\n \n \n

\n \"The

\n"}, {"id": "D", "text": "

\n \n \n

\n \"The

\n"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. The given equation a, x + b y = b can be rewritten in slope-intercept form, y = m x + k, where m represents the slope of the line represented by the equation, and k represents the y-coordinate of the y-intercept of the line. Subtracting ax from both sides of the equation yields b y = \u2212a, x + b, and dividing both sides of this equation by b yields y = the \u2212of (a)/(b, end fraction, \u00d7 x, plus, the fraction b over b, end fraction), or y = the \u2212of (a)/(b, end fraction, \u00d7 x, + 1). With the equation now in slope-intercept form, it shows that k = 1, which means the y-coordinate of the y-intercept is 1. It’s given that a and b are both greater than 0 (positive) and that a < b. Since m = the \u2212of (a)/(b), the slope of the line must be a value between \u22121 and 0. Choice C is the only graph of a line that has a y-value of the y-intercept that is 1 and a slope that is between \u22121 and 0.

Choices A, B, and D are incorrect because the slopes of the lines in these graphs aren’t between \u22121 and 0.

\n"}, {"id": "b31c3117", "domain": "Algebra", "skill": "Linear inequalities in one or two variables", "difficulty": "M", "type": "mc", "stimulus": "
\n

\n H = 120 p, + 60\n

\n
\n", "stem": "

The Karvonen formula above shows the relationship between Alice’s target heart rate H, in beats per minute (bpm), and the intensity level p of different activities. When p = 0, Alice has a resting heart rate. When p = 1, Alice has her maximum heart rate. It is recommended that p be between 0.5 and 0.85 for Alice when she trains. Which of the following inequalities describes Alice’s target training heart rate?

\n", "choices": [{"id": "A", "text": "

\n 120 < or equal to H, which < or equal to 162\n

\n"}, {"id": "B", "text": "

\n 102 < or equal to H, which < or equal to 120\n

\n"}, {"id": "C", "text": "

\n 60 < or equal to H, which < or equal to 162\n

\n"}, {"id": "D", "text": "

\n 60 < or equal to H, which < or equal to 102\n

\n"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. When Alice trains, it’s recommended that p be between 0.5 and 0.85. Therefore, her target training heart rate is represented by the values of H corresponding to 0 point 5 < or equal to p, which < or equal to 0 point 8 5. When p = 0 point 5, H = 120 \u00d7 0 point 5, + 60, or H = 120. When p = 0 point 8 5, H = 120 \u00d7 0 point 8 5, plus, 60, or H = 162. Therefore, the inequality that describes Alice’s target training heart rate is 120 < or equal to H, which < or equal to 162.

Choice B is incorrect. This inequality describes Alice’s target heart rate for 0 point 3 5 < or equal to p, which < or equal to 0 point 5. Choice C is incorrect. This inequality describes her target heart rate for 0 < or equal to p, which < or equal to 0 point 8 5. Choice D is incorrect. This inequality describes  her target heart rate for 0 < or equal to p, which < or equal to 0 point 3 5.

\n"}, {"id": "f79fffba", "domain": "Algebra", "skill": "Linear functions", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

The function h\n is defined by hx=3x-7. What is the value of h-2?

", "choices": [{"id": "A", "text": "

-13\n

"}, {"id": "B", "text": "

-10\n

"}, {"id": "C", "text": "

10\n

"}, {"id": "D", "text": "

13\n

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. The value of h-2 can be found by substituting -2\n for x\n in the equation defining h\n. Substituting -2\n for x\n in hx=3x-7 yields h-2=3-2-7, or h-2=-13. Therefore, the value of h-2 is -13\n.

\n

Choice B is incorrect. This is the value of h-1, not h-2.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

\n

Choice D is incorrect and may result from conceptual or calculation errors.
 

"}, {"id": "7d5d1b32", "domain": "Algebra", "skill": "Linear equations in one variable", "difficulty": "H", "type": "spr", "stimulus": "", "stem": "

2kx-n=\n\t-\n\t\n\t\t28\n\t\t15\n\t\n\n\n\tx\n\t-\n\t\n\t\t36\n\t\t19\n\t\n\n

\n

In the given equation, k\n and n\n are constants and n>1. The equation has no solution. What is the value of k\n?

", "choices": [], "answerId": "-.9333", "acceptedAnswers": ["-.9333", "-14/15"], "rationale": "

The correct answer is -1415. A linear equation in the form ax+b=cx+d has no solution only when the coefficients of x\n on each side of the equation are equal and the constant terms are not equal. Dividing both sides of the given equation by 2\n yields kx-n=-2830x-3638, or kx-n=-1415x-1819. Since it’s given that the equation has no solution, the coefficient of x\n on both sides of this equation must be equal, and the constant terms on both sides of this equation must not be equal. Since 1819<1, and it's given that n>1, the second condition is true. Thus, k\n must be equal to -1415. Note that -14/15, -.9333, and -0.933 are examples of ways to enter a correct answer.

"}, {"id": "e7343559", "domain": "Algebra", "skill": "Linear equations in two variables", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

\n\ty\n\t=\n\t\n\t\t\n\t\t\t-\n\t\t\t4\n\t\t\tx\n\t\t\n\t\t+\n\t\t40\n\t\n\n

\n

Which table gives three values of x\n and their corresponding values of y\n for the given equation?

", "choices": [{"id": "A", "text": "
\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
x\ny\n
0\n0\n
1\n-4\n
2\n-8\n
"}, {"id": "B", "text": "
\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
x\ny\n
0\n40\n
1\n44\n
2\n48\n
"}, {"id": "C", "text": "
\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
x\ny\n
0\n40\n
1\n36\n
2\n32\n
"}, {"id": "D", "text": "
\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
x\ny\n
0\n0\n
1\n4\n
2\n8\n
"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. Each of the given choices gives three values of x\n: 0\n, 1\n, and 2\n. Substituting 0\n for x\n in the given equation yields y=-40+40, or \n\ty\n\t=\n\t40\n\n. Therefore, when \n\tx\n\t=\n\t0\n\n, the corresponding value of y\n for the given equation is 40\n. Substituting 1\n for x\n in the given equation yields y=-41+40, or \n\ty\n\t=\n\t36\n\n. Therefore, when \n\tx\n\t=\n\t1\n\n, the corresponding value of y\n for the given equation is 36\n. Substituting 2\n for x\n in the given equation yields y=-42+40, or \n\ty\n\t=\n\t32\n\n. Therefore, when \n\tx\n\t=\n\t2\n\n, the corresponding value of y\n for the given equation is 32\n. Choice C gives three values of x\n, 0\n, 1\n, and 2\n, and their corresponding values of y\n, 40\n, 36\n, and 32\n, respectively, for the given equation.

\n

Choice A is incorrect. This table gives three values of x\n and their corresponding values of y\n for the equation \n\ty\n\t=\n\t\n\t\t-\n\t\t4\n\t\tx\n\t\n\n.

\n

Choice B is incorrect. This table gives three values of x\n and their corresponding values of y\n for the equation \n\ty\n\t=\n\t\n\t\t\n\t\t\t4\n\t\t\tx\n\t\t\n\t\t+\n\t\t40\n\t\n\n.

\n

Choice D is incorrect. This table gives three values of x\n and their corresponding values of y\n for the equation \n\ty\n\t=\n\t\n\t\t4\n\t\tx\n\t\n\n.

"}, {"id": "a9039591", "domain": "Algebra", "skill": "Linear functions", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "
\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
x\nf(x)
0\n29\n
1\n32\n
2\n35\n
\n

For the linear function f\n, the table shows three values of x\n and their corresponding values of f(x). Which equation defines f(x)?

", "choices": [{"id": "A", "text": "

f(x)=\n\t\n\t\t3\n\t\tx\n\t\n\t+\n\t29\n\n

"}, {"id": "B", "text": "

f(x)=\n\t\n\t\t29\n\t\tx\n\t\n\t+\n\t32\n\n

"}, {"id": "C", "text": "

f(x)=\n\t\n\t\t35\n\t\tx\n\t\n\t+\n\t29\n\n

"}, {"id": "D", "text": "

f(x)=\n\t\n\t\t32\n\t\tx\n\t\n\t+\n\t35\n\n

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. An equation that defines a linear function f\n can be written in the form fx=mx+b, where m\n and b\n are constants. It's given in the table that when \n\tx\n\t=\n\t0\n\n, fx=29. Substituting 0\n for x\n and 29\n for fx in the equation fx=mx+b yields 29=m0+b, or \n\t29\n\t=\n\tb\n\n. Substituting 29\n for b\n in the equation fx=mx+b yields fx=mx+29. It's also given in the table that when \n\tx\n\t=\n\t1\n\n, fx=32. Substituting 1\n for x\n and 32\n for fx in the equation fx=mx+29 yields 32=m1+29, or \n\t32\n\t=\n\t\n\t\tm\n\t\t+\n\t\t29\n\t\n\n. Subtracting 29\n from both sides of this equation yields \n\t3\n\t=\n\tm\n\n. Substituting 3\n for m\n in the equation fx=mx+29 yields fx=3x+29.

\n

Choice B is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

\n

Choice D is incorrect and may result from conceptual or calculation errors.

"}, {"id": "ee7b1de1", "domain": "Algebra", "skill": "Linear inequalities in one or two variables", "difficulty": "H", "type": "spr", "stimulus": "", "stem": "

A small business owner budgets $2,200 to purchase candles. The owner must purchase a minimum of 200\n candles to maintain the discounted pricing. If the owner pays $4.90 per candle to purchase small candles and $11.60 per candle to purchase large candles, what is the maximum number of large candles the owner can purchase to stay within the budget and maintain the discounted pricing?

", "choices": [], "answerId": "182", "acceptedAnswers": ["182"], "rationale": "

The correct answer is 182\n. Let s\n represent the number of small candles the owner can purchase, and let l represent the number of large candles the owner can purchase. It’s given that the owner pays $4.90 per candle to purchase small candles and $11.60 per candle to purchase large candles. Therefore, the owner pays 4.90s dollars for s\n small candles and 11.60l dollars for l large candles, which means the owner pays a total of 4.90s+11.60l dollars to purchase candles. It’s given that the owner budgets $2,200 to purchase candles. Therefore, 4.90s+11.60l\u22642,200. It’s also given that the owner must purchase a minimum of 200\n candles. Therefore, s+l\u2265200. The inequalities 4.90s+11.60l\u22642,200 and s+l\u2265200 can be combined into one compound inequality by rewriting the second inequality so that its left-hand side is equivalent to the left-hand side of the first inequality. Subtracting l from both sides of the inequality s+l\u2265200 yields s\u2265200-l. Multiplying both sides of this inequality by 4.90 yields 4.90s\u22654.90200-l, or 4.90s\u2265980-4.90l. Adding 11.60l to both sides of this inequality yields 4.90s+11.60l\u2265980-4.90l+11.60l, or 4.90s+11.60l\u2265980+6.70l. This inequality can be combined with the inequality 4.90s+11.60l\u22642,200, which yields the compound inequality 980+6.70l\u22644.90s+11.60l\u22642,200. It follows that 980+6.70l\u22642,200. Subtracting 980\n from both sides of this inequality yields 6.70l\u22642,200. Dividing both sides of this inequality by 6.70 yields approximately l\u2264182.09. Since the number of large candles the owner purchases must be a whole number, the maximum number of large candles the owner can purchase is the largest whole number less than 182.09\n, which is 182\n.

"}, {"id": "c17d9ba9", "domain": "Algebra", "skill": "Linear inequalities in one or two variables", "difficulty": "M", "type": "spr", "stimulus": "", "stem": "

A number x\n is at most 17\n less than 5\n times the value of y\n. If the value of y\n is 3\n, what is the greatest possible value of x\n?

", "choices": [], "answerId": "-2", "acceptedAnswers": ["-2"], "rationale": "

The correct answer is -2\n. It's given that a number x\n is at most 17\n less than 5\n times the value of y\n, or x≤5y-17. Substituting 3\n for y\n in this inequality yields x≤53-17, or x≤-2. Thus, if the value of y\n is 3\n, the greatest possible value of x\n is -2\n.

"}, {"id": "94b48cbf", "domain": "Algebra", "skill": "Linear equations in two variables", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

The graph of \n\t\n\t\t\n\t\t\t7\n\t\t\tx\n\t\t\n\t\t+\n\t\t\n\t\t\t2\n\t\t\ty\n\t\t\n\t\n\t=\n\t-31\n\n in the \n\tx\n\ty\n\n-plane has an x\n-intercept at (a\n, 0\n) and a y\n-intercept at (0\n, b\n), where a\n and b\n are constants. What is the value of \n\t\tb\n\t\ta\n\t\n?

", "choices": [{"id": "A", "text": "

\n\t-\n\t\n\t\t7\n\t\t2\n\t\n\n

"}, {"id": "B", "text": "

\n\t-\n\t\n\t\t2\n\t\t7\n\t\n\n

"}, {"id": "C", "text": "

\n\t2\n\t7\n\n

"}, {"id": "D", "text": "

\n\t7\n\t2\n\n

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. The x-coordinate a\n of the x-intercept a,0 can be found by substituting 0\n for y\n in the given equation, which gives 7x+20=-31, or 7x=-31. Dividing both sides of this equation by 7\n yields x=-317. Therefore, the value of a\n is -317. The y-coordinate b\n of the y-intercept 0,b can be found by substituting 0\n for x\n in the given equation, which gives 70+2y=-31, or 2y=-31. Dividing both sides of this equation by 2\n yields y=-312. Therefore, the value of b\n is -312. It follows that the value of \n\t\n\t\tb\n\t\ta\n\t\n\n is -312-317, which is equivalent to 312731, or \n\t7\n\t2\n\n.

\n

Choice A is incorrect and may result from conceptual or calculation errors.

\n

Choice B is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

"}, {"id": "1035faea", "domain": "Algebra", "skill": "Linear inequalities in one or two variables", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

A psychologist set up an experiment to study the tendency of a person to select the first item when presented with a series of items. In the experiment, 300 people were presented with a set of five pictures arranged in random order. Each person was asked to choose the most appealing picture. Of the first 150 participants, 36 chose the first picture in the set. Among the remaining 150 participants, p people chose the first picture in the set. If more than 20% of all participants chose the first picture in the set, which of the following inequalities best describes the possible values of p ?

\n", "choices": [{"id": "A", "text": "

p is greater than, 0 point 20 times, open parenthesis, 300 \u2212 36, close parenthesis, where p < or equal to 150

\n"}, {"id": "B", "text": "

p is greater than, 0 point 20 times, open parenthesis, 300 + 36, close parenthesis, where p < or equal to 150

\n"}, {"id": "C", "text": "

p \u2212 36 is greater than, 0 point 20 \u00d7 300, where p < or equal to 150

\n"}, {"id": "D", "text": "

p + 36 is greater than, 0 point 20 \u00d7 300, where p < or equal to 150

\n"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. Of the first 150 participants, 36 chose the first picture in the set, and of the 150 remaining participants, p chose the first picture in the set. Hence, the proportion of the participants who chose the first picture in the set is (36 + p)/(300). Since more than 20% of all the participants chose the first picture, it follows that (36 + p)/(300, > 0 point 2 0).

This inequality can be rewritten as p + 36, is greater than, 0 point 2 0 \u00d7 300. Since p is a number of people among the remaining 150 participants, p < or equal to 150.

Choices A, B, and C are incorrect and may be the result of some incorrect interpretations of the given information or of computational errors.

 

\n"}, {"id": "8339793c", "domain": "Algebra", "skill": "Linear equations in one variable", "difficulty": "E", "type": "spr", "stimulus": "", "stem": "

Nasir bought 9\n storage bins that were each the same price. He used a coupon for $63 off the entire purchase. The cost for the entire purchase after using the coupon was $27. What was the original price, in dollars, for 1\n storage bin?

", "choices": [], "answerId": "10", "acceptedAnswers": ["10"], "rationale": "

The correct answer is 10\n. It’s given that the cost for the entire purchase was $27 after a coupon was used for $63 off the entire purchase. Adding the amount of the coupon to the purchase price yields 27+63=90. Thus, the cost for the entire purchase before using the coupon was $90. It’s given that Nasir bought 9\n storage bins. The original price for 1\n storage bin can be found by dividing the total cost by 9\n. Therefore, the original price, in dollars, for 1\n storage bin is 909, or 10\n.

"}, {"id": "2e0290c3", "domain": "Algebra", "skill": "Linear equations in two variables", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n

\n

The graph shows the relationship between the number of shares of stock from Company A, x\n, and the number of shares of stock from Company B, y\n, that Simone can purchase. Which equation could represent this relationship?

", "choices": [{"id": "A", "text": "

\n\ty\n\t=\n\t\n\t\t\n\t\t\t8\n\t\t\tx\n\t\t\n\t\t+\n\t\t12\n\t\n\n

"}, {"id": "B", "text": "

\n\t\n\t\t\n\t\t\t8\n\t\t\tx\n\t\t\n\t\t+\n\t\t\n\t\t\t12\n\t\t\ty\n\t\t\n\t\n\t=\n\t480\n\n

"}, {"id": "C", "text": "

\n\ty\n\t=\n\t\n\t\t\n\t\t\t12\n\t\t\tx\n\t\t\n\t\t+\n\t\t8\n\t\n\n

"}, {"id": "D", "text": "

\n\t\n\t\t\n\t\t\t12\n\t\t\tx\n\t\t\n\t\t+\n\t\t\n\t\t\t8\n\t\t\ty\n\t\t\n\t\n\t=\n\t480\n\n

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. The graph shown is a line passing through the points 0,40 and 60,0. Since the relationship between x\n and y\n is linear, if two points on the graph make a linear equation true, then the equation represents the relationship. Substituting 0\n for x\n and 40\n for y\n in the equation in choice B, \n\t\n\t\t\n\t\t\t8\n\t\t\tx\n\t\t\n\t\t+\n\t\t\n\t\t\t12\n\t\t\ty\n\t\t\n\t\n\t=\n\t480\n\n, yields 80+1240=480, or 480=480, which is true. Substituting 60\n for x\n and 0\n for y\n in the equation \n\t\n\t\t\n\t\t\t8\n\t\t\tx\n\t\t\n\t\t+\n\t\t\n\t\t\t12\n\t\t\ty\n\t\t\n\t\n\t=\n\t480\n\n yields 860+120=480, or 480=480, which is true. Therefore, the equation \n\t\n\t\t\n\t\t\t8\n\t\t\tx\n\t\t\n\t\t+\n\t\t\n\t\t\t12\n\t\t\ty\n\t\t\n\t\n\t=\n\t480\n\n represents the relationship between x\n and y\n.

\n

Choice A is incorrect. The point 0,40 is not on the graph of this equation, since 40=80+12, or 40=12, is not true.

\n

Choice C is incorrect. The point 0,40 is not on the graph of this equation, since 40=120+8, or 40=8, is not true.

\n

Choice D is incorrect. The point 0,40 is not on the graph of this equation, since 120+840=480, or 320=480, is not true.

"}, {"id": "dd797fe2", "domain": "Algebra", "skill": "Linear equations in two variables", "difficulty": "E", "type": "mc", "stimulus": "
\n

\n 4 x + 3 y = 24\n

\n
\n", "stem": "

Mario purchased 4 binders that cost x dollars each and 3 notebooks that cost y dollars each. If the given equation represents this situation, which of the following is the best interpretation of 24 in this context?

\n", "choices": [{"id": "A", "text": "

The total cost, in dollars, for all binders purchased

\n"}, {"id": "B", "text": "

The total cost, in dollars, for all notebooks purchased

\n"}, {"id": "C", "text": "

The total cost, in dollars, for all binders and notebooks purchased

\n"}, {"id": "D", "text": "

The difference in the total cost, in dollars, between the number of binders and notebooks purchased

\n"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. Since Mario purchased 4 binders that cost x dollars each, the expression 4 x represents the total cost, in dollars, of the 4 binders he purchased. Since Mario purchased 3 notebooks that cost y dollars each, the expression 3 y represents the total cost, in dollars, of the 3 notebooks he purchased. Therefore, the expression 4 x + 3 y represents the total cost, in dollars, for all binders and notebooks he purchased. In the given equation, the expression 4 x + 3 y is equal to 24. Therefore, it follows that 24 is the total cost, in dollars, for all binders and notebooks purchased.

Choice A is incorrect. This is represented by the expression 4 x in the given equation. Choice B is incorrect. This is represented by the expression 3 y in the given equation. Choice D is incorrect. This is represented by the expression the absolute value of, 4 x \u2212 3 y, end absolute value.

\n"}, {"id": "45a534d0", "domain": "Algebra", "skill": "Systems of two linear equations in two variables", "difficulty": "H", "type": "spr", "stimulus": "", "stem": "

\n\t\n\t\t\n\t\t\t48\n\t\t\tx\n\t\t\n\t\t-\n\t\t\n\t\t\t72\n\t\t\ty\n\t\t\n\t\n\t=\n\t\n\t\t\n\t\t\t30\n\t\t\ty\n\t\t\n\t\t+\n\t\t24\n\t\n\n

\n

ry=16-16x

\n

In the given system of equations, r\n is a constant. If the system has no solution, what is the value of r\n?

", "choices": [], "answerId": "-34", "acceptedAnswers": ["-34"], "rationale": "

The correct answer is -34. A system of two linear equations in two variables, x\n and y\n, has no solution if the lines represented by the equations in the xy-plane are distinct and parallel. Two lines represented by equations in standard form Ax+By=C, where A\n, B\n, and C\n are constants, are parallel if the coefficients for x\n and y\n in one equation are proportional to the corresponding coefficients in the other equation. The first equation in the given system can be written in standard form by subtracting \n\t30\n\ty\n\n from both sides of the equation to yield 48x-102y=24. The second equation in the given system can be written in standard form by adding 16x to both sides of the equation to yield 16x+ry=16.  The coefficient of x\n in this second equation, 16\n, is 13 times the coefficient of x\n in the first equation, 48\n. For the lines to be parallel the coefficient of y\n in the second equation, r\n, must also be 13 times the coefficient of y\n in the first equation, -102. Thus, r=13(-102), or r=-34. Therefore, if the given system has no solution, the value of r\n is -34.

"}, {"id": "550b352c", "domain": "Algebra", "skill": "Linear equations in one variable", "difficulty": "E", "type": "mc", "stimulus": "
\n

\n 10 = 2 x + 4\n

\n
\n", "stem": "

How many solutions exist to the equation shown above?

\n", "choices": [{"id": "A", "text": "

None

\n"}, {"id": "B", "text": "

Exactly 1

\n"}, {"id": "C", "text": "

Exactly 3

\n"}, {"id": "D", "text": "

Infinitely many

\n"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. Subtracting 4 from each side of the given equation yields 6 = 2 x, or x = 3, so the equation has a unique solution of x = 3.

Choice A is incorrect. Since 3 is a value of x that satisfies the given equation, the equation has at least 1 solution. Choice C is incorrect. Linear equations can have 0, 1, or infinitely many solutions; no linear equation has exactly 3 solutions. Choice D is incorrect. If a linear equation has infinitely many solutions, it can be reduced to 0 = 0. This equation reduces to x = 3, so there is only 1 solution.

\n"}, {"id": "a396ed75", "domain": "Algebra", "skill": "Linear functions", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

For a training program, Juan rides his bike at an average rate of 5.7\n minutes per mile. Which function m\n models the number of minutes it will take Juan to ride x\n miles at this rate?

", "choices": [{"id": "A", "text": "

mx=x5.7

"}, {"id": "B", "text": "

mx=x+5.7

"}, {"id": "C", "text": "

mx=x-5.7

"}, {"id": "D", "text": "

mx=5.7x

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. It′s given that Juan rides his bike at an average rate of 5.7\n minutes per mile. The number of minutes it will take Juan to ride x\n miles can be determined by multiplying his average rate by the number of miles, x\n, which yields 5.7x. Therefore, the function mx=5.7x models the number of minutes it will take Juan to ride x\n miles.

\n

Choice A is incorrect and may result from conceptual errors. 

\n

Choice B is incorrect and may result from conceptual errors. 

\n

Choice C is incorrect and may result from conceptual errors. 

"}, {"id": "50f4cb9c", "domain": "Algebra", "skill": "Linear functions", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "
\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
x\nfx
1\n-64\n
2\n0\n
3\n64\n
\n

For the linear function f\n, the table shows three values of x\n and their corresponding values of fx. Function f\n is defined by fx=ax+b, where a\n and b\n are constants. What is the value of \n\ta\n\t-\n\tb\n\n?

", "choices": [{"id": "A", "text": "

-64\n

"}, {"id": "B", "text": "

62\n

"}, {"id": "C", "text": "

128\n

"}, {"id": "D", "text": "

192\n

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. The table gives that f(x)=0 when x=2. Substituting 0 for fx and 2\n for x\n into the equation f(x)=ax+b yields 0=2a+b. Subtracting \n\t2\n\ta\n\n from both sides of this equation yields b=-2a. The table gives that f(x)=-64 when x=1. Substituting -2a for b\n, -64 for fx, and 1\n for x\n into the equation f(x)=ax+b yields -64=a1+-2a. Combining like terms yields -64=-a, or a=64. Since b=-2a, substituting 64\n for a\n into this equation gives b=-264, which yields b=-128. Thus, the value of a-b can be written as 64-(-128), which is 192\n.

\n

Choice A is incorrect. This is the value of a+b, not a-b.

\n

Choice B is incorrect. This is the value of a-2, not a-b.

\n

Choice C is incorrect. This is the value of 2a, not a-b.

"}, {"id": "87071893", "domain": "Algebra", "skill": "Linear equations in one variable", "difficulty": "E", "type": "spr", "stimulus": "", "stem": "

\n\t\n\t\tx\n\t\t+\n\t\t40\n\t\n\t=\n\t95\n\n

\n

What value of x\n is the solution to the given equation?

", "choices": [], "answerId": "55", "acceptedAnswers": ["55"], "rationale": "

The correct answer is 55\n. Subtracting 40\n from both sides of the given equation yields x=55. Therefore, the value of x\n is 55\n.

"}, {"id": "ca9bb527", "domain": "Algebra", "skill": "Systems of two linear equations in two variables", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

\n\ty\n\t=\n\t\n\t\t\n\t\t\t4\n\t\t\tx\n\t\t\n\t\t-\n\t\t9\n\t\n\n
\n\ty\n\t=\n\t19\n\n

\n

What is the solution x,y to the given system of equations?

", "choices": [{"id": "A", "text": "

4,19

"}, {"id": "B", "text": "

7,19

"}, {"id": "C", "text": "

19,4

"}, {"id": "D", "text": "

19,7

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. It's given by the second equation in the system that \n\ty\n\t=\n\t19\n\n. Substituting 19\n for y\n in the first equation yields \n\t19\n\t=\n\t\n\t\t\n\t\t\t4\n\t\t\tx\n\t\t\n\t\t-\n\t\t9\n\t\n\n. Adding 9\n to both sides of this equation yields \n\t28\n\t=\n\t\n\t\t4\n\t\tx\n\t\n\n. Dividing both sides of this equation by 4\n yields \n\t7\n\t=\n\tx\n\n. Therefore, since \n\tx\n\t=\n\t7\n\n and \n\ty\n\t=\n\t19\n\n, the solution x,y to the given system of equations is 7,19.

\n

Choice A is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

\n

Choice D is incorrect and may result from conceptual or calculation errors.

"}, {"id": "16889ef3", "domain": "Algebra", "skill": "Linear functions", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

Oil and gas production in a certain area dropped from 4 million barrels in 2000 to 1.9 million barrels in 2013. Assuming that the oil and gas production decreased at a constant rate, which of the following linear functions f best models the production, in millions of barrels, t years after the year 2000?

\n", "choices": [{"id": "A", "text": "f(t) = (21)/(130, end fraction, t + 4)\n"}, {"id": "B", "text": "f(t) = (19)/(130, end fraction, t + 4)\n"}, {"id": "C", "text": "f(t) = the \u2212fraction 21 over 130, end fraction, t + 4\n"}, {"id": "D", "text": "f(t) = the \u2212fraction 19 over 130, end fraction, t + 4\n"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. It is assumed that the oil and gas production decreased at a constant rate. Therefore, the function f that best models the production t years after the year 2000 can be written as a linear function, f(t) = m, t + b, where m is the rate of change of the oil and gas production and b is the oil and gas production, in millions of barrels, in the year 2000. Since there were 4 million barrels of oil and gas produced in 2000, b = 4. The rate of change, m, can be calculated as (4 \u2212 1 point 9)/(0 \u2212 13, end fraction = the \u2212of (2 point 1)/(13)), which is equivalent to the \u2212of (21)/(130), the rate of change in choice C.

Choices A and B are incorrect because each of these functions has a positive rate of change. Since the oil and gas production decreased over time, the rate of change must be negative. Choice D is incorrect. This model may result from misinterpreting 1.9 million barrels as the amount by which the production decreased.

\n"}, {"id": "c651cc56", "domain": "Algebra", "skill": "Linear functions", "difficulty": "M", "type": "mc", "stimulus": "
\n
\n
\n \"The
\n
\n
\n", "stem": "

Some values of the linear function f are shown in the table above. What is the value of f(3)?

\n", "choices": [{"id": "A", "text": "

6

\n"}, {"id": "B", "text": "

7

\n"}, {"id": "C", "text": "

8

\n"}, {"id": "D", "text": "

9

\n"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. A linear function has a constant rate of change, and any two rows of the table shown can be used to calculate this rate. From the first row to the second, the value of x is increased by 2 and the value of f(x) is increased by 6 = 4 \u2212 \u22122. So the values of f(x) increase by 3 for every increase by 1 in the value of x. Since f(2) = 4, it follows that f of, open parenthesis, 2 + 1, close parenthesis = 4 + 3, which = 7. Therefore, f(3) = 7.

Choice A is incorrect. This is the third x-value in the table, not f(3). Choices C and D are incorrect and may result from errors when calculating the function’s rate of change.

\n"}, {"id": "adb0c96c", "domain": "Algebra", "skill": "Systems of two linear equations in two variables", "difficulty": "H", "type": "spr", "stimulus": "", "stem": "

\n\t\n\t\t\n\t\t\t24\n\t\t\tx\n\t\t\n\t\t+\n\t\ty\n\t\n\t=\n\t48\n\n

\n

\n\t\n\t\t\n\t\t\t6\n\t\t\tx\n\t\t\n\t\t+\n\t\ty\n\t\n\t=\n\t72\n\n

\n

The solution to the given system of equations is (x,y). What is the value of y\n?

", "choices": [], "answerId": "80", "acceptedAnswers": ["80"], "rationale": "

The correct answer is 80\n. Subtracting the second equation in the given system from the first equation yields 24x+y-6x+y=48-72, which is equivalent to 24x-6x+y-y=-24, or 18x=-24. Dividing each side of this equation by 3\n yields 6x=-8. Substituting -8\n for \n\t6\n\tx\n\n in the second equation yields -8+y=72. Adding 8\n to both sides of this equation yields y=80. 

\n

Alternate approach: Multiplying each side of the second equation in the given system by 4\n yields 24x+4y=288. Subtracting the first equation in the given system from this equation yields 24x+4y-24x+y=288-48, which is equivalent to 24x-24x+4y-y=240, or 3y=240. Dividing each side of this equation by 3\n yields y=80.

"}, {"id": "b4553284", "domain": "Algebra", "skill": "Linear equations in one variable", "difficulty": "E", "type": "spr", "stimulus": "", "stem": "

If \n\t\n\t\t2\n\t\tx\n\t\n\t=\n\t12\n\n, what is the value of \n\t9\n\tx\n\n?

", "choices": [], "answerId": "54", "acceptedAnswers": ["54"], "rationale": "

The correct answer is 54\n. Dividing both sides of the given equation by 2\n yields x=6. Multiplying both sides of this equation by 9\n yields 9x=54. Thus, the value of 9x is 54\n.

"}, {"id": "c22b5f25", "domain": "Algebra", "skill": "Linear functions", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

In the xy-plane, the points \u22122, 3 and 4, \u22125 lie on the graph of which of the following linear functions?

\n", "choices": [{"id": "A", "text": "

\n f(x) = x + 5\n

\n"}, {"id": "B", "text": "

\n f(x) = one half x, + 4\n

\n"}, {"id": "C", "text": "

\n f(x) = negative, four thirds x, + one third\n

\n"}, {"id": "D", "text": "

\n f(x) = negative, three halves x, + 1\n

\n"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. A linear function can be written in the form f(x) = m x + b, where m is the slope and b is the y-coordinate of the y-intercept of the line. The slope of the graph can be found using the formula m = (y sub 2 \u2212 y sub 1)/(x sub 2 \u2212 x sub 1, end fraction). Substituting the values of the given points into this formula yields m = (\u22125 \u2212 3)/(4 \u2212 \u22122, end fraction) or m = \u22128 over 6, which simplifies to m = \u2212four thirds. Only choice C shows an equation with this slope.

\nChoices A, B, and D are incorrect and may result from computation errors or misinterpreting the given information.

\n"}, {"id": "11e1ab81", "domain": "Algebra", "skill": "Linear functions", "difficulty": "M", "type": "mc", "stimulus": "
\n
\n \"The
\n
\n", "stem": "

The graph above shows the distance traveled d, in feet, by a product on a conveyor belt m minutes after the product is placed on the belt. Which of the following equations correctly relates d and m ?

\n", "choices": [{"id": "A", "text": "d = 2 m\n"}, {"id": "B", "text": "d = one-half m\n"}, {"id": "C", "text": "d = m, + 2\n"}, {"id": "D", "text": "d = 2 m, + 2\n"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. The line passes through the origin. Therefore, this is a relationship of the form d = k m, where k is a constant representing the slope of the graph. To find the value of k, choose a point m, d on the graph of the line other than the origin and substitute the values of m and d into the equation. For example, if the point 2, 4 is chosen, then 4 = k \u00d7 2, and k = 2. Therefore, the equation of the line is d = 2 m.

Choice B is incorrect and may result from calculating the slope of the line as the change in time over the change in distance traveled instead of the change in distance traveled over the change in time. Choices C and D are incorrect because each of these equations represents a line with a d-intercept of 2. However, the graph shows a line with a d-intercept of 0.

\n"}, {"id": "771bd0ca", "domain": "Algebra", "skill": "Linear equations in one variable", "difficulty": "H", "type": "spr", "stimulus": "", "stem": "

5(t+3)-7(t+3)=38

\n

What value of t\n is the solution to the given equation?

", "choices": [], "answerId": "-22", "acceptedAnswers": ["-22"], "rationale": "

The correct answer is -22\n. The given equation can be rewritten as -2t+3=38. Dividing both sides of this equation by -2\n yields t+3=-19. Subtracting 3\n from both sides of this equation yields \n\tt\n\t=\n\t-22\n\n. Therefore, -22\n is the value of t\n that is the solution to the given equation.

"}, {"id": "789975b7", "domain": "Algebra", "skill": "Linear equations in two variables", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

A gardener buys two kinds of fertilizer. Fertilizer A contains 60% filler materials by weight and Fertilizer B contains 40% filler materials by weight. Together, the fertilizers bought by the gardener contain a total of 240 pounds of filler materials. Which equation models this relationship, where x is the number of pounds of Fertilizer A and y is the number of pounds of Fertilizer B?

\n", "choices": [{"id": "A", "text": "zero point 4 x, + zero point 6 y = 240\n"}, {"id": "B", "text": "zero point 6 x, + zero point 4 y = 240\n"}, {"id": "C", "text": "40 x, plus, 60 y = 240\n"}, {"id": "D", "text": "60 x, + 40 y = 240\n"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. Since Fertilizer A contains 60% filler materials by weight, it follows that x pounds of Fertilizer A consists of 0.6x pounds of filler materials. Similarly, y pounds of Fertilizer B consists of 0.4y pounds of filler materials. When x pounds of Fertilizer A and y pounds of Fertilizer B are combined, the result is 240 pounds of filler materials. Therefore, the total amount, in pounds, of filler materials in a mixture of x pounds of Fertilizer A and y pounds of Fertilizer B can be expressed as 0 point 6 x, + 0 point 4 y = 240.

Choice A is incorrect. This choice transposes the percentages of filler materials for Fertilizer A and Fertilizer B. Fertilizer A consists of 0.6x pounds of filler materials and Fertilizer B consists of 0.4y pounds of filler materials. Therefore, 0 point 6 x, + 0 point 4 y is equal to 240, not 0 point 4 x, + 0 point 6 y. Choice C is incorrect. This choice transposes the percentages of filler materials for Fertilizer A and Fertilizer B and incorrectly represents how to take the percentage of a value mathematically. Choice D is incorrect. This choice incorrectly represents how to take the percentage of a value mathematically. Fertilizer A consists of 0.6x pounds of filler materials, not 60x pounds of filler materials, and Fertilizer B consists of 0.4y pounds of filler materials, not 40y pounds of filler materials.

\n \n

\n"}, {"id": "a309803e", "domain": "Algebra", "skill": "Linear functions", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

One gallon of paint will cover 220\n square feet of a surface. A room has a total wall area of w\n square feet. Which equation represents the total amount of paint P\n, in gallons, needed to paint the walls of the room twice?

", "choices": [{"id": "A", "text": "

\n\tP\n\t=\n\t\n\t\t\n\t\t\tw\n\t\t\t110\n\t\t\n\t\n\n

"}, {"id": "B", "text": "

\n\tP\n\t=\n\t\n\t\t440\n\t\tw\n\t\n\n

"}, {"id": "C", "text": "

\n\tP\n\t=\n\t\n\t\t\n\t\t\tw\n\t\t\t220\n\t\t\n\t\n\n

"}, {"id": "D", "text": "

\n\tP\n\t=\n\t\n\t\t220\n\t\tw\n\t\n\n

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. It's given that w\n represents the total wall area, in square feet. Since the walls of the room will be painted twice, the amount of paint, in gallons, needs to cover \n\t2\n\tw\n\n square feet. It’s also given that one gallon of paint will cover 220\n square feet. Dividing the total area, in square feet, of the surface to be painted by the number of square feet covered by one gallon of paint gives the number of gallons of paint that will be needed. Dividing \n\t2\n\tw\n\n by 220\n yields  2w220, or w110. Therefore, the equation that represents the total amount of paint P\n, in gallons, needed to paint the walls of the room twice is P=w110.

\n

Choice B is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect and may result from finding the amount of paint needed to paint the walls once rather than twice.

\n

Choice D is incorrect and may result from conceptual or calculation errors.

"}, {"id": "bf883fde", "domain": "Algebra", "skill": "Linear functions", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

For the function f\n, the graph of y=f(x) in the xy-plane has a slope of 3\n and passes through the point 0,-8. Which equation defines f\n?

", "choices": [{"id": "A", "text": "

f(x)=3x

"}, {"id": "B", "text": "

f(x)=3x-8

"}, {"id": "C", "text": "

f(x)=3x+5

"}, {"id": "D", "text": "

f(x)=3x+11

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. An equation defining a linear function can be written in the form fx=mx+b, where m\n and b\n are constants, m\n is the slope of the graph of y=fx in the xy-plane, and 0,b is the y-intercept of the graph. It's given that for the function f\n, the graph of y=fx in the xy-plane has a slope of 3\n. Therefore, m=3. It's also given that this graph passes through the point 0,-8. Therefore, the y-intercept of the graph is 0,-8, and it follows that b=-8. Substituting 3\n for m\n and -8\n for b\n in the equation fx=mx+b yields fx=3x-8. Thus, the equation that defines f\n is fx=3x-8.

\n

Choice A is incorrect. For this function, the graph of y=fx in the xy-plane passes through the point 0,0, not 0,-8.

\n

Choice C is incorrect. For this function, the graph of y=fx in the xy-plane passes through the point 0,5, not 0,-8.

\n

Choice D is incorrect. For this function, the graph of y=fx in the xy-plane passes through the point 0,11, not 0,-8.

"}, {"id": "2554b413", "domain": "Algebra", "skill": "Linear equations in two variables", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

In the xy-plane, a line has a slope of 6 and passes through the point zero, 8. Which of the following is an equation of this line?

\n", "choices": [{"id": "A", "text": "

\n y = 6 x + 8\n

\n"}, {"id": "B", "text": "

\n y = 6 x + 48\n

\n"}, {"id": "C", "text": "

\n y = 8 x + 6\n

\n"}, {"id": "D", "text": "

\n y = 8 x + 48\n

\n"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. The slope-intercept form of an equation for a line is y = m x + b, where m is the slope of the line and b is the y-coordinate of the y-intercept of the line. It’s given that the slope is 6, so m = 6. It’s also given that the line passes through the point 0, 8 on the y-axis, so b = 8. Substituting m = 6 and b = 8 into the equation y = m x + b gives y = 6 x + 8.

Choices B, C, and D are incorrect and may result from misinterpreting the slope-intercept form of an equation of a line.

\n"}, {"id": "5bf5136d", "domain": "Algebra", "skill": "Linear inequalities in one or two variables", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

The triangle inequality theorem states that the sum of any two sides of a triangle must be greater than the length of the third side. If a triangle has side lengths of 6\n and 12\n, which inequality represents the possible lengths, x\n, of the third side of the triangle?

", "choices": [{"id": "A", "text": "

x<18\n

"}, {"id": "B", "text": "

x>18\n

"}, {"id": "C", "text": "

6\n<x<18\n

"}, {"id": "D", "text": "

x<6\n or x>18\n

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. It’s given that a triangle has side lengths of 6\n and 12\n, and x\n represents the length of the third side of the triangle. It’s also given that the triangle inequality theorem states that the sum of any two sides of a triangle must be greater than the length of the third side. Therefore, the inequalities 6+x>12, 6+12>x, and 12+x>6 represent all possible values of x\n. Subtracting 6\n from both sides of the inequality 6+x>12 yields x>12-6, or x>6. Adding 6\n and 12\n in the inequality 6+12>x yields 18>x, or x<18. Subtracting 12\n from both sides of the inequality 12+x>6 yields x>6-12, or x>-6. Since all x-values that satisfy the inequality x>6 also satisfy the inequality x>-6, it follows that the inequalities x>6 and x<18 represent the possible values of x\n. Therefore, the inequality 6<x<18 represents the possible lengths, x\n, of the third side of the triangle.

\n

Choice A is incorrect. This inequality gives the upper bound for x\n but does not include its lower bound.

\n

Choice B is incorrect and may result from conceptual or calculation errors.

\n

Choice D is incorrect and may result from conceptual or calculation errors.

"}, {"id": "620abf36", "domain": "Algebra", "skill": "Linear equations in one variable", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

If 5x+4=4x+4+29, what is the value of x+4?

", "choices": [{"id": "A", "text": "

-4\n

"}, {"id": "B", "text": "

25\n

"}, {"id": "C", "text": "

29\n

"}, {"id": "D", "text": "

33\n

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. Subtracting 4x+4 from both sides of the given equation yields 1x+4=29, or \n\t\n\t\tx\n\t\t+\n\t\t4\n\t\n\t=\n\t29\n\n. Therefore, the value of \n\tx\n\t+\n\t4\n\n is 29\n.

\n

Choice A is incorrect and may result from conceptual or calculation errors.

\n

Choice B is incorrect. This is the value of x\n, not \n\tx\n\t+\n\t4\n\n.

\n

Choice D is incorrect and may result from conceptual or calculation errors.

"}, {"id": "d62ad380", "domain": "Algebra", "skill": "Linear equations in two variables", "difficulty": "M", "type": "mc", "stimulus": "
\n
\n
\n

An artist paints and sells square tiles. The selling price P, in dollars, of a painted tile is a linear function of the side length of the tile s, in inches, as shown in the table below.

\n
\n \n \n \n \n \n \n \n \n
Side length, s (inches)Price, P (dollars)
3 8.00
6 18.00
9 28.00
\n
\n
\n
\n
\n", "stem": "

Which of the following could define the relationship between s and P ?

\n", "choices": [{"id": "A", "text": "

\n P = 3 s + 10\n

\n"}, {"id": "B", "text": "

\n P = ten thirds s, + 8\n

\n"}, {"id": "C", "text": "

\n P = ten thirds s, \u2212 2\n

\n"}, {"id": "D", "text": "

\n P = three tenths s, \u2212 one tenth\n

\n"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. The relationship between s and P can be modeled by a linear equation of the form P = ks + a, where k and a are constants. The table shows that P increases by 10 when s increases by 3, so k = (10)/(3). To solve for a, substitute one of the given pairs of values for s and P: when s = 3, P = 8, so 8 = (10)/(3, end fraction, \u00d7 3, + a), which yields a = –2. The solution is therefore P = (10)/(3, end fraction, \u00d7 s \u2212 2).

Choice A is incorrect. When s = 3, P = 8, but 3(3) + 10 = 19 ≠︀ 8. Choice B is incorrect. This may result from using the first number given for P in the table as the constant term a in the linear equation P = ks + a, which is true only when s = 0. Choice D is incorrect and may result from using the reciprocal of the slope of the line.

\n"}, {"id": "ed18c4f7", "domain": "Algebra", "skill": "Linear equations in one variable", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

Cathy has n CDs. Gerry has 3 more than twice the number of CDs that Cathy has. In terms of n, how many CDs does Gerry have?

\n", "choices": [{"id": "A", "text": "

\n 3 n \u2212 2\n

\n"}, {"id": "B", "text": "

\n 3 n + 2\n

\n"}, {"id": "C", "text": "

\n 2 n \u2212 3\n

\n"}, {"id": "D", "text": "

\n 2 n + 3\n

\n"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. The term 2n represents twice the number of CDs that Cathy has, and adding 3 represents 3 more than that amount.

Choices A and B are incorrect. The expression 3n represents three times the number of CDs that Cathy has. Choice C is incorrect. Subtracting 3 represents 3 fewer than twice the number of CDs that Cathy has.

\n"}, {"id": "52a8ef85", "domain": "Algebra", "skill": "Linear equations in two variables", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

The equation \n\t\n\t\t\n\t\t\t40\n\t\t\tx\n\t\t\n\t\t+\n\t\t\n\t\t\t20\n\t\t\ty\n\t\t\n\t\n\t=\n\t160\n\n represents the number of sweaters, x\n, and number of shirts, y\n, that Yesenia purchased for $160. If Yesenia purchased 2\n sweaters, how many shirts did she purchase?  

", "choices": [{"id": "A", "text": "

3\n

"}, {"id": "B", "text": "

4\n

"}, {"id": "C", "text": "

8\n

"}, {"id": "D", "text": "

40\n

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. It's given that the equation \n\t\n\t\t\n\t\t\t40\n\t\t\tx\n\t\t\n\t\t+\n\t\t\n\t\t\t20\n\t\t\ty\n\t\t\n\t\n\t=\n\t160\n\n represents the number of sweaters, x\n, and the number of shirts, y\n, that Yesenia purchased for $160. If Yesenia purchased 2\n sweaters, the number of shirts she purchased can be calculated by substituting 2\n for x\n in the given equation, which yields 402+20y=160, or 80+20y=160. Subtracting 80\n from both sides of this equation yields \n\t\n\t\t20\n\t\ty\n\t\n\t=\n\t80\n\n. Dividing both sides of this equation by 20\n yields \n\ty\n\t=\n\t4\n\n. Therefore, if Yesenia purchased 2\n sweaters, she purchased 4\n shirts.

\n

Choice A is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect. This is the number of shirts Yesenia purchased if she purchased 0\n sweaters.

\n

Choice D is incorrect. This is the price, in dollars, for each sweater, not the number of shirts Yesenia purchased. 

"}, {"id": "3462d850", "domain": "Algebra", "skill": "Linear functions", "difficulty": "E", "type": "mc", "stimulus": "
\n
\n
\n

Marisol drove 3 hours from City A to City B. The equation below estimates the distance d, in miles, Marisol traveled after driving for t hours.

\n

\n d = 45 t\n

\n
\n
\n
\n", "stem": "

Which of the following does 45 represent in the equation?

\n", "choices": [{"id": "A", "text": "

Marisol took 45 trips from City A to City B.

\n"}, {"id": "B", "text": "

The distance between City A and City B is 45 miles.

\n"}, {"id": "C", "text": "

Marisol drove at an average speed of about 45 miles per hour.

\n"}, {"id": "D", "text": "

It took Marisol 45 hours to drive from City A to City B.

\n"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. It’s given that d is the distance, in miles, Marisol traveled after driving for t hours. Therefore, 45 represents the distance in miles traveled per hour, which is the speed she drove in miles per hour.

Choice A is incorrect and may result from misidentifying speed as the number of trips. Choice B is incorrect and may result from misidentifying speed as the total distance. Choice D is incorrect and may result from misidentifying the speed as the time, in hours.

\n"}, {"id": "0d685865", "domain": "Algebra", "skill": "Linear equations in one variable", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

If \n\tx\n\t=\n\t7\n\n, what is the value of \n\tx\n\t+\n\t20\n\n?

", "choices": [{"id": "A", "text": "

13\n

"}, {"id": "B", "text": "

20\n

"}, {"id": "C", "text": "

27\n

"}, {"id": "D", "text": "

34\n

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. It’s given that \n\tx\n\t=\n\t7\n\n. Substituting 7\n for x\n into the given expression \n\tx\n\t+\n\t20\n\n yields 7+20, which is equivalent to 27\n.

\n

Choice A is incorrect. This is the value of \n\tx\n\t+\n\t6\n\n.

\n

Choice B is incorrect. This is the value of \n\tx\n\t+\n\t13\n\n.

\n

Choice D is incorrect. This is the value of \n\tx\n\t+\n\t27\n\n.

"}, {"id": "12255364", "domain": "Algebra", "skill": "Linear equations in one variable", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

A gym charges its members a onetime $36\n enrollment fee and a membership fee of $19\n per month. If there are no charges other than the enrollment fee and the membership fee, after how many months will a member have been charged a total of $188\n at the gym?

", "choices": [{"id": "A", "text": "

4\n

"}, {"id": "B", "text": "

5\n

"}, {"id": "C", "text": "

8\n

"}, {"id": "D", "text": "

10\n

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. It’s given that a gym charges its members a onetime $36 enrollment fee and a membership fee of $19 per month. Let x\n represent the number of months at the gym after which a member will have been charged a total of $188. If there are no charges other than the enrollment fee and the membership fee, the equation 36+19x=188 can be used to represent this situation. Subtracting 36\n from both sides of this equation yields 19x=152. Dividing both sides of this equation by 19\n yields x=8. Therefore, a member will have been charged a total of $188 after 8\n months at the gym.

\n

Choice A is incorrect. A member will have been charged a total of $36+19×4, or $112, after 4\n months at the gym.

\n

Choice B is incorrect. A member will have been charged a total of $36+19×5, or $131, after 5\n months at the gym.

\n

Choice D is incorrect. A member will have been charged a total of $36+19×10, or $226, after 10\n months at the gym.

"}, {"id": "b82a943c", "domain": "Algebra", "skill": "Linear equations in one variable", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

If \n\t\n\t\t7\n\t\tx\n\t\n\t=\n\t28\n\n, what is the value of \n\t8\n\tx\n\n?

", "choices": [{"id": "A", "text": "

21\n

"}, {"id": "B", "text": "

32\n

"}, {"id": "C", "text": "

168\n

"}, {"id": "D", "text": "

224\n

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. Dividing both sides of the given equation \n\t\n\t\t7\n\t\tx\n\t\n\t=\n\t28\n\n by 7\n yields \n\tx\n\t=\n\t4\n\n. Substituting 4\n for x\n in the expression \n\t8\n\tx\n\n yields 84, which is equivalent to 32\n.

\n

Choice A is incorrect. This is the value of 214x.

\n

Choice C is incorrect. This is the value of \n\t42\n\tx\n\n.

\n

Choice D is incorrect. This is the value of \n\t56\n\tx\n\n.

"}, {"id": "092ad67d", "domain": "Algebra", "skill": "Systems of two linear equations in two variables", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

\n\t\n\t\tx\n\t\t+\n\t\t\n\t\t\t2\n\t\t\ty\n\t\t\n\t\n\t=\n\t6\n\n

\n

\n\t\n\t\tx\n\t\t-\n\t\t\n\t\t\t2\n\t\t\ty\n\t\t\n\t\n\t=\n\t4\n\n

\n

The solution to the given system of equations is x,y. What is the value of x\n?

", "choices": [{"id": "A", "text": "

2.5\n

"}, {"id": "B", "text": "

5\n

"}, {"id": "C", "text": "

6\n

"}, {"id": "D", "text": "

10\n

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. Adding the first equation to the second equation in the given system yields x+2y+x-2y=6+4, or x+x+2y-2y=10. Combining like terms in this equation yields 2x=10. Dividing both sides of this equation by 2\n yields \n\tx\n\t=\n\t5\n\n. Thus, the value of x\n is 5\n.

\n

Choice A is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

\n

Choice D is incorrect. This is the value of \n\t2\n\tx\n\n, not x\n.

"}, {"id": "90095507", "domain": "Algebra", "skill": "Linear equations in one variable", "difficulty": "H", "type": "mc", "stimulus": "
 
Townsend Realty Group Investments
Property addressPurchase price (dollars)Monthly rental price (dollars)
Clearwater Lane128,000950
Driftwood Drive176,0001,310
Edgemont Street70,000515
Glenview Street140,0001,040
Hamilton Circle450,0003,365
\n", "stem": "

The Townsend Realty Group invested in the five different properties listed in the table above. The table shows the amount, in dollars, the company paid for each property and the corresponding monthly rental price, in dollars, the company charges for the property at each of the five locations. Townsend Realty purchased the Glenview Street property and received a 40% discount off the original price along with an additional 20% off the discounted price for purchasing the property in cash. Which of the following best approximates the original price, in dollars, of the Glenview Street property?

\n", "choices": [{"id": "A", "text": "

$350,000

\n"}, {"id": "B", "text": "

$291,700

\n"}, {"id": "C", "text": "

$233,300

\n"}, {"id": "D", "text": "

$175,000

\n"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. Let x be the original price, in dollars, of the Glenview Street property. After the 40% discount, the price of the property became 0 point 6 x dollars, and after the additional 20% off the discounted price, the price of the property became 0 point 8 \u00d7 0 point 6 x. Thus, in terms of the original price of the property, x, the purchase price of the property is 0 point 4 8 x . It follows that 0 point 4 8 x = 140,000. Solving this equation for x gives x = 291,666 point 6, with the 6 repeating after the decimal point. Therefore, of the given choices, $291,700 best approximates the original price of the Glenview Street property.

Choice A is incorrect because it is the result of dividing the purchase price of the property by 0.4, as though the purchase price were 40% of the original price. Choice C is incorrect because it is the closest to dividing the purchase price of the property by 0.6, as though the purchase price were 60% of the original price. Choice D is incorrect because it is the result of dividing the purchase price of the property by 0.8, as though the purchase price were 80% of the original price.

\n"}, {"id": "eac739b2", "domain": "Algebra", "skill": "Linear equations in one variable", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

If \n\t\n\t\t\n\t\t\t4\n\t\t\tx\n\t\t\n\t\t+\n\t\t2\n\t\n\t=\n\t12\n\n, what is the value of \n\t\n\t\t16\n\t\tx\n\t\n\t+\n\t8\n\n?

", "choices": [{"id": "A", "text": "

40\n

"}, {"id": "B", "text": "

48\n

"}, {"id": "C", "text": "

56\n

"}, {"id": "D", "text": "

60\n

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. Multiplying both sides of the given equation by 4\n yields 44x+2=412, or 16x+8=48. Therefore, the value of 16x+8 is 48\n.

\n

Choice A is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

\n

Choice D is incorrect and may result from conceptual or calculation errors.

"}, {"id": "3122fc7b", "domain": "Algebra", "skill": "Linear functions", "difficulty": "M", "type": "spr", "stimulus": "", "stem": "

A linear model estimates the population of a city from 1991\n to 2015\n. The model estimates the population was 57\n thousand in 1991\n, 224\n thousand in 2011\n, and x\n thousand in 2015\n. To the nearest whole number, what is the value of x\n?

", "choices": [], "answerId": "257", "acceptedAnswers": ["257"], "rationale": "

The correct answer is 257. It’s given that a linear model estimates the population of a city from 1991 to 2015. Since the population can be estimated using a linear model, it follows that there is a constant rate of change for the model. It’s also given that the model estimates the population was 57 thousand in 1991, 224 thousand in 2011, and x thousand in 2015. The change in the population between 2011 and 1991 is 224-57, or 167, thousand. The change in the number of years between 2011 and 1991 is 2011-1991, or 20, years. Dividing 167 by 20 gives 167/20, or 8.35, thousand per year. Thus, the change in population per year from 1991 to 2015 estimated by the model is 8.35 thousand. The change in the number of years between 2015 and 2011 is 2015-2011, or 4, years. Multiplying the change in population per year by the change in number of years yields the increase in population from 2011 to 2015 estimated by the model: 8.354, or 33.4, thousand. Adding the change in population from 2011 to 2015 estimated by the model to the estimated population in 2011 yields the estimated population in 2015. Thus, the estimated population in 2015 is 33.4+224, or 257.4, thousand. Therefore to the nearest whole number, the value of x is 257.

"}, {"id": "ba79f10f", "domain": "Algebra", "skill": "Linear equations in two variables", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "
\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
x\ny\n
0\n18\n
1\n13\n
2\n8\n
\n

The table shows three values of x\n and their corresponding values of y\n. There is a linear relationship between x\n and y\n. Which of the following equations represents this relationship?

", "choices": [{"id": "A", "text": "

\n\ty\n\t=\n\t\n\t\t\n\t\t\t18\n\t\t\tx\n\t\t\n\t\t+\n\t\t13\n\t\n\n

"}, {"id": "B", "text": "

\n\ty\n\t=\n\t\n\t\t\n\t\t\t18\n\t\t\tx\n\t\t\n\t\t+\n\t\t18\n\t\n\n

"}, {"id": "C", "text": "

\n\ty\n\t=\n\t\n\t\t\n\t\t\t-\n\t\t\t5\n\t\t\tx\n\t\t\n\t\t+\n\t\t13\n\t\n\n

"}, {"id": "D", "text": "

\n\ty\n\t=\n\t\n\t\t\n\t\t\t-\n\t\t\t5\n\t\t\tx\n\t\t\n\t\t+\n\t\t18\n\t\n\n

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. A linear relationship can be represented by an equation of the form \n\ty\n\t=\n\t\n\t\t\n\t\t\tm\n\t\t\tx\n\t\t\n\t\t+\n\t\tb\n\t\n\n, where m\n and b\n are constants. It’s given in the table that when \n\tx\n\t=\n\t0\n\n, \n\ty\n\t=\n\t18\n\n. Substituting 0\n for x\n and 18\n for y\n in \n\ty\n\t=\n\t\n\t\t\n\t\t\tm\n\t\t\tx\n\t\t\n\t\t+\n\t\tb\n\t\n\n yields 18=m0+b, or \n\t18\n\t=\n\tb\n\n. Substituting 18\n for b\n in the equation \n\ty\n\t=\n\t\n\t\t\n\t\t\tm\n\t\t\tx\n\t\t\n\t\t+\n\t\tb\n\t\n\n yields \n\ty\n\t=\n\t\n\t\t\n\t\t\tm\n\t\t\tx\n\t\t\n\t\t+\n\t\t18\n\t\n\n. It’s also given in the table that when \n\tx\n\t=\n\t1\n\n, \n\ty\n\t=\n\t13\n\n. Substituting 1\n for x\n and 13\n for y\n in the equation \n\ty\n\t=\n\t\n\t\t\n\t\t\tm\n\t\t\tx\n\t\t\n\t\t+\n\t\t18\n\t\n\n yields 13=m1+18, or \n\t13\n\t=\n\t\n\t\tm\n\t\t+\n\t\t18\n\t\n\n. Subtracting 18\n from both sides of this equation yields \n\t-5\n\t=\n\tm\n\n. Therefore, the equation \n\ty\n\t=\n\t\n\t\t\n\t\t\t-\n\t\t\t5\n\t\t\tx\n\t\t\n\t\t+\n\t\t18\n\t\n\n represents the relationship between x\n and y\n.

\n

Choice A is incorrect and may result from conceptual or calculation errors.

\n

Choice B is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

"}, {"id": "d9d83c02", "domain": "Algebra", "skill": "Linear equations in one variable", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

For what value of w does w \u2212 10 = 2 times, open parenthesis, w + 5, close parenthesis ?

\n", "choices": [{"id": "A", "text": "

\"\"

\n"}, {"id": "B", "text": "

0

\n"}, {"id": "C", "text": "

\u221215

\n"}, {"id": "D", "text": "

\u221220

\n"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. To solve the equation, use the distributive property to multiply on the right-hand side of the equation which gives w – 10 = 2w + 10. Subtract w from both sides of the equation, which gives –10 = w + 10. Finally, subtract 10 from both sides of the equation, which gives –20 = w.

Choices A and B are incorrect and may result from making sign errors. Choice C is incorrect and may result from incompletely distributing the 2 in the expression 2(w + 5).

\n"}, {"id": "59a49431", "domain": "Algebra", "skill": "Linear inequalities in one or two variables", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n

\n

The shaded region shown represents solutions to an inequality. Which ordered pair x,y is a solution to this inequality?

", "choices": [{"id": "A", "text": "

0,-4

"}, {"id": "B", "text": "

0,4

"}, {"id": "C", "text": "

-4,0

"}, {"id": "D", "text": "

4,0

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. Since the shaded region shown represents solutions to an inequality, an ordered pair x,y is a solution to the inequality if it's represented by a point in the shaded region. Of the given choices, only 4,0 is represented by a point in the shaded region. Therefore, 4,0 is a solution to the inequality.

\n

Choice A is incorrect and may result from conceptual errors.

\n

Choice B is incorrect and may result from conceptual errors.

\n

Choice C is incorrect and may result from conceptual errors.

"}, {"id": "23dedddd", "domain": "Algebra", "skill": "Linear functions", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

In the linear function f\n, f0=8 and f1=12. Which equation defines f\n?

", "choices": [{"id": "A", "text": "

fx=12x+8

"}, {"id": "B", "text": "

fx=4x

"}, {"id": "C", "text": "

fx=4x+12

"}, {"id": "D", "text": "

fx=4x+8

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. Since f\n is a linear function, it can be defined by an equation of the form fx=ax+b, where a\n and b\n are constants. It's given that f0=8. Substituting 0\n for x\n and 8\n for fx in the equation fx=ax+b yields 8=a0+b, or 8=b. Substituting 8\n for b\n in the equation fx=ax+b yields fx=ax+8. It's given that f1=12. Substituting 1\n for x\n and 12\n for fx in the equation fx=ax+8 yields 12=a1+8, or 12=a+8. Subtracting 8\n from both sides of this equation yields a=4. Substituting 4\n for a\n in the equation fx=ax+8 yields fx=4x+8. Therefore, an equation that defines f\n is fx=4x+8.

\n

Choice A is incorrect and may result from conceptual or calculation errors.

\n

Choice B is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

"}, {"id": "c8fb6bcb", "domain": "Algebra", "skill": "Linear functions", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

fx=2x+244

\n

The given function f\n represents the perimeter, in centimeters cm, of a rectangle with a length of x cm and a fixed width. What is the width, in cm, of the rectangle?

", "choices": [{"id": "A", "text": "

2\n

"}, {"id": "B", "text": "

122\n

"}, {"id": "C", "text": "

244\n

"}, {"id": "D", "text": "

488\n

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. It's given that fx=2x+244 represents the perimeter, in centimeters (cm), of a rectangle with a length of x\n cm and a fixed width. If w\n represents a fixed width, in cm, then the perimeter, in cm, of a rectangle with a length of x\n cm and a fixed width of w\n cm can be given by the function fx=2x+2w. Therefore, 2x+2w=2x+244. Subtracting \n\t2\n\tx\n\n from both sides of this equation yields 2w=244. Dividing both sides of this equation by 2\n yields w=122. Therefore, the width, in cm, of the rectangle is 122\n.

\n

Choice A is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

\n

Choice D is incorrect and may result from conceptual or calculation errors.

"}, {"id": "d909cd31", "domain": "Algebra", "skill": "Systems of two linear equations in two variables", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

\n\t\n\t\t\n\t\t\t-\n\t\t\t15\n\t\t\tx\n\t\t\n\t\t+\n\t\t\n\t\t\t25\n\t\t\ty\n\t\t\n\t\n\t=\n\t65\n\n

\n

One of the two equations in a system of linear equations is given. The system has infinitely many solutions. Which of the following could be the second equation in the system?

", "choices": [{"id": "A", "text": "

\n\t\n\t\t\n\t\t\t12\n\t\t\tx\n\t\t\n\t\t+\n\t\t\n\t\t\t20\n\t\t\ty\n\t\t\n\t\n\t=\n\t52\n\n

"}, {"id": "B", "text": "

\n\t\n\t\t\n\t\t\t12\n\t\t\tx\n\t\t\n\t\t+\n\t\t\n\t\t\t20\n\t\t\ty\n\t\t\n\t\n\t=\n\t-52\n\n

"}, {"id": "C", "text": "

\n\t\n\t\t\n\t\t\t-\n\t\t\t12\n\t\t\tx\n\t\t\n\t\t+\n\t\t\n\t\t\t20\n\t\t\ty\n\t\t\n\t\n\t=\n\t52\n\n

"}, {"id": "D", "text": "

\n\t\n\t\t\n\t\t\t-\n\t\t\t12\n\t\t\tx\n\t\t\n\t\t+\n\t\t\n\t\t\t20\n\t\t\ty\n\t\t\n\t\n\t=\n\t-52\n\n

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. It's given that the system has infinitely many solutions. A system of two linear equations has infinitely many solutions when the two linear equations are equivalent. Dividing both sides of the given equation by 5\n yields \n\t\n\t\t\n\t\t\t-\n\t\t\t3\n\t\t\tx\n\t\t\n\t\t+\n\t\t\n\t\t\t5\n\t\t\ty\n\t\t\n\t\n\t=\n\t13\n\n. Dividing both sides of choice C by 4\n also yields \n\t\n\t\t\n\t\t\t-\n\t\t\t3\n\t\t\tx\n\t\t\n\t\t+\n\t\t\n\t\t\t5\n\t\t\ty\n\t\t\n\t\n\t=\n\t13\n\n, so choice C is equivalent to the given equation. Thus, choice C could be the second equation in the system.

\n

Choice A is incorrect. The system consisting of this equation and the given equation has one solution, not infinitely many solutions.

\n

Choice B is incorrect. The system consisting of this equation and the given equation has one solution, not infinitely many solutions.

\n

Choice D is incorrect. The system consisting of this equation and the given equation has no solution, not infinitely many solutions.

"}, {"id": "98d3393a", "domain": "Algebra", "skill": "Linear equations in two variables", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

Line l in the xy-plane is perpendicular to the line with equation x = 2. What is the slope of line l?

\n", "choices": [{"id": "A", "text": "

\n 0\n

\n"}, {"id": "B", "text": "

\n \u2212one half\n

\n"}, {"id": "C", "text": "

\n \u22122\n

\n"}, {"id": "D", "text": "

The slope of line l is undefined.

\n"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. It is given that line l is perpendicular to a line whose equation is x = 2. A line whose equation is a constant value of x is vertical, so l must therefore be horizontal. Horizontal lines have a slope of 0, so l has a slope of 0.

Choice B is incorrect. A line with slope \u2212one half is perpendicular to a line with slope 2. However, the line with equation x = 2 is vertical and has undefined slope (not slope of 2). Choice C is incorrect. A line with slope –2 is perpendicular to a line with slope one half. However, the line with equation x = 2 has undefined slope (not slope of one half). Choice D is incorrect; this is the slope of the line x = 2 itself, not the slope of a line perpendicular to it.

\n"}, {"id": "f88970cc", "domain": "Algebra", "skill": "Systems of two linear equations in two variables", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

\n\tx\n\t=\n\t5\n\n

\n

\n\ty\n\t=\n\t\n\t\tx\n\t\t-\n\t\t8\n\t\n\n

\n

Which of the following points x,y is the solution to the given system of equations in the xy-plane?

", "choices": [{"id": "A", "text": "

0,0

"}, {"id": "B", "text": "

5,-3

"}, {"id": "C", "text": "

5,-8

"}, {"id": "D", "text": "

5,8

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. A solution to a system of equations in the xy-plane is a point x,y that lies on the graph of each equation in the system. The first equation given is \n\tx\n\t=\n\t5\n\n. Substituting 5\n for x\n in the second given equation yields y=5-8, or \n\ty\n\t=\n\t-3\n\n. It follows that in the xy-plane, the point 5,-3 lies on the graph of each equation in the system. Therefore, the solution to the given system of equations in the xy-plane is 5,-3.

\n

Choice A is incorrect. The point 0,0 doesn't lie on the graph of either equation in the given system.

\n

Choice C is incorrect. The point 5,-8 doesn't lie on the graph of the second equation in the given system.

\n

Choice D is incorrect. The point 5,8 doesn't lie on the graph of the second equation in the given system.

"}, {"id": "56dc8045", "domain": "Algebra", "skill": "Linear functions", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

w(t)=300-4t

\n

The function w\n models the volume of liquid, in milliliters, in a container t\n seconds after it begins draining from a hole at the bottom. According to the model, what is the predicted volume, in milliliters, draining from the container each second?

", "choices": [{"id": "A", "text": "

300\n

"}, {"id": "B", "text": "

296\n

"}, {"id": "C", "text": "

75\n

"}, {"id": "D", "text": "

4\n

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. It’s given that the function w\n models the volume of liquid, in milliliters, in a container t\n seconds after it begins draining from a hole at the bottom. The given function wt=300-4t can be rewritten as wt=-4t+300. Thus, for each increase of t\n by 1\n, the value of wt decreases by 4(1), or 4\n. Therefore, the predicted volume, in milliliters, draining from the container each second is 4\n milliliters.

\n

Choice A is incorrect. This is the amount of liquid, in milliliters, in the container before the liquid begins draining.

\n

Choice B is incorrect and may result from conceptual errors.

\n

Choice C is incorrect and may result from conceptual errors.

"}, {"id": "3c4ce699", "domain": "Algebra", "skill": "Linear equations in one variable", "difficulty": "E", "type": "spr", "stimulus": "", "stem": "

If 6+x=9, what is the value of 18+3x?

", "choices": [], "answerId": "27", "acceptedAnswers": ["27"], "rationale": "

The correct answer is 27\n. Multiplying both sides of the given equation by 3\n yields 36+x=39, or 18+3x=27. Therefore, the value of 18+3x is 27\n.

"}, {"id": "f2bbd43d", "domain": "Algebra", "skill": "Linear inequalities in one or two variables", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

y>14

\n

4x+y<18

\n

The point x,53 is a solution to the system of inequalities in the xy-plane. Which of the following could be the value of x\n?

", "choices": [{"id": "A", "text": "

-9\n

"}, {"id": "B", "text": "

-5\n

"}, {"id": "C", "text": "

5\n

"}, {"id": "D", "text": "

9\n

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. It’s given that the point x,53 is a solution to the given system of inequalities in the xy-plane. This means that the coordinates of the point, when substituted for the variables x\n and y\n, make both of the inequalities in the system true. Substituting 53\n for y\n in the inequality y>14 yields 53>14, which is true. Substituting 53\n for y\n in the inequality 4x+y<18 yields 4x+53<18. Subtracting 53\n from both sides of this inequality yields 4x<-35. Dividing both sides of this inequality by 4\n yields x<-8.75. Therefore, x\n must be a value less than -8.75\n. Of the given choices, only -9\n is less than -8.75\n.

\n

Choice B is incorrect. Substituting -5\n for x\n and 53\n for y\n in the inequality 4x+y<18 yields 4-5+53<18, or 33<18, which is not true.

\n

Choice C is incorrect. Substituting 5\n for x\n and 53\n for y\n in the inequality 4x+y<18 yields 45+53<18, or 73<18, which is not true.

\n

Choice D is incorrect. Substituting 9\n for x\n and 53\n for y\n in the inequality 4x+y<18 yields 49+53<18, or 89<18, which is not true.

"}, {"id": "ffb371f5", "domain": "Algebra", "skill": "Systems of two linear equations in two variables", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

3x=12

\n

-3x+y=-6

\n

The solution to the given system of equations is x,y. What is the value of y\n?

", "choices": [{"id": "A", "text": "

-3\n

"}, {"id": "B", "text": "

6\n

"}, {"id": "C", "text": "

18\n

"}, {"id": "D", "text": "

30\n

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. Adding the second equation in the given system to the first equation in the given system yields 3x+(-3x+y)=12+-6, which is equivalent to y=6. 

\n

Choice A is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

\n

Choice D is incorrect and may result from conceptual or calculation errors.

"}, {"id": "6989c80a", "domain": "Algebra", "skill": "Linear functions", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

Fx=95x-273.15+32

\n

The function F\n gives the temperature, in degrees Fahrenheit, that corresponds to a temperature of x\n kelvins. If a temperature increased by 2.10\n kelvins, by how much did the temperature increase, in degrees Fahrenheit?

", "choices": [{"id": "A", "text": "

3.78\n

"}, {"id": "B", "text": "

35.78\n

"}, {"id": "C", "text": "

487.89\n

"}, {"id": "D", "text": "

519.89\n

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. It’s given that the function Fx=95x-273.15+32 gives the temperature, in degrees Fahrenheit, that corresponds to a temperature of x\n kelvins. A temperature that increased by 2.10 kelvins means that the value of x\n increased by 2.10 kelvins. It follows that an increase in x\n by 2.10 increases F(x) by 952.10, or 3.78. Therefore, if a temperature increased by 2.10 kelvins, the temperature increased by 3.78 degrees Fahrenheit.

\n

Choice B is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

\n

Choice D is incorrect and may result from conceptual or calculation errors.

"}, {"id": "c4d49134", "domain": "Algebra", "skill": "Linear functions", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

s=40+3t

\n

The equation gives the speed s\n, in miles per hour, of a certain car t\n seconds after it began to accelerate. What is the speed, in miles per hour, of the car 5\n seconds after it began to accelerate?

", "choices": [{"id": "A", "text": "

40\n

"}, {"id": "B", "text": "

43\n

"}, {"id": "C", "text": "

45\n

"}, {"id": "D", "text": "

55\n

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. In the given equation, s\n is the speed, in miles per hour, of a certain car t\n seconds after it began to accelerate. Therefore, the speed of the car, in miles per hour, 5\n seconds after it began to accelerate can be found by substituting 5\n for t\n in the given equation, which yields s=40+35, or s=55. Thus, the speed of the car 5\n seconds after it began to accelerate is 55\n miles per hour.

\n

Choice A is incorrect and may result from conceptual or calculation errors.

\n

Choice B is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

"}, {"id": "0cb57740", "domain": "Algebra", "skill": "Linear equations in one variable", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

Each side of a 30\n-sided polygon has one of three lengths. The number of sides with length 8 centimeters cm is 5\n times the number of sides n\n with length 3 cm. There are 6\n sides with length 4 cm. Which equation must be true for the value of n\n?

", "choices": [{"id": "A", "text": "

\n\t\n\t\t\n\t\t\t5\n\t\t\tn\n\t\t\n\t\t+\n\t\t6\n\t\n\t=\n\t30\n\n

"}, {"id": "B", "text": "

\n\t\n\t\t\n\t\t\t6\n\t\t\tn\n\t\t\n\t\t+\n\t\t6\n\t\n\t=\n\t30\n\n

"}, {"id": "C", "text": "

8n+3n+4n=30

"}, {"id": "D", "text": "

85n+3n+46=30

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. It’s given that each side of a 30\n-sided polygon has one of three lengths. It's also given that the number of sides with length 8\n centimeters cm is 5\n times the number of sides n\n with length 3 cm. Therefore, there are 5×n, or \n\t5\n\tn\n\n, sides with length 8 cm. It’s also given that there are 6\n sides with length 4 cm. Therefore, the number of 3 cm, 4 cm, and 8 cm sides are n\n, 6\n, and \n\t5\n\tn\n\n, respectively. Since there are a total of 30\n sides, the equation n+6+5n=30 represents this situation. Combining like terms on the left-hand side of this equation yields 6n+6=30. Therefore, the equation that must be true for the value of n\n is 6n+6=30.

\n

Choice A is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

\n

Choice D is incorrect and may result from conceptual or calculation errors.

"}, {"id": "ece00725", "domain": "Algebra", "skill": "Systems of two linear equations in two variables", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

Connor has c\n dollars and Maria has m\n dollars. Connor has 4\n times as many dollars as Maria, and together they have a total of $25.00\n. Which system of equations represents this situation?

", "choices": [{"id": "A", "text": "

c=4m

\n

c+m=25

"}, {"id": "B", "text": "

m=4c

\n

c+m=25

"}, {"id": "C", "text": "

c=25m

\n

c+m=4

"}, {"id": "D", "text": "

m=25c

\n

c+m=4

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. It’s given that Connor has c\n dollars, Maria has m\n dollars, and Connor has 4\n times as many dollars as Maria. This can be represented by the equation \n\tc\n\t=\n\t\n\t\t4\n\t\tm\n\t\n\n. It’s also given that together, Connor and Maria have a total of $25.00, which can be represented by the equation c+m=25. Therefore, the system consisting of the equations \n\tc\n\t=\n\t\n\t\t4\n\t\tm\n\t\n\n and c+m=25 represents this situation.

\n

Choice B is incorrect. The equation \n\tm\n\t=\n\t\n\t\t4\n\t\tc\n\t\n\n represents a situation where Maria has 4\n times as many dollars as Connor, rather than the situation where Connor has 4\n times as many dollars as Maria.

\n

Choice C is incorrect. The equation \n\tc\n\t=\n\t\n\t\t25\n\t\tm\n\t\n\n represents a situation where Connor has 25\n times, rather than 4\n times, as many dollars as Maria. The equation c+m=4 represents a situation where Connor and Maria together have a total of $4.00, rather than $25.00.

\n

Choice D is incorrect. The equation \n\tm\n\t=\n\t\n\t\t25\n\t\tc\n\t\n\n represents a situation where Maria has 25\n times as many dollars as Connor, rather than the situation where Connor has 4\n times as many dollars as Maria. The equation c+m=4 represents a situation where Connor and Maria together have a total of $4.00, rather than $25.00.

"}, {"id": "255996a6", "domain": "Algebra", "skill": "Linear functions", "difficulty": "E", "type": "mc", "stimulus": "
\n t = 1000 + 18 h\n
\n", "stem": "

In the equation above, T represents Brittany’s total take-home pay, in dollars, for her first week of work, where h represents the number of hours she worked that week and 1,000 represents a sign-on bonus. If Brittany’s total take-home pay was $1,576, for how many hours was Brittany paid for her first week of work?

\n", "choices": [{"id": "A", "text": "

16

\n"}, {"id": "B", "text": "

32

\n"}, {"id": "C", "text": "

55

\n"}, {"id": "D", "text": "

88

\n"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. Since Brittany’s total take-home pay was $1,576, the value 1,576 can be substituted for T in the given equation T = 1,000 + 18 h to give 1,576 = 1,000 + 18 h. Subtracting 1,000 from both sides of this equation gives 576 = 18 h. Dividing both sides of this equation by 18 gives 32 = h. Therefore, Brittany was paid for 32 hours for her first week of work.

Choice A is incorrect. This is half the number of hours Brittany was paid for. Choice C is incorrect and may result from dividing 1,000 by 18. Choice D is incorrect and may result from dividing 1,576 by 18.

\n"}, {"id": "a1696f3e", "domain": "Algebra", "skill": "Linear functions", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

The function \"\" is defined as g(x) = 5 x + a, where a is a constant. If g(4) = 31, what is the value of a ?

\n", "choices": [{"id": "A", "text": "

\"\"

\n"}, {"id": "B", "text": "

\"\"

\n"}, {"id": "C", "text": "

\"\"

\n"}, {"id": "D", "text": "

\u221223

\n"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. Substituting 4 for x in g(x) = 5x + a gives g(4) = 5(4) + a. Since g(4) = 31, the equation g(4) = 5(4) + a simplifies to 31 = 20 + a. It follows that a = 11.

Choices A, B, and D are incorrect and may result from arithmetic errors.

 

\n"}, {"id": "c01f4a95", "domain": "Algebra", "skill": "Linear functions", "difficulty": "M", "type": "spr", "stimulus": "", "stem": "

j(x)=mx+144

\n

For the linear function j\n, m\n is a constant and j(12)=18. What is the value of j(10)?

", "choices": [], "answerId": "39", "acceptedAnswers": ["39"], "rationale": "

The correct answer is 39\n. It’s given that for the linear function j\n, m\n is a constant and j12=18. Substituting 12\n for x\n and 18\n for jx in the given equation yields 18=m12+144. Subtracting 144\n from both sides of this equation yields -126=m12. Dividing both sides of this equation by 12\n yields -10.5=m. Substituting -10.5 for m\n in the given equation, jx=mx+144, yields jx=-10.5x+144. Substituting 10\n for x\n in this equation yields j10=-10.510+144, or j10=39. Therefore, the value of j10 is 39\n.

"}, {"id": "dfa45424", "domain": "Algebra", "skill": "Linear equations in two variables", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

Tony spends $80 per month on public transportation. A 10-ride pass costs $12.50, and a single-ride pass costs $1.50. If g represents the number of 10-ride passes Tony buys in a month and t represents the number of single-ride passes Tony buys in a month, which of the following equations best represents the relationship between g and t ?

\n", "choices": [{"id": "A", "text": "

g + t = 80

\n"}, {"id": "B", "text": "

g + t = 1 point 5 0 + 12 point 5 0

\n"}, {"id": "C", "text": "

1 point 5 0 g + 12 point 5 0 t = 80

\n"}, {"id": "D", "text": "

12 point 5 0 g + 1 point 5 0 t = 80

\n"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. Since a 10-ride pass costs $12.50 and g is the number of 10-ride passes Tony buys in a month, the expression 12 point 5 0 g represents the amount Tony spends on 10-ride passes in a month. Since a single-ride pass costs $1.50 and t is the number of single-ride passes Tony buys in a month, the expression 1 point 5 0 t represents the amount Tony spends on single-ride passes in a month. Therefore, the sum 12 point 5 0 g, + 1 point 5 0 t represents the amount he spends on the two types of passes in a month. Since Tony spends a total of $80 on passes in a month, this expression can be set equal to 80, producing 12 point 5 0 g, + 1 point 5 0 t = 80.

Choices A and B are incorrect. The expression g + t represents the total number of the two types of passes Tony buys in a month, not the amount Tony spends, which is equal to 80, nor the cost of one of each pass, which is equal to 1 point 5 0, + 12 point 5 0. Choice C is incorrect and may result from reversing the cost for each type of pass Tony buys in a month.

 

\n"}, {"id": "431c3038", "domain": "Algebra", "skill": "Linear equations in two variables", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

In an article about exercise, it is estimated that a 160-pound adult uses 200 calories for every 30 minutes of hiking and 150 calories for every 30 minutes of bicycling. An adult who weighs 160 pounds has completed 1 hour of bicycling. Based on the article, how many hours should the adult hike to use a total of 1,900 calories from bicycling and hiking?

\n", "choices": [{"id": "A", "text": "

9.5

\n"}, {"id": "B", "text": "

8.75

\n"}, {"id": "C", "text": "

6

\n"}, {"id": "D", "text": "

4

\n"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. Since a 160-pound adult uses 200 calories for every 30 minutes of hiking, then the same adult uses 200 h calories after hiking for h 30-minute periods. Similarly, the same adult uses 150 b calories after bicycling for b 30-minute periods. Therefore, the equation 200 h + 150 b = 1,900 represents the situation where a 160-pound adult uses a total of 1,900 calories from hiking for h 30-minute periods and bicycling for b 30-minute periods. It’s given that the adult completes 1 hour, or 2 30-minute periods, of bicycling. Substituting 2 for b in the equation 200 h + 150 b = 1,900 yields 200 h plus, 150 \u00d7 2 = 1,900, or 200 h + 300 = 1,900. Subtracting 300 from both sides of this equation yields 200 h = 1,600. Dividing both sides by 200 yields h = 8. Since h represents the number of 30-minute periods spent hiking and there are 2 30-minute periods in every hour, it follows that the adult will need to hike for (eight)/(2), or 4 hours to use a total of 1,900 calories from bicycling and hiking.

Choice A is incorrect and may result from solving the equation 200 h = 1,900. This represents 0 30-minute periods bicycling instead of 2. Choice B is incorrect and may result from solving the equation 200 h + 150 = 1,900. This represents 1 30-minute period of bicycling instead of 2. Choice C is incorrect. This may result from determining that the number of 30-minute periods the adult should hike is 8, but then subtracting 2 from 8, rather than dividing 8 by 2, to find the number of hours the adult should hike. 

 

\n"}, {"id": "868fc236", "domain": "Algebra", "skill": "Linear functions", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

\"The

The table above gives the typical amounts of energy per gram, expressed in both food calories and kilojoules, of the three macronutrients in food. If x food calories is equivalent to k kilojoules, of the following, which best represents the relationship between x and k ?

\n", "choices": [{"id": "A", "text": "

\n k = zero point 2 4 x\n

\n"}, {"id": "B", "text": "

\n k = 4 point 2 x\n

\n"}, {"id": "C", "text": "

\n x = 4 point 2 k\n

\n"}, {"id": "D", "text": "

\n x k = 4 point 2\n

\n"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. The relationship between x food calories and k kilojoules can be modeled as a proportional relationship. Let x sub 1, k sub 1 and x sub 2, k sub 2 represent the values in the first two rows in the table: 4 point 0, 16 point 7 and 9 point 0, 37 point 7. The rate of change, or the fraction with numerator, k sub 2 \u2212 k sub 1, and denominator x sub 2 \u2212 x sub 1, end fraction, is 21 over 5 = 4 point 2; therefore, the equation that best represents the relationship between x and k is k = 4 point 2 x.

Choice A is incorrect and may be the result of calculating the rate of change using the fraction with numerator, x sub 2 \u2212 x sub 1, and denominator k sub 2 \u2212 k sub 1, end fraction. Choice C is incorrect because the number of kilojoules is greater than the number of food calories. Choice D is incorrect and may be the result of an error when setting up the equation.

\n"}, {"id": "d8539e09", "domain": "Algebra", "skill": "Linear inequalities in one or two variables", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

y<6x+2

\n

For which of the following tables are all the values of x\n and their corresponding values of y\n solutions to the given inequality?

", "choices": [{"id": "A", "text": "
\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
x\ny\n
3\n20\n
5\n32\n
7\n44\n
"}, {"id": "B", "text": "
\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
x\ny\n
3\n16\n
5\n36\n
7\n40\n
"}, {"id": "C", "text": "
\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
x\ny\n
3\n16\n
5\n28\n
7\n40\n
"}, {"id": "D", "text": "
\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
x\ny\n
3\n24\n
5\n36\n
7\n48\n
"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. All the tables in the choices have the same three values of x\n, so each of the three values of x\n can be substituted in the given inequality to compare the corresponding values of y\n in each of the tables. Substituting 3\n for x\n in the given inequality yields y<63+2, or y<20. Therefore, when \n\tx\n\t=\n\t3\n\n, the corresponding value of y\n is less than 20\n. Substituting 5\n for x\n in the given inequality yields y<65+2, or y<32. Therefore, when \n\tx\n\t=\n\t5\n\n, the corresponding value of y\n is less than 32\n. Substituting 7\n for x\n in the given inequality yields y<67+2, or y<44. Therefore, when \n\tx\n\t=\n\t7\n\n, the corresponding value of y\n is less than 44\n. For the table in choice C, when \n\tx\n\t=\n\t3\n\n, the corresponding value of y\n is 16\n, which is less than 20\n; when \n\tx\n\t=\n\t5\n\n, the corresponding value of y\n is 28\n, which is less than 32\n; when \n\tx\n\t=\n\t7\n\n, the corresponding value of y\n is 40\n, which is less than 44\n. Therefore, the table in choice C gives values of x\n and their corresponding values of y\n that are all solutions to the given inequality.

\n

Choice A is incorrect. In the table for choice A, when \n\tx\n\t=\n\t3\n\n, the corresponding value of y\n is 20\n, which is not less than 20\n; when \n\tx\n\t=\n\t5\n\n, the corresponding value of y\n is 32\n, which is not less than 32\n; when \n\tx\n\t=\n\t7\n\n, the corresponding value of y\n is 44\n, which is not less than 44\n.

\n

Choice B is incorrect. In the table for choice B, when \n\tx\n\t=\n\t5\n\n, the corresponding value of y\n is 36\n, which is not less than 32\n.

\n

Choice D is incorrect. In the table for choice D, when \n\tx\n\t=\n\t3\n\n, the corresponding value of y\n is 24\n, which is not less than 20\n; when \n\tx\n\t=\n\t5\n\n, the corresponding value of y\n is 36\n, which is not less than 32\n; when \n\tx\n\t=\n\t7\n\n, the corresponding value of y\n is 48\n, which is not less than 44\n.

"}, {"id": "ce314070", "domain": "Algebra", "skill": "Linear equations in one variable", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

If 4 x \u2212 one half = \u22125, what is the value of 8 x \u2212 1?

\n", "choices": [{"id": "A", "text": "

\n 2\n

\n"}, {"id": "B", "text": "

\n \u2212nine eighths\n

\n"}, {"id": "C", "text": "

\n \u2212five halves\n

\n"}, {"id": "D", "text": "

\n \u221210\n

\n"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. Multiplying the given equation by 2 on each side yields 2 times, open parenthesis, 4 x \u2212 one half, close parenthesis = 2 \u00d7 \u22125. Applying the distributive property, this equation can be rewritten as 2 \u00d7 4 x, minus, 2 \u00d7 one half = 2 \u00d7 \u22125, or 8 x \u2212 1 = \u221210.

Choices A, B, and C are incorrect and may result from calculation errors in solving the given equation for x and then substituting that value of x in the expression 8 x \u2212 1.

\n"}, {"id": "7e1bff94", "domain": "Algebra", "skill": "Linear functions", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

The table gives the number of hours, h\n, of labor and a plumber\u2019s total charge fh, in dollars, for two different jobs.

\n
\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
h\nfh
1\n155\n
3\n285\n
\n

There is a linear relationship between h\n and fh. Which equation represents this relationship?

", "choices": [{"id": "A", "text": "

fh=25h+130

"}, {"id": "B", "text": "

fh=130h+25

"}, {"id": "C", "text": "

fh=65h+90

"}, {"id": "D", "text": "

fh=90h+65

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. It's given that there is a linear relationship between a plumber's hours of labor, h\n, and the plumber's total charge fh, in dollars. It follows that the relationship can be represented by an equation of the form fh=mh+b, where m\n is the rate of change of the function f\n and b\n is a constant. The rate of change of f\n can be calculated by dividing the difference in two values of fh by the difference in the corresponding values of h\n. Based on the values given in the table, the rate of change of f\n is 285-1553-1, or 65\n. Substituting 65\n for m\n in the equation fh=mh+b yields fh=65h+b. The value of b\n can be found by substituting any value of h\n and its corresponding value of fh for h\n and fh, respectively, in this equation. Substituting 1\n for h\n and 155\n for fh yields 155=651+b, or 155=65+b. Subtracting 65\n from both sides of this equation yields \n\t90\n\t=\n\tb\n\n. Substituting 90\n for b\n in the equation fh=65h+b yields f(h)=65h+90.

\n

Choice A is incorrect and may result from conceptual or calculation errors.

\n

Choice B is incorrect and may result from conceptual or calculation errors.

\n

Choice D is incorrect and may result from conceptual or calculation errors.

"}, {"id": "9f6f96ff", "domain": "Algebra", "skill": "Systems of two linear equations in two variables", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

A wire with a length of 106\n inches is cut into two parts. One part has a length of x\n inches, and the other part has a length of y\n inches. The value of x\n is 6\n more than 4\n times the value of y\n. What is the value of x\n?

", "choices": [{"id": "A", "text": "

25\n

"}, {"id": "B", "text": "

28\n

"}, {"id": "C", "text": "

56\n

"}, {"id": "D", "text": "

86\n

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. It's given that a wire with a length of 106\n inches is cut into two parts. It's also given that one part has a length of x\n inches and the other part has a length of y\n inches. This can be represented by the equation x+y=106. It's also given that the value of x\n is 6\n more than 4\n times the value of y\n. This can be represented by the equation x=4y+6. Substituting 4y+6 for x\n in the equation x+y=106 yields 4y+6+y=106, or 5y+6=106. Subtracting 6\n from each side of this equation yields 5y=100. Dividing each side of this equation by 5\n yields y=20. Substituting 20\n for y\n in the equation x=4y+6 yields x=4(20)+6, or x=86. 

\n

Choice A is incorrect. This value represents less than half of the total length of 106\n inches; however, x\n represents the length of the longer part of the wire, since it's given that the value of x\n is 6\n more than 4\n times the value of y\n.

\n

Choice B is incorrect. This value represents less than half of the total length of 106\n inches; however, x\n represents the length of the longer part of the wire, since it's given that the value of x\n is 6\n more than 4\n times the value of y\n.

\n

Choice C is incorrect. This represents a part that is 6\n more than the length of the other part, rather than 6\n more than 4\n times the length of the other part.

"}, {"id": "48fb34c8", "domain": "Algebra", "skill": "Linear inequalities in one or two variables", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

y>13x-18

\n

For which of the following tables are all the values of x\n and their corresponding values of y\n solutions to the given inequality?

", "choices": [{"id": "A", "text": "
\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
x\ny\n
3\n21\n
5\n47\n
8\n86\n
"}, {"id": "B", "text": "
\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
x\ny\n
3\n26\n
5\n42\n
8\n86\n
"}, {"id": "C", "text": "
\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
x\ny\n
3\n16\n
5\n42\n
8\n81\n
"}, {"id": "D", "text": "
\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
x\ny\n
3\n26\n
5\n52\n
8\n91\n
"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. All the tables in the choices have the same three values of x\n, so each of the three values of x\n can be substituted in the given inequality to compare the corresponding values of y\n in each of the tables. Substituting 3\n for x\n in the given inequality yields y>133-18, or y>21. Therefore, when \n\tx\n\t=\n\t3\n\n, the corresponding value of y\n is greater than 21\n. Substituting 5\n for x\n in the given inequality yields y>135-18, or y>47. Therefore, when \n\tx\n\t=\n\t5\n\n, the corresponding value of y\n is greater than 47\n. Substituting 8\n for x\n in the given inequality yields y>138-18, or y>86. Therefore, when \n\tx\n\t=\n\t8\n\n, the corresponding value of y\n is greater than 86\n. For the table in choice D, when \n\tx\n\t=\n\t3\n\n, the corresponding value of y\n is 26\n, which is greater than 21\n; when \n\tx\n\t=\n\t5\n\n, the corresponding value of y\n is 52\n, which is greater than 47\n; when \n\tx\n\t=\n\t8\n\n, the corresponding value of y\n is 91\n, which is greater than 86\n. Therefore, the table in choice D gives values of x\n and their corresponding values of y\n that are all solutions to the given inequality.

\n

Choice A is incorrect. In the table for choice A, when \n\tx\n\t=\n\t3\n\n, the corresponding value of y\n is 21\n, which is not greater than 21\n; when \n\tx\n\t=\n\t5\n\n, the corresponding value of y\n is 47\n, which is not greater than 47\n; when \n\tx\n\t=\n\t8\n\n, the corresponding value of y\n is 86\n, which is not greater than 86\n.

\n

Choice B is incorrect. In the table for choice B, when \n\tx\n\t=\n\t5\n\n, the corresponding value of y\n is 42\n, which is not greater than 47\n; when \n\tx\n\t=\n\t8\n\n, the corresponding value of y\n is 86\n, which is not greater than 86\n.

\n

Choice C is incorrect. In the table for choice C, when \n\tx\n\t=\n\t3\n\n, the corresponding value of y\n is 16\n, which is not greater than 21\n; when \n\tx\n\t=\n\t5\n\n, the corresponding value of y\n is 42\n, which is not greater than 47\n; when \n\tx\n\t=\n\t8\n\n, the corresponding value of y\n is 81\n, which is not greater than 86\n.

"}, {"id": "f718c9cf", "domain": "Algebra", "skill": "Systems of two linear equations in two variables", "difficulty": "H", "type": "spr", "stimulus": "", "stem": "

\n\t\n\t\t\n\t\t\t5\n\t\t\tx\n\t\t\n\t\t+\n\t\t\n\t\t\t14\n\t\t\ty\n\t\t\n\t\n\t=\n\t45\n\n

\n

\n\t\n\t\t\n\t\t\t10\n\t\t\tx\n\t\t\n\t\t+\n\t\t\n\t\t\t7\n\t\t\ty\n\t\t\n\t\n\t=\n\t27\n\n

\n

The solution to the given system of equations is x,y. What is the value of \n\tx\n\ty\n\n?

", "choices": [], "answerId": "1.8", "acceptedAnswers": ["1.8", "9/5"], "rationale": "

The correct answer is \n\t9\n\t5\n\n. Multiplying the first equation in the given system by 2\n yields \n\t\n\t\t\n\t\t\t10\n\t\t\tx\n\t\t\n\t\t+\n\t\t\n\t\t\t28\n\t\t\ty\n\t\t\n\t\n\t=\n\t90\n\n. Subtracting the second equation in the given system, \n\t\n\t\t\n\t\t\t10\n\t\t\tx\n\t\t\n\t\t+\n\t\t\n\t\t\t7\n\t\t\ty\n\t\t\n\t\n\t=\n\t27\n\n, from \n\t\n\t\t\n\t\t\t10\n\t\t\tx\n\t\t\n\t\t+\n\t\t\n\t\t\t28\n\t\t\ty\n\t\t\n\t\n\t=\n\t90\n\n yields 10x+28y-10x+7y=90-27, which is equivalent to 10x+28y-10x-7y=63, or \n\t\n\t\t21\n\t\ty\n\t\n\t=\n\t63\n\n. Dividing both sides of this equation by 21\n yields \n\ty\n\t=\n\t3\n\n. The value of x\n can be found by substituting 3\n for y\n in either of the two given equations. Substituting 3\n for y\n in the equation \n\t\n\t\t\n\t\t\t10\n\t\t\tx\n\t\t\n\t\t+\n\t\t\n\t\t\t7\n\t\t\ty\n\t\t\n\t\n\t=\n\t27\n\n yields 10x+73=27, or \n\t\n\t\t\n\t\t\t10\n\t\t\tx\n\t\t\n\t\t+\n\t\t21\n\t\n\t=\n\t27\n\n. Subtracting 21\n from both sides of this equation yields \n\t\n\t\t10\n\t\tx\n\t\n\t=\n\t6\n\n. Dividing both sides of this equation by 10\n yields x=610, or \n\tx\n\t=\n\t\n\t\t3\n\t\t5\n\t\n\n. Therefore, the value of \n\tx\n\ty\n\n is 353, or 95. Note that 9/5 and 1.8 are examples of ways to enter a correct answer.

"}, {"id": "915463e0", "domain": "Algebra", "skill": "Linear inequalities in one or two variables", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

Normal body temperature for an adult is between 97 point 8 degrees Fahrenheit and 99 degrees Fahrenheit, inclusive. If Kevin, an adult male, has a body temperature that is considered to be normal, which of the following could be his body temperature?

\n", "choices": [{"id": "A", "text": "

\n 96 point 7 degrees Fahrenheit\n

\n"}, {"id": "B", "text": "

\n 97 point 6 degrees Fahrenheit\n

\n"}, {"id": "C", "text": "

\n 97 point 9 degrees Fahrenheit\n

\n"}, {"id": "D", "text": "

\n 99 point 7 degrees Fahrenheit\n

\n"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. Normal body temperature must be greater than or equal to 97.8°F but less than or equal to 99°F. Of the given choices, 97.9°F is the only temperature that fits these restrictions.

Choices A and B are incorrect. These temperatures are less than 97.8°F, so they don’t fit the given restrictions. Choice D is incorrect. This temperature is greater than 99°F, so it doesn’t fit the given restrictions.

\n"}, {"id": "cc3e9528", "domain": "Algebra", "skill": "Linear equations in two variables", "difficulty": "H", "type": "spr", "stimulus": "", "stem": "

The graph of 9x-10y=19 is translated down 4\n units in the xy-plane. What is the x-coordinate of the x-intercept of the resulting graph?

", "choices": [], "answerId": "59/9", "acceptedAnswers": ["59/9", "6.555", "6.556"], "rationale": "

The correct answer is \n\t59\n\t9\n\n. When the graph of an equation in the form \n\t\n\t\t\n\t\t\tA\n\t\t\tx\n\t\t\n\t\t+\n\t\t\n\t\t\tB\n\t\t\ty\n\t\t\n\t\n\t=\n\tC\n\n, where A\n, B\n, and C\n are constants, is translated down k\n units in the xy-plane, the resulting graph can be represented by the equation Ax+By+k=C. It’s given that the graph of \n\t\n\t\t\n\t\t\t9\n\t\t\tx\n\t\t\n\t\t-\n\t\t\n\t\t\t10\n\t\t\ty\n\t\t\n\t\n\t=\n\t19\n\n is translated down 4\n units in the xy-plane. Therefore, the resulting graph can be represented by the equation 9x-10y+4=19, or 9x-10y-40=19. Adding 40\n to both sides of this equation yields \n\t\n\t\t\n\t\t\t9\n\t\t\tx\n\t\t\n\t\t-\n\t\t\n\t\t\t10\n\t\t\ty\n\t\t\n\t\n\t=\n\t59\n\n. The x-coordinate of the x-intercept of the graph of an equation in the xy-plane is the value of x\n in the equation when \n\ty\n\t=\n\t0\n\n. Substituting 0\n for y\n in the equation \n\t\n\t\t\n\t\t\t9\n\t\t\tx\n\t\t\n\t\t-\n\t\t\n\t\t\t10\n\t\t\ty\n\t\t\n\t\n\t=\n\t59\n\n yields 9x-100=59, or \n\t\n\t\t9\n\t\tx\n\t\n\t=\n\t59\n\n. Dividing both sides of this equation by 9\n yields \n\tx\n\t=\n\t\n\t\t59\n\t\t9\n\t\n\n. Therefore, the x-coordinate of the x-intercept of the resulting graph is \n\t59\n\t9\n\n. Note that 59/9, 6.555, and 6.556 are examples of ways to enter a correct answer.

"}, {"id": "520e6f5b", "domain": "Algebra", "skill": "Linear equations in two variables", "difficulty": "E", "type": "mc", "stimulus": "
 
Characteristics for Rock Types
Rock typeWeight per volume (lb/ft3)Cost per pound
Basalt180$0.18
Granite165$0.09
Limestone120$0.03
Sandstone135$0.22
\n", "stem": "

A city is planning to build a rock retaining wall, a monument, and a garden in a park. The table above shows four rock types that will be considered for use in the project. Also shown for each rock type is its weight per volume, in pounds per cubic foot (lb/ft3), and the cost per pound, in dollars. The equation 0 point 0 3 times, open parenthesis, 120 w, close parenthesis, plus, 0 point 1 8 times, open parenthesis, 180 z, close parenthesis, + 3,385 point 8 0 = 7,576 point 2 0. gives the total cost, in dollars, of the rocks used in the project in terms of the number of ft3 of limestone, w, and the number of ft3 of basalt, z. All four rock types are used in the project. Which of the following is the best interpretation of 3,385.80 in this context?

\n", "choices": [{"id": "A", "text": "

The cost of the granite and sandstone needed for the project

\n"}, {"id": "B", "text": "

The cost of the basalt and limestone needed for the project

\n"}, {"id": "C", "text": "

The cost of the basalt needed for the project

\n"}, {"id": "D", "text": "

The cost of the sandstone needed for the project

\n"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. The table shows the cost of limestone is $0.03/lb, and the weight per volume for limestone is 120 lb/ft3. Therefore, the term 0 point 0 3 \u00d7 120 w represents the cost, in dollars, of w ft3 of limestone. Similarly, the term 0 point 1 8 \u00d7 180 z represents the cost, in dollars, of z ft3 of basalt. The given equation shows that the total cost of all the rocks used in the project is $7,576.20. Since it’s given that all four rock types are used in the project, the remaining term, 3,385.80, represents the cost, in dollars, of the granite and sandstone needed for the project.

Choice B is incorrect. The cost of basalt and limestone needed for the project can be represented by 0 point 1 8 \u00d7 180 z, plus, 0 point 0 3 \u00d7 120 w. Choice C is incorrect. The cost of the basalt needed for the project can be represented by the expression 0 point 1 8 \u00d7 180 z. Choice D is incorrect and may result from neglecting to include granite in the rock types used for the project.

\n"}, {"id": "153ee763", "domain": "Algebra", "skill": "Linear equations in one variable", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

-3x+21px=84

\n

In the given equation, p\n is a constant. The equation has no solution. What is the value of p\n?

", "choices": [{"id": "A", "text": "

0\n

"}, {"id": "B", "text": "

\n\t1\n\t7\n\n

"}, {"id": "C", "text": "

\n\t4\n\t3\n\n

"}, {"id": "D", "text": "

4\n

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. A linear equation in one variable has no solution if and only if the equation is false; that is, when there is no value of x\n that produces a true statement. It's given that in the equation -3x+21px=84, p\n is a constant and the equation has no solution for x\n. Therefore, the value of the constant p\n is one that results in a false equation. Factoring out the common factor of \n\t-\n\t3\n\tx\n\n on the left-hand side of the given equation yields -3x1-7p=84. Dividing both sides of this equation by -3\n yields x1-7p=-28. Dividing both sides of this equation by 1-7p yields x=-281-7p. This equation is false if and only if 1-7p=0. Adding \n\t7\n\tp\n\n to both sides of 1-7p=0 yields 1=7p. Dividing both sides of this equation by 7\n yields 17=p. It follows that the equation x=-281-7p is false if and only if p=17. Therefore, the given equation has no solution if and only if the value of p\n is 17.

\n

Choice A is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

\n

Choice D is incorrect and may result from conceptual or calculation errors.

"}, {"id": "89541f9b", "domain": "Algebra", "skill": "Linear inequalities in one or two variables", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

Which of the following ordered pairs x, y satisfies the inequality 5 x \u2212 3 y < 4 ?

  1. \n \n Statement 1, 1, 1\n \n
    2. \n
  2. \n \n Statement 2, 2, 5\n \n
    3. \n
  3. \n \n Statement 3, 3, 2\n \n
    4. \n

\n", "choices": [{"id": "A", "text": "

I only

\n"}, {"id": "B", "text": "

II only

\n"}, {"id": "C", "text": "

I and II only

\n"}, {"id": "D", "text": "

I and III only

\n"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. Substituting 1, 1 into the inequality gives 5 \u00d7 1, minus, 3 \u00d7 1, < 4, or 2 < 4, which is a true statement. Substituting 2, 5 into the inequality gives 5 \u00d7 2, minus, 3 \u00d7 5, < 4, or \u22125 < 4, which is a true statement. Substituting 3, 2 into the inequality gives 5 \u00d7 3, minus, 3 \u00d7 2, < 4, or 9 < 4, which is not a true statement. Therefore, 1, 1 and 2, 5 are the only ordered pairs shown that satisfy the given inequality.

Choice A is incorrect because the ordered pair 2, 5 also satisfies the inequality. Choice B is incorrect because the ordered pair 1, 1 also satisfies the inequality. Choice D is incorrect because the ordered pair 3, 2 does not satisfy the inequality.

\n"}, {"id": "2875ba81", "domain": "Algebra", "skill": "Systems of two linear equations in two variables", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

\n\t\n\t\t\n\t\t\t6\n\t\t\tx\n\t\t\n\t\t+\n\t\t\n\t\t\t7\n\t\t\ty\n\t\t\n\t\n\t=\n\t28\n\n
\n\t\n\t\t\n\t\t\t2\n\t\t\tx\n\t\t\n\t\t+\n\t\t\n\t\t\t2\n\t\t\ty\n\t\t\n\t\n\t=\n\t10\n\n

\n

The solution to the given system of equations is x,y. What is the value of y?

", "choices": [{"id": "A", "text": "

-2\n

"}, {"id": "B", "text": "

7\n

"}, {"id": "C", "text": "

14\n

"}, {"id": "D", "text": "

18\n

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. The given system of linear equations can be solved by the elimination method. Multiplying each side of the second equation in the given system by 3\n yields 2x+2y(3)=103, or 6x+6y=30. Subtracting this equation from the first equation in the given system yields 6x+7y-6x+6y=28-30, which is equivalent to 6x-6x+7y-6y=28-30, or y=-2. 

\n

Choice B is incorrect. This is the value of x\n, not the value of y\n.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

\n

Choice D is incorrect and may result from conceptual or calculation errors.

\n

 

"}, {"id": "265f2a53", "domain": "Algebra", "skill": "Linear equations in two variables", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

When line n\n is graphed in the xy-plane, it has an x-intercept of -4,0 and a y-intercept of 0,863. What is the slope of line n\n?

", "choices": [{"id": "A", "text": "

\n\t3\n\t344\n\n

"}, {"id": "B", "text": "

\n\t6\n\t43\n\n

"}, {"id": "C", "text": "

\n\t43\n\t6\n\n

"}, {"id": "D", "text": "

\n\t344\n\t3\n\n

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. It's given that when line n\n is graphed in the xy-plane, it has an x-intercept of -4,0 and a y-intercept of 0,863. The slope, m\n, of a line can be found using any two points on the line, x1,y1 and x2,y2, and the slope formula m=y2-y1x2-x1. Substituting the points -4,0 and 0,863 for x1,y1 and x2,y2, respectively, in the slope formula yields m=863-00--4, or m=436. Therefore, the slope of line n\n is 436.

\n

Choice A is incorrect and may result from conceptual or calculation errors.

\n

Choice B is incorrect. This is the slope of a line that has an x-intercept of 863,0 and a y-intercept of 0,-4.

\n

Choice D is incorrect and may result from conceptual or calculation errors.

"}, {"id": "ee031767", "domain": "Algebra", "skill": "Systems of two linear equations in two variables", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

A dance teacher ordered outfits for students for a dance recital. Outfits for boys cost $26, and outfits for girls cost $35. The dance teacher ordered a total of 28 outfits and spent $881. If b represents the number of outfits the dance teacher ordered for boys and g represents the number of outfits the dance teacher ordered for girls, which of the following systems of equations can be solved to find b and g ?

\n", "choices": [{"id": "A", "text": "

\n Each option consists(t)wo equations. 26 b + 35 g = 28, and, b + g = 881\n

\n"}, {"id": "B", "text": "

\n 26 b + 35 g = 881, ; b + g = 28\n

\n"}, {"id": "C", "text": "

\n 26 g + 35 b = 28; b + g = 881\n

\n"}, {"id": "D", "text": "

\n 26 g + 35 b = 881; b + g = 28\n

\n"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. Outfits for boys cost $26 each and the teacher ordered b outfits for boys, so the teacher spent 26b dollars on outfits for boys. Similarly, outfits for girls cost $35 each and the teacher ordered g outfits for girls, so the teacher spent 35g dollars on outfits for girls. Since the teacher spent a total of $881 on outfits for boys and girls, the equation 26b + 35g = 881 must be true. And since the teacher ordered a total of 28 outfits, the equation b + g = 28 must also be true.

\n
\nChoice A is incorrect and may result from switching the constraint on the total number of outfits with the constraint on the cost of the outfits. Choice C is incorrect and may result from switching the constraint on the total number of outfits with the constraint on the cost of the outfits, as well as switching the cost of the outfits for boys with the cost of the outfits for girls. Choice D is incorrect and may result from switching the cost of the outfits for boys with the cost of the outfits for girls.

\n"}, {"id": "0cadb20e", "domain": "Algebra", "skill": "Linear functions", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

The function f\n is defined by fx=x+155, and fa=10, where a\n is a constant. What is the value of a\n?

", "choices": [{"id": "A", "text": "

5\n

"}, {"id": "B", "text": "

10\n

"}, {"id": "C", "text": "

35\n

"}, {"id": "D", "text": "

65\n

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. It's given that fx=x+155 and fa=10, where a\n is a constant. Therefore, for the given function f\n, when \n\tx\n\t=\n\ta\n\n, fx=10. Substituting a\n for x\n and 10\n for fx in the given function f\n yields 10=a+155. Multiplying both sides of this equation by 5\n yields 50=a+15. Subtracting 15\n from both sides of this equation yields 35=a. Therefore, the value of a\n is 35\n.

\n

Choice A is incorrect. This is the value of a\n if fa=4.

\n

Choice B is incorrect. This is the value of a\n if fa=5.

\n

Choice D is incorrect. This is the value of a\n if fa=16.

"}, {"id": "ce6b52d8", "domain": "Algebra", "skill": "Linear equations in one variable", "difficulty": "M", "type": "spr", "stimulus": "", "stem": "

If 2(3t-10)+t=40+4t, what is the value of 3t?

", "choices": [], "answerId": "60", "acceptedAnswers": ["60"], "rationale": "

The correct answer is 60\n. Subtracting t\n from both sides of the given equation yields 2(3t-10)=40+3t. Applying the distributive property to the left-hand side of this equation yields 6t-20=40+3t. Adding 20\n to both sides of this equation yields 6t=60+3t. Subtracting \n\t3\n\tt\n\n from both sides of this equation yields 3t=60. Therefore, the value of \n\t3\n\tt\n\n is 60\n.

"}, {"id": "aee9fd2d", "domain": "Algebra", "skill": "Linear equations in one variable", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

If x+63=x+613, the value of x+6 is between which of the following pairs of values?

", "choices": [{"id": "A", "text": "

-7\n and -3\n

"}, {"id": "B", "text": "

-2\n and 2\n

"}, {"id": "C", "text": "

2\n and 7\n

"}, {"id": "D", "text": "

8\n and 13\n

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. Multiplying both sides of the given equation by 313, or 39\n, yields 39x+63=39x+613, or 13x+6=3x+6. Subtracting 3x+6 from both sides of this equation yields 10x+6=0. Dividing both sides of this equation by 10\n yields x+6=0. Therefore, if x+63=x+613, then the value of x+6 is 0\n. It follows that of the given choices, the value of x+6 is between -2\n and 2\n.

\n

Choice A is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

\n

Choice D is incorrect and may result from conceptual or calculation errors.

"}, {"id": "84d0d07e", "domain": "Algebra", "skill": "Linear inequalities in one or two variables", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

A clothing store is having a sale on shirts and pants. During the sale, the cost of each shirt is $15 and the cost of each pair of pants is $25. Geoff can spend at most $120 at the store. If Geoff buys s shirts and p pairs of pants, which of the following must be true?

\n", "choices": [{"id": "A", "text": "

\n 15 s + 25 p, < or equal to 120\n

\n"}, {"id": "B", "text": "

\n 15 s + 25 p, > or equal to 120\n

\n"}, {"id": "C", "text": "

\n 25 s + 15 p, < or equal to 120\n

\n"}, {"id": "D", "text": "

\n 25 s + 15 p, > or equal to 120\n

\n"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. Since the cost of each shirt is $15 and Geoff buys s shirts, the expression 15 s represents the amount Geoff spends on shirts. Since the cost of each pair of pants is $25 and Geoff buys p pairs of pants, the expression 25 p represents the amount Geoff spends on pants. Therefore, the sum 15 s + 25 p represents the total amount Geoff spends at the store. Since Geoff can spend at most $120 at the store, the total amount he spends must be less than or equal to 120. Thus, 15 s + 25 p, < or equal to 120.

Choice B is incorrect. This represents the situation in which Geoff spends at least, rather than at most, $120 at the store. Choice C is incorrect and may result from reversing the cost of a shirt and that of a pair of paints. Choice D is incorrect and may result from both reversing the cost of a shirt and that of a pair of pants and from representing a situation in which Geoff spends at least, rather than at most, $120 at the store.

\n"}, {"id": "7a987ae4", "domain": "Algebra", "skill": "Linear equations in one variable", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

If 2 n over 5 = 10, what is the value of 2 n, \u2212 1 ?

\n", "choices": [{"id": "A", "text": "

24

\n"}, {"id": "B", "text": "

49

\n"}, {"id": "C", "text": "

50

\n"}, {"id": "D", "text": "

99

\n"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. Multiplying both sides of the given equation by 5 yields 2 n = 50. Substituting 50 for 2 n in the expression 2 n \u2212 1 yields 50 \u2212 1 = 49.

Alternate approach: Dividing both sides of 2 n = 50 by 2 yields n = 25. Evaluating the expression 2 n \u2212 1 for n = 25 yields 2 \u00d7 25, \u2212 1 = 49.

Choice A is incorrect and may result from finding the value of n \u2212 1 instead of 2 n \u2212 1. Choice C is incorrect and may result from finding the value of 2 n instead of 2 n \u2212 1. Choice D is incorrect and may result from finding the value of 4 n \u2212 1 instead of 2 n \u2212 1.

\n"}, {"id": "f81a0503", "domain": "Algebra", "skill": "Linear equations in two variables", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

In the xy-plane, line k\n passes through the points 0,-5 and 1,-1. Which equation defines line k\n?

", "choices": [{"id": "A", "text": "

\n\ty\n\t=\n\t\n\t\t\n\t\t\t-\n\t\t\tx\n\t\t\n\t\t+\n\t\t\n\t\t\t1\n\t\t\t4\n\t\t\n\t\n\n

"}, {"id": "B", "text": "

y=14x-5

"}, {"id": "C", "text": "

\n\ty\n\t=\n\t\n\t\t\n\t\t\t-\n\t\t\tx\n\t\t\n\t\t+\n\t\t4\n\t\n\n

"}, {"id": "D", "text": "

\n\ty\n\t=\n\t\n\t\t\n\t\t\t4\n\t\t\tx\n\t\t\n\t\t-\n\t\t5\n\t\n\n

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. An equation defining a line in the xy-plane can be written in the form \n\ty\n\t=\n\t\n\t\t\n\t\t\tm\n\t\t\tx\n\t\t\n\t\t+\n\t\tb\n\t\n\n, where m\n represents the slope and 0,b represents the y-intercept of the line. It’s given that line k\n passes through the point 0,-5; therefore, \n\tb\n\t=\n\t-5\n\n. The slope, m\n, of a line can be found using any two points on the line, x1,y1 and x2,y2, and the slope formula m=y2-y1x2-x1. Substituting the points 0,-5 and 1,-1 for x1,y1 and x2,y2, respectively, in the slope formula yields m=-1--51-0, or \n\tm\n\t=\n\t4\n\n. Substituting 4\n for m\n and -5\n for b\n in the equation \n\ty\n\t=\n\t\n\t\t\n\t\t\tm\n\t\t\tx\n\t\t\n\t\t+\n\t\tb\n\t\n\n yields \n\ty\n\t=\n\t\n\t\t\n\t\t\t4\n\t\t\tx\n\t\t\n\t\t-\n\t\t5\n\t\n\n. 

\n

Choice A is incorrect and may result from conceptual or calculation errors.

\n

Choice B is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

"}, {"id": "13909d78", "domain": "Algebra", "skill": "Linear functions", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

The function f\n is defined by the equation fx=100x+2. What is the value of fx when \n\tx\n\t=\n\t9\n\n?

", "choices": [{"id": "A", "text": "

111\n

"}, {"id": "B", "text": "

118\n

"}, {"id": "C", "text": "

900\n

"}, {"id": "D", "text": "

902\n

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. Substituting 9\n for x\n in the given equation yields f9=1009+2, or f9=902. Therefore, the value of fx when x=9 is 902\n.

\n

Choice A is incorrect. This is the value of fx when x=1.09.

\n

Choice B is incorrect. This is the value of fx when x=1.16.

\n

Choice C is incorrect. This is the value of fx when x=8.98.

"}, {"id": "10c448d6", "domain": "Algebra", "skill": "Linear equations in two variables", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

A line in the xy-plane has a slope of 19 and passes through the point 0,14. Which equation represents this line?

", "choices": [{"id": "A", "text": "

y=-19x-14

"}, {"id": "B", "text": "

y=-19x+14

"}, {"id": "C", "text": "

y=19x-14

"}, {"id": "D", "text": "

y=19x+14

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. The equation of a line in the xy-plane can be written as y=mx+b, where m\n represents the slope of the line and 0,b represents the y-intercept of the line. It's given that the slope of the line is 19. It follows that m=19. It's also given that the line passes through the point 0,14. It follows that b=14. Substituting 19 for m\n and 14\n for b\n in y=mx+b yields y=19x+14. Thus, the equation y=19x+14 represents this line.

\n

Choice A is incorrect. This equation represents a line with a slope of -19 and a y-intercept of 0,-14.

\n

Choice B is incorrect. This equation represents a line with a slope of -19 and a y-intercept of 0,14.

\n

Choice C is incorrect. This equation represents a line with a slope of 19 and a y-intercept of 0,-14.

"}, {"id": "7038b587", "domain": "Algebra", "skill": "Linear equations in two variables", "difficulty": "E", "type": "spr", "stimulus": "", "stem": "

Vivian bought party hats and cupcakes for $71\n. Each package of party hats cost $3\n, and each cupcake cost $1\n. If Vivian bought 10\n packages of party hats, how many cupcakes did she buy?

", "choices": [], "answerId": "41", "acceptedAnswers": ["41"], "rationale": "

The correct answer is 41\n. The number of cupcakes Vivian bought can be found by first finding the amount Vivian spent on cupcakes. The amount Vivian spent on cupcakes can be found by subtracting the amount Vivian spent on party hats from the total amount Vivian spent. The amount Vivian spent on party hats can be found by multiplying the cost per package of party hats by the number of packages of party hats, which yields $3\u00b710, or $30. Subtracting the amount Vivian spent on party hats, $30, from the total amount Vivian spent, $71, yields $71-$30, or $41. Since the amount Vivian spent on cupcakes was $41 and each cupcake cost $1, it follows that Vivian bought 41\n cupcakes.

"}, {"id": "4acd05cd", "domain": "Algebra", "skill": "Linear equations in two variables", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n\n

\n

The graph shows the linear relationship between x\n and y\n. Which table gives three values of x\n and their corresponding values of y\n for this relationship?

", "choices": [{"id": "A", "text": "
\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
x\ny\n
0\n0\n
1\n-7\n
2\n-9\n
"}, {"id": "B", "text": "
\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
x\ny\n
0\n0\n
1\n-3\n
2\n-1\n
"}, {"id": "C", "text": "
\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
x\ny\n
0\n-5\n
1\n-7\n
2\n-9\n
"}, {"id": "D", "text": "
\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
x\ny\n
0\n-5\n
1\n-3\n
2\n-1\n
"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. It’s given that the graph shows the linear relationship between x\n and y\n. The given graph passes through the points 0,-5, 1,-3, and 2,-1. It follows that when \n\tx\n\t=\n\t0\n\n, the corresponding value of y\n is -5\n, when \n\tx\n\t=\n\t1\n\n, the corresponding value of y\n is -3\n, and when \n\tx\n\t=\n\t2\n\n, the corresponding value of y\n is -1\n. Of the given choices, only the table in choice D gives these three values of x\n and their corresponding values of y\n for the relationship shown in the graph.

\n

Choice A is incorrect. This table represents a relationship between x\n and y\n such that the graph passes through the points 0,0, 1,-7, and 2,-9.

\n

Choice B is incorrect. This table represents a relationship between x\n and y\n such that the graph passes through the points 0,0, 1,-3, and 2,-1.

\n

Choice C is incorrect. This table represents a linear relationship between x\n and y\n such that the graph passes through the points 0,-5, 1,-7, and 2,-9.

"}, {"id": "963da34c", "domain": "Algebra", "skill": "Linear inequalities in one or two variables", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

A shipping service restricts the dimensions of the boxes it will ship for a certain type of service. The restriction states that for boxes shaped like rectangular prisms, the sum of the perimeter of the base of the box and the height of the box cannot exceed 130 inches. The perimeter of the base is determined using the width and length of the box. If a box has a height of 60 inches and its length is 2.5 times the width, which inequality shows the allowable width x, in inches, of the box?

\n", "choices": [{"id": "A", "text": "zero < x, which < or equal to 10\n"}, {"id": "B", "text": "

\n zero < x, which < or equal to 11 and two-thirds\n

\n"}, {"id": "C", "text": "

\n zero < x, which < or equal to 17 and one-half\n

\n"}, {"id": "D", "text": "

\n zero < x, which < or equal to 20\n

\n"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. If x is the width, in inches, of the box, then the length of the box is 2.5x inches. It follows that the perimeter of the base is 2 times, open parenthesis, 2 point 5 x + x, close parenthesis, or 7x inches. The height of the box is given to be 60 inches. According to the restriction, the sum of the perimeter of the base and the height of the box should not exceed 130 inches. Algebraically, this can be represented by 7 x + 60, < or equal to 130, or 7 x < or equal to 70. Dividing both sides of the inequality by 7 gives x < or equal to 10. Since x represents the width of the box, x must also be a positive number. Therefore, the inequality 0 < x, which < or equal to 10 represents all the allowable values of x that satisfy the given conditions.

Choices B, C, and D are incorrect and may result from calculation errors or misreading the given information.

\n"}, {"id": "b2de69bd", "domain": "Algebra", "skill": "Linear equations in two variables", "difficulty": "E", "type": "mc", "stimulus": "
\n\t
\n\t\t\n\t\t\t\t
\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t
xy
15
27
39
411
\n
\n", "stem": "

The table above shows some pairs of x values and y values. Which of the following equations could represent the relationship between x and y ?

\n", "choices": [{"id": "A", "text": "

y = 2 x + 3

\n"}, {"id": "B", "text": "

y = 3 x \u2212 2

\n"}, {"id": "C", "text": "

y = 4 x \u2212 one

\n"}, {"id": "D", "text": "

y = 5 x

\n"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. Each of the choices is a linear equation in the form y = mx + b, where m and b are constants. In this equation, m represents the change in y for each increase in x by 1. From the table, it can be determined that the value of y increases by 2 for each increase in x by 1. In other words, for the  pairs of x and y in the given table, m = 2. The value of b can be found by substituting the values of x and y from any row of the table and substituting the value of m into the equation y = mx + b and then solving for b. For example, using x = 1, y = 5, and m = 2 yields 5 = 2(1) + b. Solving for b yields b = 3. Therefore, the equation y = 2x + 3 could represent the relationship between x and y in the given table.

Alternatively, if an equation represents the relationship between x and y, then when each pair of x and y from the table is substituted into the equation, the result will be a true statement. Of the equations given, the equation y = 2x + 3 in choice A is the only equation that results in a true statement when each of the pairs of x and y are substituted into the equation.

Choices B, C, and D are incorrect because when at least one pair of x and y from the table is substituted into the equations given in these choices, the result is a false statement. For example, when the pair x = 4 and y = 11 is substituted into the equation in choice B, the result is 11 = 3(4) – 2, or 11 = 10, which is false.

\n"}, {"id": "28c2253f", "domain": "Algebra", "skill": "Linear equations in two variables", "difficulty": "M", "type": "mc", "stimulus": "
 
Characteristics for Rock Types
Rock typeWeight per volume (lb/ft3)Cost per pound
Basalt180$0.18
Granite165$0.09
Limestone120$0.03
Sandstone135$0.22
\n", "stem": "

A city is planning to build a rock retaining wall, a monument, and a garden in a park. The table above shows four rock types that will be considered for use in the project. Also shown for each rock type is its weight per volume, in pounds per cubic foot (lb/ft3), and the cost per pound, in dollars. Only basalt, granite, and limestone will be used in the garden. The rocks in the garden will have a total weight of 1,000 pounds. If 330 pounds of granite is used, which of the following equations could show the relationship between the amounts, x and y, in ft3, for each of the other rock types used?

 

\n", "choices": [{"id": "A", "text": "

165 x, plus, 180 y = 670

\n"}, {"id": "B", "text": "

165 x, plus, 120 y = 1,000

\n"}, {"id": "C", "text": "

120 x, plus, 180 y = 670

\n"}, {"id": "D", "text": "

120 x, plus, 180 y = 1,000

\n"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. It’s given that the weight of the granite used in the garden is 330 pounds. The weight of the limestone used in the garden is a product of its weight per volume, in lb/ft3, and its volume, in ft3. Therefore, the weight of the limestone used in the garden can be represented by 120 x, where x is the volume, in ft3, of the limestone used. Similarly, the weight of the basalt used in the garden can be represented by 180 y, where y is the volume, in ft3, of the basalt used. It’s given that the total weight of the rocks used in the garden will be 1,000 pounds. Thus, the sum of the weights of the three rock types used is 1,000 pounds, which can be represented by the equation 120 x, + 180 y, + 330 = 1,000. Subtracting 330 from both sides of this equation yields 120 x, + 180 y = 670.

Choice A is incorrect. This equation uses the weight per volume of granite instead of limestone. Choice B is incorrect. This equation uses the weight per volume of granite instead of basalt, and doesn’t take into account the 330 pounds of granite that will be used in the garden. Choice D is incorrect. This equation doesn’t take into account the 330 pounds of granite that will be used in the garden.

\n"}, {"id": "042aa429", "domain": "Algebra", "skill": "Linear functions", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

If f(x)=x+7 and g(x)=7x, what is the value of 4f(2)−g(2)?

", "choices": [{"id": "A", "text": "

-5\n

"}, {"id": "B", "text": "

1\n

"}, {"id": "C", "text": "

22\n

"}, {"id": "D", "text": "

28\n

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. The value of f(2) can be found by substituting 2\n for x\n in the given equation fx=x+7, which yields f2=2+7, or f2=9. The value of g2 can be found by substituting 2\n for x\n in the given equation gx=7x, which yields g2=72, or g2=14. The value of the expression 4f2-g2 can be found by substituting the corresponding values into the expression, which gives 4(9)−14. This expression is equivalent to 36-14, or 22\n.

\n

Choice A is incorrect. This is the value of f2-g2, not 4f2-g2.

\n

Choice B is incorrect and may result from calculating 4f2 as 4(2)+7, rather than
4(2+7).

\n

Choice D is incorrect and may result from conceptual or calculation errors.

"}, {"id": "cd33b015", "domain": "Algebra", "skill": "Systems of two linear equations in two variables", "difficulty": "E", "type": "mc", "stimulus": "
\n
\n
\n

\n Equation 1: x + y = 20. Equation 2: 2 times, open parenthesis, x + y, close parenthesis, + 3 y = 85.\n

\n
\n
\n
\n", "stem": "

If x, y is the solution to the given system of equations, what is the value of y ?

\n", "choices": [{"id": "A", "text": "

10

\n"}, {"id": "B", "text": "

15

\n"}, {"id": "C", "text": "

60

\n"}, {"id": "D", "text": "

65

\n"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. Substituting 20 for x + y in the second equation in the system yields 2 \u00d7 20, + 3y = 85, or 40 + 3 y = 85. Subtracting 40 from both sides of this equation yields 3 y = 45. Dividing both sides of this equation by 3 yields y = 15.

Choice A is incorrect. If y = 10, then x = 10 since x + y = 20. However, substituting 10 for both x and y in the second equation yields 70 = 85, which is a false statement. Choice C is incorrect. If y = 60, then x = \u221240 since x + y = 20. However, substituting these values for x and y in the second equation yields 220 = 85, which is a false statement. Choice D is incorrect. If y = 65, then x = \u221245 since x + y = 20. However, substituting these values for x and y in the second equation yields 235 = 85, which is a false statement.

\n"}, {"id": "e2e3942f", "domain": "Algebra", "skill": "Systems of two linear equations in two variables", "difficulty": "H", "type": "mc", "stimulus": "
\n

\n Equation 1: y = 2 x + 1. Equation 2: y = a, x \u2212 8.\n

\n
\n", "stem": "

In the system of equations above, a is a constant. If the system of equations has no solution, what is the value of a ?

\n", "choices": [{"id": "A", "text": "\u2212one half\n"}, {"id": "B", "text": "0\n"}, {"id": "C", "text": "1\n"}, {"id": "D", "text": "2\n"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. A system of two linear equations has no solution when the graphs of the equations have the same slope and different y-coordinates of the y-intercepts. Each of the given equations is written in the slope-intercept form of a linear equation, y = m x + b, where m is the slope and b is the y-coordinate of the y-intercept of the graph of the equation. For these two linear equations, the y-coordinates of the y-intercepts are different: 1 and \u22128. Thus, if the system of equations has no solution, the slopes of the two linear equations must be the same. The slope of the first linear equation is 2. Therefore, for the system of equations to have no solution, the value of a must be 2.

Choices A, B, and C are incorrect and may result from conceptual and computational errors.

\n"}, {"id": "f03465dc", "domain": "Algebra", "skill": "Systems of two linear equations in two variables", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

\n\t\n\t\t\n\t\t\t8\n\t\t\tx\n\t\t\n\t\t+\n\t\t\n\t\t\t7\n\t\t\ty\n\t\t\n\t\n\t=\n\t9\n\n
\n\t\n\t\t\n\t\t\t24\n\t\t\tx\n\t\t\n\t\t+\n\t\t\n\t\t\t21\n\t\t\ty\n\t\t\n\t\n\t=\n\t27\n\n

\n

For each real number r\n, which of the following points lies on the graph of each equation in the xy-plane for the given system?

", "choices": [{"id": "A", "text": "

r,-8r7+97

"}, {"id": "B", "text": "

-8r7+97,r

"}, {"id": "C", "text": "

-8r7+9,8r7+27

"}, {"id": "D", "text": "

r3+9,-r3+27

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. Dividing both sides of the second equation in the given system by 3\n yields \n\t\n\t\t\n\t\t\t8\n\t\t\tx\n\t\t\n\t\t+\n\t\t\n\t\t\t7\n\t\t\ty\n\t\t\n\t\n\t=\n\t9\n\n, which is the first equation in the given system. Therefore, the first and second equations represent the same line in the xy-plane. If the x- and y-coordinates of a point satisfy an equation, the point lies on the graph of the equation in the xy-plane. Choice A is a point with x-coordinate r\n and y-coordinate \n\t\n\t\t-\n\t\t\n\t\t\t\n\t\t\t\t8\n\t\t\t\tr\n\t\t\t\n\t\t\t7\n\t\t\n\t\n\t+\n\t\n\t\t9\n\t\t7\n\t\n\n. Substituting r\n for x\n and \n\t\n\t\t-\n\t\t\n\t\t\t\n\t\t\t\t8\n\t\t\t\tr\n\t\t\t\n\t\t\t7\n\t\t\n\t\n\t+\n\t\n\t\t9\n\t\t7\n\t\n\n for y\n in the equation \n\t\n\t\t\n\t\t\t8\n\t\t\tx\n\t\t\n\t\t+\n\t\t\n\t\t\t7\n\t\t\ty\n\t\t\n\t\n\t=\n\t9\n\n yields 8r+7-87r+97=9. Applying the distributive property to the left-hand side of this equation yields 8r-8r+9=9. Combining like terms on the left-hand side of this equation yields 9=9, so the coordinates of the point r,-87r+97 satisfy both equations in the given system. Therefore, for each real number r\n, the point r,-87r+97 lies on the graph of each equation in the xy-plane for the given system.

\n

Choice B is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

\n

Choice D is incorrect and may result from conceptual or calculation errors.

"}, {"id": "a35c7164", "domain": "Algebra", "skill": "Linear equations in two variables", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

\n\t\n\t\t\n\t\t\t5\n\t\t\tx\n\t\t\n\t\t+\n\t\t\n\t\t\t7\n\t\t\ty\n\t\t\n\t\n\t=\n\t1\n\n

\n

\n\t\n\t\t\n\t\t\ta\n\t\t\tx\n\t\t\n\t\t+\n\t\t\n\t\t\tb\n\t\t\ty\n\t\t\n\t\n\t=\n\t1\n\n

\n

In the given pair of equations, a\n and b\n are constants. The graph of this pair of equations in the xy-plane is a pair of perpendicular lines. Which of the following pairs of equations also represents a pair of perpendicular lines?

", "choices": [{"id": "A", "text": "

\n\t\n\t\t\n\t\t\t10\n\t\t\tx\n\t\t\n\t\t+\n\t\t\n\t\t\t7\n\t\t\ty\n\t\t\n\t\n\t=\n\t1\n\n

\n

\n\t\n\t\t\n\t\t\ta\n\t\t\tx\n\t\t\n\t\t-\n\t\t\n\t\t\t2\n\t\t\tb\n\t\t\ty\n\t\t\n\t\n\t=\n\t1\n\n

"}, {"id": "B", "text": "

\n\t\n\t\t\n\t\t\t10\n\t\t\tx\n\t\t\n\t\t+\n\t\t\n\t\t\t7\n\t\t\ty\n\t\t\n\t\n\t=\n\t1\n\n

\n

\n\t\n\t\t\n\t\t\ta\n\t\t\tx\n\t\t\n\t\t+\n\t\t\n\t\t\t2\n\t\t\tb\n\t\t\ty\n\t\t\n\t\n\t=\n\t1\n\n

"}, {"id": "C", "text": "

\n\t\n\t\t\n\t\t\t10\n\t\t\tx\n\t\t\n\t\t+\n\t\t\n\t\t\t7\n\t\t\ty\n\t\t\n\t\n\t=\n\t1\n\n

\n

\n\t\n\t\t\n\t\t\t2\n\t\t\ta\n\t\t\tx\n\t\t\n\t\t+\n\t\t\n\t\t\tb\n\t\t\ty\n\t\t\n\t\n\t=\n\t1\n\n

"}, {"id": "D", "text": "

\n\t\n\t\t\n\t\t\t5\n\t\t\tx\n\t\t\n\t\t-\n\t\t\n\t\t\t7\n\t\t\ty\n\t\t\n\t\n\t=\n\t1\n\n

\n

\n\t\n\t\t\n\t\t\ta\n\t\t\tx\n\t\t\n\t\t+\n\t\t\n\t\t\tb\n\t\t\ty\n\t\t\n\t\n\t=\n\t1\n\n

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. Two lines are perpendicular if their slopes are negative reciprocals, meaning that the slope of the first line is equal to -1\n divided by the slope of the second line. Each equation in the given pair of equations can be written in slope-intercept form, \n\ty\n\t=\n\t\n\t\t\n\t\t\tm\n\t\t\tx\n\t\t\n\t\t+\n\t\tb\n\t\n\n, where m\n is the slope of the graph of the equation in the xy-plane and 0,b is the y-intercept. For the first equation, \n\t\n\t\t\n\t\t\t5\n\t\t\tx\n\t\t\n\t\t+\n\t\t\n\t\t\t7\n\t\t\ty\n\t\t\n\t\n\t=\n\t1\n\n, subtracting \n\t5\n\tx\n\n from both sides gives 7y=-5x+1, and dividing both sides of this equation by 7\n gives y=-57x+17. Therefore, the slope of the graph of this equation is \n\t-\n\t\n\t\t5\n\t\t7\n\t\n\n. For the second equation, \n\t\n\t\t\n\t\t\ta\n\t\t\tx\n\t\t\n\t\t+\n\t\t\n\t\t\tb\n\t\t\ty\n\t\t\n\t\n\t=\n\t1\n\n, subtracting \n\ta\n\tx\n\n from both sides gives \n\t\n\t\tb\n\t\ty\n\t\n\t=\n\t\n\t\t\n\t\t\t-\n\t\t\ta\n\t\t\tx\n\t\t\n\t\t+\n\t\t1\n\t\n\n, and dividing both sides of this equation by b\n gives y=-abx+1b. Therefore, the slope of the graph of this equation is \n\t-\n\t\n\t\ta\n\t\tb\n\t\n\n. Since the graph of the given pair of equations is a pair of perpendicular lines, the slope of the graph of the second equation, \n\t-\n\t\n\t\ta\n\t\tb\n\t\n\n, must be the negative reciprocal of the slope of the graph of the first equation, \n\t-\n\t\n\t\t5\n\t\t7\n\t\n\n. The negative reciprocal of \n\t-\n\t\n\t\t5\n\t\t7\n\t\n\n is  -1-57, or \n\t7\n\t5\n\n. Therefore, \n\t\n\t\t-\n\t\t\n\t\t\ta\n\t\t\tb\n\t\t\n\t\n\t=\n\t\n\t\t7\n\t\t5\n\t\n\n, or \n\t\n\t\t\ta\n\t\t\tb\n\t\t\n\t=\n\t\n\t\t-\n\t\t\n\t\t\t7\n\t\t\t5\n\t\t\n\t\n\n. Similarly, rewriting the equations in choice B in slope-intercept form yields y=-107x+17 and y=-a2bx+12b. It follows that the slope of the graph of the first equation in choice B is \n\t-\n\t\n\t\t10\n\t\t7\n\t\n\n and the slope of the graph of the second equation in choice B is \n\t-\n\t\n\t\ta\n\t\t\n\t\t\t2\n\t\t\tb\n\t\t\n\t\n\n. Since \n\t\n\t\t\ta\n\t\t\tb\n\t\t\n\t=\n\t\n\t\t-\n\t\t\n\t\t\t7\n\t\t\t5\n\t\t\n\t\n\n, \n\t-\n\t\n\t\ta\n\t\t\n\t\t\t2\n\t\t\tb\n\t\t\n\t\n\n is equal to -12-75, or \n\t7\n\t10\n\n. Since \n\t7\n\t10\n\n is the negative reciprocal of \n\t-\n\t\n\t\t10\n\t\t7\n\t\n\n, the pair of equations in choice B represents a pair of perpendicular lines.

\n

Choice A is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

\n

Choice D is incorrect and may result from conceptual or calculation errors.

"}, {"id": "de6fe450", "domain": "Algebra", "skill": "Linear functions", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

On January 1, 2015, a city’s minimum hourly wage was $9.25. It will increase by $0.50 on the first day of the year for the next 5 years. Which of the following functions best models the minimum hourly wage, in dollars, x years after January 1, 2015, where x = the following five values: 1, 2, 3, 4, 5 ?

\n", "choices": [{"id": "A", "text": "

\n f(x) = 9 point 2 5, \u2212 0 point 5 0 x\n

\n"}, {"id": "B", "text": "

\n f(x) = 9 point 2 5 x, \u2212 0 point 5 0\n

\n"}, {"id": "C", "text": "

\n f(x) = 9 point 2 5, + 0 point 5 0 x\n

\n"}, {"id": "D", "text": "

\n f(x) = 9 point 2 5 x, + 0 point 5 0\n

\n"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. It’s given that the city’s minimum hourly wage will increase by $0.50 on the first day of the year for the 5 years after January 1, 2015. Therefore, the total increase, in dollars, in the minimum hourly wage x years after January 1, 2015, is represented by 0 point 5 0 x. Since the minimum hourly wage on January 1, 2015, was $9.25, it follows that the minimum hourly wage, in dollars, x years after January 1, 2015, is represented by 9 point 2 5, + 0 point 5 0 x. Therefore, the function f(x) = 9 point 2 5, + 0 point 5 0 x best models this situation.

Choices A, B, and D are incorrect. In choice A, the function models a situation where the minimum hourly wage is $9.25 on January 1, 2015, but decreases by $0.50 on the first day of the year for the next 5 years. The functions in choices B and D both model a situation where the minimum hourly wage is increasing by $9.25 on the first day of the year for the 5 years after January 1, 2015.

\n"}, {"id": "03503d49", "domain": "Algebra", "skill": "Linear inequalities in one or two variables", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

A business owner plans to purchase the same model of chair for each of the 81\n employees. The total budget to spend on these chairs is $14,000\n, which includes a 7\n% sales tax. Which of the following is closest to the maximum possible price per chair, before sales tax, the business owner could pay based on this budget?

", "choices": [{"id": "A", "text": "

$148.15

"}, {"id": "B", "text": "

$161.53

"}, {"id": "C", "text": "

$172.84

"}, {"id": "D", "text": "

$184.94

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. It’s given that a business owner plans to purchase 81\n chairs. If p\n is the price per chair, the total price of purchasing 81\n chairs is \n\t81\n\tp\n\n. It’s also given that 7% sales tax is included, which is equivalent to \n\t81\n\tp\n\n multiplied by 1.07\n, or 81(1.07)p. Since the total budget is $14,000, the inequality representing the situation is given by 81(1.07)p\u226414,000. Dividing both sides of this inequality by 81(1.07) and rounding the result to two decimal places gives  p\u2264161.53. To not exceed the budget, the maximum possible price per chair is $161.53.

\n

Choice A is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect. This is the maximum possible price per chair including sales tax, not the maximum possible price per chair before sales tax.

\n

Choice D is incorrect. This is the maximum possible price if the sales tax is added to the total budget, not the maximum possible price per chair before sales tax.

"}, {"id": "4ec95eab", "domain": "Algebra", "skill": "Systems of two linear equations in two variables", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

y=-3x

\n

4x+y=15

\n

The solution to the given system of equations is x,y. What is the value of x\n?

", "choices": [{"id": "A", "text": "

1\n

"}, {"id": "B", "text": "

5\n

"}, {"id": "C", "text": "

15\n

"}, {"id": "D", "text": "

45\n

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. The given system of linear equations can be solved by the substitution method. Substituting -3x for y\n from the first equation in the given system into the second equation yields 4x+-3x=15, or x=15.

\n

Choice A is incorrect and may result from conceptual or calculation errors.

\n

Choice B is incorrect and may result from conceptual or calculation errors.

\n

Choice D is incorrect. This is the absolute value of y\n, not the value of x\n.

"}, {"id": "2d54c272", "domain": "Algebra", "skill": "Linear equations in two variables", "difficulty": "H", "type": "spr", "stimulus": "", "stem": "

\n\t\n\t\t\n\t\t\t5\n\t\t\tG\n\t\t\n\t\t+\n\t\t\n\t\t\t45\n\t\t\tR\n\t\t\n\t\n\t=\n\t380\n\n

\n

At a school fair, students can win colored tokens that are worth a different number of points depending on the color. One student won G\n green tokens and R\n red tokens worth a total of 380\n points. The given equation represents this situation. How many more points is a red token worth than a green token?

", "choices": [], "answerId": "40", "acceptedAnswers": ["40"], "rationale": "

The correct answer is 40\n. It's given that 5G+45R=380, where G\n is the number of green tokens and R\n is the number of red tokens won by one student and these tokens are worth a total of 380\n points. Since the equation represents the situation where the student won points with green tokens and red tokens for a total of 380\n points, each term on the left-hand side of the equation represents the number of points won for one of the colors. Since the coefficient of G\n in the given equation is 5\n, a green token must be worth 5\n points. Similarly, since the coefficient of R\n in the given equation is 45\n, a red token must be worth 45\n points. Therefore, a red token is worth 45-5 points, or 40\n points, more than a green token.

"}, {"id": "cee5b352", "domain": "Algebra", "skill": "Linear functions", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

The length, y\n, of a white whale was 162 centimeters cm when it was born and increased an average of 4.8 cm per month for the first 12\n months after it was born. Which equation best represents this situation, where x\n is the number of months after the whale was born and y\n is the length, in cm, of the whale?

", "choices": [{"id": "A", "text": "

\n\ty\n\t=\n\t\n\t\t162\n\t\tx\n\t\n\n

"}, {"id": "B", "text": "

\n\ty\n\t=\n\t\n\t\t\n\t\t\t162\n\t\t\tx\n\t\t\n\t\t+\n\t\t162\n\t\n\n

"}, {"id": "C", "text": "

\n\ty\n\t=\n\t\n\t\t\n\t\t\t4.8\n\t\t\tx\n\t\t\n\t\t+\n\t\t4.8\n\t\n\n

"}, {"id": "D", "text": "

\n\ty\n\t=\n\t\n\t\t\n\t\t\t4.8\n\t\t\tx\n\t\t\n\t\t+\n\t\t162\n\t\n\n

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. It's given that the length of the whale was 162 cm when it was born and that its length increased an average of 4.8 cm per month for the first 12\n months after it was born. Since x\n represents the number of months after the whale was born, the total increase in the whale's length, in cm, is 4.8\n times x\n, or \n\t4.8\n\tx\n\n. The length of the whale y\n, in cm, can be found by adding the whale's length at birth, 162 cm, to the total increase in length, 4.8x cm. Therefore, the equation that best represents this situation is \n\ty\n\t=\n\t\n\t\t\n\t\t\t4.8\n\t\t\tx\n\t\t\n\t\t+\n\t\t162\n\t\n\n.

\n

Choice A is incorrect and may result from conceptual errors.

\n

Choice B is incorrect and may result from conceptual errors.

\n

Choice C is incorrect and may result from conceptual errors.

"}, {"id": "1e11190a", "domain": "Algebra", "skill": "Systems of two linear equations in two variables", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

Store A sells raspberries for $5.50\n per pint and blackberries for $3.00\n per pint. Store B sells raspberries for $6.50\n per pint and blackberries for $8.00\n per pint. A certain purchase of raspberries and blackberries would cost $37.00\n at Store A or $66.00\n at Store B. How many pints of blackberries are in this purchase?

", "choices": [{"id": "A", "text": "

4\n

"}, {"id": "B", "text": "

5\n

"}, {"id": "C", "text": "

8\n

"}, {"id": "D", "text": "

12\n

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice C is correct. It’s given that store A sells raspberries for $5.50 per pint and blackberries for $3.00 per pint, and a certain purchase of raspberries and blackberries at store A would cost $37.00. It’s also given that store B sells raspberries for $6.50 per pint and blackberries for $8.00 per pint, and this purchase of raspberries and blackberries at store B would cost $66.00. Let r\n represent the number of pints of raspberries and b\n represent the number of pints of blackberries in this purchase. The equation 5.50r+3.00b=37.00 represents this purchase of raspberries and blackberries from store A and the equation 6.50r+8.00b=66.00 represents this purchase of raspberries and blackberries from store B. Solving the system of equations by elimination gives the value of r\n and the value of b\n that make the system of equations true. Multiplying both sides of the equation for store A by 6.5\n yields 5.50r6.5+3.00b6.5=37.006.5, or 35.75r+19.5b=240.5. Multiplying both sides of the equation for store B by 5.5\n yields 6.50r5.5+8.00b5.5=66.005.5, or 35.75r+44b=363. Subtracting both sides of the equation for store A, 35.75r+19.5b=240.5, from the corresponding sides of the equation for store B, 35.75r+44b=363, yields 35.75r-35.75r+44b-19.5b=363-240.5, or 24.5b=122.5. Dividing both sides of this equationby 24.5\n yields b=5. Thus, 5\n pints of blackberries are in
this purchase.

\n


Choices A and B are incorrect and may result from conceptual or calculation errors. Choice D is incorrect. This is the number of pints of raspberries, not blackberries, in the purchase.

"}, {"id": "78391fcc", "domain": "Algebra", "skill": "Linear functions", "difficulty": "H", "type": "mc", "stimulus": "
\n\t\n\t\t\t\t\n\t\t\t\t\n\t\t\t\t\n\t\t\t\t\n\t\t\t\n\t\t\t\t\n\t\t\t\t\n\t\t\t\t\n\t\t\t\t\n\t\t\t
x\u221211\u221210\u22129\u22128
f(x)21181512

 

\n
\n", "stem": "

The table above shows some values of x and their corresponding values f(x) for the linear function f. What is the x-intercept of the graph of y = f(x) in the xy-plane?

\n", "choices": [{"id": "A", "text": "

the point \u22123, 0

\n"}, {"id": "B", "text": "

the point \u22124, 0

\n"}, {"id": "C", "text": "

the point \u22129, 0

\n"}, {"id": "D", "text": "

the point \u221212, 0

\n"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. The equation of a linear function can be written in the form y = m x + b, where y = f(x), m is the slope of the graph of y = f(x), and b is the y-coordinate of the y-intercept of the graph. The value of m can be found using the slope formula, m = (y sub 2 \u2212 y sub 1)/(x sub 2 \u2212 x sub 1, end fraction). According to the table, the points \u221211, 21 and \u221210, 18 lie on the graph of y = f(x). Using these two points in the slope formula yieldsm = (18 \u2212 21)/(\u221210 + 11, end fraction), or \u22123. Substituting \u22123 for m in the slope-intercept form of the equation yields y = \u22123 x + b. The value of b can be found by substituting values from the table and solving; for example, substituting the coordinates of the point \u221211, 21 into the equation y = \u22123 x + b gives 21 = \u22123 \u00d7 \u221211, + b, which yields b = \u221212. This means the function given by the table can be represented by the equation y = \u22123 x \u2212 12. The value of the x-intercept of the graph of y = f(x) can be determined by finding the value of x when y = 0. Substituting y = 0 into y = \u22123 x \u2212 12 yields 0 = \u22123 x \u2212 12, or x = \u22124. This corresponds to the point \u22124, 0.

Choice A is incorrect and may result from substituting the value of the slope for the x-coordinate of the x-intercept. Choice C is incorrect and may result from a calculation error. Choice D is incorrect and may result from substituting the y-coordinate of the y-intercept for the x-coordinate of the x-intercept.

 

\n"}, {"id": "9ff10b3b", "domain": "Algebra", "skill": "Linear equations in one variable", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

If one half x, \u2212 one sixth x = 1, what is the value of x ?

\n", "choices": [{"id": "A", "text": "

\n \u22124\n

\n"}, {"id": "B", "text": "

\n one third\n

\n"}, {"id": "C", "text": "

\n 3\n

\n"}, {"id": "D", "text": "

\n 6\n

\n"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. To make it easier to add like terms on the left-hand side of the given equation, both sides of the equation can be multiplied by 6, which is the lowest common denominator of one half and one sixth. This yields 3 x \u2212 x = 6, which can be rewritten as 2 x = 6. Dividing both sides of this equation by 2 yields x = 3.

Choice A is incorrect and may result from subtracting the denominators instead of numerators with common denominators to get \u2212one fourth x, rather than one third x, on the left-hand side of the equation. Choice B is incorrect and may result from rewriting the given equation as one half x = one sixth instead of 2 x = 6. Choice D is incorrect and may result from conceptual or computational errors.

\n"}, {"id": "e77a76ce", "domain": "Algebra", "skill": "Systems of two linear equations in two variables", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

Which of the following systems of linear equations has no solution?

", "choices": [{"id": "A", "text": "

\n\ty\n\t=\n\t\n\t\t\n\t\t\t6\n\t\t\tx\n\t\t\n\t\t+\n\t\t3\n\t\n\n

\n

\n\ty\n\t=\n\t\n\t\t\n\t\t\t6\n\t\t\tx\n\t\t\n\t\t+\n\t\t9\n\t\n\n

"}, {"id": "B", "text": "

\n\ty\n\t=\n\t10\n\n

\n

\n\ty\n\t=\n\t\n\t\t\n\t\t\t10\n\t\t\tx\n\t\t\n\t\t+\n\t\t10\n\t\n\n

"}, {"id": "C", "text": "

\n\ty\n\t=\n\t\n\t\t\n\t\t\t14\n\t\t\tx\n\t\t\n\t\t+\n\t\t14\n\t\n\n

\n

\n\ty\n\t=\n\t\n\t\t\n\t\t\t10\n\t\t\tx\n\t\t\n\t\t+\n\t\t14\n\t\n\n

"}, {"id": "D", "text": "

\n\tx\n\t=\n\t3\n\n

\n

\n\ty\n\t=\n\t10\n\n

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. A system of two linear equations in two variables, x\n and y\n, has no solution if the graphs of the lines represented by the equations in the xy-plane are distinct and parallel. The graphs of two lines in the xy-plane represented by equations in slope-intercept form, y=mx+b, where m\n and b\n are constants, are parallel if their slopes, m\n, are the same and are distinct if their y-coordinates of the y-intercepts, b\n, are different. In the equations y=6x+3 and y=6x+9, the values of m\n are each 6\n, and the values of b\n are 3\n and 9\n, respectively. Since the slopes of these lines are the same and the y-coordinates of the y-intercepts are different, it follows that the system of linear equations in choice A has no solution.

\n

Choice B is incorrect. The two lines represented by these equations are a horizontal line and a line with a slope of 10\n that have the same y-coordinate of the y-intercept. Therefore, this system has a solution, 0,10, rather than no solution.

\n

Choice C is incorrect. The two lines represented by these equations have different slopes and the same y-coordinate of the y-intercept. Therefore, this system has a solution, 0,14, rather than no solution.

\n

Choice D is incorrect. The two lines represented by these equations are a vertical line and a horizontal line. Therefore, this system has a solution, 3,10, rather than no solution.

"}, {"id": "aad7e1b9", "domain": "Algebra", "skill": "Linear functions", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

The function f\n is defined by fx=110x-2. What is the y-intercept of the graph of y=fx in the xy-plane?

", "choices": [{"id": "A", "text": "

-2,0

"}, {"id": "B", "text": "

0,-2

"}, {"id": "C", "text": "

0,110

"}, {"id": "D", "text": "

110,0

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. The y-intercept of the graph of a function in the xy-plane is the point on the graph where x=0. It′s given that fx=110x-2. Substituting 0\n for x\n in this equation yields f0=1100-2, or f0=-2. Since it′s given that y=fx, it follows that y=-2 when x=0. Therefore, the y-intercept of the graph of y=fx in the xy-plane is 0,-2.

\n

Choice A is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

\n

Choice D is incorrect and may result from conceptual or calculation errors.

"}, {"id": "1bc11c4e", "domain": "Algebra", "skill": "Linear functions", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

gm=-0.05m+12.1

\n

The given function g\n models the number of gallons of gasoline that remains from a full gas tank in a car after driving m\n miles. According to the model, about how many gallons of gasoline are used to drive each mile?

", "choices": [{"id": "A", "text": "

0.05\n

"}, {"id": "B", "text": "

12.1\n

"}, {"id": "C", "text": "

20\n

"}, {"id": "D", "text": "

242.0\n

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. It's given that the function g\n models the number of gallons that remain from a full gas tank in a car after driving m\n miles. In the given function gm=-0.05m+12.1, the coefficient of m\n is -0.05\n. This means that for every increase in the value of m\n by 1\n, the value of gm decreases by 0.05\n. It follows that for each mile driven, there is a decrease of 0.05\n gallons of gasoline. Therefore, 0.05\n gallons of gasoline are used to drive each mile.

\n

Choice B is incorrect and represents the number of gallons of gasoline in a full gas tank.

\n

Choice C is incorrect and may result from conceptual errors.

\n

Choice D is incorrect and may result from conceptual errors.

"}, {"id": "b3c7ca1d", "domain": "Algebra", "skill": "Systems of two linear equations in two variables", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

Which of the following systems of linear equations has no solution?

", "choices": [{"id": "A", "text": "

\n\tx\n\t=\n\t3\n\n

\n

\n\ty\n\t=\n\t5\n\n

"}, {"id": "B", "text": "

\n\ty\n\t=\n\t\n\t\t\n\t\t\t6\n\t\t\tx\n\t\t\n\t\t+\n\t\t6\n\t\n\n

\n

\n\ty\n\t=\n\t\n\t\t\n\t\t\t5\n\t\t\tx\n\t\t\n\t\t+\n\t\t6\n\t\n\n

"}, {"id": "C", "text": "

\n\ty\n\t=\n\t\n\t\t\n\t\t\t16\n\t\t\tx\n\t\t\n\t\t+\n\t\t3\n\t\n\n

\n

\n\ty\n\t=\n\t\n\t\t\n\t\t\t16\n\t\t\tx\n\t\t\n\t\t+\n\t\t19\n\t\n\n

"}, {"id": "D", "text": "

\n\ty\n\t=\n\t5\n\n

\n

\n\ty\n\t=\n\t\n\t\t\n\t\t\t5\n\t\t\tx\n\t\t\n\t\t+\n\t\t5\n\t\n\n

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. A system of two linear equations in two variables, x\n and y\n, has no solution if the graphs of the lines represented by the equations in the xy-plane are distinct and parallel. The graphs of two lines in the xy-plane represented by equations in slope-intercept form, y=mx+b, where m\n and b\n are constants, are parallel if their slopes, m\n, are the same and are distinct if their y-coordinates of the y-intercepts, b\n, are different. In the equations y=16x+3 and y=16x+19, the values of m\n are each 16\n, and the values of b\n are 3\n and 19\n, respectively. Since the slopes of these lines are the same, and the y-coordinates of the y-intercepts are different, it follows that the system of linear equations in choice C has no solution. 

\n

Choice A is incorrect. The lines represented by the equations in this system are a vertical line and a horizontal line. Therefore, this system has a solution, 3,5, rather than no solution.

\n

Choice B is incorrect. The two lines represented by these equations have different slopes and the same y-coordinate of the y-intercept. Therefore, this system has a solution, 0,6, rather than no solution.

\n

Choice D is incorrect. The two lines represented by these equations are a horizontal line and a line with a slope of 5\n that have the same y-coordinate of the y-intercept. Therefore, this system has a solution, 0,5, rather than no solution. 

"}, {"id": "2d0e13a6", "domain": "Algebra", "skill": "Linear equations in two variables", "difficulty": "E", "type": "spr", "stimulus": "", "stem": "

Line k\n is defined by y=14x+1. Line j\n is parallel to line k\n in the xy-plane. What is the slope of j\n?

", "choices": [], "answerId": ".25", "acceptedAnswers": [".25", "1/4"], "rationale": "

The correct answer is 14. It's given that line k\n is defined by y=14x+1. It's also given that line j\n is parallel to line k\n in the xy-plane. A line in the xy-plane represented by an equation in slope-intercept form y=mx+b has a slope of m\n and a y-intercept of 0,b. Therefore, the slope of line k\n is 14. Since parallel lines have equal slopes, the slope of line j\n is 14. Note that 1/4 and .25 are examples of ways to enter a correct answer.

"}, {"id": "b8e73b5b", "domain": "Algebra", "skill": "Linear inequalities in one or two variables", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

Ken is working this summer as part of a crew on a farm. He earned $8 per hour for the first 10 hours he worked this week. Because of his performance, his crew leader raised his salary to $10 per hour for the rest of the week. Ken saves 90% of his earnings from each week. What is the least number of hours he must work the rest of the week to save at least $270 for the week?

\n", "choices": [{"id": "A", "text": "

38

\n"}, {"id": "B", "text": "

33

\n"}, {"id": "C", "text": "

22

\n"}, {"id": "D", "text": "

16

\n"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. Ken earned $8 per hour for the first 10 hours he worked, so he earned a total of $80 for the first 10 hours he worked. For the rest of the week, Ken was paid at the rate of $10 per hour. Let x be the number of hours he will work for the rest of the week. The total of Ken’s earnings, in dollars, for the week will be 10 x + 80. He saves 90% of his earnings each week, so this week he will save 0 point 9 times, open parenthesis, 10 x + 80, close parenthesis dollars. The inequality 0 point 9 times, open parenthesis, 10 x + 80, close parenthesis, > or equal to 270 represents the condition that he will save at least $270 for the week. Factoring 10 out of the expression 10 x + 80 gives 10 times, open parenthesis, x + 8, close parenthesis. The product of 10 and 0.9 is 9, so the inequality can be rewritten as 9 times, open parenthesis, x + 8, close parenthesis, > or equal to 270. Dividing both sides of this inequality by 9 yields x + 8, > or equal to 30, so x > or equal to 22. Therefore, the least number of hours Ken must work the rest of the week to save at least $270 for the week is 22.

Choices A and B are incorrect because Ken can save $270 by working fewer hours than 38 or 33 for the rest of the week. Choice D is incorrect. If Ken worked 16 hours for the rest of the week, his total earnings for the week will be 80 dollars + 160 dollars = 240 dollars, which is less than $270. Since he saves only 90% of his earnings each week, he would save even less than $240 for the week.

\n"}, {"id": "830120b0", "domain": "Algebra", "skill": "Linear inequalities in one or two variables", "difficulty": "H", "type": "mc", "stimulus": "
 
 y > 2 x \u2212 1; 2 x > 5
 
\n", "stem": "

Which of the following consists of the y-coordinates of all the points that satisfy the system of inequalities above?

\n", "choices": [{"id": "A", "text": "

y > 6

\n"}, {"id": "B", "text": "

y > 4

\n"}, {"id": "C", "text": "

y > five-halves

\n"}, {"id": "D", "text": "

y > three-halves

\n"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. Subtracting the same number from each side of an inequality gives an equivalent inequality. Hence, subtracting 1 from each side of the inequality 2 x > 5 gives 2 x \u2212 1, > 4. So the given system of inequalities is equivalent to the system of inequalities y is greater than, 2 x \u2212 1 and 2 x \u2212 1, > 4, which can be rewritten as y is greater than, 2 x \u2212 1, which > 4. Using the transitive property of inequalities, it follows that y > 4.

Choice A is incorrect because there are points with a y-coordinate less than 6 that satisfy the given system of inequalities. For example, the point 3, 5 point 5 satisfies both inequalities. Choice C is incorrect. This may result from solving the inequality 2 x > 5 for x, then replacing x with y. Choice D is incorrect because this inequality allows y-values that are not the y-coordinate of any point that satisfies both inequalities. For example, y = 2 is contained in the set y > three halves; however, if 2 is substituted into the first inequality for y, the result is x < three halves. This cannot be true because the second inequality gives x > five halves.

 

\n"}, {"id": "c8e0f511", "domain": "Algebra", "skill": "Linear equations in two variables", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

For a camping trip a group bought x\n one-liter bottles of water and y\n three-liter bottles of water, for a total of 240\n liters of water. Which equation represents this situation?

", "choices": [{"id": "A", "text": "

x+3y=240

"}, {"id": "B", "text": "

x+y=240

"}, {"id": "C", "text": "

3x+3y=240

"}, {"id": "D", "text": "

3x+y=240

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. It's given that for a camping trip a group bought x\n one-liter bottles of water and y\n three-liter bottles of water. Since the group bought x\n one-liter bottles of water, the total number of liters bought from x\n one-liter bottles of water is represented as 1x, or x\n. Since the group bought y\n three-liter bottles of water, the total number of liters bought from y\n three-liter bottles of water is represented as \n\t3\n\ty\n\n. It's given that the group bought a total of 240\n liters; thus, the equation \n\t\n\t\tx\n\t\t+\n\t\t\n\t\t\t3\n\t\t\ty\n\t\t\n\t\n\t=\n\t240\n\n represents this situation.

\n

Choice B is incorrect and may result from conceptual errors.

\n

Choice C is incorrect and may result from conceptual errors.

\n

Choice D is incorrect. This equation represents a situation where the group bought x\n three-liter bottles of water and y\n one-liter bottles of water, for a total of 240\n liters of water.

"}, {"id": "c4ea43ef", "domain": "Algebra", "skill": "Linear equations in two variables", "difficulty": "H", "type": "mc", "stimulus": "
\n
\n \"The
\n
\n", "stem": "

To earn money for college, Avery works two part-time jobs: A and B. She earns $10 per hour working at job A and $20 per hour working at job B. In one week, Avery earned a total of s dollars for working at the two part-time jobs. The graph above represents all possible combinations of numbers of hours Avery could have worked at the two jobs to earn s dollars. What is the value of s ?

\n", "choices": [{"id": "A", "text": "

128

\n"}, {"id": "B", "text": "

160

\n"}, {"id": "C", "text": "

200

\n"}, {"id": "D", "text": "

320

\n"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. Avery earns $10 per hour working at job A. Therefore, if she works a hours at job A, she will earn 10 a dollars. Avery earns $20 per hour working at job B. Therefore, if she works b hours at job B, she will earn 20 b dollars. The graph shown represents all possible combinations of the number of hours Avery could have worked at the two jobs to earn s dollars. Therefore, if she worked a hours at job A, worked b hours at job B, and earned s dollars from both jobs, the following equation represents the graph: 10 a, + 20 b = s, where s is a constant. Identifying any point a,, b from the graph and substituting the values of the coordinates for a and b, respectively, in this equation yield the value of s. For example, the point 16, 0, where a = 16 and b = 0, lies on the graph. Substituting 16 for a and 0 for b in the equation 10 a, + 20 b = s yields 10 \u00d7 16, plus, 20 \u00d7 0 = s, or 160 = s. Similarly, the point 0, 8, where a = 0 and b = 8, lies on the graph. Substituting 0 for a and 8 for b in the equation 10 a, + 20 b = s yields 10 \u00d7 0, plus, 20 \u00d7 8 = s, or 160 = s.

Choices A, C, and D are incorrect. If the value of s is 128, 200, or 320, then no points a,, b on the graph will satisfy this equation. For example, if the value of s is 128 (choice A), then the equation 10 a, + 20 b = s becomes 10 a, + 20 b = 128. The point the point 16, 0, where a = 16 and b = 0, lies on the graph. However, substituting 16 for a and 0 for b in 10 a, + 20 b = s yields 10 \u00d7 16, plus, 20 \u00d7 0 = 128, or 160 = 128, which is false. Therefore, the point 16, 0 doesn’t satisfy the equation, and so the value of s can’t be 128. Similarly, if s = 200 (choice C) or s = 320 (choice D), then substituting 16 for a and 0 for b yields 160 = 200 and 160 = 320, respectively, which are both false.

\n"}, {"id": "4e77195b", "domain": "Algebra", "skill": "Linear equations in one variable", "difficulty": "E", "type": "spr", "stimulus": "", "stem": "

If 2+x=60, what is the value of 16+8x?

", "choices": [], "answerId": "480", "acceptedAnswers": ["480"], "rationale": "

The correct answer is 480\n. Multiplying both sides of the given equation by 8\n yields 82+x=860, or 16+8x=480. Therefore, if 2+x=60, the value of 16+8x is 480\n.

"}, {"id": "113b938e", "domain": "Algebra", "skill": "Linear functions", "difficulty": "M", "type": "mc", "stimulus": "
\n

\n y = 18, \u2212 5 x\n

\n
\n", "stem": "

The equation above represents the speed y, in feet per second, of Sheila’s bicycle x seconds after she applied the brakes at the end of a ride. If the equation is graphed in the xy-plane, which of the following is the best interpretation of the x-coordinate of the line’s x-intercept in the context of the problem?

\n", "choices": [{"id": "A", "text": "

The speed of Sheila’s bicycle, in feet per second, before Sheila applied the brakes

\n"}, {"id": "B", "text": "

The number of feet per second the speed of Sheila’s bicycle decreased each second after Sheila applied the brakes

\n"}, {"id": "C", "text": "

The number of seconds it took from the time Sheila began applying the brakes until the bicycle came to a complete stop

\n"}, {"id": "D", "text": "

The number of feet Sheila’s bicycle traveled from the time she began applying the brakes until the bicycle came to a complete stop

\n"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. It’s given that for each point x, y on the graph of the given equation, the x-coordinate represents the number of seconds after Sheila applied the brakes, and the y-coordinate represents the speed of Sheila’s bicycle at that moment in time. For the graph of the equation, the y-coordinate of the x-intercept is 0. Therefore, the x-coordinate of the x-intercept of the graph of the given equation represents the number of seconds it took from the time Sheila began applying the brakes until the bicycle came to a complete stop.

Choice A is incorrect. The speed of Sheila’s bicycle before she applied the brakes is represented by the y-coordinate of the y-intercept of the graph of the given equation, not the x-coordinate of the x-intercept. Choice B is incorrect. The number of feet per second the speed of Sheila’s bicycle decreased each second after Sheila applied the brakes is represented by the slope of the graph of the given equation, not the x-coordinate of the x-intercept. Choice D is incorrect and may result from misinterpreting x as the distance, in feet, traveled after applying the brakes, rather than the time, in seconds, after applying the brakes.

\n"}, {"id": "029c2dc2", "domain": "Algebra", "skill": "Linear equations in two variables", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

A teacher is creating an assignment worth 70\n points. The assignment will consist of questions worth 1\n point and questions worth 3\n points. Which equation represents this situation, where x\n represents the number of 1\n-point questions and y\n represents the number of 3\n-point questions?

", "choices": [{"id": "A", "text": "

\n\t\n\t\t4\n\t\tx\n\t\ty\n\t\n\t=\n\t70\n\n

"}, {"id": "B", "text": "

4x+y=70

"}, {"id": "C", "text": "

\n\t\n\t\t\n\t\t\t3\n\t\t\tx\n\t\t\n\t\t+\n\t\ty\n\t\n\t=\n\t70\n\n

"}, {"id": "D", "text": "

\n\t\n\t\tx\n\t\t+\n\t\t\n\t\t\t3\n\t\t\ty\n\t\t\n\t\n\t=\n\t70\n\n

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. Since x\n represents the number of 1\n-point questions and y\n represents the number of 3\n-point questions, the assignment is worth a total of 1·x+3·y, or x+3y, points. Since the assignment is worth 70\n points, the equation x+3y=70 represents this situation.

\n

Choice A is incorrect and may result from conceptual errors.

\n

Choice B is incorrect and may result from conceptual errors.

\n

Choice C is incorrect and may result from conceptual errors.

"}, {"id": "2e1a7f66", "domain": "Algebra", "skill": "Linear equations in two variables", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

Figure A and figure B are both regular polygons. The sum of the perimeter of figure A and the perimeter of figure B is 63\n inches. The equation \n\t\n\t\t\n\t\t\t3\n\t\t\tx\n\t\t\n\t\t+\n\t\t\n\t\t\t6\n\t\t\ty\n\t\t\n\t\n\t=\n\t63\n\n represents this situation, where x\n is the number of sides of figure A and y\n is the number of sides of figure B. Which statement is the best interpretation of 6\n in this context?

", "choices": [{"id": "A", "text": "

Each side of figure B has a length of 6\n inches.

"}, {"id": "B", "text": "

The number of sides of figure B is 6\n.

"}, {"id": "C", "text": "

Each side of figure A has a length of 6\n inches.

"}, {"id": "D", "text": "

The number of sides of figure A is 6\n.

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. It’s given that figure A and figure B (not shown) are both regular polygons and the sum of the perimeters of the two figures is 63 inches. It’s also given that x\n is the number of sides of figure A and y\n is the number of sides of figure B, and that the equation 3x+6y=63 represents this situation. Thus, 3x and 6y represent the perimeters, in inches, of figure A and figure B, respectively. Since 6y represents the perimeter, in inches, of figure B and y\n is the number of sides of figure B, it follows that each side of figure B has a length of 6 inches.

\n

Choice B is incorrect. The number of sides of figure B is y\n, not 6\n.

\n

Choice C is incorrect. Since the perimeter, in inches, of figure A is represented by 3x, each side of figure A has a length of 3 inches, not 6 inches.

\n

Choice D is incorrect. The number of sides of figure A is x\n, not 6\n.

"}, {"id": "5e422ff9", "domain": "Algebra", "skill": "Systems of two linear equations in two variables", "difficulty": "M", "type": "mc", "stimulus": "
\n

\n y = 2 x \u2212 3; 3 y = 5 x\n

\n
\n", "stem": "

In the solution to the system of equations above, what is the value of y ?

\n", "choices": [{"id": "A", "text": "\n \u221215\n \n"}, {"id": "B", "text": "\n \u22129\n \n"}, {"id": "C", "text": "\n 9\n \n"}, {"id": "D", "text": "\n 15\n \n"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. Multiplying both sides of y = 2 x \u2212 3 by 5 results in 5 y = 10 x \u2212 15. Multiplying both sides of 3 y = 5 x by 2 results in 6 y = 10 x. Subtracting the resulting equations yields 5 y \u2212 6 y = open parenthesis, 10 x \u2212 15, close parenthesis, minus, 10 x, which simplifies to \u2212y = \u221215. Dividing both sides of \u2212y = \u221215 by \u22121 results in y = 15.

Choices A and B are incorrect and may result from incorrectly subtracting the transformed equation. Choice C is incorrect and may result from finding the value of x instead of the value of y.

\n"}, {"id": "e744499e", "domain": "Algebra", "skill": "Linear inequalities in one or two variables", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

An elementary school teacher is ordering x workbooks and y sets of flash cards for a math class. The teacher must order at least 20 items, but the total cost of the order must not be over $80. If the workbooks cost $3 each and the flash cards cost $4 per set, which of the following systems of inequalities models this situation?

\n", "choices": [{"id": "A", "text": "

\n x + y, > or equal to 20; 3 x + 4 y, < or equal to 80\n

\n"}, {"id": "B", "text": "

\n x + y, > or equal to 20; 3 x + 4 y, > or equal to 80\n

\n"}, {"id": "C", "text": "

\n 3 x + 4 y, < or equal to 20; x + y, > or equal to 80\n

\n"}, {"id": "D", "text": "

\n x + y, < or equal to 20; 3 x + 4 y, > or equal to 80\n

\n"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. The total number of workbooks and sets of flash cards ordered is represented by x + y. Since the teacher must order at least 20 items, it must be true that x + y ≥ 20. Each workbook costs $3; therefore, 3x represents the cost, in dollars, of x workbooks. Each set of flashcards costs $4; therefore, 4y represents the cost, in dollars, of y sets of flashcards. It follows that the total cost for x workbooks and y sets of flashcards is 3x + 4y. Since the total cost of the order must not be over $80, it must also be true that 3x + 4y ≤ 80. Of the choices given, these inequalities are shown only in choice A.

\n
\nChoice B is incorrect. The second inequality says that the total cost must be greater, not less than or equal to $80. Choice C incorrectly limits the cost by the minimum number of items and the number of items with the maximum cost. Choice D is incorrect. The first inequality incorrectly says that at most 20 items must be ordered, and the second inequality says that the total cost of the order must be at least, not at most, $80.

\n"}, {"id": "c5479c1a", "domain": "Algebra", "skill": "Linear equations in two variables", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

A shipment consists of 5\n-pound boxes and 10\n-pound boxes with a total weight of 220\n pounds. There are 13\n 10\n-pound boxes in the shipment. How many 5\n-pound boxes are in the shipment?

", "choices": [{"id": "A", "text": "

5\n

"}, {"id": "B", "text": "

10\n

"}, {"id": "C", "text": "

13\n

"}, {"id": "D", "text": "

18\n

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. It's given that the shipment consists of 5\n-pound boxes and 10\n-pound boxes with a total weight of 220\n pounds. Let x\n represent the number of 5\n-pound boxes and y\n represent the number of 10\n-pound boxes in the shipment. Therefore, the equation \n\t\n\t\t\n\t\t\t5\n\t\t\tx\n\t\t\n\t\t+\n\t\t\n\t\t\t10\n\t\t\ty\n\t\t\n\t\n\t=\n\t220\n\n represents this situation. It's given that there are 13\n 10\n-pound boxes in the shipment. Substituting 13\n for y\n in the equation \n\t\n\t\t\n\t\t\t5\n\t\t\tx\n\t\t\n\t\t+\n\t\t\n\t\t\t10\n\t\t\ty\n\t\t\n\t\n\t=\n\t220\n\n yields 5x+1013=220, or \n\t\n\t\t\n\t\t\t5\n\t\t\tx\n\t\t\n\t\t+\n\t\t130\n\t\n\t=\n\t220\n\n. Subtracting 130\n from both sides of this equation yields \n\t\n\t\t5\n\t\tx\n\t\n\t=\n\t90\n\n. Dividing both sides of this equation by 5\n yields 18\n. Thus, there are 18\n 5\n-pound boxes in the shipment.

\n

Choice A is incorrect and may result from conceptual or calculation errors.

\n

Choice B is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect. This is the number of 10\n-pound boxes in the shipment.

"}, {"id": "14360f84", "domain": "Algebra", "skill": "Systems of two linear equations in two variables", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

\n\t\n\t\t\n\t\t\t4\n\t\t\tx\n\t\t\n\t\t-\n\t\t\n\t\t\t9\n\t\t\ty\n\t\t\n\t\n\t=\n\t\n\t\t\n\t\t\t9\n\t\t\ty\n\t\t\n\t\t+\n\t\t5\n\t\n\n

\n

hy=2+4x

\n

In the given system of equations, h\n is a constant. If the system has no solution, what is the value of h\n?

", "choices": [{"id": "A", "text": "

-9\n

"}, {"id": "B", "text": "

0\n

"}, {"id": "C", "text": "

9\n

"}, {"id": "D", "text": "

18\n

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. A system of two linear equations in two variables, x\n and y\n, has no solution if the lines represented by the equations in the xy-plane are distinct and parallel. The graphs of two lines in the xy-plane represented by equations in the form Ax+By=C, where A\n, B\n, and C\n are constants, are parallel if the coefficients for x\n and y\n in one equation are proportional to the corresponding coefficients in the other equation. The first equation in the given system can be written in the form Ax+By=C by subtracting \n\t9\n\ty\n\n from both sides of the equation to yield 4x-18y=5. The second equation in the given system can be written in the form Ax+By=C by subtracting \n\t4\n\tx\n\n from both sides of the equation to yield -4x+hy=2. The coefficient of x\n in this second equation, -4, is -1 times the coefficient of x\n in the first equation, 4\n. For the lines to be parallel, the coefficient of y\n in the second equation, h\n, must also be -1 times the coefficient of y\n in the first equation, -18. Thus, h=-1(-18), or h=18. Therefore, if the given system has no solution, the value of h\n is 18\n.

\n

Choice A is incorrect. If the value of h\n is -9\n, then the given system would have one solution, rather than no solution.

\n

Choice B is incorrect. If the value of h\n is 0\n, then the given system would have one solution, rather than no solution.

\n

Choice C is incorrect. If the value of h\n is 9\n, then the given system would have one solution, rather than no solution.

"}, {"id": "6efcc0a3", "domain": "Algebra", "skill": "Linear functions", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

In the linear function h\n, h(0)=41 and h(1)=40. Which equation defines h\n?

", "choices": [{"id": "A", "text": "

h(x)=-x+41

"}, {"id": "B", "text": "

h(x)=-x

"}, {"id": "C", "text": "

h(x)=-41x

"}, {"id": "D", "text": "

h(x)=-41

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. An equation defining a linear function can be written in the form hx=ax+b, where a\n and b\n are constants. It’s given that h0=41. Substituting 0\n for x\n and 41\n for hx in the equation hx=ax+b yields 41=a0+b, or b=41. Substituting 41\n for b\n in the equation hx=ax+b yields hx=ax+41. It’s also given that h1=40. Substituting 1\n for x\n and 40\n for hx in the equation hx=ax+41 yields 40=a1+41, or 40=a+41. Subtracting 41\n from the left- and right-hand sides of this equation yields -1=a. Substituting -1\n for a\n in the equation hx=ax+41 yields hx=-1x+41, or hx=-x+41.

\n

Choice B is incorrect. Substituting 0\n for x\n and 41\n for hx in this equation yields 41=-0, which isn't a true statement.

\n

Choice C is incorrect. Substituting 0\n for x\n and 41\n for hx in this equation yields 41=-410, or 41=0, which isn't a true statement.

\n

Choice D is incorrect. Substituting 41\n for hx in this equation yields 41=-41, which isn't a true statement.

"}, {"id": "637022d2", "domain": "Algebra", "skill": "Linear equations in two variables", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

2.5b+5r=80

\n

The given equation describes the relationship between the number of birds, b\n, and the number of reptiles, r\n, that can be cared for at a pet care business on a given day. If the business cares for 16\n reptiles on a given day, how many birds can it care for on this day?

", "choices": [{"id": "A", "text": "

0\n

"}, {"id": "B", "text": "

5\n

"}, {"id": "C", "text": "

40\n

"}, {"id": "D", "text": "

80\n

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. The number of birds can be found by calculating the value of b\n when \n\tr\n\t=\n\t16\n\n in the given equation. Substituting 16\n for r\n in the given equation yields 2.5b+516=80, or \n\t\n\t\t\n\t\t\t2.5\n\t\t\tb\n\t\t\n\t\t+\n\t\t80\n\t\n\t=\n\t80\n\n. Subtracting 80\n from both sides of this equation yields \n\t\n\t\t2.5\n\t\tb\n\t\n\t=\n\t0\n\n. Dividing both sides of this equation by 2.5\n yields \n\tb\n\t=\n\t0\n\n. Therefore, if the business cares for 16\n reptiles on a given day, it can care for 0\n birds on this day.

\n

Choice B is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

\n

Choice D is incorrect and may result from conceptual or calculation errors.

"}, {"id": "776cfa7c", "domain": "Algebra", "skill": "Linear functions", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

Hana deposited a fixed amount into her bank account each month. The function ft=100+25t gives the amount, in dollars, in Hana's bank account after t\n monthly deposits. What is the best interpretation of 25\n in this context?

", "choices": [{"id": "A", "text": "

With each monthly deposit, the amount in Hana's bank account increased by $25.

"}, {"id": "B", "text": "

Before Hana made any monthly deposits, the amount in her bank account was $25.

"}, {"id": "C", "text": "

After 1\n monthly deposit, the amount in Hana's bank account was $25.

"}, {"id": "D", "text": "

Hana made a total of 25\n monthly deposits.

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. It's given that t\n represents the number of monthly deposits. In the given function ft=100+25t, the coefficient of t\n is 25\n. This means that for every increase in the value of t\n by 1\n, the value of ft increases by 25\n. It follows that with each monthly deposit, the amount in Hana's bank account increased by $25.

\n

Choice B is incorrect. Before Hana made any monthly deposits, the amount in her bank account was $100. 

\n

Choice C is incorrect. After 1\n monthly deposit, the amount in Hana's bank account was $125. 

\n

Choice D is incorrect and may result from conceptual errors.

"}, {"id": "74c98c82", "domain": "Algebra", "skill": "Linear inequalities in one or two variables", "difficulty": "M", "type": "spr", "stimulus": "", "stem": "

An event planner is planning a party. It costs the event planner a onetime fee of $35\n to rent the venue and $10.25\n per attendee. The event planner has a budget of $200\n. What is the greatest number of attendees possible without exceeding the budget?

", "choices": [], "answerId": "16", "acceptedAnswers": ["16"], "rationale": "

The correct answer is 16\n. The total cost of the party is found by adding the onetime fee of the venue to the cost per attendee times the number of attendees. Let x\n be the number of attendees. The expression 35+10.25x thus represents the total cost of the party. It's given that the budget is $200, so this situation can be represented by the inequality 35+10.25x\u2264200. The greatest number of attendees can be found by solving this inequality for x\n. Subtracting 35\n from both sides of this inequality gives 10.25x\u2264165. Dividing both sides of this inequality by 10.25\n results in approximately x\u226416.098. Since the question is stated in terms of attendees, rounding x\n down to the nearest whole number, 16\n, gives the greatest number of attendees possible.

"}, {"id": "1efd8202", "domain": "Algebra", "skill": "Linear equations in two variables", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

\n\ty\n\t=\n\t\n\t\t\n\t\t\t70\n\t\t\tx\n\t\t\n\t\t+\n\t\t8\n\t\n\n

\n

Which table gives three values of x\n and their corresponding values of y\n for the given equation?

", "choices": [{"id": "A", "text": "
\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
x\ny\n
0\n8\n
2\n148\n
4\n288\n
"}, {"id": "B", "text": "
\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
x\ny\n
0\n70\n
2\n78\n
4\n86\n
"}, {"id": "C", "text": "
\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
x\ny\n
0\n70\n
2\n140\n
4\n280\n
"}, {"id": "D", "text": "
\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
x\ny\n
0\n8\n
2\n132\n
4\n272\n
"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. Each of the given choices gives three values of x\n: 0\n, 2\n, and 4\n. Substituting 0\n for x\n in the given equation yields y=700+8, or \n\ty\n\t=\n\t8\n\n. Therefore, when \n\tx\n\t=\n\t0\n\n, the corresponding value of y\n for the given equation is 8\n. Substituting 2\n for x\n in the given equation yields y=702+8, or \n\ty\n\t=\n\t148\n\n. Therefore, when \n\tx\n\t=\n\t2\n\n, the corresponding value of y\n for the given equation is 148\n. Substituting 4\n for x\n in the given equation yields y=704+8, or \n\ty\n\t=\n\t288\n\n. Therefore, when \n\tx\n\t=\n\t4\n\n, the corresponding value of y\n for the given equation is 288\n. Thus, if the three values of x\n are 0\n, 2\n, and 4\n, then their corresponding values of y\n are 8\n, 148\n, and 288\n, respectively, for the given equation.

\n

Choice B is incorrect. This table gives three values of x\n and their corresponding values of y\n for the equation \n\ty\n\t=\n\t\n\t\t\n\t\t\t4\n\t\t\tx\n\t\t\n\t\t+\n\t\t70\n\t\n\n.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

\n

Choice D is incorrect and may result from conceptual or calculation errors.

"}, {"id": "73b5f330", "domain": "Algebra", "skill": "Linear functions", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

The function f\n is defined by fx=5x+8. For what value of x\n does fx=58?

", "choices": [{"id": "A", "text": "

10\n

"}, {"id": "B", "text": "

13\n

"}, {"id": "C", "text": "

50\n

"}, {"id": "D", "text": "

298\n

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. It's given that the function f\n is defined by fx=5x+8. Substituting 58\n for fx in this equation yields 58=5x+8. Subtracting 8\n from both sides of this equation yields \n\t50\n\t=\n\t\n\t\t5\n\t\tx\n\t\n\n. Dividing both sides of this equation by 5\n yields \n\t10\n\t=\n\tx\n\n. Therefore, the value of x\n when fx=58 is 10\n.

\n

Choice B is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

\n

Choice D is incorrect. This is the value of f58, not the value of x\n when fx=58.

"}, {"id": "e9ef0e6b", "domain": "Algebra", "skill": "Linear inequalities in one or two variables", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

A model estimates that whales from the genus Eschrichtius travel 72\n to 77\n miles in the ocean each day during their migration. Based on this model, which inequality represents the estimated total number of miles, x\n, a whale from the genus Eschrichtius could travel in 16\n days of its migration?

", "choices": [{"id": "A", "text": "

72+16≤x≤77+16

"}, {"id": "B", "text": "

7216≤x≤7716

"}, {"id": "C", "text": "

72≤16+x≤77

"}, {"id": "D", "text": "

72≤16x≤77

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. It's given that the model estimates that whales from the genus Eschrichtius travel 72\n to 77\n miles in the ocean each day during their migration. If one of these whales travels 72\n miles each day for 16\n days, then the whale travels 7216 miles total. If one of these whales travels 77\n miles each day for 16\n days, then the whale travels 7716 miles total. Therefore, the model estimates that in 16\n days of its migration, a whale from the genus Eschrichtius could travel at least 7216 and at most 7716 miles total. Thus, the inequality 7216≤x≤7716 represents the estimated total number of miles, x\n, a whale from the genus Eschrichtius could travel in 16\n days of its migration.

\n

Choice A is incorrect and may result from conceptual errors.

\n

Choice C is incorrect and may result from conceptual errors.

\n

Choice D is incorrect and may result from conceptual errors.

"}, {"id": "c841e8e8", "domain": "Algebra", "skill": "Linear equations in one variable", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

\n\t\n\t\tk\n\t\t+\n\t\t12\n\t\n\t=\n\t336\n\n

\n

What is the solution to the given equation?

", "choices": [{"id": "A", "text": "

28\n

"}, {"id": "B", "text": "

324\n

"}, {"id": "C", "text": "

348\n

"}, {"id": "D", "text": "

4,032\n

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. Subtracting 12\n from both sides of the given equation yields k=324. Therefore, the solution to the given equation is 324\n.

\n

Choice A is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

\n

Choice D is incorrect and may result from conceptual or calculation errors.

"}, {"id": "81390d6c", "domain": "Algebra", "skill": "Linear functions", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

The function h\n is defined by hx=x+200. What is the value of h50?

", "choices": [{"id": "A", "text": "

200\n

"}, {"id": "B", "text": "

250\n

"}, {"id": "C", "text": "

10,000\n

"}, {"id": "D", "text": "

50,200\n

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. Substituting 50\n for x\n in the given function yields h50=50+200, or h50=250. Therefore, the value of h50 is 250\n.

\n

Choice A is incorrect. This is the value of h0.

\n

Choice C is incorrect. This is the value of h9,800.

\n

Choice D is incorrect. This is the value of h50,000.

"}, {"id": "567ac7ab", "domain": "Algebra", "skill": "Systems of two linear equations in two variables", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

One of the two equations in a linear system is 2 x + 6 y = 10. The system has no solution. Which of the following could be the other equation in the system?

\n", "choices": [{"id": "A", "text": "

\n x + 3 y = 5\n

\n"}, {"id": "B", "text": "

\n x + 3 y = \u221220\n

\n"}, {"id": "C", "text": "

\n 6 x \u2212 2 y = 0\n

\n"}, {"id": "D", "text": "

\n 6 x + 2 y = 10\n

\n"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. A system of two linear equations written in standard form has no solution when the equations are distinct and the ratio of the x-coefficient to the y-coefficient for one equation is equivalent to the ratio of the x-coefficient to the y-coefficient for the other equation. This ratio for the given equation is 2 to 6, or 1 to 3. Only choice B is an equation that isn’t equivalent to the given equation and whose ratio of the x-coefficient to the y-coefficient is 1 to 3.

Choice A is incorrect. Multiplying each of the terms in this equation by 2 yields an equation that is equivalent to the given equation. This system would have infinitely many solutions. Choices C and D are incorrect. The ratio of the x-coefficient to the y-coefficient in 6 x \u2212 2 y = 0 (choice C) is \u22126 to 2, or \u22123 to 1. This ratio in 6 x + 2 y = 10 (choice D) is 6 to 2, or 3 to 1. Since neither of these ratios is equivalent to that for the given equation, these systems would have exactly one solution.

\n"}, {"id": "9d0396d4", "domain": "Algebra", "skill": "Linear equations in two variables", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n\n

\n

The point with coordinates (d\n, 4\n) lies on the line shown. What is the value of d\n?

", "choices": [{"id": "A", "text": "

\n\t7\n\t2\n\n

"}, {"id": "B", "text": "

\n\t26\n\t7\n\n

"}, {"id": "C", "text": "

\n\t24\n\t7\n\n

"}, {"id": "D", "text": "

\n\t27\n\t8\n\n

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. It's given from the graph that the points 0,7 and 8,0 lie on the line. For two points on a line, x1,y1 and x2,y2, the slope of the line can be calculated using the slope formula m=y2-y1x2-x1. Substituting 0,7 for x1,y1 and 8,0 for x2,y2 in this formula, the slope of the line can be calculated as m=0-78-0, or m=-78. It's also given that the point d,4 lies on the line. Substituting d,4 for x1,y1, 8,0 for x2,y2, and -78 for m\n in the slope formula yields -78=0-48-d, or -78=-48-d. Multiplying both sides of this equation by 8-d yields -788-d=-4. Expanding the left-hand side of this equation yields -7+78d=-4. Adding 7\n to both sides of this equation yields 78d=3. Multiplying both sides of this equation by 87 yields d=247. Thus, the value of d\n is 247.

\n

Choice A is incorrect. This is the value of y\n when x=4.

\n

Choice B is incorrect and may result from conceptual or calculation errors.

\n

Choice D is incorrect and may result from conceptual or calculation errors.

"}, {"id": "5a7ab8e8", "domain": "Algebra", "skill": "Linear equations in one variable", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

66x=66x

\n

How many solutions does the given equation have?

", "choices": [{"id": "A", "text": "

Exactly one

"}, {"id": "B", "text": "

Exactly two

"}, {"id": "C", "text": "

Infinitely many

"}, {"id": "D", "text": "

Zero

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. If the two sides of a linear equation are equivalent, then the equation is true for any value. If an equation is true for any value, it has infinitely many solutions. Since the two sides of the given linear equation 66x=66x are equivalent, the given equation has infinitely many solutions.

\n

Choice A is incorrect and may result from conceptual or calculation errors.

\n

Choice B is incorrect and may result from conceptual or calculation errors.

\n

Choice D is incorrect and may result from conceptual or calculation errors.

"}, {"id": "a04050d8", "domain": "Algebra", "skill": "Linear functions", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

\"The

The table above gives the typical amounts of energy per gram, expressed in both food calories and kilojoules, of the three macronutrients in food. If the 180 food calories in a granola bar come entirely from p grams of protein, f grams of fat, and c grams of carbohydrate, which of the following expresses f in terms of p and c ?

\n", "choices": [{"id": "A", "text": "

\n f = 20 + (4)/(9, end fraction, times, open parenthesis, p + c, close parenthesis)\n

\n"}, {"id": "B", "text": "

\n f = 20 \u2212 (4)/(9, end fraction, times, open parenthesis, p + c, close parenthesis)\n

\n"}, {"id": "C", "text": "

\n f = 20 \u2212 (4)/(9, end fraction, times, open parenthesis, p \u2212 c, close parenthesis)\n

\n"}, {"id": "D", "text": "

\n f = 20 + (9)/(4, end fraction, times, open parenthesis, p + c, close parenthesis)\n

\n"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. It is given that there are 4.0 food calories per gram of protein, 9.0 food calories per gram of fat, and 4.0 food calories per gram of carbohydrate. If 180 food calories in a granola bar came from p grams of protein, f grams of fat, and c grams of carbohydrate, then the situation can be represented by the equation 180 = 4 p + 9 f, + 4 c. The equation can then be rewritten in terms of f by subtracting 4p and 4c from both sides of the equation and then dividing both sides of the equation by 9. The result is the equation f = 20 minus, four ninths times, open parenthesis, p + c, close parenthesis.

Choices A, C, and D are incorrect and may be the result of not representing the situation with the correct equation or incorrectly rewriting the equation in terms of f.

\n"}, {"id": "2704399f", "domain": "Algebra", "skill": "Systems of two linear equations in two variables", "difficulty": "M", "type": "mc", "stimulus": "
\n
\n
\n
\n \"The
\n
\n
\n
\n", "stem": "

Which of the following systems of equations has the same solution as the system of equations graphed above?

\n", "choices": [{"id": "A", "text": "

\n Equation 1: y = 0. Equation 2: x = three halves

\n"}, {"id": "B", "text": "

\n Equation 1: y = three halves. Equation 2: x = 0

\n"}, {"id": "C", "text": "

\n Equation 1: y = 0. Equation 2: x = 1

\n"}, {"id": "D", "text": "

\n Equation 1: y = 1. Equation 2: x = 0

\n"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. The solution to a system of equations is the coordinates of the intersection point of the graphs of the equations in the xy-plane. Based on the graph, the solution to the given system of equations is best approximated as the point three halves, 0. In the xy-plane, the graph of y = 0 is a horizontal line on which every y-coordinate is 0, and the graph of x = three halves is a vertical line on which every x-coordinate is three halves. These graphs intersect at the point three halves, 0. Therefore, the system of equations in choice A has the same solution as the given system.

Choices B, C, and D are incorrect. If graphed in the xy-plane, these choices would intersect at the points 0, three halves, 1, 0, and 0, 1, respectively, not the point three halves, 0.

\n"}, {"id": "f02b4509", "domain": "Algebra", "skill": "Linear inequalities in one or two variables", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

A moving truck can tow a trailer if the combined weight of the trailer and the boxes it contains is no more than 4,600\n pounds. What is the maximum number of boxes this truck can tow in a trailer with a weight of 500\n pounds if each box weighs 120\n pounds?

", "choices": [{"id": "A", "text": "

34\n

"}, {"id": "B", "text": "

35\n

"}, {"id": "C", "text": "

38\n

"}, {"id": "D", "text": "

39\n

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. It’s given that the truck can tow a trailer if the combined weight of the trailer and the boxes it contains is no more than 4,600\n pounds. If the trailer has a weight of 500\n pounds and each box weighs 120\n pounds, the expression 500+120b, where b\n is the number of boxes, gives the combined weight of the trailer and the boxes. Since the combined weight must be no more than 4,600\n pounds, the possible numbers of boxes the truck can tow are given by the inequality 500+120b\u22644,600. Subtracting 500\n from both sides of this inequality yields 120b\u22644,100. Dividing both sides of this inequality by 120\n yields b\u22642056, or b\n is less than or equal to approximately 34.17\n. Since the number of boxes, b\n, must be a whole number, the maximum number of boxes the truck can tow is the greatest whole number less than 34.17\n, which is 34\n.

\n

Choice B is incorrect. Towing the trailer and 35\n boxes would yield a combined weight of 4,700\n pounds, which is greater than 4,600\n pounds.

\n

Choice C is incorrect. Towing the trailer and 38\n boxes would yield a combined weight of 5,060\n pounds, which is greater than 4,600\n pounds.

\n

Choice D is incorrect. Towing the trailer and 39\n boxes would yield a combined weight of 5,180\n pounds, which is greater than 4,600\n pounds.

"}, {"id": "daad7c32", "domain": "Algebra", "skill": "Linear functions", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

An object hangs from a spring. The formula l = 30 + 2 w relates the length l, in centimeters, of the spring to the weight w, in newtons, of the object. Which of the following describes the meaning of the 2 in this context?

\n", "choices": [{"id": "A", "text": "

The length, in centimeters, of the spring with no weight attached

\n"}, {"id": "B", "text": "

The weight, in newtons, of an object that will stretch the spring 30 centimeters

\n"}, {"id": "C", "text": "

The increase in the weight, in newtons, of the object for each one-centimeter increase in the length of the spring

\n"}, {"id": "D", "text": "

The increase in the length, in centimeters, of the spring for each one-newton increase in the weight of the object

\n"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. The value 2 is multiplied by w, the weight of the object. When the weight is 0, the length is 30 + 2(0) = 30 centimeters. If the weight increases by w newtons, the length increases by 2w centimeters, or 2 centimeters for each one-newton increase in weight.

\n
\nChoice A is incorrect because this describes the value 30. Choice B is incorrect because 30 represents the length of the spring before it has been stretched. Choice C is incorrect because this describes the value w.

\n"}, {"id": "3f8a701b", "domain": "Algebra", "skill": "Linear equations in one variable", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

The equation 9 x + 5 = a, times, open parenthesis, x + b, close parenthesis, where a and b are constants, has no solutions. Which of the following must be true?

\n I. a = 9\n

\n II. b = 5\n

\n III. b is not equal to five ninths\n

\n", "choices": [{"id": "A", "text": "

None

\n"}, {"id": "B", "text": "

I only

\n"}, {"id": "C", "text": "

I and II only

\n"}, {"id": "D", "text": "

I and III only

\n"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. For a linear equation in a form a, x + b = c x + d to have no solutions, the x-terms must have equal coefficients and the remaining terms must not be equal. Expanding the right-hand side of the given equation yields 9 x + 5 = a, x + a, b. Inspecting the x-terms, 9 must equal a, so statement I must be true. Inspecting the remaining terms, 5 can’t equal 9 b. Dividing both of these quantities by 9 yields that b can’t equal five ninths. Therefore, statement III must be true. Since b can have any value other than five ninths, statement II may or may not be true.

Choice A is incorrect. For the given equation to have no solution, both a = 9 and b is not equal to five ninths must be true. Choice B is incorrect because it must also be true that b is not equal to five ninths. Choice C is incorrect because when a = 9, there are many values of b that lead to an equation having no solution. That is, b might be 5, but b isn’t required to be 5.

\n"}, {"id": "b9839f9e", "domain": "Algebra", "skill": "Linear equations in two variables", "difficulty": "E", "type": "mc", "stimulus": "
\n

\n F = 2 point 5 0 x, + 7 point 0 0 y\n

\n
\n", "stem": "

In the equation above, F represents the total amount of money, in dollars, a food truck charges for x drinks and y salads. The price, in dollars, of each drink is the same, and the price, in dollars, of each salad is the same. Which of the following is the best interpretation for the number 7.00 in this context?

\n", "choices": [{"id": "A", "text": "

The price, in dollars, of one drink

\n"}, {"id": "B", "text": "

The price, in dollars, of one salad

\n"}, {"id": "C", "text": "

The number of drinks bought during the day

\n"}, {"id": "D", "text": "

The number of salads bought during the day

\n"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. It’s given that 2 point 5 0 x, + 7 point 0 0 y is equal to the total amount of money, in dollars, a food truck charges for x drinks and y salads. Since each salad has the same price, it follows that the total charge for y salads is 7 point 0 0 y dollars. When y = 1, the value of the expression 7 point 0 0 y is 7 point 0 0 \u00d7 1, or 7.00. Therefore, the price for one salad is 7.00 dollars.

Choice A is incorrect. Since each drink has the same price, it follows that the total charge for x drinks is 2 point 5 0 x dollars. Therefore, the price, in dollars, for one drink is 2.50, not 7.00. Choices C and D are incorrect. In the given equation, F represents the total charge, in dollars, when x drinks and y salads are bought at the food truck. No information is provided about the number of drinks or the number of salads that are bought during the day. Therefore, 7.00 doesn’t represent either of these quantities.

\n"}, {"id": "023c0a8d", "domain": "Algebra", "skill": "Linear functions", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

For the function f, if f(o)pen parenthesis, 3 x, close parenthesis = x \u2212 6 for all values of x, what is the value of f(6) ?

\n", "choices": [{"id": "A", "text": "

\n \u22126\n

\n"}, {"id": "B", "text": "

\n \u22124\n

\n"}, {"id": "C", "text": "

\n 0\n

\n"}, {"id": "D", "text": "

\n 2\n

\n"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. It’s given that f(3) x = x \u2212 6 for all values of x. If 3 x = 6, then f(3) x will equal f(6). Dividing both sides of 3 x = 6 by 3 gives x = 2. Therefore, substituting 2 for x in the given equation yields f of, open parenthesis, 3 \u00d7 2, close parenthesis = 2 \u2212 6, which can be rewritten as f(6) = \u22124.

Choice A is incorrect. This is the value of the constant in the given equation for f. Choice C is incorrect and may result from substituting x = 6, rather than x = 2, into the given equation. Choice D is incorrect. This is the value of x that yields f(6) for the left-hand side of the given equation; it’s not the value of f(6).

\n"}, {"id": "686b7cad", "domain": "Algebra", "skill": "Systems of two linear equations in two variables", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

A proposal for a new library was included on an election ballot. A radio show stated that 3\n times as many people voted in favor of the proposal as people who voted against it. A social media post reported that 15,000\n more people voted in favor of the proposal than voted against it. Based on these data, how many people voted against the proposal?

", "choices": [{"id": "A", "text": "

7,500\n

"}, {"id": "B", "text": "

15,000\n

"}, {"id": "C", "text": "

22,500\n

"}, {"id": "D", "text": "

45,000\n

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. It's given that a radio show stated that 3\n times as many people voted in favor of the proposal as people who voted against it. Let x\n represent the number of people who voted against the proposal. It follows that \n\t3\n\tx\n\n is the number of people who voted in favor of the proposal and 3x-x, or \n\t2\n\tx\n\n, is how many more people voted in favor of the proposal than voted against it. It's also given that a social media post reported that 15,000\n more people voted in favor of the proposal than voted against it. Thus, 2x=15,000. Since 2x=15,000, the value of x\n must be half of 15,000\n, or 7,500\n. Therefore, 7,500\n people voted against the proposal.

\n

Choice B is incorrect. This is how many more people voted in favor of the proposal than voted against it, not the number of people who voted against the proposal.

\n

Choice C is incorrect. This is the number of people who voted in favor of the proposal, not the number of people who voted against the proposal.

\n

Choice D is incorrect and may result from conceptual or calculation errors.

"}, {"id": "fbb0ea7f", "domain": "Algebra", "skill": "Linear equations in one variable", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

A rocket contained 467,000\n kilograms (kg) of propellant before launch. Exactly 21\n seconds after launch, 362,105\n kg of this propellant remained. On average, approximately how much propellant, in kg, did the rocket burn each second after launch?

", "choices": [{"id": "A", "text": "

4,995\n

"}, {"id": "B", "text": "

17,243\n

"}, {"id": "C", "text": "

39,481\n

"}, {"id": "D", "text": "

104,895\n

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. It’s given that the rocket contained 467,000 kilograms (kg) of propellant before launch and had 362,105 kg remaining exactly 21\n seconds after launch. Finding the difference between the amount, in kg, of propellant before launch and the remaining amount, in kg, of propellant after launch gives the amount, in kg, of propellant burned during the 21\n seconds: 467,000-362,105=104,895. Dividing the amount of propellant burned by the number of seconds yields 104,89521=4,995. Thus, an average of 4,995 kg of propellant burned each second after launch.

\n

Choice B is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

\n

Choice D is incorrect and may result from finding the amount of propellant burned, rather than the amount of propellant burned each second.

"}, {"id": "75012ee7", "domain": "Algebra", "skill": "Systems of two linear equations in two variables", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

2x+3y=7
10x+15y=35

\n

For each real number r\n, which of the following points lies on the graph of each equation in the xy-plane for the given system?

", "choices": [{"id": "A", "text": "

r5+7,-r5+35

"}, {"id": "B", "text": "

-3r2+72, r

"}, {"id": "C", "text": "

r, 2r3+73

"}, {"id": "D", "text": "

r,-3r2+72

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. The two given equations are equivalent because the second equation can be obtained from the first equation by multiplying each side of the equation by 5\n. Thus, the graphs of the equations are coincident, so if a point lies on the graph of one of the equations, it also lies on the graph of the other equation. A point x,y lies on the graph of an equation in the xy-plane if and only if this point represents a solution to the equation. It is sufficient, therefore, to find the point that represents a solution to the first given equation. Substituting the x- and y-coordinates of choice B, -3r2+72 and r\n, for x\n and y\n, respectively, in the first equation yields 2-3r2+72+3r=7, which is equivalent to -3r+7+3r=7, or 7=7. Therefore, the point -3r2+72,r represents a solution to the first equation and thus lies on the graph of each equation in the xy-plane for the given system.

\n

Choice A is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

\n

Choice D is incorrect and may result from conceptual or calculation errors.

"}, {"id": "a7a14e87", "domain": "Algebra", "skill": "Linear equations in two variables", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

In the xy-plane, line k is defined by x + y = 0. Line j is perpendicular to line k, and the y-intercept of line j is the point 0, 3. Which of the following is an equation of line j ?

\n", "choices": [{"id": "A", "text": "

\n x + y = 3\n

\n"}, {"id": "B", "text": "

\n x + y = \u22123

\n"}, {"id": "C", "text": "

\n x \u2212 y = 3\n

\n"}, {"id": "D", "text": "

\n x \u2212 y = \u22123

\n"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. It’s given that line j is perpendicular to line k and that line k is defined by the equation x + y = 0. This equation can be rewritten in slope-intercept form, y = m x + b, where m represents the slope of the line and b represents the y-coordinate of the y-intercept of the line, by subtracting x from both sides of the equation, which yields y = \u2212x. Thus, the slope of line k is \u22121. Since line j and line k are perpendicular, their slopes are opposite reciprocals of each other. Thus, the slope of line j is 1. It’s given that the y-intercept of line j is the point 0, 3. Therefore, the equation for line j in slope-intercept form is y = x + 3, which can be rewritten as x \u2212 y = \u22123.

Choices A, B, and C are incorrect and may result from conceptual or calculation errors.

\n"}, {"id": "90bd9ef8", "domain": "Algebra", "skill": "Linear inequalities in one or two variables", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

The average annual energy cost for a certain home is $4,334. The homeowner plans to spend $25,000 to install a geothermal heating system. The homeowner estimates that the average annual energy cost will then be $2,712. Which of the following inequalities can be solved to find t, the number of years after installation at which the total amount of energy cost savings will exceed the installation cost?

\n", "choices": [{"id": "A", "text": "25,000 is greater than, open parenthesis, 4,334 \u2212 2,712, close parenthesis, \u00d7 t\n"}, {"id": "B", "text": "25,000 is less than, open parenthesis, 4,334 \u2212 2,712, close parenthesis, \u00d7 t\n"}, {"id": "C", "text": "25,000 \u2212 4,334, > 2,712 t\n"}, {"id": "D", "text": "25,000 > (4,332)/(2,712, end fraction, t)\n"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. The savings each year from installing the geothermal heating system will be the average annual energy cost for the home before the geothermal heating system installation minus the average annual energy cost after the geothermal heating system installation, which is 4,334 \u2212 2,712 dollars. In t years, the savings will be open parenthesis, 4,334 \u2212 2,712, close parenthesis, \u00d7 t dollars. Therefore, the inequality that can be solved to find the number of years after installation at which the total amount of energy cost savings will exceed (be greater than) the installation cost, $25,000, is 25,000 is less than, open parenthesis, 4,334 \u2212 2,712, close parenthesis, \u00d7 t.

Choice A is incorrect. It gives the number of years after installation at which the total amount of energy cost savings will be less than the installation cost. Choice C is incorrect and may result from subtracting the average annual energy cost for the home from the onetime cost
\nof the geothermal heating system installation. To find the predicted total savings, the predicted average cost should be subtracted from the average annual energy cost before the installation, and the result should be multiplied by the number of years, t. Choice D is incorrect and may result from misunderstanding the context. The ratio 4,332 over 2,712 compares the average energy cost before installation and the average energy cost after installation; it does not represent the savings.

\n"}, {"id": "c3989ef8", "domain": "Algebra", "skill": "Linear equations in one variable", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

Henry receives a $60.00 gift card to pay for movies online. He uses his gift card to buy 3\n movies for $7.50 each. If he spends the rest of his gift card balance on renting movies for $1.50 each, how many movies can Henry rent?

", "choices": [{"id": "A", "text": "

10\n

"}, {"id": "B", "text": "

25\n

"}, {"id": "C", "text": "

35\n

"}, {"id": "D", "text": "

40\n

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. It's given that Henry uses his $60.00 gift card to buy 3\n movies for $7.50 each. Therefore, Henry spends 3$7.50, or $22.50, of his $60.00 gift card to buy 3\n movies. After buying 3\n movies with his $60.00 gift card, Henry has a gift card balance of $60.00-$22.50, or $37.50. It's also given that Henry spends the rest of his gift card balance on renting movies for $1.50 each. Therefore, Henry can rent $37.50$1.50, or 25\n, movies.

\n

Choice A is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

\n

Choice D is incorrect and may result from conceptual or calculation errors.

"}, {"id": "6f6dfe3e", "domain": "Algebra", "skill": "Linear equations in two variables", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "
\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
x\ny\n
-6\n\n\tn\n\t+\n\t184\n\n
-3\n\n\tn\n\t+\n\t92\n\n
0\nn\n
\n

The table shows three values of x\n and their corresponding values of y\n, where n\n is a constant, for the linear relationship between x\n and y\n. What is the slope of the line that represents this relationship in the xy-plane?

", "choices": [{"id": "A", "text": "

\n\t-\n\t\n\t\t92\n\t\t3\n\t\n\n

"}, {"id": "B", "text": "

\n\t-\n\t\n\t\t3\n\t\t92\n\t\n\n

"}, {"id": "C", "text": "

n+92-3

"}, {"id": "D", "text": "

2n-923

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. The slope, m\n, of a line in the xy-plane can be found using two points on the line, x1,y1 and x2,y2, and the slope formula m=y2-y1x2-x1. Based on the given table, the line representing the relationship between x\n and y\n in the xy-plane passes through the points -6,n+184, -3,n+92, and 0,n, where n\n is a constant. Substituting two of these points, -3,n+92 and 0,n, for x1,y1 and x2,y2, respectively, in the slope formula yields m=n-n+920--3, which is equivalent to m=n-n-920+3, or m=-923. Therefore, the slope of the line that represents this relationship in the xy-plane is \n\t-\n\t\n\t\t92\n\t\t3\n\t\n\n.

\n

Choice B is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

\n

Choice D is incorrect and may result from conceptual or calculation errors.

"}, {"id": "8f0c82e2", "domain": "Algebra", "skill": "Linear inequalities in one or two variables", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

The minimum value of x\n is 12\n less than 6\n times another number n\n. Which inequality shows the possible values of x\n?

", "choices": [{"id": "A", "text": "

x≤6n-12

"}, {"id": "B", "text": "

x≥6n-12

"}, {"id": "C", "text": "

x≤12-6n

"}, {"id": "D", "text": "

x≥12-6n

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. It’s given that the minimum value of x\n is 12\n less than 6\n times another number n\n. Therefore, the possible values of x\n are all greater than or equal to the value of 12\n less than 6\n times n\n. The value of 6\n times n\n is given by the expression \n\t6\n\tn\n\n. The value of 12\n less than \n\t6\n\tn\n\n is given by the expression \n\t\n\t\t6\n\t\tn\n\t\n\t-\n\t12\n\n. Therefore, the possible values of x\n are all greater than or equal to \n\t\n\t\t6\n\t\tn\n\t\n\t-\n\t12\n\n. This can be shown by the inequality x\u22656n-12.

\n

Choice A is incorrect. This inequality shows the possible values of x\n if the maximum, not the minimum, value of x\n is 12\n less than 6\n times n\n.

\n

Choice C is incorrect. This inequality shows the possible values of x\n if the maximum, not the minimum, value of x\n is 6\n times n\n less than 12\n, not 12\n less than 6\n times n\n.

\n

Choice D is incorrect. This inequality shows the possible values of x\n if the minimum value of x\n is 6\n times n\n less than 12\n, not 12\n less than 6\n times n\n.

"}, {"id": "5ad9eff0", "domain": "Algebra", "skill": "Linear equations in one variable", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

The width of a rectangular dance floor is w feet. The length of the floor is 6 feet longer than its width. Which of the following expresses the perimeter, in feet, of the dance floor in terms of w ?

\n", "choices": [{"id": "A", "text": "2 w + 6\n"}, {"id": "B", "text": "4 w + 12\n"}, {"id": "C", "text": "w\u00b2 + 6\n"}, {"id": "D", "text": "w\u00b2 + 6 w\n"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. It is given that the width of the dance floor is w feet. The length is 6 feet longer than the width; therefore, the length of the dance floor is w + 6. So the perimeter is w + w, plus, open parenthesis, w + 6, close parenthesis, plus, open parenthesis, w + 6, close parenthesis = 4 w + 12.

Choice A is incorrect because it is the sum of one length and one width, which is only half the perimeter. Choice C is incorrect and may result from using the formula for the area instead of the formula for the perimeter and making a calculation error. Choice D is incorrect because this is the area, not the perimeter, of the dance floor.

\n"}, {"id": "038d87d7", "domain": "Algebra", "skill": "Linear equations in two variables", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

A neighborhood consists of a 2\n-hectare park and a 35\n-hectare residential area. The total number of trees in the neighborhood is 3,934\n. The equation \n\t\n\t\t\n\t\t\t2\n\t\t\tx\n\t\t\n\t\t+\n\t\t\n\t\t\t35\n\t\t\ty\n\t\t\n\t\n\t=\n\t3,934\n\n represents this situation. Which of the following is the best interpretation of x in this context?

", "choices": [{"id": "A", "text": "

The average number of trees per hectare in the park

"}, {"id": "B", "text": "

The average number of trees per hectare in the residential area

"}, {"id": "C", "text": "

The total number of trees in the park

"}, {"id": "D", "text": "

The total number of trees in the residential area

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. It's given that a neighborhood consists of a 2\n-hectare park and a 35\n-hectare residential area and that the total number of trees in the neighborhood is 3,934\n. It's also given that the equation 2x+35y=3,934 represents this situation. Since the total number of trees for a given area can be determined by taking the number of hectares times the average number of trees per hectare, this must mean that the terms \n\t2\n\tx\n\n and \n\t35\n\ty\n\n correspond to the number of trees in the park and in the residential area, respectively. Since \n\t2\n\tx\n\n corresponds to the number of trees in the park, and 2\n is the size of the park, in hectares, x\n must represent the average number of trees per hectare in the park.

\n

Choice B is incorrect and may result from conceptual errors.

\n

Choice C is incorrect and may result from conceptual errors.

\n

Choice D is incorrect and may result from conceptual errors.

"}, {"id": "174885f8", "domain": "Algebra", "skill": "Linear equations in two variables", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

Jay walks at a speed of 3\n miles per hour and runs at a speed of 5\n miles per hour. He walks for w\n hours and runs for r\n hours for a combined total of 14\n miles. Which equation represents this situation?

", "choices": [{"id": "A", "text": "

3w+5r=14\n

"}, {"id": "B", "text": "

13w+15r=14\n

"}, {"id": "C", "text": "

13w+15r=112\n

"}, {"id": "D", "text": "

3w+5r=112\n

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. Since Jay walks at a speed of 3\n miles per hour for w\n hours, Jay walks a total of \n\t3\n\tw\n\n miles. Since Jay runs at a speed of 5\n miles per hour for r\n hours, Jay runs a total of \n\t5\n\tr\n\n miles. Therefore, the total number of miles Jay travels can be represented by 3w+5r. Since the combined total number of miles is 14\n, the equation 3w+5r=14 represents this situation.

\n

Choice B is incorrect and may result from conceptual errors.

\n

Choice C is incorrect and may result from conceptual errors.

\n

Choice D is incorrect and may result from conceptual errors.

"}, {"id": "441558e7", "domain": "Algebra", "skill": "Linear functions", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

Scientists collected fallen acorns that each housed a colony of the ant species P. ohioensis and analyzed each colony's structure. For any of these colonies, if the colony has x\n worker ants, the equation y=0.67x+2.6, where 20≤x≤110, gives the predicted number of larvae, y\n, in the colony. If one of these colonies has 58\n worker ants, which of the following is closest to the predicted number of larvae in the colony?

", "choices": [{"id": "A", "text": "

41\n

"}, {"id": "B", "text": "

61\n

"}, {"id": "C", "text": "

83\n

"}, {"id": "D", "text": "

190\n

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. It's given that the equation y=0.67x+2.6, where 20≤x≤110, gives the predicted number of larvae, y\n, in a colony of ants if the colony has x\n worker ants. If one of these colonies has 58\n worker ants, the predicted number of larvae in that colony can be found by substituting 58\n for x\n in the given equation. Substituting 58\n for x\n in the given equation yields y=0.6758+2.6, or \n\ty\n\t=\n\t41.46\n\n. Of the given choices, 41\n is closest to the predicted number of larvae in the colony.

\n

Choice B is incorrect. This is closest to the predicted number of larvae in a colony with 87\n worker ants.

\n

Choice C is incorrect. This is closest to the number of worker ants for which the predicted number of larvae in a colony is 58\n.

\n

Choice D is incorrect. This is closest to the predicted number of larvae in a colony with 280\n worker ants.

"}, {"id": "2eef7e61", "domain": "Algebra", "skill": "Linear functions", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

The graph of the function f is a line in the xy-plane. If the line has slope three-fourths and f(0) = 3, which of the following defines f?

\n", "choices": [{"id": "A", "text": "

\n f(x) = three fourths x, \u2212 3\n

\n"}, {"id": "B", "text": "

\n f(x) = three fourths x, + 3\n

\n"}, {"id": "C", "text": "

\n f(x) = 4 x, \u2212 3\n

\n"}, {"id": "D", "text": "

\n f(x) = 4 x, + 3\n

\n"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. The equation for the function f in the xy-plane can be represented by f(x) = m x + b, where m is the slope and b is the y-coordinate of the y-intercept. Since it’s given that the line has a slope of three fourths, it follows that m = three fourths in f(x) = m x + b, which yields y = three fourths x, + b. It’s given that f(0) = 3. This implies that the graph of the function f in the xy-plane passes through the point 0, 3. Thus, the y-coordinate of the y-intercept of the graph is 3, so b = 3 in f(x) = three fourths x, + b, which yields f(x) = three fourths x, + 3. Therefore, the equation f(x) = three fourths x, + 3 defines the function f.

Choice A is incorrect and may result from a sign error for the y-intercept. Choice C is incorrect and may result from using the denominator of the given slope as m in f(x) = m x + b, in addition to a sign error for the y-intercept. Choice D is incorrect and may result from using the denominator of the given slope as m in f(x) = m x + b.

\n"}, {"id": "f0773a55", "domain": "Algebra", "skill": "Linear functions", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n\n

\n

The graph represents the total charge, in dollars, by an electrician for x\n hours of work. The electrician charges a onetime fee plus an hourly rate. What is the best interpretation of the slope of the graph?

", "choices": [{"id": "A", "text": "

The electrician’s hourly rate

"}, {"id": "B", "text": "

The electrician’s onetime fee

"}, {"id": "C", "text": "

The maximum amount that the electrician charges

"}, {"id": "D", "text": "

The total amount that the electrician charges

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. It’s given that the electrician charges a onetime fee plus an hourly rate. It's also given that the graph represents the total charge, in dollars, for x\n hours of work. This graph shows a linear relationship in the xy-plane. Thus, the total charge y\n, in dollars, for x\n hours of work can be represented as y=mx+b, where m\n is the slope and 0,b is the y-intercept of the graph of the equation in the xy-plane. Since the given graph represents the total charge, in dollars, by an electrician for x\n hours of work, it follows that its slope is m\n, or the electrician’s hourly rate.

\n

Choice B is incorrect. The electrician's onetime fee is represented by the y-coordinate of the y-intercept, not the slope, of the graph.

\n

Choice C is incorrect and may result from conceptual errors.

\n

Choice D is incorrect and may result from conceptual errors.

"}, {"id": "5e08a055", "domain": "Algebra", "skill": "Systems of two linear equations in two variables", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

\n\ty\n\t=\n\t\n\t\t\n\t\t\t6\n\t\t\tx\n\t\t\n\t\t+\n\t\t18\n\t\n\n

\n

One of the equations in a system of two linear equations is given. The system has no solution. Which equation could be the second equation in the system?

", "choices": [{"id": "A", "text": "

\n\t\n\t\t\n\t\t\t-\n\t\t\t6\n\t\t\tx\n\t\t\n\t\t+\n\t\ty\n\t\n\t=\n\t18\n\n

"}, {"id": "B", "text": "

\n\t\n\t\t\n\t\t\t-\n\t\t\t6\n\t\t\tx\n\t\t\n\t\t+\n\t\ty\n\t\n\t=\n\t22\n\n

"}, {"id": "C", "text": "

\n\t\n\t\t\n\t\t\t-\n\t\t\t12\n\t\t\tx\n\t\t\n\t\t+\n\t\ty\n\t\n\t=\n\t36\n\n

"}, {"id": "D", "text": "

\n\t\n\t\t\n\t\t\t-\n\t\t\t12\n\t\t\tx\n\t\t\n\t\t+\n\t\ty\n\t\n\t=\n\t18\n\n

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. A system of two linear equations in two variables, x\n and y\n, has no solution if the lines represented by the equations in the xy-plane are parallel and distinct. Lines represented by equations in standard form, Ax+By=C and Dx+Ey=F, are parallel if the coefficients for x\n and y\n in one equation are proportional to the corresponding coefficients in the other equation, meaning DA=EB; and the lines are distinct if the constants are not proportional, meaning FC is not equal to DA or EB. The given equation, y=6x+18, can be written in standard form by subtracting 6x from both sides of the equation to yield -6x+y=18. Therefore, the given equation can be written in the form Ax+By=C, where A=-6, B=1, and C=18. The equation in choice B, -6x+y=22, is written in the form Dx+Ey=F, where D=-6, E=1, and F=22. Therefore,  DA=-6-6, which can be rewritten as DA=1; EB=11, which can be rewritten as EB=1; and FC=2218, which can be rewritten as FC=119. Since DA=1, EB=1, and FC is not equal to 1\n, it follows that the given equation and the equation -6x+y=22 are parallel and distinct. Therefore, a system of two linear equations consisting of the given equation and the equation -6x+y=22 has no solution. Thus, the equation in choice B could be the second equation in the system.

\n

Choice A is incorrect. The equation -6x+y=18 and the given equation represent the same line in the xy-plane. Therefore, a system of these linear equations would have infinitely many solutions, rather than no solution. 

\n

Choice C is incorrect. The equation -12x+y=36 and the given equation represent lines in the xy-plane that are distinct and not parallel. Therefore, a system of these linear equations would have exactly one solution, rather than no solution.

\n

Choice D is incorrect. The equation -12x+y=18 and the given equation represent lines in the xy-plane that are distinct and not parallel. Therefore, a system of these linear equations would have exactly one solution, rather than no solution.

"}, {"id": "0ea7ef01", "domain": "Algebra", "skill": "Linear functions", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

Oxygen gas is placed inside a tank with a constant volume. The graph shows the estimated temperature y\n, in kelvins, of the oxygen gas when its pressure is x\n atmospheres.

\n

\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n\n

\n

What is the estimated temperature, in kelvins, of the oxygen gas when its pressure is 6\n atmospheres?

", "choices": [{"id": "A", "text": "

6\n

"}, {"id": "B", "text": "

60\n

"}, {"id": "C", "text": "

700\n

"}, {"id": "D", "text": "

760\n

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. For the graph shown, the x-axis represents pressure, in atmospheres, and the y-axis represents temperature, in kelvins. Therefore, the estimated temperature, in kelvins, of the oxygen gas when its pressure is 6\n atmospheres is represented by the y-coordinate of the point on the graph that has an x-coordinate of 6\n. The point on the graph with an x-coordinate of 6\n has a y-coordinate of approximately 700\n. Therefore, the estimated temperature, in kelvins, of the oxygen gas when its pressure is 6\n atmospheres is 700\n.

\n

Choice A is incorrect. This is the pressure, in atmospheres, not the estimated temperature, in kelvins, of the oxygen gas when its pressure is 6\n atmospheres.

\n

Choice B is incorrect and may result from conceptual or calculation errors.

\n

Choice D is incorrect and may result from conceptual or calculation errors.

"}, {"id": "0df106df", "domain": "Algebra", "skill": "Systems of two linear equations in two variables", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

An online bookstore sells novels and magazines. Each novel sells for $4, and each magazine sells for $1. If Sadie purchased a total of 11 novels and magazines that have a combined selling price of $20, how many novels did she purchase?

\n", "choices": [{"id": "A", "text": "

2

\n"}, {"id": "B", "text": "

3

\n"}, {"id": "C", "text": "

4

\n"}, {"id": "D", "text": "

5

\n"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. Let n be the number of novels and m be the number of magazines that Sadie purchased. If Sadie purchased a total of 11 novels and magazines, then n + m = 11. It is given that the combined price of 11 novels and magazines is $20. Since each novel sells for $4 and each magazine sells for $1, it follows that 4 n + m = 20. So the system of equations below must hold.

4 n + m = 20; n + m = 11

Subtracting corresponding sides of the second equation from the first equation yields 3 n = 9, so n = 3. Therefore, Sadie purchased 3 novels.

Choice A is incorrect. If 2 novels were purchased, then a total of $8 was spent on novels. That leaves $12 to be spent on magazines, which means that 12 magazines would have been purchased. However, Sadie purchased a total of 11 novels and magazines. Choices C and D are incorrect. If 4 novels were purchased, then a total of $16 was spent on novels. That leaves $4 to be spent on magazines, which means that 4 magazines would have been purchased. By the same logic, if Sadie purchased 5 novels, she would have no money at all ($0) to buy magazines. However, Sadie purchased a total of 11 novels and magazines.

 

\n"}, {"id": "628300a9", "domain": "Algebra", "skill": "Linear equations in one variable", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

A science teacher is preparing the 5 stations of a science laboratory. Each station will have either Experiment A materials or Experiment B materials, but not both. Experiment A requires 6 teaspoons of salt, and Experiment B requires 4 teaspoons of salt. If x is the number of stations that will be set up for Experiment A and the remaining stations will be set up for Experiment B, which of the following expressions represents the total number of teaspoons of salt required?

\n", "choices": [{"id": "A", "text": "5 x\n"}, {"id": "B", "text": "10 x\n"}, {"id": "C", "text": "2 x + 20\n"}, {"id": "D", "text": "10 x + 20\n"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. It is given that x represents the number of stations that will be set up for Experiment A and that there will be 5 stations total, so it follows that 5 – x is the number of stations that will be set up for Experiment B. It is also given that Experiment A requires 6 teaspoons of salt and that Experiment B requires 4 teaspoons of salt, so the total number of teaspoons of salt required is 6x + 4(5 – x), which simplifies to 2x + 20.

Choices A, B, and D are incorrect and may be the result of not understanding the description of the context.

\n"}, {"id": "9ed4c1a2", "domain": "Algebra", "skill": "Linear equations in two variables", "difficulty": "M", "type": "spr", "stimulus": "", "stem": "

What is the slope of the graph of y=1427x+15+7x in the xy-plane?

", "choices": [], "answerId": "13.75", "acceptedAnswers": ["13.75", "55/4"], "rationale": "

The correct answer is 554. In the xy-plane, the graph of an equation in the form \n\ty\n\t=\n\t\n\t\t\n\t\t\tm\n\t\t\tx\n\t\t\n\t\t+\n\t\tb\n\t\n\n, where m\n and b\n are constants, has a slope of m\n and a y-intercept of 0,b. Applying the distributive property to the right-hand side of the given equation yields y=274x+154+7x. Combining like terms yields y=554x+154. This equation is in the form \n\ty\n\t=\n\t\n\t\t\n\t\t\tm\n\t\t\tx\n\t\t\n\t\t+\n\t\tb\n\t\n\n, where \n\tm\n\t=\n\t\n\t\t55\n\t\t4\n\t\n\n and \n\tb\n\t=\n\t\n\t\t15\n\t\t4\n\t\n\n. It follows that the slope of the graph of y=1427x+15+7x in the xy-plane is 554. Note that 55/4 and 13.75 are examples of ways to enter a correct answer.

"}, {"id": "45bba652", "domain": "Algebra", "skill": "Linear equations in one variable", "difficulty": "M", "type": "mc", "stimulus": "
\n

\n
\n", "stem": "

If 2 times, open parenthesis, x \u2212 5, close parenthesis, + 3 times, open parenthesis, x \u2212 5, close parenthesis = 10, what is the value of x \u2212 5 ?

\n", "choices": [{"id": "A", "text": "

2

\n"}, {"id": "B", "text": "

5

\n"}, {"id": "C", "text": "

7

\n"}, {"id": "D", "text": "

12

\n"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. Adding the like terms on the left-hand side of the given equation yields 5 times, open parenthesis, x \u2212 5, close parenthesis = 10. Dividing both sides of this equation by 5 yields x \u2212 5 = 2.

Choice B is incorrect and may result from subtracting 5, not dividing by 5, on both sides of the equation 5 times, open parenthesis, x \u2212 5, close parenthesis = 10. Choice C is incorrect. This is the value of x, not the value of x \u2212 5. Choice D is incorrect. This is the value of x + 5, not the value of x \u2212 5.

\n"}, {"id": "1ecaa9c0", "domain": "Algebra", "skill": "Linear functions", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

Robert rented a truck to transport materials he purchased from a hardware store. He was charged an initial fee of $20.00 plus an additional $0.70 per mile driven. If the truck was driven 38 miles, what was the total amount Robert was charged?

\n", "choices": [{"id": "A", "text": "

$46.60

\n"}, {"id": "B", "text": "

$52.90

\n"}, {"id": "C", "text": "

$66.90

\n"}, {"id": "D", "text": "

$86.50

\n"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. It’s given that Robert was charged an initial fee of $20.00 to rent the truck plus an additional $0.70 per mile driven. Let m represent the number of miles the truck was driven. Since the rental charge is $0.70 per mile driven, 0 point 7 0 m represents the amount Robert was charged for m miles driven. Let c equal the total amount, in dollars, Robert was charged to rent the truck. The total amount can be represented by the equation c = 20 point 0 0 + 0 point 7 0 m. It’s given that the truck was driven 38 miles, thus m = 38. Substituting 38 into the equation gives c = 20 point 0 0 + 0 point 7 0, \u00d7 38. Multiplying 0 point 7 0 \u00d7 38 gives c = 20 point 0 0 + 26 point 6 0. Adding these values gives c = 46 point 6 0, so the total amount Robert was charged is $46.60.

Choices B, C, and D are incorrect and may result from setting up the equation incorrectly or from making calculation errors.

 

\n"}, {"id": "fb43b85f", "domain": "Algebra", "skill": "Linear equations in two variables", "difficulty": "M", "type": "spr", "stimulus": "", "stem": "

A line passes through the points 4,6 and 15,24 in the xy-plane. What is the slope of the line?

", "choices": [], "answerId": "1.636", "acceptedAnswers": ["1.636", "18/11"], "rationale": "

The correct answer is \n\t18\n\t11\n\n. For a line that passes through the points x1,y1 and x2,y2 in the xy-plane, the slope of the line can be calculated using the slope formula, m=y2-y1x2-x1. It's given that a line passes through the points 4,6 and 15,24 in the xy-plane. Substituting 4,6 for x1,y1 and 15,24 for x2,y2 in the slope formula, m=y2-y1x2-x1, yields m=24-615-4, or m=1811. Therefore, the slope of the line is \n\t18\n\t11\n\n. Note that 18/11 and 1.636 are examples of ways to enter a correct answer.

"}, {"id": "eafdbbbd", "domain": "Algebra", "skill": "Linear equations in one variable", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

14x+5-13x+5=-7

\n

What value of x\n is the solution to the given equation?

", "choices": [{"id": "A", "text": "

-12\n

"}, {"id": "B", "text": "

-5\n

"}, {"id": "C", "text": "

79\n

"}, {"id": "D", "text": "

204\n

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. For the given equation, x+5 is a factor of both terms on the left-hand side. Therefore, the given equation can be rewritten as 14-13x+5=-7, or 312-412x+5=-7, which is equivalent to -112x+5=-7. Multiplying both sides of this equation by -12\n yields x+5=84. Subtracting 5\n from both sides of this equation yields x=79. 

\n

Choice A is incorrect. This is the value of x\n for which the left-hand side of the given equation equals \n\t7\n\t12\n\n, not -7\n.

\n

Choice B is incorrect. This is the value of x\n for which the left-hand side of the given equation equals 0\n, not -7\n.

\n

Choice D is incorrect. This is the value of x\n for which the left-hand side of the given equation equals \n\t-\n\t\n\t\t209\n\t\t12\n\t\n\n, not -7\n.

"}, {"id": "7d89376f", "domain": "Algebra", "skill": "Systems of two linear equations in two variables", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

\n A discount airline sells a certain number of tickets, x, for a flight for $90 each. It sells the number of remaining tickets, y, for $250 each. For a particular flight, the airline sold 120 tickets and collected a total of $27,600 from the sale of those tickets. Which system of equations represents this relationship between x and y ?\n

\n", "choices": [{"id": "A", "text": "

\n open brace, x + y = 120; 90 x + 250 y = 27,600\n

\n"}, {"id": "B", "text": "

\n open brace, x + y = 120; 90 x + 250 y = 120 \u00d7 27,600\n

\n"}, {"id": "C", "text": "

\n open brace, x + y = 27,600; 90 x + 250 y = 120 \u00d7 27,600\n

\n"}, {"id": "D", "text": "

\n open brace, 90 x = 250 y; 120 x + 120 y = 27,600\n

\n"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. The airline sold two types of tickets for this flight: x tickets at $90 each and the remaining  tickets, y, at $250 each. Because the airline sold a total of 120 tickets for this flight, it must be true that x + y = 120. The amount, in dollars, collected from the sale of x tickets at $90 each is represented by 90x. The amount, in dollars, collected from the sale of the remaining y tickets at $250 each is represented by 250y. It is given that a total of $27,600 was collected from the sale of all tickets. Therefore, it must also be true that 90x + 250y = 27,600.

Choice B is incorrect. The total number of tickets sold is represented correctly as x + y = 120. The total amount, in dollars, collected from the sale of the x tickets at $90 each and the remaining tickets, y, at $250 has been correctly represented as 90x + 250y. However, according to the information given, this total should be equal to 27,600, not 120(27,600) dollars. Choice C is incorrect. The total number of tickets sold has been correctly represented as x + y. However, according to the information given, this total should be equal to 120, not 27,600, as shown in choice C. The total amount, in dollars, collected from the sale of the x tickets at $90 each and the remaining tickets, y, at $250 has been correctly represented as 90x + 250y. However, according to the information given, this total should be equal to 27,600, not 120(27,600) dollars. Choice D is incorrect. The two equations given in choice D have no meaning in this context.

\n"}, {"id": "3ce92ce8", "domain": "Algebra", "skill": "Linear functions", "difficulty": "M", "type": "spr", "stimulus": "", "stem": "

fx=2x+3

\n

For the given function f\n, the graph of y=fx in the xy-plane is parallel to line j\n. What is the slope of line j\n?

", "choices": [], "answerId": "2", "acceptedAnswers": ["2"], "rationale": "

The correct answer is 2\n. It’s given that function f\n is defined by fx=2x+3. Therefore, the equation representing the graph of y=fx in the xy-plane is y=2x+3, and the graph is a line. For a linear equation in the form y=mx+b, m\n represents the slope of the line. Since the value of m\n in the equation y=2x+3 is 2\n, the slope of the line defined by function f\n is 2\n. It's given that line j\n is parallel to the line defined by function f\n. The slopes of parallel lines are equal. Therefore, the slope of line j\n is also 2\n.

"}, {"id": "f40552a9", "domain": "Algebra", "skill": "Linear equations in two variables", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n\n

\n

What is the y-intercept of the line graphed?

", "choices": [{"id": "A", "text": "

0,-8

"}, {"id": "B", "text": "

0,-18

"}, {"id": "C", "text": "

0,0

"}, {"id": "D", "text": "

0,8

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. The y-intercept of a line graphed in the xy-plane is the point where the line intersects the y-axis. The line graphed intersects the y-axis at the point 0,8. Therefore, the y-intercept of the line graphed is 0,8.

\n

Choice A is incorrect and may result from conceptual errors.

\n

Choice B is incorrect and may result from conceptual errors.

\n

Choice C is incorrect and may result from conceptual errors.

"}, {"id": "12ae3452", "domain": "Algebra", "skill": "Linear equations in two variables", "difficulty": "E", "type": "spr", "stimulus": "", "stem": "

The equation \n\t46\n\t=\n\t\n\t\t\n\t\t\t2\n\t\t\ta\n\t\t\n\t\t+\n\t\t\n\t\t\t2\n\t\t\tb\n\t\t\n\t\n\n gives the relationship between the side lengths a\n and b\n of a certain parallelogram. If \n\ta\n\t=\n\t9\n\n, what is the value of b\n?

", "choices": [], "answerId": "14", "acceptedAnswers": ["14"], "rationale": "

The correct answer is 14\n. It's given that the equation 46=2a+2b gives the relationship between the side lengths a\n and b\n of a certain parallelogram. Substituting 9\n for a\n in the given equation yields 46=29+2b, or 46=18+2b. Subtracting 18\n from both sides of this equation yields 28=2b. Dividing both sides of this equation by 2\n yields 14=b. Therefore, if a=9, the value of b\n is 14\n.

"}, {"id": "17f176ec", "domain": "Algebra", "skill": "Systems of two linear equations in two variables", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

A movie theater charges $11 for each full-price ticket and $8.25 for each reduced-price ticket. For one movie showing, the theater sold a total of 214 full-price and reduced-price tickets for $2,145. Which of the following systems of equations could be used to determine the number of full-price tickets, f, and the number of reduced-price tickets, r, sold?

\n", "choices": [{"id": "A", "text": "f + r = 2,145; 11 f + 8 point 2 5 r = 214\n"}, {"id": "B", "text": "f + r = 214; 11 f + 8 point 2 5 r = 2,145\n"}, {"id": "C", "text": "f + r = 214; 8 point 2 5 f + 11 r = 2,145\n"}, {"id": "D", "text": "f + r = 2,145; 8 point 2 5 f + 11 r = 214\n"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. The movie theater sells f full-price tickets and r reduced-price tickets, so the total number of tickets sold is f + r. Since the movie theater sold a total of 214 full-price and reduced-price tickets for one movie showing, it follows that f + r = 214. The movie theater charges $11 for each full-price ticket; thus, the sales for full-price tickets, in dollars, is given by 11f. The movie theater charges $8.25 for each reduced-price ticket; thus, the sales for reduced-price tickets, in dollars, is given by 8.25r. Therefore, the total sales, in dollars, for the movie showing is given by 11f + 8.25r. Since the total sales for all full-price and reduced-price tickets is $2,145, it follows that 11f + 8.25r = 2,145.

Choice A is incorrect. This system of equations suggests that the movie theater sold a total of 2,145 full-price and reduced-price tickets for a total of $214. Choice C is incorrect. This system suggests that the movie theater charges $8.25 for each full-price ticket and $11 for each reduced-price ticket. Choice D is incorrect. This system suggests that the movie theater charges $8.25 for each full-price ticket and $11 for each reduced-price ticket and sold a total of 2,145 tickets for a total of $214.

\n"}, {"id": "8643d906", "domain": "Algebra", "skill": "Linear functions", "difficulty": "E", "type": "mc", "stimulus": "
\n

\n P(t) = 250 + 10 t\n

\n
\n", "stem": "

The population of snow leopards in a certain area can be modeled by the function P defined above, where P(t) is the population t years after 1990. Of the following, which is the best interpretation of the equation P(3)0 = 550 ?

\n", "choices": [{"id": "A", "text": "

The snow leopard population in this area is predicted to be 30 in the year 2020.

\n"}, {"id": "B", "text": "

The snow leopard population in this area is predicted to be 30 in the year 2030.

\n"}, {"id": "C", "text": "

The snow leopard population in this area is predicted to be 550 in the year 2020.

\n"}, {"id": "D", "text": "

The snow leopard population in this area is predicted to be 550 in the year 2030.

\n"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. It’s given that P(t) represents the population of snow leopards t years after 1990. P(3)0 = 550 corresponds to t = 30 and P(t) = 550. It follows that t = 30 corresponds to 30 years after 1990, or 2020. Thus, the best interpretation of P(3)0 = 550 is that the snow leopard population in this area is predicted to be 550 in the year 2020.

Choices A and B are incorrect and may result from reversing the interpretations of t and P(t). Choice D is incorrect and may result from determining that 30 years after 1990 is 2030, not 2020.

\n"}, {"id": "bbf9e5ce", "domain": "Algebra", "skill": "Linear functions", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

For groups of 25\n or more people, a museum charges $21\n per person for the first 25\n people and $14\n for each additional person. Which function f\n gives the total charge, in dollars, for a tour group with n\n people, where n≥25?

", "choices": [{"id": "A", "text": "

fn=\n\t\n\t\t14\n\t\tn\n\t\n\t+\n\t175\n\n

"}, {"id": "B", "text": "

fn=\n\t\n\t\t14\n\t\tn\n\t\n\t+\n\t525\n\n

"}, {"id": "C", "text": "

fn=\n\t\n\t\t35\n\t\tn\n\t\n\t-\n\t350\n\n

"}, {"id": "D", "text": "

fn=\n\t\n\t\t14\n\t\tn\n\t\n\t+\n\t21\n\n

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. A tour group with n\n people, where n\u226525, can be split into two subgroups: the first 25\n people and the additional \n\tn\n\t-\n\t25\n\n people. Since the museum charges $21 per person for the first 25\n people and $14 for each additional person, the charge for the first 25\n people is $21(25) and the charge for the additional \n\tn\n\t-\n\t25\n\n people is $14(n-25). Therefore, the total charge, in dollars, is given by the function f(n)=21(25)+14(n-25), or f(n)=14n+175.

\n

Choice B is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

\n

Choice D is incorrect and may result from conceptual or calculation errors.

"}, {"id": "a4d6fbec", "domain": "Algebra", "skill": "Linear functions", "difficulty": "E", "type": "spr", "stimulus": "", "stem": "

If \n\ty\n\t=\n\t\n\t\t\n\t\t\t5\n\t\t\tx\n\t\t\n\t\t+\n\t\t10\n\t\n\n, what is the value of y\n when \n\tx\n\t=\n\t8\n\n?

", "choices": [], "answerId": "50", "acceptedAnswers": ["50"], "rationale": "

The correct answer is 50\n. Substituting 8\n for x\n in the given equation yields y=58+10, or y=50. Therefore, the value of y\n is 50\n when x=8.

"}, {"id": "d02193fb", "domain": "Algebra", "skill": "Linear inequalities in one or two variables", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n

\n

The shaded region shown represents the solutions to which inequality?

", "choices": [{"id": "A", "text": "

y<1+4x

"}, {"id": "B", "text": "

y<1-4x

"}, {"id": "C", "text": "

y>1+4x

"}, {"id": "D", "text": "

y>1-4x

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. The equation for the line representing the boundary of the shaded region can be written in slope-intercept form y=b+mx, where m\n is the slope and 0,b is the y-intercept of the line. For the graph shown, the boundary line passes through the points 0,1 and 1,-3. Given two points on a line, x1,y1 and x2,y2, the slope of the line can be calculated using the equation m=y2-y1x2-x1. Substituting the points 0,1 and 1,-3 for x1,y1 and x2,y2 in this equation yields m=-3-11-0, which is equivalent to m=-41, or m=-4. Since the point 0,1 represents the y-intercept, it follows that \n\tb\n\t=\n\t1\n\n. Substituting -4\n for m\n and 1\n for b\n in the equation y=b+mx yields y=1-4x as the equation of the boundary line. Since the shaded region represents all the points above this boundary line, it follows that the shaded region shown represents the solutions to the inequality y>1-4x.

\n

Choice A is incorrect. This inequality represents a region below, not above, a boundary line with a slope of 4\n, not -4\n.

\n

Choice B is incorrect. This inequality represents a region below, not above, the boundary line shown.

\n

Choice C is incorrect. This inequality represents a region whose boundary line has a slope of 4\n, not -4\n.

"}, {"id": "768b2425", "domain": "Algebra", "skill": "Linear equations in two variables", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

Last week, an interior designer earned a total of $1,258 from consulting for x\n hours and drawing up plans for y\n hours. The equation 68x+85y=1,258 represents this situation. Which of the following is the best interpretation of 68\n in this context?

", "choices": [{"id": "A", "text": "

The interior designer earned $68 per hour consulting last week.

"}, {"id": "B", "text": "

The interior designer worked 68\n hours drawing up plans last week.

"}, {"id": "C", "text": "

The interior designer earned $68 per hour drawing up plans last week.

"}, {"id": "D", "text": "

The interior designer worked 68\n hours consulting last week.

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. It's given that 68x+85y=1,258 represents the situation where an interior designer earned a total of $1,258 last week from consulting for x\n hours and drawing up plans for y\n hours. Thus, \n\t68\n\tx\n\n represents the amount earned, in dollars, from consulting for x\n hours, and \n\t85\n\ty\n\n represents the amount earned, in dollars, from drawing up plans for y\n hours. Since \n\t68\n\tx\n\n represents the amount earned, in dollars, from consulting for x\n hours, it follows that the interior designer earned $68 per hour consulting last week.

\n

Choice B is incorrect. The interior designer worked y\n hours, not 68\n hours, drawing up plans last week.

\n

Choice C is incorrect. The interior designer earned $85 per hour, not $68 per hour, drawing up plans last week.

\n

Choice D is incorrect. The interior designer worked x\n hours, not 68\n hours, consulting last week.

"}, {"id": "e53688cb", "domain": "Algebra", "skill": "Systems of two linear equations in two variables", "difficulty": "M", "type": "spr", "stimulus": "", "stem": "

\n\t\n\t\tx\n\t\t+\n\t\t\n\t\t\t3\n\t\t\ty\n\t\t\n\t\n\t=\n\t29\n\n

\n

\n\t\n\t\t3\n\t\ty\n\t\n\t=\n\t11\n\n

\n

The solution to the given system of equations is x,y. What is the value of x\n?

", "choices": [], "answerId": "18", "acceptedAnswers": ["18"], "rationale": "

The correct answer is 18\n. It's given by the second equation in the system that \n\t\n\t\t3\n\t\ty\n\t\n\t=\n\t11\n\n. Substituting 11\n for \n\t3\n\ty\n\n in the first equation in the system, \n\t\n\t\tx\n\t\t+\n\t\t\n\t\t\t3\n\t\t\ty\n\t\t\n\t\n\t=\n\t29\n\n, yields \n\t\n\t\tx\n\t\t+\n\t\t11\n\t\n\t=\n\t29\n\n. Subtracting 11\n from both sides of this equation yields \n\tx\n\t=\n\t18\n\n.

"}, {"id": "44d65912", "domain": "Algebra", "skill": "Systems of two linear equations in two variables", "difficulty": "E", "type": "mc", "stimulus": "

Angela is playing a video game. In this game, players can score points only by collecting coins and stars. Each coin is worth c points, and each star is worth s points.

  • The first time she played, Angela scored 700 points. She collected 20 coins and 10 stars.
  • The second time she played, Angela scored 850 points. She collected 25 coins and 12 stars.
\n", "stem": "

Which system of equations can be used to correctly determine the values of c and s ?

\n", "choices": [{"id": "A", "text": "

This answer choice consists(t)wo equations. 10 c, + 20 s = 700; 12 c, + 25 s = 850

\n"}, {"id": "B", "text": "

This answer choice consists(t)wo equations. 20 c, + 10 s = 700; 25 c, + 12 s = 850

\n"}, {"id": "C", "text": "

This answer choice consists(t)wo equations. 20 c, + 700 s = 10; 25 c, + 850 s = 12

\n"}, {"id": "D", "text": "

This answer choice consists(t)wo equations. 700 c, + 20 s = 10; 850 c, + 25 s = 12

\n"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. The number of coins collected can be multiplied by c to give the score from the points earned from coins. Similarly, the number of stars collected can be multiplied by s to give the score from the points earned from the stars. Therefore, the total score each time Angela played is 20 c, + 10 s = 700, and the total score the second time she played is 25 c, + 12 s = 850.

Choices A, C, and D are incorrect and may result from misidentifying the terms of the equation. Choice A switches coins and stars, choice C switches stars and points, and choice D misidentifies coins, stars, and points.

 

\n"}, {"id": "41fdc0b8", "domain": "Algebra", "skill": "Linear functions", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

\"The

The table above shows the population of Greenleaf, Idaho, for the years 2000 and 2010. If the relationship between population and year is linear, which of the following functions P models the population of Greenleaf t years after 2000?

\n", "choices": [{"id": "A", "text": "P(t) = 862 \u2212 1 point 6 \u00d7 t\n"}, {"id": "B", "text": "P(t) = 862 \u2212 16 \u00d7 t\n"}, {"id": "C", "text": "\n P(t) = 862 + 16 times, open parenthesis, t \u2212 2,000, close parenthesis\n"}, {"id": "D", "text": "P(t) = 862 \u2212 1 point 6 times, open parenthesis, t \u2212 2,000, close parenthesis\n"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. It is given that the relationship between population and year is linear; therefore, the function that models the population t years after 2000 is of the form P(t) = m, t + b, where m is the slope and b is the population when t = 0. In the year 2000, t = 0. Therefore, b = 862. The slope is given by m = (P(1)0, \u2212 P(0))/(10 \u2212 0, end fraction, which = (with numerator 846 \u2212 862, and denominator 10 \u2212 0, end fraction, which = \u221216)/(10, which = \u22121 point 6)). Therefore, P(t) = \u22121 point 6, t, + 862, which is equivalent to the equation in choice A.

Choice B is incorrect and may be the result of incorrectly calculating the slope as just the change in the value of P. Choice C is incorrect and may be the result of the same error as in choice B, in addition to incorrectly using t to represent the year, instead of the number of years after 2000. Choice D is incorrect and may be the result of incorrectly using t to represent the year instead of the number of years after 2000.

\n"}, {"id": "8b2a2a63", "domain": "Algebra", "skill": "Linear equations in two variables", "difficulty": "E", "type": "spr", "stimulus": "", "stem": "

The y-intercept of the graph of \n\ty\n\t=\n\t\n\t\t\n\t\t\t-\n\t\t\t6\n\t\t\tx\n\t\t\n\t\t-\n\t\t32\n\t\n\n in the xy-plane is 0,y. What is the value of y\n?

", "choices": [], "answerId": "-32", "acceptedAnswers": ["-32"], "rationale": "

The correct answer is -32. It’s given that the y-intercept of the graph of y=-6x-32 is 0,y. Substituting 0\n for x\n in this equation yields y=-60-32, or y=-32. Therefore, the value of y\n that corresponds to the y-intercept of the graph of y=-6x-32 in the xy-plane is -32.

"}, {"id": "70774aa4", "domain": "Algebra", "skill": "Linear equations in one variable", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

If \n\t\n\t\t5\n\t\tx\n\t\n\t=\n\t20\n\n, what is the value of \n\t15\n\tx\n\n?

", "choices": [{"id": "A", "text": "

7\n

"}, {"id": "B", "text": "

12\n

"}, {"id": "C", "text": "

23\n

"}, {"id": "D", "text": "

60\n

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. It’s given that 5x=20. Multiplying both sides of this equation by 3\n yields 15x=60. Therefore, the value of 15x is 60\n.

\n

Choice A is incorrect and may result from conceptual errors.

\n

Choice B is incorrect and may result from conceptual errors.

\n

Choice C is incorrect and may result from conceptual errors.

"}, {"id": "8a1544f1", "domain": "Algebra", "skill": "Linear equations in two variables", "difficulty": "E", "type": "mc", "stimulus": "
\n
\n \"The
\n
\n", "stem": "

What is the equation of the line shown in the xy-plane above?

\n", "choices": [{"id": "A", "text": "y = 3 x \u2212 3\n"}, {"id": "B", "text": "y = \u22123 x + 3\n"}, {"id": "C", "text": "y = one-third x \u2212 3\n"}, {"id": "D", "text": "y = \u2212one-third x + 3\n"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. Any line in the xy-plane can be defined by an equation in the form y = mx + b, where m is the slope of the line and b is the y-coordinate of the y-intercept of the line. From the graph, the y-intercept of the line is (0, 3). Therefore, b = 3. The slope of the line is the change in the value of y divided by the change in the value of x for any two points on the line. The line shown passes through (0, 3) and (1, 0), so m = (3 \u2212 zero)/(zero \u2212 1), or m = –3. Therefore, the equation of the line is y = –3x + 3.

Choices A and C are incorrect because the equations given in these choices represent a line with a positive slope. However, the line shown has a negative slope. Choice D is incorrect because the equation given in this choice represents a line with slope of \u2212one third. However, the line shown has a slope of  –3.

\n"}, {"id": "a9c04a21", "domain": "Algebra", "skill": "Linear equations in one variable", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

What is the solution to the equation 2 x + 3 = 7?

\n", "choices": [{"id": "A", "text": "

1

\n"}, {"id": "B", "text": "

1.5

\n"}, {"id": "C", "text": "

2

\n"}, {"id": "D", "text": "

4

\n"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. Subtracting 3 from both sides of the given equation yields 2 x = 4. Dividing both sides by 2 results in x = 2.

Choices A and B are incorrect and may result from computational errors. Choice D is incorrect. This is the value of 2 x.

\n"}, {"id": "27f5fff3", "domain": "Algebra", "skill": "Systems of two linear equations in two variables", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n\n

\n

If a new graph of three linear equations is created using the system of equations shown and the equation \n\t\n\t\tx\n\t\t+\n\t\t\n\t\t\t4\n\t\t\ty\n\t\t\n\t\n\t=\n\t-16\n\n, how many solutions x,y will the resulting system of three equations have?

", "choices": [{"id": "A", "text": "

Zero

"}, {"id": "B", "text": "

Exactly one

"}, {"id": "C", "text": "

Exactly two

"}, {"id": "D", "text": "

Infinitely many

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. A solution to a system of equations must satisfy each equation in the system. It follows that if an ordered pair x,y is a solution to the system, the point x,y lies on the graph in the xy-plane of each equation in the system. The only point that lies on each graph of the system of two linear equations shown is their intersection point 8,2.  It follows that if a new graph of three linear equations is created using the system of equations shown and the graph of x+4y=-16, this system has either zero solutions or one solution, the point 8,2. Substituting 8\n for x\n and 2\n for y\n in the equation x+4y=-16 yields 8+42=-16, or 16=-16. Since this equation is not true, the point 8,2 does not lie on the graph of x+4y=-16. Therefore, 8,2 is not a solution to the system of three equations. It follows that there are zero solutions to this system.

\n

Choice B is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

\n

Choice D is incorrect and may result from conceptual or calculation errors.

"}, {"id": "535fa6e6", "domain": "Algebra", "skill": "Linear equations in two variables", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

Davio bought some potatoes and celery. The potatoes cost $0.69 per pound, and the celery cost $0.99 per pound. If Davio spent $5.34 in total and bought twice as many pounds of celery as pounds of potatoes, how many pounds of celery did Davio buy?

", "choices": [{"id": "A", "text": "

2\n

"}, {"id": "B", "text": "

2.5

"}, {"id": "C", "text": "

2.67\n

"}, {"id": "D", "text": "

4\n

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. Let p represent the number of pounds of potatoes and let c represent the number of pounds of celery that Davio bought. It’s given that potatoes cost $0.69 per pound and celery costs $0.99 per pound. If Davio spent $5.34 in total, then the equation 0.69p+0.99c=5.34 represents this situation. It’s also given that Davio bought twice as many pounds of celery as pounds of potatoes; therefore, c=2p. Substituting 2p for c in the equation 0.69p+0.99c=5.34 yields 0.69p+0.992p=5.34, which is equivalent to 0.69p+1.98p=5.34, or 2.67p=5.34. Dividing both sides of this equation by 2.67 yields p=2. Substituting 2 for p in the equation c=2p yields c=22, or c=4. Therefore, Davio bought 4 pounds of celery.

\n

Choice A is incorrect. This is the number of pounds of potatoes, not the number of pounds of celery, Davio bought.

\n

Choice B is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

"}, {"id": "a73a5c22", "domain": "Algebra", "skill": "Linear functions", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

The function g\n is defined by gx=10x+8. What is the value of gx when \n\tx\n\t=\n\t8\n\n?

", "choices": [{"id": "A", "text": "

0\n

"}, {"id": "B", "text": "

8\n

"}, {"id": "C", "text": "

10\n

"}, {"id": "D", "text": "

88\n

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. The value of gx when x=8 can be found by substituting 8\n for x\n in the given equation gx=10x+8. This yields g8=108+8, or g8=88. Therefore, when x=8, the value of gx is 88\n.

\n

Choice A is incorrect. This is the value of x\n when gx=8, rather than the value of gx when x=8.

\n

Choice B is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

"}, {"id": "6fa593f1", "domain": "Algebra", "skill": "Linear equations in one variable", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

If \n\tx\n\t=\n\t40\n\n, what is the value of \n\tx\n\t+\n\t6\n\n?

", "choices": [{"id": "A", "text": "

34\n

"}, {"id": "B", "text": "

40\n

"}, {"id": "C", "text": "

46\n

"}, {"id": "D", "text": "

64\n

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. It's given that x=40. Adding 6\n to both sides of this equation yields x+6=40+6, or x+6=46. Therefore, the value of x+6 is 46\n.

\n

Choice A is incorrect. This is the value of x-6, not x+6.

\n

Choice B is incorrect. This is the value of x\n, not x+6.

\n

Choice D is incorrect. This is the value of x+24, not x+6.
 

"}, {"id": "8c515062", "domain": "Algebra", "skill": "Linear equations in one variable", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

A candle is made of 17\n ounces of wax. When the candle is burning, the amount of wax in the candle decreases by 1\n ounce every 4\n hours. If 6\n ounces of wax remain in this candle, for how many hours has it been burning?

", "choices": [{"id": "A", "text": "

3\n

"}, {"id": "B", "text": "

6\n

"}, {"id": "C", "text": "

24\n

"}, {"id": "D", "text": "

44\n

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. It’s given that the candle starts with 17\n ounces of wax and has 6\n ounces of wax remaining after a period of time has passed. The amount of wax the candle has lost during the time period can be found by subtracting the remaining amount of wax from the amount of wax the candle was made of, which yields 17-6 ounces, or 11\n ounces. This means the candle loses 11\n ounces of wax during that period of time. It’s given that the amount of wax decreases by 1\n ounce every 4\n hours. If h\n represents the number of hours the candle has been burning, it follows that 14=11h. Multiplying both sides of this equation by \n\t4\n\th\n\n yields \n\th\n\t=\n\t44\n\n. Therefore, the candle has been burning for 44\n hours. 

\n

Choice A is incorrect and may result from using the equation 14=h11 rather than 14=11h to represent the situation, and then rounding to the nearest whole number. 

\n

Choice B is incorrect. This is the amount of wax, in ounces, remaining in the candle, not the number of hours it has been burning. 

\n

Choice C is incorrect and may result from using the equation 14=6h rather than 14=11h to represent the situation. 

"}, {"id": "4b76c7f1", "domain": "Algebra", "skill": "Systems of two linear equations in two variables", "difficulty": "E", "type": "mc", "stimulus": "
\n

\n Equation 1: 2 x, + 7 y = 9. Equation 2: 8 x, + 28 y = a\n

\n
\n", "stem": "

In the given system of equations, a is a constant. If the system has infinitely many solutions, what is the value of a ?

\n", "choices": [{"id": "A", "text": "

4

\n"}, {"id": "B", "text": "

9

\n"}, {"id": "C", "text": "

36

\n"}, {"id": "D", "text": "

54

\n"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. A system of two linear equations has infinitely many solutions if one equation is equivalent to the other. This means that when the two equations are written in the same form, each coefficient or constant in one equation is equal to the corresponding coefficient or constant in the other equation multiplied by the same number. The equations in the given system of equations are written in the same form, with x and y on the left-hand side of the equation and a constant on the right-hand side of the equation. The coefficients of x and y in the second equation are equal to the coefficients of x and y, respectively, in the first equation multiplied by 4: 8 = 2 \u00d7 4 and 28 = 7 \u00d7 4. Therefore, the constant in the second equation must be equal to 4 times the constant in the first equation: a = 9 \u00d7 4, or a = 36.

Choices A, B, and D are incorrect. When a = 4, a = 9, or a = 54, the given system of equations has no solution.

\n"}, {"id": "b64e2c7f", "domain": "Algebra", "skill": "Linear inequalities in one or two variables", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

Monarch butterflies can fly only with a body temperature of at least 55.0 degrees Fahrenheit °F. If a monarch butterfly's body temperature is 51.3\n°F, what is the minimum increase needed in its body temperature, in °F, so that it can fly?

", "choices": [{"id": "A", "text": "

1.3\n

"}, {"id": "B", "text": "

3.7\n

"}, {"id": "C", "text": "

5.0\n

"}, {"id": "D", "text": "

6.3\n

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. It's given that monarch butterflies can fly only with a body temperature of at least 55.0 degrees Fahrenheit °F. Let x\n represent the minimum increase needed in the monarch butterfly's body temperature to fly. If the monarch butterfly's body temperature is 51.3°F, the inequality 51.3+x≥55.0 represents this situation. Subtracting 51.3 from both sides of this inequality yields x≥3.7. Therefore, if the monarch butterfly's body temperature is 51.3°F, the minimum increase needed in its body temperature, in °F, so that it can fly is 3.7.

\n

Choice A is incorrect. This is the minimum increase needed in body temperature if the monarch butterfly's body temperature is 53.7°F, not 51.3°F.

\n

Choice C is incorrect. This is the minimum increase needed in body temperature if the monarch butterfly's body temperature is 50.0°F, not 51.3°F.

\n

Choice D is incorrect. This is the minimum increase needed in body temperature if the monarch butterfly's body temperature is 48.7°F, not 51.3°F.

"}, {"id": "7d6928bd", "domain": "Algebra", "skill": "Linear inequalities in one or two variables", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

A cleaning service that cleans both offices and homes can clean at most 14\n places per day. Which inequality represents this situation, where f\n is the number of offices and h\n is the number of homes?

", "choices": [{"id": "A", "text": "

f+h≤14

"}, {"id": "B", "text": "

f+h≥14

"}, {"id": "C", "text": "

f-h≤14

"}, {"id": "D", "text": "

f-h≥14

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. It's given that the cleaning service cleans both offices and homes, where f\n is the number of offices and h\n is the number of homes the cleaning service can clean per day. Therefore, the expression \n\tf\n\t+\n\th\n\n represents the number of places the cleaning service can clean per day. It's also given that the cleaning service can clean at most 14\n places per day. Since \n\tf\n\t+\n\th\n\n represents the number of places the cleaning service can clean per day and the service can clean at most 14\n places per day, it follows that the inequality f+h≤14 represents this situation.

\n

Choice B is incorrect. This inequality represents a cleaning service that cleans at least 14\n places per day.

\n

Choice C is incorrect. This inequality represents a cleaning service that cleans at most 14\n more offices than homes per day.

\n

Choice D is incorrect. This inequality represents a cleaning service that cleans at least 14\n more offices than homes per day.

"}, {"id": "5ad6bc97", "domain": "Algebra", "skill": "Linear functions", "difficulty": "E", "type": "spr", "stimulus": "", "stem": "

fx=7x+1

\n

The function gives the total number of people on a company retreat with x\n managers. What is the total number of people on a company retreat with 7\n managers?

", "choices": [], "answerId": "50", "acceptedAnswers": ["50"], "rationale": "

The correct answer is 50\n. It's given that the function f\n gives the total number of people on a company retreat with x\n managers. It's also given that 7\n managers are on the company retreat. Substituting 7\n for x\n in the given function yields f7=77+1, or f7=50. Therefore, there are a total of 50\n people on a company retreat with 7\n managers.

"}, {"id": "a8e6bd75", "domain": "Algebra", "skill": "Linear functions", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

Which of the following is the graph of the equation y = 2 x \u2212 5 in the xy-plane?

\n", "choices": [{"id": "A", "text": "

 

\"The

 

\n"}, {"id": "B", "text": "

 

\"The

 

\n"}, {"id": "C", "text": "

 

\"The

 

\n"}, {"id": "D", "text": "

 

\"The

 

\n"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. In the xy-plane, the graph of the equation y = m x + b, where m and b are constants, is a line with slope m and y-intercept 0, b. Therefore, the graph of y = 2 x \u2212 5 in the xy-plane is a line with slope 2 and a y-intercept 0, \u22125. Having a slope of 2 means that for each increase in x by 1, the value of y increases by 2. Only the graph in choice D has a slope of 2 and crosses the y-axis at the point 0, \u22125. Therefore, the graph shown in choice D must be the correct answer.

Choices A, B, and C are incorrect. The graph of y = 2 x \u2212 5 in the xy-plane is a line with slope 2 and a y-intercept at the point 0, \u22125. The graph in choice A crosses the y-axis at the point 0, 2 point 5, not the point 0, \u22125, and it has a slope of one-half, not 2. The graph in choice B crosses the y-axis at the point 0, \u22125; however, the slope of this line is \u22122, not 2. The graph in choice C has a slope of 2; however, the graph crosses the y-axis at the point 0, 5, not the point 0, \u22125.

 

\n"}, {"id": "948087f2", "domain": "Algebra", "skill": "Linear inequalities in one or two variables", "difficulty": "M", "type": "mc", "stimulus": "
\n\t\n\t\t\t\n\t\t\t
y < or equal to, 3 x + 1
x \u2212 y > 1
\n", "stem": "

Which of the following ordered pairs (x, y) satisfies the system of inequalities above?

\n", "choices": [{"id": "A", "text": "

\u22122, \u22121

 

\n"}, {"id": "B", "text": "

\u22121, 3

 

\n"}, {"id": "C", "text": "

1, 5

 

\n"}, {"id": "D", "text": "

2, \u22121

 

\n"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. Any point (x, y) that is a solution to the given system of inequalities must satisfy both inequalities in the system. The second inequality in the system can be rewritten as x is greater than, y + 1. Of the given answer choices, only choice D satisfies this inequality, because inequality 2 is greater than, \u22121 + 1 is a true statement. The point 2, \u22121 also satisfies the first inequality.

Alternate approach: Substituting 2, \u22121 into the first inequality gives \u22121 < or equal to, 3 \u00d7 2, + 1, or \u22121 < or equal to 7, which is a true statement. Substituting 2, \u22121 into the second inequality gives 2 \u2212 \u22121, > 1, or 3 > 1, which is a true statement. Therefore, since 2, \u22121 satisfies both inequalities, it is a solution to the system.

Choice A is incorrect because substituting −2 for x and −1 for y in the first inequality gives \u22121 < or equal to, 3 \u00d7 \u22122, + 1, or \u22121 < or equal to \u22125, which is false. Choice B is incorrect because substituting −1 for x and 3 for y in the first inequality gives 3 < or equal to, 3 \u00d7 \u22121, + 1, or 3 < or equal to \u22122, which is false. Choice C is incorrect because substituting 1 for x and 5 for y in the first inequality gives 5 < or equal to, 3 \u00d7 1, + 1, or 5 < or equal to 4, which is false.

 

\n"}, {"id": "beca03de", "domain": "Advanced Math", "skill": "Nonlinear functions", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

A rectangle has a length that is 15\n times its width. The function y=15ww represents this situation, where y\n is the area, in square feet, of the rectangle and y>0. Which of the following is the best interpretation of 15w in this context?

", "choices": [{"id": "A", "text": "

The length of the rectangle, in feet

"}, {"id": "B", "text": "

The area of the rectangle, in square feet

"}, {"id": "C", "text": "

The difference between the length and the width of the rectangle, in feet

"}, {"id": "D", "text": "

 The width of the rectangle, in feet

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. It's given that a rectangle has a length that is 15\n times its width. It's also given that the function y=15ww represents this situation, where y\n is the area, in square feet, of the rectangle and y>0. The area of a rectangle can be calculated by multiplying the rectangle's length by its width. Since the rectangle has a length that is 15\n times its width, it follows that w\n represents the width of the rectangle, in feet, and \n\t15\n\tw\n\n represents the length of the rectangle, in feet. Therefore, the best interpretation of \n\t15\n\tw\n\n in this context is that it's the length of the rectangle, in feet.

\n

Choice B is incorrect. This is the best interpretation of y\n, not \n\t15\n\tw\n\n, in the given function.

\n

Choice C is incorrect and may result from conceptual errors.

\n

Choice D is incorrect. This is the best interpretation of w\n, not \n\t15\n\tw\n\n, in the given function.

"}, {"id": "f5c3e3b8", "domain": "Advanced Math", "skill": "Equivalent expressions", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

Which expression is equivalent to m4q4z-1mq5z3, where m\n, q\n, and z\n are positive?

", "choices": [{"id": "A", "text": "

m4q20z-3

"}, {"id": "B", "text": "

\n\t\n\t\tm\n\t\t5\n\t\n\t\n\t\tq\n\t\t9\n\t\n\t\n\t\tz\n\t\t2\n\t\n\n

"}, {"id": "C", "text": "

m6q8z-1

"}, {"id": "D", "text": "

m20q12z-2

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. Applying the commutative property of multiplication, the expression m4q4z-1mq5z3 can be rewritten as m4mq4q5z-1z3. For positive values of x\n, xaxb=xa+b. Therefore, the expression m4mq4q5z-1z3 can be rewritten as m4+1q4+5z-1+3, or m5q9z2.

\n

Choice A is incorrect and may result from multiplying, not adding, the exponents.

\n

Choice C is incorrect and may result from conceptual or calculation errors. 

\n

Choice D is incorrect and may result from conceptual or calculation errors. 

"}, {"id": "a5663025", "domain": "Advanced Math", "skill": "Nonlinear equations in one variable and systems of equations in two variables ", "difficulty": "M", "type": "mc", "stimulus": "
\n
\n \"The
\n
\n", "stem": "

A system of equations consists of a quadratic equation and a linear equation. The equations in this system are graphed in the xy-plane above. How many solutions does this system have?

\n", "choices": [{"id": "A", "text": "

0

\n"}, {"id": "B", "text": "

1

\n"}, {"id": "C", "text": "

2

\n"}, {"id": "D", "text": "

3

\n"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. The solutions to a system of two equations correspond to points where the graphs of the equations intersect. The given graphs intersect at 2 points; therefore, the system has 2 solutions.

Choice A is incorrect because the graphs intersect. Choice B is incorrect because the graphs intersect more than once. Choice D is incorrect. It’s not possible for the graph of a quadratic equation and the graph of a linear equation to intersect more than twice.

\n"}, {"id": "3c95093c", "domain": "Advanced Math", "skill": "Nonlinear equations in one variable and systems of equations in two variables ", "difficulty": "E", "type": "mc", "stimulus": "
\n

\n 6 x \u2212 9 y, > 12\n

\n
\n", "stem": "

Which of the following inequalities is equivalent to the inequality above?

\n", "choices": [{"id": "A", "text": "x \u2212 y, > 2\n"}, {"id": "B", "text": "2 x \u2212 3 y, > 4\n"}, {"id": "C", "text": "3 x \u2212 2 y, > 4\n"}, {"id": "D", "text": "3 y \u2212 2 x, > 2\n"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. Both sides of the given inequality can be divided by 3 to yield 2 x \u2212 3 y, > 4.

Choices A, C, and D are incorrect because they are not equivalent to (do not have the same solution set as) the given inequality. For example, the ordered pair 0, \u22121 point 5 is a solution to the given inequality, but it is not a solution to any of the inequalities in choices A, C, or D.

\n"}, {"id": "d0a7871e", "domain": "Advanced Math", "skill": "Nonlinear equations in one variable and systems of equations in two variables ", "difficulty": "M", "type": "mc", "stimulus": "
\n\t

y = x + 1, ; y = x\u00b2 + x

\n
\n", "stem": "

If x, y is a solution to the system of equations above, which of the following could be the value of x ?

\n", "choices": [{"id": "A", "text": "

–1

\n"}, {"id": "B", "text": "

0

\n"}, {"id": "C", "text": "

2

\n"}, {"id": "D", "text": "

3

\n"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. It is given that y = x + 1 and y = x2 + x. Setting the values for y equal to each other yields x + 1 = x2 + x. Subtracting x from each side of this equation yields x2 = 1. Therefore, x can equal 1 or –1. Of these, only –1 is given as a choice.

Choice B is incorrect. If x = 0, then x + 1 = 1, but x2 + x = 02 + 0 = 0 ≠︀ 1. Choice C is incorrect. If x = 2, then x + 1 = 3, but x2 + x = 22 + 2 = 6 ≠︀ 3. Choice D is incorrect. If x = 3, then x + 1 = 4, but x2 + x = 32 + 3 = 12 ≠︀ 4.

 

\n"}, {"id": "dd4ab4c4", "domain": "Advanced Math", "skill": "Equivalent expressions", "difficulty": "M", "type": "mc", "stimulus": "
\n

\n 4 a\u00b2, + 20 a b, + 25 b\u00b2\n

\n
\n", "stem": "

Which of the following is a factor of the polynomial above?

\n", "choices": [{"id": "A", "text": "

\n a + b\n

\n"}, {"id": "B", "text": "

\n 2 a + 5 b\n

\n"}, {"id": "C", "text": "

\n 4 a + 5 b\n

\n"}, {"id": "D", "text": "

\n 4 a + 25 b\n

\n"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. The first and last terms of the polynomial are both squares such that 4 a, squared = open parenthesis, 2 a, close parenthesis, squared and 25 b\u00b2 = open parenthesis, 5 b, close parenthesis, squared. The second term is twice the product of the square root of the first and last terms: 20 a, b = 2, \u00d7 2 a, \u00d7 5 b. Therefore, the polynomial is the square of a binomial such that 4 a, squared, + 20 a, b, + 25 b\u00b2 = open parenthesis, 2 a, + 5 b, close parenthesis, squared, and open parenthesis, 2 a, + 5 b, close parenthesis is a factor.

Choice A is incorrect and may be the result of incorrectly factoring the polynomial. Choice C is incorrect and may be the result of dividing the second and third terms of the polynomial by their greatest common factor. Choice D is incorrect and may be the result of not factoring the coefficients.

\n"}, {"id": "b8caaf84", "domain": "Advanced Math", "skill": "Equivalent expressions", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

If p = 3 x, + 4 and v = x + 5, which of the following is equivalent to p v, \u2212 2 p, + v ?

\n", "choices": [{"id": "A", "text": "

\n 3 x\u00b2, plus, 12 x, + 7\n

\n"}, {"id": "B", "text": "

\n 3 x\u00b2, plus, 14 x, + 17\n

\n"}, {"id": "C", "text": "

\n 3 x\u00b2, plus, 19 x, + 20\n

\n"}, {"id": "D", "text": "

\n 3 x\u00b2, plus, 26 x, + 33\n

\n"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. It’s given that p = 3 x + 4 and v = x + 5. Substituting the values for p and v into the expression p v, \u2212 2 p, + v yields open parenthesis, 3 x + 4, close parenthesis, times, open parenthesis, x + 5, close parenthesis, minus, 2 times, open parenthesis, 3 x + 4, close parenthesis, + x, + 5. Multiplying the terms open parenthesis, 3 x + 4, close parenthesis, times, open parenthesis, x + 5, close parenthesis yields 3 x\u00b2, + 4 x, + 15 x, + 20. Using the distributive property to rewrite \u22122 times, open parenthesis, 3 x + 4, close parenthesis yields \u22126 x \u2212 8. Therefore, the entire expression can be represented as 3 x\u00b2, + 4 x, + 15 x, + 20, \u2212 6 x, \u2212 8, + x, + 5. Combining like terms yields 3 x\u00b2, + 14 x, + 17.

Choice A is incorrect and may result from subtracting, instead of adding, the term x + 5. Choice C is incorrect. This is the result of multiplying the terms open parenthesis, 3 x + 4, close parenthesis, times, open parenthesis, x + 5, close parenthesis. Choice D is incorrect and may result from distributing 2, instead of \u22122, to the term 3 x + 4.

\n"}, {"id": "7f81d0c3", "domain": "Advanced Math", "skill": "Nonlinear equations in one variable and systems of equations in two variables ", "difficulty": "M", "type": "mc", "stimulus": "
\n

\n x\u00b2, \u2212 x, \u2212 1 = 0\n

\n
\n", "stem": "

What values satisfy the equation above?

\n", "choices": [{"id": "A", "text": "

\n x = 1 and x = 2

\n"}, {"id": "B", "text": "

\n x = \u2212one half and x = three halves

\n"}, {"id": "C", "text": "

\n x = (1 + the square root(5))/(2) and x = (1 \u2212 the square root(5))/(2)

\n"}, {"id": "D", "text": "

\n x = (\u22121 + the square root(5))/(2) and x = (\u22121 \u2212 the square root(5))/(2)

\n"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. Using the quadratic formula to solve the given expression yields x = (negative, open parenthesis, \u22121, close parenthesis, + or minus, the square root(o)pen parenthesis, \u22121, close parenthesis, squared, minus, 4 \u00d7 1 \u00d7 \u22121, end root, and denominator, 2 \u00d7 1, end fraction, which = the fraction with numerator 1, + or minus, the square root(5))/(2). Therefore, x = (1 + the square root(5))/(2) and x = (1 \u2212 the square root(5))/(2) satisfy the given equation.

Choices A and B are incorrect and may result from incorrectly factoring or incorrectly applying the quadratic formula. Choice D is incorrect and may result from a sign error.

\n"}, {"id": "e312081b", "domain": "Advanced Math", "skill": "Equivalent expressions", "difficulty": "E", "type": "mc", "stimulus": "
\n\t

\"\"

\n
\n", "stem": "

Which of the following is equivalent to the given expression?

\n", "choices": [{"id": "A", "text": "

3 x \u2212 2

\n"}, {"id": "B", "text": "

3 x + 2

\n"}, {"id": "C", "text": "

3 x \u2212 8

\n"}, {"id": "D", "text": "

3 x + 8

\n"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. Using the associative and commutative properties of addition, the given expression open parenthesis, x + 5, close parenthesis, plus, open parenthesis, 2 x \u2212 3, close parenthesis can be rewritten as open parenthesis, x + 2 x, close parenthesis, plus, open parenthesis, 5 \u2212 3, close parenthesis. Adding these like terms results in 3 x + 2.

Choice A is incorrect and may result from adding open parenthesis, x \u2212 5, close parenthesis, plus, open parenthesis, 2 x + 3, close parenthesis. Choice C is incorrect and may result from adding open parenthesis, x \u2212 5, close parenthesis, plus, open parenthesis, 2 x \u2212 3, close parenthesis. Choice D is incorrect and may result from adding open parenthesis, x + 5, close parenthesis, plus, open parenthesis, 2 x + 3, close parenthesis.

 

\n"}, {"id": "52931bfa", "domain": "Advanced Math", "skill": "Equivalent expressions", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

Which expression is equivalent to 8xx-7-3x-72x-14, where x>7?

", "choices": [{"id": "A", "text": "

x-75

"}, {"id": "B", "text": "

8x-32

"}, {"id": "C", "text": "

8x2-3x-142x-14

"}, {"id": "D", "text": "

8x2-3x-772x-14

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. The given expression has a common factor of 2\n in the denominator, so the expression can be rewritten as 8xx-7-3x-72x-7. The three terms in this expression have a common factor of x-7. Since it's given that x>7, x\n can't be equal to 7\n, which means x-7 can't be equal to 0\n. Therefore, each term in the expression, 8xx-7-3x-72x-7, can be divided by x-7, which gives 8x-32.

\n

Choice A is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

\n

Choice D is incorrect and may result from conceptual or calculation errors.

"}, {"id": "1e003284", "domain": "Advanced Math", "skill": "Nonlinear equations in one variable and systems of equations in two variables ", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

x=49

\n

y=x+9

\n

The graphs of the given equations intersect at the point x,y in the xy-plane. What is the value of y\n?

", "choices": [{"id": "A", "text": "

16\n

"}, {"id": "B", "text": "

40\n

"}, {"id": "C", "text": "

81\n

"}, {"id": "D", "text": "

130\n

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. It's given that the graphs of the given equations intersect at the point x,y in the xy-plane. It follows that x,y represents a solution to the system consisting of the given equations. The first equation given is \n\tx\n\t=\n\t49\n\n. Substituting 49\n for x\n in the second equation given, \n\ty\n\t=\n\t\n\t\t\n\t\t\tx\n\t\t\n\t\t+\n\t\t9\n\t\n\n, yields y=49+9, which is equivalent to y=7+9, or y=16. It follows that the graphs of the given equations intersect at the point 49,16. Therefore, the value of y\n is 16\n.

\n

Choice B is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

\n

Choice D is incorrect and may result from conceptual or calculation errors.

"}, {"id": "91e7ea5e", "domain": "Advanced Math", "skill": "Nonlinear functions", "difficulty": "H", "type": "mc", "stimulus": "
\n

\n h(x) = 2 times, open parenthesis, x \u2212 4, close parenthesis, squared, \u2212 32\n

\n
\n", "stem": "

The quadratic function h is defined as shown. In the xy-plane, the graph of y = h(x) intersects the x-axis at the points 0, 0and t, 0, where t is a constant. What is the value of t ?

\n", "choices": [{"id": "A", "text": "

1

\n"}, {"id": "B", "text": "

2

\n"}, {"id": "C", "text": "

4

\n"}, {"id": "D", "text": "

8

\n"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. It’s given that the graph of y = h(x) intersects the x-axis at the point 0, 0 and the point t, 0, where t is a constant. Since this graph intersects the x-axis when y = 0 or when h(x) = 0, it follows that h(0) = 0 and h(t) = 0. If h(t) = 0, then 0 = 2 times, open parenthesis, t \u2212 4, close parenthesis, squared, \u2212 32. Adding 32 to both sides of this equation yields 32 = 2 times, open parenthesis, t \u2212 4, close parenthesis, squared. Dividing both sides of this equation by 2 yields 16 = open parenthesis, t \u2212 4, close parenthesis, squared. Taking the square root of both sides of this equation yields 4 = t \u2212 4. Adding 4 to both sides of this equation yields 8 = t. Therefore, the value of t is 8.

Choices A, B, and C are incorrect and may result from calculation errors.

\n"}, {"id": "3a9d60b2", "domain": "Advanced Math", "skill": "Nonlinear equations in one variable and systems of equations in two variables ", "difficulty": "H", "type": "spr", "stimulus": "", "stem": "

24-x+34-x=25

\n

What is the positive solution to the given equation?

", "choices": [], "answerId": "9", "acceptedAnswers": ["9"], "rationale": "

The correct answer is 9\n. The given equation can be rewritten as 54-x=25. Dividing each side of this equation by 5\n yields 4-x=5. By the definition of absolute value, if 4-x=5, then 4-x=5 or 4-x=-5. Subtracting 4\n from each side of the equation 4-x=5 yields -x=1. Dividing each side of this equation by -1\n yields x=-1. Similarly, subtracting 4\n from each side of the equation 4-x=-5 yields -x=-9. Dividing each side of this equation by -1\n yields x=9. Therefore, since the two solutions to the given equation are -1\n and 9\n, the positive solution to the given equation is 9\n.

"}, {"id": "8490cc45", "domain": "Advanced Math", "skill": "Nonlinear functions", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

The function f\n is defined by f(x)=(-8)(2)x+22. What is the y-intercept of the graph of y=f(x) in the xy-plane?

", "choices": [{"id": "A", "text": "

(0,14)

"}, {"id": "B", "text": "

(0,2)

"}, {"id": "C", "text": "

(0,22)

"}, {"id": "D", "text": "

(0,-8)

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. The y-intercept of the graph of y=fx in the xy-plane occurs at the point on the graph where \n\tx\n\t=\n\t0\n\n. In other words, when \n\tx\n\t=\n\t0\n\n, the corresponding value of fx is the y-coordinate of the y-intercept. Substituting 0\n for x\n in the given equation yields f0=-820+22, which is equivalent to f0=-81+22, or f0=14. Thus, when \n\tx\n\t=\n\t0\n\n, the corresponding value of fx is 14\n. Therefore, the y-intercept of the graph of y=fx in the xy-plane is 0,14.

\n

Choice B is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

\n

Choice D is incorrect. This could be the y-intercept for fx=-82x, not fx=-82x+22.

"}, {"id": "4fbffc0a", "domain": "Advanced Math", "skill": "Nonlinear functions", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n

\n

The graph shows the height above ground, in meters, of a ball x\n seconds after the ball was launched upward from a platform. Which statement is the best interpretation of the marked point 1.0,4.8 in this context?

", "choices": [{"id": "A", "text": "

1.0\n second after being launched, the ball's height above ground is 4.8\n meters.

"}, {"id": "B", "text": "

4.8\n seconds after being launched, the ball's height above ground is 1.0\n meter.

"}, {"id": "C", "text": "

The ball was launched from an initial height of 1.0\n meter with an initial velocity of 4.8\n meters per second.

"}, {"id": "D", "text": "

The ball was launched from an initial height of 4.8\n meters with an initial velocity of 1.0\n meter per second.

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. It's given that the graph shows the height above ground, in meters, of a ball x\n seconds after the ball was launched upward from a platform. In the graph shown, the x-axis represents time, in seconds, and the y-axis represents the height of the ball above ground, in meters. It follows that for the marked point 1.0,4.8, 1.00\n represents the time, in seconds, after the ball was launched upward from a platform and 4.80\n represents the height of the ball above ground, in meters. Therefore, the best interpretation of the marked point 1.0,4.8 is 1.00\n second after being launched, the ball's height above ground is 4.80\n meters.

\n

Choice B is incorrect and may result from conceptual errors.

\n

Choice C is incorrect and may result from conceptual errors.

\n

Choice D is incorrect and may result from conceptual errors.

"}, {"id": "ba0edc30", "domain": "Advanced Math", "skill": "Nonlinear equations in one variable and systems of equations in two variables ", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

\n\t\n\t\t\n\t\t\tx\n\t\t\t2\n\t\t\n\t\t-\n\t\t\n\t\t\t2\n\t\t\tx\n\t\t\n\t\t-\n\t\t9\n\t\n\t=\n\t0\n\n

\n

One solution to the given equation can be written as 1+k, where k\n is a constant. What is the value of k\n?

", "choices": [{"id": "A", "text": "

8\n

"}, {"id": "B", "text": "

10\n

"}, {"id": "C", "text": "

20\n

"}, {"id": "D", "text": "

40\n

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. Adding 9\n to each side of the given equation yields \n\t\n\t\t\n\t\t\tx\n\t\t\t2\n\t\t\n\t\t-\n\t\t\n\t\t\t2\n\t\t\tx\n\t\t\n\t\n\t=\n\t9\n\n. To complete the square, adding 1\n to each side of this equation yields x2-2x+1=9+1, or x-12=10. Taking the square root of each side of this equation yields x-1=\u00b110. Adding 1\n to each side of this equation yields x=1\u00b110. Since it's given that one of the solutions to the equation can be written as 1+k, the value of k\n must be 10\n.

\n

Alternate approach: It's given that 1+k is a solution to the given equation. It follows that x=1+k. Substituting 1+k for x\n in the given equation yields 1+k2-21+k-9=0, or 1+k1+k-21+k-9=0. Expanding the products on the left-hand side of this equation yields 1+2k+k-2-2k-9=0, or \n\t\n\t\tk\n\t\t-\n\t\t10\n\t\n\t=\n\t0\n\n. Adding 10\n to each side of this equation yields \n\tk\n\t=\n\t10\n\n.

\n

Choice A is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

\n

Choice D is incorrect and may result from conceptual or calculation errors.

"}, {"id": "fc3d783a", "domain": "Advanced Math", "skill": "Nonlinear equations in one variable and systems of equations in two variables ", "difficulty": "H", "type": "spr", "stimulus": "", "stem": "

In the \n\tx\n\ty\n\n-plane, a line with equation \n\t\n\t\t2\n\t\ty\n\t\n\t=\n\t4.5\n\n intersects a parabola at exactly one point. If the parabola has equation \n\ty\n\t=\n\t\n\t\t\n\t\t\t-\n\t\t\t4\n\t\t\t\n\t\t\t\tx\n\t\t\t\t2\n\t\t\t\n\t\t\n\t\t+\n\t\t\n\t\t\tb\n\t\t\tx\n\t\t\n\t\n\n, where b\n is a positive constant, what is the value of b\n?

", "choices": [], "answerId": "6", "acceptedAnswers": ["6"], "rationale": "

The correct answer is 6\n. It’s given that a line with equation 2y=4.5 intersects a parabola with equation y=-4x2+bx, where b\n is a positive constant, at exactly one point in the xy-plane. It follows that the system of equations consisting of 2y=4.5 and y=-4x2+bx has exactly one solution. Dividing both sides of the equation of the line by 2\n yields y=2.25. Substituting 2.25\n for y\n in the equation of the parabola yields 2.25=-4x2+bx. Adding 4x2 and subtracting bx from both sides of this equation yields 4x2-bx+2.25=0. A quadratic equation in the form of ax2+bx+c=0, where a\n, b\n, and c\n are constants, has exactly one solution when the discriminant, b2-4ac, is equal to zero. Substituting 4\n for a\n and 2.25\n for c\n in the expression b2-4ac and setting this expression equal to 0\n yields b2-4(4)(2.25)=0, or b2-36=0. Adding 36\n to each side of this equation yields b2=36. Taking the square root of each side of this equation yields b=±6. It’s given that b\n is positive, so the value of b\n is 6\n.

"}, {"id": "a9084ca4", "domain": "Advanced Math", "skill": "Nonlinear functions", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

fx=9,0000.66x

\n

The given function f\n models the number of advertisements a company sent to its clients each year, where x\n represents the number of years since 1997, and 0≤x≤5. If y=fx is graphed in the xy-plane, which of the following is the best interpretation of the y-intercept of the graph in this context?

", "choices": [{"id": "A", "text": "

The minimum estimated number of advertisements the company sent to its clients during the 5\n years was 1,708\n.

"}, {"id": "B", "text": "

The minimum estimated number of advertisements the company sent to its clients during the 5\n years was 9,000\n.

"}, {"id": "C", "text": "

The estimated number of advertisements the company sent to its clients in 1997 was 1,708\n.

"}, {"id": "D", "text": "

The estimated number of advertisements the company sent to its clients in 1997 was 9,000\n.

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. The y-intercept of a graph in the xy-plane is the point where \n\tx\n\t=\n\t0\n\n. For the given function f, the y-intercept of the graph of y=fx in the xy-plane can be found by substituting 0\n for x\n in the equation y=9,0000.66x, which gives y=9,0000.660. This is equivalent to y=9,0001, or \n\ty\n\t=\n\t9,000\n\n. Therefore, the y-intercept of the graph of y=fx is 0,9,000. It’s given that the function f models the number of advertisements a company sent to its clients each year. Therefore, fx represents the estimated number of advertisements the company sent to its clients each year. It's also given that x\n represents the number of years since 1997. Therefore, \n\tx\n\t=\n\t0\n\n represents 0\n years since 1997, or 1997. Thus, the best interpretation of the y-intercept of the graph of y=fx is that the estimated number of advertisements the company sent to its clients in 1997 was 9,000\n.

\n

Choice A is incorrect and may result from conceptual or calculation errors.

\n

Choice B is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

"}, {"id": "2c6f214f", "domain": "Advanced Math", "skill": "Nonlinear functions", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

The first term of a sequence is 9\n. Each term after the first is 4\n times the preceding term. If w\n represents the n\nth term of the sequence, which equation gives w\n in terms of n\n?

", "choices": [{"id": "A", "text": "

w=49n

"}, {"id": "B", "text": "

w=49n-1

"}, {"id": "C", "text": "

w=94n

"}, {"id": "D", "text": "

w=94n-1

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. Since w\n represents the n\nth term of the sequence and 9\n is the first term of the sequence, the value of w\n is 9\n when the value of n\n is 1\n. Since each term after the first is 4\n times the preceding term, the value of w\n is 94 when the value of n\n is 2\n. Therefore, the value of w\n is 944, or 942, when the value of n\n is 3\n. More generally, the value of w\n is 94n-1 for a given value of n\n. Therefore, the equation w=94n-1 gives w\n in terms of n\n.

\n

Choice A is incorrect. This equation describes a sequence for which the first term is 36\n, rather than 9\n, and each term after the first is 9\n, rather than 4\n, times the preceding term. 

\n

Choice B is incorrect. This equation describes a sequence for which the first term is 4\n, rather than 9\n, and each term after the first is 9\n, rather than 4\n, times the preceding term.

\n

Choice C is incorrect. This equation describes a sequence for which the first term is 36\n, rather than 9\n.

"}, {"id": "4661e2a9", "domain": "Advanced Math", "skill": "Nonlinear equations in one variable and systems of equations in two variables ", "difficulty": "H", "type": "mc", "stimulus": "
\n

\n Equation 1: x \u2212 y = 1. Equation 2: x + y = x\u00b2 \u2212 3\n

\n
\n", "stem": "

Which ordered pair is a solution to the system of equations above?

\n", "choices": [{"id": "A", "text": "

\n 1 + the square root(3), comma, the square root(3)

\n"}, {"id": "B", "text": "

\n the square root(3), comma, the negative(t)he square root(3)

\n"}, {"id": "C", "text": "

\n 1 + the square root(5), comma, the square root(5)

\n"}, {"id": "D", "text": "

\n the square root(5), comma, \u22121 + the square root(5)

\n"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. The solution to the given system of equations can be found by solving the first equation for x, which gives x = y + 1, and substituting that value of x into the second equation which gives y + 1, + y = open parenthesis, y + 1, close parenthesis, squared, \u2212 3. Rewriting this equation by adding like terms and expanding open parenthesis, y + 1, close parenthesis, squared gives 2 y + 1 = y\u00b2 + 2 y, \u2212 2. Subtracting 2 y from both sides of this equation gives 1 = y\u00b2 \u2212 2. Adding to 2 to both sides of this equation gives 3 = y\u00b2. Therefore, it follows that y = + or \u2212 the square root(3). Substituting the square root(3) for y in the first equation yields x \u2212 the square root(3) = 1. Adding the square root(3) to both sides of this equation yields x = 1 + the square root(3). Therefore, the ordered pair 1 + the square root(3), end root,, the square root(3) is a solution to the given system of equations.

Choice B is incorrect. Substituting the square root(3) for x and the negative(t)he square root(3) for y in the first equation yields the square root(3), end root, minus, the negative(t)he square root(3) = 1, or 2 \u00d7 the square root(3) = 1, which isn’t a true statement. Choice C is incorrect. Substituting 1 + the square root(5) for x and the square root(5) for y in the second equation yields open parenthesis, 1 + the square root(5), close parenthesis, + the square root(5) = open parenthesis, 1 + the square root(5), close parenthesis, squared, \u2212 3, or 1 plus, 2 \u00d7 the square root(5) = 2 \u00d7 the square root(5), + 3, which isn’t a true statement. Choice D is incorrect. Substituting the square root(5) for x and open parenthesis, \u22121 + the square root(5), close parenthesis for y in the second equation yields the square root(5) plus, open parenthesis, \u22121 + the square root(5), close parenthesis = the square root(5), squared, \u2212 3, or 2 \u00d7 the square root(5), \u2212 1 = 2, which isn’t a true statement.

\n"}, {"id": "6abec9a8", "domain": "Advanced Math", "skill": "Nonlinear functions", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n

\n

What is the y\n-intercept of the graph shown?

", "choices": [{"id": "A", "text": "

-1,-9

"}, {"id": "B", "text": "

0,-5

"}, {"id": "C", "text": "

0,-4

"}, {"id": "D", "text": "

0,0

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. The y-intercept of a graph in the xy-plane is the point x,y on the graph where \n\tx\n\t=\n\t0\n\n. At \n\tx\n\t=\n\t0\n\n, the corresponding value of y\n is -5\n. Therefore, the y-intercept of the graph shown is 0,-5.

\n

Choice A is incorrect and may result from conceptual errors.

\n

Choice C is incorrect. This is the y-intercept of a graph in the xy-plane that intersects the y-axis at \n\ty\n\t=\n\t-4\n\n, not \n\ty\n\t=\n\t-5\n\n.

\n

Choice D is incorrect. This is the y-intercept of a graph in the xy-plane that intersects the y-axis at \n\ty\n\t=\n\t0\n\n, not \n\ty\n\t=\n\t-5\n\n.

"}, {"id": "ad2ec615", "domain": "Advanced Math", "skill": "Equivalent expressions", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

Which of the following is equivalent to the expression x to the fourth power, \u2212 x\u00b2, \u2212 6 ?

\n", "choices": [{"id": "A", "text": "

\n open parenthesis, x\u00b2 + 1, close parenthesis, times, open parenthesis, x\u00b2 \u2212 6, close parenthesis\n

\n"}, {"id": "B", "text": "

\n open parenthesis, x\u00b2 + 2, close parenthesis, times, open parenthesis, x\u00b2 \u2212 3, close parenthesis\n

\n"}, {"id": "C", "text": "

\n open parenthesis, x\u00b2 + 3, close parenthesis, times, open parenthesis, x\u00b2 \u2212 2, close parenthesis\n

\n"}, {"id": "D", "text": "

\n open parenthesis, x\u00b2 + 6, close parenthesis, times, open parenthesis, x\u00b2 \u2212 1, close parenthesis\n

\n"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. The term x4 can be factored as x\u00b2, times, x\u00b2. Factoring –6 as 2 \u00d7 \u22123 yields values that add to –1, the coefficient of x2 in the expression.

Choices A, C, and D are incorrect and may result from finding factors of –6 that don’t add to the coefficient of x2 in the original expression.

\n"}, {"id": "42c71eb5", "domain": "Advanced Math", "skill": "Equivalent expressions", "difficulty": "M", "type": "mc", "stimulus": "
\n

\n open parenthesis, 2 x + 5, close parenthesis, squared, minus, open parenthesis, x \u2212 2, close parenthesis, + 2 times, open parenthesis, x + 3, close parenthesis\n

\n
\n", "stem": "

Which of the following is equivalent to the expression above?

\n", "choices": [{"id": "A", "text": "

\n 4 x\u00b2, + 21 x, + 33\n

\n"}, {"id": "B", "text": "

\n 4 x\u00b2, + 21 x, + 29\n

\n"}, {"id": "C", "text": "

\n 4 x\u00b2, + x, + 29\n

\n"}, {"id": "D", "text": "

\n 4 x\u00b2, + x, + 33\n

\n"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. The given expression can be rewritten as open parenthesis, 2 x + 5, close parenthesis, squared, plus, \u22121 times, open parenthesis, x \u2212 2, close parenthesis, plus, 2 times, open parenthesis, x + 3, close parenthesis. Applying the distributive property, the expression  \u22121 times, open parenthesis, x \u2212 2, close parenthesis, plus, 2 times, open parenthesis, x + 3, close parenthesiscan be rewritten as \u2212one \u00d7 x, plus, \u22121 \u00d7 \u22122, plus, 2 \u00d7 x, plus, 2 \u00d7 3, or \u2212x + 2, + 2 x, + 6. Adding like terms yields x + 8. Substituting x + 8 for  \u22121, times, open parenthesis, x \u2212 2, close parenthesis, plus, 2 times, open parenthesis, x + 3, close parenthesis in the given expression yields open parenthesis, 2 x + 5, close parenthesis, squared, + x, + 8. By the rules of exponents, the expression open parenthesis, 2 x + 5, close parenthesis, squared is equivalent to open parenthesis, 2 x + 5, close parenthesis, times, open parenthesis, 2 x + 5, close parenthesis. Applying the distributive property, this expression can be rewritten as 2 x \u00d7 2x, plus, 2 x \u00d7 5, plus, 5 \u00d7 2 x, plus, 5 \u00d7 5, or 4 x\u00b2, + 10 x, + 10 x, + 25. Adding like terms gives 4 x\u00b2, + 20 x, + 25. Substituting 4 x\u00b2, + 20 x, + 25 for open parenthesis, 2 x + 5, close parenthesis, squared in the rewritten expression yields 4 x\u00b2, + 20 x, + 25, + x, + 8, and adding like terms yields 4 x\u00b2, + 21 x, + 33.

Choices B, C, and D are incorrect. Choices C and D may result from rewriting the expression open parenthesis, 2 x + 5, close parenthesis, squared as 4 x\u00b2, + 25, instead of as 4 x\u00b2, + 20 x, + 25. Choices B and C may result from rewriting the expression negative, open parenthesis, x \u2212 2, close parenthesis as \u2212x \u2212 2, instead of \u2212x + 2.

\n"}, {"id": "52b1700c", "domain": "Advanced Math", "skill": "Nonlinear functions", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
Time (years)Total amount (dollars)
0604.00\n
1606.42\n
2608.84\n
\n

Rosa opened a savings account at a bank. The table shows the exponential relationship between the time t\n, in years, since Rosa opened the account and the total amount n\n, in dollars, in the account. If Rosa made no additional deposits or withdrawals, which of the following equations best represents the relationship between t\n and n\n?

", "choices": [{"id": "A", "text": "

n=1+604t

"}, {"id": "B", "text": "

n=1+0.004t

"}, {"id": "C", "text": "

n=6041+0.004t

"}, {"id": "D", "text": "

n=0.0041+604t

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. It’s given that the relationship between t\n and n\n is exponential. The table shows that the value of n\n increases as the value of t\n increases. Therefore, the relationship between t\n and n\n can be represented by an increasing exponential equation of the form n=a1+bt, where a\n and b\n are positive constants. The table shows that when \n\tt\n\t=\n\t0\n\n, \n\tn\n\t=\n\t604\n\n. Substituting 0\n for t\n and 604\n for n\n in the equation n=a1+bt yields 604=a1+b0, which is equivalent to 604=a1, or 604=a. Substituting 604\n for a\n in the equation n=a1+bt yields n=6041+bt. The table also shows that when \n\tt\n\t=\n\t1\n\n, \n\tn\n\t=\n\t606.42\n\n. Substituting 1\n for t\n and 606.42\n for n\n in the equation n=6041+bt yields 606.42=6041+b1, or 606.42=6041+b. Dividing both sides of this equation by 604\n yields approximately 1.004=1+b. Subtracting 1\n from both sides of this equation yields that the value of b\n is approximately 0.004\n. Substituting 0.004\n for b\n in the equation n=6041+bt yields n=6041+0.004t. Therefore, of the choices, choice C best represents the relationship between t\n and n\n.

\n

Choice A is incorrect and may result from conceptual or calculation errors.

\n

Choice B is incorrect and may result from conceptual or calculation errors.

\n

Choice D is incorrect and may result from conceptual or calculation errors.

"}, {"id": "371cbf6b", "domain": "Advanced Math", "skill": "Equivalent expressions", "difficulty": "H", "type": "mc", "stimulus": "
\n

\n open parenthesis, a x + 3, close parenthesis, times, open parenthesis, 5 x\u00b2, \u2212 b x, + 4, close parenthesis = 20 x\u00b3, \u2212 9 x\u00b2, \u2212 2 x, + 12\n

\n
\n", "stem": "

The equation above is true for all x, where a and b are constants. What is the value of ab ?

\n", "choices": [{"id": "A", "text": "

18

\n"}, {"id": "B", "text": "

20

\n"}, {"id": "C", "text": "

24

\n"}, {"id": "D", "text": "

40

\n"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. If the equation is true for all x, then the expressions on both sides of the equation will be equivalent. Multiplying the polynomials on the left-hand side of the equation gives 5 a, x\u00b3, \u2212 a, b x\u00b2, + 4 a, x, + 15 x\u00b2, \u2212 3 b x, + 12. On the right-hand side of the equation, the only x\u00b2-term is \u22129 x\u00b2. Since the expressions on both sides of the equation are equivalent, it follows that \u2212a, b x\u00b2, + 15 x\u00b2 = \u22129 x\u00b2, which can be rewritten as open parenthesis, \u2212a, b + 15, close parenthesis, \u00d7 x\u00b2 = \u22129 x\u00b2. Therefore, \u2212a, b + 15 = \u22129, which gives a, b = 24.

Choice A is incorrect. If a, b = 18, then the coefficient of x\u00b2 on the left-hand side of the equation would be \u221218 + 15 = \u22123, which doesn’t equal the coefficient of x\u00b2, \u22129, on the right-hand side. Choice B is incorrect. If a, b = 20, then the coefficient of x\u00b2 on the left-hand side of the equation would be \u221220 + 15 = \u22125, which doesn’t equal the coefficient of x\u00b2, \u22129, on the right-hand side. Choice D is incorrect. If a, b = 40, then the coefficient of x\u00b2 on the left-hand side of the equation would be \u221240 + 15 = \u221225, which doesn’t equal the coefficient of x\u00b2, \u22129, on the right-hand side.

\n"}, {"id": "a05bd3a4", "domain": "Advanced Math", "skill": "Equivalent expressions", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

Which of the following expressions is equivalent to x\u00b2 \u2212 5 ?

\n", "choices": [{"id": "A", "text": "open parenthesis, x + the square root(5), close parenthesis, squared\n"}, {"id": "B", "text": "open parenthesis, x \u2212 the square root(5), close parenthesis, squared\n"}, {"id": "C", "text": "open parenthesis, x + the square root(5), close parenthesis, times, open parenthesis, x \u2212 the square root(5), close parenthesis\n"}, {"id": "D", "text": "open parenthesis, x + 5, close parenthesis, times, open parenthesis, x \u2212 1, close parenthesis\n"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. The expression can be written as a difference of squares x2 – y2, which can be factored as (x + y)(x – y). Here, y2 = 5, so y = the square root(5), and the expression therefore factors as open parenthesis, x + the square root(5), close parenthesis, times, open parenthesis, x \u2212 the square root(5), close parenthesis.

Choices A and B are incorrect and may result from misunderstanding how to factor a difference of squares. Choice D is incorrect; (x + 5)(x – 1) can be rewritten as x2 + 4x – 5, which is not equivalent to the original expression.

\n"}, {"id": "c3b116d7", "domain": "Advanced Math", "skill": "Equivalent expressions", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

Which of the following expressions is(are) a factor of \n\t\n\t\t3\n\t\t\n\t\t\tx\n\t\t\t2\n\t\t\n\t\n\t+\n\t\n\t\t20\n\t\tx\n\t\n\t-\n\t63\n\n?

\n
    \n
  1.  \n\tx\n\t-\n\t9\n\n
    2. \n
  2. \n\t\n\t\t3\n\t\tx\n\t\n\t-\n\t7\n\n
    3. \n
", "choices": [{"id": "A", "text": "

I only

"}, {"id": "B", "text": "

II only

"}, {"id": "C", "text": "

I and II

"}, {"id": "D", "text": "

Neither I nor II

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. The given expression can be factored by first finding two values whose sum is 20\n and whose product is 3-63, or -189\n. Those two values are 27\n and -7\n. It follows that the given expression can be rewritten as 3x2+27x-7x-63. Since the first two terms of this expression have a common factor of \n\t3\n\tx\n\n and the last two terms of this expression have a common factor of -7\n, this expression can be rewritten as 3xx+9-7x+9. Since the two terms of this expression have a common factor of x+9, it can be rewritten as 3x-7x+9. Therefore, expression II, 3x-7, is a factor of 3x2+20x-63, but expression I, x-9, is not a factor of 3x2+20x-63. 

\n

Choice A is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

\n

Choice D is incorrect and may result from conceptual or calculation errors.

"}, {"id": "b8f13a3a", "domain": "Advanced Math", "skill": "Nonlinear functions", "difficulty": "H", "type": "spr", "stimulus": "", "stem": "

Function f\n is defined by fx=-ax+b, where a\n and b\n are constants. In the xy-plane, the graph of y=fx-12 has a y-intercept at 0,-757. The product of a\n and b\n is \n\t320\n\t7\n\n. What is the value of a\n?

", "choices": [], "answerId": "20", "acceptedAnswers": ["20"], "rationale": "

The correct answer is 20\n. It’s given that fx=-ax+b. Substituting -ax+b for fx in the equation y=fx-12 yields y=-ax+b-12. It’s given that the y-intercept of the graph of y=fx-12 is 0,-757. Substituting 0\n for x\n and -757 for y\n in the equation y=-ax+b-12 yields -757=-a0+b-12, which is equivalent to -757=-1+b-12, or -757=b-13. Adding 13\n to both sides of this equation yields 167=b. It’s given that the product of a\n and b\n is \n\t320\n\t7\n\n, or \n\t\n\t\ta\n\t\tb\n\t\n\t=\n\t\n\t\t320\n\t\t7\n\t\n\n. Substituting \n\t16\n\t7\n\n for b\n in this equation yields a167=3207. Dividing both sides of this equation by \n\t16\n\t7\n\n yields \n\ta\n\t=\n\t20\n\n.

"}, {"id": "1ee962ec", "domain": "Advanced Math", "skill": "Nonlinear functions", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n\n

\n

Scientists recorded data about the ocean water levels at a certain location over a period of 6\n hours. The graph shown models the data, where \n\ty\n\t=\n\t0\n\n represents sea level. Which table gives values of x\n and their corresponding values of y\n based on the model?

", "choices": [{"id": "A", "text": "
\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
x\ny\n
0\n-12\n
0\n3\n
3\n6\n
"}, {"id": "B", "text": "
\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
x\ny\n
0\n0\n
3\n12\n
0\n-6\n
"}, {"id": "C", "text": "
\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
x\ny\n
0\n0\n
3\n-12\n
6\n0\n
"}, {"id": "D", "text": "
\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
x\ny\n
0\n0\n
12\n3\n
-6\n0\n
"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. Each point x,y on the graph represents an elapsed time x\n, in hours, and the corresponding ocean water level y\n, in feet, at a certain location based on the model. The graph shown passes through the points 0,0, 3,-12, and 6,0. Thus, the table in choice C gives the values of x\n and their corresponding values of y\n based on the model.

\n

Choice A is incorrect and may result from conceptual or calculation errors.

\n

Choice B is incorrect and may result from conceptual or calculation errors.

\n

Choice D is incorrect and may result from conceptual or calculation errors.

"}, {"id": "ad03127d", "domain": "Advanced Math", "skill": "Nonlinear equations in one variable and systems of equations in two variables ", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

6r=7s+t

\n

The given equation relates the variables r\n, s\n, and t\n. Which equation correctly expresses s\n in terms of r\n and t\n?

", "choices": [{"id": "A", "text": "

s=42r-t

"}, {"id": "B", "text": "

s=76r-t

"}, {"id": "C", "text": "

s=67r-t

"}, {"id": "D", "text": "

s=6r-t7

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. Subtracting t\n from both sides of the given equation yields 6r-t=7s. Dividing both sides of this equation by 7\n yields 6r-t7=s. Therefore, the equation s=6r-t7 correctly expresses s\n in terms of r\n and t\n.

\n

Choice A is incorrect and may result from conceptual or calculation errors.

\n

Choice B is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

"}, {"id": "f65288e8", "domain": "Advanced Math", "skill": "Nonlinear equations in one variable and systems of equations in two variables ", "difficulty": "H", "type": "mc", "stimulus": "
\n

\n (1)/(x\u00b2, + 10 x, + 25, end fraction = 4)\n

\n
\n", "stem": "

If x is a solution to the given equation, which of the following is a possible value of x + 5 ?

\n", "choices": [{"id": "A", "text": "

\n one half

\n"}, {"id": "B", "text": "

\n five halves

\n"}, {"id": "C", "text": "

\n nine halves

\n"}, {"id": "D", "text": "

\n eleven halves

\n"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. The given equation can be rewritten as the fraction 1 over, open parenthesis, x + 5, close parenthesis, squared, end fraction = 4. Multiplying both sides of this equation by open parenthesis, x + 5, close parenthesis, squared yields 1 = 4 times, open parenthesis, x + 5, close parenthesis, squared. Dividing both sides of this equation by 4 yields one fourth = open parenthesis, x + 5, close parenthesis, squared. Taking the square root of both sides of this equation yields one half = x + 5 or \u2212one half = x + 5. Therefore, a possible value of x + 5 is one half.
\nChoices B, C, and D are incorrect and may result from computational or conceptual errors.

\n"}, {"id": "788bfd56", "domain": "Advanced Math", "skill": "Nonlinear functions", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

The function f\n is defined by f(x)=4+x. What is the value of f144?

", "choices": [{"id": "A", "text": "

0\n

"}, {"id": "B", "text": "

16\n

"}, {"id": "C", "text": "

40\n

"}, {"id": "D", "text": "

76\n

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. The value of f144 is the value of fx when x=144. It's given that the function f\n is defined by fx=4+x. Substituting 144\n for x\n in this equation yields f144=4+144. Since the positive square root of 144\n is 12\n, it follows that this equation can be rewritten as f144=4+12, or f144=16. Therefore, the value of f144 is 16\n.

\n

Choice A is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect. This is the value of f1,296, not f144.

\n

Choice D is incorrect. This is the value of f5,184, not f144.

"}, {"id": "f89af023", "domain": "Advanced Math", "skill": "Nonlinear functions", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

A rectangular volleyball court has an area of 162 square meters. If the length of the court is twice the width, what is the width of the court, in meters?

\n", "choices": [{"id": "A", "text": "

9

\n"}, {"id": "B", "text": "

18

\n"}, {"id": "C", "text": "

27

\n"}, {"id": "D", "text": "

54

\n"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. It’s given that the volleyball court is rectangular and has an area of 162 square meters. The formula for the area of a rectangle is A = l w, where A is the area, l is the length, and w is the width of the rectangle. It’s also given that the length of the volleyball court is twice the width, thus l = 2 w. Substituting the given value into the formula for the area of a rectangle and using the relationship between length and width for this rectangle yields 162 = 2 w \u00d7 w. This equation can be rewritten as 162 = 2 w\u00b2. Dividing both sides of this equation by 2 yields 81 = w\u00b2. Taking the square root of both sides of this equation yields plus or \u2212 9 = w. Since the width of a rectangle is a positive number, the width of the volleyball court is 9 meters.

\n\tChoice B is incorrect because this is the length of the rectangle. Choice C is incorrect because this is the result of using 162 as the perimeter rather than the area. Choice D is incorrect because this is the result of calculating w in the equation 162 = 2 w + w instead of 162 = 2 w \u00d7 w.

\n"}, {"id": "7902bed0", "domain": "Advanced Math", "skill": "Nonlinear functions", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

A machine launches a softball from ground level. The softball reaches a maximum height of 51.84\n meters above the ground at 1.8\n seconds and hits the ground at 3.6\n seconds. Which equation represents the height above ground h\n, in meters, of the softball t\n seconds after it is launched?

", "choices": [{"id": "A", "text": "

\n\th\n\t=\n\t\n\t\t\n\t\t\t-\n\t\t\t\n\t\t\t\tt\n\t\t\t\t2\n\t\t\t\n\t\t\n\t\t+\n\t\t3.6\n\t\n\n

"}, {"id": "B", "text": "

\n\th\n\t=\n\t\n\t\t\n\t\t\t-\n\t\t\t\n\t\t\t\tt\n\t\t\t\t2\n\t\t\t\n\t\t\n\t\t+\n\t\t51.84\n\t\n\n

"}, {"id": "C", "text": "

\n\th\n\t=\n\t\n\t\t\n\t\t\t-\n\t\t\t16\n\t\t\t\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\tt\n\t\t\t\t\t\t-\n\t\t\t\t\t\t1.8\n\t\t\t\t\t\n\t\t\t\t\n\t\t\t\t2\n\t\t\t\n\t\t\n\t\t-\n\t\t3.6\n\t\n\n

"}, {"id": "D", "text": "

\n\th\n\t=\n\t\n\t\t\n\t\t\t-\n\t\t\t16\n\t\t\t\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\tt\n\t\t\t\t\t\t-\n\t\t\t\t\t\t1.8\n\t\t\t\t\t\n\t\t\t\t\n\t\t\t\t2\n\t\t\t\n\t\t\n\t\t+\n\t\t51.84\n\t\n\n

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. An equation representing the height above ground h\n, in meters, of a softball t\n seconds after it is launched by a machine from ground level can be written in the form h=-at-b2+c, where a\n, b\n, and c\n are positive constants. In this equation, b\n represents the time, in seconds, at which the softball reaches its maximum height of c\n meters above the ground. It's given that this softball reaches a maximum height of 51.84\n meters above the ground at 1.8 seconds; therefore, b=1.8 and \n\tc\n\t=\n\t51.84\n\n. Substituting 1.8 for b\n and 51.84\n for c\n in the equation h=-at-b2+c yields h=-at-1.82+51.84. It's also given that this softball hits the ground at 3.6 seconds; therefore, h=0 when t=3.6. Substituting 0\n for h\n and 3.6 for t\n in the equation h=-at-1.82+51.84 yields 0=-a3.6-1.82+51.84, which is equivalent to 0=-a1.82+51.84, or 0=-3.24a+51.84. Adding \n\t3.24\n\ta\n\n to both sides of this equation yields 3.24a=51.84. Dividing both sides of this equation by 3.24\n yields a=16. Substituting 16\n for a\n in the equation h=-at-1.82+51.84 yields h=-16t-1.82+51.84. Therefore, h=-16t-1.82+51.84 represents the height above ground h\n, in meters, of this softball t\n seconds after it is launched.

\n

Choice A is incorrect. This equation represents a situation where the maximum height is 3.6 meters above the ground at 0\n seconds, not 51.84\n meters above the ground at 1.8 seconds.

\n

Choice B is incorrect. This equation represents a situation where the maximum height is 51.84\n meters above the ground at 0\n seconds, not 1.8 seconds.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

"}, {"id": "4a0d0399", "domain": "Advanced Math", "skill": "Nonlinear functions", "difficulty": "H", "type": "spr", "stimulus": "", "stem": "

The function f\n is defined by f(x)=ax+b, where a\n and b\n are constants. In the \n\tx\n\ty\n\n-plane, the graph of y=fx has an x\n-intercept at 2,0 and a y\n-intercept at 0,-323. What is the value of b\n?

", "choices": [], "answerId": "-324", "acceptedAnswers": ["-324"], "rationale": "

The correct answer is -324. It's given that the function f is defined by fx=ax+b, where a and b are constants. It's also given that the graph of y=fx has a y-intercept at 0,-323. It follows that f0=-323. Substituting 0 for x and -323 for fx in fx=ax+b yields -323=a0+b, or -323=1+b. Subtracting 1 from each side of this equation yields -324=b. Therefore, the value of b is -324.

"}, {"id": "e53add44", "domain": "Advanced Math", "skill": "Nonlinear functions", "difficulty": "M", "type": "mc", "stimulus": "
\n

\n S(n) = 38,000 \u00d7 a, to the n power\n

\n
\n", "stem": "

The function S above models the annual salary, in dollars, of an employee n years after starting a job, where a is a constant. If the employee’s salary increases by 4% each year, what is the value of a ?

\n", "choices": [{"id": "A", "text": "

0.04

\n"}, {"id": "B", "text": "

0.4

\n"}, {"id": "C", "text": "

1.04

\n"}, {"id": "D", "text": "

1.4

\n"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. A model for a quantity S that increases by a certain percentage per time period n is an exponential function in the form S(n) = I times, open parenthesis, 1 + r over 100, close parenthesis, to the n power, where I is the initial value at time n = 0 for r% annual increase. It’s given that the annual increase in an employee’s salary is 4%, so r = 4. The initial value can be found by substituting 0 for n in the given function, which yields S(0) = 38,000. Therefore, I = 38,000. Substituting these values for r and I into the form of the exponential function S(n) = I times, open parenthesis, 1 + r over 100, close parenthesis, to the n power yields S(n) = 38,000 times, open parenthesis, 1 + 4 over 100, close parenthesis, to the n power, or S(n) = 38,000 times, 1 point 0 4 to the n power. Therefore, the value of a in the given function is 1.04.

Choices A, B, and D are incorrect and may result from incorrectly representing the annual increase in the exponential function.

\n"}, {"id": "b4a6ed81", "domain": "Advanced Math", "skill": "Equivalent expressions", "difficulty": "M", "type": "spr", "stimulus": "", "stem": "

The expression \n\t\n\t\t90\n\t\t\n\t\t\ty\n\t\t\t5\n\t\t\n\t\n\t-\n\t\n\t\t54\n\t\t\n\t\t\ty\n\t\t\t4\n\t\t\n\t\n\n is equivalent to ry415y-9, where r\n is a constant. What is the value of r\n?

", "choices": [], "answerId": "6", "acceptedAnswers": ["6"], "rationale": "

The correct answer is 6\n. Applying the distributive property to the expression ry415y-9 yields 15ry5-9ry4. Since 90y5-54y4 is equivalent to ry415y-9, it follows that 90y5-54y4 is also equivalent to 15ry5-9ry4. Since these expressions are equivalent, it follows that corresponding coefficients are equivalent. Therefore, \n\t90\n\t=\n\t\n\t\t15\n\t\tr\n\t\n\n and \n\t-54\n\t=\n\t\n\t\t-\n\t\t9\n\t\tr\n\t\n\n. Solving either of these equations for r\n will yield the value of r\n. Dividing both sides of \n\t90\n\t=\n\t\n\t\t15\n\t\tr\n\t\n\n by 15\n yields \n\t6\n\t=\n\tr\n\n. Therefore, the value of r\n is 6\n.  

"}, {"id": "9654add7", "domain": "Advanced Math", "skill": "Nonlinear functions", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

\n f(x) = \u2212500, x\u00b2, + 25,000 x\n

The revenue f(x), in dollars, that a company receives from sales of a product is given by the function f above, where x is the unit price, in dollars, of the product. The graph of y = f(x) in the xy-plane intersects the x-axis at 0 and a. What does a represent?

\n", "choices": [{"id": "A", "text": "

The revenue, in dollars, when the unit price of the product is $0

\n"}, {"id": "B", "text": "

The unit price, in dollars, of the product that will result in maximum revenue

\n"}, {"id": "C", "text": "

The unit price, in dollars, of the product that will result in a revenue of $0

\n"}, {"id": "D", "text": "

The maximum revenue, in dollars, that the company can make

\n"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. By definition, the y-value when a function intersects the x-axis is 0. It’s given that the graph of the function intersects the x-axis at 0 and a, that x is the unit price, in dollars, of a product, and that f(x), where y = f(x), is the revenue, in dollars, that a company receives from the sales of the product. Since the value of a occurs when y = 0, a is the unit price, in dollars, of the product that will result in a revenue of $0.

Choice A is incorrect. The revenue, in dollars, when the unit price of the product is $0 is represented by f(x), when x = 0. Choice B is incorrect. The unit price, in dollars, of the product that will result in maximum revenue is represented by the x-coordinate of the maximum of f. Choice D is incorrect. The maximum revenue, in dollars, that the company can make is represented by the y-coordinate of the maximum of f.

\n"}, {"id": "34847f8a", "domain": "Advanced Math", "skill": "Equivalent expressions", "difficulty": "H", "type": "mc", "stimulus": "
\n

\n (2)/(x \u2212 2, end fraction, plus, the fraction with numerator 3, and denominator x + 5, end fraction = the fraction with numerator r x + t, and denominator, open parenthesis, x \u2212 2, close parenthesis, times, open parenthesis, x + 5, close parenthesis, end fraction)\n

\n
\n", "stem": "

The equation above is true for all x greater than 2, where r and t are positive constants. What is the value of rt ?

\n", "choices": [{"id": "A", "text": "\u221220\n"}, {"id": "B", "text": "15\n"}, {"id": "C", "text": "20\n"}, {"id": "D", "text": "60\n"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. To express the sum of the two rational expressions on the left-hand side of the equation as the single rational expression on the right-hand side of the equation, the expressions on the left-hand side must have the same denominator. Multiplying the first expression by (x + 5)/(x \u2212 5, end fraction) results in the fraction with numerator 2 times, open parenthesis, x + 5, close parenthesis, and denominator, open parenthesis, x \u2212 2, close parenthesis, times, open parenthesis, x + 5, close parenthesis, end fraction, and multiplying the second expression by (x \u2212 2)/(x \u2212 2, end fraction) results in the fraction with numerator 3 times, open parenthesis, x \u2212 2, close parenthesis, and denominator, open parenthesis, x \u2212 2, close parenthesis, times, open parenthesis, x + 5, close parenthesis, end fraction, so the given equation can be rewritten as the fraction with numerator 2 times, open parenthesis, x + 5, close parenthesis, and denominator, open parenthesis, x \u2212 2, close parenthesis, times, open parenthesis, x + 5, close parenthesis, end fraction, plus, the fraction with numerator 3 times, open parenthesis, x \u2212 2, close parenthesis, and denominator, open parenthesis, x \u2212 2, close parenthesis, times, open parenthesis, x + 5, close parenthesis, end fraction = the fraction with numerator r x + t, and denominator, open parenthesis, x \u2212 2, close parenthesis, times, open parenthesis, x + 5, close parenthesis, end fraction, or the fraction with numerator 2 x + 10, and denominator, open parenthesis, x \u2212 2, close parenthesis, times, open parenthesis, x + 5, close parenthesis, end fraction, plus, the fraction with numerator 3 x \u2212 6, and denominator, open parenthesis, x \u2212 2, close parenthesis, times, open parenthesis, x + 5, close parenthesis, end fraction = the fraction with numerator r x + t, and denominator, open parenthesis, x \u2212 2, close parenthesis, times, open parenthesis, x + 5, close parenthesis, end fraction. Since the two rational expressions on the left-hand side of the equation have the same denominator as the rational expression on the right-hand side of the equation, it follows that open parenthesis, 2 x + 10, close parenthesis, plus, open parenthesis, 3 x \u2212 6, close parenthesis = r x + t. Combining like terms on the left-hand side yields 5 x + 4 = r x + t, so it follows that r = 5 and t = 4. Therefore, the value of r t is 5 \u00d7 4, which = 20.

Choice A is incorrect and may result from an error when determining the sign of either r or t. Choice B is incorrect and may result from not distributing the 2 and 3 to their respective terms in the fraction with numerator 2 times, open parenthesis, x + 5, close parenthesis, and denominator, open parenthesis, x \u2212 2, close parenthesis, times, open parenthesis, x + 5, close parenthesis, end fraction, plus, the fraction with numerator 3 times, open parenthesis, x \u2212 2, close parenthesis, and denominator, open parenthesis, x \u2212 2, close parenthesis, times, open parenthesis, x + 5, close parenthesis, end fraction = the fraction with numerator r x + t, and denominator, open parenthesis, x \u2212 2, close parenthesis, times, open parenthesis, x + 5, close parenthesis, end fraction. Choice D is incorrect and may result from a calculation error.

\n"}, {"id": "cc776a04", "domain": "Advanced Math", "skill": "Equivalent expressions", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

Which of the following is an equivalent form of open parenthesis, 1 point 5 x \u2212 2 point 4, close parenthesis, squared, minus, open parenthesis, 5 point 2, x\u00b2, \u2212 6 point 4, close parenthesis ?

\n", "choices": [{"id": "A", "text": "\u22122 point 2, x\u00b2, + 1 point 6\n"}, {"id": "B", "text": "\u22122 point 2, x\u00b2, + 11 point 2\n"}, {"id": "C", "text": "\u22122 point 95, x\u00b2, \u2212 7 point 2 x, + 12 point 16\n"}, {"id": "D", "text": "\u22122 point 95, x\u00b2, \u2212 7 point 2 x, + 0 point 64\n"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. The first expression open parenthesis, 1 point 5 x \u2212 2 point 4, close parenthesis, squared can be rewritten as open parenthesis, 1 point 5 x \u2212 2 point 4, close parenthesis, times, open parenthesis, 1 point 5 x \u2212 2 point 4, close parenthesis . Applying the distributive property to this product yields open parenthesis, 2 point 2 5, x\u00b2, \u2212 3 point 6 x, \u2212 3 point 6 x, + 5 point 7 6, close parenthesis, minus, open parenthesis, 5 point 2, x\u00b2, \u2212 6 point 4, close parenthesis . This difference can be rewritten as open parenthesis, 2 point 2 5, x\u00b2, \u2212 3 point 6 x, \u2212 3 point 6 x, + 5 point 7 6, close parenthesis, plus, \u22121 times, open parenthesis, 5 point 2 x\u00b2, \u2212 6 point 4, close parenthesis . Distributing the factor of \u22121 through the second expression yields 2 point 2 5 x, squared, \u2212 3 point 6 x, \u2212 3 point 6 x, + 5 point 7 6, \u2212 5 point 2, x\u00b2, + 6 point 4 . Regrouping like terms, the expression becomes open parenthesis, 2 point 2 5, x\u00b2, \u2212 5 point 2, x\u00b2, close parenthesis, plus, open parenthesis, \u22123 point 6 x \u2212 3 point 6 x, close parenthesis, plus, open parenthesis, 5 point 7 6 + 6 point 4, close parenthesis . Combining like terms yields \u22122 point 9 5, x\u00b2, \u2212 7 point 2 x, + 12 point 1 6 .

Choices A, B, and D are incorrect and likely result from errors made when applying the distributive property or combining the resulting like terms.

\n"}, {"id": "263f9937", "domain": "Advanced Math", "skill": "Nonlinear functions", "difficulty": "H", "type": "mc", "stimulus": "
\n
\n
\n
\n \n \n \n \n \n \n \n \n \n
Growth of a Culture of Bacteria
DayNumber of bacteria per
\n\tmilliliter at end of day
1\n 2 point 5 \u00d7 10 to the power 5
2\n 5 point 0 \u00d7 10 to the power 5
3\n 1 point 0 \u00d7 10 to the power 6
\n
\n
\n
\n", "stem": "

A culture of bacteria is growing at an exponential rate, as shown in the table above. At this rate, on which day would the number of bacteria per milliliter reach 5 point 1 2, \u00d7 10, to the power 8?

\n", "choices": [{"id": "A", "text": "

Day 5

\n"}, {"id": "B", "text": "

Day 9

\n"}, {"id": "C", "text": "

Day 11

\n"}, {"id": "D", "text": "

Day 12

\n"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. The number of bacteria per milliliter is doubling each day. For example, from day 1 to day 2, the number of bacteria increased from 2.5 × 105 to 5.0 × 105. At the end of day 3 there are 106 bacteria per milliliter. At the end of day 4, there will be 106 × 2 bacteria per milliliter. At the end of day 5, there will be (106 × 2) × 2, or 106 × (22) bacteria per milliliter, and so on. At the end of day d, the number of bacteria will be 106 × (2d – 3). If the number of bacteria per milliliter will reach 5.12 × 108 at the end of day d, then the equation 10 to the power 6, end power, \u00d7 2 to the power d \u2212 3, end power = 5 point 1 2, \u00d7 10 to the power 8 must hold. Since 5.12 × 108 can be rewritten as 512 × 106,  the equation is equivalent to 2 to the power d \u2212 3, end power = 512. Rewriting 512 as 29 gives d – 3 = 9, so d = 12. The number of bacteria per milliliter would reach 5.12 × 108 at the end of day 12.

Choices A, B, and C are incorrect. Given the growth rate of the bacteria, the number of bacteria will not reach 5.12 × 108 per milliliter by the end of any of these days.

\n"}, {"id": "926c246b", "domain": "Advanced Math", "skill": "Nonlinear functions", "difficulty": "M", "type": "mc", "stimulus": "
\n

\n D = 5,640 times, open parenthesis, 1 point 9, close parenthesis, to the t power\n

\n
\n", "stem": "

The equation above estimates the global data traffic D, in terabytes, for the year that is t years after 2010. What is the best interpretation of the number 5,640 in this context?

\n", "choices": [{"id": "A", "text": "

The estimated amount of increase of data traffic, in terabytes, each year

\n"}, {"id": "B", "text": "

The estimated percent increase in the data traffic, in terabytes, each year

\n"}, {"id": "C", "text": "

The estimated data traffic, in terabytes, for the year that is t years after 2010

\n"}, {"id": "D", "text": "

The estimated data traffic, in terabytes, in 2010

\n"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. Since t represents the number of years after 2010, the estimated data traffic, in terabytes, in 2010 can be calculated using the given equation when t = 0. Substituting 0 for t in the given equation yields D = 5,640 times, open parenthesis, 1 point 9, close parenthesis, to the 0 power, or 5,640 \u00d7 1 = 5,640. Thus, 5,640 represents the estimated data traffic, in terabytes, in 2010.

Choice A is incorrect. Since the equation is exponential, the amount of increase of data traffic each year isn’t constant. Choice B is incorrect. According to the equation, the percent increase in data traffic each year is 90%. Choice C is incorrect. The estimated data traffic, in terabytes, for the year that is t years after 2010 is represented by D, not the number 5,640.

\n"}, {"id": "84e5e36c", "domain": "Advanced Math", "skill": "Nonlinear equations in one variable and systems of equations in two variables ", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

\n\ty\n\t=\n\t76\n\n
\n\ty\n\t=\n\t\n\t\t\n\t\t\tx\n\t\t\t2\n\t\t\n\t\t-\n\t\t5\n\t\n\n

\n

The graphs of the given equations in the xy-plane intersect at the point (x,y). What is a possible value of x\n?

", "choices": [{"id": "A", "text": "

\n\t-\n\t\n\t\t76\n\t\t5\n\t\n\n

"}, {"id": "B", "text": "

-9\n

"}, {"id": "C", "text": "

5\n

"}, {"id": "D", "text": "

76\n

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. Since the point x,y is an intersection point of the graphs of the given equations in the xy-plane, the pair x,y should satisfy both equations, and thus is a solution of the given system. According to the first equation, \n\ty\n\t=\n\t76\n\n. Substituting 76\n in place of y\n in the second equation yields \n\t\n\t\t\n\t\t\tx\n\t\t\t2\n\t\t\n\t\t-\n\t\t5\n\t\n\t=\n\t76\n\n. Adding 5\n to both sides of this equation yields \n\t\n\t\tx\n\t\t2\n\t\n\t=\n\t81\n\n. Taking the square root of both sides of this equation yields two solutions: \n\tx\n\t=\n\t9\n\n and \n\tx\n\t=\n\t-9\n\n. Of these two solutions, only -9\n is given as a choice.

\n

Choice A is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

\n

Choice D is incorrect. This is the value of coordinate y\n, rather than x\n, of the intersection point x,y.

"}, {"id": "ff2c1431", "domain": "Advanced Math", "skill": "Nonlinear equations in one variable and systems of equations in two variables ", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

7m=5n+p

\n

The given equation relates the positive numbers m\n, n\n, and p\n. Which equation correctly gives n\n in terms of m\n and p\n?

", "choices": [{"id": "A", "text": "

n=5p7m

"}, {"id": "B", "text": "

n=7m5-p

"}, {"id": "C", "text": "

n=57m+p

"}, {"id": "D", "text": "

n=7m-5-p

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. It's given that the equation 7m=5n+p relates the positive numbers m\n, n\n, and p\n. Dividing both sides of the given equation by 5\n yields 7m5=n+p. Subtracting p\n from both sides of this equation yields 7m5-p=n, or n=7m5-p. It follows that the equation n=7m5-p correctly gives n\n in terms of m\n and p\n.

\n

Choice A is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

\n

Choice D is incorrect and may result from conceptual or calculation errors.

"}, {"id": "137cc6fd", "domain": "Advanced Math", "skill": "Equivalent expressions", "difficulty": "H", "type": "spr", "stimulus": "", "stem": "

70n570n62

\n

For what value of x\n is the given expression equivalent to 70n30x, where n>1?

", "choices": [], "answerId": ".0177", "acceptedAnswers": [".0177", ".0178", "4/225"], "rationale": "

The correct answer is \n\t4\n\t225\n\n. An expression of the form ak, where k\n is an integer greater than 1\n and a≥0, is equivalent to a1k. Therefore, the given expression, where n>1, is equivalent to 70n1570n162. Applying properties of exponents, this expression can be rewritten as 70n1570n16·2, or 70n1570n13, which can be rewritten as 70n15+13, or 70n815. It's given that the expression 70n570n62 is equivalent to 70n30x, where n>1. It follows that 70n815 is equivalent to 70n30x. Therefore, 815=30x. Dividing both sides of this equation by 30\n yields 8450=x, or 4225=x. Thus, the value of x\n for which the given expression is equivalent to 70n30x, where n>1, is \n\t4\n\t225\n\n. Note that 4/225, .0177, .0178, 0.017, and 0.018 are examples of ways to enter a correct answer.

"}, {"id": "6ce95fc8", "domain": "Advanced Math", "skill": "Nonlinear equations in one variable and systems of equations in two variables ", "difficulty": "H", "type": "mc", "stimulus": "
\n

\n 2 x\u00b2, \u2212 2 = 2 x + 3\n

\n
\n", "stem": "

Which of the following is a solution to the equation above?

\n", "choices": [{"id": "A", "text": "

\n 2

\n"}, {"id": "B", "text": "

\n 1 \u2212 the square root(1)1

\n"}, {"id": "C", "text": "

\n one half + the square root(1)1

\n"}, {"id": "D", "text": "

\n (1 + the square root(1)1)/(2)

\n"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. A quadratic equation in the form a, x\u00b2, + b x, + c = 0, where a, b, and c are constants, can be solved using the quadratic formula: x = (\u2212b + or \u2212 the square root(b) squared, \u2212 4 a c, end root)/(2 a, end fraction). Subtracting 2 x + 3 from both sides of the given equation yields 2 x\u00b2, \u2212 2 x, \u2212 5 = 0. Applying the quadratic formula, where a = 2, b = \u22122, and c = \u22125, yields x = (negative, open parenthesis, \u22122, close parenthesis, + or \u2212 the square root of, open parenthesis, \u22122, close parenthesis, squared, \u2212 4 \u00d7 2, \u00d7 \u22125, end root)/(2 \u00d7 2, end fraction). This can be rewritten as x = (2 + or \u2212 the square root(4)4, end root)/(4). Since the square root(4)4 = the square root(2) squared, \u00d7 11, end root, or 2 \u00d7 the square root(1)1, the equation can be rewritten as x = (2 + or \u2212 2 \u00d7 the square root(1)1, end root)/(4). Dividing 2 from both the numerator and denominator yields (1 + the square root(1)1, end root)/(2) or (1 \u2212 the square root(1)1, end root)/(2). Of these two solutions, only (1 + the square root(1)1, end root)/(2) is present among the choices. Thus, the correct choice is D.

Choice A is incorrect and may result from a computational or conceptual error. Choice B is incorrect and may result from using x = (\u2212b + or \u2212 the square root(b) squared, \u2212 4 a c, end root)/(a, end fraction) instead of x = (\u2212b, + or \u2212 the square root(b) squared, \u2212 4 a c, end root)/(2 a, end fraction) as the quadratic formula. Choice C is incorrect and may result from rewriting the square root(4)4 as 4 \u00d7 the square root(1)1 instead of 2 \u00d7 the square root(1)1.

\n"}, {"id": "4dd4efcf", "domain": "Advanced Math", "skill": "Nonlinear functions", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

fx=ax2+4x+c

\n

In the given quadratic function, a\n and c\n are constants. The graph of y=fx in the xy-plane is a parabola that opens upward and has a vertex at the point h,k, where h\n and k\n are constants. If k<0 and f-9=f3, which of the following must be true?

\n
    \n
  1. c<0
    2. \n
  2. a≥1
    3. \n
", "choices": [{"id": "A", "text": "

I only

"}, {"id": "B", "text": "

II only

"}, {"id": "C", "text": "

I and II

"}, {"id": "D", "text": "

Neither I nor II

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. It's given that the graph of y=fx in the xy-plane is a parabola with vertex h,k. If f-9=f3, then for the graph of y=fx, the point with an x-coordinate of -9\n and the point with an x-coordinate of 3\n have the same y-coordinate. In the xy-plane, a parabola is a symmetric graph such that when two points have the same y-coordinate, these points are equidistant from the vertex, and the x-coordinate of the vertex is halfway between the x-coordinates of these two points. Therefore, for the graph of y=fx, the points with x-coordinates -9\n and 3\n are equidistant from the vertex, h,k, and h\n is halfway between -9\n and 3\n. The value that is halfway between -9\n and 3\n is -9+32, or -3\n. Therefore, \n\th\n\t=\n\t-3\n\n. The equation defining f\n can also be written in vertex form, fx=ax-h2+k. Substituting -3\n for h\n in this equation yields fx=ax--32+k, or fx=ax+32+k. This equation is equivalent to fx=ax2+6x+9+k, or fx=ax2+6ax+9a+k. Since fx=ax2+4x+c, it follows that \n\t\n\t\t6\n\t\ta\n\t\n\t=\n\t4\n\n and \n\t\n\t\t\n\t\t\t9\n\t\t\ta\n\t\t\n\t\t+\n\t\tk\n\t\n\t=\n\tc\n\n. Dividing both sides of the equation \n\t\n\t\t6\n\t\ta\n\t\n\t=\n\t4\n\n by 6\n yields a=46, or \n\ta\n\t=\n\t\n\t\t2\n\t\t3\n\t\n\n. Since 23<1, it's not true that a\u22651. Therefore, statement II isn't true. Substituting \n\t2\n\t3\n\n for a\n in the equation \n\t\n\t\t\n\t\t\t9\n\t\t\ta\n\t\t\n\t\t+\n\t\tk\n\t\n\t=\n\tc\n\n yields 923+k=c, or 6+k=c. Subtracting 6\n from both sides of this equation yields \n\tk\n\t=\n\t\n\t\tc\n\t\t-\n\t\t6\n\t\n\n. If k<0, then c-6<0, or c<6. Since c\n could be any value less than 6\n, it's not necessarily true that c<0. Therefore, statement I isn't necessarily true. Thus, neither I nor II must be true.

\n

Choice A is incorrect and may result from conceptual or calculation errors.

\n

Choice B is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

"}, {"id": "cc2601cb", "domain": "Advanced Math", "skill": "Nonlinear functions", "difficulty": "E", "type": "spr", "stimulus": "", "stem": "

\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n\n

\n

The x-intercept of the graph shown is x,0. What is the value of x\n?

", "choices": [], "answerId": "7", "acceptedAnswers": ["7"], "rationale": "

The correct answer is 7\n. It’s given that the x-intercept of the graph shown is x,0. The graph passes through the point 7,0. Therefore, the value of x\n is 7\n. 

"}, {"id": "f5aa5040", "domain": "Advanced Math", "skill": "Nonlinear equations in one variable and systems of equations in two variables ", "difficulty": "H", "type": "spr", "stimulus": "", "stem": "

In the xy-plane, a line with equation \n\t\n\t\t2\n\t\ty\n\t\n\t=\n\tc\n\n for some constant c\n intersects a parabola at exactly one point. If the parabola has equation \n\ty\n\t=\n\t\n\t\t\n\t\t\t-\n\t\t\t2\n\t\t\t\n\t\t\t\tx\n\t\t\t\t2\n\t\t\t\n\t\t\n\t\t+\n\t\t\n\t\t\t9\n\t\t\tx\n\t\t\n\t\n\n, what is the value of c\n?

", "choices": [], "answerId": "20.25", "acceptedAnswers": ["20.25", "81/4"], "rationale": "

The correct answer is 814. The given linear equation is 2y=c. Dividing both sides of this equation by 2\n yields y=c2. Substituting c2 for y\n in the equation of the parabola yields c2=-2x2+9x. Adding 2x2 and \n\t-\n\t9\n\tx\n\n to both sides of this equation yields 2x2-9x+c2=0. Since it’s given that the line and the parabola intersect at exactly one point, the equation 2x2-9x+c2=0 must have exactly one solution. An equation of the form Ax2+Bx+C=0, where A\n, B\n, and C\n are constants, has exactly one solution when the discriminant, B2-4AC, is equal to 0\n. In the equation 2x2-9x+c2=0, where A=2, B=-9, and C=c2, the discriminant is -92-42c2. Setting the discriminant equal to 0\n yields -92-42c2=0, or 81-4c=0. Adding \n\t4\n\tc\n\n to both sides of this equation yields 81=4c. Dividing both sides of this equation by 4\n yields c=814. Note that 81/4 and 20.25 are examples of ways to enter a correct answer.

"}, {"id": "252a3b3a", "domain": "Advanced Math", "skill": "Nonlinear functions", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n\n

\n

Which of the following could be the equation of the graph shown in the xy-plane?

", "choices": [{"id": "A", "text": "

y=-110xx-4x+5

"}, {"id": "B", "text": "

y=-110xx-4x+52

"}, {"id": "C", "text": "

y=-110xx-5x+4

"}, {"id": "D", "text": "

y=-110xx-52x+4

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. Each of the given choices is an equation of the form y=-110xx-amx+bn, where a\n, b\n, m\n, and n\n are positive constants. In the xy-plane, the graph of an equation of this form has x-intercepts at \n\tx\n\t=\n\t0\n\n, \n\tx\n\t=\n\ta\n\n, and \n\tx\n\t=\n\t\n\t\t-\n\t\tb\n\t\n\n. The graph shown has x-intercepts at \n\tx\n\t=\n\t0\n\n, \n\tx\n\t=\n\t4\n\n, and \n\tx\n\t=\n\t-5\n\n. Therefore, \n\ta\n\t=\n\t4\n\n and \n\tb\n\t=\n\t5\n\n. Of the given choices, only choices A and B have \n\ta\n\t=\n\t4\n\n and \n\tb\n\t=\n\t5\n\n. For an equation in the form y=-110xx-amx+bn, if all values of x\n that are less than \n\t-\n\tb\n\n or greater than a\n correspond to negative y-values, then the sum of all the exponents of the factors on the right-hand side of the equation is even. In the graph shown, all values of x\n less than -5\n or greater than 4\n correspond to negative y-values. Therefore, the sum of all the exponents of the factors on the right-hand side of the equation y=-110xx-4mx+5n must be even. For choice A, the sum of these exponents is 1+1+1, or 3\n, which is odd. For choice B, the sum of these exponents is 1+1+2, or 4\n, which is even. Therefore, y=-110xx-4x+52 could be the equation of the graph shown.

\n

Choice A is incorrect. For the graph of this equation, all values of x\n less than -5\n correspond to positive, not negative, y-values.

\n

Choice C is incorrect. The graph of this equation has x-intercepts at \n\tx\n\t=\n\t-4\n\n, \n\tx\n\t=\n\t0\n\n, and \n\tx\n\t=\n\t5\n\n, rather than x-intercepts at \n\tx\n\t=\n\t-5\n\n, \n\tx\n\t=\n\t0\n\n, and \n\tx\n\t=\n\t4\n\n.

\n

Choice D is incorrect. The graph of this equation has x-intercepts at \n\tx\n\t=\n\t-4\n\n, \n\tx\n\t=\n\t0\n\n, and \n\tx\n\t=\n\t5\n\n, rather than x-intercepts at \n\tx\n\t=\n\t-5\n\n, \n\tx\n\t=\n\t0\n\n, and \n\tx\n\t=\n\t4\n\n.

"}, {"id": "841ef26c", "domain": "Advanced Math", "skill": "Nonlinear functions", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

fx=\n\t\n\t\t4\n\t\t\n\t\t\tx\n\t\t\t2\n\t\t\n\t\n\t+\n\t\n\t\t64\n\t\tx\n\t\n\t+\n\t262\n\n

\n

The function g\n is defined by gx=fx+5. For what value of x\n does gx reach its minimum?

", "choices": [{"id": "A", "text": "

-13\n

"}, {"id": "B", "text": "

-8\n

"}, {"id": "C", "text": "

-5\n

"}, {"id": "D", "text": "

-3\n

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. It's given that gx=fx+5. Since fx=4x2+64x+262, it follows that fx+5=4x+52+64x+5+262. Expanding the quantity x+52 in this equation yields fx+5=4x2+10x+25+64x+5+262. Distributing the 4\n and the 64\n yields fx+5=4x2+40x+100+64x+320+262. Combining like terms yields fx+5=4x2+104x+682. Therefore, gx=4x2+104x+682. For a quadratic function defined by an equation of the form gx=ax-h2+k, where a\n, h\n, and k\n are constants and a\n is positive, gx reaches its minimum, k\n, when the value of x\n is h\n. The equation gx=4x2+104x+682 can be rewritten in this form by completing the square. This equation is equivalent to gx=4x2+26+682, or gx=4x2+26x+169-169+682. This equation can be rewritten as gx=4x+132-169+682, or gx=4x+132-4169+682, which is equivalent to gx=4x+132+6. This equation is in the form gx=ax-h2+k, where \n\ta\n\t=\n\t4\n\n, \n\th\n\t=\n\t-13\n\n, and \n\tk\n\t=\n\t6\n\n. Therefore, gx reaches its minimum when the value of x\n is -13\n.

\n

Choice B is incorrect. This is the value of x\n for which fx, rather than gx, reaches its minimum.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

\n

Choice D is incorrect. This is the value of x\n for which fx-5, rather than fx+5, reaches its minimum.

"}, {"id": "cc6ccd71", "domain": "Advanced Math", "skill": "Nonlinear functions", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n\n

\n

The graph of y=fx is shown, where the function f\n is defined by fx=ax3+bx2+cx+d and a\n, b\n, c\n, and d\n are constants. For how many values of x\n does fx=0?

", "choices": [{"id": "A", "text": "

One

"}, {"id": "B", "text": "

Two

"}, {"id": "C", "text": "

Three

"}, {"id": "D", "text": "

Four

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. If a value of x\n satisfies f(x)=0, the graph of y=fx will contain a point x,0 and thus touch the x-axis. Since there are 3\n points at which this graph touches the x-axis, there are 3\n values of x\n for which f(x)=0.

\n

Choice A is incorrect and may result from conceptual or calculation errors.

\n

Choice B is incorrect and may result from conceptual or calculation errors.

\n

Choice D is incorrect and may result from conceptual or calculation errors.

"}, {"id": "70482e20", "domain": "Advanced Math", "skill": "Equivalent expressions", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

Which expression is equivalent to 11x3-5x3?

", "choices": [{"id": "A", "text": "

\n\t16\n\t\n\t\tx\n\t\t3\n\t\n\n

"}, {"id": "B", "text": "

\n\t6\n\t\n\t\tx\n\t\t3\n\t\n\n

"}, {"id": "C", "text": "

\n\t6\n\t\n\t\tx\n\t\t6\n\t\n\n

"}, {"id": "D", "text": "

\n\t16\n\t\n\t\tx\n\t\t6\n\t\n\n

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. The given expression can be rewritten as 11x3+-5x3. Since the two terms of this expression are both constant multiples of x3, they are like terms and can, therefore, be combined through addition. Adding like terms in the expression 11x3+-5x3 yields 6x3.

\n

Choice A is incorrect. This is equivalent to 11x3+5x3, not 11x3-5x3.

\n

Choice C is incorrect. This is equivalent to 11x6-5x6, not 11x3-5x3. 

\n

Choice D is incorrect. This is equivalent to 11x6+5x6, not 11x3-5x3. 

"}, {"id": "8452c42b", "domain": "Advanced Math", "skill": "Equivalent expressions", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

Which expression is equivalent to 50x2+5x2?

", "choices": [{"id": "A", "text": "

\n\t250\n\t\n\t\tx\n\t\t2\n\t\n\n

"}, {"id": "B", "text": "

\n\t10\n\t\n\t\tx\n\t\t2\n\t\n\n

"}, {"id": "C", "text": "

\n\t45\n\t\n\t\tx\n\t\t2\n\t\n\n

"}, {"id": "D", "text": "

\n\t55\n\t\n\t\tx\n\t\t2\n\t\n\n

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. The given expression shows addition of two like terms. Therefore, the given expression is equivalent to 50+5x2, or 55x2.

\n

Choice A is incorrect. This expression is equivalent to 505x2, not 50+5x2.

\n

Choice B is incorrect. This expression is equivalent to 505x2, not 50+5x2.

\n

Choice C is incorrect. This expression is equivalent to 50-5x2, not 50+5x2.

"}, {"id": "b39d74a0", "domain": "Advanced Math", "skill": "Nonlinear functions", "difficulty": "E", "type": "mc", "stimulus": "
\n\t
\n\t\t
\n\t\t\t
\n\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t
xy
00
11
28
327
\n\t\t
\n\t
\n
\n", "stem": "

The table shown includes some values of x and their corresponding values of y. Which of the following graphs in the xy-plane could represent the relationship between x and y ?

\n", "choices": [{"id": "A", "text": "

 

\"The

 

\n"}, {"id": "B", "text": "

 

\"The

 

\n"}, {"id": "C", "text": "

 

\"The

 

\n"}, {"id": "D", "text": "

 

\"The

 

\n"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. Each pair of values shown in the table gives the ordered pair of coordinates for a point that lies on the graph that represents the relationship between x and y in the xy-plane: the point 0, 0, the point 1, 1, the point 2, 8, and the point 3, 27. Only the graph in choice B passes through the points listed in the table that are visible in the given choices.

Choices A, C, and D are incorrect. None of these graphs passes through the point 1, 1.

 

\n"}, {"id": "ea6d05bb", "domain": "Advanced Math", "skill": "Equivalent expressions", "difficulty": "H", "type": "spr", "stimulus": "", "stem": "

The expression 3x-2319x+6 is equivalent to the expression ax2+bx+c, where a\n, b\n, and c\n are constants. What is the value of b\n?

", "choices": [], "answerId": "-419", "acceptedAnswers": ["-419"], "rationale": "

The correct answer is -419\n. It's given that the expression 3x-2319x+6 is equivalent to the expression \n\t\n\t\ta\n\t\t\n\t\t\tx\n\t\t\t2\n\t\t\n\t\n\t+\n\t\n\t\tb\n\t\tx\n\t\n\t+\n\tc\n\n, where a\n, b\n, and c\n are constants. Applying the distributive property to the given expression, 3x-2319x+6, yields 3x19x+3x6-2319x-236, which can be rewritten as 57x2+18x-437x-138. Combining like terms yields 57x2-419x-138. Since this expression is equivalent to \n\t\n\t\ta\n\t\t\n\t\t\tx\n\t\t\t2\n\t\t\n\t\n\t+\n\t\n\t\tb\n\t\tx\n\t\n\t+\n\tc\n\n, it follows that the value of b\n is -419\n.

"}, {"id": "0536ad4f", "domain": "Advanced Math", "skill": "Equivalent expressions", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

Which expression is equivalent to 20w-4w+3w?

", "choices": [{"id": "A", "text": "

\n\t10\n\tw\n\n

"}, {"id": "B", "text": "

\n\t13\n\tw\n\n

"}, {"id": "C", "text": "

\n\t19\n\tw\n\n

"}, {"id": "D", "text": "

\n\t21\n\tw\n\n

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. Combining like terms inside the parentheses of the given expression, 20w-4w+3w, yields 20w-7w. Combining like terms in this resulting expression yields \n\t13\n\tw\n\n.

\n

Choice A is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

\n

Choice D is incorrect and may result from conceptual or calculation errors.

"}, {"id": "433184f1", "domain": "Advanced Math", "skill": "Equivalent expressions", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

Which expression is equivalent to \n\t\n\t\t\n\t\t\t4\n\t\t\t\n\t\t\t\t\n\t\t\t\t\t4\n\t\t\t\t\tx\n\t\t\t\t\n\t\t\t\t-\n\t\t\t\t5\n\t\t\t\n\t\t\n\t\n\t-\n\t\n\t\t1\n\t\t\n\t\t\tx\n\t\t\t+\n\t\t\t1\n\t\t\n\t\n\n?

", "choices": [{"id": "A", "text": "

\n\t\n\t\t1\n\t\t\n\t\t\t\n\t\t\t\t\n\t\t\t\t\tx\n\t\t\t\t\t+\n\t\t\t\t\t1\n\t\t\t\t\n\t\t\t\n\t\t\t\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t4\n\t\t\t\t\t\tx\n\t\t\t\t\t\n\t\t\t\t\t-\n\t\t\t\t\t5\n\t\t\t\t\n\t\t\t\n\t\t\n\t\n\n

"}, {"id": "B", "text": "

\n\t\n\t\t3\n\t\t\n\t\t\t\n\t\t\t\t3\n\t\t\t\tx\n\t\t\t\n\t\t\t-\n\t\t\t6\n\t\t\n\t\n\n

"}, {"id": "C", "text": "

\n\t-\n\t\n\t\t1\n\t\t\n\t\t\t\n\t\t\t\t\n\t\t\t\t\tx\n\t\t\t\t\t+\n\t\t\t\t\t1\n\t\t\t\t\n\t\t\t\n\t\t\t\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t4\n\t\t\t\t\t\tx\n\t\t\t\t\t\n\t\t\t\t\t-\n\t\t\t\t\t5\n\t\t\t\t\n\t\t\t\n\t\t\n\t\n\n

"}, {"id": "D", "text": "

\n\t\n\t\t9\n\t\t\n\t\t\t\n\t\t\t\t\n\t\t\t\t\tx\n\t\t\t\t\t+\n\t\t\t\t\t1\n\t\t\t\t\n\t\t\t\n\t\t\t\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t4\n\t\t\t\t\t\tx\n\t\t\t\t\t\n\t\t\t\t\t-\n\t\t\t\t\t5\n\t\t\t\t\n\t\t\t\n\t\t\n\t\n\n

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. The expression 44x-5-1x+1 can be rewritten as 44x-5+-1x+1. To add the two terms of this expression, the terms can be rewritten with a common denominator. Since x+1x+1=1, the expression 44x-5 can be rewritten as x+14x+14x-5. Since 4x-54x-5=1, the expression -1x+1 can be rewritten as 4x-5-14x-5x+1. Therefore, the expression 44x-5+-1x+1 can be rewritten as x+14x+14x-5+4x-5-14x-5x+1, which is equivalent to x+14+4x-5-1x+14x-5. Applying the distributive property to each term of the numerator yields 4x+4+-4x+5x+14x-5, or  4x+-4x+4+5x+14x-5. Adding like terms in the numerator yields 9x+14x-5.

\n

Choice A is incorrect and may result from conceptual or calculation errors.

\n

Choice B is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

"}, {"id": "d135f4bf", "domain": "Advanced Math", "skill": "Nonlinear functions", "difficulty": "H", "type": "spr", "stimulus": "", "stem": "

The function f\n is defined by fx=\n\t\n\t\t\n\t\t\tx\n\t\t\t-\n\t\t\t6\n\t\t\n\t\n\t\n\t\t\n\t\t\tx\n\t\t\t-\n\t\t\t2\n\t\t\n\t\n\t\n\t\t\n\t\t\tx\n\t\t\t+\n\t\t\t6\n\t\t\n\t\n\n. In the xy-plane, the graph of y=gx is the result of translating the graph of y=fx up 4\n units. What is the value of g0?

", "choices": [], "answerId": "76", "acceptedAnswers": ["76"], "rationale": "

The correct answer is 76\n. It's given that the graph of y=gx is the result of translating the graph of y=fx up 4\n units in the xy-plane. It follows that the graph of y=gx is the same as the graph of y=fx+4. Substituting gx for y\n in the equation y=fx+4 yields gx=fx+4. It's given that fx=x-6x-2x+6. Substituting x-6x-2x+6 for fx in the equation gx=fx+4 yields gx=x-6x-2x+6+4. Substituting 0\n for x\n in this equation yields g0=0-60-20+6+4, or g0=76. Thus, the value of g0 is 76\n.

"}, {"id": "1d3fee25", "domain": "Advanced Math", "skill": "Equivalent expressions", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

Which of the following is equivalent to 3 times, open parenthesis, x + 5, close parenthesis, \u2212 6 ?

\n", "choices": [{"id": "A", "text": "3 x \u2212 3\n"}, {"id": "B", "text": "3 x \u2212 1\n"}, {"id": "C", "text": "3 x + 9\n"}, {"id": "D", "text": "15 x \u2212 6\n"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. Using the distributive property to multiply 3 and open parenthesis, x + 5, close parenthesis gives 3 x + 15, \u2212 6, which can be rewritten as 3 x + 9.

Choice A is incorrect and may result from rewriting the given expression as 3 times, open parenthesis, x + 5, \u2212 6, close parenthesis. Choice B is incorrect and may result from incorrectly rewriting the expression as open parenthesis, 3 x + 5, close parenthesis, \u2212 6. Choice D is incorrect and may result from incorrectly rewriting the expression as 3 \u00d7 5 x, \u2212 6.

\n"}, {"id": "4ca30186", "domain": "Advanced Math", "skill": "Nonlinear equations in one variable and systems of equations in two variables ", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n

\n

The graph of a system of a linear equation and a nonlinear equation is shown. What is the solution x,y to this system?

", "choices": [{"id": "A", "text": "

0,0

"}, {"id": "B", "text": "

0,2

"}, {"id": "C", "text": "

2,4

"}, {"id": "D", "text": "

4,0

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. The solution to the system of two equations corresponds to the point where the graphs of the equations intersect. The graphs of the linear equation and the nonlinear equation shown intersect at the point 2,4. Thus, the solution to the system is 2,4.

\n

Choice A is incorrect and may result from conceptual or calculation errors.

\n

Choice B is incorrect and may result from conceptual or calculation errors.

\n

Choice D is incorrect and may result from conceptual or calculation errors.

"}, {"id": "911383f2", "domain": "Advanced Math", "skill": "Nonlinear equations in one variable and systems of equations in two variables ", "difficulty": "M", "type": "mc", "stimulus": "
\n

\n open parenthesis, x \u2212 4, close parenthesis, times, open parenthesis, x + 2, close parenthesis, times, open parenthesis, x \u2212 1, close parenthesis = 0\n

\n
\n", "stem": "

What is the product of the solutions to the given equation?

\n", "choices": [{"id": "A", "text": "

\n 8

\n"}, {"id": "B", "text": "

\n 3

\n"}, {"id": "C", "text": "

\n \u22123

\n"}, {"id": "D", "text": "

\n \u22128

\n"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. By the zero-product property, if open parenthesis, x \u2212 4, close parenthesis, times, open parenthesis, x + 2, close parenthesis, times, open parenthesis, x \u2212 1, close parenthesis = 0, then x \u2212 4 = 0, x + 2 = 0, or x \u2212 1 = 0. Solving each of these equations for x yields x = 4, x = \u22122, or x = 1. The product of these solutions is 4 \u00d7 \u22122, \u00d7 1 = \u22128.

Choice A is incorrect and may result from sign errors made when solving the given equation. Choice B is incorrect and may result from finding the sum, not the product, of the solutions. Choice C is incorrect and may result from finding the sum, not the product, of the solutions in addition to making sign errors when solving the given equation.

\n"}, {"id": "d8789a4c", "domain": "Advanced Math", "skill": "Equivalent expressions", "difficulty": "H", "type": "mc", "stimulus": "
\n

\n (x\u00b2, \u2212 c)/(x \u2212 b, end fraction)\n

\n
\n", "stem": "

In the expression above, b and c are positive integers. If the expression is equivalent to x + b and x is not equal to b, which of the following could be the value of c ?

\n", "choices": [{"id": "A", "text": "

4

\n"}, {"id": "B", "text": "

6

\n"}, {"id": "C", "text": "

8

\n"}, {"id": "D", "text": "

10

\n"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. If the given expression is equivalent to x + b, then (x\u00b2, \u2212 c)/(x \u2212 b, end fraction = x + b), where x isn’t equal to b. Multiplying both sides of this equation by x \u2212 b yields x\u00b2, \u2212 c = open parenthesis, x + b, close parenthesis, times, open parenthesis, x \u2212 b, close parenthesis. Since the right-hand side of this equation is in factored form for the difference of squares, the value of c must be a perfect square. Only choice A gives a perfect square for the value of c.

Choices B, C, and D are incorrect. None of these values of c produces a difference of squares. For example, when 6 is substituted for c in the given expression, the result is (x\u00b2, \u2212 6)/(x \u2212 b, end fraction). The expression x\u00b2, \u2212 6 can’t be factored with integer values, and therefore (x\u00b2, \u2212 6)/(x \u2212 b, end fraction) isn’t equivalent to x + b.

\n"}, {"id": "b80d10d7", "domain": "Advanced Math", "skill": "Nonlinear equations in one variable and systems of equations in two variables ", "difficulty": "M", "type": "mc", "stimulus": "
\n

\n (2 times, open parenthesis, x + 1, close parenthesis)/(x + 5, end fraction = 1 \u2212 the fraction with numerator 1, and denominator x + 5, end fraction)\n

\n
\n", "stem": "

What is the solution to the equation above?

\n", "choices": [{"id": "A", "text": "

0

\n"}, {"id": "B", "text": "

2

\n"}, {"id": "C", "text": "

3

\n"}, {"id": "D", "text": "

5

\n"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. Since (x + 5)/(x + 5, end fraction) is equivalent to 1, the right-hand side of the given equation can be rewritten as (x + 5)/(x + 5, end fraction, minus, the fraction 1 over, x + 5, end fraction), or (x + 4)/(x + 5, end fraction). Since the left- and right-hand sides of the equation (2 times, open parenthesis, x + 1, close parenthesis)/(x + 5, end fraction = the fraction with numerator x + 4, and denominator x + 5, end fraction) have the same denominator, it follows that 2 times, open parenthesis, x + 1, close parenthesis = x + 4. Applying the distributive property of multiplication to the expression 2 times, open parenthesis, x + 1, close parenthesis yields 2 \u00d7 x, plus, 2 \u00d7 1, or 2 x + 2. Therefore, 2 x + 2 = x + 4. Subtracting x and 2 from both sides of this equation yields x = 2.

Choices A, C, and D are incorrect. If x = 0, then (2 times, open parenthesis, 0 + 1, close parenthesis)/(0 + 5, end fraction = 1 minus, the fraction with numerator 1, and denominator 0 + 5, end fraction). This can be rewritten as 2 over 5 = 4 over 5, which is a false statement. Therefore, 0 isn’t a solution to the given equation. Substituting 3 and 5 into the given equation yields similarly false statements.

\n"}, {"id": "d4950429", "domain": "Advanced Math", "skill": "Nonlinear functions", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

A rectangle has a length of x\n units and a width of x-15 units. If the rectangle has an area of 76\n square units, what is the value of x\n?

", "choices": [{"id": "A", "text": "

4\n

"}, {"id": "B", "text": "

19\n

"}, {"id": "C", "text": "

23\n

"}, {"id": "D", "text": "

76\n

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. The area of a rectangle is equal to its length multiplied by its width. Multiplying the given length, x\n units, by the given width, x-15 units, yields xx-15 square units. If the rectangle has an area of 76\n square units, it follows that xx-15=76, or x2-15x=76. Subtracting 76\n from both sides of this equation yields x2-15x-76=0. Factoring the left-hand side of this equation yields x-19x+4=0. Applying the zero product property to this equation yields two solutions: \n\tx\n\t=\n\t19\n\n and \n\tx\n\t=\n\t-4\n\n. Since x\n is the rectangle’s length, in units, which must be positive, the value of x\n is 19\n.

\n

Choice A is incorrect. This is the width, in units, of the rectangle, not the value of x\n.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

\n

Choice D is incorrect. This is the area, in square units, of the rectangle, not the value of x\n.

"}, {"id": "752055d1", "domain": "Advanced Math", "skill": "Nonlinear functions", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

A scientist initially measures 12,000\n bacteria in a growth medium. 4\n hours later, the scientist measures 24,000\n bacteria. Assuming exponential growth, the formula P=C2rt gives the number of bacteria in the growth medium, where r\n and C\n are constants and P\n is the number of bacteria t\n hours after the initial measurement. What is the value of r\n?

", "choices": [{"id": "A", "text": "

\n\t1\n\t12,000\n\n

"}, {"id": "B", "text": "

\n\t1\n\t4\n\n

"}, {"id": "C", "text": "

4\n

"}, {"id": "D", "text": "

12,000\n

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. It’s given that the formula P=C2rt gives the number of bacteria in a growth medium, where r\n and C\n are constants and P\n is the number of bacteria t\n hours after the initial measurement. It’s also given that a scientist initially measures 12,000\n bacteria in the growth medium. Since the initial measurement is 0\n hours after the initial measurement, it follows that when \n\tt\n\t=\n\t0\n\n, \n\tP\n\t=\n\t12,000\n\n. Substituting 0\n for t\n and 12,000\n for P\n in the given equation yields 12,000=C2r0, or 12,000=C20, which is equivalent to 12,000=C.  It’s given that 4\n hours later, the scientist measures 24,000\n bacteria, or when \n\tt\n\t=\n\t4\n\n, \n\tP\n\t=\n\t24,000\n\n. Substituting 4\n for t\n, 24,000\n for P\n, and 12,000\n for C\n in the given equation yields 24,000=12,00024r. Dividing each side of this equation by 12,000\n yields \n\t2\n\t=\n\t\n\t\t2\n\t\t\n\t\t\t4\n\t\t\tr\n\t\t\n\t\n\n, or 21=24r, which is equivalent to \n\t1\n\t=\n\t\n\t\t4\n\t\tr\n\t\n\n. Dividing both sides of this equation by 4\n yields \n\t\n\t\t1\n\t\t4\n\t\n\t=\n\tr\n\n. Therefore, the value of r\n is \n\t1\n\t4\n\n.

\n

Choice A is incorrect. This is the value of the reciprocal of C\n.

\n

Choice C is incorrect. This is the value of the reciprocal of r\n.

\n

Choice D is incorrect. This is the value of C\n.

"}, {"id": "d0a53ef5", "domain": "Advanced Math", "skill": "Nonlinear equations in one variable and systems of equations in two variables ", "difficulty": "H", "type": "spr", "stimulus": "", "stem": "

\n\t\n\t\t\n\t\t\t\n\t\t\t\t\n\t\t\t\t\tx\n\t\t\t\t\t-\n\t\t\t\t\t2\n\t\t\t\t\n\t\t\t\n\t\t\t2\n\t\t\n\t\n\t=\n\t\n\t\t\n\t\t\t\n\t\t\t\t3\n\t\t\t\tx\n\t\t\t\n\t\t\t+\n\t\t\t34\n\t\t\n\t\n\n

\n

What is the smallest solution to the given equation?

", "choices": [], "answerId": "-3", "acceptedAnswers": ["-3"], "rationale": "

The correct answer is -3. Squaring both sides of the given equation yields x-22=3x+34, which can be rewritten as x2-4x+4=3x+34. Subtracting \n\t3\n\tx\n\n and 34\n from both sides of this equation yields x2-7x-30=0. This quadratic equation can be rewritten as x-10x+3=0. According to the zero product property, x-10x+3 equals zero when either x-10=0 or x+3=0. Solving each of these equations for x\n yields x=10 or x=-3. Therefore, the given equation has two solutions, 10\n and -3\n. Of these two solutions, -3\n is the smallest solution to the given equation.

"}, {"id": "271ffad7", "domain": "Advanced Math", "skill": "Nonlinear functions", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

A quadratic function models a projectile's height, in meters, above the ground in terms of the time, in seconds, after it was launched. The model estimates that the projectile was launched from an initial height of 7\n meters above the ground and reached a maximum height of 51.1\n meters above the ground 3\n seconds after the launch. How many seconds after the launch does the model estimate that the projectile will return to a height of 7\n meters?

", "choices": [{"id": "A", "text": "

3\n

"}, {"id": "B", "text": "

6\n

"}, {"id": "C", "text": "

7\n

"}, {"id": "D", "text": "

9\n

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. It's given that a quadratic function models the projectile's height, in meters, above the ground in terms of the time, in seconds, after it was launched. It follows that an equation representing the model can be written in the form fx=ax-h2+k, where fx is the projectile's estimated height above the ground, in meters, x\n seconds after the launch, a\n is a constant, and k\n is the maximum height above the ground, in meters, the model estimates the projectile reached h\n seconds after the launch. It's given that the model estimates the projectile reached a maximum height of 51.1\n meters above the ground 3\n seconds after the launch. Therefore, \n\tk\n\t=\n\t51.1\n\n and \n\th\n\t=\n\t3\n\n. Substituting 51.1\n for k\n and 3\n for h\n in the equation fx=ax-h2+k yields fx=ax-32+51.1. It's also given that the model estimates that the projectile was launched from an initial height of 7\n meters above the ground. Therefore, when \n\tx\n\t=\n\t0\n\n, fx=7. Substituting 0\n for x\n and 7\n for fx in the equation fx=ax-32+51.1 yields 7=a0-32+51.1, or 7=9a+51.1. Subtracting 51.1\n from both sides of this equation yields \n\t-44.1\n\t=\n\t\n\t\t9\n\t\ta\n\t\n\n. Dividing both sides of this equation by 9\n yields \n\t-4.9\n\t=\n\ta\n\n. Substituting -4.9\n for a\n in the equation fx=ax-32+51.1 yields fx=-4.9x-32+51.1. Therefore, the equation fx=-4.9x-32+51.1 models the projectile's height, in meters, above the ground x\n seconds after it was launched. The number of seconds after the launch that the model estimates that the projectile will return to a height of 7\n meters is the value of x\n when fx=7. Substituting 7\n for fx in fx=-4.9x-32+51.1 yields 7=-4.9x-32+51.1. Subtracting 51.1\n from both sides of this equation yields -44.1=-4.9x-32. Dividing both sides of this equation by -4.9\n yields 9=x-32. Taking the square root of both sides of this equation yields two equations: \n\t3\n\t=\n\t\n\t\tx\n\t\t-\n\t\t3\n\t\n\n and \n\t-3\n\t=\n\t\n\t\tx\n\t\t-\n\t\t3\n\t\n\n. Adding 3\n to both sides of the equation \n\t3\n\t=\n\t\n\t\tx\n\t\t-\n\t\t3\n\t\n\n yields \n\t6\n\t=\n\tx\n\n. Adding 3\n to both sides of the equation \n\t-3\n\t=\n\t\n\t\tx\n\t\t-\n\t\t3\n\t\n\n yields \n\t0\n\t=\n\tx\n\n. Since 0\n seconds after the launch represents the time at which the projectile was launched, 6\n must be the number of seconds the model estimates that the projectile will return to a height of 7\n meters.

\n

Alternate approach: It's given that a quadratic function models the projectile's height, in meters, above the ground in terms of the time, in seconds, after it was launched. It's also given that the model estimates that the projectile was launched from an initial height of 7\n meters above the ground and reached a maximum height of 51.1\n meters above the ground 3\n seconds after the launch. Since the model is quadratic, and quadratic functions are symmetric, the model estimates that for any given height less than the maximum height, the time the projectile takes to travel from the given height to the maximum height is the same as the time the projectile takes to travel from the maximum height back to the given height. Thus, since the model estimates the projectile took 3\n seconds to travel from 7\n meters above the ground to its maximum height of 51.1\n meters above the ground, the model also estimates the projectile will take 3\n more seconds to travel from its maximum height of 51.1\n meters above the ground back to 7\n meters above the ground. Thus, the model estimates that the projectile will return to a height of 7\n meters 3\n seconds after it reaches its maximum height, which is 6\n seconds after the launch.

\n

Choice A is incorrect. The model estimates that 3\n seconds after the launch, the projectile reached a height of 51.1\n meters, not 7\n meters.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

\n

Choice D is incorrect and may result from conceptual or calculation errors.

"}, {"id": "ee857afb", "domain": "Advanced Math", "skill": "Nonlinear functions", "difficulty": "H", "type": "spr", "stimulus": "", "stem": "

\n\ty\n\t=\n\t\n\t\t\n\t\t\tx\n\t\t\t2\n\t\t\n\t\t-\n\t\t\n\t\t\t14\n\t\t\tx\n\t\t\n\t\t+\n\t\t22\n\t\n\n

\n

The given equation relates the variables x\n and y\n. For what value of x\n does the value of y\n reach its minimum?

", "choices": [], "answerId": "7", "acceptedAnswers": ["7"], "rationale": "

The correct answer is 7\n. When an equation is of the form y=ax2+bx+c, where a\n, b\n, and c\n are constants, the value of y\n reaches its minimum when x=-b2a. Since the given equation is of the form y=ax2+bx+c, it follows that \n\ta\n\t=\n\t1\n\n, \n\tb\n\t=\n\t-14\n\n, and \n\tc\n\t=\n\t22\n\n. Therefore, the value of y\n reaches its minimum when x=--1421, or \n\tx\n\t=\n\t7\n\n.

"}, {"id": "a520ba07", "domain": "Advanced Math", "skill": "Equivalent expressions", "difficulty": "M", "type": "mc", "stimulus": "
\n

\n the cube root(x) to the power 3, \u00d7 y to the power 6, end root\n

\n
\n", "stem": "

Which of the following expressions is equivalent to the expression above?

\n", "choices": [{"id": "A", "text": "y\u00b2\n"}, {"id": "B", "text": "x \u00d7 y\u00b2\n"}, {"id": "C", "text": "y\u00b3\n"}, {"id": "D", "text": "x \u00d7 y\u00b3\n"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. One of the properties of radicals is the nth root(a) \u00d7 b, end root = the nth root(a), end root, \u00d7 the nth root(b), end root. Thus, the given expression can be rewritten as the cube root(x) cubed, end root, \u00d7 the cube root(y) to the power 6, end root. Simplifying by taking the cube root of each part gives x1 ⋅ y2, or xy2.

Choices A, C, and D are incorrect and may be the result of incorrect application of the properties of exponents and radicals.

\n"}, {"id": "5b6af6b1", "domain": "Advanced Math", "skill": "Equivalent expressions", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

Which expression is equivalent to d-68d2-3?

", "choices": [{"id": "A", "text": "

\n\t\n\t\t8\n\t\t\n\t\t\td\n\t\t\t3\n\t\t\n\t\n\t-\n\t\n\t\t14\n\t\t\n\t\t\td\n\t\t\t2\n\t\t\n\t\n\t-\n\t\n\t\t3\n\t\td\n\t\n\t+\n\t18\n\n

"}, {"id": "B", "text": "

\n\t\n\t\t8\n\t\t\n\t\t\td\n\t\t\t3\n\t\t\n\t\n\t-\n\t\n\t\t17\n\t\t\n\t\t\td\n\t\t\t2\n\t\t\n\t\n\t+\n\t48\n\n

"}, {"id": "C", "text": "

\n\t\n\t\t8\n\t\t\n\t\t\td\n\t\t\t3\n\t\t\n\t\n\t-\n\t\n\t\t48\n\t\t\n\t\t\td\n\t\t\t2\n\t\t\n\t\n\t-\n\t\n\t\t3\n\t\td\n\t\n\t+\n\t18\n\n

"}, {"id": "D", "text": "

\n\t\n\t\t8\n\t\t\n\t\t\td\n\t\t\t3\n\t\t\n\t\n\t-\n\t\n\t\t51\n\t\t\n\t\t\td\n\t\t\t2\n\t\t\n\t\n\t+\n\t48\n\n

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. Applying the distributive property to the given expression yields d8d2-3-68d2-3. Applying the distributive property once again to this expression yields d8d2+d-3+-68d2+-6-3, or 8d3+-3d+-48d2+18. This expression can be rewritten as 8d3-48d2-3d+18. Thus, d-68d2-3 is equivalent to 8d3-48d2-3d+18.

\n

Choice A is incorrect and may result from conceptual or calculation errors.

\n

Choice B is incorrect and may result from conceptual or calculation errors.

\n

Choice D is incorrect and may result from conceptual or calculation errors.

"}, {"id": "652054da", "domain": "Advanced Math", "skill": "Nonlinear equations in one variable and systems of equations in two variables ", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

An oceanographer uses the equation s = three halves p to model the speed s, in knots, of an ocean wave, where p represents the period of the wave, in seconds. Which of the following represents the period of the wave in terms of the speed of the wave?

\n", "choices": [{"id": "A", "text": "

\n p = two thirds s\n

\n"}, {"id": "B", "text": "

\n p = three halves s\n

\n"}, {"id": "C", "text": "

\n p = two thirds + s\n

\n"}, {"id": "D", "text": "

\n p = three halves + s\n

\n"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. It’s given that p represents the period of the ocean wave, so the equation s = three halves p can be solved for p to represent the period of the wave in terms of the speed of the wave. Multiplying both sides of the equation by the reciprocal of three halves will isolate p. This yields two thirds s = two thirds times, three halves p, which simplifies to two thirds s = p. Therefore, p = two thirds s.

Choices B, C, and D are incorrect and may result from errors made when rearranging the equation to solve for p.

\n"}, {"id": "837e9da7", "domain": "Advanced Math", "skill": "Nonlinear functions", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

The function f\n is defined by fx=16x. What is the value of fx when \n\tx\n\t=\n\t3\n\n?

", "choices": [{"id": "A", "text": "

\n\t1\n\t3\n\n

"}, {"id": "B", "text": "

\n\t1\n\t6\n\n

"}, {"id": "C", "text": "

\n\t1\n\t9\n\n

"}, {"id": "D", "text": "

\n\t1\n\t18\n\n

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. It's given that fx=16x. Substituting 3\n for x\n in this equation yields f3=163, or f3=118. Therefore, when \n\tx\n\t=\n\t3\n\n, the value of fx is 118.

\n

Choice A is incorrect. This is the value of fx when x=0.5.

\n

Choice B is incorrect. This is the value of fx when \n\tx\n\t=\n\t1\n\n. 

\n

Choice C is incorrect. This is the value of fx when x=1.5.

"}, {"id": "a255ae72", "domain": "Advanced Math", "skill": "Equivalent expressions", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

If x\u00b2 = a, + b and y\u00b2 = a, + c, which of the following is equal to open parenthesis, x\u00b2, \u2212 y\u00b2, close parenthesis, squared ?

\n", "choices": [{"id": "A", "text": "

\n a, squared, \u2212 2 a, c, + c\u00b2\n

\n"}, {"id": "B", "text": "

\n b\u00b2, \u2212 2 b c, + c\u00b2\n

\n"}, {"id": "C", "text": "

\n 4, a, squared, \u2212 4 a, b c, + c\u00b2\n

\n"}, {"id": "D", "text": "

\n 4 a, squared, \u2212 2 a, b c, + b\u00b2 c\u00b2\n

\n"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. It’s given that x\u00b2 = a, + b and y\u00b2 = a, + c. Using the distributive property, the expression open parenthesis, x\u00b2, \u2212 y\u00b2, close parenthesis, squared can be rewritten as open parenthesis, x\u00b2, close parenthesis, squared, \u2212 2 x\u00b2, \u00d7 y\u00b2, plus, open parenthesis, y\u00b2, close parenthesis, squared. Substituting a, + b and a, + c for x\u00b2 and y\u00b2, respectively, in this expression yields open parenthesis, a, + b, close parenthesis, squared, minus, 2 times, open parenthesis, open parenthesis, a, + b, close parenthesis, times, open parenthesis, a, + c, close parenthesis, close parenthesis, plus, open parenthesis, a, + c, close parenthesis, squared. Expanding this expression yields open parenthesis, a, squared, + 2 a, b, + b\u00b2, close parenthesis, minus, open parenthesis, 2 a, squared, + 2 b c, + 2 a, c, + 2 a, b, close parenthesis, plus, open parenthesis, a, squared, + 2 a, c, + c\u00b2, close parenthesis. Combining like terms, this expression can be rewritten as b\u00b2, \u2212 2 b c, + c\u00b2.

Choices A, C, and D are incorrect and may result from an error in using the distributive property, substituting, or combining like terms.

\n"}, {"id": "3de7a7d7", "domain": "Advanced Math", "skill": "Nonlinear equations in one variable and systems of equations in two variables ", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

Which of the following is a solution to the equation 2 x\u00b2, \u2212 4 = x\u00b2 ?

\n", "choices": [{"id": "A", "text": "

1

\n"}, {"id": "B", "text": "

2

\n"}, {"id": "C", "text": "

3

\n"}, {"id": "D", "text": "

4

\n"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. Subtracting x2 from both sides of the given equation yields x2 – 4 = 0. Adding 4 to both sides of the equation gives x2 = 4. Taking the square root of both sides of the equation gives x = 2 or x = –2. Therefore, x = 2 is one solution to the original equation.

Alternative approach: Subtracting x2 from both sides of the given equation yields x2 – 4 = 0. Factoring this equation gives x2 – 4 = (x + 2)(x – 2) = 0, such that x = 2 or x = –2. Therefore, x = 2 is one solution to the original equation.

Choices A, C, and D are incorrect and may be the result of computation errors.

\n"}, {"id": "70f98ab4", "domain": "Advanced Math", "skill": "Nonlinear equations in one variable and systems of equations in two variables ", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

q-29r=s

\n

The given equation relates the positive numbers q\n, r\n, and s\n. Which equation correctly expresses q\n in terms of r\n and s\n?

", "choices": [{"id": "A", "text": "

q=s-29r

"}, {"id": "B", "text": "

q=s+29r

"}, {"id": "C", "text": "

q=29rs

"}, {"id": "D", "text": "

q=-s29r

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. Adding \n\t29\n\tr\n\n to each side of the given equation yields q=s+29r. Therefore, the equation q=s+29r correctly expresses q\n in terms of r\n and s\n.

\n

Choice A is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

\n

Choice D is incorrect and may result from conceptual or calculation errors.

"}, {"id": "2c05d312", "domain": "Advanced Math", "skill": "Nonlinear equations in one variable and systems of equations in two variables ", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

57x2+(57b+a)x+ab=0

\n

In the given equation, a\n and b\n are positive constants. The product of the solutions to the given equation is kab, where k\n is a constant. What is the value of k\n?

", "choices": [{"id": "A", "text": "

\n\t1\n\t57\n\n

"}, {"id": "B", "text": "

\n\t1\n\t19\n\n

"}, {"id": "C", "text": "

1\n

"}, {"id": "D", "text": "

57\n

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. The left-hand side of the given equation is the expression 57x2+57b+ax+ab. Applying the distributive property to this expression yields 57x2+57bx+ax+ab. Since the first two terms of this expression have a common factor of \n\t57\n\tx\n\n and the last two terms of this expression have a common factor of a\n, this expression can be rewritten as 57xx+b+ax+b. Since the two terms of this expression have a common factor of x+b, it can be rewritten as x+b57x+a. Therefore, the given equation can be rewritten as x+b57x+a=0. By the zero product property, it follows that x+b=0 or 57x+a=0. Subtracting b\n from both sides of the equation x+b=0 yields x=-b. Subtracting a\n from both sides of the equation 57x+a=0 yields 57x=-a. Dividing both sides of this equation by 57\n yields x=-a57. Therefore, the solutions to the given equation are \n\t-\n\tb\n\n and -a57. It follows that the product of the solutions of the given equation is -b-a57, or ab57. It’s given that the product of the solutions of the given equation is kab. It follows that ab57=kab, which can also be written as ab157=abk. It’s given that a\n and b\n are positive constants. Therefore, dividing both sides of the equation ab157=abk by \n\ta\n\tb\n\n yields 157=k. Thus, the value of k\n is 157.

\n

Choice B is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

\n

Choice D is incorrect and may result from conceptual or calculation errors.

"}, {"id": "1fe32f7d", "domain": "Advanced Math", "skill": "Nonlinear equations in one variable and systems of equations in two variables ", "difficulty": "H", "type": "spr", "stimulus": "", "stem": "

\n\t\n\t\t\n\t\t\t-\n\t\t\t\n\t\t\t\tx\n\t\t\t\t2\n\t\t\t\n\t\t\n\t\t+\n\t\t\n\t\t\tb\n\t\t\tx\n\t\t\n\t\t-\n\t\t676\n\t\n\t=\n\t0\n\n

\n

In the given equation, b\n is a positive integer. The equation has no real solution. What is the greatest possible value of b\n?

", "choices": [], "answerId": "51", "acceptedAnswers": ["51"], "rationale": "

The correct answer is 51\n. A quadratic equation of the form \n\t\n\t\t\n\t\t\ta\n\t\t\t\n\t\t\t\tx\n\t\t\t\t2\n\t\t\t\n\t\t\n\t\t+\n\t\t\n\t\t\tb\n\t\t\tx\n\t\t\n\t\t+\n\t\tc\n\t\n\t=\n\t0\n\n, where a\n, b\n, and c\n are constants, has no real solution if and only if its discriminant, \n\t\n\t\t-\n\t\t4\n\t\ta\n\t\tc\n\t\n\t+\n\t\n\t\tb\n\t\t2\n\t\n\n, is negative. In the given equation, \n\ta\n\t=\n\t-1\n\n and \n\tc\n\t=\n\t-676\n\n. Substituting -1\n for a\n and -676\n for c\n in this expression yields a discriminant of b2-4-1-676, or \n\t\n\t\tb\n\t\t2\n\t\n\t-\n\t2,704\n\n. Since this value must be negative, b2-2,704<0, or b2<2,704. Taking the positive square root of each side of this inequality yields b<52. Since b\n is a positive integer, and the greatest integer less than 52\n is 51\n, the greatest possible value of b\n is 51\n.

"}, {"id": "a45ffacb", "domain": "Advanced Math", "skill": "Nonlinear functions", "difficulty": "H", "type": "spr", "stimulus": "", "stem": "

Function f\n is defined by fx=-ax+b, where a\n and b\n are constants. In the xy-plane, the graph of y=fx-15 has a y-intercept at 0,-997. The product of a\n and b\n is \n\t65\n\t7\n\n. What is the value of a\n?

", "choices": [], "answerId": "5", "acceptedAnswers": ["5"], "rationale": "

The correct answer is 5\n. It’s given that fx=-ax+b. Substituting -ax+b for fx in the equation y=fx-15 yields y=-ax+b-15. It’s given that the y-intercept of the graph of y=fx-15 is 0,-997. Substituting 0\n for x\n and -997 for y\n in the equation y=-ax+b-15 yields -997=-a0+b-15, which is equivalent to -997=-1+b-15, or -997=b-16. Adding 16\n to both sides of this equation yields 137=b. It’s given that the product of a\n and b\n is \n\t65\n\t7\n\n, or \n\t\n\t\ta\n\t\tb\n\t\n\t=\n\t\n\t\t65\n\t\t7\n\t\n\n. Substituting \n\t13\n\t7\n\n  for b\n in this equation yields a137=657. Dividing both sides of this equation by \n\t13\n\t7\n\n yields \n\ta\n\t=\n\t5\n\n.

"}, {"id": "95ed0b69", "domain": "Advanced Math", "skill": "Nonlinear equations in one variable and systems of equations in two variables ", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

\n\tp\n\t=\n\t\n\t\t\n\t\t\tk\n\t\t\t\n\t\t\t\t\n\t\t\t\t\t4\n\t\t\t\t\tj\n\t\t\t\t\n\t\t\t\t+\n\t\t\t\t9\n\t\t\t\n\t\t\n\t\n\n

\n

The given equation relates the distinct positive numbers p\n, k\n, and j\n. Which equation correctly expresses \n\t\n\t\t4\n\t\tj\n\t\n\t+\n\t9\n\n in terms of p\n and k\n?

", "choices": [{"id": "A", "text": "

\n\t\n\t\t\n\t\t\t4\n\t\t\tj\n\t\t\n\t\t+\n\t\t9\n\t\n\t=\n\t\n\t\t\n\t\t\tk\n\t\t\tp\n\t\t\n\t\n\n

"}, {"id": "B", "text": "

\n\t\n\t\t\n\t\t\t4\n\t\t\tj\n\t\t\n\t\t+\n\t\t9\n\t\n\t=\n\t\n\t\tk\n\t\tp\n\t\n\n

"}, {"id": "C", "text": "

4j+9=k-p

"}, {"id": "D", "text": "

\n\t\n\t\t\n\t\t\t4\n\t\t\tj\n\t\t\n\t\t+\n\t\t9\n\t\n\t=\n\t\n\t\t\n\t\t\tp\n\t\t\tk\n\t\t\n\t\n\n

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. To express 4j+9 in terms of p\n and k\n, the given equation must be solved for 4j+9. Since it's given that j\n is a positive number, 4j+9 is not equal to zero. Therefore, multiplying both sides of the given equation by 4j+9 yields the equivalent equation p4j+9=k. Since it's given that p\n is a positive number, p\n is not equal to zero. Therefore, dividing each side of the equation p4j+9=k by p\n yields the equivalent equation 4j+9=kp.

\n

Choice B is incorrect. This equation is equivalent to p=4j+9k.

\n

Choice C is incorrect. This equation is equivalent to p=k-4j-9.

\n

Choice D is incorrect. This equation is equivalent to p=k4j+9.

"}, {"id": "463eec13", "domain": "Advanced Math", "skill": "Equivalent expressions", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

If x is not equal to 0, which of the following expressions is equivalent to (the square root(1)6 x to the fourth power, y to the eighth power, end root)/(x\u00b3, end fraction) ?

\n", "choices": [{"id": "A", "text": "

\n 8 x\u00b2, y to the fourth power\n

\n"}, {"id": "B", "text": "

\n 4 x, y to the fourth power\n

\n"}, {"id": "C", "text": "

\n 4 x raised to the \u22122 power, y\u00b2\n

\n"}, {"id": "D", "text": "

\n 4 x raised to the \u22121 power, y to the fourth power\n

\n"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. Taking the square root of an exponential expression halves the exponent, so (the square root of, 16 x to the fourth power \u00d7 y to the eighth power, end root)/(x\u00b3, end fraction = the fraction with numerator 4 x\u00b2, \u00d7 y to the fourth power, and denominator x\u00b3), which further reduces to (4, y to the fourth power)/(x). This can be rewritten as 4, x to the \u22121 power, \u00d7 y to the fourth power.

Choice A is incorrect and may result from neglecting the denominator of the given expression and from incorrectly calculating the square root of 16. Choice B is incorrect and may result from rewriting 1 over x as x to the first power rather than x to the \u22121 power. Choice C is incorrect and may result from taking the square root of the variables in the numerator twice instead of once.

\n"}, {"id": "341ba5db", "domain": "Advanced Math", "skill": "Nonlinear functions", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

gx=x2+55

\n

What is the minimum value of the given function?

", "choices": [{"id": "A", "text": "

0\n

"}, {"id": "B", "text": "

55\n

"}, {"id": "C", "text": "

110\n

"}, {"id": "D", "text": "

3,025\n

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. For a quadratic function defined by an equation of the form gx=ax-h2+k, where a\n, h\n, and k\n are constants and a>0, the minimum value of the function is k\n. In the given function, \n\ta\n\t=\n\t1\n\n, \n\th\n\t=\n\t0\n\n, and \n\tk\n\t=\n\t55\n\n. Therefore, the minimum value of the given function is 55\n.

\n

Choice A is incorrect. This is the value of x\n for which the given function reaches its minimum value, not the minimum value of the function.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

\n

Choice D is incorrect and may result from conceptual or calculation errors.

"}, {"id": "18e35375", "domain": "Advanced Math", "skill": "Nonlinear functions", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

fx=\n\t\n\t\t\n\t\t\tx\n\t\t\t-\n\t\t\t14\n\t\t\n\t\n\t\n\t\t\n\t\t\tx\n\t\t\t+\n\t\t\t19\n\t\t\n\t\n\n

\n

The function f\n is defined by the given equation. For what value of x\n does fx reach its minimum?

", "choices": [{"id": "A", "text": "

-266\n

"}, {"id": "B", "text": "

-19\n

"}, {"id": "C", "text": "

\n\t-\n\t\n\t\t33\n\t\t2\n\t\n\n

"}, {"id": "D", "text": "

\n\t-\n\t\n\t\t5\n\t\t2\n\t\n\n

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. It's given that fx=x-14x+19, which can be rewritten as fx=x2+5x-266. Since the coefficient of the x2-term is positive, the graph of y=fx in the xy-plane opens upward and reaches its minimum value at its vertex. The x-coordinate of the vertex is the value of x\n such that fx reaches its minimum. For an equation in the form fx=ax2+bx+c, where a\n, b\n, and c\n are constants, the x-coordinate of the vertex is -b2a. For the equation fx=x2+5x-266, a=1, b=5, and c=-266. It follows that the x-coordinate of the vertex is -521, or -52. Therefore, fx reaches its minimum when the value of x\n is -52.

\n

Alternate approach: The value of x\n for the vertex of a parabola is the x-value of the midpoint between the two x-intercepts of the parabola. Since it’s given that fx=x-14x+19, it follows that the two x-intercepts of the graph of y=fx in the xy-plane occur when x=14 and x=-19, or at the points 14,0 and -19,0. The midpoint between two points, x1,y1 and x2,y2, is x1+x22,y1+y22. Therefore, the midpoint between 14,0 and -19,0 is 14+-192,0+02, or -52,0. It follows that fx reaches its minimum when the value of x\n is -52.

\n

Choice A is incorrect. This is the y-coordinate of the y-intercept of the graph of y=fx in the xy-plane.

\n

Choice B is incorrect. This is one of the x-coordinates of the x-intercepts of the graph of y=fx in the xy-plane.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

"}, {"id": "c303ad23", "domain": "Advanced Math", "skill": "Nonlinear equations in one variable and systems of equations in two variables ", "difficulty": "H", "type": "spr", "stimulus": "", "stem": "

If \n\t\n\t\t\n\t\t\t3\n\t\t\t\n\t\t\t\tx\n\t\t\t\t2\n\t\t\t\n\t\t\n\t\t-\n\t\t\n\t\t\t18\n\t\t\tx\n\t\t\n\t\t-\n\t\t15\n\t\n\t=\n\t0\n\n, what is the value of \n\t\n\t\tx\n\t\t2\n\t\n\t-\n\t\n\t\t6\n\t\tx\n\t\n\n?

", "choices": [], "answerId": "5", "acceptedAnswers": ["5"], "rationale": "

The correct answer is 5\n. Dividing each side of the given equation by 3\n yields x2-6x-5=0. Adding 5\n to each side of this equation yields x2-6x=5. Therefore, if 3x2-18x-15=0, the value of x2-6x is 5\n.

"}, {"id": "b5c43226", "domain": "Advanced Math", "skill": "Nonlinear functions", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n\n

\n

What is the y-intercept of the graph shown?

", "choices": [{"id": "A", "text": "

0,0

"}, {"id": "B", "text": "

0,2

"}, {"id": "C", "text": "

2,0

"}, {"id": "D", "text": "

2,2

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. The y-intercept of a graph in the xy-plane is the point at which the graph crosses the y-axis. The graph shown crosses the y-axis at the point 0,2. Therefore, the y-intercept of the graph shown is 0,2. 

\n

Choice A is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

\n

Choice D is incorrect and may result from conceptual or calculation errors.

"}, {"id": "7bd10ef3", "domain": "Advanced Math", "skill": "Nonlinear equations in one variable and systems of equations in two variables ", "difficulty": "H", "type": "mc", "stimulus": "
\n

\n 2 x\u00b2, \u2212 4 x = t\n

\n
\n", "stem": "

In the equation above, t is a constant. If the equation has no real solutions, which of the following could be the value of t ?

\n", "choices": [{"id": "A", "text": "\n \u22123\n \n"}, {"id": "B", "text": "\n \u22121\n \n"}, {"id": "C", "text": "\n 1\n \n"}, {"id": "D", "text": "\n 3\n \n"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. The number of solutions to any quadratic equation in the form a, x\u00b2, + b x, + c = 0, where a, b, and c are constants, can be found by evaluating the expression b\u00b2, \u2212 4 a, c, which is called the discriminant. If the value of b\u00b2, \u2212 4 a, c is a positive number, then there will be exactly two real solutions to the equation. If the value of b\u00b2, \u2212 4 a, c is zero, then there will be exactly one real solution to the equation. Finally, if the value of b\u00b2, \u2212 4 a, c is negative, then there will be no real solutions to the equation.

The given equation 2 x\u00b2, \u2212 4 x = t is a quadratic equation in one variable, where t is a constant. Subtracting t from both sides of the equation gives 2 x\u00b2, \u2212 4 x, \u2212 t = 0. In this form, a = 2, b = \u22124, and c = \u2212t. The values of t for which the equation has no real solutions are the same values of t for which the discriminant of this equation is a negative value. The discriminant is equal to open parenthesis, \u22124, close parenthesis, squared, \u2212 4 \u00d7 2, \u00d7 \u2212t; therefore, open parenthesis, \u22124, close parenthesis, squared, minus, 4 \u00d7 2, \u00d7 \u2212t, < 0. Simplifying the left side of the inequality gives 16 + 8, t, < 0. Subtracting 16 from both sides of the inequality and then dividing both sides by 8 gives t < \u22122. Of the values given in the options, \u22123 is the only value that is less than \u22122. Therefore, choice A must be the correct answer.

Choices B, C, and D are incorrect and may result from a misconception about how to use the discriminant to determine the number of solutions of a quadratic equation in one variable.

\n \n

\n"}, {"id": "e166aca6", "domain": "Advanced Math", "skill": "Nonlinear functions", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n

\n

What is the x-intercept of the graph shown?

", "choices": [{"id": "A", "text": "

-5,0

"}, {"id": "B", "text": "

5,0

"}, {"id": "C", "text": "

-4,0

"}, {"id": "D", "text": "

4,0

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. The x-intercept of the graph shown is the point x,y on the graph where \n\ty\n\t=\n\t0\n\n. At \n\ty\n\t=\n\t0\n\n, the corresponding value of x\n is 4\n. Therefore, the x-intercept of the graph shown is 4,0.

\n

Choice A is incorrect. This is the x-intercept of a graph in the xy-plane that intersects the x-axis at \n\tx\n\t=\n\t-5\n\n, not \n\tx\n\t=\n\t4\n\n.

\n

Choice B is incorrect. This is the x-intercept of a graph in the xy-plane that intersects the x-axis at \n\tx\n\t=\n\t5\n\n, not \n\tx\n\t=\n\t4\n\n.

\n

Choice C is incorrect. This is the x-intercept of a graph in the xy-plane that intersects the x-axis at \n\tx\n\t=\n\t-4\n\n, not \n\tx\n\t=\n\t4\n\n.

"}, {"id": "11ccf3e1", "domain": "Advanced Math", "skill": "Nonlinear equations in one variable and systems of equations in two variables ", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

\n\t\n\t\t\n\t\t\t14\n\t\t\tj\n\t\t\n\t\t+\n\t\t\n\t\t\t5\n\t\t\tk\n\t\t\n\t\n\t=\n\tm\n\n

\n

The given equation relates the numbers j\n, k\n, and m\n. Which equation correctly expresses k\n in terms of j\n and m\n?

", "choices": [{"id": "A", "text": "

k=m-14j5

"}, {"id": "B", "text": "

k=15m-14j

"}, {"id": "C", "text": "

k=14j-m5

"}, {"id": "D", "text": "

k=5m-14j

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. Subtracting 14j from each side of the given equation results in 5k=m-14j. Dividing each side of this equation by 5\n results in k=m-14j5.

\n

Choice B is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

\n

Choice D is incorrect and may result from conceptual or calculation errors.

"}, {"id": "50e40f08", "domain": "Advanced Math", "skill": "Nonlinear functions", "difficulty": "M", "type": "spr", "stimulus": "", "stem": "

fx=x+6x-4

\n

If the given function f\n is graphed in the xy-plane, where y=fx, what is the x-coordinate of an x-intercept of the graph?

", "choices": [], "answerId": "-6", "acceptedAnswers": ["-6", "4"], "rationale": "

The correct answer is either -6\n or 4\n. The x-intercepts of a graph in the xy-plane are the points where \n\ty\n\t=\n\t0\n\n. Thus, for an x-intercept of the graph of y=fx, 0=fx. Substituting 0\n for fx in the equation fx=x+6x-4 yields 0=x+6x-4. By the zero product property, \n\t\n\t\tx\n\t\t+\n\t\t6\n\t\n\t=\n\t0\n\n and \n\t\n\t\tx\n\t\t-\n\t\t4\n\t\n\t=\n\t0\n\n. Subtracting 6\n from both sides of the equation \n\t\n\t\tx\n\t\t+\n\t\t6\n\t\n\t=\n\t0\n\n yields \n\tx\n\t=\n\t-6\n\n. Adding 4\n to both sides of the equation \n\t\n\t\tx\n\t\t-\n\t\t4\n\t\n\t=\n\t0\n\n yields \n\tx\n\t=\n\t4\n\n. Therefore, the x-coordinates of the x-intercepts of the graph of y=fx are -6\n and 4\n. Note that -6 and 4 are examples of ways to enter a correct answer.

"}, {"id": "03ff48d2", "domain": "Advanced Math", "skill": "Nonlinear equations in one variable and systems of equations in two variables ", "difficulty": "H", "type": "spr", "stimulus": "", "stem": "

\n\t\n\t\tx\n\t\t\n\t\t\t\n\t\t\t\t\n\t\t\t\t\tk\n\t\t\t\t\tx\n\t\t\t\t\n\t\t\t\t-\n\t\t\t\t56\n\t\t\t\n\t\t\n\t\n\t=\n\t-16\n\n

\n

In the given equation, k\n is an integer constant. If the equation has no real solution, what is the least possible value of k\n?

", "choices": [], "answerId": "50", "acceptedAnswers": ["50"], "rationale": "

The correct answer is 50\n. An equation of the form ax2+bx+c=0, where a\n, b\n, and c\n are constants, has no real solutions if and only if its discriminant, b2-4ac, is negative. Applying the distributive property to the left-hand side of the equation xkx-56=-16 yields kx2-56x=-16. Adding 16\n to each side of this equation yields kx2-56x+16=0. Substituting k\n for a\n, -56\n for b\n, and 16\n for c\n in b2-4ac yields a discriminant of -562-4k16, or 3,136-64k. If the given equation has no real solution, it follows that the value of 3,136-64k must be negative. Therefore, 3,136-64k<0. Adding \n\t64\n\tk\n\n to both sides of this inequality yields 3,136<64k. Dividing both sides of this inequality by 64\n yields 49<k, or k>49. Since it's given that k\n is an integer, the least possible value of k\n is 50\n. 

"}, {"id": "13e57f0a", "domain": "Advanced Math", "skill": "Nonlinear equations in one variable and systems of equations in two variables ", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

\n\t\n\t\t\n\t\t\t-\n\t\t\t4\n\t\t\t\n\t\t\t\tx\n\t\t\t\t2\n\t\t\t\n\t\t\n\t\t-\n\t\t\n\t\t\t7\n\t\t\tx\n\t\t\n\t\n\t=\n\t-36\n\n

\n

What is the positive solution to the given equation?

", "choices": [{"id": "A", "text": "

\n\t7\n\t4\n\n

"}, {"id": "B", "text": "

\n\t9\n\t4\n\n

"}, {"id": "C", "text": "

4\n

"}, {"id": "D", "text": "

7\n

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. Multiplying each side of the given equation by -16\n yields \n\t\n\t\t\n\t\t\t64\n\t\t\t\n\t\t\t\tx\n\t\t\t\t2\n\t\t\t\n\t\t\n\t\t+\n\t\t\n\t\t\t112\n\t\t\tx\n\t\t\n\t\n\t=\n\t576\n\n. To complete the square, adding 49\n to each side of this equation yields 64x2+112x+49=576+49, or 8x+72=625. Taking the square root of each side of this equation yields two equations: \n\t\n\t\t\n\t\t\t8\n\t\t\tx\n\t\t\n\t\t+\n\t\t7\n\t\n\t=\n\t25\n\n and \n\t\n\t\t\n\t\t\t8\n\t\t\tx\n\t\t\n\t\t+\n\t\t7\n\t\n\t=\n\t-25\n\n. Subtracting 7\n from each side of the equation \n\t\n\t\t\n\t\t\t8\n\t\t\tx\n\t\t\n\t\t+\n\t\t7\n\t\n\t=\n\t25\n\n yields \n\t\n\t\t8\n\t\tx\n\t\n\t=\n\t18\n\n. Dividing each side of this equation by 8\n yields x=188, or \n\tx\n\t=\n\t\n\t\t9\n\t\t4\n\t\n\n. Therefore, \n\t9\n\t4\n\n is a solution to the given equation. Subtracting 7\n from each side of the equation \n\t\n\t\t\n\t\t\t8\n\t\t\tx\n\t\t\n\t\t+\n\t\t7\n\t\n\t=\n\t-25\n\n yields \n\t\n\t\t8\n\t\tx\n\t\n\t=\n\t-32\n\n. Dividing each side of this equation by 8\n yields \n\tx\n\t=\n\t-4\n\n. Therefore, the given equation has two solutions, \n\t9\n\t4\n\n and -4\n. Since \n\t9\n\t4\n\n is positive, it follows that \n\t9\n\t4\n\n is the positive solution to the given equation.

\n

Alternate approach: Adding \n\t4\n\t\n\t\tx\n\t\t2\n\t\n\n and \n\t7\n\tx\n\n to each side of the given equation yields \n\t0\n\t=\n\t\n\t\t\n\t\t\t4\n\t\t\t\n\t\t\t\tx\n\t\t\t\t2\n\t\t\t\n\t\t\n\t\t+\n\t\t\n\t\t\t7\n\t\t\tx\n\t\t\n\t\t-\n\t\t36\n\t\n\n. The right-hand side of this equation can be rewritten as 4x2+16x-9x-36. Factoring out the common factor of \n\t4\n\tx\n\n from the first two terms of this expression and the common factor of -9\n from the second two terms yields 4xx+4-9x+4. Factoring out the common factor of x+4 from these two terms yields the expression 4x-9x+4. Since this expression is equal to 0\n, it follows that either \n\t\n\t\t\n\t\t\t4\n\t\t\tx\n\t\t\n\t\t-\n\t\t9\n\t\n\t=\n\t0\n\n or \n\t\n\t\tx\n\t\t+\n\t\t4\n\t\n\t=\n\t0\n\n. Adding 9\n to each side of the equation \n\t\n\t\t\n\t\t\t4\n\t\t\tx\n\t\t\n\t\t-\n\t\t9\n\t\n\t=\n\t0\n\n yields \n\t\n\t\t4\n\t\tx\n\t\n\t=\n\t9\n\n. Dividing each side of this equation by 4\n yields \n\tx\n\t=\n\t\n\t\t9\n\t\t4\n\t\n\n. Therefore, \n\t9\n\t4\n\n is a positive solution to the given equation. Subtracting 4\n from each side of the equation \n\t\n\t\tx\n\t\t+\n\t\t4\n\t\n\t=\n\t0\n\n yields \n\tx\n\t=\n\t-4\n\n. Therefore, the given equation has two solutions, \n\t9\n\t4\n\n and -4\n. Since \n\t9\n\t4\n\n is positive, it follows that \n\t9\n\t4\n\n is the positive solution to the given equation.

\n

Choice A is incorrect. Substituting \n\t7\n\t4\n\n for x\n in the given equation yields -492=-36, which is false.

\n

Choice C is incorrect. Substituting 4\n for x\n in the given equation yields -92=-36, which is false.

\n

Choice D is incorrect. Substituting 7\n for x\n in the given equation yields -245=-36, which is false.

"}, {"id": "be0c419e", "domain": "Advanced Math", "skill": "Nonlinear functions", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

Immanuel purchased a certain rare coin on January 1. The function f(x)=651.03x, where 0≤x≤10, gives the predicted value, in dollars, of the rare coin x\n years after Immanuel purchased it. What is the best interpretation of the statement “f8 is approximately equal to 82\n” in this context?

", "choices": [{"id": "A", "text": "

When the rare coin's predicted value is approximately 82\n dollars, it is 8\n% greater than the predicted value, in dollars, on January 1 of the previous year.

"}, {"id": "B", "text": "

When the rare coin’s predicted value is approximately 82\n dollars, it is 8\n times the predicted value, in dollars, on January 1 of the previous year.

"}, {"id": "C", "text": "

From the day Immanuel purchased the rare coin to 8\n years after Immanuel purchased the coin, its predicted value increased by a total of approximately 82\n dollars.

"}, {"id": "D", "text": "

8\n years after Immanuel purchased the rare coin, its predicted value is approximately 82\n dollars.

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. It’s given that the function fx=651.03x gives the predicted value, in dollars, of a certain rare coin x\n years after Immanuel purchased it. It follows that fx represents the predicted value, in dollars, of the coin x\n years after Immanuel purchased it. Since the value of f8 is the value of fx when \n\tx\n\t=\n\t8\n\n, it follows that “f8 is approximately equal to 82\n” means that fx is approximately equal to 82\n when \n\tx\n\t=\n\t8\n\n. Therefore, the best interpretation of the statement “f8 is approximately equal to 82\n” in this context is 8\n years after Immanuel purchased the rare coin, its predicted value is approximately 82\n dollars.

\n

Choice A is incorrect and may result from conceptual errors.

\n

Choice B is incorrect and may result from conceptual errors.

\n

Choice C is incorrect and may result from conceptual errors.

"}, {"id": "ce579859", "domain": "Advanced Math", "skill": "Nonlinear functions", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

A model estimates that at the end of each year from 2015 to 2020, the number of squirrels in a population was 150\n% more than the number of squirrels in the population at the end of the previous year. The model estimates that at the end of 2016, there were 180\n squirrels in the population. Which of the following equations represents this model, where n\n is the estimated number of squirrels in the population t\n years after the end of 2015 and t≤5?

", "choices": [{"id": "A", "text": "

n=721.5t

"}, {"id": "B", "text": "

n=722.5t

"}, {"id": "C", "text": "

n=1801.5t

"}, {"id": "D", "text": "

n=1802.5t

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. Since the model estimates that the number of squirrels in the population increased by a fixed percentage, 150%, each year, the model can be represented by an exponential equation of the form n=a1+p100t, where a\n is the estimated number of squirrels in the population at the end of 2015, and the model estimates that at the end of each year, the number is p% more than the number at the end of the previous year. Since the model estimates that at the end of each year, the number was 150% more than the number at the end of the previous year, \n\tp\n\t=\n\t150\n\n. Substituting 150\n for p\n in the equation n=a1+p100t yields n=a1+150100t, which is equivalent to n=a1+1.5t, or n=a2.5t. It’s given that the estimated number of squirrels at the end of 2016 was 180\n. This means that when \n\tt\n\t=\n\t1\n\n, \n\tn\n\t=\n\t180\n\n. Substituting 1\n for t\n and 180\n for n\n in the equation n=a2.5t yields 180=a2.51, or \n\t180\n\t=\n\t\n\t\t2.5\n\t\ta\n\t\n\n. Dividing each side of this equation by 2.5\n yields \n\t72\n\t=\n\ta\n\n. Substituting 72\n for a\n in the equation n=a2.5t yields n=722.5t.

\n

Choice A is incorrect. This equation represents a model where at the end of each year, the estimated number of squirrels was 150% of, not 150% more than, the estimated number at the end of the previous year.

\n

Choice C is incorrect. This equation represents a model where at the end of each year, the estimated number of squirrels was 150% of, not 150% more than, the estimated number at the end of the previous year, and the estimated number of squirrels at the end of 2015, not the end of 2016, was 180\n.

\n

Choice D is incorrect. This equation represents a model where the estimated number of squirrels at the end of 2015, not the end of 2016, was 180\n.

"}, {"id": "5355c0ef", "domain": "Advanced Math", "skill": "Equivalent expressions", "difficulty": "H", "type": "spr", "stimulus": "", "stem": "

\n\t\n\t\t0.36\n\t\t\n\t\t\tx\n\t\t\t2\n\t\t\n\t\n\t+\n\t\n\t\t0.63\n\t\tx\n\t\n\t+\n\t1.17\n\n

\n

The given expression can be rewritten as a4x2+7x+13, where a\n is a constant. What is the value of a\n?

", "choices": [], "answerId": ".09", "acceptedAnswers": [".09", "9/100"], "rationale": "

The correct answer is .09. It's given that the expression 0.36x2+0.63x+1.17 can be rewritten as a4x2+7x+13. Applying the distributive property to the expression a4x2+7x+13 yields 4ax2+7ax+13a. Therefore, 0.36x2+0.63x+1.17 can be rewritten as 4ax2+7ax+13a. It follows that in the expressions 0.36x2+0.63x+1.17 and 4ax2+7ax+13a, the coefficients of x2 are equivalent, the coefficients of x\n are equivalent, and the constant terms are equivalent. Therefore, \n\t0.36\n\t=\n\t\n\t\t4\n\t\ta\n\t\n\n, \n\t0.63\n\t=\n\t\n\t\t7\n\t\ta\n\t\n\n, and \n\t1.17\n\t=\n\t\n\t\t13\n\t\ta\n\t\n\n. Solving any of these equations for a\n yields the value of a\n. Dividing both sides of the equation \n\t0.36\n\t=\n\t\n\t\t4\n\t\ta\n\t\n\n by 4\n yields \n\t0.09\n\t=\n\ta\n\n. Therefore, the value of a\n is 0.09\n. Note that .09 and 9/100 are examples of ways to enter a correct answer.

"}, {"id": "2f51abc2", "domain": "Advanced Math", "skill": "Nonlinear functions", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

fx=59-2x

\n

The function f\n is defined by the given equation. For which of the following values of k\n does fk=3k?

", "choices": [{"id": "A", "text": "

\n\t59\n\t5\n\n

"}, {"id": "B", "text": "

\n\t59\n\t2\n\n

"}, {"id": "C", "text": "

\n\t177\n\t5\n\n

"}, {"id": "D", "text": "

59\n

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. The value of k\n for which fk=3k can be found by substituting k\n for x\n and \n\t3\n\tk\n\n for fx in the given equation, fx=59-2x, which yields 3k=59-2k. For this equation to be true, either -3k=59-2k or 3k=59-2k. Adding \n\t2\n\tk\n\n to both sides of the equation -3k=59-2k yields -k=59. Dividing both sides of this equation by -1\n yields k=-59. To check whether -59\n is the value of k\n, substituting -59\n for k\n in the equation 3k=59-2k yields 3-59=59-2-59, which is equivalent to -177=177, or -177=177, which isn't a true statement. Therefore, -59\n isn't the value of k\n. Adding \n\t2\n\tk\n\n to both sides of the equation 3k=59-2k yields 5k=59. Dividing both sides of this equation by 5\n yields k=595. To check whether \n\t59\n\t5\n\n is the value of k\n, substituting \n\t59\n\t5\n\n for k\n in the equation 3k=59-2k yields 3595=59-2595, which is equivalent to 1775=1775, or 1775=1775, which is a true statement. Therefore, the value of k\n for which fk=3k is 595.

\n

Choice B is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

\n

Choice D is incorrect and may result from conceptual or calculation errors.

"}, {"id": "17d0e87d", "domain": "Advanced Math", "skill": "Nonlinear equations in one variable and systems of equations in two variables ", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

14x7y=2w+19

\n

The given equation relates the distinct positive real numbers w\n, x\n, and y\n. Which equation correctly expresses w\n in terms of x\n and y\n?

", "choices": [{"id": "A", "text": "

w=xy-19

"}, {"id": "B", "text": "

w=28x14y-19

"}, {"id": "C", "text": "

w=xy2-19

"}, {"id": "D", "text": "

w=28x14y2-19

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. Dividing each side of the given equation by 2\n yields 14x14y=2w+192, or xy=w+19. Because it's given that each of the variables is positive, squaring each side of this equation yields the equivalent equation xy2=w+19. Subtracting 19\n from each side of this equation yields xy2-19=w, or w=xy2-19.

\n

Choice A is incorrect. This equation isn't equivalent to the given equation. 

\n

Choice B is incorrect. This equation isn't equivalent to the given equation. 

\n

Choice D is incorrect. This equation isn't equivalent to the given equation. 

"}, {"id": "a1bf1c4e", "domain": "Advanced Math", "skill": "Equivalent expressions", "difficulty": "M", "type": "mc", "stimulus": "
\n

\n x\u00b2, + 6 x, + 4\n

\n
\n", "stem": "

Which of the following is equivalent to the expression above?

\n", "choices": [{"id": "A", "text": "

\n (x + 3)2 + 5\n

\n"}, {"id": "B", "text": "

\n (x + 3)2 – 5\n

\n"}, {"id": "C", "text": "

\n (x – 3)2 + 5\n

\n"}, {"id": "D", "text": "

\n (x – 3)2 – 5\n

\n"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. The given quadratic expression is in standard form, and each answer choice is in vertex form. Completing the square converts the expression from standard form to vertex form. The first step is to rewrite the expression as follows: x\u00b2, + 6 x, + 4 = x\u00b2, + 6 x, + 9, + 4, \u2212 9. The first three terms of the revised expression can be rewritten as a perfect square as follows: x\u00b2, + 6 x, + 9, + 4, \u2212 9 = open parenthesis, x + 3, close parenthesis, squared, + 4, \u2212 9. Combining the constant terms gives open parenthesis, x + 3, close parenthesis, squared, \u2212 5.

Choice A is incorrect. Squaring the binomial and simplifying the expression in choice A gives x\u00b2, + 6 x, + 9, + 5. Combining like terms gives x\u00b2, \u2212 6 x, + 14, not x\u00b2, + 6 x, + 4. Choice C is incorrect. Squaring the binomial and simplifying the expression in choice C gives x\u00b2, \u2212 6 x, + 9, + 5. Combining like terms gives x\u00b2, \u2212 6 x, + 14, not x\u00b2, + 6 x, + 4. Choice D is incorrect. Squaring the binomial and simplifying the expression in choice D gives x\u00b2, \u2212 6 x, + 9, \u2212 5. Combining like terms gives x\u00b2, \u2212 6 x, + 4, not x\u00b2, + 6 x, + 4.

\n"}, {"id": "c81b6c57", "domain": "Advanced Math", "skill": "Equivalent expressions", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

In the expression \"\" , p is a constant. This expression is equivalent to the expression 6 x\u00b2 \u2212 155 x + 24. What is the value of p ?

\n", "choices": [{"id": "A", "text": "

\u22123

\n"}, {"id": "B", "text": "

7

\n"}, {"id": "C", "text": "

13

\n"}, {"id": "D", "text": "

155

\n"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. Using the distributive property, the first given expression can be rewritten as 6x2 + 3px + 24 – 16px – 64x + 24, and then rewritten as 6x2 + (3p – 16p – 64)x + 24. Since the expression 6x2 + (3p – 16p – 64)x + 24 is equivalent to 6x2 – 155x + 24, the coefficients of the x terms from each expression are equivalent to each other; thus 3p – 16p – 64 = –155. Combining like terms gives –13p  – 64 = –155. Adding 64 to both sides of the equation gives –13p = –71. Dividing both sides of the equation by –13 yields p = 7.

Choice A is incorrect. If p = –3, then the first expression would be equivalent to 6x2 – 25x + 24. Choice C is incorrect. If p = 13, then the first expression would be equivalent to 6x2 – 233x + 24. Choice D is incorrect. If p = 155, then the first expression would be equivalent to 6x2 – 2,079x + 24.

\n"}, {"id": "802549ac", "domain": "Advanced Math", "skill": "Nonlinear equations in one variable and systems of equations in two variables ", "difficulty": "M", "type": "mc", "stimulus": "
\n

\n open parenthesis, x + 2, close parenthesis, times, open parenthesis, x + 3, close parenthesis = open parenthesis, x \u2212 2, close parenthesis, times, open parenthesis, x \u2212 3, close parenthesis, + 10\n

\n
\n", "stem": "

Which of the following is a solution to the given equation?

\n", "choices": [{"id": "A", "text": "

\n 1

\n"}, {"id": "B", "text": "

\n 0

\n"}, {"id": "C", "text": "

\n \u22122

\n"}, {"id": "D", "text": "

\n \u22125

\n"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. Applying the distributive property on the left- and right-hand sides of the given equation yields x\u00b2, + 2 x, + 3 x, + 6 = x\u00b2, \u2212 2 x, \u2212 3 x, + 6, + 10, or x\u00b2, + 5 x, + 6 = x\u00b2, \u2212 5 x, + 16. Subtracting x\u00b2 from and adding 5 x to both sides of this equation yields 10 x + 6 = 16. Subtracting 6 from both sides of this equation and then dividing both sides by 10 yields x = 1.

Choices B, C, and D are incorrect. Substituting 0, \u22122, or \u22125 for x in the given equation will result in a false statement. If x = 0, the given equation becomes 6 = 16; if x = \u22122, the given equation becomes 0 = 30; and if x = \u22125, the given equation becomes 6 = 66. Therefore, the values 0, \u22122, and \u22125 aren’t solutions to the given equation.

\n"}, {"id": "a31417d1", "domain": "Advanced Math", "skill": "Nonlinear functions", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

From 2005 through 2014, the number of music CDs sold in the United States declined each year by approximately 15% of the number sold the preceding year. In 2005, approximately 600 million CDs were sold in the United States. Of the following, which best models C, the number of millions of CDs sold in the United States, t years after 2005?

\n", "choices": [{"id": "A", "text": "

\n C = 600 times, open parenthesis, 0 point 1 5, close parenthesis, raised to the t power\n

\n"}, {"id": "B", "text": "

\n C = 600 times, open parenthesis, 0 point 8 5, close parenthesis, raised to the t power\n

\n"}, {"id": "C", "text": "

\n C = 600 times, open parenthesis, 1 point 1 5, close parenthesis, raised to the t power\n

\n"}, {"id": "D", "text": "

\n C = 600 times, open parenthesis, 1 point 8 5, close parenthesis, raised to the t power\n

\n"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. A model for a quantity C that decreases by a certain percentage per time period t is an exponential equation in the form C = I times, open parenthesis, 1 minus, (r)/(100, close parenthesis, to the t power), where I is the initial value at time t = 0 for r% annual decline. It’s given that C is the number of millions of CDs sold in the United States and that t is the number of years after 2005. It’s also given that 600 million CDs were sold at time t = 0, so I = 600. This number declines by 15% per year, so r = 15. Substituting these values into the equation produces C = 600 times, open parenthesis, 1 \u2212 (15)/(100, close parenthesis, to the t power), or C = 600 times, open parenthesis, 0 point 8 5, close parenthesis, to the t power.

Choice A is incorrect and may result from errors made when representing the percent decline. Choices C and D are incorrect. These equations model exponential increases in CD sales, not exponential decreases.

\n"}, {"id": "66bce0c1", "domain": "Advanced Math", "skill": "Nonlinear equations in one variable and systems of equations in two variables ", "difficulty": "H", "type": "mc", "stimulus": "
\n\t

The square root(2) x + 6, end root, + 4 = x + 3

\n
\n", "stem": "

What is the solution set of the equation above?

\n", "choices": [{"id": "A", "text": "

set consisting(n)egative 1

\n"}, {"id": "B", "text": "

set consisting(5)

\n"}, {"id": "C", "text": "

set consisting(n)egative 1 and 5

\n"}, {"id": "D", "text": "

set consisting(0), \u22121, and 5

\n"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. Subtracting 4 from both sides of the square root(2) x + 6, end root, + 4 = x + 3 isolates the radical expression on the left side of the equation as follows: the square root(2) x + 6, end root = x \u2212 1. Squaring both sides of the square root(2) x + 6, end root = x \u2212 1 yields 2 x + 6 = x\u00b2, \u2212 2 x, + 1. This equation can be rewritten as a quadratic equation in standard form: x\u00b2, \u2212 4 x, \u2212 5 = 0. One way to solve this quadratic equation is to factor the expression x\u00b2, \u2212 4 x, \u2212 5 by identifying two numbers with a sum of \u22124 and a product of \u22125. These numbers are \u22125 and 1. So the quadratic equation can be factored as open parenthesis, x \u2212 5, close parenthesis, times, open parenthesis, x + 1, close parenthesis = 0. It follows that 5 and \u22121 are the solutions to the quadratic equation. However, the solutions must be verified by checking whether 5 and\u22121 satisfy the original equation, the square root(2) x + 6, end root, + 4 = x + 3. When x = \u22121, the original equation gives the square root(2) \u00d7 \u22121, + 6, end root, + 4 = \u22121 + 3, or 6 = 2, which is false. Therefore, \u22121 does not satisfy the original equation. When x = 5, the original equation gives the square root(2) \u00d7 5, + 6, end root, + 4 = 5 + 3, or 8 = 8, which is true. Therefore, x = 5 is the only solution to the original equation, and so the solution set is 5.

Choices A, C, and D are incorrect because each of these sets contains at least one value that results in a false statement when substituted into the given equation. For instance, in choice D, when 0 is substituted for x into the given equation, the result is the square root(2) \u00d7 0, + 6, + 4, end root = 0 + 3, or the square root(6), end root, + 4 = 3. This is not a true statement, so 0 is not a solution to the given equation.

 

\n"}, {"id": "6d04c89d", "domain": "Advanced Math", "skill": "Equivalent expressions", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

The expression \n\t\t24\n\t\t\n\t\t\t\n\t\t\t\t6\n\t\t\t\tx\n\t\t\t\n\t\t\t+\n\t\t\t42\n\t\t\n\t\n is equivalent to \n\t\t4\n\t\t\n\t\t\tx\n\t\t\t+\n\t\t\tb\n\t\t\n\t\n, where b is a constant and x>0. What is the value of b?

", "choices": [{"id": "A", "text": "

7\n

"}, {"id": "B", "text": "

10\n

"}, {"id": "C", "text": "

24\n

"}, {"id": "D", "text": "

252\n

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. Since the given expressions are equivalent and the numerator of the second expression is 16 of the numerator of the first expression, the denominator of the second expression must also be 16 of the denominator of the first expression. By the distributive property,  166x+42 is equivalent to 166x+1642, or x+7. Therefore, the value of b\n is 7\n.

\n

Choice B is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

\n

Choice D is incorrect and may result from conceptual or calculation errors.

"}, {"id": "ebb717ab", "domain": "Advanced Math", "skill": "Nonlinear equations in one variable and systems of equations in two variables ", "difficulty": "H", "type": "spr", "stimulus": "", "stem": "

\n\t\n\t\t\n\t\t\tx\n\t\t\t2\n\t\t\n\t\t-\n\t\t\n\t\t\t34\n\t\t\tx\n\t\t\n\t\t+\n\t\tc\n\t\n\t=\n\t0\n\n

\n

In the given equation, c\n is a constant. The equation has no real solutions if c>n. What is the least possible value of n\n?

", "choices": [], "answerId": "289", "acceptedAnswers": ["289"], "rationale": "

The correct answer is 289\n. A quadratic equation of the form ax2+bx+c=0, where a\n, b\n, and c\n are constants, has no real solutions when the value of the discriminant, b2-4ac, is less than 0\n. In the given equation, x2-34x+c=0, a=1 and b=-34. Therefore, the discriminant of the given equation can be expressed as -342-41c, or 1,156-4c. It follows that the given equation has no real solutions when 1,156-4c<0. Adding \n\t4\n\tc\n\n to both sides of this inequality yields 1,156<4c. Dividing both sides of this inequality by 4\n yields 289<c, or c>289. It's given that the equation x2-34x+c=0 has no real solutions when c>n. Therefore, the least possible value of n\n is 289\n.

"}, {"id": "9afe2370", "domain": "Advanced Math", "skill": "Nonlinear functions", "difficulty": "H", "type": "mc", "stimulus": "
\n
\n
\n

The population P of a certain city y years after the last census is modeled by the equation below, where r is a constant and P subscript 0 is the population when y = 0.

\n
\n
\n

\n P = P subscript 0, times, open parenthesis, 1 + r, close parenthesis, to the power y\n

\n
\n", "stem": "

If during this time the population of the city decreases by a fixed percent each year, which of the following must be true?

\n", "choices": [{"id": "A", "text": "r < \u22121\n"}, {"id": "B", "text": "\u22121 < r, which < 0\n"}, {"id": "C", "text": "0 < r, which < 1\n"}, {"id": "D", "text": "r > 1\n"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. The term (1 + r) represents a percent change. Since the population is decreasing, the percent change must be between 0% and 100%. When the percent change is expressed as a decimal rather than as a percent, the percentage change must be between 0 and 1. Because (1 + r) represents percent change, this can be expressed as 0 < 1 + r < 1. Subtracting 1 from all three terms of this compound inequality results in –1 < r < 0.

Choice A is incorrect. If r < –1, then after 1 year, the population P would be a negative value, which is not possible. Choices C and D are incorrect. For any value of r > 0, 1 + r > 1, and the exponential function models growth for positive values of the exponent. This contradicts the given information that the population is decreasing.

\n"}, {"id": "60fdb4d4", "domain": "Advanced Math", "skill": "Equivalent expressions", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

Which expression is equivalent to parenthesis, 2 x\u00b2 \u2212 4, close parenthesis, minus, parenthesis, \u22123 x\u00b2, + 2 x, \u2212 7, close parenthesis ?

\n", "choices": [{"id": "A", "text": "5 x\u00b2 \u2212 2 x + 3\n"}, {"id": "B", "text": "5 x\u00b2 + 2 x \u2212 3\n"}, {"id": "C", "text": "\u2212x\u00b2 \u2212 2 x \u2212 11\n"}, {"id": "D", "text": "\u2212x\u00b2 + 2 x \u2212 11\n"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. The given expression open parenthesis, 2 x\u00b2, \u2212 4, close parenthesis, minus, open parenthesis, \u22123, x\u00b2, + 2 x, \u2212 7, close parenthesis can be rewritten as 2 x\u00b2, \u2212 4, + 3 x\u00b2, \u2212 2 x, + 7. Combining like terms yields 5 x\u00b2, \u2212 2 x, + 3.

Choices B, C, and D are incorrect and may be the result of errors when applying the distributive property.

\n \n

\n"}, {"id": "ad376f1a", "domain": "Advanced Math", "skill": "Nonlinear functions", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n\n

\n

The graph of y=fx is shown in the xy-plane. What is the value of f0?

", "choices": [{"id": "A", "text": "

-3\n

"}, {"id": "B", "text": "

0\n

"}, {"id": "C", "text": "

\n\t3\n\t5\n\n

"}, {"id": "D", "text": "

3\n

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. Because the graph of y=fx is shown, the value of f0 is the value of y\n on the graph that corresponds with \n\tx\n\t=\n\t0\n\n. When \n\tx\n\t=\n\t0\n\n, the corresponding value of y\n is 3\n. Therefore, the value of f0 is 3\n.

\n

Choice A is incorrect and may result from conceptual errors.

\n

Choice B is incorrect and may result from conceptual errors.

\n

Choice C is incorrect and may result from conceptual errors.

"}, {"id": "db888cd6", "domain": "Advanced Math", "skill": "Nonlinear functions", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n\n

\n

The graph gives the estimated number of catalogs y\n, in thousands, a company sent to its customers at the end of each year, where x\n represents the number of years since the end of 1992\n, where 0≤x≤10. Which statement is the best interpretation of the y-intercept in this context?

", "choices": [{"id": "A", "text": "

The estimated total number of catalogs the company sent to its customers during the first 10\n years was 9,000\n.

"}, {"id": "B", "text": "

The estimated total number of catalogs the company sent to its customers from the end of 1992\n to the end of 2002\n was 90\n.

"}, {"id": "C", "text": "

The estimated number of catalogs the company sent to its customers at the end of 1992\n was 9\n.

"}, {"id": "D", "text": "

The estimated number of catalogs the company sent to its customers at the end of 1992\n was 9,000\n.

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. The y-intercept of the graph is the point at which the graph crosses the y-axis, or the point for which the value of x\n is 0\n. Therefore, the y-intercept of the given graph is the point 0,9. It's given that x\n represents the number of years since the end of 1992. Therefore, x=0 represents 0\n years since the end of 1992, which is the same as the end of 1992. It's also given that y\n represents the estimated number of catalogs, in thousands, that the company sent to its customers at the end of the year. Therefore, y=9 represents 9,000\n catalogs. It follows that the y-intercept 0,9 means that the estimated number of catalogs the company sent to its customers at the end of 1992 was 9,000\n. 

\n

Choice A is incorrect and may result from conceptual or calculation errors.

\n

Choice B is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

"}, {"id": "6ecdbcb4", "domain": "Advanced Math", "skill": "Nonlinear functions", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

f(x)=(x+6)(x+5)(x-4)

\n

The function f\n is given. Which table of values represents y=f(x)-3?

", "choices": [{"id": "A", "text": "\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
x\ny\n
-6\n-9\n
-5\n-8\n
4\n1\n
"}, {"id": "B", "text": "\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
x\ny\n
-6\n-3\n
-5\n-3\n
4\n-3\n
"}, {"id": "C", "text": "\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
x\ny\n
-6\n-3\n
-5\n-2\n
4\n7\n
"}, {"id": "D", "text": "\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
x\ny\n
-6\n3\n
-5\n3\n
4\n3\n
"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. It’s given that fx=(x+6)(x+5)(x-4) and y=f(x)-3. Substituting (x+6)(x+5)(x-4) for fx in the equation y=f(x)-3 yields y=(x+6)(x+5)(x-4)-3. Substituting -6\n for x\n in this equation yields y=(-6+6)(-6+5)(-6-4)-3, or \n\ty\n\t=\n\t-3\n\n. Substituting -5\n for x\n in the equation y=(x+6)(x+5)(x-4)-3 yields y=(-5+6)(-5+5)(-5-4)-3, or \n\ty\n\t=\n\t-3\n\n. Substituting 4\n for x\n in the equation y=(x+6)(x+5)(x-4)-3 yields y=(4+6)(4+5)(4-4)-3, or \n\ty\n\t=\n\t-3\n\n. Therefore, when \n\tx\n\t=\n\t-6\n\n then \n\ty\n\t=\n\t-3\n\n, when \n\tx\n\t=\n\t-5\n\n then \n\ty\n\t=\n\t-3\n\n, and when \n\tx\n\t=\n\t4\n\n then \n\ty\n\t=\n\t-3\n\n. Thus, the table of values in choice B represents y=f(x)-3.

\n

Choice A is incorrect. This table represents \n\ty\n\t=\n\t\n\t\tx\n\t\t-\n\t\t3\n\t\n\n rather than y=f(x)-3.

\n

Choice C is incorrect. This table represents \n\ty\n\t=\n\t\n\t\tx\n\t\t+\n\t\t3\n\t\n\n rather than y=f(x)-3.

\n

Choice D is incorrect. This table represents y=fx+3 rather than y=f(x)-3.

"}, {"id": "7cb3a8ee", "domain": "Advanced Math", "skill": "Nonlinear equations in one variable and systems of equations in two variables ", "difficulty": "E", "type": "spr", "stimulus": "", "stem": "

\n\t\n\t\t\n\t\t\t\n\t\t\t\tx\n\t\t\t\t-\n\t\t\t\t5\n\t\t\t\n\t\t\n\t\n\t=\n\t10\n\n

\n

What is one possible solution to the given equation?

", "choices": [], "answerId": "15", "acceptedAnswers": ["15", "-5"], "rationale": "

The correct answer is 15\n or -5\n. By the definition of absolute value, if x-5=10, then x-5=10 or x-5=-10. Adding 5\n to both sides of the first equation yields x=15. Adding 5\n to both sides of the second equation yields x=-5. Thus, the given equation has two possible solutions, 15\n and -5\n. Note that 15 and -5 are examples of ways to enter a correct answer.

"}, {"id": "203774bc", "domain": "Advanced Math", "skill": "Nonlinear functions", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

The product of two positive integers is 546\n. If the first integer is 11\n greater than twice the second integer, what is the smaller of the two integers?

", "choices": [{"id": "A", "text": "

7\n

"}, {"id": "B", "text": "

14\n

"}, {"id": "C", "text": "

39\n

"}, {"id": "D", "text": "

78\n

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. Let x\n be the first integer and let y\n be the second integer. If the first integer is 11\n greater than twice the second integer, then \n\tx\n\t=\n\t\n\t\t\n\t\t\t2\n\t\t\ty\n\t\t\n\t\t+\n\t\t11\n\t\n\n. If the product of the two integers is 546\n, then xy=546. Substituting \n\t\n\t\t2\n\t\ty\n\t\n\t+\n\t11\n\n for x\n in this equation results in 2y+11y=546. Distributing the y\n to both terms in the parentheses results in \n\t\n\t\t\n\t\t\t2\n\t\t\t\n\t\t\t\ty\n\t\t\t\t2\n\t\t\t\n\t\t\n\t\t+\n\t\t\n\t\t\t11\n\t\t\ty\n\t\t\n\t\n\t=\n\t546\n\n. Subtracting 546\n from both sides of this equation results in \n\t\n\t\t\n\t\t\t2\n\t\t\t\n\t\t\t\ty\n\t\t\t\t2\n\t\t\t\n\t\t\n\t\t+\n\t\t\n\t\t\t11\n\t\t\ty\n\t\t\n\t\t-\n\t\t546\n\t\n\t=\n\t0\n\n. The left-hand side of this equation can be factored by finding two values whose product is 2-546, or -1,092\n, and whose sum is 11\n. The two values whose product is -1,092\n and whose sum is 11\n are 39\n and -28\n. Thus, the equation \n\t\n\t\t\n\t\t\t2\n\t\t\t\n\t\t\t\ty\n\t\t\t\t2\n\t\t\t\n\t\t\n\t\t+\n\t\t\n\t\t\t11\n\t\t\ty\n\t\t\n\t\t-\n\t\t546\n\t\n\t=\n\t0\n\n can be rewritten as 2y2+28y-39y-546=0, which is equivalent to 2yy-14+39y-14=0, or 2y+39y-14=0. By the zero product property, it follows that \n\t\n\t\t\n\t\t\t2\n\t\t\ty\n\t\t\n\t\t+\n\t\t39\n\t\n\t=\n\t0\n\n and \n\t\n\t\ty\n\t\t-\n\t\t14\n\t\n\t=\n\t0\n\n. Subtracting 39\n from both sides of the equation \n\t\n\t\t\n\t\t\t2\n\t\t\ty\n\t\t\n\t\t+\n\t\t39\n\t\n\t=\n\t0\n\n yields \n\t\n\t\t2\n\t\ty\n\t\n\t=\n\t-39\n\n. Dividing both sides of this equation by 2\n yields \n\ty\n\t=\n\t\n\t\t-\n\t\t\n\t\t\t39\n\t\t\t2\n\t\t\n\t\n\n. Since y\n is a positive integer, the value of y\n is not \n\t-\n\t\n\t\t39\n\t\t2\n\t\n\n. Adding 14\n to both sides of the equation \n\t\n\t\ty\n\t\t-\n\t\t14\n\t\n\t=\n\t0\n\n yields \n\ty\n\t=\n\t14\n\n. Substituting 14\n for y\n in the equation xy=546 yields x14=546. Dividing both sides of this equation by 14\n results in \n\tx\n\t=\n\t39\n\n. Therefore, the two integers are 14\n and 39\n, so the smaller of the two integers is 14\n.

\n

Choice A is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect. This is the larger of the two integers.

\n

Choice D is incorrect and may result from conceptual or calculation errors.

"}, {"id": "b7c74b73", "domain": "Advanced Math", "skill": "Nonlinear functions", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

fx=5,4700.64x12

\n

The function f\n gives the value, in dollars, of a certain piece of equipment after x\n months of use. If the value of the equipment decreases each year by p% of its value the preceding year, what is the value of p\n?

", "choices": [{"id": "A", "text": "

4\n

"}, {"id": "B", "text": "

5\n

"}, {"id": "C", "text": "

36\n

"}, {"id": "D", "text": "

64\n

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. For a function of the form fx=arxk, where a\n, r\n, and k\n are constants and r<1, the value of fx decreases by 1001-r% for every increase of x\n by k\n. In the given function, \n\ta\n\t=\n\t5,470\n\n, \n\tr\n\t=\n\t0.64\n\n, and \n\tk\n\t=\n\t12\n\n. Therefore, for the given function, the value of fx decreases by 1001-0.64%, or 36%, for every increase of x\n by 12\n. Since fx represents the value, in dollars, of the equipment after x\n months of use, it follows that the value of the equipment decreases every 12\n months by 36% of its value the preceding 12\n months. Since there are 12\n months in a year, the value of the equipment decreases each year by 36% of its value the preceding year. Thus, the value of p\n is 36\n.

\n

Choice A is incorrect and may result from conceptual or calculation errors.

\n

Choice B is incorrect and may result from conceptual or calculation errors.

\n

Choice D is incorrect and may result from conceptual or calculation errors.

"}, {"id": "3d12b1e0", "domain": "Advanced Math", "skill": "Nonlinear equations in one variable and systems of equations in two variables ", "difficulty": "H", "type": "spr", "stimulus": "", "stem": "

\n\t\n\t\t\n\t\t\t-\n\t\t\t16\n\t\t\t\n\t\t\t\tx\n\t\t\t\t2\n\t\t\t\n\t\t\n\t\t-\n\t\t\n\t\t\t8\n\t\t\tx\n\t\t\n\t\t+\n\t\tc\n\t\n\t=\n\t0\n\n

\n

In the given equation, c\n is a constant. The equation has exactly one solution. What is the value of c\n?

", "choices": [], "answerId": "-1", "acceptedAnswers": ["-1"], "rationale": "

The correct answer is -1\n. A quadratic equation in the form ax2+bx+c=0, where a\n, b\n, and c\n are constants, has exactly one solution when its discriminant, b2-4ac, is equal to 0\n. In the given equation, -16x2-8x+c=0, \n\ta\n\t=\n\t-16\n\n and \n\tb\n\t=\n\t-8\n\n. Substituting -16\n for a\n and -8\n for b\n in b2-4ac yields -82-4-16c, or 64+64c. Since the given equation has exactly one solution, 64+64c=0. Subtracting 64\n from both sides of this equation yields 64c=-64. Dividing both sides of this equation by 64\n yields \n\tc\n\t=\n\t-1\n\n. Therefore, the value of c\n is -1\n.

"}, {"id": "2c88af4d", "domain": "Advanced Math", "skill": "Equivalent expressions", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

The expression (x to the power \u22122, end power, \u00d7 y to the power one-half)/(x to the power one-third, end power, \u00d7 y to the power \u22121, end fraction), where x > 1 and y > 1, is equivalent to which of the following?

\n", "choices": [{"id": "A", "text": "\n The fraction with numerator the square root(y) and denominator the cube root(x) squared\n \n"}, {"id": "B", "text": "\n The fraction with numerator y \u00d7 the square root(y) and denominator the cube root(x) squared\n \n"}, {"id": "C", "text": "\n The fraction with numerator y \u00d7 the square root(y) and denominator x \u00d7 the square root(x)\n \n"}, {"id": "D", "text": "\n The fraction with numerator y \u00d7 the square root(y) and denominator x\u00b2 \u00d7 the cube root(x)\n \n"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. For x > 1 and y > 1, x to the one third power and y to the one half power are equivalent to the cube root(x) and the square root(y), respectively. Also, x to the \u22122 power and y to the \u22121 power are equivalent to (1)/(x\u00b2, end fraction) and 1 over y, respectively. Therefore, the given expression can be rewritten as the fraction with numerator, y \u00d7 the square root(y), and denominator x\u00b2, \u00d7 the cube root(x), end fraction.

Choices A, B, and C are incorrect because these choices are not equivalent to the given expression for x > 1 and y > 1.

For example, for x = 2 and y = 2, the value of the given expression is 2 to the \u2212five sixths power; the values of the choices, however, are 2 to the \u2212one third power, 2 to the five sixths power, and 1, respectively.

\n"}, {"id": "c4cd5bcc", "domain": "Advanced Math", "skill": "Nonlinear functions", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

In the xy-plane, the y-coordinate of the y-intercept of the graph of the function f is c. Which of the following must be equal to c ?

\n", "choices": [{"id": "A", "text": "

f(0)

\n"}, {"id": "B", "text": "

f(1)

\n"}, {"id": "C", "text": "

f(2)

\n"}, {"id": "D", "text": "

f(3)

\n"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. A y-intercept is the point in the xy-plane where the graph of the function crosses the y-axis, which is where x = 0. It’s given that the y-coordinate of the y-intercept of the graph of function f is c. It follows that the coordinate pair representing the y-intercept must be the point 0, c. Therefore, c must equal f(0).

Choices B, C, and D are incorrect because f(1), f(2), and f(3)would represent the y-value of the coordinate where x = 1, x = 2, and x = 3, respectively.

 

\n"}, {"id": "062f86db", "domain": "Advanced Math", "skill": "Nonlinear equations in one variable and systems of equations in two variables ", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

\n\t\n\t\t\n\t\t\t5\n\t\t\t\n\t\t\t\tx\n\t\t\t\t2\n\t\t\t\n\t\t\n\t\t-\n\t\t\n\t\t\t37\n\t\t\tx\n\t\t\n\t\t-\n\t\t24\n\t\n\t=\n\t0\n\n

\n

What is the positive solution to the given equation?

", "choices": [{"id": "A", "text": "

\n\t3\n\t5\n\n

"}, {"id": "B", "text": "

3\n

"}, {"id": "C", "text": "

8\n

"}, {"id": "D", "text": "

37\n

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. The left-hand side of the given equation can be factored as 5x+3x-8. Therefore, the given equation, 5x2-37x-24=0, can be written as 5x+3x-8=0. Applying the zero product property to this equation yields 5x+3=0 and x-8=0. Subtracting 3\n from both sides of the equation 5x+3=0 yields 5x=-3. Dividing both sides of this equation by 5\n yields x=-35. Adding 8\n to both sides of the equation x-8=0 yields x=8. Therefore, the two solutions to the given equation, 5x2-37x-24=0, are -35 and 8\n. It follows that 8\n is the positive solution to the given equation.

\n

Choice A is incorrect and may result from conceptual or calculation errors.

\n

Choice B is incorrect and may result from conceptual or calculation errors.

\n

Choice D is incorrect and may result from conceptual or calculation errors.

"}, {"id": "ffdbcad4", "domain": "Advanced Math", "skill": "Equivalent expressions", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

The expression \n\t\n\t\t4\n\t\t\n\t\t\tx\n\t\t\t2\n\t\t\n\t\n\t+\n\t\n\t\tb\n\t\tx\n\t\n\t-\n\t45\n\n, where b\n is a constant, can be rewritten as hx+kx+j, where h\n, k\n, and j\n are integer constants. Which of the following must be an integer?

", "choices": [{"id": "A", "text": "

\n\t\n\t\tb\n\t\th\n\t\n\n

"}, {"id": "B", "text": "

\n\t\n\t\tb\n\t\tk\n\t\n\n

"}, {"id": "C", "text": "

\n\t\n\t\t45\n\t\th\n\t\n\n

"}, {"id": "D", "text": "

\n\t\n\t\t45\n\t\tk\n\t\n\n

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. It's given that 4x2+bx-45 can be rewritten as hx+kx+j. The expression hx+kx+j can be rewritten as hx2+jhx+kx+kj, or hx2+jh+kx+kj. Therefore, hx2+jh+kx+kj is equivalent to 4x2+bx-45. It follows that kj=-45. Dividing each side of this equation by k\n yields j=-45k. Since j\n is an integer, \n\t-\n\t\n\t\t45\n\t\tk\n\t\n\n must be an integer. Therefore, \n\t\t45\n\t\tk\n\t\n must also be an integer.

\n

Choice A is incorrect and may result from conceptual or calculation errors.

\n

Choice B is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

"}, {"id": "735a0a00", "domain": "Advanced Math", "skill": "Nonlinear functions", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

\n\ty\n\t=\n\t\n\t\t\n\t\t\t0.25\n\t\t\t\n\t\t\t\tx\n\t\t\t\t2\n\t\t\t\n\t\t\n\t\t-\n\t\t\n\t\t\t7.5\n\t\t\tx\n\t\t\n\t\t+\n\t\t90.25\n\t\n\n

\n

The equation gives the estimated stock price y\n, in dollars, for a certain company x\n days after a new product launched, where 0≤x≤20. Which statement is the best interpretation of x,y=1,83  in this context?

", "choices": [{"id": "A", "text": "

The company's estimated stock price increased $83\n every day after the new product launched.

"}, {"id": "B", "text": "

The company's estimated stock price increased $1 every 83\n days after the new product launched.

"}, {"id": "C", "text": "

1 day after the new product launched, the company's estimated stock price is $83\n.

"}, {"id": "D", "text": "

83\n days after the new product launched, the company's estimated stock price is $1.

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. In the given equation, x\n represents the number of days after a new product launched, where 0≤x≤20, and y\n represents the estimated stock price, in dollars, for a certain company. Therefore, the best interpretation of x,y=1,83 in this context is that 1\n day after the new product launched, the company's estimated stock price is $83.

\n

Choice A is incorrect and may result from conceptual errors.

\n

Choice B is incorrect and may result from conceptual errors.

\n

Choice D is incorrect and may result from conceptual errors.
 

"}, {"id": "71014fb1", "domain": "Advanced Math", "skill": "Nonlinear equations in one variable and systems of equations in two variables ", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

\n\t\n\t\t\n\t\t\t\n\t\t\t\tx\n\t\t\t\t-\n\t\t\t\t1\n\t\t\t\n\t\t\n\t\t2\n\t\n\t=\n\t-4\n\n

\n

How many distinct real solutions does the given equation have?

", "choices": [{"id": "A", "text": "

Exactly one

"}, {"id": "B", "text": "

Exactly two

"}, {"id": "C", "text": "

Infinitely many

"}, {"id": "D", "text": "

Zero

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. Any quantity that is positive or negative in value has a positive value when squared. Therefore, the left-hand side of the given equation is either positive or zero for any value of x\n. Since the right-hand side of the given equation is negative, there is no value of x\n for which the given equation is true. Thus, the number of distinct real solutions for the given equation is zero.

\n

Choices A, B, and C are incorrect and may result from conceptual errors.

"}, {"id": "4a5af623", "domain": "Advanced Math", "skill": "Equivalent expressions", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

Which expression is a factor of \n\t\n\t\t2\n\t\t\n\t\t\tx\n\t\t\t2\n\t\t\n\t\n\t+\n\t\n\t\t38\n\t\tx\n\t\n\t+\n\t10\n\n?

", "choices": [{"id": "A", "text": "

2\n

"}, {"id": "B", "text": "

\n\t5\n\tx\n\n

"}, {"id": "C", "text": "

\n\t38\n\tx\n\n

"}, {"id": "D", "text": "

\n\t2\n\t\n\t\tx\n\t\t2\n\t\n\n

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. Since 2\n is a common factor of each of the terms in the given expression, the expression can be rewritten as 2x2+19x+5. Therefore, the factors of the given expression are 2\n and \n\t\n\t\tx\n\t\t2\n\t\n\t+\n\t\n\t\t19\n\t\tx\n\t\n\t+\n\t5\n\n. Of these two factors, only 2\n is listed as a choice.

\n

Choice B is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect. This is a term of the given expression, not a factor of the given expression.

\n

Choice D is incorrect. This is a term of the given expression, not a factor of the given expression.

"}, {"id": "22fd3e1f", "domain": "Advanced Math", "skill": "Equivalent expressions", "difficulty": "H", "type": "mc", "stimulus": "
\n\t

f(x) = x\u00b3 minus, 9 x; g(x) = x\u00b2 minus, 2 x \u2212 3

\n
\n", "stem": "

Which of the following expressions is equivalent to (f(x))/(g(x)), for x > 3 ?

\n", "choices": [{"id": "A", "text": "

(1)/(x + 1, end fraction)

\n"}, {"id": "B", "text": "

(x + 3)/(x + 1, end fraction)

\n"}, {"id": "C", "text": "

(x times, open parenthesis, x \u2212 3, close parenthesis)/(x + 1, end fraction)

\n"}, {"id": "D", "text": "

(x times, open parenthesis, x + 3, close parenthesis)/(x + 1, end fraction)

\n"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. Since x\u00b3, \u2212 9 x = x times, open parenthesis, x + 3, close parenthesis, times, open parenthesis, x \u2212 3, close parenthesis and x\u00b2, \u2212 2 x, \u2212 3 = open parenthesis, x + 1, close parenthesis, times, open parenthesis, x \u2212 3, close parenthesis, the fractionf(x), over g(x) can be written as the fraction with numerator x times, open parenthesis, x + 3, close parenthesis, times, open parenthesis, x \u2212 3, close parenthesis, and denominator, open parenthesis, x + 1, close parenthesis, times, open parenthesis, x \u2212 3, close parenthesis, end fraction. It is given that x > 3, so the common factor x \u2212 3 is not equal to 0. Therefore, the fraction can be further simplified to (x times, open parenthesis, x + 3, close parenthesis)/(x + 1, end fraction).

Choice A is incorrect. The expression the fraction 1 over, x + 1, end fraction is not equivalent to (f(x),)/(g(x)) because at x = 0, the fraction 1 over, x + 1, end fraction as a value of 1 and (f(x),)/(g(x)) has a value of 0.

Choice B is incorrect and results from omitting the factor x in the factorization of f(x). Choice C is incorrect and may result from incorrectly factoring g(x) as open parenthesis, x + 1, close parenthesis, times, open parenthesis, x + 3, close parenthesis instead of open parenthesis, x + 1, close parenthesis, times, open parenthesis, x \u2212 3, close parenthesis.

 

\n"}, {"id": "717a1964", "domain": "Advanced Math", "skill": "Nonlinear equations in one variable and systems of equations in two variables ", "difficulty": "M", "type": "spr", "stimulus": "", "stem": "

\n\t\n\t\t\n\t\t\tz\n\t\t\t2\n\t\t\n\t\t+\n\t\t\n\t\t\t10\n\t\t\tz\n\t\t\n\t\t-\n\t\t24\n\t\n\t=\n\t0\n\n

\n

What is one of the solutions to the given equation?

", "choices": [], "answerId": "2", "acceptedAnswers": ["2", "-12"], "rationale": "

The correct answer is either 2\n or -12\n. The left-hand side of the given equation can be rewritten by factoring. The two values that multiply to -24\n and add to 10\n are 12\n and -2\n. It follows that the given equation can be rewritten as z+12z-2=0. Setting each factor equal to 0\n yields two equations: \n\t\n\t\tz\n\t\t+\n\t\t12\n\t\n\t=\n\t0\n\n and \n\t\n\t\tz\n\t\t-\n\t\t2\n\t\n\t=\n\t0\n\n. Subtracting 12\n from both sides of the equation \n\t\n\t\tz\n\t\t+\n\t\t12\n\t\n\t=\n\t0\n\n results in \n\tz\n\t=\n\t-12\n\n. Adding 2\n to both sides of the equation \n\t\n\t\tz\n\t\t-\n\t\t2\n\t\n\t=\n\t0\n\n results in \n\tz\n\t=\n\t2\n\n. Note that 2 and -12 are examples of ways to enter a correct answer.

"}, {"id": "78d5f91a", "domain": "Advanced Math", "skill": "Nonlinear functions", "difficulty": "M", "type": "mc", "stimulus": "
f(x) = x\u00b3, + 3 x\u00b2, \u2212 6 x, \u2212 1
\n", "stem": "

For the function f defined above, what is the value of f(n)egative 1?

\n", "choices": [{"id": "A", "text": "

\u221211

 

\n"}, {"id": "B", "text": "

\u22127

 

\n"}, {"id": "C", "text": "

7

 

\n"}, {"id": "D", "text": "

11

 

\n"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. Substituting \u22121 for x in the given function f gives f(n)egative 1 = open parenthesis, \u22121, close parenthesis, cubed, + 3 times, open parenthesis, \u22121, close parenthesis, squared, minus, 6 \u00d7 \u22121, \u2212 1, which simplifies to f(n)egative 1 = \u22121 plus, 3 \u00d7 1, minus, 6 \u00d7 \u22121, \u2212 1. This further simplifies to f(n)egative 1 = \u22121 + 3, + 6, \u2212 1, or f(n)egative 1 = 7.

Choice A is incorrect and may result from correctly substituting \u22121 for x in the function but incorrectly simplifying the resulting expression to f(n)egative 1 = \u22121 \u2212 3, \u2212 6, \u2212 1, or \u221211. Choice B is incorrect and may result from arithmetic errors. Choice D is incorrect and may result from correctly substituting \u22121 for x in the function but incorrectly simplifying the expression to f(n)egative 1 = 1 + 3, + 6, + 1, or 11.

 

\n"}, {"id": "d675744f", "domain": "Advanced Math", "skill": "Nonlinear functions", "difficulty": "M", "type": "mc", "stimulus": "
\n

\n y = 4 times, open parenthesis, 2 to the x power, close parenthesis\n

\n
\n", "stem": "

Which of the following is the graph in the xy-plane of the given equation?

\n", "choices": [{"id": "A", "text": "

\n \n \n

\n \"The

\n"}, {"id": "B", "text": "

\n \n \n

\n \"The

\n"}, {"id": "C", "text": "

\n \n \n

\n \"The

\n"}, {"id": "D", "text": "

\n \n \n

\n \"The

\n"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. The y-intercept of the graph of an equation is the point 0, b, where b is the value of y when x = 0. For the given equation, y = 4 when x = 0. It follows that the y-intercept of the graph of the given equation is the point 0, 4. Additionally, for the given equation, the value of y doubles for each increase of 1 in the value of x. Therefore, the graph contains the points 1, 8, 2, 16, 3, 32, and 4, 64. Only the graph shown in choice D passes through these points.

Choices A and B are incorrect because these are graphs of decreasing, not increasing, exponential functions. Choice C is incorrect because the value of y increases by a growth factor greater than 2 for each increase of 1 in the value of x.

\n"}, {"id": "a0b4103e", "domain": "Advanced Math", "skill": "Equivalent expressions", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

The expression one-third x\u00b2, \u2212 2 can be rewritten as one-third times, open parenthesis, x \u2212 k, close parenthesis, times, open parenthesis, x + k, close parenthesis, where k is a positive constant. What is the value of k ?

\n", "choices": [{"id": "A", "text": "2\n"}, {"id": "B", "text": "6\n"}, {"id": "C", "text": "\n the square root(2)\n \n"}, {"id": "D", "text": "\n the square root(6)\n \n"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. Factoring out the coefficient one third, the given expression can be rewritten as one third times, open parenthesis, x\u00b2, \u2212 6, close parenthesis. The expression x\u00b2, \u2212 6 can be approached as a difference of squares and rewritten as open parenthesis, x \u2212 the square root(6), close parenthesis, times, open parenthesis, x + the square root(6), close parenthesis. Therefore, k must be the square root(6).

Choice A is incorrect. If k were 2, then the expression given would be rewritten as one third times, open parenthesis, x \u2212 2, close parenthesis, times, open parenthesis, x + 2, close parenthesis, which is equivalent to one third, x\u00b2, \u2212 four thirds, not one third, x\u00b2, \u2212 2.

Choice B is incorrect. This may result from incorrectly factoring the expression and finding open parenthesis, x \u2212 6, close parenthesis, times, open parenthesis, x + 6, close parenthesis as the factored form of the expression. Choice C is incorrect. This may result from incorrectly distributing the one third and rewriting the expression as one third times, open parenthesis, x\u00b2, \u2212 2, close parenthesis.

\n"}, {"id": "5377d9cf", "domain": "Advanced Math", "skill": "Nonlinear functions", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

If f(x) = (x\u00b2 \u2212 6 x + 3)/(x \u2212 1, end fraction), what is f(n)egative 1 ?

\n", "choices": [{"id": "A", "text": "

–5

\n"}, {"id": "B", "text": "

–2

\n"}, {"id": "C", "text": "

2

\n"}, {"id": "D", "text": "

5

\n"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. Substituting –1 for x in the equation that defines f gives f(n)egative 1 = the fraction with numerator, open parenthesis, \u22121, close parenthesis, squared, \u2212 6, times, open parenthesis, \u22121, close parenthesis, + 3, and denominator \u22121 \u2212 1, end fraction. Simplifying the expressions in the numerator and denominator yields (1 + 6, + 3)/(\u22122), which is equal to 10 over \u22122 or –5.

Choices B, C, and D are incorrect and may result from misapplying the order of operations when substituting –1 for x.

 

\n"}, {"id": "2cd6b22d", "domain": "Advanced Math", "skill": "Nonlinear equations in one variable and systems of equations in two variables ", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

\n\t\n\t\t\n\t\t\t5\n\t\t\t\n\t\t\t\tx\n\t\t\t\t2\n\t\t\t\n\t\t\n\t\t+\n\t\t\n\t\t\t10\n\t\t\tx\n\t\t\n\t\t+\n\t\t16\n\t\n\t=\n\t0\n\n

\n

How many distinct real solutions does the given equation have?

", "choices": [{"id": "A", "text": "

Exactly one

"}, {"id": "B", "text": "

Exactly two

"}, {"id": "C", "text": "

Infinitely many

"}, {"id": "D", "text": "

Zero

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. The number of solutions of a quadratic equation of the form ax2+bx+c=0, where a\n, b\n, and c\n are constants, can be determined by the value of the discriminant, b2-4ac. If the value of the discriminant is positive, then the quadratic equation has exactly two distinct real solutions. If the value of the discriminant is equal to zero, then the quadratic equation has exactly one real solution. If the value of the discriminant is negative, then the quadratic equation has zero real solutions. In the given equation, 5x2+10x+16=0, a= 5, b=10, and c=16. Substituting these values for a\n, b\n, and c\n in b2-4ac yields 102-4516, or -220. Since the value of its discriminant is negative, the given equation has zero real solutions. Therefore, the number of distinct real solutions the given equation has is zero.

\n

Choice A is incorrect and may result from conceptual or calculation errors.

\n

Choice B is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

"}, {"id": "f2d60b99", "domain": "Advanced Math", "skill": "Nonlinear functions", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

The function fx=19x-72+3 gives a metal ball's height above the ground fx, in inches, x\n seconds after it started moving on a track, where 0≤x≤10. Which of the following is the best interpretation of the vertex of the graph of y=fx in the xy-plane?

", "choices": [{"id": "A", "text": "

The metal ball's minimum height was 3\n inches above the ground.

"}, {"id": "B", "text": "

The metal ball's minimum height was 7\n inches above the ground.

"}, {"id": "C", "text": "

The metal ball's height was 3\n inches above the ground when it started moving.

"}, {"id": "D", "text": "

The metal ball's height was 7\n inches above the ground when it started moving.

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. The graph of a quadratic equation in the form y=ax-h2+k, where a\n, h\n, and k\n are positive constants, is a parabola that opens upward with vertex h,k. The given function fx=19x-72+3 is in the form y=ax-h2+k, where y=fx, a=19, \n\th\n\t=\n\t7\n\n, and \n\tk\n\t=\n\t3\n\n. Therefore, the graph of y=fx is a parabola that opens upward with vertex 7,3. Since the parabola opens upward, the vertex is the lowest point on the graph. It follows that the y-coordinate of the vertex of the graph of y=fx is the minimum value of fx. Therefore, the minimum value of fx is 3\n. It’s given that fx=19x-72+3 represents the metal ball’s height above the ground, in inches, x\n seconds after it started moving on a track. Therefore, the best interpretation of the vertex of the graph of y=fx is that the metal ball’s minimum height was 3\n inches above the ground.

\n

Choice B is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

\n

Choice D is incorrect and may result from conceptual or calculation errors.

"}, {"id": "e9349667", "domain": "Advanced Math", "skill": "Nonlinear equations in one variable and systems of equations in two variables ", "difficulty": "H", "type": "mc", "stimulus": "
\n

\n y = x\u00b2 + 2 x + 1; x + y + 1 = 0\n

\n
\n", "stem": "

If x subscript 1, y subscript 1 and x subscript 2, y subscript 2 are the two solutions to the system of equations above, what is the value of y subscript 1, plus, y subscript 2 ?

\n", "choices": [{"id": "A", "text": "\u22123\n"}, {"id": "B", "text": "\u22122\n"}, {"id": "C", "text": "\u22121\n"}, {"id": "D", "text": "1\n"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. The system of equations can be solved using the substitution method. Solving the second equation for y gives y = –x – 1. Substituting the expression –x – 1 for y into the first equation gives –x – 1 = x2 + 2x + 1. Adding x + 1 to both sides of the equation yields x2 + 3x + 2 = 0. The left-hand side of the equation can be factored by finding two numbers whose sum is 3 and whose product is 2, which gives (x + 2)(x + 1) = 0. Setting each factor equal to 0 yields x + 2 = 0 and x + 1 = 0, and solving for x yields x = –2 or x = –1. These values of x can be substituted for x in the equation y = –x – 1 to find the corresponding y-values: y = –(–2) – 1 = 2 – 1 = 1 and y = –(–1) – 1 = 1 – 1 = 0. It follows that (–2, 1) and (–1, 0) are the solutions to the given system of equations. Therefore, (x1, y1) = (–2, 1), (x2, y2) = (–1, 0), and y1 + y2 = 1 + 0 = 1.

\n \n

Choice A is incorrect. The solutions to the system of equations are (x1, y1) = (–2, 1) and (x2, y2) = (–1, 0). Therefore, –3 is the sum of the x-coordinates of the solutions, not the sum of the y-coordinates of the solutions. Choices B and C are incorrect and may be the result of computation or substitution errors.

\n"}, {"id": "67f4b449", "domain": "Advanced Math", "skill": "Nonlinear functions", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

The function fw=6w2 gives the area of a rectangle, in square feet ft2, if its width is w ft and its length is 6\n times its width. Which of the following is the best interpretation of f14=1,176\n?

", "choices": [{"id": "A", "text": "

If the width of the rectangle is 14 ft, then the area of the rectangle is 1,176 ft2.

"}, {"id": "B", "text": "

If the width of the rectangle is 14 ft, then the length of the rectangle is 1,176 ft.

"}, {"id": "C", "text": "

If the width of the rectangle is 1,176 ft, then the length of the rectangle is 14 ft.

"}, {"id": "D", "text": "

If the width of the rectangle is 1,176 ft, then the area of the rectangle is 14 ft2.

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. The function f\n gives the area of the rectangle, in ft2, if its width is w ft. Since the value of f14 is the value of fw if \n\tw\n\t=\n\t14\n\n, it follows that f14=1,176 means that fw is 1,176 if \n\tw\n\t=\n\t14\n\n. In the given context, this means that if the width of the rectangle is 14 ft, then the area of the rectangle is 1,176 ft2.

\n

Choice B is incorrect and may result from conceptual errors.

\n

Choice C is incorrect and may result from conceptual errors.

\n

Choice D is incorrect and may result from interpreting fw as the width, in ft, of the rectangle if its area is w ft2, rather than as the area, in ft2, of the rectangle if its width is w ft.

"}, {"id": "49efde89", "domain": "Advanced Math", "skill": "Equivalent expressions", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

The expression 2 x\u00b2, + a, x is equivalent to x times, open parenthesis, 2 x, + 7, close parenthesis for some constant a. What is the value of a ?

\n", "choices": [{"id": "A", "text": "

2

\n"}, {"id": "B", "text": "

3

\n"}, {"id": "C", "text": "

4

\n"}, {"id": "D", "text": "

7

\n"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. It’s given that 2 x\u00b2, + a, x is equivalent to x times, open parenthesis, 2 x + 7, close parenthesis for some constant a. Distributing the x over each term in the parentheses gives 2 x\u00b2, + 7 x, which is in the same form as the first given expression, 2 x\u00b2, + a, x. The coefficient of the second term in 2 x\u00b2, + 7 x is 7. Therefore, the value of a is 7.

Choice A is incorrect. If the value of a were 2, then 2 x\u00b2, + a, x would be equivalent to 2 x\u00b2, + 2 x, which isn’t equivalent to x times, open parenthesis, 2 x + 7, close parenthesis. Choice B is incorrect. If the value of a were 3, then 2 x\u00b2, + a, x would be equivalent to 2 x\u00b2, + 3 x, which isn’t equivalent to x times, open parenthesis, 2 x + 7, close parenthesis. Choice C is incorrect. If the value of a were 4, then 2 x\u00b2, + a, x would be equivalent to 2 x\u00b2, + 4 x, which isn’t equivalent to x times, open parenthesis, 2 x + 7, close parenthesis.

 

\n"}, {"id": "44076c7d", "domain": "Advanced Math", "skill": "Nonlinear functions", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
x\nfx
-1\n10\n
0\n14\n
1\n20\n
\n

For the quadratic function f\n, the table shows three values of x\n and their corresponding values of fx. Which equation defines f\n?

", "choices": [{"id": "A", "text": "

fx=3x2+3x+14

"}, {"id": "B", "text": "

fx=5x2+x+14

"}, {"id": "C", "text": "

fx=9x2-x+14

"}, {"id": "D", "text": "

fx=x2+5x+14

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. The equation of a quadratic function can be written in the form fx=ax-h2+k, where a\n, h\n, and k\n are constants. It’s given in the table that when \n\tx\n\t=\n\t-1\n\n, the corresponding value of fx is 10\n. Substituting -1\n for x\n and 10\n for fx in the equation fx=ax-h2+k gives 10=a-1-h2+k, which is equivalent to 10=a1+2h+h2+k, or 10=a+2ah+ah2+k. It’s given in the table that when \n\tx\n\t=\n\t0\n\n, the corresponding value of fx is 14\n. Substituting 0\n for x\n and 14\n for fx in the equation fx=ax-h2+k gives 14=a0-h2+k, or 14=ah2+k. It’s given in the table that when \n\tx\n\t=\n\t1\n\n, the corresponding value of fx is 20\n. Substituting 1\n for x\n and 20\n for fx in the equation fx=ax-h2+k gives 20=a1-h2+k, which is equivalent to 20=a1-2h+h2+k, or 20=a-2ah+ah2+k. Adding 20=a-2ah+ah2+k to the equation 10=a+2ah+ah2+k gives 30=2a+2ah2+2k. Dividing both sides of this equation by 2\n gives 15=a+ah2+k. Since 14=ah2+k, substituting 14\n for ah2+k  into the equation 15=a+ah2+k gives 15=a+14. Subtracting 14\n from both sides of this equation gives \n\ta\n\t=\n\t1\n\n. Substituting 1\n for a\n in the equations \n\t14\n\t=\n\t\n\t\t\n\t\t\ta\n\t\t\t\n\t\t\t\th\n\t\t\t\t2\n\t\t\t\n\t\t\n\t\t+\n\t\tk\n\t\n\n and \n\t20\n\t=\n\t\n\t\t\n\t\t\ta\n\t\t\t\n\t\t\t\th\n\t\t\t\t2\n\t\t\t\n\t\t\n\t\t-\n\t\t\n\t\t\t2\n\t\t\ta\n\t\t\th\n\t\t\n\t\t+\n\t\ta\n\t\t+\n\t\tk\n\t\n\n gives 14=h2+k and 20=1-2h+h2+k, respectively. Since \n\t14\n\t=\n\t\n\t\t\n\t\t\th\n\t\t\t2\n\t\t\n\t\t+\n\t\tk\n\t\n\n, substituting 14\n for \n\t\n\t\th\n\t\t2\n\t\n\t+\n\tk\n\n in the equation 20=1-2h+h2+k gives 20=1-2h+14, or 20=15-2h. Subtracting 15\n from both sides of this equation gives 5=-2h. Dividing both sides of this equation by -2\n gives -52=h. Substituting \n\t-\n\t\n\t\t5\n\t\t2\n\t\n\n for h\n into the equation 14=h2+k gives 14=-522+k, or 14=254+k. Subtracting 254 from both sides of this equation gives 314=k. Substituting 1\n for a\n, -52 for h\n, and 314 for k\n in the equation fx=ax-h2+k gives fx=x+522+314, which is equivalent to fx=x2+5x+254+314, or fx=x2+5x+14. Therefore, fx=x2+5x+14 defines f\n.

\n

Choice A is incorrect. If fx=3x2+3x+14, then when \n\tx\n\t=\n\t-1\n\n, the corresponding value of fx is 14\n, not 10\n.

\n

Choice B is incorrect. If fx=5x2+x+14, then when \n\tx\n\t=\n\t-1\n\n, the corresponding value of fx is 18\n, not 10\n.

\n

Choice C is incorrect. If fx=9x2-x+14, then when \n\tx\n\t=\n\t-1\n\n, the corresponding value of fx is 24\n, not 10\n, and when \n\tx\n\t=\n\t1\n\n, the corresponding value of fx is 22\n, not 20\n.

"}, {"id": "1f353a9e", "domain": "Advanced Math", "skill": "Nonlinear functions", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

ft=8,0000.65t

\n

The given function f\n models the number of coupons a company sent to their customers at the end of each year, where t\n represents the number of years since the end of 1998, and 0≤t≤5. If y=ft is graphed in the ty-plane, which of the following is the best interpretation of the y-intercept of the graph in this context?

", "choices": [{"id": "A", "text": "

The minimum estimated number of coupons the company sent to their customers during the 5\n years was 1,428\n.

"}, {"id": "B", "text": "

The minimum estimated number of coupons the company sent to their customers during the 5\n years was 8,000\n.

"}, {"id": "C", "text": "

The estimated number of coupons the company sent to their customers at the end of 1998 was 1,428\n.

"}, {"id": "D", "text": "

The estimated number of coupons the company sent to their customers at the end of 1998 was 8,000\n.

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. The y-intercept of a graph in the ty-plane is the point where \n\tt\n\t=\n\t0\n\n. For the given function f, the y-intercept of the graph of y=ft in the ty-plane can be found by substituting 0\n for t\n in the equation y=8,0000.65t, which gives y=8,0000.650. This is equivalent to y=8,0001, or \n\ty\n\t=\n\t8,000\n\n. Therefore, the y-intercept of the graph of y=ft is 0,8,000. It’s given that the function f models the number of coupons a company sent to their customers at the end of each year. Therefore, ft represents the estimated number of coupons the company sent to their customers at the end of each year. It's also given that t\n represents the number of years since the end of 1998. Therefore, \n\tt\n\t=\n\t0\n\n represents 0\n years since the end of 1998, or the end of 1998. Thus, the best interpretation of the y-intercept of the graph of y=ft is that the estimated number of coupons the company sent to their customers at the end of 1998 was 8,000\n.

\n

Choice A is incorrect and may result from conceptual or calculation errors. 

\n

Choice B is incorrect and may result from conceptual or calculation errors. 

\n

Choice C is incorrect and may result from conceptual or calculation errors. 

"}, {"id": "b03adde3", "domain": "Advanced Math", "skill": "Nonlinear equations in one variable and systems of equations in two variables ", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

If u \u2212 3 = the fraction 6 over, t \u2212 2, end fraction, what is t in terms of u ?

\n", "choices": [{"id": "A", "text": "

\n t = (1)/(u)\n

\n"}, {"id": "B", "text": "

\n t = (2 u + 9,)/(u)\n

\n"}, {"id": "C", "text": "

\n t = the fraction 1 over, u \u2212 3, end fraction\n

\n"}, {"id": "D", "text": "

\n t = (2 u,)/(u \u2212 3, end fraction)\n

\n"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. Multiplying both sides of the given equation by t \u2212 2 yields open parenthesis, t \u2212 2, close parenthesis, times, open parenthesis, u \u2212 3, close parenthesis = 6. Dividing both sides of this equation by u \u2212 3 yields t \u2212 2 = (6)/(u \u2212 3, end fraction). Adding 2 to both sides of this equation yields t = (6)/(u \u2212 3, end fraction, + 2), which can be rewritten as t = (6)/(u \u2212 3, end fraction, plus, the fraction with numerator 2 times, open parenthesis, u \u2212 3, close parenthesis, and denominator u \u2212 3, end fraction). Since the fractions on the right-hand side of this equation have a common denominator, adding the fractions yields t = (6 + 2, times, open parenthesis, u \u2212 3, close parenthesis)/(u \u2212 3, end fraction). Applying the distributive property to the numerator on the right-hand side of this equation yields t = (6 + 2 u, \u2212 6)/(u \u2212 3, end fraction), which is equivalent to t = (2 u)/(u \u2212 3, end fraction).

Choices A, B, and C are incorrect and may result from various misconceptions or miscalculations.

\n"}, {"id": "1ce9ffcd", "domain": "Advanced Math", "skill": "Nonlinear equations in one variable and systems of equations in two variables ", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

\n\t\n\t\t\n\t\t\t-\n\t\t\t9\n\t\t\t\n\t\t\t\tx\n\t\t\t\t2\n\t\t\t\n\t\t\n\t\t+\n\t\t\n\t\t\t30\n\t\t\tx\n\t\t\n\t\t+\n\t\tc\n\t\n\t=\n\t0\n\n

\n

In the given equation, c\n is a constant. The equation has exactly one solution. What is the value of c\n?

", "choices": [{"id": "A", "text": "

3\n

"}, {"id": "B", "text": "

0\n

"}, {"id": "C", "text": "

-25\n

"}, {"id": "D", "text": "

-53\n

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. It's given that the equation -9x2+30x+c=0 has exactly one solution. A quadratic equation of the form \n\t\n\t\t\n\t\t\ta\n\t\t\t\n\t\t\t\tx\n\t\t\t\t2\n\t\t\t\n\t\t\n\t\t+\n\t\t\n\t\t\tb\n\t\t\tx\n\t\t\n\t\t+\n\t\tc\n\t\n\t=\n\t0\n\n has exactly one solution if and only if its discriminant, \n\t\n\t\t-\n\t\t4\n\t\ta\n\t\tc\n\t\n\t+\n\t\n\t\tb\n\t\t2\n\t\n\n, is equal to zero. It follows that for the given equation, \n\ta\n\t=\n\t-9\n\n and \n\tb\n\t=\n\t30\n\n. Substituting -9\n for a\n and 30\n for b\n into b2-4ac  yields 302-4-9c, or 900+36c. Since the discriminant must equal zero, 900+36c=0. Subtracting \n\t36\n\tc\n\n from both sides of this equation yields \n\t900\n\t=\n\t\n\t\t-\n\t\t36\n\t\tc\n\t\n\n. Dividing each side of this equation by -36\n yields \n\t-25\n\t=\n\tc\n\n. Therefore, the value of c\n is -25\n. 

\n

Choice A is incorrect. If the value of c\n is 3\n, this would yield a discriminant that is greater than zero. Therefore, the given equation would have two solutions, rather than exactly one solution.

\n

Choice B is incorrect. If the value of c\n is 0\n, this would yield a discriminant that is greater than zero. Therefore, the given equation would have two solutions, rather than exactly one solution.

\n

Choice D is incorrect. If the value of c\n is -53\n, this would yield a discriminant that is less than zero. Therefore, the given equation would have no real solutions, rather than exactly one solution.

"}, {"id": "104bff62", "domain": "Advanced Math", "skill": "Nonlinear equations in one variable and systems of equations in two variables ", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

\n\t\n\t\t\n\t\t\t\n\t\t\t\tx\n\t\t\t\t2\n\t\t\t\n\t\t\t\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\tx\n\t\t\t\t\t\t2\n\t\t\t\t\t\n\t\t\t\t\t-\n\t\t\t\t\t\n\t\t\t\t\t\tc\n\t\t\t\t\t\t2\n\t\t\t\t\t\n\t\t\t\t\n\t\t\t\n\t\t\n\t\n\t=\n\t\n\t\t\n\t\t\t\n\t\t\t\t\n\t\t\t\t\tc\n\t\t\t\t\t2\n\t\t\t\t\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tx\n\t\t\t\t\t\t\t2\n\t\t\t\t\t\t\n\t\t\t\t\t\t-\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tc\n\t\t\t\t\t\t\t2\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\n\t\t\t\n\t\t\n\t\t+\n\t\t39\n\t\n\n

\n

In the given equation, c\n is a positive constant. Which of the following is one of the solutions to the given equation?

", "choices": [{"id": "A", "text": "

\n\t-\n\tc\n\n

"}, {"id": "B", "text": "

-c2-392

"}, {"id": "C", "text": "

-392-c2

"}, {"id": "D", "text": "

-c2+392

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. If x2-c2\u22640, then neither side of the given equation is defined and there can be no solution. Therefore, x2-c2>0. Subtracting c2x2-c2 from both sides of the given equation yields x2x2-c2-c2x2-c2=39, or x2-c2x2-c2=39. Squaring both sides of this equation yields x2-c2x2-c22=392, or x2-c2x2-c2x2-c2=392. Since x2-c2 is positive and, therefore, nonzero, the expression x2-c2x2-c2 is defined and equivalent to 1\n. It follows that the equation x2-c2x2-c2x2-c2=392 can be rewritten as x2-c2x2-c2x2-c2=392, or 1x2-c2=392, which is equivalent to x2-c2=392. Adding c2 to both sides of this equation yields x2=c2+392. Taking the square root of both sides of this equation yields two solutions: x=c2+392 and x=-c2+392. Therefore, of the given choices, -c2+392 is one of the solutions to the given equation.

\n

Choice A is incorrect and may result from conceptual or calculation errors.

\n

Choice B is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

"}, {"id": "75915e3c", "domain": "Advanced Math", "skill": "Nonlinear functions", "difficulty": "E", "type": "mc", "stimulus": "
\n

\n f(x) = 2 times, open parenthesis, 3 raised to the x power, close parenthesis\n

\n
\n", "stem": "

For the function f defined above, what is the value of f(2)?

\n", "choices": [{"id": "A", "text": "

9

\n"}, {"id": "B", "text": "

12

\n"}, {"id": "C", "text": "

18

\n"}, {"id": "D", "text": "

36

\n"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. The value of f(2) is found by evaluating the expression 2 \u00d7 3 raised to the x power when x = 2. Substituting 2 for x in the given equation yields f(2) = 2 times, 3\u00b2. Simplifying 3\u00b2 in the equation results in f(2) = 2 \u00d7 9. Evaluating the right-hand side of the equation yields f(2) = 18. Therefore, the value of f(2) is 18.

Choice A is incorrect and may result from evaluating the expression as 3\u00b2. Choice B is incorrect and may result from evaluating the expression as 2 times, open parenthesis, 3 \u00d7 2, close parenthesis. Choice D is incorrect and may result from evaluating the expression as open parenthesis, 2 \u00d7 3, close parenthesis, squared.

\n"}, {"id": "f44a29a8", "domain": "Advanced Math", "skill": "Nonlinear functions", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

An object’s kinetic energy, in joules, is equal to the product of one-half the object’s mass, in kilograms, and the square of the object’s speed, in meters per second. What is the speed, in meters per second, of an object with a mass of 4 kilograms and kinetic energy of 18 joules?

\n", "choices": [{"id": "A", "text": "

3

\n"}, {"id": "B", "text": "

6

\n"}, {"id": "C", "text": "

9

\n"}, {"id": "D", "text": "

36

\n"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. It’s given that an object’s kinetic energy, in joules, is equal to the product of one-half the object’s mass, in kilograms, and the square of the object’s speed, in meters per second. This relationship can be represented by the equation K = one half m v\u00b2, where K is the kinetic energy, m is the mass, and v is the speed. Substituting a mass of 4 kilograms for m and a kinetic energy of 18 joules for K results in the equation 18 = one half \u00d7 4, \u00d7 v\u00b2, or 18 = 2 v\u00b2. Dividing both sides of this equation by 2 yields 9 = v\u00b2. Taking the square root of both sides yields v = \u22123 and v = 3. Since speed can’t be expressed as a negative number, the speed of the object is 3 meters per second.

Choice B is incorrect and may result from computation errors. Choice C is incorrect. This is the value of v\u00b2 rather than v. Choice D is incorrect. This is the value of 4 v\u00b2 rather than v.

 

\n"}, {"id": "92f812bb", "domain": "Advanced Math", "skill": "Nonlinear functions", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

In the xy-plane, a parabola has vertex (9,-14) and intersects the x-axis at two points. If the equation of the parabola is written in the form \n\ty\n\t=\n\t\n\t\t\n\t\t\ta\n\t\t\t\n\t\t\t\tx\n\t\t\t\t2\n\t\t\t\n\t\t\n\t\t+\n\t\t\n\t\t\tb\n\t\t\tx\n\t\t\n\t\t+\n\t\tc\n\t\n\n, where a\n, b\n, and c\n are constants, which of the following could be the value of \n\ta\n\t+\n\tb\n\t+\n\tc\n\n?

", "choices": [{"id": "A", "text": "

-23\n

"}, {"id": "B", "text": "

-19\n

"}, {"id": "C", "text": "

-14\n

"}, {"id": "D", "text": "

-12\n

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. The equation of a parabola in the xy-plane can be written in the form y=ax-h2+k, where a\n is a constant and h,k is the vertex of the parabola. If a\n is positive, the parabola will open upward, and if a\n is negative, the parabola will open downward. It’s given that the parabola has vertex 9,-14. Substituting 9\n for h\n and -14\n for k\n in the equation y=ax-h2+k gives y=ax-92-14, which can be rewritten as y=ax-9x-9-14, or y=ax2-18x+81-14. Distributing the factor of a\n on the right-hand side of this equation yields y=ax2-18ax+81a-14. Therefore, the equation of the parabola, y=ax2-18ax+81a-14, can be written in the form y=ax2+bx+c, where a=a, b=-18a, and c=81a-14. Substituting \n\t-\n\t18\n\ta\n\n for b\n and \n\t\n\t\t81\n\t\ta\n\t\n\t-\n\t14\n\n for c\n in the expression a+b+c yields a+-18a+81a-14, or 64a-14. Since the vertex of the parabola, 9,-14, is below the x-axis, and it’s given that the parabola intersects the x-axis at two points, the parabola must open upward. Therefore, the constant a\n must have a positive value. Setting the expression \n\t\n\t\t64\n\t\ta\n\t\n\t-\n\t14\n\n equal to the value in choice D yields 64a-14=-12. Adding 14\n to both sides of this equation yields \n\t\n\t\t64\n\t\ta\n\t\n\t=\n\t2\n\n. Dividing both sides of this equation by 64\n yields a=264, which is a positive value. Therefore, if the equation of the parabola is written in the form y=ax2+bx+c, where a\n, b\n, and c\n are constants, the value of a+b+c could be -12.

\n

Choice A is incorrect. If the equation of a parabola with a vertex at 9,-14 is written in the form y=ax2+bx+c, where a\n, b\n, and c\n are constants and a+b+c=-23, then the value of a\n will be negative, which means the parabola will open downward, not upward, and will intersect the x-axis at zero points, not two points. 

\n

Choice B is incorrect. If the equation of a parabola with a vertex at 9,-14 is written in the form y=ax2+bx+c, where a\n, b\n, and c\n are constants and a+b+c=-19, then the value of a\n will be negative, which means the parabola will open downward, not upward, and will intersect the x-axis at zero points, not two points.

\n

Choice C is incorrect. If the equation of a parabola with a vertex at 9,-14 is written in the form y=ax2+bx+c, where a\n, b\n, and c\n are constants and a+b+c=-14, then the value of a\n will be 0\n, which is inconsistent with the equation of a parabola.

"}, {"id": "f547a8b1", "domain": "Advanced Math", "skill": "Nonlinear functions", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n\n

\n

What is the y-intercept of the graph shown?

", "choices": [{"id": "A", "text": "

-8,0

"}, {"id": "B", "text": "

-6,0

"}, {"id": "C", "text": "

0,6

"}, {"id": "D", "text": "

0,8

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. The y-intercept of a graph in the xy-plane is the point at which the graph crosses the y-axis. The graph shown crosses the y-axis at the point 0,8. Therefore, the y-intercept of the graph shown is 0,8.

\n

Choice A is incorrect and may result from conceptual or calculation errors.

\n

Choice B is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

"}, {"id": "b8c4a1cd", "domain": "Advanced Math", "skill": "Nonlinear equations in one variable and systems of equations in two variables ", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

8j=k+15m

\n

The given equation relates the distinct positive numbers j\n, k\n, and m\n. Which equation correctly expresses j\n in terms of k\n and m\n?

", "choices": [{"id": "A", "text": "

j=k8+15m

"}, {"id": "B", "text": "

j=k+15m8

"}, {"id": "C", "text": "

j=8(k+15m)

"}, {"id": "D", "text": "

j=k+15m8

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. To express j\n in terms of k\n and m\n, the given equation must be solved for j\n. Dividing each side of the given equation by 8\n yields  j=k+15m8.

\n

Choice A is incorrect. This is equivalent to 8j=k+120m.

\n

Choice B is incorrect. This is equivalent to 8j=8k+15m.

\n

Choice C is incorrect. This is equivalent to j8=k+15m.

"}, {"id": "7dbd46d9", "domain": "Advanced Math", "skill": "Nonlinear equations in one variable and systems of equations in two variables ", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

\n\t\n\t\t\n\t\t\t8\n\t\t\tx\n\t\t\n\t\t+\n\t\ty\n\t\n\t=\n\t-11\n\n

\n

\n\t\n\t\t2\n\t\t\n\t\t\tx\n\t\t\t2\n\t\t\n\t\n\t=\n\t\n\t\ty\n\t\t+\n\t\t341\n\t\n\n

\n

The graphs of the equations in the given system of equations intersect at the point (x\n, y\n) in the \n\tx\n\ty\n\n-plane. What is a possible value of x\n?

", "choices": [{"id": "A", "text": "

-15\n

"}, {"id": "B", "text": "

-11\n

"}, {"id": "C", "text": "

2\n

"}, {"id": "D", "text": "

8\n

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. It's given that the graphs of the equations in the given system of equations intersect at the point x,y. Therefore, this intersection point is a solution to the given system. The solution can be found by isolating y\n in each equation. The given equation 8x+y=-11 can be rewritten to isolate y\n by subtracting \n\t8\n\tx\n\n from both sides of the equation, which gives y=-8x-11. The given equation 2x2=y+341 can be rewritten to isolate y\n by subtracting 341\n from both sides of the equation, which gives 2x2-341=y. With each equation solved for y\n, the value of y\n from one equation can be substituted into the other, which gives 2x2-341=-8x-11. Adding \n\t8\n\tx\n\n and 11\n to both sides of this equation results in 2x2+8x-330=0. Dividing both sides of this equation by 2\n results in x2+4x-165=0. This equation can be rewritten by factoring the left-hand side, which yields x+15x-11=0. By the zero-product property, if x+15x-11=0, then x+15=0, or x-11=0. It follows that x=-15, or x=11. Since only -15 is given as a choice, a possible value of x\n is -15. 

\n

Choice B is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

\n

Choice D is incorrect and may result from conceptual or calculation errors.

"}, {"id": "0121a235", "domain": "Advanced Math", "skill": "Nonlinear functions", "difficulty": "H", "type": "mc", "stimulus": "
\n
\n \n \n \n \n \n \n \n \n \n \n \n \n
x\n p(x)
\n x is \u22122\n \n p(x) is 5\n
\n x is \u22121\n \n p(x) is 0\n
\n x is 0\n \n p(x) is \u22123\n
\n x is 1\n \n p(x) is \u22121\n
\n x is 2\n \n p(x) is 0\n
\n
\n", "stem": "

The table above gives selected values of a polynomial function p. Based on the values in the table, which of the following must be a factor of p ?

\n", "choices": [{"id": "A", "text": "

\n open parenthesis, x \u2212 3, close parenthesis\n

\n"}, {"id": "B", "text": "

\n open parenthesis, x + 3, close parenthesis\n

\n"}, {"id": "C", "text": "

\n open parenthesis, x \u2212 1, close parenthesis, times, open parenthesis, x + 2, close parenthesis\n

\n"}, {"id": "D", "text": "

\n open parenthesis, x + 1, close parenthesis, times, open parenthesis, x \u2212 2, close parenthesis\n

\n"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. According to the table, when x is \u22121 or 2, p(x) = 0. Therefore, two x-intercepts of the graph of p are the points \u22121, 0 and 2, 0. Since the points \u22121, 0 and 2, 0 are x-intercepts, it follows that open parenthesis, x + 1, close parenthesis and open parenthesis, x \u2212 2, close parenthesis are factors of the polynomial equation. This is because when x = \u22121, the value of x + 1 is 0. Similarly, when x = 2, the value of x \u2212 2 is 0. Therefore, the product open parenthesis, x + 1, close parenthesis, times, open parenthesis, x \u2212 2, close parenthesis is a factor of the polynomial function p.

Choice A is incorrect. The factor x \u2212 3 corresponds to an x-intercept of the point 3, 0, which isn’t present in the table. Choice B is incorrect. The factor x + 3 corresponds to an x-intercept of the point \u22123, 0, which isn’t present in the table. Choice C is incorrect. The factors x \u2212 1 and x + 2 correspond to x-intercepts 1, 0 and \u22122, 0, respectively, which aren’t present in the table.

\n"}, {"id": "9da41c80", "domain": "Advanced Math", "skill": "Nonlinear functions", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

A ball is dropped from an initial height of 22\n feet and bounces off the ground repeatedly. The function h\n estimates that the maximum height reached after each time the ball hits the ground is 85\n% of the maximum height reached after the previous time the ball hit the ground. Which equation defines h\n, where h(n) is the estimated maximum height of the ball after it has hit the ground n\n times and n\n is a whole number greater than 1\n and less than 10\n?

", "choices": [{"id": "A", "text": "

h(n)=22(0.22)n

"}, {"id": "B", "text": "

h(n)=22(0.85)n

"}, {"id": "C", "text": "

h(n)=850.22n

"}, {"id": "D", "text": "

h(n)=85(0.85)n

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. It's given that for the function h\n, hn is the estimated maximum height, in feet, of the ball after it has hit the ground n\n times. It's also given that the function h\n estimates that the maximum height reached after each time the ball hits the ground is 85% of the maximum height reached after the previous time the ball hit the ground. It follows that h\n is a decreasing exponential function that can be written in the form hn=ap100n, where a\n is the initial height, in feet, the ball was dropped from and the function estimates that the maximum height reached after each time the ball hits the ground is p% of the maximum height reached after the previous time the ball hit the ground. It's given that the ball is dropped from an initial height of 22\n feet. Therefore, \n\ta\n\t=\n\t22\n\n. Since the function h\n estimates that the maximum height reached after each time the ball hits the ground is 85% of the maximum height reached after the previous time the ball hit the ground, \n\tp\n\t=\n\t85\n\n. Substituting 22\n for a\n and 85\n for p\n in the equation hn=ap100n yields hn=2285100n, or hn=220.85n.

\n

Choice A is incorrect. This function estimates that the maximum height reached after each time the ball hits the ground is 22%, not 85%, of the maximum height reached after the previous time the ball hit the ground.

\n

Choice C is incorrect. This function estimates that the ball is dropped from an initial height of 85\n feet, not 22\n feet, and that the maximum height reached after each time the ball hits the ground is 22%, not 85%, of the maximum height reached after the previous time the ball hit the ground.

\n

Choice D is incorrect. This function estimates that the ball is dropped from an initial height of 85\n feet, not 22\n feet.

"}, {"id": "7160cbb3", "domain": "Advanced Math", "skill": "Nonlinear functions", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n\n

\n

What is the y-intercept of the graph shown?

", "choices": [{"id": "A", "text": "

0,-6

"}, {"id": "B", "text": "

-6,0

"}, {"id": "C", "text": "

0,0

"}, {"id": "D", "text": "

-5,-5

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. The y-intercept of a graph in the xy-plane is the point x,y on the graph where \n\tx\n\t=\n\t0\n\n. For the graph shown, at \n\tx\n\t=\n\t0\n\n, the corresponding value of y is -6\n. Therefore, the y-intercept of the graph shown is 0,-6.

\n

Choice B is incorrect and may result from conceptual errors.

\n

Choice C is incorrect and may result from conceptual errors.

\n

Choice D is incorrect and may result from conceptual errors.

"}, {"id": "d71f6dbf", "domain": "Advanced Math", "skill": "Nonlinear functions", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

The height, in feet, of an object x seconds after it is thrown straight up in the air can be modeled by the function h(x) = \u221216 x\u00b2, + 20 x, + 5. Based on the model, which of the following statements best interprets the equation h(1) point 4 = 1 point 6 4 ?

\n", "choices": [{"id": "A", "text": "

The height of the object 1.4 seconds after being thrown straight up in the air is 1.64 feet.

\n"}, {"id": "B", "text": "

The height of the object 1.64 seconds after being thrown straight up in the air is 1.4 feet.

\n"}, {"id": "C", "text": "

The height of the object 1.64 seconds after being thrown straight up in the air is approximately 1.4 times as great as its initial height.

\n"}, {"id": "D", "text": "

The speed of the object 1.4 seconds after being thrown straight up in the air is approximately 1.64 feet per second.

\n"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. The value 1.4 is the value of x, which represents the number of seconds after the object was thrown straight up in the air. When the function h is evaluated for x = 1.4, the function has a value of 1.64, which is the height, in feet, of the object.

Choices B and C are incorrect and may result from misidentifying seconds as feet and feet as seconds. Additionally, choice C may result from incorrectly including the initial height of the object as the input x. Choice D is incorrect and may result from misidentifying height as speed.

\n"}, {"id": "630897df", "domain": "Advanced Math", "skill": "Nonlinear equations in one variable and systems of equations in two variables ", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

The speed of sound in dry air, v, can be modeled by the formula v = 331 point 3 + 0 point 6 0 6 \u00d7 T, where T is the temperature in degrees Celsius and v is measured in meters per second. Which of the following correctly expresses T in terms of v ?

\n", "choices": [{"id": "A", "text": "T = the fraction with numerator, v + 0 point 6 0 6, and denominator, 331 point 3\n"}, {"id": "B", "text": "T = the fraction with numerator, v \u2212 0 point 6 0 6, and denominator, 331 point 3\n"}, {"id": "C", "text": "T = the fraction with numerator, v + 331 point 3, and denominator, 0 point 6 0 6\n"}, {"id": "D", "text": "T = the fraction with numerator, v \u2212 331 point 3, and denominator, 0 point 6 0 6\n"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. To express T in terms of v, subtract 331.3 from both sides of the equation, which gives v – 331.3 = 0.606T. Dividing both sides of the equation by 0.606 gives (v \u2212 331 point 3)/(0 point 6 0 6 = T).

Choices A, B, and C are incorrect and are the result of incorrect steps while solving for T.

\n"}, {"id": "20722644", "domain": "Advanced Math", "skill": "Nonlinear functions", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

The function f\n is defined by fx=x3+9. What is the value of f2?

", "choices": [{"id": "A", "text": "

14\n

"}, {"id": "B", "text": "

15\n

"}, {"id": "C", "text": "

17\n

"}, {"id": "D", "text": "

18\n

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. It's given that fx=x3+9. Substituting 2\n for x\n in this equation yields f2=23+9. This is equivalent to f2=8+9, or f2=17.

\n

Choice A is incorrect. This is the value of 2+3+9, not 23+9.

\n

Choice B is incorrect. This is the value of 23+9, not 23+9.

\n

Choice D is incorrect. This is the value of 32+9, not 23+9.

"}, {"id": "5805e747", "domain": "Advanced Math", "skill": "Equivalent expressions", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

Which expression is equivalent to 7x3+7x-6x3-3x?

", "choices": [{"id": "A", "text": "

\n\t\n\t\tx\n\t\t3\n\t\n\t+\n\t\n\t\t10\n\t\tx\n\t\n\n

"}, {"id": "B", "text": "

\n\t\n\t\t-\n\t\t13\n\t\t\n\t\t\tx\n\t\t\t3\n\t\t\n\t\n\t+\n\t\n\t\t10\n\t\tx\n\t\n\n

"}, {"id": "C", "text": "

\n\t\n\t\t-\n\t\t13\n\t\t\n\t\t\tx\n\t\t\t3\n\t\t\n\t\n\t+\n\t\n\t\t4\n\t\tx\n\t\n\n

"}, {"id": "D", "text": "

\n\t\n\t\tx\n\t\t3\n\t\n\t+\n\t\n\t\t4\n\t\tx\n\t\n\n

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. Applying the distributive property, the given expression can be written as 7x3+7x-6x3+3x. Grouping like terms in this expression yields 7x3-6x3+7x+3x. Combining like terms in this expression yields x3+10x.

\n

Choice B is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

\n

Choice D is incorrect and may result from conceptual or calculation errors.

"}, {"id": "158591f0", "domain": "Advanced Math", "skill": "Nonlinear equations in one variable and systems of equations in two variables ", "difficulty": "H", "type": "spr", "stimulus": "", "stem": "

\n\t\n\t\t\n\t\t\tx\n\t\t\t\n\t\t\t\t\n\t\t\t\t\tx\n\t\t\t\t\t+\n\t\t\t\t\t1\n\t\t\t\t\n\t\t\t\n\t\t\n\t\t-\n\t\t56\n\t\n\t=\n\t\n\t\t4\n\t\tx\n\t\t\n\t\t\t\n\t\t\t\tx\n\t\t\t\t-\n\t\t\t\t7\n\t\t\t\n\t\t\n\t\n\n

\n

What is the sum of the solutions to the given equation?

", "choices": [], "answerId": "29/3", "acceptedAnswers": ["29/3", "9.666", "9.667"], "rationale": "

The correct answer is 293. Applying the distributive property to the left-hand side of the given equation, xx+1-56, yields x2+x-56. Applying the distributive property to the right-hand side of the given equation, 4xx-7, yields 4x2-28x. Thus, the equation becomes x2+x-56=4x2-28x. Combining like terms on the left- and right-hand sides of this equation yields 0=4x2-x2+-28x-x+56, or 3x2-29x+56=0. For a quadratic equation in the form ax2+bx+c=0, where a\n, b\n, and c\n are constants, the quadratic formula gives the solutions to the equation in the form x=-b\u00b1b2-4ac2a. Substituting 3\n for a\n, -29\n for b\n, and 56\n for c\n from the equation 3x2-29x+56=0 into the quadratic formula yields x=29\u00b1-292-435623, or x=296\u00b1136. It follows that the solutions to the given equation are 296+136 and 296-136. Adding these two solutions gives the sum of the solutions: 296+136+296-136, which is equivalent to 296+296, or 293. Note that 29/3, 9.666, and 9.667 are examples of ways to enter a correct answer.

"}, {"id": "bba18ecb", "domain": "Advanced Math", "skill": "Nonlinear functions", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

When the quadratic function f\n is graphed in the xy-plane, where y=fx, its vertex is -3,6. One of the x-intercepts of this graph is -174,0. What is the other x-intercept of the graph?

", "choices": [{"id": "A", "text": "

-294,0

"}, {"id": "B", "text": "

-74,0

"}, {"id": "C", "text": "

54,0

"}, {"id": "D", "text": "

174,0

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. Since the line of symmetry for the graph of a quadratic function contains the vertex of the graph, the x-coordinate of the vertex of the graph of y=fx is the x-coordinate of the midpoint of its two x-intercepts. The midpoint of two points with x-coordinates x1 and x2 has x-coordinate xm, where xm=x1+x22. It′s given that the vertex is -3,6 and one of the x-intercepts is -174,0. Substituting -3 for xm and -174 for x1 in the equation xm=x1+x22 yields -3=-174+x22. Multiplying each side of this equation by 2\n yields -6=-174+x2. Adding 174 to each side of this equation yields -74=x2. Therefore, the other x-intercept is -74,0.  

\n

Choice A is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

\n

Choice D is incorrect and may result from conceptual or calculation errors.

"}, {"id": "70753f99", "domain": "Advanced Math", "skill": "Nonlinear functions", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

The function f is defined by f(x) = open parenthesis, x + 3, close parenthesis, times, open parenthesis, x + 1, close parenthesis. The graph of f in the xy-plane is a parabola. Which of the following intervals contains the x-coordinate of the vertex of the graph of f ?

\n", "choices": [{"id": "A", "text": "

\n \u22124 < x, which < \u22123\n

\n"}, {"id": "B", "text": "

\n \u22123 < x, which < 1\n

\n"}, {"id": "C", "text": "

\n 1 < x, which < 3\n

\n"}, {"id": "D", "text": "

\n 3 < x, which < 4\n

\n"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. The graph of a quadratic function in the xy-plane is a parabola. The axis of symmetry of the parabola passes through the vertex of the parabola. Therefore, the vertex of the parabola and the midpoint of the segment between the two x-intercepts of the graph have the same x-coordinate. Since f(n)egative 3 = f(n)egative 1, which = 0, the x-coordinate of the vertex is (\u22123 + \u22121)/(2 = \u22122). Of the shown intervals, only the interval in choice B contains –2. Choices A, C, and D are incorrect and may result from either calculation errors or misidentification of the graph’s x-intercepts.

\n"}, {"id": "568aaf27", "domain": "Advanced Math", "skill": "Nonlinear equations in one variable and systems of equations in two variables ", "difficulty": "E", "type": "mc", "stimulus": "
\n

\n Equation 1: x + y = 12. Equation 2: y = x\u00b2.\n

\n
\n", "stem": "

If x, y is a solution to the system of equations above, which of the following is a possible value of x?

\n", "choices": [{"id": "A", "text": "

0

\n"}, {"id": "B", "text": "

1

\n"}, {"id": "C", "text": "

2

\n"}, {"id": "D", "text": "

3

\n"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. Substituting x\u00b2 from the second equation for y in the first equation yields x + x\u00b2 = 12. Subtracting 12 from both sides of this equation and rewriting the equation results in x\u00b2, + x, \u2212 12 = 0. Factoring the left-hand side of this equation yields open parenthesis, x \u2212 3, close parenthesis, times, open parenthesis, x + 4, close parenthesis = 0. Using the zero product property to solve for x, it follows that x \u2212 3 = 0 and x + 4 = 0. Solving each equation for x yields x = 3 and x = \u22124, respectively. Thus, two possible values of x are 3 and \u22124. Of the choices given, 3 is the only possible value of x.

Choices A, B, and C are incorrect. Substituting 0 for x in the first equation gives 0 + y = 12, or y = 12; then, substituting 12 for y and 0 for x in the second equation gives 12 = 0\u00b2, or 12 = 0, which is false. Similarly, substituting 1 or 2 for x in the first equation yields y = 11 or y = 10, respectively; then, substituting 11 or 10 for y in the second equation yields a false statement.

\n"}, {"id": "6676f055", "domain": "Advanced Math", "skill": "Nonlinear functions", "difficulty": "M", "type": "mc", "stimulus": "
\n

\n f(t)heta = \u22120 point 2 8, times, open parenthesis, theta \u2212 27, close parenthesis, squared, + 880\n

\n
\n", "stem": "

An engineer wanted to identify the best angle for a cooling fan in an engine in order to get the greatest airflow. The engineer discovered that the function above models the airflow f(t)heta, in cubic feet per minute, as a function of the angle of the fan theta, in degrees. According to the model, what angle, in degrees, gives the greatest airflow?

\n", "choices": [{"id": "A", "text": "

–0.28

\n"}, {"id": "B", "text": "

0.28

\n"}, {"id": "C", "text": "

27

\n"}, {"id": "D", "text": "

880

\n"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. The function f is quadratic, so it will have either a maximum or a minimum at the vertex of the graph. Since the coefficient of the quadratic term (–0.28) is negative, the vertex will be at a maximum. The equation f(theta) = –0.28(theta – 27)2 + 880 is given in vertex form, so the vertex is at theta = 27. Therefore, an angle of 27 degrees gives the greatest airflow.

Choices A and B are incorrect and may be the result of misidentifying which value in a quadratic equation in vertex form represents the vertex. Choice D is incorrect. This choice identifies the maximum value of f(theta) rather than the value of theta for which f(theta) is maximized.

\n"}, {"id": "29ed5d39", "domain": "Advanced Math", "skill": "Nonlinear equations in one variable and systems of equations in two variables ", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

\n\tp\n\t=\n\t\n\t\t20\n\t\t+\n\t\t\n\t\t\t\n\t\t\t\t16\n\t\t\t\tn\n\t\t\t\n\t\t\n\t\n\n

\n

The given equation relates the numbers p\n and n\n, where n\n is not equal to 0\n and p>20. Which equation correctly expresses n\n in terms of p\n?

", "choices": [{"id": "A", "text": "

n=p-2016

"}, {"id": "B", "text": "

\n\tn\n\t=\n\t\n\t\t\n\t\t\t\n\t\t\t\tp\n\t\t\t\t16\n\t\t\t\n\t\t\n\t\t+\n\t\t20\n\t\n\n

"}, {"id": "C", "text": "

\n\tn\n\t=\n\t\n\t\t\n\t\t\t\n\t\t\t\tp\n\t\t\t\t16\n\t\t\t\n\t\t\n\t\t-\n\t\t20\n\t\n\n

"}, {"id": "D", "text": "

\n\tn\n\t=\n\t\n\t\t\n\t\t\t16\n\t\t\t\n\t\t\t\tp\n\t\t\t\t-\n\t\t\t\t20\n\t\t\t\n\t\t\n\t\n\n

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. To express n\n in terms of p\n, the given equation must be solved for n\n. Subtracting 9\n from both sides of the given equation yields p-9=14n. Since n\n is not equal to 0\n, multiplying both sides of this equation by n\n yields p-9n=14. It's given that p>9, which means \n\tp\n\t-\n\t9\n\n is not equal to 0\n. Therefore, dividing both sides of p-9n=14 by p-9 yields p-9np-9=14p-9, or n=14p-9.

\n

Choice A is incorrect and may result from conceptual or calculation errors.

\n

Choice B is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

"}, {"id": "90bcaa61", "domain": "Advanced Math", "skill": "Nonlinear functions", "difficulty": "M", "type": "spr", "stimulus": "", "stem": "

The function ft=60,0002t410 gives the number of bacteria in a population t\n minutes after an initial observation. How much time, in minutes, does it take for the number of bacteria in the population to double?

", "choices": [], "answerId": "410", "acceptedAnswers": ["410"], "rationale": "

The correct answer is 410\n. It's given that t\n minutes after an initial observation, the number of bacteria in a population is 60,0002t410. This expression consists of the initial number of bacteria, 60,000, multiplied by the expression 2t410. The time it takes for the number of bacteria to double is the increase in the value of t\n that causes the expression 2t410 to double. Since the base of the expression 2t410 is 2\n, the expression 2t410 will double when the exponent increases by 1\n. Since the exponent of the expression 2t410 is t410, the exponent will increase by 1\n when t\n increases by 410\n. Therefore the time, in minutes, it takes for the number of bacteria in the population to double is 410\n.

"}, {"id": "895628b5", "domain": "Advanced Math", "skill": "Nonlinear equations in one variable and systems of equations in two variables ", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

y=x-2x+4

\n

y=6x-12

\n

Which ordered pair x,y is the solution to the given system of equations?

", "choices": [{"id": "A", "text": "

0,2

"}, {"id": "B", "text": "

-4,2

"}, {"id": "C", "text": "

2,0

"}, {"id": "D", "text": "

2,-4

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. The second equation in the given system of equations is \n\ty\n\t=\n\t\n\t\t\n\t\t\t6\n\t\t\tx\n\t\t\n\t\t-\n\t\t12\n\t\n\n. Substituting \n\t\n\t\t6\n\t\tx\n\t\n\t-\n\t12\n\n for y\n in the first equation of the given system yields 6x-12=x-2x+4. Factoring 6\n out of the left-hand side of this equation yields 6x-2=x-2x+4. An expression with a factor of the form x-a is equal to zero when \n\tx\n\t=\n\ta\n\n. Each side of this equation has a factor of x-2, so each side of the equation is equal to zero when \n\tx\n\t=\n\t2\n\n. Substituting 2\n for x\n into the equation 6x-2=x-2x+4 yields 62-2=2-22+4, or 0=0, which is true. Substituting 2\n for x\n into the second equation in the given system of equations yields y=62-12, or \n\ty\n\t=\n\t0\n\n. Therefore, the solution to the system of equations is the ordered pair 2,0.

\n

Choice A is incorrect and may result from switching the order of the solutions for x\n and y\n.

\n

Choice B is incorrect and may result from conceptual or calculation errors.

\n

Choice D is incorrect and may result from conceptual or calculation errors.

"}, {"id": "26eb61c1", "domain": "Advanced Math", "skill": "Equivalent expressions", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

Which expression is equivalent to \n\t\n\t\t6\n\t\t\n\t\t\tx\n\t\t\t8\n\t\t\n\t\t\n\t\t\ty\n\t\t\t2\n\t\t\n\t\n\t+\n\t\n\t\t12\n\t\t\n\t\t\tx\n\t\t\t2\n\t\t\n\t\t\n\t\t\ty\n\t\t\t2\n\t\t\n\t\n\n?

", "choices": [{"id": "A", "text": "

6x2y22x6

"}, {"id": "B", "text": "

6x2y2x4

"}, {"id": "C", "text": "

\n\t6\n\t\n\t\tx\n\t\t2\n\t\n\t\n\t\ty\n\t\t2\n\t\n\t\n\t\t\n\t\t\t\n\t\t\t\tx\n\t\t\t\t6\n\t\t\t\n\t\t\t+\n\t\t\t2\n\t\t\n\t\n\n

"}, {"id": "D", "text": "

\n\t6\n\t\n\t\tx\n\t\t2\n\t\n\t\n\t\ty\n\t\t2\n\t\n\t\n\t\t\n\t\t\t\n\t\t\t\tx\n\t\t\t\t4\n\t\t\t\n\t\t\t+\n\t\t\t2\n\t\t\n\t\n\n

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. Since each term of the given expression has a common factor of 6x2y2, it may be rewritten as 6x2y2(x6)+6x2y2(2), or 6x2y2(x6+2).

\n

Choice A is incorrect. This expression is equivalent to 12x8y2, not 6x8y2+12x2y2.

\n

Choice B is incorrect. This expression is equivalent to 6x6y2, not 6x8y2+12x2y2.

\n

Choice D is incorrect. This expression is equivalent to 6x6y2+12x2y2, not 6x8y2+12x2y2.

"}, {"id": "8f65cddc", "domain": "Advanced Math", "skill": "Nonlinear equations in one variable and systems of equations in two variables ", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

17b=11xy

\n

The given equation relates the positive numbers b\n, x\n, and y\n. Which equation correctly expresses x\n in terms of b\n and y\n?

", "choices": [{"id": "A", "text": "

x=7by11

"}, {"id": "B", "text": "

\n\tx\n\t=\n\t\n\t\ty\n\t\t-\n\t\t\n\t\t\t77\n\t\t\tb\n\t\t\n\t\n\n

"}, {"id": "C", "text": "

\n\tx\n\t=\n\t\n\t\t\n\t\t\ty\n\t\t\t\n\t\t\t\t77\n\t\t\t\tb\n\t\t\t\n\t\t\n\t\n\n

"}, {"id": "D", "text": "

\n\tx\n\t=\n\t\n\t\t77\n\t\tb\n\t\ty\n\t\n\n

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. Multiplying each side of the given equation by y\n yields the equivalent equation y7b=11x. Dividing each side of this equation by 11\n yields y77b=x, or x=y77b.

\n

Choice A is incorrect. This equation is not equivalent to the given equation. 

\n

Choice B is incorrect. This equation is not equivalent to the given equation. 

\n

Choice D is incorrect. This equation is not equivalent to the given equation. 

"}, {"id": "dd8ac009", "domain": "Advanced Math", "skill": "Nonlinear functions", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
Time (years)Total amount (dollars)
0670.00
1674.02
2678.06
\n

Sara opened a savings account at a bank. The table shows the exponential relationship between the time t\n, in years, since Sara opened the account and the total amount d\n, in dollars, in the account. If Sara made no additional deposits or withdrawals, which of the following equations best represents the relationship between t\n and d\n?

", "choices": [{"id": "A", "text": "

d=0.0061+670t

"}, {"id": "B", "text": "

d=6701+0.006t

"}, {"id": "C", "text": "

d=1+0.006t

"}, {"id": "D", "text": "

d=1+670t

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. It’s given that the relationship between t\n and d\n is exponential. The table shows that the value of d\n increases as the value of t\n increases. Therefore, the relationship between t\n and d\n can be represented by an increasing exponential equation of the form d=a1+bt, where a\n and b\n are positive constants. The table shows that when \n\tt\n\t=\n\t0\n\n, \n\td\n\t=\n\t670\n\n. Substituting 0\n for t\n and 670\n for d\n in the equation d=a1+bt yields 670=a1+b0, which is equivalent to 670=a1, or 670=a. Substituting 670\n for a\n in the equation d=a1+bt yields d=6701+bt. The table also shows that when \n\tt\n\t=\n\t1\n\n, \n\td\n\t=\n\t674.02\n\n. Substituting 1\n for t\n and 674.02\n for d\n in the equation d=6701+bt yields 674.02=6701+b1, or 674.02=6701+b. Dividing both sides of this equation by 670\n yields 1.006=1+b. Subtracting 1\n from both sides of this equation yields \n\tb\n\t=\n\t0.006\n\n. Substituting 0.006\n for b\n in the equation d=6701+bt yields d=6701+0.006t. Therefore, of the choices, choice B best represents the relationship between t\n and d\n.

\n

Choice A is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

\n

Choice D is incorrect and may result from conceptual or calculation errors.

"}, {"id": "2d1614a1", "domain": "Advanced Math", "skill": "Nonlinear functions", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

Pt=2901.0446t

\n

The function P\n models the population, in thousands, of a certain city t\n years after 2005\n. According to the model, the population is predicted to increase by n% every 18\n months. What is the value of n\n?

", "choices": [{"id": "A", "text": "

0.38\n

"}, {"id": "B", "text": "

1.04\n

"}, {"id": "C", "text": "

4\n

"}, {"id": "D", "text": "

6\n

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. It's given that the function P\n models the population of the city t\n years after 2005. Since there are 12\n months in a year, 18\n months is equivalent to 1812 years. Therefore, the expression 1812x can represent the number of years in x\n 18\n-month periods. Substituting 1812x for t\n in the given equation yields P1812x=2901.04461812x, which is equivalent to P1812x=2901.04x. Therefore, for each 18\n-month period, the predicted population of the city is 1.04\n times, or 104% of, the previous population. This means that the population is predicted to increase by 4% every 18\n months.

\n

Choice A is incorrect and may result from conceptual or calculation errors. 

\n

Choice B is incorrect. Each year, the predicted population of the city is 1.04\n times the previous year's predicted population, which is not the same as an increase of 1.04%.

\n

Choice D is incorrect and may result from conceptual or calculation errors.

"}, {"id": "9ed9f54d", "domain": "Advanced Math", "skill": "Equivalent expressions", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

Which of the following is equivalent to 2 times, open parenthesis, x\u00b2 \u2212 x, close parenthesis, + 3 times, open parenthesis, x\u00b2 \u2212 x, close parenthesis ?

\n", "choices": [{"id": "A", "text": "

\n 5 x\u00b2, \u2212 5 x\n

\n"}, {"id": "B", "text": "

\n 5 x\u00b2, + 5 x\n

\n"}, {"id": "C", "text": "

5x

\n"}, {"id": "D", "text": "

5x2

\n"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. Since open parenthesis, x\u00b2, \u2212 x, close parenthesis is a common term in the original expression, like terms can be added: 2 times, open parenthesis, x\u00b2, \u2212 x, close parenthesis, plus, 3 times, open parenthesis, x\u00b2, \u2212 x, close parenthesis = 5 times, open parenthesis, x\u00b2, \u2212 x, close parenthesis. Distributing the constant term 5 yields 5 x\u00b2, \u2212 5 x.

Choice B is incorrect and may result from not distributing the negative signs in the expressions within the parentheses. Choice C is incorrect and may result from not distributing the negative signs in the expressions within the parentheses and from incorrectly eliminating the x\u00b2-term. Choice D is incorrect and may result from incorrectly eliminating the x-term.

\n"}, {"id": "30281058", "domain": "Advanced Math", "skill": "Nonlinear equations in one variable and systems of equations in two variables ", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

In the xy-plane, the graph of y = x\u00b2 \u2212 9 intersects line p at the point 1, a and the point 5, b, where a and b are constants. What is the slope of line p ?

\n", "choices": [{"id": "A", "text": "\n 6\n \n"}, {"id": "B", "text": "\n 2\n \n"}, {"id": "C", "text": "\n \u22122\n \n"}, {"id": "D", "text": "\n \u22126\n \n"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. It’s given that the graph of y = x\u00b2, \u2212 9 and line p intersect at the point 1, a and the point 5, b. Therefore, the value of y when x = 1 is the value of a, and the value of y when x = 5 is the value of b. Substituting 1 for x in the given equation yields y = 1\u00b2 \u2212 9, or y = \u22128. Similarly, substituting 5 for x in the given equation yields y = 5\u00b2 \u2212 9, or y = 16. Therefore, the intersection points are the point 1, \u22128 and the point 5, 16. The slope of line p is the ratio of the change in y to the change in x between these two points: (16 \u2212 \u22128)/(5 \u2212 1, end fraction = (24)/(4)), or 6.

Choices B, C, and D are incorrect and may result from conceptual or calculation errors in determining the values of a, b, or the slope of line p.

\n"}, {"id": "42f19012", "domain": "Advanced Math", "skill": "Equivalent expressions", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

Which expression is equivalent to \n\ta\n\t\n\t\t11\n\t\t12\n\t\n\n, where a>0?

", "choices": [{"id": "A", "text": "

\n\t\n\t\ta\n\t\t132\n\t\n\t12\n\n

"}, {"id": "B", "text": "

\n\t\n\t\ta\n\t\t132\n\t\n\t144\n\n

"}, {"id": "C", "text": "

\n\t\n\t\ta\n\t\t132\n\t\n\t121\n\n

"}, {"id": "D", "text": "

\n\t\n\t\ta\n\t\t132\n\t\n\t11\n\n

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. Since 1212=1, multiplying the exponent of the given expression by 1212 yields an equivalent expression: a11121212=a132144. Since 132144=1321144, the expression a132144 can be rewritten as a1321144. Applying properties of exponents, this expression can be rewritten as a1321144. An expression of the form m1k, where m>0 and k>0, is equivalent to mk. Therefore, a1321144 is equivalent to a132144.

\n

Choice A is incorrect and may result from conceptual or calculation errors. 

\n

Choice C is incorrect and may result from conceptual or calculation errors. 

\n

Choice D is incorrect and may result from conceptual or calculation errors. 

"}, {"id": "294db8ec", "domain": "Advanced Math", "skill": "Equivalent expressions", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

Which of the following is equivalent to 2 x\u00b3, + 4?

\n", "choices": [{"id": "A", "text": "

\n 4 \u00d7 open parenthesis, x\u00b3, + 4, close parenthesis\n

\n"}, {"id": "B", "text": "

\n 4 \u00d7 open parenthesis, x\u00b3, + 2, close parenthesis\n

\n"}, {"id": "C", "text": "

\n 2 \u00d7 open parenthesis, x\u00b3, + 4, close parenthesis\n

\n"}, {"id": "D", "text": "

\n 2 \u00d7 open parenthesis, x\u00b3, + 2, close parenthesis

\n"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. The expression 2 x\u00b3, + 4 has two terms, 2 x\u00b3 and 4. The greatest common factor of these two terms is 2. Factoring 2 from each of these terms yields 2 \u00d7 x\u00b3, plus, 2 \u00d7 2, or 2 times, open parenthesis, x\u00b3 + 2, close parenthesis.

Choices A and B are incorrect because 4 is not a factor of the term 2 x\u00b3. Choice C is incorrect and may result from factoring 2 from 2 x\u00b3 but not from 4.

\n"}, {"id": "84dd43f8", "domain": "Advanced Math", "skill": "Nonlinear functions", "difficulty": "H", "type": "spr", "stimulus": "", "stem": "

For the function f\n, f0=86, and for each increase in x\n by 1\n, the value of fx decreases by 80%. What is the value of f2?

", "choices": [], "answerId": "3.44", "acceptedAnswers": ["3.44", "86/25"], "rationale": "

The correct answer is 3.44\n. It’s given that f0=86 and that for each increase in x\n by 1\n, the value of fx decreases by 80%. Because the output of the function decreases by a constant percentage for each 1\n-unit increase in the value of x\n, this relationship can be represented by an exponential function of the form fx=abx, where a\n represents the initial value of the function and b\n represents the rate of decay,
expressed as a decimal. Because f0=86, the value of a\n must be 86\n. Because the value of fx decreases by 80% for each 1\n-unit increase in x\n, the value of b\n must be (1−0.80), or 0.2. Therefore, the function f\n can be defined by fx=860.2x. Substituting 2\n for x\n in this function yields f2=860.22, which is equivalent to f2=860.04, or f2=3.44. Either 3.44\n or 86/25 may be entered as the correct answer.

\n

Alternate approach: It’s given that f0=86 and that for each increase in x\n by 1\n, the value of fx decreases by 80%. Therefore, when x=1, the value of fx is (100−80)%, or 20%, of 86\n, which can be expressed as 0.2086. Since 0.2086=17.2, the value of f1 is 17.2\n. Similarly, when x=2, the value of fx is 20% of 17.2\n, which can be expressed as 0.2017.2. Since 0.2017.2=3.44, the value of f2 is 3.44\n. Either 3.44\n or 86/25 may be entered as the correct answer.

"}, {"id": "59d1f4b5", "domain": "Advanced Math", "skill": "Nonlinear functions", "difficulty": "H", "type": "mc", "stimulus": "
\n\t

M = 1,800 times, 1 point 0 2, to the power t

\n
\n", "stem": "

The equation above models the number of members, M, of a gym t years after the gym opens. Of the following, which equation models the number of members of the gym q quarter years after the gym opens?

\n", "choices": [{"id": "A", "text": "

M = 1,800 times, 1 point 0 2, to the power of (q)/(4)

\n"}, {"id": "B", "text": "

M = 1,800 times, 1 point 0 2, to the power 4 q

\n"}, {"id": "C", "text": "

M = 1,800 times, 1 point 0 0 5, to the power 4 q

\n"}, {"id": "D", "text": "

M = 1,800 times, 1 point 0 8 2, to the power q

\n"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. In 1 year, there are 4 quarter years, so the number of quarter years, q, is 4 times the number of years, t ; that is, q = 4, t. This is equivalent to t = q over 4, and substituting this into the expression for M in terms of t gives M = 1,800 times, 1 point 0 2 raised to (q)/(4 power).

Choices B and D are incorrect and may be the result of incorrectly using t = 4 q instead of q = 4, t. (Choices B and D are nearly the same since 1 point 0 2 raised to the 4 q power is equivalent to open parenthesis, 1 point 0 2 to the fourth power, close parenthesis, raised to the q power, which is approximately 1 point 0 8 2 to the q power.) Choice C is incorrect and may be the result of incorrectly using t = 4 q and unnecessarily dividing 0.02 by 4.

 

\n"}, {"id": "281a4f3b", "domain": "Advanced Math", "skill": "Nonlinear functions", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

A certain college had 3,000 students enrolled in 2015. The college predicts that after 2015, the number of students enrolled each year will be 2% less than the number of students enrolled the year before. Which of the following functions models the relationship between the number of students enrolled, f(x), and the number of years after 2015, x ?

\n", "choices": [{"id": "A", "text": "

\n f(x) = 0 point 0 2, \u00d7 open parenthesis, 3,000, close parenthesis, to the x power\n

\n"}, {"id": "B", "text": "

\n f(x) = 0 point 9 8, \u00d7 open parenthesis, 3,000, close parenthesis, to the x power\n

\n"}, {"id": "C", "text": "

\n f(x) = 3,000, \u00d7 open parenthesis, 0 point 0 2, close parenthesis, to the x power

\n"}, {"id": "D", "text": "

\n f(x) = 3,000, \u00d7 open parenthesis, 0 point 9 8, close parenthesis, to the x power\n

\n"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. Because the change in the number of students decreases by the same percentage each year, the relationship between the number of students and the number of years can be modeled with a decreasing exponential function in the form f(x) = a, times, open parenthesis, 1 \u2212 r, close parenthesis, to the x power, where f(x) is the number of students, a is the number of students in 2015, r is the rate of decrease each year, and x is the number of years since 2015. It’s given that 3,000 students were enrolled in 2015 and that the rate of decrease is predicted to be 2%, or 0.02. Substituting these values into the decreasing exponential function yields f(x) = 3,000 times, open parenthesis, 1 \u2212 0 point 0 2, close parenthesis, to the x power, which is equivalent to f(x) = 3,000 times, open parenthesis, 0 point 9 8, close parenthesis, to the x power.

Choices A, B, and C are incorrect and may result from conceptual errors when translating the given information into a decreasing exponential function.

\n"}, {"id": "72ae8a87", "domain": "Advanced Math", "skill": "Nonlinear functions", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

The function f(x)=200,0001.21x gives a company’s predicted annual revenue, in dollars, x\n years after the company started selling light bulbs online, where 0<x≤10. What is the best interpretation of the statement “f5 is approximately equal to 518,748\n” in this context?

", "choices": [{"id": "A", "text": "

5\n years after the company started selling light bulbs online, its predicted annual revenue is approximately 518,748\n dollars.

"}, {"id": "B", "text": "

5\n years after the company started selling light bulbs online, its predicted annual revenue will have increased by a total of approximately 518,748\n dollars.

"}, {"id": "C", "text": "

When the company’s predicted annual revenue is approximately 518,748\n dollars, it is 5\n times the predicted annual revenue for the previous year.

"}, {"id": "D", "text": "

When the company’s predicted annual revenue is approximately 518,748\n dollars, it is 5\n% greater than the predicted annual revenue for the previous year.

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. It's given that the function fx=200,0001.21x gives a company's predicted annual revenue, in dollars, x years after the company started selling light bulbs online. It follows that fx represents the company's predicted annual revenue, in dollars, x years after the company started selling light bulbs online. Since the value of f5 is the value of fx when x=5, it follows that \"f5 is approximately equal to 518,748\" means that fx is approximately equal to 518,748 when x=5. Therefore, the best interpretation of the statement \"f5 is approximately equal to 518,748\" in this context is 5 years after the company started selling light bulbs online, its predicted annual revenue is approximately 518,748 dollars.

\n

Choice B is incorrect and may result from conceptual errors.

\n

Choice C is incorrect and may result from conceptual errors.

\n

Choice D is incorrect and may result from conceptual errors.

"}, {"id": "01668cd6", "domain": "Advanced Math", "skill": "Nonlinear functions", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

The functions f\n and g\n are defined by the given equations, where x≥0. Which of the following equations displays, as a constant or coefficient, the maximum value of the function it defines, where x≥0?

\n
    \n
  1. fx=330.4x+3
    2. \n
  2. gx=330.160.4x-2
    3. \n
", "choices": [{"id": "A", "text": "

I only

"}, {"id": "B", "text": "

II only

"}, {"id": "C", "text": "

I and II

"}, {"id": "D", "text": "

Neither I nor II

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. Functions f\n and g\n are both exponential functions with a base of 0.40\n. Since 0.40\n is less than 1\n, functions f\n and g\n are both decreasing exponential functions. This means that fx and gx decrease as x\n increases. Since fx and gx decrease as x\n increases, the maximum value of each function occurs at the least value of x\n for which the function is defined. It's given that functions f\n and g\n are defined for x≥0. Therefore, the maximum value of each function occurs at \n\tx\n\t=\n\t0\n\n. Substituting 0\n for x\n in the equation defining f\n yields f0=330.40+3, which is equivalent to f0=330.43, or f0=2.112. Therefore, the maximum value of f\n is 2.112\n. Since the equation fx=330.4x+3 doesn't display the value 2.112\n, the equation defining f\n doesn't display the maximum value of f\n. Substituting 0\n for x\n in the equation defining g\n yields g0=330.160.40-2, which can be rewritten as g0=330.1610.42, or g0=330.1610.16, which is equivalent to g0=33. Therefore, the maximum value of g\n is 33\n. Since the equation gx=330.160.4x-2 displays the value 33\n, the equation defining g\n displays the maximum value of g\n. Thus, only equation II displays, as a constant or coefficient, the maximum value of the function it defines.

\n

Choice A is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

\n

Choice D is incorrect and may result from conceptual or calculation errors.

"}, {"id": "c77ef2fb", "domain": "Advanced Math", "skill": "Nonlinear equations in one variable and systems of equations in two variables ", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

Blood volume,V sub B, in a human can be determined using the equation V sub B = (V sub P)/(1 \u2212 H, end fraction), where V sub P is the plasma volume and H is the hematocrit (the fraction of blood volume that is red blood cells). Which of the following correctly expresses the hematocrit in terms of the blood volume and the plasma volume?

\n", "choices": [{"id": "A", "text": "

\n H = 1 \u2212 (V sub P)/(V sub B)\n

\n"}, {"id": "B", "text": "

\n H = (V sub B)/(V sub P)\n

\n"}, {"id": "C", "text": "

\n H = 1 + (V sub B)/(V sub P)\n

\n"}, {"id": "D", "text": "

\n H = V sub B, \u2212 V sub P\n

\n"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. The hematocrit can be expressed in terms of the blood volume and the plasma volume by solving the given equation V sub B = (V sub P)/(1 \u2212 H, end fraction) for H. Multiplying both sides of this equation by open parenthesis, 1 \u2212 H, close parenthesis yields V sub B, times, open parenthesis, 1 \u2212 H, close parenthesis = V sub P. Dividing both sides by V sub B yields 1 \u2212 H = (V sub P,)/(V sub B). Subtracting 1 from both sides yields \u2212H = \u22121 plus, (V sub P)/(V sub B). Dividing both sides by \u22121 yields H = 1 minus, (V sub P)/(V sub B).

Choices B, C, and D are incorrect and may result from errors made when manipulating the equation.

\n"}, {"id": "5ae186b4", "domain": "Advanced Math", "skill": "Nonlinear equations in one variable and systems of equations in two variables ", "difficulty": "M", "type": "spr", "stimulus": "", "stem": "

-54w=6

\n

What is the solution to the given equation?

", "choices": [], "answerId": "-9", "acceptedAnswers": ["-9"], "rationale": "

The correct answer is -9\n. Since w\n is in the denominator of a fraction in the given equation, w\n can't be equal to 0\n. Since w\n isn't equal to 0\n, multiplying both sides of the given equation by w\n yields an equivalent equation, \n\t-54\n\t=\n\t\n\t\t6\n\t\tw\n\t\n\n. Dividing both sides of this equation by 6\n yields \n\t-9\n\t=\n\tw\n\n. Therefore, -9\n is the solution to the given equation.

"}, {"id": "b76a2815", "domain": "Advanced Math", "skill": "Nonlinear equations in one variable and systems of equations in two variables ", "difficulty": "E", "type": "mc", "stimulus": "
\n

\n P = (W)/(t)\n

\n
\n", "stem": "

The power P produced by a machine is represented by the equation above, where W is the work performed during an amount of time t. Which of the following correctly expresses W in terms of P and t ?

\n", "choices": [{"id": "A", "text": "

\n W = P t\n

\n"}, {"id": "B", "text": "

\n W = (P)/(t)\n

\n"}, {"id": "C", "text": "

\n W = (t)/(P)\n

\n"}, {"id": "D", "text": "

\n W = P + t\n

\n"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. Multiplying both sides of the equation by t yields P \u00d7 t = open parenthesis, (w)/(t, close parenthesis, \u00d7 t), or P t = W, which expresses W in terms of P and t. This is equivalent to W = Pt.

\n
\nChoices B, C, and D are incorrect. Each of the expressions given in these answer choices gives W in terms of P and t but doesn’t maintain the given relationship between W, P, and t. These expressions may result from performing different operations with t on each side of the equation. In choice B, W has been multiplied by t, and P has been divided by t. In choice C, W has been multiplied by t, and the quotient of P divided by t has been reciprocated. In choice D, W has been multiplied by t, and P has been added to t. However, in order to maintain the relationship between the variables in the given equation, the same operation must be performed with t on each side of the equation. 

\n"}, {"id": "09f58996", "domain": "Advanced Math", "skill": "Nonlinear functions", "difficulty": "E", "type": "spr", "stimulus": "", "stem": "

The function f\n is defined by f(x)=6+x. What is the value of f36?

", "choices": [], "answerId": "12", "acceptedAnswers": ["12"], "rationale": "

The correct answer is 12\n. The value of f36 is the value of fx when x=36. Substituting 36\n for x\n in the given equation yields f36=6+36, which is equivalent to f36=6+6, or f36=12. Thus, the value of f36 is 12\n.

"}, {"id": "beb86a0c", "domain": "Advanced Math", "skill": "Equivalent expressions", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

Which expression is equivalent to \n\t\n\t\t9\n\t\t\n\t\t\tx\n\t\t\t2\n\t\t\n\t\n\t+\n\t\n\t\t5\n\t\tx\n\t\n\n?

", "choices": [{"id": "A", "text": "

\n\tx\n\t\n\t\t\n\t\t\t\n\t\t\t\t9\n\t\t\t\tx\n\t\t\t\n\t\t\t+\n\t\t\t5\n\t\t\n\t\n\n

"}, {"id": "B", "text": "

\n\t5\n\tx\n\t\n\t\t\n\t\t\t\n\t\t\t\t9\n\t\t\t\tx\n\t\t\t\n\t\t\t+\n\t\t\t1\n\t\t\n\t\n\n

"}, {"id": "C", "text": "

\n\t9\n\tx\n\t\n\t\t\n\t\t\tx\n\t\t\t+\n\t\t\t5\n\t\t\n\t\n\n

"}, {"id": "D", "text": "

\n\t\n\t\tx\n\t\t2\n\t\n\t\n\t\t\n\t\t\t\n\t\t\t\t9\n\t\t\t\tx\n\t\t\t\n\t\t\t+\n\t\t\t5\n\t\t\n\t\n\n

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. Since x\n is a factor of each term in the given expression, the expression is equivalent to x9x+x5, or x9x+5.

\n

Choice B is incorrect. This expression is equivalent to \n\t\n\t\t45\n\t\t\n\t\t\tx\n\t\t\t2\n\t\t\n\t\n\t+\n\t\n\t\t5\n\t\tx\n\t\n\n, not \n\t\n\t\t9\n\t\t\n\t\t\tx\n\t\t\t2\n\t\t\n\t\n\t+\n\t\n\t\t5\n\t\tx\n\t\n\n.

\n

Choice C is incorrect. This expression is equivalent to \n\t\n\t\t9\n\t\t\n\t\t\tx\n\t\t\t2\n\t\t\n\t\n\t+\n\t\n\t\t45\n\t\tx\n\t\n\n, not \n\t\n\t\t9\n\t\t\n\t\t\tx\n\t\t\t2\n\t\t\n\t\n\t+\n\t\n\t\t5\n\t\tx\n\t\n\n.

\n

Choice D is incorrect. This expression is equivalent to \n\t\n\t\t9\n\t\t\n\t\t\tx\n\t\t\t3\n\t\t\n\t\n\t+\n\t\n\t\t5\n\t\t\n\t\t\tx\n\t\t\t2\n\t\t\n\t\n\n, not \n\t\n\t\t9\n\t\t\n\t\t\tx\n\t\t\t2\n\t\t\n\t\n\t+\n\t\n\t\t5\n\t\tx\n\t\n\n.

"}, {"id": "5910bfff", "domain": "Advanced Math", "skill": "Nonlinear equations in one variable and systems of equations in two variables ", "difficulty": "H", "type": "mc", "stimulus": "
\n

\n
\n", "stem": "

\n D = T minus, (9)/(25, end fraction, \u00d7 open parenthesis, 100 \u2212 H, close parenthesis)

The formula above can be used to approximate the dew point D, in degrees Fahrenheit, given the temperature T, in degrees Fahrenheit, and the relative humidity of H percent, where H > 50. Which of the following expresses the relative humidity in terms of the temperature and the dew point?

\n", "choices": [{"id": "A", "text": "H = (25)/(9, end fraction, \u00d7 open parenthesis, D \u2212 T, close parenthesis, + 100)\n"}, {"id": "B", "text": "H = (25)/(9, end fraction, \u00d7 open parenthesis, D \u2212 T, close parenthesis, \u2212 100)\n"}, {"id": "C", "text": "H = (25)/(9, end fraction, \u00d7 open parenthesis, D + T, close parenthesis, + 100)\n"}, {"id": "D", "text": "H = (25)/(9, end fraction, \u00d7 open parenthesis, D + T, close parenthesis, \u2212 100)\n"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. It’s given that D = T \u2212 (9)/(25, end fraction, times, open parenthesis, 100 \u2212 H, close parenthesis). Solving this formula for H expresses the relative humidity in terms of the temperature and the dew point. Subtracting T from both sides of this equation yields D \u2212 T = the \u2212of (9)/(25, end fraction, times, open parenthesis, 100 \u2212 H, close parenthesis). Multiplying both sides by the \u2212of (25)/(9) yields the \u2212of (25)/(9, end fraction, times, open parenthesis, D \u2212 T, close parenthesis = 100 \u2212 H). Subtracting 100 from both sides yields the \u2212of (25)/(9, end fraction, times, open parenthesis, D \u2212 T, close parenthesis, \u2212 100 = \u2212H). Multiplying both sides by \u22121 results in the formula (25)/(9, end fraction, times, open parenthesis, D \u2212 T, close parenthesis, + 100 = H.).

Choices B, C, and D are incorrect and may result from errors made when rewriting the given formula.

\n"}, {"id": "7ba694f3", "domain": "Advanced Math", "skill": "Nonlinear functions", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

The number of bacteria in a liquid medium doubles every day. There are 44,000\n bacteria in the liquid medium at the start of an observation. Which represents the number of bacteria, y\n, in the liquid medium t\n days after the start of the observation? 

", "choices": [{"id": "A", "text": "

y=1244,000t

"}, {"id": "B", "text": "

y=244,000t

"}, {"id": "C", "text": "

y=44,00012t

"}, {"id": "D", "text": "

y=44,0002t

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. Since the number of bacteria doubles every day, the relationship between t\n and y\n can be represented by an exponential equation of the form y=abt, where a\n is the number of bacteria at the start of the observation and the number of bacteria increases by a factor of b\n every day. It’s given that there are 44,000\n bacteria at the start of the observation. Therefore, \n\ta\n\t=\n\t44,000\n\n. It’s also given that the number of bacteria doubles, or increases by a factor of 2\n, every day. Therefore, \n\tb\n\t=\n\t2\n\n. Substituting 44,000\n for a\n and 2\n for b\n in the equation y=abt yields y=44,0002t.

\n

Choice A is incorrect and may result from conceptual or calculation errors.

\n

Choice B is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect. This equation represents a situation where the number of bacteria is decreasing by half, not doubling, every day.

"}, {"id": "fbb96bb1", "domain": "Advanced Math", "skill": "Nonlinear equations in one variable and systems of equations in two variables ", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

x-29=x-ax-29

\n

Which of the following are solutions to the given equation, where a\n is a constant and a>30?

\n
    \n
  1. a\n
    2. \n
  2. \n\ta\n\t+\n\t1\n\n
    3. \n
  3. 29\n
    4. \n
", "choices": [{"id": "A", "text": "

I and II only

"}, {"id": "B", "text": "

I and III only

"}, {"id": "C", "text": "

II and III only

"}, {"id": "D", "text": "

I, II, and III

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. Subtracting the expression x-29 from both sides of the given equation yields 0=x-ax-29-x-29, which can be rewritten as 0=x-ax-29+-1x-29. Since the two terms on the right-hand side of this equation have a common factor of x-29, it can be rewritten as 0=x-29x-a+-1, or 0=x-29x-a-1. Since x-a-1 is equivalent to x-a+1, the equation 0=x-29x-a-1 can be rewritten as 0=x-29x-a+1. By the zero product property, it follows that x-29=0 or x-a+1=0. Adding 29\n to both sides of the equation x-29=0 yields \n\tx\n\t=\n\t29\n\n. Adding a+1 to both sides of the equation x-a+1=0 yields x=a+1. Therefore, the two solutions to the given equation are 29\n and \n\ta\n\t+\n\t1\n\n. Thus, only \n\ta\n\t+\n\t1\n\n and 29\n, not a\n, are solutions to the given equation.

\n

Choice A is incorrect and may result from conceptual or calculation errors.

\n

Choice B is incorrect and may result from conceptual or calculation errors.

\n

Choice D is incorrect and may result from conceptual or calculation errors.

"}, {"id": "6e06a0a7", "domain": "Advanced Math", "skill": "Equivalent expressions", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

Which of the following expressions is equivalent to 2, a\u00b2, times, open parenthesis, a, + 3, close parenthesis ?

\n", "choices": [{"id": "A", "text": "

5, a\u00b3

\n"}, {"id": "B", "text": "

8, a to the fifth power

\n"}, {"id": "C", "text": "

2, a\u00b3, + 3

\n"}, {"id": "D", "text": "

2, a\u00b3, + 6, a\u00b2

\n"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. Expanding the given expression using the distributive property yields 2 a, squared times, a, + 2 a, squared times, 3. Combining like terms yields 2 a, squared times, open parenthesis, a, to the first power, close parenthesis, plus, open parenthesis, 2 \u00d7 3, close parenthesis, times, open parenthesis, a, squared, close parenthesis, or 2 a, raised to the 2 + 1 power, + 6 a, squared, which is equivalent to 2 a, cubed, + 6 a, squared.

Choices A and B are incorrect and may result from incorrectly combining like terms. Choice C is incorrect and may result from distributing 2 a, squared only to a, and not to 3, in the given expression.

 

\n"}, {"id": "ad038c19", "domain": "Advanced Math", "skill": "Equivalent expressions", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

Which of the following is equivalent to parenthesis, a, + (b)/(2, close parenthesis, squared) ?

\n", "choices": [{"id": "A", "text": "a, squared, + (b\u00b2)/(2)\n"}, {"id": "B", "text": "a, squared, + (b\u00b2)/(4)\n"}, {"id": "C", "text": "a, squared, + (a, \u00d7 b,)/(2, end fraction, + the fraction b\u00b2 over 2)\n"}, {"id": "D", "text": "a, squared, + a, \u00d7 b, + (b\u00b2)/(4)\n"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. The expression open parenthesis, a, + (b)/(2, close parenthesis, squared) can be rewritten as open parenthesis, a, + (b)/(2, close parenthesis, times, open parenthesis, a, + the fraction b over 2, close parenthesis). Using the distributive property, the expression yields open parenthesis, a, + (b)/(2, close parenthesis, times, open parenthesis, a, + the fraction b over 2, close parenthesis = a, squared, + (a, b)/(2, end fraction, + the fraction with numerator a, b and denominator 2, end fraction, + the fraction b\u00b2, over 4)). Combining like terms gives a, squared, + a, b, + (b\u00b2)/(4).

Choices A, B, and C are incorrect and may result from errors using the distributive property on the given expression or combining like terms.

\n"}, {"id": "c7a187a7", "domain": "Advanced Math", "skill": "Nonlinear functions", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

fx=\n\t\n\t\tx\n\t\t2\n\t\n\t-\n\t\n\t\t18\n\t\tx\n\t\n\t-\n\t360\n\n

\n

If the given function f\n is graphed in the xy-plane, where y=fx, what is an x-intercept of the graph?

", "choices": [{"id": "A", "text": "

-12,0

"}, {"id": "B", "text": "

-30,0

"}, {"id": "C", "text": "

-360,0

"}, {"id": "D", "text": "

12,0

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. It's given that y=fx. The x-intercepts of a graph in the xy-plane are the points where \n\ty\n\t=\n\t0\n\n. Thus, for an x-intercept of the graph of function f\n, 0=fx. Substituting 0\n for fx in the equation fx=x2-18x-360 yields \n\t0\n\t=\n\t\n\t\t\n\t\t\tx\n\t\t\t2\n\t\t\n\t\t-\n\t\t\n\t\t\t18\n\t\t\tx\n\t\t\n\t\t-\n\t\t360\n\t\n\n. Factoring the right-hand side of this equation yields 0=x+12x-30. By the zero product property, \n\t\n\t\tx\n\t\t+\n\t\t12\n\t\n\t=\n\t0\n\n and \n\t\n\t\tx\n\t\t-\n\t\t30\n\t\n\t=\n\t0\n\n. Subtracting 12\n from both sides of the equation \n\t\n\t\tx\n\t\t+\n\t\t12\n\t\n\t=\n\t0\n\n yields \n\tx\n\t=\n\t-12\n\n. Adding 30\n to both sides of the equation \n\t\n\t\tx\n\t\t-\n\t\t30\n\t\n\t=\n\t0\n\n yields \n\tx\n\t=\n\t30\n\n. Therefore, the x-intercepts of the graph of y=fx are -12,0 and 30,0. Of these two x-intercepts, only -12,0 is given as a choice.

\n

Choice B is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

\n

Choice D is incorrect and may result from conceptual or calculation errors.

"}, {"id": "ebe4bde0", "domain": "Advanced Math", "skill": "Nonlinear functions", "difficulty": "E", "type": "mc", "stimulus": "
\n\t
\"The
\n
\n", "stem": "

The quadratic function graphed above models a particular measure of plant diversity as a function of the elevation in a region of Switzerland. According to the model, which of the following is closest to the elevation, in meters, at which plant diversity is greatest?

\n", "choices": [{"id": "A", "text": "

13,500

\n"}, {"id": "B", "text": "

3,000

\n"}, {"id": "C", "text": "

1,250

\n"}, {"id": "D", "text": "

250

\n"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. Each point x, y on the graph represents the elevation x, in meters, and the corresponding measure of plant diversity y in a region of Switzerland. Therefore, the point on the graph with the greatest y-coordinate represents the location that has the greatest measure of plant diversity in the region. The greatest y-coordinate of any point on the graph is approximately 13,500. The x-coordinate of that point is approximately 1,250. Therefore, the closest elevation at which the plant diversity is the greatest is 1,250 meters.

Choice A is incorrect. This value is closest to the greatest y-coordinate of any point on the graph and therefore represents the greatest measure of plant diversity, not the elevation where the greatest measure of plant diversity occurs. Choice B is incorrect. At an elevation of 3,000 meters the measure of plant diversity is approximately 4,000. Because there are points on the graph with greater y-coordinates, 4,000 can’t be the greatest measure of plant diversity, and 3,000 meters isn’t the elevation at which the greatest measure of plant diversity occurs. Choice D is incorrect. At an elevation of 250 meters, the measure of plant diversity is approximately 11,000. Because there are points on the graph with greater y-coordinates, 11,000 can’t be the greatest measure of plant diversity and 250 meters isn’t the elevation at which the greatest measure of plant diversity occurs.

 

\n"}, {"id": "ef926848", "domain": "Advanced Math", "skill": "Nonlinear functions", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

Square P has a side length of x\n inches. Square Q has a perimeter that is 176\n inches greater than the perimeter of square P. The function f\n gives the area of square Q, in square inches. Which of the following defines f\n?

", "choices": [{"id": "A", "text": "

fx=x+442

"}, {"id": "B", "text": "

fx=x+1762

"}, {"id": "C", "text": "

fx=176x+442

"}, {"id": "D", "text": "

fx=176x+1762

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. Let x\n represent the side length, in inches, of square P. It follows that the perimeter of square P is 4x inches. It's given that square Q has a perimeter that is 176\n inches greater than the perimeter of square P. Thus, the perimeter of square Q is 176\n inches greater than 4x inches, or 4x+176 inches. Since the perimeter of a square is 4\n times the side length of the square, each side length of Q is 4x+1764, or x+44 inches. Since the area of a square is calculated by multiplying the length of two sides, the area of square Q is x+44x+44, or x+442 square inches. It follows that function f\n is defined by fx=x+442. 

\n

Choice B is incorrect. This function represents a square with side lengths x+176 inches.

\n

Choice C is incorrect. This function represents a square with side lengths 176x+44 inches.

\n

Choice D is incorrect. This function represents a square with side lengths 176x+176 inches.

"}, {"id": "77c0cced", "domain": "Advanced Math", "skill": "Nonlinear equations in one variable and systems of equations in two variables ", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

\n\ty\n\t=\n\t\n\t\t\n\t\t\t2\n\t\t\t\n\t\t\t\tx\n\t\t\t\t2\n\t\t\t\n\t\t\n\t\t-\n\t\t\n\t\t\t21\n\t\t\tx\n\t\t\n\t\t+\n\t\t64\n\t\n\n

\n

\n\ty\n\t=\n\t\n\t\t\n\t\t\t3\n\t\t\tx\n\t\t\n\t\t+\n\t\ta\n\t\n\n

\n

In the given system of equations, a\n is a constant. The graphs of the equations in the given system intersect at exactly one point, (x,y), in the xy-plane. What is the value of x\n?

", "choices": [{"id": "A", "text": "

-8\n

"}, {"id": "B", "text": "

-6\n

"}, {"id": "C", "text": "

6\n

"}, {"id": "D", "text": "

8\n

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. It's given that the graphs of the equations in the given system intersect at exactly one point, x,y, in the xy-plane. Therefore, x,y is the only solution to the given system of equations. The given system of equations can be solved by subtracting the second equation, y=3x+a, from the first equation, y=2x2-21x+64. This yields y-y=2x2-21x+64-3x+a, or 0=2x2-24x+64-a. Since the given system has only one solution, this equation has only one solution. A quadratic equation in the form rx2+sx+t=0, where r\n, s\n, and t\n are constants, has one solution if and only if the discriminant, s2-4rt, is equal to zero. Substituting 2\n for r\n, -24 for s\n, and \n\t\n\t\t-\n\t\ta\n\t\n\t+\n\t64\n\n for t\n in the expression s2-4rt yields -242-4264-a. Setting this expression equal to zero yields -242-4264-a=0, or \n\t\n\t\t\n\t\t\t8\n\t\t\ta\n\t\t\n\t\t+\n\t\t64\n\t\n\t=\n\t0\n\n. Subtracting 64\n from both sides of this equation yields 8a=-64. Dividing both sides of this equation by 8\n yields a=-8. Substituting -8 for a\n in the equation 0=2x2-24x+64-a yields 0=2x2-24x+64+8, or 0=2x2-24x+72. Factoring 2\n from the right-hand side of this equation yields 0=2x2-12x+36. Dividing both sides of this equation by 2\n yields 0=x2-12x+36, which is equivalent to 0=x-6x-6, or 0=x-62. Taking the square root of both sides of this equation yields \n\t0\n\t=\n\t\n\t\tx\n\t\t-\n\t\t6\n\t\n\n. Adding 6\n to both sides of this equation yields \n\tx\n\t=\n\t6\n\n. 

\n

Choice A is incorrect. This is the value of a\n, not x\n.

\n

Choice B is incorrect and may result from conceptual or calculation errors.

\n

Choice D is incorrect and may result from conceptual or calculation errors.

"}, {"id": "635f54ee", "domain": "Advanced Math", "skill": "Nonlinear functions", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

The surface area of a cube is 6 times, open parenthesis, (a,)/(4, close parenthesis, squared), where a is a positive constant. Which of the following gives the perimeter of one face of the cube?

\n", "choices": [{"id": "A", "text": "(a,)/(4)\n"}, {"id": "B", "text": "a\n"}, {"id": "C", "text": "4 a\n"}, {"id": "D", "text": "6 a\n"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. A cube has 6 faces of equal area, so if the total surface area of a cube is 6 times, open parenthesis, a, over 4, close parenthesis, squared, then the area of one face is open parenthesis, a, over 4, close parenthesis, squared. Likewise, the area of one face of a cube is the square of one of its edges; therefore, if the area of one face is open parenthesis, a, over 4, close parenthesis, squared, then the length of one edge of the cube is a, over 4. Since the perimeter of one face of a cube is four times the length of one edge, the perimeter is 4 \u00d7 (a,)/(4 = a).
\nChoice A is incorrect because if the perimeter of one face of the cube is a, over 4, then the total surface area of the cube is 6 times, open parenthesis, (a, over 4)/(4, close parenthesis, squared = 6 times, open parenthesis, a, over 16, close parenthesis, squared), which is not 6 times, open parenthesis, a, over 4, close parenthesis, squared. Choice C is incorrect because if the perimeter of one face of the cube is 4a, then the total surface area of the cube is 6 times, open parenthesis, (4 a,)/(4, close parenthesis, squared = 6 a, squared), which is not 6 times, open parenthesis, a, over 4, close parenthesis, squared. Choice D is incorrect because if the perimeter of one face of the cube is 6a, then the total surface area of the cube is 6 times, open parenthesis, (6 a,)/(4, close parenthesis, squared = 6 times, open parenthesis, the fraction 3 a, over 2, close parenthesis, squared), which is not 6 times, open parenthesis, a, over 4, close parenthesis, squared.

\n"}, {"id": "a26c29f7", "domain": "Advanced Math", "skill": "Nonlinear functions", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

The function f\n is defined by fx=7x3. In the xy-plane, the graph of y=gx is the result of shifting the graph of y=fx down 2\n units. Which equation defines function g\n?

", "choices": [{"id": "A", "text": "

gx=72x3

"}, {"id": "B", "text": "

gx=7x32

"}, {"id": "C", "text": "

gx=7x3+2

"}, {"id": "D", "text": "

gx=7x3-2

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. If the graph of y=gx is the result of shifting the graph of y=fx down k\n units in the xy-plane, the function g\n can be defined by an equation of the form gx=fx-k. It’s given that fx=7x3 and the graph of y=gx is the result of shifting the graph of y=fx down 2\n units. Substituting 7x3 for fx and 2\n for k\n in the equation gx=fx-k yields gx=7x3-2. 

\n

Choice A is incorrect and may result from conceptual errors.

\n

Choice B is incorrect and may result from conceptual errors.

\n

Choice C is incorrect. This equation defines a function g\n for which the graph of y=gx is the result of shifting the graph of y=fx up, not down, 2\n units.

"}, {"id": "0980fcdd", "domain": "Advanced Math", "skill": "Nonlinear equations in one variable and systems of equations in two variables ", "difficulty": "M", "type": "mc", "stimulus": "
\n

\n Equation 1: x\u00b2 = 6 x + y. Equation 2: y = \u22126 x, + 36.

\n
\n", "stem": "

A solution to the given system of equations is x, y. Which of the following is a possible value of xy ?

\n", "choices": [{"id": "A", "text": "

0

\n"}, {"id": "B", "text": "

6

\n"}, {"id": "C", "text": "

12

\n"}, {"id": "D", "text": "

36

\n"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. Solutions to the given system of equations are ordered pairs x, y that satisfy both equations in the system. Adding the left-hand and right-hand sides of the equations in the system yields x\u00b2, + y = 6 x + \u22126 x, + y, + 36, or x\u00b2, + y = y + 36. Subtracting y from both sides of this equation yields x\u00b2 = 36. Taking the square root of both sides of this equation yields x = 6 and x = \u22126. Therefore, there are two solutions to this system of equations, one with an x-coordinate of 6 and the other with an x-coordinate of \u22126. Substituting 6 for x in the second equation yields y = \u22126 \u00d7 6, + 36, or y = 0; therefore, one solution is 6, 0. Similarly, substituting \u22126 for x in the second equation yields y = \u22126 \u00d7 \u22126, + 36, or y = 72; therefore, the other solution is \u22126, 72. It follows then that if x, y is a solution to the system, then possible values of x y are 6 \u00d7 0 = 0 and \u22126 \u00d7 72 = \u2212432. Only 0 is among the given choices.

Choice B is incorrect. This is the x-coordinate of one of the solutions, 6, 0. Choice C is incorrect and may result from conceptual or computational errors. Choice D is incorrect. This is the square of the x-coordinate of one of the solutions, 6, 0.

\n"}, {"id": "3c600337", "domain": "Advanced Math", "skill": "Nonlinear functions", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

The function f\n is defined by fx=2700.1x. What is the value of f0?

", "choices": [{"id": "A", "text": "

0\n

"}, {"id": "B", "text": "

1\n

"}, {"id": "C", "text": "

27\n

"}, {"id": "D", "text": "

270\n

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. The value of f0 is the value of fx when \n\tx\n\t=\n\t0\n\n. Substituting 0\n for x\n in the given function yields f0=2700.10, or f0=2701, which is equivalent to f0=270. Therefore, the value of f0 is 270\n.

\n

Choice A is incorrect. This is the value of x\n, not fx.

\n

Choice B is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect. This is the value of f1, not f0.

"}, {"id": "3ea87153", "domain": "Advanced Math", "skill": "Nonlinear functions", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

The function g\n is defined by gx=x2+9. For which value of x\n is gx=25?

", "choices": [{"id": "A", "text": "

4\n

"}, {"id": "B", "text": "

5\n

"}, {"id": "C", "text": "

9\n

"}, {"id": "D", "text": "

13\n

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. It's given that gx=x2+9. Substituting 25\n for gx in this equation yields 25=x2+9. Subtracting 9\n from both sides of this equation yields 16=x2. Taking the square root of each side of this equation yields x=\u00b14. It follows that gx=25 when the value of x\n is 4\n or -4\n. Only 4\n is listed among the choices.

\n

Choice B is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

\n

Choice D is incorrect and may result from conceptual or calculation errors.

"}, {"id": "499cb491", "domain": "Advanced Math", "skill": "Equivalent expressions", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

Which expression is equivalent to \n\t\n\t\t5\n\t\t\n\t\t\tx\n\t\t\t2\n\t\t\n\t\n\t-\n\t\n\t\t50\n\t\tx\n\t\t\n\t\t\ty\n\t\t\t2\n\t\t\n\t\n\n?

", "choices": [{"id": "A", "text": "

5xx-10y2

"}, {"id": "B", "text": "

5xx-50y2

"}, {"id": "C", "text": "

5x210xy2

"}, {"id": "D", "text": "

5x250xy2

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. Since each term of the given expression has a factor of \n\t5\n\tx\n\n, it can be rewritten as 5xx-5x10y2, or 5xx-10y2.

\n

Choice B is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

\n

Choice D is incorrect and may result from conceptual or calculation errors.

"}, {"id": "d46da42c", "domain": "Advanced Math", "skill": "Nonlinear functions", "difficulty": "E", "type": "mc", "stimulus": "
\n

\n f(x) = x\u00b2, + 4\n

\n
\n", "stem": "

The function f is defined as shown. Which of the following graphs in the xy-plane could be the graph of y = f(x) ?

\n", "choices": [{"id": "A", "text": "

\n \n \n

\n \"The

\n"}, {"id": "B", "text": "

\n \n \n

\n \"The

\n"}, {"id": "C", "text": "

\n \n \n

\n \"The

\n"}, {"id": "D", "text": "

\n \n \n

\n \"The

\n"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. For the quadratic function f(x) = x\u00b2, + 4, the vertex of the graph is the point 0, 4, and because the x\u00b2 term is positive, the vertex is the minimum of the function. Choice D is the only option that meets these conditions.

Choices A, B, and C are incorrect. The vertex of each of these graphs doesn’t correspond to the minimum of the given function.

\n"}, {"id": "4209aefe", "domain": "Advanced Math", "skill": "Nonlinear functions", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

The function f(x)=206(1.034)x models the value, in dollars, of a certain bank account by the end of each year from 1957\n through 1972\n, where x\n is the number of years after 1957\n. Which of the following is the best interpretation of “f(5) is approximately equal to 243\n” in this context?

", "choices": [{"id": "A", "text": "

The value of the bank account is estimated to be approximately 5\n dollars greater in 1962\n than in 1957\n.

"}, {"id": "B", "text": "

The value of the bank account is estimated to be approximately 243\n dollars in 1962\n.

"}, {"id": "C", "text": "

The value, in dollars, of the bank account is estimated to be approximately 5\n times greater in 1962\n than in 1957\n.

"}, {"id": "D", "text": "

The value of the bank account is estimated to increase by approximately 243\n dollars every 5\n years between 1957\n and 1972\n.

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. It’s given that the function fx=2061.034x models the value, in dollars, of a certain bank account by the end of each year from 19\n57\n through 19\n72\n, where x\n is the number of years after 19\n57\n. It follows that fx represents the estimated value, in dollars, of the bank account x\n years after 19\n57\n. Since the value of f5 is the value of fx when \n\tx\n\t=\n\t5\n\n, it follows that “f5 is approximately equal to 243\n” means that fx is approximately equal to 243\n when \n\tx\n\t=\n\t5\n\n. In the given context, this means that the value of the bank account is estimated to be approximately 243\n dollars 5\n years after 19\n57\n. Therefore, the best interpretation of the statement “f5 is approximately equal to 243\n” in this context is the value of the bank account is estimated to be approximately 243\n dollars in 19\n62\n.

\n

Choice A is incorrect and may result from conceptual errors.

\n

Choice C is incorrect and may result from conceptual errors.

\n

Choice D is incorrect and may result from conceptual errors.

"}, {"id": "5bf0f84a", "domain": "Advanced Math", "skill": "Nonlinear functions", "difficulty": "M", "type": "mc", "stimulus": "
\n

\n h(t) = \u221216 t\u00b2, + 110 t, + 72\n

\n
\n", "stem": "

The function above models the height h, in feet, of an object above ground t seconds after being launched straight up in the air. What does the number 72 represent in the function?

\n", "choices": [{"id": "A", "text": "

The initial height, in feet, of the object

\n"}, {"id": "B", "text": "

The maximum height, in feet, of the object

\n"}, {"id": "C", "text": "

The initial speed, in feet per second, of the object

\n"}, {"id": "D", "text": "

The maximum speed, in feet per second, of the object

\n"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. The variable t represents the seconds after the object is launched. Since h(0) = 72, this means that the height, in feet, at 0 seconds, or the initial height, is 72 feet.

Choices B, C, and D are incorrect and may be the result of misinterpreting the function in context.

\n"}, {"id": "c048055c", "domain": "Advanced Math", "skill": "Nonlinear functions", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

A model predicts that the population of Springfield was 15,000\n in 2005. The model also predicts that each year for the next 5\n years, the population p\n increased by 4% of the previous year's population. Which equation best represents this model, where x\n is the number of years after 2005, for x≤5?

", "choices": [{"id": "A", "text": "

p=0.9615,000x

"}, {"id": "B", "text": "

p=1.0415,000x

"}, {"id": "C", "text": "

p=15,0000.96x

"}, {"id": "D", "text": "

p=15,0001.04x

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. It's given that a model predicts the population of Springfield in 2005 was 15,000\n. The model also predicts that each year for the next 5\n years, the population increased by 4% of the previous year's population. The predicted population in one of these years can be found by multiplying the predicted population from the previous year by 1.04\n. Since the predicted population in 2005 was 15,000\n, the predicted population 1\n year later is 15,000(1.04). The predicted population 2\n years later is this value times 1.04\n, which is 15,0001.041.04, or 15,0001.042. The predicted population 3\n years later is this value times 1.04\n, or 15,0001.043. More generally, the predicted population, p\n, x\n years after 2005 is represented by the equation p=15,0001.04x. 

\n

Choice A is incorrect. Substituting 0\n for x\n in this equation indicates the predicted population in 2005 was 0.96\n rather than 15,000\n.

\n

Choice B is incorrect. Substituting 0\n for x\n in this equation indicates the predicted population in 2005 was 1.04\n rather than 15,000\n.

\n

Choice C is incorrect. This equation indicates the predicted population is decreasing, rather than increasing, by 4% each year.

"}, {"id": "70ebd3d0", "domain": "Advanced Math", "skill": "Nonlinear functions", "difficulty": "M", "type": "mc", "stimulus": "
\n\t

N(d) = 115 times, open parenthesis, 0.90, close parenthesis, raised to the d power.

\n
\n", "stem": "

The function N defined above can be used to model the number of species of brachiopods at various ocean depths d, where d is in hundreds of meters. Which of the following does the model predict?

\n", "choices": [{"id": "A", "text": "

For every increase in depth by 1 meter, the number of brachiopod species decreases by 115.

\n"}, {"id": "B", "text": "

For every increase in depth by 1 meter, the number of brachiopod species decreases by 10%.

\n"}, {"id": "C", "text": "

For every increase in depth by 100 meters, the number of brachiopod species decreases by 115.

\n"}, {"id": "D", "text": "

For every increase in depth by 100 meters, the number of brachiopod species decreases by 10%.

\n"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. The function N is exponential, so it follows that N(d) changes by a fixed percentage for each increase in d by 1. Since d is measured in hundreds of meters, it also follows that the number of brachiopod species changes by a fixed percentage for each increase in ocean depth by 100 meters. Since the base of the exponent in the model is 0.90, which is less than 1, the number of brachiopod species decreases as the ocean depth increases. Specifically, the number of brachiopod species at a depth of d + 100 meters is 90% of the number of brachiopod species at a depth of d meters. This means that for each increase in ocean depth by 100 meters, the number of brachiopod species decreases by 10%.

Choices A and C are incorrect. These describe situations where the number of brachiopod species are decreasing linearly rather than exponentially. Choice B is incorrect and results from interpreting the decrease in the number of brachiopod species as 10% for every 1-meter increase in ocean depth rather than for every 100-meter increase in ocean depth.

 

\n"}, {"id": "20291f47", "domain": "Advanced Math", "skill": "Equivalent expressions", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

Which expression is equivalent to y+12x-8+yx-8x2y-8xy?

", "choices": [{"id": "A", "text": "

\n\t\n\t\t\n\t\t\t\n\t\t\t\tx\n\t\t\t\ty\n\t\t\t\n\t\t\t+\n\t\t\ty\n\t\t\t+\n\t\t\t4\n\t\t\n\t\t\n\t\t\t\n\t\t\t\t\n\t\t\t\t\tx\n\t\t\t\t\t3\n\t\t\t\t\n\t\t\t\ty\n\t\t\t\n\t\t\t-\n\t\t\t\n\t\t\t\t16\n\t\t\t\t\n\t\t\t\t\tx\n\t\t\t\t\t2\n\t\t\t\t\n\t\t\t\ty\n\t\t\t\n\t\t\t+\n\t\t\t\n\t\t\t\t64\n\t\t\t\tx\n\t\t\t\ty\n\t\t\t\n\t\t\n\t\n\n

"}, {"id": "B", "text": "

\n\t\n\t\t\n\t\t\t\n\t\t\t\tx\n\t\t\t\ty\n\t\t\t\n\t\t\t+\n\t\t\t\n\t\t\t\t9\n\t\t\t\ty\n\t\t\t\n\t\t\t+\n\t\t\t12\n\t\t\n\t\t\n\t\t\t\n\t\t\t\t\n\t\t\t\t\tx\n\t\t\t\t\t2\n\t\t\t\t\n\t\t\t\ty\n\t\t\t\n\t\t\t-\n\t\t\t\n\t\t\t\t8\n\t\t\t\tx\n\t\t\t\ty\n\t\t\t\n\t\t\t+\n\t\t\tx\n\t\t\t-\n\t\t\t8\n\t\t\n\t\n\n

"}, {"id": "C", "text": "

\n\t\n\t\t\n\t\t\t\n\t\t\t\tx\n\t\t\t\t\n\t\t\t\t\ty\n\t\t\t\t\t2\n\t\t\t\t\n\t\t\t\n\t\t\t+\n\t\t\t\n\t\t\t\t13\n\t\t\t\tx\n\t\t\t\ty\n\t\t\t\n\t\t\t-\n\t\t\t\n\t\t\t\t8\n\t\t\t\ty\n\t\t\t\n\t\t\n\t\t\n\t\t\t\n\t\t\t\t\n\t\t\t\t\tx\n\t\t\t\t\t2\n\t\t\t\t\n\t\t\t\ty\n\t\t\t\n\t\t\t-\n\t\t\t\n\t\t\t\t8\n\t\t\t\tx\n\t\t\t\ty\n\t\t\t\n\t\t\n\t\n\n

"}, {"id": "D", "text": "

\n\t\n\t\t\n\t\t\t\n\t\t\t\tx\n\t\t\t\t\n\t\t\t\t\ty\n\t\t\t\t\t2\n\t\t\t\t\n\t\t\t\n\t\t\t+\n\t\t\t\n\t\t\t\t13\n\t\t\t\tx\n\t\t\t\ty\n\t\t\t\n\t\t\t-\n\t\t\t\n\t\t\t\t8\n\t\t\t\ty\n\t\t\t\n\t\t\n\t\t\n\t\t\t\n\t\t\t\t\n\t\t\t\t\tx\n\t\t\t\t\t3\n\t\t\t\t\n\t\t\t\ty\n\t\t\t\n\t\t\t-\n\t\t\t\n\t\t\t\t16\n\t\t\t\t\n\t\t\t\t\tx\n\t\t\t\t\t2\n\t\t\t\t\n\t\t\t\ty\n\t\t\t\n\t\t\t+\n\t\t\t\n\t\t\t\t64\n\t\t\t\tx\n\t\t\t\ty\n\t\t\t\n\t\t\n\t\n\n

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. Factoring the denominator in the second term of the given expression gives y+12x-8+yx-8xyx-8. This expression can be rewritten with common denominators by multiplying the first term by xyxy, giving xyy+12xyx-8+yx-8xyx-8. Adding these two terms yields xyy+12+yx-8xyx-8. Using the distributive property to rewrite this expression gives xy2+12xy+xy-8yx2y-8xy. Combining the like terms in the numerator of this expression gives xy2+13xy-8yx2y-8xy.

\n

Choice A is incorrect and may result from conceptual or calculation errors.

\n

Choice B is incorrect and may result from conceptual or calculation errors.

\n

Choice D is incorrect and may result from conceptual or calculation errors.

"}, {"id": "42f8e4b4", "domain": "Advanced Math", "skill": "Equivalent expressions", "difficulty": "H", "type": "spr", "stimulus": "", "stem": "

One of the factors of \n\t\n\t\t2\n\t\t\n\t\t\tx\n\t\t\t3\n\t\t\n\t\n\t+\n\t\n\t\t42\n\t\t\n\t\t\tx\n\t\t\t2\n\t\t\n\t\n\t+\n\t\n\t\t208\n\t\tx\n\t\n\n is \n\tx\n\t+\n\tb\n\n, where b\n is a positive constant. What is the smallest possible value of b\n?

", "choices": [], "answerId": "8", "acceptedAnswers": ["8"], "rationale": "

The correct answer is 8\n. Since each term of the given expression, 2x3+42x2+208x, has a factor of \n\t2\n\tx\n\n, the expression can be rewritten as 2xx2+2x21x+2x104, or 2xx2+21x+104. Since the values 8\n and 13\n have a sum of 21\n and a product of 104\n, the expression x2+21x+104 can be factored as x+8x+13. Therefore, the given expression can be factored as 2xx+8x+13. It follows that the factors of the given expression are 2\n, x\n, \n\tx\n\t+\n\t8\n\n, and \n\tx\n\t+\n\t13\n\n. Of these factors, only \n\tx\n\t+\n\t8\n\n and \n\tx\n\t+\n\t13\n\n are of the form \n\tx\n\t+\n\tb\n\n, where b\n is a positive constant. Therefore, the possible values of b\n are 8\n and 13\n. Thus, the smallest possible value of b\n is 8\n.

"}, {"id": "a67a439d", "domain": "Advanced Math", "skill": "Nonlinear equations in one variable and systems of equations in two variables ", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

\n\t\n\t\tx\n\t\t+\n\t\t7\n\t\n\t=\n\t10\n\n

\n

x+72=y

\n

Which ordered pair x,y is a solution to the given system of equations?

", "choices": [{"id": "A", "text": "

3,100

"}, {"id": "B", "text": "

3,3

"}, {"id": "C", "text": "

3,10

"}, {"id": "D", "text": "

3,70

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. The solution to a system of equations is the ordered pair x,y that satisfies all equations in the system. It's given by the first equation in the system that x+7=10. Substituting 10\n for \n\tx\n\t+\n\t7\n\n into the second equation yields 102=y, or y=100. The x-coordinate of the solution to the system of equations can be found by subtracting 7\n from both sides of the equation x+7=10, which yields x=3. Therefore, the ordered pair 3,100 is a solution to the given system of equations.

\n

Choice B is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

\n

Choice D is incorrect and may result from conceptual or calculation errors.

"}, {"id": "de39858a", "domain": "Advanced Math", "skill": "Nonlinear functions", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

The function h\n is defined by h(x)=ax+b, where a\n and b\n are positive constants. The graph of y=h(x) in the \n\tx\n\ty\n\n-plane passes through the points (0\n, 10\n) and (-2\n, \n\t325\n\t36\n\n). What is the value of \n\ta\n\tb\n\n?

", "choices": [{"id": "A", "text": "

\n\t1\n\t4\n\n

"}, {"id": "B", "text": "

\n\t1\n\t2\n\n

"}, {"id": "C", "text": "

54\n

"}, {"id": "D", "text": "

60\n

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. It’s given that the function h\n is defined by hx=ax+b and that the graph of y=h(x) in the xy-plane passes through the points 0,10 and -2, 32536. Substituting 0\n for x\n and 10\n for hx in the equation hx=ax+b yields 10=a0+b, or 10=1+b. Subtracting 1\n from both sides of this equation yields 9=b. Substituting -2 for x\n and 32536 for hx in the equation h(x)=ax+9 yields 32536=a-2+9. Subtracting 9\n from both sides of this equation yields 136=a-2, which can be rewritten as a2=36. Taking the square root of both sides of this equation yields a=6 and a=-6, but because it’s given that a\n is a positive constant, a\n must equal 6\n. Because the value of a\n is 6\n and the value of b\n is 9\n, the value of \n\ta\n\tb\n\n is (6)(9), or 54\n.

\n


Choice A is incorrect and may result from finding the value of a-2b rather than the value of ab.

\n

Choice B is incorrect and may result from conceptual or calculation errors.

\n

Choice D is incorrect and may result from correctly finding the value of a\n as 6\n, but multiplying it by the y-value in the first ordered pair rather than by the value of b\n.

"}, {"id": "2683b5db", "domain": "Advanced Math", "skill": "Nonlinear equations in one variable and systems of equations in two variables ", "difficulty": "M", "type": "mc", "stimulus": "
\n

\n T = 0 point 0 1 times, open parenthesis, P \u2212 40,000, close parenthesis\n

\n
\n", "stem": "

In a city, the property tax T, in dollars, is calculated using the formula above, where P is the value of the property, in dollars. Which of the following expresses the value of the property in terms of the property tax?

\n", "choices": [{"id": "A", "text": "

\n P = 100 T, \u2212 400

\n"}, {"id": "B", "text": "

\n P = 100 T, + 400

\n"}, {"id": "C", "text": "

\n P = 100 T, \u2212 40,000

\n"}, {"id": "D", "text": "

\n P = 100 T, + 40,000

\n"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. To express the value of the property in terms of the property tax, the given equation must be solved for P. Multiplying both sides of the equation by 100 gives 100 T = P \u2212 40,000. Adding 40,000 to both sides of the equation gives 100 T + 40,000 = P. Therefore, P = 100 T + 40,000.

Choice A is incorrect and may result from multiplying 40,000 by 0.01, then subtracting 400 from, instead of adding 400 to, the left-hand side of the equation. Choice B is incorrect and may result from multiplying 40,000 by 0.01. Choice C is incorrect and may result from subtracting instead of adding 40,000 from the left-hand side of the equation.

\n"}, {"id": "1178f2df", "domain": "Advanced Math", "skill": "Nonlinear functions", "difficulty": "H", "type": "spr", "stimulus": "", "stem": "
\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
x\ny\n
21\n-8\n
23\n8\n
25\n-8\n
\n

The table shows three values of x\n and their corresponding values of y\n, where y=fx+4 and f\n is a quadratic function. What is the y-coordinate of the y-intercept of the graph of y=fx in the xy-plane?

", "choices": [], "answerId": "-2112", "acceptedAnswers": ["-2112"], "rationale": "

The correct answer is -2,112. It's given that f\n is a quadratic function. It follows that f\n can be defined by an equation of the form fx=ax-h2+k, where a\n, h\n, and k\n are constants. It's also given that the table shows three values of x\n and their corresponding values of y\n, where y=fx+4. Substituting ax-h2+k for fx in this equation yields y=ax-h2+k+4. This equation represents a quadratic relationship between x\n and y\n, where \n\tk\n\t+\n\t4\n\n is either the maximum or the minimum value of y\n, which occurs when \n\tx\n\t=\n\th\n\n. For quadratic relationships between x\n and y\n, the maximum or minimum value of y\n occurs at the value of x\n halfway between any two values of x\n that have the same corresponding value of y\n. The table shows that x-values of 21\n and 25\n correspond to the same y-value, -8. Since 23\n is halfway between 21\n and 25\n, the maximum or minimum value of y\n occurs at an x-value of 23\n. The table shows that when \n\tx\n\t=\n\t23\n\n, \n\ty\n\t=\n\t8\n\n. It follows that \n\th\n\t=\n\t23\n\n and \n\t\n\t\tk\n\t\t+\n\t\t4\n\t\n\t=\n\t8\n\n. Subtracting 4\n from both sides of the equation \n\t\n\t\tk\n\t\t+\n\t\t4\n\t\n\t=\n\t8\n\n yields \n\tk\n\t=\n\t4\n\n. Substituting 23\n for h\n and 4\n for k\n in the equation y=ax-h2+k+4 yields y=ax-232+4+4, or y=ax-232+8. The value of a\n can be found by substituting any x-value and its corresponding y-value for x\n and y\n, respectively, in this equation. Substituting 25\n for x\n and -8 for y\n in this equation yields -8=a25-232+8, or -8=a22+8. Subtracting 8\n from both sides of this equation yields -16=a22, or -16=4a. Dividing both sides of this equation by 4\n yields -4=a. Substituting -4 for a\n, 23\n for h\n, and 4\n for k\n in the equation fx=ax-h2+k yields fx=-4x-232+4. The y-intercept of the graph of y=fx in the xy-plane is the point on the graph where \n\tx\n\t=\n\t0\n\n. Substituting 0\n for x\n in the equation fx=-4x-232+4 yields f0=-40-232+4, or f0=-4-232+4. This is equivalent to f0=-2,112, so the y-intercept of the graph of y=fx in the xy-plane is 0,-2,112. Thus, the y-coordinate of the y-intercept of the graph of y=fx in the xy-plane is -2,112.

"}, {"id": "ce940f80", "domain": "Advanced Math", "skill": "Nonlinear equations in one variable and systems of equations in two variables ", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

x225=36

\n

What is a solution to the given equation?

", "choices": [{"id": "A", "text": "

6\n

"}, {"id": "B", "text": "

30\n

"}, {"id": "C", "text": "

450\n

"}, {"id": "D", "text": "

900\n

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. Multiplying the left- and right-hand sides of the given equation by 25\n yields x2=900. Taking the square root of the left- and right-hand sides of this equation yields x=30 or x=-30. Of these two solutions, only 30\n is given as a choice.

\n

Choice A is incorrect. This is a solution to the equation x2=36.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

\n

Choice D is incorrect and may result from conceptual or calculation errors.

"}, {"id": "45df91ee", "domain": "Advanced Math", "skill": "Nonlinear functions", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

gx=11\n\t\n\t\t\n\t\t\t1\n\t\t\t12\n\t\t\n\t\n\tx\n\n

\n

If the given function g\n is graphed in the xy-plane, where y=gx, what is the y-intercept of the graph?

", "choices": [{"id": "A", "text": "

0,11

"}, {"id": "B", "text": "

0,132

"}, {"id": "C", "text": "

0,1

"}, {"id": "D", "text": "

0,12

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. The x-coordinate of any y-intercept of a graph is 0\n. Substituting 0\n for x\n in the given equation yields g0=111120. Since any nonzero number raised to the 0th power is 1\n, this gives g(0)=11\u00b71, or g(0)=11. The y-intercept of the graph is, therefore, the point 0,11.

\n

Choice B is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

\n

Choice D is incorrect and may result from conceptual or calculation errors.

"}, {"id": "67e866b5", "domain": "Advanced Math", "skill": "Equivalent expressions", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

Which expression is equivalent to 9x2+7x2+9x?

", "choices": [{"id": "A", "text": "

\n\t\n\t\t63\n\t\t\n\t\t\tx\n\t\t\t4\n\t\t\n\t\n\t+\n\t\n\t\t9\n\t\tx\n\t\n\n

"}, {"id": "B", "text": "

\n\t\n\t\t9\n\t\t\n\t\t\tx\n\t\t\t2\n\t\t\n\t\n\t+\n\t\n\t\t16\n\t\tx\n\t\n\n

"}, {"id": "C", "text": "

\n\t25\n\t\n\t\tx\n\t\t5\n\t\n\n

"}, {"id": "D", "text": "

\n\t\n\t\t16\n\t\t\n\t\t\tx\n\t\t\t2\n\t\t\n\t\n\t+\n\t\n\t\t9\n\t\tx\n\t\n\n

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. In the given expression, the first two terms, 9x2 and 7x2, are like terms. Combining these like terms yields 9x2+7x2, or 16x2. It follows that the expression 9x2+7x2+9x is equivalent to 16x2+9x.

\n

Choice A is incorrect and may result from conceptual or calculation errors.

\n

Choice B is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

"}, {"id": "fd65f47f", "domain": "Advanced Math", "skill": "Equivalent expressions", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

Which expression is equivalent to 2x2+x-9+x2+6x+1?

", "choices": [{"id": "A", "text": "

\n\t\n\t\t2\n\t\t\n\t\t\tx\n\t\t\t2\n\t\t\n\t\n\t+\n\t\n\t\t7\n\t\tx\n\t\n\t+\n\t10\n\n

"}, {"id": "B", "text": "

\n\t\n\t\t2\n\t\t\n\t\t\tx\n\t\t\t2\n\t\t\n\t\n\t+\n\t\n\t\t6\n\t\tx\n\t\n\t-\n\t8\n\n

"}, {"id": "C", "text": "

\n\t\n\t\t3\n\t\t\n\t\t\tx\n\t\t\t2\n\t\t\n\t\n\t+\n\t\n\t\t7\n\t\tx\n\t\n\t-\n\t10\n\n

"}, {"id": "D", "text": "

\n\t\n\t\t3\n\t\t\n\t\t\tx\n\t\t\t2\n\t\t\n\t\n\t+\n\t\n\t\t7\n\t\tx\n\t\n\t-\n\t8\n\n

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. The given expression is equivalent to 2x2+x+-9+x2+6x+1, which can be rewritten as 2x2+x2+x+6x+-9+1. Adding like terms in this expression yields 3x2+7x+-8, or 3x2+7x-8.

\n

Choice A is incorrect and may result from conceptual or calculation errors.

\n

Choice B is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

"}, {"id": "97158b3a", "domain": "Advanced Math", "skill": "Nonlinear functions", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

The area A, in square centimeters, of a rectangular painting can be represented by the expression ww+29, where w\n is the width, in centimeters, of the painting.  Which expression represents the length, in centimeters, of the painting?

", "choices": [{"id": "A", "text": "

w\n

"}, {"id": "B", "text": "

29\n

"}, {"id": "C", "text": "

w+29

"}, {"id": "D", "text": "

ww+29

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. It's given that the expression ww+29 represents the area, in square centimeters, of a rectangular painting, where w\n is the width, in centimeters, of the painting. The area of a rectangle can be calculated by multiplying its length by its width. It follows that the length, in centimeters, of the painting is represented by the expression w+29.

\n

Choice A is incorrect. This expression represents the width, in centimeters, of the painting, not its length, in centimeters.

\n

Choice B is incorrect. This is the difference between the length, in centimeters, and the width, in centimeters, of the painting, not its length, in centimeters.

\n

Choice D is incorrect. This expression represents the area, in square centimeters, of the painting, not its length, in centimeters.

"}, {"id": "84e8cc72", "domain": "Advanced Math", "skill": "Nonlinear functions", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

A quadratic function models the height, in feet, of an object above the ground in terms of the time, in seconds, after the object is launched off an elevated surface. The model indicates the object has an initial height of 10\n feet above the ground and reaches its maximum height of 1,034\n feet above the ground 8\n seconds after being launched. Based on the model, what is the height, in feet, of the object above the ground 10\n seconds after being launched?

", "choices": [{"id": "A", "text": "

234\n

"}, {"id": "B", "text": "

778\n

"}, {"id": "C", "text": "

970\n

"}, {"id": "D", "text": "

1,014\n

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. It's given that a quadratic function models the height, in feet, of an object above the ground in terms of the time, in seconds, after the object is launched off an elevated surface. This quadratic function can be defined by an equation of the form fx=ax-h2+k, where fx is the height of the object x\n seconds after it was launched, and a\n, h\n, and k\n are constants such that the function reaches its maximum value, k\n, when \n\tx\n\t=\n\th\n\n. Since the model indicates the object reaches its maximum height of 1,034\n feet above the ground 8\n seconds after being launched, fx reaches its maximum value, 1,034\n, when \n\tx\n\t=\n\t8\n\n. Therefore, \n\tk\n\t=\n\t1,034\n\n and \n\th\n\t=\n\t8\n\n. Substituting 8\n for h\n and 1,034\n for k\n in the function fx=ax-h2+k yields fx=ax-82+1,034. Since the model indicates the object has an initial height of 10\n feet above the ground, the value of fx is 10\n when \n\tx\n\t=\n\t0\n\n. Substituting 0\n for x\n and 10\n for fx in the equation fx=ax-82+1,034 yields 10=a0-82+1,034, or 10=64a+1,034. Subtracting 1,034\n from both sides of this equation yields 64a=-1,024. Dividing both sides of this equation by 64\n yields \n\ta\n\t=\n\t-16\n\n. Therefore, the model can be represented by the equation fx=-16x-82+1,034. Substituting 10\n for x\n in this equation yields f10=-1610-82+1,034, or f10=970. Therefore, based on the model, 10\n seconds after being launched, the height of the object above the ground is 970\n feet.

\n

Choice A is incorrect and may result from conceptual or calculation errors.

\n

Choice B is incorrect and may result from conceptual or calculation errors.

\n

Choice D is incorrect and may result from conceptual or calculation errors.

"}, {"id": "12e7faf8", "domain": "Advanced Math", "skill": "Equivalent expressions", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

The equation (x\u00b2, + 6 x, \u2212 7)/(x + 7, end fraction = a x + d) is true for all x not equal to \u22127, where a and d are integers. What is the value of a + d ?

\n", "choices": [{"id": "A", "text": "\n \u22126\n \n"}, {"id": "B", "text": "\n \u22121\n \n"}, {"id": "C", "text": "\n 0\n \n"}, {"id": "D", "text": "\n 1\n \n"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. Since the expression x\u00b2, + 6 x, \u2212 7 can be factored as open parenthesis, x + 7, close parenthesis, times, open parenthesis, x \u2212 1, close parenthesis, the given equation can be rewritten as (open parenthesis, x + 7, close parenthesis, times, open parenthesis, x \u2212 1, close parenthesis)/(x + 7, end fraction = a, x + d). Since x is not equal to \u22127, x + 7 is also not equal to 0, so both the numerator and denominator of (open parenthesis, x + 7, close parenthesis, times, open parenthesis, x \u2212 1, close parenthesis)/(x + 7, end fraction) can be divided by x + 7. This gives x \u2212 1 = a x + d. Equating the coefficient of x on each side of the equation gives a = 1. Equating the constant terms gives d = \u22121. The sum is 1 + \u22121 = 0.

Choice A is incorrect and may result from incorrectly simplifying the equation. Choices B and D are incorrect. They are the values of d and a, respectively, not a, + d.

\n"}, {"id": "89fc23af", "domain": "Advanced Math", "skill": "Equivalent expressions", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

Which of the following expressions is equivalent to (x\u00b2, \u2212 2 x, \u2212 5)/(x \u2212 3) ?

\n", "choices": [{"id": "A", "text": "

x \u2212 5, \u2212 (20)/(x \u2212 3)

\n"}, {"id": "B", "text": "

x \u2212 5, \u2212 (10)/(x \u2212 3)

\n"}, {"id": "C", "text": "

x + 1, \u2212 (8)/(x \u2212 3)

\n"}, {"id": "D", "text": "

x + 1, \u2212 (2)/(x \u2212 3)

\n"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. The numerator of the given expression can be rewritten in terms of the denominator, x \u2212 3, as follows: x\u00b2, \u2212 2 x, \u2212 5 = x\u00b2, \u2212 3 x, + x, \u2212 3, \u2212 2, which is equivalent to x times, open parenthesis, x \u2212 3, close parenthesis, plus, open parenthesis, x \u2212 3, close parenthesis, \u2212 2. So the given expression is equivalent to (x times, open parenthesis, x \u2212 3, close parenthesis, plus, open parenthesis, x \u2212 3, close parenthesis, \u2212 2)/(x \u2212 3, end fraction = the fraction with numerator x times, open parenthesis, x \u2212 3, close parenthesis, and denominator x \u2212 3, end fraction, + the fraction with numerator x \u2212 3, and denominator x \u2212 3, end fraction, \u2212 the fraction with numerator 2, and denominator x \u2212 3, end fraction). Since the given expression is defined for x is not equal to 3, the expression can be rewritten as x + 1, minus, (2)/(x \u2212 3, end fraction).

Long division can also be used as an alternate approach. Choices A, B, and C are incorrect and may result from errors made when dividing the two polynomials or making use of structure.

 

\n"}, {"id": "d8ace155", "domain": "Advanced Math", "skill": "Nonlinear functions", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

A company opens an account with an initial balance of $36,100.00\n. The account earns interest, and no additional deposits or withdrawals are made. The account balance is given by an exponential function A\n, where A(t) is the account balance, in dollars, t\n years after the account is opened. The account balance after 13\n years is $68,071.93\n. Which equation could define A\n?

", "choices": [{"id": "A", "text": "

At=36,100.00\n1.05t

"}, {"id": "B", "text": "

At=31,971.93\n1.05t

"}, {"id": "C", "text": "

At=31,971.93\n0.05t

"}, {"id": "D", "text": "

At=36,100.00\n0.05t

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. Since it's given that the account balance, At, in dollars, after t\n years can be modeled by an exponential function, it follows that function A\n can be written in the form At=Nrt, where N\n is the initial value of the function and r\n is a constant related to the growth of the function. It's given that the initial balance of the account is $36,100.00, so it follows that the initial value of the function, or N\n, must be 36,100.00. Substituting 36,100.00 for N\n in the equation At=Nrt yields At=36,100.00rt. It's given that the account balance after 13\n years, or when t=13, is $68,071.93. It follows that A13=68,071.93, or 36,100.00r13=68,071.93. Dividing each side of the equation 36,100.00r13=68,071.93 by 36,100.00 yields r13=68,071.9336,100.00. Taking the 13\nth root of both sides of this equation yields r=68,071.9336,100.0013, or r\n is approximately equal to 1.05\n. Substituting 1.05\n for r\n in the equation At=36,100.00rt yields At=36,100.001.05t, so the equation At=36,100.001.05t could define A\n. 

\n

Choice B is incorrect. Substituting 0\n for t\n in this function indicates an initial balance of $31,971.93, rather than $36,100.00.

\n

Choice C is incorrect. Substituting 0\n for t\n in this function indicates an initial balance of $31,971.93, rather than $36,100.00. Additionally, this function indicates the account balance is decreasing, rather than increasing, over time. 

\n

Choice D is incorrect. This function indicates the account balance is decreasing, rather than increasing, over time.

"}, {"id": "c3a72da5", "domain": "Advanced Math", "skill": "Equivalent expressions", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

Which of the following is equivalent to the sum of 3 x to the fourth power, + 2 x\u00b3 and 4 x to the fourth power, + 7 x\u00b3?

\n", "choices": [{"id": "A", "text": "

\n 16 x to the fourteenth power\n

\n"}, {"id": "B", "text": "

\n 7 x to the eighth power, + 9 x to the sixth power\n

\n"}, {"id": "C", "text": "

\n 12 x to the fourth power, + 14 x\u00b3\n

\n"}, {"id": "D", "text": "

\n 7 x to the fourth power, + 9 x\u00b3\n

\n"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. Adding the two expressions yields 3 x to the fourth power, + 2 x to the third power, + 4 x to the fourth power, + 7 x to the third power. Because the pair of terms 3 x to the fourth power and 4 x to the fourth power and the pair of terms 2 x to the third power and 7 x to the third power each contain the same variable raised to the same power, they are like terms and can be combined as 7 x to the fourth power and 9 x to the third power, respectively. The sum of the given expressions therefore simplifies to 7 x to the fourth power, + 9 x to the third power.

Choice A is incorrect and may result from adding the coefficients and the exponents in the given expressions. Choice B is incorrect and may result from adding the exponents as well as the coefficients of the like terms in the given expressions. Choice C is incorrect and may result from multiplying, rather than adding, the coefficients of the like terms in the given expressions.

\n"}, {"id": "dba7432e", "domain": "Advanced Math", "skill": "Nonlinear functions", "difficulty": "M", "type": "mc", "stimulus": "
\n \n \n \n \n \n \n \n \n \n \n
\n \n x\n \n \n \n f\n (x)
05
1\n \n five halves\n \n
2\n five fourths\n
3\n \n five eighths\n \n
\n", "stem": "

The table above gives the values of the function f for some values of x. Which of the following equations could define f ?

\n", "choices": [{"id": "A", "text": "

\n f(x) = 5 times, open parenthesis, 2 raised to the x + 1 power, close parenthesis\n

\n"}, {"id": "B", "text": "

\n f(x) = 5 times, open parenthesis, 2 to the x power, close parenthesis\n

\n"}, {"id": "C", "text": "

\n f(x) = 5 times, open parenthesis, 2 raised to the negative, open parenthesis, x + 1, close parenthesis, power, close parenthesis\n

\n"}, {"id": "D", "text": "

\n f(x) = 5 times, open parenthesis, 2 to the \u2212x power, close parenthesis\n

\n"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. Each choice has a function with coefficient 5 and base 2, so the exponents must be analyzed. When the input value of x increases, the output value of f(x) decreases, so the exponent must be negative. An exponent of –x yields the values in the table: first value, 5, which = 5 \u00d7 open parenthesis, 2 to the \u22120 power, close parenthesis, second value, five halves, which = 5 \u00d7 open parenthesis, 2 to the \u22121 power, close parenthesis, third value, five fourths, which = 2 to the \u22122 power, and fourth value, five eighths, which = 5 \u00d7 open parenthesis, 2 to the \u22123 power, close parenthesis.

Choices A and B are incorrect and may result from choosing equations that yield an increasing, rather than decreasing, output value of f(x) when the input value of x increases. Choice C is incorrect and may result from choosing an equation that doesn’t yield the values in the table.

\n"}, {"id": "b74f2feb", "domain": "Advanced Math", "skill": "Equivalent expressions", "difficulty": "H", "type": "spr", "stimulus": "", "stem": "

The expression 635x455·28x8 is equivalent to \n\ta\n\t\n\t\tx\n\t\tb\n\t\n\n, where a\n and b\n are positive constants and x>1. What is the value of \n\ta\n\t+\n\tb\n\n?

", "choices": [], "answerId": "361/8", "acceptedAnswers": ["361/8", "45.12", "45.13"], "rationale": "

The correct answer is 3618. The rational exponent property is ymn=ymn, where y>0, m\n and n\n are integers, and n>0. This property can be applied to rewrite the given expression 635x455·28x8 as 6355x455288x18, or 63x92x18. This expression can be rewritten by multiplying the constants, which gives 36x9x18. The multiplication exponent property is yn·ym=yn+m, where y>0. This property can be applied to rewrite the expression 36x9x18 as 36x9+18, or 36x738. Therefore, 635x455·28x8=36x738. It's given that 635x455·28x8 is equivalent to axb; therefore, a=36 and b=738. It follows that a+b=36+738. Finding a common denominator on the right-hand side of this equation gives a+b=2888+738, or a+b=3618. Note that 361/8, 45.12, and 45.13 are examples of ways to enter a correct answer.

"}, {"id": "2f958af9", "domain": "Advanced Math", "skill": "Nonlinear equations in one variable and systems of equations in two variables ", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

\n v\u00b2 = (L T)/(m)\n

The formula above expresses the square of the speed v of a wave moving along a string in terms of tension T, mass m, and length L of the string. What is T in terms of m, v, and L ?

\n", "choices": [{"id": "A", "text": "T = (m v\u00b2)/(L)\n"}, {"id": "B", "text": "T = (m)/(v\u00b2 L, end fraction)\n"}, {"id": "C", "text": "T = (m L)/(v\u00b2, end fraction)\n"}, {"id": "D", "text": "T = (L)/(m v\u00b2, end fraction)\n"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. To write the formula as T in terms of m, v, and L means to isolate T on one side of the equation. First, multiply both sides of the equation by m, which gives m v\u00b2 = (m L T)/(m), which simplifies to mv2 = LT. Next, divide both sides of the equation by L, which gives (m v\u00b2)/(L = the fraction with numerator L T, and denominator L), which simplifies to T = (m v\u00b2)/(L).

Choices B, C, and D are incorrect and may be the result of incorrectly applying operations to each side of the equation.

\n"}, {"id": "5edc8c98", "domain": "Advanced Math", "skill": "Nonlinear equations in one variable and systems of equations in two variables ", "difficulty": "H", "type": "spr", "stimulus": "", "stem": "

64x2-16a+4bx+ab=0

\n

In the given equation, a\n and b\n are positive constants. The sum of the solutions to the given equation is  k4a+b, where k\n is a constant. What is the value of k\n?

", "choices": [], "answerId": ".0625", "acceptedAnswers": [".0625", "1/16"], "rationale": "

The correct answer is \n\t1\n\t16\n\n. Let p\n and q\n represent the solutions to the given equation. Then, the given equation can be rewritten as 64x-px-q=0, or 64x2-64p+q+pq=0. Since this equation is equivalent to the given equation, it follows that -16a+4b=-64p+q. Dividing both sides of this equation by -64\n yields 16a+4b64=p+q, or 1164a+b=p+q. Therefore, the sum of the solutions to the given equation, p+q, is equal to 1164a+b. Since it's given that the sum of the solutions to the given equation is k4a+b, where k\n is a constant, it follows that \n\tk\n\t=\n\t\n\t\t1\n\t\t16\n\t\n\n. Note that 1/16, .0625, 0.062, and 0.063 are examples of ways to enter a correct answer.

\n

Alternate approach: The given equation can be rewritten as 64x2-44a+bx+ab=0, where a\n and b\n are positive constants. Dividing both sides of this equation by 4\n yields 16x2-4a+bx+ab4=0. The solutions for a quadratic equation in the form Ax2+Bx+C=0, where A\n, B\n, and C\n are constants, can be calculated using the quadratic formula, x=-B+B2-4AC2A and x=-B-B2-4AC2A. It follows that the sum of the solutions to a quadratic equation in the form \n\t\n\t\t\n\t\t\tA\n\t\t\t\n\t\t\t\tx\n\t\t\t\t2\n\t\t\t\n\t\t\n\t\t+\n\t\t\n\t\t\tB\n\t\t\tx\n\t\t\n\t\t+\n\t\tC\n\t\n\t=\n\t0\n\n is -B+B2-4AC2A+-B-B2-4AC2A, which can be rewritten as -B+-B+B2-4AC-B2-4AC2A, which is equivalent to -2B2A, or \n\t-\n\t\n\t\tB\n\t\tA\n\t\n\n. In the equation 16x2-4a+bx+ab4=0, \n\tA\n\t=\n\t16\n\n, B=-4a+b, and \n\tC\n\t=\n\t\n\t\t\n\t\t\t\n\t\t\t\ta\n\t\t\t\tb\n\t\t\t\n\t\t\t4\n\t\t\n\t\n\n. Substituting 16\n for A\n and -4a+b for B\n in \n\t-\n\t\n\t\tB\n\t\tA\n\t\n\n yields --4a+b16, which can be rewritten as 1164a+b. Thus, the sum of the solutions to the given equation is 1164a+b. Since it's given that the sum of the solutions to the given equation is k4a+b, where k\n is a constant, it follows that \n\tk\n\t=\n\t\n\t\t1\n\t\t16\n\t\n\n. 

"}, {"id": "c7789423", "domain": "Advanced Math", "skill": "Nonlinear equations in one variable and systems of equations in two variables ", "difficulty": "E", "type": "spr", "stimulus": "", "stem": "

\n\t\n\t\t\n\t\t\t\n\t\t\t\tx\n\t\t\t\t-\n\t\t\t\t2\n\t\t\t\n\t\t\n\t\n\t=\n\t9\n\n

\n

What is one possible solution to the given equation?

", "choices": [], "answerId": "11", "acceptedAnswers": ["11", "-7"], "rationale": "

The correct answer is 11\n or -7\n. By the definition of absolute value, if x-2=9, then x-2=9 or x-2=-9. Adding 2\n to both sides of the equation x-2=9 yields x=11. Adding 2\n to both sides of the equation x-2=-9 yields x=-7. Thus, the given equation, x-2=9, has two possible solutions, 11\n and -7\n. Note that 11 and -7 are examples of ways to enter a correct answer.

"}, {"id": "d9137a84", "domain": "Advanced Math", "skill": "Equivalent expressions", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

Which expression represents the product of x-6y3z5 and x4z5+y8z-7?

", "choices": [{"id": "A", "text": "

x-2z10+y11z-2

"}, {"id": "B", "text": "

x-2z10+x-6z-2

"}, {"id": "C", "text": "

x-2y3z10+y8z-7

"}, {"id": "D", "text": "

x-2y3z10+x-6y11z-2

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. The product of x-6y3z5 and x4z5+y8z-7 can be represented by the expression x-6y3z5x4z5+y8z-7. Applying the distributive property to this expression yields x-6y3z5x4z5+x-6y3z5y8z-7, or x-6x4y3z5z5+x-6y3y8z5z-7. This expression is equivalent to x-6+4y3z5+5+x-6y3+8z5-7, or x-2y3z10+x-6y11z-2.

\n

Choice A is incorrect and may result from conceptual or calculation errors.

\n

Choice B is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

"}, {"id": "876a731c", "domain": "Advanced Math", "skill": "Nonlinear equations in one variable and systems of equations in two variables ", "difficulty": "M", "type": "mc", "stimulus": "
\n\t\n\t\t\t\n\t\t\t
y = x\u00b2
2 y + 6 = 2 times, open parenthesis, x + 3, close parenthesis
\n", "stem": "

If (x, y) is a solution of the system of equations above and x > 0, what is the value of xy ?

\n", "choices": [{"id": "A", "text": "

1

\n"}, {"id": "B", "text": "

2

\n"}, {"id": "C", "text": "

3

\n"}, {"id": "D", "text": "

9

\n"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. Substituting x\u00b2 for y in the second equation gives 2 times, x\u00b2, + 6 = 2 times, open parenthesis, x + 3, close parenthesis. This equation can be solved as follows:

\n\t\n\t\t\t\t\n\t\t\t\n\t\t\t\t\n\t\t\t\n\t\t\t\t\n\t\t\t\n\t\t\t\t\n\t\t\t
2 x\u00b2, + 6 = 2 x + 6Apply the distributive property.
2 x\u00b2, + 6, \u2212 2 x, \u2212 6 = 0Subtract 2x and 6 from both sides of the equation.
2 x\u00b2, \u2212 2 x = 0Combine like terms.
2 x times, open parenthesis, x \u2212 1, close parenthesis = 0Factor both terms on the left side of the equation
\n\t\t\t\t\tby 2x.

Thus, x = 0 and x = 1 are the solutions to the system. Since x > 0, only x = 1 needs to be considered. The value of y when x = 1 is y = x\u00b2, which = 1\u00b2, which = 1. Therefore, the value of xy is 1 \u00d7 1 = 1.

Choices B, C, and D are incorrect and likely result from a computational or conceptual error when solving this system of equations.

 

\n"}, {"id": "cd358b89", "domain": "Advanced Math", "skill": "Nonlinear functions", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

Function f\n is defined by fx=x+6x+5x+1. Function g\n is defined by gx=fx-1. The graph of y=gx in the xy-plane has x-intercepts at a,0, b,0, and c,0, where a\n, b\n, and c\n are distinct constants. What is the value of \n\ta\n\t+\n\tb\n\t+\n\tc\n\n?

", "choices": [{"id": "A", "text": "

-15\n

"}, {"id": "B", "text": "

-9\n

"}, {"id": "C", "text": "

11\n

"}, {"id": "D", "text": "

15\n

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. It's given that gx=fx-1. Since fx=x+6x+5x+1, it follows that fx-1=x-1+6x-1+5x-1+1. Combining like terms yields fx-1=x+5x+4x. Therefore, gx=xx+5x+4. The x-intercepts of a graph in the xy-plane are the points where \n\ty\n\t=\n\t0\n\n. The x-coordinates of the x-intercepts of the graph of y=gx in the xy-plane can be found by solving the equation 0=xx+5x+4. Applying the zero product property to this equation yields three equations: \n\tx\n\t=\n\t0\n\n, \n\t\n\t\tx\n\t\t+\n\t\t5\n\t\n\t=\n\t0\n\n, and \n\t\n\t\tx\n\t\t+\n\t\t4\n\t\n\t=\n\t0\n\n. Solving each of these equations for x\n yields \n\tx\n\t=\n\t0\n\n, \n\tx\n\t=\n\t-5\n\n, and \n\tx\n\t=\n\t-4\n\n, respectively. Therefore, the x-intercepts of the graph of y=gx are 0,0, -5,0, and -4,0. It follows that the values of a\n, b\n, and c\n are 0\n, -5\n, and -4\n. Thus, the value of \n\ta\n\t+\n\tb\n\t+\n\tc\n\n is 0+-5+-4, which is equal to -9\n.

\n

Choice A is incorrect. This is the value of \n\ta\n\t+\n\tb\n\t+\n\tc\n\n if gx=fx+1.

\n

Choice C is incorrect. This is the value of \n\ta\n\t+\n\tb\n\t+\n\tc\n\t-\n\t1\n\n if gx=x-6x-5x-1.

\n

Choice D is incorrect. This is the value of \n\ta\n\t+\n\tb\n\t+\n\tc\n\n if fx=x-6x-5x-1.

"}, {"id": "f89e1d6f", "domain": "Advanced Math", "skill": "Equivalent expressions", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

If a = c + d, which of the following is equivalent to the expression x\u00b2, \u2212 c\u00b2, \u2212 2 c d, \u2212 d\u00b2?

\n", "choices": [{"id": "A", "text": "open parenthesis, x + a, close parenthesis, squared\n"}, {"id": "B", "text": "open parenthesis, x \u2212 a, close parenthesis, squared\n"}, {"id": "C", "text": "open parenthesis, x + a, close parenthesis, times, open parenthesis, x \u2212 a, close parenthesis\n"}, {"id": "D", "text": "x\u00b2, \u2212 a \u00d7 x, \u2212 a\u00b2\n"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. Factoring –1 from the second, third, and fourth terms gives x2 – c2 – 2cd – d2 = x2 – (c2 + 2cd + d2). The expression c2 + 2cd + d2 is the expanded form of a perfect square: c2 + 2cd + d2 = (c + d)2. Therefore, x2 – (c2 + 2cd + d2) = x2 – (c + d)2. Since a = c + d, x2 – (c + d)2 = x2 – a2. Finally, because x2 – a2 is the difference of squares, it can be expanded as x2 – a2 = (x + a)(x – a).

Choices A and B are incorrect and may be the result of making an error in factoring the difference of squares x2 – a2. Choice D is incorrect and may be the result of incorrectly combining terms.

\n"}, {"id": "ff2e5c76", "domain": "Advanced Math", "skill": "Nonlinear equations in one variable and systems of equations in two variables ", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

\n\t\n\t\t\n\t\t\tx\n\t\t\t2\n\t\t\n\t\t-\n\t\t\n\t\t\t40\n\t\t\tx\n\t\t\n\t\t-\n\t\t10\n\t\n\t=\n\t0\n\n

\n

What is the sum of the solutions to the given equation?

", "choices": [{"id": "A", "text": "

0\n

"}, {"id": "B", "text": "

5\n

"}, {"id": "C", "text": "

10\n

"}, {"id": "D", "text": "

40\n

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. Adding 10\n to each side of the given equation yields \n\t\n\t\t\n\t\t\tx\n\t\t\t2\n\t\t\n\t\t-\n\t\t\n\t\t\t40\n\t\t\tx\n\t\t\n\t\n\t=\n\t10\n\n. To complete the square, adding 4022, or 202, to each side of this equation yields x2-40x+202=10+202, or \n\t\n\t\t\n\t\t\t\n\t\t\t\tx\n\t\t\t\t-\n\t\t\t\t20\n\t\t\t\n\t\t\n\t\t2\n\t\n\t=\n\t410\n\n. Taking the square root of each side of this equation yields x-20=±410. Adding 20\n to each side of this equation yields x=20±410. Therefore, the solutions to the given equation are x=20+410 and x=20-410. The sum of these solutions is 20+410+20-410, or 40\n.

\n

Choice A is incorrect and may result from conceptual or calculation errors.

\n

Choice B is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

"}, {"id": "c8bf5313", "domain": "Advanced Math", "skill": "Nonlinear equations in one variable and systems of equations in two variables ", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

\n\tx\n\t=\n\t8\n\n

\n

\n\ty\n\t=\n\t\n\t\t\n\t\t\tx\n\t\t\t2\n\t\t\n\t\t+\n\t\t8\n\t\n\n

\n

The graphs of the equations in the given system of equations intersect at the point x,y in the xy-plane. What is the value of y\n?

", "choices": [{"id": "A", "text": "

8\n

"}, {"id": "B", "text": "

24\n

"}, {"id": "C", "text": "

64\n

"}, {"id": "D", "text": "

72\n

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. Since the graphs of the equations in the given system intersect at the point x,y, the point x,y represents a solution to the given system of equations. The first equation of the given system of equations states that \n\tx\n\t=\n\t8\n\n. Substituting 8\n for x\n in the second equation of the given system of equations yields y=82+8, or \n\ty\n\t=\n\t72\n\n. Therefore, the value of y\n is 72\n.

\n

Choice A is incorrect. This is the value of x\n, not y\n.

\n

Choice B is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

"}, {"id": "df0ef054", "domain": "Advanced Math", "skill": "Equivalent expressions", "difficulty": "E", "type": "mc", "stimulus": "
\n

\n open parenthesis, 2 x\u00b3, + 3 x, close parenthesis, times, open parenthesis, x\u00b3, \u2212 2 x, close parenthesis\n

\n
\n", "stem": "

Which of the following is equivalent to the expression above?

\n", "choices": [{"id": "A", "text": "

\n x\u00b3, + 5 x\n

\n"}, {"id": "B", "text": "

\n 3 x\u00b3, + x\n

\n"}, {"id": "C", "text": "

\n 2 x to the sixth power, \u2212 x to the fourth power, \u2212 6 x\u00b2\n

\n"}, {"id": "D", "text": "

\n 3 x to the sixth power, \u2212 x to the fourth power, \u2212 6 x\u00b2\n

\n"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. Using the distributive property to multiply the terms in the parentheses yields open parenthesis, 2 x\u00b3, \u00d7 x\u00b3, close parenthesis, plus, open parenthesis, 2 x\u00b3, \u00d7 \u22122 x, close parenthesis, plus, open parenthesis, 3 x \u00d7 x\u00b3, close parenthesis, plus, open parenthesis, 3 x \u00d7 \u22122 x, close parenthesis, which is equivalent to 2 x to the sixth power \u2212 4 x to the fourth power, + 3 x to the fourth power, \u2212 6 x\u00b2. Combining like terms results in  2 x to the sixth power \u2212 x to the fourth power, \u2212 6 x\u00b2.

Choices A and D are incorrect and may result from conceptual errors when multiplying the terms in the given expression. Choice B is incorrect and may result from adding, instead of multiplying, open parenthesis, 2 x\u00b3, + 3 x, close parenthesis and open parenthesis, x\u00b3, \u2212 2 x, close parenthesis.

\n"}, {"id": "f1c81b3b", "domain": "Advanced Math", "skill": "Nonlinear functions", "difficulty": "M", "type": "spr", "stimulus": "", "stem": "

The exponential function g\n is defined by gx=19·ax, where a\n is a positive constant. If g3=2,375\n, what is the value of g4?

", "choices": [], "answerId": "11875", "acceptedAnswers": ["11875"], "rationale": "

The correct answer is 11,875\n. It's given that the exponential function g\n is defined by gx=19\u00b7ax, where a\n is a positive constant, and g3=2,375. It follows that when \n\tx\n\t=\n\t3\n\n, gx=2,375. Substituting 3\n for x\n and 2,375\n for gx in the given equation yields 2,375=19\u00b7a3. Dividing each side of this equation by 19\n yields 125=a3. Taking the cube root of both sides of this equation gives \n\ta\n\t=\n\t5\n\n. Substituting 4\n for x\n and 5\n for a\n in the equation gx=19\u00b7ax yields g4=19\u00b754, or g4=11,875. Therefore, the value of g4 is 11,875\n. 

"}, {"id": "bef4b1c6", "domain": "Advanced Math", "skill": "Nonlinear equations in one variable and systems of equations in two variables ", "difficulty": "M", "type": "spr", "stimulus": "", "stem": "

\n\t\n\t\t\n\t\t\t55\n\t\t\t\n\t\t\t\tx\n\t\t\t\t+\n\t\t\t\t6\n\t\t\t\n\t\t\n\t\n\t=\n\tx\n\n

\n

What is the positive solution to the given equation?

", "choices": [], "answerId": "5", "acceptedAnswers": ["5"], "rationale": "

The correct answer is 5\n. Multiplying both sides of the given equation by \n\tx\n\t+\n\t6\n\n results in 55=xx+6. Applying the distributive property of multiplication to the right-hand side of this equation results in \n\t55\n\t=\n\t\n\t\t\n\t\t\tx\n\t\t\t2\n\t\t\n\t\t+\n\t\t\n\t\t\t6\n\t\t\tx\n\t\t\n\t\n\n. Subtracting 55\n from both sides of this equation results in \n\t0\n\t=\n\t\n\t\t\n\t\t\tx\n\t\t\t2\n\t\t\n\t\t+\n\t\t\n\t\t\t6\n\t\t\tx\n\t\t\n\t\t-\n\t\t55\n\t\n\n. The right-hand side of this equation can be rewritten by factoring. The two values that multiply to -55\n and add to 6\n are 11\n and -5\n. It follows that the equation \n\t0\n\t=\n\t\n\t\t\n\t\t\tx\n\t\t\t2\n\t\t\n\t\t+\n\t\t\n\t\t\t6\n\t\t\tx\n\t\t\n\t\t-\n\t\t55\n\t\n\n can be rewritten as 0=x+11x-5. Setting each factor equal to 0\n yields two equations: \n\t\n\t\tx\n\t\t+\n\t\t11\n\t\n\t=\n\t0\n\n and \n\t\n\t\tx\n\t\t-\n\t\t5\n\t\n\t=\n\t0\n\n. Subtracting 11\n from both sides of the equation \n\t\n\t\tx\n\t\t+\n\t\t11\n\t\n\t=\n\t0\n\n results in \n\tx\n\t=\n\t-11\n\n. Adding 5\n to both sides of the equation \n\t\n\t\tx\n\t\t-\n\t\t5\n\t\n\t=\n\t0\n\n results in \n\tx\n\t=\n\t5\n\n. Therefore, the positive solution to the given equation is 5\n.

"}, {"id": "3e9cc0c2", "domain": "Advanced Math", "skill": "Equivalent expressions", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

Which of the following is equivalent to \"\" ?

\n", "choices": [{"id": "A", "text": "

1 \u2212 p to the power 8

\n"}, {"id": "B", "text": "

1 \u2212 p to the power 7

\n"}, {"id": "C", "text": "

1 \u2212 p to the power 6

\n"}, {"id": "D", "text": "

1 \u2212 p to the power 5

\n"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. Multiplying (1 – p) by each term of the polynomial within the second pair of parentheses gives (1 – p)1 = 1 – p; (1 – p)p = p – p2; (1 – p)p2 = p2 – p3; (1 – p)p3 = p3 – p4; (1 – p)p4 = p4 – p5; (1 – p)p5 = p5 – p6; and (1 – p)p6 = p6 – p7. Adding these seven expressions together and combining like terms gives 1 + (p – p) + (p2 – p2) + (p3 – p3) + (p4 – p4) + (p5 – p5) + (p6 – p6) – p7, which can be simplified to 1 – p7.


\n\tChoices A, C, and D are incorrect and may result from incorrectly identifying the highest power of p in the expressions or incorrectly combining like terms.

 

\n"}, {"id": "2c5c22d0", "domain": "Advanced Math", "skill": "Nonlinear equations in one variable and systems of equations in two variables ", "difficulty": "H", "type": "mc", "stimulus": "
\n

\n y = x\u00b2, + 3 x, \u2212 7; y \u2212 5 x, + 8 = 0\n

\n
\n", "stem": "

How many solutions are there to the system of equations above?

\n", "choices": [{"id": "A", "text": "

There are exactly 4 solutions.

\n"}, {"id": "B", "text": "

There are exactly 2 solutions.

\n"}, {"id": "C", "text": "

There is exactly 1 solution.

\n"}, {"id": "D", "text": "

There are no solutions.

\n"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. The second equation of the system can be rewritten as y = 5 x \u2212 8. Substituting 5 x \u2212 8 for y in the first equation gives 5 x \u2212 8 = x\u00b2, + 3 x, \u2212 7. This equation can be solved as shown below:

\n x\u00b2, + 3 x, \u2212 7, \u2212 5 x, + 8 = 0

\n x\u00b2, \u2212 2 x, + 1 = 0

\n open parenthesis, x \u2212 1, close parenthesis, squared = 0

\n x = 1

Substituting 1 for x in the equation y = 5 x \u2212 8 gives y = \u22123. Therefore, 1, \u22123 is the only solution to the system of equations.

Choice A is incorrect. In the xy-plane, a parabola and a line can intersect at no more than two points. Since the graph of the first equation is a parabola and the graph of the second equation is a line, the system cannot have more than 2 solutions. Choice B is incorrect. There is a single ordered pair x, y that satisfies both equations of the system. Choice D is incorrect because the ordered pair 1, \u22123 satisfies both equations of the system.

\n"}, {"id": "7348f046", "domain": "Advanced Math", "skill": "Equivalent expressions", "difficulty": "M", "type": "mc", "stimulus": "
\n

\n open parenthesis, 2 x + 3, close parenthesis, minus, open parenthesis, x \u2212 7, close parenthesis

\n
\n", "stem": "

Which of the following is equivalent to the given expression?

\n", "choices": [{"id": "A", "text": "

\n x \u2212 4

\n"}, {"id": "B", "text": "

\n 3 x \u2212 4

\n"}, {"id": "C", "text": "

\n x + 10

\n"}, {"id": "D", "text": "

\n 2 x\u00b2, + 21

\n"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. Distributing the negative sign to the terms in the second parentheses yields open parenthesis, 2 x + 3, close parenthesis, \u2212 x, + 7. This expression can be rewritten as 2 x \u2212 x, + 3, + 7. Combining like terms results in x + 10.

Choice A is incorrect and may result from not distributing the negative sign to the 7. Choice B is incorrect and may result from adding x \u2212 7 to 2 x + 3 instead of subtracting x \u2212 7. Choice D is incorrect and may result from adding the product of 2 x and x to the product of 3 and 7.

\n"}, {"id": "0aaef7aa", "domain": "Advanced Math", "skill": "Nonlinear functions", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

The function p\n is defined by pn=7n3. What is the value of n\n when p(n) is equal to 56\n?

", "choices": [{"id": "A", "text": "

2\n

"}, {"id": "B", "text": "

\n\t8\n\t3\n\n

"}, {"id": "C", "text": "

7\n

"}, {"id": "D", "text": "

8\n

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. It's given that pn=7n3. Substituting 56\n for pn in this equation yields 56=7n3. Dividing each side of this equation by 7\n yields 8=n3. Taking the cube root of each side of this equation yields 2=n. Therefore, when pn is equal to 56\n, the value of n\n is 2\n.

\n

Choice B is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

\n

Choice D is incorrect and may result from conceptual or calculation errors.

"}, {"id": "928498f3", "domain": "Advanced Math", "skill": "Nonlinear equations in one variable and systems of equations in two variables ", "difficulty": "M", "type": "mc", "stimulus": "
\n

\n 6 x\u00b2, + 5 x, \u2212 7 = 0\n

\n
\n", "stem": "

What are the solutions to the given equation?

\n", "choices": [{"id": "A", "text": "

\n (\u22125, + or \u2212 the square root(2)5 + 168, end root)/(12)\n

\n"}, {"id": "B", "text": "

\n (\u22126, + or \u2212 the square root(2)5 + 168, end root)/(12)\n

\n"}, {"id": "C", "text": "

\n (\u22125, + or \u2212 the square root(3)6 \u2212 168, end root)/(12)\n

\n"}, {"id": "D", "text": "

\n (\u22126, + or \u2212 the square root(3)6 \u2212 168, end root)/(12)\n

\n"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. The quadratic formula, x = (\u2212b + or minus, the square root of, b\u00b2, \u2212 4 a, c, end root)/(2 a, end fraction), can be used to find the solutions to an equation in the form a, x\u00b2, + b x, + c = 0. In the given equation, a = 6, b = 5, and c = \u22127. Substituting these values into the quadratic formula gives (\u22125 + or minus, the square root of, 5\u00b2 \u2212 4, \u00d7 6, \u00d7 7, end root)/(2 \u00d7 6, end fraction), or (\u22125 + or minus, the square root of, 25 \u2212 168, end root)/(12, end fraction).

Choice B is incorrect and may result from using (\u2212a, + or minus, the square root of, b\u00b2, \u2212 4 a, c, end root)/(2 a, end fraction) as the quadratic formula. Choice C is incorrect and may result from using(\u2212b + or minus, the square root of, a, squared, + 4 a, c, end root)/(2 a, end fraction) as the quadratic formula. Choice D is incorrect and may result from using (\u2212a, + or minus, the square root of, a, squared, + 4 a, c, end root)/(2 a, end fraction) as the quadratic formula.

\n"}, {"id": "b7cd6ca6", "domain": "Advanced Math", "skill": "Nonlinear functions", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

The equation Et=51.8t gives the estimated number of employees at a restaurant, where t\n is the number of years since the restaurant opened. Which of the following is the best interpretation of the number 5\n in this context?

", "choices": [{"id": "A", "text": "

The estimated number of employees when the restaurant opened

"}, {"id": "B", "text": "

The increase in the estimated number of employees each year

"}, {"id": "C", "text": "

The number of years the restaurant has been open

"}, {"id": "D", "text": "

The percent increase in the estimated number of employees each year

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. For an exponential function of the form Et=abt, where a\n and b\n are constants, the initial value of the function—that is, the value of the function when \n\tt\n\t=\n\t0\n\n—is a\n and the value of the function increases by a factor of b\n each time t\n increases by 1\n. Since the function Et=51.8t gives the estimated number of employees at a restaurant and t\n is the number of years since the restaurant opened, the best interpretation of the number 5\n in this context is the estimated number of employees when \n\tt\n\t=\n\t0\n\n, or when the restaurant opened.

\n

Choice B is incorrect and may result from conceptual errors.

\n

Choice C is incorrect and may result from conceptual errors.

\n

Choice D is incorrect and may result from conceptual errors.

"}, {"id": "b47419f4", "domain": "Advanced Math", "skill": "Equivalent expressions", "difficulty": "M", "type": "mc", "stimulus": "
\n

\n open parenthesis, one-half x, + 3, close parenthesis, minus, open parenthesis, two-thirds x, \u2212 5, close parenthesis\n

\n
\n", "stem": "

Which of the following is equivalent to the expression above?

\n", "choices": [{"id": "A", "text": "\u2212one sixth x, + 8\n"}, {"id": "B", "text": "\u2212one sixth x, \u2212 2\n"}, {"id": "C", "text": "\u2212one-third x\u00b2, + one-half x, + 15\n"}, {"id": "D", "text": "\u2212one-third x\u00b2, \u2212 nine halves x, \u2212 15\n"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. By distributing the minus sign through the expression two thirds x \u2212 5, the given expression can be rewritten as open parenthesis, one half x + 3, close parenthesis, \u2212 two thirds x, + 5, which is equivalent to one half x, \u2212 two thirds x, + 3, + 5. Combining like terms gives open parenthesis, one half \u2212 two thirds, close parenthesis, \u00d7 x, plus, open parenthesis, 3 + 5, close parenthesis, or \u2212one sixth x + 8.

Choice B is incorrect and may be the result of failing to distribute the minus sign appropriately through the second term and simplifying the expression one half x, + 3, \u2212 two thirds x, \u2212 5. Choice C is incorrect and may be the result of multiplying the expressions one half x + 3 and \u2212two thirds x + 5. Choice D is incorrect and may be the result of multiplying the expressions one half x + 3 and \u2212two thirds x \u2212 5.

\n"}, {"id": "fc3dfa26", "domain": "Advanced Math", "skill": "Nonlinear equations in one variable and systems of equations in two variables ", "difficulty": "H", "type": "mc", "stimulus": "
\n

\n (4 x\u00b2)/(x\u00b2 \u2212 9, end fraction, \u2212 the fraction with numerator 2 x, and denominator x + 3, end fraction = the fraction with numerator 1, and denominator x \u2212 3, end fraction)\n

\n
\n", "stem": "

What value of x satisfies the equation above?

\n", "choices": [{"id": "A", "text": "\n \u22123\n \n"}, {"id": "B", "text": "\n \u2212one half\n \n"}, {"id": "C", "text": "\n one half\n \n"}, {"id": "D", "text": "3\n"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. Each fraction in the given equation can be expressed with the common denominator x\u00b2, \u2212 9. Multiplying (2 x)/(x + 3, end fraction) by (x \u2212 3)/(x \u2212 3, end fraction) yields (2 x\u00b2, \u2212 6)/(x\u00b2 \u2212 9, end fraction), and multiplying (1)/(x \u2212 3, end fraction) by (x + 3)/(x + 3, end fraction) yields (x + 3)/(x\u00b2 \u2212 9, end fraction). Therefore, the given equation can be written as (4 x\u00b2)/(x\u00b2 \u2212 9, minus, the fraction with numerator 2 x\u00b2, \u2212 6 x, and denominator x\u00b2 \u2212 9, end fraction = the fraction with numerator x + 3, and denominator x\u00b2 \u2212 9, end fraction). Multiplying each fraction by the denominator results in the equation 4 x\u00b2 minus, open parenthesis, 2 x\u00b2, \u2212 6 x, close parenthesis = x + 3, or 2 x\u00b2, + 6 x = x + 3. This equation can be solved by setting a quadratic expression equal to 0, then solving for x. Subtracting x + 3 from both sides of this equation yields 2 x\u00b2, + 5 x, \u2212 3 = 0. The expression 2 x\u00b2, + 5 x, \u2212 3 can be factored, resulting in the equation open parenthesis, 2 x \u2212 1, close parenthesis, times, open parenthesis, x + 3, close parenthesis = 0. By the zero product property, 2 x \u2212 1 = 0 or x + 3 = 0. To solve for x in 2 x \u2212 1 = 0, 1 can be added to both sides of the equation, resulting in 2 x = 1. Dividing both sides of this equation by 2 results in x = one half. Solving for x in x + 3 = 0 yields x = \u22123. However, this value of x would result in the second fraction of the original equation having a denominator of 0. Therefore, x = \u22123 is an extraneous solution. Thus, the only value of x that satisfies the given equation is x = one half.

Choice A is incorrect and may result from solving x + 3 = 0 but not realizing that this solution is extraneous because it would result in a denominator of 0 in the second fraction. Choice B is incorrect and may result from a sign error when solving 2 x \u2212 1 = 0 for x. Choice D is incorrect and may result from a calculation error.

\n"}, {"id": "8838a672", "domain": "Advanced Math", "skill": "Equivalent expressions", "difficulty": "M", "type": "mc", "stimulus": "
\n

\n open parenthesis, 4, x\u00b3, \u2212 5, x\u00b2, + 3, close parenthesis, minus, open parenthesis, 6, x\u00b3, + 2, x\u00b2, \u2212 x, close parenthesis\n

\n
\n", "stem": "

Which of the following expressions is equivalent to the expression above?

\n", "choices": [{"id": "A", "text": "

\n \u221210, x\u00b3, \u2212 3, x\u00b2, + x, + 3

\n"}, {"id": "B", "text": "

\n \u22122, x\u00b3, \u2212 7, x\u00b2, + x, + 3

\n"}, {"id": "C", "text": "

\n \u22122, x\u00b3, \u2212 3, x\u00b2, + x, + 3

\n"}, {"id": "D", "text": "

\n 10, x\u00b3, \u2212 7, x\u00b2, \u2212 x, + 3

\n"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. Using the distributive property, the given expression can be rewritten as 4 x\u00b3, \u2212 5 x\u00b2, + 3, \u2212 6 x\u00b3, \u2212 2 x\u00b2, + x. Combining like terms, this expression can be rewritten as open parenthesis, 4 \u2212 6, close parenthesis, \u00d7 x\u00b3, plus, open parenthesis, \u22125 \u2212 2, close parenthesis, \u00d7 x\u00b2, + x, + 3, which is equivalent to \u22122 x\u00b3, \u2212 7 x\u00b2, + x, + 3.

Choices A, C, and D are incorrect and may result from an error when applying the distributive property or an error when combining like terms.

\n"}, {"id": "eb268057", "domain": "Advanced Math", "skill": "Nonlinear equations in one variable and systems of equations in two variables ", "difficulty": "E", "type": "mc", "stimulus": "
\n

\n x\u00b2 = 64\n

\n
\n", "stem": "

Which of the following values of x satisfies the given equation?

\n", "choices": [{"id": "A", "text": "

\n \u22128

\n"}, {"id": "B", "text": "

\n 4

\n"}, {"id": "C", "text": "

\n 32

\n"}, {"id": "D", "text": "

\n 128

\n"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. Solving for x by taking the square root of both sides of the given equation yields x = 8 or x = \u22128. Of the choices given, \u22128 satisfies the given equation.

Choice B is incorrect and may result from a calculation error when solving for x. Choice C is incorrect and may result from dividing 64 by 2 instead of taking the square root. Choice D is incorrect and may result from multiplying 64 by 2 instead of taking the square root.

\n"}, {"id": "6d9e01a2", "domain": "Advanced Math", "skill": "Nonlinear functions", "difficulty": "H", "type": "spr", "stimulus": "", "stem": "

fx=\n\t\n\t\t4\n\t\t\n\t\t\tx\n\t\t\t2\n\t\t\n\t\n\t-\n\t\n\t\t50\n\t\tx\n\t\n\t+\n\t126\n\n

\n

The given equation defines the function f\n. For what value of x\n does fx reach its minimum?

", "choices": [], "answerId": "25/4", "acceptedAnswers": ["25/4", "6.25"], "rationale": "

The correct answer is \n\t25\n\t4\n\n. The given equation can be rewritten in the form fx=ax-h2+k, where a\n, h\n, and k\n are constants. When a>0, h\n is the value of x\n for which fx reaches its minimum. The given equation can be rewritten as fx=4x2-504x+126, which is equivalent to fx=4x2-504x+5082-5082+126. This equation can be rewritten as fx=4x-5082-5082+126, or fx=4x-5082-45082+126, which is equivalent to fx=4x-2542-1214. Therefore, \n\th\n\t=\n\t\n\t\t25\n\t\t4\n\t\n\n, so the value of x\n for which fx reaches its minimum is \n\t25\n\t4\n\n. Note that 25/4 and 6.25 are examples of ways to enter a correct answer.

"}, {"id": "2cf7f039", "domain": "Advanced Math", "skill": "Nonlinear functions", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

The function f\n is defined by fx=8x. For what value of x\n does fx=48?

", "choices": [{"id": "A", "text": "

6\n

"}, {"id": "B", "text": "

8\n

"}, {"id": "C", "text": "

36\n

"}, {"id": "D", "text": "

64\n

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. It's given that fx=8x. Substituting 48\n for fx in this equation yields 48=8x. Dividing both sides of this equation by 8\n yields 6=x. This can be rewritten as x=6. Squaring both sides of this equation yields x=36. Therefore, the value of x\n for which fx=48 is 36\n.

\n

Choice A is incorrect. If x=6, fx=86, not 48\n.

\n

Choice B is incorrect. If x=8, fx=88, not 48\n.

\n

Choice D is incorrect. If x=64, fx=864, which is equivalent to 64\n, not 48\n.

"}, {"id": "0b3d25c5", "domain": "Advanced Math", "skill": "Equivalent expressions", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

Which of the following is equivalent to the fourth root of, x\u00b2, + 8 x, + 16, end root, where x > 0?

\n", "choices": [{"id": "A", "text": "

\n open parenthesis, x + 4, close parenthesis, to the fourth power\n

\n"}, {"id": "B", "text": "

\n open parenthesis, x + 4, close parenthesis, squared\n

\n"}, {"id": "C", "text": "

\n open parenthesis, x + 4, close parenthesis

\n"}, {"id": "D", "text": "

\n open parenthesis, x + 4, close parenthesis, raised to the one half power\n

\n"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. The given expression can also be written as open parenthesis, x\u00b2, + 8, x, + 16, close parenthesis, raised to the one fourth power. The trinomial x\u00b2, + 8, x, + 16 can be rewritten in factored form as open parenthesis, x + 4, close parenthesis, squared. Thus, the entire expression can be rewritten as open parenthesis, open parenthesis, x + 4, close parenthesis, squared, close parenthesis, raised to the one fourth power. Simplifying the exponents yields open parenthesis, x + 4, close parenthesis, raised to the one half power.

Choices A, B, and C are incorrect and may result from errors made when simplifying the exponents in the expression open parenthesis, open parenthesis, x + 4, close parenthesis, squared, close parenthesis, raised to the one fourth power.

\n"}, {"id": "6011a3f8", "domain": "Advanced Math", "skill": "Nonlinear equations in one variable and systems of equations in two variables ", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

\n\t\n\t\t\n\t\t\t64\n\t\t\t\n\t\t\t\tx\n\t\t\t\t2\n\t\t\t\n\t\t\n\t\t+\n\t\t\n\t\t\tb\n\t\t\tx\n\t\t\n\t\t+\n\t\t25\n\t\n\t=\n\t0\n\n

\n

In the given equation, b\n is a constant. For which of the following values of b\n will the equation have more than one real solution?

", "choices": [{"id": "A", "text": "

-91\n

"}, {"id": "B", "text": "

-80\n

"}, {"id": "C", "text": "

5\n

"}, {"id": "D", "text": "

40\n

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. A quadratic equation of the form ax2+bx+c=0, where a\n, b\n, and c\n are constants, has either no real solutions, exactly one real solution, or exactly two real solutions. That is, for the given equation to have more than one real solution, it must have exactly two real solutions. When the value of the discriminant, or b2-4ac, is greater than 0, the given equation has exactly two real solutions. In the given equation, 64x2+bx+25=0, a=64 and c=25. Therefore, the given equation has exactly two real solutions when b2-46425>0, or b2-6,400>0. Adding 6,400\n to both sides of this inequality yields b2>6,400. Taking the square root of both sides of b2>6,400 yields two possible inequalities: b<-80 or b>80. Of the choices, only choice A satisfies b<-80 or b>80.

\n

Choice B is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

\n

Choice D is incorrect and may result from conceptual or calculation errors.

"}, {"id": "0e61101e", "domain": "Advanced Math", "skill": "Nonlinear functions", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

fx=9(4)x

\n

The function f\n is defined by the given equation. If g(x)=f(x+2), which of the following equations defines the function g\n?

", "choices": [{"id": "A", "text": "

gx=184x

"}, {"id": "B", "text": "

gx=1444x

"}, {"id": "C", "text": "

gx=188x

"}, {"id": "D", "text": "

gx=8116x

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. It’s given that fx=94x and gx=fx+2. Substituting x+2 for x\n in fx=94x gives fx+2=94x+2. Rewriting this equation using properties of exponents gives fx+2=94x42, which is equivalent to fx+2=94x16. Multiplying 9\n and 16\n in this equation gives fx+2=1444x. Since gx=fx+2, gx=1444x.

\n

Choice A is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

\n

Choice D is incorrect and may result from conceptual or calculation errors.

"}, {"id": "e117d3b8", "domain": "Advanced Math", "skill": "Equivalent expressions", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

If a and c are positive numbers, which of the following is equivalent to the square root of, open parenthesis, a + c, close parenthesis, cubed, end root, times, the square root(a) + c, end root?

\n", "choices": [{"id": "A", "text": "a + c\n"}, {"id": "B", "text": "a\u00b2 + c\u00b2\n"}, {"id": "C", "text": "a\u00b2 + 2 a c + c\u00b2\n"}, {"id": "D", "text": "a\u00b2 \u00d7 c\u00b2\n"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. Using the property that the square root(x), end root, \u00d7 the square root(y), end root = the square root(x) y, end root for positive numbers x and y, with x = (a + c)3 and y = a + c, it follows that the square root of, open parenthesis, a, + c, close parenthesis, cubed, end root, times, the square root(a), + c, end root = the square root of, open parenthesis a, + c, end parenthesis to the power 4, end root. By rewriting (a + c)4 as ((a + c)2)2, it is possible to simplify the square root expression as follows: the square root of, open outer parenthesis, open inner parenthesis, a, + c, close inner parenthesis, squared, close outer parenthesis, squared, end root = open parenthesis, a, + c, close parenthesis, squared, which = a, squared, + 2 a, c, + c\u00b2.

\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n Choice A is incorrect and may be the result of the square root of, open parenthesis, a, + c, close parenthesis, cubed, end root, divided by the square root of, a, + c, end root. Choice B is incorrect and may be the result of incorrectly rewriting (a + c)2 as a2 + c2. Choice D is incorrect and may be the result of incorrectly applying properties of exponents.

\n"}, {"id": "04bbce67", "domain": "Advanced Math", "skill": "Nonlinear functions", "difficulty": "H", "type": "spr", "stimulus": "", "stem": "

fx=\n\t\n\t\t\n\t\t\t\n\t\t\t\tx\n\t\t\t\t+\n\t\t\t\t7\n\t\t\t\n\t\t\n\t\t2\n\t\n\t+\n\t4\n\n

\n

The function f\n is defined by the given equation. For what value of x\n does fx reach its minimum?

", "choices": [], "answerId": "-7", "acceptedAnswers": ["-7"], "rationale": "

The correct answer is -7\n. For a quadratic function defined by an equation of the form  fx=ax-h2+k, where a\n, h\n, and k\n are constants and a>0, the function reaches its minimum when \n\tx\n\t=\n\th\n\n. In the given function, \n\ta\n\t=\n\t1\n\n, \n\th\n\t=\n\t-7\n\n, and \n\tk\n\t=\n\t4\n\n. Therefore, the value of x\n for which fx reaches its minimum is -7\n.

"}, {"id": "e8779461", "domain": "Advanced Math", "skill": "Nonlinear equations in one variable and systems of equations in two variables ", "difficulty": "M", "type": "spr", "stimulus": "", "stem": "

\n\ty\n\t=\n\t\n\t\t\n\t\t\tx\n\t\t\t2\n\t\t\n\t\t+\n\t\t\n\t\t\t14\n\t\t\tx\n\t\t\n\t\t+\n\t\t48\n\t\n\n

\n

\n\t\n\t\tx\n\t\t+\n\t\t8\n\t\n\t=\n\t11\n\n

\n

The solution to the given system of equations is x,y. What is the value of y\n?

", "choices": [], "answerId": "99", "acceptedAnswers": ["99"], "rationale": "

The correct answer is 99\n. In the given system of equations, the second equation is x+8=11. Subtracting 8\n from both sides of this equation yields x=3. In the given system of equations, the first equation is y=x2+14x+48. Substituting 3\n for x\n in this equation yields y=32+143+48, or y=99. Therefore, the solution to the given system of equations is x,y=3,99. Thus, the value of y\n is 99\n.

"}, {"id": "98f735f2", "domain": "Advanced Math", "skill": "Nonlinear equations in one variable and systems of equations in two variables ", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

The total revenue from sales of a product can be calculated using the formula T = P Q, where T is the total revenue, P is the price of the product, and Q is the quantity of the product sold. Which of the following equations gives the quantity of product sold in terms of P and T ?

\n", "choices": [{"id": "A", "text": "

\n Q = P over T\n

\n"}, {"id": "B", "text": "

\n Q = T over P\n

\n"}, {"id": "C", "text": "

\n Q = P T\n

\n"}, {"id": "D", "text": "

\n Q = T \u2212 P\n

\n"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. Solving the given equation for Q gives the quantity of the product sold in terms of P and T. Dividing both sides of the given equation by P yields T over P = Q, or Q = T over P. Therefore, Q = T over P gives the quantity of product sold in terms of P and T.

Choice A is incorrect and may result from an error when dividing both sides of the given equation by P. Choice C is incorrect and may result from multiplying, rather than dividing, both sides of the given equation by P. Choice D is incorrect and may result from subtracting P from both sides of the equation rather than dividing both sides by P.

\n"}, {"id": "79ba511a", "domain": "Advanced Math", "skill": "Nonlinear functions", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

The function f\n is defined by fx=x3+15. What is the value of f2?

", "choices": [{"id": "A", "text": "

20\n

"}, {"id": "B", "text": "

21\n

"}, {"id": "C", "text": "

23\n

"}, {"id": "D", "text": "

24\n

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. The value of f2 is the value of fx when \n\tx\n\t=\n\t2\n\n. Substituting 2\n for x\n in the given function yields f2=23+15, or f2=8+15, which is equivalent to f2=23. Therefore, the value of f2 is 23\n.

\n

Choice A is incorrect and may result from conceptual or calculation errors.

\n

Choice B is incorrect. This is the value of f2 when fx=x3+15, rather than fx=x3+15.

\n

Choice D is incorrect and may result from conceptual or calculation errors.

"}, {"id": "6f5540a5", "domain": "Advanced Math", "skill": "Nonlinear functions", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

Kao measured the temperature of a cup of hot chocolate placed in a room with a constant temperature of 70 degrees Fahrenheit (°F). The temperature of the hot chocolate was 185°F at 6:00 p.m. when it started cooling. The temperature of the hot chocolate was 156°F at 6:05 p.m. and 135°F at 6:10 p.m. The hot chocolate’s temperature continued to decrease. Of the following functions, which best models the temperature T(m), in degrees Fahrenheit, of Kao’s hot chocolate m minutes after it started cooling?

\n", "choices": [{"id": "A", "text": "

\n T(m) = 185 times, 1 point 2 5 to the m power\n

\n"}, {"id": "B", "text": "

\n T(m) = 185 times, 0 point 8 5 to the m power\n

\n"}, {"id": "C", "text": "

\n T(m) = open parenthesis, 185 \u2212 70, close parenthesis, times, 0 point 7 5 raised to the m over 5 power\n

\n"}, {"id": "D", "text": "

\n T(m) = 70 plus, 115 times, 0 point 7 5 raised to the m over 5 power\n

\n"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. The hot chocolate cools from 185°F over time, never going lower than the room temperature, 70°F. Since the base of the exponent in this function, 0.75, is less than 1, T(m) decreases as time increases. Using the function, the temperature, in °F, at 6:00 p.m. can be estimated as T(0) and is equal to 70 + 115, times, open parenthesis, 0 point 7 5, close parenthesis, raised to the power zero fifths = 185. The temperature, in °F, at 6:05 p.m. can be estimated as T(5) and is equal to 70 + 115, times, open parenthesis, 0 point 7 5, close parenthesis raised to the power five fifths, which is approximately 156°F. Finally, the temperature, in °F, at 6:10 p.m. can be estimated as T(1)0 and is equal to 70 + 115, times, open parenthesis, 0 point 7 5, close parenthesis, raised to the power ten fifths, which is approximately 135°F. Since these three given values of m and their corresponding values for T(m) can be verified using the function T(m) = 70 + 115, times, open parenthesis, 0 point 7 5, close parenthesis, raised to the power (m)/(5), this is the best function out of the given choices to model the temperature of Kao’s hot chocolate after m minutes.

Choice A is incorrect because the base of the exponent,1 point 2 5, results in the value of T(m) increasing over time rather than decreasing. Choice B is incorrect because when m is large enough, T(m) becomes less than 70. Choice C is incorrect because the maximum value of T(m) at 6:00 p.m. is 115°F, not 185°F.

\n"}, {"id": "50418728", "domain": "Advanced Math", "skill": "Nonlinear functions", "difficulty": "E", "type": "spr", "stimulus": "", "stem": "

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n

\n

The graph of the polynomial function f\n, where y=fx, is shown. The y-intercept of the graph is 0,y. What is the value of y\n?

", "choices": [], "answerId": "-3", "acceptedAnswers": ["-3"], "rationale": "

The correct answer is -3. The y-intercept of the graph of a function in the xy-plane is the point where the graph crosses the y-axis. The graph of the polynomial function shown crosses the y-axis at the point 0,-3. It's given that the y-intercept of the graph is 0,y. Thus, the value of y\n is -3.

"}, {"id": "9cb9beec", "domain": "Advanced Math", "skill": "Nonlinear equations in one variable and systems of equations in two variables ", "difficulty": "H", "type": "spr", "stimulus": "", "stem": "

\n\ty\n\t=\n\t-1.50\n\n

\n

\n\ty\n\t=\n\t\n\t\t\n\t\t\tx\n\t\t\t2\n\t\t\n\t\t+\n\t\t\n\t\t\t8\n\t\t\tx\n\t\t\n\t\t+\n\t\ta\n\t\n\n

\n

In the given system of equations, a\n is a positive constant. The system has exactly one distinct real solution. What is the value of a\n?

", "choices": [], "answerId": "14.5", "acceptedAnswers": ["14.5", "29/2"], "rationale": "

The correct answer is 292. According to the first equation in the given system, the value of y\n is -1.5\n. Substituting -1.5\n for y\n in the second equation in the given system yields -1.5=x2+8x+a. Adding 1.5\n to both sides of this equation yields 0=x2+8x+a+1.5. If the given system has exactly one distinct real solution, it follows that 0=x2+8x+a+1.5 has exactly one distinct real solution. A quadratic equation in the form 0=px2+qx+r, where p\n, q\n, and r\n are constants, has exactly one distinct real solution if and only if the discriminant, q2-4pr, is equal to 0\n. The equation 0=x2+8x+a+1.5 is in this form, where p=1, q=8, and r=a+1.5. Therefore, the discriminant of the equation 0=x2+8x+a+1.5 is 82-41a+1.5, or 58-4a. Setting the discriminant equal to 0\n to solve for a\n yields 58-4a=0. Adding \n\t4\n\ta\n\n to both sides of this equation yields 58=4a. Dividing both sides of this equation by 4\n yields 584=a, or 292=a. Therefore, if the given system of equations has exactly one distinct real solution, the value of a\n is 292. Note that 29/2 and 14.5 are examples of ways to enter a correct answer.

"}, {"id": "f5e8ccf1", "domain": "Advanced Math", "skill": "Nonlinear functions", "difficulty": "M", "type": "mc", "stimulus": "
\n

\n f(x) = open parenthesis, x + 4, close parenthesis, times, open parenthesis, x \u2212 1, close parenthesis, times, open parenthesis, 2 x \u2212 3, close parenthesis

\n
\n", "stem": "

The function f is defined above. Which of the following is NOT an x-intercept of the graph of the function in the xy-plane?

\n", "choices": [{"id": "A", "text": "the point \u22124, 0\n"}, {"id": "B", "text": "the point \u2212two thirds, 0\n"}, {"id": "C", "text": "the point 1, 0\n"}, {"id": "D", "text": "the point three halves, 0\n"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. The graph of the function f in the xy-plane has x-intercepts at the points x, y, where y = f(x), which = 0. Substituting 0 for f(x) in the given equation yields 0 = open parenthesis, x + 4, close parenthesis, times, open parenthesis, x \u2212 1, close parenthesis, times, open parenthesis, 2 x \u2212 3, close parenthesis. By the zero product property, if 0 = open parenthesis, x + 4, close parenthesis, times, open parenthesis, x \u2212 1, close parenthesis, times, open parenthesis, 2 x \u2212 3, close parenthesis, then x + 4 = 0, x \u2212 1 = 0, or 2 x \u2212 3 = 0. Solving each of these linear equations for x, it follows that x = \u22124, x = 1, and x = three halves, respectively. This means that the graph of the function f in the xy-plane has three x-intercepts: the point \u22124, 0, the point 1, 0, and the point three halves, 0. Therefore, the point \u2212two thirds, 0 isn’t an x-intercept of the graph of the function f.
\nAlternate approach: Substitution may be used. Since by definition an x-intercept of any graph is a point in the form k, 0 where k is a constant, and since all points in the options are in this form, it need only be checked whether the points in the options lie on the graph of the function f. Substituting \u2212two thirds for x and 0 for f(x) in the given equation yields 0 = open parenthesis, \u2212two thirds + 4, close parenthesis, times, open parenthesis, \u2212two thirds \u2212 1, close parenthesis, times, open parenthesis, 2 \u00d7 \u2212two thirds, \u2212 3, close parenthesis, or 0 = (650)/(27). Therefore, the point \u2212two thirds, 0 doesn’t lie on the graph of the function f and can’t be an x-intercept of the graph.

Choices A, C, and D are incorrect because each of these points is an x-intercept of the graph of the function f in the xy-plane. By definition, an x-intercept is a point on the graph of the form k, 0, where k is a constant. Substituting \u22124 for x and 0 for f(x) in the given equation yields 0 = open parenthesis, \u22124 + 4, close parenthesis, times, open parenthesis, \u22124 \u2212 1, close parenthesis, times, open parenthesis, 2 \u00d7 \u22124, \u2212 3, close parenthesis, or 0 = 0. Since this is a true statement, the point \u22124, 0 lies on the graph of the function f and is an x-intercept of the graph. Performing similar substitution using the points 1, 0 and three halves, 0 also yields the true statement 0 = 0, illustrating that these points also lie on the graph of the function f and are x-intercepts of the graph.

\n"}, {"id": "127b2759", "domain": "Advanced Math", "skill": "Equivalent expressions", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

Which expression is equivalent to 8+d2+3?

", "choices": [{"id": "A", "text": "

\n\t\n\t\td\n\t\t2\n\t\n\t+\n\t24\n\n

"}, {"id": "B", "text": "

\n\t\n\t\td\n\t\t2\n\t\n\t+\n\t11\n\n

"}, {"id": "C", "text": "

\n\t\n\t\td\n\t\t2\n\t\n\t+\n\t5\n\n

"}, {"id": "D", "text": "

\n\t\n\t\td\n\t\t2\n\t\n\t-\n\t11\n\n

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. The given expression can be rewritten as d2+8+3. Adding 8\n and 3\n in this expression yields \n\t\n\t\td\n\t\t2\n\t\n\t+\n\t11\n\n.

\n

Choice A is incorrect. This expression is equivalent to d2+83.

\n

Choice C is incorrect. This expression is equivalent to 8+d2-3.

\n

Choice D is incorrect. This expression is equivalent to -8+d2-3.

"}, {"id": "fb96a5b3", "domain": "Advanced Math", "skill": "Equivalent expressions", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

Which of the following expressions is equivalent to 2 times, open parenthesis, a, b \u2212 3, close parenthesis, + 2 ?

\n", "choices": [{"id": "A", "text": "

\n 2 a, b, \u2212 1\n

\n"}, {"id": "B", "text": "

\n 2 a, b, \u2212 4\n

\n"}, {"id": "C", "text": "

\n 2 a, b, \u2212 5\n

\n"}, {"id": "D", "text": "

\n 2 a, b, \u2212 8\n

\n"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. Applying the distributive property to the given expression yields 2 \u00d7 a, b, plus, 2 \u00d7 \u22123, + 2, or 2 a, b \u2212 6, + 2. Adding the like terms \u22126 and 2 results in the expression 2 a, b \u2212 4.

Choice A is incorrect and may result from multiplying a, b by 2 without multiplying \u22123 by 2 when applying the distributive property. Choices C and D are incorrect and may result from computational or conceptual errors.

\n"}, {"id": "1fe10d97", "domain": "Advanced Math", "skill": "Nonlinear functions", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

pt=90,0001.06t

\n

The given function p\n models the population of Lowell t\n years after a census. Which of the following functions best models the population of Lowell m\n months after the census?

", "choices": [{"id": "A", "text": "

rm=90,000121.06m

"}, {"id": "B", "text": "

rm=90,0001.0612m

"}, {"id": "C", "text": "

rm=90,0001.0612m12

"}, {"id": "D", "text": "

rm=90,0001.06m12

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. It’s given that the function p\n models the population of Lowell t\n years after a census. Since there are 12\n months in a year, m\n months after the census is equivalent to m12 years after the census. Substituting m12 for t\n in the equation pt=90,0001.06t yields pm12=90,0001.06m12. Therefore, the function r\n that best models the population of Lowell m\n months after the census is rm=90,0001.06m12.

\n

Choice A is incorrect and may result from conceptual or calculation errors.

\n

Choice B is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

"}, {"id": "b73ee6cf", "domain": "Advanced Math", "skill": "Nonlinear functions", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

The population of a town is currently 50,000, and the population is estimated to increase each year by 3% from the previous year. Which of the following equations can be used to estimate the number of years, t, it will take for the population of the town to reach 60,000 ?

\n", "choices": [{"id": "A", "text": "

\n 50,000 = 60,000 times, open parenthesis, 0 point 0 3, close parenthesis, to the power t\n

\n"}, {"id": "B", "text": "

\n 50,000 = 60,000 times, open parenthesis, 3, close parenthesis, to the power t\n

\n"}, {"id": "C", "text": "

\n 60,000 = 50,000 times, open parenthesis, 0 point 0 3, close parenthesis, to the power t\n

\n"}, {"id": "D", "text": "

\n 60,000 = 50,000 times, open parenthesis, 1 point 0 3, close parenthesis, to the power t\n

\n"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. Stating that the population will increase each year by 3% from the previous year is equivalent to saying that the population each year will be 103% of the population the year before. Since the initial population is 50,000, the population after t years is given by 50,000(1.03)t. It follows that the equation 60,000 = 50,000(1.03)t can be used to estimate the number of years it will take for the population to reach 60,000.

Choice A is incorrect. This equation models how long it will take the population to decrease from 60,000 to 50,000, which is impossible given the growth factor. Choice B is incorrect and may result from misinterpreting a 3% growth as growth by a factor of 3. Additionally, this equation attempts to model how long it will take the population to decrease from 60,000 to 50,000. Choice C is incorrect and may result from misunderstanding how to model percent growth by multiplying the initial amount by a factor greater than 1.

\n"}, {"id": "08d03fe4", "domain": "Advanced Math", "skill": "Nonlinear functions", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

For the exponential function f\n, the value of f1 is k\n, where k\n is a constant. Which of the following equivalent forms of the function f\n shows the value of k\n as the coefficient or the base?

", "choices": [{"id": "A", "text": "

fx=502x+1

"}, {"id": "B", "text": "

fx=802x

"}, {"id": "C", "text": "

fx=1282x-1

"}, {"id": "D", "text": "

fx=2052x-2

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. For the form of the function in choice C, fx=1281.6x-1, the value of f1 can be found as 1281.61-1, which is equivalent to 1281.60, or 128\n. Therefore, \n\tk\n\t=\n\t128\n\n, which is shown in fx=1281.6x-1 as the coefficient.

\n

Choice A is incorrect and may result from conceptual or calculation errors.

\n

Choice B is incorrect and may result from conceptual or calculation errors.

\n

Choice D is incorrect and may result from conceptual or calculation errors.

"}, {"id": "3918e8bc", "domain": "Advanced Math", "skill": "Nonlinear functions", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

An object is kicked from a platform. The equation h=-4.9t2+7t+9 represents this situation, where h\n is the height of the object above the ground, in meters, t\n seconds after it is kicked. Which number represents the height, in meters, from which the object was kicked?

", "choices": [{"id": "A", "text": "

0\n

"}, {"id": "B", "text": "

4.9\n

"}, {"id": "C", "text": "

7\n

"}, {"id": "D", "text": "

9\n

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. It’s given that the equation \n\th\n\t=\n\t\n\t\t\n\t\t\t-\n\t\t\t4.9\n\t\t\t\n\t\t\t\tt\n\t\t\t\t2\n\t\t\t\n\t\t\n\t\t+\n\t\t\n\t\t\t7\n\t\t\tt\n\t\t\n\t\t+\n\t\t9\n\t\n\n represents this situation, where h\n is the height, in meters, of the object t\n seconds after it is kicked. It follows that the height, in meters, from which the object was kicked is the value of h\n when \n\tt\n\t=\n\t0\n\n. Substituting 0\n for t\n in the equation \n\th\n\t=\n\t\n\t\t\n\t\t\t-\n\t\t\t4.9\n\t\t\t\n\t\t\t\tt\n\t\t\t\t2\n\t\t\t\n\t\t\n\t\t+\n\t\t\n\t\t\t7\n\t\t\tt\n\t\t\n\t\t+\n\t\t9\n\t\n\n yields h=-4.902+70+9, or \n\th\n\t=\n\t9\n\n. Therefore, the object was kicked from a height of 9\n meters.

\n

Choice A is incorrect and may result from conceptual or calculation errors.

\n

Choice B is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

"}, {"id": "1dd13816", "domain": "Advanced Math", "skill": "Equivalent expressions", "difficulty": "M", "type": "spr", "stimulus": "", "stem": "

(5x3-3)-(-4x3+8)

\n

The given expression is equivalent to \n\t\n\t\tb\n\t\t\n\t\t\tx\n\t\t\t3\n\t\t\n\t\n\t-\n\t11\n\n, where b\n is a constant. What is the value of b\n?

", "choices": [], "answerId": "9", "acceptedAnswers": ["9"], "rationale": "

The correct answer is 9\n. The given expression can be rewritten as 5x3-3+-1-4x3+8. By applying the distributive property, this expression can be rewritten as 5x3-3+4x3+-8, which is equivalent to 5x3+4x3+-3+-8. Adding like terms in this expression yields 9x3-11. Since it's given that 5x3-3--4x3+8 is equivalent to bx3-11, it follows that 9x3-11 is equivalent to bx3-11. Therefore, the coefficients of x3 in these two expressions must be equivalent, and the value of b\n must be 9\n.

"}, {"id": "e597050f", "domain": "Advanced Math", "skill": "Equivalent expressions", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

Which expression is equivalent to 9x+6x+2y+3y?

", "choices": [{"id": "A", "text": "

3\n\n\tx\n\t+\n\t\n\t\t5\n\t\ty\n\t\n\n

"}, {"id": "B", "text": "

6\n\n\tx\n\t+\n\t\n\t\t8\n\t\ty\n\t\n\n

"}, {"id": "C", "text": "

12\n\n\tx\n\t+\n\t\n\t\t8\n\t\ty\n\t\n\n

"}, {"id": "D", "text": "

15\n\n\tx\n\t+\n\t\n\t\t5\n\t\ty\n\t\n\n

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. Combining like terms in the given expression yields 9x+6x+2y+3y, or 15x+5y.

\n

Choice A is incorrect and may result from conceptual or calculation errors.

\n

Choice B is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

"}, {"id": "7eed640d", "domain": "Advanced Math", "skill": "Nonlinear functions", "difficulty": "H", "type": "mc", "stimulus": "
\n

\n h(x) = \u221216 x\u00b2, + 100 x, + 10\n

\n
\n", "stem": "

The quadratic function above models the height above the ground h, in feet, of a projectile x seconds after it had been launched vertically. If y = h(x) is graphed in the xy-plane, which of the following represents the real-life meaning of the positive x-intercept of the graph?

\n", "choices": [{"id": "A", "text": "

The initial height of the projectile

\n"}, {"id": "B", "text": "

The maximum height of the projectile

\n"}, {"id": "C", "text": "

The time at which the projectile reaches its maximum height

\n"}, {"id": "D", "text": "

The time at which the projectile hits the ground

\n"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. The positive x-intercept of the graph of y = h(x) is a point x, y for which y = 0. Since y = h(x) models the height above the ground, in feet, of the projectile, a y-value of 0 must correspond to the height of the projectile when it is 0 feet above ground or, in other words, when the projectile is on the ground. Since x represents the time since the projectile was launched, it follows that the positive x-intercept, the point x, 0, represents the time at which the projectile hits the ground.

Choice A is incorrect and may result from misidentifying the y-intercept as a positive x-intercept. Choice B is incorrect and may result from misidentifying the y-value of the vertex of the graph of the function as an x-intercept. Choice C is incorrect and may result from misidentifying the x-value of the vertex of the graph of the function as an x-intercept.

\n"}, {"id": "2d2ab76b", "domain": "Advanced Math", "skill": "Nonlinear equations in one variable and systems of equations in two variables ", "difficulty": "M", "type": "mc", "stimulus": "
\n

\n y = x\u00b2, \u2212 1 and y = 3\n

\n
\n", "stem": "

When the equations above are graphed in the xy-plane, what are the coordinates (x, y) of the points of intersection of the two graphs?

\n", "choices": [{"id": "A", "text": "\n 2, 3

and \u22122, 3\n

\n"}, {"id": "B", "text": "\n 2, 4

and \u22122, 4\n

\n"}, {"id": "C", "text": "\n 3, 8

and \u22123, 8\n

\n"}, {"id": "D", "text": "\n the square root(2), 3

and the \u2212square root(2), 3\n

\n"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. The two equations form a system of equations, and the solutions to the system correspond to the points of intersection of the graphs. The solutions to the system can be found by substitution. Since the second equation gives y = 3, substituting 3 for y in the first equation gives 3 = x2 – 1. Adding 1 to both sides of the equation gives 4 = x2. Solving by taking the square root of both sides of the equation gives x = ±2. Since y = 3 for all values of x for the second equation, the solutions are (2, 3) and (–2, 3). Therefore, the points of intersection of the two graphs are (2, 3) and (–2, 3).

Choices B, C, and D are incorrect and may be the result of calculation errors.

\n"}, {"id": "de362c2f", "domain": "Advanced Math", "skill": "Nonlinear functions", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

The function f\n is defined by fx=5x2. What is the value of f8?

", "choices": [{"id": "A", "text": "

40\n

"}, {"id": "B", "text": "

50\n

"}, {"id": "C", "text": "

80\n

"}, {"id": "D", "text": "

320\n

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. It's given that the function f\n is defined by fx=5x2. Substituting 8\n for x\n in fx=5x2 yields f8=582, which is equivalent to f8=564, or f8=320. Therefore, the value of f8 is 320\n.

\n

Choice A is incorrect. This is the value of f8 if fx=5x.

\n

Choice B is incorrect. This is the value of f8 if fx=5x+2.

\n

Choice C is incorrect. This is the value of f8 if fx=5x2.

"}, {"id": "da602115", "domain": "Advanced Math", "skill": "Nonlinear equations in one variable and systems of equations in two variables ", "difficulty": "M", "type": "spr", "stimulus": "", "stem": "

If 4x-4=112, what is the positive value of \n\tx\n\t-\n\t1\n\n?

", "choices": [], "answerId": "28", "acceptedAnswers": ["28"], "rationale": "

The correct answer is 28\n. The given absolute value equation can be rewritten as two linear equations: \n\t\n\t\t\n\t\t\t4\n\t\t\tx\n\t\t\n\t\t-\n\t\t4\n\t\n\t=\n\t112\n\n and -4x-4=112, or \n\t\n\t\t\n\t\t\t4\n\t\t\tx\n\t\t\n\t\t-\n\t\t4\n\t\n\t=\n\t-112\n\n. Adding 4\n to both sides of the equation \n\t\n\t\t\n\t\t\t4\n\t\t\tx\n\t\t\n\t\t-\n\t\t4\n\t\n\t=\n\t112\n\n results in \n\t\n\t\t4\n\t\tx\n\t\n\t=\n\t116\n\n. Dividing both sides of this equation by 4\n results in \n\tx\n\t=\n\t29\n\n. Adding 4\n to both sides of the equation \n\t\n\t\t\n\t\t\t4\n\t\t\tx\n\t\t\n\t\t-\n\t\t4\n\t\n\t=\n\t-112\n\n results in \n\t\n\t\t4\n\t\tx\n\t\n\t=\n\t-108\n\n. Dividing both sides of this equation by 4\n results in \n\tx\n\t=\n\t-27\n\n. Therefore, the two values of \n\tx\n\t-\n\t1\n\n are 29-1, or 28\n, and -27-1, or -28\n. Thus, the positive value of \n\tx\n\t-\n\t1\n\n is 28\n.

\n

Alternate approach: The given equation can be rewritten as 4x-1=112, which is equivalent to 4x-1=112. Dividing both sides of this equation by 4\n yields x-1=28. This equation can be rewritten as two linear equations: \n\t\n\t\tx\n\t\t-\n\t\t1\n\t\n\t=\n\t28\n\n and -x-1=28, or \n\t\n\t\tx\n\t\t-\n\t\t1\n\t\n\t=\n\t-28\n\n. Therefore, the positive value of \n\tx\n\t-\n\t1\n\n is 28\n.

"}, {"id": "1e8d7183", "domain": "Advanced Math", "skill": "Equivalent expressions", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

Which expression is equivalent to \n\t\n\t\t256\n\t\t\n\t\t\tw\n\t\t\t2\n\t\t\n\t\n\t-\n\t676\n\n?

", "choices": [{"id": "A", "text": "

(16w-26)(16w-26)

"}, {"id": "B", "text": "

\n\t\n\t\t\n\t\t\t\n\t\t\t\t8\n\t\t\t\tw\n\t\t\t\n\t\t\t-\n\t\t\t13\n\t\t\n\t\n\t\n\t\t\n\t\t\t\n\t\t\t\t8\n\t\t\t\tw\n\t\t\t\n\t\t\t+\n\t\t\t13\n\t\t\n\t\n\n

"}, {"id": "C", "text": "

(8w-13)(8w-13)

"}, {"id": "D", "text": "

\n\t\n\t\t\n\t\t\t\n\t\t\t\t16\n\t\t\t\tw\n\t\t\t\n\t\t\t-\n\t\t\t26\n\t\t\n\t\n\t\n\t\t\n\t\t\t\n\t\t\t\t16\n\t\t\t\tw\n\t\t\t\n\t\t\t+\n\t\t\t26\n\t\t\n\t\n\n

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. The given expression follows the difference of two squares pattern, x2-y2, which factors as x-yx+y. Therefore, the expression 256w2-676 can be written as 16w2-262, or 16w16w-2626, which factors as 16w-2616w+26.

\n

Choice A is incorrect. This expression is equivalent to 256w2-832w+676.

\n

Choice B is incorrect. This expression is equivalent to 64w2-169.

\n

Choice C is incorrect. This expression is equivalent to 64w2-208w+169.

"}, {"id": "044c1cb7", "domain": "Advanced Math", "skill": "Nonlinear functions", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

hx=x2-3

\n

Which table gives three values of x\n and their corresponding values of hx for the given function h\n?

", "choices": [{"id": "A", "text": "
\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
x\n1\n2\n3\n
hx4\n5\n6\n
"}, {"id": "B", "text": "
\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
x\n1\n2\n3\n
hx-2\n1\n6\n
"}, {"id": "C", "text": "
\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
x\n1\n2\n3\n
hx-1\n1\n3\n
"}, {"id": "D", "text": "
\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
x\n1\n2\n3\n
hx-2\n1\n3\n
"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. It′s given that hx=x2-3. Each table gives 1\n, 2\n, and 3\n as the three given values of x\n. Substituting 1\n for x\n in the equation hx=x2-3 yields h1=12-3, or h1=-2. Substituting 2\n for x\n in the equation hx=x2-3 yields h2=22-3, or h2=1. Finally, substituting 3\n for x\n in the equation hx=x2-3 yields h3=32-3, or h3=6. Therefore, hx is -2 when x\n is 1\n, hx is 1\n when x\n is 2\n, and hx is 6\n when x\n is 3\n. Choice B is a table with these values of x\n and their corresponding values of hx.

\n

Choice A is incorrect. This is a table of values for the function hx=x+3, not hx=x2-3.

\n

Choice C is incorrect. This is a table of values for the function hx=2x-3, not hx=x2-3.

\n

Choice D is incorrect and may result from conceptual or calculation errors.

"}, {"id": "7e5a3640", "domain": "Advanced Math", "skill": "Nonlinear functions", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

Bacteria are growing in a liquid growth medium. There were 300,000\n cells per milliliter during an initial observation. The number of cells per milliliter doubles every 3\n hours. How many cells per milliliter will there be 15\n hours after the initial observation?

", "choices": [{"id": "A", "text": "

1,500,000\n

"}, {"id": "B", "text": "

2,400,000\n

"}, {"id": "C", "text": "

4,500,000\n

"}, {"id": "D", "text": "

9,600,000\n

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. Let y\n represent the number of cells per milliliter x\n hours after the initial observation. Since the number of cells per milliliter doubles every 3\n hours, the relationship between x\n and y\n can be represented by an exponential equation of the form y=abxk, where a\n is the number of cells per milliliter during the initial observation and the number of cells per milliliter increases by a factor of b\n every k\n hours. It’s given that there were 300,000\n cells per milliliter during the initial observation. Therefore, \n\ta\n\t=\n\t300,000\n\n. It’s also given that the number of cells per milliliter doubles, or increases by a factor of 2\n, every 3\n hours. Therefore, \n\tb\n\t=\n\t2\n\n and \n\tk\n\t=\n\t3\n\n. Substituting 300,000\n for a\n, 2\n for b\n, and 3\n for k\n in the equation y=abxk yields y=300,0002x3. The number of cells per milliliter there will be 15\n hours after the initial observation is the value of y\n in this equation when \n\tx\n\t=\n\t15\n\n. Substituting 15\n for x\n in the equation y=300,0002x3 yields y=300,0002153, or y=300,00025. This is equivalent to y=300,00032, or \n\ty\n\t=\n\t9,600,000\n\n. Therefore, 15\n hours after the initial observation, there will be 9,600,000\n cells per milliliter.

\n

Choice A is incorrect and may result from conceptual or calculation errors.

\n

Choice B is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

"}, {"id": "0354c7de", "domain": "Advanced Math", "skill": "Equivalent expressions", "difficulty": "E", "type": "mc", "stimulus": "
\n

\n 5 x + 15\n

\n
\n", "stem": "

Which of the following is equivalent to the given expression?

\n", "choices": [{"id": "A", "text": "

\n 5 times, open parenthesis, x + 3, close parenthesis

\n"}, {"id": "B", "text": "

\n 5 times, open parenthesis, x + 10, close parenthesis

\n"}, {"id": "C", "text": "

\n 5 times, open parenthesis, x + 15, close parenthesis

\n"}, {"id": "D", "text": "

\n 5 times, open parenthesis, x + 20, close parenthesis

\n"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. Since 5 is a factor of both terms, 5 x and 15, the given expression can be factored and rewritten as 5 times, open parenthesis, x + 3, close parenthesis.

Choice B is incorrect and may result from subtracting 5 from the constant when factoring 5 from the given expression. Choice C is incorrect and may result from factoring 5 from only the first term, not both terms, of the given expression. Choice D is incorrect and may result from adding 5 to the constant when factoring 5 from the given expression.

\n"}, {"id": "4d037075", "domain": "Advanced Math", "skill": "Nonlinear functions", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n\n

\n

The rational function f\n is defined by an equation in the form fx=ax+b, where a\n and b\n are constants. The partial graph of y=fx is shown. If  gx=fx+4, which equation could define function g\n?

", "choices": [{"id": "A", "text": "

gx=6x

"}, {"id": "B", "text": "

gx=6x+4

"}, {"id": "C", "text": "

gx=6x+8

"}, {"id": "D", "text": "

gx=6(x+4)x+4

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. It's given that fx=ax+b and that the graph shown is a partial graph of y=fx. Substituting y\n for fx in the equation fx=ax+b yields \n\ty\n\t=\n\t\n\t\t\ta\n\t\t\t\n\t\t\t\tx\n\t\t\t\t+\n\t\t\t\tb\n\t\t\t\n\t\t\n\n. The graph passes through the point -7,-2. Substituting -7\n for x\n and -2\n for y\n in the equation \n\ty\n\t=\n\t\n\t\t\ta\n\t\t\t\n\t\t\t\tx\n\t\t\t\t+\n\t\t\t\tb\n\t\t\t\n\t\t\n\n yields -2=a-7+b. Multiplying each side of this equation by -7+b yields -2-7+b=a, or 14-2b=a. The graph also passes through the point -5,-6. Substituting -5\n for x\n and -6\n for y\n in the equation \n\ty\n\t=\n\t\n\t\t\ta\n\t\t\t\n\t\t\t\tx\n\t\t\t\t+\n\t\t\t\tb\n\t\t\t\n\t\t\n\n yields -6=a-5+b. Multiplying each side of this equation by -5+b yields -6-5+b=a, or 30-6b=a. Substituting 14-2b for a\n in this equation yields 30-6b=14-2b. Adding \n\t6\n\tb\n\n to each side of this equation yields 30=14+4b. Subtracting 14\n from each side of this equation yields \n\t16\n\t=\n\t\n\t\t4\n\t\tb\n\t\n\n. Dividing each side of this equation by 4\n yields \n\t4\n\t=\n\tb\n\n. Substituting 4\n for b\n in the equation 14-2b=a yields 14-24=a, or \n\t6\n\t=\n\ta\n\n. Substituting 6\n for a\n and 4\n for b\n in the equation fx=ax+b yields fx=6x+4. It's given that gx=fx+4. Substituting \n\tx\n\t+\n\t4\n\n for x\n in the equation fx=6x+4 yields fx+4=6x+4+4, which is equivalent to fx+4=6x+8. It follows that gx=6x+8.

\n

Choice A is incorrect. This could define function g\n if gx=fx-4.

\n

Choice B is incorrect. This could define function g\n if gx=fx.

\n

Choice D is incorrect. This could define function g\n if gx=fx\u00b7x+4.

"}, {"id": "4d7064a6", "domain": "Advanced Math", "skill": "Nonlinear functions", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

fx=\n\t\n\t\t\n\t\t\tx\n\t\t\t-\n\t\t\t10\n\t\t\n\t\n\t\n\t\t\n\t\t\tx\n\t\t\t+\n\t\t\t13\n\t\t\n\t\n\n

\n

The function f\n is defined by the given equation. For what value of x\n does fx reach its minimum?

", "choices": [{"id": "A", "text": "

-130\n

"}, {"id": "B", "text": "

-13\n

"}, {"id": "C", "text": "

\n\t-\n\t\n\t\t23\n\t\t2\n\t\n\n

"}, {"id": "D", "text": "

\n\t-\n\t\n\t\t3\n\t\t2\n\t\n\n

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. It's given that fx=x-10x+13, which can be rewritten as  fx=x2+3x-130. Since the coefficient of the x2-term is positive, the graph of y=fx in the xy-plane opens upward and reaches its minimum value at its vertex. The x-coordinate of the vertex is the value of x\n such that fx reaches its minimum. For an equation in the form fx=ax2+bx+c, where a\n, b\n, and c\n are constants, the x-coordinate of the vertex is -b2a. For the equation fx=x2+3x-130, a=1, b=3, and c=-130. It follows that the x-coordinate of the vertex is -321, or -32. Therefore, fx reaches its minimum when the value of x\n is -32.

\n

Alternate approach: The value of x\n for the vertex of a parabola is the x-value of the midpoint between the two x-intercepts of the parabola. Since it’s given that fx=x-10x+13, it follows that the two x-intercepts of the graph of y=fx in the xy-plane occur when x=10 and x=-13, or at the points 10,0 and -13,0. The midpoint between two points, x1,y1 and x2,y2, is x1+x22,y1+y22. Therefore, the midpoint between 10,0 and -13,0 is 10+-132,0+02, or -32,0. It follows that fx reaches its minimum when the value of x\n is -32.

\n

Choice A is incorrect. This is the y-coordinate of the y-intercept of the graph of y=fx in the xy-plane.

\n

Choice B is incorrect. This is one of the x-coordinates of the x-intercepts of the graph of y=fx in the xy-plane.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

"}, {"id": "4eaf0a3a", "domain": "Advanced Math", "skill": "Equivalent expressions", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

Which expression is equivalent to \n\t\n\t\t\n\t\t\tx\n\t\t\t9\n\t\t\n\t\t\n\t\t\ty\n\t\t\t9\n\t\t\n\t\n\t7\n\n, where x\n and y\n are positive?

", "choices": [{"id": "A", "text": "

xy79

"}, {"id": "B", "text": "

xy97

"}, {"id": "C", "text": "

xy16

"}, {"id": "D", "text": "

xy63

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. For positive values of a\n and b\n, ambm=abm, an=a1n, and ajk=ajk. Therefore, the given expression, x9y97, can be rewritten as xy97. This expression is equivalent to xy917, which can be rewritten as xy9\u00b717, or xy97. 

\n

Choice A is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

\n

Choice D is incorrect and may result from conceptual or calculation errors.

"}, {"id": "4993b828", "domain": "Advanced Math", "skill": "Nonlinear functions", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

The area A\n, in square centimeters, of a rectangular cutting board can be represented by the expression ww+9, where w\n is the width, in centimeters, of the cutting board. Which expression represents the length, in centimeters, of the cutting board?

", "choices": [{"id": "A", "text": "

ww+9

"}, {"id": "B", "text": "

w\n

"}, {"id": "C", "text": "

9\n

"}, {"id": "D", "text": "

w+9

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. It's given that the expression ww+9 represents the area, in square centimeters, of a rectangular cutting board, where w\n is the width, in centimeters, of the cutting board. The area of a rectangle can be calculated by multiplying its length by its width. It follows that the length, in centimeters, of the cutting board is represented by the expression w+9. 

\n

Choice A is incorrect. This expression represents the area, in square centimeters, of the cutting board, not its length, in centimeters.

\n

Choice B is incorrect. This expression represents the width, in centimeters, of the cutting board, not its length.

\n

Choice C is incorrect. This is the difference between the length, in centimeters, and the width, in centimeters, of the cutting board, not its length, in centimeters.

"}, {"id": "1853bb35", "domain": "Advanced Math", "skill": "Nonlinear functions", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

For the function q\n, the value of qx decreases by 45\n% for every increase in the value of x\n by 1\n. If q0=14, which equation defines q\n?

", "choices": [{"id": "A", "text": "

qx=0.5514x

"}, {"id": "B", "text": "

qx=1.4514x

"}, {"id": "C", "text": "

qx=140.55x

"}, {"id": "D", "text": "

qx=141.45x

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. Since the value of qx decreases by a fixed percentage, 45%, for every increase in the value of x\n by 1\n, the function q\n is a decreasing exponential function. A decreasing exponential function can be written in the form qx=a1-p100x, where a\n is the value of q0 and the value of qx decreases by p% for every increase in the value of x\n by 1\n. If q0=14, then \n\ta\n\t=\n\t14\n\n. Since the value of qx decreases by 45% for every increase in the value of x\n by 1\n, \n\tp\n\t=\n\t45\n\n. Substituting 14\n for a\n and 45\n for p\n in the equation qx=a1-p100x yields qx=141-45100x, which is equivalent to qx=141-0.45x, or qx=140.55x.

\n

Choice A is incorrect and may result from conceptual or calculation errors.

\n

Choice B is incorrect and may result from conceptual or calculation errors.

\n

Choice D is incorrect. For this function, the value of qx increases, rather than decreases, by 45% for every increase in the value of x\n by 1\n.

"}, {"id": "a54753ca", "domain": "Advanced Math", "skill": "Nonlinear equations in one variable and systems of equations in two variables ", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

In the xy-plane, the graph of the equation \n\ty\n\t=\n\t\n\t\t\n\t\t\t-\n\t\t\t\n\t\t\t\tx\n\t\t\t\t2\n\t\t\t\n\t\t\n\t\t+\n\t\t\n\t\t\t9\n\t\t\tx\n\t\t\n\t\t-\n\t\t100\n\t\n\n intersects the line \n\ty\n\t=\n\tc\n\n at exactly one point. What is the value of c\n?

", "choices": [{"id": "A", "text": "

\n\t-\n\t\n\t\t481\n\t\t4\n\t\n\n

"}, {"id": "B", "text": "

-100\n

"}, {"id": "C", "text": "

\n\t-\n\t\n\t\t319\n\t\t4\n\t\n\n

"}, {"id": "D", "text": "

\n\t-\n\t\n\t\t9\n\t\t2\n\t\n\n

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. In the xy-plane, the graph of the line y=c is a horizontal line that crosses the y-axis at y=c and the graph of the quadratic equation y=-x2+9x-100 is a parabola. A parabola can intersect a horizontal line at exactly one point only at its vertex. Therefore, the value of c\n should be equal to the y-coordinate of the vertex of the graph of the given equation. For a quadratic equation in vertex form, y=ax-h2+k, the vertex of its graph in the xy-plane is h,k. The given quadratic equation, y=-x2+9x-100, can be rewritten as y=-x2-292x+922+922-100, or y=-x-922+-3194. Thus, the value of c\n is equal to -3194.

\n

Choice A is incorrect and may result from conceptual or calculation errors.

\n

Choice B is incorrect and may result from conceptual or calculation errors.

\n

Choice D is incorrect and may result from conceptual or calculation errors.

\n

 

"}, {"id": "c602140f", "domain": "Advanced Math", "skill": "Equivalent expressions", "difficulty": "M", "type": "mc", "stimulus": "
\n

\n open parenthesis, x \u2212 11 y, close parenthesis, times, open parenthesis, 2 x \u2212 3 y, close parenthesis, minus, 12 y, times, open parenthesis, \u22122 x, + 3 y, close parenthesis\n

\n
\n", "stem": "

Which of the following is equivalent to the expression above?

\n", "choices": [{"id": "A", "text": "

\n x \u2212 23 y\n

\n"}, {"id": "B", "text": "

\n 2 x\u00b2, \u2212 x y, \u2212 3 y\u00b2\n

\n"}, {"id": "C", "text": "

\n 2 x\u00b2, + 24 x y, + 36 y\u00b2\n

\n"}, {"id": "D", "text": "

\n 2 x\u00b2, \u2212 49 x y, + 69 y\u00b2\n

\n"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. Expanding all terms yields (x – 11y)(2x – 3y) – 12y(–2x + 3y), which is equivalent to 2x2 – 22xy – 3xy + 33y2 + 24xy – 36y2. Combining like terms gives 2x2 – xy – 3y2.

Choice A is incorrect and may be the result of using the sums of the coefficients of the existing x and y terms as the coefficients of the x and y terms in the new expressions. Choice C is incorrect and may be the result of incorrectly combining like terms. Choice D is incorrect and may be the result of using the incorrect sign in front of the 12y term.

\n"}, {"id": "fcb78856", "domain": "Advanced Math", "skill": "Nonlinear equations in one variable and systems of equations in two variables ", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

\n\tb\n\t=\n\t\n\t\t42\n\t\tc\n\t\tf\n\t\n\n

\n

The given equation relates the positive numbers b\n, c\n, and f\n. Which equation correctly expresses c\n in terms of b\n and f\n?

", "choices": [{"id": "A", "text": "

\n\tc\n\t=\n\t\n\t\t\n\t\t\tb\n\t\t\t\n\t\t\t\t42\n\t\t\t\tf\n\t\t\t\n\t\t\n\t\n\n

"}, {"id": "B", "text": "

\n\tc\n\t=\n\t\n\t\t\n\t\t\t\n\t\t\t\tb\n\t\t\t\t-\n\t\t\t\t42\n\t\t\t\n\t\t\tf\n\t\t\n\t\n\n

"}, {"id": "C", "text": "

\n\tc\n\t=\n\t\n\t\t42\n\t\tb\n\t\tf\n\t\n\n

"}, {"id": "D", "text": "

c=42-b-f

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. It's given that the equation b=42cf relates the positive numbers b\n, c\n, and f\n. Dividing each side of the given equation by \n\t42\n\tf\n\n yields b42f=c, or c=b42f. Thus, the equation c=b42f correctly expresses c\n in terms of b\n and f\n.

\n

Choice B is incorrect. This equation can be rewritten as b=cf+42.

\n

Choice C is incorrect. This equation can be rewritten as b=c42f.

\n

Choice D is incorrect. This equation can be rewritten as b=42-c-f.

"}, {"id": "a8ae0d22", "domain": "Advanced Math", "skill": "Nonlinear functions", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

Two variables, x\n and y\n, are related such that for each increase of 1\n in the value of x\n, the value of y\n increases by a factor of 4\n. When \n\tx\n\t=\n\t0\n\n, \n\ty\n\t=\n\t200\n\n. Which equation represents this relationship?

", "choices": [{"id": "A", "text": "

y=4x200

"}, {"id": "B", "text": "

y=4200x

"}, {"id": "C", "text": "

y=200x4

"}, {"id": "D", "text": "

y=2004x

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. Since the value of y\n increases by a constant factor, 4\n, for each increase of 1\n in the value of x\n, the relationship between x\n and y\n is exponential. An exponential relationship between x\n and y\n can be represented by an equation of the form y=abx, where a\n is the value of x\n when \n\ty\n\t=\n\t0\n\n and y\n increases by a factor of b\n for each increase of 1\n in the value of x\n. Since \n\ty\n\t=\n\t200\n\n when \n\tx\n\t=\n\t0\n\n, \n\ta\n\t=\n\t200\n\n. Since y\n increases by a factor of 4\n for each increase of 1\n in the value of x\n, \n\tb\n\t=\n\t4\n\n. Substituting 200\n for a\n and 4\n for b\n in the equation y=abx yields y=2004x. Thus, the equation y=2004x represents the relationship between x\n and y\n.

\n

Choice A is incorrect and may result from conceptual errors.

\n

Choice B is incorrect. This equation represents a relationship where for each increase of 1\n in the value of x\n, the value of y\n increases by a factor of 200\n, not 4\n, and when \n\tx\n\t=\n\t0\n\n, y\n is equal to 4\n, not 200\n.

\n

Choice C is incorrect and may result from conceptual errors.

"}, {"id": "fd4b2aa0", "domain": "Advanced Math", "skill": "Equivalent expressions", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

Which expression is equivalent to 12x3-5x3?

", "choices": [{"id": "A", "text": "

\n\t7\n\t\n\t\tx\n\t\t6\n\t\n\n

"}, {"id": "B", "text": "

\n\t17\n\t\n\t\tx\n\t\t3\n\t\n\n

"}, {"id": "C", "text": "

\n\t7\n\t\n\t\tx\n\t\t3\n\t\n\n

"}, {"id": "D", "text": "

\n\t17\n\t\n\t\tx\n\t\t6\n\t\n\n

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. The given expression shows subtraction of two like terms. The two terms can be subtracted as follows: 12x3-5x3=12-5x3, or 7x3.

\n

Choice A is incorrect and may result from conceptual or calculation errors.

\n

Choice B is incorrect. This is the result of adding, not subtracting, the two like terms.

\n

Choice D is incorrect and may result from conceptual or calculation errors.

"}, {"id": "981aca65", "domain": "Advanced Math", "skill": "Nonlinear functions", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

fx=a-19x+5

\n

In the given function f\n, a\n is a constant. The graph of function f\n in the xy-plane, where y=fx, is translated 3\n units down and 4\n units to the right to produce the graph of y=gx. Which equation defines function g\n?

", "choices": [{"id": "A", "text": "

gx=a-19x+4+2

"}, {"id": "B", "text": "

gx=a-19x-4+2

"}, {"id": "C", "text": "

gx=a-22x+4+5

"}, {"id": "D", "text": "

gx=a-22x-4+5

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. It's given that the graph of y=gx is produced by translating the graph of y=fx 3\n units down and 4\n units to the right in the xy-plane. Therefore, function g\n can be defined by an equation in the form gx=fx-4-3. Function f is defined by the equation fx=a-19x+5, where a\n is a constant. Substituting x-4 for x\n in the equation fx=a-19x+5 yields fx-4=a-19x-4+5. Substituting a-19x-4+5 for fx-4 in the equation gx=fx-4-3 yields gx=a-19x-4+5-3, or gx=a-19x-4+2. Therefore, the equation that defines function g\n is gx=a-19x-4+2.

\n

Choice A is incorrect. This equation defines a function whose graph is produced by translating the graph of y=fx 3\n units down and 4\n units to the left, not 3\n units down and 4\n units to the right.

\n

Choice C is incorrect. This equation defines a function whose graph is produced by translating the graph of  y=fx 4\n units to the left, not 3\n units down and 4\n units to the right.

\n

Choice D is incorrect. This equation defines a function whose graph is produced by translating the graph of y=fx 4\n units to the right, not 3\n units down and 4\n units to the right.

"}, {"id": "4236c5a3", "domain": "Advanced Math", "skill": "Nonlinear equations in one variable and systems of equations in two variables ", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

If open parenthesis, x + 5, close parenthesis, squared = 4, which of the following is a possible value of x ?

\n", "choices": [{"id": "A", "text": "1 \n"}, {"id": "B", "text": "\n \u22121\n \n"}, {"id": "C", "text": "\n \u22122\n \n"}, {"id": "D", "text": "\n \u22123\n \n"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. If open parenthesis, x + 5, close parenthesis, squared = 4, then taking the square root of each side of the equation gives x + 5 = 2 or x + 5 = \u22122. Solving these equations for x gives x = \u22123 or x = \u22127. Of these, \u22123 is the only solution given as a choice.

Choice A is incorrect and may result from solving the equation x + 5 = 4 and making a sign error. Choice B is incorrect and may result from solving the equation x + 5 = 4. Choice C is incorrect and may result from finding a possible value of x + 5.

\n"}, {"id": "a7711fe8", "domain": "Advanced Math", "skill": "Nonlinear functions", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

What is the minimum value of the function f defined by f(x) = open parenthesis, x \u2212 2, close parenthesis, squared, \u2212 4 ?

\n", "choices": [{"id": "A", "text": "

\u22124

\n"}, {"id": "B", "text": "

\u22122

\n"}, {"id": "C", "text": "

2

\n"}, {"id": "D", "text": "

4

\n"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. The given quadratic function f is in vertex form, f(x) = open parenthesis, x \u2212 h, close parenthesis, squared, + k, where the point h, k is the vertex of the graph of y = f(x) in the xy-plane. Therefore, the vertex of the graph of y = f(x) is the point 2, \u22124. In addition, the y-coordinate of the vertex represents either the minimum or maximum value of a quadratic function, depending on whether the graph of the function opens upward or downward. Since the leading coefficient of f (the coefficient of the term open parenthesis, x \u2212 2, close parenthesis, squared) is 1, which is positive, the graph of y = f(x) opens upward. It follows that at x = 2, the minimum value of the function f is \u22124.

Choice B is incorrect and may result from making a sign error and from using the x-coordinate of the vertex. Choice C is incorrect and may result from using the x-coordinate of the vertex. Choice D is incorrect and may result from making a sign error.

 

\n"}, {"id": "3b4b8831", "domain": "Advanced Math", "skill": "Nonlinear equations in one variable and systems of equations in two variables ", "difficulty": "M", "type": "spr", "stimulus": "", "stem": "

38x2=389

\n

What is the negative solution to the given equation?

", "choices": [], "answerId": "-3", "acceptedAnswers": ["-3"], "rationale": "

The correct answer is -3\n. Dividing both sides of the given equation by 38\n yields \n\t\n\t\tx\n\t\t2\n\t\n\t=\n\t9\n\n. Taking the square root of both sides of this equation yields the solutions \n\tx\n\t=\n\t3\n\n and \n\tx\n\t=\n\t-3\n\n. Therefore, the negative solution to the given equation is -3\n.

"}, {"id": "f5247e52", "domain": "Advanced Math", "skill": "Nonlinear equations in one variable and systems of equations in two variables ", "difficulty": "M", "type": "mc", "stimulus": "
\n

\n y = a \u00d7 x\u00b2 \u2212 c\n

\n
\n", "stem": "

In the equation above, a and c are positive constants. How many times does the graph of the equation above intersect the graph of the equation y = a + c in the xy-plane?

\n", "choices": [{"id": "A", "text": "

Zero

\n"}, {"id": "B", "text": "

One

\n"}, {"id": "C", "text": "

Two

\n"}, {"id": "D", "text": "

More than two

\n"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. It is given that the constants a and c are both positive; therefore, the graph of the given quadratic equation is a parabola that opens up with a vertex on the y-axis at a point below the x-axis. The graph of the second equation provided is a horizontal line that lies above the x-axis. A horizontal line above the x-axis will intersect a parabola that opens up and has a vertex below the x-axis in exactly two points.

Choices A, B, and D are incorrect and are the result of not understanding the relationships of the graphs of the two equations given. Choice A is incorrect because the two graphs intersect. Choice B is incorrect because in order for there to be only one intersection point, the horizontal line would have to intersect the parabola at the vertex, but the vertex is below the x-axis and the line is above the x-axis. Choice D is incorrect because a line cannot intersect a parabola in more than two points.

\n"}, {"id": "1a722d7d", "domain": "Advanced Math", "skill": "Nonlinear functions", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

Let the function p be defined as p(x) = the fraction with numerator, open parenthesis, x \u2212 c, close parenthesis, squared, plus, 160, and denominator, 2 c , end fraction, where c is a constant. If p(c) = 10, what is the value of p(1)2 ?

\n", "choices": [{"id": "A", "text": "

10.00

\n"}, {"id": "B", "text": "

10.25

\n"}, {"id": "C", "text": "

10.75

\n"}, {"id": "D", "text": "

11.00

\n"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. The value of p(12) depends on the value of the constant c, so the value of c must first be determined. It is given that p(c) = 10. Based on the definition of p, it follows that:

\n p(c) = (open parenthesis, c \u2212 c, close parenthesis, squared, + 160)/(2 c, end fraction, which = 10)

\n (160)/(2 c, end fraction = 10)

\n 2 c = 16

\n c = 8

This means that p(x) = (open parenthesis, x \u2212 8, close parenthesis, squared, + 160)/(16) for all values of x. Therefore:

\n p(1)2 = (open parenthesis, 12 \u2212 8, close parenthesis, squared, + 160)/(16)

\n which = (16 + 160)/(16)

\n which = 11

Choice A is incorrect. It is the value of p(8), not p(12). Choices B and C are incorrect. If one of these values were correct, then x = 12 and the selected value of p(12) could be substituted into the equation to solve for c. However, the values of c that result from choices B and C each result in p(c) < 10.

\n"}, {"id": "ee05c84e", "domain": "Advanced Math", "skill": "Nonlinear functions", "difficulty": "E", "type": "mc", "stimulus": "
\n\t

f(x) = open parenthesis, x + 0 point 2 5 x, close parenthesis, times, open parenthesis, 50 \u2212 x, close parenthesis

\n
\n", "stem": "

The function f is defined above. What is the value of f(2)0 ?

\n", "choices": [{"id": "A", "text": "

250

\n"}, {"id": "B", "text": "

500

\n"}, {"id": "C", "text": "

750

\n"}, {"id": "D", "text": "

2,000

\n"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. Adding the like terms x and 0 point 2 5 x yields the equation f(x) = 1 point 2 5 x times, open parenthesis, 50 \u2212 x, close parenthesis. Substituting 20 for x yields f(2)0 = open parenthesis, 1 point 2 5 \u00d7 20, close parenthesis, times, open parenthesis, 50 \u2212 20, close parenthesis. The product 1 point 2 5 \u00d7 20 is equal to 25, and the difference 50 \u2212 20 is equal to 30. Substituting these values in the given equation gives f(2)0 = 25 \u00d7 30, and multiplying 25 by 30 results in f(2)0 = 750.

Choices A, B, and D are incorrect and may result from conceptual or computational errors when finding the value of f(2)0.

 

\n"}, {"id": "5d93c782", "domain": "Advanced Math", "skill": "Equivalent expressions", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

Which expression is equivalent to \n\t\n\t\tx\n\t\t2\n\t\n\t+\n\t\n\t\t3\n\t\tx\n\t\n\t-\n\t40\n\n?

", "choices": [{"id": "A", "text": "

\n\t\n\t\t\n\t\t\tx\n\t\t\t-\n\t\t\t4\n\t\t\n\t\n\t\n\t\t\n\t\t\tx\n\t\t\t+\n\t\t\t10\n\t\t\n\t\n\n

"}, {"id": "B", "text": "

\n\t\n\t\t\n\t\t\tx\n\t\t\t-\n\t\t\t5\n\t\t\n\t\n\t\n\t\t\n\t\t\tx\n\t\t\t+\n\t\t\t8\n\t\t\n\t\n\n

"}, {"id": "C", "text": "

\n\t\n\t\t\n\t\t\tx\n\t\t\t-\n\t\t\t8\n\t\t\n\t\n\t\n\t\t\n\t\t\tx\n\t\t\t+\n\t\t\t5\n\t\t\n\t\n\n

"}, {"id": "D", "text": "

\n\t\n\t\t\n\t\t\tx\n\t\t\t-\n\t\t\t10\n\t\t\n\t\n\t\n\t\t\n\t\t\tx\n\t\t\t+\n\t\t\t4\n\t\t\n\t\n\n

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. The given expression may be rewritten as x2+8x-5x-40. Since the first two terms of this expression have a common factor of x\n and the last two terms of this expression have a common factor of -5\n, this expression may be rewritten as xx+x8-5x-58, or xx+8-5x+8. Since each term of this expression has a common factor of x+8, it may be rewritten as x-5x+8.

\n

Alternate approach: An expression of the form x2+bx+c, where b\n and c\n are constants, can be factored if there are two values that add to give b\n and multiply to give c\n. In the given expression, b=3 and c=-40. The values of -5\n and 8\n add to give 3\n and multiply to give -40\n, so the expression can be factored as x-5x+8.

\n

Choice A is incorrect. This expression is equivalent to x2+6x-40, not x2+3x-40.

\n

Choice C is incorrect. This expression is equivalent to x2-3x-40, not x2+3x-40.

\n

Choice D is incorrect. This expression is equivalent to x2-6x-40, not x2+3x-40.

"}, {"id": "5c00c2c1", "domain": "Advanced Math", "skill": "Nonlinear functions", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

There were no jackrabbits in Australia before 1788 when 24 jackrabbits were introduced. By 1920 the population of jackrabbits had reached 10 billion. If the population had grown exponentially, this would correspond to a 16.2% increase, on average, in the population each year. Which of the following functions best models the population p(t) of jackrabbits t years after 1788?

\n", "choices": [{"id": "A", "text": "

\n p(t) = 1 point 1 6 2 times, 24 raised to the t power\n

\n"}, {"id": "B", "text": "

\n p(t) = 24 times, 2 raised to the 1 point 1 6 2, t power\n

\n"}, {"id": "C", "text": "

\n p(t) = 24 times, 1 point 1 6 2 raised to the t power\n

\n"}, {"id": "D", "text": "

\n p(t) = open parenthesis, 24 \u00d7 1 point 1 6 2, close parenthesis, raised to the t power\n

\n"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. This exponential growth model can be written in the form p(t) = A, times, open parenthesis, 1 + r, close parenthesis, raised to the t power, where p(t) is the population t years after 1788, A is the initial population, and r is the yearly growth rate, expressed as a decimal. Since there were 24 jackrabbits in Australia in 1788, A = 24. Since the number of jackrabbits increased by an average of 16.2% each year, r = 0 point 1 6 2. Therefore, the equation that best models this situation is p(t) = 24 times, 1 point 1 6 2 raised to the t power.

Choices A, B, and D are incorrect and may result from misinterpreting the form of an exponential growth model.

\n"}, {"id": "974d33dc", "domain": "Advanced Math", "skill": "Equivalent expressions", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

Which of the following expressions is equivalent to the sum of open parenthesis, r\u00b3, + 5 r\u00b2, + 7, close parenthesis and open parenthesis, r\u00b2, + 8 r, + 12, close parenthesis ?

\n", "choices": [{"id": "A", "text": "

r to the fifth power, + 13 r\u00b3, + 19

\n"}, {"id": "B", "text": "

2 r\u00b3, + 13 r\u00b2, + 19

\n"}, {"id": "C", "text": "

r\u00b3, + 5 r\u00b2, + 7 r, + 12

\n"}, {"id": "D", "text": "

r\u00b3, + 6 r\u00b2, + 8 r, + 19

\n"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. Grouping like terms, the given expressions can be rewritten as r\u00b3 plus, open parenthesis, 5, r\u00b2 + r\u00b2, close parenthesis, + 8 r, plus, open parenthesis, 7 + 12, close parenthesis. This can be rewritten as r\u00b3, + 6, r\u00b2, + 8 r, + 19.

Choice A is incorrect and may result from adding the two sets of unlike terms, r\u00b3 and r\u00b2 as well as 5, r\u00b2 and 8 r, and then adding the respective exponents. Choice B is incorrect and may result from adding the unlike terms r\u00b3 and r\u00b2 as if they were r\u00b3 and r\u00b3 and adding the unlike terms 5, r\u00b2 and 8 r as if they were 5, r\u00b2 and 8, r\u00b2. Choice C is incorrect and may result from errors when combining like terms.

 

\n"}, {"id": "d4d513ff", "domain": "Advanced Math", "skill": "Equivalent expressions", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

Which expression is equivalent to \n\t\n\t\t12\n\t\tx\n\t\n\t+\n\t27\n\n?

", "choices": [{"id": "A", "text": "

129x+1

"}, {"id": "B", "text": "

2712x+1

"}, {"id": "C", "text": "

34x+9

"}, {"id": "D", "text": "

39x+24

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. Each term in the given expression, \n\t\n\t\t12\n\t\tx\n\t\n\t+\n\t27\n\n, has a common factor of 3\n. Therefore, the expression can be rewritten as 34x+39, or 34x+9. Thus, the expression 34x+9 is equivalent to the given expression.

\n

Choice A is incorrect. This expression is equivalent to \n\t\n\t\t108\n\t\tx\n\t\n\t+\n\t12\n\n, not \n\t\n\t\t12\n\t\tx\n\t\n\t+\n\t27\n\n.

\n

Choice B is incorrect. This expression is equivalent to \n\t\n\t\t324\n\t\tx\n\t\n\t+\n\t27\n\n, not \n\t\n\t\t12\n\t\tx\n\t\n\t+\n\t27\n\n.

\n

Choice D is incorrect. This expression is equivalent to \n\t\n\t\t27\n\t\tx\n\t\n\t+\n\t72\n\n, not \n\t\n\t\t12\n\t\tx\n\t\n\t+\n\t27\n\n.

"}, {"id": "58b109d4", "domain": "Advanced Math", "skill": "Nonlinear equations in one variable and systems of equations in two variables ", "difficulty": "H", "type": "spr", "stimulus": "", "stem": "

\n\t\n\t\t\n\t\t\tx\n\t\t\t2\n\t\t\n\t\t+\n\t\ty\n\t\t+\n\t\t7\n\t\n\t=\n\t7\n\n

\n

20x+100-y=0

\n

The solution to the given system of equations is x,y. What is the value of x\n?

", "choices": [], "answerId": "-10", "acceptedAnswers": ["-10"], "rationale": "

The correct answer is -10\n. Adding y\n to both sides of the second equation in the given system yields \n\t\n\t\t\n\t\t\t20\n\t\t\tx\n\t\t\n\t\t+\n\t\t100\n\t\n\t=\n\ty\n\n. Substituting \n\t\n\t\t20\n\t\tx\n\t\n\t+\n\t100\n\n for y\n in the first equation in the given system yields x2+20x+100+7=7. Subtracting 7\n from both sides of this equation yields \n\t\n\t\t\n\t\t\tx\n\t\t\t2\n\t\t\n\t\t+\n\t\t\n\t\t\t20\n\t\t\tx\n\t\t\n\t\t+\n\t\t100\n\t\n\t=\n\t0\n\n. Factoring the left-hand side of this equation yields x+10x+10=0, or x+102=0. Taking the square root of both sides of this equation yields \n\t\n\t\tx\n\t\t+\n\t\t10\n\t\n\t=\n\t0\n\n. Subtracting 10\n from both sides of this equation yields \n\tx\n\t=\n\t-10\n\n. Therefore, the value of x\n is -10\n.

"}, {"id": "85939da5", "domain": "Problem-Solving and Data Analysis", "skill": "Inference from sample statistics and margin of error ", "difficulty": "H", "type": "mc", "stimulus": "
Texting behaviorTalks on cell phone dailyDoes not talk on cell phone dailyTotal
Light110146256
Medium139164303
Heavy16674240
Total415384799
\n", "stem": "

In a study of cell phone use, 799 randomly selected US teens were asked how often they talked on a cell phone and about their texting behavior. The data are summarized in the table above. Based on the data from the study, an estimate of the percent of US teens who are heavy texters is 30% and the associated margin of error is 3%. Which of the following is a correct statement based on the given margin of error?

\n", "choices": [{"id": "A", "text": "

Approximately 3% of the teens in the study who are classified as heavy texters are not really heavy texters.

\n"}, {"id": "B", "text": "

It is not possible that the percent of all US teens who are heavy texters is less than 27%.

\n"}, {"id": "C", "text": "

The percent of all US teens who are heavy texters is 33%.

\n"}, {"id": "D", "text": "

It is doubtful that the percent of all US teens who are heavy texters is 35%.

\n"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. The given margin of error of 3% indicates that the actual percent of all US teens who are heavy texters is likely within 3% of the estimate of 30%, or between 27% and 33%. Therefore, it is unlikely, or doubtful, that the percent of all US teens who are heavy texters would be 35%.

Choice A is incorrect. The margin of error doesn’t provide any information about the accuracy of reporting in the study. Choice B is incorrect. Based on the estimate and given margin of error, it is unlikely that the percent of all US teens who are heavy texters would be less than 27%, but it is possible. Choice C is incorrect. While the percent of all US teens who are heavy texters is likely between 27% and 33%, any value within this interval is equally likely. We can’t be certain that the value is exactly 33%.

\n"}, {"id": "3c8fdc40", "domain": "Problem-Solving and Data Analysis", "skill": "Ratios, rates, proportional relationships, and units", "difficulty": "E", "type": "spr", "stimulus": "", "stem": "

A printer produces posters at a constant rate of 42\n posters per minute. At what rate, in posters per hour, does the printer produce the posters?

", "choices": [], "answerId": "2520", "acceptedAnswers": ["2520"], "rationale": "

The correct answer is 2,520\n. There are 60\n minutes in one hour. At a rate of 42\n posters per minute, the number of posters produced in one hour can be determined by 42 posters1  minute60 minutes1 hour, which is 2,520\n posters per hour.

"}, {"id": "eccbf957", "domain": "Problem-Solving and Data Analysis", "skill": "Probability and conditional probability", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

Each face of a fair 14\n-sided die is labeled with a number from 1\n through 14\n, with a different number appearing on each face. If the die is rolled one time, what is the probability of rolling a 2\n?

", "choices": [{"id": "A", "text": "

\n\t1\n\t14\n\n

"}, {"id": "B", "text": "

214

"}, {"id": "C", "text": "

1214

"}, {"id": "D", "text": "

\n\t13\n\t14\n\n

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. The total number of possible outcomes for rolling a fair 14\n-sided die is 14\n. The number of possible outcomes for rolling a 2\n is 1\n. The probability of rolling a 2\n is the number of possible outcomes for rolling a 2\n divided by the total number of possible outcomes, or 114.

\n

Choice B is incorrect. This is the probability of rolling a number no greater than 2\n.

\n

Choice C is incorrect. This is the probability of rolling a number greater than 2\n.

\n

Choice D is incorrect. This is the probability of rolling a number other than 2\n.

"}, {"id": "affb2315", "domain": "Problem-Solving and Data Analysis", "skill": "Inference from sample statistics and margin of error ", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

There are 55\n students in Spanish club. A sample of the Spanish club students was selected at random and asked whether they intend to enroll in a new study program. Of those surveyed, 20% responded that they intend to enroll in the study program. Based on this survey, which of the following is the best estimate of the total number of Spanish club students who intend to enroll in the study program?

", "choices": [{"id": "A", "text": "

11\n

"}, {"id": "B", "text": "

20\n

"}, {"id": "C", "text": "

44\n

"}, {"id": "D", "text": "

55\n

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. It’s given that 20% of the students surveyed responded that they intend to enroll in the study program. Therefore, the proportion of students in Spanish club who intend to enroll in the study program, based on the survey, is 0.20. Since there are 55\n total students in Spanish club, the best estimate for the total number of these students who intend to enroll in the study program is 550.20, or 11\n.

\n

Choice B is incorrect. This is the best estimate for the percentage, rather than the total number, of students in Spanish club who intend to enroll in the study program.

\n

Choice C is incorrect. This is the best estimate for the total number of Spanish club students who do not intend to enroll in the study program.

\n

Choice D is incorrect. This is the total number of students in Spanish club.

"}, {"id": "954943a4", "domain": "Problem-Solving and Data Analysis", "skill": "Percentages", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

Jennifer bought a box of Crunchy Grain cereal. The nutrition facts on the box state that a serving size of the cereal is three fourths cup and provides 210 calories, 50 of which are calories from fat. In addition, each serving of the cereal provides 180 milligrams of potassium, which is 5% of the daily allowance for adults. If p percent of an adult’s daily allowance of potassium is provided by x servings of Crunchy Grain cereal per day, which of the following expresses p in terms of x ?

\n", "choices": [{"id": "A", "text": "

\n p = 0 point 5 x\n

\n"}, {"id": "B", "text": "

\n p = 5 x\n

\n"}, {"id": "C", "text": "

\n p = open parenthesis, 0 point 0 5, close parenthesis, to the x power\n

\n"}, {"id": "D", "text": "

\n p = open parenthesis, 1 point 0 5, close parenthesis, to the x power\n

\n"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. It’s given that each serving of Crunchy Grain cereal provides 5% of an adult’s daily allowance of potassium, so x servings would provide x times 5%. The percentage of an adult’s daily allowance of potassium, p, is 5 times the number of servings, x. Therefore, the percentage of an adult’s daily allowance of potassium can be expressed as p = 5 x.

Choices A, C, and D are incorrect and may result from incorrectly converting 5% to its decimal equivalent, which isn’t necessary since p is expressed as a percentage. Additionally, choices C and D are incorrect because the context should be represented by a linear relationship, not by an exponential relationship.

\n"}, {"id": "b1b5300b", "domain": "Problem-Solving and Data Analysis", "skill": "Probability and conditional probability", "difficulty": "M", "type": "mc", "stimulus": "
\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n
Prices of 14 Different Cars
Type of carPriced at no more
 than $25,000		Priced greater
 than $25,000		Total
Nonhybrid538
Hybrid246
Total7714
\n", "stem": "
The table above shows information about 14 cars listed for sale on an auto dealership’s website. If one of the cars listed for sale is selected at random, what is the probability that the car selected will be a hybrid car priced at no more than $25,000 ?
\n", "choices": [{"id": "A", "text": "

\n one seventh\n

\n"}, {"id": "B", "text": "

\n two sevenths\n

\n"}, {"id": "C", "text": "

\n one third\n

\n"}, {"id": "D", "text": "

\n four sevenths\n

\n"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. It’s given that there are 2 hybrid cars priced at no more than $25,000. It’s also given that there are 14 cars total for sale. Therefore, the probability of selecting a hybrid priced at no more than $25,000 when one car is chosen at random is 2 over 14 = one seventh.

Choice B is incorrect. This is the probability of selecting a hybrid car priced greater than $25,000 when choosing one car at random. Choice C is incorrect. This is the probability, when choosing randomly from only the hybrid cars, of selecting one priced at no more than $25,000. Choice D is incorrect. This is the probability of selecting a hybrid car when selecting at random from only the cars priced greater than $25,000.

\n"}, {"id": "d28c29e1", "domain": "Problem-Solving and Data Analysis", "skill": "Ratios, rates, proportional relationships, and units", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

The International Space Station orbits Earth at an average speed of 4.76 miles per second. What is the space station’s average speed in miles per hour?

\n", "choices": [{"id": "A", "text": "

285.6

\n"}, {"id": "B", "text": "

571.2

\n"}, {"id": "C", "text": "

856.8

\n"}, {"id": "D", "text": "

17,136.0

\n"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. Since 1 minute = 60 seconds and 1 hour = 60 minutes, it follows that 1 hour = (60)(60), or 3,600 seconds. Using this conversion factor, the space station’s average speed of 4.76 miles per second is equal to an average speed of (4 point 7 6 miles)/(second, times, the fraction with numerator 3,600 seconds, and denominator hour = the fraction with numerator 17,136 miles, and denominator hour), or 17,136 miles per hour.

Choice A is incorrect. This is the space station’s average speed in miles per minute. Choice B is incorrect. This is double the space station’s average speed in miles per minute, or the number of miles the space station travels on average in 2 minutes. Choice C is incorrect. This is triple the space station’s average speed in miles per minute, or the number of miles the space station travels on average in 3 minutes. 

\n"}, {"id": "1adb39f0", "domain": "Problem-Solving and Data Analysis", "skill": "Two-variable data: Models and scatterplots", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

The scatterplot shows the relationship between two variables, x and y. A line of best fit for the data is also shown. Which of the following is closest to the difference between the y-coordinate of the data point with x = 1 and the y-value predicted by the line of best fit at x = 1 ?

\n \"The

\n", "choices": [{"id": "A", "text": "

1

\n"}, {"id": "B", "text": "

2

\n"}, {"id": "C", "text": "

5

\n"}, {"id": "D", "text": "

12

\n"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. The data point with x = 1 has a y-coordinate of 12. The y-value predicted by the line of best fit at x = 1 is approximately 11. The difference between the y-coordinate of the data point and the y-value predicted by the line of best fit at x = 1 is 12 \u2212 11, or 1.

Choices B and C are incorrect and may result from incorrectly reading the scatterplot. Choice D is incorrect. This is the y-coordinate of the data point at x = 1.

\n"}, {"id": "b4912cc5", "domain": "Problem-Solving and Data Analysis", "skill": "Ratios, rates, proportional relationships, and units", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

The population density of Iceland, in people per square kilometer of land area, increased from 2.5 in 1990 to 3.3 in 2014. During this time period, the land area of Iceland was 100,250 square kilometers. By how many people did Iceland’s population increase from 1990 to 2014?

\n", "choices": [{"id": "A", "text": "

330,825

\n"}, {"id": "B", "text": "

132,330

\n"}, {"id": "C", "text": "

125,312

\n"}, {"id": "D", "text": "

80,200

\n"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. The increase in Iceland’s population can be found by multiplying the increase in population density, in people per square kilometer, by the area, in square kilometers. It’s given that the population density of Iceland was 2.5 people per square kilometer in 1990 and 3.3 people per square kilometer in 2014. The increase in population density can be found by subtracting 2.5 from 3.3, which yields 0.8. It’s given that the land area of Iceland was 100,250 square kilometers. Thus, the increase in population is 0 point 8 \u00d7 100,250, or 80,200.

Alternate approach: It’s given that the population density of Iceland, in people per square kilometer of land area, in 1990 was 2.5. Since the land area of Iceland was 100,250 square kilometers, it follows that the population of Iceland in 1990 was 2 point 5 \u00d7 100,250, or 250,625. Similarly, the population of Iceland in 2014 was 3 point 3 \u00d7 100,250, or 330,825. The population increase is the difference in the population from 1990 to 2014, or 330,825 \u2212 250,625, which yields 80,200. Therefore, Iceland’s population increased by 80,200 from 1990 to 2014.

Choice A is incorrect. This is the population of Iceland in 2014. Choice B is incorrect and may result from dividing 3.3 by 2.5, instead of subtracting 2.5 from 3.3. Choice C is incorrect and may result from dividing the population of Iceland in 1990 by 2.

\n"}, {"id": "f890dc20", "domain": "Problem-Solving and Data Analysis", "skill": "One-variable data: Distributions and measures of center and spread", "difficulty": "E", "type": "mc", "stimulus": "
\n

\n The seven data values 2, 2, 2, 3, 4, 4, 11 are shown.

\n
\n", "stem": "

What is the median of the seven data values shown?

\n", "choices": [{"id": "A", "text": "

2

\n"}, {"id": "B", "text": "

3

\n"}, {"id": "C", "text": "

4

\n"}, {"id": "D", "text": "

9

\n"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. When a data set has an odd number of values, the median can be found by ordering the values from least to greatest and determining the value in the middle. Since the values are already presented in order from least to greatest and there are 7 values, the median is the fourth value in the list. Therefore, the median is 3.

Choice A is incorrect. This is the mode. Choice C is incorrect. This is the mean. Choice D is incorrect. This is the range.

\n"}, {"id": "d3b9c8d8", "domain": "Problem-Solving and Data Analysis", "skill": "One-variable data: Distributions and measures of center and spread", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

\n

The box plots summarize the masses, in kilograms, of two groups of gazelles. Based on the box plots, which of the following statements must be true?

", "choices": [{"id": "A", "text": "

The mean mass of group 1 is greater than the mean mass of group 2.

"}, {"id": "B", "text": "

The mean mass of group 1 is less than the mean mass of group 2.

"}, {"id": "C", "text": "

The median mass of group 1 is greater than the median mass of group 2.

"}, {"id": "D", "text": "

The median mass of group 1 is less than the median mass of group 2.

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. The median of a data set represented in a box plot is represented by the vertical line within the box. It follows that the median mass of the gazelles in group 1\n is 25\n kilograms, and the median mass of the gazelles in group 2\n is 24\n kilograms. Since 25\n kilograms is greater than 24\n kilograms, the median mass of group 1\n is greater than the median mass of group 2\n.

\n

Choice A is incorrect. The mean mass of each of the two groups cannot be determined from the box plots.

\n

Choice B is incorrect. The mean mass of each of the two groups cannot be determined from the box plots.

\n

Choice D is incorrect and may result from conceptual or calculation errors.

"}, {"id": "86636d8f", "domain": "Problem-Solving and Data Analysis", "skill": "Ratios, rates, proportional relationships, and units", "difficulty": "E", "type": "spr", "stimulus": "", "stem": "

A customer spent $27 to purchase oranges at $3 per pound. How many pounds of oranges did the customer purchase?

", "choices": [], "answerId": "9", "acceptedAnswers": ["9"], "rationale": "

The correct answer is 9\n. It’s given that the customer spent $27 to purchase oranges at $3 per pound. Therefore, the number of pounds of oranges the customer purchased is $271 pound$3, or 9\n pounds.

"}, {"id": "1ea09200", "domain": "Problem-Solving and Data Analysis", "skill": "Evaluating statistical claims: Observational studies and experiments ", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

A sample of 40 fourth-grade students was selected at random from a certain school. The 40 students completed a survey about the morning announcements, and 32 thought the announcements were helpful. Which of the following is the largest population to which the results of the survey can be applied?

\n", "choices": [{"id": "A", "text": "

The 40 students who were surveyed

\n"}, {"id": "B", "text": "

All fourth-grade students at the school

\n"}, {"id": "C", "text": "

All students at the school

\n"}, {"id": "D", "text": "

All fourth-grade students in the county in which the school is located

\n"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. Selecting a sample of a reasonable size at random to use for a survey allows the results from that survey to be applied to the population from which the sample was selected, but not beyond this population. In this case, the population from which the sample was selected is all fourth-grade students at a certain school. Therefore, the results of the survey can be applied to all fourth-grade students at the school.

Choice A is incorrect. The results of the survey can be applied to the 40 students who were surveyed. However, this isn’t the largest group to which the results of the survey can be applied. Choices C and D are incorrect. Since the sample was selected at random from among the fourth-grade students at a certain school, the results of the survey can’t be applied to other students at the school or to other fourth-grade students who weren’t represented in the survey results. Students in other grades in the school or other fourth-grade students in the country may feel differently about announcements than the fourth-grade students at the school.

\n"}, {"id": "82aaa0a1", "domain": "Problem-Solving and Data Analysis", "skill": "Two-variable data: Models and scatterplots", "difficulty": "E", "type": "mc", "stimulus": "
\n\t
\"The
\n
\n", "stem": "

Of the following, which is the best model for the data in the scatterplot?

\n", "choices": [{"id": "A", "text": "

y = 2 x\u00b2, \u2212 11 x, \u2212 20

\n"}, {"id": "B", "text": "

y = 2 x\u00b2, \u2212 11 x, + 20

\n"}, {"id": "C", "text": "

y = 2 x\u00b2, \u2212 5 x, \u2212 3

\n"}, {"id": "D", "text": "

y = 2 x\u00b2, \u2212 5 x, + 3

\n"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. The graphical model that most closely fits the data in the scatterplot is a model in which the number of data points above and below the model are approximately balanced. Fitting a graphical model to the data shown results in an upward-facing parabola with a y-intercept near the point 0, 20 and a vertex with an approximate x-value of 2.5. Of the given choices, only choice B gives an equation of an upward-facing parabola with a y-intercept at the point 0, 20. Furthermore, substituting 2.5 for x into the equation in choice B yields y = 5. This is approximately the y-value of the vertex of the model.

Choices A, C, and D are incorrect. These equations don’t give a graphical model that best fits the data. At x = 0, they have y-values of \u221220, \u22123, and 3, respectively. At x = 2 point 5, they have y-values of \u221235, \u22123, and 3, respectively.

 

\n"}, {"id": "37930b2a", "domain": "Problem-Solving and Data Analysis", "skill": "Evaluating statistical claims: Observational studies and experiments ", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

Residents of a town were surveyed to determine whether they are satisfied with the concession stand at the local park. A random sample of 200 residents was selected. All 200 responded, and 87% said they are satisfied. Based on this information, which of the following statements must be true?

I. Of all the town residents, 87% would say they are satisfied with the concession stand at the local park.
\nII. If another random sample of 200 residents were surveyed, 87% would say they are satisfied.

\n", "choices": [{"id": "A", "text": "

Neither

\n"}, {"id": "B", "text": "

I only

\n"}, {"id": "C", "text": "

II only

\n"}, {"id": "D", "text": "

I and II

\n"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. The purpose of surveying a random sample of residents is to approximate the percent of the town residents that are satisfied with the concession stand. The sample doesn’t necessarily get the same result as surveying every resident of the town, nor would another sample necessarily have identical results. Therefore, although it’s possible that either statement I or statement II could prove true by surveying every resident of the town, these statements cannot be proven true solely based on the results of the sample.

Choice B is incorrect because surveying a sample of the town residents may not have the same result as surveying all the town residents. Choices C and D are incorrect because surveying a different sample of residents could yield different results.

\n"}, {"id": "83272c51", "domain": "Problem-Solving and Data Analysis", "skill": "Two-variable data: Models and scatterplots", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

\"The

In an experiment, a heated cup of coffee is removed from a heat source, and the cup of coffee is then left in a room that is kept at a constant temperature. The graph above shows the temperature, in degrees Fahrenheit (°F), of the coffee immediately after being removed from the heat source and at 10-minute intervals thereafter. During which of the following 10-minute intervals does the temperature of the coffee decrease at the greatest average rate?

\n", "choices": [{"id": "A", "text": "

Between 0 and 10 minutes

\n"}, {"id": "B", "text": "

Between 30 and 40 minutes

\n"}, {"id": "C", "text": "

Between 50 and 60 minutes

\n"}, {"id": "D", "text": "

Between 90 and 100 minutes

\n"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. The average rate of change in temperature of the coffee in degrees Fahrenheit per minute is calculated by dividing the difference between two recorded temperatures by the number of minutes in the corresponding interval of time. Since the time intervals given are all 10 minutes, the average rate of change is greatest for the points with the greatest difference in temperature. Of the choices, the greatest difference in temperature occurs between 0 and 10 minutes.

Choices B, C, and D are incorrect and may result from misinterpreting the average rate of change from the graph.

\n"}, {"id": "4c774b00", "domain": "Problem-Solving and Data Analysis", "skill": "One-variable data: Distributions and measures of center and spread", "difficulty": "M", "type": "mc", "stimulus": "
\n
\n \n
\n

Ages of 20 Students Enrolled in a College Class 

\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n
AgeFrequency
186
195
204
212
221
231
301
\n
\n", "stem": "

The table above shows the distribution of ages of the 20 students enrolled in a college class. Which of the following gives the correct order of the mean, median, and mode of the ages?

\n", "choices": [{"id": "A", "text": "

mode < median < mean

\n"}, {"id": "B", "text": "

mode < mean < median

\n"}, {"id": "C", "text": "

median < mode < mean

\n"}, {"id": "D", "text": "

mean < mode < median

\n"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. The mode is the data value with the highest frequency. So for the data shown, the mode is 18. The median is the middle data value when the data values are sorted from least to greatest. Since there are 20 ages ordered, the median is the average of the two middle values, the 10th and 11th, which for these data are both 19. Therefore, the median is 19. The mean is the sum of the data values divided by the number of the data values. So for these data, the mean is the fraction with numerator, open parenthesis, 18 \u00d7 6, close parenthesis, plus, open parenthesis, 19 \u00d7 5, close parenthesis, plus, open parenthesis, 20 \u00d7 4, close parenthesis, plus, open parenthesis, 21 \u00d7 2, close parenthesis, plus, open parenthesis, 22 \u00d7 1, close parenthesis, plus, open parenthesis, 23 \u00d7 1, close parenthesis, plus, open parenthesis, 30 \u00d7 1, close parenthesis, and denominator 20 = 20.

Since the mode is 18, the median is 19, and the mean is 20, mode < median, which < mean.

Choices B and D are incorrect because the mean is greater than the median. Choice C is incorrect because the median is greater than the mode.

Alternate approach: After determining the mode, 18, and the median, 19, it remains to determine whether the mean is less than 19 or more than 19. Because the mean is a balancing point, there is as much deviation below the mean as above the mean. It is possible to compare the data to 19 to determine the balance of deviation above and below the mean. There is a total deviation of only 6 below 19 (the 6 values of 18); however, the data value 30 alone deviates by 11 above 19. Thus the mean must be greater than 19.

\n"}, {"id": "1353b86e", "domain": "Problem-Solving and Data Analysis", "skill": "Probability and conditional probability", "difficulty": "E", "type": "mc", "stimulus": "
\n\t
\n\t\t
\n\t\t\t\n\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t
Colors of Marbles in a Bag
ColorNumber
Red8
Blue10
Green22
Total40
\n\t
\n
\n", "stem": "

The table shows the number of different colors of marbles in a bag. If a marble is chosen at random from the bag, what is the probability that the marble will be blue?

\n", "choices": [{"id": "A", "text": "

30 over 40

\n"}, {"id": "B", "text": "

22 over 40

\n"}, {"id": "C", "text": "

18 over 40

\n"}, {"id": "D", "text": "

10 over 40

\n"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. If a marble is chosen at random from the bag, the probability of choosing a marble of a certain color is the number of marbles of that color divided by the total number of marbles in the bag. Since there are 10 blue marbles in the bag, and there are 40 total marbles in the bag, the probability that the marble chosen will be blue is 10 over 40.

Choices A, B, and C are incorrect. These represent the probability that the marble chosen won’t be blue (choice A), will be green (choice B), and won’t be green (choice C).

 

\n"}, {"id": "d89c1513", "domain": "Problem-Solving and Data Analysis", "skill": "Probability and conditional probability", "difficulty": "E", "type": "mc", "stimulus": "
\n
\n
\n
\n
\n", "stem": "
\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n
Customer Purchases at a Gas Station
Beverage purchasedBeverage not purchasedTotal
Gasoline purchased602585
Gasoline not purchased351550
Total9040135

On Tuesday, a local gas station had 135 customers. The table above summarizes whether or not the customers on Tuesday purchased gasoline, a beverage, both, or neither. Based on the data in the table, what is the probability that a gas station customer selected at random on that day did not purchase gasoline?

\n", "choices": [{"id": "A", "text": "

\n 15 over 50\n

\n"}, {"id": "B", "text": "

\n 15 over 40\n

\n"}, {"id": "C", "text": "

\n 35 over 50\n

\n"}, {"id": "D", "text": "

\n 50 over 135\n

\n"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. The total number of gas station customers on Tuesday was 135. The table shows that the number of customers who did not purchase gasoline was 50. Finding the ratio of the number of customers who did not purchase gasoline to the total number of customers gives the probability that a customer selected at random on that day did not purchase gasoline, which is 50 over 135.

Choice A is incorrect and may result from finding the probability that a customer did not purchase a beverage, given that the customer did not purchase gasoline. Choice B is incorrect and may result from finding the probability that a customer did not purchase gasoline, given that the customer did not purchase a beverage. Choice C is incorrect and may result from finding the probability that a customer did purchase a beverage, given that the customer did not purchase gasoline.

\n"}, {"id": "52f9a246", "domain": "Problem-Solving and Data Analysis", "skill": "One-variable data: Distributions and measures of center and spread", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

4\n, 4\n, 4\n, 4\n, 8\n, 8\n, 8\n, 13\n, 13\n

\n

Which frequency table correctly represents the data listed?

", "choices": [{"id": "A", "text": "
\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
NumberFrequency
4\n4\n
8\n3\n
13\n2\n
"}, {"id": "B", "text": "
\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
NumberFrequency
4\n4\n
3\n8\n
2\n13\n
"}, {"id": "C", "text": "
\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
NumberFrequency
4\n16\n
8\n24\n
13\n26\n
"}, {"id": "D", "text": "
\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
NumberFrequency
16\n4\n
24\n8\n
26\n13\n
"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. A frequency table is a table that lists the data value and shows the number of times the data value occurs. In the data listed, the number 4\n occurs four times, the number 8\n occurs three times, and the number 13\n occurs two times. This corresponds to the table in choice A.

\n

Choice B is incorrect. This table has the values for number and frequency reversed.

\n

Choice C is incorrect because the frequency values don't represent the data listed.

\n

Choice D is incorrect. This table represents the listed number values as the frequency values.

"}, {"id": "a456cfd2", "domain": "Problem-Solving and Data Analysis", "skill": "One-variable data: Distributions and measures of center and spread", "difficulty": "M", "type": "spr", "stimulus": "", "stem": "
\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
Data valueFrequency
6\n3\n
7\n3\n
8\n8\n
9\n8\n
10\n9\n
11\n11\n
12\n9\n
13\n0\n
14\n6\n
\n

The frequency table summarizes the 57\n data values in a data set. What is the maximum data value in the data set?

", "choices": [], "answerId": "14", "acceptedAnswers": ["14"], "rationale": "

The correct answer is 14\n. The maximum value is the largest value in the data set. The frequency refers to the number of times a data value occurs. The given frequency table shows that for this data set, the data value 6\n occurs three times, the data value 7\n occurs three times, the data value 8\n occurs eight times, the data value 9\n occurs eight times, the data value 10\n occurs nine times, the data value 11\n occurs eleven times, the data value 12\n occurs nine times, the data value 13\n occurs zero times, and the data value 14\n occurs six times. Therefore, the maximum data value in the data set is 14\n.

"}, {"id": "e1ad3d41", "domain": "Problem-Solving and Data Analysis", "skill": "Probability and conditional probability", "difficulty": "M", "type": "mc", "stimulus": "
\n
\n \n
\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n
Coat colorEye color
\n Deep blueLight brownTotal
Cream-tortoiseshell161632
Chocolate12  416
Total282048
\n
\n", "stem": "

The data on the coat color and eye color for 48 Himalayan kittens available for adoption were collected and summarized in the table above. What fraction of the chocolate-colored kittens has deep blue eyes?

\n", "choices": [{"id": "A", "text": "(12)/(48)\n"}, {"id": "B", "text": "(12)/(28)\n"}, {"id": "C", "text": "(16)/(32)\n"}, {"id": "D", "text": "(12)/(16)\n"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. The table shows that there are a total of 16 kittens that have a chocolate-colored coat. Of the 16 with a chocolate-colored coat, 12 have deep blue eyes. Therefore, the fraction of chocolate-colored kittens with deep blue eyes is simply the ratio of those two numbers, or (12)/(16).

Choice A is incorrect; this is the fraction of all chocolate-colored kittens. Choice B is incorrect; this is the fraction of kittens with deep blue eyes that have a chocolate-colored coat. Choice C is incorrect; this is the fraction of cream-tortoiseshell-colored kittens with deep blue eyes.

\n"}, {"id": "3726e079", "domain": "Problem-Solving and Data Analysis", "skill": "Ratios, rates, proportional relationships, and units", "difficulty": "M", "type": "spr", "stimulus": "", "stem": "

If \n\t\n\t\t\n\t\t\tx\n\t\t\ty\n\t\t\n\t\n\t=\n\t4\n\n and \n\t\n\t\t\n\t\t\t\n\t\t\t\t24\n\t\t\t\tx\n\t\t\t\n\t\t\t\n\t\t\t\tn\n\t\t\t\ty\n\t\t\t\n\t\t\n\t\n\t=\n\t4\n\n, what is the value of n\n?

", "choices": [], "answerId": "24", "acceptedAnswers": ["24"], "rationale": "

The correct answer is 24\n. The equation 24xny=4 can be rewritten as 24nxy=4. It's given that \n\t\n\t\t\tx\n\t\t\ty\n\t\t\n\t=\n\t4\n\n. Substituting 4\n for \n\t\tx\n\t\ty\n\t\n in the equation 24nxy=4 yields 24n4=4. Multiplying both sides of this equation by n\n yields 244=4n. Dividing both sides of this equation by 4\n yields \n\t24\n\t=\n\tn\n\n. Therefore, the value of n\n is 24\n.

"}, {"id": "8baf2118", "domain": "Problem-Solving and Data Analysis", "skill": "Two-variable data: Models and scatterplots", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

The scatterplot shows the relationship between two variables, x\n and y\n. A line of best fit is also shown.

\n

\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n\n

\n

Which of the following equations best represents the line of best fit shown?

", "choices": [{"id": "A", "text": "

y=13.5+0.8x

"}, {"id": "B", "text": "

y=13.5-0.8x

"}, {"id": "C", "text": "

y=-13.5+0.8x

"}, {"id": "D", "text": "

y=-13.5-0.8x

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. The line of best fit shown intersects the y-axis at a positive y-value and has a negative slope. The graph of an equation of the form y=a+bx, where a\n and b\n are constants, intersects the y-axis at a y-value of a\n and has a slope of b\n. Of the given choices, only choice B represents a line that intersects the y-axis at a positive y-value, 13.5\n, and has a negative slope, -0.8\n.

\n

Choice A is incorrect. This equation represents a line that has a positive slope, not a negative slope.

\n

Choice C is incorrect. This equation represents a line that intersects the y-axis at a negative y-value, not a positive y-value, and has a positive slope, not a negative slope.

\n

Choice D is incorrect. This equation represents a line that intersects the y-axis at a negative y-value, not a positive y-value.

"}, {"id": "ac5b6558", "domain": "Problem-Solving and Data Analysis", "skill": "Two-variable data: Models and scatterplots", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

\"The

The scatterplot above shows the high temperature on a certain day and the elevation of 8 different locations in the Lake Tahoe Basin. A line of best fit for the data is also shown. What temperature is predicted by the line of best fit for a location in the Lake Tahoe Basin with an elevation of 8,500 feet?

\n", "choices": [{"id": "A", "text": "

37°F

\n"}, {"id": "B", "text": "

39°F

\n"}, {"id": "C", "text": "

41°F

\n"}, {"id": "D", "text": "

43°F

\n"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. The line of best fit passes through the point 8,500, 39. Therefore, the line of best fit predicts a temperature of 39°F for a location in Lake Tahoe Basin with an elevation of 8,500 feet.

Choice A is incorrect. This is the lowest temperature listed on the scatterplot, and the line of best fit never crosses this value for any of the elevations shown. Choice C is incorrect. According to the line of best fit, the temperature of 41°F is predicted for an elevation of slightly greater than 7,500 feet, not an elevation of 8,500 feet. Choice D is incorrect. According to the line of best fit, the temperature of 43°F is predicted for an elevation of roughly 6,700 feet, not an elevation of 8,500 feet.

\n"}, {"id": "46545dd6", "domain": "Problem-Solving and Data Analysis", "skill": "Probability and conditional probability", "difficulty": "E", "type": "mc", "stimulus": "
Number of High School Students Who
Completed Summer Internships
High schoolYear
20082009201020112012
Foothill8780757670
Valley4454657682
Total131134140152152
\n", "stem": "

The table above shows the number of students from two different high schools who completed summer internships in each of five years. No student attended both schools. Of the students who completed a summer internship in 2010, which of the following represents the fraction of students who were from Valley High School?

\n", "choices": [{"id": "A", "text": "

10 over 140

\n"}, {"id": "B", "text": "

65 over 140

\n"}, {"id": "C", "text": "

75 over 140

\n"}, {"id": "D", "text": "

65 over 75

\n"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. According to the table, 140 students from the two high schools completed summer internships in 2010. Of these, 65 were from Valley High School. Therefore, of the students who completed summer internships in 2010, (65)/(140) represents the fraction who were from Valley High School.

Choice A is incorrect. This is the difference between the numbers of students from the two high schools who completed internships in 2010 divided by the total number of students from the two schools who completed internships that year. Choice C is incorrect. This is the fraction of students from Foothill High School who completed internships out of all the students who completed internships in 2010. Choice D is incorrect. This is the number of students from Valley High School who completed internships in 2010 divided by the number of students from Foothill High School who completed internships in 2010.

\n"}, {"id": "16cea46c", "domain": "Problem-Solving and Data Analysis", "skill": "Probability and conditional probability", "difficulty": "E", "type": "mc", "stimulus": "
\n \n \n \n \n \n \n \n \n \n \n
Voice typeNumber of singers
Countertenor4
Tenor6
Baritone10
Bass5
\n", "stem": "

A total of 25 men registered for singing lessons. The frequency table shows how many of these singers have certain voice types. If one of these singers is selected at random, what is the probability he is a baritone?

\n", "choices": [{"id": "A", "text": "

0.10

\n"}, {"id": "B", "text": "

0.40

\n"}, {"id": "C", "text": "

0.60

\n"}, {"id": "D", "text": "

0.67

\n"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. This probability is calculated by dividing the number of baritone singers by the total number of men registered for singing lessons. It’s given that a total of 25 men registered for singing lessons and that there are 10 baritones. Therefore, the probability of selecting a baritone from this group at random is 10 over 25, which is equivalent to 0.40.

Choice A is incorrect. This would be the probability of selecting a baritone at random if there were 100 total men who registered for singing lessons. Choice C is incorrect. This is the probability of selecting a singer at random who isn’t a baritone. Choice D is incorrect. This would be the probability of selecting a baritone at random if there were 15 total men registered for singing lessons.

\n"}, {"id": "bd90f87e", "domain": "Problem-Solving and Data Analysis", "skill": "Percentages", "difficulty": "E", "type": "mc", "stimulus": "

A table of the US minimum wage for 6 different years is shown below.
YearUS minimum wage
  (dollars per hour)
19601.00
19701.60
19803.10
19903.80
20005.15
20107.25

 

\n", "stem": "

What was the percent increase of the minimum wage from 1960 to 1970?

\n", "choices": [{"id": "A", "text": "

30%

\n"}, {"id": "B", "text": "

60%

\n"}, {"id": "C", "text": "

62.5%

\n"}, {"id": "D", "text": "

120%

\n"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. According to the table, the minimum wage in 1960 was $1.00 per hour, and in 1970 it was $1.60 per hour. The percentage change is therefore 100 \u00d7 open parenthesis, (1 point 6 0 \u2212 1 point 0 0)/(1 point 0 0, close parenthesis = 60 percent).

Choice A is incorrect and may result from averaging the two wages before calculating the percentage change. Choice C is incorrect. This is the 1960 wage expressed as a percentage of the 1970 wage, not the percentage change between the two. Choice D is incorrect and may result from a calculation error.

\n"}, {"id": "312ba47c", "domain": "Problem-Solving and Data Analysis", "skill": "Ratios, rates, proportional relationships, and units", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

In a box of pens, the ratio of black pens to red pens is 8\n to 1\n. There are 40\n black pens in the box. How many red pens are in the box?

", "choices": [{"id": "A", "text": "

5\n

"}, {"id": "B", "text": "

8\n

"}, {"id": "C", "text": "

40\n

"}, {"id": "D", "text": "

320\n

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. It’s given that the ratio of black pens to red pens is 8\n to 1\n. Therefore, there are 18 as many red pens as black pens in the box. It’s also given that there are 40\n black pens in the box. Therefore, the number of red pens is 18 of the 40\n black pens. Thus, the number of red pens is 4018, or 5\n.

\n

Choice B is incorrect. This is the number of black pens in the box for every red pen.

\n

Choice C is incorrect. This is the number of black pens in the box.

\n

Choice D is incorrect. This is the number of red pens in the box if the ratio of black pens to red pens is 1\n to 8\n.

"}, {"id": "0ea56bb2", "domain": "Problem-Solving and Data Analysis", "skill": "Percentages", "difficulty": "H", "type": "mc", "stimulus": "
\n
\n \n
\n
\n \n \n \n \n \n \n
YearSubscriptions
\n\t\tsold
20125,600
20135,880
\n
\n
\n", "stem": "

The manager of an online news service received the report above on the number of subscriptions sold by the service. The manager estimated that the percent increase from 2012 to 2013 would be double the percent increase from 2013 to 2014. How many subscriptions did the manager expect would be sold in 2014?

\n", "choices": [{"id": "A", "text": "

6,020

\n"}, {"id": "B", "text": "

6,027

\n"}, {"id": "C", "text": "

6,440

\n"}, {"id": "D", "text": "

6,468

\n"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. The percent increase from 2012 to 2013 was (5,880 \u2212 5,600)/(5,600 = 0 point 0 5), or 5%. Since the percent increase from 2012 to 2013 was estimated to be double the percent increase from 2013 to 2014, the percent increase from 2013 to 2014 was expected to be 2.5%.
\nTherefore, the number of subscriptions sold in 2014 is expected to be the number of subscriptions sold in 2013 multiplied by 1 + 0 point 0 2 5, or 5,880 \u00d7 1 point 0 2 5 = 6,027.

Choice A is incorrect and is the result of adding half of the value of the increase from 2012 to 2013 to the 2013 result. Choice C is incorrect and is the result adding twice the value of the increase from 2012 to 2013 to the 2013 result. Choice D is incorrect and is the result of interpreting the percent increase from 2013 to 2014 as double the percent increase from 2012 to 2013.

\n"}, {"id": "15617f62", "domain": "Problem-Solving and Data Analysis", "skill": "Ratios, rates, proportional relationships, and units", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

The population density of Worthington is 290\n people per square mile. Worthington has a population of 92,800\n people. What is the area, in square miles, of Worthington?

", "choices": [{"id": "A", "text": "

102,400\n

"}, {"id": "B", "text": "

93,090\n

"}, {"id": "C", "text": "

320\n

"}, {"id": "D", "text": "

32\n

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. It’s given that the population density of Worthington is 290\n people per square mile and Worthington has a population of 92,800\n people. Therefore, the area of Worthington is 92,800 people1 square mile290 people, which is equivalent to 92,800 square miles290, or 320\n square miles.

\n

Choice A is incorrect and may result from conceptual or calculation errors.

\n

Choice B is incorrect and may result from conceptual or calculation errors.

\n

Choice D is incorrect and may result from conceptual or calculation errors.

"}, {"id": "8736334b", "domain": "Problem-Solving and Data Analysis", "skill": "One-variable data: Distributions and measures of center and spread", "difficulty": "E", "type": "mc", "stimulus": "
\n

\n Data set A consists(t)he 5 numbers: 72, 73, 73, 76, and 76. Data set B consists(t)he 5 numbers: 61, 64, 74, 85, and x.

\n
\n", "stem": "

Data set A and data set B each contain 5 numbers. If the mean of data set A is equal to the mean of data set B, what is the value of x ?

\n", "choices": [{"id": "A", "text": "

77

\n"}, {"id": "B", "text": "

85

\n"}, {"id": "C", "text": "

86

\n"}, {"id": "D", "text": "

95

\n"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. The mean of a data set is found by dividing the sum of the values in the data set by the number of values in the data set. Therefore, the mean of data set A is (72, + 73, + 73, + 76, + 76)/(5), which simplifies to 74. The mean of data set B is represented by the equation (61, + 64, + 74, + 85, + x)/(5), or (284 + x)/(5). It’s given that the mean of data set A is equal to the mean of data set B. Therefore, the equation 74 = (284 + x)/(5) can be used to solve for x. Multiplying both sides of this equation by 5 yields 370 = 284 + x. Subtracting 284 from both sides of this equation yields 86 = x.

Choices A, B, and D are incorrect and may result from calculation errors.

\n"}, {"id": "be35c117", "domain": "Problem-Solving and Data Analysis", "skill": "Ratios, rates, proportional relationships, and units", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

A wind turbine completes 900\n revolutions in 50\n minutes. At this rate, how many revolutions per minute does this turbine complete?

", "choices": [{"id": "A", "text": "

18\n

"}, {"id": "B", "text": "

850\n

"}, {"id": "C", "text": "

950\n

"}, {"id": "D", "text": "

1,400\n

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. Dividing the number of revolutions by the number of minutes gives the number of revolutions the turbine completes per minute. It’s given that the wind turbine completes 900\n revolutions in 50\n minutes. Therefore, at this rate, this turbine completes 90050, or 18\n, revolutions per minute.

\n

Choice B is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

\n

Choice D is incorrect and may result from conceptual or calculation errors.

"}, {"id": "4a2264b3", "domain": "Problem-Solving and Data Analysis", "skill": "Two-variable data: Models and scatterplots", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

The line graph shows the percent of cars for sale at a used car lot on a given day by model year.

\n

\n

For what model year is the percent of cars for sale the smallest?

", "choices": [{"id": "A", "text": "

2012

"}, {"id": "B", "text": "

2013

"}, {"id": "C", "text": "

2014

"}, {"id": "D", "text": "

2015

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. For the given line graph, the percent of cars for sale at a used car lot on a given day is represented on the vertical axis. The percent of cars for sale is the smallest when the height of the line graph is the lowest. The lowest height of the line graph occurs for cars with a model year of 2014.

\n

Choice A is incorrect and may result from conceptual errors.

\n

Choice B is incorrect and may result from conceptual errors.

\n

Choice D is incorrect and may result from conceptual errors.

"}, {"id": "b680e76d", "domain": "Problem-Solving and Data Analysis", "skill": "Probability and conditional probability", "difficulty": "E", "type": "mc", "stimulus": "
\n
\n
\n

A survey taken by 1,000 students at a school asked whether they played school sports. The table below summarizes all 1,000 responses from the students surveyed.

\n
\n
\n
\n \"The
\n
\n", "stem": "

How many of the males surveyed responded that they do not play a school sport?

\n", "choices": [{"id": "A", "text": "

109

\n"}, {"id": "B", "text": "

252

\n"}, {"id": "C", "text": "

468

\n"}, {"id": "D", "text": "

688

\n"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. The table summarizes all 1,000 responses from the students surveyed. If 312 are males who play a sport, 220 are females who play a sport, and 216 are females who do not play a sport, then 1,000 – 312 – 220 – 216 = 252 males who do not play a sport.

Choices A, C, and D are incorrect. If 109 males who do not play a sport responded, then the table summary would be 109 + 312 + 220 + 216 = 857 total student responses rather than 1,000. If 468 males who do not play a sport responded, then the table summary would be 468 + 312 + 220 + 216 = 1,216 total student responses rather than 1,000. If 688 males who do not play a sport responded, then the table summary would be 688 + 312 + 220 + 216 = 1,436 total student responses rather than 1,000.
\n 

\n"}, {"id": "53d97af5", "domain": "Problem-Solving and Data Analysis", "skill": "Inference from sample statistics and margin of error ", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

A study was done on the weights of different types of fish in a pond. A random sample of fish were caught and marked in order to ensure that none were weighed more than once. The sample contained 150 largemouth bass, of which 30% weighed more than 2 pounds. Which of the following conclusions is best supported by the sample data?

\n", "choices": [{"id": "A", "text": "

The majority of all fish in the pond weigh less than 2 pounds.

\n"}, {"id": "B", "text": "

The average weight of all fish in the pond is approximately 2 pounds.

\n"}, {"id": "C", "text": "

Approximately 30% of all fish in the pond weigh more than 2 pounds.

\n"}, {"id": "D", "text": "

Approximately 30% of all largemouth bass in the pond weigh more than 2 pounds.

\n"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

\n \n

Choice D is correct. The sample of 150 largemouth bass was selected at random from all the largemouth bass in the pond, and since 30% of the fish in the sample weighed more than 2 pounds, it can be concluded that approximately 30% of all largemouth bass in the pond weigh more than 2 pounds.

Choices A, B, and C are incorrect. Since the sample contained 150 largemouth bass, of which 30% weighed more than 2 pounds, this result can be generalized only to largemouth bass in the pond, not to all fish in the pond.

\n \n

\n"}, {"id": "0301c5dc", "domain": "Problem-Solving and Data Analysis", "skill": "Probability and conditional probability", "difficulty": "M", "type": "mc", "stimulus": "
\n\t
\n\t\t
\n\t\t\t

The table below shows the number of state parks in a certain state that contain camping facilities and bicycle paths.

\n\n\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t
 Has bicycle pathsDoes not have bicycle paths
Has camping facilities205
Does not have camping facilities84
\n\t
\n
\n", "stem": "

If one of these state parks is selected at random, what is the probability that it has camping facilities but does not have bicycle paths?

\n", "choices": [{"id": "A", "text": "

5 over 37

\n"}, {"id": "B", "text": "

5 over 25

\n"}, {"id": "C", "text": "

8 over 28

\n"}, {"id": "D", "text": "

5 over 9

\n"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. The total number of state parks in the state is 20, + 5, + 8, + 4 = 37. According to the table, 5 of these have camping facilities but not bicycle paths. Therefore, if a state park is selected at random, the probability that it has camping facilities but not bicycle paths is 5 over 37.

Choice B is incorrect. This is the probability that a state park selected at random from the state parks with camping facilities does not have bicycle paths. Choice C is incorrect. This is the probability that a state park selected at random from the state parks with bicycle paths does not have camping facilities. Choice D is incorrect. This is the probability that a state park selected at random from the state parks without bicycle paths does have camping facilities.

 

\n"}, {"id": "0ae37ff3", "domain": "Problem-Solving and Data Analysis", "skill": "Probability and conditional probability", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

In a bag, there are 7\n red, 4\n white, 33\n blue, and 33\n yellow cubes. If one of these cubes is selected at random, what is the probability of selecting a cube that is neither blue nor yellow?

", "choices": [{"id": "A", "text": "

67

"}, {"id": "B", "text": "

711

"}, {"id": "C", "text": "

13

"}, {"id": "D", "text": "

17

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. It’s given that there are 7\n red, 4\n white, 33\n blue, and 33\n yellow cubes in the bag. Therefore, there are a total of 7+4+33+33, or 77\n, cubes in the bag. If the cube is neither blue nor yellow, then it must be either red or white. Therefore, the probability of selecting a cube that is neither blue nor yellow is equivalent to the probability of selecting a cube that is either red or white. If one of these cubes is selected at random, the probability of selecting a cube that is either red or white is equal to the sum of the number of red cubes and white cubes divided by the total number of cubes in the bag. There are 7\n red cubes, 4\n white cubes, and 77\n total cubes in the bag. Therefore, the probability of selecting a red or white cube is 7+477, which is equivalent to 1177, or \n\t1\n\t7\n\n. Thus, if one cube is selected at random, the probability of selecting a cube that is neither blue nor yellow is \n\t1\n\t7\n\n.

\n

Choice A is incorrect. This is the probability of selecting a cube that is either blue or yellow, rather than the probability of selecting a cube that is neither blue nor yellow.

\n

Choice B is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

"}, {"id": "c88e0663", "domain": "Problem-Solving and Data Analysis", "skill": "One-variable data: Distributions and measures of center and spread", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

For a school fund-raiser, 10 students sold a total of 90 boxes of cookies. Which of the following can be calculated from this information?

\n", "choices": [{"id": "A", "text": "

The average number of boxes sold per student

\n"}, {"id": "B", "text": "

The median number of boxes sold per student

\n"}, {"id": "C", "text": "

The greatest number of boxes sold by one student

\n"}, {"id": "D", "text": "

The least number of boxes sold by one student

\n"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. The average can be found by dividing the total number of boxes sold by the number of students, which is (90)/(10 = 9).

Choices B, C, and D are incorrect. Each results from choosing measures that require the results of individual students, which are not given.

\n"}, {"id": "9bb4107c", "domain": "Problem-Solving and Data Analysis", "skill": "Two-variable data: Models and scatterplots", "difficulty": "M", "type": "spr", "stimulus": "", "stem": "

\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n\n

\n

The graph shows the momentum y\n, in newton-seconds, of an object x\n seconds after the object started moving, for 0≤x≤8. What is the average rate of change, in newton-seconds per second, in the momentum of the object from \n\tx\n\t=\n\t2\n\n to \n\tx\n\t=\n\t6\n\n?

", "choices": [], "answerId": ".5", "acceptedAnswers": [".5", "1/2"], "rationale": "

The correct answer is 12. For the graph shown, x\n represents time, in seconds, and y\n represents momentum, in newton-seconds. Therefore, the average rate of change, in newton-seconds per second, in the momentum of the object between two x-values is the difference in the corresponding y-values divided by the difference in the x-values. The graph shows that at \n\tx\n\t=\n\t2\n\n, the corresponding y-value is 6\n. The graph also shows that at \n\tx\n\t=\n\t6\n\n, the corresponding y-value is 8\n. It follows that the average rate of change, in newton-seconds per second, from \n\tx\n\t=\n\t2\n\n to \n\tx\n\t=\n\t6\n\n is 8-66-2, which is equivalent to 24, or 12. Note that 1/2 and .5 are examples of ways to enter a correct answer.

"}, {"id": "3f2ee20a", "domain": "Problem-Solving and Data Analysis", "skill": "One-variable data: Distributions and measures of center and spread", "difficulty": "M", "type": "mc", "stimulus": "
\n
\n
\n

The results of two independent surveys are shown in the table below.

\n \n \n \n \n \n \n \n \n \n \n \n \n \n
Men's Height
GroupSample sizeMean (centimeters)Standard deviation (centimeters)
A2,50018612.5
B2,500186 19.1
\n
\n
\n", "stem": "

Which statement is true based on the table?

\n", "choices": [{"id": "A", "text": "

The Group A data set was identical to the Group B data set.

\n"}, {"id": "B", "text": "

Group B contained the tallest participant.

\n"}, {"id": "C", "text": "

The heights of the men in Group B had a larger spread than the heights of the men in Group A.

\n"}, {"id": "D", "text": "

The median height of Group B is larger than the median height of Group A.

\n"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. Standard deviation is a measure of spread, so data sets with larger standard deviations tend to have larger spread. The standard deviation of the heights of the men in Group B is larger than the standard deviation of the heights of the men in Group A. Therefore, the heights of the men in Group B had a larger spread than the heights of the men in Group A.

Choice A is incorrect. If two data sets are identical, they will have equivalent means and equivalent standard deviations. Since the two data sets have different standard deviations, they cannot be identical. Choice B is incorrect. Without knowing the maximum value for each data set, it’s impossible to know which group contained the tallest participant. Choice D is incorrect. Since the means of the two groups are equivalent, the medians could also be the same or could be different, but it's impossible to tell from the given information.

\n"}, {"id": "d0efc1dd", "domain": "Problem-Solving and Data Analysis", "skill": "One-variable data: Distributions and measures of center and spread", "difficulty": "M", "type": "mc", "stimulus": "
\n\t

15, 14, 18, 17, x

\n
\n", "stem": "

The mean and the median of the five numbers above are equal. Which of the following is NOT a possible value of x ?

\n", "choices": [{"id": "A", "text": "

6

\n"}, {"id": "B", "text": "

11

\n"}, {"id": "C", "text": "

16

\n"}, {"id": "D", "text": "

21

\n"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. If x is 6, then the five numbers in the given list are 15, 14, 18, 17, 6. The mean of these five numbers is the sum of all the values divided by the number of values, or (15 + 14, + 18, + 17, + 6)/(5, end fraction = 70 over 5, which = 14). The median of these five numbers can be found by ordering the numbers from least to greatest and determining the middle value. When ordered from least to greatest, the numbers in the given list are 6, 14, 15, 17, 18, and the middle value is 15. Since the mean is 14 and the median is 15, the mean and median aren’t equal when x is 6.

Choices B, C, and D are incorrect. If any of these values is substituted for x, the mean and median of the data set would be equal.

 

\n"}, {"id": "e9fb7774", "domain": "Problem-Solving and Data Analysis", "skill": "Percentages", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

What percentage of 300\n is 75\n?

", "choices": [{"id": "A", "text": "

25\n%

"}, {"id": "B", "text": "

50\n%

"}, {"id": "C", "text": "

75\n%

"}, {"id": "D", "text": "

225\n%

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. Let x\n represent the percentage of 300\n that is 75\n. This can be written as x100300=75, or \n\t\n\t\t3\n\t\tx\n\t\n\t=\n\t75\n\n. Dividing both sides of this equation by 3\n yields \n\tx\n\t=\n\t25\n\n. Therefore, 25% of 300\n is 75\n.

\n

Choice B is incorrect. 50% of 300\n is 150\n, not 75\n.

\n

Choice C is incorrect. 75% of 300\n is 225\n, not 75\n.

\n

Choice D is incorrect. 225% of 300\n is 675\n, not 75\n.

"}, {"id": "190be2fc", "domain": "Problem-Solving and Data Analysis", "skill": "One-variable data: Distributions and measures of center and spread", "difficulty": "H", "type": "spr", "stimulus": "", "stem": "

Data set A consists of 10\n positive integers less than 60\n. The list shown gives 9\n of the integers from data set A.

\n

43\n, 45\n, 44\n, 43\n, 38\n, 39\n, 40\n, 46\n, 40\n

\n

The mean of these 9\n integers is 42\n. If the mean of data set A is an integer that is greater than 42\n, what is the value of the largest integer from data set A?

", "choices": [], "answerId": "52", "acceptedAnswers": ["52"], "rationale": "

The correct answer is 52\n. The mean of a data set is calculated by dividing the sum of the data values by the number of values. It’s given that data set A consists of 10\n values, 9\n of which are shown. Let x\n represent the 10th data value in data set A, which isn’t shown. The mean of data set A can be found using the expression 43+45+44+43+38+39+40+46+40+x10, or 378+x10. It’s given that the mean of the 9\n values shown is 42\n and that the mean of all 10\n numbers is greater than 42\n. Consequently, the 10th data value, x\n, is larger than 42\n. It’s also given that the data values in data set A are positive integers less than 60\n. Thus, 42<x<60. Finally, it’s given that the mean of data set A is an integer. This means that the sum of the 10\n data values, 378+x, is divisible by 10\n. Thus, 378+x must have a ones digit of 0\n. It follows that x\n must have a ones digit of 2\n. Since 42<x<60 and x\n has a ones digit of 2\n, the only possible value of x\n is 52\n. Since 52\n is larger than any of the integers shown, the largest integer from data set A is 52\n.

"}, {"id": "3f236a64", "domain": "Problem-Solving and Data Analysis", "skill": "Ratios, rates, proportional relationships, and units", "difficulty": "E", "type": "mc", "stimulus": "
\n
\n \n \n \n \n \n \n \n \n \n \n
\n x\n \n y\n
14
312
520
40\n k\n
\n
\n", "stem": "

In the table above, the ratio of y to x for each ordered pair is constant. What is the value of k ?

\n", "choices": [{"id": "A", "text": "

28

\n"}, {"id": "B", "text": "

36

\n"}, {"id": "C", "text": "

80

\n"}, {"id": "D", "text": "

160

\n"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. Since the ratio of y to x is constant for each ordered pair in the table, the first row can be used to determine that the ratio of y to x is 4 to 1. The proportion 4 over 1 = k over 40 can be used to solve for k. Multiplying each side of the equation by 40 yields 160 = k.

Choice A is incorrect. This is the value of y when the value of x is 7, not 40. Choice B is incorrect and may result from subtracting 4 from 40 instead of multiplying 40 by 4. Choice C is incorrect and may result from incorrectly setting up the proportion.

\n"}, {"id": "8705ecba", "domain": "Problem-Solving and Data Analysis", "skill": "Percentages", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

The cost of a certain shirt is $20 before a 5% sales tax is added. What is the total cost, including sales tax, to purchase the shirt?

\n", "choices": [{"id": "A", "text": "

$20.05

\n"}, {"id": "B", "text": "

$20.50

\n"}, {"id": "C", "text": "

$21.00

\n"}, {"id": "D", "text": "

$25.00

\n"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. The total cost to purchase the shirt is the $20 cost of the shirt plus the 5% sales tax. The value of the 5% sales tax on the $20 shirt is equivalent to0 point 0 5 \u00d7 20 dollars, or $1. Therefore, the total cost to purchase the shirt is 20 dollars + 1 dollar, or $21.

Choice A is incorrect and may result from neglecting to multiply by $20 when finding the value of the sales tax. Choice B is incorrect and may result from dividing by 10, instead of by 100, and then neglecting to multiply by $20 when finding the sales tax. Choice D is incorrect and may result from interpreting the sales tax of 5% as $5.

\n"}, {"id": "2e74e403", "domain": "Problem-Solving and Data Analysis", "skill": "Two-variable data: Models and scatterplots", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

In the given scatterplot, a line of best fit for the data is shown.

\n

\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n\n

\n

Which of the following is closest to the slope of this line of best fit?

", "choices": [{"id": "A", "text": "

7\n

"}, {"id": "B", "text": "

0.7\n

"}, {"id": "C", "text": "

-0.7\n

"}, {"id": "D", "text": "

-7\n

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. A line of best fit is shown in the scatterplot such that as the value of x\n increases, the value of y\n decreases. It follows that the slope of the line of best fit shown is negative. The slope of a line in the xy-plane that passes through the points x1,y1 and x2,y2 can be calculated as y2-y1x2-x1. The line of best fit shown passes approximately through the points 0,8 and 10,1. Substituting 0,8 for x1,y1 and 10,1 for x2,y2 in y2-y1x2-x1 yields the slope of the line being approximately 1-810-0, which is equivalent to -710, or -0.7. Therefore, of the given choices, -0.7 is the closest to the slope of this line of best fit.

\n

Choice A is incorrect. The line of best fit shown has a negative slope, not a positive slope.

\n

Choice B is incorrect. The line of best fit shown has a negative slope, not a positive slope.

\n

Choice D is incorrect and may result from conceptual or calculation errors.

"}, {"id": "f8f79e11", "domain": "Problem-Solving and Data Analysis", "skill": "Inference from sample statistics and margin of error ", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

A park ranger asked a random sample of visitors how far they hiked during their visit. Based on the responses, the estimated mean was found to be 4.5 miles, with an associated margin of error of 0.5 miles. Which of the following is the best conclusion from these data?

\n", "choices": [{"id": "A", "text": "

It is likely that all visitors hiked between 4 and 5 miles.

\n"}, {"id": "B", "text": "

It is likely that most visitors hiked exactly 4.5 miles.

\n"}, {"id": "C", "text": "

It is not possible that any visitor hiked less than 3 miles.

\n"}, {"id": "D", "text": "

It is plausible that the mean distance hiked for all visitors is between 4 and 5 miles.

\n"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. The given estimated mean has an associated margin of error because from sample data, the population mean can’t be determined precisely. Rather, from the sample mean, an interval can be determined within which it’s plausible that the population’s mean is likely to lie. Since the estimated mean is 4.5 miles with an associated margin of error of 0.5 miles, it follows that between 4 point 5 \u2212 0 point 5 miles and 4 point 5 + 0 point 5 miles, or between 4 and 5 miles, is plausibly the mean distance hiked for all visitors.

Choices A, B, and C are incorrect. Based on the estimated mean, no determination can be made about the number of miles hiked for all visitors to the park.

\n"}, {"id": "707db2d3", "domain": "Problem-Solving and Data Analysis", "skill": "Percentages", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

For the finale of a TV show, viewers could use either social media or a text message to vote for their favorite of two contestants. The contestant receiving more than 50% of the vote won. An estimated 10% of the viewers voted, and 30% of the votes were cast on social media. Contestant 2 earned 70% of the votes cast using social media and 40% of the votes cast using a text message. Based on this information, which of the following is an accurate conclusion?

\n", "choices": [{"id": "A", "text": "

If all viewers had voted, Contestant 2 would have won.

\n"}, {"id": "B", "text": "

Viewers voting by social media were likely to be younger than viewers voting by text message.

\n"}, {"id": "C", "text": "

If all viewers who voted had voted by social media instead of by text message, Contestant 2 would have won.

\n"}, {"id": "D", "text": "

Viewers voting by social media were more likely to prefer Contestant 2 than were viewers voting by text message.

\n"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. It is given that Contestant 2 earned 70% of the votes cast using social media and 40% of the votes cast using a text message. Based on this information, viewers voting by social media were more likely to prefer Contestant 2 than were viewers voting by text message.

Choices A, B, and C are incorrect. There is not enough information about the viewers to reach these conclusions.

\n"}, {"id": "c178d4da", "domain": "Problem-Solving and Data Analysis", "skill": "One-variable data: Distributions and measures of center and spread", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "
\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
ValueData set A frequencyData set B frequency
30\n2\n9\n
34\n4\n7\n
38\n5\n5\n
42\n7\n4\n
46\n9\n2\n
\n

Data set A and data set B each consist of 27\n values. The table shows the frequencies of the values for each data set. Which of the following statements best compares the means of the two data sets?

", "choices": [{"id": "A", "text": "

The mean of data set A is greater than the mean of data set B.

"}, {"id": "B", "text": "

The mean of data set A is less than the mean of data set B.

"}, {"id": "C", "text": "

The mean of data set A is equal to the mean of data set B.

"}, {"id": "D", "text": "

There is not enough information to compare the means of the data sets.

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. The mean value of a data set is the sum of the values of the data set divided by the number of values in the data set. When a data set is represented in a frequency table, the sum of the values in the data set is the sum of the products of each value and its frequency. For data set A, the sum of products of each value and its frequency is 302+344+385+427+469, or 1,094. It's given that there are 27\n values in data set A. Therefore, the mean of data set A is 1,09427, or approximately 40.52. Similarly, the mean of data B is 95827, or approximately 35.48. Therefore, the mean of data set A is greater than the mean of data set B.

\n

Choice B is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

\n

Choice D is incorrect and may result from conceptual or calculation errors.

"}, {"id": "9a144a01", "domain": "Problem-Solving and Data Analysis", "skill": "Two-variable data: Models and scatterplots", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

Which of the following is true about the values of 2 to the x power and 2 x + 2 for x greater than 0?

\n", "choices": [{"id": "A", "text": "

For all x greater than 0, it is true that 2 to the x power, < 2 x + 2.

\n"}, {"id": "B", "text": "

For all x greater than 0, it is true that 2 to the x power, > 2 x + 2.

\n"}, {"id": "C", "text": "

There is a constant c such that if 0 < x, which < c, then 2 to the x power, < 2 x + 2, but if x > c, then 2 to the x power, > 2 x + 2.

\n"}, {"id": "D", "text": "

There is a constant c such that if 0 < x, which < c, then 2 to the x power, > 2 x + 2, but if x > c, then 2 to the x power, < 2 x + 2.

\n"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. At x = 0, the value of 2 raised to the x power is less than the value of 2 x + 2, where 2 to the 0 power is less than, 2 \u00d7 0, + 2, which is equivalent to 1 < 2. As the value of x increases, the value of 2 raised to the x power remains less than the value of 2 x + 2 until x = 3, which is when the two values are equal: 2\u00b3 = 2 \u00d7 3, + 2, which is equivalent to 8 is equal to 8. Then, for x greater than 3, the value of 2 raised to the x power is greater than the value of 2 x + 2. So there is a constant, 3, such that when 0 < x, which < 3, then 2 raised to the x power is less than, 2 x + 2, but when x > 3, then 2 raised to the x power is greater than, 2 x + 2.

Choice A is incorrect because 2 raised to the x power is greater than, 2 x + 2 when x > 3. Choice B is incorrect because 2 raised to the x power is less than, 2 x + 2 when 0 < x, which < 3. Choice D is incorrect because 2 raised to the x power is less than, 2 x + 2 when 0 < x, which < 3 and 2 raised to the x power is greater than, 2 x + 2 when x > 3.

 

\n"}, {"id": "457d2f2c", "domain": "Problem-Solving and Data Analysis", "skill": "One-variable data: Distributions and measures of center and spread", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

A data set of 27 different numbers has a mean of 33 and a median of 33. A new data set is created by adding 7 to each number in the original data set that is greater than the median and subtracting 7 from each number in the original data set that is less than the median. Which of the following measures does NOT have the same value in both the original and new data sets?

\n", "choices": [{"id": "A", "text": "

Median

\n"}, {"id": "B", "text": "

Mean

\n"}, {"id": "C", "text": "

Sum of the numbers

\n"}, {"id": "D", "text": "

Standard deviation

\n"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. When a data set has an odd number of elements, the median can be found by ordering the values from least to greatest and determining the middle value. Out of the 27 different numbers in this data set, 13 numbers are below the median, one number is exactly 33, and 13 numbers are above the median. When 7 is subtracted from each number below the median and added to each number above the median, the data spread out from the median. Since the median of this data set, 33, is equivalent to the mean of the data set, the data also spread out from the mean. Since standard deviation is a measure of how spread out the data are from the mean, a greater spread from the mean indicates an increased standard deviation.

Choice A is incorrect. All the numbers less than the median decrease and all the numbers greater than the median increase, but the median itself doesn’t change. Choices B and C are incorrect. The mean of a data set is found by dividing the sum of the values by the number of values. The net change from subtracting 7 from 13 numbers and adding 7 to 13 numbers is zero. Therefore, neither the mean nor the sum of the numbers changes.

 

\n"}, {"id": "c9fb15ad", "domain": "Problem-Solving and Data Analysis", "skill": "Ratios, rates, proportional relationships, and units", "difficulty": "H", "type": "mc", "stimulus": "

 

Species of treeGrowth factor
Red maple4.5
River birch3.5
Cottonwood2.0
Black walnut4.5
White birch5.0
American elm4.0
Pin oak3.0
Shagbark hickory7.5
\n", "stem": "

One method of calculating the approximate age, in years, of a tree of a particular species is to multiply the diameter of the tree, in inches, by a constant called the growth factor for that species. The table above gives the growth factors for eight species of trees. If a white birch tree and a pin oak tree each now have a diameter of 1 foot, which of the following will be closest to the difference, in inches, of their diameters 10 years from now? (1 foot = 12 inches)

\n", "choices": [{"id": "A", "text": "

1.0

\n"}, {"id": "B", "text": "

1.2

\n"}, {"id": "C", "text": "

1.3

\n"}, {"id": "D", "text": "

1.4

\n"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. According to the given information, multiplying a tree species’ growth factor by the tree’s diameter is a method to approximate the age of the tree. A white birch with a diameter of 12 inches (or 1 foot) has a given growth factor of 5 and is approximately 60 years old. A pin oak with a diameter of 12 inches (or 1 foot) has a given growth factor of 3 and is approximately 36 years old. The diameters of the two trees 10 years from now can be found by dividing each tree’s age in 10 years, 70 years, and 46 years, by its respective growth factor. This yields 14 inches and 15 and one third inches. The difference between 15 and one third and 14 is 1 and one third, or approximately 1.3 inches.

Alternate approach: Since a white birch has a growth factor of 5, the age increases at a rate of 5 years per inch or, equivalently, the diameter increases at a rate of one fifth of an inch per year. Likewise, the pin oak has a growth factor of 3, so its diameter increases at a rate of one third of an inch per year. Thus, the pin oak grows two fifteenths of an inch per year more than the white birch. In 10 years it will grow two fifteenths \u00d7 10 = four thirds of an inch more, which is approximately 1.3 inches.

Choices A, B, and D are incorrect and a result of incorrectly calculating the diameters of the two trees in 10 years.

\n"}, {"id": "47624288", "domain": "Problem-Solving and Data Analysis", "skill": "Probability and conditional probability", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

The table gives the distribution of votes for a new school mascot and grade level for 80\n students.

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
MascotGrade level
SixthSeventhEighthTotal
Badger4\n9\n9\n22\n
Lion9\n2\n9\n20\n
Longhorn4\n6\n4\n14\n
Tiger6\n9\n9\n24\n
Total23\n26\n31\n80\n
\n

If one of these students is selected at random, what is the probability of selecting a student whose vote for new mascot was for a lion? 

", "choices": [{"id": "A", "text": "

\n\t1\n\t9\n\n

"}, {"id": "B", "text": "

\n\t1\n\t5\n\n

"}, {"id": "C", "text": "

\n\t1\n\t4\n\n

"}, {"id": "D", "text": "

\n\t2\n\t3\n\n

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. If one of these students is selected at random, the probability of selecting a student whose vote for the new mascot was for a lion is given by the number of votes for a lion divided by the total number of votes. The given table indicates that the number of votes for a lion is 20\n votes, and the total number of votes is 80\n votes. The table gives the distribution of votes for 80\n students, and the table shows a total of 80 votes were counted. It follows that each of the 80\n students voted exactly once. Thus, the probability of selecting a student whose vote for the new mascot was for a lion is 2080, or 14.

\n

Choice A is incorrect and may result from conceptual or computational errors.

\n

Choice B is incorrect and may result from conceptual or computational errors.

\n

Choice D is incorrect and may result from conceptual or computational errors.

"}, {"id": "6310adbc", "domain": "Problem-Solving and Data Analysis", "skill": "Ratios, rates, proportional relationships, and units", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

The ratio of t to u is 1 to 2, and t = 10. What is the value of u ?

\n", "choices": [{"id": "A", "text": "

2

\n"}, {"id": "B", "text": "

5

\n"}, {"id": "C", "text": "

10

\n"}, {"id": "D", "text": "

20

\n"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. It’s given that the ratio of t to u is 1 to 2. Since t = 10, it follows that the ratio of 10 to u is also 1 to 2. The relationship between these ratios can be represented by the proportion 10 over u = one half. Multiplying both sides of this equation by 2 and then by u yields 20 = u.

Choice A is incorrect. This is the value of u when t = 1. Choice B is incorrect. This would be the value of u if the ratio of t to u were 2 to 1. Choice C is incorrect. This is the value of t, not u.

\n"}, {"id": "63573fea", "domain": "Problem-Solving and Data Analysis", "skill": "Percentages", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

During the first month of sales, a company sold 1,300,000 units of a certain type of smartphone. During the same month, 15% of the units sold were returned. If sales and the return rate remain the same for each of the next 5 months, about how many units of this smartphone will be returned to the company during this 6-month period?

\n", "choices": [{"id": "A", "text": "

195,000

\n"}, {"id": "B", "text": "

975,000

\n"}, {"id": "C", "text": "

1,170,000

\n"}, {"id": "D", "text": "

6,630,000

\n"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. Of the 1,300,000 units sold during the first month, 15% were returned, so 1,300,000 \u00d7 0 point 1 5 = 195,000 units were returned during the first month. If the units were sold and returned at the same rate for the next 5 months, then a total of 195,000 \u00d7 6 = 1,170,000 smartphone units were returned during the 6-month period.

Choice A is incorrect. This is the number of units that were returned in 1 month. Choice B is incorrect. This is the number of units that were returned in 5 months. Choice D is incorrect. This is the number of units sold and not returned during the first 6 months.

\n"}, {"id": "191d167b", "domain": "Problem-Solving and Data Analysis", "skill": "Percentages", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

Last year, 200\n students enrolled in an interior design program. This year, the number of students enrolled is 147% of last year’s number. How many students are enrolled in the interior design program this year?

", "choices": [{"id": "A", "text": "

247\n

"}, {"id": "B", "text": "

294\n

"}, {"id": "C", "text": "

347\n

"}, {"id": "D", "text": "

394\n

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. It's given that the number of students enrolled in an interior design program this year is 147% of last year's number, which is 200\n. 147% of 200\n can be expressed as 147100200, or 1.47200, which is equivalent to 294\n. Therefore, 294\n students are enrolled in the interior design program this year.

\n

Choice A is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

\n

Choice D is incorrect and may result from conceptual or calculation errors.

"}, {"id": "03a16790", "domain": "Problem-Solving and Data Analysis", "skill": "Two-variable data: Models and scatterplots", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

The scatterplot shows the relationship between two variables, x\n and y\n. A line of best fit is also shown.

\n

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n

\n

Which of the following is closest to the slope of the line of best fit shown?

", "choices": [{"id": "A", "text": "

-2.4\n

"}, {"id": "B", "text": "

-0.8\n

"}, {"id": "C", "text": "

0.8\n

"}, {"id": "D", "text": "

2.4\n

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. A line of best fit is shown in the scatterplot such that as the value of x\n increases, the value of y\n decreases. Thus, the slope of the line of best fit shown is negative. The slope of a line passing through two points, x1,y1 and x2,y2, can be calculated as y2-y1x2-x1. The line of best fit shown passes approximately through the points 1,12 and 11,4. Substituting 1,12 and 11,4 for x1,y1 and x2,y2, respectively, in y2-y1x2-x1 gives 4-1211-1, which is equivalent to -810, or -0.8. Therefore, of the given choices, -0.8 is closest to the slope of the line of best fit shown.

\n

Choice A is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect. The line of best fit shown has a negative slope, not a positive slope.

\n

Choice D is incorrect. The line of best fit shown has a negative slope, not a positive slope.

"}, {"id": "60caadfd", "domain": "Problem-Solving and Data Analysis", "skill": "Probability and conditional probability", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

Each rock in a collection of 70\n rocks was classified as either igneous, metamorphic, or sedimentary, as shown in the frequency table.

\n
\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
ClassificationFrequency
igneous10\n
metamorphic33\n
sedimentary27\n
\n

If one of these rocks is selected at random, what is the probability of selecting a rock that is igneous?

", "choices": [{"id": "A", "text": "

1027

"}, {"id": "B", "text": "

1033

"}, {"id": "C", "text": "

1060

"}, {"id": "D", "text": "

1070

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. If one of the rocks in the collection is selected at random, the probability of selecting a rock that is igneous is equal to the number of igneous rocks in the collection divided by the total number of rocks in the collection. According to the table, there are 10\n igneous rocks in the collection, and it's given that there's a total of 70\n rocks in the collection. Therefore, if one of the rocks in the collection is selected at random, the probability of selecting a rock that is igneous is 1070.

\n

Choice A is incorrect. This is the number of igneous rocks in the collection divided by the number of sedimentary rocks in the collection, not divided by the total number of rocks in the collection.

\n

Choice B is incorrect. This is the number of igneous rocks in the collection divided by the number of metamorphic rocks in the collection, not divided by the total number of rocks in the collection.

\n

Choice C is incorrect. This is the number of igneous rocks in the collection divided by the number of rocks in the collection that aren't igneous, not divided by the total number of rocks in the collection.

"}, {"id": "b4f5a7ca", "domain": "Problem-Solving and Data Analysis", "skill": "Evaluating statistical claims: Observational studies and experiments ", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

A survey was conducted using a sample of history professors selected at random from the California State Universities. The professors surveyed were asked to name the publishers of their current texts. What is the largest population to which the results of the survey can be generalized?

\n", "choices": [{"id": "A", "text": "

All professors in the United States

\n"}, {"id": "B", "text": "

All history professors in the United States

\n"}, {"id": "C", "text": "

All history professors at all California State Universities

\n"}, {"id": "D", "text": "

All professors at all California State Universities

\n"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. Selecting a sample at random when conducting a survey allows the results to be generalized to the population from which the sample was selected, but not beyond this population. In this situation, the population that the sample was selected from is history professors from the California State Universities. Therefore, the largest population to which the results of the survey can be generalized is all history professors at all California State Universities.

Choices A, B, and D are incorrect. Since the sample was selected at random from history professors from the California State Universities, the results of the survey can’t be generalized to all professors in the United States, all history professors in the United States, or all professors at all California State Universities. All three of these populations may use different texts and therefore may name different publishers.

 

\n"}, {"id": "d6af3572", "domain": "Problem-Solving and Data Analysis", "skill": "Two-variable data: Models and scatterplots", "difficulty": "H", "type": "mc", "stimulus": "
\n
\n
\n
\n
\n
\n
\n", "stem": "
\n \"The

The scatterplot above shows the federal-mandated minimum wage every 10 years between 1940 and 2010. A line of best fit is shown, and its equation is y = 0 point 0 9 6 x, \u2212 0 point 4 8 8. What does the line of best fit predict about the increase in the minimum wage over the 70-year period?

\n", "choices": [{"id": "A", "text": "

Each year between 1940 and 2010, the average increase in minimum wage was 0.096 dollars.

\n"}, {"id": "B", "text": "

Each year between 1940 and 2010, the average increase in minimum wage was 0.49 dollars.

\n"}, {"id": "C", "text": "

Every 10 years between 1940 and 2010, the average increase in minimum wage was 0.096 dollars.

\n"}, {"id": "D", "text": "

Every 10 years between 1940 and 2010, the average increase in minimum wage was 0.488 dollars.

\n"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. The given equation is in slope-intercept form, or y = m x + b, where m is the value of the slope of the line of best fit. Therefore, the slope of the line of best fit is 0.096. From the definition of slope, it follows that an increase of 1 in the x-value corresponds to an increase of 0.096 in the y-value. Therefore, the line of best fit predicts that for each year between 1940 and 2010, the minimum wage will increase by 0.096 dollar per hour.

Choice B is incorrect and may result from using the y-coordinate of the y-intercept as the average increase, instead of the slope. Choice C is incorrect and may result from using the 10-year increments given on the x-axis to incorrectly interpret the slope of the line of best fit. Choice D is incorrect and may result from using the y-coordinate of the y-intercept as the average increase, instead of the slope, and from using the 10-year increments given on the x-axis to incorrectly interpret the slope of the line of best fit.

\n"}, {"id": "2d16d62c", "domain": "Problem-Solving and Data Analysis", "skill": "Ratios, rates, proportional relationships, and units", "difficulty": "E", "type": "spr", "stimulus": "", "stem": "

A special camera is used for underwater ocean research. When the camera is at a depth of 58\n fathoms, what is the camera's depth in feet? 1 fathom=6 feet

", "choices": [], "answerId": "348", "acceptedAnswers": ["348"], "rationale": "

The correct answer is 348\n. It's given that 1\n fathom is equivalent to 6\n feet. Therefore, 58\n fathoms is equivalent to 58 fathoms6 feet1 fathom, or 348\n feet. Thus, when the camera is at a depth of 58\n fathoms, the camera's depth, in feet, is 348\n.

"}, {"id": "69f6717f", "domain": "Problem-Solving and Data Analysis", "skill": "Ratios, rates, proportional relationships, and units", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

A sample of oak has a density of 807\n kilograms per cubic meter. The sample is in the shape of a cube, where each edge has a length of 0.90 meters. To the nearest whole number, what is the mass, in kilograms, of this sample? 

", "choices": [{"id": "A", "text": "

588\n

"}, {"id": "B", "text": "

726\n

"}, {"id": "C", "text": "

897\n

"}, {"id": "D", "text": "

1,107\n

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. It’s given that the sample is in the shape of a cube with edge lengths of 0.9\n meters. Therefore, the volume of the sample is 0.903, or 0.729\n, cubic meters. It’s also given that the sample has a density of 807\n kilograms per 1\n cubic meter. Therefore, the mass of this sample is 0.729 cubic meters807 kilograms1 cubic meter, or 588.303\n kilograms. Rounding this mass to the nearest whole number gives 588\n kilograms. Therefore, to the nearest whole number, the mass, in kilograms, of this sample is 588\n.

\n

Choice B is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

\n

Choice D is incorrect and may result from conceptual or calculation errors.

"}, {"id": "35bec412", "domain": "Problem-Solving and Data Analysis", "skill": "One-variable data: Distributions and measures of center and spread", "difficulty": "E", "type": "spr", "stimulus": "", "stem": "

73\n, 74\n, 75\n, 77\n, 79\n, 82\n, 84\n, 85\n, 91\n

\n

What is the median of the data shown?

", "choices": [], "answerId": "79", "acceptedAnswers": ["79"], "rationale": "

The correct answer is 79\n. The median of a data set with an odd number of values is the middle value of the set when the values are ordered from least to greatest. Because the given data set consists of nine values that are ordered from least to greatest, the median is the fifth value in the data set. Therefore, the median of the data shown is 79\n.

"}, {"id": "74dee52b", "domain": "Problem-Solving and Data Analysis", "skill": "Two-variable data: Models and scatterplots", "difficulty": "E", "type": "mc", "stimulus": "
\n
\n
\n
\n \"The
\n
\n
\n
\n", "stem": "

The line graph shows the number of graduates from the classes of 2001 through 2007 at a certain school who enrolled in college within 24 months of graduation. Of the following, which class had the fewest graduates who enrolled in college within 24 months of graduation?

\n", "choices": [{"id": "A", "text": "

2002

\n"}, {"id": "B", "text": "

2004

\n"}, {"id": "C", "text": "

2005

\n"}, {"id": "D", "text": "

2007

\n"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. The year with the fewest graduates who enrolled in college within 24 months of graduation is the point with the lowest value on the vertical axis. This occurs at 2002.

Choice B, C, and D are incorrect. The years 2004, 2005, and 2007 each had a greater number of graduates who enrolled in college within 24 months of graduation than did the year 2002.

\n"}, {"id": "aeeaec96", "domain": "Problem-Solving and Data Analysis", "skill": "Ratios, rates, proportional relationships, and units", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

How many yards are equivalent to 612\n inches? 1 yard=36 inches

", "choices": [{"id": "A", "text": "

0.059\n

"}, {"id": "B", "text": "

17\n

"}, {"id": "C", "text": "

576\n

"}, {"id": "D", "text": "

22,032\n

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. It’s given that 1 yard=36 inches. Therefore, 612\n inches is equivalent to 612 inches1 yard36 inches, which can be rewritten as 612 yards36, or 17\n yards.

\n

Choice A is incorrect. This is the number of yards that are equivalent to 2.124\n inches.

\n

Choice C is incorrect. This is the number of yards that are equivalent to 20,736\n inches.

\n

Choice D is incorrect. This is the number of yards that are equivalent to 793,152\n inches.

"}, {"id": "9d88a3e3", "domain": "Problem-Solving and Data Analysis", "skill": "Two-variable data: Models and scatterplots", "difficulty": "E", "type": "mc", "stimulus": "
\n
\n \"The
\n
\n", "stem": "

Theresa ran on a treadmill for thirty minutes, and her time and speed are shown on the graph above. According to the graph, which of the following statements is NOT true concerning Theresa’s run?

\n", "choices": [{"id": "A", "text": "

Theresa ran at a constant speed for five minutes.

\n"}, {"id": "B", "text": "

Theresa’s speed was increasing for a longer period of time than it was decreasing.

\n"}, {"id": "C", "text": "

Theresa’s speed decreased at a constant rate during the last five minutes.

\n"}, {"id": "D", "text": "

Theresa’s speed reached its maximum during the last ten minutes.

\n"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. Theresa’s speed was increasing from 0 to 5 minutes and from 20 to 25 minutes, which is a total of 10 minutes. Theresa’s speed was decreasing from 10 minutes to 20 minutes and from 25 to 30 minutes, which is a total of 15 minutes. Therefore, Theresa’s speed was NOT increasing for a longer period of time than it was decreasing.

Choice A is incorrect. Theresa ran at a constant speed for the 5-minute period from 5 to 10 minutes. Choice C is incorrect. Theresa’s speed decreased at a constant rate during the last 5 minutes, which can be seen since the graph is linear during that time. Choice D is incorrect. Theresa’s speed reached its maximum at 25 minutes, which is within the last 10 minutes.

\n"}, {"id": "e03f3477", "domain": "Problem-Solving and Data Analysis", "skill": "Inference from sample statistics and margin of error ", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

A sample consisting of 720\n adults who own televisions was selected at random for a study. Based on the sample, it is estimated that 32\n% of all adults who own televisions use their televisions to watch nature shows, with an associated margin of error of 3.41\n%. Which of the following is the most plausible conclusion about all adults who own televisions?

", "choices": [{"id": "A", "text": "

More than 35.41\n% of all adults who own televisions use their televisions to watch nature shows.

"}, {"id": "B", "text": "

Between 28.59\n% and 35.41\n% of all adults who own televisions use their televisions to watch nature shows. 

"}, {"id": "C", "text": "

Since the sample included adults who own televisions and not just those who use their televisions to watch nature shows, no conclusion can be made.

"}, {"id": "D", "text": "

Since the sample did not include all the people who watch nature shows, no conclusion can be made.

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. It's given that based on a sample selected at random, it's estimated that 32% of all adults who own televisions use their televisions to watch nature shows, with an associated margin of error of 3.41%. Subtracting the margin of error from the estimate and adding the margin of error to the estimate gives an interval of plausible values for the true percentage of adults who own televisions who use their televisions to watch nature shows. This means it's plausible that between 32%-3.41%, or 28.59%, and 32%+3.41%, or 35.41%, of all adults who own televisions use their televisions to watch nature shows. Therefore, of the given choices, the most plausible conclusion is that between 28.59% and 35.41% of all adults who own televisions use their televisions to watch nature shows.

\n

Choice A is incorrect and may result from conceptual errors.

\n

Choice C is incorrect. To make a plausible conclusion about all adults who own televisions, the sample must be selected at random from all adults who own televisions, not just those who use their televisions to watch nature shows.

\n

Choice D is incorrect. Since the sample was selected at random from all adults who own televisions, a plausible conclusion can be made about all adults who own televisions.

"}, {"id": "d693f563", "domain": "Problem-Solving and Data Analysis", "skill": "Percentages", "difficulty": "M", "type": "spr", "stimulus": "", "stem": "

Last year, Cedric had 35\n plants in his garden. This year, the number of plants in Cedric’s garden is 60\n% greater than the number of plants in his garden last year. How many plants does Cedric have in his garden this year?

", "choices": [], "answerId": "56", "acceptedAnswers": ["56"], "rationale": "

The correct answer is 56\n. It’s given that Cedric had 35\n plants in his garden last year and that the number of plants in Cedric's garden this year is 60% greater than the number of plants in his garden last year. It follows that the number of plants in Cedric’s garden this year is 35\n plus 60% of 35\n, which is equal to 35+3560100, or 35+350.6. This expression is equivalent to 35+21, or 56\n. Therefore, Cedric has 56\n plants in his garden this year.

"}, {"id": "f46139df", "domain": "Problem-Solving and Data Analysis", "skill": "Two-variable data: Models and scatterplots", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

The scatterplot shows the relationship between two variables, x\n and y\n. A line of best fit for the data is also shown.

\n

\n

At \n\tx\n\t=\n\t25.5\n\n, which of the following is closest to the y-value predicted by the line of best fit?

", "choices": [{"id": "A", "text": "

6.2\n

"}, {"id": "B", "text": "

7.3\n

"}, {"id": "C", "text": "

8.2\n

"}, {"id": "D", "text": "

9.1\n

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. On the line of best fit, an x-value of 25.5\n corresponds to a y-value between 8\n and 8.5\n. Therefore, at \n\tx\n\t=\n\t25.5\n\n, 8.2\n is closest to the y-value predicted by the line of best fit.

\n

Choice A is incorrect and may result from conceptual errors.

\n

Choice B is incorrect and may result from conceptual errors.

\n

Choice D is incorrect and may result from conceptual errors.

"}, {"id": "e5b5fbdd", "domain": "Problem-Solving and Data Analysis", "skill": "Probability and conditional probability", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

Of the 8 planets in our solar system, 4 are considered rocky. If a student randomly selects 1 of those 8 planets as a topic for a report, what is the probability that the selected planet will be rocky?

\n", "choices": [{"id": "A", "text": "

\n one eighth\n

\n"}, {"id": "B", "text": "

\n one fourth\n

\n"}, {"id": "C", "text": "

\n one half\n

\n"}, {"id": "D", "text": "

\n 2\n

\n"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. If one of these planets is selected at random, the probability that the selected planet will be rocky is calculated by dividing the number of planets that are considered rocky by the total number of planets. It’s given that 4 of the 8 total planets are considered rocky. Therefore, the probability that the selected planet will be rocky is four eighths, which is equivalent to one half.

Choices A and B are incorrect. These represent the probability if 1 of the 8 planets was considered rocky (choice A) and if 2 of the 8 planets were considered rocky (choice B). Choice D is incorrect and may result from dividing the total number of planets by the number of planets that are considered rocky.

\n"}, {"id": "d65b9a87", "domain": "Problem-Solving and Data Analysis", "skill": "One-variable data: Distributions and measures of center and spread", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

The dot plots represent the distributions of values in data sets A and B.

\n

\n

Which of the following statements must be true?

\n
    \n
  1. The median of data set A is equal to the median of data set B.
    2. \n
  2. The standard deviation of data set A is equal to the standard deviation of data set B.
    3. \n
", "choices": [{"id": "A", "text": "

I only

"}, {"id": "B", "text": "

II only

"}, {"id": "C", "text": "

I and II

"}, {"id": "D", "text": "

Neither I nor II

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. The median of a data set with an odd number of values that are in ascending or descending order is the middle value of the data set. Since the distribution of the values of both data set A and data set B form symmetric dot plots, and each data set has an odd number of values, it follows that the median is given by the middle value in each of the dot plots. Thus, the median of data set A is 13\n, and the median of data set B is 13\n. Therefore, statement I is true. Data set A and data set B have the same frequency for each of the values 11\n, 12\n, 14\n, and 15\n. Data set A has a frequency of 1\n for values 10\n and 16\n, whereas data set B has a frequency of 2\n for values 10\n and 16\n. Standard deviation is a measure of the spread of a data set; it is larger when there are more values further from the mean, and smaller when there are more values closer to the mean. Since both distributions are symmetric with an odd number of values, the mean of each data set is equal to its median. Thus, each data set has a mean of 13\n. Since more of the values in data set A are closer to 13\n than data set B, it follows that data set A has a smaller standard deviation than data set B. Thus, statement II is false. Therefore, only statement I must be true.

\n

Choice B is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

\n

Choice D is incorrect and may result from conceptual or calculation errors.

"}, {"id": "bb7c8186", "domain": "Problem-Solving and Data Analysis", "skill": "Percentages", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

What is 23% of 100\n?

", "choices": [{"id": "A", "text": "

23\n

"}, {"id": "B", "text": "

46\n

"}, {"id": "C", "text": "

77\n

"}, {"id": "D", "text": "

123\n

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. 23% of 100\n can be calculated by multiplying 23100 by 100\n, which yields 23100100, or 23\n.

\n

Choice B is incorrect. This is 46%, not 23%, of 100\n.

\n

Choice C is incorrect. This is 23% less than 100\n, not 23% of 100\n.

\n

Choice D is incorrect. This is 23% greater than 100\n, not 23% of 100\n.

"}, {"id": "d230e963", "domain": "Problem-Solving and Data Analysis", "skill": "Two-variable data: Models and scatterplots", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

The scatterplot shows the relationship between two variables, x\n and y\n. A line of best fit is also shown.

\n

\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n\n

\n

Which of the following equations best represents the line of best fit shown?

", "choices": [{"id": "A", "text": "

y=2.8+1.7x

"}, {"id": "B", "text": "

y=2.8-1.7x

"}, {"id": "C", "text": "

y=-2.8+1.7x

"}, {"id": "D", "text": "

y=-2.8-1.7x

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. The line of best fit shown intersects the y-axis at a positive y-value and has a positive slope. The graph of an equation of the form y=a+bx, where a\n and b\n are constants, intersects the y-axis at a y-value of a\n and has a slope of b\n. Of the given choices, only choice A represents a line that intersects the y-axis at a positive y-value, 2.8\n, and has a positive slope, 1.7\n.

\n

Choice B is incorrect. This equation represents a line that has a negative slope, not a positive slope.

\n

Choice C is incorrect. This equation represents a line that intersects the y-axis at a negative y-value, not a positive y-value.

\n

Choice D is incorrect. This equation represents a line that intersects the y-axis at a negative y-value, not a positive y-value, and has a negative slope, not a positive slope.

"}, {"id": "181cc4d6", "domain": "Problem-Solving and Data Analysis", "skill": "Ratios, rates, proportional relationships, and units", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

Rectangle A has length 15 and width w. Rectangle B has length 20 and the same length-to-width ratio as rectangle A. What is the width of rectangle B in terms of w ?

\n", "choices": [{"id": "A", "text": "

four-thirds w

\n"}, {"id": "B", "text": "

w + 5

\n"}, {"id": "C", "text": "

three-fourths w

\n"}, {"id": "D", "text": "

w \u2212 5

\n"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. It’s given that rectangle A has length 15 and width w. Therefore, the length-to-width ratio of rectangle A is 15 to w. It’s also given that rectangle B has length 20 and the same length-to-width ratio as rectangle A. Let x represent the width of rectangle B. The proportion 15 over w = 20 over x can be used to solve for x in terms of w. Multiplying both sides of this equation by x yields (15 x)/(w = 20), and then multiplying both sides of this equation by w yields 15 x = 20 w. Dividing both sides of this equation by 15 yields x = (20 w)/(15). Simplifying this fraction yields x = four thirds w.

Choices B and D are incorrect and may result from interpreting the difference in the lengths of rectangle A and rectangle B as equivalent to the difference in the widths of rectangle A and rectangle B. Choice C is incorrect and may result from using a length-to-width ratio of w to 15, instead of 15 to w.

 

\n"}, {"id": "e9841407", "domain": "Problem-Solving and Data Analysis", "skill": "Ratios, rates, proportional relationships, and units", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

Shaquan has 7 red cards and 28 blue cards. What is the ratio of red cards to blue cards that Shaquan has?

\n", "choices": [{"id": "A", "text": "

1 to 4

\n"}, {"id": "B", "text": "

4 to 1

\n"}, {"id": "C", "text": "

1 to 7

\n"}, {"id": "D", "text": "

7 to 1

\n"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. It’s given that Shaquan has 7 red cards and 28 blue cards. Therefore, the ratio of red cards to blue cards that Shaquan has is 7 to 28. This ratio can be reduced by dividing both parts of the ratio by 7, which yields the ratio 1 to 4.

Choice B is incorrect. This is the ratio of blue cards to red cards that Shaquan has. Choice C is incorrect and may result from a calculation error when reducing the ratio. Choice D is incorrect. This may result from finding the ratio of blue cards to red cards, or 28 to 7, and then making a calculation error when reducing the ratio.

\n"}, {"id": "7fd284ac", "domain": "Problem-Solving and Data Analysis", "skill": "Two-variable data: Models and scatterplots", "difficulty": "M", "type": "mc", "stimulus": "
\n
\n \"The\n
\n
\n", "stem": "

\n The scatterplot above shows data for ten charities along with the line of best fit. For the charity with the greatest percent of total expenses spent on programs, which of the following is closest to the difference of the actual percent and the percent predicted by the line of best fit?\n

\n", "choices": [{"id": "A", "text": "

\n 10 percent

\n"}, {"id": "B", "text": "

\n 7 percent

\n"}, {"id": "C", "text": "

\n 4 percent

\n"}, {"id": "D", "text": "

\n 1 percent

\n"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. The charity with the greatest percent of total expenses spent on programs is represented by the highest point on the scatterplot; this is the point that has a vertical coordinate slightly less than halfway between 90 and 95 and a horizontal coordinate slightly less than halfway between 3,000 and 4,000. Thus, the charity represented by this point has a total income of about $3,400 million and spends about 92% of its total expenses on programs. The percent predicted by the line of best fit is the vertical coordinate of the point on the line of best fit with horizontal coordinate $3,400 million; this vertical coordinate is very slightly more than 85. Thus, the line of best fit predicts that the charity with the greatest percent of total expenses spent on programs will spend slightly more than 85% on programs. Therefore, the difference between the actual percent (92%) and the prediction (slightly more than 85%) is slightly less than 7%.

Choice A is incorrect. There is no charity represented in the scatterplot for which the difference between the actual percent of total expenses spent on programs and the percent predicted by the line of best fit is as much as 10%. Choices C and D are incorrect. These choices may result from misidentifying in the scatterplot the point that represents the charity with the greatest percent of total expenses spent on programs.

\n"}, {"id": "f8a322d9", "domain": "Problem-Solving and Data Analysis", "skill": "One-variable data: Distributions and measures of center and spread", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

\n

Two data sets of 23\n integers each are summarized in the histograms shown. For each of the histograms, the first interval represents the frequency of integers greater than or equal to 10\n, but less than 20\n. The second interval represents the frequency of integers greater than or equal to 20\n, but less than 30\n, and so on. What is the smallest possible difference between the mean of data set A and the mean of data set B?

", "choices": [{"id": "A", "text": "

0\n

"}, {"id": "B", "text": "

1\n

"}, {"id": "C", "text": "

10\n

"}, {"id": "D", "text": "

23\n

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. The histograms shown have the same shape, but data set A contains values between 20\n and 60\n and data set B contains values between 10\n and 50\n. Thus, the mean of data set A is greater than the mean of data set B. Therefore, the smallest possible difference between the mean of data set A and the mean of data set B is the difference between the smallest possible mean of data set A and the greatest possible mean of data set B. In data set A, since there are 3\n integers in the interval greater than or equal to 20\n but less than 30\n, 4\n integers greater than or equal to 30\n but less than 40\n, 7\n integers greater than or equal to 40\n but less than 50\n, and 9\n integers greater than or equal to 50\n but less than 60\n, the smallest possible mean for data set A is 3\u00b720+4\u00b730+7\u00b740+9\u00b75023. In data set B, since there are 3\n integers greater than or equal to 10\n but less than 20\n, 4\n integers greater than or equal to 20\n but less than 30\n, 7\n integers greater than or equal to 30\n but less than 40\n, and 9\n integers greater than or equal to 40\n but less than 50\n, the largest possible mean for data set B is 3\u00b719+4\u00b729+7\u00b739+9\u00b74923. Therefore, the smallest possible difference between the mean of data set A and the mean of data set B is 3\u00b720+4\u00b730+7\u00b740+9\u00b75023-3\u00b719+4\u00b729+7\u00b739+9\u00b74923, which is equivalent to 3\u00b720-3\u00b719+4\u00b730-4\u00b729+7\u00b740-7\u00b739+9\u00b750-9\u00b74923. This expression can be rewritten as 320-19+430-29+740-39+950-4923, or 2323, which is equal to 1\n. Therefore, the smallest possible difference between the mean of data set A and the mean of data set B is 1\n.

\n

Choice A is incorrect. This is the smallest possible difference between the ranges, not the means, of the data sets.

\n

Choice C is incorrect. This is the difference between the greatest possible mean, not the smallest possible mean, of data set A and the greatest possible mean of data set B.

\n

Choice D is incorrect. This is the smallest possible difference between the sum of the values in data set A and the sum of the values in data set B, not the smallest possible difference between the means.

"}, {"id": "e7d9649f", "domain": "Problem-Solving and Data Analysis", "skill": "Inference from sample statistics and margin of error ", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

A random sample of 50 people from a town with a population of 14,878 were asked to name their favorite flavor of ice cream. If 7 people in the sample named chocolate as their favorite ice‑cream flavor, about how many people in the town would be expected to name chocolate?

\n", "choices": [{"id": "A", "text": "350\n"}, {"id": "B", "text": "2,100\n"}, {"id": "C", "text": "7,500\n"}, {"id": "D", "text": "10,500\n"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. Let x be the number of people in the entire town that would be expected to name chocolate. Since the sample of 50 people was selected at random, it is reasonable to expect that the proportion of people who named chocolate as their favorite ice-cream flavor would be the same for both the sample and the town population. Symbolically, this can be expressed as (7)/(50, end fraction = the fraction x over 14,878). Using cross multiplication, 7 \u00d7 14,878 = x \u00d7 50; solving for x yields 2,083. The choice closest to the value of 2,083 is choice B, 2,100.

Choices A, C, and D are incorrect and may be the result of errors when setting up the proportion, solving for the unknown, or incorrectly comparing the choices to the number of people expected to name chocolate, 2,083.

\n"}, {"id": "2df8f293", "domain": "Problem-Solving and Data Analysis", "skill": "Probability and conditional probability", "difficulty": "M", "type": "spr", "stimulus": "", "stem": "

Each vertex of a 14\n-sided polygon is labeled with one of the 14\n letters A\n through N\n, with a different letter at each vertex. If one vertex is selected at random, what is the probability that the letter D\n will be at the selected vertex? (Express your answer as a decimal or fraction, not as a percent.)

", "choices": [], "answerId": ".0714", "acceptedAnswers": [".0714", "1/14"], "rationale": "

The correct answer is \n\t1\n\t14\n\n. If one vertex of the polygon is selected at random, the probability that the letter D\n will be at the selected vertex is equal to the number of vertices labeled with the letter D\n divided by the total number of vertices. It's given that each vertex is labeled with one of the 14\n letters A\n through N\n, with a different letter at each vertex. It follows that there is 1\n vertex labeled with the letter D\n. It's also given that the polygon is 14\n-sided. It follows that there are a total of 14\n vertices. Thus, the probability that the letter D\n will be at the selected vertex is \n\t1\n\t14\n\n. Note that 1/14, .0714, and 0.071 are examples of ways to enter a correct answer.

"}, {"id": "7cab9fe1", "domain": "Problem-Solving and Data Analysis", "skill": "Percentages", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

Which expression represents the result of increasing a positive quantity w\n by 43%?

", "choices": [{"id": "A", "text": "

1.43w

"}, {"id": "B", "text": "

0.57w

"}, {"id": "C", "text": "

\n\t43\n\tw\n\n

"}, {"id": "D", "text": "

0.43w

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. The result of increasing a positive quantity w\n by x% can be represented by the expression 1+x100w. Therefore, the result of increasing a positive quantity w\n by 43% can be found by substituting 43\n for x\n in the expression 1+x100w, which gives 1+43100w, or 1.43w. Thus, the expression 1.43w represents the result of increasing a positive quantity w\n by 43%.

\n

Choice B is incorrect. This is the result of decreasing a positive quantity w\n by 43%.

\n

Choice C is incorrect. This is the result of increasing a positive quantity w\n by 4,200%.

\n

Choice D is incorrect. This is the result of decreasing a positive quantity w\n by 57%.

"}, {"id": "ec7b0eb8", "domain": "Problem-Solving and Data Analysis", "skill": "Probability and conditional probability", "difficulty": "E", "type": "mc", "stimulus": "
Texting behaviorTalks on cell phone dailyDoes not talk on cell phone dailyTotal
Light110146256
Medium139164303
Heavy16674240
Total415384799
 
\n", "stem": "

In a study of cell phone use, 799 randomly selected US teens were asked how often they talked on a cell phone and about their texting behavior. The data are summarized in the table above. If one of the 799 teens surveyed is selected at random, what is the probability that the teen talks on a cell phone daily?

\n", "choices": [{"id": "A", "text": "

1 over 799

\n"}, {"id": "B", "text": "

415 over 799

\n"}, {"id": "C", "text": "

384 over 415

\n"}, {"id": "D", "text": "

384 over 799

\n"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. If one of the teens surveyed is selected at random, the probability that the teen talks on a cell phone daily is equal to the quotient of the total number of teens who reported that they talk on a cell phone daily, 415, and the total number of teens surveyed, 799. Therefore, this probability is equal to 415 over 799.

Choice A is incorrect. This fraction represents the probability of selecting at random any one of the 799 teens surveyed. Choice C is incorrect and may result from conceptual errors. Choice D is incorrect. This fraction represents the probability of selecting at random one of the 799 teens surveyed who doesn’t talk on a cell phone daily. 

\n"}, {"id": "12dae628", "domain": "Problem-Solving and Data Analysis", "skill": "One-variable data: Distributions and measures of center and spread", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

2\n, 9\n, 14\n, 23\n, 32\n

\n

What is the mean of the data shown?

", "choices": [{"id": "A", "text": "

14\n

"}, {"id": "B", "text": "

16\n

"}, {"id": "C", "text": "

17\n

"}, {"id": "D", "text": "

32\n

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. The mean of a set of data values is the sum of all the data values divided by the number of data values in the set. The sum of the data values shown is 2+9+14+23+32, or 80\n. Since there are 5\n data values in the set, the mean of the data shown is 805, or 16\n.

\n

Choice A is incorrect. This is the median, not the mean, of the data shown.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

\n

Choice D is incorrect. This is the maximum, not the mean, of the data shown.

"}, {"id": "1142af44", "domain": "Problem-Solving and Data Analysis", "skill": "One-variable data: Distributions and measures of center and spread", "difficulty": "H", "type": "mc", "stimulus": "
\n\t
\n\t\t\n\t\t\t\t\t\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t
ValueFrequency
1a
22a
33a
42a
5a
\n
\n", "stem": "

The frequency distribution above summarizes a set of data, where a is a positive integer. How much greater is the mean of the set of data than the median?

\n", "choices": [{"id": "A", "text": "

0

\n"}, {"id": "B", "text": "

1

\n"}, {"id": "C", "text": "

2

\n"}, {"id": "D", "text": "

3

\n"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. Since the frequencies of values less than the middle value, 3, are the same as the frequencies of the values greater than 3, the set of data has a symmetric distribution. When a set of data has a symmetric distribution, the mean and median values are equal. Therefore, the mean is 0 greater than the median.

Choices B, C, and D are incorrect and may result from misinterpreting the set of data.

 

\n"}, {"id": "79201024", "domain": "Problem-Solving and Data Analysis", "skill": "Probability and conditional probability", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

A band with 45\n members has 11\n members who play saxophone. If one band member is selected at random, what is the probability of selecting a band member who plays saxophone?

", "choices": [{"id": "A", "text": "

145

"}, {"id": "B", "text": "

1145

"}, {"id": "C", "text": "

3445

"}, {"id": "D", "text": "

4545

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. The probability of an event occurring is the ratio of the number of favorable outcomes to the total number of possible outcomes. It’s given that there are 45\n band members, which is the total number of possible outcomes. It's also given that there are 11\n band members who play saxophone. Therefore, the number of favorable outcomes is 11\n. Thus, the probability of selecting a band member who plays saxophone is 1145.

\n

Choice A is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect. This is the probability of selecting a band member who does not play saxophone.

\n

Choice D is incorrect and may result from conceptual or calculation errors.

"}, {"id": "445dd032", "domain": "Problem-Solving and Data Analysis", "skill": "Ratios, rates, proportional relationships, and units", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

Tanya earns $13.50 per hour at her part-time job. When she works z hours, she earns 13 point 5 0 z dollars. Which of the following expressions gives the amount, in dollars, Tanya will earn if she works 3 z hours?

\n", "choices": [{"id": "A", "text": "

\n 3 times, open parenthesis, 13 point 5 0 z, close parenthesis\n

\n"}, {"id": "B", "text": "

\n 3 + 13 point 5 0 z\n

\n"}, {"id": "C", "text": "

\n 3 z + 13 point 5 0 z\n

\n"}, {"id": "D", "text": "

\n 13 point 5 0 times, open parenthesis, z + 3, close parenthesis\n

\n"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. It’s given that when Tanya works z hours, she earns 13 point 5 0 z dollars. Since her hourly rate is constant, if she works 3 times as many hours, or 3 z hours, she will earn 3 times as many dollars, or 3 times, open parenthesis, 13 point 5 0 z, close parenthesis.

Choice B is incorrect. This expression represents adding 3 dollars to the 13 point 5 0 z dollars Tanya will earn. Choice C is incorrect. This expression can be rewritten as 16 point 5 0 z, which implies that Tanya earns $16.50 per hour, not $13.50. Choice D is incorrect. This expression adds 3 to the number of hours Tanya works, rather than multiplying the hours she works by 3.

\n"}, {"id": "651d83bb", "domain": "Problem-Solving and Data Analysis", "skill": "One-variable data: Distributions and measures of center and spread", "difficulty": "H", "type": "mc", "stimulus": "
\n
\n
\n

Two different teams consisting of 10 members each ran in a race. Each member’s completion time of the race was recorded. The mean of the completion times for each team was calculated and is shown below.

\n
\n
\n

Team A: 3.41 minutes
Team B: 3.79 minutes

\n
\n", "stem": "

Which of the following MUST be true?

  1. Every member of team A completed the race in less time than any member of team B.
    2. \n
  2. The median time it took the members of team B to complete the race is greater than the median time it took the members of team A to complete the race.
    3. \n
  3. There is at least one member of team B who took more time to complete the race than some member of team A.
    4. \n

\n", "choices": [{"id": "A", "text": "

III only

\n"}, {"id": "B", "text": "

I and III only

\n"}, {"id": "C", "text": "

II and III only

\n"}, {"id": "D", "text": "

I, II, and III

\n"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. Since the average time for the 10 members of team A is 3.41 minutes, the sum of the 10 times for team A is equal to 10 \u00d7 3 point 4 1 = 34 point 1 minutes. Since the average time for the 10 members of team B is 3.79 minutes, the sum of the 10 times for team B is equal to 10 \u00d7 3 point 7 9 = 37 point 9 minutes. Since the sum of the 10 times for team B is greater than the sum of the 10 times for team A, it must be true that at least one of the times for team B must be greater than one of the times for team A. Thus, statement III is true. However, it’s possible that at least some of the times for team A were greater than some of the times for team B. For example, all of team A’s times could be 3.41 minutes, and team B could have 1 time of 3.34 minutes and 9 times of 3.84 minutes. Thus, statement I need not be true. It’s also possible that the median of the times for team B is less than the median of the times for team A. For example, all of team A’s times could be 3.41 minutes, and team B could have 6 times of 3.37 minutes and 4 times of 4.42 minutes; then the median of team B’s times would be 3.37 minutes and the median of team A’s times would be 3.41 minutes. Thus, statement II need not be true.

Choices B, C, and D are incorrect because neither statement I nor statement II must be true.

\n"}, {"id": "121dc44f", "domain": "Problem-Solving and Data Analysis", "skill": "Percentages", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

The population of City A increased by 7% from 2015 to 2016. If the 2016 population is k\n times the 2015 population, what is the value of k\n?

", "choices": [{"id": "A", "text": "

0.07

"}, {"id": "B", "text": "

0.7

"}, {"id": "C", "text": "

1.07

"}, {"id": "D", "text": "

1.7

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. It's given that the population of City A increased by 7% from 20\n15\n to 20\n16\n. Therefore, the population of City A in 20\n16\n includes 100% of the population of City A in 20\n15\n plus an additional 7% of the population of City A in 20\n15\n. This means that the population of City A in 20\n16\n is 107% of the population in 20\n15\n. Thus, the population of City A in 20\n16\n is \n\t107\n\t100\n\n, or 1.07\n, times the 20\n15\n population. Therefore, the value of k\n is 1.07\n.

\n

Choice A is incorrect. This would be the value of k\n if the population in 20\n16\n was 7% of the population in 20\n15\n.

\n

Choice B is incorrect. This would be the value of k\n if the population in 20\n16\n was 70% of the population in 20\n15\n.

\n

Choice D is incorrect. This would be the value of k\n if the population increased by 70%, not 7%, from 20\n15\n to 20\n16\n.

"}, {"id": "1e8ccffd", "domain": "Problem-Solving and Data Analysis", "skill": "One-variable data: Distributions and measures of center and spread", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

The mean score of 8 players in a basketball game was 14.5 points. If the highest individual score is removed, the mean score of the remaining 7 players becomes 12 points. What was the highest score?

\n", "choices": [{"id": "A", "text": "

20

\n"}, {"id": "B", "text": "

24

\n"}, {"id": "C", "text": "

32

\n"}, {"id": "D", "text": "

36

\n"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. If the mean score of 8 players is 14.5, then the total of all 8 scores is 14 point 5 \u00d7 8 = 116. If the mean of 7 scores is 12, then the total of all 7 scores is 12 \u00d7 7 = 84. Since the set of 7 scores was made by removing the highest score of the set of 8 scores, then the difference between the total of all 8 scores and the total of all 7 scores is equal to the removed score: 116 \u2212 84 = 32.

Choice A is incorrect because if 20 is removed from the group of 8 scores, then the mean score of the remaining 7 players is the fraction with numerator, open parenthesis, 14 point 5 \u00d7 8, close parenthesis, \u2212 20, and denominator 7 is approximately 13.71, not 12. Choice B is incorrect because if 24 is removed from the group of 8 scores, then the mean score of the remaining 7 players is the fraction with numerator, open parenthesis, 14 point 5 \u00d7 8, close parenthesis, \u2212 24, and denominator 7 is approximately 13.14, not 12. Choice D is incorrect because if 36 is removed from the group of 8 scores, then the mean score of the remaining 7 players is the fraction with numerator, open parenthesis, 14 point 5 \u00d7 8, close parenthesis, \u2212 36, and denominator 7 or approximately 11.43, not 12.

 

\n"}, {"id": "1e1027a7", "domain": "Problem-Solving and Data Analysis", "skill": "Two-variable data: Models and scatterplots", "difficulty": "H", "type": "mc", "stimulus": "
\n\t
\"The
\n
\n", "stem": "

The scatterplot above shows a company’s ice cream sales d, in dollars, and the high temperature t, in degrees Celsius (°C), on 12 different days. A line of best fit for the data is also shown. Which of the following could be an equation of the line of best fit?

\n", "choices": [{"id": "A", "text": "

d = 0 point 0 3 t + 402

\n"}, {"id": "B", "text": "

d = 10 t + 402

\n"}, {"id": "C", "text": "

d = 33 t + 300

\n"}, {"id": "D", "text": "

d = 33 t + 84

\n"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. On the line of best fit, d increases from approximately 480 to 880 between t = 12 and t = 24. The slope of the line of best fit is the difference in d-values divided by the difference in t-values, which gives (880 \u2212 480)/(24 \u2212 12, end fraction = (400)/(12)), or approximately 33. Writing the equation of the line of best fit in slope-intercept form gives d = 33 t + b, where b is the y-coordinate of the y-intercept. This equation is satisfied by all points on the line, so d = 480 when t = 12. Thus, 480 = 33 \u00d7 12, + b, which is equivalent to 480 = 396 + b. Subtracting 396 from both sides of this equation gives b = 84. Therefore, an equation for the line of best fit could be d = 33 t + 84.

Choice A is incorrect and may result from an error in calculating the slope and misidentifying the y-coordinate of the y-intercept of the graph as the value of d at \"\" rather than the value of d at t = 0. Choice B is incorrect and may result from using the smallest value of t on the graph as the slope and misidentifying the y-coordinate of the y-intercept of the graph as the value of d at t = 10 rather than the value of d at t = 0. Choice C is incorrect and may result from misidentifying the y-coordinate of the y-intercept as the smallest value of d on the graph.

 

\n"}, {"id": "fe1ec415", "domain": "Problem-Solving and Data Analysis", "skill": "Ratios, rates, proportional relationships, and units", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

A cherry pitting machine pits 12\n pounds of cherries in 3\n minutes. At this rate, how many minutes does it take the machine to pit 96\n pounds of cherries?

", "choices": [{"id": "A", "text": "

8\n

"}, {"id": "B", "text": "

15\n

"}, {"id": "C", "text": "

24\n

"}, {"id": "D", "text": "

36\n

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. It's given that the cherry pitting machine pits 12\n pounds of cherries in 3\n minutes. This rate can be written as 12 pounds of cherries3 minutes. If the number of minutes it takes the machine to pit 96\n pounds of cherries is represented by x\n, the value of x\n can be calculated by solving the equation 12 pounds of cherries3 minutes=96 pounds of cherriesx minutes, which can be rewritten as 123=96x, or 4=96x. Multiplying each side of this equation by x\n yields 4x=96. Dividing each side of this equation by 4\n yields x=24. Therefore, it takes the machine 24\n minutes to pit 96\n pounds of cherries.

\n

Choice A is incorrect. This is the number of minutes it takes the machine to pit 32\n, not 96\n, pounds of cherries. 

\n

Choice B is incorrect. This is the number of minutes it takes the machine to pit 60\n, not 96\n, pounds of cherries. 

\n

Choice D is incorrect. This is the number of minutes it takes the machine to pit 144\n, not 96\n, pounds of cherries. 

"}, {"id": "ba62b0b0", "domain": "Problem-Solving and Data Analysis", "skill": "Ratios, rates, proportional relationships, and units", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

A kangaroo has a mass of 28\n kilograms. What is the kangaroo's mass, in grams? (1 kilogram=1,000 grams)

", "choices": [{"id": "A", "text": "

28,000\n

"}, {"id": "B", "text": "

1,028\n

"}, {"id": "C", "text": "

972\n

"}, {"id": "D", "text": "

784\n

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. It's given that a kangaroo has a mass of 28\n kilograms and that 1\n kilogram is equal to 1,000\n grams. Therefore, the kangaroo's mass, in grams, is 28 kilograms1,000 grams1 kilogram, which is equivalent to 28,000\n grams.

\n

Choice B is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

\n

Choice D is incorrect and may result from conceptual or calculation errors.

"}, {"id": "939c46d1", "domain": "Problem-Solving and Data Analysis", "skill": "Ratios, rates, proportional relationships, and units", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

\"The

The glass pictured above can hold a maximum volume of 473 cubic centimeters, which is approximately 16 fluid ounces. Jenny has a pitcher that contains 1 gallon of water. How many times could Jenny completely fill the glass with 1 gallon of water? 1 gallon = 128 fluid ounces

\n", "choices": [{"id": "A", "text": "

16

\n"}, {"id": "B", "text": "

  8

\n"}, {"id": "C", "text": "

  4

\n"}, {"id": "D", "text": "

  3

\n"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. It is given that the volume of the glass is approximately 16 fluid ounces. If Jenny has 1 gallon of water, which is 128 fluid ounces, she could fill the glass 128 over 16, which = 8 times.

Choice A is incorrect because Jenny would need 16 \u00d7 16 fluid ounces = 256 fluid ounces, or 2 gallons, of water to fill the glass 16 times. Choice C is incorrect because Jenny would need only 4 \u00d7 16 fluid ounces = 64 fluid ounces of water to fill the glass 4 times. Choice D is incorrect because Jenny would need only 3 \u00d7 16 fluid ounces = 48 fluid ounces to fill the glass 3 times.

\n"}, {"id": "29c177e6", "domain": "Problem-Solving and Data Analysis", "skill": "Percentages", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

What is 10% of 470\n?

", "choices": [{"id": "A", "text": "

37\n

"}, {"id": "B", "text": "

47\n

"}, {"id": "C", "text": "

423\n

"}, {"id": "D", "text": "

460\n

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. 10% of a quantity means 10100 times the quantity. Therefore, 10% of 470\n can be represented as 10100470, which is equivalent to 0.10470, or 47\n. Therefore, 10% of 470\n is 47\n.

\n

Choice A is incorrect. This is 10% of 370\n, not 10% of 470\n.

\n

Choice C is incorrect. This is 90% of 470\n, not 10% of 470\n.

\n

Choice D is incorrect. This is 470-10, not 10% of 470\n.

"}, {"id": "fc46af57", "domain": "Problem-Solving and Data Analysis", "skill": "Inference from sample statistics and margin of error ", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

A bag containing 10,000 beads of assorted colors is purchased from a craft store. To estimate the percent of red beads in the bag, a sample of beads is selected at random. The percent of red beads in the bag was estimated to be 15%, with an associated margin of error of 2%. If r is the actual number of red beads in the bag, which of the following is most plausible?

\n", "choices": [{"id": "A", "text": "

\n r > 1,700\n

\n"}, {"id": "B", "text": "

\n 1,300 < r, which < 1,700\n

\n"}, {"id": "C", "text": "

\n 200 < r, which < 1,500\n

\n"}, {"id": "D", "text": "

\n r < 1,300\n

\n"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. It was estimated that 15% of the beads in the bag are red. Since the bag contains 10,000 beads, it follows that there are an estimated 10,000 \u00d7 0 point 1 5 = 1,500 red beads. It’s given that the margin of error is 2%, or 10,000 \u00d7 0 point 0 2 = 200 beads. If the estimate is too high, there could plausibly be 1,500 \u2212 200 = 1,300 red beads. If the estimate is too low, there could plausibly be 1,500 + 200 = 1,700 red beads. Therefore, the most plausible statement of the actual number of red beads in the bag is 1,300 < r, which < 1,700.

Choices A and D are incorrect and may result from misinterpreting the margin of error. It’s unlikely that more than 1,700 beads or fewer than 1,300 beads in the bag are red. Choice C is incorrect because 200 is the margin of error for the number of red beads, not the lower bound of the range of red beads.

\n"}, {"id": "7b65bb28", "domain": "Problem-Solving and Data Analysis", "skill": "One-variable data: Distributions and measures of center and spread", "difficulty": "M", "type": "mc", "stimulus": "
\n
\n \n
\n
\n \n \n \n \n \n \n \n \n \n \n
Station 1Station 2Station 3Station 4Station 5
$3.699$3.609$3.729$3.679$3.729
\n
\n
\n", "stem": "

In the table above, Melissa recorded the price of one gallon of regular gas from five different local gas stations on the same day. What is the median of the gas prices Melissa recorded?

\n", "choices": [{"id": "A", "text": "

$3.679

\n"}, {"id": "B", "text": "

$3.689

\n"}, {"id": "C", "text": "

$3.699

\n"}, {"id": "D", "text": "

$3.729

\n"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. The median of a data set is the middle value when the data is in ascending or descending order. In ascending order, the gas prices are $3.609, $3.679, $3.699, $3.729, and $3.729. The middle number of this list is 3.699, so it follows that $3.699 is the median gas price.

Choice A is incorrect. When the gas prices are listed in ascending order, this value isn’t the middle number. Choice B is incorrect. This value represents the mean gas price. Choice D is incorrect. This value represents both the mode and the maximum gas price.

\n"}, {"id": "8a714fa1", "domain": "Problem-Solving and Data Analysis", "skill": "Percentages", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

Which of the following represents the result of increasing the quantity x by 9%, where x > 0 ?

\n", "choices": [{"id": "A", "text": "

\n 1 point 0 9 x\n

\n"}, {"id": "B", "text": "

\n 0 point 0 9 x\n

\n"}, {"id": "C", "text": "

\n x + 9\n

\n"}, {"id": "D", "text": "

\n x + 0 point 0 9\n

\n"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. Increasing the positive quantity x by 9% is the result of adding 9% of x to x. 9% of x can be represented algebraically as the fraction, 9 over 100, end fraction, \u00d7 x, or 0 point 0 9 x. Adding this expression to x yields x + 0 point 0 9 x, or 1 point 0 9 x.

Choice B is incorrect. This represents 9% of x. Choice C is incorrect. This represents increasing x by 9, not by 9%. Choice D is incorrect. This represents increasing x by 0.09, not by 9%.

\n"}, {"id": "7cd1c6db", "domain": "Problem-Solving and Data Analysis", "skill": "Ratios, rates, proportional relationships, and units", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

An object travels at a constant speed of 12\n centimeters per second. At this speed, what is the time, in seconds, that it would take for the object to travel 108\n centimeters?

", "choices": [{"id": "A", "text": "

9\n

"}, {"id": "B", "text": "

96\n

"}, {"id": "C", "text": "

120\n

"}, {"id": "D", "text": "

972\n

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. If the object travels 108\n centimeters at a speed of 12\n centimeters per second, the time of travel can be determined by dividing the total distance by the speed. This results in 108 centimeters12 centimeters/second, which is 9\n seconds.

\n

Choice B is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

\n

Choice D is incorrect and may result from conceptual or calculation errors.

"}, {"id": "3f775bbf", "domain": "Problem-Solving and Data Analysis", "skill": "Ratios, rates, proportional relationships, and units", "difficulty": "H", "type": "mc", "stimulus": "
 
StatePower capacity
LowMediumHighTotal
Texas4239
California1012
Oregon1012
Indiana0202
Colorado1102
Iowa2002
Oklahoma1001
Total105520
\n", "stem": "

The table shows the distribution, by location and power capacity (maximum rate of power generation) of the twenty largest wind projects in the United States in 2013. The total power capacity of the nine wind projects located in Texas was 4,952 megawatts (MW), and the total power capacity of the twenty wind projects was 11,037 MW in 2013. The amount of energy produced in one hour at a rate of one megawatt is one megawatt-hour. If each of the nine Texas wind projects in 2013 had operated continuously for 24 hours at the maximum rate of power generation, approximately how many megawatt-hours of energy would the nine projects have produced?

\n", "choices": [{"id": "A", "text": "

200

\n"}, {"id": "B", "text": "

5,000

\n"}, {"id": "C", "text": "

11,000

\n"}, {"id": "D", "text": "

120,000

\n"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. It’s given that the total power capacity of the nine wind projects in Texas was 4,952 megawatts. Therefore, if all nine Texas projects operated continuously for 1 hour, the amount of energy produced would be 4,952 megawatt-hours. It follows that, if all nine Texas projects operated continuously for 24 hours, the amount of energy produced, in megawatt-hours, would be 4,952 \u00d7 24 = 118,848, which is closest to 120,000.

Choice A is incorrect. This is approximately the amount of energy produced for the nine projects divided by 24 hours. Choice B is incorrect. This is approximately the amount of energy produced for the nine projects. Choice C is incorrect. This is approximately the given amount of energy produced for all twenty projects in the table.

\n"}, {"id": "8637294f", "domain": "Problem-Solving and Data Analysis", "skill": "Ratios, rates, proportional relationships, and units", "difficulty": "H", "type": "spr", "stimulus": "", "stem": "

If \n\t\n\t\t\n\t\t\t\n\t\t\t\t4\n\t\t\t\ta\n\t\t\t\n\t\t\tb\n\t\t\n\t\n\t=\n\t6.7\n\n and \n\t\n\t\t\n\t\t\ta\n\t\t\t\n\t\t\t\tb\n\t\t\t\tn\n\t\t\t\n\t\t\n\t\n\t=\n\t26.8\n\n, what is the value of n\n?

", "choices": [], "answerId": ".0625", "acceptedAnswers": [".0625", "1/16"], "rationale": "

The correct answer is .0625. It's given that 4ab=6.7 and abn=26.8. The equation 4ab=6.7 can be rewritten as 4ab=6.7. Dividing both sides of this equation by 4\n yields ab=1.675. The equation abn=26.8 can be rewritten as ab1n=26.8. Substituting 1.675 for ab in this equation yields 1.6751n=26.8, or 1.675n=26.8. Multiplying both sides of this equation by n\n yields 1.675=26.8n. Dividing both sides of this equation by 26.8 yields n=0.0625. Therefore, the value of n\n is 0.0625. Note that .0625, 0.062, 0.063, and 1/16 are examples of ways to enter a correct answer.

"}, {"id": "8e2e424e", "domain": "Problem-Solving and Data Analysis", "skill": "Percentages", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

The number k is 36% greater than 50. If k is the product of 50 and r, what is the value of r ?

\n", "choices": [{"id": "A", "text": "

36

\n"}, {"id": "B", "text": "

3.6

\n"}, {"id": "C", "text": "

1.36

\n"}, {"id": "D", "text": "

0.36

\n"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. It’s given that the number k is 36% greater than 50. Therefore, the value of k is the number 50 plus 36% of 50. This can be rewritten as k = 50 plus, (36)/(100, end fraction, \u00d7 50). Multiplying the terms (36)/(100, end fraction, \u00d7 50) yields 18, so k = 50 + 18, or k = 68. It’s also given that k is the product of 50 and r, which can be rewritten as k = 50 r. Substituting 68 for k yields 68 = 50 r. Dividing both sides of this equation by 50 yields r = 1 point 3 6.

Choice A is incorrect. This is the percentage that k is greater than 50. Choice B is incorrect and may result from a calculation error. Choice D is incorrect. This would be the value of r if k were 36% of 50, instead of 36% greater than 50.

 

\n"}, {"id": "24ad9dcb", "domain": "Problem-Solving and Data Analysis", "skill": "Ratios, rates, proportional relationships, and units", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

The weight of an object on Venus is approximately (9)/(10) of its weight on Earth. The weight of an object on Jupiter is approximately (23)/(10) of its weight on Earth. If an object weighs 100 pounds on Earth, approximately how many more pounds does it weigh on Jupiter than it weighs on Venus?

\n", "choices": [{"id": "A", "text": "90\n"}, {"id": "B", "text": "111\n"}, {"id": "C", "text": "140\n"}, {"id": "D", "text": "230\n"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. The weight of an object on Venus is approximately nine tenths of its weight on Earth. If an object weighs 100 pounds on Earth, then the object’s weight on Venus is approximately nine tenths \u00d7 100 = 90 pounds. The same object’s weight on Jupiter is approximately twenty three tenths of its weight on Earth; therefore, the object weighs approximately twenty three tenths \u00d7 100 = 230 pounds on Jupiter. The difference between the object’s weight on Jupiter and the object’s weight on Venus is approximately 230 \u2212 90 = 140 pounds. Therefore, an object that weighs 100 pounds on Earth weighs 140 more pounds on Jupiter than it weighs on Venus.

Choice A is incorrect because it is the weight, in pounds, of the object on Venus. Choice B is incorrect because it is the weight, in pounds, of an object on Earth if it weighs 100 pounds on Venus. Choice D is incorrect because it is the weight, in pounds, of the object on Jupiter.

\n"}, {"id": "be00d896", "domain": "Problem-Solving and Data Analysis", "skill": "One-variable data: Distributions and measures of center and spread", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

For which of the following data sets is the mean greater than the median?

\n", "choices": [{"id": "A", "text": "

5, 5, 5, 5, 5, 5, 5, 5, 5

\n"}, {"id": "B", "text": "

0, 10, 20, 30, 40, 50, 60, 70, 80

\n"}, {"id": "C", "text": "

2, 4, 8, 16, 32, 64, 128, 256, 512

\n"}, {"id": "D", "text": "

7, 107, 107, 207, 207, 207, 307, 307, 307

\n"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. If the values in a data set are ordered from least to greatest, the median of the data set will be the middle value. Since each data set in the choices is ordered and contains exactly 9 data values, the 5th value in each is the median. It follows that the median of the data set in choice C is 32. The sum of the positive differences between 32 and each of the values that are less than 32 is significantly smaller than the sum of the positive differences between 32 and each of the values that are greater than 32. If 32 were the mean, these sums would have been equal to each other. Therefore, the mean of this data set must be greater than 32. This can also be confirmed by calculating the mean as the sum of the values divided by the number of values in the data set:  The fraction with numerator 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256, + 512, and denominator 9 = 113 and five ninths.

Choices A and B are incorrect. Each of the data sets in these choices is symmetric with respect to its median, so the mean and the median for each of these choices are equivalent. Choice D is incorrect. The median of this data set is 207. Since the sum of the positive differences between 207 and each of the values less than 207 is greater than the sum of the positive differences between 207 and each value greater than 207 in this data set, the mean must be less than the median.

\n"}, {"id": "3d985614", "domain": "Problem-Solving and Data Analysis", "skill": "Two-variable data: Models and scatterplots", "difficulty": "M", "type": "mc", "stimulus": "
\n
\n \"The
\n
\n", "stem": "

Each dot in the scatterplot above represents the height x, in feet, in the high jump, and the distance y, in feet, in the long jump, made by each student in a group of twenty students. The graph of which of the following equations is a line that most closely fits the data?

\n", "choices": [{"id": "A", "text": "

\n y = 0 point 8 2 x, + 3 point 3 0\n

\n"}, {"id": "B", "text": "

\n y = 0 point 8 2 x, \u2212 0 point 8 2\n

\n"}, {"id": "C", "text": "

\n y = 3 point 3 0 x, + 0 point 8 2\n

\n"}, {"id": "D", "text": "

\n y = 3 point 3 0 x, \u2212 3 point 3 0\n

\n"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. A line that most closely fits the data is a line with an approximately balanced number of data points above and below the line. Fitting a line to the data shown results in a line with an approximate slope of 3 and a y-intercept near the point 0, 1. An equation for the line can be written in slope-intercept form, y = m x + b, where m is the slope and b is the y-coordinate of the y-intercept. The equation y = 3 point 3 0 x + 0 point 8 2 in choice C fits the data most closely.

Choices A and B are incorrect because the slope of the lines of these equations is 0.82, which is a value that is too small to be the slope of the line that fits the data shown. Choice D is incorrect. The graph of this equation has a y-intercept at the point 0, \u22123 point 3 0, not the point 0, 0 point 8 2. This line would lie below all of the data points, and therefore would not closely fit the data.

\n"}, {"id": "560fab82", "domain": "Problem-Solving and Data Analysis", "skill": "One-variable data: Distributions and measures of center and spread", "difficulty": "M", "type": "spr", "stimulus": "", "stem": "

The table shows the frequency of values in a data set.

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
ValueFrequency
19\n7\n
21\n1\n
23\n7\n
25\n4\n
\n

What is the minimum value of the data set?

", "choices": [], "answerId": "19", "acceptedAnswers": ["19"], "rationale": "

The correct answer is 19\n. The minimum value of a data set is the least value in the data set. The frequency refers to the number of times a value occurs. The given table shows that for this data set, the value 19\n occurs 7\n times, the value 21\n occurs 1\n time, the value 23\n occurs 7\n times, and the value 25\n occurs 4\n times. Therefore, of the values 19\n, 21\n, 23\n, and 25\n given in the data set, the minimum value of the data set is 19\n.

"}, {"id": "308084c5", "domain": "Problem-Solving and Data Analysis", "skill": "Inference from sample statistics and margin of error ", "difficulty": "H", "type": "mc", "stimulus": "
\n
\n \n \n \n \n \n \n \n \n \n
SamplePercent in favorMargin of error
A52%4.2%
B48%1.6%
\n
\n", "stem": "

The results of two random samples of votes for a proposition are shown above. The samples were selected from the same population, and the margins of error were calculated using the same method. Which of the following is the most appropriate reason that the margin of error for sample A is greater than the margin of error for sample B?

\n", "choices": [{"id": "A", "text": "

Sample A had a smaller number of votes that could not be recorded.

\n"}, {"id": "B", "text": "

Sample A had a higher percent of favorable responses.

\n"}, {"id": "C", "text": "

Sample A had a larger sample size.

\n"}, {"id": "D", "text": "

Sample A had a smaller sample size.

\n"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. Sample size is an appropriate reason for the margin of error to change. In general, a smaller sample size increases the margin of error because the sample may be less representative of the whole population.

Choice A is incorrect. The margin of error will depend on the size of the sample of recorded votes, not the number of votes that could not be recorded. In any case, the smaller number of votes that could not be recorded for sample A would tend to decrease, not increase, the comparative size of the margin of error. Choice B is incorrect. Since the percent in favor for sample A is the same distance from 50% as the percent in favor for sample B, the percent of favorable responses doesn’t affect the comparative size of the margin of error for the two samples. Choice C is incorrect. If sample A had a larger margin of error than sample B, then sample A would tend to be less representative of the population. Therefore, sample A is not likely to have a larger sample size.

\n"}, {"id": "d94018fd", "domain": "Problem-Solving and Data Analysis", "skill": "One-variable data: Distributions and measures of center and spread", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

\n

Each of the dot plots shown represents the number of glue sticks brought in by each student for two classes, class A and class B. Which statement best compares the standard deviations of the numbers of glue sticks brought in by each student for these two classes?

", "choices": [{"id": "A", "text": "

The standard deviation of the number of glue sticks brought in by each student for class A is less than the standard deviation of the number of glue sticks brought in by each student for class B.

"}, {"id": "B", "text": "

The standard deviation of the number of glue sticks brought in by each student for class A is equal to the standard deviation of the number of glue sticks brought in by each student for class B.

"}, {"id": "C", "text": "

The standard deviation of the number of glue sticks brought in by each student for class A is greater than the standard deviation of the number of glue sticks brought in by each student for class B.

"}, {"id": "D", "text": "

There is not enough information to compare these standard deviations.

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. Standard deviation is a measure of the spread of a data set from its mean. The dot plot for class A and the dot plot for class B have the same shape. Thus, the frequency distributions for both class A and class B are the same. Since both class A and class B have the same frequency distribution of glue sticks brought in by each student, it follows that both class A and class B have the same spread of the number of glue sticks brought in by each student from their respective means. Therefore, the standard deviation of the number of glue sticks brought in by each student for class A is equal to the standard deviation of the number of glue sticks brought in by each student for class B.

\n

Choice A is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

\n

Choice D is incorrect and may result from conceptual or calculation errors.

"}, {"id": "e21d10a7", "domain": "Problem-Solving and Data Analysis", "skill": "Ratios, rates, proportional relationships, and units", "difficulty": "M", "type": "spr", "stimulus": "", "stem": "

One of a planet's moons orbits the planet every 252\n days. A second moon orbits the planet every 287\n days. How many more days does it take the second moon to orbit the planet 29\n times than it takes the first moon to orbit the planet 29\n times?

", "choices": [], "answerId": "1015", "acceptedAnswers": ["1015"], "rationale": "

The correct answer is 1,015\n. It’s given that the first moon orbits the planet every 252\n days. Therefore, it takes the first moon 25229, or 7,308\n, days to orbit the planet 29\n times. It’s also given that the second moon orbits the planet every 287\n days. Therefore, it takes the second moon 28729, or 8,323\n, days to orbit the planet 29\n times. Since it takes the first moon 7,308\n days and the second moon 8,323\n days, it takes the second moon 8,323-7,308, or 1,015\n, more days than it takes the first moon to orbit the planet 29\n times.

"}, {"id": "7d721177", "domain": "Problem-Solving and Data Analysis", "skill": "Ratios, rates, proportional relationships, and units", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

The density of a certain type of wood is 353\n kilograms per cubic meter. A sample of this type of wood is in the shape of a cube and has a mass of 345\n kilograms. To the nearest hundredth of a meter, what is the length of one edge of this sample? 

", "choices": [{"id": "A", "text": "

0.98\n

"}, {"id": "B", "text": "

0.99\n

"}, {"id": "C", "text": "

1.01\n

"}, {"id": "D", "text": "

1.02\n

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. It’s given that the density of a certain type of wood is 353\n kilograms per cubic meter kg/m3, and a sample of this type of wood has a mass of 345 kg. Let x\n represent the volume, in m3, of the sample. It follows that the relationship between the density, mass, and volume of this sample can be written
as 353 kg1 m3=345 kgx m3, or 353=345x. Multiplying both sides of this equation by x\n yields 353x=345. Dividing both sides of this equation by 353\n yields x=345353. Therefore, the volume of this sample is 345353 m3. Since it’s given that the sample of this type of wood is a cube, it follows that the length of one edge of this sample can be found using the volume formula for a cube, V=s3, where V\n represents the volume, in m3, and s\n represents the length, in m, of one edge of the cube. Substituting 345353for V\n in this formula yields 345353=s3. Taking the cube root of both sides of this equation yields 3453533=s, or s≈0.99. Therefore, the length of one edge of this sample to the nearest hundredth of a meter is 0.99\n.

\n

Choices A, C, and D are incorrect and may result from conceptual or calculation errors.

"}, {"id": "d0d9ede4", "domain": "Problem-Solving and Data Analysis", "skill": "Ratios, rates, proportional relationships, and units", "difficulty": "E", "type": "spr", "stimulus": "", "stem": "

How many feet are equivalent to 34\n yards? 1 yard=3 feet

", "choices": [], "answerId": "102", "acceptedAnswers": ["102"], "rationale": "

The correct answer is 102\n. It’s given that 1\n yard is equivalent to 3\n feet. Therefore, 34\n yards is equivalent to 34 yards3 feet1 yard, or 102\n feet.

"}, {"id": "4b09f783", "domain": "Problem-Solving and Data Analysis", "skill": "One-variable data: Distributions and measures of center and spread", "difficulty": "E", "type": "spr", "stimulus": "", "stem": "

A list of 10\n data values is shown.

\n

6\n, 8\n, 16\n, 4\n, 17\n, 26\n, 8\n, 5\n, 5\n, 5\n

\n

What is the mean of these data?

", "choices": [], "answerId": "10", "acceptedAnswers": ["10"], "rationale": "

The correct answer is 10\n. The mean of a data set is calculated by dividing the sum of the data values by the number of data values in the data set. For this data set, the mean can be calculated as 6+8+16+4+17+26+8+5+5+510, which is equivalent to 10010, or 10\n.

"}, {"id": "67c0200a", "domain": "Problem-Solving and Data Analysis", "skill": "Percentages", "difficulty": "H", "type": "spr", "stimulus": "", "stem": "

The number a\n is 70% less than the positive number b\n. The number c\n is 80% greater than a\n. The number c\n is how many times b\n?

", "choices": [], "answerId": ".54", "acceptedAnswers": [".54", "27/50"], "rationale": "

The correct answer is .54. It's given that the number a\n is 70% less than the positive number b\n. Therefore, a=1-70100b, which is equivalent to a=1-0.70b, or a=0.30b. It's also given that the number c\n is 80% greater than a\n. Therefore, c=1+80100a, which is equivalent to c=1+0.80a, or c=1.80a. Since \n\ta\n\t=\n\t\n\t\t0.30\n\t\tb\n\t\n\n, substituting \n\t0.30\n\tb\n\n for a\n in the equation \n\tc\n\t=\n\t\n\t\t1.80\n\t\ta\n\t\n\n yields c=1.800.30b, or c=0.54b. Thus, c\n is 0.54\n times b\n. Note that .54 and 27/50 are examples of ways to enter a correct answer.

"}, {"id": "f04d40b2", "domain": "Problem-Solving and Data Analysis", "skill": "Inference from sample statistics and margin of error ", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

From a population of 50,000\n people, 1,000\n were chosen at random and surveyed about a proposed piece of legislation. Based on the survey, it is estimated that 35\n% of people in the population support the legislation, with an associated margin of error of 3\n%. Based on these results, which of the following is a plausible value for the total number of people in the population who support the proposed legislation?

", "choices": [{"id": "A", "text": "

350\n

"}, {"id": "B", "text": "

650\n

"}, {"id": "C", "text": "

16,750\n

"}, {"id": "D", "text": "

31,750\n

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. It’s given that an estimated 35% of people in the population support the legislation, with an associated margin of error of 3%. Subtracting and adding the margin of error from the estimate gives an interval of plausible values for the true percentage of people in the population who support the legislation. Therefore, it’s plausible that between 32% and 38% of people in this population support the legislation. The corresponding numbers of people represented by these percentages in the population can be calculated by multiplying the total population, 50,000\n, by 0.32\n and by 0.38\n, which gives 50,0000.32=16,000 and 50,0000.38=19,000, respectively. It follows that any value in the interval 16,000\n to 19,000\n is a plausible value for the total number of people in the population who support the proposed legislation. Of the choices given, only 16,750\n is in this interval.

\n

Choice A is incorrect. This is the number of people in the sample, rather than in the population, who support the legislation.

\n

Choice B is incorrect. This is the number of people in the sample who do not support the legislation.

\n

Choice D is incorrect. This is a plausible value for the total number of people in the population who do not support the proposed legislation.

"}, {"id": "bfa8a85c", "domain": "Problem-Solving and Data Analysis", "skill": "One-variable data: Distributions and measures of center and spread", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

6\n, 6\n, 8\n, 8\n, 8\n, 10\n, 21\n

\n

Which of the following lists represents a data set that has the same median as the data set shown?

", "choices": [{"id": "A", "text": "

4\n, 6\n, 6\n, 6\n, 8\n, 8\n

"}, {"id": "B", "text": "

6\n, 6\n, 8\n, 8\n, 10\n, 10\n

"}, {"id": "C", "text": "

6\n, 8\n, 10\n, 10\n, 10\n, 12\n

"}, {"id": "D", "text": "

8\n, 8\n, 10\n, 10\n, 21\n, 21\n

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. If a data set contains an odd number of data values, the median is represented by the middle data value in the list when the data values are listed in ascending or descending order. Since the data set shown has 7\n data values and is in ascending order, it follows that the median is the fourth data value in the list, or 8\n. If a data set contains an even number of data values, the median is between the two middle data values when the values are listed in ascending or descending order. Since each of the choices consists of a data set with 6\n data values in ascending order, it follows that the median is between the third and fourth data value. The third and fourth data values in choice B are 8\n and 8\n. Thus, choice B represents a data set with a median of 8\n. Since the median of the data set shown is 8\n and choice B represents a data set with a median of 8\n, it follows that choice B represents a data set that has the same median as the data set shown.

\n

Choice A is incorrect. This list represents a data set with a median of 6\n, not 8\n.

\n

Choice C is incorrect. This list represents a data set with a median of 10\n, not 8\n.

\n

Choice D is incorrect. This list represents a data set with a median of 10\n, not 8\n.

"}, {"id": "c9dd92b1", "domain": "Problem-Solving and Data Analysis", "skill": "Two-variable data: Models and scatterplots", "difficulty": "E", "type": "mc", "stimulus": "
\n
\n \"The
\n
\n", "stem": "

The densities of different concentrations of grape juice are shown in the scatterplot above. According to the trend shown by the data, which of the following is closest to the predicted density, in kilograms per cubic meter (kg/m3), for grape juice with a concentration of 60%?

\n", "choices": [{"id": "A", "text": "

1,200

\n"}, {"id": "B", "text": "

1,250

\n"}, {"id": "C", "text": "

1,300

\n"}, {"id": "D", "text": "

1,350

\n"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. The data in the scatterplot show an increasing linear trend. The density when the juice concentration is 60% will be between the densities shown at about 53% and 67% concentration, or between about 1,255 and 1,340 kg/m3. Of the choices given, only 1,300 falls within this range.

Choices A, B, and D are incorrect. These are the approximate densities of grape juice with a concentration of 45%, 55%, and 70%, respectively.

\n"}, {"id": "9bf4c545", "domain": "Problem-Solving and Data Analysis", "skill": "Evaluating statistical claims: Observational studies and experiments ", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

The members of a city council wanted to assess the opinions of all city residents about converting an open field into a dog park. The council surveyed a sample of 500 city residents who own dogs. The survey showed that the majority of those sampled were in favor of the dog park. Which of the following is true about the city council’s survey?

\n", "choices": [{"id": "A", "text": "

It shows that the majority of city residents are in favor of the dog park.

\n"}, {"id": "B", "text": "

The survey sample should have included more residents who are dog owners.

\n"}, {"id": "C", "text": "

The survey sample should have consisted entirely of residents who do not own dogs.

\n"}, {"id": "D", "text": "

The survey sample is biased because it is not representative of all city residents.

\n"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. The members of the city council wanted to assess opinions of all city residents. To gather an unbiased sample, the council should have used a random sampling design to select subjects from all city residents. The given survey introduced a sampling bias because the 500 city residents surveyed were all dog owners. This sample is not representative of all city residents because not all city residents are dog owners.

Choice A is incorrect because when the sampling method isn’t random, there is no guarantee that the survey results will be reliable; hence, they cannot be generalized to the entire population. Choice B is incorrect because a larger sample of residents who are dog owners would not correct the sampling bias. Choice C is incorrect because a survey sample of entirely non–dog owners would likely have a biased opinion, just as a sample of dog owners would likely have a biased opinion.

\n \n

\n"}, {"id": "fa7a0164", "domain": "Problem-Solving and Data Analysis", "skill": "One-variable data: Distributions and measures of center and spread", "difficulty": "E", "type": "mc", "stimulus": "
\n
\n
\n

The table below shows the high and low temperatures in Houston, Texas, during a five-day period.

\n
\n
\n
\n \"The
\n
\n", "stem": "

What was the mean low temperature, in degrees Fahrenheit, during the five-day period?

\n", "choices": [{"id": "A", "text": "

48.8

\n"}, {"id": "B", "text": "

49

\n"}, {"id": "C", "text": "

59

\n"}, {"id": "D", "text": "

59.1

\n"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. The mean low temperature can be calculated by finding the sum of the low temperatures for all the days shown in the table, 49 + 37 + 41 + 54 + 63 = 244, and then dividing the sum by the number of days the temperature was recorded, 244 divided by 5 = 48 point 8.

Choice B is incorrect. This may be the result of choosing the median rather than calculating the mean. Choices C and D are incorrect and may be the result of calculation errors.

\n"}, {"id": "40e7a1a9", "domain": "Problem-Solving and Data Analysis", "skill": "Percentages", "difficulty": "H", "type": "spr", "stimulus": "", "stem": "

210\n is p% greater than 30\n. What is the value of p\n?

", "choices": [], "answerId": "600", "acceptedAnswers": ["600"], "rationale": "

The correct answer is 600\n. It’s given that 210\n is p% greater than 30\n. It follows that 210=1+p10030. Dividing both sides of this equation by 30\n yields 7=1+p100. Subtracting 1\n from both sides of this equation yields 6=p100. Multiplying both sides of this equation by 100\n yields \n\tp\n\t=\n\t600\n\n. Therefore, the value of p\n is 600\n.

"}, {"id": "708590d7", "domain": "Problem-Solving and Data Analysis", "skill": "One-variable data: Distributions and measures of center and spread", "difficulty": "E", "type": "mc", "stimulus": "
\n

\n Data set A is the set consisting(t)he following seven numbers: 1, 2,, 3,, 4,, 5,, 6,, 7. Data set B is the set consisting(t)he following seven numbers: 1, 1,, 2,, 2,, 3,, 3,, 4.\n

\n
\n", "stem": "

Which of the following statements correctly compares the means of data set A and data set B?

\n", "choices": [{"id": "A", "text": "

The mean of each data set is 2.

\n"}, {"id": "B", "text": "

The mean of each data set is 4.

\n"}, {"id": "C", "text": "

The mean of data set A is less than the mean of data set B.

\n"}, {"id": "D", "text": "

The mean of data set A is greater than the mean of data set B.

\n"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. The mean of a data set is found by dividing the sum of the values in the data set by the number of values in the data set. Therefore, the mean of data set A is (1 + 2, + 3, + 4, + 5, + 6, + 7)/(7 = (28)/(7)), or 4. The mean of data set B is (1 + 1, + 2, + 2, + 3, + 3, + 4)/(7 = (16)/(7)), or approximately 2.2857. Therefore, the mean of data set A is greater than the mean of data set B.

Alternate approach: Data set A and data set B are both ordered from least to greatest value. Besides the first value in each data set, which is 1, each value in ordered data set B is less than the respective value in ordered data set A. Therefore, conceptually, the mean of data set A must be greater than the mean of data set B.

Choices A, B, and C are incorrect and may result from various misconceptions or miscalculations.

\n"}, {"id": "bf47ad54", "domain": "Problem-Solving and Data Analysis", "skill": "One-variable data: Distributions and measures of center and spread", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

Each of the following frequency tables represents a data set. Which data set has the greatest mean?

", "choices": [{"id": "A", "text": "
\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
ValueFrequency
70\n4\n
80\n5\n
90\n6\n
100\n7\n
"}, {"id": "B", "text": "
\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
ValueFrequency
70\n6\n
80\n6\n
90\n6\n
100\n6\n
"}, {"id": "C", "text": "
\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
ValueFrequency
70\n7\n
80\n6\n
90\n6\n
100\n7\n
"}, {"id": "D", "text": "
\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
ValueFrequency
70\n8\n
80\n5\n
90\n5\n
100\n8\n
"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. The tables in choices B, C, and D each represent a data set where the values 80\n and 90\n have the same frequency and the values 70\n and 100\n have the same frequency. It follows that each of these data sets is symmetric around the value halfway between 80\n and 90\n, or 85\n. When a data set is symmetric around a value, that value is the mean of the data set. Therefore, the data sets represented by the tables in choices B, C, and D each have a mean of 85\n. The table in choice A represents a data set where the value 90\n has a greater frequency than the value 80\n and the value 100\n has a greater frequency than the value 70\n. It follows that this data set has a mean greater than 85\n. Therefore, of the given choices, choice A represents the data set with the greatest mean.

\n

Choice B is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

\n

Choice D is incorrect and may result from conceptual or calculation errors.

"}, {"id": "a6b2fcce", "domain": "Problem-Solving and Data Analysis", "skill": "Two-variable data: Models and scatterplots", "difficulty": "E", "type": "mc", "stimulus": "
\n
\n \"The
\n
\n", "stem": "

According to the line graph above, between which two consecutive years was there the greatest change in the number of 3‑D movies released?

\n", "choices": [{"id": "A", "text": "

2003–2004

\n"}, {"id": "B", "text": "

2008–2009

\n"}, {"id": "C", "text": "

2009–2010

\n"}, {"id": "D", "text": "

2010–2011

\n"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. The change in the number of 3-D movies released between any two consecutive years can be found by first estimating the number of 3-D movies released for each of the two years and then finding the positive difference between these two estimates. Between 2003 and 2004, this change is approximately 2 \u2212 2 = 0 movies; between 2008 and 2009, this change is approximately 20 \u2212 8 = 12 movies; between 2009 and 2010, this change is approximately 26 \u2212 20 = 6 movies; and between 2010 and 2011, this change is approximately 46 \u2212 26 = 20 movies. Therefore, of the pairs of consecutive years in the choices, the greatest increase in the number of 3-D movies released occurred during the time period between 2010 and 2011.

Choices A, B, and C are incorrect. Between 2010 and 2011, approximately 20 more 3-D movies were released. The change in the number of 3-D movies released between any of the other pairs of consecutive years is significantly smaller than 20.

\n"}, {"id": "06a152cd", "domain": "Problem-Solving and Data Analysis", "skill": "Ratios, rates, proportional relationships, and units", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

To make a bakery’s signature chocolate muffins, a baker needs 2.5 ounces of chocolate for each muffin. How many pounds of chocolate are needed to make 48 signature chocolate muffins? (1 pound = 16 ounces)

\n", "choices": [{"id": "A", "text": "

7.5

\n"}, {"id": "B", "text": "

10

\n"}, {"id": "C", "text": "

50.5

\n"}, {"id": "D", "text": "

120

\n"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. If 2.5 ounces of chocolate are needed for each muffin, then the number of ounces of chocolate needed to make 48 muffins is 48 \u00d7 2 point 5 = 120 ounces. Since 1 pound = 16 ounces, the number of pounds that is equivalent to 120 ounces is120 over 16 = 7 point 5 pounds. Therefore, 7.5 pounds of chocolate are needed to make the 48 muffins.

Choice B is incorrect. If 10 pounds of chocolate were needed to make 48 muffins, then the total number of ounces of chocolate needed would be 10 \u00d7 16 = 160 ounces. The number of ounces of chocolate per muffin would then be160 over 48 = 3 point 3 3 ounces per muffin, not 2.5 ounces per muffin. Choices C and D are also incorrect. Following the same procedures as used to test choice B gives 16.8 ounces per muffin for choice C and 40 ounces per muffin for choice D, not 2.5 ounces per muffin. Therefore, 50.5 and 120 pounds cannot be the number of pounds needed to make 48 signature chocolate muffins.

 

\n"}, {"id": "7d68096f", "domain": "Problem-Solving and Data Analysis", "skill": "Evaluating statistical claims: Observational studies and experiments ", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

A trivia tournament organizer wanted to study the relationship between the number of points a team scores in a trivia round and the number of hours that a team practices each week. For the study, the organizer selected 55\n teams at random from all trivia teams in a certain tournament. The table displays the information for the 40\n teams in the sample that practiced for at least 3\n hours per week.

\n
\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
Hours practicedNumber of points per round
6 to 13 points14 or more pointsTotal
3 to 5 hours6\n4\n10\n
More than 5 hours4\n26\n30\n
Total10\n30\n40\n
\n

Which of the following is the largest population to which the results of the study can be generalized?

", "choices": [{"id": "A", "text": "

All trivia teams in the tournament that scored 14\n or more points in the round

"}, {"id": "B", "text": "

The 55\n trivia teams in the sample

"}, {"id": "C", "text": "

The 40\n trivia teams in the sample that practiced for at least 3\n hours per week

"}, {"id": "D", "text": "

All trivia teams in the tournament

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. It's given that the organizer selected 55\n teams at random from all trivia teams in the tournament. A table is also given displaying the information for the 40\n teams in the sample that practiced for at least 3\n hours per week. Selecting a sample of a reasonable size at random to use for a survey allows the results from that survey to be applied to the population from which the sample was selected, but not beyond this population. Thus, only the sampling method information is necessary to determine the largest population to which the results of the study can be generalized. Since the organizer selected the sample at random from all trivia teams in the tournament, the largest population to which the results of the study can be generalized is all trivia teams in the tournament.

\n

Choice A is incorrect. The sample was selected at random from all trivia teams in the tournament, not just from the teams that scored an average of 14\n or more points per round.

\n

Choice B is incorrect. If a study uses a sample selected at random from a population, the results of the study can be generalized to the population, not just the sample.

\n

Choice C is incorrect. If a study uses a sample selected at random from a population, the results of the study can be generalized to the population, not just a subset of the sample.

"}, {"id": "7760c516", "domain": "Problem-Solving and Data Analysis", "skill": "One-variable data: Distributions and measures of center and spread", "difficulty": "E", "type": "spr", "stimulus": "", "stem": "

Each value in the data set shown represents the height, in centimeters, of a plant. 

\n

6\n, 10\n, 13\n, 2\n, 15\n, 22\n, 10\n, 4\n, 4\n, 4\n

\n

What is the mean height, in centimeters, of these plants?

", "choices": [], "answerId": "9", "acceptedAnswers": ["9"], "rationale": "

The correct answer is 9\n. The mean of a data set is the sum of the values in the data set divided by the number of values in the data set. It follows that the mean height, in centimeters, of these plants is the sum of the heights, in centimeters, of each plant, 6+10+13+2+15+22+10+4+4+4, or 90\n, divided by the number of plants in the data set, 10\n. Therefore, the mean height, in centimeters, of these plants is 9010, or 9\n. 

"}, {"id": "8917ce38", "domain": "Problem-Solving and Data Analysis", "skill": "Ratios, rates, proportional relationships, and units", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

Which of the following speeds is equivalent to 90 kilometers per hour? (1 kilometer = 1,000 meters)

\n", "choices": [{"id": "A", "text": "

25 meters per second

\n"}, {"id": "B", "text": "

32 meters per second

\n"}, {"id": "C", "text": "

250 meters per second

\n"}, {"id": "D", "text": "

324 meters per second

\n"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. Since 1 kilometer is equal to 1,000 meters, it follows that 90 kilometers is equal to 90 \u00d7 1,000 = 90,000 meters. Since 1 hour is equal to 60 minutes and 1 minute is equal to 60 seconds, it follows that 1 hour is equal to 60 \u00d7 60 = 3,600 seconds. Now (90 kilometers)/(1 hour) is equal to (90,000 meters)/(3,600 seconds), which reduces to (25 meters)/(1 second) or 25 meters per second.

Choices B, C, and D are incorrect and may result from conceptual or calculation errors.

 

\n"}, {"id": "f4b3672a", "domain": "Problem-Solving and Data Analysis", "skill": "Inference from sample statistics and margin of error ", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

A certain forest is 253 acres. To estimate the number of trees in the forest, a ranger randomly selects 5 different 1-acre parcels in the forest and determines the number of trees in each parcel. The numbers of trees in the sample acres are 51, 59, 45, 52, and 73. Based on the mean of the sample, which of the following ranges contains the best estimate for the number of trees in the entire forest?

\n", "choices": [{"id": "A", "text": "

11,000 to 12,000

\n"}, {"id": "B", "text": "

12,500 to 13,500

\n"}, {"id": "C", "text": "

13,500 to 14,500

\n"}, {"id": "D", "text": "

18,000 to 19,000

\n"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. The mean of the 5 samples is the fraction with numerator, 51 + 59 + 45 + 52 + 73, and denominator 5 = 56 trees per acre. The best estimate for the total number of trees in the forest is the product of the mean number of trees per acre in the sample and the total number of acres in the forest. This is (56)(253) = 14,168, which is between 13,500 and 14,500.

Choice A is incorrect and may result from multiplying the minimum number of trees per acre in the sample, 45, by the number of acres, 253. Choice B is incorrect and may result from multiplying the median number of trees per acre in the sample, 52, by the number of acres, 253. Choice D is incorrect and may result from multiplying the maximum number of trees per acre in the sample, 73, by the number of acres, 253.

 

\n"}, {"id": "374b18f9", "domain": "Problem-Solving and Data Analysis", "skill": "One-variable data: Distributions and measures of center and spread", "difficulty": "E", "type": "mc", "stimulus": "
\n
\n \"The
\n
\n", "stem": "

The number of acres of useful timberland in 13 counties in California is summarized in the box plot above. Which of the following is closest to the median number of acres?

\n", "choices": [{"id": "A", "text": "

4,399

\n"}, {"id": "B", "text": "

7,067

\n"}, {"id": "C", "text": "

8,831

\n"}, {"id": "D", "text": "

10,595

\n"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. The median of the data summarized by a box plot is the value associated with the vertical line segment within the box. According to the box plot shown, this value is slightly greater than 7,000. Therefore, the closest value for the median number of acres is 7,067.

Choice A is incorrect. This is the value associated with the vertical line segment forming the left-hand side of the box. Choice C is incorrect. This value is greater than the value associated with the vertical line segment within the box. Choice D is incorrect. This is the value associated with the vertical line segment forming the right-hand side of the box.

\n"}, {"id": "4ff597db", "domain": "Problem-Solving and Data Analysis", "skill": "One-variable data: Distributions and measures of center and spread", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

The mean amount of time that the 20 employees of a construction company have worked for the company is 6.7 years. After one of the employees leaves the company, the mean amount of time that the remaining employees have worked for the company is reduced to 6.25 years. How many years did the employee who left the company work for the company?

\n", "choices": [{"id": "A", "text": "

0.45

\n"}, {"id": "B", "text": "

2.30

\n"}, {"id": "C", "text": "

9.00

\n"}, {"id": "D", "text": "

15.25

\n"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. The mean amount of time that the 20 employees worked for the company is 6.7 years. This means that the total number of years all 20 employees worked for the company is (6.7)(20) = 134 years. After the employee left, the mean amount of time that the remaining 19 employees worked for the company is 6.25 years. Therefore, the total number of years all 19 employees worked for the company is (6.25)(19) = 118.75 years. It follows that the number of years that the employee who left had worked for the company is 134 – 118.75 = 15.25 years.

Choice A is incorrect; this is the change in the mean, which isn’t the same as the amount of time worked by the employee who left. Choice B is incorrect and likely results from making the assumption that there were still 20 employees, rather than 19, at the company after the employee left and then subtracting the original mean of 6.7 from that result. Choice C is incorrect and likely results from making the assumption that there were still 20 employees, rather than 19, at the company after the employee left.

\n"}, {"id": "ec787383", "domain": "Problem-Solving and Data Analysis", "skill": "Ratios, rates, proportional relationships, and units", "difficulty": "M", "type": "spr", "stimulus": "", "stem": "

A distance of 61\n furlongs is equivalent to how many feet? 1 furlong=220 yards and 1 yard=3 feet

", "choices": [], "answerId": "40260", "acceptedAnswers": ["40260"], "rationale": "

The correct answer is 40,260\n. It's given that 1 furlong=220 yards and 1 yard=3 feet. It follows that a distance of 61\n furlongs is equivalent to 61 furlongs220 yards1 furlong3 feet1 yard, or 40,260\n feet.

"}, {"id": "7e6c745f", "domain": "Problem-Solving and Data Analysis", "skill": "Ratios, rates, proportional relationships, and units", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "
\n \n
\n
\n \n \n \n \n \n \n \n \n \n
FoodProtein Cost
1 large egg6 grams$0.36
1 cup of milk8 grams$0.24
\n

The table above shows the amount of protein in two foods and the cost of each food. Based on the table, what is the ratio of the cost per gram of protein in a large egg to the cost per gram of protein in a cup of milk?

\n", "choices": [{"id": "A", "text": "

1 : 2

\n"}, {"id": "B", "text": "

2 : 3

\n"}, {"id": "C", "text": "

3 : 4

\n"}, {"id": "D", "text": "

2 : 1

\n"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. The cost per gram of protein in 1 large egg is $0.36 ÷ 6 = $0.06. The cost per gram of protein in 1 cup of milk is $0.24 ÷ 8 = $0.03. It follows that the ratio of the cost per gram of protein in a large egg to the cost per gram of protein in a cup of milk is 0.06:0.03, which can be rewritten as 2:1.

Choice A is incorrect and may result from finding the ratio of the cost per gram of protein in a cup of milk to the cost per gram of protein in a large egg (the reciprocal of the ratio specified in the question). Choices B and C are incorrect and may result from incorrectly calculating the unit rates or from errors made when simplifying the ratio.

\n"}, {"id": "7b52985c", "domain": "Problem-Solving and Data Analysis", "skill": "Two-variable data: Models and scatterplots", "difficulty": "H", "type": "spr", "stimulus": "", "stem": "

The scatterplot shows the relationship between the length of time y\n, in hours, a certain bird spent in flight and the number of days after January 11\n, x\n.

\n

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n

\n

What is the average rate of change, in hours per day, of the length of time the bird spent in flight on January 13\n to the length of time the bird spent in flight on January 15\n?

", "choices": [], "answerId": "4.5", "acceptedAnswers": ["4.5", "9/2"], "rationale": "

The correct answer is \n\t9\n\t2\n\n. It's given that the scatterplot shows the relationship between the length of time y\n, in hours, a certain bird spent in flight and the number of days after January 11\n, x\n. Since January 13\n is 2\n days after January 11\n, it follows that January 13\n corresponds to an x-value of 2\n in the scatterplot. In the scatterplot, when \n\tx\n\t=\n\t2\n\n, the corresponding value of y\n is 6\n. In other words, on January 13\n, the bird spent 6\n hours in flight. Since January 15\n is 4\n days after January 11\n, it follows that January 15\n corresponds to an x-value of 4\n in the scatterplot. In the scatterplot, when \n\tx\n\t=\n\t4\n\n, the corresponding value of y\n is 15\n. In other words, on January 15\n, the bird spent 15\n hours in flight. Therefore, the average rate of change, in hours per day, of the length of time the bird spent in flight on January 13\n to the length of time the bird spent in flight on January 15\n is the difference in the length of time, in hours, the bird spent in flight divided by the difference in the number of days after January 11\n, or 15-64-2, which is equivalent to \n\t9\n\t2\n\n. Note that 9/2 and 4.5 are examples of ways to enter a correct answer.

"}, {"id": "7ce2830a", "domain": "Problem-Solving and Data Analysis", "skill": "Evaluating statistical claims: Observational studies and experiments ", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

A psychologist designed and conducted a study to determine whether playing a certain educational game increases middle school students’ accuracy in adding fractions. For the study, the psychologist chose a random sample of 35 students from all of the students at one of the middle schools in a large city. The psychologist found that students who played the game showed significant improvement in accuracy when adding fractions. What is the largest group to which the results of the study can be generalized?

\n", "choices": [{"id": "A", "text": "

The 35 students in the sample

\n"}, {"id": "B", "text": "

All students at the school

\n"}, {"id": "C", "text": "

All middle school students in the city

\n"}, {"id": "D", "text": "

All students in the city

\n"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. The largest group to which the results of a study can be generalized is the population from which the random sample was chosen. In this case, the psychologist chose a random sample from all students at one particular middle school. Therefore, the largest group to which the results can be generalized is all the students at the school.

Choice A is incorrect because this isn’t the largest group the results can be generalized to. Choices C and D are incorrect because these groups are larger than the population from which the random sample was chosen. Therefore, the sample isn’t representative of these groups.

 

\n"}, {"id": "12dbe3de", "domain": "Problem-Solving and Data Analysis", "skill": "Probability and conditional probability", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

A store received a shipment of 1,000 MP3 players, 4 of which were defective. If an MP3 player is randomly selected from this shipment, what is the probability that it is defective?

\n", "choices": [{"id": "A", "text": "

0.004

\n"}, {"id": "B", "text": "

0.04

\n"}, {"id": "C", "text": "

0.4

\n"}, {"id": "D", "text": "

4

\n"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. The probability of randomly selecting a defective MP3 player from the shipment is equal to the number of defective MP3 players divided by the total number of MP3 players in the shipment. Therefore, the probability is 4 over 1,000, which is equivalent to 0.004.

Choice B is incorrect because 0.04 represents 4 defective MP3 players out of 100 rather than out of 1,000. Choice C is incorrect because 0.4 represents 4 defective MP3 players out of 10 rather than out of 1,000. Choice D is incorrect. This is the number of defective MP3 players in the shipment.

 

\n"}, {"id": "709e04de", "domain": "Problem-Solving and Data Analysis", "skill": "Percentages", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

The value of z\n is 1.13\n times 100\n. The value of z\n is what percent greater than 100\n?

", "choices": [{"id": "A", "text": "

11.3\n

"}, {"id": "B", "text": "

13\n

"}, {"id": "C", "text": "

130\n

"}, {"id": "D", "text": "

213\n

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. It’s given that the value of z\n is 1.13 times 100\n. This can be written as z=1.13100, which is equivalent to z=1+0.13(100), or z=1+13100100. It follows that the value of z\n is 100% of 100\n plus 13% of 100\n. Therefore, the value of z\n is 13% greater than 100\n.

\n

Choice A is incorrect. This gives a value of z\n that is 1.113\n, not 1.13\n, times 100\n.

\n

Choice C is incorrect. This gives a value of z\n that is 2.30\n, not 1.13\n, times 100\n.

\n

Choice D is incorrect. This gives a value of z\n that is 3.13\n, not 1.13\n, times 100\n.

"}, {"id": "642519d7", "domain": "Problem-Solving and Data Analysis", "skill": "Evaluating statistical claims: Observational studies and experiments ", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

A polling agency recently surveyed 1,000 adults who were selected at random from a large city and asked each of the adults, “Are you satisfied with the quality of air in the city?” Of those surveyed, 78 percent responded that they were satisfied with the quality of air in the city. Based on the results of the survey, which of the following statements must be true?

  1. Of all adults in the city, 78 percent are satisfied with the quality of air in the city.
    2. \n
  2. If another 1,000 adults selected at random from the city were surveyed, 78 percent of them would report they are satisfied with the quality of air in the city.
    3. \n
  3. If 1,000 adults selected at random from a different city were surveyed, 78 percent of them would report they are satisfied with the quality of air in the city.
    4. \n

\n", "choices": [{"id": "A", "text": "

None

\n"}, {"id": "B", "text": "

II only

\n"}, {"id": "C", "text": "

I and II only

\n"}, {"id": "D", "text": "

I and III only

\n"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. Statement I need not be true. The fact that 78% of the 1,000 adults who were surveyed responded that they were satisfied with the air quality in the city does not mean that the exact same percentage of all adults in the city will be satisfied with the air quality in the city. Statement II need not be true because random samples, even when they are of the same size, are not necessarily identical with regard to percentages of people in them who have a certain opinion. Statement III need not be true for the same reason that statement II need not be true: results from different samples can vary. The variation may be even bigger for this sample since it would be selected from a different city. Therefore, none of the statements must be true.

Choices B, C, and D are incorrect because none of the statements must be true.

\n"}, {"id": "0108ac2d", "domain": "Problem-Solving and Data Analysis", "skill": "Inference from sample statistics and margin of error ", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

At a large high school, 300 students were selected at random and were asked in a survey about a menu change in the school cafeteria. All 300 students completed the survey. It was estimated that 38% of the students were in support of a menu change, with a margin of error of 5.5%. Which of the following is the best interpretation of the survey results?

\n", "choices": [{"id": "A", "text": "

The percent of the students at the school who support a menu change is 38%.

\n"}, {"id": "B", "text": "

The percent of the students at the school who support a menu change is greater than 38%.

\n"}, {"id": "C", "text": "

Plausible values of the percent of the students at the school who support a menu change are between 32.5% and 43.5%.

\n"}, {"id": "D", "text": "

Plausible values of the number of the students at the school who support a menu change are between 295 and 305.

\n"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. It’s given that an estimated 38% of sampled students at the school were in support of a menu change, with a margin of error of 5.5%. It follows that the percent of the students at the school who support a menu change is 38% plus or minus 5.5%. The lower bound of this estimation is 38 \u2212 5 point 5, or 32.5%. The upper bound of this estimation is 38 + 5 point 5, or 43.5%. Therefore, plausible values of the percent of the students at the school who support a menu change are between 32.5% and 43.5%.

Choice A is incorrect. This is the percent of the sampled students at the school who support a menu change. Choices B and D are incorrect and may result from misinterpreting the margin of error.

 

\n"}, {"id": "949cd96b", "domain": "Problem-Solving and Data Analysis", "skill": "Percentages", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

The length of the base of a certain parallelogram is 89% of the height of the parallelogram. Which expression represents the length of the base of the parallelogram, where h\n is the height of the parallelogram?

", "choices": [{"id": "A", "text": "

\n\t89\n\th\n\n

"}, {"id": "B", "text": "

\n\t0.089\n\th\n\n

"}, {"id": "C", "text": "

\n\t8.9\n\th\n\n

"}, {"id": "D", "text": "

\n\t0.89\n\th\n\n

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. It's given that the length of the base of the parallelogram is 89% of the height of the parallelogram. Since h\n is the height of the parallelogram, it follows that the length of the base of the parallelogram can be represented by the expression 89100h, or \n\t0.89\n\th\n\n.

\n

Choice A is incorrect. This expression represents 8,900%, not 89%, of the height of the parallelogram.

\n

Choice B is incorrect. This expression represents 8.9%, not 89%, of the height of the parallelogram.

\n

Choice C is incorrect. This expression represents 890%, not 89%, of the height of the parallelogram.

"}, {"id": "28c6bd8c", "domain": "Problem-Solving and Data Analysis", "skill": "Percentages", "difficulty": "E", "type": "mc", "stimulus": "
\n
\n
\n \"The
\n
\n
\n", "stem": "

The table above shows a summary of 1,200 responses to a survey question. Based on the table, how many of those surveyed get most of their medical information from either a doctor or the Internet?

\n", "choices": [{"id": "A", "text": "

865

\n"}, {"id": "B", "text": "

887

\n"}, {"id": "C", "text": "

912

\n"}, {"id": "D", "text": "

926

\n"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. According to the table, 63% of survey respondents get most of their medical information from a doctor and 13% get most of their medical information from the Internet. Therefore, 76% of the 1,200 survey respondents get their information from either a doctor or the Internet, and 76% of 1,200 is 912.

Choices A, B, and D are incorrect. According to the table, 76% of survey respondents get their information from either a doctor or the Internet. Choice A is incorrect because 865 is about 72% (the percent of survey respondents who get most of their medical information from a doctor or from magazines/brochures), not 76%, of 1,200. Choice B is incorrect because 887 is about 74%, not 76%, of 1,200. Choice D is incorrect because 926 is about 77%, not 76%, of 1,200.

\n"}, {"id": "912cd125", "domain": "Problem-Solving and Data Analysis", "skill": "Probability and conditional probability", "difficulty": "M", "type": "mc", "stimulus": "
\n
\n
\n

For a science project, Anka recorded whether it rained each weekday and weekend day for 12 weeks. Her results are summarized in the table below.

\n
\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n
Weekday and Weekend Day Rain for 12 Weeks
RainNo rainTotal
Number of weekdays124860
Number of weekend days81624
Total206484
\n
\n
\n
\n", "stem": "

If one of the days on which there was no rain is selected at random, what is the probability the day was a weekend day?

\n", "choices": [{"id": "A", "text": "(4)/(21)\n"}, {"id": "B", "text": "(1)/(4)\n"}, {"id": "C", "text": "(2)/(3)\n"}, {"id": "D", "text": "(3)/(4)\n"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. There were 64 days with no rain. It was a weekend day for 16 of those 64 days. So 16 out of 64 of the days with no rain were weekend days. Because the day is selected at random, each day has an equal chance of being selected, so the probability is (16)/(64 = the fraction 1 over 4).

\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n Choice A is incorrect. It is the probability that a day selected at random from any one of the days during the 12 weeks is a weekend day with no rain. Choice C is incorrect. It is the probability that a day selected at random from the weekend days has no rain. Choice D is incorrect. It is the probability that a day selected at random from the days with no rain is a weekday.

\n"}, {"id": "3a6ed720", "domain": "Problem-Solving and Data Analysis", "skill": "Percentages", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

Of 900,000\n beads, 828,000\n are silver. What percentage of the beads are silver?

", "choices": [{"id": "A", "text": "

8\n%

"}, {"id": "B", "text": "

36\n%

"}, {"id": "C", "text": "

72\n%

"}, {"id": "D", "text": "

92\n%

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. The proportion of the beads that are silver can be written as 828,000900,000, or 0.92\n. Therefore, the percentage of the beads that are silver is 0.92100, or 92%.

\n

Choice A is incorrect. This is the percentage of the beads that are not silver.

\n

Choice B is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

"}, {"id": "85b33aa8", "domain": "Problem-Solving and Data Analysis", "skill": "Ratios, rates, proportional relationships, and units", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

A fish swam a distance of 5,104\n yards. How far did the fish swim, in miles? 1 mile=1,760 yards 

", "choices": [{"id": "A", "text": "

0.3\n

"}, {"id": "B", "text": "

2.9\n

"}, {"id": "C", "text": "

3,344\n

"}, {"id": "D", "text": "

6,864\n

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. It’s given that the fish swam 5,104\n yards and that 1\n mile is equal to 1,760\n yards. Therefore, the fish swam 5,104 yards1 mile1,760 yards, which is equivalent to 5,1041,760 miles, or 2.9\n miles. 

\n

Choice A is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

\n

Choice D is incorrect and may result from conceptual or calculation errors.

"}, {"id": "ba61d95f", "domain": "Problem-Solving and Data Analysis", "skill": "Percentages", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

The population of Greenville increased by 7\n% from 2015 to 2016. If the 2016 population is k\n times the 2015 population, what is the value of k\n?

", "choices": [{"id": "A", "text": "

0.07\n

"}, {"id": "B", "text": "

0.7\n

"}, {"id": "C", "text": "

1.07\n

"}, {"id": "D", "text": "

1.7\n

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. Let x\n be the 2015 population of Greenville. It's given that the population increased by 7% from 2015 to 2016. The increase in population can be written as 0.07x. The 2016 population of Greenville is given as the sum of the 2015 population of Greenville and the increase in population from 2015 to 2016. This can be rewritten as x+0.07x, or 1.07x. Therefore, the value of k\n is 1.07\n.

\n

Choice A is incorrect. This is the percent, represented as a decimal, that the population increased from 2015 to 2016, not the value of k\n.

\n

Choice B is incorrect and may result from conceptual or calculation errors.

\n

Choice D is incorrect. This is the value of k\n if the population increased by 70%, not 7%, from 2015 to 2016.

"}, {"id": "873d2838", "domain": "Problem-Solving and Data Analysis", "skill": "Ratios, rates, proportional relationships, and units", "difficulty": "M", "type": "spr", "stimulus": "", "stem": "

The population density of Cedar County is 230\n people per square mile. The county has a population of 85,100\n people. What is the area, in square miles, of Cedar County?

", "choices": [], "answerId": "370", "acceptedAnswers": ["370"], "rationale": "

The correct answer is 370\n. It’s given that the population density of Cedar County is 230\n people per square mile and the county has a population of 85,100\n people. Based on the population density, it follows that the area of Cedar County is 85,100 people1 square mile230 people, or 370\n square miles.

"}, {"id": "2cdefcb1", "domain": "Problem-Solving and Data Analysis", "skill": "Ratios, rates, proportional relationships, and units", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

What length, in centimeters, is equivalent to a length of 51\n meters? 1 meter=100 centimeters

", "choices": [{"id": "A", "text": "

0.051\n

"}, {"id": "B", "text": "

0.51\n

"}, {"id": "C", "text": "

5,100\n

"}, {"id": "D", "text": "

51,000\n

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. Since 1\n meter is equal to 100\n centimeters, 51\n meters is equal to 51 meters100 centimeters1 meter, or 5,100\n centimeters. 

\n

Choice A is incorrect and may result from conceptual or calculation errors.

\n

Choice B is incorrect and may result from dividing, rather than multiplying, 51\n by 100\n.

\n

Choice D is incorrect. This is the length, in millimeters rather than centimeters, that is equivalent to a length of 51\n meters. 

"}, {"id": "6a715bed", "domain": "Problem-Solving and Data Analysis", "skill": "Probability and conditional probability", "difficulty": "H", "type": "spr", "stimulus": "", "stem": "

The table summarizes the distribution of age and assigned group for 90\n participants in a study.

\n
\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
 0\n\u20139\n years10\n\u201319\n years20+ yearsTotal
Group A7\n14\n9\n30\n
Group B6\n4\n20\n30\n
Group C17\n12\n1\n30\n
Total30\n30\n30\n90\n
\n

One of these participants will be selected at random. What is the probability of selecting a participant from group A, given that the participant is at least 10\n years of age? (Express your answer as a decimal or fraction, not as a percent.)

", "choices": [], "answerId": ".3833", "acceptedAnswers": [".3833", "23/60"], "rationale": "

The correct answer is \n\t23\n\t60\n\n. It's given that one of the participants will be selected at random. The probability of selecting a participant from group A given that the participant is at least 10\n years of age is the number of participants in group A who are at least 10\n years of age divided by the total number of participants who are at least 10\n years of age. The table shows that in group A, there are 14\n participants who are 10\n–19\n years of age and 9\n participants who are 20+ years of age. Therefore, there are 14+9, or 23\n, participants in group A who are at least 10\n years of age. The table also shows that there are a total of 30\n participants who are 10\n–19\n years of age and 30\n participants who are 20+ years of age. Therefore, there are a total of 30+30, or 60\n, participants who are at least 10\n years of age. It follows that the probability of selecting a participant from group A given that the participant is at least 10\n years of age is \n\t23\n\t60\n\n. Note that 23/60, .3833, and 0.383 are examples of ways to enter a correct answer.

"}, {"id": "8cbf1415", "domain": "Problem-Solving and Data Analysis", "skill": "Percentages", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

In a group, 40\n% of the items are red. Of all the red items in the group, 30\n% also have stripes. What percentage of the items in the group are red with stripes?

", "choices": [{"id": "A", "text": "

10\n%

"}, {"id": "B", "text": "

12\n%

"}, {"id": "C", "text": "

70\n%

"}, {"id": "D", "text": "

75\n%

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. It’s given that in a group, 40% of the items are red. It follows that the number of red items in the group can be represented by 0.4x, where x\n represents the total number of items in the group. It’s also given that of all the red items in the group, 30% also have stripes. It follows that the number of items in the group that are red and have stripes can be represented by 0.30.4x, or 0.12x. The expression 0.12x represents 12% of x\n. Since x\n represents the total number of items in the group, it follows that 12% of the items in the group are red and have stripes.

\n

Choice A is incorrect and may result from subtracting 30% from 40% rather than calculating 30% of 40%.

\n

Choice C is incorrect and may result from adding 30% and 40% rather than calculating 30% of 40%.

\n

Choice D is incorrect and may result from calculating the percentage that 30% is of 40% rather than calculating 30% of 40%.

"}, {"id": "c7c6445f", "domain": "Problem-Solving and Data Analysis", "skill": "Ratios, rates, proportional relationships, and units", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

A certain town has an area of 4.36\n square miles. What is the area, in square yards, of this town? 1 mile=1,760 yards

", "choices": [{"id": "A", "text": "

404\n

"}, {"id": "B", "text": "

7,674\n

"}, {"id": "C", "text": "

710,459\n

"}, {"id": "D", "text": "

13,505,536\n

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. Since the number of yards in 1\n mile is 1,760\n, the number of square yards in 1\n square mile is (1,760)(1,760)=3,097,600. Therefore, if the area of the town is 4.36\n square miles, it is 4.36(3,097,600)=13,505,536, in square yards.

\n

Choice A is incorrect and may result from dividing the number of yards in a mile by the square mileage of the town.

\n

Choice B is incorrect and may result from multiplying the number of yards in a mile by the square mileage of the town.

\n

Choice C is incorrect and may result from dividing the number of square yards in a square mile by the square mileage of the town.

"}, {"id": "c54b92a2", "domain": "Problem-Solving and Data Analysis", "skill": "One-variable data: Distributions and measures of center and spread", "difficulty": "E", "type": "mc", "stimulus": "

A study was conducted on the production rates for a company that produces tractor wheels. The table below shows the number of wheels made during 11 consecutive one-hour production periods.

One-hour
period		Number
of wheels
made
A24
B24
C21
D21
E21
F19
G24
H24
I19
J22
K23

\n", "stem": "

What is the range of the number of wheels made for the 11 one-hour periods?

\n", "choices": [{"id": "A", "text": "

5.5

\n"}, {"id": "B", "text": "

5.0

\n"}, {"id": "C", "text": "

4.5

\n"}, {"id": "D", "text": "

4.0

\n"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. Range is defined as the difference between the greatest and least values from a set of data. The greatest number of wheels made during a one-hour period was 24 wheels. The least number of wheels was 19. Hence, the range is 24 \u2212 19 = 5, or 5.0.

Choices A, C, and D are incorrect and may be the result of arithmetic errors or incorrectly identifying the greatest or least number of wheels made during a one-hour period.

\n"}, {"id": "3c5b19ef", "domain": "Problem-Solving and Data Analysis", "skill": "Two-variable data: Models and scatterplots", "difficulty": "M", "type": "mc", "stimulus": "
\n
\n \"The
\n
\n", "stem": "

The scatterplot above shows the number of visitors to a railroad museum in Pennsylvania each year from 1968 to 1980, where t is the number of years since 1968 and n is the number of visitors. A line of best fit is also shown. Which of the following could be an equation of the line of best fit shown?

\n", "choices": [{"id": "A", "text": "

\n n = 16,090, + 4,680, t\n

\n"}, {"id": "B", "text": "

\n n = 4,690, + 16,090, t\n

\n"}, {"id": "C", "text": "

\n n = 16,090, + 9,060, t\n

\n"}, {"id": "D", "text": "

\n n = 9,060, + 16,090, t\n

\n"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. An equation of a line of best fit can be written in the form y = a, + b x, where a is the y-intercept of the line and b is the slope. In the scatterplot shown, the line of best fit intersects the y-axis just over halfway between 10,000 and 20,000, or approximately 16,000. The line of best fit also intersects the graph at the point 5, 40,000. Using the slope formula b = (y sub 2 \u2212 y sub 1)/(x sub 2 \u2212 x sub 1, end fraction) and two points that lie on the graph such as the point 5, 40,000 and the point 0, 16,000, the slope can be approximated as (40,000 \u2212 16,000)/(5 \u2212 0, end fraction), or 4,800. Only choice A has a y-intercept near the estimate of 16,000 and a slope near the estimate of 4,800. Therefore, an equation of the line of best fit could be n = 16,090 + 4,680 t.

Choice B is incorrect because the values for the slope and the y-coordinate of the y-intercept are switched. Choice C is incorrect because the value for the slope is approximately double the actual slope. Choice D is incorrect because the values for the slope and the y-intercept are switched and because the slope is approximately double the actual slope.

\n"}, {"id": "73ddfdac", "domain": "Problem-Solving and Data Analysis", "skill": "Ratios, rates, proportional relationships, and units", "difficulty": "M", "type": "spr", "stimulus": "", "stem": "

A distance of 112\n furlongs is equivalent to how many feet? 1 furlong=220 yards and 1 yard=3 feet

", "choices": [], "answerId": "73920", "acceptedAnswers": ["73920"], "rationale": "

The correct answer is 73,920\n. It's given that 1 furlong=220 yards and 1 yard=3 feet. It follows that a distance of 112 furlongs is equivalent to 112 furlongs220 yards1 furlong3 feet1 yard, or 73,920 feet.

"}, {"id": "96a45430", "domain": "Problem-Solving and Data Analysis", "skill": "Percentages", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

A number n is increased 6%. If the result is 318, what is the value of n ?

\n", "choices": [{"id": "A", "text": "

199

\n"}, {"id": "B", "text": "

299

\n"}, {"id": "C", "text": "

300

\n"}, {"id": "D", "text": "

337

\n"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. The decimal equivalent of 6% is 0.06. Since increasing the number n by 6% yields the number 318, this situation can be represented by the equation n times, open parenthesis, 1 + 0 point 0 6, close parenthesis = 318, or n \u00d7 1 point 0 6 = 318. Dividing both sides of this equation by 1.06 yields n = 300.

Choice A is incorrect. This is the result when n is increased by 60%, not by 6%. Choice B is incorrect. This is the approximate result of decreasing 318 by 6%. Choice D is incorrect. This is the approximate result of increasing 318 by 6%.

 

\n"}, {"id": "82dfb646", "domain": "Problem-Solving and Data Analysis", "skill": "Evaluating statistical claims: Observational studies and experiments ", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

A market researcher selected 200 people at random from a group of people who indicated that they liked a certain book. The 200 people were shown a movie based on the book and then asked whether they liked or disliked the movie. Of those surveyed, 95% said they disliked the movie. Which of the following inferences can appropriately be drawn from this survey result?

\n", "choices": [{"id": "A", "text": "

At least 95% of people who go see movies will dislike this movie.

\n"}, {"id": "B", "text": "

At least 95% of people who read books will dislike this movie.

\n"}, {"id": "C", "text": "

Most people who dislike this book will like this movie.

\n"}, {"id": "D", "text": "

Most people who like this book will dislike this movie.

\n"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. The sample was selected from a group of people who indicated that they liked the book. It is inappropriate to generalize the result of the survey beyond the population from which the participants were selected. Choice D is the most appropriate inference from the survey results because it describes a conclusion about people who liked the book, and the results of the survey indicate that most people who like the book disliked the movie.

Choices A, B, and C are incorrect because none of these inferences can be drawn from the survey results. Choices A and B need not be true. The people surveyed all liked the book on which the movie was based, which is not necessarily true of all people who go see movies or all people who read books. Thus, the people surveyed are not representative of all people who go see movies or all people who read books. Therefore, the results of this survey cannot appropriately be extended to at least 95% of people who go see movies or to at least 95% of people who read books. Choice C need not be true because the sample includes only people who liked the book, and so the results do not extend to people who dislike the book.

\n"}, {"id": "5c3c2e3c", "domain": "Problem-Solving and Data Analysis", "skill": "One-variable data: Distributions and measures of center and spread", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

The weights, in pounds, for 15 horses in a stable were reported, and the mean, median, range, and standard deviation for the data were found. The horse with the lowest reported weight was found to actually weigh 10 pounds less than its reported weight. What value remains unchanged if the four values are reported using the corrected weight?

\n", "choices": [{"id": "A", "text": "

Mean

\n"}, {"id": "B", "text": "

Median

\n"}, {"id": "C", "text": "

Range

\n"}, {"id": "D", "text": "

Standard deviation

\n"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. The median weight is found by ordering the horses’ weights from least to greatest and then determining the middle value from this list of weights. Decreasing the value for the horse with the lowest weight doesn’t affect the median since it’s still the lowest value.

Choice A is incorrect. The mean is calculated by finding the sum of all the weights of the horses and then dividing by the number of horses. Decreasing one of the weights would decrease the sum and therefore decrease the mean. Choice C is incorrect. Range is the difference between the highest and lowest weights, so decreasing the lowest weight would increase the range. Choice D is incorrect. Standard deviation is calculated based on the mean weight of the horses. Decreasing one of the weights decreases the mean and therefore would affect the standard deviation.

 

\n"}, {"id": "61b87506", "domain": "Problem-Solving and Data Analysis", "skill": "Ratios, rates, proportional relationships, and units", "difficulty": "M", "type": "spr", "stimulus": "", "stem": "

For the values j\n and k\n, the ratio of j\n to k\n is 11\n to 12\n. If j\n is multiplied by 17\n, what is k\n multiplied by in order to maintain the same ratio?

", "choices": [], "answerId": "17", "acceptedAnswers": ["17"], "rationale": "

The correct answer is 17\n. If one value is multiplied by a number, then the other value must be multiplied by the same number in order to maintain the same ratio. It’s given that j\n is multiplied by 17\n. Therefore, in order to maintain the same ratio, k\n must also be multiplied by 17\n.

"}, {"id": "30db8f77", "domain": "Problem-Solving and Data Analysis", "skill": "Probability and conditional probability", "difficulty": "M", "type": "spr", "stimulus": "", "stem": "

At a conference, there are a total of 275\n attendees. Each attendee is assigned to either group A, group B, or group C. If one of these attendees is selected at random, the probability of selecting an attendee who is assigned to group A is 0.44\n and the probability of selecting an attendee who is assigned to group B is 0.24\n. How many attendees are assigned to group C?

", "choices": [], "answerId": "88", "acceptedAnswers": ["88"], "rationale": "

The correct answer is 88\n. It's given that there are a total of 275\n attendees and each attendee is assigned to either group A, group B, or group C. It's also given that if one of these attendees is selected at random, the probability of selecting an attendee who is assigned to group A is 0.44\n and the probability of selecting an attendee who is assigned to group B is 0.24\n. It follows that there are 0.44275, or 121\n, attendees who are assigned to group A and 0.24275, or 66\n, attendees who are assigned to group B. The number of attendees who are assigned to group C is the number of attendees who are not assigned to group A or group B. In other words, the number of attendees who are assigned to group C is the total number of attendees minus the number of attendees who are assigned to group A and group B. Therefore, the number of attendees who are assigned to group C is 275-121-66, or 88\n.

"}, {"id": "43744269", "domain": "Problem-Solving and Data Analysis", "skill": "Two-variable data: Models and scatterplots", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

An airplane descends from an altitude of 9,500\n feet to 5,000\n feet at a constant rate of 400\n feet per minute. What type of function best models the relationship between the descending airplane's altitude and time?

", "choices": [{"id": "A", "text": "

Decreasing exponential

"}, {"id": "B", "text": "

Decreasing linear

"}, {"id": "C", "text": "

Increasing exponential

"}, {"id": "D", "text": "

Increasing linear

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. It′s given that the airplane descends at a constant rate of 400 feet per minute. Since the altitude decreases by a constant amount during each fixed time period, the relationship between the airplane′s altitude and time is linear. Since the airplane descends from an altitude of 9,500 feet to 5,000 feet, the airplane′s altitude is decreasing with time. Thus, the relationship is best modeled by a decreasing linear function.

\n

Choice A is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

\n

Choice D is incorrect and may result from conceptual or calculation errors.

"}, {"id": "3ac09984", "domain": "Problem-Solving and Data Analysis", "skill": "Ratios, rates, proportional relationships, and units", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

Marta has 7,500 pesos she will convert to US dollars using a currency exchange service. At this time, the currency exchange rate is 1 peso = 0.075 US dollars. The exchange service will charge Marta a 2% fee on the converted US dollar amount. How many US dollars will Marta receive from the currency exchange after the 2% fee is applied?

\n", "choices": [{"id": "A", "text": "$551

.25\n

\n"}, {"id": "B", "text": "$562

.50\n

\n"}, {"id": "C", "text": "$5,625

.00\n

\n"}, {"id": "D", "text": "$98,000

.00\n

\n"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. At the exchange rate of 1 peso = 0.075 US dollars, 7,500 pesos would be converted to 7,500 × 0.075 = $562.50. However, since Maria pays a 2% fee on the converted US dollar amount, she receives only (100 – 2)%, or 98%, of the converted US dollars, and 562.50 × 0.98 = $551.25.

Choice B is incorrect. This is the number of US dollars Maria would receive if the exchange service did not charge a 2% fee. Choice C is incorrect and may result from a decimal point error made when calculating the conversion to US dollars and from not assessing the 2% fee. Choice D is incorrect and may result from reversing the units of the exchange rate.

\n"}, {"id": "66f03086", "domain": "Problem-Solving and Data Analysis", "skill": "One-variable data: Distributions and measures of center and spread", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

71\n, 72\n, 73\n, 76\n, 77\n, 79\n, 83\n, 87\n, 93\n

\n

What is the median of the data shown?

", "choices": [{"id": "A", "text": "

71\n

"}, {"id": "B", "text": "

77\n

"}, {"id": "C", "text": "

78\n

"}, {"id": "D", "text": "

79\n

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. The median of a data set with an odd number of data values is defined as the middle value of the ordered list of values. The data set shown has nine values, so the median is the fifth value in the ordered list, which is 77\n.

\n

Choice A is incorrect. This is the minimum value of the data set, not the median.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

\n

Choice D is incorrect. This is the mean of the data set, not the median.

"}, {"id": "9110c120", "domain": "Problem-Solving and Data Analysis", "skill": "One-variable data: Distributions and measures of center and spread", "difficulty": "M", "type": "mc", "stimulus": "
\n

\n Data set A consists(9) data values, each(w)hich is the integer 5. Data set B consists(1)0 data values, nine(w)hich are the integer 5, and one(w)hich is the integer 100.

\n
\n", "stem": "

Which of the following statements about the means and medians of data set A and data set B is true?

\n", "choices": [{"id": "A", "text": "

Only the means are different.

\n"}, {"id": "B", "text": "

Only the medians are different.

\n"}, {"id": "C", "text": "

Both the means and the medians are different.

\n"}, {"id": "D", "text": "

Neither the means nor the medians are different.

\n"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. The mean of a data set is the sum of the values divided by the number of values. The mean of data set A is (45)/(9), or 5. The mean of data set B is (145)/(10), or 14.5. Thus, the means are different. The median of a data set is the middle value when the values are ordered from least to greatest. The medians of data sets A and B are both 5. Therefore, the medians are the same, so only the means are different.

Choices B, C, and D are incorrect and may result from conceptual or calculation errors.

\n"}, {"id": "9296553d", "domain": "Problem-Solving and Data Analysis", "skill": "Two-variable data: Models and scatterplots", "difficulty": "E", "type": "mc", "stimulus": "
\n
\n \"The
\n
\n", "stem": "

Which of the following could be an equation for a line of best fit for the data in the scatterplot?

\n", "choices": [{"id": "A", "text": "

\n y = \u2212x, + 6\n

\n"}, {"id": "B", "text": "

\n y = \u2212x, \u2212 6\n

\n"}, {"id": "C", "text": "

\n y = 6 x, + 1\n

\n"}, {"id": "D", "text": "

\n y = 6 x, \u2212 1\n

\n"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. A line of best fit for the data in a scatterplot is a line that follows the trend of the data with approximately half the data points above and half the data points below the line. Based on the given data, a line of best fit will have a positive y-intercept on or near the point 0, 6 and a negative slope. All of the choices are in slope-intercept form y = m x + b, where m is the slope and b is the y-coordinate of the y-intercept. Only choice A is an equation of a line with a positive y-intercept at the point 0, 6 and a negative slope, \u22121.

Choice B is incorrect. This equation is for a line that has a negative y-intercept, not a positive y-intercept. Choices C and D are incorrect and may result from one or more sign errors and from switching the values of the y-intercept and the slope in the equation.

\n"}, {"id": "d1db8def", "domain": "Problem-Solving and Data Analysis", "skill": "One-variable data: Distributions and measures of center and spread", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "
\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
ResponseFrequency
Once a week or more3\n
Two or three times a month16\n
About once a month26\n
A few times a year73\n
Almost never53\n
Never29\n
Total200\n
\n

The table gives the results of a survey of 200\n people who were asked how often they see a movie in a theater. How many people responded either \u201cnever\u201d or \u201calmost never\u201d?

", "choices": [{"id": "A", "text": "

24\n

"}, {"id": "B", "text": "

53\n

"}, {"id": "C", "text": "

82\n

"}, {"id": "D", "text": "

118\n

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. The table gives the results of 200\n people who were asked how often they see a movie in a theater. The table shows that 29\n people responded “never” and 53\n people responded “almost never.” Therefore, 29+53, or 82\n, people responded either “never” or “almost never.”

\n

Choice A is incorrect. This is the difference between the number of people who responded “almost never” and the number of people who responded “never.”

\n

Choice B is incorrect. This is the number of people who responded “almost never” but doesn't include those who responded “never.”

\n

Choice D is incorrect. This is the number of people who responded something other than “never” or “almost never,” rather than the number of people who responded either “never” or “almost never.”

"}, {"id": "b2f6f17d", "domain": "Problem-Solving and Data Analysis", "skill": "Percentages", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

A customer’s monthly water bill was $75.74. Due to a rate increase, her monthly bill is now $79.86. To the nearest tenth of a percent, by what percent did the amount of the customer’s water bill increase?

\n", "choices": [{"id": "A", "text": "

4.1%

\n"}, {"id": "B", "text": "

5.1%

\n"}, {"id": "C", "text": "

5.2%

\n"}, {"id": "D", "text": "

5.4%

\n"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. To find the percent increase of the customer’s water bill, the absolute increase of the bill, in dollars, is divided by the original amount of the bill, and the result is multiplied by 100%, as follows: (79 point 8 6 \u2212 75 point 7 4)/(75 point 7 4, is approximately equal to, 0 point 0 5 4;); 0 point 0 5 4 \u00d7 100 percent = 5 point 4 percent.

Choice A is incorrect. This choice is the difference 79 point 8 6, \u2212 75 point 7 4 rounded to the nearest tenth, which is the (absolute) increase of the bill’s amount, not its percent increase. Choice B is incorrect and may be the result of some calculation errors. Choice C is incorrect and is the result of dividing the difference between the two bill amounts by the new bill amount instead of the original bill amount.

\n"}, {"id": "4626102e", "domain": "Problem-Solving and Data Analysis", "skill": "One-variable data: Distributions and measures of center and spread", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

\n

The dot plot represents the 15\n values in data set A. Data set B is created by adding 56\n to each of the values in data set A. Which of the following correctly compares the medians and the ranges of data sets A and B?

", "choices": [{"id": "A", "text": "

The median of data set B is equal to the median of data set A, and the range of data set B is equal to the range of data set A.

"}, {"id": "B", "text": "

The median of data set B is equal to the median of data set A, and the range of data set B is greater than the range of data set A.

"}, {"id": "C", "text": "

The median of data set B is greater than the median of data set A, and the range of data set B is equal to the range of data set A.

"}, {"id": "D", "text": "

The median of data set B is greater than the median of data set A, and the range of data set B is greater than the range of data set A.

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. The median of a data set with an odd number of values, in ascending or descending order, is the middle value of the data set, and the range of a data set is the positive difference between the maximum and minimum values in the data set. Since the dot plot shown gives the values in data set A in ascending order and there are 15\n values in the data set, the eighth value in data set A, 23\n, is the median. The maximum value in data set A is 26\n and the minimum value is 22\n, so the range of data set A is 26-22, or 4\n. It’s given that data set B is created by adding 56\n to each of the values in data set A. Increasing each of the 15\n values in data set A by 56\n will also increase its median value by 56\n making the median of data set B 79\n. Increasing each value of data set A by 56\n does not change the range, since the maximum value of data set B is 26+56, or 82\n, and the minimum value is 22+56, or 78\n, making the range of data set B 82-78, or 4\n. Therefore, the median of data set B is greater than the median of data set A, and the range of data set B is equal to the range of data set A.

\n

Choice A is incorrect and may result from conceptual or calculation errors.

\n

Choice B is incorrect and may result from conceptual or calculation errors.

\n

Choice D is incorrect and may result from conceptual or calculation errors.

"}, {"id": "d6121490", "domain": "Problem-Solving and Data Analysis", "skill": "Two-variable data: Models and scatterplots", "difficulty": "E", "type": "mc", "stimulus": "
\n
\n \"The
\n
\n", "stem": "

The graph above shows the relationship between the speed of a particular car, in miles per hour, and its corresponding braking distance, in feet. Approximately how many feet greater will the car’s braking distance be when the car is traveling at 50 miles per hour than when the car is traveling at 30 miles per hour?

\n", "choices": [{"id": "A", "text": "

75

\n"}, {"id": "B", "text": "

125

\n"}, {"id": "C", "text": "

175

\n"}, {"id": "D", "text": "

250

\n"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. According to the graph, when the car is traveling at 50 miles per hour, the braking distance is approximately 225 feet, and when the car is traveling at 30 miles per hour, the braking distance is approximately 100 feet. The difference between these braking distances is 225 \u2212 100, or 125 feet.

Choice A is incorrect and may result from finding the braking distance for 20 miles per hour, the difference between the given speeds. Choice C is incorrect and may result from subtracting the speed from the braking distance at 50 miles per hour. Choice D is incorrect and may result from finding the difference in the braking distances at 60 and 20 miles per hour.

\n"}, {"id": "55cfaf22", "domain": "Problem-Solving and Data Analysis", "skill": "One-variable data: Distributions and measures of center and spread", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

Data set X: 5\n, 9\n, 9\n, 13\n

\n

Data set Y: 5\n, 9\n, 9\n, 13\n, 27\n

\n

The lists give the values in data sets X and Y. Which statement correctly compares the mean of data set X and the mean of data set Y?

", "choices": [{"id": "A", "text": "

The mean of data set X is greater than the mean of data set Y.

"}, {"id": "B", "text": "

The mean of data set X is less than the mean of data set Y.

"}, {"id": "C", "text": "

The means of data set X and data set Y are equal.

"}, {"id": "D", "text": "

There is not enough information to compare the means.

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. \u200b\u200bThe mean of a data set is the sum of the values in the data set divided by the number of values in the data set. It follows that the mean of data set X is 5+9+9+134, or 9\n, and the mean of data set Y is 5+9+9+13+275, or 12.6\n. Since 9\n is less than 12.6\n, the mean of data set X is less than the mean of data set Y.

\n

Alternate approach: Data set Y consists of the 4\n values in data set X and one additional value, 27\n. Since the additional value, 27\n, is larger than any value in data set X, the mean of data set X is less than the mean of data set Y.

\n

Choice A is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

\n

Choice D is incorrect and may result from conceptual or calculation errors.

"}, {"id": "ab7740a8", "domain": "Problem-Solving and Data Analysis", "skill": "Two-variable data: Models and scatterplots", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

In which of the following tables is the relationship between the values of x and their corresponding y-values nonlinear?

\n", "choices": [{"id": "A", "text": "

\n \n \n

\n \"The

\n"}, {"id": "B", "text": "

\n \n \n

\n \"The

\n"}, {"id": "C", "text": "

\n \n \n

\n \"The

\n"}, {"id": "D", "text": "

\n \n \n

\n \"The

\n"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. The relationship between the values of x and their corresponding y-values is nonlinear if the rate of change between these pairs of values isn’t constant. The table for choice D gives four pairs of values: the point 1, 6,the point 2, 12, the point 3, 24, and the point 4, 48. Finding the rate of change, or slope, between the point 1, 6 and the point 2, 12 by using the slope formula, (y sub 2 \u2212 y sub 1)/(x sub 2 \u2212 x sub 1, end fraction), yields (12 \u2212 6)/(2 \u2212 1, end fraction), or 6. Finding the rate of change between the point 2, 12 and the point 3, 24 yields (24 \u2212 12)/(3 \u2212 2, end fraction), or 12. Finding the rate of change between the point 3, 24 and the point 4, 48 yields (48 \u2212 24)/(4 \u2212 3, end fraction), or 24. Since the rate of change isn’t constant for these pairs of values, this table shows a nonlinear relationship.

Choices A, B, and C are incorrect. The rate of change between the values of x and their corresponding y-values in each of these tables is constant, being 3, 4, and 5, respectively. Therefore, each of these tables shows a linear relationship.

\n"}, {"id": "2a08d878", "domain": "Problem-Solving and Data Analysis", "skill": "Probability and conditional probability", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

There are n nonfiction books and 12 fiction books on a bookshelf. If one of these books is selected at random, what is the probability of selecting a nonfiction book, in terms of n ?

\n", "choices": [{"id": "A", "text": "

\n (n)/(12)\n

\n"}, {"id": "B", "text": "

\n (n)/(n + 12, end fraction)\n

\n"}, {"id": "C", "text": "

\n (12)/(n)\n

\n"}, {"id": "D", "text": "

\n (12)/(n + 12, end fraction)\n

\n"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. Since there are n nonfiction and 12 fiction books on the bookshelf, n + 12 represents the total number of books. If one of these books is selected at random, the probability of selecting a nonfiction book is equivalent to the number of nonfiction books divided by the total number of books. Therefore, the probability of selecting a nonfiction book, in terms of n, is (n)/(n + 12, end fraction).

Choice A is incorrect. This expression represents the number of nonfiction books divided by the number of fiction books. Choice C is incorrect. This expression represents the number of fiction books divided by the number of nonfiction books. Choice D is incorrect. This expression represents the probability of selecting a fiction book.

\n"}, {"id": "820d7a73", "domain": "Problem-Solving and Data Analysis", "skill": "One-variable data: Distributions and measures of center and spread", "difficulty": "E", "type": "spr", "stimulus": "", "stem": "

\n

The bar graph shows the distribution of 419\n cans collected by 10\n different groups for a food drive. How many cans were collected by group 6\n?

", "choices": [], "answerId": "40", "acceptedAnswers": ["40"], "rationale": "

The correct answer is 40\n. The height of each bar in the bar graph shown represents the number of cans collected by the group specified at the bottom of the bar. The bar for group 6\n reaches a height of 40\n. Therefore, group 6\n collected 40\n cans.

"}, {"id": "38a9ac45", "domain": "Problem-Solving and Data Analysis", "skill": "Probability and conditional probability", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

If 1,200 customers register for new accounts at a social media website every day, what fraction of the first 60,000 new accounts are registered in the first 5 days?

\n", "choices": [{"id": "A", "text": "

\n one fifth\n

\n"}, {"id": "B", "text": "

\n one tenth\n

\n"}, {"id": "C", "text": "

\n one twelfth\n

\n"}, {"id": "D", "text": "

\n 1 over 50\n

\n"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. If 1,200 customers register for new accounts every day, then (1,200)(5) = 6,000 customers registered for new accounts in the first 5 days. Therefore, of the first 60,000 new accounts that were registered, (6,000)/(60,000), or (1)/(10), were registered in the first 5 days.

Choice A is incorrect. The fraction one fifth represents the fraction of accounts registered in 1 of the first 5 days. Choice C is incorrect and may result from conceptual or computation errors. Choice D is incorrect. The fraction 1 over 50 represents the fraction of the first 60,000 accounts that were registered in 1 day.

\n"}, {"id": "9c44f828", "domain": "Problem-Solving and Data Analysis", "skill": "Percentages", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

There are a total of 840\n seats in a school auditorium. During an assembly, students occupied 50% of the seats in the auditorium. How many seats did the students occupy during this assembly?

", "choices": [{"id": "A", "text": "

25\n

"}, {"id": "B", "text": "

50\n

"}, {"id": "C", "text": "

420\n

"}, {"id": "D", "text": "

790\n

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. It's given that during an assembly, students occupied 50% of the 840\n seats in the school auditorium. Therefore, the number of seats that the students occupied during this assembly can be calculated by multiplying the number of seats in the school auditorium by 50100. Thus, the students occupied 84050100, or 420\n, seats during this assembly.

\n

Choice A is incorrect. This is approximately 3%, not 50%, of 840\n.

\n

Choice B is incorrect. This is approximately 6%, not 50%, of 840\n.

\n

Choice D is incorrect. This is approximately 94%, not 50%, of 840\n.

"}, {"id": "eb672707", "domain": "Problem-Solving and Data Analysis", "skill": "Ratios, rates, proportional relationships, and units", "difficulty": "M", "type": "spr", "stimulus": "", "stem": "

How many tablespoons are equivalent to 14\n teaspoons? 3 teaspoons=1 tablespoon

", "choices": [], "answerId": "14/3", "acceptedAnswers": ["14/3", "4.666", "4.667"], "rationale": "

The correct answer is 143. It's given that 3\n teaspoons is equivalent to 1\n tablespoon. Therefore, 14\n teaspoons is equivalent to 14 teaspoons1 tablespoon3 teaspoons, or 143 tablespoons. Note that 14/3, 4.666, and 4.667 are examples of ways to enter a correct answer.

"}, {"id": "273b7f37", "domain": "Problem-Solving and Data Analysis", "skill": "Percentages", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

Isabel grows potatoes in her garden. This year, she harvested 760\n potatoes and saved 10% of them to plant next year. How many of the harvested potatoes did Isabel save to plant next year?

", "choices": [{"id": "A", "text": "

66\n

"}, {"id": "B", "text": "

76\n

"}, {"id": "C", "text": "

84\n

"}, {"id": "D", "text": "

86\n

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. The number of harvested potatoes Isabel saved to plant next year can be calculated by multiplying the total number of potatoes Isabel harvested, 760\n, by the proportion of potatoes she saved. Since she saved 10% of the potatoes she harvested, the proportion of potatoes she saved is 10100, or 0.1\n. Multiplying 760\n by this proportion gives 7600.1, or 76\n, potatoes that she saved to plant next year.

\n

Choice A is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

\n

Choice D is incorrect and may result from conceptual or calculation errors.

"}, {"id": "2e511919", "domain": "Problem-Solving and Data Analysis", "skill": "Two-variable data: Models and scatterplots", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

The line graph shows the estimated number of chipmunks in a state park on April 1 of each year from 1989 to 1999.

\n

\n

Based on the line graph, in which year was the estimated number of chipmunks in the state park the greatest?

", "choices": [{"id": "A", "text": "

1989

"}, {"id": "B", "text": "

1994

"}, {"id": "C", "text": "

1995

"}, {"id": "D", "text": "

1998

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. For the given line graph, the estimated number of chipmunks is represented on the vertical axis. The greatest estimated number of chipmunks in the state park is indicated by the greatest height in the line graph. This height is achieved when the year is 1994.

\n

Choice A is incorrect and may result from conceptual errors.

\n

Choice C is incorrect and may result from conceptual errors.

\n

Choice D is incorrect and may result from conceptual errors.

"}, {"id": "55818046", "domain": "Problem-Solving and Data Analysis", "skill": "Percentages", "difficulty": "H", "type": "mc", "stimulus": "

According to the 2010 Census, the adult population aged 18 years or greater of the United States in 2010 was 234,564,071. In 2010, a survey was conducted among a randomly chosen sample of adults aged 18 years or greater in the United States about their preference to live in a warm climate or a cool climate. The table below displays a summary of the survey results.

Climate Preferences
 WarmCoolNo preferenceTotal
18–35 years old29516845508
36–50 years old24612341410
51–65 years old23811748403
Greater than 65 years old1377864279
Total9164861981,600
 

\n", "stem": "

Which of the following is closest to the difference between the percentage of adults aged 18–50 years who responded “warm” and the percentage of adults aged 51 years or greater who responded “warm”?

\n", "choices": [{"id": "A", "text": "

4%

\n"}, {"id": "B", "text": "

5%

\n"}, {"id": "C", "text": "

10%

\n"}, {"id": "D", "text": "

18%

\n"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. The percentage of adults aged 18–50 who responded “warm” is (295 + 246)/(508 + 410, end fraction = (541)/(918)), or about 58.9%. The percentage of adults aged 51 years or greater who responded “warm” is (238 + 137)/(403 + 279, end fraction = (375)/(682)), or about 55.0%. The difference between 58.9% and 55.0% is 3.9%. Of the answer choices, 4% is closest to this number.

Choices B, C, and D are incorrect and may result from calculation errors.

\n"}, {"id": "7ed0d098", "domain": "Problem-Solving and Data Analysis", "skill": "Percentages", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

Lani spent 15% of her 8-hour workday in meetings. How many minutes of her workday did she spend in meetings?

\n", "choices": [{"id": "A", "text": "

1.2

\n"}, {"id": "B", "text": "

15

\n"}, {"id": "C", "text": "

48

\n"}, {"id": "D", "text": "

72

\n"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. There are 60 minutes in one hour, so an 8-hour workday has 60 \u00d7 8 = 480 minutes. To calculate 15% of 480, multiply 0.15 by 480: 0 point 1 5 \u00d7 480 = 72. Therefore, Lani spent 72 minutes of her workday in meetings.

Choice A is incorrect because 1.2 is 15% of 8, which gives the time Lani spent of her workday in meetings in hours, not minutes. Choices B and C are incorrect and may be the result of computation errors.

 

\n"}, {"id": "20845d36", "domain": "Problem-Solving and Data Analysis", "skill": "Percentages", "difficulty": "H", "type": "spr", "stimulus": "", "stem": "

The number a\n is 70% less than the positive number b\n. The number c\n is 60% greater than a\n. The number c\n is how many times b\n?

", "choices": [], "answerId": ".48", "acceptedAnswers": [".48", "12/25"], "rationale": "

The correct answer is .48. It's given that the number a\n is 70% less than the positive number b\n. Therefore, a=1-70100b, which is equivalent to a=1-0.70b, or a=0.30b. It's also given that the number c\n is 60% greater than a\n. Therefore, c=1+60100a, which is equivalent to c=1+0.60a, or c=1.60a. Since \n\ta\n\t=\n\t\n\t\t0.30\n\t\tb\n\t\n\n, substituting \n\t0.30\n\tb\n\n for a\n in the equation \n\tc\n\t=\n\t\n\t\t1.60\n\t\ta\n\t\n\n yields c=1.600.30b, or c=0.48b. Thus, c\n is 0.48\n times b\n. Note that .48 and 12/25 are examples of ways to enter a correct answer.

"}, {"id": "4bb25495", "domain": "Problem-Solving and Data Analysis", "skill": "One-variable data: Distributions and measures of center and spread", "difficulty": "E", "type": "mc", "stimulus": "
\n\t
\n\t\t\n\t\t\t\n\t\t\t\t\t\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t
\n\t\t\t\t

Five Smallest Countries in 2016

\n\t\t\t
CountryLand area
\n\t\t\t\t\t\t (square kilometers)
Monaco2.0
Nauru21
San Marino61
Tuvalu26
Vatican City0.44
\n
\n", "stem": "

The table above shows the land area, in square kilometers, of the five smallest countries of the world in 2016. Based on the table, what is the mean land area of the 5 smallest countries in 2016, to the nearest square kilometer?

\n", "choices": [{"id": "A", "text": "

20

\n"}, {"id": "B", "text": "

22

\n"}, {"id": "C", "text": "

61

\n"}, {"id": "D", "text": "

110

\n"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. The mean land area of these 5 countries is equal to the sum of the land areas of these countries, or 2 point 0, + 21, + 61, + 26, + 0 point 4 4, divided by the number of countries in the table, 5, or (2 point 0, + 21, + 61, + 26, + 0 point 4 4)/(5). Combining like terms in the numerator yields 110 point 4 4 over 5, which simplifies to 22.088 square kilometers. This value, when rounded to the nearest square kilometer, is 22.

Choice A is incorrect and may result from a calculation error. Choice C is incorrect. This is the greatest land area of the 5 countries in the table. Choice D is incorrect. This is the sum of the land areas of the 5 countries in the table, rounded to the nearest square kilometer.

 

\n"}, {"id": "aa43b41f", "domain": "Problem-Solving and Data Analysis", "skill": "Evaluating statistical claims: Observational studies and experiments ", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

Near the end of a US cable news show, the host invited viewers to respond to a poll on the show’s website that asked, “Do you support the new federal policy discussed during the show?” At the end of the show, the host reported that 28% responded “Yes,” and 70% responded “No.” Which of the following best explains why the results are unlikely to represent the sentiments of the population of the United States?

\n", "choices": [{"id": "A", "text": "

The percentages do not add up to 100%, so any possible conclusions from the poll are invalid.

\n"}, {"id": "B", "text": "

Those who responded to the poll were not a random sample of the population of the United States.

\n"}, {"id": "C", "text": "

There were not 50% “Yes” responses and 50% “No” responses.

\n"}, {"id": "D", "text": "

The show did not allow viewers enough time to respond to the poll.

\n"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. In order for the poll results from a sample of a population to represent the entire population, the sample must be representative of the population. A sample that is randomly selected from a population is more likely than a sample of the type described to represent the population. In this case, the people who responded were people with access to cable television and websites, which aren’t accessible to the entire population. Moreover, the people who responded also chose to watch the show and respond to the poll. The people who made these choices aren’t representative of the entire population of the United States because they were not a random sample of the population of the United States.

Choices A, C, and D are incorrect because they present reasons unrelated to whether the sample is representative of the population of the United States.

 

\n"}, {"id": "cb4894f9", "domain": "Problem-Solving and Data Analysis", "skill": "Ratios, rates, proportional relationships, and units", "difficulty": "M", "type": "spr", "stimulus": "", "stem": "

A triathlon is a multisport race consisting of three different legs. A triathlon participant completed the cycling leg with an average speed of 19.700 miles per hour. What was the average speed, in yards per hour, of the participant during the cycling leg? 1 mile=1,760 yards

", "choices": [], "answerId": "34672", "acceptedAnswers": ["34672"], "rationale": "

The correct answer is 34,672\n. It's given that 1 mile=1,760 yards. It follows that an average speed of 19.700 miles per hour is equivalent to 19.700 miles1 hour1,760 yards1 mile, or 34,672\n yards per hour.

"}, {"id": "b6569d0e", "domain": "Problem-Solving and Data Analysis", "skill": "Probability and conditional probability", "difficulty": "M", "type": "mc", "stimulus": "
\n
\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n
\n United States Presidents
\nfrom 1789 to 2015\n
AgesNumber
40–442
45–497
50–5413
55–5911
60–647
65–693
\n
\n", "stem": "

The table above gives the number of United States presidents from 1789 to 2015 whose age at the time they first took office is within the interval listed. Of those presidents who were at least 50 years old when they first took office, what fraction were at least 60 years old?

\n", "choices": [{"id": "A", "text": "

\n 10 over 43\n

\n"}, {"id": "B", "text": "

\n 10 over 34\n

\n"}, {"id": "C", "text": "

\n 10 over 24\n

\n"}, {"id": "D", "text": "

\n 25 over 34\n

\n"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. The sample space is restricted to the presidents who were at least 50 years old when they first took office. Therefore, the sum of the values in the final four rows of the table, 13 + 11, + 7, + 3 = 34, is the total number of presidents in the sample space. The number of presidents who were at least 60 years old is the sum of the values in the final two rows of the table: 7 + 3 = 10. Thus, the fraction of the 34 presidents who were at least 50 years old when they first took office who were at least 60 years old is 10 over 34.

Choice A is incorrect. This is the fraction of all presidents in the table who were at least 60 years old when they first took office. Choice C is incorrect and may result from treating the number of presidents who were between 50 and 59 years old when they first took office, instead of the number of presidents who were at least 50 years old, as the sample space. Choice D is incorrect and may result from a calculation error.

\n"}, {"id": "5dc386fb", "domain": "Problem-Solving and Data Analysis", "skill": "Probability and conditional probability", "difficulty": "H", "type": "mc", "stimulus": "
\n\t
\n\t\t
\n\t\t\t

The table below shows the distribution of US states according to whether they have a state-level sales tax and a state-level income tax.

\n\n\t\t\t\n\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t
2013 State-Level Taxes
 State sales taxNo state sales tax
State income tax394
No state income tax61

 

\n\t\t
\n\t
\n
\n", "stem": "

To the nearest tenth of a percent, what percent of states with a state-level sales tax do not have a state-level income tax?

\n", "choices": [{"id": "A", "text": "

6.0%

\n"}, {"id": "B", "text": "

12.0%

\n"}, {"id": "C", "text": "

13.3%

\n"}, {"id": "D", "text": "

14.0%

\n"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. The sum of the number of states with a state-level sales tax is 39 + 6 = 45. Of these states, 6 don’t have a state-level income tax. Therefore, 6 over 45 = 0 point 1 3 3 3 dot dot dot, or about 13.3%, of states with a state-level sales tax don’t have a state-level income tax.


\n\tChoice A is incorrect. This is the number of states that have a state-level sales tax and no state-level income tax. Choice B is incorrect. This is the percent of states that have a state-level sales tax and no state-level income tax. Choice D is incorrect. This is the percent of states that have no state-level income tax.

 

\n"}, {"id": "551c52b9", "domain": "Problem-Solving and Data Analysis", "skill": "Ratios, rates, proportional relationships, and units", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

Tilly earns p\n dollars for every w\n hours of work. Which expression represents the amount of money, in dollars, Tilly earns for \n\t39\n\tw\n\n hours of work?

", "choices": [{"id": "A", "text": "

\n\t39\n\tp\n\n

"}, {"id": "B", "text": "

p39

"}, {"id": "C", "text": "

\n\tp\n\t+\n\t39\n\n

"}, {"id": "D", "text": "

\n\tp\n\t-\n\t39\n\n

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. It’s given that Tilly earns p\n dollars for every w\n hours of work. This can be represented by the proportion pw. The amount of money, x\n, Tilly earns for \n\t39\n\tw\n\n hours of work can be found by setting up the proportion pw=x39w. This can be rewritten as 39pw=xw. Dividing both sides by w\n results in \n\tx\n\t=\n\t\n\t\t39\n\t\tp\n\t\n\n. 

\n

Choice B is incorrect. This is the amount of money Tilly earns in dollars per hour, not the amount of money Tilly earns for \n\t39\n\tw\n\n hours of work.

\n

Choice C is incorrect. This is the amount of money Tilly earns for w\n hours of work plus 39\n, not the amount of money Tilly earns for \n\t39\n\tw\n\n hours of work.

\n

Choice D is incorrect. This is the amount of money Tilly earns for w\n hours of work minus 39\n, not the amount of money Tilly earns for \n\t39\n\tw\n\n hours of work.

"}, {"id": "1180401d", "domain": "Problem-Solving and Data Analysis", "skill": "Ratios, rates, proportional relationships, and units", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

The total area of a coastal city is 92.1 square miles, of which 11.3 square miles is water. If the city had a population of 621,000 people in the year 2010, which of the following is closest to the population density, in people per square mile of land area, of the city at that time?

\n", "choices": [{"id": "A", "text": "

6,740

\n"}, {"id": "B", "text": "

7,690

\n"}, {"id": "C", "text": "

55,000

\n"}, {"id": "D", "text": "

76,000

\n"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. The land area of the coastal city can be found by subtracting the area of the water from the total area of the coastal city; that is, 92 point 1, \u2212 11 point 3 = 80 point 8 square miles. The population density is the population divided by the land area, or (621,000)/(80 point 8, end fraction = 7,686), which is closest to 7,690 people per square mile.

Choice A is incorrect and may be the result of dividing the population by the total area, instead of the land area. Choice C is incorrect and may be the result of dividing the population by the area of water. Choice D is incorrect and may be the result of making a computational error with the decimal place.

\n"}, {"id": "f6cbb04a", "domain": "Problem-Solving and Data Analysis", "skill": "Ratios, rates, proportional relationships, and units", "difficulty": "M", "type": "mc", "stimulus": "
\n

\n d = 55 t\n

\n
\n", "stem": "

The equation above can be used to calculate the distance d, in miles, traveled by a car moving at a speed of 55 miles per hour over a period of t hours. For any positive constant k, the distance the car would have traveled after 9 k hours is how many times the distance the car would have traveled after 3 k hours?

\n", "choices": [{"id": "A", "text": "3\n"}, {"id": "B", "text": "6\n"}, {"id": "C", "text": "3k\n"}, {"id": "D", "text": "6 k\n"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. Since the distance is equal to the amount of time multiplied by a constant, the given equation d = 55 t represents a proportional relationship between distance and time in this situation. Since 9 k = 3 \u00d7 3 k, the time when t = 9 k hours is 3 times the time when t = 3 k hours. Therefore, the distance traveled after 9 k hours is 3 times the distance after 3 k hours.

Choices B and D are incorrect and may result from interpreting the proportional relationship between time and distance as additive rather than multiplicative. Choice C is incorrect and may result from an arithmetic error.

\n"}, {"id": "96c3e32d", "domain": "Problem-Solving and Data Analysis", "skill": "Ratios, rates, proportional relationships, and units", "difficulty": "M", "type": "spr", "stimulus": "", "stem": "

One side of a flat board has an area of 874\n square inches. If a pressure of 19\n pounds per square inch of area is exerted on this side of the board, what is the total force, in pounds, exerted on this side of the board?

", "choices": [], "answerId": "16606", "acceptedAnswers": ["16606"], "rationale": "

The correct answer is 16,606\n. It's given that one side of a flat board has an area of 874\n square inches. If a pressure of 19\n pounds per square inch of area is exerted on this side of the board, the total force exerted on this side of the board is 874 square inches19 pounds1 square inch, or 16,606\n pounds.

"}, {"id": "98958ae8", "domain": "Problem-Solving and Data Analysis", "skill": "One-variable data: Distributions and measures of center and spread", "difficulty": "H", "type": "spr", "stimulus": "", "stem": "

Data set A consists of the heights of 75\n objects and has a mean of 25\n meters. Data set B consists of the heights of 50\n objects and has a mean of 65\n meters. Data set C consists of the heights of the 125\n objects from data sets A and B. What is the mean, in meters, of data set C?

", "choices": [], "answerId": "41", "acceptedAnswers": ["41"], "rationale": "

The correct answer is 41\n. The mean of a data set is computed by dividing the sum of the values in the data set by the number of values in the data set. It’s given that data set A consists of the heights of 75\n objects and has a mean of 25\n meters. This can be represented by the equation \n\t\n\t\t\n\t\t\tx\n\t\t\t75\n\t\t\n\t\n\t=\n\t25\n\n, where x\n represents the sum of the heights of the objects, in meters, in data set A. Multiplying both sides of this equation by 75\n yields x=7525, or \n\tx\n\t=\n\t1,875\n\n meters. Therefore, the sum of the heights of the objects in data set A is 1,875\n meters. It’s also given that data set B consists of the heights of 50\n objects and has a mean of 65\n meters. This can be represented by the equation \n\t\n\t\t\n\t\t\ty\n\t\t\t50\n\t\t\n\t\n\t=\n\t65\n\n, where y\n represents the sum of the heights of the objects, in meters, in data set B. Multiplying both sides of this equation by 50\n yields y=5065, or \n\ty\n\t=\n\t3,250\n\n meters. Therefore, the sum of the heights of the objects in data set B is 3,250\n meters. Since it’s given that data set C consists of the heights of the 125\n objects from data sets A and B, it follows that the mean of data set C is the sum of the heights of the objects, in meters, in data sets A and B divided by the number of objects represented in data sets A and B, or 1,875+3,250125, which is equivalent to 41\n meters. Therefore, the mean, in meters, of data set C is 41\n.

"}, {"id": "391ae4b2", "domain": "Problem-Solving and Data Analysis", "skill": "One-variable data: Distributions and measures of center and spread", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

Data set F consists of 55\n integers between 170\n and 290\n. Data set G consists of all the integers in data set F as well as the integer 10\n. Which of the following must be less for data set F than for data set G?

\n
    \n
  1. The mean
    2. \n
  2. The median
    3. \n
", "choices": [{"id": "A", "text": "

I only

"}, {"id": "B", "text": "

II only

"}, {"id": "C", "text": "

I and II

"}, {"id": "D", "text": "

Neither I nor II

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. It's given that data set F consists of 55\n integers between 170\n and 290\n and data set G consists of all the integers in data set F as well as the integer 10\n. Since the integer 10\n is less than all the integers in data set F, the mean of data set G must be less than the mean of data set F. Thus, the mean of data set F isn't less than the mean of data set G. When a data set is in ascending order, the median is between the two middle values when there is an even number of values and the median is the middle value when there is an odd number of values. It follows that the median of data set F is either greater than or equal to the median of data set G. Therefore, the median of data set F isn't less than the median of data set G. Thus, neither the mean nor the median must be less for data set F than for data set G.

\n

Choice A is incorrect and may result from conceptual or calculation errors.

\n

Choice B is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

"}, {"id": "4096a482", "domain": "Problem-Solving and Data Analysis", "skill": "Inference from sample statistics and margin of error ", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

Based on a random sample from a population, a researcher estimated that the mean value of a certain variable for the population is 20.5\n, with an associated margin of error of 1\n. Which of the following is the most appropriate conclusion?

", "choices": [{"id": "A", "text": "

It is plausible that the actual mean value of the variable for the population is between 19.5\n and 21.5\n.

"}, {"id": "B", "text": "

It is not possible that the mean value of the variable for the population is less than 19.5\n or greater than 21.5\n.

"}, {"id": "C", "text": "

Every value of the variable in the population is between 19.5\n and 21.5\n.

"}, {"id": "D", "text": "

The mean value of the variable for the population is 20.5\n.

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. It's given that based on a random sample from a population, the estimated mean value for a certain variable for the population is 20.5, with an associated margin of error of 1\n. This means that it is plausible that the actual mean value of the variable for the population is between 20.5-1 and 20.5+1. Therefore, the most appropriate conclusion is that it is plausible that the actual mean value of the variable for the population is between 19.5 and 21.5.

\n

Choice B is incorrect. The estimated mean value and associated margin of error describe only plausible values, not all the possible values, for the actual mean value of the variable, so this is not an appropriate conclusion.

\n

Choice C is incorrect. The estimated mean value and associated margin of error describe only plausible values for the actual mean value of the variable, not all the possible values of the variable, so this is not an appropriate conclusion.

\n

Choice D is incorrect. Since 20.5 is the estimated mean value of the variable based on a random sample, the actual mean value of the variable may not be exactly 20.5. Therefore, this is not an appropriate conclusion.

"}, {"id": "57f45509", "domain": "Problem-Solving and Data Analysis", "skill": "One-variable data: Distributions and measures of center and spread", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

\n

 

\n

The box plot summarizes 15\n data values. What is the median of this data set?

", "choices": [{"id": "A", "text": "

2\n

"}, {"id": "B", "text": "

3\n

"}, {"id": "C", "text": "

5\n

"}, {"id": "D", "text": "

8\n

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. The median of a data set represented in a box plot is given by the vertical line within the box. In the given box plot, the vertical line within the box occurs at 5\n. Therefore, the median of this data set is 5\n.

\n

Choice A is incorrect. This is the minimum value of the data set.

\n

Choice B is incorrect and may result from conceptual errors.

\n

Choice D is incorrect. This is the maximum value of the data set.

"}, {"id": "2a59eb45", "domain": "Problem-Solving and Data Analysis", "skill": "One-variable data: Distributions and measures of center and spread", "difficulty": "H", "type": "spr", "stimulus": "", "stem": "

Data set A consists of the heights of 75\n buildings and has a mean of 32\n meters. Data set B consists of the heights of 50\n buildings and has a mean of 62\n meters. Data set C consists of the heights of the 125\n buildings from data sets A and B. What is the mean, in meters, of data set C?

", "choices": [], "answerId": "44", "acceptedAnswers": ["44"], "rationale": "

The correct answer is 44\n. The mean of a data set is computed by dividing the sum of the values in the data set by the number of values in the data set. It's given that data set A consists of the heights of 75\n buildings and has a mean of 32\n meters. This can be represented by the equation \n\t\n\t\t\tx\n\t\t\t75\n\t\t\n\t=\n\t32\n\n, where x\n represents the sum of the heights of the buildings, in meters, in data set A. Multiplying both sides of this equation by 75\n yields x=7532, or \n\tx\n\t=\n\t2,400\n\n meters. Therefore, the sum of the heights of the buildings in data set A is 2,400\n meters. It's also given that data set B consists of the heights of 50\n buildings and has a mean of 62\n meters. This can be represented by the equation \n\t\n\t\t\ty\n\t\t\t50\n\t\t\n\t=\n\t62\n\n, where y\n represents the sum of the heights of the buildings, in meters, in data set B. Multiplying both sides of this equation by 50\n yields y=5062, or \n\ty\n\t=\n\t3,100\n\n meters. Therefore, the sum of the heights of the buildings in data set B is 3,100\n meters. Since it's given that data set C consists of the heights of the 125\n buildings from data sets A and B, it follows that the mean of data set C is the sum of the heights of the buildings, in meters, in data sets A and B divided by the number of buildings represented in data sets A and B, or 2,400+3,100125, which is equivalent to 44\n meters. Therefore, the mean, in meters, of data set C is 44\n.

"}, {"id": "2e92cc21", "domain": "Problem-Solving and Data Analysis", "skill": "Percentages", "difficulty": "H", "type": "spr", "stimulus": "", "stem": "

The number a\n is 110% greater than the number b\n. The number b\n is 90% less than 47\n. What is the value of a\n?

", "choices": [], "answerId": "9.87", "acceptedAnswers": ["9.87", "987/100"], "rationale": "

The correct answer is 9.87\n. It’s given that the number a\n is 110% greater than the number b\n. It follows that a=1+110100b, or \n\ta\n\t=\n\t\n\t\t2.1\n\t\tb\n\t\n\n. It’s also given that the number b\n is 90% less than 47\n. It follows that b=1-9010047, or b=0.147, which yields \n\tb\n\t=\n\t4.7\n\n. Substituting 4.7\n for b\n in the equation \n\ta\n\t=\n\t\n\t\t2.1\n\t\tb\n\t\n\n yields a=2.14.7, which is equivalent to \n\ta\n\t=\n\t9.87\n\n. Therefore, the value of a\n is 9.87\n.

"}, {"id": "77cf4fa6", "domain": "Problem-Solving and Data Analysis", "skill": "Percentages", "difficulty": "E", "type": "spr", "stimulus": "", "stem": "

There are 170\n blocks in a container. Of these blocks, 10% are green. How many blocks in the container are green?

", "choices": [], "answerId": "17", "acceptedAnswers": ["17"], "rationale": "

The correct answer is 17\n. It's given that there are 170\n blocks in a container, and of these blocks, 10% are green. Since 10% can be rewritten as 10100, or 0.1, the number of green blocks in the container is 0.1170, or 17\n.

"}, {"id": "2d31caae", "domain": "Problem-Solving and Data Analysis", "skill": "Percentages", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "
\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n
Call Ratings
1 Star2 Stars3 Stars4 StarsTotal
Employee A 1649728145
Employee B\n

4

\n 		10223470
Employee C8564516125
Employee D22428412160
Total5015722370500

\n

A supervisor at a call center reviewed 500 calls taken by four employees and rated the employees’ performance on each call on a scale from 1 star to 4 stars. The ratings for each employee are shown in the table above. According to the table, to the nearest whole percent, what percent of Employee A’s calls received a rating of 1 star?

\n", "choices": [{"id": "A", "text": "

3%

\n"}, {"id": "B", "text": "

11%

\n"}, {"id": "C", "text": "

16%

\n"}, {"id": "D", "text": "

32%

\n"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. The percent of Employee A’s calls that received a rating of 1 star is the number of Employee A’s 1-star calls divided by the total number of Employee A’s calls. This quotient, 16 over 145, is approximately equal to 0 point 1 1 0 3, or 11 point 0 3 percent. To the nearest whole percent, this is 11%.

\nChoice A is incorrect. This is the percent of all calls taken by Employee A that received a rating of 1 star. Choice C is incorrect and may result from a conceptual error. For example, 16 is the number, not the percent, of calls taken by Employee A that received a rating of 1 star. Choice D is incorrect. This is the percent of all calls that received a rating of 1 star that were taken by Employee A.

\n"}, {"id": "4a422e3e", "domain": "Problem-Solving and Data Analysis", "skill": "Evaluating statistical claims: Observational studies and experiments ", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

To determine the mean number of children per household in a community, Tabitha surveyed 20 families at a playground. For the 20 families surveyed, the mean number of children per household was 2.4. Which of the following statements must be true?

\n", "choices": [{"id": "A", "text": "

The mean number of children per household in the community is 2.4.

\n"}, {"id": "B", "text": "

A determination about the mean number of children per household in the community should not be made because the sample size is too small.

\n"}, {"id": "C", "text": "

The sampling method is flawed and may produce a biased estimate of the mean number of children per household in the community.

\n"}, {"id": "D", "text": "

The sampling method is not flawed and is likely to produce an unbiased estimate of the mean number of children per household in the community.

\n"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. In order to use a sample mean to estimate the mean for a population, the sample must be representative of the population (for example, a simple random sample). In this case, Tabitha surveyed 20 families in a playground. Families in the playground are more likely to have children than other households in the community. Therefore, the sample isn’t representative of the population. Hence, the sampling method is flawed and may produce a biased estimate.

Choices A and D are incorrect because they incorrectly assume the sampling method is unbiased. Choice B is incorrect because a sample of size 20 could be large enough to make an estimate if the sample had been representative of all the families in the community.

\n"}, {"id": "e821a26d", "domain": "Problem-Solving and Data Analysis", "skill": "Two-variable data: Models and scatterplots", "difficulty": "H", "type": "mc", "stimulus": "
\n
\n
\n

The scatterplot below shows the amount of electric energy generated, in millions of megawatt-hours, by nuclear sources over a 10‑year period.

\n
\n
\n
\n
\n \"The
\n

\n
\n
\n", "stem": "

\n Of the following equations, which best models the data in the scatterplot?

\n", "choices": [{"id": "A", "text": "y = 1 point six seven four x\u00b2, + 19 point seven six x, \u2212 745 point seven three\n"}, {"id": "B", "text": "y = \u22121 point six seven four x\u00b2, \u2212 19 point seven six x, \u2212 745 point seven three\n"}, {"id": "C", "text": "y = 1 point six seven four x\u00b2, + 19 point seven six x, + 745 point seven three\n"}, {"id": "D", "text": "y = \u22121 point six seven four x\u00b2, + 19 point seven six x, + 745 point seven three\n"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. The data in the scatterplot roughly fall in the shape of a downward-opening parabola; therefore, the coefficient for the x\u00b2 term must be negative. Based on the location of the data points, the y-intercept of the parabola should be somewhere between 740 and 760. Therefore, of the equations given, the best model is y = \u22121 point 6 7 4, x\u00b2, + 19 point 7 6 x, + 745 point 7 3.

Choices A and C are incorrect. The positive coefficient of the x\u00b2 term means that these equations each define upward-opening parabolas, whereas a parabola that fits the data in the scatterplot must open downward. Choice B is incorrect because it defines a parabola with a y-intercept that has a negative y-coordinate, whereas a parabola that fits the data in the scatterplot must have a y-intercept with a positive y-coordinate.

\n"}, {"id": "9eb896c5", "domain": "Problem-Solving and Data Analysis", "skill": "Two-variable data: Models and scatterplots", "difficulty": "M", "type": "mc", "stimulus": "
\n
\n
\n
\n \"The
\n
\n
\n
\n", "stem": "

Which of the following could be the equation for a line of best fit for the data shown in the scatterplot above?

\n", "choices": [{"id": "A", "text": "

\n y = 3 x + 0 point 8\n

\n"}, {"id": "B", "text": "

\n y = 0 point 8 x, + 3\n

\n"}, {"id": "C", "text": "

\n y = \u22120 point 8 x, + 3\n

\n"}, {"id": "D", "text": "

\n y = \u22123 x + 0 point 8\n

\n"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. The data show a strong linear relationship between x and y. The line of best fit for a set of data is a linear equation that minimizes the distances from the data points to the line. An equation for the line of best fit can be written in slope-intercept form, y = m x + b, where m is the slope of the graph of the line and b is the y-coordinate of the y-intercept of the graph. Since, for the data shown, the y-values increase as the x-values increase, the slope of a line of best fit must be positive. The data shown lie almost in a line, so the slope can be roughly estimated using the formula for slope, m = (y sub 2 \u2212 y sub 1)/(x sub 2 \u2212 x sub 1, end fraction). The leftmost and rightmost data points have coordinates of about 1, 4 and 8, 26, so the slope is approximately (26 \u2212 4)/(8 \u2212 1, end fraction = (22)/(7)), which is a little greater than 3. Extension of the line to the left would intersect the y-axis at about the point 0, 1. Only choice A represents a line with a slope close to 3 and a y-intercept close to the point 0, 1.

Choice B is incorrect and may result from switching the slope and y-intercept. The line with a y-intercept of 0, 3 and a slope of 0.8 is farther from the data points than the line with a slope of 3 and a y-intercept of 0, 0 point 8. Choices C and D are incorrect. They represent lines with negative slopes, not positive slopes.

\n"}, {"id": "194ae3b1", "domain": "Problem-Solving and Data Analysis", "skill": "Percentages", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

There were approximately 113,000 occupational therapy jobs in the United States in 2012. The Bureau of Labor Statistics has projected that this number will increase by 29% from 2012 to 2022. Of the following, which is closest to the number of occupational therapy jobs the bureau has projected for the United States in 2022?

\n", "choices": [{"id": "A", "text": "

115,900

\n"}, {"id": "B", "text": "

116,300

\n"}, {"id": "C", "text": "

142,000

\n"}, {"id": "D", "text": "

145,800

\n"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. The decimal equivalent of 29% is 0.29. It’s given that the 113,000 occupational therapy jobs in the United States in 2012 are projected to increase by 29% by 2022. Increasing 113,000 by 29% can be expressed as 113,000 times, open parenthesis, 1 + 0 point 2 9, close parenthesis, or 113,000 \u00d7 1 point 2 9. Evaluating this expression yields 145,770. The closest number is 145,800 in choice D.

Choice A is incorrect and may result from increasing 113,000 by 2,900 instead of by 29%. Choice B is incorrect and may result from increasing 113,000 by 2.9% instead of by 29%. Choice C is incorrect and may result from increasing 113,000 by 29,000 instead of by 29%.

 

\n"}, {"id": "79340403", "domain": "Problem-Solving and Data Analysis", "skill": "One-variable data: Distributions and measures of center and spread", "difficulty": "E", "type": "spr", "stimulus": "", "stem": "

\n

The bar graph shows the distribution of 414\n books collected by 10\n different groups for a book drive. How many books were collected by group 1\n?

", "choices": [], "answerId": "30", "acceptedAnswers": ["30"], "rationale": "

The correct answer is 30\n. The height of each bar in the bar graph shown represents the number of books collected by the group specified at the bottom of the bar. The bar for group 1\n reaches a height of 30\n. Therefore, group 1\n collected 30\n books.

"}, {"id": "a8fabad0", "domain": "Problem-Solving and Data Analysis", "skill": "Percentages", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

A waiter receives tips from each customer. On average, the tip is 15% of the customer’s bill. At this rate, which of the following is closest to the tip the waiter can expect when a customer has a bill that is $78.20?

\n", "choices": [{"id": "A", "text": "

$8.00

\n"}, {"id": "B", "text": "

$10.00

\n"}, {"id": "C", "text": "

$12.00

\n"}, {"id": "D", "text": "

$14.00

\n"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. If the bill is $78.20, 15% of the bill can be found by multiplying 78.20 by the decimal conversion of 15%, 78.20 × 0.15 = $11.73. The exact amount $11.73 is closest in value to $12.00.

Choices A, B, and D are incorrect and may be the result of errors when calculating 15% of the total $78.20.

\n"}, {"id": "d112bc9d", "domain": "Problem-Solving and Data Analysis", "skill": "Two-variable data: Models and scatterplots", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

The scatterplot shows the temperature y\n, in °F, recorded by a meteorologist at various times x\n, in days since June 1\n. 

\n

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n

\n

During which of the following time periods did the greatest increase in recorded temperature take place?

", "choices": [{"id": "A", "text": "

From x=6 to x=7

"}, {"id": "B", "text": "

From x=5 to x=6

"}, {"id": "C", "text": "

From x=2 to x=3

"}, {"id": "D", "text": "

From x=1 to x=2

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. The scatterplot shows that there was an increase in recorded temperature from x=2 to x=3 and from x=6 to x=7. When x=2, the recorded temperature was approximately 60°F and when x=3, the recorded temperature was greater than 70°F. This means that the increase in recorded temperature from x=2 to x=3 was greater than (70-60)°F, or 10°F. When x=6, the recorded temperature was greater than 60°F and when x=7, the recorded temperature was less than 70°F. This means that the increase in recorded temperature from x=6 to x=7 was less than (70-60)°F, or 10°F. It follows that the greatest increase in recorded temperature took place from x=2 to x=3.

\n

Choice A is incorrect. The increase in recorded temperature from x=6 to x=7 was less than the increase in recorded temperature from x=2 to x=3.

\n

Choice B is incorrect. From x=5 to x=6, a decrease, not an increase, in recorded temperature took place.

\n

Choice D is incorrect. From x=1 to x=2, a decrease, not an increase, in recorded temperature took place.

"}, {"id": "99550621", "domain": "Problem-Solving and Data Analysis", "skill": "Ratios, rates, proportional relationships, and units", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

Makayla is planning an event in a 5,400-square-foot room. If there should be at least 8 square feet per person, what is the maximum number of people that could attend this event?

\n", "choices": [{"id": "A", "text": "

588

\n"}, {"id": "B", "text": "

675

\n"}, {"id": "C", "text": "

15,274

\n"}, {"id": "D", "text": "

43,200

\n"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. It’s given that the event will be in a 5,400-square-foot room and that there should be at least 8 square feet per person. The maximum number of people that could attend the event can be found by dividing the total square feet in the room by the minimum number of square feet needed per person, which gives (5,400)/(8 = 675).

Choices A and C are incorrect and may result from conceptual or computational errors. Choice D is incorrect and may result from multiplying, rather than dividing, 5,400 by 8.

\n"}, {"id": "93779b53", "domain": "Problem-Solving and Data Analysis", "skill": "One-variable data: Distributions and measures of center and spread", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

\n

A group of students voted on five after-school activities. The bar graph shows the number of students who voted for each of the five activities. How many students chose activity 3\n?

", "choices": [{"id": "A", "text": "

25\n

"}, {"id": "B", "text": "

39\n

"}, {"id": "C", "text": "

48\n

"}, {"id": "D", "text": "

50\n

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. The height of each bar in the bar graph given represents the number of students that voted for the activity specified at the bottom of the bar. The bar for activity 3\n has a height that is between 35\n and 40\n. In other words, the number of students that chose activity 3\n is between 35\n students and 40\n students. Of the given choices, 39\n is the only value between 35\n and 40\n. Therefore, 39\n students chose activity 3\n.

\n

Choice A is incorrect and may result from conceptual errors.

\n

Choice C is incorrect. This is the number of students that chose activity 5\n, not activity 3\n.

\n

Choice D is incorrect and may result from conceptual errors.

"}, {"id": "9d935bd8", "domain": "Problem-Solving and Data Analysis", "skill": "One-variable data: Distributions and measures of center and spread", "difficulty": "H", "type": "mc", "stimulus": "
\n
\n \"The
\n
\n", "stem": "

A survey was given to residents of all 50 states asking if they had earned a bachelor’s degree or higher. The results from 7 of the states are given in the table above. The median percent of residents who earned a bachelor’s degree or higher for all 50 states was 26.95%. What is the difference between the median percent of residents who earned a bachelor’s degree or higher for these 7 states and the median for all 50 states?

\n", "choices": [{"id": "A", "text": "

0.05%

\n"}, {"id": "B", "text": "

0.95%

\n"}, {"id": "C", "text": "

1.22%

\n"}, {"id": "D", "text": "

7.45%

\n"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. The median of a set of numbers is the middle value of the set values when ordered from least to greatest. If the percents in the table are ordered from least to greatest, the middle value is 27.9%. The difference between 27.9% and 26.95% is 0.95%.

Choice A is incorrect and may be the result of calculation errors or not finding the median of the data in the table correctly. Choice C is incorrect and may be the result of finding the mean instead of the median. Choice D is incorrect and may be the result of using the middle value of the unordered list.

\n"}, {"id": "8c5dbd3e", "domain": "Problem-Solving and Data Analysis", "skill": "Percentages", "difficulty": "H", "type": "spr", "stimulus": "", "stem": "

The number w\n is 110% greater than the number z\n. The number z\n is 55% less than 50\n. What is the value of w\n?

", "choices": [], "answerId": "189/4", "acceptedAnswers": ["189/4", "47.25"], "rationale": "

The correct answer is 47.25\n. It’s given that the number w\n is 110% greater than the number z\n. It follows that w=1+110100z, or w=2.1z. It’s also given that the number z\n is 55% less than 50\n. It follows that z=1-5510050, or z=0.4550, which yields z=22.5. Substituting 22.5 for z\n in the equation w=2.1z yields w=2.122.5, which is equivalent to \n\tw\n\t=\n\t47.25\n\n. Therefore, the value of w\n is 47.25\n. Note that 47.25 and 189/4 are examples of ways to enter a correct answer.

"}, {"id": "94c65646", "domain": "Problem-Solving and Data Analysis", "skill": "Percentages", "difficulty": "M", "type": "spr", "stimulus": "", "stem": "

432\n is 96\n% of what number?

", "choices": [], "answerId": "450", "acceptedAnswers": ["450"], "rationale": "

The correct answer is 450\n. Let x\n represent the number that 432\n is 96% of. This can be written as 96100x=432, or 0.96x=432. Dividing both sides of this equation by 0.96\n yields \n\tx\n\t=\n\t450\n\n. Therefore, 432\n is 96% of 450\n.

"}, {"id": "5c24c861", "domain": "Problem-Solving and Data Analysis", "skill": "Two-variable data: Models and scatterplots", "difficulty": "E", "type": "mc", "stimulus": "
\n
\n
\n

A study was done to determine a new car’s stopping distance when it was traveling at different speeds. The study was done on a dry road with good surface conditions. The results are shown below, along with the graph of a quadratic function that models the data.

\n
\n
\n
\n \"The
\n
\n", "stem": "

According to the model, which of the following is the best estimate for the stopping distance, in feet, if the vehicle was traveling 55 miles per hour?

\n", "choices": [{"id": "A", "text": "25\n"}, {"id": "B", "text": "30\n"}, {"id": "C", "text": "

\n 210\n

\n"}, {"id": "D", "text": "

\n 250\n

\n"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Correct Answer Rationale
\nChoice C is correct. According to the model, the stopping distance, in feet, of a vehicle traveling 55 miles per hour is about 200 feet. Of the choices given, the best estimate of the stopping distance for a car traveling 55 miles per hour is 210 feet.

Incorrect Answer Rationale
\nChoices A, B, and D are incorrect and may be the result of incorrectly reading the given quadratic model. The corresponding x-values to the y-values of 25 and 30 are not part of the model. The corresponding x-value to a y-value of 250 is approximately 60 mph, not 55 mph.

\n"}, {"id": "5f3ee607", "domain": "Problem-Solving and Data Analysis", "skill": "Two-variable data: Models and scatterplots", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n\n

\n

Which of the following equations is the most appropriate linear model for the data shown in the scatterplot?

", "choices": [{"id": "A", "text": "

\n\ty\n\t=\n\t\n\t\t\n\t\t\t-\n\t\t\t1.9\n\t\t\tx\n\t\t\n\t\t-\n\t\t10.1\n\t\n\n

"}, {"id": "B", "text": "

\n\ty\n\t=\n\t\n\t\t\n\t\t\t-\n\t\t\t1.9\n\t\t\tx\n\t\t\n\t\t+\n\t\t10.1\n\t\n\n

"}, {"id": "C", "text": "

\n\ty\n\t=\n\t\n\t\t\n\t\t\t1.9\n\t\t\tx\n\t\t\n\t\t-\n\t\t10.1\n\t\n\n

"}, {"id": "D", "text": "

\n\ty\n\t=\n\t\n\t\t\n\t\t\t1.9\n\t\t\tx\n\t\t\n\t\t+\n\t\t10.1\n\t\n\n

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. The equation representing a linear model can be written in the form y=a+bx, or y=bx+a, where b\n is the slope of the graph of the model and 0,a is the y-intercept of the graph of the model. The scatterplot shows that as the x-values of the data points increase, the y-values of the data points decrease, which means the graph of an appropriate linear model has a negative slope. Therefore, b<0. The scatterplot also shows that the data points are close to the y-axis at a positive value of y\n. Therefore, the y-intercept of the graph of an appropriate linear model has a positive y-coordinate, which means a>0. Of the given choices, only choice B, y=-1.9x+10.1, has a negative value for b\n, the slope, and a positive value for a\n, the y-coordinate of the y-intercept. 

\n

Choice A is incorrect. The graph of this model has a y-intercept with a negative y-coordinate, not a positive y-coordinate.

\n

Choice C is incorrect. The graph of this model has a positive slope, not a negative slope, and a y-intercept with a negative y-coordinate, not a positive y-coordinate.

\n

Choice D is incorrect. The graph of this model has a positive slope, not a negative slope.

"}, {"id": "9e2bf782", "domain": "Problem-Solving and Data Analysis", "skill": "One-variable data: Distributions and measures of center and spread", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

A fish hatchery has three tanks for holding fish before they are introduced into the wild. Ten fish weighing less than 5 ounces are placed in tank A. Eleven fish weighing at least 5 ounces but no more than 13 ounces are placed in tank B. Twelve fish weighing more than 13 ounces are placed in tank C. Which of the following could be the median of the weights, in ounces, of these 33 fish?

\n", "choices": [{"id": "A", "text": "

4.5

\n"}, {"id": "B", "text": "

8

\n"}, {"id": "C", "text": "

13.5

\n"}, {"id": "D", "text": "

15

\n"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. The median of a set of numbers is the middle number when the values in the set are ordered from least to greatest. There are 33 fish, so in an ordered list of the weights, the 17th value would be the median weight. The 10 fish in tank A weigh the least, and these 10 weights would be the first 10 values on the ordered list. The 11 fish in tank B have the next set of higher weights, and so would be the 11th through 21st weights in the ordered list, which includes the median weight as the 17th value. The fish in tank B weigh at least 5 ounces but no more than 13 ounces; of the given choices, only 8 ounces falls within this range of values.

Choice A is incorrect. It’s given that tank A has ten fish weighing less than 5 ounces. Since there are more than ten fish in tanks B and C combined, the median weight cannot be less than 5 ounces. Choice C and D are incorrect. It’s given that tank C has twelve fish weighing more than 13 ounces. There are more than twelve fish in tanks A and B combined, so the median weight can’t be more than 13 ounces.

 

\n"}, {"id": "9ba3e283", "domain": "Problem-Solving and Data Analysis", "skill": "Inference from sample statistics and margin of error ", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

In State X, Mr. Camp’s eighth-grade class consisting of 26 students was surveyed and 34.6 percent of the students reported that they had at least two siblings. The average eighth‑grade class size in the state is 26. If the students in Mr. Camp’s class are representative of students in the state’s eighth-grade classes and there are 1,800 eighth-grade classes in the state, which of the following best estimates the number of eighth‑grade students in the state who have fewer than two siblings?

\n", "choices": [{"id": "A", "text": "

16,200

\n"}, {"id": "B", "text": "

23,400

\n"}, {"id": "C", "text": "

30,600

\n"}, {"id": "D", "text": "

46,800

\n"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. It is given that 34.6% of 26 students in Mr. Camp’s class reported that they had at least two siblings. Since 34.6% of 26 is 8.996, there must have been 9 students in the class who reported having at least two siblings and 17 students who reported that they had fewer than two siblings. It is also given that the average eighth-grade class size in the state is 26 and that Mr. Camp’s class is representative of all eighth-grade classes in the state. This means that in each eighth-grade class in the state there are about 17 students who have fewer than two siblings. Therefore, the best estimate of the number of eighth-grade students in the state who have fewer than two siblings is 17 × (number of eighth-grade classes in the state), or 17 \u00d7 1,800 = 30,600.

Choice A is incorrect because 16,200 is the best estimate for the number of eighth-grade students in the state who have at least, not fewer than, two siblings. Choice B is incorrect because 23,400 is half of the estimated total number of eighth-grade students in the state; however, since the students in Mr. Camp’s class are representative of students in the eighth-grade classes in the state and more than half of the students in Mr. Camp’s class have fewer than two siblings, more than half of the students in each eighth-grade class in the state have fewer than two siblings, too. Choice D is incorrect because 46,800 is the estimated total number of eighth-grade students in the state.

\n"}, {"id": "a9647302", "domain": "Problem-Solving and Data Analysis", "skill": "One-variable data: Distributions and measures of center and spread", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

\"The

For quality control, a company that manufactures lightbulbs conducted five different trials. In each trial, 500 different lightbulbs were tested. The bar graph above shows the number of defective lightbulbs found in each trial. What is the mean number of defective lightbulbs for the five trials?

\n", "choices": [{"id": "A", "text": "

4.0

\n"}, {"id": "B", "text": "

4.2

\n"}, {"id": "C", "text": "

4.6

\n"}, {"id": "D", "text": "

5.0

\n"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. The numbers of defective lightbulbs found for the five trials are 4, 7, 1, 3, and 6, respectively. The mean is therefore (4, + 7, + 1, + 3, + 6)/(5 = 4 point 2).

Choice A is incorrect. This is the median number of defective lightbulbs for the five trials. Choice C is incorrect and may result from an arithmetic error. Choice D is incorrect and may result from mistaking the number of trials for the number of defective lightbulbs.

\n"}, {"id": "7b731fc3", "domain": "Problem-Solving and Data Analysis", "skill": "Percentages", "difficulty": "M", "type": "spr", "stimulus": "", "stem": "

What number is 40\n% greater than 115\n?

", "choices": [], "answerId": "161", "acceptedAnswers": ["161"], "rationale": "

The correct answer is 161\n. For a number to be 40% greater than 115\n, it follows that the number is 100% of 115+40% of 115, which can be written as 100100115+40100115. This expression is equivalent to 1115+0.4115, or 1.4115, which is equal to 161\n. Therefore, 161\n is 40% greater than 115\n.

"}, {"id": "e9f4521a", "domain": "Problem-Solving and Data Analysis", "skill": "Percentages", "difficulty": "M", "type": "spr", "stimulus": "", "stem": "

13\n is p% of 25\n. What is the value of p\n?

", "choices": [], "answerId": "52", "acceptedAnswers": ["52"], "rationale": "

The correct answer is 52\n. It's given that 13\n is p% of 25\n. It follows that \n\t\n\t\t13\n\t\t25\n\t\n\t=\n\t\n\t\t\tp\n\t\t\t100\n\t\t\n\n. Multiplying both sides of this equation by 100\n gives \n\t52\n\t=\n\tp\n\n. Therefore, the value of p\n is 52\n.

"}, {"id": "1c2f50a6", "domain": "Problem-Solving and Data Analysis", "skill": "Percentages", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

During a sale, the original prices of all the items in a clothing store have been reduced by 20%. What is the sale price of a jacket with an original price of $50 ?

\n", "choices": [{"id": "A", "text": "

$12

\n"}, {"id": "B", "text": "

$30

\n"}, {"id": "C", "text": "

$36

\n"}, {"id": "D", "text": "

$40

\n"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. It’s given that the original price of the jacket has been reduced by 20%. Multiplying the original price, $50, by 20% gives the amount, in dollars, that the price of the jacket is reduced by: 50 \u00d7 point 2 0 = 10. Subtracting this value from the original price results in the sale price of the jacket: 50 dollars \u2212 10 dollars, or $40.

Choices A, B, and C are incorrect and may result from a conceptual or calculation error.

 

\n"}, {"id": "89c39d77", "domain": "Problem-Solving and Data Analysis", "skill": "Ratios, rates, proportional relationships, and units", "difficulty": "M", "type": "spr", "stimulus": "", "stem": "

A competition consisted of four different events. One participant completed the first event with an average speed of 20.300 miles per hour. What was this average speed, in yards per hour? 1 mile=1,760 yards

", "choices": [], "answerId": "35728", "acceptedAnswers": ["35728"], "rationale": "

The correct answer is 35,728\n. It's given that 1 mile=1,760 yards. It follows that an average speed of 20.300 miles per hour is equivalent to 20.300 miles1 hour1,760 yards1 mile, or 35,728\n yards per hour.

"}, {"id": "661dfddd", "domain": "Problem-Solving and Data Analysis", "skill": "Two-variable data: Models and scatterplots", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

\"The

The scatterplot above shows the high temperature on a certain day and the elevation of 8 different locations in the Lake Tahoe Basin. A line of best fit for the data is also shown. Which of the following statements best describes the association between the elevation and the temperature of locations in the Lake Tahoe Basin?

\n", "choices": [{"id": "A", "text": "

As the elevation increases, the temperature tends to increase.

\n"}, {"id": "B", "text": "

As the elevation increases, the temperature tends to decrease.

\n"}, {"id": "C", "text": "

As the elevation decreases, the temperature tends to decrease.

\n"}, {"id": "D", "text": "

There is no association between the elevation and the temperature.

\n"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. The association between the elevation and the temperature of locations in the Lake Tahoe Basin can be described by looking at the direction of the line of best fit. The line of best fit slopes downward, which corresponds to the temperature decreasing as the elevation increases.

Choices A and C are incorrect. Both of these choices would be represented by a line of best fit that slopes from the lower left to the upper right of the graph, which isn’t what’s shown on the graph. Choice D is incorrect. This choice would be represented by a line of best fit that is horizontal or has a slope very close to 0. This is not what’s shown on the graph.

\n"}, {"id": "3d73a58b", "domain": "Problem-Solving and Data Analysis", "skill": "Percentages", "difficulty": "H", "type": "spr", "stimulus": "", "stem": "

A gift shop buys souvenirs at a wholesale price of 7.00 dollars each and resells them each at a retail price that is 290% of the wholesale price. At the end of the season, any remaining souvenirs are marked at a discounted price that is 80% off the retail price. What is the discounted price of each remaining souvenir, in dollars?

", "choices": [], "answerId": "203/50", "acceptedAnswers": ["203/50", "4.06"], "rationale": "

The correct answer is 4.06\n. It's given that the retail price is 290% of the wholesale price of $7.00. Thus, the retail price is $7.00290100, which is equivalent to $7.002.9, or $20.30. It's also given that the discounted price is 80% off the retail price. Thus, the discounted price is $20.301-80100, which is equivalent to $20.300.20, or $4.06.

"}, {"id": "79137c1b", "domain": "Problem-Solving and Data Analysis", "skill": "Two-variable data: Models and scatterplots", "difficulty": "H", "type": "mc", "stimulus": "
\n
\n \"The
\n
\n", "stem": "

The scatterplot above shows the size x and the sale price y of 25 houses for sale in Town H. Which of the following could be an equation for a line of best fit for the data?

\n", "choices": [{"id": "A", "text": "

\n y = 200 x + 100\n

\n"}, {"id": "B", "text": "

\n y = 100 x + 100\n

\n"}, {"id": "C", "text": "

\n y = 50 x + 100\n

\n"}, {"id": "D", "text": "

\n y = 100 x\n

\n"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. From the shape of the cluster of points, the line of best fit should pass roughly through the points 1, 200 and 2 point 5, 350. Therefore, these two points can be used to find an approximate equation for the line of best fit. The slope of this line of best fit is therefore (y sub 2, \u2212 y sub 1)/(x sub 2, \u2212 x sub 1, end fraction = the fraction with numerator 350 \u2212 200, and denominator 2 point 5 \u2212 1, end fraction), or 100. The equation for the line of best fit, in slope-intercept form, is y = 100 x + b for some value of b. Using the point 1, 200, 1 can be substituted for x and 200 can be substituted for y: 200 = 100 \u00d7 1, + b, or b = 100. Substituting this value into the slope-intercept form of the equation gives y = 100 x + 100.

Choice A is incorrect. The line defined by y = 200 x + 100 passes through the points 1, 300 and 2, 500, both of which are well above the cluster of points, so it cannot be a line of best fit. Choice C is incorrect. The line defined by y = 50 x + 100 passes through the points 1, 150 and 2, 200, both of which lie at the bottom of the cluster of points, so it cannot be a line of best fit. Choice D is incorrect and may result from correctly calculating the slope of a line of best fit but incorrectly assuming the y-intercept is at the point 0, 0.

\n"}, {"id": "b8150b17", "domain": "Problem-Solving and Data Analysis", "skill": "Probability and conditional probability", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

For a particular machine that produces beads, 29\n out of every 100\n beads it produces have a defect. A bead produced by the machine will be selected at random. What is the probability of selecting a bead that has a defect?

", "choices": [{"id": "A", "text": "

\n\t1\n\t2,900\n\n

"}, {"id": "B", "text": "

\n\t1\n\t29\n\n

"}, {"id": "C", "text": "

\n\t29\n\t100\n\n

"}, {"id": "D", "text": "

\n\t29\n\t10\n\n

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. It’s given that 29\n out of every 100\n beads that the machine produces have a defect. It follows that if the machine produces k\n beads, then the number of beads that have a defect is 29100k, for some constant k\n. If a bead produced by the machine will be selected at random, the probability of selecting a bead that has a defect is given by the number of beads with a defect, 29100k, divided by the number of beads produced by the machine, k\n. Therefore, the probability of selecting a bead that has a defect is 29100kk, or 29100.

\n

Choice A is incorrect and may result from conceptual or computational errors.

\n

Choice B is incorrect and may result from conceptual or computational errors.

\n

Choice D is incorrect and may result from conceptual or computational errors.

"}, {"id": "fdfc90e4", "domain": "Problem-Solving and Data Analysis", "skill": "Two-variable data: Models and scatterplots", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

The scatterplot shows the relationship between two variables, x\n and y\n. A line of best fit for the data is also shown.

\n

\n

At \n\tx\n\t=\n\t32\n\n, which of the following is closest to the y-value predicted by the line of best fit?

", "choices": [{"id": "A", "text": "

0.4\n

"}, {"id": "B", "text": "

1.5\n

"}, {"id": "C", "text": "

2.4\n

"}, {"id": "D", "text": "

3.3\n

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. At x=32, the line of best fit has a y-value between 2\n and 3\n. The only choice with a value between 2\n and 3\n is choice C.

\n

Choice A is incorrect. This is the difference between the y-value predicted by the line of best fit and the actual y-value at x=32 rather than the y-value predicted by the line of best fit at x=32.

\n

Choice B is incorrect. This is the y-value predicted by the line of best fit at x=31 rather than at x=32.

\n

Choice D is incorrect. This is the y-value predicted by the line of best fit at x=33 rather than at x=32.

"}, {"id": "1e562f24", "domain": "Problem-Solving and Data Analysis", "skill": "Inference from sample statistics and margin of error ", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

To estimate the proportion of a population that has a certain characteristic, a random sample was selected from the population. Based on the sample, it is estimated that the proportion of the population that has the characteristic is 0.49\n, with an associated margin of error of 0.04\n. Based on this estimate and margin of error, which of the following is the most appropriate conclusion about the proportion of the population that has the characteristic?

", "choices": [{"id": "A", "text": "

It is plausible that the proportion is between 0.45\n and 0.53\n.

"}, {"id": "B", "text": "

It is plausible that the proportion is less than 0.45\n.

"}, {"id": "C", "text": "

The proportion is exactly 0.49\n.

"}, {"id": "D", "text": "

It is plausible that the proportion is greater than 0.53\n.

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. It’s given that the estimate for the proportion of the population that has the characteristic is 0.49\n with an associated margin of error of 0.04\n. Subtracting the margin of error from the estimate and adding the margin of error to the estimate gives an interval of plausible values for the true proportion of the population that has the characteristic. Therefore, it’s plausible that the proportion of the population that has this characteristic is between 0.45\n and 0.53\n.

\n

Choice B is incorrect. A value less than 0.45\n is outside the interval of plausible values for the proportion of the population that has the characteristic.

\n

Choice C is incorrect. The value 0.49\n is an estimate for the proportion based on this sample. However, since the margin of error for this estimate is known, the most appropriate conclusion is not that the proportion is exactly one value but instead lies in an interval of plausible values.

\n

Choice D is incorrect. A value greater than 0.53\n is outside the interval of plausible values for the proportion of the population that has the characteristic.

"}, {"id": "89f8d08a", "domain": "Problem-Solving and Data Analysis", "skill": "Inference from sample statistics and margin of error ", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

A store manager reviewed the receipts from 80 customers who were selected at random from all the customers who made purchases last Thursday. Of those selected, 20 receipts showed that the customer had purchased fruit. If 1,500 customers made purchases last Thursday, which of the following is the most appropriate conclusion?

\n", "choices": [{"id": "A", "text": "

Exactly 75 customers must have purchased fruit last Thursday.

\n"}, {"id": "B", "text": "

Exactly 375 customers must have purchased fruit last Thursday.

\n"}, {"id": "C", "text": "

The best estimate for the number of customers who purchased fruit last Thursday is 75.

\n"}, {"id": "D", "text": "

The best estimate for the number of customers who purchased fruit last Thursday is 375.

\n"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. It’s given that the manager took a random selection of the receipts of 80 customers from a total of 1,500. It’s also given that of those 80 receipts, 20 showed that the customer had purchased fruit. This means that an appropriate estimate of the fraction of customers who purchased fruit is (20)/(80), or one fourth. Multiplying this fraction by the total number of customers yields one fourth \u00d7 1,500 = 375. Therefore, the best estimate for the number of customers who purchased fruit is 375.

Choices A and B are incorrect because an exact number of customers can’t be known from taking a random selection. Additionally, choice A may also be the result of a calculation error. Choice C is incorrect and may result from a calculation error. 

 

\n"}, {"id": "6a305cd0", "domain": "Problem-Solving and Data Analysis", "skill": "Inference from sample statistics and margin of error ", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

In a study, the data from a random sample of a population had a mean of 37, with an associated margin of error of 3. Which of the following is the most appropriate conclusion that can be made about the population mean?

\n", "choices": [{"id": "A", "text": "

It is less than 37.

\n"}, {"id": "B", "text": "

It is greater than 37.

\n"}, {"id": "C", "text": "

It is between 34 and 40.

\n"}, {"id": "D", "text": "

It is less than 34 or greater than 40.

\n"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. It’s given that the mean of the data from a random sample of a population is 37, with an associated margin of error of 3. The most appropriate conclusion that can be made is that the mean of the entire population will fall between 37, plus or minus 3. Therefore, the population mean is between 37 \u2212 3, which = 34 and 37 + 3, which = 40.

Choice A is incorrect. While it’s an appropriate conclusion that the population mean is as low as 37 \u2212 3, or 34, it isn’t appropriate to conclude that the population mean is less than 34. Choice B is incorrect. While it’s an appropriate conclusion that the population mean is as high as 37 + 3, or 40, it isn’t appropriate to conclude that the population mean is greater than 40. Choice D is incorrect. It isn’t an appropriate conclusion that the population mean is less than 34 or greater than 40.

\n"}, {"id": "048811bd", "domain": "Problem-Solving and Data Analysis", "skill": "Percentages", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

What is 10% of 370\n?

", "choices": [{"id": "A", "text": "

27\n

"}, {"id": "B", "text": "

37\n

"}, {"id": "C", "text": "

333\n

"}, {"id": "D", "text": "

360\n

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. 10% of a quantity means 10100 times the quantity. Therefore, 10% of 370\n can be represented as 10100370, which is equivalent to 0.10370, or 37\n. Therefore, 10% of 370\n is 37\n.

\n

Choice A is incorrect. This is 10% of 270\n, not 10% of 370\n.

\n

Choice C is incorrect. This is 90% of 370\n, not 10% of 370\n.

\n

Choice D is incorrect. This is 370-10, not 10% of 370\n.

"}, {"id": "869a32f1", "domain": "Problem-Solving and Data Analysis", "skill": "One-variable data: Distributions and measures of center and spread", "difficulty": "E", "type": "mc", "stimulus": "
\n\t
\n\t\t
\n\t\t\t

The high temperature, in degrees Fahrenheit (°F), in a certain city was recorded for each of 5 days. The data are shown below.

\n\n\t\t\t
\n\t\t\t\t\n\t\t\t\t\t\t
\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t
Day12345
High temperature (°F)8180818182
\n\t\t
\n\t
\n
\n", "stem": "

Over this 5-day period, which of the following is NOT equal to 81°F?

\n", "choices": [{"id": "A", "text": "

Median of the high temperatures

\n"}, {"id": "B", "text": "

Mean of the high temperatures

\n"}, {"id": "C", "text": "

Mode of the high temperatures

\n"}, {"id": "D", "text": "

Range of the high temperatures

\n"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. The range of a data set is the difference between the maximum and the minimum values in the set. The maximum value among the high temperatures in the table is 82°F and the minimum value is 80°F. Therefore, the range is 82°F – 80°F = 2°F.

Choice A is incorrect. The median of a data set is the middle value when the values in the set are ordered from least to greatest. Ordering the high temperatures this way gives the list 80, 81, 81, 81, 82. Therefore, the median high temperature is 81°F. Choice B is incorrect. The mean high temperature is (81, + 80, + 81, + 81, + 82)/(5 = (405)/(5, which = 81)). Choice C is incorrect. The mode is the value that occurs the greatest number of times. For the set of high temperatures shown, 81 is the value that occurs 3 times, and therefore, 81°F is the mode of the high temperatures.

\n"}, {"id": "916ffe9b", "domain": "Problem-Solving and Data Analysis", "skill": "Inference from sample statistics and margin of error ", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "
\n\n\n\n\n\n\n\n\n\n\n\n

Poll Results

Angel Cruz483\n
Terry Smith320\n
\n

The table shows the results of a poll. A total of 803\n voters selected at random were asked which candidate they would vote for in the upcoming election. According to the poll, if 6,424\n people vote in the election, by how many votes would Angel Cruz be expected to win?

", "choices": [{"id": "A", "text": "

163\n

"}, {"id": "B", "text": "

1,304\n

"}, {"id": "C", "text": "

3,864\n

"}, {"id": "D", "text": "

5,621\n

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. It's given that 483\n out of 803\n voters responded that they would vote for Angel Cruz. Therefore, the proportion of voters from the poll who responded they would vote for Angel Cruz is 483803. It’s also given that there are a total of 6,424\n voters in the election. Therefore, the total number of people who would be expected to vote for Angel Cruz is 6,424483803, or 3,864\n. Since 3,864\n of the 6,424\n total voters would be expected to vote for Angel Cruz, it follows that 6,424-3,864, or 2,560\n voters would be expected not to vote for Angel Cruz. The difference in the number of votes for and against Angel Cruz is 3,864-2,560, or 1,304\n votes. Therefore, if 6,424\n people vote in the election, Angel Cruz would be expected to win by 1,304\n votes.

\n

Choice A is incorrect. This is the difference in the number of voters from the poll who responded that they would vote for and against Angel Cruz.

\n

Choice C is incorrect. This is the total number of people who would be expected to vote for Angel Cruz.

\n

Choice D is incorrect. This is the difference between the total number of people who vote in the election and the number of voters from the poll.

"}, {"id": "a3384df0", "domain": "Problem-Solving and Data Analysis", "skill": "Probability and conditional probability", "difficulty": "M", "type": "mc", "stimulus": "
\n
\n \n \n
\n

Penguin Exhibit

\n
\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n
Type of penguinMaleFemaleTotal
     Chinstrap  41  59100
     Emperor    8  27  35
     Gentoo  49  54103
     Macaroni  42  40  82
     Total140180320
\n
\n", "stem": "

The number of penguins in a zoo exhibit, sorted by gender and type of penguin, is shown in the table above. Which type of penguin has a female population that is the closest to being one-third of the total female penguin population in the exhibit?

\n", "choices": [{"id": "A", "text": "

Chinstrap

\n"}, {"id": "B", "text": "

Emperor

\n"}, {"id": "C", "text": "

Gentoo

\n"}, {"id": "D", "text": "

Macaroni

\n"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. It is given that there are 180 female penguins in the exhibit. Therefore, one third of the female penguins is one third \u00d7 180 = 60 penguins. According to the table, there are 59 female chinstrap penguins, 27 female emperor penguins, 54 female gentoo penguins, and 40 female macaroni penguins. So the female chinstrap penguin population is the closest to 60, or one third of the total female population in the exhibit.

Choices B, C, and D are incorrect and may result from reading data from the table incorrectly. Since the total female penguin population is 180, one third of the total female penguin population is 60. The numbers of female emperor (27), female gentoo (54), and female macaroni (40) penguins are not as close to 60 as the number of female chinstrap penguins (59).

\n"}, {"id": "6670e407", "domain": "Problem-Solving and Data Analysis", "skill": "One-variable data: Distributions and measures of center and spread", "difficulty": "E", "type": "mc", "stimulus": "
Number of High School Students Who
Completed Summer Internships
High schoolYear
20082009201020112012
Foothill8780757670
Valley4454657682
Total131134140152152
\n", "stem": "

The table above shows the number of students from two different high schools who completed summer internships in each of five years. No student attended both schools. Which of the following statements are true about the number of students who completed summer internships for the 5 years shown?

  1. The mean number from Foothill High School is greater than the mean number from Valley High School.
  2. The median number from Foothill High School is greater than the median number from Valley High School.

\n", "choices": [{"id": "A", "text": "

I only

\n"}, {"id": "B", "text": "

II only

\n"}, {"id": "C", "text": "

I and II

\n"}, {"id": "D", "text": "

Neither I nor II

\n"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. The mean of a data set is found by dividing the sum of the values by the number of values. Therefore, the mean number of students who completed summer internships from Foothill High School is (87 + 80, + 75, + 76, + 70)/(5 = (388)/(5)), or 77.6. Similarly, the mean number from Valley High School is (44 + 54, + 65, + 76, + 82)/(5 = (321)/(5)), or 64.2. Thus, the mean number from Foothill High School is greater than the mean number from Valley High School. When a data set has an odd number of elements, the median can be found by ordering the values from least to greatest and determining the value in the middle. Since there are five values in each data set, the third value in each ordered list is the median. Therefore, the median number from Foothill High School is 76 and the median number from Valley High School is 65. Thus, the median number from Foothill High School is greater than the median number from Valley High School.

Choices A, B, and D are incorrect and may result from various misconceptions or miscalculations.

\n"}, {"id": "9b5b23fc", "domain": "Problem-Solving and Data Analysis", "skill": "Two-variable data: Models and scatterplots", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

For x>0, the function f\n is defined as follows:

\n

f(x) equals 201% of x\n

\n

Which of the following could describe this function?

", "choices": [{"id": "A", "text": "

Decreasing exponential

"}, {"id": "B", "text": "

Decreasing linear

"}, {"id": "C", "text": "

Increasing exponential

"}, {"id": "D", "text": "

Increasing linear

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. It's given that for x>0, fx is equal to 201% of x\n. This is equivalent to fx=201100x, or fx=2.01x, for x>0. This function indicates that as x\n increases, fx also increases, which means f\n is an increasing function. Furthermore,  fx increases at a constant rate of 2.01\n for each increase of x\n by 1\n. A function with a constant rate of change is linear. Thus, the function f\n can be described as an increasing linear function.

\n

Choice A is incorrect and may result from conceptual errors.

\n

Choice B is incorrect and may result from conceptual errors.

\n

Choice C is incorrect. This could describe the function fx=2.01x, where fx is equal to 201% of fx-1, not x\n, for x>0.

"}, {"id": "4e527894", "domain": "Problem-Solving and Data Analysis", "skill": "Probability and conditional probability", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

There are 20\n buttons in a bag: 8\n white buttons, 2\n orange buttons, and 10\n brown buttons. If one of these buttons is selected at random, what is the probability of selecting a white button?

", "choices": [{"id": "A", "text": "

220

"}, {"id": "B", "text": "

820

"}, {"id": "C", "text": "

1020

"}, {"id": "D", "text": "

1220

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. It’s given that there are 20\n buttons in a bag and 8\n of the buttons are white. If one button from the bag is selected at random, the probability of selecting a white button is the number of white buttons in the bag divided by the total number of buttons in the bag. Therefore, if one button from the bag is selected at random, the probability of selecting a white button is 820.

\n

Choice A is incorrect. This is the probability of selecting an orange button from the bag.

\n

Choice C is incorrect. This is the probability of selecting a brown button from the bag.

\n

Choice D is incorrect. This is the probability of selecting a button that isn't white from the bag.

"}, {"id": "808f7d6c", "domain": "Problem-Solving and Data Analysis", "skill": "Ratios, rates, proportional relationships, and units", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

If t = 4 u, which of the following is equivalent to 2 t?

\n", "choices": [{"id": "A", "text": "

\n 8 u\n

\n"}, {"id": "B", "text": "

\n 2 u\n

\n"}, {"id": "C", "text": "

\n u\n

\n"}, {"id": "D", "text": "

\n one-half u\n

\n"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. It’s given that t = 4 u. Multiplying both sides of this equation by 2 yields 2 t = 2 times, 4 u, or 2 t = 8 u.

Choice B is incorrect and may result from dividing, instead of multiplying, the right-hand side of the equation by 2. Choices C and D are incorrect and may result from calculation errors.

\n"}, {"id": "af142f8d", "domain": "Problem-Solving and Data Analysis", "skill": "Two-variable data: Models and scatterplots", "difficulty": "H", "type": "mc", "stimulus": "
\n
\n \n
\n \n \n \n \n \n \n \n \n \n
Amount investedBalance increase
Account A   $5006% annual interest
Account B$1,000$25 per year
\n
\n", "stem": "

Two investments were made as shown in the table above. The interest in Account A is compounded once per year. Which of the following is true about the investments?

\n", "choices": [{"id": "A", "text": "

Account A always earns more money per year than Account B.

\n"}, {"id": "B", "text": "

Account A always earns less money per year than Account B.

\n"}, {"id": "C", "text": "

Account A earns more money per year than Account B at first but eventually earns less money per year.

\n"}, {"id": "D", "text": "

Account A earns less money per year than Account B at first but eventually earns more money per year.

\n"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. Account A starts with $500 and earns interest at 6% per year, so in the first year Account A earns (500)(0.06) = $30, which is greater than the $25 that Account B earns that year. Compounding interest can be modeled by an increasing exponential function, so each year Account A will earn more money than it did the previous year. Therefore, each year Account A earns at least $30 in interest. Since Account B always earns $25 each year, Account A always earns more money per year than Account B.

Choices B and D are incorrect. Account A earns $30 in the first year, which is greater than the $25 Account B earns in the first year. Therefore, neither the statement that Account A always earns less money per year than Account B nor the statement that Account A earns less money than Account B at first can be true. Choice C is incorrect. Since compounding interest can be modeled by an increasing exponential function, each year Account A will earn more money than it did the previous year. Therefore, Account A always earns at least $30 per year, which is more than the $25 per year that Account B earns.

\n"}, {"id": "6e4a60dd", "domain": "Problem-Solving and Data Analysis", "skill": "Percentages", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

Rita’s total bill at a restaurant was $25.00, including tax. If she left a tip of 20% of the total bill, what was the amount of the tip?

\n", "choices": [{"id": "A", "text": "

$3.50

\n"}, {"id": "B", "text": "

$4.00

\n"}, {"id": "C", "text": "

$4.50

\n"}, {"id": "D", "text": "

$5.00

\n"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. The total bill was $25.00. The percentage 20% is equivalent to the decimal 0.2. The tip is the product of the percentage and the total bill; therefore, 0 point 2 \u00d7 25 = 5, so the tip was $5.00.

Choices A, B, and C are incorrect and may be the result of incorrectly converting the given percentage or a calculation error.

\n"}, {"id": "040f2a84", "domain": "Problem-Solving and Data Analysis", "skill": "Percentages", "difficulty": "H", "type": "spr", "stimulus": "", "stem": "

The regular price of a shirt at a store is $11.70\n. The sale price of the shirt is 80\n% less than the regular price, and the sale price is 30\n% greater than the store's cost for the shirt. What was the store’s cost, in dollars, for the shirt? (Disregard the $ sign when entering your answer. For example, if your answer is $4.97\n, enter 4.97\n)

", "choices": [], "answerId": "1.8", "acceptedAnswers": ["1.8", "9/5"], "rationale": "

The correct answer is 1.8\n. It’s given that the regular price of a shirt at a store is $11.70, and the sale price of the shirt is 80% less than the regular price. It follows that the sale price of the shirt is $11.701-80100, or $11.701-0.8, which is equivalent to $2.34. It’s also given that the sale price of the shirt is 30% greater than the store’s cost for the shirt. Let x\n represent the store’s cost for the shirt. It follows that 2.34=1+30100x, or 2.34=1.3x. Dividing both sides of this equation by 1.3\n yields x=1.80. Therefore, the store’s cost, in dollars, for the shirt is 1.80. Note that 1.8 and 9/5 are examples of ways to enter a correct answer.

"}, {"id": "41b71b4e", "domain": "Problem-Solving and Data Analysis", "skill": "Percentages", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

What number is 20% greater than 60 ?

\n", "choices": [{"id": "A", "text": "

50

\n"}, {"id": "B", "text": "

72

\n"}, {"id": "C", "text": "

75

\n"}, {"id": "D", "text": "

132

\n"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. The decimal equivalent of 20% is 0.2. The number that is 20% greater than 60 is also 120% of 60. The decimal equivalent of 120% is 1.2, and 1 point 2 \u00d7 60 = 72.

Alternate approach: 10% of 60 is 6, and 20% of 60 is double that amount, or 12. It follows that the number that is 20% greater than 60 is 12 more than 60, or 60 + 12 = 72.

Choice A is incorrect and may result from dividing, instead of multiplying, 60 by 1.2. Choice C is incorrect because it’s 25% greater than 60, rather than 20% greater than 60. Choice D is incorrect and may result from multiplying 60 by 2.2 instead of 1.2.

 

\n"}, {"id": "eaab8bc1", "domain": "Problem-Solving and Data Analysis", "skill": "Percentages", "difficulty": "E", "type": "spr", "stimulus": "", "stem": "

Out of 300\n seeds that were planted, 80% sprouted. How many of these seeds sprouted?

", "choices": [], "answerId": "240", "acceptedAnswers": ["240"], "rationale": "

The correct answer is 240\n. It’s given that 80% of the 300\n seeds sprouted. Therefore, the number of seeds that sprouted can be calculated by multiplying the number of seeds that were planted by 80100, which gives 30080100, or 240\n.

"}, {"id": "46b2e169", "domain": "Problem-Solving and Data Analysis", "skill": "Probability and conditional probability", "difficulty": "M", "type": "spr", "stimulus": "", "stem": "

A box contains 13\n red pens and 37\n blue pens. If one of these pens is selected at random, what is the probability of selecting a red pen? (Express your answer as a decimal or fraction, not as a percent.)

", "choices": [], "answerId": ".26", "acceptedAnswers": [".26", "13/50"], "rationale": "

The correct answer is 1350. It's given that a box contains 13\n red pens and 37\n blue pens. If one of these pens is selected at random, the probability of selecting a red pen is the number of red pens in the box divided by the number of red and blue pens in the box. The number of red and blue pens in the box is 13+37, or 50\n. Since there are 13\n red pens in the box, it follows that the probability of selecting a red pen is \n\t13\n\t50\n\n. Note that 13/50 and .26 are examples of ways to enter a correct answer.

"}, {"id": "8213b1b3", "domain": "Problem-Solving and Data Analysis", "skill": "Percentages", "difficulty": "H", "type": "spr", "stimulus": "", "stem": "

According to a set of standards, a certain type of substance can contain a maximum of 0.001% phosphorus by mass. If a sample of this substance has a mass of 140\n grams, what is the maximum mass, in grams, of phosphorus the sample can contain to meet these standards?

", "choices": [], "answerId": ".0014", "acceptedAnswers": [".0014"], "rationale": "

The correct answer is .0014. It's given that a certain type of substance can contain a maximum of 0.001% phosphorus by mass to meet a set of standards. If a sample of the substance has a mass of 140\n grams, it follows that the maximum mass, in grams, of phosphorus the sample can contain to meet the standards is 0.001% of 140\n, or 0.001100140, which is equivalent to 0.00001140, or 0.0014\n. Note that .0014 and 0.001 are examples of ways to enter a correct answer.

"}, {"id": "f8696cd8", "domain": "Problem-Solving and Data Analysis", "skill": "Probability and conditional probability", "difficulty": "M", "type": "mc", "stimulus": "
\n
\n \n
\n \n \n \n \n \n \n \n \n \n
Human ResourcesAccounting
Bachelor’s degree43
Master’s degree26
\n
\n", "stem": "

The table above shows the number of people who work in the Human Resources and Accounting departments of a company and the highest level of education they have completed. A person from one of these departments is to be chosen at random. If the person chosen works in the Human Resources department, what is the probability that the highest level of education the person completed is a master’s degree?

\n", "choices": [{"id": "A", "text": "(2)/(15)\n"}, {"id": "B", "text": "one-third\n"}, {"id": "C", "text": "one-fourth\n"}, {"id": "D", "text": "(8)/(15)\n"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. In total, there are 6 people in the Human Resources department. Of those 6, 2 have a master’s degree as their highest level of education. Therefore, the probability of an employee selected at random from the Human Resources department having a master’s degree is  two sixths, which simplifies to one third.

Choice A is incorrect; it is the probability that an employee selected at random from either department will be in the Human Resources department and have a master’s degree. Choice C is incorrect; it is the probability that an employee with a master’s degree selected at random will be in the Human Resources department. Choice D is incorrect; it is the probability that an employee selected at random from either department will have a master’s degree.

\n"}, {"id": "50b2807e", "domain": "Problem-Solving and Data Analysis", "skill": "Two-variable data: Models and scatterplots", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

The scatterplot shows the relationship between two variables, x\n and y\n.

\n

\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n\n

\n

Which of the following equations is the most appropriate linear model for the data shown?

", "choices": [{"id": "A", "text": "

y=0.9+\n\t9.4\n\tx\n\n

"}, {"id": "B", "text": "

y=0.9-\n\t9.4\n\tx\n\n

"}, {"id": "C", "text": "

y=9.4\n+0.9x

"}, {"id": "D", "text": "

y=9.4\n-0.9x

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. The data points suggest that as the variable x\n increases, the variable y\n decreases, which implies that an appropriate linear model for the data has a negative slope. The data points also show that when x\n is close to 0\n, y\n is greater than 9\n. Therefore, the y-intercept of the graph of an appropriate linear model has a y-coordinate greater than 9\n. The graph of an equation of the form y=a+bx, where a\n and b\n are constants, has a y-intercept with a y-coordinate of a\n and has a slope of b\n. Of the given choices, only choice D represents a graph that has a negative slope, -0.9\n, and a y-intercept with a y-coordinate greater than 9\n, 9.4\n.

\n

Choice A is incorrect. The graph of this equation has a positive slope, not a negative slope, and a y-intercept with a y-coordinate less than 1\n, not greater than 9\n.

\n

Choice B is incorrect. The graph of this equation has a y-intercept with a y-coordinate less than 1\n, not greater than 9\n.

\n

Choice C is incorrect. The graph of this equation has a positive slope, not a negative slope.

"}, {"id": "34f8cd89", "domain": "Problem-Solving and Data Analysis", "skill": "Percentages", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

37\n% of the items in a box are green. Of those, 37\n% are also rectangular. Of the green rectangular items, 42\n% are also metal. Which of the following is closest to the percentage of the items in the box that are not rectangular green metal items?

", "choices": [{"id": "A", "text": "

1.16\n%

"}, {"id": "B", "text": "

57.50\n%

"}, {"id": "C", "text": "

94.25\n%

"}, {"id": "D", "text": "

98.84\n%

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. It's given that 37% of the items in a box are green. Let x\n represent the total number of items in the box. It follows that 37100x, or 0.37x, items in the box are green. It's also given that of those, 37% are also rectangular. Therefore, 371000.37x, or 0.1369x, items in the box are green rectangular items. It's also given that of the green rectangular items, 42% are also metal. Therefore, 421000.1369x, or 0.057498x, items in the box are rectangular green metal items. The number of the items in the box that are not rectangular green metal items is the total number of items in the box minus the number of rectangular green metal items in the box. Therefore, the number of items in the box that are not rectangular green metal items is x-0.057498x, or 0.942502x. The percentage of items in the box that are not rectangular green metal items is the percentage that 0.942502x is of x\n. If p% represents this percentage, the value of p\n is 1000.942502xx, or 94.2502. Of the given choices, 94.25% is closest to the percentage of items in the box that are not rectangular green metal items.

\n

Choice A is incorrect and may result from conceptual or calculation errors.

\n

Choice B is incorrect and may result from conceptual or calculation errors.

\n

Choice D is incorrect and may result from conceptual or calculation errors.

"}, {"id": "20b69297", "domain": "Problem-Solving and Data Analysis", "skill": "Ratios, rates, proportional relationships, and units", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

Anita created a batch of green paint by mixing 2 ounces of blue paint with 3 ounces of yellow paint. She must mix a second batch using the same ratio of blue and yellow paint as the first batch. If she uses 5 ounces of blue paint for the second batch, how much yellow paint should Anita use?

\n", "choices": [{"id": "A", "text": "

Exactly 5 ounces

\n"}, {"id": "B", "text": "

3 ounces more than the amount of yellow paint used in the first batch

\n"}, {"id": "C", "text": "

1.5 times the amount of yellow paint used in the first batch

\n"}, {"id": "D", "text": "

1.5 times the amount of blue paint used in the second batch

\n"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. It’s given that Anita used a ratio of 2 ounces of blue paint to 3 ounces of yellow paint for the first batch. For any batch of paint that uses the same ratio, the amount of yellow paint used will be three halves, or 1.5, times the amount of blue paint used in the batch. Therefore, the amount of yellow paint Anita will use in the second batch will be 1.5 times the amount of blue paint used in the second batch.

Alternate approach: It’s given that Anita used a ratio of 2 ounces of blue paint to 3 ounces of yellow paint for the first batch and that she will use 5 ounces of blue paint for the second batch. A proportion can be set up to solve for x, the amount of yellow paint she will use for the second batch: 2 over 3 = 5 over x. Multiplying both sides of this equation by 3 yields 2 = 15 over x, and multiplying both sides of this equation by x yields 2 x = 15. Dividing both sides of this equation by 2 yields x = 7 point 5. Since Anita will use 7.5 ounces of yellow paint for the second batch, this is 7 point 5 over 5 = 1 point 5 times the amount of blue paint (5 ounces) used in the second batch.

Choices A, B, and C are incorrect and may result from incorrectly interpreting the ratio of blue paint to yellow paint used.

 

\n"}, {"id": "9d95e7ad", "domain": "Problem-Solving and Data Analysis", "skill": "Two-variable data: Models and scatterplots", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "
\"The

The scatterplot above shows the numbers of grams of both total protein and total fat for eight sandwiches on a restaurant menu. The line of best fit for the data is also shown. According to the line of best fit, which of the following is closest to the predicted increase in total fat, in grams, for every increase of 1 gram in total protein?

\n
\n", "choices": [{"id": "A", "text": "

2.5

\n"}, {"id": "B", "text": "

2.0

\n"}, {"id": "C", "text": "

1.5

\n"}, {"id": "D", "text": "

1.0

\n"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. The predicted increase in total fat, in grams, for every increase of 1 gram in total protein is represented by the slope of the line of best fit. Any two points on the line can be used to calculate the slope of the line as the change in total fat over the change in total protein. For instance, it can be estimated that the points 20, 34 and 30, 48 are on the line of best fit, and the slope of the line that passes through them is (48 \u2212 34)/(30 \u2212 20, end fraction = 14 over 10), or 1.4. Of the choices given, 1.5 is the closest to the slope of the line of best fit.

Choices A, B, and D are incorrect and may be the result of incorrectly finding ordered pairs that lie on the line of best fit or of incorrectly calculating the slope.

 

\n"}, {"id": "39aa146d", "domain": "Problem-Solving and Data Analysis", "skill": "Two-variable data: Models and scatterplots", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

The scatterplot shows the relationship between x\n and y\n. A line of best fit is also shown.

\n

\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n\n

\n

Which of the following is closest to the slope of the line of best fit shown?

", "choices": [{"id": "A", "text": "

-2.27\n

"}, {"id": "B", "text": "

-0.44\n

"}, {"id": "C", "text": "

0.44\n

"}, {"id": "D", "text": "

2.27\n

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. It's given that the scatterplot shows the relationship between two variables, x\n and y\n, and a line of best fit is shown. For the line of best fit shown, for each increase in the value of x\n by 1\n, the corresponding value of y\n increases by a constant rate. It follows that the relationship between the variables x\n and y\n has a positive linear trend. A line in the xy-plane that passes through the points a,b and c,d has a slope of d-bc-a. The line of best fit shown passes approximately through the points 0,0.25 and 4,2. It follows that the slope of this line is approximately 2-0.254-0, which is equivalent to 0.4375\n. Therefore, of the given choices, 0.44\n is closest to the slope of the line of best fit shown.

\n

Choice A is incorrect. This is the slope of a line of best fit for a relationship between x\n and y\n that has a negative, rather than a positive, linear trend.

\n

Choice B is incorrect. This is the slope of a line of best fit for a relationship between x\n and y\n that has a negative, rather than a positive, linear trend.

\n

Choice D is incorrect and may result from conceptual or calculation errors.

"}, {"id": "58171b5e", "domain": "Problem-Solving and Data Analysis", "skill": "Two-variable data: Models and scatterplots", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

Each year, the value of an investment increases by 0.49\n% of its value the previous year. Which of the following functions best models how the value of the investment changes over time?

", "choices": [{"id": "A", "text": "

Decreasing exponential

"}, {"id": "B", "text": "

Decreasing linear

"}, {"id": "C", "text": "

Increasing exponential

"}, {"id": "D", "text": "

Increasing linear

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. Because the value of the investment increases each year, the function that best models how the value of the investment changes over time is an increasing function. It′s given that each year, the value of the investment increases by 0.49% of its value the previous year. Since the value of the investment changes by a fixed percentage each year, the function that best models how the value of the investment changes over time is an exponential function. Therefore, the function that best models how the value of the investment changes over time is an increasing exponential function.

\n

Choice A is incorrect and may result from conceptual errors.

\n

Choice B is incorrect and may result from conceptual errors.

\n

Choice D is incorrect and may result from conceptual errors.

"}, {"id": "d6456c7a", "domain": "Problem-Solving and Data Analysis", "skill": "Ratios, rates, proportional relationships, and units", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

A certain park has an area of 11,863,808\n square yards. What is the area, in square miles, of this park? 1 mile=1,760 yards

", "choices": [{"id": "A", "text": "

1.96\n

"}, {"id": "B", "text": "

3.83\n

"}, {"id": "C", "text": "

3,444.39\n 

"}, {"id": "D", "text": "

6,740.8\n

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. Since 1\n mile is equal to 1,760 yards, 1\n square mile is equal to 1,7602, or 3,097,600, square yards. It’s given that the park has an area of 11,863,808 square yards. Therefore, the park has an area of 11,863,808 square yards1 square mile3,097,600 square yards, or 11,863,8083,097,600 square miles. Thus, the area, in square miles, of the park is 3.83\n.

\n

Choice A is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect. This is the square root of the area of the park in square yards, not the area of the park in square miles.

\n

Choice D is incorrect and may result from converting 11,863,808 yards to miles, rather than converting 11,863,808 square yards to square miles.

"}, {"id": "4347a032", "domain": "Problem-Solving and Data Analysis", "skill": "Ratios, rates, proportional relationships, and units", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

How many teaspoons are equivalent to 44\n tablespoons? 3 teaspoons=1 tablespoon

", "choices": [{"id": "A", "text": "

47\n

"}, {"id": "B", "text": "

88\n

"}, {"id": "C", "text": "

132\n

"}, {"id": "D", "text": "

176\n

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. It's given that 3\n teaspoons is equivalent to 1\n tablespoon. Therefore, 44\n tablespoons is equivalent to 44 tablespoons3 teaspoons1 tablespoon, or 132\n teaspoons.

\n

Choice A is incorrect. This is equivalent to approximately 15.66\n tablespoons, not 44\n tablespoons.

\n

Choice B is incorrect. This is equivalent to approximately 29.33\n tablespoons, not 44\n tablespoons.

\n

Choice D is incorrect. This is equivalent to approximately 58.66\n tablespoons, not 44\n tablespoons.

"}, {"id": "51c9d65f", "domain": "Problem-Solving and Data Analysis", "skill": "Ratios, rates, proportional relationships, and units", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

For a certain rectangular region, the ratio of its length to its width is 35\n to 10\n. If the width of the rectangular region increases by 7\n units, how must the length change to maintain this ratio?

", "choices": [{"id": "A", "text": "

It must decrease by 24.5\n units.

"}, {"id": "B", "text": "

It must increase by 24.5\n units.

"}, {"id": "C", "text": "

It must decrease by 7\n units.

"}, {"id": "D", "text": "

It must increase by 7\n units.

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. It’s given that the ratio of the rectangular region’s length to its width is 35\n to 10\n. This can be written as a proportion: lengthwidth=3510, or lw=3510. This proportion can be rewritten as 10l=35w, or l=3.5w. If the width of the rectangular region increases by 7\n, then the length will increase by some number x\n in order to maintain this ratio. The value of x\n can be found by replacing l with l+x and w\n with \n\tw\n\t+\n\t7\n\n in the equation, which gives l+x=3.5w+7. This equation can be rewritten using the distributive property as l+x=3.5w+24.5. Since l=3.5w, the right-hand side of this equation can be rewritten by substituting l for \n\t3.5\n\tw\n\n, which gives l+x=l+24.5, or \n\tx\n\t=\n\t24.5\n\n. Therefore, if the width of the rectangular region increases by 7\n units, the length must increase by 24.5\n units in order to maintain the given ratio.

\n

Choice A is incorrect. If the width of the rectangular region increases, the length must also increase, not decrease.

\n

Choice C is incorrect. If the width of the rectangular region increases, the length must also increase, not decrease.

\n

Choice D is incorrect. Since the ratio of the length to the width of the rectangular region is 35\n to 10\n, if the width of the rectangular region increases by 7\n units, the length would have to increase by a proportional amount, which would have to be greater than 7\n units.

"}, {"id": "763e6769", "domain": "Problem-Solving and Data Analysis", "skill": "Ratios, rates, proportional relationships, and units", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

The ratio x\n to y\n is equivalent to the ratio 12\n to t\n. When \n\tx\n\t=\n\t156\n\n, what is the value of y\n in terms of t\n?

", "choices": [{"id": "A", "text": "

\n\t13\n\tt\n\n

"}, {"id": "B", "text": "

\n\t12\n\tt\n\n

"}, {"id": "C", "text": "

\n\t144\n\tt\n\n

"}, {"id": "D", "text": "

\n\t168\n\tt\n\n

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. It's given that the ratio x\n to y\n is equivalent to the ratio 12\n to t\n. This can be represented by xy=12t. Substituting 156\n for x\n in this equation yields 156y=12t. This can be rewritten as 12y=156t. Dividing both sides of this equation by 12\n yields \n\ty\n\t=\n\t\n\t\t13\n\t\tt\n\t\n\n. Therefore, when \n\tx\n\t=\n\t156\n\n, the value of y\n in terms of t\n is \n\t13\n\tt\n\n.

\n

Choice B is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

\n

Choice D is incorrect and may result from conceptual or calculation errors.

"}, {"id": "25faa756", "domain": "Problem-Solving and Data Analysis", "skill": "Percentages", "difficulty": "H", "type": "spr", "stimulus": "", "stem": "

The number a\n is 60\n% greater than the positive number b\n. The number c\n is 45\n% less than a\n. The number c\n is how many times b\n?

", "choices": [], "answerId": ".88", "acceptedAnswers": [".88", "22/25"], "rationale": "

The correct answer is .88. It’s given that the number a\n is 60% greater than the positive number b\n. Therefore, a=1+60100b, which is equivalent to a=1+0.60b, or \n\ta\n\t=\n\t\n\t\t1.60\n\t\tb\n\t\n\n. It’s also given that the number c\n is 45% less than a\n. Therefore, c=1-45100a, which is equivalent to c=1-0.45a, or \n\tc\n\t=\n\t\n\t\t0.55\n\t\ta\n\t\n\n. Since \n\ta\n\t=\n\t\n\t\t1.60\n\t\tb\n\t\n\n, substituting \n\t1.60\n\tb\n\n for a\n in the equation \n\tc\n\t=\n\t\n\t\t0.55\n\t\ta\n\t\n\n yields c=0.551.60b, or \n\tc\n\t=\n\t\n\t\t0.88\n\t\tb\n\t\n\n. Thus, the number c\n is 0.88\n times the number b\n. Note that .88 and 22/25 are examples of ways to enter a correct answer. 

"}, {"id": "ad911622", "domain": "Problem-Solving and Data Analysis", "skill": "Percentages", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

The value of a collectible comic book increased by 167% from the end of 2011 to the end of 2012 and then decreased by 16% from the end of 2012 to the end of 2013. What was the net percentage increase in the value of the collectible comic book from the end of 2011 to the end of 2013?

", "choices": [{"id": "A", "text": "

124.28%

"}, {"id": "B", "text": "

140.28%

"}, {"id": "C", "text": "

151.00%

"}, {"id": "D", "text": "

209.72%

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. It’s given that the value of the comic book increased by 167% from the end of 2011 to the end of 2012. Therefore, if the value of the comic book at the end of 2011 was x\n dollars, then the value, in dollars, of the comic book at the end of 2012 was x+167100x, which can be rewritten as 1x+1.67x, or \n\t2.67\n\tx\n\n. It’s also given that the value of the comic book decreased by 16% from the end of 2012 to the end of 2013. Therefore, the value, in dollars, of the comic book at the end of 2013 was 2.67x-2.67x16100, which can be rewritten as 2.67x-2.67x0.16, or 2.2428x. Thus, if the value of the comic book at the end of 2011 was x\n dollars, and the value of the comic book at the end of 2013 was \n\t2.2428\n\tx\n\n dollars, then from the end of 2011 to the end of 2013, the value of the comic book increased by 2.2428x-1x, or \n\t1.2428\n\tx\n\n, dollars. Therefore, the increase in the value of the comic book from the end of 2011 to the end of 2013 is equal to 1.2428\n times the value of the comic book at the end of 2011. It follows that from the end of 2011 to the end of 2013, the net percentage increase in the value of the comic book was 1.2428100%, or 124.28%.

\n

Choice B is incorrect and may result from conceptual or calculation errors. 

\n

Choice C is incorrect. This is the difference between the net percentage increase in the value of the comic book from the end of 2011 to the end of 2012 and the net percentage decrease in the value of the comic book from the end of 2012 to the end of 2013, not the net percentage increase in the value of the comic book from the end of 2011 to the end of 2013.

\n

Choice D is incorrect. This is the net percentage increase in the value of the comic book from the end of 2011 to the end of 2013, if the value of the comic book increased by 167% from the end of 2011 to the end of 2012 and then increased, not decreased, by 16% from the end of 2012 to the end of 2013.

"}, {"id": "ecd09c38", "domain": "Problem-Solving and Data Analysis", "skill": "Probability and conditional probability", "difficulty": "H", "type": "mc", "stimulus": "
\n
\n
\n

Employees working for a customer service line at an electric company recorded all the calls last Monday and noted whether the caller asked for repairs and whether the caller asked about a bill. The results are summarized in the table below.

\n
\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n
Asked for
 repairs		Did not ask
 for repairs		Total
Asked
 about a bill		48623671
Did not ask
 about a bill		13090220
Total178713891
\n
\n
\n
\n", "stem": "

If a caller last Monday who asked about his or her bill is selected at random, which of the following is closest to the probability that the customer also asked for repairs?

\n", "choices": [{"id": "A", "text": "

0.05

\n"}, {"id": "B", "text": "

0.07

\n"}, {"id": "C", "text": "

0.20

\n"}, {"id": "D", "text": "

0.27

\n"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. According to the table, a total of 671 customers asked about a bill. Of these, 48 also asked for repairs. Therefore, if a customer who asked about a bill is selected at random, the probability that the customer also asked for repairs is 48 over 671 is approximately equal to 0 point 0 7.

Choice A is incorrect. This is the probability that a customer selected at random from all customers who called on Monday both asked for repairs and asked about a bill. Choice C is incorrect. This is the probability that a customer selected at random from all customers who called on Monday asked for repairs, regardless of whether or not the customer asked about a bill. Choice D is incorrect. This is the probability that a customer selected at random from those who asked for repairs also asked about a bill.

\n"}, {"id": "cf0ae57a", "domain": "Problem-Solving and Data Analysis", "skill": "Two-variable data: Models and scatterplots", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

\"The

The scatterplot above shows the densities of 7 planetoids, in grams per cubic centimeter, with respect to their average distances from the Sun in astronomical units (AU). The line of best fit is also shown. An astronomer has discovered a new planetoid about 1.2 AU from the Sun. According to the line of best fit, which of the following best approximates the density of the planetoid, in grams per cubic centimeter?

\n", "choices": [{"id": "A", "text": "

3.6

\n"}, {"id": "B", "text": "

4.1

\n"}, {"id": "C", "text": "

4.6

\n"}, {"id": "D", "text": "

5.5

\n"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. According to the line of best fit, a planetoid with a distance from the Sun of 1.2 AU has a predicted density between 4 point 5 grams per cubic centimeter and 4 point 7 5 grams per cubic centimeter. The only choice in this range is 4.6.

Choices A, B, and D are incorrect and may result from misreading the information in the scatterplot.

\n"}, {"id": "e9ed719f", "domain": "Problem-Solving and Data Analysis", "skill": "Probability and conditional probability", "difficulty": "M", "type": "spr", "stimulus": "", "stem": "

The table summarizes the distribution of color and shape for 100\n tiles of equal area.

\n
\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
 RedBlueYellowTotal
Square10\n20\n25\n55\n
Pentagon20\n10\n15\n45\n
Total30\n30\n40\n100\n
\n

If one of these tiles is selected at random, what is the probability of selecting a red tile? (Express your answer as a decimal or fraction, not as a percent.)

", "choices": [], "answerId": ".3", "acceptedAnswers": [".3", "3/10"], "rationale": "

The correct answer is 310. It’s given that there are a total of 100\n tiles of equal area, which is the total number of possible outcomes. According to the table, there are a total of 30\n red tiles. The probability of an event occurring is the ratio of the number of favorable outcomes to the total number of possible outcomes. By definition, the probability of selecting a red tile is given by 30100, or 310. Note that 3/10 and .3 are examples of ways to enter a correct answer.

"}, {"id": "6d99b141", "domain": "Geometry and Trigonometry", "skill": "Lines, angles, and triangles", "difficulty": "H", "type": "spr", "stimulus": "", "stem": "

\n

 

\n

In the figure, \n\t\n\t\tA\n\t\tC\n\t\n\t=\n\t\n\t\tC\n\t\tD\n\t\n\n. The measure of angle EBC is 45°, and the measure of angle ACD is 104°. What is the value of x\n?

", "choices": [], "answerId": "83", "acceptedAnswers": ["83"], "rationale": "

The correct answer is 83\n. It's given that in the figure, \n\t\n\t\tA\n\t\tC\n\t\n\t=\n\t\n\t\tC\n\t\tD\n\t\n\n. Thus, triangle \n\tA\n\tC\n\tD\n\n is an isosceles triangle and the measure of angle CDA is equal to the measure of angle CAD. The sum of the measures of the interior angles of a triangle is 180°. Thus, the sum of the measures of the interior angles of triangle \n\tA\n\tC\n\tD\n\n is 180°. It's given that the measure of angle \n\tA\n\tC\n\tD\n\n is 104°. It follows that the sum of the measures of angles CDA and CAD is 180-104°, or 76°. Since the measure of angle CDA is equal to the measure of angle CAD, the measure of angle CDA is half of 76°, or 38°. The sum of the measures of the interior angles of triangle \n\tB\n\tD\n\tE\n\n is 180°. It's given that the measure of angle EBC is 45°. Since the measure of angle BDE, which is the same angle as angle CDA, is 38°, it follows that the measure of angle DEB is 180-45-38°, or 97°. Since angle DEB and angle AEB form a straight line, the sum of the measures of these angles is 180°. It's given in the figure that the measure of angle AEB is x°. It follows that 97+x=180. Subtracting 97\n from both sides of this equation yields \n\tx\n\t=\n\t83\n\n.

"}, {"id": "e10d8313", "domain": "Geometry and Trigonometry", "skill": "Lines, angles, and triangles", "difficulty": "H", "type": "spr", "stimulus": "", "stem": "

\n

In the figure shown, points Q\n, R\n, S\n, and T\n lie on line segment \n\tP\n\tV\n\n, and line segment \n\tR\n\tU\n\n intersects line segment \n\tS\n\tX\n\n at point W\n. The measure of ∠SQX is 48°, the measure of ∠SXQ is 86°, the measure of ∠SWU is 85°, and the measure of ∠VTU is 162°. What is the measure, in degrees, of ∠TUR? 

", "choices": [], "answerId": "123", "acceptedAnswers": ["123"], "rationale": "

The correct answer is 123\n. The triangle angle sum theorem states that the sum of the measures of the interior angles of a triangle is 180\n degrees. It's given that the measure of ∠SQX is 48° and the measure of ∠SXQ is 86°. Since points S\n, Q\n, and X\n form a triangle, it follows from the triangle angle sum theorem that the measure, in degrees, of ∠QSX is 180-48-86, or 46\n. It's also given that the measure of ∠SWU is 85°. Since ∠SWU and ∠SWR are supplementary angles, the sum of their measures is 180\n degrees. It follows that the measure, in degrees, of ∠SWR is 180-85, or 95\n. Since points R\n, S\n, and W\n form a triangle, and ∠RSW is the same angle as ∠QSX, it follows from the triangle angle sum theorem that the measure, in degrees, of ∠WRS is 180-46-95, or 39\n. It's given that the measure of ∠VTU is 162°. Since ∠VTU and ∠STU are supplementary angles, the sum of their measures is 180\n degrees. It follows that the measure, in degrees, of ∠STU is 180-162, or 18. Since points R\n, T\n, and U\n form a triangle, and ∠URT is the same angle as ∠WRS, it follows from the triangle angle sum theorem that the measure, in degrees, of ∠TUR is 180-39-18, or 123.

"}, {"id": "bcb66188", "domain": "Geometry and Trigonometry", "skill": "Right triangles and trigonometry", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

Triangle \n\tF\n\tG\n\tH\n\n is similar to triangle \n\tJ\n\tK\n\tL\n\n, where angle F\n corresponds to angle J\n and angles G\n and K\n are right angles. If sinF=308317, what is the value of sin(J)?

", "choices": [{"id": "A", "text": "

\n\t75\n\t317\n\n

"}, {"id": "B", "text": "

\n\t308\n\t317\n\n

"}, {"id": "C", "text": "

\n\t317\n\t308\n\n

"}, {"id": "D", "text": "

\n\t317\n\t75\n\n

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. If two triangles are similar, then their corresponding angles are congruent. It's given that right triangle \n\tF\n\tG\n\tH\n\n is similar to right triangle \n\tJ\n\tK\n\tL\n\n and angle F\n corresponds to angle J\n. It follows that angle F\n is congruent to angle J\n and, therefore, the measure of angle F\n is equal to the measure of angle J\n. The sine ratios of angles of equal measure are equal. Since the measure of angle F\n is equal to the measure of angle J\n, sinF=sinJ. It's given that sinF=308317. Therefore,  sinJ is 308317.

\n

Choice A is incorrect. This is the value of cosJ, not the value of sinJ.

\n

Choice C is incorrect. This is the reciprocal of the value of sinJ, not the value of sinJ.

\n

Choice D is incorrect. This is the reciprocal of the value of cosJ, not the value of sinJ.

"}, {"id": "5207e508", "domain": "Geometry and Trigonometry", "skill": "Lines, angles, and triangles", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

\n

In the figure, line m\n is parallel to line n\n. What is the value of w\n?

", "choices": [{"id": "A", "text": "

17\n

"}, {"id": "B", "text": "

30\n

"}, {"id": "C", "text": "

70\n

"}, {"id": "D", "text": "

170\n

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. It's given that lines m\n and n\n are parallel. Since line t\n intersects both lines m\n and n\n, it's a transversal. The angles in the figure marked as 170\u00b0 and w\u00b0 are on the same side of the transversal, where one is an interior angle with line m\n as a side, and the other is an exterior angle with line n\n as a side. Thus, the marked angles are corresponding angles. When two parallel lines are intersected by a transversal, corresponding angles are congruent and, therefore, have equal measure. It follows that w\u00b0=170\u00b0. Therefore, the value of w\n is 170\n. 

\n

Choice A is incorrect and may result from conceptual or calculation errors.

\n

Choice B is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

"}, {"id": "f67e4efc", "domain": "Geometry and Trigonometry", "skill": "Area and volume", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

A right circular cylinder has a volume of 45 pi. If the height of the cylinder is 5, what is the radius of the cylinder?

\n", "choices": [{"id": "A", "text": "

3

\n"}, {"id": "B", "text": "

4.5

\n"}, {"id": "C", "text": "

9

\n"}, {"id": "D", "text": "

40

\n"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. The volume of a right circular cylinder with a radius of r is the product of the area of the base, pi, r\u00b2, and the height, h. The volume of the right circular cylinder described is 45 pi and its height is 5. If the radius is r, it follows that 45 pi = pi times, r, squared, \u00d7 5. Dividing both sides of this equation by 5 pi yields 9 = r\u00b2. Taking the square root of both sides yields r = 3 or r = \u22123. Since r represents the radius, the value must be positive. Therefore, the radius is 3.

Choice B is incorrect and may result from finding that the square of the radius is 9, but then from dividing 9 by 2, rather than taking the square root of 9. Choice C is incorrect. This represents the square of the radius. Choice D is incorrect and may result from solving the equation 45 pi = pi times, r, squared, \u00d7 5 for r\u00b2, not r, by dividing by pi on both sides and then by subtracting, not dividing, 5 from both sides.

 

\n"}, {"id": "e5c57163", "domain": "Geometry and Trigonometry", "skill": "Area and volume", "difficulty": "H", "type": "spr", "stimulus": "", "stem": "

Square A has side lengths that are 166\n times the side lengths of square B. The area of square A is k\n times the area of square B. What is the value of k\n?

", "choices": [], "answerId": "27556", "acceptedAnswers": ["27556"], "rationale": "

The correct answer is 27,556\n. The area of a square is \n\ts\n\t2\n\n, where s\n is the side length of the square. Let x\n represent the length of each side of square B. Substituting x\n for s\n in \n\ts\n\t2\n\n yields \n\tx\n\t2\n\n. It follows that the area of square B is \n\tx\n\t2\n\n. It’s given that square A has side lengths that are 166\n times the side lengths of square B. Since x\n represents the length of each side of square B, the length of each side of square A can be represented by the expression \n\t166\n\tx\n\n. It follows that the area of square A is 166x2, or \n\t27,556\n\t\n\t\tx\n\t\t2\n\t\n\n. It’s given that the area of square A is k\n times the area of square B. Since the area of square A is equal to \n\t27,556\n\t\n\t\tx\n\t\t2\n\t\n\n, and the area of square B is equal to \n\tx\n\t2\n\n, an equation representing the given statement is \n\t\n\t\t27,556\n\t\t\n\t\t\tx\n\t\t\t2\n\t\t\n\t\n\t=\n\t\n\t\tk\n\t\t\n\t\t\tx\n\t\t\t2\n\t\t\n\t\n\n. Since x\n represents the length of each side of square B, the value of x\n must be positive. Therefore, the value of \n\tx\n\t2\n\n is also positive, so it does not equal 0\n. Dividing by \n\tx\n\t2\n\n on both sides of the equation \n\t\n\t\t27,556\n\t\t\n\t\t\tx\n\t\t\t2\n\t\t\n\t\n\t=\n\t\n\t\tk\n\t\t\n\t\t\tx\n\t\t\t2\n\t\t\n\t\n\n yields 27,556=k. Therefore, the value of k\n is 27,556\n.

"}, {"id": "33e29881", "domain": "Geometry and Trigonometry", "skill": "Right triangles and trigonometry", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

In right triangle \n\tR\n\tS\n\tT\n\n, the sum of the measures of angle R\n and angle S\n is 90\n degrees. The value of sinR is \n\t\n\t\t\n\t\t\t15\n\t\t\n\t\t4\n\t\n\n. What is the value of cosS?

", "choices": [{"id": "A", "text": "

\n\t\n\t\t\n\t\t\t15\n\t\t\n\t\t15\n\t\n\n

"}, {"id": "B", "text": "

\n\t\n\t\t\n\t\t\t15\n\t\t\n\t\t4\n\t\n\n

"}, {"id": "C", "text": "

\n\t\n\t\t\n\t\t\t4\n\t\t\t\n\t\t\t\t15\n\t\t\t\n\t\t\n\t\t15\n\t\n\n

"}, {"id": "D", "text": "

\n\t15\n\n

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. The sine of any acute angle is equal to the cosine of its complement. It’s given that in right triangle \n\tR\n\tS\n\tT\n\n, the sum of the measures of angle R\n and angle S\n is 90\n degrees. Therefore, angle R\n and angle S\n are complementary, and the value of sinR is equal to the value of cosS. It's given that the value of sinR is 154, so the value of cosS is also 154.

\n

Choice A is incorrect. This is the value of tanS.

\n

Choice C is incorrect. This is the value of 1cosS.

\n

Choice D is incorrect. This is the value of 1tanS.

"}, {"id": "5252e606", "domain": "Geometry and Trigonometry", "skill": "Area and volume", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

The side length of a square is 55 centimeters cm. What is the area, in cm2, of the square?

", "choices": [{"id": "A", "text": "

110\n

"}, {"id": "B", "text": "

220\n

"}, {"id": "C", "text": "

3,025\n

"}, {"id": "D", "text": "

12,100\n

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. The area A\n, in square centimeters (cm2), of a square with side length s\n, in cm, is given by the formula \n\tA\n\t=\n\t\n\t\ts\n\t\t2\n\t\n\n. It’s given that the square has a side length of 55 cm. Substituting 55\n for s\n in the formula \n\tA\n\t=\n\t\n\t\ts\n\t\t2\n\t\n\n yields A=552, or \n\tA\n\t=\n\t3,025\n\n. Therefore, the area, in cm2, of the square is 3,025\n.

\n

Choice A is incorrect and may result from conceptual or calculation errors.

\n

Choice B is incorrect. This is the perimeter, in cm, of the square, not its area, in cm2.

\n

Choice D is incorrect and may result from conceptual or calculation errors.

"}, {"id": "5afbdc8e", "domain": "Geometry and Trigonometry", "skill": "Area and volume", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

What is the length of one side of a square that has the same area as a circle with radius 2 ?

\n", "choices": [{"id": "A", "text": "

2

\n"}, {"id": "B", "text": "

\n the square root(2) pi, end root\n

\n"}, {"id": "C", "text": "

\n 2 \u00d7 the square root(p)i\n

\n"}, {"id": "D", "text": "

\n 2 pi\n

\n"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. The area A of a circle with radius r is given by the formula A = pi \u00d7 r\u00b2. Thus, a circle with radius 2 has area pi \u00d7 2\u00b2, which can be rewritten as 4 pi. The area of a square with side length s is given by the formula A = s\u00b2. Thus, if a square has the same area as a circle with radius 2, then s\u00b2 = 4 pi. Since the side length of a square must be a positive number, taking the square root of both sides of s\u00b2 = 4 pi gives s = the square root(4) pi, end root. Using the properties of square roots, the square root(4) pi, end root can be rewritten as open parenthesis, the square root(4), close parenthesis, times, open parenthesis, the square root(p)i, close parenthesis, which is equivalent to 2 \u00d7 the square root(p)i. Therefore, s = 2 \u00d7 the square root(p)i.

Choice A is incorrect. The side length of the square isn’t equal to the radius of the circle. Choices B and D are incorrect and may result from incorrectly simplifying the expression the square root(4) pi, end root.

\n"}, {"id": "c8d60e48", "domain": "Geometry and Trigonometry", "skill": "Lines, angles, and triangles", "difficulty": "E", "type": "mc", "stimulus": "
\n
\n \"The
\n
\n", "stem": "

In the given triangle, the length(s)ide A, B = the length(s)ide A, C and angle A, B C has a measure of 67 degrees. What is the value of x ?

\n", "choices": [{"id": "A", "text": "

36

\n"}, {"id": "B", "text": "

46

\n"}, {"id": "C", "text": "

58

\n"}, {"id": "D", "text": "

70

\n"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. Since the length(A), B = the length(A), C, the measures of their corresponding angles, angle A, B C and angle A, C B, are equal. Since angle A, B C has a measure of 67 degrees, the measure of angle A, C B is also 67 degrees. Since the sum of the measures of the interior angles in a triangle is 180 degrees, it follows that 67 + 67, + x = 180, or 134 + x = 180. Subtracting by 134 on both sides of this equation yields x = 46.

Choices A, C, and D are incorrect and may result from calculation errors.

\n"}, {"id": "1f0b582e", "domain": "Geometry and Trigonometry", "skill": "Area and volume", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

Square X has a side length of 12\n centimeters. The perimeter of square Y is 2\n times the perimeter of square X. What is the length, in centimeters, of one side of square Y?

", "choices": [{"id": "A", "text": "

6\n

"}, {"id": "B", "text": "

10\n

"}, {"id": "C", "text": "

14\n

"}, {"id": "D", "text": "

24\n

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. The perimeter, P\n, of a square can be found using the formula \n\tP\n\t=\n\t\n\t\t4\n\t\ts\n\t\n\n, where s\n is the length of each side of the square. It's given that square X has a side length of 12\n centimeters. Substituting 12\n for s\n in the formula for the perimeter of a square yields P=412, or \n\tP\n\t=\n\t48\n\n. Therefore, the perimeter of square X is 48\n centimeters. It’s also given that the perimeter of square Y is 2\n times the perimeter of square X. Therefore, the perimeter of square Y is 248, or 96\n, centimeters. Substituting 96\n for P\n in the formula P=4s gives 96=4s. Dividing both sides of this equation by 4\n gives \n\t24\n\t=\n\ts\n\n. Therefore, the length of one side of square Y is 24\n centimeters.

\n

Choice A is incorrect and may result from conceptual or calculation errors.

\n

Choice B is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

"}, {"id": "d5f349b7", "domain": "Geometry and Trigonometry", "skill": "Lines, angles, and triangles", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

\n

Right triangles \n\tP\n\tQ\n\tR\n\n and \n\tS\n\tT\n\tU\n\n are similar, where P\n corresponds to S\n. If the measure of angle Q\n is 18°, what is the measure of angle S\n?

", "choices": [{"id": "A", "text": "

18°

"}, {"id": "B", "text": "

72°

"}, {"id": "C", "text": "

82°

"}, {"id": "D", "text": "

162°

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. In similar triangles, corresponding angles are congruent. It’s given that right triangles \n\tP\n\tQ\n\tR\n\n and \n\tS\n\tT\n\tU\n\n are similar, where angle P\n corresponds to angle S\n. It follows that angle P\n is congruent to angle S\n. In the triangles shown, angle R\n and angle U\n are both marked as right angles, so angle R\n and angle U\n are corresponding angles. It follows that angle Q\n and angle T\n are corresponding angles, and thus, angle Q\n is congruent to angle T\n. It’s given that the measure of angle Q\n is 18\u00b0, so the measure of angle T\n is also 18\u00b0. Angle U\n is a right angle, so the measure of angle U\n is 90\u00b0. The sum of the measures of the interior angles of a triangle is 180\u00b0. Thus, the sum of the measures of the interior angles of triangle \n\tS\n\tT\n\tU\n\n is 180\n degrees. Let s\n represent the measure, in degrees, of angle S\n. It follows that s+18+90=180, or \n\t\n\t\ts\n\t\t+\n\t\t108\n\t\n\t=\n\t180\n\n. Subtracting 108\n from both sides of this equation yields \n\ts\n\t=\n\t72\n\n. Therefore, if the measure of angle Q\n is 18\n degrees, then the measure of angle S\n is 72\n degrees.

\n

Choice A is incorrect. This is the measure of angle T\n.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

\n

Choice D is incorrect. This is the sum of the measures of angle S\n and angle U\n.

"}, {"id": "686b5212", "domain": "Geometry and Trigonometry", "skill": "Lines, angles, and triangles", "difficulty": "M", "type": "spr", "stimulus": "", "stem": "

\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n\n

\n

In the figure, line q\n is parallel to line r\n, and both lines are intersected by line s\n. If \n\ty\n\t=\n\t\n\t\t\n\t\t\t2\n\t\t\tx\n\t\t\n\t\t+\n\t\t8\n\t\n\n, what is the value of x\n?

", "choices": [], "answerId": "57", "acceptedAnswers": ["57"], "rationale": "

The correct answer is 57\n. Based on the figure, the angle with measure y° and the angle vertical to the angle with measure 58° are same side interior angles. Since vertical angles are congruent, the angle vertical to the angle with measure 58° also has measure 58°. It’s given that lines q\n and r\n are parallel. Therefore, same side interior angles between lines q\n and r\n are supplementary. It follows that \n\t\n\t\ty\n\t\t+\n\t\t58\n\t\n\t=\n\t180\n\n. If \n\ty\n\t=\n\t\n\t\t\n\t\t\t2\n\t\t\tx\n\t\t\n\t\t+\n\t\t8\n\t\n\n, then the value of x\n can be found by substituting \n\t\n\t\t2\n\t\tx\n\t\n\t+\n\t8\n\n for y\n in the equation \n\t\n\t\ty\n\t\t+\n\t\t58\n\t\n\t=\n\t180\n\n, which yields 2x+8+58=180, or 2x+66=180. Subtracting 66\n from both sides of this equation yields \n\t\n\t\t2\n\t\tx\n\t\n\t=\n\t114\n\n. Dividing both sides of this equation by 2\n yields \n\tx\n\t=\n\t57\n\n. Thus, if \n\ty\n\t=\n\t\n\t\t\n\t\t\t2\n\t\t\tx\n\t\t\n\t\t+\n\t\t8\n\t\n\n, the value of x\n is 57\n.

"}, {"id": "a6dbad6b", "domain": "Geometry and Trigonometry", "skill": "Lines, angles, and triangles", "difficulty": "E", "type": "mc", "stimulus": "
\n
\n
\n", "stem": "

\"The

In the figure above, lines l and m are parallel, y = 20, and z = 60. What is the value of x ?

\n", "choices": [{"id": "A", "text": "

120

\n"}, {"id": "B", "text": "

100

\n"}, {"id": "C", "text": "

90

\n"}, {"id": "D", "text": "

80

\n"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. Let the measure of the third angle in the smaller triangle be a, degrees. Since lines l and m are parallel and cut by transversals, it follows that the corresponding angles formed are congruent. So a degrees = y degrees, which = 20 degrees. The sum of the measures of the interior angles of a triangle is 180 degrees, which for the interior angles in the smaller triangle yields a, + x, + z = 180. Given that z = 60 and a = 20, it follows that 20 + x, + 60 = 180. Solving for x gives x = 180 \u2212 60, \u2212 20, or x = 100.

Choice A is incorrect and may result from incorrectly assuming that angles x + z = 180. Choice C is incorrect and may result from incorrectly assuming that the smaller triangle is a right triangle, with x as the right angle. Choice D is incorrect and may result from a misunderstanding of the exterior angle theorem and incorrectly assuming that x = y + z.

\n"}, {"id": "81b664bc", "domain": "Geometry and Trigonometry", "skill": "Lines, angles, and triangles", "difficulty": "M", "type": "mc", "stimulus": "
\n
\n
\n", "stem": "

\"The

In the figure above, side A, F, line segment B E, and side C D are parallel. Points B and E lie on side A, C and side F D, respectively. If the length(l)ine segment A, B = 9, the length(l)ine segment B C = 18 point 5, and the length(l)ine segment F E = 8 point 5, what is the length of line segment E D, to the nearest tenth?

\n", "choices": [{"id": "A", "text": "

16.8

\n"}, {"id": "B", "text": "

17.5

\n"}, {"id": "C", "text": "

18.4

\n"}, {"id": "D", "text": "

19.6

\n"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. Since line segment A F, line segment B E, and line segment C D are parallel, quadrilaterals A F E B and B E D C are similar. Let x represent the length of line segment E D. With similar figures, the ratios of the lengths of corresponding sides are equal. It follows that 9 over 18 point 5 = 8 point 5 over x. Multiplying both sides of this equation by 18.5 and by x yields 9 x = 18 point 5, \u00d7 8 point 5, or 9 x = 157 point 2 5. Dividing both sides of this equation by 9 yields x = 17 point 4 7, which to the nearest tenth is 17.5.

Choices A, C, and D are incorrect and may result from errors made when setting up the proportion.

\n"}, {"id": "59cb654c", "domain": "Geometry and Trigonometry", "skill": "Area and volume", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

The area of a square is 64\n square inches. What is the side length, in inches, of this square?

", "choices": [{"id": "A", "text": "

8\n

"}, {"id": "B", "text": "

16\n

"}, {"id": "C", "text": "

64\n

"}, {"id": "D", "text": "

128\n

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. It's given that the area of a square is 64\n square inches. The area A\n, in square inches, of a square is given by the formula A=s2, where s\n is the side length, in inches, of the square. Substituting 64\n for A\n in this formula yields 64=s2. Taking the positive square root of both sides of this equation yields 8=s. Thus, the side length, in inches, of this square is 8\n.

\n

Choice B is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect. This is the area, in square inches, of the square, not the side length, in inches, of the square.

\n

Choice D is incorrect and may result from conceptual or calculation errors.

"}, {"id": "902dc959", "domain": "Geometry and Trigonometry", "skill": "Right triangles and trigonometry", "difficulty": "M", "type": "mc", "stimulus": "
\n
\n \"The
\n
\n", "stem": "

In the figure above, what is the value of tangent A?

\n", "choices": [{"id": "A", "text": "

\n 20 over 29\n

\n"}, {"id": "B", "text": "

\n 21 over 29\n

\n"}, {"id": "C", "text": "

\n 20 over 21\n

\n"}, {"id": "D", "text": "

\n 21 over 20\n

\n"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. Angle A is an acute angle in a right triangle, so the value of tan(A) is equivalent to the ratio of the length of the side opposite angle A, 20, to the length of the nonhypotenuse side adjacent to angle A, 21. Therefore,  tangent A = 20 over 21.

Choice A is incorrect. This is the value of sin(A). Choice B is incorrect. This is the value of cos(A). Choice D is incorrect. This is the value of tan(B).

\n"}, {"id": "9966235e", "domain": "Geometry and Trigonometry", "skill": "Area and volume", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

A cube has an edge length of 68\n inches. A solid sphere with a radius of 34\n inches is inside the cube, such that the sphere touches the center of each face of the cube. To the nearest cubic inch, what is the volume of the space in the cube not taken up by the sphere?

", "choices": [{"id": "A", "text": "

149,796\n

"}, {"id": "B", "text": "

164,500\n

"}, {"id": "C", "text": "

190,955\n

"}, {"id": "D", "text": "

310,800\n

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. The volume of a cube can be found by using the formula V=s3, where V\n is the volume and s\n is the edge length of the cube. Therefore, the volume of the given cube is V=683, or 314,432\n cubic inches. The volume of a sphere can be found by using the formula V=43\u03c0r3 , where V\n is the volume and r\n is the radius of the sphere. Therefore, the volume of the given sphere is V=43\u03c0343, or approximately 164,636\n cubic inches. The volume of the space in the cube not taken up by the sphere is the difference between the volume of the cube and volume of the sphere. Subtracting the approximate volume of the sphere from the volume of the cube gives 314,432-164,636=149,796 cubic inches.

\n

Choice B is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

\n

Choice D is incorrect and may result from conceptual or calculation errors.

"}, {"id": "a0369739", "domain": "Geometry and Trigonometry", "skill": "Lines, angles, and triangles", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

In triangle \n\tA\n\tB\n\tC\n\n, the measure of angle B\n is 90° and BD is an altitude of the triangle. The length of AB is 15\n and the length of AC is 23\n greater than the length of AB. What is the value of BCBD?

", "choices": [{"id": "A", "text": "

\n\t15\n\t38\n\n

"}, {"id": "B", "text": "

\n\t15\n\t23\n\n

"}, {"id": "C", "text": "

\n\t23\n\t15\n\n

"}, {"id": "D", "text": "

\n\t38\n\t15\n\n

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. It's given that in triangle ABC, the measure of angle B\n is 90° and  BD is an altitude of the triangle. Therefore, the measure of angle BDC is 90°. It follows that angle B\n is congruent to angle D\n and angle C\n is congruent to angle C\n. By the angle-angle similarity postulate, triangle ABC is similar to triangle BDC. Since triangles ABC and BDC are similar, it follows that ACAB=BCBD. It's also given that the length of AB¯ is 15\n and the length of AC¯ is 23\n greater than the length of AB¯. Therefore, the length of AC¯ is 15+23, or 38\n. Substituting 15\n for AB and 38\n for AC in the equation ACAB=BCBD yields 3815=BCBD. Therefore, the value of BCBD is 3815.

\n

Choice A is incorrect. This is the value of BDBC.

\n

Choice B is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect and may result from conceptual or calculation errors.
 

"}, {"id": "a07ed090", "domain": "Geometry and Trigonometry", "skill": "Area and volume", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

\n

The figure shown is a right circular cylinder with a radius of r\n and height of h\n. A second right circular cylinder (not shown) has a volume that is 392\n times as large as the volume of the cylinder shown. Which of the following could represent the radius R\n, in terms of r\n, and the height H\n, in terms of h\n, of the second cylinder?

", "choices": [{"id": "A", "text": "

\n\tR\n\t=\n\t\n\t\t8\n\t\tr\n\t\n\n and \n\tH\n\t=\n\t\n\t\t7\n\t\th\n\t\n\n

"}, {"id": "B", "text": "

\n\tR\n\t=\n\t\n\t\t8\n\t\tr\n\t\n\n and \n\tH\n\t=\n\t\n\t\t49\n\t\th\n\t\n\n

"}, {"id": "C", "text": "

\n\tR\n\t=\n\t\n\t\t7\n\t\tr\n\t\n\n and \n\tH\n\t=\n\t\n\t\t8\n\t\th\n\t\n\n

"}, {"id": "D", "text": "

\n\tR\n\t=\n\t\n\t\t49\n\t\tr\n\t\n\n and \n\tH\n\t=\n\t\n\t\t8\n\t\th\n\t\n\n

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. The volume of a right circular cylinder is equal to πa2b, where a\n is the radius of a base of the cylinder and b\n is the height of the cylinder. It’s given that the cylinder shown has a radius of r\n and a height of h\n. It follows that the volume of the cylinder shown is equal to πr2h. It’s given that the second right circular cylinder has a radius of R\n and a height of H\n. It follows that the volume of the second cylinder is equal to πR2H. Choice C gives \n\tR\n\t=\n\t\n\t\t7\n\t\tr\n\t\n\n and \n\tH\n\t=\n\t\n\t\t8\n\t\th\n\t\n\n. Substituting \n\t7\n\tr\n\n for R\n and \n\t8\n\th\n\n for H\n in the expression that represents the volume of the second cylinder yields π7r28h, or π49r28h, which is equivalent to π392r2h, or 392πr2h. This expression is equal to 392\n times the volume of the cylinder shown, πr2h. Therefore, \n\tR\n\t=\n\t\n\t\t7\n\t\tr\n\t\n\n and \n\tH\n\t=\n\t\n\t\t8\n\t\th\n\t\n\n could represent the radius R\n, in terms of r\n, and the height H\n, in terms of h\n, of the second cylinder.

\n

Choice A is incorrect. Substituting \n\t8\n\tr\n\n for R\n and \n\t7\n\th\n\n for H\n in the expression that represents the volume of the second cylinder yields π8r27h, or π64r27h, which is equivalent to π448r2h, or 448πr2h. This expression is equal to 448\n, not 392\n, times the volume of the cylinder shown. 

\n

Choice B is incorrect. Substituting \n\t8\n\tr\n\n for R\n and \n\t49\n\th\n\n for H\n in the expression that represents the volume of the second cylinder yields π8r249h, or π64r249h, which is equivalent to π3,136r2h, or 3,136πr2h. This expression is equal to 3,136\n, not 392\n, times the volume of the cylinder shown.

\n

Choice D is incorrect. Substituting \n\t49\n\tr\n\n for R\n and \n\t8\n\th\n\n for H\n in the expression that represents the volume of the second cylinder yields π49r28h, or π2,401r28h, which is equivalent to π19,208r2h, or 19,208πr2h. This expression is equal to 19,208\n, not 392\n, times the volume of the cylinder shown.

"}, {"id": "cbe8ca31", "domain": "Geometry and Trigonometry", "skill": "Lines, angles, and triangles", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

In △XYZ, the measure of ∠X is 24\n° and the measure of ∠Y is 98\n°. What is the measure of ∠Z?

", "choices": [{"id": "A", "text": "

58\n°

"}, {"id": "B", "text": "

74\n°

"}, {"id": "C", "text": "

122\n°

"}, {"id": "D", "text": "

212\n°

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. The triangle angle sum theorem states that the sum of the measures of the interior angles of a triangle is 180°. It's given that in △XYZ, the measure of ∠X is 24° and the measure of ∠Y is 98°. It follows that the measure of ∠Z is 180-24-98°, or 58°.

\n

Choice B is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect. This is the sum of the measures of ∠X and ∠Y, not the measure of ∠Z.

\n

Choice D is incorrect and may result from conceptual or calculation errors.

"}, {"id": "94364a79", "domain": "Geometry and Trigonometry", "skill": "Lines, angles, and triangles", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

Two nearby trees are perpendicular to the ground, which is flat. One of these trees is 10\n feet tall and has a shadow that is 5\n feet long. At the same time, the shadow of the other tree is 2\n feet long. How tall, in feet, is the other tree?

", "choices": [{"id": "A", "text": "

3\n

"}, {"id": "B", "text": "

4\n

"}, {"id": "C", "text": "

8\n

"}, {"id": "D", "text": "

27\n

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. Each tree and its shadow can be modeled using a right triangle, where the height of the tree and the length of its shadow are the legs of the triangle. At a given point in time, the right triangles formed by two nearby trees and their respective shadows will be similar. Therefore, if the height of the other tree is x\n, in feet, the value of x\n can be calculated by solving the proportional relationship 10 feet tall5 feet long=x feet tall2 feet long. This equation is equivalent to105=x2, or 2=x2. Multiplying each side of the equation 2=x2 by 2\n yields 4=x. Therefore, the other tree is 4 feet tall.

\n

Choice A is incorrect and may result from calculating the difference between the lengths of the shadows, rather than the height of the other tree.

\n

Choice C is incorrect and may result from calculating the difference between the height of the 10\n-foot-tall tree and the length of the shadow of the other tree, rather than calculating the height of the other tree.

\n

Choice D is incorrect and may result from a conceptual or calculation error.

"}, {"id": "c24e1bda", "domain": "Geometry and Trigonometry", "skill": "Lines, angles, and triangles", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

\n

In the figure, line m\n is parallel to line n\n. What is the value of w\n?

", "choices": [{"id": "A", "text": "

13\n

"}, {"id": "B", "text": "

34\n

"}, {"id": "C", "text": "

66\n

"}, {"id": "D", "text": "

134\n

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. It's given that lines m\n and n\n are parallel. Since line t\n intersects both lines m\n and n\n, it's a transversal. The angles in the figure marked as 134° and w° are on the same side of the transversal, where one is an interior angle with line m\n as a side, and the other is an exterior angle with line n\n as a side. Thus, the marked angles are corresponding angles. When two parallel lines are intersected by a transversal, corresponding angles are congruent and, therefore, have equal measure. It follows that w°=134°. Therefore, the value of w\n is 134\n.

\n

Choice A is incorrect and may result from conceptual or calculation errors.

\n

Choice B is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

"}, {"id": "c8345903", "domain": "Geometry and Trigonometry", "skill": "Circles", "difficulty": "H", "type": "mc", "stimulus": "
\n
\n \"The
\n
\n", "stem": "

The circle above has center O, the length of arc A, D C is 5 pi, and x = 100. What is the length of arc A, B C ?

\n", "choices": [{"id": "A", "text": "

\n 9 pi\n

\n"}, {"id": "B", "text": "

\n 13 pi\n

\n"}, {"id": "C", "text": "

\n 18 pi\n

\n"}, {"id": "D", "text": "

\n 13 halves pi\n

\n"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. The ratio of the lengths of two arcs of a circle is equal to the ratio of the measures of the central angles that subtend the arcs. It’s given that arc A D C is subtended by a central angle with measure 100°. Since the sum of the measures of the angles about a point is 360°, it follows that arc A B C is subtended by a central angle with measure 360 degrees \u2212 100 degrees = 260 degrees. If s is the length of arc A B C, then s must satisfy the ratio (s)/(5 pi, end fraction = the fraction 260 over 100). Reducing the fraction 260 over 100 to its simplest form gives (13)/(5). Therefore, (s)/(5 pi, end fraction = the fraction 13 over 5). Multiplying both sides of (s)/(5 pi, end fraction = the fraction 13 over 5) by 5 pi yields s = 13 pi.

Choice A is incorrect. This is the length of an arc consisting of exactly half of the circle, but arc A B C is greater than half of the circle. Choice C is incorrect. This is the total circumference of the circle. Choice D is incorrect. This is half the length of arc A B C, not its full length.

\n"}, {"id": "901c3215", "domain": "Geometry and Trigonometry", "skill": "Lines, angles, and triangles", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

In triangles \n\tA\n\tB\n\tC\n\n and \n\tD\n\tE\n\tF\n\n, angles B\n and E\n each have measure 27° and angles C\n and F\n each have measure 41°. Which additional piece of information is sufficient to determine whether triangle \n\tA\n\tB\n\tC\n\n is congruent to triangle \n\tD\n\tE\n\tF\n\n?

", "choices": [{"id": "A", "text": "

The measure of angle A\n

"}, {"id": "B", "text": "

The length of side \n\tA\n\tB\n\n

"}, {"id": "C", "text": "

The lengths of sides \n\tB\n\tC\n\n and \n\tE\n\tF\n\n

"}, {"id": "D", "text": "

No additional information is necessary.

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. Since angles B\n and E\n each have the same measure and angles C\n and F\n each have the same measure, triangles \n\tA\n\tB\n\tC\n\n and \n\tD\n\tE\n\tF\n\n are similar, where side \n\tB\n\tC\n\n corresponds to side \n\tE\n\tF\n\n. To determine whether two similar triangles are congruent, it is sufficient to determine whether one pair of corresponding sides are congruent. Therefore, to determine whether triangles \n\tA\n\tB\n\tC\n\n and \n\tD\n\tE\n\tF\n\n are congruent, it is sufficient to determine whether sides \n\tB\n\tC\n\n and \n\tE\n\tF\n\n have equal length. Thus, the lengths of \n\tB\n\tC\n\n and \n\tE\n\tF\n\n are sufficient to determine whether triangle \n\tA\n\tB\n\tC\n\n is congruent to triangle \n\tD\n\tE\n\tF\n\n.

\n

Choice A is incorrect and may result from conceptual errors.

\n

Choice B is incorrect and may result from conceptual errors.

\n

Choice D is incorrect. The given information is sufficient to determine that triangles \n\tA\n\tB\n\tC\n\n and \n\tD\n\tE\n\tF\n\n are similar, but not whether they are congruent.

"}, {"id": "f7dbde16", "domain": "Geometry and Trigonometry", "skill": "Lines, angles, and triangles", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

In triangles \n\tL\n\tM\n\tN\n\n and \n\tR\n\tS\n\tT\n\n, angles L\n and R\n each have measure 60\n°, \n\t\n\t\tL\n\t\tN\n\t\n\t=\n\t10\n\n, and \n\t\n\t\tR\n\t\tT\n\t\n\t=\n\t30\n\n. Which additional piece of information is sufficient to prove that triangle \n\tL\n\tM\n\tN\n\n is similar to triangle \n\tR\n\tS\n\tT\n\n?

", "choices": [{"id": "A", "text": "

\n\t\n\t\tM\n\t\tN\n\t\n\t=\n\t7\n\n and \n\t\n\t\tS\n\t\tT\n\t\n\t=\n\t7\n\n

"}, {"id": "B", "text": "

\n\t\n\t\tM\n\t\tN\n\t\n\t=\n\t7\n\n and \n\t\n\t\tS\n\t\tT\n\t\n\t=\n\t21\n\n

"}, {"id": "C", "text": "

The measures of angles M\n and S\n are 70\n° and 60\n°, respectively.

"}, {"id": "D", "text": "

The measures of angles M\n and T\n are 70\n° and 50\n°, respectively.

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. Two triangles are similar if they have three pairs of congruent corresponding angles. It’s given that angles L\n and R\n each measure 60\u00b0, and so these corresponding angles are congruent. If angle M\n is 70\u00b0, then angle N\n must be 50\u00b0 so that the sum of the angles in triangle \n\tL\n\tM\n\tN\n\n is 180\u00b0. If angle T\n is 50\u00b0, then angle S\n must be 70\u00b0 so that the sum of the angles in triangle \n\tR\n\tS\n\tT\n\n is 180\u00b0. Therefore, if the measures of angles M\n and T\n are 70\u00b0 and 50\u00b0, respectively, then corresponding angles M\n and S\n are both 70\u00b0, and corresponding angles N\n and T\n are both 50\u00b0. It follows that triangles \n\tL\n\tM\n\tN\n\n and \n\tR\n\tS\n\tT\n\n have three pairs of congruent corresponding angles, and so the triangles are similar. Therefore, the additional piece of information that is sufficient to prove that triangle \n\tL\n\tM\n\tN\n\n is similar to triangle \n\tR\n\tS\n\tT\n\n is that the measures of angles M\n and T\n are 70\u00b0 and 50\u00b0, respectively.

\n

Choice A is incorrect. If the measures of two sides in one triangle are proportional to the corresponding sides in another triangle and the included angles are congruent, then the triangles are similar. However, the two sides given are not proportional and the angle given is not included by the given sides.

\n

Choice B is incorrect. If the measures of two sides in one triangle are proportional to the corresponding sides in another triangle and the included angles are congruent, then the triangles are similar. However, the angle given is not included between the proportional sides.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

"}, {"id": "b0c5ece5", "domain": "Geometry and Trigonometry", "skill": "Right triangles and trigonometry", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n\n \n \n \n\n \n\n

\n

Which equation shows the relationship between the side lengths of the given triangle?

", "choices": [{"id": "A", "text": "

4b=19

"}, {"id": "B", "text": "

4+b=19

"}, {"id": "C", "text": "

42+b2=192

"}, {"id": "D", "text": "

42-b2=192

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. The Pythagorean theorem states that in a right triangle, the sum of the squares of the lengths of the two legs is equal to the square of the length of the hypotenuse. Therefore, a2+b2=c2, where a\n and b\n are the lengths of the legs and c\n is the length of the hypotenuse. For the given right triangle, the lengths of the legs are 4\n and b\n, and the length of the hypotenuse is 19\n. Substituting 4\n for a\n and 19\n for c\n in the equation a2+b2=c2 yields 42+b2=192. Thus, the relationship between the side lengths of the given triangle is 42+b2=192.

\n

Choice A is incorrect and may result from conceptual or calculation errors.

\n

Choice B is incorrect and may result from conceptual or calculation errors.

\n

Choice D is incorrect and may result from conceptual or calculation errors.

"}, {"id": "76c73dbf", "domain": "Geometry and Trigonometry", "skill": "Circles", "difficulty": "H", "type": "spr", "stimulus": "", "stem": "

The graph of \n\t\n\t\t\n\t\t\tx\n\t\t\t2\n\t\t\n\t\t+\n\t\tx\n\t\t+\n\t\t\n\t\t\ty\n\t\t\t2\n\t\t\n\t\t+\n\t\ty\n\t\n\t=\n\t\n\t\t199\n\t\t2\n\t\n\n in the xy-plane is a circle. What is the length of the circle’s radius?

", "choices": [], "answerId": "10", "acceptedAnswers": ["10"], "rationale": "

The correct answer is 10\n. It's given that the graph of x2+x+y2+y=1992 in the xy-plane is a circle. The equation of a circle in the xy-plane can be written in the form x-h2+y-k2=r2, where the coordinates of the center of the circle are h,k and the length of the radius of the circle is r\n. The term x-h2 in this equation can be obtained by adding the square of half the coefficient of x\n to both sides of the given equation to complete the square. The coefficient of x\n is 1\n. Half the coefficient of x\n is \n\t1\n\t2\n\n. The square of half the coefficient of x\n is \n\t1\n\t4\n\n. Adding \n\t1\n\t4\n\n to each side of x2+x+y2+y=1992 yields x2+x+14+y2+y=1992+14, or x+122+y2+y=1992+14. Similarly, the term y-k2 can be obtained by adding the square of half the coefficient of y\n to both sides of this equation, which yields x+122+y2+y+14=1992+14+14, or x+122+y+122=1992+14+14. This equation is equivalent to x+122+y+122=100, or x+122+y+122=102. Therefore, the length of the circle's radius is 10\n.

"}, {"id": "e336a1d2", "domain": "Geometry and Trigonometry", "skill": "Area and volume", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

A cube has an edge length of 41\n inches. What is the volume, in cubic inches, of the cube?

", "choices": [{"id": "A", "text": "

164\n

"}, {"id": "B", "text": "

1,681\n

"}, {"id": "C", "text": "

10,086\n

"}, {"id": "D", "text": "

68,921\n

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. The volume, V\n, of a cube can be found using the formula V=s3, where s\n is the edge length of the cube. It's given that a cube has an edge length of 41\n inches. Substituting 41\n inches for s\n in this equation yields V=413 cubic inches, or \n\tV\n\t=\n\t68,921\n\n cubic inches. Therefore, the volume of the cube is 68,921\n cubic inches.

\n

Choice A is incorrect. This is the perimeter, in inches, of the cube.

\n

Choice B is incorrect. This is the area, in square inches, of a face of the cube.

\n

Choice C is incorrect. This is the surface area, in square inches, of the cube.

"}, {"id": "c0586eb5", "domain": "Geometry and Trigonometry", "skill": "Area and volume", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

A cylinder has a diameter of 8\n inches and a height of 12\n inches. What is the volume, in cubic inches, of the cylinder?

", "choices": [{"id": "A", "text": "

\n\t16\n\tπ\n\n

"}, {"id": "B", "text": "

\n\t96\n\tπ\n\n

"}, {"id": "C", "text": "

\n\t192\n\tπ\n\n

"}, {"id": "D", "text": "

\n\t768\n\tπ\n\n

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. The base of a cylinder is a circle with a diameter equal to the diameter of the cylinder. The volume, V\n, of a cylinder can be found by multiplying the area of the circular base, A\n, by the height of the cylinder, h\n, or V=Ah. The area of a circle can be found using the formula A=\u03c0r2, where r\n is the radius of the circle. It’s given that the diameter of the cylinder is 8\n inches. Thus, the radius of this circle is 4\n inches. Therefore, the area of the circular base of the cylinder is A=\u03c042, or 16\u03c0 square inches. It’s given that the height h\n of the cylinder is 12\n inches. Substituting 16\u03c0 for A\n and 12\n for h\n in the formula V=Ah gives V=16\u03c012, or 192\u03c0 cubic inches.

\n

Choice A is incorrect. This is the area of the circular base of the cylinder.

\n

Choice B is incorrect and may result from using 8\n, instead of 16\n, as the value of r2 in the formula for the area of a circle.

\n

Choice D is incorrect and may result from using 8\n, instead of 4\n, for the radius of the circular base.

"}, {"id": "151eda3c", "domain": "Geometry and Trigonometry", "skill": "Area and volume", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

A manufacturing company produces two sizes of cylindrical containers that each have a height of 50 centimeters. The radius of container A is 16 centimeters, and the radius of container B is 25% longer than the radius of container A. What is the volume, in cubic centimeters, of container B?

\n", "choices": [{"id": "A", "text": "

\n 16,000 pi\n

\n"}, {"id": "B", "text": "

\n 20,000 pi\n

\n"}, {"id": "C", "text": "

\n 25,000 pi\n

\n"}, {"id": "D", "text": "

\n 31,250 pi\n

\n"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. If the radius of container A is 16 centimeters and the radius of container B is 25% longer than the radius of container A, then the radius of container B is 16 plus, 0 point 2 5 \u00d7 16 = 20 centimeters. The volume of a cylinder is pi, \u00d7 r\u00b2, \u00d7 h, where r is the radius of the cylinder and h is its height. Substituting r = 20 and h = 50 into pi, \u00d7 r\u00b2, \u00d7 h yields that the volume of cylinder B is pi \u00d7 open parenthesis, 20, close parenthesis, squared, \u00d7 50 = 20,000 pi cubic centimeters.

Choice A is incorrect and may result from multiplying the radius of cylinder B by the radius of cylinder A rather than squaring the radius of cylinder B. Choice C is incorrect and may result from multiplying the radius of cylinder B by 25 rather than squaring it. Choice D is incorrect and may result from taking the radius of cylinder B to be 25 centimeters rather than 20 centimeters.

\n"}, {"id": "2266984b", "domain": "Geometry and Trigonometry", "skill": "Circles", "difficulty": "H", "type": "mc", "stimulus": "
\n\t

x\u00b2, + 20 x, + y\u00b2, + 16 y = \u221220

\n
\n", "stem": "

The equation above defines a circle in the xy-plane. What are the coordinates of the center of the circle?

\n", "choices": [{"id": "A", "text": "

\u221220, \u221216

\n"}, {"id": "B", "text": "

\u221210, \u22128

\n"}, {"id": "C", "text": "

10, 8

\n"}, {"id": "D", "text": "

20, 16

\n"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. The standard equation of a circle in the xy-plane is of the form open parenthesis, x \u2212 h, close parenthesis, squared, plus, open parenthesis, y \u2212 k, close parenthesis, squared = r\u00b2, where h, k are the coordinates of the center of the circle and r is the radius. The given equation can be rewritten in standard form by completing the squares. So the sum of the first two terms, x\u00b2, + 20 x, needs a 100 to complete the square, and the sum of the second two terms, y\u00b2, + 16 y, needs a 64 to complete the square. Adding 100 and 64 to both sides of the given equation yields open parenthesis, x\u00b2, + 20 x, + 100, close parenthesis, plus, open parenthesis, y\u00b2, + 16 y, + 64, close parenthesis = \u221220, + 100, + 64, which is equivalent to open parenthesis, x + 10, close parenthesis, squared, plus, open parenthesis, y + 8, close parenthesis, squared = 144. Therefore, the coordinates of the center of the circle are \u221210, \u22128.

Choices A, C, and D are incorrect and may result from computational errors made when attempting to complete the squares or when identifying the coordinates of the center.

 

\n"}, {"id": "d0b6d927", "domain": "Geometry and Trigonometry", "skill": "Area and volume", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

A rectangle has an area of 63\n square meters and a length of 9\n meters. What is the width, in meters, of the rectangle?

", "choices": [{"id": "A", "text": "

7\n

"}, {"id": "B", "text": "

54\n

"}, {"id": "C", "text": "

81\n

"}, {"id": "D", "text": "

567\n

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. The area A\n, in square meters, of a rectangle is the product of its length l, in meters, and its width w\n, in meters; thus, A=lw. It's given that a rectangle has an area of 63\n square meters and a length of 9\n meters. Substituting 63\n for A\n and 9\n for l in the equation A=lw yields \n\t63\n\t=\n\t\n\t\t9\n\t\tw\n\t\n\n. Dividing both sides of this equation by 9\n yields \n\t7\n\t=\n\tw\n\n. Therefore, the width, in meters, of the rectangle is 7\n.

\n

Choice B is incorrect. This is the difference between the area, in square meters, and the length, in meters, of the rectangle, not the width, in meters, of the rectangle.

\n

Choice C is incorrect. This is the square of the length, in meters, not the width, in meters, of the rectangle.

\n

Choice D is incorrect. This is the product of the area, in square meters, and the length, in meters, of the rectangle, not the width, in meters, of the rectangle.

"}, {"id": "1429dcdf", "domain": "Geometry and Trigonometry", "skill": "Right triangles and trigonometry", "difficulty": "H", "type": "spr", "stimulus": "", "stem": "

\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n\n \n \n \n \n \n \n \n \n\n \n\n

\n

In the triangle shown, what is the value of sinx°?

", "choices": [], "answerId": ".6956", "acceptedAnswers": [".6956", ".6957", "16/23"], "rationale": "

The correct answer is \n\t16\n\t23\n\n. In a right triangle, the sine of an acute angle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. In the triangle shown, the length of the side opposite the angle with measure x° is 16\n units and the length of the hypotenuse is 23\n units. Therefore, the value of sinx° is \n\t16\n\t23\n\n. Note that 16/23, .6956, .6957, 0.695, and 0.696 are examples of ways to enter a correct answer.

"}, {"id": "69b0d79d", "domain": "Geometry and Trigonometry", "skill": "Circles", "difficulty": "H", "type": "mc", "stimulus": "
\n
\n \"The
\n
\n", "stem": "

Point O is the center of the circle above, and the measure of angle O A, B is 30 degrees. If the length of line segment O C is 18, what is the length of arc A, B?

\n", "choices": [{"id": "A", "text": "

\n 9 pi\n

\n"}, {"id": "B", "text": "

\n 12 pi\n

\n"}, {"id": "C", "text": "

\n 15 pi\n

\n"}, {"id": "D", "text": "

\n 18 pi\n

\n"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. Because segments OA and OB are radii of the circle centered at point O, these segments have equal lengths. Therefore, triangle AOB is an isosceles triangle, where angles OAB and OBA are congruent base angles of the triangle. It’s given that angle OAB measures 30 degrees. Therefore, angle OBA also measures 30 degrees. Let x degrees represent the measure of angle AOB. Since the sum of the measures of the three angles of any triangle is 180 degrees, it follows that 30 degrees + 30 degrees, + x degrees = 180 degrees, or 60 degrees + x degrees = 180 degrees. Subtracting 60 degrees from both sides of this equation yields x degrees = 120 degrees, or (2 pi)/(3) radians. Therefore, the measure of angle AOB, and thus the measure of arc A, B, is (2 pi)/(3) radians. Since the line segment O C is a radius of the given circle and its length is 18, the length of the radius of the circle is 18. Therefore, the length of arc A, B can be calculated as (2 pi)/(3, end fraction, \u00d7 18), or 12 pi.

Choices A, C, and D are incorrect and may result from conceptual or computational errors.

\n"}, {"id": "ebbf23ae", "domain": "Geometry and Trigonometry", "skill": "Circles", "difficulty": "H", "type": "spr", "stimulus": "", "stem": "

A circle in the xy-plane has a diameter with endpoints 2,4 and 2,14. An equation of this circle is \n\t\n\t\t\n\t\t\t\n\t\t\t\t\n\t\t\t\t\tx\n\t\t\t\t\t-\n\t\t\t\t\t2\n\t\t\t\t\n\t\t\t\n\t\t\t2\n\t\t\n\t\t+\n\t\t\n\t\t\t\n\t\t\t\t\n\t\t\t\t\ty\n\t\t\t\t\t-\n\t\t\t\t\t9\n\t\t\t\t\n\t\t\t\n\t\t\t2\n\t\t\n\t\n\t=\n\t\n\t\tr\n\t\t2\n\t\n\n, where r\n is a positive constant. What is the value of r\n?

", "choices": [], "answerId": "5", "acceptedAnswers": ["5"], "rationale": "

The correct answer is 5\n. The standard form of an equation of a circle in the xy-plane is x-h2+y-k2=r2, where h\n, k\n, and r\n are constants, the coordinates of the center of the circle are h,k, and the length of the radius of the circle is r\n. It′s given that an equation of the circle is x-22+y-92=r2. Therefore, the center of this circle is 2,9. It’s given that the endpoints of a diameter of the circle are 2,4 and 2,14. The length of the radius is the distance from the center of the circle to an endpoint of a diameter of the circle, which can be found using the distance formula, x1-x22+y1-y22. Substituting the center of the circle 2,9 and one endpoint of the diameter 2,4 in this formula gives a distance of 2-22+9-42, or 02+52, which is equivalent to 5\n. Since the distance from the center of the circle to an endpoint of a diameter is 5\n, the value of r\n is 5\n.

"}, {"id": "4c95c7d4", "domain": "Geometry and Trigonometry", "skill": "Right triangles and trigonometry", "difficulty": "H", "type": "mc", "stimulus": "
\n
\n \"The
\n
\n", "stem": "

A graphic designer is creating a logo for a company. The logo is shown in the figure above. The logo is in the shape of a trapezoid and consists of three congruent equilateral triangles. If the perimeter of the logo is 20 centimeters, what is the combined area of the shaded regions, in square centimeters, of the logo?

\n", "choices": [{"id": "A", "text": "

\n 2 \u00d7 the square root(3)\n

\n"}, {"id": "B", "text": "

\n 4 \u00d7 the square root(3)\n

\n"}, {"id": "C", "text": "

\n 8 \u00d7 the square root(3)\n

\n"}, {"id": "D", "text": "

\n 16\n

\n"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. It’s given that the logo is in the shape of a trapezoid that consists of three congruent equilateral triangles, and that the perimeter of the trapezoid is 20 centimeters (cm). Since the perimeter of the trapezoid is the sum of the lengths of 5 of the sides of the triangles, the length of each side of an equilateral triangle is (20)/(5 = 4 centimeters). Dividing up one equilateral triangle into two right triangles yields a pair of congruent 30°-60°-90° triangles. The shorter leg of each right triangle is half the length of the side of an equilateral triangle, or 2 cm. Using the Pythagorean Theorem, a, squared, + b\u00b2 = c\u00b2, the height of the equilateral triangle can be found. Substituting a = 2 and c = 4 and solving for b yields the square root of, 4\u00b2, \u2212 2\u00b2, end root = the square root(1)2, which = 2 \u00d7 the square root(3) centimeters cm. The area of one equilateral triangle is one half b h, where b = 2 and h = 2 \u00d7 the square root(3). Therefore, the area of one equilateral triangle is one half \u00d7 4, times, open parenthesis, 2 \u00d7 the square root(3), close parenthesis = 4 \u00d7 the square root(3) centimeters\u00b2. The shaded area consists of two such triangles, so its area is 2 \u00d7 4, \u00d7 the square root(3) = 8 \u00d7 the square root(3) centimeters\u00b2.

Alternate approach: The area of a trapezoid can be found by evaluating the expression one half times, open parenthesis, b sub 1 + b sub 2, close parenthesis, \u00d7 h, where b sub 1is the length of one base, b sub 2 is the length of the other base, and h is the height of the trapezoid. Substituting b sub 1 = 8, b sub 2 = 4, and h = 2 \u00d7 the square root(3) yields the expression one half times, open parenthesis, 8 + 4, close parenthesis, times, open parenthesis, 2 \u00d7 the square root(3), close parenthesis, or one half \u00d7 12, times, open parenthesis, 2 \u00d7 the square root(3), close parenthesis, which gives an area of 12 \u00d7 the square root(3) centimeters\u00b2 for the trapezoid. Since two-thirds of the trapezoid is shaded, the area of the shaded region is two thirds times, 12 \u00d7 the square root(3) = 8 \u00d7 the square root(3).

Choice A is incorrect. This is the height of the trapezoid. Choice B is incorrect. This is the area of one of the equilateral triangles, not two. Choice D is incorrect and may result from using a height of 4 for each triangle rather than the height of 2 \u00d7 the square root(3).

\n"}, {"id": "b8a225ff", "domain": "Geometry and Trigonometry", "skill": "Circles", "difficulty": "H", "type": "spr", "stimulus": "", "stem": "

Circle A in the xy-plane has the equation \n\t\n\t\t\n\t\t\t\n\t\t\t\t\n\t\t\t\t\tx\n\t\t\t\t\t+\n\t\t\t\t\t5\n\t\t\t\t\n\t\t\t\n\t\t\t2\n\t\t\n\t\t+\n\t\t\n\t\t\t\n\t\t\t\t\n\t\t\t\t\ty\n\t\t\t\t\t-\n\t\t\t\t\t5\n\t\t\t\t\n\t\t\t\n\t\t\t2\n\t\t\n\t\n\t=\n\t4\n\n. Circle B has the same center as circle A. The radius of circle B is two times the radius of circle A. The equation defining circle B in the xy-plane is \n\t\n\t\t\n\t\t\t\n\t\t\t\t\n\t\t\t\t\tx\n\t\t\t\t\t+\n\t\t\t\t\t5\n\t\t\t\t\n\t\t\t\n\t\t\t2\n\t\t\n\t\t+\n\t\t\n\t\t\t\n\t\t\t\t\n\t\t\t\t\ty\n\t\t\t\t\t-\n\t\t\t\t\t5\n\t\t\t\t\n\t\t\t\n\t\t\t2\n\t\t\n\t\n\t=\n\tk\n\n, where k\n is a constant. What is the value of k\n?

", "choices": [], "answerId": "16", "acceptedAnswers": ["16"], "rationale": "

The correct answer is 16\n. An equation of a circle in the xy-plane can be written as x-t2+y-u2=r2, where the center of the circle is t,u , the radius of the circle is r\n, and where t\n, u\n, and r\n are constants. It’s given that the equation of circle A is x+52+y-52=4, which is equivalent to x+52+y-52=22. Therefore, the center of circle A is -5,5 and the radius of circle A is 2\n. It’s given that circle B has the same center as circle A and that the radius of circle B is two times the radius of circle A. Therefore, the center of circle B is -5,5 and the radius of circle B is 22, or 4\n. Substituting -5\n for t\n, 5\n for u\n, and 4\n for r\n into the equation x-t2+y-u2=r2  yields x+52+y-52=42, which is equivalent to x+52+y-52=16. It follows that the equation of circle B in the xy-plane is x+52+y-52=16. Therefore, the value of k\n is 16\n.

"}, {"id": "b0a72bdc", "domain": "Geometry and Trigonometry", "skill": "Circles", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

What is the diameter of the circle in the xy-plane with equation \n\t\n\t\t\n\t\t\t\n\t\t\t\t\n\t\t\t\t\tx\n\t\t\t\t\t-\n\t\t\t\t\t5\n\t\t\t\t\n\t\t\t\n\t\t\t2\n\t\t\n\t\t+\n\t\t\n\t\t\t\n\t\t\t\t\n\t\t\t\t\ty\n\t\t\t\t\t-\n\t\t\t\t\t3\n\t\t\t\t\n\t\t\t\n\t\t\t2\n\t\t\n\t\n\t=\n\t16\n\n?

", "choices": [{"id": "A", "text": "

4\n

"}, {"id": "B", "text": "

8\n

"}, {"id": "C", "text": "

16\n

"}, {"id": "D", "text": "

32\n

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. The standard form of an equation of a circle in the xy-plane is x-h2+y-k2=r2, where the coordinates of the center of the circle are h,k and the length of the radius of the circle is r\n. For the circle in the xy-plane with equation x-52+y-32=16, it follows that r2=16. Taking the square root of both sides of this equation yields \n\tr\n\t=\n\t4\n\n or \n\tr\n\t=\n\t-4\n\n. Because r\n represents the length of the radius of the circle and this length must be positive, \n\tr\n\t=\n\t4\n\n. Therefore, the radius of the circle is 4\n. The diameter of a circle is twice the length of the radius of the circle. Thus, 24 yields 8\n. Therefore, the diameter of the circle is 8\n.

\n

Choice A is incorrect. This is the radius of the circle. 

\n

Choice C is incorrect. This is the square of the radius of the circle. 

\n

Choice D is incorrect and may result from conceptual or calculation errors.

"}, {"id": "933fee1a", "domain": "Geometry and Trigonometry", "skill": "Lines, angles, and triangles", "difficulty": "M", "type": "mc", "stimulus": "
\n
\n
\n \"The
\n
\n
\n", "stem": "

Triangles ABC and DEF are shown above. Which of the following is equal to the ratio B C over A, B?

\n", "choices": [{"id": "A", "text": "D E over D F\n"}, {"id": "B", "text": "D F over D E\n"}, {"id": "C", "text": "D F over E F\n"}, {"id": "D", "text": "E F over D E\n"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. In right triangle ABC, the measure of angle B must be 58° because the sum of the measure of angle A, which is 32°, and the measure of angle B is 90°. Angle D in the right triangle DEF has measure 58°. Hence, triangles ABC and DEF are similar (by angle-angle similarity). Since side B C is the side opposite to the angle with measure 32° and AB is the hypotenuse in right triangle ABC, the ratio the length(s)ide B C over the length(s)ide A, B is equal to the length(s)ide D F over the length(s)ide D E.

Alternate approach: The trigonometric ratios can be used to answer this question. In right triangle ABC, the ratio the length(s)ide B C over the length(s)ide A, B = the sine(3)2 degrees. The angle E in triangle DEF has measure 32° because the measure(a)ngle D, + the measure(a)ngle E = 90 degrees. In triangle DEF, the ratio the length(s)ide D F over the length(s)ide D E = the sine(3)2 degrees. Therefore, the length(s)ide D F over the length(s)ide D E = the length(s)ide B C over the length(s)ide A, B.

Choice A is incorrect because the length(s)ide D E over the length(s)ide D F is the reciprocal of the ratio the length(s)ide B C over the length(s)ide A, B. Choice C is incorrect because the length(s)ide D F over the length(s)ide D E = the length(s)ide B C over the length(s)ide A, C, not the length(s)ide B C over the length(s)ide A, B. Choice D is incorrect because the length(s)ide E F over the length(s)ide D E = the length(s)ide A, C over the length(s)ide A, B, not the length(s)ide B C over the length(s)ide A, B.

\n"}, {"id": "64c1f044", "domain": "Geometry and Trigonometry", "skill": "Right triangles and trigonometry", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n\n \n \n \n \n \n \n \n \n\n \n\n

\n

In the triangle shown, what is the value of tan x°?

", "choices": [{"id": "A", "text": "

126

"}, {"id": "B", "text": "

1926

"}, {"id": "C", "text": "

267

"}, {"id": "D", "text": "

337

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. The tangent of an acute angle in a right triangle is defined as the ratio of the length of the side opposite the angle to the length of the shorter side adjacent to the angle. In the triangle shown, the length of the side opposite the angle with measure x° is 26\n units and the length of the side adjacent to the angle with measure x° is 7\n units. Therefore, the value of tanx° is 267.

\n

Choice A is incorrect and may result from conceptual or calculation errors.

\n

Choice B is incorrect and may result from conceptual or calculation errors.

\n

Choice D is incorrect and may result from conceptual or calculation errors.

"}, {"id": "ba8ca563", "domain": "Geometry and Trigonometry", "skill": "Area and volume", "difficulty": "H", "type": "spr", "stimulus": "", "stem": "

A cube has a volume of 474,552\n cubic units. What is the surface area, in square units, of the cube?

", "choices": [], "answerId": "36504", "acceptedAnswers": ["36504"], "rationale": "

The correct answer is 36,504\n. The volume of a cube can be found using the formula \n\tV\n\t=\n\t\n\t\ts\n\t\t3\n\t\n\n, where s\n represents the edge length of a cube. It’s given that this cube has a volume of 474,552\n cubic units. Substituting 474,552\n for V\n in V=s3 yields \n\t474,552\n\t=\n\t\n\t\ts\n\t\t3\n\t\n\n. Taking the cube root of both sides of this equation yields 78=s. Thus, the edge length of the cube is 78\n units. Since each face of a cube is a square, it follows that each face has an edge length of 78\n units. The area of a square can be found using the formula \n\tA\n\t=\n\t\n\t\ts\n\t\t2\n\t\n\n. Substituting 78\n for s\n in this formula yields A=782, or \n\tA\n\t=\n\t6,084\n\n. Therefore, the area of one face of this cube is 6,084\n square units. Since a cube has 6\n faces, the surface area, in square units, of this cube is 66,084, or 36,504\n.

"}, {"id": "a4bd60a3", "domain": "Geometry and Trigonometry", "skill": "Right triangles and trigonometry", "difficulty": "H", "type": "spr", "stimulus": "", "stem": "

The perimeter of an equilateral triangle is 624\n centimeters. The height of this triangle is k3 centimeters, where k\n is a constant. What is the value of k\n?

", "choices": [], "answerId": "104", "acceptedAnswers": ["104"], "rationale": "

The correct answer is 104\n. An equilateral triangle is a triangle in which all three sides have the same length and all three angles have a measure of 60\u00b0. The height of the triangle, k3, is the length of the altitude from one vertex. The altitude divides the equilateral triangle into two congruent 30-60-90 right triangles, where the altitude is the side across from the 60\u00b0 angle in each 30-60-90 right triangle. Since the altitude has a length of k3, it follows from the properties of 30-60-90 right triangles that the side across from each 30\u00b0 angle has a length of k\n and each hypotenuse has a length of \n\t2\n\tk\n\n. In this case, the hypotenuse of each 30-60-90 right triangle is a side of the equilateral triangle; therefore, each side length of the equilateral triangle is \n\t2\n\tk\n\n. The perimeter of a triangle is the sum of the lengths of each side. It's given that the perimeter of the equilateral triangle is 624\n; therefore, 2k+2k+2k=624, or 6k=624. Dividing both sides of this equation by 6\n yields \n\tk\n\t=\n\t104\n\n.

"}, {"id": "899c6042", "domain": "Geometry and Trigonometry", "skill": "Area and volume", "difficulty": "H", "type": "spr", "stimulus": "", "stem": "

A right circular cone has a height of 22 centimeters cm and a base with a diameter of 6 cm. The volume of this cone is nπ cm3. What is the value of n\n?

", "choices": [], "answerId": "66", "acceptedAnswers": ["66"], "rationale": "

The correct answer is 66\n. It’s given that the right circular cone has a height of 22\n centimeters cm and a base with a diameter of 6 cm. Since the diameter of the base of the cone is 6 cm, the radius of the base is 3 cm. The volume V\n, in cm3, of a right circular cone can be found using the formula V=13πr2h, where h\n is the height, in cm, and r\n is the radius, in cm, of the base of the cone. Substituting 22\n for h\n and 3\n for r\n in this formula yields V=13π3222, or V=66π. Therefore, the volume of the cone is 66π cm3. It’s given that the volume of the cone is nπ cm3. Therefore, the value of n\n is 66\n.

"}, {"id": "740bf79f", "domain": "Geometry and Trigonometry", "skill": "Lines, angles, and triangles", "difficulty": "H", "type": "mc", "stimulus": "
\n\t
\"The
\n
\n", "stem": "

In the figure above, what is the length of line segment NQ ?

\n", "choices": [{"id": "A", "text": "

2.2

\n"}, {"id": "B", "text": "

2.3

\n"}, {"id": "C", "text": "

2.4

\n"}, {"id": "D", "text": "

2.5

\n"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. First, line segment M P is the hypotenuse of right triangle M N P, whose legs have lengths 3 and 4. Therefore, open parenthesis, the length(l)ine segment M P, close parenthesis, squared = 3\u00b2 + 4\u00b2, so open parenthesis, the length(l)ine segment M P, close parenthesis, squared = 25 and the length(l)ine segment M P = 5. Second, because angle M N P corresponds to angle N Q P and because angle M P N corresponds to angle N P Q, triangle M N P is similar to triangle N Q P. The ratio of corresponding sides of similar triangles is constant, so the length(l)ine segment N Q over the length(l)ine segment M N = the length(l)ine segment N P over the length(l)ine segment M P. Since M P = 5 and it’s given that the length(l)ine segment M N = 3 and the length(l)ine segment N P = 4, the length(l)ine segment N Q, over 3 = 4 over 5. Solving for NQ results in the length(l)ine segment N Q = 12 over 5, or 2.4.

Choices A, B, and D are incorrect and may result from setting up incorrect ratios.

 

\n"}, {"id": "3b225698", "domain": "Geometry and Trigonometry", "skill": "Lines, angles, and triangles", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

Triangle \n\tX\n\tY\n\tZ\n\n is similar to triangle \n\tR\n\tS\n\tT\n\n such that X\n, Y\n, and Z\n correspond to R\n, S\n, and T\n, respectively. The measure of ∠Z is 20\n° and \n\t\n\t\t2\n\t\tX\n\t\tY\n\t\n\t=\n\t\n\t\tR\n\t\tS\n\t\n\n. What is the measure of ∠T?

", "choices": [{"id": "A", "text": "

2\n°

"}, {"id": "B", "text": "

10\n°

"}, {"id": "C", "text": "

20\n°

"}, {"id": "D", "text": "

40\n°

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. It’s given that triangle \n\tX\n\tY\n\tZ\n\n is similar to triangle \n\tR\n\tS\n\tT\n\n, such that X\n, Y\n, and Z\n correspond to R\n, S\n, and T\n, respectively. Since corresponding angles of similar triangles are congruent, it follows that the measure of \u2220Z is congruent to the measure of \u2220T. It’s given that the measure of \u2220Z is 20\u00b0. Therefore, the measure of \u2220T is 20\u00b0.

\n

Choice A is incorrect and may result from a conceptual error.

\n

Choice B is incorrect. This is half the measure of \u2220Z.

\n

Choice D is incorrect. This is twice the measure of \u2220Z.

"}, {"id": "249d3f80", "domain": "Geometry and Trigonometry", "skill": "Circles", "difficulty": "H", "type": "spr", "stimulus": "", "stem": "

Point O\n is the center of a circle. The measure of arc \n\tR\n\tS\n\n on this circle is 100°. What is the measure, in degrees, of its associated angle ROS?

", "choices": [], "answerId": "100", "acceptedAnswers": ["100"], "rationale": "

The correct answer is 100\n. It's given that point O\n is the center of a circle and the measure of arc RS on the circle is 100\u00b0. It follows that points R\n and S\n lie on the circle. Therefore, OR\u00af and OS\u00af are radii of the circle. A central angle is an angle formed by two radii of a circle, with its vertex at the center of the circle. Therefore, \u2220ROS is a central angle. Because the degree measure of an arc is equal to the measure of its associated central angle, it follows that the measure, in degrees, of \u2220ROS is 100\n.

"}, {"id": "a4c05a1b", "domain": "Geometry and Trigonometry", "skill": "Lines, angles, and triangles", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n\n

\n

In the figure shown, lines r\n and s\n are parallel, and line m\n intersects both lines. If y<65, which of the following must be true?

", "choices": [{"id": "A", "text": "

x<115

"}, {"id": "B", "text": "

x>115

"}, {"id": "C", "text": "

x+y<180

"}, {"id": "D", "text": "

x+y>180

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. In the figure shown, the angle measuring y° is congruent to its vertical angle formed by lines s\n and m\n, so the measure of the vertical angle is also y°. The vertical angle forms a same-side interior angle pair with the angle measuring x°. It's given that lines r\n and s\n are parallel. Therefore, same-side interior angles in the figure are supplementary, which means the sum of the measure of the vertical angle and the measure of the angle measuring x° is 180°, or \n\t\n\t\tx\n\t\t+\n\t\ty\n\t\n\t=\n\t180\n\n. Subtracting x\n from both sides of this equation yields y=180-x. Substituting 180-x for y\n in the inequality y<65 yields 180-x<65. Adding x\n to both sides of this inequality yields 180<65+x. Subtracting 65\n from both sides of this inequality yields 115<x, or x>115. Thus, if y<65, it must be true that x>115.

\n

Choice A is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect. \n\tx\n\t+\n\ty\n\n must be equal to, not less than, 180\n.

\n

Choice D is incorrect. \n\tx\n\t+\n\ty\n\n must be equal to, not greater than, 180\n.

"}, {"id": "38517165", "domain": "Geometry and Trigonometry", "skill": "Area and volume", "difficulty": "M", "type": "spr", "stimulus": "", "stem": "

A circle has a circumference of 31π centimeters. What is the diameter, in centimeters, of the circle?

", "choices": [], "answerId": "31", "acceptedAnswers": ["31"], "rationale": "

The correct answer is 31\n. The circumference of a circle is equal to 2πr centimeters, where r\n represents the radius, in centimeters, of the circle, and the diameter of the circle is equal to \n\t2\n\tr\n\n centimeters. It's given that a circle has a circumference of 31π centimeters. Therefore, 31π=2πr. Dividing both sides of this equation by π yields \n\t31\n\t=\n\t\n\t\t2\n\t\tr\n\t\n\n. Since the diameter of the circle is equal to \n\t2\n\tr\n\n centimeters, it follows that the diameter, in centimeters, of the circle is 31\n.

"}, {"id": "d3fe472f", "domain": "Geometry and Trigonometry", "skill": "Lines, angles, and triangles", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

Triangle \n\tA\n\tB\n\tC\n\n is similar to triangle \n\tX\n\tY\n\tZ\n\n, such that A\n, B\n, and C\n correspond to X\n, Y\n, and Z\n respectively. The length of each side of triangle \n\tX\n\tY\n\tZ\n\n is 2\n times the length of its corresponding side in triangle \n\tA\n\tB\n\tC\n\n. The measure of side \n\tA\n\tB\n\n is 16. What is the measure of side \n\tX\n\tY\n\n?

", "choices": [{"id": "A", "text": "

14\n

"}, {"id": "B", "text": "

16\n

"}, {"id": "C", "text": "

18\n

"}, {"id": "D", "text": "

32\n

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. It's given that triangle ABC is similar to triangle XYZ, such that A\n, B\n, and C\n correspond to X\n, Y\n, and Z\n, respectively. Therefore, side \n\tA\n\tB\n\n corresponds to side \n\tX\n\tY\n\n. Since the length of each side of triangle XYZ is 2\n times the length of its corresponding side in triangle ABC, it follows that the measure of side \n\tX\n\tY\n\n is 2\n times the measure of side \n\tA\n\tB\n\n. Thus, since the measure of side \n\tA\n\tB\n\n is 16\n, then the measure of side \n\tX\n\tY\n\n is 216, or 32\n.

\n

Choice A is incorrect and may result from conceptual or calculation errors.

\n

Choice B is incorrect. This is the measure of side \n\tA\n\tB\n\n, not side \n\tX\n\tY\n\n.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

"}, {"id": "f9d40000", "domain": "Geometry and Trigonometry", "skill": "Lines, angles, and triangles", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

In △XYZ, the measure of ∠X is 23\n° and the measure of ∠Y is 66\n°. What is the measure of ∠Z?

", "choices": [{"id": "A", "text": "

43\n°

"}, {"id": "B", "text": "

89\n°

"}, {"id": "C", "text": "

91\n°

"}, {"id": "D", "text": "

179\n°

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. The triangle angle sum theorem states that the sum of the measures of the interior angles of a triangle is 180°. It's given that in △XYZ, the measure of ∠X is 23° and the measure of ∠Y is 66°. It follows that the measure of ∠Z is 180-23-66°, or 91°.

\n

Choice A is incorrect and may result from conceptual or calculation errors.

\n

Choice B is incorrect. This is the sum of the measures of ∠X and ∠Y, not the measure of ∠Z.

\n

Choice D is incorrect and may result from conceptual or calculation errors.

"}, {"id": "0d3f51dc", "domain": "Geometry and Trigonometry", "skill": "Lines, angles, and triangles", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n\n

\n

In the figure, line m\n is parallel to line n\n, and line t\n intersects both lines. What is the value of x\n? 

", "choices": [{"id": "A", "text": "

33\n

"}, {"id": "B", "text": "

57\n

"}, {"id": "C", "text": "

123\n

"}, {"id": "D", "text": "

147\n

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. It’s given that line m\n is parallel to line n\n, and line t\n intersects both lines. It follows that line t\n is a transversal. When two lines are parallel and intersected by a transversal, exterior angles on the same side of the transversal are supplementary. Thus, \n\t\n\t\tx\n\t\t+\n\t\t33\n\t\n\t=\n\t180\n\n. Subtracting 33\n from both sides of this equation yields \n\tx\n\t=\n\t147\n\n. Therefore, the value of x\n is 147\n.

\n

Choice A is incorrect and may result from conceptual or calculation errors.

\n

Choice B is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

"}, {"id": "fd8745fc", "domain": "Geometry and Trigonometry", "skill": "Lines, angles, and triangles", "difficulty": "M", "type": "spr", "stimulus": "", "stem": "

In triangle JKL, the measures of ∠K and ∠L are each 48°. What is the measure of ∠J, in degrees? (Disregard the degree symbol when entering your answer.)

", "choices": [], "answerId": "84", "acceptedAnswers": ["84"], "rationale": "

The correct answer is 84\n. The sum of the measures of the interior angles of a triangle is 180°. It's given that in triangle JKL, the measures of ∠Kand ∠L are each 48°. Adding the measures, in degrees, of ∠K and ∠L gives 48+48, or 96\n. Therefore, the measure of ∠J, in degrees, is 180-96, or 84\n.

"}, {"id": "3e577e4a", "domain": "Geometry and Trigonometry", "skill": "Circles", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

A circle in the xy-plane has its center at -4,-6. Line k\n is tangent to this circle at the point -7,-7. What is the slope of line k\n?

", "choices": [{"id": "A", "text": "

-3\n

"}, {"id": "B", "text": "

\n\t-\n\t\n\t\t1\n\t\t3\n\t\n\n

"}, {"id": "C", "text": "

\n\t1\n\t3\n\n

"}, {"id": "D", "text": "

3\n

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. A line that's tangent to a circle is perpendicular to the radius of the circle at the point of tangency. It's given that the circle has its center at -4,-6 and line k\n is tangent to the circle at the point -7,-7. The slope of a radius defined by the points q,r and s,t can be calculated as t-rs-q. The points -7,-7 and -4,-6 define the radius of the circle at the point of tangency. Therefore, the slope of this radius can be calculated as -6--7-4--7, or 13. If a line and a radius are perpendicular, the slope of the line must be the negative reciprocal of the slope of the radius. The negative reciprocal of 13 is -3. Thus, the slope of line k\n is -3.

\n

Choice B is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect. This is the slope of the radius of the circle at the point of tangency, not the slope of line k\n.

\n

Choice D is incorrect and may result from conceptual or calculation errors.

"}, {"id": "b0dc920d", "domain": "Geometry and Trigonometry", "skill": "Area and volume", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

A manufacturer determined that right cylindrical containers with a height that is 4 inches longer than the radius offer the optimal number of containers to be displayed on a shelf. Which of the following expresses the volume, V, in cubic inches, of such containers, where r is the radius, in inches?

\n", "choices": [{"id": "A", "text": "

\n V = 4 pi r\u00b3\n

\n"}, {"id": "B", "text": "

\n V = pi times, open parenthesis, 2 r, close parenthesis, cubed

\n"}, {"id": "C", "text": "

\n V = pi r\u00b2, + 4 pi r\n

\n"}, {"id": "D", "text": "

\n V = pi r\u00b3, + 4 pi r\u00b2\n

\n"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. The volume, V, of a right cylinder is given by the formula V = pi r\u00b2, \u00d7 h, where r represents the radius of the base of the cylinder and h represents the height. Since the height is 4 inches longer than the radius, the expression r + 4 represents the height of each cylindrical container. It follows that the volume of each container is represented by the equation V = pi r\u00b2 times, open parenthesis, r + 4, close parenthesis. Distributing the expression pi r\u00b2 into each term in the parentheses yields V = pi r\u00b3, + 4 pi r\u00b2.

Choice A is incorrect and may result from representing the height as 4 r instead of r + 4. Choice B is incorrect and may result from representing the height as 2 r instead of r + 4. Choice C is incorrect and may result from representing the volume of a right cylinder as V = pi r h instead of V = pi r\u00b2, \u00d7 h.

\n"}, {"id": "c7bed21d", "domain": "Geometry and Trigonometry", "skill": "Lines, angles, and triangles", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

Quadrilateral P'Q'R'S' is similar to quadrilateral \n\tP\n\tQ\n\tR\n\tS\n\n, where P\n, Q\n, R\n, and S\n correspond to P', Q', R', and S', respectively. The measure of angle P\n is 30°, the measure of angle Q\n is 50°, and the measure of angle R\n is 70°. The length of each side of P'Q'R'S' is 3\n times the length of each corresponding side of \n\tP\n\tQ\n\tR\n\tS\n\n. What is the measure of angle P'?

", "choices": [{"id": "A", "text": "

10°

"}, {"id": "B", "text": "

30°

"}, {"id": "C", "text": "

40°

"}, {"id": "D", "text": "

90°

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. It's given that quadrilateral P'Q'R'S' is similar to quadrilateral PQRS, where P\n, Q\n, R\n, and S\n correspond to P', Q', R', and S', respectively. Since corresponding angles of similar quadrilaterals are congruent, it follows that the measure of angle P\n is equal to the measure of angle P'. It's given that the measure of angle P\n is 30°. Therefore, the measure of angle P' is 30°.

\n

Choice A is incorrect. This is 13 the measure of angle P'.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

\n

Choice D is incorrect. This is 3\n times the measure of angle P'.

"}, {"id": "dfc420b2", "domain": "Geometry and Trigonometry", "skill": "Lines, angles, and triangles", "difficulty": "E", "type": "mc", "stimulus": "
\n
\n \"The
\n
\n", "stem": "

In the figure above, line segment A, D intersects line segment B E at C. If x = 100, what is the value of y ?

\n", "choices": [{"id": "A", "text": "

100

\n"}, {"id": "B", "text": "

90

\n"}, {"id": "C", "text": "

80

\n"}, {"id": "D", "text": "

60

\n"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. It’s given that x = 100; therefore, substituting 100 for x in triangle ABC gives two known angle measures for this triangle. The sum of the measures of the interior angles of any triangle equals 180°. Subtracting the two known angle measures of triangle ABC from 180° gives the third angle measure: 180 degrees \u2212 100 degrees, \u2212 20 degrees = 60 degrees. This is the measure of angle BCA. Since vertical angles are congruent, the measure of angle DCE is also 60°. Subtracting the two known angle measures of triangle CDE from 180° gives the third angle measure: 180 degrees \u2212 60 degrees, \u2212 40 degrees = 80 degrees. Therefore, the value of y is 80.

Choice A is incorrect and may result from a calculation error. Choice B is incorrect and may result from classifying angle CDE as a right angle. Choice D is incorrect and may result from finding the measure of angle BCA or DCE instead of the measure of angle CDE.

\n"}, {"id": "de550be0", "domain": "Geometry and Trigonometry", "skill": "Right triangles and trigonometry", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n\n \n \n \n\n \n\n

\n

For the triangle shown, which expression represents the value of a\n?

", "choices": [{"id": "A", "text": "

212-62

"}, {"id": "B", "text": "

212-62

"}, {"id": "C", "text": "

21-6

"}, {"id": "D", "text": "

21-6

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. For the right triangle shown, the lengths of the legs are a\n units and 6\n units, and the length of the hypotenuse is 21\n units. The Pythagorean theorem states that in a right triangle, the sum of the squares of the lengths of the two legs is equal to the square of the length of the hypotenuse. Therefore, a2+62=212. Subtracting 62 from both sides of this equation yields a2=212-62. Taking the square root of both sides of this equation yields a=±212-62. Since a\n is a length, a\n must be positive. Therefore, a=212-62. Thus, for the triangle shown, 212-62 represents the value of a\n.

\n

Choice B is incorrect. For the triangle shown, this expression represents the value of \n\ta\n\t2\n\n, not a\n.

\n

Choice C is incorrect and may result from conceptual errors.

\n

Choice D is incorrect and may result from conceptual errors.

"}, {"id": "901e3285", "domain": "Geometry and Trigonometry", "skill": "Lines, angles, and triangles", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

In triangle ABC, the measure of angle A is 50 degrees. If triangle ABC is isosceles, which of the following is NOT a possible measure of angle B ?

\n", "choices": [{"id": "A", "text": "\n 50 degrees\n \n"}, {"id": "B", "text": "\n 65 degrees\n \n"}, {"id": "C", "text": "\n 80 degrees\n \n"}, {"id": "D", "text": "\n 100 degrees\n \n"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. The sum of the three interior angles in a triangle is 180 degrees. It’s given that angle A measures 50 degrees. If angle B measured 100 degrees, the measure of angle C would be 180 degrees minus, open parenthesis, 50 degrees + 100 degrees, close parenthesis = 30 degrees. Thus, the measures of the angles in the triangle would be 50 degrees, 100 degrees, and 30 degrees. However, an isosceles triangle has two angles of equal measure. Therefore, angle B can’t measure 100 degrees.

Choice A is incorrect. If angle B has measure 50 degrees, then angle C would measure 180 degrees minus, open parenthesis, 50 degrees + 50 degrees, close parenthesis = 80 degrees, and 50 degrees, 50 degrees, and 80 degrees could be the angle measures of an isosceles triangle. Choice B is incorrect. If angle B has measure 65 degrees, then angle C would measure 180 degrees minus, open parenthesis, 65 degrees + 50 degrees, close parenthesis = 65 degrees, and 50 degrees, 65 degrees, and 65 degrees could be the angle measures of an isosceles triangle. Choice C is incorrect. If angle B has measure 80 degrees, then angle C would measure 180 degrees minus, open parenthesis, 80 degrees + 50 degrees, close parenthesis = 50 degrees, and 50 degrees, 80 degrees, and 50 degrees could be the angle measures of an isosceles triangle.

\n"}, {"id": "bd7f6e30", "domain": "Geometry and Trigonometry", "skill": "Lines, angles, and triangles", "difficulty": "H", "type": "mc", "stimulus": "
\n\t
\"The
\n
\n", "stem": "

In the figure above, R T = T U. What is the value of x ?

\n", "choices": [{"id": "A", "text": "

72

\n"}, {"id": "B", "text": "

66

\n"}, {"id": "C", "text": "

64

\n"}, {"id": "D", "text": "

58

\n"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. Since the length(s)ide R T = the length(s)ide T U, it follows that triangle R T U is an isosceles triangle with base RU. Therefore, angle T R U and angle T U R are the base angles of an isosceles triangle and are congruent. Let the measures of both angle T R U and angle T U R be t degrees. According to the triangle sum theorem, the sum of the measures of the three angles of a triangle is 180 degrees. Therefore, 114 degrees + 2 t degrees = 180 degrees, so t = 33.

Note that angle T U R is the same angle as angle S U V. Thus, the measure of angle S U V is 33 degrees. According to the triangle exterior angle theorem, an external angle of a triangle is equal to the sum of the opposite interior angles. Therefore, x degrees is equal to the sum of the measures of angle V S U and angle S U V; that is, 31 degrees + 33 degrees = 64 degrees. Thus, the value of x is 64.

Choice B is incorrect. This is the measure of angle S T R, but angle S T R is not congruent to angle S V R. Choices A and D are incorrect and may result from a calculation error.

 

\n"}, {"id": "2adbf1b1", "domain": "Geometry and Trigonometry", "skill": "Lines, angles, and triangles", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n\n

\n

In the figure, lines m\n and n\n are parallel. If x=6k+13 and y=8k-29, what is the value of z\n?

", "choices": [{"id": "A", "text": "

3\n

"}, {"id": "B", "text": "

21\n

"}, {"id": "C", "text": "

41\n

"}, {"id": "D", "text": "

139\n

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. Vertical angles, which are angles that are opposite each other when two lines intersect, are congruent. The figure shows that lines t\n and m\n intersect. It follows that the angle with measure x\u00b0 and the angle with measure y\u00b0 are vertical angles, so \n\tx\n\t=\n\ty\n\n. It's given that \n\tx\n\t=\n\t\n\t\t\n\t\t\t6\n\t\t\tk\n\t\t\n\t\t+\n\t\t13\n\t\n\n and \n\ty\n\t=\n\t\n\t\t\n\t\t\t8\n\t\t\tk\n\t\t\n\t\t-\n\t\t29\n\t\n\n. Substituting \n\t\n\t\t6\n\t\tk\n\t\n\t+\n\t13\n\n for x\n and \n\t\n\t\t8\n\t\tk\n\t\n\t-\n\t29\n\n for y\n in the equation \n\tx\n\t=\n\ty\n\n yields \n\t\n\t\t\n\t\t\t6\n\t\t\tk\n\t\t\n\t\t+\n\t\t13\n\t\n\t=\n\t\n\t\t\n\t\t\t8\n\t\t\tk\n\t\t\n\t\t-\n\t\t29\n\t\n\n. Subtracting \n\t6\n\tk\n\n from both sides of this equation yields \n\t13\n\t=\n\t\n\t\t\n\t\t\t2\n\t\t\tk\n\t\t\n\t\t-\n\t\t29\n\t\n\n. Adding 29\n to both sides of this equation yields \n\t42\n\t=\n\t\n\t\t2\n\t\tk\n\t\n\n, or \n\t\n\t\t2\n\t\tk\n\t\n\t=\n\t42\n\n. Dividing both sides of this equation by 2\n yields \n\tk\n\t=\n\t21\n\n. It's given that lines m\n and n\n are parallel, and the figure shows that lines m\n and n\n are intersected by a transversal, line t\n. If two parallel lines are intersected by a transversal, then the same-side interior angles are supplementary. It follows that the same-side interior angles with measures y\u00b0 and z\u00b0 are supplementary, so \n\t\n\t\ty\n\t\t+\n\t\tz\n\t\n\t=\n\t180\n\n. Substituting \n\t\n\t\t8\n\t\tk\n\t\n\t-\n\t29\n\n for y\n in this equation yields 8k-29+z=180. Substituting 21\n for k\n in this equation yields 821-29+z=180, or 139+z=180. Subtracting 139\n from both sides of this equation yields \n\tz\n\t=\n\t41\n\n. Therefore, the value of z\n is 41\n.

\n

Choice A is incorrect and may result from conceptual or calculation errors.

\n

Choice B is incorrect. This is the value of k\n, not z\n.

\n

Choice D is incorrect. This is the value of x\n or y\n, not z\n.

"}, {"id": "ffe862a3", "domain": "Geometry and Trigonometry", "skill": "Right triangles and trigonometry", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

An isosceles right triangle has a hypotenuse of length 58\n inches. What is the perimeter, in inches, of this triangle?

", "choices": [{"id": "A", "text": "

\n\t29\n\t\n\t\t2\n\t\n\n

"}, {"id": "B", "text": "

\n\t58\n\t\n\t\t2\n\t\n\n

"}, {"id": "C", "text": "

\n\t58\n\t+\n\t\n\t\t58\n\t\t\n\t\t\t2\n\t\t\n\t\n\n

"}, {"id": "D", "text": "

\n\t58\n\t+\n\t\n\t\t116\n\t\t\n\t\t\t2\n\t\t\n\t\n\n

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. Since the triangle is an isosceles right triangle, the two sides that form the right angle must be the same length. Let x\n be the length, in inches, of each of those sides. The Pythagorean theorem states that in a right triangle, \n\t\n\t\t\n\t\t\ta\n\t\t\t2\n\t\t\n\t\t+\n\t\t\n\t\t\tb\n\t\t\t2\n\t\t\n\t\n\t=\n\t\n\t\tc\n\t\t2\n\t\n\n, where c\n is the length of the hypotenuse and a\n and b\n are the lengths of the other two sides. Substituting x\n for a\n, x\n for b\n, and 58\n for c\n in this equation yields x2+x2=582, or 2x2=582. Dividing each side of this equation by 2\n yields x2=5822, or x2=2\u00b75824. Taking the square root of each side of this equation yields two solutions: x=5822 and x=-5822. The value of x\n must be positive because it represents a side length. Therefore, x=5822, or \n\tx\n\t=\n\t\n\t\t29\n\t\t\n\t\t\t2\n\t\t\n\t\n\n. The perimeter, in inches, of the triangle is 58+x+x, or 58+2x. Substituting \n\t29\n\t\n\t\t2\n\t\n\n for x\n in this expression gives a perimeter, in inches, of 58+2292, or \n\t58\n\t+\n\t\n\t\t58\n\t\t\n\t\t\t2\n\t\t\n\t\n\n.

\n

Choice A is incorrect. This is the length, in inches, of each of the congruent sides of the triangle, not the perimeter, in inches, of the triangle.

\n

Choice B is incorrect. This is the sum of the lengths, in inches, of the congruent sides of the triangle, not the perimeter, in inches, of the triangle.

\n

Choice D is incorrect and may result from conceptual or calculation errors.

"}, {"id": "24cec8d1", "domain": "Geometry and Trigonometry", "skill": "Circles", "difficulty": "H", "type": "spr", "stimulus": "", "stem": "

A circle has center O\n, and points R\n and S\n lie on the circle. In triangle \n\tO\n\tR\n\tS\n\n, the measure of ∠ROS is 88°. What is the measure of ∠RSO, in degrees? (Disregard the degree symbol when entering your answer.)

", "choices": [], "answerId": "46", "acceptedAnswers": ["46"], "rationale": "

The correct answer is 46\n. It's given that O\n is the center of a circle and that points R\n and S\n lie on the circle. Therefore, OR\u00af and OS\u00af are radii of the circle. It follows that OR=OS. If two sides of a triangle are congruent, then the angles opposite them are congruent. It follows that the angles \u2220RSO and \u2220ORS, which are across from the sides of equal length, are congruent. Let x\u00b0 represent the measure of \u2220RSO. It follows that the measure of \u2220ORS is also x\u00b0. It's given that the measure of \u2220ROS is 88\u00b0. Because the sum of the measures of the interior angles of a triangle is 180\u00b0, the equation x\u00b0+x\u00b0+88\u00b0=180\u00b0, or 2x+88=180, can be used to find the measure of \u2220RSO. Subtracting 88\n from both sides of this equation yields 2x=92. Dividing both sides of this equation by 2\n yields x=46. Therefore, the measure of \u2220RSO, in degrees, is 46\n.

"}, {"id": "0837c3b9", "domain": "Geometry and Trigonometry", "skill": "Area and volume", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

Triangle ABC and triangle DEF are similar triangles, where line segment A B and line segment D E are corresponding sides. If the length(l)ine segment D E = 2 \u00d7 the length(l)ine segment A B and the perimeter of triangle ABC is 20, what is the perimeter of triangle DEF ?

\n", "choices": [{"id": "A", "text": "

10

\n"}, {"id": "B", "text": "

40

\n"}, {"id": "C", "text": "

80

\n"}, {"id": "D", "text": "

120

\n"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. Since triangles ABC and DEF are similar and the length(s)ide D E = 2 \u00d7 the length(s)ide A B, the length of each side of triangle DEF is two times the length of its corresponding side in triangle ABC. Therefore, the perimeter of triangle DEF is two times the perimeter of triangle ABC. Since the perimeter of triangle ABC is 20, the perimeter of triangle DEF is 40.

Choice A is incorrect. This is half, not two times, the perimeter of triangle ABC. Choice C is incorrect. This is two times the perimeter of triangle DEF rather than two times the perimeter of triangle ABC. Choice D is incorrect. This is six times, not two times, the perimeter of triangle ABC.

\n"}, {"id": "9e44284b", "domain": "Geometry and Trigonometry", "skill": "Circles", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

In the xy-plane, the graph of 2 x\u00b2, \u2212 6 x, + 2 y\u00b2, + 2 y = 45 is a circle. What is the radius of the circle?

\n", "choices": [{"id": "A", "text": "

5

\n"}, {"id": "B", "text": "

6.5

\n"}, {"id": "C", "text": "

square root(4)0

 

\n"}, {"id": "D", "text": "

square root(5)0

 

\n"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. One way to find the radius of the circle is to rewrite the given equation in standard form, open parenthesis, x \u2212 h, close parenthesis, squared, plus, open parenthesis, y \u2212 k, close parenthesis, squared = r\u00b2, where h, k is the center of the circle and the radius of the circle is r. To do this, divide the original equation, 2 x\u00b2, \u2212 6 x, + 2 y\u00b2, + 2 y = 45, by 2 to make the leading coefficients of x\u00b2 and y\u00b2 each equal to 1: as follows: x\u00b2, \u2212 3 x, + y\u00b2, + y = 22 point 5. Then complete the square to put the equation in standard form. To do so, first rewrite x\u00b2, \u2212 3 x, + y\u00b2, + y = 22 point 5 as open parenthesis, x\u00b2, \u2212 3 x, + 2 point 2 5, close parenthesis, \u2212 2 point 2 5, plus, open parenthesis, y\u00b2, + y, + 0 point 2 5, close parenthesis, \u2212 0 point 2 5 = 22 point 5. Second, add 2.25 and 0.25 to both sides of the equation: open parenthesis, x\u00b2, \u2212 3 x, + 2 point 2 5, close parenthesis, plus, open parenthesis, y\u00b2, + y, + 0 point 2 5, close parenthesis = 25. Since x\u00b2, \u2212 3 x, + 2 point 2 5 = open parenthesis, x \u2212 1 point 5, close parenthesis, squared, y\u00b2, + y, + 0 point 2 5 = open parenthesis, y + 0 point 5, close parenthesis, squared, and 25 = 5\u00b2, it follows that open parenthesis, x \u2212 1 point 5, close parenthesis, squared, plus, open parenthesis, y + 0 point 5, close parenthesis, squared = 5\u00b2. Therefore, the radius of the circle is 5.

Choices B, C, and D are incorrect and may be the result of errors in manipulating the equation or of a misconception about the standard form of the equation of a circle in the xy-plane.

 

\n"}, {"id": "568d66a7", "domain": "Geometry and Trigonometry", "skill": "Right triangles and trigonometry", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

An isosceles right triangle has a perimeter of \n\t94\n\t+\n\t\n\t\t94\n\t\t\n\t\t\t2\n\t\t\n\t\n\n inches. What is the length, in inches, of one leg of this triangle?

", "choices": [{"id": "A", "text": "

47\n

"}, {"id": "B", "text": "

\n\t47\n\t\n\t\t2\n\t\n\n

"}, {"id": "C", "text": "

94\n

"}, {"id": "D", "text": "

\n\t94\n\t\n\t\t2\n\t\n\n

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. It's given that the right triangle is isosceles. In an isosceles right triangle, the two legs have equal lengths, and the length of the hypotenuse is \n\t2\n\n times the length of one of the legs. Let l represent the length, in inches, of each leg of the isosceles right triangle. It follows that the length of the hypotenuse is l2 inches. The perimeter of a figure is the sum of the lengths of the sides of the figure. Therefore, the perimeter of the isosceles right triangle is l+l+l2 inches. It's given that the perimeter of the triangle is 94+942 inches. It follows that l+l+l2=94+942. Factoring the left-hand side of this equation yields 1+1+2l=94+942, or 2+2l=94+942. Dividing both sides of this equation by 2+2 yields l=94+9422+2. Rationalizing the denominator of the right-hand side of this equation by multiplying the right-hand side of the equation by 2-22-2 yields l=94+9422-22+22-2. Applying the distributive property to the numerator and to the denominator of the right-hand side of this equation yields l=188-942+1882-9444-22+22-4. This is equivalent to l=9422, or l=472. Therefore, the length, in inches, of one leg of the isosceles right triangle is \n\t47\n\t\n\t\t2\n\t\n\n.

\n

Choice A is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect. This is the length, in inches, of the hypotenuse.

\n

Choice D is incorrect and may result from conceptual or calculation errors.

"}, {"id": "0e709a29", "domain": "Geometry and Trigonometry", "skill": "Right triangles and trigonometry", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

RS=440\n

\n

ST=384\n

\n

TR=584\n

\n

The side lengths of right triangle \n\tR\n\tS\n\tT\n\n are given. Triangle \n\tR\n\tS\n\tT\n\n  is similar to triangle \n\tU\n\tV\n\tW\n\n, where S\n corresponds to V\n and T\n corresponds to W\n. What is the value of tanW?

", "choices": [{"id": "A", "text": "

\n\t48\n\t73\n\n

"}, {"id": "B", "text": "

\n\t55\n\t73\n\n

"}, {"id": "C", "text": "

\n\t48\n\t55\n\n

"}, {"id": "D", "text": "

\n\t55\n\t48\n\n

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. The hypotenuse of triangle RST is the longest side and is across from the right angle. The longest side length given is 584\n, which is the length of side TR. Therefore, the hypotenuse of triangle RST is side TR, so the right angle is angle S\n. The tangent of an acute angle in a right triangle is the ratio of the length of the opposite side, which is the side across from the angle, to the length of the adjacent side, which is the side closest to the angle that is not the hypotenuse. It follows that the opposite side of angle T\n is side RS and the adjacent side of angle T\n is side ST. Therefore, tanT=RSST. Substituting 440\n for RS and 384\n for ST in this equation yields tanT=440384. This is equivalent to tanT=5548. It’s given that triangle RST is similar to triangle UVW, where S\n corresponds to V\n and T\n corresponds to W\n. It follows that R\n corresponds to U\n. Therefore, the hypotenuse of triangle UVW is side WU, which means tanW=UVVW. Since the lengths of corresponding sides of similar triangles are proportional, RSST=UVVW. Therefore, tanW=UVVW is equivalent to tanW=RSST, or tanW=tanT. Thus, tanW=5548.

\n

Choice A is incorrect. This is the value of cosW, not tanW.

\n

Choice B is incorrect. This is the value of sinW, not tanW.

\n

Choice C is incorrect. This is the value of 1tanW, not tanW.

"}, {"id": "5b2b8866", "domain": "Geometry and Trigonometry", "skill": "Area and volume", "difficulty": "H", "type": "spr", "stimulus": "", "stem": "

A rectangular poster has an area of 360\n square inches. A copy of the poster is made in which the length and width of the original poster are each increased by 20\n%. What is the area of the copy, in square inches?

", "choices": [], "answerId": "2592/5", "acceptedAnswers": ["2592/5", "518.4"], "rationale": "

The correct answer is 518.4\n. It's given that the area of the original poster is 360\n square inches. Let l represent the length, in inches, of the original poster, and let w\n represent the width, in inches, of the original poster. Since the area of a rectangle is equal to its length times its width, it follows that 360=lw. It's also given that a copy of the poster is made in which the length and width of the original poster are each increased by 20%. It follows that the length of the copy is the length of the original poster plus 20% of the length of the original poster, which is equivalent to l+20100l inches. This length can be rewritten as l+0.2l inches, or 1.2l inches. Similarly, the width of the copy is the width of the original poster plus 20% of the width of the original poster, which is equivalent to w+20100w inches. This width can be rewritten as w+0.2w inches, or 1.2w inches. Since the area of a rectangle is equal to its length times its width, it follows that the area, in square inches, of the copy is equal to 1.2l1.2w, which can be rewritten as 1.21.2lw. Since 360=lw, the area, in square inches, of the copy can be found by substituting 360\n for lw in the expression 1.21.2lw, which yields 1.21.2360, or 518.4\n. Therefore, the area of the copy, in square inches, is 518.4\n.

"}, {"id": "9f934297", "domain": "Geometry and Trigonometry", "skill": "Area and volume", "difficulty": "H", "type": "spr", "stimulus": "", "stem": "

A right rectangular prism has a length of 28 centimeters cm, a width of 15 cm, and a height of 16 cm. What is the surface area, in cm2, of the right rectangular prism?

", "choices": [], "answerId": "2216", "acceptedAnswers": ["2216"], "rationale": "

The correct answer is 2,216\n. The surface area of a prism is the sum of the areas of all its faces. A right rectangular prism consists of six rectangular faces, where opposite faces are congruent. It's given that this prism has a length of 28 cm, a width of 15 cm, and a height of 16 cm. Thus, for this prism, there are two faces with area 2815 cm2, two faces with area 2816 cm2, and two faces with area 1516 cm2. Therefore, the surface area, in cm2, of the right rectangular prism is 22815+22816+21516, or 2,216\n.

"}, {"id": "575f1e12", "domain": "Geometry and Trigonometry", "skill": "Area and volume", "difficulty": "E", "type": "spr", "stimulus": "", "stem": "

What is the area, in square centimeters, of a rectangle with a length of 34 centimeters cm and a width of 29 cm?

", "choices": [], "answerId": "986", "acceptedAnswers": ["986"], "rationale": "

The correct answer is 986\n. The area, A\n, of a rectangle is given by A=lw, where l is the length of the rectangle and w\n is its width. It’s given that the length of the rectangle is 34\n centimeters (cm) and the width is 29\n cm. Substituting 34\n for l and 29\n for w\n in the equation A=lw yields A=3429, or A=986. Therefore, the area, in square centimeters, of this rectangle is 986\n.

"}, {"id": "74d8b897", "domain": "Geometry and Trigonometry", "skill": "Circles", "difficulty": "M", "type": "spr", "stimulus": "", "stem": "

An angle has a measure of 9π20 radians. What is the measure of the angle in degrees?

", "choices": [], "answerId": "81", "acceptedAnswers": ["81"], "rationale": "

The correct answer is 81\n. The measure of an angle, in degrees, can be found by multiplying its measure, in radians, by 180 degreesπ radians. Multiplying the given angle measure, 9π20 radians, by 180 degreesπ radians yields 9π20 radians180 degreesπ radians, which is equivalent to 81\n degrees.

"}, {"id": "dc71597b", "domain": "Geometry and Trigonometry", "skill": "Area and volume", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

A right circular cone has a volume of one third, pi cubic feet and a height of 9 feet. What is the radius, in feet, of the base of the cone?

\n", "choices": [{"id": "A", "text": "\n one third\n \n"}, {"id": "B", "text": "\n (1)/(the square root(3), end fraction)\n \n"}, {"id": "C", "text": "\n the square root(3)\n \n"}, {"id": "D", "text": "3\n"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. The equation for the volume of a right circular cone is V = one third pi r\u00b2 \u00d7 h. It’s given that the volume of the right circular cone is one third pi cubic feet and the height is 9 feet. Substituting these values for V and h, respectively, gives one third pi = one third pi r\u00b2, \u00d7 9. Dividing both sides of the equation by one third pi gives 1 = r\u00b2 \u00d7 9. Dividing both sides of the equation by 9 gives one ninth = r\u00b2. Taking the square root of both sides results in two possible values for the radius, the square root(o)ne ninth or the negative(t)he square root(o)ne ninth. Since the radius can’t have a negative value, that leaves the square root(o)ne ninth as the only possibility. Applying the quotient property of square roots, the square root of (a,)/(b = the fraction the square root(a), over the square root(b)), results in r = (the square root(1))/(the square root(9)), or r = one third.

Choices B and C are incorrect and may result from incorrectly evaluating the square root(o)ne ninth. Choice D is incorrect and may result from solving r\u00b2 = 9 instead of r\u00b2 = one ninth.

\n"}, {"id": "410bdbe6", "domain": "Geometry and Trigonometry", "skill": "Lines, angles, and triangles", "difficulty": "E", "type": "mc", "stimulus": "
\n
\n \"The
\n
\n", "stem": "

In the triangle above, a = 45. What is the value of b ?

\n", "choices": [{"id": "A", "text": "

52

\n"}, {"id": "B", "text": "

59

\n"}, {"id": "C", "text": "

76

\n"}, {"id": "D", "text": "

104

\n"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. The sum of the measures of the three interior angles of a triangle is 180°. Therefore, 31 + 2 b, + a = 180. Since it’s given that a = 45, it follows that 31 + 2 b, + 45 = 180, or 2 b = 104. Dividing both sides of this equation by 2 yields b = 52.

Choice B is incorrect and may result from a calculation error. Choice C is incorrect. This is the value of a, + 31. Choice D is incorrect. This is the value of 2 b.

\n"}, {"id": "a0cacec1", "domain": "Geometry and Trigonometry", "skill": "Circles", "difficulty": "M", "type": "spr", "stimulus": "", "stem": "

An angle has a measure of \n\t\n\t\t\n\t\t\t16\n\t\t\tπ\n\t\t\n\t\t15\n\t\n\n radians. What is the measure of the angle, in degrees?

\n

 

", "choices": [], "answerId": "192", "acceptedAnswers": ["192"], "rationale": "

The correct answer is 192\n. The measure of an angle, in degrees, can be found by multiplying its measure, in radians, by 180 degrees\u03c0 radians. Multiplying the given angle measure, 16\u03c015radians, by 180 degrees\u03c0 radians yields 16\u03c015radians180 degrees\u03c0 radians, which simplifies to 192\n degrees.

"}, {"id": "f811d345", "domain": "Geometry and Trigonometry", "skill": "Right triangles and trigonometry", "difficulty": "H", "type": "spr", "stimulus": "", "stem": "

A right triangle has legs with lengths of 24\n centimeters and 21\n centimeters. If the length of this triangle's hypotenuse, in centimeters, can be written in the form 3d, where d\n is an integer, what is the value of d\n?

", "choices": [], "answerId": "113", "acceptedAnswers": ["113"], "rationale": "

The correct answer is 113\n. It's given that the legs of a right triangle have lengths 24\n centimeters and 21\n centimeters. In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the two legs. It follows that if h\n represents the length, in centimeters, of the hypotenuse of the right triangle, h2=242+212. This equation is equivalent to \n\t\n\t\th\n\t\t2\n\t\n\t=\n\t1,017\n\n. Taking the square root of each side of this equation yields h=1,017. This equation can be rewritten as h=9\u00b7113, or h=9\u00b7113. This equation is equivalent to \n\th\n\t=\n\t\n\t\t3\n\t\t\n\t\t\t113\n\t\t\n\t\n\n. It's given that the length of the triangle's hypotenuse, in centimeters, can be written in the form \n\t3\n\t\n\t\td\n\t\n\n. It follows that the value of d\n is 113\n.

"}, {"id": "c9931030", "domain": "Geometry and Trigonometry", "skill": "Right triangles and trigonometry", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

RS=20\n

\n

ST=48\n

\n

TR=52\n

\n

The side lengths of right triangle RST are given. Triangle RST is similar to triangle UVW, where S\n corresponds to V\n and T\n corresponds to W\n. What is the value of tanW?

", "choices": [{"id": "A", "text": "

\n\t5\n\t13\n\n

"}, {"id": "B", "text": "

\n\t5\n\t12\n\n

"}, {"id": "C", "text": "

\n\t12\n\t13\n\n

"}, {"id": "D", "text": "

\n\t12\n\t5\n\n

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. It's given that right triangle \n\tR\n\tS\n\tT\n\n is similar to triangle \n\tU\n\tV\n\tW\n\n, where S\n corresponds to V\n and T\n corresponds to W\n. It's given that the side lengths of the right triangle \n\tR\n\tS\n\tT\n\n are \n\t\n\t\tR\n\t\tS\n\t\n\t=\n\t20\n\n, \n\t\n\t\tS\n\t\tT\n\t\n\t=\n\t48\n\n, and TR=52. Corresponding angles in similar triangles are equal. It follows that the measure of angle T\n is equal to the measure of angle W\n. The hypotenuse of a right triangle is the longest side. It follows that the hypotenuse of triangle RST is side TR. The hypotenuse of a right triangle is the side opposite the right angle. Therefore, angle S\n is a right angle. The adjacent side of an acute angle in a right triangle is the side closest to the angle that is not the hypotenuse. It follows that the adjacent side of angle T\n is side \n\tS\n\tT\n\n. The opposite side of an acute angle in a right triangle is the side across from the acute angle. It follows that the opposite side of angle T\n is side \n\tR\n\tS\n\n. The tangent of an acute angle in a right triangle is the ratio of the length of the opposite side to the length of the adjacent side. Therefore, tan T=RSST. Substituting 20\n for \n\tR\n\tS\n\n and 48\n for \n\tS\n\tT\n\n in this equation yields tan T=2048, or tan T=512. The tangents of two acute angles with equal measures are equal. Since the measure of angle T\n is equal to the measure of angle W\n, it follows that tan T=tan W. Substituting 512 for tan T in this equation yields 512=tan W. Therefore, the value of tan W is 512.

\n

Choice A is incorrect. This is the value of sin W.

\n

Choice C is incorrect. This is the value of cos W.

\n

Choice D is incorrect. This is the value of 1tan W.

"}, {"id": "087cdcfd", "domain": "Geometry and Trigonometry", "skill": "Lines, angles, and triangles", "difficulty": "E", "type": "mc", "stimulus": "
\n
\n \"The
\n
\n", "stem": "

In the figure, three lines intersect at point P. If x = 65 and y = 75, what is the value of z ?

\n", "choices": [{"id": "A", "text": "

140

\n"}, {"id": "B", "text": "

80

\n"}, {"id": "C", "text": "

40

\n"}, {"id": "D", "text": "

20

\n"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. The angle that is shown as lying between the y° angle and the z° angle is a vertical angle with the x° angle. Since vertical angles are congruent and x = 65, the angle between the y° angle and the z° angle measures 65°. Since the 65° angle, the y° angle, and the z° angle are adjacent and form a straight angle, it follows that the sum of the measures of these three angles is 180°, which is represented by the equation 65 degrees, + y degrees, + z degrees = 180 degrees. It’s given that y = 75. Substituting 75 for y yields 65 degrees, + 75 degrees, + z degrees = 180 degrees, which can be rewritten as 140 degrees, + z degrees = 180 degrees. Subtracting 140° from both sides of this equation yields z degrees = 40 degrees. Therefore, z = 40.

Choice A is incorrect and may result from finding the value of x + y rather than z. Choices B and D are incorrect and may result from conceptual or computational errors.

\n"}, {"id": "c88183f7", "domain": "Geometry and Trigonometry", "skill": "Area and volume", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

A rectangle has a length of 13\n and a width of 6\n. What is the perimeter of the rectangle?

", "choices": [{"id": "A", "text": "

12\n

"}, {"id": "B", "text": "

26\n

"}, {"id": "C", "text": "

38\n

"}, {"id": "D", "text": "

52\n

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. The perimeter of a quadrilateral is the sum of the lengths of its four sides. It's given that the rectangle has a length of 13\n and a width of 6\n. It follows that the rectangle has two sides with length 13\n and two sides with length 6\n. Therefore, the perimeter of the rectangle is 13+13+6+6, or 38\n.

\n

Choice A is incorrect. This is the sum of the lengths of the two sides with length 6\n, not the sum of the lengths of all four sides of the rectangle.

\n

Choice B is incorrect. This is the sum of the lengths of the two sides with length 13\n, not the sum of the lengths of all four sides of the rectangle.

\n

Choice D is incorrect. This is the perimeter of a rectangle that has four sides with length 13\n, not two sides with length 13\n and two sides with length 6\n.

"}, {"id": "afa3c48b", "domain": "Geometry and Trigonometry", "skill": "Lines, angles, and triangles", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n\n

\n

In the figure shown, line m\n is parallel to line n\n. What is the value of x\n?

", "choices": [{"id": "A", "text": "

13\n

"}, {"id": "B", "text": "

26\n

"}, {"id": "C", "text": "

52\n

"}, {"id": "D", "text": "

154\n

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. The sum of consecutive interior angles between two parallel lines and on the same side of the transversal is 180\n degrees. Since it's given that line m\n is parallel to line n\n, it follows that \n\t\n\t\tx\n\t\t+\n\t\t26\n\t\n\t=\n\t180\n\n. Subtracting 26\n from both sides of this equation yields 154\n. Therefore, the value of x\n is 154\n.

\n

Choice A is incorrect. This is half of the given angle measure.

\n

Choice B is incorrect. This is the value of the given angle measure.

\n

Choice C is incorrect. This is twice the value of the given angle measure.

"}, {"id": "9ec76b54", "domain": "Geometry and Trigonometry", "skill": "Right triangles and trigonometry", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

A right triangle has legs with lengths of 28\n centimeters and 20\n centimeters. What is the length of this triangle's hypotenuse, in centimeters?

", "choices": [{"id": "A", "text": "

\n\t8\n\t\n\t\t6\n\t\n\n

"}, {"id": "B", "text": "

\n\t4\n\t\n\t\t74\n\t\n\n

"}, {"id": "C", "text": "

48\n

"}, {"id": "D", "text": "

1,184\n

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. The Pythagorean theorem states that in a right triangle, the sum of the squares of the lengths of the two legs is equal to the square of the length of the hypotenuse. It's given that the right triangle has legs with lengths of 28\n centimeters and 20\n centimeters. Let c\n represent the length of this triangle's hypotenuse, in centimeters. Therefore, by the Pythagorean theorem, 282+202=c2, or 1,184=c2. Taking the positive square root of both sides of this equation yields 1,184=c, or 474=c. Therefore, the length of this triangle's hypotenuse, in centimeters, is 474.

\n

Choice A is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

\n

Choice D is incorrect. This is the square of the length of the triangle’s hypotenuse.

"}, {"id": "992f4e93", "domain": "Geometry and Trigonometry", "skill": "Lines, angles, and triangles", "difficulty": "E", "type": "mc", "stimulus": "
\n
\n \"The
\n
\n", "stem": "

In the figure above, lines l and k are parallel. What is the value of a ?

\n", "choices": [{"id": "A", "text": "

26

\n"}, {"id": "B", "text": "

64

\n"}, {"id": "C", "text": "

116

\n"}, {"id": "D", "text": "

154

\n"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. Since lines l and k are parallel, corresponding angles formed by the intersection of line j with lines l and k are congruent. Therefore, the angle with measure a° must be the supplement of the angle with measure 64°. The sum of two supplementary angles is 180°, so a = 180 – 64 = 116.

Choice A is incorrect and likely results from thinking the angle with measure a° is the complement of the angle with measure 64°. Choice B is incorrect and likely results from thinking the angle with measure a° is congruent to the angle with measure 64°. Choice D is incorrect and likely results from a conceptual or computational error.

\n"}, {"id": "f1747a6a", "domain": "Geometry and Trigonometry", "skill": "Lines, angles, and triangles", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

In triangle \n\tA\n\tB\n\tC\n\n, the measure of angle B\n is 52° and the measure of angle C\n is 17°. What is the measure of angle A\n?

", "choices": [{"id": "A", "text": "

21\n°

"}, {"id": "B", "text": "

35\n°

"}, {"id": "C", "text": "

69\n°

"}, {"id": "D", "text": "

111\n°

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. The sum of the angle measures of a triangle is 180\u00b0. Adding the measures of angles B\n and C\n gives 52+17=69\u00b0. Therefore, the measure of angle A\n is 180-69=111\u00b0.

\n

Choice A is incorrect and may result from subtracting the sum of the measures of angles B\n and C\n from 90\u00b0, instead of from 180\u00b0.

\n

Choice B is incorrect and may result from subtracting the measure of angle C\n from the measure of angle B\n.

\n

Choice C is incorrect and may result from adding the measures of angles B\n and C\n but not subtracting the result from 180\u00b0.

"}, {"id": "23c5fcce", "domain": "Geometry and Trigonometry", "skill": "Circles", "difficulty": "E", "type": "mc", "stimulus": "
\n\t
\"The
\n
\n", "stem": "

The circle above with center O has a circumference of 36. What is the length of minor arc A, C?

\n", "choices": [{"id": "A", "text": "

9

\n"}, {"id": "B", "text": "

12

\n"}, {"id": "C", "text": "

18

\n"}, {"id": "D", "text": "

36

\n"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. A circle has 360 degrees of arc. In the circle shown, O is the center of the circle and angle A, O C is a central angle of the circle. From the figure, the two diameters that meet to form angle A, O C are perpendicular, so the measure of angle A, O C is 90 degrees. Therefore, the length of minor arc A, C is (90)/(360) of the circumference of the circle. Since the circumference of the circle is 36, the length of minor arc A, C is (90)/(360, end fraction, \u00d7 36 = 9).

Choices B, C, and D are incorrect. The perpendicular diameters divide the circumference of the circle into four equal arcs; therefore, minor arc A, C is one fourth of the circumference. However, the lengths in choices B and C are, respectively, one third and one half the circumference of the circle, and the length in choice D is the length of the entire circumference. None of these lengths is one fourth the circumference.

 

\n"}, {"id": "f1c1e971", "domain": "Geometry and Trigonometry", "skill": "Circles", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

The measure of angle R\n is \n\t\n\t\t\n\t\t\t2\n\t\t\tπ\n\t\t\n\t\t3\n\t\n\n radians. The measure of angle T\n is \n\t\n\t\t\n\t\t\t5\n\t\t\tπ\n\t\t\n\t\t12\n\t\n\n radians greater than the measure of angle R\n. What is the measure of angle T\n, in degrees?

", "choices": [{"id": "A", "text": "

75\n

"}, {"id": "B", "text": "

120\n

"}, {"id": "C", "text": "

195\n

"}, {"id": "D", "text": "

390\n

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. It’s given that the measure of angle R\n is 2\u03c03 radians, and the measure of angle T\n is 5\u03c012 radians greater than the measure of angle R\n. Therefore, the measure of angle T\n is equal to 2\u03c03+5\u03c012 radians. Multiplying 2\u03c03 by 44 to get a common denominator with 5\u03c012 yields 8\u03c012. Therefore, 2\u03c03+5\u03c012 is equivalent to 8\u03c012+5\u03c012, or 13\u03c012. Therefore, the measure of angle T\n is 13\u03c012 radians. The measure of angle T\n, in degrees, can be found by multiplying its measure, in radians, by 180\u03c0. This yields 13\u03c012\u00d7180\u03c0, which is equivalent to 195\n degrees. Therefore, the measure of angle T\n is 195\n degrees.

\n

Choice A is incorrect. This is the number of degrees that the measure of angle T\n is greater than the measure of angle R\n.

\n

Choice B is incorrect. This is the measure of angle R\n, in degrees.

\n

Choice D is incorrect and may result from conceptual or calculation errors.

"}, {"id": "6ab30ce3", "domain": "Geometry and Trigonometry", "skill": "Right triangles and trigonometry", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

Triangle \n\tA\n\tB\n\tC\n\n is similar to triangle \n\tD\n\tE\n\tF\n\n, where A\n corresponds to D\n and C\n corresponds to F\n. Angles C\n and F\n are right angles. If tanA=3 and DF=125, what is the length of DE¯?

", "choices": [{"id": "A", "text": "

12533

"}, {"id": "B", "text": "

12532

"}, {"id": "C", "text": "

1253

"}, {"id": "D", "text": "

250\n

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. Corresponding angles in similar triangles have equal measures. It's given that triangle ABC is similar to triangle DEF, where A\n corresponds to D\n, so the measure of angle A\n is equal to the measure of angle D\n. Therefore, if tanA=3, then tanD=3. It's given that angles C\n and F\n are right angles, so triangles ABC and DEF are right triangles. The adjacent side of an acute angle in a right triangle is the side closest to the angle that is not the hypotenuse. It follows that the adjacent side of angle D\n is side \n\tD\n\tF\n\n. The opposite side of an acute angle in a right triangle is the side across from the acute angle. It follows that the opposite side of angle D\n is side \n\tE\n\tF\n\n. The tangent of an acute angle in a right triangle is the ratio of the length of the opposite side to the length of the adjacent side. Therefore, tanD=EFDF. If DF=125, the length of side \n\tE\n\tF\n\n can be found by substituting 3 for tanD and 125\n for \n\tD\n\tF\n\n in the equation tanD=EFDF, which yields 3=EF125. Multiplying both sides of this equation by 125\n yields 1253=EF. Since the length of side \n\tE\n\tF\n\n is 3 times the length of side \n\tD\n\tF\n\n, it follows that triangle DEF is a special right triangle with angle measures 30°, 60°, and 90°. Therefore, the length of the hypotenuse, DE¯, is 2\n times the length of side \n\tD\n\tF\n\n, or DE=2DF. Substituting 125\n for \n\tD\n\tF\n\n in this equation yields DE=2125, or DE=250. Thus, if tanA=3 and DF=125, the length of DE¯ is 250\n.

\n

Choice A is incorrect and may result from conceptual or calculation errors.

\n

Choice B is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect. This is the length of EF¯, not DE¯.

"}, {"id": "9acd101f", "domain": "Geometry and Trigonometry", "skill": "Circles", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

The equation \n\t\n\t\t\n\t\t\tx\n\t\t\t2\n\t\t\n\t\t+\n\t\t\n\t\t\t\n\t\t\t\t\n\t\t\t\t\ty\n\t\t\t\t\t-\n\t\t\t\t\t1\n\t\t\t\t\n\t\t\t\n\t\t\t2\n\t\t\n\t\n\t=\n\t49\n\n represents circle A. Circle B is obtained by shifting circle A down 2\n units in the xy-plane. Which of the following equations represents circle B?

", "choices": [{"id": "A", "text": "

\n\t\n\t\t\n\t\t\t\n\t\t\t\t\n\t\t\t\t\tx\n\t\t\t\t\t-\n\t\t\t\t\t2\n\t\t\t\t\n\t\t\t\n\t\t\t2\n\t\t\n\t\t+\n\t\t\n\t\t\t\n\t\t\t\t\n\t\t\t\t\ty\n\t\t\t\t\t-\n\t\t\t\t\t1\n\t\t\t\t\n\t\t\t\n\t\t\t2\n\t\t\n\t\n\t=\n\t49\n\n

"}, {"id": "B", "text": "

\n\t\n\t\t\n\t\t\tx\n\t\t\t2\n\t\t\n\t\t+\n\t\t\n\t\t\t\n\t\t\t\t\n\t\t\t\t\ty\n\t\t\t\t\t-\n\t\t\t\t\t3\n\t\t\t\t\n\t\t\t\n\t\t\t2\n\t\t\n\t\n\t=\n\t49\n\n

"}, {"id": "C", "text": "

\n\t\n\t\t\n\t\t\t\n\t\t\t\t\n\t\t\t\t\tx\n\t\t\t\t\t+\n\t\t\t\t\t2\n\t\t\t\t\n\t\t\t\n\t\t\t2\n\t\t\n\t\t+\n\t\t\n\t\t\t\n\t\t\t\t\n\t\t\t\t\ty\n\t\t\t\t\t-\n\t\t\t\t\t1\n\t\t\t\t\n\t\t\t\n\t\t\t2\n\t\t\n\t\n\t=\n\t49\n\n

"}, {"id": "D", "text": "

\n\t\n\t\t\n\t\t\tx\n\t\t\t2\n\t\t\n\t\t+\n\t\t\n\t\t\t\n\t\t\t\t\n\t\t\t\t\ty\n\t\t\t\t\t+\n\t\t\t\t\t1\n\t\t\t\t\n\t\t\t\n\t\t\t2\n\t\t\n\t\n\t=\n\t49\n\n

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. The graph in the xy-plane of an equation of the form x-h2+y-k2=r2 is a circle with center h,k and a radius of length r\n. It's given that circle A is represented by x2+y-12=49, which can be rewritten as x2+y-12=72. Therefore, circle A has center 0,1 and a radius of length 7\n. Shifting circle A down two units is a rigid vertical translation of circle A that does not change its size or shape. Since circle B is obtained by shifting circle A down two units, it follows that circle B has the same radius as circle A, and for each point x,y on circle A, the point x,y-2 lies on circle B. Moreover, if h,k is the center of circle A, then h,k-2 is the center of circle B. Therefore, circle B has a radius of 7\n and the center of circle B is 0,1-2, or 0,-1. Thus, circle B can be represented by the equation x2+y+12=72, or x2+y+12=49.

\n

Choice A is incorrect. This is the equation of a circle obtained by shifting circle A right 2\n units.

\n

Choice B is incorrect. This is the equation of a circle obtained by shifting circle A up 2\n units.

\n

Choice C is incorrect. This is the equation of a circle obtained by shifting circle A left 2\n units.

"}, {"id": "08b7a3f5", "domain": "Geometry and Trigonometry", "skill": "Area and volume", "difficulty": "M", "type": "spr", "stimulus": "", "stem": "

A triangular prism has a height of 8 centimeters cm and a volume of 216 cm3. What is the area, in cm2, of the base of the prism? (The volume of a triangular prism is equal to \n\tB\n\th\n\n, where B\n is the area of the base and h\n is the height of the prism.)

", "choices": [], "answerId": "27", "acceptedAnswers": ["27"], "rationale": "

The correct answer is 27\n. It's given that a triangular prism has a volume of 216 cubic centimeters cm3 and the volume of a triangular prism is equal to \n\tB\n\th\n\n, where B\n is the area of the base and h\n is the height of the prism. Therefore, 216=Bh. It's also given that the triangular prism has a height of 8 cm. Therefore, h=8. Substituting 8\n for h\n in the equation 216=Bh yields 216=B8. Dividing both sides of this equation by 8\n yields 27=B. Therefore, the area, in cm2, of the base of the prism is 27\n.

"}, {"id": "5733ce30", "domain": "Geometry and Trigonometry", "skill": "Lines, angles, and triangles", "difficulty": "E", "type": "mc", "stimulus": "
\n
\n \"The
\n
\n", "stem": "

In the given figure, side A C extends to point D. If the measure of angle B A C is equal to the measure of angle B C A, what is the value of x ?

\n", "choices": [{"id": "A", "text": "

110

\n"}, {"id": "B", "text": "

70

\n"}, {"id": "C", "text": "

55

\n"}, {"id": "D", "text": "

40

\n"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. Since angle B C D and angle B C A form a linear pair of angles, their measures sum to 180°. It’s given that the measure of angle B C D is 110°. Therefore, 110 degrees + angle B C A = 180 degrees. Subtracting 110° from both sides of this equation gives the measure of angle B C A as 70°. It’s also given that the measure of angle B A C is equal to the measure of angle B C A. Thus, the measure of angle B A C is also 70°. The measures of the interior angles of a triangle sum to 180°. Thus, 70 degrees, + 70 degrees, + x degrees = 180 degrees. Combining like terms on the left-hand side of this equation yields 140 degrees + x degrees = 180 degrees. Subtracting 140° from both sides of this equation yields x degrees = 40 degrees, or x = 40.

Choice A is incorrect. This is the value of the measure of angle B C D. Choice B is incorrect. This is the value of the measure of each of the other two interior angles, angle B C A and angle B A C. Choice C is incorrect and may result from an error made when identifying the relationship between the exterior angle of a triangle and the interior angles of the triangle.

\n"}, {"id": "3b4b5b1e", "domain": "Geometry and Trigonometry", "skill": "Lines, angles, and triangles", "difficulty": "E", "type": "spr", "stimulus": "", "stem": "

\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n\n

\n

In the figure, line j\n is parallel to line k\n. What is the value of x\n?

", "choices": [], "answerId": "47", "acceptedAnswers": ["47"], "rationale": "

The correct answer is 47\n. Based on the figure, the angle with measure x\u00b0 and the angle with measure 133\u00b0 together form a straight line. Therefore, these two angles are supplementary, so the sum of their measures is 180\u00b0. It follows that \n\t\n\t\tx\n\t\t+\n\t\t133\n\t\n\t=\n\t180\n\n. Subtracting 133\n from both sides of this equation yields \n\tx\n\t=\n\t47\n\n.

"}, {"id": "29e9b28c", "domain": "Geometry and Trigonometry", "skill": "Area and volume", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

\n

 

\n

The triangle shown has a perimeter of 22\n units. If x=9 units and y=7 units, what is the value of z\n, in units?

", "choices": [{"id": "A", "text": "

6\n

"}, {"id": "B", "text": "

7\n

"}, {"id": "C", "text": "

9\n

"}, {"id": "D", "text": "

16\n

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. The perimeter of a triangle is the sum of the lengths of its three sides. The triangle shown has side lengths x\n, y\n, and z\n. It's given that the triangle has a perimeter of 22\n units. Therefore, \n\t\n\t\tx\n\t\t+\n\t\ty\n\t\t+\n\t\tz\n\t\n\t=\n\t22\n\n. If \n\tx\n\t=\n\t9\n\n units and \n\ty\n\t=\n\t7\n\n units, the value of z\n, in units, can be found by substituting 9\n for x\n and 7\n for y\n in the equation \n\t\n\t\tx\n\t\t+\n\t\ty\n\t\t+\n\t\tz\n\t\n\t=\n\t22\n\n, which yields 9+7+z=22, or 16+z=22. Subtracting 16\n from both sides of this equation yields \n\tz\n\t=\n\t6\n\n. Therefore, if \n\tx\n\t=\n\t9\n\n units and \n\ty\n\t=\n\t7\n\n units, the value of z\n, in units, is 6\n.

\n

Choice B is incorrect. This is the value of y\n, in units, not the value of z\n, in units.

\n

Choice C is incorrect. This is the value of x\n, in units, not the value of z\n, in units.

\n

Choice D is incorrect. This is the value of \n\tx\n\t+\n\ty\n\n, in units, not the value of z\n, in units.

"}, {"id": "5b4757df", "domain": "Geometry and Trigonometry", "skill": "Lines, angles, and triangles", "difficulty": "H", "type": "spr", "stimulus": "", "stem": "

In triangle RST, angle T\n is a right angle, point L\n lies on RS¯, point K\n lies on ST¯, and LK¯ is parallel to RT¯. If the length of RT¯ is 72\n units, the length of LK¯ is 24\n units, and the area of triangle RST is 792\n square units, what is the length of KT¯, in units?

", "choices": [], "answerId": "14.66", "acceptedAnswers": ["14.66", "14.67", "44/3"], "rationale": "

The correct answer is \n\t44\n\t3\n\n. It's given that in triangle \n\tR\n\tS\n\tT\n\n, angle T\n is a right angle. The area of a right triangle can be found using the formula A=12l1l2, where A\n represents the area of the right triangle, l1 represents the length of one leg of the triangle, and l2 represents the length of the other leg of the triangle. In triangle \n\tR\n\tS\n\tT\n\n, the two legs are RT¯ and ST¯. Therefore, if the length of RT¯ is 72\n and the area of triangle RST is 792\n, then 792=1272ST, or 792=36ST. Dividing both sides of this equation by 36\n yields 22=ST. Therefore, the length of ST¯ is 22\n. It's also given that point L\n lies on RS¯, point K\n lies on ST¯, and LK¯ is parallel to RT¯. It follows that angle LKS is a right angle. Since triangles RST and LSK share angle S\n and have right angles T\n and K\n, respectively, triangles RST and LSK are similar triangles. Therefore, the ratio of the length of RT¯ to the length of LK¯ is equal to the ratio of the length of ST¯ to the length of SK¯. If the length of RT¯ is 72\n and the length of LK¯ is 24\n, it follows that the ratio of the length of RT¯ to the length of LK¯ is 7224, or 3\n, so the ratio of the length of ST¯ to the length of SK¯ is 3\n. Therefore, 22SK=3. Multiplying both sides of this equation by SK yields 22=3SK. Dividing both sides of this equation by 3\n yields 223=SK. Since the length of ST¯, 22\n, is the sum of the length of SK¯, \n\t22\n\t3\n\n, and the length of KT¯, it follows that the length of KT¯ is 22-223, or \n\t44\n\t3\n\n. Note that 44/3, 14.66, and 14.67 are examples of ways to enter a correct answer.

"}, {"id": "ca2235f6", "domain": "Geometry and Trigonometry", "skill": "Circles", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

A circle has center O\n, and points A\n and B\n lie on the circle. The measure of arc \n\tA\n\tB\n\n is 45∘ and the length of arc \n\tA\n\tB\n\n is 3\n inches. What is the circumference, in inches, of the circle?

", "choices": [{"id": "A", "text": "

3\n

"}, {"id": "B", "text": "

6\n

"}, {"id": "C", "text": "

9\n

"}, {"id": "D", "text": "

24\n

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. It’s given that the measure of arc AB is 45° and the length of arc AB is 3 inches. The arc measure of the full circle is 360°. If x\n represents the circumference, in inches, of the circle, it follows that 45°360°=3 inchesx inches. This equation is equivalent to 45360=3x, or 18=3x. Multiplying both sides of this equation by 8x yields 1(x)=3(8), or x=24. Therefore, the circumference of the circle is 24 inches.

\n

Choice A is incorrect. This is the length of arc AB.

\n

Choice B is incorrect and may result from multiplying the length of arc AB by 2\n.

\n

Choice C is incorrect and may result from squaring the length of arc AB.

"}, {"id": "856372ca", "domain": "Geometry and Trigonometry", "skill": "Circles", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

In the xy-plane, a circle with radius 5 has center \u22128, 6. Which of the following is an equation of the circle?

\n", "choices": [{"id": "A", "text": "

\n open parenthesis, x \u2212 8, close parenthesis, squared, plus, open parenthesis, y + 6, close parenthesis, squared = 25\n

\n"}, {"id": "B", "text": "

\n \n open parenthesis, x + 8, close parenthesis, squared, plus, open parenthesis, y \u2212 6, close parenthesis, squared = 25\n \n

\n"}, {"id": "C", "text": "

\n \n \n open parenthesis, x \u2212 8, close parenthesis, squared, plus, open parenthesis, y + 6, close parenthesis, squared = 5\n \n \n

\n"}, {"id": "D", "text": "

\n \n \n \n \n open parenthesis, x + 8, close parenthesis, squared, plus, open parenthesis, y \u2212 6, close parenthesis, squared = 5\n \n \n \n \n

\n"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. An equation of a circle is open parenthesis, x \u2212 h, close parenthesis, squared, plus, open parenthesis, y \u2212 k, close parenthesis, squared = r\u00b2, where the center of the circle is the point h, k and the radius is r. It’s given that the center of this circle is the point \u22128, 6 and the radius is 5. Substituting these values into the equation gives open parenthesis, x \u2212 \u22128, close parenthesis, squared, plus, open parenthesis, y \u2212 6, close parenthesis, squared = 5\u00b2, or open parenthesis, x + 8, close parenthesis, squared, plus, open parenthesis, y \u2212 6, close parenthesis, squared = 25.

Choice A is incorrect. This is an equation of a circle that has center 8, \u22126. Choice C is incorrect. This is an equation of a circle that has center 8, \u22126 and radius the square root(5). Choice D is incorrect. This is an equation of a circle that has radius  the square root(5).

\n"}, {"id": "cf0d3050", "domain": "Geometry and Trigonometry", "skill": "Lines, angles, and triangles", "difficulty": "E", "type": "spr", "stimulus": "", "stem": "

\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n\n

\n

In the figure shown, line c\n intersects parallel lines s\n and t\n. What is the value of x\n?

", "choices": [], "answerId": "70", "acceptedAnswers": ["70"], "rationale": "

The correct answer is 70\n. Based on the figure, the angle with measure 110\u00b0 and the angle vertical to the angle with measure x\u00b0 are same side interior angles. Since vertical angles are congruent, the angle vertical to the angle with measure x\u00b0 also has measure x\u00b0. It’s given that lines s\n and t\n are parallel. Therefore, same side interior angles between lines s\n and t\n are supplementary. It follows that \n\t\n\t\tx\n\t\t+\n\t\t110\n\t\n\t=\n\t180\n\n. Subtracting 110\n from both sides of this equation yields \n\tx\n\t=\n\t70\n\n.

"}, {"id": "0bb39de4", "domain": "Geometry and Trigonometry", "skill": "Lines, angles, and triangles", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

Triangles \n\tA\n\tB\n\tC\n\n and \n\tD\n\tE\n\tF\n\n are congruent, where A\n corresponds to D\n, and B\n and E\n are right angles. The measure of angle A\n is 18°. What is the measure of angle F\n?

", "choices": [{"id": "A", "text": "

18\n°

"}, {"id": "B", "text": "

72\n°

"}, {"id": "C", "text": "

90\n°

"}, {"id": "D", "text": "

162\n°

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. It’s given that triangle \n\tA\n\tB\n\tC\n\n is congruent to triangle \n\tD\n\tE\n\tF\n\n. Corresponding angles of congruent triangles are congruent and, therefore, have equal measure. It’s given that angle A\n corresponds to angle D\n, and that the measure of angle A\n is 18\u00b0. It's also given that the measures of angles B\n and E\n are 90\u00b0. Since these angles have equal measure, they are corresponding angles. It follows that angle C\n corresponds to angle F\n. Let x\u00b0 represent the measure of angle C\n. Since the sum of the measures of the interior angles of a triangle is 180\u00b0, it follows that 18\u00b0+90\u00b0+x\u00b0=180\u00b0, or 108\u00b0+x\u00b0=180\u00b0. Subtracting 108\u00b0 from both sides of this equation yields x\u00b0=72\u00b0. Therefore, the measure of angle C\n is 72\u00b0. Since angle C\n corresponds to angle F\n, it follows that the measure of angle F\n is also 72\u00b0.

\n

Choice A is incorrect. This is the measure of angle D\n, not the measure of angle F\n.

\n

Choice C is incorrect. This is the measure of angle E\n, not the measure of angle F\n.

\n

Choice D is incorrect. This is the sum of the measures of angles E\n and F\n, not the measure of angle F\n.

"}, {"id": "9d159400", "domain": "Geometry and Trigonometry", "skill": "Circles", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

Which of the following equations represents a circle in the xy-plane that intersects the y-axis at exactly one point?

", "choices": [{"id": "A", "text": "

\n\t\n\t\t\n\t\t\t\n\t\t\t\t\n\t\t\t\t\tx\n\t\t\t\t\t-\n\t\t\t\t\t8\n\t\t\t\t\n\t\t\t\n\t\t\t2\n\t\t\n\t\t+\n\t\t\n\t\t\t\n\t\t\t\t\n\t\t\t\t\ty\n\t\t\t\t\t-\n\t\t\t\t\t8\n\t\t\t\t\n\t\t\t\n\t\t\t2\n\t\t\n\t\n\t=\n\t16\n\n

"}, {"id": "B", "text": "

\n\t\n\t\t\n\t\t\t\n\t\t\t\t\n\t\t\t\t\tx\n\t\t\t\t\t-\n\t\t\t\t\t8\n\t\t\t\t\n\t\t\t\n\t\t\t2\n\t\t\n\t\t+\n\t\t\n\t\t\t\n\t\t\t\t\n\t\t\t\t\ty\n\t\t\t\t\t-\n\t\t\t\t\t4\n\t\t\t\t\n\t\t\t\n\t\t\t2\n\t\t\n\t\n\t=\n\t16\n\n

"}, {"id": "C", "text": "

\n\t\n\t\t\n\t\t\t\n\t\t\t\t\n\t\t\t\t\tx\n\t\t\t\t\t-\n\t\t\t\t\t4\n\t\t\t\t\n\t\t\t\n\t\t\t2\n\t\t\n\t\t+\n\t\t\n\t\t\t\n\t\t\t\t\n\t\t\t\t\ty\n\t\t\t\t\t-\n\t\t\t\t\t9\n\t\t\t\t\n\t\t\t\n\t\t\t2\n\t\t\n\t\n\t=\n\t16\n\n

"}, {"id": "D", "text": "

\n\t\n\t\t\n\t\t\tx\n\t\t\t2\n\t\t\n\t\t+\n\t\t\n\t\t\t\n\t\t\t\t\n\t\t\t\t\ty\n\t\t\t\t\t-\n\t\t\t\t\t9\n\t\t\t\t\n\t\t\t\n\t\t\t2\n\t\t\n\t\n\t=\n\t16\n\n

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. The graph of the equation x-h2+y-k2=r2 in the xy-plane is a circle with center h,k and a radius of length r\n. The radius of a circle is the distance from the center of the circle to any point on the circle. If a circle in the xy-plane intersects the y-axis at exactly one point, then the perpendicular distance from the center of the circle to this point on the y-axis must be equal to the length of the circle's radius. It follows that the x-coordinate of the circle's center must be equivalent to the length of the circle's radius. In other words, if the graph of x-h2+y-k2=r2 is a circle that intersects the y-axis at exactly one point, then r=h must be true. The equation in choice C is x-42+y-92=16, or x-42+y-92=42. This equation is in the form x-h2+y-k2=r2, where h=4, k=9, and r=4, and represents a circle in the xy-plane with center 4,9 and radius of length 4\n. Substituting 4\n for r\n and 4\n for h\n in the equation r=h yields 4=4, or 4=4, which is true. Therefore, the equation in choice C represents a circle in the xy-plane that intersects the y-axis at exactly one point. 

\n

Choice A is incorrect. This is the equation of a circle that does not intersect the y-axis at any point.

\n

Choice B is incorrect. This is an equation of a circle that intersects the x-axis, not the y-axis, at exactly one point.

\n

Choice D is incorrect. This is the equation of a circle with the center located on the y-axis and thus intersects the y-axis at exactly two points, not exactly one point.

"}, {"id": "bf8d843e", "domain": "Geometry and Trigonometry", "skill": "Right triangles and trigonometry", "difficulty": "M", "type": "mc", "stimulus": "
\n
\n \"The
\n
\n", "stem": "

In triangle A, B C above, what is the length of  segment A, D?

\n", "choices": [{"id": "A", "text": "

4

\n"}, {"id": "B", "text": "

6

\n"}, {"id": "C", "text": "6 \u00d7 the square root(2)\n"}, {"id": "D", "text": "6 \u00d7 the square root(3)\n"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. Triangles ADB and CDB are both 30 degree 60 degree 90 degree triangles and share side B D . Therefore, triangles ADB and CDB are congruent by the angle-side-angle postulate. Using the properties of 30 degree 60 degree 90 degree triangles, the length of side A, D is half the length of hypotenuse A, B . Since the triangles are congruent, the length(s)ide A, B = the length(s)ide B C, which = 12. So the length of side A, D is twelve halves = 6.

Alternate approach: Since angle CBD has a measure of 30 degrees, angle ABC must have a measure of 60 degrees. It follows that triangle ABC is equilateral, so side AC also has length 12. It also follows that the altitude BD is also a median, and therefore the length of AD is half of the length of AC, which is 6.

Choice A is incorrect. If the length of side A, D were 4, then the length of side A, B would be 8. However, this is incorrect because side A, B is congruent to side B C, which has a length of 12. Choices C and D are also incorrect. Following the same procedures as used to test choice A gives side A, B a length of 12 \u00d7 the square root(2) for choice C and 12 \u00d7 the square root(3) for choice D. However, these results cannot be true because side A, B is congruent to side B C, which has a length of 12.

\n"}, {"id": "3453aafc", "domain": "Geometry and Trigonometry", "skill": "Area and volume", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

What is the area, in square centimeters, of a rectangle with a length of 36\n centimeters and a width of 34\n centimeters?

", "choices": [{"id": "A", "text": "

70\n

"}, {"id": "B", "text": "

140\n

"}, {"id": "C", "text": "

1,156\n

"}, {"id": "D", "text": "

1,224\n

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. The area A\n, in square centimeters, of a rectangle can be found using the formula A=lw, where l is the length, in centimeters, of the rectangle and w\n is its width, in centimeters. It's given that the rectangle has a length of 36\n centimeters and a width of 34\n centimeters. Substituting 36\n for l and 34\n for w\n in the formula A=lw yields A=3634, or A=1,224. Therefore, the area, in square centimeters, of this rectangle is 1,224.

\n

Choice A is incorrect and may result from conceptual or calculation errors.

\n

Choice B is incorrect. This is the perimeter, in centimeters, not the area, in square centimeters, of the rectangle.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

"}, {"id": "981275d2", "domain": "Geometry and Trigonometry", "skill": "Circles", "difficulty": "H", "type": "mc", "stimulus": "
\n\t

Open parenthesis, x \u2212 6, close parenthesis, squared, plus, open parenthesis, y + 5, close parenthesis, squared = 16

\n
\n", "stem": "

In the xy-plane, the graph of the equation above is a circle. Point P is on the circle and has coordinates 10, \u22125. If line segment P Q is a diameter of the circle, what are the coordinates of point Q ?

\n", "choices": [{"id": "A", "text": "

2, \u22125

\n"}, {"id": "B", "text": "

6, \u22121

\n"}, {"id": "C", "text": "

6, \u22125

\n"}, {"id": "D", "text": "

6, \u22129

\n"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. The standard form for the equation of a circle is open parenthesis, x \u2212 h, close parenthesis, squared, plus, open parenthesis, y \u2212 k, close parenthesis, squared = r\u00b2, where h, k are the coordinates of the center and r is the length of the radius. According to the given equation, the center of the circle is the point 6, \u22125. Let x sub 1, y sub 1 represent the coordinates of point Q. Since point P 10, \u22125 and point Q x sub 1, y sub 1 are the endpoints of a diameter of the circle, the center 6, \u22125 lies on the diameter, halfway between P and Q. Therefore, the following relationships hold: (x sub 1, + 10)/(2 = 6) and (y sub 1, + \u22125)/(2 = \u22125). Solving the equations for x sub 1 and y sub 1, respectively, yields x sub 1 = 2 and y sub 1 = \u22125. Therefore, the coordinates of point Q are 2, \u22125.

Alternate approach: Since point P 10, \u22125 on the circle and the center of the circle 6, \u22125 have the same y-coordinate, it follows that the radius of the circle is 10 \u2212 6 = 4. In addition, the opposite end of the diameter P Q must have the same y-coordinate as P and be 4 units away from the center. Hence, the coordinates of point Q must be 2, \u22125.

Choices B and D are incorrect because the points given in these choices lie on a diameter that is perpendicular to the diameter P Q. If either of these points were point Q, then line segment P Q would not be the diameter of the circle. Choice C is incorrect because the point 6, \u22125 is the center of the circle and does not lie on the circle.

 

\n"}, {"id": "89661424", "domain": "Geometry and Trigonometry", "skill": "Circles", "difficulty": "H", "type": "spr", "stimulus": "", "stem": "

A circle in the xy-plane has its center at -5,2 and has a radius of 9\n. An equation of this circle is x2+y2+ax+by+c=0, where a\n, b\n, and c\n are constants. What is the value of c\n?

", "choices": [], "answerId": "-52", "acceptedAnswers": ["-52"], "rationale": "

The correct answer is -52\n. The equation of a circle in the xy-plane with its center at h,k and a radius of r\n can be written in the form x-h2+y-k2=r2. It's given that a circle in the xy-plane has its center at -5,2 and has a radius of 9\n. Substituting -5\n for h\n, 2\n for k\n, and 9\n for r\n in the equation x-h2+y-k2=r2 yields x--52+y-22=92, or x+52+y-22=81. It's also given that an equation of this circle is x2+y2+ax+by+c=0, where a\n, b\n, and c\n are constants. Therefore, x+52+y-22=81 can be rewritten in the form x2+y2+ax+by+c=0. The equation x+52+y-22=81, or x+5x+5+y-2y-2=81, can be rewritten as x2+5x+5x+25+y2-2y-2y+4=81. Combining like terms on the left-hand side of this equation yields x2+y2+10x-4y+29=81. Subtracting 81\n from both sides of this equation yields x2+y2+10x-4y-52=0, which is equivalent to x2+y2+10x+-4y+-52=0. This equation is in the form x2+y2+ax+by+c=0. Therefore, the value of c\n is -52\n.

"}, {"id": "7c25b0dc", "domain": "Geometry and Trigonometry", "skill": "Right triangles and trigonometry", "difficulty": "H", "type": "spr", "stimulus": "", "stem": "

The length of a rectangle’s diagonal is \n\t3\n\t\n\t\t17\n\t\n\n, and the length of the rectangle’s shorter side is 3\n. What is the length of the rectangle’s longer side?

", "choices": [], "answerId": "12", "acceptedAnswers": ["12"], "rationale": "

The correct answer is 12\n. The diagonal of a rectangle forms a right triangle, where the shorter side and the longer side of the rectangle are the legs of the triangle and the diagonal of the rectangle is the hypotenuse of the triangle. It's given that the length of the rectangle's diagonal is 317 and the length of the rectangle's shorter side is 3\n. Thus, the length of the hypotenuse of the right triangle formed by the diagonal is 317 and the length of one of the legs is 3\n. By the Pythagorean theorem, if a right triangle has a hypotenuse with length c\n and legs with lengths a\n and b\n, then a2+b2=c2. Substituting 317 for c\n and 3\n for b\n in this equation yields a2+32=3172, or a2+9=153. Subtracting 9\n from both sides of this equation yields a2=144. Taking the square root of both sides of this equation yields a=±144, or a=±12. Since a\n represents a length, which must be positive, the value of a\n is 12\n. Thus, the length of the rectangle's longer side is 12\n.

"}, {"id": "e80d62c6", "domain": "Geometry and Trigonometry", "skill": "Circles", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

The equation \n\t\n\t\t\n\t\t\tx\n\t\t\t2\n\t\t\n\t\t+\n\t\t\n\t\t\t\n\t\t\t\t\n\t\t\t\t\ty\n\t\t\t\t\t-\n\t\t\t\t\t2\n\t\t\t\t\n\t\t\t\n\t\t\t2\n\t\t\n\t\n\t=\n\t36\n\n represents circle A. Circle B is obtained by shifting circle A down 4\n units in the xy-plane. Which of the following equations represents circle B?

", "choices": [{"id": "A", "text": "

\n\t\n\t\t\n\t\t\tx\n\t\t\t2\n\t\t\n\t\t+\n\t\t\n\t\t\t\n\t\t\t\t\n\t\t\t\t\ty\n\t\t\t\t\t+\n\t\t\t\t\t2\n\t\t\t\t\n\t\t\t\n\t\t\t2\n\t\t\n\t\n\t=\n\t36\n\n

"}, {"id": "B", "text": "

\n\t\n\t\t\n\t\t\tx\n\t\t\t2\n\t\t\n\t\t+\n\t\t\n\t\t\t\n\t\t\t\t\n\t\t\t\t\ty\n\t\t\t\t\t-\n\t\t\t\t\t6\n\t\t\t\t\n\t\t\t\n\t\t\t2\n\t\t\n\t\n\t=\n\t36\n\n

"}, {"id": "C", "text": "

\n\t\n\t\t\n\t\t\t\n\t\t\t\t\n\t\t\t\t\tx\n\t\t\t\t\t-\n\t\t\t\t\t4\n\t\t\t\t\n\t\t\t\n\t\t\t2\n\t\t\n\t\t+\n\t\t\n\t\t\t\n\t\t\t\t\n\t\t\t\t\ty\n\t\t\t\t\t-\n\t\t\t\t\t2\n\t\t\t\t\n\t\t\t\n\t\t\t2\n\t\t\n\t\n\t=\n\t36\n\n

"}, {"id": "D", "text": "

\n\t\n\t\t\n\t\t\t\n\t\t\t\t\n\t\t\t\t\tx\n\t\t\t\t\t+\n\t\t\t\t\t4\n\t\t\t\t\n\t\t\t\n\t\t\t2\n\t\t\n\t\t+\n\t\t\n\t\t\t\n\t\t\t\t\n\t\t\t\t\ty\n\t\t\t\t\t-\n\t\t\t\t\t2\n\t\t\t\t\n\t\t\t\n\t\t\t2\n\t\t\n\t\n\t=\n\t36\n\n

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. The standard form of an equation of a circle in the xy-plane is x-h2+y-k2=r2, where the coordinates of the center of the circle are h,k and the length of the radius of the circle is r\n. The equation of circle A, x2+y-22=36, can be rewritten as x-02+y-22=62. Therefore, the center of circle A is at 0,2 and the length of the radius of circle A is 6\n. If circle A is shifted down 4\n units, the y-coordinate of its center will decrease by 4\n; the radius of the circle and the x-coordinate of its center will not change. Therefore, the center of circle B is at 0,2-4, or 0,-2, and its radius is 6\n. Substituting 0\n for h\n, -2\n for k\n, and 6\n for r\n in the equation x-h2+y-k2=r2 yields x-02+y--22=62, or x2+y+22=36. Therefore, the equation x2+y+22=36 represents circle B.

\n

Choice B is incorrect. This equation represents a circle obtained by shifting circle A up, rather than down, 4\n units.

\n

Choice C is incorrect. This equation represents a circle obtained by shifting circle A right, rather than down, 4\n units.

\n

Choice D is incorrect. This equation represents a circle obtained by shifting circle A left, rather than down, 4\n units.

"}, {"id": "f243c383", "domain": "Geometry and Trigonometry", "skill": "Area and volume", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

Two identical rectangular prisms each have a height of 90 centimeters cm. The base of each prism is a square, and the surface area of each prism is K cm2. If the prisms are glued together along a square base, the resulting prism has a surface area of 9247K cm2. What is the side length, in cm, of each square base?

", "choices": [{"id": "A", "text": "

4\n

"}, {"id": "B", "text": "

8\n

"}, {"id": "C", "text": "

9\n

"}, {"id": "D", "text": "

16\n

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. Let x\n represent the side length, in cm, of each square base. If the two prisms are glued together along a square base, the resulting prism has a surface area equal to twice the surface area of one of the prisms, minus the area of the two square bases that are being glued together, which yields 2K-2x2 cm2 . It’s given that this resulting surface area is equal to 9247K cm2, so 2K-2x2=9247K. Subtracting 9247K from both sides of this equation yields 2K-9247K-2x2=0. This equation can be rewritten by multiplying \n\t2\n\tK\n\n on the left-hand side by 4747, which yields 9447K-9247K-2x2=0, or 247K-2x2=0. Adding 2x2 to both sides of this equation yields 247K=2x2. Multiplying both sides of this equation by 472 yields K=47x2. The surface area K\n, in cm2, of each rectangular prism is equivalent to the sum of the areas of the two square bases and the areas of the four lateral faces. Since the height of each rectangular prism is 90 cm and the side length of each square base is x cm, it follows that the area of each square base is x2 cm2 and the area of each lateral face is 90x cm2. Therefore, the surface area of each rectangular prism can be represented by the expression 2x2+490x, or 2x2+360x. Substituting this expression for K\n in the equation K=47x2 yields 2x2+360x=47x2. Subtracting 2x2 and \n\t360\n\tx\n\n from both sides of this equation yields 0=45x2-360x. Factoring x\n from the right-hand side of this equation yields 0=x45x-360. Applying the zero product property, it follows that x=0 and 45x-360=0. Adding 360\n to both sides of the equation 45x-360=0 yields 45x=360. Dividing both sides of this equation by 45\n yields x=8. Since a side length of a rectangular prism can’t be 0\n, the length of each square base is 8\n cm.

\n

Choice A is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

\n

Choice D is incorrect and may result from conceptual or calculation errors.

"}, {"id": "95ba2d09", "domain": "Geometry and Trigonometry", "skill": "Circles", "difficulty": "M", "type": "mc", "stimulus": "
\n\t
\"The
\n
\n", "stem": "

In the xy-plane above, points P, Q, R, and T lie on the circle with center O. The degree measures of angles P O Q and R O T are each 30°. What is the radian measure of angle Q O R ?

\n", "choices": [{"id": "A", "text": "

five sixths, pi

\n"}, {"id": "B", "text": "

three fourths, pi

\n"}, {"id": "C", "text": "

two thirds, pi

\n"}, {"id": "D", "text": "

one third, pi

\n"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. Because points T, O, and P all lie on the x-axis, they form a line. Since the angles on a line add up to 180 degrees, and it’s given that angles POQ and ROT each measure 30 degrees, it follows that the measure of angle QOR is 180 degrees \u2212 30 degrees, \u2212 30 degrees = 120 degrees. Since the arc of a complete circle is 360 degrees or 2 pi radians, a proportion can be set up to convert the measure of angle QOR from degrees to radians: (360 degrees)/(2 pi radians = the fraction 120 degrees over x radians), where x is the radian measure of angle QOR. Multiplying each side of the proportion by 2 pi x gives 360 x = 240 pi. Solving for x gives (240)/(360 \u00d7 pi), or two thirds pi.

Choice A is incorrect and may result from subtracting only angle POQ from 180 degreesto get a value of 150 degreesand then finding the radian measure equivalent to that value. Choice B is incorrect and may result from a calculation error. Choice D is incorrect and may result from calculating the sum of the angle measures, in radians, of angles POQ and ROT.

 

\n"}, {"id": "6dd463ca", "domain": "Geometry and Trigonometry", "skill": "Lines, angles, and triangles", "difficulty": "M", "type": "mc", "stimulus": "
\n
\n \"The
\n
\n", "stem": "

In the figure above, segments AE and BD are parallel. If angle BDC measures 58° and angle ACE measures 62°, what is the measure of angle CAE ?

\n", "choices": [{"id": "A", "text": "

58°

\n"}, {"id": "B", "text": "

60°

\n"}, {"id": "C", "text": "

62°

\n"}, {"id": "D", "text": "

120°

\n"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. It’s given that angle ACE measures 62 degrees. Since segments AE and BD are parallel, angles BDC and CEA are congruent. Therefore, angle CEA measures 58 degrees. The sum of the measures of angles ACE, CEA, and CAE is 180 degrees since the sum of the interior angles of triangle ACE is equal to 180 degrees. Let the measure of angle CAE be x degrees. Therefore, 62 + 58, + x = 180, which simplifies to x = 60. Thus, the measure of angle CAE is 60 degrees.

Choice A is incorrect. This is the measure of angle AEC, not that of angle CAE. Choice C is incorrect. This is the measure of angle ACE, not that of CAE. Choice D is incorrect. This is the sum of the measures of angles ACE and CEA.

\n"}, {"id": "0815a5af", "domain": "Geometry and Trigonometry", "skill": "Circles", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

\n

The circle shown has center O\n, circumference 144π, and diameters PR¯ and QS¯. The length of arc \n\tP\n\tS\n\n is twice the length of arc \n\tP\n\tQ\n\n. What is the length of arc \n\tQ\n\tR\n\n?

", "choices": [{"id": "A", "text": "

24π

"}, {"id": "B", "text": "

48π

"}, {"id": "C", "text": "

72π

"}, {"id": "D", "text": "

96π

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. Since PR\u00af and QS\u00af are diameters of the circle shown, OS\u00af, OR\u00af, OP\u00af, and OQ\u00af are radii of the circle and are therefore congruent. Since \u2220SOP and \u2220ROQ are vertical angles, they are congruent. Therefore, arc PS and arc QR are formed by congruent radii and have the same angle measure, so they are congruent arcs. Similarly, \u2220SOR and \u2220POQ are vertical angles, so they are congruent. Therefore, arc SR and arc PQ are formed by congruent radii and have the same angle measure, so they are congruent arcs. Let x\n represent the length of arc SR. Since arc SR and arc PQ are congruent arcs, the length of arc PQ can also be represented by x\n. It’s given that the length of arc PS is twice the length of arc PQ. Therefore, the length of arc PS can be represented by the expression 2x. Since arc PS and arc QR are congruent arcs, the length of arc QR can also be represented by 2x. This gives the expression x+x+2x+2x. Since it's given that the circumference is 144\u03c0, the expression x+x+2x+2x is equal to 144\u03c0. Thus x+x+2x+2x=144\u03c0, or 6x=144\u03c0. Dividing both sides of this equation by 6\n yields x=24\u03c0. Therefore, the length of arc QR is 224\u03c0, or 48\u03c0.

\n

Choice A is incorrect. This is the length of arc PQ, not arc QR.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

\n

Choice D is incorrect and may result from conceptual or calculation errors.

"}, {"id": "93de3f84", "domain": "Geometry and Trigonometry", "skill": "Area and volume", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

The volume of right circular cylinder A is 22 cubic centimeters. What is the volume, in cubic centimeters, of a right circular cylinder with twice the radius and half the height of cylinder A?

\n", "choices": [{"id": "A", "text": "

11

\n"}, {"id": "B", "text": "

22

\n"}, {"id": "C", "text": "

44

\n"}, {"id": "D", "text": "

66

\n"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. The volume of right circular cylinder A is given by the expression pi r\u00b2 \u00d7 h, where r is the radius of its circular base and h is its height. The volume of a cylinder with twice the radius and half the height of cylinder A is given by pi times, open parenthesis, 2 r, close parenthesis, squared, \u00d7 one half h, which is equivalent to 4 pi r\u00b2, times, one half h, and = 2 pi r\u00b2 \u00d7 h. Therefore, the volume is twice the volume of cylinder A, or 2 \u00d7 22 = 44.

Choice A is incorrect and likely results from not multiplying the radius of cylinder A by 2. Choice B is incorrect and likely results from not squaring the 2 in 2r when applying the volume formula. Choice D is incorrect and likely results from a conceptual error.

 

\n"}, {"id": "c9f8d1e9", "domain": "Geometry and Trigonometry", "skill": "Right triangles and trigonometry", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n\n \n \n \n \n \n \n \n \n\n \n\n

\n

For the right triangle shown, a=4 and b=5. Which expression represents the value of c\n?

", "choices": [{"id": "A", "text": "

4+5

"}, {"id": "B", "text": "

45

"}, {"id": "C", "text": "

4+5

"}, {"id": "D", "text": "

42+52

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. By the Pythagorean theorem, if a right triangle has a hypotenuse with length c\n and legs with lengths a\n and b\n, then c2=a2+b2. In the right triangle shown, the hypotenuse has length c\n and the legs have lengths a\n and b\n. It's given that a=4 and b=5. Substituting 4\n for a\n and 5\n for b\n in the Pythagorean theorem yields c2=42+52. Taking the square root of both sides of this equation yields c=\u00b142+52. Since the length of a side of a triangle must be positive, the value of c\n is 42+52.

\n

Choice A is incorrect and may result from conceptual or calculation errors.

\n

Choice B is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

"}, {"id": "f60bb551", "domain": "Geometry and Trigonometry", "skill": "Area and volume", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

The area of a rectangle is 630\n square inches. The length of the rectangle is 70\n inches. What is the width, in inches, of this rectangle?

", "choices": [{"id": "A", "text": "

9\n

"}, {"id": "B", "text": "

70\n

"}, {"id": "C", "text": "

315\n

"}, {"id": "D", "text": "

560\n

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. The area A\n, in square inches, of a rectangle is the product of its length l, in inches, and its width w\n, in inches; thus, A=lw. It's given that the area of a rectangle is 630\n square inches and the length of the rectangle is 70\n inches. Substituting 630\n for A\n and 70\n for l in the equation A=lw yields \n\t630\n\t=\n\t\n\t\t70\n\t\tw\n\t\n\n. Dividing both sides of this equation by 70\n yields \n\t9\n\t=\n\tw\n\n. Therefore, the width, in inches, of this rectangle is 9\n.

\n

Choice B is incorrect. This is the length, not the width, in inches, of the rectangle.

\n

Choice C is incorrect. This is half the area, in square inches, not the width, in inches, of the rectangle.

\n

Choice D is incorrect. This is the difference between the area, in square inches, and the length, in inches, of the rectangle, not the width, in inches, of the rectangle.

"}, {"id": "d2047497", "domain": "Geometry and Trigonometry", "skill": "Area and volume", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

What is the area of a rectangle with a length of 17 centimeters cm and a width of 7 cm?

", "choices": [{"id": "A", "text": "

24\n cm2

"}, {"id": "B", "text": "

48\n cm2

"}, {"id": "C", "text": "

119\n cm2

"}, {"id": "D", "text": "

576\n cm2

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. The area of a rectangle with length l\n and width w\n can be found using the formula A=lw. It’s given that the rectangle has a length of 17 cm and a width of 7 cm. Therefore, the area of this rectangle is A=177, or 119 cm2.

\n

Choice A is incorrect. This is the sum of the length and width of the rectangle, not the area.

\n

Choice B is incorrect. This is the perimeter of the rectangle, not the area.

\n

Choice D is incorrect. This is the sum of the length and width of the rectangle squared, not the area.

"}, {"id": "a5aee181", "domain": "Geometry and Trigonometry", "skill": "Right triangles and trigonometry", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

The length of a rectangle’s diagonal is \n\t5\n\t\n\t\t17\n\t\n\n, and the length of the rectangle’s shorter side is 5\n. What is the length of the rectangle’s longer side?

", "choices": [{"id": "A", "text": "

\n\t17\n\n

"}, {"id": "B", "text": "

20\n

"}, {"id": "C", "text": "

\n\t15\n\t\n\t\t2\n\t\n\n

"}, {"id": "D", "text": "

400\n

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. A rectangle’s diagonal divides a rectangle into two congruent right triangles, where the diagonal is the hypotenuse of both triangles. It’s given that the length of the diagonal is 517 and the length of the rectangle’s shorter side is 5\n. Therefore, each of the two right triangles formed by the rectangle’s diagonal has a hypotenuse with length 517, and a shorter leg with length 5\n. To calculate the length of the longer leg of each right triangle, the Pythagorean theorem, a2+b2=c2, can be used, where a and b are the lengths of the legs and c is the length of the hypotenuse of the triangle. Substituting 5\n for a and 517 for c in the equation a2+b2=c2  yields 52+b2=5172, which is equivalent to 25+b2=2517, or 25+b2=425. Subtracting 25\n from each side of this equation yields b2=400. Taking the positive square root of each side of this equation yields b=20. Therefore, the length of the longer leg of each right triangle formed by the diagonal of the rectangle is 20\n. It follows that the length of the rectangle’s longer side is 20\n.

\n

Choice A is incorrect and may result from dividing the length of the rectangle’s diagonal by the length of the rectangle’s shorter side, rather than substituting these values into the Pythagorean theorem.

\n

Choice C is incorrect and may result from using the length of the rectangle’s diagonal as the length of a leg of the right triangle, rather than the length of the hypotenuse.

\n

Choice D is incorrect. This is the square of the length of the rectangle’s longer side.

"}, {"id": "ae041e52", "domain": "Geometry and Trigonometry", "skill": "Right triangles and trigonometry", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

A square is inscribed in a circle. The radius of the circle is 2022 inches. What is the side length, in inches, of the square?

", "choices": [{"id": "A", "text": "

20\n

"}, {"id": "B", "text": "

2022

"}, {"id": "C", "text": "

202

"}, {"id": "D", "text": "

40\n

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. When a square is inscribed in a circle, a diagonal of the square is a diameter of the circle. It's given that a square is inscribed in a circle and the length of a radius of the circle is 2022 inches. Therefore, the length of a diameter of the circle is 22022 inches, or 202 inches. It follows that the length of a diagonal of the square is 202 inches. A diagonal of a square separates the square into two right triangles in which the legs are the sides of the square and the hypotenuse is a diagonal. Since a square has 4\n congruent sides, each of these two right triangles has congruent legs and a hypotenuse of length 202 inches. Since each of these two right triangles has congruent legs, they are both 45\n-45\n-90\n triangles. In a 45\n-45\n-90\n triangle, the length of the hypotenuse is 2 times the length of a leg. Let s\n represent the length of a leg of one of these 45\n-45\n-90\n triangles. It follows that 202=2s. Dividing both sides of this equation by 2 yields 20=s. Therefore, the length of a leg of one of these 45\n-45\n-90\n triangles is 20\n inches. Since the legs of these two 45\n-45\n-90\n triangles are the sides of the square, it follows that the side length of the square is 20\n inches.

\n

Choice B is incorrect. This is the length of a radius, in inches, of the circle.

\n

Choice C is incorrect. This is the length of a diameter, in inches, of the circle.

\n

Choice D is incorrect and may result from conceptual or calculation errors.

"}, {"id": "c6dff223", "domain": "Geometry and Trigonometry", "skill": "Right triangles and trigonometry", "difficulty": "H", "type": "spr", "stimulus": "", "stem": "

Triangle ABC is similar to triangle DEF, where angle A\n corresponds to angle D\n and angles C\n and F\n are right angles. The length of AB¯ is 2.9\n times the length of DE¯. If tanA=2120, what is the value of sinD?

", "choices": [], "answerId": ".7241", "acceptedAnswers": [".7241", "21/29"], "rationale": "

The correct answer is \n\t21\n\t29\n\n. It's given that triangle \n\tA\n\tB\n\tC\n\n is similar to triangle \n\tD\n\tE\n\tF\n\n, where angle A\n corresponds to angle D\n and angles C\n and F\n are right angles. In similar triangles, the tangents of corresponding angles are equal. Therefore, if tanA=2120, then tanD=2120. In a right triangle, the tangent of an acute angle is the ratio of the length of the leg opposite the angle to the length of the leg adjacent to the angle. Therefore, in triangle \n\tD\n\tE\n\tF\n\n, if tanD=2120, the ratio of the length of EF¯ to the length of DF¯ is \n\t21\n\t20\n\n. If the lengths of EF¯ and DF¯ are 21\n and 20\n, respectively, then the ratio of the length of EF¯ to the length of DF¯ is \n\t21\n\t20\n\n. In a right triangle, the sine of an acute angle is the ratio of the length of the leg opposite the angle to the length of the hypotenuse. Therefore, the value of sinD is the ratio of the length of EF¯ to the length of DE¯. The length of DE¯ can be calculated using the Pythagorean theorem, which states that if the lengths of the legs of a right triangle are a\n and b\n and the length of the hypotenuse is c\n, then \n\t\n\t\t\n\t\t\ta\n\t\t\t2\n\t\t\n\t\t+\n\t\t\n\t\t\tb\n\t\t\t2\n\t\t\n\t\n\t=\n\t\n\t\tc\n\t\t2\n\t\n\n. Therefore, if the lengths of EF¯ and DF¯ are 21\n and 20\n, respectively, then 212+202=DE2, or 841=DE2. Taking the positive square root of both sides of this equation yields 29=DE. Therefore, if the lengths of EF¯ and DF¯ are 21\n and 20\n, respectively, then the length of DE¯ is 29\n and the ratio of the length of EF¯ to the length of DE¯ is \n\t21\n\t29\n\n. Thus, if tanA=2120, the value of sinD is \n\t21\n\t29\n\n. Note that 21/29, .7241, and 0.724 are examples of ways to enter a correct answer.

"}, {"id": "eb70d2d0", "domain": "Geometry and Trigonometry", "skill": "Area and volume", "difficulty": "H", "type": "spr", "stimulus": "", "stem": "

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n

\n

What is the area, in square units, of the triangle formed by connecting the three points shown?

", "choices": [], "answerId": "24.5", "acceptedAnswers": ["24.5", "49/2"], "rationale": "

The correct answer is 24.5. It's given that a triangle is formed by connecting the three points shown, which are -3,4, 5,3, and 4,-3. Let this triangle be triangle A. The area of triangle A can be found by calculating the area of the rectangle that circumscribes it and subtracting the areas of the three triangles that are inside the rectangle but outside triangle A. The rectangle formed by the points -3,4, 5,4, 5,-3, and -3,-3 circumscribes triangle A. The width, in units, of this rectangle can be found by calculating the distance between the points 5,4 and 5,-3. This distance is 4--3, or 7\n. The length, in units, of this rectangle can be found by calculating the distance between the points 5,4 and -3,4. This distance is 5--3, or 8\n. It follows that the area, in square units, of the rectangle is 78, or 56\n. One of the triangles that lies inside the rectangle but outside triangle A is formed by the points -3,4, 5,4, and 5,3. The length, in units, of a base of this triangle can be found by calculating the distance between the points 5,4 and 5,3. This distance is 4-3, or 1\n. The corresponding height, in units, of this triangle can be found by calculating the distance between the points 5,4 and -3,4. This distance is 5--3, or 8\n. It follows that the area, in square units, of this triangle is 1281, or 4\n. A second triangle that lies inside the rectangle but outside triangle A is formed by the points 4,-3, 5,3, and 5,-3. The length, in units, of a base of this triangle can be found by calculating the distance between the points 5,3 and 5,-3. This distance is 3--3 , or 6\n. The corresponding height, in units, of this triangle can be found by calculating the distance between the points 5,-3 and 4,-3. This distance is 5-4, or 1\n. It follows that the area, in square units, of this triangle is 1216, or 3\n. The third triangle that lies inside the rectangle but outside triangle A is formed by the points -3,4, -3,-3, and 4,-3. The length, in units, of a base of this triangle can be found by calculating the distance between the points 4,-3 and -3,-3. This distance is 4--3, or 7\n. The corresponding height, in units, of this triangle can be found by calculating the distance between the points -3,4 and -3,-3. This distance is 4--3, or 7\n. It follows that the area, in square units, of this triangle is 1277, or 24.5. Thus, the area, in square units, of the triangle formed by connecting the three points shown is 56-4-3-24.5, or 24.5. Note that 24.5 and 49/2 are examples of ways to enter a correct answer.

"}, {"id": "f329442c", "domain": "Geometry and Trigonometry", "skill": "Area and volume", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

Circle A\n has a radius of \n\t3\n\tn\n\n and circle B\n has a radius of \n\t129\n\tn\n\n, where n\n is a positive constant. The area of circle B\n is how many times the area of circle A\n?

", "choices": [{"id": "A", "text": "

43\n

"}, {"id": "B", "text": "

86\n

"}, {"id": "C", "text": "

129\n

"}, {"id": "D", "text": "

1,849\n

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. The area of a circle can be found by using the formula A=\u03c0r2, where A\n is the area and r\n is the radius of the circle. It’s given that the radius of circle A is 3n. Substituting this value for r\n into the formula A=\u03c0r2 gives A=\u03c03n2, or 9\u03c0n2. It’s also given that the radius of circle B is 129n. Substituting this value for r\n into the formula A=\u03c0r2 gives A=\u03c0129n2, or 16,641\u03c0n2. Dividing the area of circle B by the area of circle A gives 16,641\u03c0n29\u03c0n2, which simplifies to 1,849\n. Therefore, the area of circle B is 1,849\n times the area of circle A.

\n

Choice A is incorrect. This is how many times greater the radius of circle B is than the radius of circle A.

\n

Choice B is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect. This is the coefficient on the term that describes the radius of circle B.

"}, {"id": "92eb236a", "domain": "Geometry and Trigonometry", "skill": "Right triangles and trigonometry", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

In a right triangle, the tangent of one of the two acute angles is (the square root(3))/(3). What is the tangent of the other acute angle?

\n", "choices": [{"id": "A", "text": "\n the \u2212of (the square root(3))/(3)\n \n"}, {"id": "B", "text": "\n the \u2212of (3)/(the square root(3))\n \n"}, {"id": "C", "text": "\n (the square root(3))/(3)\n \n"}, {"id": "D", "text": "\n (3)/(the square root(3))\n \n"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. The tangent of a nonright angle in a right triangle is defined as the ratio of the length of the leg opposite the angle to the length of the leg adjacent to the angle. Using that definition for tangent, in a right triangle with legs that have lengths a and b, the tangent of one acute angle is (a,)/(b) and the tangent for the other acute angle is (b)/(a). It follows that the tangents of the acute angles in a right triangle are reciprocals of each other. Therefore, the tangent of the other acute angle in the given triangle is the reciprocal of the fraction, the square root(3), end root, over 3, end fraction or the fraction, 3 over the square root(3), end fraction.

Choice A is incorrect and may result from assuming that the tangent of the other acute angle is the negative of the tangent of the angle described. Choice B is incorrect and may result from assuming that the tangent of the other acute angle is the negative of the reciprocal of the tangent of the angle described. Choice C is incorrect and may result from interpreting the tangent of the other acute angle as equal to the tangent of the angle described.

\n"}, {"id": "76670c80", "domain": "Geometry and Trigonometry", "skill": "Area and volume", "difficulty": "E", "type": "spr", "stimulus": "", "stem": "

Each side of a square has a length of 45\n. What is the perimeter of this square?

", "choices": [], "answerId": "180", "acceptedAnswers": ["180"], "rationale": "

The correct answer is 180\n. The perimeter of a polygon is equal to the sum of the lengths of the sides of the polygon. It’s given that each side of the square has a length of 45\n. Since a square is a polygon with 4\n sides, the perimeter of this square is 45+45+45+45, or 180\n.

"}, {"id": "17912810", "domain": "Geometry and Trigonometry", "skill": "Lines, angles, and triangles", "difficulty": "H", "type": "spr", "stimulus": "", "stem": "

\n

In the figure, parallel lines q\n and t\n are intersected by lines r\n and s\n. If \n\ta\n\t=\n\t43\n\n and \n\tb\n\t=\n\t122\n\n, what is the value of w\n?

", "choices": [], "answerId": "101/2", "acceptedAnswers": ["101/2", "50.5"], "rationale": "

The correct answer is \n\t101\n\t2\n\n. In the figure, lines q\n, r\n, and s\n form a triangle. One interior angle of this triangle is vertical to the angle marked a°; therefore, the interior angle also has measure a°. It's given that \n\ta\n\t=\n\t43\n\n. Therefore, the interior angle of the triangle has measure 43°. A second interior angle of the triangle forms a straight line, q\n, with the angle marked b°. Therefore, the sum of the measures of these two angles is 180°. It's given that \n\tb\n\t=\n\t122\n\n. Therefore, the angle marked b° has measure 122° and the second interior angle of the triangle has measure 180-122°, or 58°. The sum of the interior angles of a triangle is 180°. Therefore, the measure of the third interior angle of the triangle is 180-43-58°, or 79°. It's given that parallel lines q\n and t\n are intersected by line r\n. It follows that the triangle's interior angle with measure 79° is congruent to the same side interior angle between lines q\n and t\n formed by lines t\n and r\n. Since this angle is supplementary to the two angles marked w°, the sum of 79°, w°, and w° is 180°. It follows that 79+w+w=180, or 79+2w=180. Subtracting 79\n from both sides of this equation yields 2w=101. Dividing both sides of this equation by 2\n yields \n\tw\n\t=\n\t\n\t\t101\n\t\t2\n\t\n\n. Note that 101/2 and 50.5 are examples of ways to enter a correct answer.

"}, {"id": "4420e500", "domain": "Geometry and Trigonometry", "skill": "Area and volume", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

What is the area of a rectangle with a length of 4 centimeters cm and a width of 2 cm?

", "choices": [{"id": "A", "text": "

6\n cm2

"}, {"id": "B", "text": "

8\n cm2

"}, {"id": "C", "text": "

12\n cm2

"}, {"id": "D", "text": "

36\n cm2

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. The area of a rectangle with length l and width w\n can be found using the formula A=lw. It’s given that the rectangle has a length of 4 cm and a width of 2 cm. Therefore, the area of this rectangle is 4 cm(2 cm), or 8 cm2.

\n

Choice A is incorrect. This is the sum, in cm, of the length and width of the rectangle, not the area, in cm2.

\n

Choice C is incorrect. This is the perimeter, in cm, of the rectangle, not the area, in cm2.

\n

Choice D is incorrect. This is the sum of the length and width of the rectangle squared, not the area.

"}, {"id": "165c30c4", "domain": "Geometry and Trigonometry", "skill": "Area and volume", "difficulty": "E", "type": "spr", "stimulus": "", "stem": "

A rectangle has a length of 64\n inches and a width of 32\n inches. What is the area, in square inches, of the rectangle?

", "choices": [], "answerId": "2048", "acceptedAnswers": ["2048"], "rationale": "

The correct answer is 2,048\n. The area A\n, in square inches, of a rectangle is equal to the product of its length l, in inches, and its width w\n, in inches, or A=lw. It's given that the rectangle has a length of 64\n inches and a width of 32\n inches. Substituting 64\n for l and 32\n for w\n in the equation A=lw yields A=6432, or \n\tA\n\t=\n\t2,048\n\n. Therefore, the area, in square inches, of the rectangle is 2,048\n.

"}, {"id": "2be01bd9", "domain": "Geometry and Trigonometry", "skill": "Right triangles and trigonometry", "difficulty": "H", "type": "spr", "stimulus": "", "stem": "

Triangle \n\tA\n\tB\n\tC\n\n is similar to triangle \n\tD\n\tE\n\tF\n\n, where angle A\n corresponds to angle D\n and angle C\n corresponds to angle F\n.  Angles C\n and F\n are right angles. If \n\t\n\t\ttan\n\t\t\n\t\t\tA\n\t\t\n\t\n\t=\n\t\n\t\t50\n\t\t7\n\t\n\n, what is the value of  \n\ttan\n\t\n\t\tE\n\t\n\n?

", "choices": [], "answerId": ".14", "acceptedAnswers": [".14", "7/50"], "rationale": "

The correct answer is \n\t7\n\t50\n\n. It's given that triangle \n\tA\n\tB\n\tC\n\n is similar to triangle \n\tD\n\tE\n\tF\n\n, where angle A\n corresponds to angle D\n and angle C\n corresponds to angle F\n. In similar triangles, the tangents of corresponding angles are equal. Since angle A\n and angle D\n are corresponding angles, if tanA=507, then tanD=507. It's also given that angles C\n and F\n are right angles. It follows that triangle \n\tD\n\tE\n\tF\n\n is a right triangle with acute angles D\n and E\n. The tangent of one acute angle in a right triangle is the inverse of the tangent of the other acute angle in the triangle. Therefore, tanE=1tanD. Substituting \n\t50\n\t7\n\n for tanD in this equation yields tanE=1507, or tanE=750. Thus, if tanA=507, the value of tanE is \n\t7\n\t50\n\n. Note that 7/50 and .14 are examples of ways to enter a correct answer.

"}, {"id": "3828f53d", "domain": "Geometry and Trigonometry", "skill": "Lines, angles, and triangles", "difficulty": "E", "type": "mc", "stimulus": "
\n
\n \"The
\n
\n", "stem": "

In the figure above, lines m and n are parallel. What is the value of b ?

\n", "choices": [{"id": "A", "text": "

40

\n"}, {"id": "B", "text": "

50

\n"}, {"id": "C", "text": "

65

\n"}, {"id": "D", "text": "

80

\n"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. Given that lines m and n are parallel, the angle marked 130° must be supplementary to the leftmost angle marked a° because they are same-side interior angles. Therefore, 130° + a° = 180°, which yields a = 50°. Lines l and m intersect at a right angle, so lines j, l, and m form a right triangle where the two acute angles are a° and b°. The acute angles of a right triangle are complementary, so a° + b° = 90°, which yields 50° + b° = 90°, and b = 40.

Choice B is incorrect. This is the value of a, not b. Choice C is incorrect and may be the result of dividing 130° by 2. Choice D is incorrect and may be the result of multiplying b by 2.

\n"}, {"id": "acd30391", "domain": "Geometry and Trigonometry", "skill": "Circles", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

A circle in the xy-plane has equation open parenthesis, x + 3, close parenthesis, squared, plus, open parenthesis, y \u2212 1, close parenthesis, squared = 25. Which of the following points does NOT lie in the interior of the circle?

\n", "choices": [{"id": "A", "text": "

\n \u22127, 3\n

\n"}, {"id": "B", "text": "

\n \u22123, 1\n

\n"}, {"id": "C", "text": "

\n zero, zero\n

\n"}, {"id": "D", "text": "

\n 3, 2\n

\n"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. The circle with equation open parenthesis, x + 3, close parenthesis, squared, plus, open parenthesis, y \u2212 1, close parenthesis, squared = 25 has center \u22123, 1 and radius 5. For a point to be inside of the circle, the distance from that point to the center must be less than the radius, 5. The distance between the point 3, 2 and the point \u22123, 1 is the square root of, open parenthesis, \u22123 \u2212 3, close parenthesis, squared, plus, open parenthesis, 1 \u2212 2, close parenthesis, squared, end root = the square root of, open parenthesis, \u22126, close parenthesis, squared, plus, open parenthesis, \u22121, close parenthesis, squared, end root, which = the square root(3)7, which is greater than 5. Therefore, the point 3, 2 does NOT lie in the interior of the circle.

Choice A is incorrect. The distance between the point \u22127, 3 and the point \u22123, 1 is the square root of, open parenthesis, \u22127 + 3, close parenthesis, squared, plus, open parenthesis, 3 \u2212 1, close parenthesis, squared, end root = the square root of, open parenthesis, \u22124, close parenthesis, squared, plus, open parenthesis, 2, close parenthesis, squared, end root, which = the square root(2)0, which is less than 5, and therefore the point \u22127, 3 lies in the interior of the circle. Choice B is incorrect because it is the center of the circle. Choice C is incorrect because the distance between the point 0, 0 and the point \u22123, 1 is the square root of, open parenthesis, 0 + 3, close parenthesis, squared, plus, open parenthesis, 0 \u2212 1, close parenthesis, squared, end root = the square root of, open parenthesis, 3, close parenthesis, squared, + open parenthesis, 1, close parenthesis, squared, end root, which = the square root(8), which is less than 5, and therefore the point 0, 0 in the interior of the circle.

\n"}, {"id": "4ff7b652", "domain": "Geometry and Trigonometry", "skill": "Lines, angles, and triangles", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

Right triangles \n\tL\n\tM\n\tN\n\n and \n\tP\n\tQ\n\tR\n\n are similar, where L\n and M\n correspond to P\n and Q\n, respectively. Angle M\n has a measure of 53\n°. What is the measure of angle Q\n?

", "choices": [{"id": "A", "text": "

37\n°

"}, {"id": "B", "text": "

53\n°

"}, {"id": "C", "text": "

127\n°

"}, {"id": "D", "text": "

143\n°

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. It’s given that triangle \n\tL\n\tM\n\tN\n\n is similar to triangle \n\tP\n\tQ\n\tR\n\n. Corresponding angles of similar triangles are congruent. Since angle M\n and angle Q\n correspond to each other, they must be congruent. Therefore, if the measure of angle M\n is 53\u00b0, then the measure of angle Q\n is also 53\u00b0.

\n

Choice A is incorrect and may result from concluding that angle M\n and angle Q\n are complementary rather than congruent.

\n

Choice C is incorrect and may result from concluding that angle M\n and angle Q\n are supplementary rather than congruent.

\n

Choice D is incorrect and may result from conceptual or calculation errors.

"}, {"id": "8027db3f", "domain": "Geometry and Trigonometry", "skill": "Right triangles and trigonometry", "difficulty": "H", "type": "spr", "stimulus": "", "stem": "

In triangle \n\tJ\n\tK\n\tL\n\n, \n\tcos\n\t\n\t\tK\n\t\n\n=2451 and angle J\n is a right angle. What is the value of \n\tcos\n\t\n\t\tL\n\t\n\n?

", "choices": [], "answerId": ".8823", "acceptedAnswers": [".8823", ".8824", "15/17"], "rationale": "

The correct answer is 1517. It's given that angle J\n is the right angle in triangle JKL. Therefore, the acute angles of triangle JKL are angle K\n and angle L\n. The hypotenuse of a right triangle is the side opposite its right angle. Therefore, the hypotenuse of triangle JKL is side KL. The cosine of an acute angle in a right triangle is the ratio of the length of the side adjacent to the angle to the length of the hypotenuse. It's given that cosK=2451. This can be written as cosK=817. Since the cosine of angle K\n is a ratio, it follows that the length of the side adjacent to angle K\n is \n\t8\n\tn\n\n and the length of the hypotenuse is \n\t17\n\tn\n\n, where n\n is a constant. Therefore, JK=8n and KL=17n. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. For triangle JKL, it follows that JK2+JL2=KL2. Substituting \n\t8\n\tn\n\n for \n\tJ\n\tK\n\n and \n\t17\n\tn\n\n for \n\tK\n\tL\n\n yields 8n2+JL2=17n2. This is equivalent to 64n2+JL2=289n2. Subtracting 64n2 from each side of this equation yields JL2=225n2. Taking the square root of each side of this equation yields JL=15n. Since cosL=JLKL, it follows that cosL=15n17n, which can be rewritten as cosL=1517. Note that 15/17, .8824, .8823, and 0.882 are examples of ways to enter a correct answer.

"}, {"id": "42b4493b", "domain": "Geometry and Trigonometry", "skill": "Lines, angles, and triangles", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

In a right triangle, the measure of one of the acute angles is 51°. What is the measure, in degrees, of the other acute angle?

", "choices": [{"id": "A", "text": "

6\n

"}, {"id": "B", "text": "

39\n

"}, {"id": "C", "text": "

49\n

"}, {"id": "D", "text": "

51\n

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. The sum of the measures of the interior angles of a triangle is 180\n degrees. Since the triangle is a right triangle, it has one angle that measures 90\n degrees. Therefore, the sum of the measures, in degrees, of the remaining two angles is 180-90, or 90\n. It’s given that the measure of one of the acute angles in the triangle is 51\n degrees. Therefore, the measure, in degrees, of the other acute angle is 90-51, or 39\n.

\n

Choice A is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

\n

Choice D is incorrect. This is the measure, in degrees, of the acute angle whose measure is given.

"}, {"id": "d683a9cc", "domain": "Geometry and Trigonometry", "skill": "Area and volume", "difficulty": "E", "type": "mc", "stimulus": "
\n
\n
\n
\n \"The
\n
\n
\n
\n", "stem": "

The figure shows the lengths, in centimeters (cm), of the edges of a right rectangular prism. The volume V of a right rectangular prism is l w h, where l is the length of the prism, w is the width of the prism, and h is the height of the prism. What is the volume, in cubic centimeters, of the prism?

\n", "choices": [{"id": "A", "text": "

36

\n"}, {"id": "B", "text": "

24

\n"}, {"id": "C", "text": "

12

\n"}, {"id": "D", "text": "

11

\n"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is correct. It’s given that the volume of a right rectangular prism is l w h. The prism shown has a length of 6 cm, a width of 2 cm, and a height of 3 cm. Thus, l w h = 6 \u00d7 2, \u00d7 3, or 36 cubic centimeters.

Choice B is incorrect. This is the volume of a rectangular prism with edge lengths of 6, 2, and 2. Choice C is incorrect and may result from only finding the product of the length and width of the base of the prism. Choice D is incorrect and may result from finding the sum, not the product, of the edge lengths of the prism.

\n"}, {"id": "a2e76b60", "domain": "Geometry and Trigonometry", "skill": "Area and volume", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

A cylindrical can containing pieces of fruit is filled to the top with syrup before being sealed. The base of the can has an area of 75 centimeters\u00b2, and the height of the can is 10 cm. If 110 centimeters\u00b3 of syrup is needed to fill the can to the top, which of the following is closest to the total volume of the pieces of fruit in the can?

\n", "choices": [{"id": "A", "text": "

\n \n 7 point 5 centimeters\u00b3

\n"}, {"id": "B", "text": "

\n \n 185 centimeters\u00b3

\n"}, {"id": "C", "text": "640 centimeters\u00b3\n"}, {"id": "D", "text": "750 centimeters\u00b3\n"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. The total volume of the cylindrical can is found by multiplying the area of the base of the can, 75 square centimeters, by the height of the can, 10 cm, which yields 750 cubic centimeters. If the syrup needed to fill the can has a volume of 110 cubic centimeters, then the remaining volume for the pieces of
\nfruit is 750 \u2212 110 = 640 cubic centimeters.

Choice A is incorrect because if the fruit had a volume of 7 point 5 cubic centimeters, there would be 750 \u2212 7 point 5 = 742 point 5 cubic centimeters of syrup needed to fill the can to the top. Choice B is incorrect because if the fruit had a volume of 185 cubic centimeters, there would be 750 \u2212 185 = 565 cubic centimeters of syrup needed to fill the can to the top. Choice D is incorrect because it is the total volume of the can, not just of the pieces of fruit.

\n"}, {"id": "36200a38", "domain": "Geometry and Trigonometry", "skill": "Lines, angles, and triangles", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

\"The

In the figure above, two sides of a triangle are extended. What is the value of x ?

\n", "choices": [{"id": "A", "text": "

110

\n"}, {"id": "B", "text": "

120

\n"}, {"id": "C", "text": "

130

\n"}, {"id": "D", "text": "

140

\n"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. The sum of the interior angles of a triangle is 180°. The measures of the two interior angles of the given triangle are shown. Therefore, the measure of the third interior angle is 180° – 70° – 50° = 60°. The angles of measures x° and 60° are supplementary, so their sum is 180°. Therefore, x = 180 – 60 = 120.

Choice A is incorrect and may be the result of misinterpreting x° as supplementary to 70°. Choice C is incorrect and may be the result of misinterpreting x° as supplementary to 50°. Choice D is incorrect and may be the result of a calculation error.

\n"}, {"id": "306264ab", "domain": "Geometry and Trigonometry", "skill": "Area and volume", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

A right triangle has sides of length \n\t2\n\t\n\t\t2\n\t\n\n, \n\t6\n\t\n\t\t2\n\t\n\n, and 80 units. What is the area of the triangle, in square units?

", "choices": [{"id": "A", "text": "

\n\t8\n\t\n\t\t2\n\t\n\n+80

"}, {"id": "B", "text": "

12\n

"}, {"id": "C", "text": "

24\n80

"}, {"id": "D", "text": "

24\n

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. The area, A\n, of a triangle can be found using the formula A=12bh, where b\n is the length of the base of the triangle and h\n is the height of the triangle. It's given that the triangle is a right triangle. Therefore, its base and height can be represented by the two legs. It’s also given that the triangle has sides of length 22, 62, and 80 units. Since 80 units is the greatest of these lengths, it's the length of the hypotenuse. Therefore, the two legs have lengths 22 and 62 units. Substituting these values for b\n and h\n in the formula A=12bh gives A=122262, which is equivalent to A=64 square units, or \n\tA\n\t=\n\t12\n\n square units.

\n

Choice A is incorrect. This expression represents the perimeter, rather than the area, of the triangle.

\n

Choice C is incorrect and may result from conceptual or calculation errors. 

\n

Choice D is incorrect and may result from conceptual or calculation errors. 

"}, {"id": "37dde49f", "domain": "Geometry and Trigonometry", "skill": "Area and volume", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

\"The

The glass pictured above can hold a maximum volume of 473 cubic centimeters, which is approximately 16 fluid ounces. What is the value of k, in centimeters?

\n", "choices": [{"id": "A", "text": "

  2.52

\n"}, {"id": "B", "text": "

  7.67

\n"}, {"id": "C", "text": "

  7.79

\n"}, {"id": "D", "text": "

10.11

\n"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. Using the volume formula V = (7 pi \u00d7 k\u00b3)/(48) and the given information that the volume of the glass is 473 cubic centimeters, the value of k can be found as follows:

\n 473 = (7 pi \u00d7 k\u00b3)/(48)

\n k\u00b3 = (473 \u00d7 48)/(7 pi, end fraction)

\n k = the cube root of (473 \u00d7 48)/(7 pi, end fraction, end root, which is approximately equal to 10 point 1 0 6 9 0)

Therefore, the value of k is approximately 10.11 centimeters.

Choices A, B, and C are incorrect. Substituting the values of k from these choices in the formula results in volumes of approximately 7 cubic centimeters, 207 cubic centimeters, and 217 cubic centimeters, respectively, all of which contradict the given information that the volume of the glass is 473 cubic centimeters.

\n"}, {"id": "02b02213", "domain": "Geometry and Trigonometry", "skill": "Area and volume", "difficulty": "E", "type": "mc", "stimulus": "", "stem": "

What is the perimeter, in inches, of a rectangle with a length of 4\n inches and a width of 9\n inches?

", "choices": [{"id": "A", "text": "

13\n

"}, {"id": "B", "text": "

17\n

"}, {"id": "C", "text": "

22\n

"}, {"id": "D", "text": "

26\n

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. The perimeter of a figure is equal to the sum of the measurements of the sides of the figure. It’s given that the rectangle has a length of 4\n inches and a width of 9\n inches. Since a rectangle has 4\n sides, of which opposite sides are parallel and equal, it follows that the rectangle has two sides with a length of 4\n inches and two sides with a width of 9\n inches. Therefore, the perimeter of this rectangle is 4+4+9+9, or 26\n inches.

\n

Choice A is incorrect. This is the sum, in inches, of the length and the width of the rectangle.

\n

Choice B is incorrect. This is the sum, in inches, of the two lengths and the width of the rectangle.

\n

Choice C is incorrect. This is the sum, in inches, of the length and the two widths of the rectangle.

"}, {"id": "82c8325f", "domain": "Geometry and Trigonometry", "skill": "Circles", "difficulty": "M", "type": "mc", "stimulus": "", "stem": "

A circle in the xy-plane has its center at -4,5 and the point -8,8 lies on the circle. Which equation represents this circle?

", "choices": [{"id": "A", "text": "

x-42+y+52=5

"}, {"id": "B", "text": "

x+42+y-52=5

"}, {"id": "C", "text": "

x-42+y+52=25

"}, {"id": "D", "text": "

x+42+y-52=25

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. A circle in the xy-plane can be represented by an equation of the form x-h2+y-k2=r2, where h,k is the center of the circle and r\n is the length of a radius of the circle. It's given that the circle has its center at -4,5. Therefore, \n\th\n\t=\n\t-4\n\n and \n\tk\n\t=\n\t5\n\n. Substituting -4\n for h\n and 5\n for k\n in the equation x-h2+y-k2=r2 yields x--42+y-52=r2, or x+42+y-52=r2. It's also given that the point -8,8 lies on the circle. Substituting -8\n for x\n and 8\n for y\n in the equation x+42+y-52=r2 yields -8+42+8-52=r2, or -42+32=r2, which is equivalent to 16+9=r2, or 25=r2. Substituting 25\n for \n\tr\n\t2\n\n in the equation x+42+y-52=r2 yields x+42+y-52=25. Thus, the equation x+42+y-52=25 represents the circle.

\n

Choice A is incorrect. The circle represented by this equation has its center at 4,-5, not -4,5, and the point -8,8 doesn't lie on the circle.

\n

Choice B is incorrect. The point -8,8 doesn't lie on the circle represented by this equation.

\n

Choice C is incorrect. The circle represented by this equation has its center at 4,-5, not -4,5, and the point -8,8 doesn't lie on the circle.

"}, {"id": "459dd6c5", "domain": "Geometry and Trigonometry", "skill": "Area and volume", "difficulty": "H", "type": "spr", "stimulus": "", "stem": "

Triangles ABC and DEF are similar. Each side length of triangle ABC is 4\n times the corresponding side length of triangle DEF. The area of triangle ABC is 270\n square inches. What is the area, in square inches, of triangle DEF?

", "choices": [], "answerId": "135/8", "acceptedAnswers": ["135/8", "16.87", "16.88"], "rationale": "

The correct answer is \n\t135\n\t8\n\n. It's given that triangles ABC and DEF are similar and each side length of triangle ABC is 4\n times the corresponding side length of triangle DEF. For two similar triangles, if each side length of the first triangle is k\n times the corresponding side length of the second triangle, then the area of the first triangle is \n\tk\n\t2\n\n times the area of the second triangle. Therefore, the area of triangle ABC is 42, or 16\n, times the area of triangle DEF. It's given that the area of triangle ABC is 270\n square inches. Let a\n represent the area, in square inches, of triangle DEF. It follows that 270\n is 16\n times a\n, or \n\t270\n\t=\n\t\n\t\t16\n\t\ta\n\t\n\n. Dividing both sides of this equation by 16\n yields 27016=a, which is equivalent to 1358=a. Thus, the area, in square inches, of triangle DEF is \n\t135\n\t8\n\n. Note that 135/8, 16.87, and 16.88 are examples of ways to enter a correct answer.

"}, {"id": "310c87fe", "domain": "Geometry and Trigonometry", "skill": "Area and volume", "difficulty": "H", "type": "mc", "stimulus": "", "stem": "

A cube has a surface area of 54 square meters. What is the volume, in cubic meters, of the cube?

\n", "choices": [{"id": "A", "text": "

18

\n"}, {"id": "B", "text": "

27

\n"}, {"id": "C", "text": "

36

\n"}, {"id": "D", "text": "

81

\n"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is correct. The surface area of a cube with side length s is equal to 6 s\u00b2. Since the surface area is given as 54 square meters, the equation 54 = 6 s\u00b2 can be used to solve for s. Dividing both sides of the equation by 6 yields 9 = s\u00b2. Taking the square root of both sides of this equation yields 3 = s and \u22123 = s. Since the side length of a cube must be a positive value, s = \u22123 can be discarded as a possible solution, leaving s = 3. The volume of a cube with side length s is equal to s\u00b3. Therefore, the volume of this cube, in cubic meters, is 3\u00b3, or 27.

Choices A, C, and D are incorrect and may result from calculation errors.

 

\n"}, {"id": "cf53cb56", "domain": "Geometry and Trigonometry", "skill": "Area and volume", "difficulty": "M", "type": "mc", "stimulus": "
\n
\n \"The
\n
\n", "stem": "

In the xy-plane shown, square ABCD has its diagonals on the x- and y-axes. What is the area, in square units, of the square?

\n", "choices": [{"id": "A", "text": "

20

\n"}, {"id": "B", "text": "

25

\n"}, {"id": "C", "text": "

50

\n"}, {"id": "D", "text": "

100

\n"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is correct. The two diagonals of square ABCD divide the square into 4 congruent right triangles, where each triangle has a vertex at the origin of the graph shown. The formula for the area of a triangle is A = one half \u00d7 b h, where b is the base length of the triangle and h is the height of the triangle. Each of the 4 congruent right triangles has a height of 5 units and a base length of 5 units. Therefore, the area of each triangle is A = one half times, 5 \u00d7 5, or 12.5 square units. Since the 4 right triangles are congruent, the area of each is one fourth of the area of square ABCD. It follows that the area of the square ABCD is equal to 4 \u00d7 12 point 5, or 50 square units.

Choices A and D are incorrect and may result from using 5 or 25, respectively, as the area of one of the 4 congruent right triangles formed by diagonals of square ABCD. However, the area of these triangles is 12.5. Choice B is incorrect and may result from using 5 as the length of one side of square ABCD. However, the length of a side of square ABCD is 5 \u00d7 the square root(2).

\n"}], "rw": [{"id": "f1bfbed3", "domain": "Information and Ideas", "skill": "Inferences", "difficulty": "H", "type": "mc", "stimulus": "

Marta Coll and colleagues’ 2010 Mediterranean Sea biodiversity census reported approximately 17,000 species, nearly double the number reported in Carlo Bianchi and Carla Morri’s 2000 census—a difference only partly attributable to the description of new invertebrate species in the interim. Another factor is that the morphological variability of microorganisms is poorly understood compared to that of vertebrates, invertebrates, plants, and algae, creating uncertainty about how to evaluate microorganisms as species. Researchers’ decisions on such matters therefore can be highly consequential. Indeed, the two censuses reported similar counts of vertebrate, plant, and algal species, suggesting that ______blank

", "stem": "

Which choice most logically completes the text?

", "choices": [{"id": "A", "text": "

Coll and colleagues reported a much higher number of species than Bianchi and Morri did largely due to the inclusion of invertebrate species that had not been described at the time of Bianchi and Morri’s census.

"}, {"id": "B", "text": "

some differences observed in microorganisms may have been treated as variations within species by Bianchi and Morri but treated as indicative of distinct species by Coll and colleagues.

"}, {"id": "C", "text": "

Bianchi and Morri may have been less sensitive to the degree of morphological variation displayed within a typical species of microorganism than Coll and colleagues were.

"}, {"id": "D", "text": "

the absence of clarity regarding how to differentiate among species of microorganisms may have resulted in Coll and colleagues underestimating the number of microorganism species.

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer because it presents the conclusion that most logically completes the text’s discussion of the different counts of species in the Mediterranean Sea. The text states that Coll and colleagues reported almost double the number of species that Bianchi and Morri reported in their study ten years earlier. According to the text, this difference can only be partly attributed to new invertebrate species being described in the years between the two studies, which means there must be an additional factor that made Coll and colleagues’ count so much higher than Bianchi and Morri’s count. The text goes on to explain that factor: researchers have a relatively poor understanding of microorganisms’ morphological variability, or the differences in microorganisms’ structure and form. This poor understanding makes it hard to classify microorganisms by species and means that researchers’ decisions about classifying microorganisms can have a large effect on the overall species counts that researchers report. Additionally, the text says that the two censuses reported similar numbers of vertebrate, plant, and algal species, which means that the difference in overall species did not come from differences in those categories. Given all this information, it most logically follows that Coll and colleagues may have treated some of the differences among microorganisms as indicative of the microorganisms being different species, whereas Bianchi and Morri treated those differences as variations within species, resulting in Coll and colleagues reporting many more species than Bianchi and Morri did.

Choice A is incorrect because the text explicitly addresses this issue by stating that the description of new invertebrate species in the years between the two studies can explain only part of the difference in the number of species reported by the studies. The focus of the text is on explaining the difference between Coll and colleagues’ count and Bianchi and Morri’s count that cannot be accounted for by the inclusion of invertebrate species that had not been described at the time of Bianchi and Morri’s study. Choice C is incorrect because nothing in the text suggests that Bianchi and Morri may have been less sensitive to how much the form and structure of microorganisms vary within the same species than Coll and colleagues were. If Bianchi and Morri had been less sensitive to within-species variation than Coll and colleagues were, Bianchi and Morri would likely have reported more species than Coll and colleagues did, since less sensitivity to within-species variation would lead researchers to classify as different species microorganisms that more sensitive researchers would classify as variations within the same species. The text indicates, however, that Bianchi and Morri reported far fewer species than Coll and colleagues did; since the text also excludes other explanations for this difference, it suggests that in fact Bianchi and Morri were more sensitive to within-species variation than Coll and colleagues were, leading Bianchi and Morri to report fewer overall species. Choice D is incorrect because the text is focused on explaining why Coll and colleagues reported many more species than Bianchi and Morri did, and an underestimate of the number of microorganism species by Coll and colleagues would not explain that difference—it would suggest, in fact, that the difference in the number of species should have been even larger. 

"}, {"id": "87aa7bab", "domain": "Information and Ideas", "skill": "Central Ideas and Details", "difficulty": "M", "type": "mc", "stimulus": "

A common assumption among art historians is that the invention of photography in the mid-nineteenth century displaced the painted portrait in the public consciousness. The diminishing popularity of the portrait miniature, which coincided with the rise of photography, seems to support this claim. However, photography’s impact on the portrait miniature may be overstated. Although records from art exhibitions in the Netherlands from 1820 to 1892 show a decrease in the number of both full-sized and miniature portraits submitted, this trend was established before the invention of photography.

", "stem": "

Based on the text, what can be concluded about the diminishing popularity of the portrait miniature in the nineteenth century?  

", "choices": [{"id": "A", "text": "

Factors other than the rise of photography may be more directly responsible for the portrait miniature’s decline.

"}, {"id": "B", "text": "

Although portrait miniatures became less common than photographs, they were widely regarded as having more artistic merit.     

"}, {"id": "C", "text": "

The popularity of the portrait miniature likely persisted for longer than art historians have assumed. 

"}, {"id": "D", "text": "

As demand for portrait miniatures decreased, portrait artists likely shifted their creative focus to photography. 

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. The text says that the impact of photography on the portrait miniature might be \"overstated,\" as some records show a decrease in the number of portrait miniatures before the invention of photography. From this, we can conclude that factors other than the rise of photography may be more directly responsible for the portrait miniature’s decline.

Choice B is incorrect. The text never discusses the \"artistic merit\" of either art form. Choice C is incorrect. The text never suggests that the portrait miniature was popular for longer than historians thought—if anything, it suggests that the portrait miniature started losing its popularity earlier than historians thought. Choice D is incorrect. The text never suggests that portrait painters shifted to become photographers.

"}, {"id": "d73a908a", "domain": "Information and Ideas", "skill": "Central Ideas and Details", "difficulty": "M", "type": "mc", "stimulus": "

Believing that living in an impractical space can heighten awareness and even improve health, conceptual artists Madeline Gins and Shusaku Arakawa designed an apartment building in Japan to be more fanciful than functional. A kitchen counter is chest-high on one side and knee-high on the other; a ceiling has a door to nowhere. The effect is disorienting but invigorating: after four years there, filmmaker Nobu Yamaoka reported significant health benefits.

", "stem": "

Which choice best states the main idea of the text?

", "choices": [{"id": "A", "text": "

Although inhabiting a home surrounded by fanciful features such as those designed by Gins and Arakawa can be rejuvenating, it is unsustainable.

"}, {"id": "B", "text": "

Designing disorienting spaces like those in the Gins and Arakawa building is the most effective way to create a physically stimulating environment. 

"}, {"id": "C", "text": "

As a filmmaker, Yamaoka has long supported the designs of conceptual artists such as Gins and Arakawa.

"}, {"id": "D", "text": "

Although impractical, the design of the apartment building by Gins and Arakawa may improve the well-being of the building’s residents. 

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer because it most accurately states the main idea of the text. According to the text, conceptual artists Gins and Arakawa have designed an apartment building that is disorienting because of several unconventional elements, such as uneven kitchen counters and “a door to nowhere.” The text goes on to suggest that there may be benefits to this kind of design because filmmaker Yamaoka lived in the apartment building for four years and reported health benefits. Thus, although the design is impractical, it may improve the well-being of the apartment building’s residents. 

Choice A is incorrect. Although the text mentions that Yamaoka lived in the apartment for four years, it doesn’t address how long someone can beneficially live in a home surrounded by fanciful features or whether doing so can be sustained. Choice B is incorrect. Although the text mentions the potential benefits of living in a home with disorienting design features, it doesn’t suggest that this is the most effective method to create a physically stimulating environment. Choice C is incorrect because the text refers to Yamaoka to support the claim that Gins and Arakawa’s apartment building design may be beneficial, but the text doesn’t indicate that Yamaoka supports the designs of other conceptual artists. 

"}, {"id": "d748c3fd", "domain": "Information and Ideas", "skill": "Inferences", "difficulty": "M", "type": "mc", "stimulus": "

In her 2021 article “Throwaway History: Towards a Historiography of Ephemera,” scholar Anne Garner discusses John Johnson (1882–1956), a devoted collector of items intended to be discarded, including bus tickets and campaign pamphlets. Johnson recognized that scholarly institutions considered his expansive collection of ephemera to be worthless—indeed, it wasn’t until 1968, after Johnson’s death, that Oxford University’s Bodleian Library acquired the collection, having grasped the items’ potential value to historians and other researchers. Hence, the example of Johnson serves to ______blank

", "stem": "

Which choice most logically completes the text?

", "choices": [{"id": "A", "text": "

demonstrate the difficulties faced by contemporary historians in conducting research at the Bodleian Library without access to ephemera.

"}, {"id": "B", "text": "

represent the challenge of incorporating examples of ephemera into the collections of libraries and other scholarly institutions.

"}, {"id": "C", "text": "

lend support to arguments by historians and other researchers who continue to assert that ephemera holds no value for scholars.

"}, {"id": "D", "text": "

illustrate both the relatively low scholarly regard in which ephemera was once held and the later recognition of ephemera’s possible utility.

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. Johnson collected “ephemera,” or things that are meant to be thrown away. Scholars thought his collection was worthless to them, then later realized that it was potentially valuable. This suggests that scholars went from disregarding ephemera to recognizing their usefulness.

Choice A is incorrect. This inference isn’t supported. The text tells us that the Bodleian Library acquired Johnson’s large collection of ephemera back in 1968, so we can assume that contemporary historians conducting research there do have access to that collection. Choice B is incorrect. This inference isn’t supported. The text tells us that “Oxford University’s Bodleian Library acquired the collection,” but it never suggests that it was a challenge to do so. Choice C is incorrect. This inference isn’t supported. The text actually suggests the opposite: the example of Johnson’s collection lends support to arguments that ephemera does hold value for scholars.

"}, {"id": "a15b3219", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "H", "type": "mc", "stimulus": "
\n\n\n\n\n1,3001,2001,1001,0009008007006005004003002001000Number of municipalitiesno responseresponded to inquiryoffered incentiveMunicipalities\u2019 Responses to Inquiries about Potential Incentives for Firm announcement before election announcement after election
\n

In the United States, firms often seek incentives from municipal governments to expand to those municipalities. A team of political scientists hypothesized that municipalities are much more likely to respond to firms and offer incentives if expansions can be announced in time to benefit local elected officials than if they can\u2019t. The team contacted officials in thousands of municipalities, inquiring about incentives for a firm looking to expand and indicating that the firm would announce its expansion on a date either just before or just after the next election.\u00a0

", "stem": "

Which choice best describes data from the graph that weaken the team’s hypothesis?

", "choices": [{"id": "A", "text": "

A large majority of the municipalities that received an inquiry mentioning plans for an announcement before the next election didn’t respond to the inquiry.

"}, {"id": "B", "text": "

The proportion of municipalities that responded to the inquiry or offered incentives didn’t substantially differ across the announcement timing conditions. 

"}, {"id": "C", "text": "

Only around half the municipalities that responded to inquiries mentioning plans for an announcement before the next election offered incentives. 

"}, {"id": "D", "text": "

Of the municipalities that received an inquiry mentioning plans for an announcement date after the next election, more than 1,200 didn’t respond and only around 100 offered incentives.

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. The lighter bars show what happened when the announcement was to come before the election, and the darker bars show what happened when the announcement was to come after the election. For all three of the outcomes, the light and dark bars are virtually the same, demonstrating that the announcement timing didn’t actually make a difference.

Choice A is incorrect. This accurately describes some data from the graph, but it doesn’t weaken the hypothesis. It doesn’t include the “announcement after election” data for comparison. Choice C is incorrect. This accurately describes some data from the graph, but it doesn’t weaken the hypothesis. It doesn’t include the “announcement after election” data for comparison. Choice D is incorrect. This accurately describes some data from the graph, but it doesn’t weaken the hypothesis. It doesn’t include the “announcement before election” data for comparison.

"}, {"id": "ed314256", "domain": "Information and Ideas", "skill": "Central Ideas and Details", "difficulty": "H", "type": "mc", "stimulus": "

The most recent iteration of the immersive theater experience Sleep No More, which premiered in New York City in 2011, transforms its performance space—a five-story warehouse—into a 1930s-era hotel. Audience members, who wander through the labyrinthine venue at their own pace and follow the actors as they play out simultaneous, interweaving narrative loops, confront the impossibility of experiencing the production in its entirety. The play’s refusal of narrative coherence thus hinges on the sense of spatial fragmentation that the venue’s immense and intricate layout generates.

", "stem": "

What does the text most strongly suggest about Sleep No More’s use of its performance space? 

", "choices": [{"id": "A", "text": "

The choice of a New York City venue likely enabled the play’s creators to experiment with the use of theatrical space in a way that venues from earlier productions could not. 

"}, {"id": "B", "text": "

Audience members likely find the experience of the play disappointing because they generally cannot make their way through the entire venue.

"}, {"id": "C", "text": "

The production’s dependence on a particular performance environment would likely make it difficult to reproduce exactly in a different theatrical space. 

"}, {"id": "D", "text": "

Audience members who navigate the space according to a recommended itinerary will likely have a better grasp of the play’s narrative than audience members who depart from that itinerary.

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. The text says that the production’s use of its large, winding space has a very specific effect on the audience. Given that the space itself is so important to creating this effect, it would be difficult to reproduce the production in a different space.

Choice A is incorrect. The fact that the venue is in New York City isn’t connected to the experimental nature of the performance. It’s the size of the venue, not its location in New York, that affects the theatrical experience. Choice B is incorrect. The text never suggests that audience members are disappointed because they can’t see the entire production. In fact, it suggests that that’s an important part of the experience. Choice D is incorrect. The text doesn’t mention a recommended itinerary for audience members.

"}, {"id": "92c2564d", "domain": "Information and Ideas", "skill": "Central Ideas and Details", "difficulty": "M", "type": "mc", "stimulus": "

Utah is home to Pando, a colony of about 47,000 quaking aspen trees that all share a single root system. Pando is one of the largest single organisms by mass on Earth, but ecologists are worried that its growth is declining in part because of grazing by animals. The ecologists say that strong fences could prevent deer from eating young trees and help Pando start thriving again.

", "stem": "

According to the text, why are ecologists worried about Pando?

", "choices": [{"id": "A", "text": "

It isn’t growing at the same rate it used to.

"}, {"id": "B", "text": "

It isn’t producing young trees anymore.

"}, {"id": "C", "text": "

It can’t grow into new areas because it is blocked by fences.

"}, {"id": "D", "text": "

Its root system can’t support many more new trees.

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer because it presents an explanation that is directly stated in the text for why ecologists are worried about Pando. The text states that Pando is a colony of about 47,000 quaking aspen trees that represents one of the largest organisms on Earth. According to the text, ecologists are worried that Pando’s growth is declining, partly because animals are feeding on the trees. In other words, the ecologists are worried that Pando isn’t growing at the same rate it used to.

Choice B is incorrect. Rather than indicating that Pando isn’t producing young trees anymore, the text reveals that Pando is indeed producing young trees, stating that those trees can be protected from grazing deer by strong fences. Choice C is incorrect because the text states that fences can be used to prevent deer from eating Pando’s young trees, not that Pando itself can’t grow in new areas because it’s blocked by fences. Choice D is incorrect because the text offers no evidence that Pando’s root system is incapable of supporting new trees or is otherwise a cause of worry for ecologists.

"}, {"id": "22e4d633", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "M", "type": "mc", "stimulus": "

Although many transposons, DNA sequences that move within an organism’s genome through shuffling or duplication, have become corrupted and inactive over time, those from the long interspersed nuclear elements (LINE) family appear to remain active in the genomes of some species. In humans, they are functionally important within the hippocampus, a brain structure that supports complex cognitive processes. When the results of molecular analysis of two species of octopus—an animal known for its intelligence—were announced in 2022, the confirmation of a LINE transposon in Octopus vulgaris and Octopus bimaculoides genomes prompted researchers to hypothesize that that transposon family is tied to a species’ capacity for advanced cognition.

", "stem": "

Which finding, if true, would most directly support the researchers’ hypothesis?

", "choices": [{"id": "A", "text": "

The LINE transposon in O. vulgaris and O. bimaculoides genomes is active in an octopus brain structure that functions similarly to the human hippocampus.

"}, {"id": "B", "text": "

The human genome contains multiple transposons from the LINE family that are all primarily active in the hippocampus.

"}, {"id": "C", "text": "

A consistent number of copies of LINE transposons is present across the genomes of most octopus species, with few known corruptions.

"}, {"id": "D", "text": "

O. vulgaris and O. bimaculoides have smaller brains than humans do relative to body size, but their genomes contain sequences from a wider variety of transposon families.

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. The text says that LINE transposons are important in the human hippocampus, which supports complex cognition. If the LINE transposon found in octopuses is active in a similar part of their brain, that would suggest that LINE transposons support complex cognition in octopuses too, which in turn supports the hypothesis that LINE transposons are linked to advanced cognition in general.

Choice B is incorrect. This choice doesn’t support the hypothesis. It doesn’t include anything about how LINE transposons function in species other than humans. Choice C is incorrect. This choice doesn’t support the hypothesis. It doesn’t include anything about how the LINE transposon in octopuses might support advanced cognition. Choice D is incorrect. This choice doesn’t support the hypothesis. It doesn’t include anything about how the LINE transposon in octopuses might support advanced cognition.

"}, {"id": "3543e6e2", "domain": "Information and Ideas", "skill": "Central Ideas and Details", "difficulty": "E", "type": "mc", "stimulus": "

The following text is from Jane Austen’s 1811 novel Sense and Sensibility. Elinor lives with her younger sisters and her mother, Mrs. Dashwood.

\n

Elinor, this eldest daughter, whose advice was so effectual, possessed a strength of understanding, and coolness of judgment, which qualified her, though only nineteen, to be the counsellor of her mother, and enabled her frequently to counteract, to the advantage of them all, that eagerness of mind in Mrs. Dashwood which must generally have led to imprudence. She had an excellent heart;—her disposition was affectionate, and her feelings were strong; but she knew how to govern them: it was a knowledge which her mother had yet to learn; and which one of her sisters had resolved never to be taught.

", "stem": "

According to the text, what is true about Elinor?

", "choices": [{"id": "A", "text": "

Elinor often argues with her mother but fails to change her mind.

"}, {"id": "B", "text": "

Elinor can be overly sensitive with regard to family matters.

"}, {"id": "C", "text": "

Elinor thinks her mother is a bad role model.

"}, {"id": "D", "text": "

Elinor is remarkably mature for her age.

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer because it provides a detail about Elinor that is established in the text. The text indicates that although Elinor is “only nineteen,” she gives good advice and exhibits such a high level of understanding and judgment that she serves as “the counsellor of her mother.” Thus, Elinor is mature beyond her years.   

Choice A is incorrect because it isn’t supported by the text: although the text says that Elinor advises her mother and often counteracts her mother’s impulses, there’s no mention of Elinor arguing with her mother or failing to change her mother’s mind. Choice B is incorrect because it isn’t supported by the text: although the text mentions that Elinor has strong feelings, it doesn’t indicate that she’s excessively sensitive when it comes to family issues. Choice C is incorrect because it isn’t supported by the text: there’s no mention of what Elinor thinks about her mother and no suggestion that she thinks her mother is a bad role model. Because she’s described as having “an excellent heart,” Elinor likely doesn’t think ill of her mother.

"}, {"id": "75e07a4d", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "E", "type": "mc", "stimulus": "

Sample of Food Items from Gemini Mission Menus

Food itemDayMeal
Sugar cookie cubes1B
Chicken and vegetables2B
Shrimp cocktail4C
Hot cocoa3A

\n

To make sure they got the nutrition they needed while in space, the astronauts of NASA’s Gemini missions were given menus for three meals a day (meals A, B, and C) on a four-day rotating schedule. Looking at the sample of food items from these menus, a student notes that on day 1, the menu included ______blank

", "stem": "

Which choice most effectively uses data from the table to complete the statement?

", "choices": [{"id": "A", "text": "

shrimp cocktail for meal B.

"}, {"id": "B", "text": "

hot cocoa for meal C.

"}, {"id": "C", "text": "

sugar cookie cubes for meal B.

"}, {"id": "D", "text": "

chicken and vegetables for meal A.

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer because it most effectively uses data from the table to complete the statement. The table shows that on day 1, the menu for NASA’s Gemini missions included sugar cookie cubes for meal B.

Choice A is incorrect because according to the table, shrimp cocktail was served on day 4, not day 1; moreover, the item was served for meal C, not meal B, as this choice claims. Choice B is incorrect because according to the table, hot cocoa was served on day 3, not on day 1; moreover, the item was served for meal A, not for meal C, as this choice claims. Choice D is incorrect because according to the table, chicken and vegetables were served on day 2, not on day 1; moreover, the item was served for meal B, not for meal A, as this choice claims.

"}, {"id": "602b47c7", "domain": "Information and Ideas", "skill": "Central Ideas and Details", "difficulty": "M", "type": "mc", "stimulus": "

Biologists have predicted that birds’ feather structures vary with habitat temperature, but this hadn’t been tested in mountain environments. Ornithologist Sahas Barve studied feathers from 249 songbird species inhabiting different elevations—and thus experiencing different temperatures—in the Himalaya Mountains. He found that feathers of high-elevation species not only have a greater proportion of warming downy sections to flat and smooth sections than do feathers of low-elevation species, but high-elevation species’ feathers also tend to be longer, providing a thicker layer of insulation.

", "stem": "

Which choice best states the main idea of the text?

", "choices": [{"id": "A", "text": "

Barve’s investigation shows that some species of Himalayan songbirds have evolved feathers that better regulate body temperature than do the feathers of other species, contradicting previous predictions.

"}, {"id": "B", "text": "

Barve found an association between habitat temperature and feather structure among Himalayan songbirds, lending new support to a general prediction.

"}, {"id": "C", "text": "

Barve discovered that songbirds have adapted to their environment by growing feathers without flat and smooth sections, complicating an earlier hypothesis.

"}, {"id": "D", "text": "

The results of Barve’s study suggest that the ability of birds to withstand cold temperatures is determined more strongly by feather length than feather structure, challenging an established belief.

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. The text describes how Barve found an association between habitat temperature and feather structure among Himalayan songbirds, which supports the general prediction that birds’ feather structures vary with habitat temperature.

Choice A is incorrect. Barve’s study isn’t said to contradict previous predictions. In fact, the study supports the prediction described in the first sentence, which is that birds’ feather structures vary with habitat temperature. Choice C is incorrect. Barve’s study isn’t said to “complicate an earlier hypothesis.” In fact, the study supports the earlier prediction described in the first sentence, which is that birds’ feather structures vary with habitat temperature. Choice D is incorrect. The text doesn’t compare the importance of feather length and feather structure, and it doesn’t say that Barve’s study challenges any established beliefs. In fact, the study supports the prediction described in the first sentence, which is that birds’ feather structures vary with habitat temperature.

"}, {"id": "702eb7e3", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "H", "type": "mc", "stimulus": "
\n\n\n\n\n200150100500Uncertainty(larger values = more uncertainty)\u2002\u20022005\u2002\u20022006\u2002\u20022007\u2002\u20022008\u2002\u20022009\u2002\u20022010Economic Policy Uncertainty in the United Kingdom, 2005\u20132010Year tax and public spending policy trade policy general economic policy
\n

High levels of public uncertainty about which economic policies a country will adopt can make planning difficult for businesses, but measures of such uncertainty have not tended to be very detailed. Recently, however, economist Sandile Hlatshwayo analyzed trends in news reports to derive measures not only for general economic policy uncertainty but also for uncertainty related to specific areas of economic policy, like tax or trade policy. One revelation of her work is that a general measure may not fully reflect uncertainty about specific areas of policy, as in the case of the United Kingdom, where general economic policy uncertainty ______blank

", "stem": "

Which choice most effectively uses data from the graph to illustrate the claim?

", "choices": [{"id": "A", "text": "

aligned closely with uncertainty about tax and public spending policy in 2005 but differed from uncertainty about tax and public spending policy by a large amount in 2009.

"}, {"id": "B", "text": "

was substantially lower than uncertainty about tax and public spending policy each year from 2005 to 2010.

"}, {"id": "C", "text": "

reached its highest level between 2005 and 2010 in the same year that uncertainty about trade policy and tax and public spending policy reached their lowest levels.

"}, {"id": "D", "text": "

was substantially lower than uncertainty about trade policy in 2005 and substantially higher than uncertainty about trade policy in 2010.

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer because it uses data from the graph to effectively illustrate the text’s claim about general economic policy uncertainty in the United Kingdom. The graph presents values for economic policy uncertainty in tax and public spending policy, trade policy, and general economic policy in the UK from 2005 to 2010. The graph shows that in 2005, the value for general economic policy uncertainty (approximately 90) was substantially lower than the value for uncertainty about trade policy specifically (approximately 160). It also shows that in 2010, the value for general economic policy uncertainty (approximately 120) was substantially higher than the value for uncertainty about trade policy (approximately 70). The substantial differences between these values in 2005 and 2010 support the claim that a general measure may not fully reflect uncertainty about specific areas of policy.

Choice A is incorrect because the graph shows that the level of general economic policy uncertainty was similar to the level of uncertainty about tax and public spending policy in both 2005 (with values of approximately 90 and 100, respectively) and 2009 (with values of approximately 80 and 75, respectively). Choice B is incorrect because the graph shows that general economic policy uncertainty was higher than uncertainty about tax and public spending policy in 2006, 2007, and 2009, not that it was lower each year from 2005 to 2010. Choice C is incorrect because the graph shows that general economic policy uncertainty reached its highest level in 2010, which was when uncertainty about tax and public spending policy also reached its highest level, not its lowest level.

"}, {"id": "d83c3d54", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "M", "type": "mc", "stimulus": "
\n\n\n\n\n140,000120,000100,00080,00060,00040,00020,0000Area (square meters)198719932006Characteristics of the Banks of the Provo River Downstream of the Jordanelle DamYear grass cover bare soil forest cover
\n

The Jordanelle Dam was built on the Provo River in Utah in 1992. Earth scientist Adriana E. Martinez and colleagues tracked changes to the environment on the banks of the river downstream of the dam, including how much grass and forest cover were present. They concluded that the dam changed the flow of the river in ways that benefited grass plants but didn\u2019t benefit trees.

", "stem": "

Which choice best describes data from the graph that support Martinez and colleagues’ conclusion?

", "choices": [{"id": "A", "text": "

The lowest amount of grass cover was approximately 58,000 square meters, and the highest amount of forest cover was approximately 75,000 square meters.

"}, {"id": "B", "text": "

There was more grass cover than forest cover in 1987, and this difference increased dramatically in 1993 and again in 2006.

"}, {"id": "C", "text": "

There was less grass cover than bare soil in 1987 but more grass cover than bare soil in 1993 and 2006, whereas there was more forest cover than bare soil in all three years.

"}, {"id": "D", "text": "

Grass cover increased from 1987 to 1993 and from 1993 to 2006, whereas forest cover decreased in those periods.

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer because it describes data from the graph that support Martinez and colleagues’ conclusion that the Jordanelle Dam led to changes that benefited grass plants but not trees. The graph shows characteristics of the banks of the Provo River downstream of the Jordanelle Dam in three different years—1987, 1993, and 2006. Specifically, the graph shows the amount of grass cover, bare soil, and forest cover in those years. The text indicates that the Jordanelle Dam was built in 1992, meaning that the data from the graph for 1987 reflect conditions before the dam was built, whereas the data for 1993 and 2006 reflect conditions after the dam was built. The data show that grass cover increased substantially from 1987 to 1993 and again from 1993 to 2006. The data also show that forest cover declined over those periods. Together, these data support Martinez and colleagues’ conclusion that the dam was beneficial for grass plants but not for trees—grass cover increased significantly after the dam was built, while forest cover declined. 

Choice A is incorrect. Although it is true that, in the graph, the lowest value for grass cover is approximately 58,000 square meters and the highest value for forest cover is approximately 75,000 square meters, both values are from 1987, before the Jordanelle Dam was built in 1992. Therefore, this information alone cannot support Martinez and colleagues’ conclusion about changes in grass and tree cover following the construction of the dam. Choice B is incorrect because it presents an inaccurate description of data from the graph. The graph shows that there was more forest cover than grass cover in 1987, not that there was more grass cover than forest cover that year. Choice C is incorrect because, while it accurately reflects data from the graph when it compares grass cover and forest cover to bare soil, these data alone cannot support Martinez and colleagues’ conclusion that the dam led to changes that benefited grass plants but not trees. An increase in grass cover relative to bare soil following the construction of the dam might indicate that the dam benefited grass plants, but the fact that there was more forest cover than bare soil in all three years doesn’t indicate that the dam failed to benefit trees. 

"}, {"id": "403fb4e4", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "H", "type": "mc", "stimulus": "
\n\n\n\n\n605550454035302520151050Female farmersas a percentage of totalnorth Ondocentral Ondosouth OndoPercentage of Ondo State Small-Scale Farmers Who Are Female, by Main Crop GrownOndo State region cereals root crops non\u2013root vegetables
\n

Geographer Adebayo Oluwole Eludoyin and his colleagues surveyed small-scale farmers in three locations in Ondo State, Nigeria\u2014which has mountainous terrain in the north, an urbanized center, and coastal terrain in the south\u2014to learn more about their practices, like the types of crops they mainly cultivated. In some regions, female farmers were found to be especially prominent in the cultivation of specific types of crops and even constituted the majority of farmers who cultivated those crops; for instance, ______blank

", "stem": "

Which choice most effectively uses data from the graph to complete the example?

", "choices": [{"id": "A", "text": "

most of the farmers who mainly cultivated cereals and most of the farmers who mainly cultivated non–root vegetables in south Ondo were women. 

"}, {"id": "B", "text": "

more women in central Ondo mainly cultivated root crops than mainly cultivated cereals.

"}, {"id": "C", "text": "

most of the farmers who mainly cultivated non–root vegetables in north and south Ondo were women.  

"}, {"id": "D", "text": "

a relatively equal proportion of women across the three regions of Ondo mainly cultivated cereals. 

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer because it uses data from the graph to effectively complete the example of Eludoyin and his colleagues’ findings concerning female farmers in some regions of Ondo State, Nigeria. The graph presents values for the percentage of Ondo State small-scale farmers who are female, by type of crop and region. The graph shows that of the farmers mainly cultivating non-root vegetables, approximately 57% in north Ondo and approximately 54% in south Ondo are female; in other words, most of those farmers are female, which exemplifies the idea that female farmers make up the majority (more than half) of the farmers cultivating specific types of crops in some regions.

Choice A is incorrect because it inaccurately cites data from the graph: the graph shows that in south Ondo, most of the farmers mainly cultivating non-root vegetables are women (approximately 54%), but that only about 35% (less than half) of the farmers mainly cultivating cereals are women. Choice B is incorrect because it inaccurately cites data from the graph: the graph shows that more women in central Ondo mainly cultivate cereals than mainly cultivate root crops (approximately 36% and 20%, respectively). Additionally, it doesn’t effectively complete the example because the graph shows that female farmers don’t make up the majority (more than half) of the farmers for any type of crop in central Ondo. Choice D is incorrect because it doesn’t effectively complete the example; it simply states that a relatively equal proportion of women across the three regions mainly cultivate cereals, which doesn’t address the value for that proportion and thus doesn’t show that a majority (more than half) of the farmers cultivating certain crops are female.

"}, {"id": "94c54577", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "H", "type": "mc", "stimulus": "

While attending school in New York City in the 1980s, Okwui Enwezor encountered few works by African artists in exhibitions, despite New York’s reputation as one of the best places to view contemporary art from around the world. According to an arts journalist, later in his career as a renowned curator and art historian, Enwezor sought to remedy this deficiency, not by focusing solely on modern African artists, but by showing how their work fits into the larger context of global modern art and art history.

", "stem": "

Which finding, if true, would most directly support the journalist’s claim?

", "choices": [{"id": "A", "text": "

As curator of the Haus der Kunst in Munich, Germany, Enwezor organized a retrospective of Ghanaian sculptor El Anatsui’s work entitled El Anatsui: Triumphant Scale, one of the largest art exhibitions devoted to a Black artist in Europe’s history. 

"}, {"id": "B", "text": "

In the exhibition Postwar: Art Between the Pacific and the Atlantic, 1945–1965, Enwezor and cocurator Katy Siegel brought works by African artists such as Malangatana Ngwenya together with pieces by major figures from other countries, like US artist Andy Warhol and Mexico’s David Siqueiros.

"}, {"id": "C", "text": "

Enwezor’s work as curator of the 2001 exhibition The Short Century: Independence and Liberation Movements in Africa, 1945–1994 showed how African movements for independence from European colonial powers following the Second World War profoundly influenced work by African artists of the period, such as Kamala Ibrahim Ishaq and Thomas Mukarobgwa.

"}, {"id": "D", "text": "

Enwezor organized the exhibition In/sight: African Photographers, 1940 to the Present not to emphasize a particular aesthetic trend but to demonstrate the broad range of ways in which African artists have approached the medium of photography.

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer because it presents a finding that, if true, would most directly support the arts journalist’s claim about Enwezor’s work as a curator and art historian. In the text, the arts journalist asserts that Enwezor wished not just to focus on modern African artists but also to show “how their work fits into the larger context of global modern art and art history,” or how their work relates to artistic developments and work by other artists elsewhere in the world. The description of Postwar: Art Between the Pacific and the Atlantic, 1945–1965 indicates that Enwezor and Siegel’s exhibition brought works by African artists together with works by artists from other countries, thus supporting the arts journalist’s claim that Enwezor sought to show works by African artists in a context of global modern art and art history.

Choice A is incorrect because it describes a retrospective that wouldn’t support the arts journalist’s claim that Enwezor wanted to show how works by modern African artists fit into the larger context of global modern art and art history. The description of El Anatsui: Triumphant Scale indicates that the retrospective focused only on the work of a single African artist, El Anatsui. The description doesn’t suggest that the exhibition showed how El Anatsui’s works fit into a global artistic context. Choice C is incorrect because it describes an exhibition that wouldn’t support the arts journalist’s claim that Enwezor wanted to show how works by modern African artists relate to the larger context of global modern art and art history. The description of The Short Century: Independence and Liberation Movements in Africa, 1945–1994 indicates that the exhibition showed how African artists were influenced by movements for independence from European colonial powers following the Second World War. Although this suggests that Enwezor intended the exhibition to place works by African artists in a political context, it doesn’t indicate that the works were placed in a global artistic context. Choice D is incorrect because it describes an exhibition that wouldn’t support the arts journalist’s claim that Enwezor wanted to show how works by modern African artists relate to the larger context of global modern art and art history. The description of In/sight: African Photographers, 1940 to the Present indicates that the exhibition was intended to reveal the broad range of approaches taken by African photographers, not that the exhibition showed how photography by African artists fits into a global artistic context.

"}, {"id": "ce4448b7", "domain": "Information and Ideas", "skill": "Inferences", "difficulty": "H", "type": "mc", "stimulus": "

Researchers recently found that disruptions to an enjoyable experience, like a short series of advertisements during a television show, often increase viewers’ reported enjoyment. Suspecting that disruptions to an unpleasant experience would have the opposite effect, the researchers had participants listen to construction noise for 30 minutes and anticipated that those whose listening experience was frequently interrupted with short breaks of silence would thus ______blank

", "stem": "

Which choice most logically completes the text?

", "choices": [{"id": "A", "text": "

find the disruptions more irritating as time went on. 

"}, {"id": "B", "text": "

rate the listening experience as more negative than those whose listening experience was uninterrupted.

"}, {"id": "C", "text": "

rate the experience of listening to construction noise as lasting for less time than it actually lasted.

"}, {"id": "D", "text": "

perceive the volume of the construction noise as growing softer over time.

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. It most logically completes the text. The text tells us that disruptions to an enjoyable experience increase viewers’ enjoyment. It also says that researchers suspect the opposite is true for disruptions to an unpleasant experience. Thus, we can infer that the researchers expect to find that the interrupted unpleasant experience was worse for listeners than the uninterrupted unpleasant experience.  

Choice A is incorrect. It doesn’t logically complete the text. The text never makes any claims about how irritating the disruptions themselves are perceived to be. Rather, the text says that pleasant experiences are perceived as more enjoyable with interruptions, and that the opposite is suspected to be true of unpleasant experiences. Choice C is incorrect. It doesn’t logically complete the text. The text never makes any claims about how long any experience is perceived to be. Rather, the text says that pleasant experiences are perceived as more enjoyable with interruptions, and that the opposite is suspected to be true of unpleasant experiences. Choice D is incorrect. It doesn’t logically complete the text. The text never makes any claims about how interruptions affect the perceived volume of the unpleasant or pleasant experience. Rather, the text says that pleasant experiences are perceived as more enjoyable with interruptions, and that the opposite is suspected to be true of unpleasant experiences. 

"}, {"id": "1f3be847", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "M", "type": "mc", "stimulus": "

“Loon Point” is a 1912 poem by Amy Lowell. In the poem, which presents a nighttime scene on a body of water, Lowell describes an element of nature as an active participant in the experience, writing, ______blank

", "stem": "

Which quotation from “Loon Point” most effectively illustrates the claim?

", "choices": [{"id": "A", "text": "

“Through the water the moon writes her legends / In light, on the smooth, wet sand.”

"}, {"id": "B", "text": "

“Softly the water ripples / Against the canoe’s curving side.”

"}, {"id": "C", "text": "

“Or like the snow-white petals / Which drop from an overblown rose.”

"}, {"id": "D", "text": "

“But the moon in her wayward beauty / Is ever and always the same.”

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer because it most effectively illustrates the claim that Lowell describes an element of nature as an active participant in the experience of a nighttime scene on a body of water. The quotation presents the image of the moon shining on a body of water. However, instead of describing the moon in passive terms or simply stating that it reflects through the water and onto the sandy shore, the quotation portrays the moon as being engaged in the humanlike action of writing a legend. In other words, the moon is participating actively in the nighttime scene.

Choice B is incorrect. Although the quotation describes a nighttime scene on a body of water, the element of nature in these lines—the waves—isn’t portrayed as an active participant in an experience; instead, the waves merely ripple softly against a canoe, as waves would normally do. Choice C is incorrect because the quotation doesn’t present a nighttime scene on a body of water; instead, it describes petals falling from a rose. Choice D is incorrect. Although the quotation presents an image of an element of nature—the moon—it doesn’t mention a body of water; moreover, it portrays the moon not as an active participant in a scene but instead as static or unchanging (“ever and always the same”).

"}, {"id": "7a1877be", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "H", "type": "mc", "stimulus": "

Nucleobase Concentrations from Murchison Meteorite and Soil Samples in Parts per Billion

NucleobaseMurchison meteorite sample 1Murchison meteorite sample 2Murchison soil sample
Isoguanine0.50.04not detected
Purine0.20.02not detected
Xanthine3931
Adenine15140
Hypoxanthine2412

\n

Employing high-performance liquid chromatography—a process that uses pressurized water to separate material into its component molecules—astrochemist Yashiro Oba and colleagues analyzed two samples of the Murchison meteorite that landed in Australia as well as soil from the landing zone of the meteorite to determine the concentrations of various organic molecules. By comparing the relative concentrations of types of molecules known as nucleobases in the Murchison meteorite with those in the soil, the team concluded that there is evidence that the nucleobases in the Murchison meteorite formed in space and are not the result of contamination on Earth.

", "stem": "

Which choice best describes data from the table that support the team’s conclusion?

", "choices": [{"id": "A", "text": "

Isoguanine and purine were detected in both meteorite samples but not in the soil sample.

"}, {"id": "B", "text": "

Adenine and xanthine were detected in both of the meteorite samples and in the soil sample.

"}, {"id": "C", "text": "

Hypoxanthine and purine were detected in both the Murchison meteorite sample 2 and in the soil sample.

"}, {"id": "D", "text": "

Isoguanine and hypoxanthine were detected in the Murchison meteorite sample 1 but not in sample 2.

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. The researchers concluded that the meteorite’s nucleobases weren’t the result of soil contamination. Presence of nucleobases in the meteorite and not in soil provides evidence that those nucleobases likely didn’t come from the soil.

Choice B is incorrect. This choice doesn’t justify the conclusion. The researchers concluded that the meteorite’s nucleobases weren’t the result of soil contamination. If the nucleobases are present in both the soil and meteorite, then it’s possible that these nucleobases came from the soil. Choice C is incorrect. This choice misreads the table. Purine was not detected in the soil sample. Choice D is incorrect. This choice misreads the table. Both isoguanine and hypoxanthine were detected in both Murchison meteorite samples.

"}, {"id": "11a9f635", "domain": "Information and Ideas", "skill": "Central Ideas and Details", "difficulty": "M", "type": "mc", "stimulus": "

Paleontologists searching for signs of ancient life have found many fossilized specimens of prehistoric human ancestors, including several from the Pleistocene era discovered in a geological formation in the Minatogawa quarry in Japan. However, to study the emergence of the earliest multicellular organisms to appear on Earth, researchers must turn elsewhere, such as to the Ediacaran geological formation at Mistaken Point in Canada. A UNESCO World Heritage Site, the 146-hectare reserve contains more than 10,000 fossils that together document a critical moment in evolutionary history.

", "stem": "

What does the text indicate about the geological formation at Mistaken Point? 

", "choices": [{"id": "A", "text": "

It holds a greater number of fossils but from a smaller variety of species than the formation in the Minatogawa quarry does.

"}, {"id": "B", "text": "

It has provided evidence that the earliest human species may have emerged before the Pleistocene era.

"}, {"id": "C", "text": "

It is widely considered by paleontologists to be the most valuable source of information about prehistoric life forms.

"}, {"id": "D", "text": "

It contains specimens from an older time period than those found in the formation in the Minatogawa quarry.

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. The text says that the formation at Mistaken Point contains fossils of “the earliest multicellular organisms,” which implies that these fossils are from an older time period than the fossils of “prehistoric human ancestors” found in the Minatogawa quarry.

Choice A is incorrect. The text says that the formation at Mistake Point contains “more than 10,000 fossils,” but it doesn’t compare this number to the number of fossils in the Minatogawa quarry. It also doesn’t say anything about the variety of species in either formation. Choice B is incorrect. The text says that the formation at Mistaken Point contains fossils of “the earliest multicellular organisms,” but it never says that the site contains early human fossils too. Rather, the early human fossils mentioned in the text were found in the formation at Minatogawa quarry. Choice C is incorrect. The text says that the fossils at Mistaken Point “document a critical moment in evolutionary history,” but it never says that Mistaken Point is the most valuable source of information about prehistoric life forms.

"}, {"id": "57485f5e", "domain": "Information and Ideas", "skill": "Central Ideas and Details", "difficulty": "E", "type": "mc", "stimulus": "

The following text is adapted from Johanna Spyri’s 1881 novel Heidi (translated by Elisabeth Stork in 1915). Eight-year-old Heidi and her friend’s grandmother are looking at some illustrated books.

\n
\n

Heidi had come and was looking with wondering eyes at the splendid pictures in the large books, that Grandmama was showing her. Suddenly she screamed aloud, for there on the picture she saw a peaceful flock grazing on a green pasture. In the middle a shepherd was standing, leaning on his crook. The setting sun was shedding a golden light over everything. With glowing eyes Heidi devoured the scene.

\n
", "stem": "

Which choice best states the main idea of the text?

", "choices": [{"id": "A", "text": "

Heidi is upset until she sees a serene image of a pasture in one of Grandmama’s books.

"}, {"id": "B", "text": "

Heidi is delighted and fascinated by an image she sees in one of Grandmama’s books.

"}, {"id": "C", "text": "

Heidi is initially frightened by an image in one of Grandmama’s books but quickly comes to appreciate its beauty.

"}, {"id": "D", "text": "

Heidi is inspecting an image in one of Grandmama’s books because she has never seen a shepherd with his sheep before.

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer because it most effectively states the main idea of the text, which is that Heidi is delighted and fascinated by an image she sees in one of Grandmama’s books. In the text, Heidi screams upon first seeing the picture of the green pasture. In another context, such a reaction might suggest fear, but here the reaction is followed by descriptions of an image that’s peaceful rather than scary. The text goes on to describe Heidi’s eyes as “glowing” and states that she “devoured the scene,” suggesting that the image delights and fascinates her so much that she wants to examine every detail. Together, these descriptions suggest that Heidi is thrilled and intrigued by the image in the book.

Choice A is incorrect because there’s nothing in the text to suggest that Heidi is upset before seeing the peaceful image of the green pasture. Before Heidi sees that image, the text describes her as “looking with wondering eyes at the splendid pictures” in the book, suggesting that Heidi is intrigued, not that she’s unhappy. Choice C is incorrect. Although Heidi screams upon first seeing the image, the text’s description of the image and Heidi’s other reactions to it suggest that she is screaming with delight, not fear. The text describes the images in the book as “splendid” and the particular image that causes her to scream as peaceful rather than frightening. It also describes Heidi’s eyes as “glowing” and states that she “devoured the scene,” suggesting that the image of the green pasture delights and fascinates her so much that she wants to examine every detail. Choice D is incorrect because it’s unclear from the text whether Heidi has ever seen a shepherd with his sheep before. The text merely suggests that she is delighted and fascinated by the image of the shepherd and his sheep.

"}, {"id": "a68fd3e7", "domain": "Information and Ideas", "skill": "Inferences", "difficulty": "H", "type": "mc", "stimulus": "

Many of William Shakespeare’s tragedies address broad themes that still appeal to today’s audiences. For instance, Romeo and Juliet, which is set in the Italy of Shakespeare’s time, tackles the themes of parents versus children and love versus hate, and the play continues to be read and produced widely around the world. But understanding Shakespeare’s so-called history plays can require a knowledge of several centuries of English history. Consequently, ______blank

", "stem": "

Which choice most logically completes the text?

", "choices": [{"id": "A", "text": "

many theatergoers and readers today are likely to find Shakespeare’s history plays less engaging than the tragedies.

"}, {"id": "B", "text": "

some of Shakespeare’s tragedies are more relevant to today’s audiences than twentieth-century plays.

"}, {"id": "C", "text": "

Romeo and Juliet is the most thematically accessible of all Shakespeare’s tragedies.

"}, {"id": "D", "text": "

experts in English history tend to prefer Shakespeare’s history plays to his other works.

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer because it most logically completes the text’s discussion of the relative appeal of different kinds of plays by Shakespeare to today’s audiences. According to the text, Shakespeare’s tragedies address broad themes that continue to appeal to today’s audiences. Indeed, the text suggests that these themes are timeless, as illustrated by the example of Romeo and Juliet, which the text states is still read and widely performed despite being set in the Italy of Shakespeare’s time. In contrast, the text indicates that audiences and readers may need to be familiar with several centuries of English history in order to understand Shakespeare’s history plays. Because many theatergoers and readers are unlikely to possess such extensive historical knowledge, it follows that they are likely to find Shakespeare’s history plays less engaging than his more accessible tragedies.

Choice B is incorrect because the text never introduces a comparison between Shakespeare’s tragedies and twentieth-century plays, only between Shakespeare’s tragedies and his history plays. Since twentieth-century plays aren’t mentioned, there’s no basis in the text for the idea that some of Shakespeare’s tragedies are more relevant than twentieth-century plays to today’s audiences. Choice C is incorrect. Although the text indicates that Romeo and Juliet is thematically accessible to today’s audiences, it doesn’t suggest that Romeo and Juliet is more accessible than Shakespeare’s other tragedies. Rather, the text presents Romeo and Juliet as an example to support the idea that Shakespeare’s tragedies hold continued appeal for today’s readers and theatergoers. Choice D is incorrect. Although experts in English history would likely possess the knowledge needed to understand Shakespeare’s history plays, the text never mentions such experts or suggests that they would enjoy the history plays more than Shakespeare’s other works.

"}, {"id": "e677fa6c", "domain": "Information and Ideas", "skill": "Central Ideas and Details", "difficulty": "M", "type": "mc", "stimulus": "

The following text is adapted from Edgar Allan Poe’s 1849 story “Landor’s Cottage.”

\n
\n

During a pedestrian trip last summer, through one or two of the river counties of New York, I found myself, as the day declined, somewhat embarrassed about the road I was pursuing. The land undulated very remarkably; and my path, for the last hour, had wound about and about so confusedly, in its effort to keep in the valleys, that I no longer knew in what direction lay the sweet village of B——, where I had determined to stop for the night.

\n
", "stem": "

Which choice best states the main idea of the text?

", "choices": [{"id": "A", "text": "

The narrator remembers a trip he took and admits to getting lost.

"}, {"id": "B", "text": "

The narrator recalls fond memories of a journey that he took through some beautiful river counties.

"}, {"id": "C", "text": "

The narrator describes what he saw during a long trip through a frequently visited location.

"}, {"id": "D", "text": "

The narrator explains the difficulties he encountered on a trip and how he overcame them.

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. The narrator is “embarrassed” about the route he took, which ends up leaving him lost and confused about how to get to his destination for the evening.

Choice B is incorrect. This choice doesn’t match the passage. The narrator is embarrassed, rather than fond, and he doesn’t describe the beauty of the place. Choice C is incorrect. This choice doesn’t match the passage. We don’t know from this excerpt whether or not the narrator has visited this part of New York multiple times. Choice D is incorrect. This choice doesn’t match the passage. The narrator doesn’t explain how he overcame being lost in this excerpt.

"}, {"id": "3d91c973", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "H", "type": "mc", "stimulus": "

Mosasaurs were large marine reptiles that lived in the Late Cretaceous period, approximately 100 million to 66 million years ago. Celina Suarez, Alberto Pérez-Huerta, and T. Lynn Harrell Jr. examined oxygen-18 isotopes in mosasaur tooth enamel in order to calculate likely mosasaur body temperatures and determined that mosasaurs were endothermic—that is, they used internal metabolic processes to maintain a stable body temperature in a variety of ambient temperatures. Suarez, Pérez-Huerta, and Harrell claim that endothermy would have enabled mosasaurs to include relatively cold polar waters in their range.

", "stem": "

Which finding, if true, would most directly support Suarez, Pérez-Huerta, and Harrell’s claim?

", "choices": [{"id": "A", "text": "

Mosasaurs’ likely body temperatures are easier to determine from tooth enamel oxygen-18 isotope data than the body temperatures of nonendothermic Late Cretaceous marine reptiles are.

"}, {"id": "B", "text": "

Fossils of both mosasaurs and nonendothermic marine reptiles have been found in roughly equal numbers in regions known to be near the poles during the Late Cretaceous, though in lower concentrations than elsewhere.

"}, {"id": "C", "text": "

Several mosasaur fossils have been found in regions known to be near the poles during the Late Cretaceous, while relatively few fossils of nonendothermic marine reptiles have been found in those locations. 

"}, {"id": "D", "text": "

During the Late Cretaceous, seawater temperatures were likely higher throughout mosasaurs’ range, including near the poles, than seawater temperatures at those same latitudes are today. 

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer because it presents the finding that, if true, would best support Suarez, Pérez-Huerta, and Harrell’s claim about mosasaurs. The text states that Suarez, Pérez-Huerta, and Harrell’s research on mosasaur tooth enamel led them to conclude that mosasaurs were endothermic, which means that they could live in waters at many different temperatures and still maintain a stable body temperature. The researchers claim that endothermy enabled mosasaurs to live in relatively cold waters near the poles. If several mosasaur fossils have been found in areas that were near the poles during the period when mosasaurs were alive and fossils of nonendothermic marine reptiles are rare in such locations, that would support the researchers’ claim: it would show that mosasaurs inhabited polar waters but nonendothermic marine mammals tended not to, suggesting that endothermy may have been the characteristic that enabled mosasaurs to include polar waters in their range.

Choice A is incorrect because finding that it’s easier to determine mosasaur body temperatures from tooth enamel data than it is to determine nonendothermic reptile body temperatures wouldn’t support the researchers’ claim. Whether one research process is more difficult than another indicates nothing about the results of those processes and therefore is irrelevant to the issue of where mosasaurs lived and what enabled them to live in those locations. \n Choice B is incorrect because finding roughly equal numbers of mosasaur and nonendothermic marine reptile fossils in areas that were near the poles in the Late Cretaceous would suggest that endothermy didn’t give mosasaurs any particular advantage when it came to expanding their range to include relatively cold polar waters, thereby weakening the researchers’ claim rather than supporting it. Choice D is incorrect because finding that the temperature of seawater in the Late Cretaceous was warmer than seawater today wouldn’t weaken the researchers’ claim. Seawater in the Late Cretaceous could have been warmer than seawater today but still cold enough for endothermy to be advantageous to mosasaurs, so this finding wouldn’t provide enough information to either support or weaken the researchers’ claim.

"}, {"id": "7cbb9764", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "M", "type": "mc", "stimulus": "

Accomplished printmaker and sculptor Elizabeth Catlett (1915–2012) used her art to explore the Black experience in the United States. In a paper for an art history class, a student claims that Catlett had a particular talent for unifying various artistic traditions and styles in her work.

", "stem": "

Which quotation from a scholar describing Catlett’s work would best support the student’s claim?

", "choices": [{"id": "A", "text": "

“In Mother and Child, a sculpture of two Black figures, Catlett used an ancient Indigenous sculpting technique and combined the visual aesthetic of modern Mexican muralists with that of German artist Kathe Kollwitz.” 

"}, {"id": "B", "text": "

“In her collage New Generation, Catlett overlaid fabric onto the canvas to represent the clothing of a father and his toddler, positioned to evoke classic images of a mother and child.”

"}, {"id": "C", "text": "

“Created in 1968, Catlett’s sculpture Black Unity, a stylized fist sculpted from mahogany and measuring two feet across, remains an important piece and has received renewed and well-deserved attention in recent years.”

"}, {"id": "D", "text": "

“One series of Catlett’s prints, made by the artist using the linoleum cut method, depicts several notable African American women, including Harriet Tubman and Sojourner Truth.” 

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer because it presents a quotation about Elizabeth Catlett that supports the student’s claim that this artist had a talent for unifying various traditions and styles in her work. The quotation explains that to create the work, Catlett combined Indigenous sculpture with the visual aesthetic of modern muralists from Mexico as well as that of German artist Kathe Kollwitz. In other words, Catlett was able to unify several artistic traditions and styles within a single sculpture.

Choice B is incorrect because in discussing the technique and subject matter of Catlett’s collage, the quotation makes no reference to particular traditions or styles. Choice C is incorrect because in describing the sculpture, the quotation doesn’t mention any artistic traditions or styles that Catlett may have synthesized to create the work. Choice D is incorrect because in discussing Catlett’s prints of notable African American women, the quotation doesn’t characterize those prints as having fused different traditions or styles.

"}, {"id": "94ca8ebd", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "M", "type": "mc", "stimulus": "

A student is examining a long, challenging poem that was initially published in a quarterly journal without explanatory notes, then later republished in a stand-alone volume containing only that poem and accompanying explanatory notes written by the poet. The student asserts that the explanatory notes were included in the republication primarily as a marketing device to help sell the stand-alone volume.

", "stem": "

Which statement, if true, would most directly support the student’s claim?

", "choices": [{"id": "A", "text": "

The text of the poem as published in the quarterly journal is not identical to the text of the poem published in the stand-alone volume.

"}, {"id": "B", "text": "

Many critics believe that the poet’s explanatory notes remove certain ambiguities of the poem and make it less interesting as a result.

"}, {"id": "C", "text": "

The publishers of the stand-alone volume requested the explanatory notes from the poet in order to make the book attractive to readers who already had a copy of the poem in a journal issue.

"}, {"id": "D", "text": "

Correspondence between the poet and the publisher reveals that the poet’s explanatory notes went through several drafts.

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer because it would most directly support the student’s claim about the motivation for including explanatory notes with the stand-alone volume of the poem. The text explains that the poem had previously been published without the notes in a quarterly journal. It stands to reason that readers who had purchased the journal issue containing the poem would be unlikely to purchase an unchanged version of the poem in a stand-alone volume. However, the inclusion of notes in that volume would encourage the purchase of a stand-alone volume, since the later text would differ from the original by including the author’s own explanation of the poem. Therefore, if it were true that the publishers of the stand-alone volume had requested the notes to make the book attractive to readers who already had a copy of the journal issue, this fact would support the student’s claim that the notes were included primarily as a marketing device.

Choice A is incorrect because the student’s claim is about the motivation for including the explanatory notes in the stand-alone volume, not about changes that might have been made to the poem itself for publication in that volume; moreover, the text never suggests that such changes were made. Choice B is incorrect because the student’s claim is about why the explanatory notes were included in the stand-alone volume, not about how the notes affected readers’ and critics’ subsequent experience of the poem. Choice D is incorrect because the fact that the poet drafted multiple versions of the explanatory notes doesn’t directly address the issue of whether the notes were intended as a marketing device, as the student claims; the correspondence would support this claim only if it showed that the poet had revised the notes specifically to make them useful to the marketing of the stand-alone volume.

"}, {"id": "66c47028", "domain": "Information and Ideas", "skill": "Central Ideas and Details", "difficulty": "M", "type": "mc", "stimulus": "

In 1934 physicist Eugene Wigner posited the existence of a crystal consisting entirely of electrons in a honeycomb-like structure. The so-called Wigner crystal remained largely conjecture, however, until Feng Wang and colleagues announced in 2021 that they had captured an image of one. The researchers trapped electrons between two semiconductors and then cooled the apparatus, causing the electrons to settle into a crystalline structure. By inserting an ultrathin sheet of graphene above the crystal, the researchers obtained an impression—the first visual confirmation of the Wigner crystal.

", "stem": "

Which choice best states the main idea of the text?

", "choices": [{"id": "A", "text": "

Researchers have obtained the most definitive evidence to date of the existence of the Wigner crystal.

"}, {"id": "B", "text": "

Researchers have identified an innovative new method for working with unusual crystalline structures.

"}, {"id": "C", "text": "

Graphene is the most important of the components required to capture an image of a Wigner crystal.

"}, {"id": "D", "text": "

 It’s difficult to acquire an image of a Wigner crystal because of the crystal’s honeycomb structure.

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer because it most accurately states the main idea of the text. According to the text, Eugene Wigner hypothesized that a crystal could exist that would be composed of electrons and have a honeycomb-like shape. The text goes on to say that the existence of the Wigner crystal remained unconfirmed until Feng Wang and colleagues were able to make an impression of one using two semiconductors and an ultrathin sheet of graphene. Thus, the main idea is that researchers have obtained the most definitive evidence to date of the existence of the Wigner crystal.

Choice B is incorrect because the text focuses on one kind of crystal—the Wigner crystal— and doesn’t discuss crystalline structures in general. And although the text conveys that Wang and colleagues figured out a way to capture an image of a Wigner crystal, it doesn’t address the idea of applying this approach to other types of crystals. Choice C is incorrect because the text describes in general the process Wang and colleagues followed to obtain an impression of the Wigner crystal; it doesn’t address the relative importance of each component in that process. Choice D is incorrect because the text doesn’t state that researchers had a hard time getting an impression of the Wigner crystal because of its honeycomb structure. Nothing in the text indicates why it took so long to prove the existence of this crystal or take an impression of it.

"}, {"id": "0770b53d", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "E", "type": "mc", "stimulus": "

O Pioneers! is a 1913 novel by Willa Cather. In the novel, Cather portrays Alexandra Bergson as having a deep emotional connection to her natural surroundings: ______blank

", "stem": "

Which quotation from O Pioneers! most effectively illustrates the claim?

", "choices": [{"id": "A", "text": "

“She had never known before how much the country meant to her. The chirping of the insects down in the long grass had been like the sweetest music. She had felt as if her heart were hiding down there, somewhere, with the quail and the plover and all the little wild things that crooned or buzzed in the sun. Under the long shaggy ridges, she felt the future stirring.”

"}, {"id": "B", "text": "

“Alexandra talked to the men about their crops and to the women about their poultry. She spent a whole day with one young farmer who had been away at school, and who was experimenting with a new kind of clover hay. She learned a great deal.”

"}, {"id": "C", "text": "

“Alexandra drove off alone. The rattle of her wagon was lost in the howling of the wind, but her lantern, held firmly between her feet, made a moving point of light along the highway, going deeper and deeper into the dark country.”

"}, {"id": "D", "text": "

“It was Alexandra who read the papers and followed the markets, and who learned by the mistakes of their neighbors. It was Alexandra who could always tell about what it had cost to fatten each steer, and who could guess the weight of a hog before it went on the scales closer than John Bergson [her father] himself.”

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer because it presents the quotation that most directly illustrates the claim that Cather portrays Alexandra as having a deep emotional connection to her natural surroundings. This quotation states that the country meant a great deal to Alexandra and then goes on to detail several ways in which her natural surroundings affect her emotionally: the insects sound like “the sweetest music,” she feels as though “her heart were hiding” in the grass “with the quail and the plover,” and near the ridges she feels “the future stirring.”

Choice B is incorrect because the quotation doesn’t suggest that Alexandra had a deep emotional connection to her natural surroundings but instead describes how she interacts with the people around her to learn more about crops, poultry, and experiments with clover hay. Choice C is incorrect because the quotation doesn’t suggest that Alexandra has a deep emotional connection to her natural surroundings but instead describes her nighttime departure in a wagon. The quotation says nothing about Alexandra’s emotional state. Choice D is incorrect because the quotation doesn’t convey Alexandra’s deep emotional connection to her natural surroundings; instead, this quotation describes how well she understands the markets and livestock. 

"}, {"id": "58e9e497", "domain": "Information and Ideas", "skill": "Inferences", "difficulty": "H", "type": "mc", "stimulus": "

In the early nineteenth century, some Euro-American farmers in the northeastern United States used agricultural techniques developed by the Haudenosaunee (Iroquois) people centuries earlier, but it seems that few of those farmers had actually seen Haudenosaunee farms firsthand. Barring the possibility of several farmers of the same era independently developing techniques that the Haudenosaunee people had already invented, these facts most strongly suggest that ______blank

", "stem": "

Which choice most logically completes the text?

", "choices": [{"id": "A", "text": "

those farmers learned the techniques from other people who were more directly influenced by Haudenosaunee practices.

"}, {"id": "B", "text": "

the crops typically cultivated by Euro-American farmers in the northeastern United States were not well suited to Haudenosaunee farming techniques.

"}, {"id": "C", "text": "

Haudenosaunee farming techniques were widely used in regions outside the northeastern United States.

"}, {"id": "D", "text": "

Euro-American farmers only began to recognize the benefits of Haudenosaunee farming techniques late in the nineteenth century.

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer because it most logically completes the text’s discussion of Euro-American farmers’ use of Haudenosaunee agricultural techniques. According to the text, some Euro-American farmers were using these techniques in the early nineteenth century despite few of the farmers having seen Haudenosaunee farms. One explanation for these facts might be that the farmers developed techniques on their own that already had been invented centuries earlier by the Haudenosaunee people, but the text explicitly bars, or rules out, this explanation. If Euro-American farmers didn’t learn these techniques from direct observation of Haudenosaunee practices and didn’t invent the techniques independently, then the most logical explanation is that they learned the techniques from other people who were more directly influenced by Haudenosaunee practices than the farmers themselves were. Once they learned about Haudenosaunee agricultural practices, Euro-American farmers could then apply those practices to their own farming.

Choice B is incorrect because the fact that some Euro-American farmers in the northeastern United States were using Haudenosaunee techniques suggests that the techniques were likely useful for the crops the farmers raised, not that the crops typically cultivated by the farmers were not well suited to Haudenosaunee farming techniques. If the farmers’ crops were ill suited to the techniques, it’s unlikely that the farmers would have used those techniques. Choice C is incorrect because the text indicates only that Haudenosaunee agricultural techniques were used by Euro-American farmers in the northeastern United States, not that these techniques were widely used outside this region. Choice D is incorrect because the text states that some Euro-American farmers were using Haudenosaunee farming techniques early in the nineteenth century. This suggests that some Euro-American farmers were beginning to recognize the benefits of these techniques near the start of the century, not that such farmers only began to recognize the benefits of the techniques much later.

"}, {"id": "1a2b29c9", "domain": "Information and Ideas", "skill": "Central Ideas and Details", "difficulty": "H", "type": "mc", "stimulus": "

The following text is adapted from María Cristina Mena’s 1914 short story “The Vine-Leaf.”

\n
\n

It is a saying in the capital of Mexico that Dr. Malsufrido carries more family secrets under his hat than any archbishop.

\n

The doctor’s hat is, appropriately enough, uncommonly capacious, rising very high, and sinking so low that it seems to be supported by his ears and eyebrows, and it has a furry look, as if it had been brushed the wrong way, which is perhaps what happens to it if it is ever brushed at all. When the doctor takes it off, the family secrets do not fly out like a flock of parrots, but remain nicely bottled up beneath a dome of old and highly polished ivory.

\n
", "stem": "

Based on the text, how do people in the capital of Mexico most likely regard Dr. Malsufrido?

", "choices": [{"id": "A", "text": "

Many have come to tolerate him despite his disheveled appearance.

"}, {"id": "B", "text": "

Few feel concerned that he will divulge their confidences.

"}, {"id": "C", "text": "

Some dislike how freely he discusses his own family.

"}, {"id": "D", "text": "

Most would be unimpressed by him were it not for his professional expertise.

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. The text describes a saying in the capital that Malsufrido keeps more secrets than an archbishop. It also says that when he takes off his hat, “the family secrets do not fly out… but remain nicely bottled up,” suggesting that he will not betray his confidences.

Choice A is incorrect. This choice doesn’t reflect the text. While his hat is large and appears to have been brushed in the wrong direction, Dr. Malsufrido does not seem to be regarded as ill-dressed or disheveled. Choice C is incorrect. This choice is the opposite of what the text says. The secrets of families (his and others’) remain “bottled up” in his head. Choice D is incorrect. This choice isn’t supported by the text. His professional expertise is not discussed in the passage.

"}, {"id": "71904085", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "H", "type": "mc", "stimulus": "

Linguist Deborah Tannen has cautioned against framing contentious issues in terms of two highly competitive perspectives, such as pro versus con. According to Tannen, this debate-driven approach can strip issues of their complexity and, when used in front of an audience, can be less informative than the presentation of multiple perspectives in a noncompetitive format. To test Tannen’s hypothesis, students conducted a study in which they showed participants one of three different versions of local news commentary about the same issue. Each version featured a debate between two commentators with opposing views, a panel of three commentators with various views, or a single commentator.

", "stem": "

Which finding from the students’ study, if true, would most strongly support Tannen’s hypothesis?

", "choices": [{"id": "A", "text": "

On average, participants perceived commentators in the debate as more knowledgeable about the issue than commentators in the panel.

"}, {"id": "B", "text": "

On average, participants perceived commentators in the panel as more knowledgeable about the issue than the single commentator.

"}, {"id": "C", "text": "

On average, participants who watched the panel correctly answered more questions about the issue than those who watched the debate or the single commentator did.

"}, {"id": "D", "text": "

On average, participants who watched the single commentator correctly answered more questions about the issue than those who watched the debate did.

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer because it presents the finding that, if true, would most strongly support Tannen’s hypothesis. According to the text, Tannen’s hypothesis is that multiple perspectives presented in a noncompetitive format is more informative than a debate between opposing viewpoints is. If participants who saw a panel of three commentators with various views about an issue answered more questions about the issue correctly than did participants who saw a debate, that would support Tannen’s hypothesis since it would show that participants who heard multiple varied perspectives were better informed than were participants who heard a debate between opposing viewpoints.

Choice A is incorrect because finding that participants perceived commentators in the debate as more knowledgeable than commentators in the panel is irrelevant to Tannen’s hypothesis, which is that presenting multiple perspectives on an issue is more informative to the audience than presenting opposing views of the issue is. Participants’ perception of how knowledgeable panelists are has no bearing on how much participants learn from the panelists. Choice B is incorrect because finding that participants perceived commentators in the panel as more knowledgeable than a single commentator is irrelevant to Tannen’s hypothesis, which is that presenting multiple perspectives on an issue is more informative to the audience than presenting opposing views of the issue is. Participants’ perception of how knowledgeable panelists are has no bearing on how much participants learn from the panelists, and Tannen’s hypothesis says nothing about how informative single commentators are. Choice D is incorrect because finding that participants who watched a single commentator answered more questions correctly than participants who watched the debate did wouldn’t be relevant to Tannen’s hypothesis, which is that hearing multiple varying perspectives is more informative than hearing a debate. Tannen’s hypothesis says nothing about how informative single commentators are.

"}, {"id": "3190835d", "domain": "Information and Ideas", "skill": "Inferences", "difficulty": "M", "type": "mc", "stimulus": "

Some businesses believe that when employees are interrupted while doing their work, they experience a decrease in energy and productivity. However, a team led by Harshad Puranik, who studies management, has found that interruptions by colleagues can have a social component that increases employees’ sense of belonging, resulting in greater job satisfaction that benefits employees and employers. Therefore, businesses should recognize that ______blank

", "stem": "

Which choice most logically completes the text?

", "choices": [{"id": "A", "text": "

the interpersonal benefits of some interruptions in the workplace may offset the perceived negative effects.

"}, {"id": "B", "text": "

in order to maximize productivity, employers should be willing to interrupt employees frequently throughout the day.

"}, {"id": "C", "text": "

most employees avoid interrupting colleagues because they don’t appreciate being interrupted themselves.

"}, {"id": "D", "text": "

in order to cultivate an ideal workplace environment, interruptions of work should be discouraged.

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer because it most logically completes the text’s discussion of potential benefits of interruptions in the workplace. The text indicates that a common belief in business is that interruptions to working employees decrease energy and productivity levels. However, the text goes on to explain that a research team led by Harshad Puranik has found that there could be a social benefit to these interruptions.  Since the team found that workplace interruptions can increase employees’ sense of belonging and job satisfaction, it follows that the interpersonal benefits of some interruptions can offset the perceived negative effects. 

Choice B is incorrect. Although the text presents research findings that suggest some workplace interruptions can have a positive effect on employee job satisfaction, no further information is presented to suggest at what frequency these interruptions are ideal. Furthermore, the text doesn’t tie workplace interruptions to increased productivity, but rather links it to social benefits such as sense of belonging. Choice C is incorrect because the text doesn’t address employees’ motives for choosing not to interrupt their colleagues. The text presents research findings that suggest that there are some positive interpersonal effects of workplace interruptions that can increase employee job satisfaction. Choice D is incorrect because asking businesses to discourage workplace interruptions doesn’t follow from the team’s research about the benefits of workplace interruptions, nor does the text describe an ideal work environment. Instead, the text presents research suggesting that there may be positive aspects to workplace interruptions that haven’t previously been considered.

"}, {"id": "04cbeca3", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "H", "type": "mc", "stimulus": "

In 1534 CE, King Henry VIII of England split with the Catholic Church and declared himself head of the Church of England, in part because Pope Clement VII refused to annul his marriage to Catherine of Aragon. Two years later, Henry VIII introduced a policy titled the Dissolution of the Monasteries that by 1540 had resulted in the closure of all Catholic monasteries in England and the confiscation of their estates. Some historians assert that the enactment of the policy was primarily motivated by perceived financial opportunities.

", "stem": "

Which quotation from a scholarly article best supports the assertion of the historians mentioned in the text?

", "choices": [{"id": "A", "text": "

“At the time of the Dissolution of the Monasteries, about 2 percent of the adult male population of England were monks; by 1690, the proportion of the adult male population who were monks was less than 1 percent.”

"}, {"id": "B", "text": "

“A contemporary description of the Dissolution of the Monasteries, Michael Sherbrook’s Falle of the Religious Howses, recounts witness testimony that monks were allowed to keep the contents of their cells and that the monastery timber was purchased by local yeomen.”

"}, {"id": "C", "text": "

“In 1535, the year before enacting the Dissolution of the Monasteries, Henry commissioned a survey of the value of church holdings in England—the work, performed by sheriffs, bishops, and magistrates, began that January and was swiftly completed by the summer.”

"}, {"id": "D", "text": "

“The October 1536 revolt known as the Pilgrimage of Grace had several economic motives: high food prices due to a poor harvest the prior year; the Dissolution of the Monasteries, which closed reliable sources of food and shelter for many; and rents and taxes throughout Northern England that were not merely high but predatory.”

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. The fact that Henry VIII commissioned a survey of church holdings just before enacting the Dissolution of the Monasteries suggests that he was interested in the potential profits from claiming their assets. This supports the historians’ assertion.

Choice A is incorrect. This choice describes a potential effect of the Dissolution of the Monasteries. The decrease in the proportion of monks in England isn’t relevant to the question of Henry VIII’s motivations. Choice B is incorrect. Details about how the monks were treated during the dissolution don’t address Henry VIII’s motivations for enacting the policy in the first place. That the monks could keep the content of their cells (their rooms) and sell off the timber they’d harvested has no impact on the value of the monasteries’ estates—their land holdings. Choice D is incorrect. This choice mentions one impact that the Dissolution of the Monasteries contributed to, two years after it happened. But it doesn’t help explain why Henry VIII might have wanted to enact the policy in the first place.

"}, {"id": "d5b9ed0d", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "M", "type": "mc", "stimulus": "
\n\n\n\n\n76543210Participants\u2019 mean rating(1\u20139; higher values = more positive)Helpfulness of reviewAttitude toward reviewed productParticipants\u2019 Responses to Three Review Conditions no anger (control) high anger low anger
\n

To understand how expressions of anger in reviews of products affect readers of those reviews, business scholar Dezhi Yin and colleagues measured study participants\u2019 responses to three versions of the same negative review\u2014a control review expressing no anger, a review expressing a high degree of anger, and a review expressing a low degree of anger. Reviewing the data, a student concludes that the mere presence of anger in a review may not negatively affect readers\u2019 perceptions of the review, but a high degree of anger in a review does worsen readers\u2019 perceptions of the review.

", "stem": "

Which choice best describes data from the graph that support the students’ conclusion?

", "choices": [{"id": "A", "text": "

On average, participants’ ratings of the helpfulness of the review were substantially higher than were participants’ ratings of the reviewed product regardless of which type of review participants had seen.

"}, {"id": "B", "text": "

Compared with participants who saw the control review, participants who saw the low-anger review rated the review as slightly more helpful, whereas participants who saw the high-anger review rated the review as less helpful. 

"}, {"id": "C", "text": "

Participants who saw the low-anger review rated the review as slightly more helpful than participants who saw the control review did, but participants’ attitude toward the reviewed product was slightly worse when participants saw the low-anger review than when they saw the no-anger review. 

"}, {"id": "D", "text": "

Compared with participants who saw the low-anger review, participants who saw the high-anger review rated the review as less helpful and had a less positive attitude toward the reviewed product. 

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. The claim is that low anger does not negatively affect readers’ perceptions of the review, while high anger does negatively affect readers’ perceptions of the review. This choice accurately expresses the supporting data from the “helpfulness of review” part of the graph: that low-anger reviews were rated as slightly more helpful than no-anger reviews, while high-anger reviews were rated as less helpful than no-anger reviews.

Choice A is incorrect. This choice does not support the conclusion. The conclusion is only about how participants feel about the review itself—the participants’ ratings of the reviewed product are not relevant. Choice C is incorrect. This choice does not support the conclusion. The conclusion is only about how participants feel about the review itself—the participants’ attitude towards the reviewed product is not relevant. Choice D is incorrect. This choice does not support the conclusion. The conclusion is only about how participants feel about the review itself—the participants’ attitude towards the reviewed product is not relevant.

"}, {"id": "2fdfe002", "domain": "Information and Ideas", "skill": "Central Ideas and Details", "difficulty": "H", "type": "mc", "stimulus": "

The following text is adapted from Countee Cullen’s 1926 poem “Thoughts in a Zoo.” 

\n
\n

They in their cruel traps, and we in ours,  

\n

Survey each other’s rage, and pass the hours  

\n

Commiserating each the other’s woe,  

\n

To mitigate his own pain’s fiery glow.  

\n

Man could but little proffer in exchange  

\n

Save that his cages have a larger range.  

\n

That lion with his lordly, untamed heart  

\n

Has in some man his human counterpart,

\n

Some lofty soul in dreams and visions wrapped,  

\n

But in the stifling flesh securely trapped.

\n
", "stem": "

Based on the text, what challenge do humans sometimes experience?

", "choices": [{"id": "A", "text": "

They cannot effectively tame certain wild animals because of a lack of compassion.

"}, {"id": "B", "text": "

They cannot focus on setting attainable goals because of a lack of motivation.

"}, {"id": "C", "text": "

They quickly become frustrated when faced with difficult tasks because of a lack of self-control.

"}, {"id": "D", "text": "

They have aspirations that cannot be fulfilled because of certain limitations.

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. The text metaphorically likens humans to animals in a zoo, suggesting that humans have dreams that they cannot fulfill because they are trapped.

Choice A is incorrect. The speaker says that the lion has an “untamed heart,” but the speaker doesn’t actually mention anything about humans taming wild animals or a lack of compassion. Choice B is incorrect. The speaker doesn’t suggest that humans lack motivation. Rather, the speaker thinks that humans are “trapped” and prevented from achieving their dreams. Choice C is incorrect. The speaker doesn’t mention anything about humans becoming frustrated or lacking self-control. Rather, the speaker thinks that humans are “trapped” and prevented from achieving their dreams.

"}, {"id": "6a6bbac3", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "H", "type": "mc", "stimulus": "

Number and Origin of Clamshell Tools Found at Different Levels Below the Surface in Neanderthal Cave

Depth of tools found below surface in cave (meters)Clamshells that Neanderthals collected from the beachClamshells that Neanderthals harvested from the seafloor
3–49933
6–710
4–520
2–370
5–6187

\n

Studying tools unearthed at a cave site on the western coast of Italy, archaeologist Paola Villa and colleagues have determined that prehistoric Neanderthal groups fashioned them from shells of clams that they harvested from the seafloor while wading or diving or that washed up on the beach. Clamshells become thin and eroded as they wash up on the beach, while those on the seafloor are smooth and sturdy, so the research team suspects that Neanderthals prized the tools made with seafloor shells. However, the team also concluded that those tools were likely more challenging to obtain, noting that ______blank

", "stem": "

Which choice most effectively uses data from the table to support the research team’s conclusion?

", "choices": [{"id": "A", "text": "

at each depth below the surface in the cave, the difference in the numbers of tools of each type suggests that shells were easier to collect from the beach than to harvest from the seafloor. 

"}, {"id": "B", "text": "

the highest number of tools were at a depth of 3–4 meters below the surface, which suggests that the Neanderthal population at the site was highest during the related period of time.

"}, {"id": "C", "text": "

at each depth below the surface in the cave, the difference in the numbers of tools of each type suggests that Neanderthals preferred to use clamshells from the beach because of their durability.

"}, {"id": "D", "text": "

the higher number of tools at depths of 5–6 meters below the surface in the cave than at depths of 4–5 meters below the surface suggests that the size of clam populations changed over time.

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer because it most effectively uses data from the table to support the researchers’ conclusion about the harvesting of clamshells by Neanderthals for use as tools. The text explains that Neanderthals used clamshells to make tools and that the sturdiest, and therefore the most desirable, shells for this purpose are found on the seafloor, not on the beach. However, the researchers also concluded that the clamshell tools made from shells from the seafloor are rarer than those made from shells from the beach. Meanwhile the table shows that at each depth, the number of tools made from shells from the beach exceeds the number made from the more desirable shells from the seafloor. The fact that the more desirable shells are less common suggests that it was significantly more difficult to harvest shells from the seafloor than from the beach.

Choice B is incorrect because knowing which depth represents the period of time with the highest Neanderthal population does not help answer the question of why the Neanderthals consistently made more tools from the less desirable shells from the beach than they made from the more desirable shells from the seafloor. Choice C is incorrect because it claims that the beach shells are more durable than the seafloor shells, which contradicts the text’s description of shells from the seafloor as smoother and sturdier than shells from the beach. Choice D is incorrect because knowing which depth has the most artifacts or whether the clam population fluctuated does not help explain why tools made from the less desirable shells from the beach outnumber tools made from the more desirable shells from the seafloor.

"}, {"id": "6f626ae5", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "E", "type": "mc", "stimulus": "

“To You” is an 1856 poem by Walt Whitman. In the poem, Whitman suggests that readers, whom he addresses directly, have not fully understood themselves, writing, ______blank

", "stem": "

Which quotation from “To You” most effectively illustrates the claim?

", "choices": [{"id": "A", "text": "

“You have not known what you are, you have slumber’d upon yourself / all your life, / Your eyelids have been the same as closed most of the time.”

"}, {"id": "B", "text": "

“These immense meadows, these interminable rivers, you are immense / and interminable as they.”

"}, {"id": "C", "text": "

“I should have made my way straight to you long ago, / I should have blabb’d nothing but you, I should have chanted nothing / but you.”

"}, {"id": "D", "text": "

“I will leave all and come and make the hymns of you, / None has understood you, but I understand you.”

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer because it presents the quotation that most directly illustrates the claim that Whitman’s poem suggests that its readers haven’t fully understood themselves. This quotation makes that point directly by saying to readers, “You have not known what you are.” The quotation goes on to reinforce this point using a metaphor of sleep, saying that readers have “slumber’d” and that their “eyelids have been the same as closed most of the time.” 

Choice B is incorrect because this quotation doesn’t suggest that readers haven’t fully understood themselves but instead characterizes readers as “immense” and “interminable.” Although immense and interminable things can be difficult to understand, this quotation doesn’t make that point. Choice C is incorrect because this quotation doesn’t suggest that readers haven’t fully understood themselves but instead conveys the speaker’s regret over not having celebrated readers sooner. In fact, this quotation says nothing at all about readers themselves—it’s focused solely on the speaker’s feelings about readers. Choice D is incorrect because this quotation doesn’t suggest that readers haven’t fully understood themselves; instead, this quotation makes the point that the speaker has understood readers and is determined to create “hymns” about them.

"}, {"id": "ccb1ab92", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "H", "type": "mc", "stimulus": "

\n\n\n\n\n180160140120100806040200REM sleep as % of baseline (mean difference from baseline was not statisticallysignificant)Day 1Day 2Fur Seal REM Sleep on Land after an Extended Period in WaterSleep on land Seal B Seal A Seal C

\n

Research suggests that REM sleep in animals is homeostatically regulated: animals compensate for periods of REM sleep deprivation by increasing subsequent REM sleep. When on land, fur seals get enough REM sleep, but during the weeks they\u2019re in the water, they get almost none. In a study of fur seals\u2019 sleep habits, researchers recorded the REM sleep (as a percentage of baseline) of fur seals once they had returned to land. They concluded that REM sleep may not be homeostatically regulated in fur seals, citing as evidence the fact that the seals in the study ______blank

", "stem": "

Which choice most effectively uses data from the graph to complete the text?

", "choices": [{"id": "A", "text": "

didn’t show significantly less REM sleep during the second day after returning to land than they did during the first day.

"}, {"id": "B", "text": "

showed no significant differences from one another in baseline levels of REM sleep.

"}, {"id": "C", "text": "

didn’t consistently demonstrate a significant increase in REM sleep after their period of deprivation in the water.

"}, {"id": "D", "text": "

showed no significant difference between REM sleep after returning to land and REM sleep while in the water.

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. If REM sleep were homeostatically regulated in fur seals, then all the seals would compensate with REM levels significantly over baseline after going weeks without REM. We’d also expect the seals to maintain those elevated REM levels for some time. Since seals B and C return very quickly to baseline REM levels, this suggests that REM sleep in fur seals may not be regulated homeostatically.

Choice A is incorrect. This doesn’t support the conclusion. If REM sleep were homeostatically regulated in fur seals, then we’d suspect the seals to sustain REM levels well above baseline for a prolonged period in order to compensate for weeks of REM deprivation while in the water. Whether or not there’s a reduction in REM sleep from day 1 to day 2 doesn’t tell us how REM sleep on those days relates to baseline, which is where our focus should be. Choice B is incorrect. The y-axis of this graph doesn’t depict baseline levels of REM sleep, but rather shows REM sleep as a percent of baseline. Choice D is incorrect. The graph doesn’t depict REM sleep while in the water for the seals in the study. Additionally, we’re told fur seals get no REM sleep while in the water, which is significantly different to the values shown in the graph for after they return to land.

"}, {"id": "be19faa1", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "H", "type": "mc", "stimulus": "

\n\n\n\n\n9080706050403020100Percentage of all sites analyzed0%Up to 25%More than 25%Home Heating Needs Met with Subsurface Thermal Pollution for Two Temperature Conditions, by Percentage of SitesLocal heating needs met Current surface temperature Maximum plausible surface, temperature

\n

Urbanization, industrialization, and the warming climate create thermal pollution (excess heat) in the shallow subsurface soil. Susanne A. Benz and colleagues analyzed thousands of sites on three continents under one scenario in which surface temperature remains at the current level and under another in which the surface reaches the maximum plausible temperature. They then categorized each site according to the percentage of local home heating needs that could be met using this excess subsurface heat. The team concluded that if surface temperature approaches the maximum plausible level, the percentage of sites where thermal pollution could feasibly contribute to meeting home heating needs will increase.

", "stem": "

Which choice best describes data in the graph that support Benz and colleagues’ conclusion?

", "choices": [{"id": "A", "text": "

Under both temperature conditions, less than 10% of sites were in the up-to-25% group, but at the maximum plausible surface temperature, almost 80% of sites could have all their local heating needs met by thermal pollution.

"}, {"id": "B", "text": "

At current surface temperatures, more than 80% of the sites have no need for supplemental local home heating from subsurface thermal pollution, but at the maximum plausible surface temperature, more than 70% of sites exhibit significantly greater home heating needs.

"}, {"id": "C", "text": "

At current surface temperatures, more than 80% of sites can meet, at most, 25% of local home heating needs with subsurface thermal pollution, but at the maximum plausible surface temperature, more than 80% of sites can meet greater than 25% of local home heating needs.

"}, {"id": "D", "text": "

At current surface temperatures, more than 80% of the sites cannot use subsurface thermal pollution to meet any portion of local home heating needs, but at the maximum plausible surface temperature, that percentage drops below 20%. 

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. The researchers concluded that as we approach maximum plausible surface temperatures, there will be a larger percentage of sites where thermal pollution could contribute to meeting home heating needs. By showing that only a small percentage of homes can currently use thermal pollution for home heating, and that this percentage would grow much larger at maximum plausible surface temperatures, this choice supports the researchers’ conclusion.

Choice A is incorrect. We do not know how many sites could have all (i.e., 100%) of their local heating needs met by thermal pollution, as the graph only classifies sites by whether \"0%,\" \"Up to 25%,\" and \"More than 25%\" of heating needs could be met. Choice B is incorrect. The graph is not depicting need for supplemental heating from thermal pollution, but rather potential to use thermal pollution for supplemental heating. Choice C is incorrect. The graph indicates that, at current surface temperatures, less than 10% of sites can meet 25% of local home heating needs and that more than 80% of sites cannot meet any local home heating needs.

"}, {"id": "645fd11a", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "H", "type": "mc", "stimulus": "
\n\n\n\n\n76543210Average number of individuals directly reporting to CEO1991\u201319951996\u201320012001\u20132008Average Number of IndividualsReporting Directly to CEOsYears managers department leaders
\n

Considering a large sample of companies, economics experts Maria Guadalupe, Julie Wulf, and Raghuram Rajan assessed the number of managers and leaders from different departments who reported directly to a chief executive officer (CEO). According to the researchers, the findings suggest that across the years analyzed, there was a growing interest among CEOs in connecting with more departments in their companies.

", "stem": "

Which choice best describes data from the graph that support the researchers’ conclusion?

", "choices": [{"id": "A", "text": "

The average numbers of managers and department leaders reporting directly to their CEO didn’t fluctuate from the 1991–1995 period to the 2001–2008 period.

"}, {"id": "B", "text": "

The average number of managers reporting directly to their CEO was highest in the 1996–2001 period.

"}, {"id": "C", "text": "

The average number of department leaders reporting directly to their CEO was greater than the average number of managers reporting directly to their CEO in each of the three periods studied.

"}, {"id": "D", "text": "

The average number of department leaders reporting directly to their CEO rose over the three periods studied.

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer because it describes data from the graph that support the researchers’ conclusion that there is a growing interest among CEOs in connecting with more departments in their companies. The graph shows the average number of individuals reporting directly to CEOs during three different time periods: the individuals are divided into managers and department leaders. The average number of department leaders directly reporting to their CEO during the 1991–1995 period was slightly more than three, during the 1996–2001 period it was four, and during the 2001–2008 period it was almost seven. Thus, the average number of department leaders reporting directly to their CEO rose over the three periods studied, which suggests that CEOs were connecting with more departments.

Choice A is incorrect because the average number of managers and department leaders reporting directly to their CEO rose for both categories between the 1991–1995 and 2001–2008 periods; thus, it isn’t true that the average numbers didn’t fluctuate. Choice B is incorrect because the average number of managers reporting directly to their CEO was highest in the 2001–2008 period, not in the 1996–2001 period. Choice C is incorrect. Although it correctly describes a feature of the graph, the observation that more department leaders than managers are reporting to CEOs does not by itself address the question of whether CEOs are connecting with more departments over time—to address that question, one needs to know whether the number of department leaders reporting to CEOs is increasing over time.

"}, {"id": "85439572", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "E", "type": "mc", "stimulus": "

Roasted green chiles are a popular ingredient in Southwestern cuisine, but the traditional roasting method of burning propane is not environmentally friendly. To see if solar power could provide a better alternative, engineer Kenneth Armijo and his team roasted batches of green chiles using between 38 and 42 heliostats, which are devices that concentrate sunlight. The team was successful in reaching the same roasting temperature used in traditional propane roasting, but they found that propane yielded faster results. While the fastest solar-roasted green chiles took six minutes, batches using propane took only four. Armijo hypothesizes that they can reduce the roasting time for solar-roasted green chiles by using more heliostats. 

", "stem": "

Which finding, if true, would most directly support Armijo’s hypothesis?

", "choices": [{"id": "A", "text": "

The temperature inside the roasting drum is distributed more evenly when roasting green chiles with solar power than with propane.

"}, {"id": "B", "text": "

Attempts to roast green chiles using 50 heliostats yields results in fewer than six minutes.

"}, {"id": "C", "text": "

Green chile connoisseurs prefer the flavor of solar-roasted green chiles over the flavor of propane-roasted green chiles.

"}, {"id": "D", "text": "

The skins of solar-roasted green chiles are easier to peel than the skins of propane-roasted green chiles.

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. Armijo believes that using more heliostats will speed up the roasting process, and this finding shows that with 50 heliostats—more than the number of heliostats already used—the roasting time is indeed reduced.

Choice A is incorrect. The evenness of temperature in the roasting drum doesn’t tell us about the speed of the roasting process, which is what Armijo’s hypothesis is concerned with. Choice C is incorrect. Armijo’s hypothesis is focused on the speed of the roasting process, not the flavor of the resulting roasted chiles. Choice D is incorrect. Though Armijo’s hypothesis mentions a benefit of solar-roasting green chiles (easier peeling), it doesn’t address the speed of the roasting process.

"}, {"id": "701126bc", "domain": "Information and Ideas", "skill": "Central Ideas and Details", "difficulty": "H", "type": "mc", "stimulus": "

In superfluorescence, electrical charges known as dipoles emit light in synchronized bursts so intense that they are visible to the eye. Until recently, this phenomenon has only been observed at extremely cold temperatures because dipoles cannot synchronize at higher temperatures. But in a study, Melike Biliroglu and colleagues observed superfluorescence at room temperature in thin films made of perovskite and other similarly crystalline materials; the researchers propose that the formation of shock-absorbing quasiparticles called polarons in the material protects dipoles from thermal interference.

", "stem": "

Based on the text, how are polarons believed to be involved in the superfluorescence observed in Biliroglu and colleagues’ study?

", "choices": [{"id": "A", "text": "

Polarons enable superfluorescent bursts to cross from one crystalline material to another.

"}, {"id": "B", "text": "

Polarons allow for the dipoles to synchronize despite higher temperatures. 

"}, {"id": "C", "text": "

Polarons accelerate the dipoles’ release of superfluorescent bursts.

"}, {"id": "D", "text": "

Polarons decrease the intensity of the superfluorescent burst.

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer because it most accurately describes Biliroglu and colleagues’ claim about how the polarons function in relation to superfluorescence. The text indicates that “until recently,” superfluorescence (intense, synchronized bursts of light emitted by dipoles) has solely been observed at very cold temperatures. However, it also states that, recently, Biliroglu and colleagues report observing the phenomenon at room temperature. They achieved this using “thin films made of perovskite and other similarly crystalline materials,” which the researchers claim allows for the formation of polarons. They also suggest that these polarons might absorb the thermal shocks that typically disrupt dipole synchronization at warmer temperatures. Thus, based on the text, Biliroglu and colleagues believe that polarons help dipoles synchronize at temperatures well above those at which superfluorescence had previously been observed.

Choice A is incorrect because the text doesn’t address the prospect of a superfluorescent burst moving between crystalline materials or any other mediums. Choice C is incorrect because the text’s discussion of polarons is about how they might enable superfluorescence at higher temperatures than those at which it had previously been observed. Rather than suggesting that polarons speed up superfluorescent bursts, the text suggests that no superfluorescence can occur at room temperature in the absence of polarons. Thus, the text indicates that polarons make superfluorescent bursts more likely to occur at higher temperatures than those at which it had previously been observed, not that polarons accelerate the bursts. Choice D is incorrect because the text’s discussion of polarons is about how they might enable superfluorescence at higher temperatures than those at which it had previously been observed. In the absence of polarons, the text suggests there would be no superfluorescence at room temperature. Thus, rather than decrease the intensity of superfluorescent bursts, polarons make them more likely to occur under certain circumstances.  

"}, {"id": "c83e0b43", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "H", "type": "mc", "stimulus": "

O Pioneers! is a 1913 novel by Willa Cather. In the novel, Cather depicts Alexandra Bergson as a person who takes comfort in understanding the world around her: ______blank

\n", "stem": "\n

Which quotation from O Pioneers! most effectively illustrates the claim?

", "choices": [{"id": "A", "text": "

“She looked fixedly up the bleak street as if she were gathering her strength to face something, as if she were trying with all her might to grasp a situation which, no matter how painful, must be met and dealt with somehow.“

"}, {"id": "B", "text": "

“She had never known before how much the country meant to her. The chirping of the insects down in the long grass had been like the sweetest music. She had felt as if her heart were hiding down there, somewhere, with the quail and the plover and all the little wild things that crooned or buzzed in the sun. Under the long shaggy ridges, she felt the future stirring.“

"}, {"id": "C", "text": "

“Alexandra drove off alone. The rattle of her wagon was lost in the howling of the wind, but her lantern, held firmly between her feet, made a moving point of light along the highway, going deeper and deeper into the dark country.”

"}, {"id": "D", "text": "

“Alexandra drew her shawl closer about her and stood leaning against the frame of the mill, looking at the stars which glittered so keenly through the frosty autumn air. She always loved to watch them, to think of their vastness and distance, and of their ordered march. It fortified her to reflect upon the great operations of nature, and when she thought of the law that lay behind them, she felt a sense of personal security.”

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer because it most effectively uses a quotation from O Pioneers! to illustrate the claim that Alexandra Bergson takes comfort in understanding the world around her. In the quotation, Alexandra is described as enjoying looking at the stars and feeling a “sense of personal security” when she contemplates nature’s order and its governing laws. This suggests that Alexandra takes comfort in understanding the world around her. 

Choice A is incorrect because the quotation expresses how Alexandra Bergson attempts to meet difficult situations with determination, not how she takes comfort in understanding the world around her. Choice B is incorrect because the quotation expresses “how much the country meant to” Alexandra Bergson, not how she takes comfort in understanding the world around her. In detailing some of the wildlife surrounding Alexandra, the quotation conveys that nature is important to her but not necessarily that it gives her comfort. Choice C is incorrect because the quotation describes Alexandra driving her wagon down a highway at night; it doesn’t describe how she takes comfort in understanding the world around her or address how she’s feeling as she drives off. 

"}, {"id": "a9040290", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "E", "type": "mc", "stimulus": "
\n\n\n\n\n2001751501251007550250Electricity (in thousands of MWh)\u2002Amount of Additional Electricity WindTurbines Could Generate WhenWinds Were Stronger Than ForecastWestMidwest
\n

Electric companies that use wind turbines rely on weather forecasts to predict the maximum amount of power, in megawatt-hours (MWh), they can generate using wind so that they can determine how much they\u2019ll need to generate from other sources. When winds are stronger than they were forecast to be, however, the predicted maximum amount of electricity wind turbines could generate will be too low. For example, the graph shows that for the West region, the winds were ______blank

", "stem": "

Which choice most effectively uses data from the graph to complete the example?

", "choices": [{"id": "A", "text": "

strong enough to generate about 150 thousand more MWh of electricity from wind turbines.

"}, {"id": "B", "text": "

so weak that the electricity from wind turbines was about 175 thousand MWh less than predicted.

"}, {"id": "C", "text": "

so weak that the electricity from wind turbines was about 150 thousand MWh less than predicted.

"}, {"id": "D", "text": "

strong enough to generate about 175 thousand more MWh of electricity from wind turbines.

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. The claim is that when winds are stronger than forecasted, wind turbines can generate more energy than predicted. The supporting graph shows the additional amount (above the predicted amount) that the turbines generated under those conditions, with the West generating about 150 thousand additional MWh.

Choice B is incorrect. This choice doesn’t complete the example. The graph shows the additional amount of electricity that the wind turbines generated. The West bar is greater than 0, so the West generated more than the predicted amount. Choice C is incorrect. This choice doesn’t complete the example. The graph shows the additional amount of electricity that the wind turbines generated. The West bar is greater than 0, so the West generated more than the predicted amount. Choice D is incorrect. This choice misreads the graph. The graph shows us that the West (the bar on the left) generated about 150 thousand additional MWh.

"}, {"id": "ac285054", "domain": "Information and Ideas", "skill": "Inferences", "difficulty": "H", "type": "mc", "stimulus": "

The domestic sweet potato (Ipomoea batatas) descends from a wild plant native to South America. It also populates the Polynesian Islands, where evidence confirms that Native Hawaiians and other Indigenous peoples were cultivating the plant centuries before seafaring first occurred over the thousands of miles of ocean separating them from South America. To explain how the sweet potato was first introduced in Polynesia, botanist Pablo Muñoz-Rodríguez and colleagues analyzed the DNA of numerous varieties of the plant, concluding that Polynesian varieties diverged from South American ones over 100,000 years ago. Given that Polynesia was peopled only in the last three thousand years, the team concluded that ______blank

", "stem": "

Which choice most logically completes the text?

", "choices": [{"id": "A", "text": "

the cultivation of the sweet potato in Polynesia likely predates its cultivation in South America.

"}, {"id": "B", "text": "

Polynesian peoples likely acquired the sweet potato from South American peoples only within the last three thousand years.

"}, {"id": "C", "text": "

human activity likely played no role in the introduction of the sweet potato in Polynesia.

"}, {"id": "D", "text": "

Polynesian sweet potato varieties likely descend from a single South American variety that was domesticated, not wild.

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer because it most logically completes the text’s discussion of the sweet potato in Polynesia. The text indicates that the sweet potato is found in Polynesia but originated in South America, and that the sweet potato was being cultivated by Native Hawaiians and other Indigenous peoples in Polynesia long before sea voyages between South America and Polynesia began. The text goes on to note that research by Muñoz-Rodríguez and colleagues has established that the Polynesian varieties of sweet potato split from South American varieties more than 100,000 years ago, which is thousands of years before humans settled in Polynesia. If Polynesian peoples were cultivating the sweet potato before sea voyages between Polynesia and South America began, and if Polynesian varieties of sweet potato diverged from South American varieties well before people were in Polynesia, it can reasonably be concluded that humans didn’t play a role in bringing the sweet potato to Polynesia. 

Choice A is incorrect. The text doesn’t provide any information about when the sweet potato began to be cultivated in South America, so there’s no support for the conclusion that cultivation began in Polynesia before it began in South America. Choice B is incorrect because the text indicates that the sweet potato was being cultivated in Polynesia long before sea journeys between Polynesia and South America began. Therefore, it wouldn’t be reasonable to conclude that Polynesian peoples acquired the sweet potato from South American peoples. Additionally, the text indicates that the Polynesian varieties of sweet potato diverged from the South American varieties thousands of years before people settled in Polynesia, which suggests that the sweet potato was already present in Polynesia when people arrived. Choice D is incorrect because the text states that the domestic sweet potato, which is found in Polynesia, descends from a wild South American plant, not from a domesticated South American plant. The only people that the text describes as cultivating the sweet potato are Native Hawaiians and other Indigenous peoples of Polynesia. 

"}, {"id": "01989d77", "domain": "Information and Ideas", "skill": "Inferences", "difficulty": "E", "type": "mc", "stimulus": "

Microbes that live in shallow lakes and ponds produce methane, a harmful greenhouse gas. Ecologist Ralf Aben and his team wanted to see how different types of shallow-water plants might affect the amount of methane that escapes into the atmosphere. Aben’s team set up some water tanks with soil and microbes from local ponds. Some tanks had a type of underwater plant that grows in the soil called watermilfoil. Other tanks had either duckweed, a type of plant that floats on the water’s surface, or algae. Aben and his team found that tanks with duckweed and algae released higher levels of methane than tanks with watermilfoil did. This finding suggests that ______blank

", "stem": "

Which choice most logically completes the text?

", "choices": [{"id": "A", "text": "

the presence of some kinds of underwater plants like watermilfoil helps prevent methane from escaping shallow lakes and ponds.

"}, {"id": "B", "text": "

shallow lakes and ponds release more methane than deeper bodies of water because shallow bodies of water usually have more plants than deep bodies of water do.    

"}, {"id": "C", "text": "

shallow lakes and ponds are more likely to contain algae than to contain either watermilfoil or duckweed.

"}, {"id": "D", "text": "

having a mix of algae, underwater plants, and floating plants is the best way to reduce the amount of methane in shallow lakes and ponds. 

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. The passage tells us that “tanks with duckweed (a floating plant) and algae released higher levels of methane than tanks with watermilfoil (an underwater plant) did.” This suggests that the presence of some kinds of underwater plants like watermilfoil may help prevent methane from escaping shallow lakes and ponds.

Choice B is incorrect. The passage doesn’t mention deeper bodies of water at all, so there’s no basis for this inference. Choice C is incorrect. The passage doesn’t compare the likelihood of shallow lakes and ponds containing algae, watermilfoil, or duckweed. Choice D is incorrect. The study didn’t include any tanks with a mix of plants, so there’s no basis for this inference.

"}, {"id": "a13541c0", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "M", "type": "mc", "stimulus": "

Sandra Cisneros’s 1984 novella The House on Mango Street made a lasting impact on US literature. Its depiction of Mexican American culture inspired later authors to examine their own heritage within their fictional works. Also influential was the book’s portrayal of the main character, Esperanza, during a pivotal year of her youth. This insightful depiction of a preteen girl encouraged authors who, like Cisneros herself, are Latina to use fictional works to examine experiences from their own youth.

", "stem": "

Which statement, if true, would most strongly support the claim in the underlined sentence?

", "choices": [{"id": "A", "text": "

In interviews, a number of Latina authors say that The House on Mango Street inspired them to write about their own adolescence in their novels.

"}, {"id": "B", "text": "

In published writings, several prominent authors who are not Latina say that reading The House on Mango Street influenced their approach to writing fiction.

"}, {"id": "C", "text": "

The House on Mango Street has sold over six million copies and is one of the most commonly read books among high school and university students in the US.

"}, {"id": "D", "text": "

Since 1984, new novels about young Latina characters by Latina authors have often been compared to The House on Mango Street. 

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer because it presents a finding that, if true, would most strongly support the claim in the underlined sentence. The text begins by explaining that the portrayal of Mexican American culture in Sandra Cisneros’s The House on Mango Street inspired later authors to explore their own heritage. Noting that Cisneros’s novella was also influential for its depiction of a formative year in a female character’s youth, the text then claims that this depiction inspired other Latina authors to use fiction to explore their own experiences of youth. Since this claim addresses how Cisneros encouraged Latina authors specifically to portray their youthful experiences, it would be directly supported by such authors stating that her novella influenced them to write about their own adolescence, or the transitional period between childhood and adulthood.

Choice B is incorrect. The text states that with its portrayal of Mexican American culture, The House on Mango Street inspired later authors to explore their own heritage, and since this statement isn’t limited to only Latina authors, it can be inferred that authors who aren’t Latina were also likely influenced by the novella. But because the claim in the underlined sentence concerns the novella’s influence on Latina authors specifically, the finding that the book also influenced authors who weren’t Latina would fail to provide support for the claim. Choice C is incorrect because the finding that The House on Mango Street has sold millions of copies and is widely read among students in the US doesn’t relate directly to the text’s claim that the novella has influenced Latina authors specifically. Choice D is incorrect. While comparisons of new novels about young Latina characters by Latina authors to Cisneros’s The House on Mango Street would likely be founded on similarities between those novels and Cisneros’s novella, such similarities wouldn’t necessarily be evidence of the novella’s influence; such similarities might arise if Cisneros and younger Latina authors alike depicted certain basic cultural and historical features of their communities. Testimony from younger Latina authors about how The House on Mango Street had inspired them would be far more persuasive evidence of the novella’s influence. 

"}, {"id": "8a8236e1", "domain": "Information and Ideas", "skill": "Central Ideas and Details", "difficulty": "E", "type": "mc", "stimulus": "

Scent is tightly interwoven with our daily lives, often evoking significant memories and important social events. This connection is of growing interest to archaeologists who hope to use it to better understand ancient rituals, trade, social hierarchies, and medicine. Although the speed at which odor molecules dissipate makes identifying ancient scents challenging, advancements in biomolecular technologies show promise in unlocking ancient aromas from preserved artifacts. Archaeological studies making use of these advancements may provide new insights into past societies.

", "stem": "

According to the text, what is one reason some archaeologists are interested in recovering scents from ancient artifacts?

", "choices": [{"id": "A", "text": "

They are investigating whether people’s sense of smell has declined in recent centuries.

"}, {"id": "B", "text": "

They believe the scents could illuminate important aspects of ancient life.

"}, {"id": "C", "text": "

They think that ancient scents would be enjoyable to people today. 

"}, {"id": "D", "text": "

They hope to develop new medicines using ancient scent molecules. 

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. The text states that archaeologists are interested in using scents to better understand \"ancient rituals, trade, social hierarchies, and medicine,\" all of which are important aspects of ancient life.

Choice A is incorrect. The text doesn’t say anything about investigating if people’s sense of smell has declined in recent centuries. It says that scents fade over time—not that people have gotten worse at smelling scents. Choice C is incorrect. The text says that archaeologists are interested in using scents to better understand \"ancient rituals, trade, social hierarchies, and medicine,\" but it doesn’t say anything about ancient scents being enjoyable to people today. Choice D is incorrect. The text doesn’t say anything about developing new medicines. Rather, it says that archaeologists are interested in using scents to better understand \"ancient rituals, trade, social hierarchies, and medicine.\"

"}, {"id": "7c1e5880", "domain": "Information and Ideas", "skill": "Inferences", "difficulty": "M", "type": "mc", "stimulus": "

Scholars have noted that F. Scott Fitzgerald’s writings were likely influenced in part by his marriage to Zelda Fitzgerald, but many don’t recognize Zelda as a writer in her own right. Indeed, Zelda authored several works herself, such as the novel Save Me the Waltz and numerous short stories. Thus, those who primarily view Zelda as an inspiration for F. Scott’s writings ______blank

", "stem": "

Which choice most logically completes the text?

", "choices": [{"id": "A", "text": "

overlook the many other factors that motivated F. Scott to write.

"}, {"id": "B", "text": "

risk misrepresenting the full range of Zelda’s contributions to literature.

"}, {"id": "C", "text": "

may draw inaccurate conclusions about how F. Scott and Zelda viewed each other’s works.

"}, {"id": "D", "text": "

tend to read the works of F. Scott and Zelda in an overly autobiographical light.

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer because it most logically completes the text’s discussion of Zelda Fitzgerald’s contributions to literature. The text begins by saying that many scholars view Zelda mainly in terms of her marriage to F. Scott Fitzgerald and “don’t recognize Zelda as a writer in her own right.” The text then mentions a novel and “numerous short stories” that she wrote and that such scholars tend to ignore. Therefore, those scholars who focus on Zelda only as an inspiration for F. Scott’s writings risk misrepresenting the full range of Zelda’s contributions to literature.

Choice A is incorrect. Although the text does mention that Zelda Fitzgerald “likely influenced” her husband’s literary work, its focus is on Zelda’s own writing, not on her husband’s writing or factors that might have influenced it. Choice C is incorrect because the text does not discuss F. Scott and Zelda Fitzgerald’s opinions of each other’s works. Choice D is incorrect. Although the text does suggest that F. Scott Fitzgerald’s works were “likely influenced in part” by his marriage to Zelda, it does not discuss autobiographical interpretations of the works of either F. Scott or Zelda.

"}, {"id": "dd1757fd", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "H", "type": "mc", "stimulus": "

Neural networks are computer models intended to reflect the organization of human brains and are often used in studies of brain function. According to an analysis of 11,000 such networks, Rylan Schaeffer and colleagues advise caution when drawing conclusions about brains from observations of neural networks. They found that when attempting to mimic grid cells (brain cells used in navigation), while 90% of the networks could accomplish navigation-related tasks, only about 10% of those exhibited any behaviors similar to those of grid cells. But even this approximation of grid-cell activity has less to do with similarity between the neural networks and biological brains than it does with the rules programmed into the networks.

", "stem": "

Which finding, if true, would most directly support the claim in the underlined sentence?

", "choices": [{"id": "A", "text": "

The rules that allow for networks to exhibit behaviors like those of grid cells have no equivalent in the function of biological brains.

"}, {"id": "B", "text": "

The networks that do not exhibit behaviors like those of grid cells were nonetheless programmed with rules that had proven useful in earlier neural-network studies.

"}, {"id": "C", "text": "

Neural networks can often accomplish tasks that biological brains do, but they are typically programmed with rules to model multiple types of brain cells simultaneously.

"}, {"id": "D", "text": "

Once a neural network is programmed, it is trained on certain tasks to see if it can independently arrive at processes that are similar to those performed by biological brains.

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. While many networks can perform navigation tasks, or even mimic grid cells, it doesn’t mean they’re actually behaving like biological brains—this finding suggests that the rules that govern neural network behavior are completely unlike the way real brains work.

Choice B is incorrect. Although it mentions the rules that are programmed into the networks, this finding wouldn’t clarify whether or not these rules have anything to do with the function of biological brains. Choice C is incorrect. This choice suggests that neural networks are modeled after multiple types of brain cells, which sidesteps the question of whether these rule-based networks are genuinely similar to biological brains. Choice D is incorrect. This choice doesn’t address the key point of the claim, which is that the apparent similarity between neural networks and biological brains is only due to the rules programmed into the networks. It focuses on training tasks, not the originally programmed rules.

"}, {"id": "8a584241", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "M", "type": "mc", "stimulus": "

\n\n\n\n\n\n\n\n\n\n\n\n\n1009080706050403020100Seeds germinated (%)244872168Seed Germination with and withoutH\u2082S Treatment Time (hours) 500 micromoles per liter 10 micromoles per liter untreated

\n

In high concentrations, hydrogen sulfide (H\u2082S) is typically toxic to many plants. Frederick D. Dooley and colleagues wanted to understand what effects low doses of H\u2082S might have on plant growth. They treated bean, corn, wheat, and pea seeds with various concentrations (measured in micromoles per liter) of H\u2082S and tracked the germination of those seeds along with the germination of untreated seeds. Treatment with particular concentrations of H\u2082S was associated with accelerated germination: for example, ______blank

", "stem": "

Which choice most effectively uses data from the graph to complete the statement?

", "choices": [{"id": "A", "text": "

at 24 hours, less than 10% of seeds treated with H\u2082S at a concentration of 10 micromoles per liter had germinated, whereas more than 90% of those seeds had germinated at 168 hours.

"}, {"id": "B", "text": "

at 48 hours, more than 70% of seeds treated with H\u2082S at a concentration of 10 micromoles per liter had germinated, whereas only approximately 50% of untreated seeds had germinated. 

"}, {"id": "C", "text": "

at 168 hours, more than 90% of seeds treated with H\u2082S at concentrations of 10 or 500 micromoles per liter had germinated, whereas less than 70% of untreated seeds had germinated.

"}, {"id": "D", "text": "

at 48 hours, approximately 50% of seeds treated with H\u2082S at a concentration of 10 micromoles per liter had germinated, whereas only approximately 30% of untreated seeds had germinated.

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. The claim is that some concentrations of H\u2082S led to increased germination rates, and this choice accurately shows that seeds treated with 10 micromoles per liter of H\u2082S tended to germinate faster than untreated seeds.

Choice A is incorrect. This choice doesn’t justify the claim. The claim compares the germination rates of seeds exposed to certain concentrations of H\u2082S to untreated seeds, but this choice only discusses one concentration of H\u2082S, so it can’t support any comparison between treated and untreated groups. Choice C is incorrect. This choice misreads the graph. At 168 hours, only about 85% of seeds treated with H\u2082S at 500 micromoles per liter and well over 70% of untreated seeds had germinated (about 80%). Choice D is incorrect. This choice misreads the graph. At 48 hours, about 70% of seeds treated with H\u2082S at 10 micromoles per liter and about 50% of untreated seeds had germinated.

"}, {"id": "dd72993d", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "M", "type": "mc", "stimulus": "

Rivers rich in sediment appear yellow, while increases in red algae make rivers appear red. To track things like the sediment or algae content of large US rivers, John R. Gardner and colleagues used satellite data to determine the dominant visible wavelengths of light measured for various segments of these rivers. The researchers classified wavelengths of 495 nanometers (nm) and below as red, wavelengths between 495 and 560 nm as blue, and wavelengths of 560 nm and above as yellow. The researchers concluded that for the Missouri River, segments flowing into lakes tend to carry more sediment than those flowing out of lakes.  

", "stem": "

Which finding, if true, would most directly support the researchers’ conclusion?

", "choices": [{"id": "A", "text": "

The segments of the Missouri River that had higher levels of chlorophyll-a, which contributes to the green color of photosynthetic organisms, have dominant wavelengths of light between 490 and 560 nm.

"}, {"id": "B", "text": "

In lakes through which segments of the Missouri River pass, the dominant wavelength of light tended to be above 560 nm near the lakes’ shores and below 560 nm in the lakes’ centers.

"}, {"id": "C", "text": "

The majority of the segments of the Missouri River were found to have dominant wavelengths of light significantly higher than 560 nm.  

"}, {"id": "D", "text": "

Segments of the Missouri River flowing into lakes typically had dominant wavelengths of light above 560 nm, while segments flowing out of lakes typically had dominant wavelengths below 560 nm.

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer because it presents a finding that, if true, would support Gardner and colleagues’ conclusion that segments of the Missouri River flowing into lakes tend to carry more sediment than do segments of the river flowing out of lakes. The text says that rivers appear yellow when they contain a lot of sediment and appear red when they contain a lot of algae. It goes on to explain that Gardner and colleagues measured the wavelengths of light for different segments of rivers in the United States and classified those wavelength measurements into colors: red for wavelengths of 495 nanometers and below, blue for wavelengths between 495 and 560 nanometers, and yellow for wavelengths of 560 nanometers and above. Combined with the earlier information about river colors, this suggests that rivers rich in sediment will have wavelengths of 560 nanometers and above (since such rivers appear yellow). If researchers found that Missouri River segments flowing into lakes tend to have wavelengths above 560 nanometers and segments flowing out of lakes tend to have wavelengths below 560 nanometers, this finding would support Gardner and colleagues’ conclusion, since it would suggest that the river tends to carry more sediment when it flows into lakes than when it flows out of lakes. 

Choice A is incorrect because finding that sections of the Missouri River with high chlorophyll-a levels have wavelengths between 490 and 560 nanometers would be irrelevant to the researchers’ conclusion that segments of the river flowing into lakes are richer in sediment than are segments of the river flowing out of lakes. This finding would not indicate anything about segments flowing into or out of lakes. Choice B is incorrect because finding that lakes through which the Missouri River passes have higher wavelengths near their shores than in the center would not support the researchers’ conclusion that segments of the river flowing into lakes have more sediment than segments flowing out of lakes. This finding would suggest only that there is more sediment around the edges of lakes than in their centers, which does not have any direct bearing on the researchers’ conclusion about river segments flowing into and out of lakes. Choice C is incorrect because finding that most segments of the Missouri River have wavelengths significantly higher than 560 nanometers would suggest that most segments of the river are high in sediment, not that segments flowing into lakes are higher in sediment than segments flowing out of lakes. Only a comparison of river segments flowing into lakes with segments flowing out of lakes can support the researchers’ conclusion. 

"}, {"id": "4603d1f7", "domain": "Information and Ideas", "skill": "Inferences", "difficulty": "E", "type": "mc", "stimulus": "

In their book Smart Pricing, Jagmohan Raju and Z. John Zhang consider musicians’ use of the nontraditional “pay as you wish” pricing model. This model generally offers listeners the choice to pay more or less than a suggested price for a song or album—or even to pay nothing at all. As the authors note, that’s the option most listeners chose for an album by the band Harvey Danger. Only about 1% opted to pay for the album, resulting in earnings below the band’s expectations. But the authors also discuss musician Jane Siberry, who saw significant earnings from her “pay as you wish” online music store as a result of many listeners choosing to pay more than the store’s suggested prices. Hence, the “pay as you wish” model may ______blank

", "stem": "

Which choice most logically completes the text?

", "choices": [{"id": "A", "text": "

prove financially successful for some musicians but disappointing for others.

"}, {"id": "B", "text": "

hold greater financial appeal for bands than for individual musicians.

"}, {"id": "C", "text": "

cause most musicians who use the model to lower the suggested prices of their songs and albums over time.

"}, {"id": "D", "text": "

more strongly reflect differences in certain musicians’ popularity than traditional pricing models do.

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. In one example, musicians made less money than expected by using the “pay as you wish” model. In the other example, a musician made more money than expected. This suggests that some musicians may have more success than others using the “pay as you wish” model.

Choice B is incorrect. This inference isn’t supported. In the examples provided, the individual musician was more successful with the “pay as you wish” model than the band was. Choice C is incorrect. This inference isn’t supported. The passage provides no instances in which musicians changed the suggested prices of their songs or albums, nor does it mention this as a possibility. Choice D is incorrect. This inference isn’t supported. The text never discusses the differences in popularity of different musicians, so there is no basis to make this inference.

"}, {"id": "e185a21f", "domain": "Information and Ideas", "skill": "Inferences", "difficulty": "H", "type": "mc", "stimulus": "

One theory behind human bipedalism speculates that it originated in a mostly ground-based ancestor that practiced four-legged “knuckle-walking,” like chimpanzees and gorillas do today, and eventually evolved into moving upright on two legs. But recently, researchers observed orangutans, another relative of humans, standing on two legs on tree branches and using their arms for balance while they reached for fruits. These observations may suggest that ______blank

", "stem": "

Which choice most logically completes the text?

", "choices": [{"id": "A", "text": "

bipedalism evolved because it was advantageous to a tree-dwelling ancestor of humans.

"}, {"id": "B", "text": "

bipedalism must have evolved simultaneously with knuckle-walking and tree-climbing.

"}, {"id": "C", "text": "

moving between the ground and the trees would have been difficult without bipedalism.

"}, {"id": "D", "text": "

a knuckle-walking human ancestor could have easily moved bipedally in trees.  

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer because it most logically completes the text’s discussion of the evolution of bipedalism in humans. According to the text, one potential explanation for humans walking upright on two legs is that the behavior evolved from an ancestor that mostly stayed on the ground and walked on four limbs, as modern chimpanzees and gorillas do. However, the finding that orangutans, also a relative of humans, sometimes stand on two legs in trees while using their arms to balance and reach for fruits suggests another possible explanation: perhaps a tree-dwelling ancestor of humans began moving on two legs because it offered an advantage, such as access to certain foods.

Choice B is incorrect because the finding that modern orangutans (a relative of humans) sometimes stand on two legs in trees doesn’t offer any insight into when either bipedalism or tree-climbing behavior emerged in human ancestors. Additionally, the text indicates that one theory is that bipedalism evolved from a mostly ground-based ancestor that was already practicing knuckle-walking, not that bipedalism and knuckle-walking developed at the same time. Choice C is incorrect because the finding that orangutans (a relative of humans) sometimes stand on two legs in trees doesn’t offer any insight into how difficult it would’ve been to move between the ground and the trees without bipedalism; there’s no suggestion that climbing or moving in trees depends on the ability to walk on two legs rather than four, even if that ability might be helpful in certain circumstances. Choice D is incorrect because the finding that orangutans (a relative of humans) sometimes stand on two legs in trees doesn’t suggest that a knuckle-walking human ancestor could’ve easily moved on two legs in trees. Although the text indicates that bipedalism may have evolved from a human ancestor that mostly stayed on the ground and walked on four limbs, it gives no indication of how easy it would’ve been for such an ancestor to move bipedally in trees. 

"}, {"id": "20000f5f", "domain": "Information and Ideas", "skill": "Inferences", "difficulty": "E", "type": "mc", "stimulus": "

Arthur Conan Doyle’s stories about detective Sherlock Holmes were published between 1887 and 1927. They have inspired countless successful adaptations, including comic strips, movies, and a television series Sherlock Hound, directed by Hayao Miyazaki, who is celebrated for his animated movies. Until 2014, these stories were copyrighted. The right to adapt was only available to those who could afford the copyright fee and gain approval from the strict copyright holders of Doyle’s estate. Some journalists predict that the number of Sherlock Holmes adaptations is likely to increase since the end of copyright means that ______blank

", "stem": "

Which choice most logically completes the text?

", "choices": [{"id": "A", "text": "

Doyle’s original stories will become hard to find.

"}, {"id": "B", "text": "

people will become more interested in detective stories than they were in the 1800s.

"}, {"id": "C", "text": "

producing adaptations will become easier and less expensive.

"}, {"id": "D", "text": "

the former copyright holders of Doyle’s estate will return fees they collected.

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. The text tells us that because of the copyright, adapting Sherlock Holmes stories used to be expensive and difficult. This suggests that after the copyright ends, it will be less expensive and less difficult to adapt these stories.

Choice A is incorrect. This inference isn’t supported. The text never suggests that the copyright ending will make Sherlock Holmes stories harder to find. Instead, it suggests that adaptations of these stories will be easier and less expensive to make. Choice B is incorrect. This inference isn’t supported. The text never discusses people’s interest in detective stories, so there is no basis to make this inference. Choice D is incorrect. This inference isn’t supported. The text never suggests that copyright fees from the past are returned after a copyright ends, so there is no basis to make this inference.

"}, {"id": "25176ff8", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "M", "type": "mc", "stimulus": "

“Mrs. Spring Fragrance” is a 1912 short story by Sui Sin Far. In the story, Mrs. Spring Fragrance, a Chinese immigrant living in Seattle, is traveling in California. In letters to her husband and friend, she demonstrates her concern for what’s happening at her home in Seattle while she is away: ______blank

", "stem": "

Which quotation from Mrs. Spring Fragrance’s letters most effectively illustrates the claim?

", "choices": [{"id": "A", "text": "

“My honorable cousin is preparing for the Fifth Moon Festival, and wishes me to compound for the occasion some American ‘fudge,’ for which delectable sweet, made by my clumsy hands, you have sometimes shown a slight prejudice.”

"}, {"id": "B", "text": "

“Next week I accompany Ah Oi to the beauteous town of San José. There will we be met by the son of the Illustrious Teacher.”

"}, {"id": "C", "text": "

“Forget not to care for the cat, the birds, and the flowers. Do not eat too quickly nor fan too vigorously now that the weather is warming.”

"}, {"id": "D", "text": "

“I am enjoying a most agreeable visit, and American friends, as also our own, strive benevolently for the accomplishment of my pleasure.”

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer because it presents a quotation that illustrates the claim that Mrs. Spring Fragrance demonstrates concern for what’s happening at home while she’s in California. By giving reminders to “care for the cat, the birds, and the flowers,” “not eat too quickly,” and avoid engaging in strenuous activity in the heat, Mrs. Spring Fragrance shows that she’s thinking about what’s happening at home and wants to ensure everything is taken care of.

Choice A is incorrect because the quotation, while it does suggest that Mrs. Spring Fragrance has made fudge at home before, is focused on preparations for an upcoming festival, not on concerns for anything happening at home while Mrs. Spring Fragrance is away. Choice B is incorrect because the quotation has to do with an upcoming event during Mrs. Spring Fragrance’s trip—visiting San José and meeting someone new—rather than her concern for what’s happening at home. Choice D is incorrect because the quotation is focused on how Mrs. Spring Fragrance feels about her trip and the friends she’s seeing, not on her concern for what’s happening at home.

"}, {"id": "67b59a67", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "M", "type": "mc", "stimulus": "

Plants like potatoes, tomatoes, and soybeans are susceptible to bacterial wilt disease caused by the bacteria Ralstonia solanacearum. A multinational team of scientists led by Zhong Wei studied whether other microbes in the soil might influence the degree to which plants are affected by the disease. The team sampled soil surrounding individual tomato plants over time and compared the results of plants that became diseased with those that remained healthy. They concluded that the presence of certain microbes in the soil might explain the difference between healthy and diseased plants.

", "stem": "

Which finding, if true, would most directly support the team’s conclusion?

", "choices": [{"id": "A", "text": "

The soil surrounding healthy plants contained significantly higher concentrations of microbes known to inhibit Ralstonia solanacearum than the soil surrounding diseased plants did.

"}, {"id": "B", "text": "

The soil surrounding the plants contained high concentrations of Ralstonia solanacearum regardless of whether the plants were affected by wilt disease.

"}, {"id": "C", "text": "

The soil surrounding healthy plants tended to have significantly higher moisture levels than the soil surrounding diseased plants did. 

"}, {"id": "D", "text": "

By the end of the experiment, over half the plants had been affected by wilt disease regardless of differences in the types and concentrations of microbes in the surrounding soil. 

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. This choice provides evidence that directly links the presence of R. solanacearum-inhibiting microbes in the soil to the health of tomato plants.

Choice B is incorrect. This choice would weaken the team’s conclusion. It suggests that the presence of the disease-causing bacteria had no effect on the health of the tomato plants. Choice C is incorrect. This choice doesn’t support the team’s conclusion. The conclusion is about microbes, not soil moisture. Choice D is incorrect. This choice would weaken the team’s conclusion. It suggests that the presence of the bacteria-inhibiting microbe in soil had no effect on the health of the tomato plants.

"}, {"id": "c228bd45", "domain": "Information and Ideas", "skill": "Central Ideas and Details", "difficulty": "E", "type": "mc", "stimulus": "

The following text is adapted from Edith Nesbit’s 1906 novel The Railway Children.

\n\n

Mother did not spend all her time in paying dull [visits] to dull ladies, and sitting dully at home waiting for dull ladies to pay [visits] to her. She was almost always there, ready to play with the children, and read to them, and help them to do their home-lessons. Besides this she used to write stories for them while they were at school, and read them aloud after tea, and she always made up funny pieces of poetry for their birthdays and for other great occasions.

", "stem": "

According to the text, what is true about Mother?

", "choices": [{"id": "A", "text": "

She wishes that more ladies would visit her.

"}, {"id": "B", "text": "

Birthdays are her favorite special occasion. 

"}, {"id": "C", "text": "

She creates stories and poems for her children.

"}, {"id": "D", "text": "

Reading to her children is her favorite activity. 

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer because it describes something that is true of Mother, as presented in the text. The text indicates that in addition to other activities, Mother writes stories for her children while they are at school and makes up “funny pieces of poetry” for certain occasions. 

Choice A is incorrect because the text suggests that Mother prefers to spend her time with her children and doesn’t sit at home hoping that ladies will visit her. Choice B is incorrect because the text says only that Mother makes up poetry for the children’s birthdays, not that she likes birthdays more than other special occasions. Choice D is incorrect because the text doesn’t suggest that Mother prefers reading to her children over the other activities she does with them, such as playing with them and writing stories and poems for them. 

"}, {"id": "7edfb2c5", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "M", "type": "mc", "stimulus": "

\n\n\n\n\n7006005004003002001000Temperature (\u00b0C)L5_239K5_106K3_18K3_9Estimated Temperatures to which Evron Quarry Artifacts Were Exposedartifact

\n

Flint artifacts dating to 800,000 to 1,000,000 years ago have been recovered from the Evron Quarry in Israel. Likely created by the hominin Homo erectus, the artifacts have no visual features suggesting that they were exposed to fire, leading some scholars to conclude that these hominins had not acquired control of fire. But Zane Stepka and colleagues recently used a new method to determine whether these artifacts had been exposed to temperatures above 400\u00b0C (the typical temperature campfires reach) and concluded that the hominins who inhabited the site may have had control of fire.\u00a0

", "stem": "

Which choice best describes data in the graph that support the team’s conclusion?

", "choices": [{"id": "A", "text": "

Artifacts K5_106 and K3_9 were exposed to temperatures above 400°C.

"}, {"id": "B", "text": "

Artifacts L5_239 and K3_18 were exposed to temperatures of approximately 550°C and 650°C, respectively.

"}, {"id": "C", "text": "

All of the artifacts were exposed to temperatures above 100°C.

"}, {"id": "D", "text": "

Artifact K3_9 was exposed to a higher temperature than was artifact K5_106.

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. Campfires typically reach over 400°C, so human artifacts that were exposed to temperatures higher than this may indicate some human control over fire.

Choice A is incorrect. This choice misreads the graph. Neither artifact K3_9 nor K5_106 was exposed to temperatures above even 200°C. Choice C is incorrect. This choice doesn’t support the claim. Campfires typically reach over 400°C, so exposure to temperatures of 100°C wouldn’t demonstrate exposure to fire. Choice D is incorrect. This choice doesn’t support the claim. Both artifacts K3_9 and K5_106 were exposed to temperatures of less than 200°C. Since campfires typically reach over 400°C, this wouldn’t demonstrate exposure to fire.

"}, {"id": "0c622cfb", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "M", "type": "mc", "stimulus": "

Although it’s clear that Mars once had liquid water on its surface, astronomers have debated whether the evidence of ancient water reflects a prolonged phase of warm, wet conditions—the so-called wet and warm scenario—or a brief period of melting in an otherwise consistently frozen environment. Researchers Benjamin T. Cardenas and Michael P. Lamb recently added to this debate by using data from NASA and the Mars Orbiter Laser Altimeter to map the topography of what is now a large basin in Mars’s northern hemisphere. Cardenas and Lamb concluded that the wet and warm scenario is likely correct.  

", "stem": "

Which finding about the basin, if true, would most directly support Cardenas and Lamb’s conclusion?

", "choices": [{"id": "A", "text": "

Its dimensions and shape indicate that it is unlikely to have formed as the result of an asteroid or comet impact. 

"}, {"id": "B", "text": "

It has features suggesting that it once held an ocean that underwent gradual sea-level changes over an extended time.

"}, {"id": "C", "text": "

Its physical characteristics are most consistent with it having formed as a result of a massive but short-lived influx of liquid water.

"}, {"id": "D", "text": "

It is surrounded by channels that could have been formed either by running water or by flowing lava. 

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. This choice provides direct support for the researchers’ conclusion. If the basin once held an ocean of liquid water for \"an extended time,\" that supports the \"wet and warm scenario\" on Mars, which involved a \"prolonged\" period of temperate conditions (and not just a \"brief period of melting\").

Choice A is incorrect. This choice doesn’t provide support for the researchers’ conclusions. The dimensions of the basin have little bearing on whether or not it was filled with liquid water, and for how long, and that’s the evidence that would support the \"wet and warm\" theory. Similarly, whether or not the basin was formed by an asteroid or a comet is irrelevant to the question of whether or not there was water in the basin for a long period. Choice C is incorrect. This choice does not provide support for the researchers’ conclusions, but rather the opposite. A \"massive but short lived influx\" of liquid water is not the same as a \"prolonged phase of warm, wet conditions.\" It more reflects the opposing theory, a \"brief period of melting.\" Choice D is incorrect. This choice does not support Cardenas and Lamb’s conclusion. Both theories about liquid water on Mars (\"wet and warm\" and \"brief period of melting\") involve flowing water, but lava isn’t mentioned at all in the text. Therefore, this choice doesn’t provide exclusive support for either theory.

"}, {"id": "5fb6ed10", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "M", "type": "mc", "stimulus": "

The Land of Enchantment is a 1906 travel book by Lilian Whiting. In the book, which describes the experience of traveling through the southwestern United States by train, Whiting reflects on the escape from everyday life that such a journey provides: ______blank 

", "stem": "

Which quotation from The Land of Enchantment most effectively illustrates the claim?

", "choices": [{"id": "A", "text": "

“The opportunities and advantages already offered and constantly increasing are greater than would at first be considered possible.”

"}, {"id": "B", "text": "

“The social and the picturesque charm of the long journey is singularly enhanced by the leisurely stops made for refreshment.” 

"}, {"id": "C", "text": "

“The real journey begins, of course, at Chicago, and as these trains leave in the evening the traveller fares forth in the seclusion of his berth.”

"}, {"id": "D", "text": "

“One experiences a certain sense of detachment from ordinary day and daylight duties that is exhilarating.” 

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer because. This quotation specifically describes a \"sense of detachment from ordinary day,\" which matches the claim’s focus on \"escape from everyday life.\"

Choice A is incorrect. While this quotation describes new opportunities associated with Whiting’s experience, it doesn’t frame these opportunities as \"an escape,\" and it doesn’t directly compare Whiting’s journey with \"everyday life.\" Choice B is incorrect. While this quotation includes a positive characterization of Whiting’s journey, it doesn’t specifically address the idea of an \"escape from everyday life,\" which is the focus of the claim. Choice C is incorrect. This quotation focuses on where the journey begins, not on how it feels like an \"escape from everyday life.\"

"}, {"id": "f452410b", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "E", "type": "mc", "stimulus": "

Results of Footprint Analysis for Two Sets of Theropod Tracks

TracksEstimated footprint length (centimeters)Average stride length (meters)Estimated mean speed (meters per second)
La Torre 6A32.85.236.5–10.3
La Torre 6B28.95.578.8–12.4

\n

The table shows data from paleontologist Angélica Torices and colleagues’ 2021 study of two sets of dinosaur tracks preserved in a fossilized lake bed in Spain. The tracks, referred to as La Torre 6A and La Torre 6B, were left by two individual theropods (dinosaurs that walked on two legs). The team’s findings suggest that of the two theropods, the one that left the La Torre 6B tracks had a higher maximum mean speed, ______blank

", "stem": "

Which choice most effectively uses data from the table to complete the claim?

", "choices": [{"id": "A", "text": "

a longer footprint, and a longer average stride.

"}, {"id": "B", "text": "

a longer footprint, and a shorter average stride.

"}, {"id": "C", "text": "

a shorter footprint, and a longer average stride.

"}, {"id": "D", "text": "

a shorter footprint, and a shorter average stride.

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer because it most effectively uses data from the table to complete the claim about the tracks left by two therapods. The table indicates that the set of tracks labeled La Torre 6A has an estimated footprint length of 32.8 centimeters, an average stride length of 5.23 meters, and an estimated mean speed of 6.5–10.3 meters per second. For the set of tracks labeled La Torre 6B, on the other hand, the estimated footprint length is 28.9 centimeters, the average stride length is 5.57 meters, and the estimated mean speed is 8.8–12.4 meters per second. Therefore, the therapod that left the La Torre 6B tracks had a shorter footprint and a longer average stride than the one that left the La Torre 6A tracks.

Choice A is incorrect. While it is true that of the two therapods, the one that left the La Torre 6B tracks had a longer average stride, it didn’t have a longer footprint: the table shows that its estimated footprint length is 28.9 centimeters, while La Torre 6A’s estimated footprint length is 32.8 centimeters. Choice B is incorrect because the table shows that of the two therapods, the one that left the La Torre 6B tracks had a footprint length estimated at 28.9 centimeters, which is shorter than the 32.8 centimeters estimated for the other set of tracks. Moreover, the therapod that left the La Torre 6B tracks had a longer average stride, not shorter: 5.57 meters, compared with 5.23 meters for the other set of tracks. Choice D is incorrect. While it is true that of the two therapods, the one that left the La Torre 6B tracks had a shorter footprint, it didn’t have a shorter average stride: the table shows that its average stride length is 5.57 meters, while La Torre 6A’s average stride length is 5.23 meters.

"}, {"id": "9731a22b", "domain": "Information and Ideas", "skill": "Central Ideas and Details", "difficulty": "H", "type": "mc", "stimulus": "

Paleontologist Lucas E. Fiorelli and colleagues have reported the discovery at a mine in Brazil of several egg clutches, partially preserved single eggs, and egg shells from the Late Cretaceous period. The researchers have concluded that the area was once a nesting and breeding site for titanosaurs, a group of sauropod dinosaurs. The finding is significant given the previous lack of known nesting sites in northern regions of South America, which led many paleontologists to assume that titanosaurs migrated south to lay eggs.

", "stem": "

What does the text most strongly suggest about the site discovered by the researchers?

", "choices": [{"id": "A", "text": "

It is the earliest known example of a titanosaur nesting and breeding site.

"}, {"id": "B", "text": "

It was very difficult to excavate given that it was discovered in a mine.

"}, {"id": "C", "text": "

It may have been occupied by other sauropods in addition to titanosaurs.

"}, {"id": "D", "text": "

It is farther north than any other nesting site discovered in South America.

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer because it presents a statement about the site discovered by the researchers that is supported by the text. The text discusses Fiorelli and colleagues’ discovery of egg clutches, single eggs, and eggshells in a Brazilian mine. According to the text, the presence of these eggs, which are from the Late Cretaceous period, led the researchers to conclude that the location was once a nesting and breeding site for titanosaurs. The text then explains that the finding is important because of the “previous lack of known nesting sites in northern regions of South America.” If there haven’t been any other discoveries of a nesting site in South America’s northern regions and the site in the Brazilian mine is the first, then the text strongly suggests that the site is farther north than other nesting sites that have been discovered in South America. 

Choice A is incorrect because the text doesn’t suggest that the site discovered by Fiorelli and colleagues is the earliest titanosaur nesting and breeding site known to paleontologists but rather that it’s the first nesting site found in northern regions of South America. Moreover, the text doesn’t suggest how the timeline of the newly discovered site compares with that of other titanosaur nesting and breeding sites. Choice B is incorrect because there is no mention in the text about any difficulties that Fiorelli and colleagues faced when they were excavating the nesting and breeding site in the Brazilian mine. Choice C is incorrect because the text doesn’t support the idea that the nesting and breeding site in the Brazilian mine was occupied by sauropods other than titanosaurs. The text simply mentions that titanosaurs are sauropod dinosaurs and presents the researchers’ conclusion that the site they discovered was for titanosaurs. 

"}, {"id": "db876fd5", "domain": "Information and Ideas", "skill": "Inferences", "difficulty": "M", "type": "mc", "stimulus": "

Songbirds learn to respond to and imitate their species’ songs from an early age. With each generation, small differences are introduced that result in distinct variations—called dialects—among geographically isolated populations of the same species. A research study examined whether twelve-day-old Ficedula hypoleuca (pied flycatcher) nestlings prefer local dialects over the unfamiliar dialects of nonlocal F. hypoleuca populations: the more begging calls the nestlings made in response to a song, the stronger their preference. The researchers found that nestlings produced more begging calls in response to their own dialect than to nonlocal dialects. Since song preference plays a role in songbird mate selection, the finding suggests that ______blank

", "stem": "

Which choice most logically completes the text?

", "choices": [{"id": "A", "text": "

F. hypoleuca nestlings’ preference for their own dialect likely disappears as they mature to promote socialization between different F. hypoleuca populations.

"}, {"id": "B", "text": "

F. hypoleuca nestlings who show an early preference for their own dialect are likely to receive more food from their caretakers than nestlings who show no preferences among any F. hypoleuca dialects. 

"}, {"id": "C", "text": "

F. hypoleuca nestlings’ preference for their own dialect likely drives them when they mature to reproduce with other F. hypoleuca from local rather than nonlocal populations.  

"}, {"id": "D", "text": "

F. hypoleuca nestlings show a preference for both local F. hypoleuca dialects and the songs of other local songbirds over the songs of nonlocal birds of any species.

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. Because “song preference plays a role in songbird mate selection,” and because F. hypoleuca nestlings display a preference for local dialects, we can infer that they will be more likely to choose mates from local populations.

Choice A is incorrect. We don’t have any information suggesting that this preference disappears, so there’s no basis for this inference. Choice B is incorrect. Although the passage discusses the number of begging calls made in response to various F. hypoleuca dialects, no mention is made about the amount of food received based on dialect preference. Therefore, there’s no basis for this inference. Choice D is incorrect. There’s no mention in the passage of methods of other types of local songbirds, so there’s no basis for this inference.

"}, {"id": "09f9edb0", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "H", "type": "mc", "stimulus": "

In the 1980s, many musicians and journalists in the English-speaking world began to draw attention to music from around the globe—such as mbaqanga from South Africa and quan h\u1ecd from Vietnam—that can’t be easily categorized according to British or North American popular music genres, typically referring to such music as “world music.” While some scholars have welcomed this development for bringing diverse musical forms to prominence in countries where they’d previously been overlooked, musicologist Su Zheng claims that the concept of world music homogenizes highly distinct traditions by reducing them all to a single category.

", "stem": "

Which finding about mbaqanga and quan h\u1ecd, if true, would most directly support Zheng’s claim?

", "choices": [{"id": "A", "text": "

Mbaqanga and quan h\u1ecd developed independently of each other and have little in common musically.

"}, {"id": "B", "text": "

Mbaqanga is significantly more popular in the English-speaking world than quan h\u1ecd is. 

"}, {"id": "C", "text": "

Mbaqanga and quan h\u1ecd are now performed by a diverse array of musicians with no direct connections to South Africa or Vietnam. 

"}, {"id": "D", "text": "

Mbaqanga and quan h\u1ecd are highly distinct from British and North American popular music genres but similar to each other.

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. Zheng’s claim is that the idea of world music “homogenizes” (meaning makes similar) distinct kinds of music by reducing them to one category. In other words, Zheng thinks the concept of world music is a harmful oversimplification of diverse musical forms. To support this claim, we need evidence that these musical traditions are so different from one another that they should not fall into the same category. If it’s true that mbaqanga and quan h\u1ecd developed separately and have little in common musically, then it wouldn’t make sense to lump them into the same category.

Choice B is incorrect. If true, this wouldn’t affect the claim. To support the claim, we need evidence that these musical traditions are so different from one another that they should not fall into the same category. A difference in popularity doesn’t necessarily mean that the two musical traditions shouldn’t be categorized together: instead, we need to know if the music itself is similar or different. Choice C is incorrect. If true, this wouldn’t affect the claim. To support the claim, we need evidence that these musical traditions are so different from each other that they should not fall into the same category. This choice doesn’t do that. Choice D is incorrect. If true, this would actually weaken the claim. Zheng thinks it’s reductive or oversimplifying to put distinct musical traditions into a single category. But if mbaqanga and quan h\u1ecd are similar to each other, then it would make sense to put them in the same category.

"}, {"id": "f39507a3", "domain": "Information and Ideas", "skill": "Inferences", "difficulty": "H", "type": "mc", "stimulus": "

One challenge when researching whether holding elected office changes a person’s behavior is the problem of ensuring that the experiment has an appropriate control group. To reveal the effect of holding office, researchers must compare people who hold elected office with people who do not hold office but who are otherwise similar to the office-holders. Since researchers are unable to control which politicians win elections, they therefore ______blank

", "stem": "

Which choice most logically completes the text?

", "choices": [{"id": "A", "text": "

struggle to find valid data about the behavior of politicians who do not currently hold office.

"}, {"id": "B", "text": "

can only conduct valid studies with people who have previously held office rather than people who presently hold office.

"}, {"id": "C", "text": "

should select a control group of people who differ from office holders in several significant ways.

"}, {"id": "D", "text": "

will find it difficult to identify a group of people who can function as an appropriate control group for their studies.

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer because it presents the conclusion that most logically follows from the text’s discussion of the challenge researchers face when studying the effects of holding elected office on a person’s behavior. The text explains that it’s hard for researchers to test for the effects that elected office has on people because finding people to serve as a control group is difficult. The text indicates that a control group needs to be made up of people who share characteristics of the group being tested but don’t have the variable being tested (in this case, holding elected office). Because researchers aren’t able to influence who wins elections, they’re also unable to determine who would serve as an appropriately similar member of a control group. Thus, it logically follows that researchers will find it difficult to identify a group of people who can function as an appropriate control group for their studies.

Choice A is incorrect because the text focuses on the struggle to put together a control group for experiments; it doesn’t suggest that finding information about politicians’ behavior is difficult. Choice B is incorrect because the experiments mentioned in the text are testing the effects of holding elected office on a person’s behavior. Studying people who have already held elected office wouldn’t provide an opportunity to note any behavioral changes that the position might cause. Choice C is incorrect because the text defines people in a control group as those “who are otherwise similar to the office-holders”; selecting people who differ from the office-holders wouldn’t fit the criteria for an appropriate control group. 

"}, {"id": "5325b3cc", "domain": "Information and Ideas", "skill": "Central Ideas and Details", "difficulty": "M", "type": "mc", "stimulus": "

Philadelphia’s Black Pearl Chamber Orchestra, founded by Jeri Lynne Johnson, performs classical music, from well-known compositions by Beethoven to contemporary works by Jessie Montgomery. For the orchestra’s iConduct! program, Johnson invites community members to learn some basic elements of conducting and then experience conducting the Black Pearl orchestra themselves.

", "stem": "

Which choice best states the main idea of the text?

", "choices": [{"id": "A", "text": "

The Black Pearl orchestra performs music from all over the world but mostly performs music composed by Philadelphians.

"}, {"id": "B", "text": "

Johnson founded the Black Pearl orchestra to perform classical music by contemporary artist Jessie Montgomery. 

"}, {"id": "C", "text": "

The Black Pearl orchestra gives community members the chance to both listen to and participate in classical music performance. 

"}, {"id": "D", "text": "

Johnson has community members conduct an orchestra to demonstrate how difficult the task is.

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer because it most accurately states the main idea of the text. The text begins by stating that the Black Pearl orchestra performs classical music, and then goes on to explain that the orchestra offers an iConduct! program. According to the text, this program offers community members the opportunity to learn some basics about conducting and then apply what they learn by conducting the orchestra themselves. Thus, the main idea of the text is that community members can both listen to and participate in a classical music performance.

Choice A is incorrect. Although the text states that the Black Pearl orchestra is based in Philadelphia, it doesn’t indicate that most of the music it plays was composed by Philadelphians. Choice B is incorrect. Although the text does state that Johnson founded the Black Pearl orchestra, this is just a detail and not the main focus of the text. Moreover, while the text does say that the orchestra sometimes plays music by Montgomery, it doesn’t assert that the orchestra was founded solely for the purpose of performing Montgomery’s work. Choice D is incorrect. Although the text explains that community members are invited to conduct the Black Pearl orchestra after participating in the iConduct! program, the text doesn’t indicate that Johnson allows community members to do this for the specific purpose of showing how difficult the task is.

"}, {"id": "6bc0e595", "domain": "Information and Ideas", "skill": "Inferences", "difficulty": "E", "type": "mc", "stimulus": "

One aspect of in-person shopping that online shopping can’t replicate is the opportunity to touch a product before buying it. Does this difference matter? In an experiment, researchers asked one group of participants to touch a mug and a toy, while another group was prohibited from touching the two items. The participants were then asked how much money they’d pay for the items. People who got to touch the items were willing to pay much more money for them than were people who weren’t allowed to touch the items. This finding suggests that ______blank

", "stem": "

Which choice most logically completes the text?

", "choices": [{"id": "A", "text": "

people who mainly shop online probably spend more money every month than people who mainly shop in person do.

"}, {"id": "B", "text": "

in-person shopping may make products seem more valuable than they seem if only viewed online. 

"}, {"id": "C", "text": "

retailers with in-person and online stores should charge the same price for a given product in both places.

"}, {"id": "D", "text": "

online retailers may be able to raise the prices they charge for products that are only available online.

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. The text tells us that “people who got to touch the items were willing to pay much more money for them than people who weren’t allowed to touch” them. This suggests that being able to interact with a product in person may make it seem more valuable to a shopper.

Choice A is incorrect. The text doesn’t discuss how much people spend each month, so there’s not much basis for this claim. Furthermore, since being able to touch a product tends to make people “willing to pay much more money” for it, we might predict that an online shopper would be willing to spend less on the same purchases as an in-person shopper. Choice C is incorrect. The text doesn’t discuss what retailers “should charge,” so there’s not much basis for this claim. Furthermore, the study in the text suggests that in-person stores may actually be able to charge more for a given product, since shoppers can touch it. Choice D is incorrect. The text doesn’t discuss products that are only available online, so there’s not much basis for this claim. Furthermore, products only available online would still have the problem of shoppers not being able to touch them, and the study suggests that this lowers the prices shoppers are willing to pay.

"}, {"id": "c538954d", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "M", "type": "mc", "stimulus": "

Sense and Sensibility is an 1811 novel by Jane Austen. In the novel, Austen describes Marianne Dashwood’s ability to persuade others of the rightness of her artistic judgments, as is evident when Marianne visits with John Willoughby, a potential suitor: ______blank

", "stem": "

Which quotation from Sense and Sensibility most effectively illustrates the claim?

", "choices": [{"id": "A", "text": "

“Above all, when she heard him declare, that of music and dancing he was passionately fond, she gave him such a look of approbation as secured the largest share of his discourse to herself for the rest of his stay.”

"}, {"id": "B", "text": "

“Their taste was strikingly alike. The same books, the same passages were idolized by each—or if any difference appeared, any objection arose, it lasted no longer than till the force of her arguments and the brightness of her eyes could be displayed.”

"}, {"id": "C", "text": "

“It was only necessary to mention any favourite amusement to engage her to talk. She could not be silent when such points were introduced, and she had neither shyness nor reserve in their discussion.”

"}, {"id": "D", "text": "

“They speedily discovered that their enjoyment of dancing and music was mutual, and that it arose from a general conformity of judgment in all that related to either. Encouraged by this to a further examination of his opinions, she proceeded to question him on the subject of books.”

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. By showing that \"any difference\" in taste was quickly overcome by \"the force of [Marianne’s] arguments,\" this choice effectively demonstrates Marianne’s \"ability to persuade others.\"

Choice A is incorrect. This choice doesn’t effectively illustrate the claim. This choice shows that Marianne and John share an interest in music and dancing, but it doesn’t provide evidence of Marianne’s \"ability to persuade others.\" Choice C is incorrect. This choice doesn’t effectively illustrate the claim. This choice shows that Marianne enjoys talking about her interests, but it doesn’t provide evidence of Marianne’s \"ability to persuade others.\" Choice D is incorrect. This choice doesn’t effectively illustrate the claim. This choice shows that Marianne and John share many interests and generally agree on music and dancing, but it doesn’t provide evidence of Marianne’s \"ability to persuade others.\"

"}, {"id": "9debe79a", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "E", "type": "mc", "stimulus": "

Average Temperatures in July in Four Locations in the Navajo Nation

LocationAverage highest temperature (Fahrenheit)Average lowest temperature (Fahrenheit)
Teec Nos Pos94°65°
Cameron99°65°
Ramah83°50°
Tuba City83°50°

\n

The Navajo Nation has the largest land area of any tribal nation in the United States: over 27,000 square miles in the Southwest. Because this area is so huge and its communities are located at various elevations, the people of the Navajo Nation can experience different climate conditions depending on where they live. For example, in July, ______blank

", "stem": "

Which choice most effectively uses data from the table to complete the statement?

", "choices": [{"id": "A", "text": "

the lowest temperature for both Cameron and Teec Nos Pos was 65°.

"}, {"id": "B", "text": "

Tuba City’s average highest temperature was 94°, while Teec Nos Pos’s was 93°.

"}, {"id": "C", "text": "

Ramah’s average highest temperature was 83°, while Cameron’s was 99°.

"}, {"id": "D", "text": "

the lowest temperature for both Ramah and Tuba City was 50°.

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer because it effectively uses data from the table to complete the statement, providing an example of how the people of the Navajo Nation can experience different climate conditions depending on where they live. The table shows the average highest temperatures and average lowest temperatures in four locations in the Navajo Nation in July. According to the table, Ramah’s average highest temperature for July was 83°, whereas Cameron’s average highest temperature was much higher, at 99°. This difference illustrates the statement that the people of the Navajo Nation can experience different climate conditions depending on where they live.

Choice A is incorrect because it states that Cameron and Teec Nos Pos had the same average lowest temperature (65°) for July, which suggests a similarity in climate conditions in those locations rather than a difference. Choice B is incorrect because it misrepresents the data from the table, which shows that the average highest temperature in July for Tuba City was 83°, not 94°, and for Teec Nos Pos it was 94°, not 93°. Even if the cited data accurately reflected the data in the table, the similarity between the two values for average highest temperature would suggest that people in the two locations likely experience similar climate conditions, not different climate conditions. Choice D is incorrect because it states that Ramah and Tuba City had the same average lowest temperature (50°) for July, which suggests a similarity in climate conditions in those locations rather than a difference.

"}, {"id": "f9bd4e61", "domain": "Information and Ideas", "skill": "Inferences", "difficulty": "H", "type": "mc", "stimulus": "

German theater practitioner Bertolt Brecht (1898–1956) believed that theater should elicit an intellectual rather than an emotional response from audiences, provoking them to consider social and political realities that extend beyond the characters and events depicted onstage. Brecht’s influence can be seen in English playwright Caryl Churchill’s 1979 play Cloud 9: although the play sometimes invites empathetic reactions, it primarily works to engage audiences in an interrogation of patriarchy and colonialism, which it does by placing audiences at a distance, thereby encouraging them to ______blank

", "stem": "

Which choice most logically completes the text?

", "choices": [{"id": "A", "text": "

focus on the characters’ beliefs about social and political issues as revealed by the characters’ actions.

"}, {"id": "B", "text": "

reflect on social and political phenomena not directly related to patriarchy and colonialism.

"}, {"id": "C", "text": "

recognize pertinent social and political parallels between Germany during Brecht’s time and England at the time when Churchill was writing Cloud 9.

"}, {"id": "D", "text": "

be dispassionate as they think critically about the social and political questions raised by the play.

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. Churchill’s play was influenced by Brecht’s belief that theater should elicit an intellectual rather than an emotional response from audiences, making them think about social and political issues that also exist outside of the play. Therefore, it makes sense that Churchill would strive to have audiences think dispassionately (i.e., without emotion) and critically about the social and political questions raised by the play.

Choice A is incorrect. The passage mentions that Churchill was influenced by Brecht’s belief that plays should provoke audience members “to consider social and political realities that extend beyond the characters and events depicted onstage,” so there’s no basis for an inference about audience members deeply engaging with characters’ beliefs and actions. Choice B is incorrect. Reflecting on things that aren’t related to patriarchy and colonialism wouldn’t “engage audiences in an interrogation of patriarchy and colonialism.” That creates a confusing contradiction. Choice C is incorrect. No mention is made of social and political issues in Germany during Brecht’s time, so there’s no basis for this inference.

"}, {"id": "f7bd14de", "domain": "Information and Ideas", "skill": "Central Ideas and Details", "difficulty": "H", "type": "mc", "stimulus": "

Several scholars have argued that conditions in England in the late ninth through early eleventh centuries—namely, burgeoning literacy amid running conflicts between England’s Anglo-Saxon kingdoms and Danish invaders—were especially conducive to the production of the Old English epic poem Beowulf, and they have dated the poem’s composition accordingly. It is not inconceivable that Beowulf emerged from such a context, but privileging contextual fit over the linguistic evidence of an eighth- or even seventh-century composition requires a level of justification that thus far has not been presented.

", "stem": "

Which choice best states the main idea of the text?

", "choices": [{"id": "A", "text": "

Although there are some grounds for believing that Beowulf was composed between the late ninth and early eleventh centuries, advocates for that view tend to rely on evidence that has been called into question by advocates for an earlier date. 

"}, {"id": "B", "text": "

Although several scholars have dated Beowulf to the late ninth through early eleventh centuries, others have argued that doing so privileges a controversial interpretation of the social conditions of the period.

"}, {"id": "C", "text": "

Although Beowulf fits well with the historical context of England in the late ninth through early eleventh centuries, it fits equally well with the historical context of England in the seventh and eighth centuries. 

"}, {"id": "D", "text": "

Although the claim of a late ninth- through early eleventh-century composition date for Beowulf has some plausibility, advocates for the claim have not compellingly addressed evidence suggesting an earlier date.

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer because it most accurately states the main idea of the text. The text states that some scholars have dated the composition of Beowulf to the late ninth through early eleventh centuries due to the poem’s fit with that period’s historical context. The text goes on to say that while it is “not inconceivable that Beowulf emerged from such a context”—that is, it is possible that Beowulf was composed during the late ninth through eleventh centuries—there is linguistic evidence that the poem was composed earlier, in the seventh or eighth century. According to the text, favoring the historical context over the linguistic evidence requires justification that scholars have not yet supplied. In other words, the text suggests that scholars who favor the later composition date need to explain why the poem’s fit with historical context should take precedence over the linguistic evidence, but they have not yet done so. Thus, the main idea of the text is that while there is some plausibility to the later composition date, advocates for the later date have not compellingly addressed evidence suggestive of an earlier date. 

Choice A is incorrect because the text says that scholars who date the poem to the late ninth through early eleventh centuries have failed to account for the linguistic evidence that the poem may have been composed earlier, not that the evidence those scholars cite in favor of their view is unreliable or that anyone has cast doubt on that evidence. In other words, the text does not suggest that there are problems with the evidence cited by advocates of the later composition date, only that there is other evidence of an earlier composition date that those advocates need to consider. Choice B is incorrect because nothing in the text suggests that those scholars who date the poem to the late ninth through early eleventh centuries are giving priority to a controversial view of the social conditions at that time. The text makes no reference to any controversy about how scholars interpret that historical period. Instead, the text suggests that scholars who date the poem on the basis of its fit with the historical context of England in the late ninth through early eleventh centuries have failed to account for linguistic evidence that the poem may have been composed earlier. Choice C is incorrect because the text says nothing about how well the poem fits the historical context of England in the seventh and eighth centuries, let alone that it fits that historical context as well as it fits the historical context of the late ninth through early eleventh centuries. Rather, the text says that there is linguistic evidence that the poem may have been composed in the seventh or eighth century. 

"}, {"id": "baef99a5", "domain": "Information and Ideas", "skill": "Central Ideas and Details", "difficulty": "E", "type": "mc", "stimulus": "

The following text is adapted from Oscar Wilde’s 1891 novel The Picture of Dorian Gray. Dorian Gray is taking his first look at a portrait that Hallward has painted of him.

\n

Dorian passed listlessly in front of his picture and turned towards it. When he saw it he drew back, and his cheeks flushed for a moment with pleasure. A look of joy came into his eyes, as if he had recognized himself for the first time. He stood there motionless and in wonder, dimly conscious that Hallward was speaking to him, but not catching the meaning of his words. The sense of his own beauty came on him like a revelation. He had never felt it before.

", "stem": "

According to the text, what is true about Dorian?

", "choices": [{"id": "A", "text": "

He wants to know Hallward’s opinion of the portrait.

"}, {"id": "B", "text": "

He is delighted by what he sees in the portrait.

"}, {"id": "C", "text": "

He prefers portraits to other types of paintings.

"}, {"id": "D", "text": "

He is uncertain of Hallward’s talent as an artist.

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer because it presents a statement about Dorian that is directly supported by the text. The narrator of the text says that when Dorian sees his portrait, “his cheeks flushed for a moment with pleasure” and “a look of joy came into his eyes.” The narrator goes on to say that Dorian looked at the portrait “in wonder” and presents him as being so entranced by the portrait that he doesn’t notice what Hallward is saying to him. All these details support the description of Dorian as being delighted by what he sees in the portrait.

Choice A is incorrect because Dorian isn’t depicted as interested in Hallward’s opinion of the portrait but rather as so enraptured by the painting that he’s hardly even aware of Hallward. Choice C is incorrect because the portrait of Dorian is the only painting that is mentioned in the text, so there’s no evidence that Dorian prefers portraits to other types of paintings. Although Dorian is depicted as delighted with this particular portrait, there’s no way of knowing from the text whether he likes portraits better than other kinds of paintings. Choice D is incorrect because nothing in the text suggests that Dorian is uncertain about Hallward’s talent. Instead, the text is focused on Dorian’s delight with the portrait. 

"}, {"id": "3fc06a91", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "H", "type": "mc", "stimulus": "

Employment by Sector in France and the United States, 1800–2012 (% of total employment)

YearAgriculture in FranceManufacturing in FranceServices in FranceAgriculture in USManufacturing in USServices in US
1800642214681813
1900432928412831
1950323335143353
20123217621880

\n

Rows in table may not add up to 100 due to rounding.

\n

Over the past two hundred years, the percentage of the population employed in the agricultural sector has declined in both France and the United States, while employment in the service sector (which includes jobs in retail, consulting, real estate, etc.) has risen. However, this transition happened at very different rates in the two countries. This can be seen most clearly by comparing the employment by sector in both countries in ______blank

", "stem": "

Which choice most effectively uses data from the table to complete the statement?

", "choices": [{"id": "A", "text": "

1900 with the employment by sector in 1950.

"}, {"id": "B", "text": "

1800 with the employment by sector in 2012.

"}, {"id": "C", "text": "

1900 with the employment by sector in 2012.

"}, {"id": "D", "text": "

1800 with the employment by sector in 1900.

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer because it presents data from the table that most effectively complete the statement about the rates at which employment shifted in France and the United States. The text states that over the last two hundred years employment in the agricultural sector has declined while employment in the service sector has risen in both France and the US, and the data from the table reflect these trends. The text asserts, however, that the transition from agriculture to services “happened at very different rates in the two countries.” This assertion is best supported by a comparison of data from 1900 and 1950: the table shows that in those years, employment in agriculture went from 43% to 32% in France (a decline of 11 percentage points) and from 41% to 14% in the US (a decline of 27 percentage points), and that employment in services went from 28% to 35% in France (an increase of 7 percentage points) and from 31% to 53% in the US (an increase of 22 percentage points). In other words, the rate of change was greater in the US than in France for both sectors.

Choice B is incorrect because comparing the data for 1800 and 2012 would suggest a similar rate of change in the two countries, not very different rates: employment in agriculture went from 64% in 1800 to 3% in 2012 in France, which is close to the change from 68% in 1800 to 2% in 2012 in the US, while employment in services went from 14% in 1800 to 76% in 2012 in France, which is close to the change from 13% in 1800 to 80% in 2012 in the US. Choice C is incorrect because comparing the data for 1900 and 2012 would suggest a similar rate of change in the two countries rather than very different rates: employment in agriculture went from 43% in 1900 to 3% in 2012 in France, which is close to the change from 41% in 1900 to 2% in 2012 in the US, while employment in services went from 28% in 1900 to 76% in 2012 in France, which is close to the change from 31% in 1900 to 80% in 2012 in the US. Choice D is incorrect because comparing the data for 1800 and 1900 would suggest a similar rate of change in the two countries, not very different rates: employment in agriculture went from 64% in 1800 to 43% in 1900 in France, which is fairly close to the change from 68% in 1800 to 41% in 1900 in the US, while employment in services went from 14% in 1800 to 28% in 1900 in France, which is close to the change from 13% in 1800 to 31% in 1900 in the US.

"}, {"id": "96802cc0", "domain": "Information and Ideas", "skill": "Central Ideas and Details", "difficulty": "H", "type": "mc", "stimulus": "

For centuries, the widespread acknowledgment of the involvement of the cerebellum—a dense brain structure in vertebrates—in coordinating motor control in humans has hindered recognition of other possible functions of the structure. Neuroscience research from the last two decades now suggests that the cerebellum regulates emotion and social behavior, and recent research by Ilaria Carta and colleagues has identified a pathway connecting the cerebellum to a center for motivation and reward processing known as the ventral tegmental area (VTA).

", "stem": "

Which choice best states the main idea of the text?

", "choices": [{"id": "A", "text": "

The recent verification of a pathway between the VTA and the cerebellum confirms the cerebellum’s long-suspected role in motor coordination.

"}, {"id": "B", "text": "

Recent advances in the field of neuroscience have challenged widely accepted claims about the function of a pathway connecting the VTA and the cerebellum. 

"}, {"id": "C", "text": "

The cerebellum has primarily been thought to regulate motor functioning, but in recent years neuroscience researchers have been uncovering additional functions.

"}, {"id": "D", "text": "

Technological limitations have historically hindered the study of the cerebellum, but the recent development of new technologies has led to greater insights into its functions. 

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. The text says that the cerebellum has long been thought to regulate motor functioning, but new research shows that it may also have other functions—including regulating emotion and social behavior and some connection to motivation and rewards processing.

Choice A is incorrect. The VTA is described as “a center for motivation and reward processing,” and the discovery of the pathway between the VTA and the cerebellum supports the theory that the cerebellum is involved in functions other than motor coordination. Choice B is incorrect. The text says that recent research has identified this pathway, but it doesn’t discuss any previous “widely accepted claims” about the pathway’s function. The “widespread acknowledgement” mentioned early in the passage is about the cerebellum alone, not its connection to the VTA. Choice D is incorrect. The text never discusses any technological limitations or any new technologies.

"}, {"id": "8a668840", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "M", "type": "mc", "stimulus": "
\n\n\n\n\n\n\n\n\n\n\n\n\n350300250200150100500Hours of sunshineAprilMayJuneJulyAugustSeptemberMonthly Hours of Sunshine from April toSeptember in Anchorage and Fairbanks, AlaskaMonth Anchorage Fairbanks
\n

A student is researching monthly hours of sunshine in different cities in Alaska. When comparing trends in Anchorage and Fairbanks, the student concludes that the two cities show a similar pattern in the monthly hours of sunshine from April to September.

", "stem": "

Which choice best describes data from the graph that support the student’s conclusion?

", "choices": [{"id": "A", "text": "

The monthly hours of sunshine in both Anchorage and Fairbanks hold steady in June and July before beginning to decline in August.

"}, {"id": "B", "text": "

The monthly hours of sunshine in both Anchorage and Fairbanks increase from April to June and then decrease from June to September.

"}, {"id": "C", "text": "

Anchorage and Fairbanks both have less than 200 monthly hours of sunshine from April to September.

"}, {"id": "D", "text": "

Anchorage and Fairbanks both have more than 300 monthly hours of sunshine from April to June and less than 200 hours from July to September.

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer because it best describes data from the graph that support the student’s conclusion about weather patterns in Anchorage and Fairbanks. According to the graph, the amount of sunshine increases in both cities from April to June: in Anchorage, the number of monthly hours increases from about 250 to just under 300, and in Fairbanks the number of monthly hours increases from about 300 to just under 350. Also according to the graph, the amount of sunshine decreases in both cities from June to September: in Anchorage the number of monthly hours decreases from just under 300 to about 125, and in Fairbanks the number of monthly hours decreases from just under 350 to about 125. Thus, the monthly hours of sunshine in both cities follow a similar pattern, increasing from April to June and then decreasing from June to September.

Choice A is incorrect because, according to the graph, the monthly hours of sunshine in both Anchorage and Fairbanks decrease from June to July. They don’t hold steady. In June there are slightly less than 300 hours of sunshine in Anchorage and slightly less than 350 hours in Fairbanks. Then, in July there are approximately 250 hours of sunshine in both cities. Choice C is incorrect because the graph shows that Anchorage and Fairbanks have less than 200 monthly hours of sunshine only in August and September. For the rest of the months represented in the graph, both cities have more than 200 monthly hours of sunshine. Choice D is incorrect because, according to the graph, Anchorage doesn’t have more than 300 monthly hours of sunshine from April to June. In addition, both cities have more than 200 hours of sunshine in July, although the amount of sunshine does decrease to less than 200 monthly hours in August and September.

"}, {"id": "ec93e52c", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "H", "type": "mc", "stimulus": "

Archaeologist Petra Vaiglova, anthropologist Xinyi Liu, and their colleagues investigated the domestication of farm animals in China during the Bronze Age (approximately 2000 to 1000 BCE). By analyzing the chemical composition of the bones of sheep, goats, and cattle from this era, the team determined that wild plants made up the bulk of sheep’s and goats’ diets, while the cattle’s diet consisted largely of millet, a crop cultivated by humans. The team concluded that cattle were likely raised closer to human settlements, whereas sheep and goats were allowed to roam farther away.

", "stem": "

Which finding, if true, would most strongly support the team’s conclusion?

", "choices": [{"id": "A", "text": "

Analysis of the animal bones showed that the cattle’s diet also consisted of wheat, which humans widely cultivated in China during the Bronze Age.

"}, {"id": "B", "text": "

Further investigation of sheep and goat bones revealed that their diets consisted of small portions of millet as well.

"}, {"id": "C", "text": "

Cattle’s diets generally require larger amounts of food and a greater variety of nutrients than do sheep’s and goats’ diets.

"}, {"id": "D", "text": "

The diets of sheep, goats, and cattle were found to vary based on what the farmers in each Bronze Age settlement could grow.

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer because it presents a finding that, if true, would most strongly support the team’s conclusion that cattle were likely raised closer to human settlements than sheep and goats were. The text explains that Vaiglova, Liu, and their colleagues analyzed the chemical composition of sheep, goat, and cattle bones from the Bronze Age in China in order to investigate the animals’ domestication, or their adaptation from a wild state to a state in which they existed in close connection with humans. According to the text, the team’s analysis showed that sheep and goats of the era fed largely on wild plants, whereas cattle fed on millet—importantly, a crop cultivated by humans. If analysis of the animal bones shows that the cattle’s diet also consisted of wheat, another crop cultivated by humans in China during the Bronze Age, the finding would support the team’s conclusion by offering additional evidence that cattle during this era fed on human-grown crops—and, by extension, that humans raised cattle relatively close to the settlements where they grew these crops, leaving goats and sheep to roam farther away in areas with wild vegetation, uncultivated by humans.

Choice B is incorrect because if it were true that sheep’s and goats’ diets consisted of small portions of millet, which the text states was a crop cultivated by humans, the finding would suggest that sheep and goats were raised relatively close to human settlements, weakening the team’s conclusion that cattle were likely raised closer to those settlements than sheep and goats were. Choice C is incorrect because the finding that cattle generally require more food and nutrients than do sheep and goats wouldn’t support the team’s conclusion that cattle were likely raised closer to human settlements than sheep and goats were. Nothing in the text suggests that cattle were incapable of obtaining sufficient food and nutrients without access to human-grown crops. Hence, even if cattle’s diets are found to have different requirements than the diets of sheep and goats, the cattle could have met those requirements from food located far from human settlements. Choice D is incorrect because if it were true that the diets of sheep, goats, and cattle varied based on what the farmers in each Bronze Age settlement could grow, the finding would weaken the team’s conclusion that cattle were likely raised closer to human settlements than sheep and goats were, suggesting instead that all three types of animals were raised close enough to human settlements to feed on those settlements’ crops.

"}, {"id": "4889580c", "domain": "Information and Ideas", "skill": "Inferences", "difficulty": "H", "type": "mc", "stimulus": "

Archaeologists and historians used to believe that the Maya civilization during its Classic period (roughly 250–900) lacked agricultural marketplaces. One reason for this belief was that these scholars misunderstood the ecology of the regions the Maya inhabited. Marketplaces typically emerge because different individuals or groups want to trade resources they control for resources they don’t control. Scholars seriously underestimated the ecological diversity of the Maya landscape and thus assumed that ______blank

", "stem": "

Which choice most logically completes the text?

", "choices": [{"id": "A", "text": "

marketplaces likely would not have attracted many traders from outside the regions controlled by the Maya.

"}, {"id": "B", "text": "

farming practices would have been largely the same throughout Maya lands even if the crops people produced varied significantly. 

"}, {"id": "C", "text": "

marketplaces would not have enabled Maya people to acquire many products different from those they already produced.

"}, {"id": "D", "text": "

farmers would trade agricultural products only if they had already produced enough to meet their own needs. 

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer because it presents the conclusion that most logically follows from the text’s discussion of scholars’ understanding of Maya ecology and agricultural marketplaces. The text indicates that scholars used to believe that during the Classic period, the Maya civilization didn’t have agricultural marketplaces. According to the text, scholars held this view because they misunderstood the ecology of areas where the Maya lived. The text points out that people tend to create marketplaces in order to acquire resources they don’t otherwise control. Agricultural marketplaces would have allowed farmers who produced one type of crop to trade that crop for other types of crops that they didn’t produce. The text goes on to say, however, that scholars underestimated the ecological diversity of the Maya areas, meaning that scholars thought that the Maya landscape produced a smaller range of resources than it actually produced. Taken together, then, this information suggests that scholars assumed that marketplaces wouldn’t have allowed Maya people to acquire products different from the products they already produced: that is, if everyone produced the same array of crops, as scholars mistakenly believed, then there wouldn’t have been any need for marketplaces where people could trade those crops.

Choice A is incorrect because the text doesn’t say anything about trade between the Maya and people from outside the regions controlled by the Maya. Although scholars’ mistaken belief that the Maya lands weren’t very ecologically diverse would give those scholars a reason to think that the Maya didn’t have marketplaces, it wouldn’t lead scholars to assume that traders from outside Maya lands were uninterested in acquiring resources produced by the Maya. Even if the Maya actually did produce only a small array of resources throughout their lands, there is no reason to believe from the text that people outside Maya lands also produced these same resources and thus would have no need to trade with the Maya people. Choice B is incorrect because the text indicates that scholars underestimated the ecological diversity of the Maya lands, which suggests that they mistakenly believed that the Maya produced a relatively small array of resources throughout their territory, not that the crops the Maya produced varied significantly throughout the Maya lands. Although the scholars might have assumed that a lack of ecological diversity suggests that Maya farming practices were largely the same everywhere, the text does not support that they also assumed there was a lot of variation in the crops that Maya people produced. In fact, the text states that marketplaces emerge when people want to obtain resources they don’t already control. If it were the case that scholars assumed that the crops Maya people produced varied significantly, this would have led them to conclude that Maya people likely established marketplaces so they could trade for resources they didn’t already possess, not that the Maya civilization lacked marketplaces. Choice D is incorrect because nothing in the text suggests that scholars assumed that farmers wouldn’t trade their agricultural products unless they had already met their own needs with those products. Instead, the text says that scholars thought that the Maya lands produced a smaller array of resources than they actually did, which the text suggests led scholars to assume that the Maya didn’t have any need for marketplaces. The scholars’ mistaken belief has no bearing on the issue of whether farmers met their own needs before trading their products.

"}, {"id": "b7d51f84", "domain": "Information and Ideas", "skill": "Central Ideas and Details", "difficulty": "M", "type": "mc", "stimulus": "

In West Africa, jalis have traditionally been keepers of information about family histories and records of important events. They have often served as teachers and advisers, too. New technologies may have changed some aspects of the role today, but jalis continue to be valued for knowing and protecting their peoples’ stories.

", "stem": "

Which choice best states the main idea of the text?

", "choices": [{"id": "A", "text": "

Even though there have been some changes in their role, jalis continue to preserve their communities’ histories.

"}, {"id": "B", "text": "

Although jalis have many roles, many of them like teaching best.

"}, {"id": "C", "text": "

Jalis have been entertaining the people within their communities for centuries.

"}, {"id": "D", "text": "

Technology can now do some of the things jalis used to be responsible for.

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer because it best states the main idea of the text. According to the text, jalis’ traditional role has been to maintain information about families’ histories and significant events. The text goes on to say that although technological changes have altered jalis’ role somewhat, jalis are still valued for preserving the histories of their communities. 

Choice B is incorrect because the text says nothing about jalis’ views of the various tasks they perform. There is no information to support the idea that many jalis prefer teaching to other tasks. Choice C is incorrect because the text doesn’t describe jalis as being sources of entertainment. Rather, jalis are presented as valued sources of knowledge. Additionally, the text gives no indication of how long jalis have been serving their communities. Choice D is incorrect because the main focus of the text is on jalis’ role and their continued value despite the effects of technology, not on what technology can now do. Although the text indicates that jalis’ role has changed as a result of technological changes, the text doesn’t present any specific information about technology performing tasks that jalis once performed. 

"}, {"id": "78b265b2", "domain": "Information and Ideas", "skill": "Central Ideas and Details", "difficulty": "E", "type": "mc", "stimulus": "

In 2014, Amelia Quon and her team at NASA set out to build a helicopter capable of flying on Mars. Because Mars’s atmosphere is only one percent as dense as Earth’s, the air of Mars would not provide enough resistance to the rotating blades of a standard helicopter for the aircraft to stay aloft. For five years, Quon’s team tested designs in a lab that mimicked Mars’s atmospheric conditions. The craft the team ultimately designed can fly on Mars because its blades are longer and rotate faster than those of a helicopter of the same size built for Earth.

", "stem": "

According to the text, why would a helicopter built for Earth be unable to fly on Mars?

", "choices": [{"id": "A", "text": "

Because Mars and Earth have different atmospheric conditions

"}, {"id": "B", "text": "

Because the blades of helicopters built for Earth are too large to work on Mars

"}, {"id": "C", "text": "

Because the gravity of Mars is much weaker than the gravity of Earth

"}, {"id": "D", "text": "

Because helicopters built for Earth are too small to handle the conditions on Mars

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer because it presents an explanation about a helicopter that is directly supported by the text. The text states that Mars’s atmosphere is much less dense than Earth’s, and as a result, the air on Mars doesn’t provide the resistance required to support the blades of a helicopter built for Earth and to keep the helicopter aloft. In other words, a helicopter built for Earth can’t fly on Mars because of the differences in the two planets’ atmospheres.

Choice B is incorrect because instead of stating that the blades of helicopters built for Earth are too large to work on Mars, the text indicates that the helicopter built to fly on Mars actually has even longer blades than a helicopter built for Earth. Choice C is incorrect because the text never addresses the role of gravity on Mars or on Earth; instead, it focuses on atmospheric conditions. Choice D is incorrect because the text doesn’t indicate that helicopters built for Earth are too small to operate in the conditions on Mars. In fact, the text states that the size of the helicopter built to fly on Mars is the same size as a helicopter built for Earth, even though it has longer blades that rotate faster.

"}, {"id": "e7dc27dc", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "E", "type": "mc", "stimulus": "

As a monthly newsletter formed in 1969 by a group of Asian American students at the University of California, Los Angeles, Gidra helped raise awareness about social and political issues concerning the Asian American community on campus and at large. The newsletter had an expansive reach for a publication of its kind: around 4,000 copies were published each month. A student writing a history paper, however, hypothesizes that Gidra’s influence cannot be measured by the number of newsletters published monthly alone.

", "stem": "

Which finding, if true, would most directly support the student’s hypothesis?

", "choices": [{"id": "A", "text": "

The students who initially formed Gidra each contributed financially to its creation.

"}, {"id": "B", "text": "

In addition to covering current events, Gidra also featured works of art and literature.

"}, {"id": "C", "text": "

Gidra was initially based out of the Asian American Studies Center at UCLA.

"}, {"id": "D", "text": "

People would often give their copies of Gidra to others once they had finished reading an issue.

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. If there were more Gidra readers than there were copies of the newsletter, then the newsletter’s influence would be much greater than its 4,000 monthly copies.

Choice A is incorrect. Information about the newsletter’s initial funding doesn’t tell us about the influence that the newsletter eventually had. Choice B is incorrect. While the content of Gidra was undoubtedly related to the newsletter’s influence, this information isn’t relevant to the specific hypothesis about monthly circulation numbers. Choice C is incorrect. Where the publishers of Gidra were initially based doesn’t tell us about the newsletter’s overall influence.

"}, {"id": "30c3aa98", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "E", "type": "mc", "stimulus": "

\n\n\n\n\n\n\n\n\n\n\n\n\n4003002001000Yearly copper production (in millions of pounds)188919021909Copper Production for Three States, 1889-1909Year Montana Arizona Michigan

\n

Copper had been mined in the US for thousands of years, but large-scale commercial mining of copper took off starting in the late 1800s. This was due to several factors. Technological advancements in the mining industry led to improvements in the production of copper. This helped the country keep up with the growing number of people wanting to buy copper starting in the 1890s. At the same time, the growth of the railroad system made the transportation of copper in large batches much easier. Several states saw rapid growth in the production of this resource, for example: ______blank

", "stem": "

Which choice most effectively uses the data in the graph to complete the example?

", "choices": [{"id": "A", "text": "

The rise in copper production in Michigan slowed from 1902 to 1909.

"}, {"id": "B", "text": "

Montana and Arizona produced more copper than Michigan did in 1909.

"}, {"id": "C", "text": "

Fewer than 100 million pounds of copper were produced in Arizona in 1889.

"}, {"id": "D", "text": "

Copper production rose significantly from 1889 to 1909 for Arizona, Michigan, and Montana.

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. The text asks us to provide examples of several states that saw rapid growth in copper production from the 1890s onward. The graph depicts Arizona, Michigan, and Montana all experiencing such rapid growth during this time period.

Choice A is incorrect. The claim is about states experiencing rapid growth in copper production. This statement only discusses one state and does not provide evidence of rapid growth—in fact, it discusses a slow-down of growth. Choice B is incorrect. The claim is about states experiencing rapid growth in copper production, and this statement provides a comparison of production rates between states, rather than an example of rapid growth. Choice C is incorrect. The claim is about several states experiencing rapid growth in copper production. This statement only discusses one state and does not provide evidence of growth in copper production.

"}, {"id": "d0f51067", "domain": "Information and Ideas", "skill": "Central Ideas and Details", "difficulty": "H", "type": "mc", "stimulus": "

Modern dog breeds are largely the result of 160 years of owners crossbreeding certain dogs in order to select for particular physical appearances. Owners often say that some breeds are also more likely than others to have particular personality traits—basset hounds are affectionate; boxers are easy to train—but Kathleen Morrill and colleagues found through a combination of owner surveys and DNA sequencing of 2,000 dogs that while physical traits are predictably heritable among purebred dogs, behavior varies widely among dogs of the same breed.

", "stem": "

Which choice best states the main idea of the text?

", "choices": [{"id": "A", "text": "

Dog breeds would not exist without many years of human intervention in dogs’ reproduction.

"}, {"id": "B", "text": "

Research fails to confirm a commonly held belief about dog breeds and behavior.

"}, {"id": "C", "text": "

The dog breeds most popular among owners have often changed over the past 160 years.

"}, {"id": "D", "text": "

A study of dog breeds is notable for its usage of both opinion surveys and DNA sequencing.

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer because it most accurately states the main idea of the text. The text indicates that dog owners typically claim that some dog breeds are “more likely than others to have particular personality traits.” In other words, the text points out that a commonly held belief about dog breeds is that their personality traits are heritable. The text then states that Kathleen Morrill and colleagues undertook research about dog trait heritability and found that “behavior varies widely among dogs of the same breed.” Because Morrill and colleagues found evidence for variability rather than consistency in the behavior of dogs of the same breed, the statement that research fails to uphold a commonly held belief about dog breeds and behavior accurately reflects the main idea of the text.

Choice A is incorrect. Although the text mentions that humans have long intervened in dogs’ reproduction by intentionally crossbreeding certain dogs, it doesn’t argue that such intervention is essential to the existence of dog breeds. Choice C is incorrect because the text doesn’t discuss the popularity of any dog breeds; breeds are mentioned as having certain traits, but the text says nothing about the popularity of these breeds or traits. Choice D is incorrect. Although the text briefly mentions that Morrill and colleagues conducted a study about dog traits using both surveys and DNA sequencing, this is not the main focus of the text. The text concerns the study’s results about the heritability of dog traits, not the particular methodology used by Morrill and colleagues.

"}, {"id": "3cc2eacc", "domain": "Information and Ideas", "skill": "Inferences", "difficulty": "M", "type": "mc", "stimulus": "

In a study of the mechanisms underlying associative memory—or the ability to learn and remember connections between inherently unrelated things—neuroscientists Kei Igarashi, Jasmine Chavez, and others presented mice with memory tests. The team discovered that fan cells, a type of cell found in the medial temporal lobe of the brain, are necessary for the acquisition of new associative memories. They also found that fan cell activity requires dopamine, a chemical the brain produces in response to pleasure and rewards. Consequently, receiving a reward should likely help to ______blank

", "stem": "

Which choice most logically completes the text?

", "choices": [{"id": "A", "text": "

decrease an individual’s capacity to utilize dopamine.

"}, {"id": "B", "text": "

increase an individual’s capacity to recognize differences between unrelated things.

"}, {"id": "C", "text": "

increase an individual’s capacity to form associative memories.

"}, {"id": "D", "text": "

decrease an individual’s capacity to create fan cells.

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer because it most logically completes the text’s discussion of the mechanisms underlying associative memory. The text explains that fan cells—a type of brain cell—are necessary for the acquisition of new associative memories, and that activity among these cells requires a chemical known as dopamine, which the brain produces in response to rewards. Since the brain cells that enable the formation of associative memories require dopamine in order to function, and since the brain produces dopamine in response to rewards, it can be inferred that receiving a reward should likely help to increase an individual’s capacity to form associative memories.

Choice A is incorrect because the relationship between rewards and dopamine sketched by the text is that rewards result in the production of dopamine, not that they cause an individual’s capacity to utilize dopamine to decrease. Choice B is incorrect. The text suggests that receiving a reward would produce dopamine and thereby assist with associative memory formation. However, the text never suggests that associative memory involves the capacity to recognize differences between unrelated things, indicating only that associative memory involves remembering what connects those things. Choice D is incorrect because the text never discusses how fan cells are initially created and therefore provides no evidence for a conclusion about how receiving a reward would affect their creation. 

"}, {"id": "54057e3f", "domain": "Information and Ideas", "skill": "Inferences", "difficulty": "M", "type": "mc", "stimulus": "

Although military veterans make up a small proportion of the total population of the United States, they occupy a significantly higher proportion of the jobs in the civilian government. One possible explanation for this disproportionate representation is that military service familiarizes people with certain organizational structures that are also reflected in the civilian government bureaucracy, and this familiarity thus ______blank

", "stem": "

Which choice most logically completes the text?

", "choices": [{"id": "A", "text": "

makes civilian government jobs especially appealing to military veterans.

"}, {"id": "B", "text": "

alters the typical relationship between military service and subsequent career preferences.

"}, {"id": "C", "text": "

encourages nonveterans applying for civilian government jobs to consider military service instead.

"}, {"id": "D", "text": "

increases the number of civilian government jobs that require some amount of military experience to perform.

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer because it presents the conclusion that most logically follows from the text’s discussion of military veterans working in civilian government jobs in the United States. The text indicates that the proportion of military veterans working in civilian government jobs is considerably higher than the proportion of military veterans in the population as a whole. The text also notes that the unusually high representation of military veterans in these jobs may be a result of the organizational structures  shared by civilian government entities and the military. Hence, it’s reasonable to infer that it’s the familiarity of the structures of civilian government that makes jobs there particularly attractive to military veterans. 

Choice B is incorrect because the text doesn’t address what a typical relationship between military service and later career preferences would be, and there’s no indication that it’s atypical for veterans to work in civilian government jobs after they’ve left the military. On the contrary, the text suggests that many military veterans are drawn to such jobs. Choice C is incorrect because the text is focused on the high representation of military veterans in civilian government jobs and doesn’t address nonveterans or their possible interest in military service. Choice D is incorrect because the text conveys that military veterans may be particularly interested in civilian government jobs due to the familiarity of organizational structures that are already in place, but there’s no reason to think that this interest would mean that more civilian government jobs will start to require military experience.

"}, {"id": "aaddd60f", "domain": "Information and Ideas", "skill": "Inferences", "difficulty": "H", "type": "mc", "stimulus": "

Scientists studying Mars long thought the history of its crust was relatively simple. One reason for this is that geologic and climate data collected by a spacecraft showed that the crust was largely composed of basalt, likely as a result of intense volcanic activity that brought about a magma ocean, which then cooled to form the planet’s surface. A study led by Valerie Payré focused on additional information—further analysis of data collected by the spacecraft and infrared wavelengths detected from Mars’s surface—that revealed the presence of surprisingly high concentrations of silica in certain regions on Mars. Since a planetary surface that formed in a mostly basaltic environment would be unlikely to contain large amounts of silica, Payré concluded that ______blank

", "stem": "

Which choice most logically completes the text?

", "choices": [{"id": "A", "text": "

the information about silica concentrations collected by the spacecraft is likely more reliable than the silica information gleaned from infrared wavelengths detected from Mars’s surface.

"}, {"id": "B", "text": "

high silica concentrations on Mars likely formed from a different process than that which formed the crusts of other planets.

"}, {"id": "C", "text": "

having a clearer understanding of the composition of Mars’s crust and the processes by which it formed will provide more insight into how Earth’s crust formed.  

"}, {"id": "D", "text": "

Mars’s crust likely formed as a result of other major geological events in addition to the cooling of a magma ocean. 

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. Cooling magma would create basalt, but “a planetary surface that formed in a mostly basaltic environment would be unlikely to contain large amounts of silica.” Since Mars’s crust does contain large amounts of silica, it is unlikely that Mars’s crust was formed exclusively by cooling magma. Therefore, there were likely other major geological events that created the high silica concentrations.

Choice A is incorrect. Although the passage discusses these two methods of collecting data about Mars’s crust, it never compares their reliability, so there’s no basis for this inference. Choice B is incorrect. The passage never mentions anything about the crusts of other planets, so there’s no basis for this inference. Choice C is incorrect. The passage never mentions Earth’s crust, so there’s no basis for this inference.

"}, {"id": "1c69ff20", "domain": "Information and Ideas", "skill": "Central Ideas and Details", "difficulty": "H", "type": "mc", "stimulus": "

For many years, the only existing fossil evidence of mixopterid eurypterids—an extinct family of large aquatic arthropods known as sea scorpions and related to modern arachnids and horseshoe crabs—came from four species living on the paleocontinent of Laurussia. In a discovery that expands our understanding of the geographical distribution of mixopterids, paleontologist Bo Wang and others have identified fossilized remains of a new mixopterid species, Terropterus xiushanensis, that lived over 400 million years ago on the paleocontinent of Gondwana.

", "stem": "

According to the text, why was Wang and his team’s discovery of the Terropterus xiushanensis fossil significant?

", "choices": [{"id": "A", "text": "

The fossil constitutes the first evidence found by scientists that mixopterids lived more than 400 million years ago.

"}, {"id": "B", "text": "

The fossil helps establish that mixopterids are more closely related to modern arachnids and horseshoe crabs than previously thought.

"}, {"id": "C", "text": "

The fossil helps establish a more accurate timeline of the evolution of mixopterids on the paleocontinents of Laurussia and Gondwana.

"}, {"id": "D", "text": "

The fossil constitutes the first evidence found by scientists that mixopterids existed outside the paleocontinent of Laurussia.

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer because it states why Wang and his team’s discovery of the Terropterus xiushanensis fossil was significant. The text explains that up until Wang and his team’s discovery, the only fossil evidence of mixopterids came from the paleocontinent of Laurussia. Wang and his team, however, identified fossil remains of a mixopterid species from the paleocontinent Gondwana. Therefore, the team’s discovery was significant because the fossil remains of a mixopterid species were outside of the paleocontinent Laurussia.

Choice A is incorrect. Although the text states that Wang and his team identified fossilized remains of a mixopterid species that lived more than 400 million years ago, it doesn’t indicate that mixopterid fossils previously found by scientists dated to a more recent period than that. Choice B is incorrect. Although the text states that mixopterids are related to modern arachnids and horseshoe crabs, it doesn’t suggest that the fossil discovered by Wang and his team confirmed that this relationship is closer than scientists had previously thought. Choice C is incorrect because the team’s fossil established the presence of mixopterids on Gondwana, not on Laurussia. Moreover, the text only discusses the fossil in relation to the geographical distribution of mixopterids, not in relation to their evolution.

"}, {"id": "39e440e4", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "H", "type": "mc", "stimulus": "

Archaeologists have held that the Casarabe culture, which emerged in the southwestern Amazon basin in the first millennium CE, was characterized by a sparse, widely distributed population and little intervention in the surrounding wilderness. Recently, however, archaeologist Heiko Prümers and colleagues conducted a study of the region using remote-sensing technology that enabled them to create three-dimensional images of the jungle-covered landscape from above, and the researchers concluded that the Casarabe people developed a form of urbanism in the Amazon basin.

", "stem": "

Which finding about the remote-sensing images, if true, would most directly support Prümers and colleagues’ conclusion?

", "choices": [{"id": "A", "text": "

They show shapes consistent with widely separated settlements of roughly equal small size surrounded by uncultivated jungle.

"}, {"id": "B", "text": "

They show shapes consistent with long-distance footpaths running from Casarabe territories to large cities outside the region inhabited by the Casarabe people.

"}, {"id": "C", "text": "

 They show shapes consistent with scattered small farms created by clearing jungle areas near sources of fresh water.

"}, {"id": "D", "text": "

They show shapes consistent with monumental platforms and dense central settlements linked to smaller settlements by a system of canals and roadways.

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. This finding, if true, would support the archaeologists’ conclusion. Dense central settlements linked to smaller ones would provide evidence of cities and suburbs—in other words, “a form of urbanism.”

Choice A is incorrect. This finding, if true, would weaken the archaeologists’ conclusion. Widely separated, small settlements with jungle in between would support the long-held belief that the Casarabe culture “was characterized by a sparse, widely distributed population and little intervention in the surrounding wilderness.” Choice B is incorrect. This choice wouldn’t support the researchers’ conclusion. These large cities are located outside Casarabe territory, which doesn’t show evidence of Casarabe urbanism. Choice C is incorrect. This finding wouldn’t support the archaeologists’ conclusion. Scattered small farms in jungle clearings are not good evidence to support the existence of cities (“a form of urbanism”).

"}, {"id": "29cde5fa", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "M", "type": "mc", "stimulus": "

“Mr. Cornelius Johnson, Office-Seeker” is a 1900 short story by Paul Laurence Dunbar. In the story, the narrator describes Mr. Cornelius Johnson’s appearance as conveying his exaggerated sense of his importance: ______blank

", "stem": "

Which quotation from “Mr. Cornelius Johnson, Office-Seeker” most effectively illustrates the claim?

", "choices": [{"id": "A", "text": "

“He carried himself always as if he were passing under his own triumphal arch.”

"}, {"id": "B", "text": "

“The grey Prince Albert was scrupulously buttoned about his form, and a shiny top hat replaced the felt of the afternoon.”

"}, {"id": "C", "text": "

“It was a beautiful day in balmy May and the sun shone pleasantly on Mr. Cornelius Johnson’s very spruce Prince Albert suit of grey as he alighted from the train in Washington.”

"}, {"id": "D", "text": "

“Mr. Cornelius Johnson always spoke in a large and important tone.”

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. This quote most effectively illustrates the claim. The claim is that the narrator describes Mr. Johnson as arrogant and self-important. This basically says that Mr. Johnson always looks like he’s congratulating himself for something, which definitely supports the idea that Mr. Johnson is arrogant! .

Choice B is incorrect. This quote doesn’t illustrate the claim. The claim is that the narrator describes Mr. Johnson’s appearance as conveying his arrogance. This describes his appearance, but the description doesn’t suggest a sense of arrogance. Choice C is incorrect. This quote doesn’t illustrate the claim. The claim is that the narrator describes Mr. Johnson’s appearance as conveying his arrogance. This doesn’t describe Mr. Johnson’s appearance very much, and it doesn’t suggest a sense of arrogance. Choice D is incorrect. This quote doesn’t effectively illustrate the claim. It describes Mr. Johnson’s tone of voice as “large and important,” but it doesn’t describe his appearance as conveying a sense of self-importance. 

"}, {"id": "c4d43991", "domain": "Information and Ideas", "skill": "Inferences", "difficulty": "E", "type": "mc", "stimulus": "

Archaeologists have been debating the origin of a rare form of lead found in Shang dynasty (1766–1046 BCE) bronze artifacts since its presence was discovered in China in the 1990s. Different researchers have proposed theories on which regions of the world would have had the raw materials containing the specific lead in these artifacts, but no conclusive evidence has been presented. What is intriguing is that bronze artifacts from China dated after the Shang dynasty do not contain this form of lead, suggesting that ______blank

", "stem": "

Which choice most logically completes the text?

", "choices": [{"id": "A", "text": "

Shang dynasty bronze pieces are rare and therefore more valuable than those from other time periods.

"}, {"id": "B", "text": "

the source of some of the raw materials used to make bronze was exploited only until the end of the Shang dynasty.

"}, {"id": "C", "text": "

bronze was used for a short time during the Shang dynasty before different metals were used to make artifacts.

"}, {"id": "D", "text": "

methods used to analyze bronze artifacts are not useful on pieces that are dated after the Shang dynasty.

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. The passage tells us that Shang dynasty bronze artifacts contained \"a rare form of lead,\" but that bronze artifacts after this time did not contain that lead. Although we don’t know where that specific type of bronze came from, we can conclude that that source was not used after the end of the Shang dynasty—otherwise, post-Shang dynasty pieces would also contain that rare form of lead.

Choice A is incorrect. Despite these pieces containing \"a rare form of lead,\" there is no direct claim in the passage that Shang dynasty bronze is itself more rare or valuable than bronze pieces from other periods. Therefore, there’s no basis for this inference. Choice C is incorrect. Although the passage mentions that the nature of the bronze in Chinese artifacts changed after the Shang dynasty, bronze was still used to create artifacts after this time. The passage in fact explicitly states \"bronze artifacts from China dated after the Shang dynasty…,\" indicating that bronze was still used in China after the Shang dynasty. Choice D is incorrect. There’s no mention in the passage of methods used to analyze bronze artifacts, so there’s no basis for this inference.

"}, {"id": "4042ff0b", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "E", "type": "mc", "stimulus": "

Comfort Ratings and Temperature-Adjustment Preferences from One Survey

ParticipantComfort ratingPreferred temperature adjustment
20−2negative 2Cooler
11Cooler
211Cooler

\n

Nan Gao and her team conducted multiple surveys to determine participants’ levels of comfort in a room where the temperature was regulated by a commercial climate control system. Participants filled out surveys several times a day to indicate their level of comfort on a scale from −3negative 3 (very cold) to +3positive 3 (very hot), with 0 indicating neutral (neither warm nor cool), and to indicate how they would prefer the temperature to be adjusted. The table shows three participants’ responses in one of the surveys. According to the table, all three participants wanted the room to be cooler, ______blank 

", "stem": "

Which choice most effectively uses data from the table to complete the statement?

", "choices": [{"id": "A", "text": "

and they each reported the same level of comfort.

"}, {"id": "B", "text": "

even though each participant’s ratings varied throughout the day.

"}, {"id": "C", "text": "

but participant 20 reported feeling significantly colder than the other two participants did.

"}, {"id": "D", "text": "

but participant 1 reported feeling warmer than the other two participants did.

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. The text describes the comfort rating scale: from −3 (very cold) to +3 (very hot), with 0 being neutral. Participant 20 gave a −2 comfort rating, a full three points colder on the scale than the other two participants.

Choice A is incorrect. This choice misreads the table. Participant 1 and participant 21 reported the same level of comfort, but participant 20’s comfort level was three points lower. Choice B is incorrect. This choice doesn’t use data from the table. The table only shows us one survey, so we don’t know if the participants’ ratings varied throughout the day. Choice D is incorrect. This choice misreads the table. Participant 1 and participant 21 reported the same level of comfort.

"}, {"id": "d0fbf1ae", "domain": "Information and Ideas", "skill": "Central Ideas and Details", "difficulty": "H", "type": "mc", "stimulus": "

Algae living within the tissues of corals play a critical role in keeping corals, and the marine ecosystems they are part of, thriving. Some coral species appear brown in color when healthy due to the algae colonies living in their tissues. In the event of an environmental stressor, the algae can die or be expelled, causing the corals to appear white. To recover the algae, the bleached corals then begin to produce bright colors, which block intense sunlight, encouraging the light-sensitive algae to recolonize the corals.

", "stem": "

What does the text most strongly suggest about corals that produce bright colors?

", "choices": [{"id": "A", "text": "

These corals have likely been subjected to stressful environmental conditions.

"}, {"id": "B", "text": "

These corals are likely more vulnerable to exposure from intense sunlight than white corals are.

"}, {"id": "C", "text": "

These corals have likely recovered from an environmental event without the assistance of algae colonies.

"}, {"id": "D", "text": "

These corals are more likely to survive without algae colonies than brown corals are.

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. The text says that corals produce bright colors to block sunlight and encourage algae to recolonize after “an environmental stressor.” From this, we can infer that corals that produce bright colors have probably been subjected to an environmental stressor.

Choice B is incorrect. The text says that corals produce bright colors to block intense sunlight, which protects the light-sensitive algae that keep the coral healthy. In other words, bright colors make the coral’s health less vulnerable to intense sunlight. Choice C is incorrect. The text says that corals produce bright colors to encourage algae to recolonize, not that they have recovered without the assistance of algae colonies. Choice D is incorrect. The text never compares the likelihood of differently colored corals surviving without algae colonies.

"}, {"id": "b30a2613", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "M", "type": "mc", "stimulus": "
\n\n\n\n\n9080706050403020100Spider count1102030Spider Population CountDay of experimentno lizardswith lizards
\n

To investigate the effect of lizard predation on spider populations, a student in a biology class placed spiders in two enclosures, one with lizards and one without, and tracked the number of spiders in the enclosures for 30 days. The student concluded that the reduction in the spider population count in the enclosure with lizards by day 30 was entirely attributable to the presence of the lizards.

", "stem": "

Which choice best describes data from the graph that weaken the student’s conclusion?

", "choices": [{"id": "A", "text": "

The spider population count was the same in both enclosures on day 1.

"}, {"id": "B", "text": "

The spider population count also substantially declined by day 30 in the enclosure without lizards.

"}, {"id": "C", "text": "

The largest decline in spider population count in the enclosure with lizards occurred from day 1 to day 10.

"}, {"id": "D", "text": "

The spider population count on day 30 was lower in the enclosure with lizards than in the enclosure without lizards.

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer because it describes data from the graph that weaken the student’s conclusion about the reduction in the spider population in the enclosure with lizards. The graph shows that the enclosure with lizards and the enclosure without lizards each began with about 85 spiders, and that the number of spiders in each enclosure fell over the 30 days of the study. The student’s claim is that the reduction in spiders in the enclosure with lizards is “entirely attributable to the presence of the lizards,” meaning that the spider population wouldn’t have declined except for the presence of the lizards. This claim is weakened, however, by the fact that the enclosure without lizards also saw a substantial reduction in the number of spiders. Since the number of spiders fell in the enclosure without lizards as well as in the enclosure with lizards, there must be some other factor than just the presence of the lizards that contributed to the reduction in the spider population. 

Choice A is incorrect because the fact that the two enclosures started with the same number of spiders is irrelevant to the claim that the reduction in spider population by day 30 in the enclosure with lizards can be entirely attributed to the lizards. Choice C is incorrect because the fact that the spider population in the enclosure with lizards fell more between days 1 and 10 than in other periods has nothing to do with the student’s claim that the reduction in spiders in that enclosure by day 30 can be entirely attributed to the lizards. Choice D is incorrect. Although it’s true that on day 30 the spider population was lower in the enclosure with lizards than in the enclosure without lizards, this fact doesn’t weaken the student’s claim that the reduction in the spider population in the enclosure with lizards can be entirely attributed to the lizards. Indeed, the lower spider population in the enclosure with lizards suggests that the lizards are contributing to the reduction in the spider population, though the fact that the spider population also fell substantially in the other enclosure means that the lizards aren’t the only cause of the reduction. 

"}, {"id": "123bd312", "domain": "Information and Ideas", "skill": "Inferences", "difficulty": "M", "type": "mc", "stimulus": "

Herbivorous sauropod dinosaurs could grow more than 100 feet long and weigh up to 80 tons, and some researchers have attributed the evolution of sauropods to such massive sizes to increased plant production resulting from high levels of atmospheric carbon dioxide during the Mesozoic era. However, there is no evidence of significant spikes in carbon dioxide levels coinciding with relevant periods in sauropod evolution, such as when the first large sauropods appeared, when several sauropod lineages underwent further evolution toward gigantism, or when sauropods reached their maximum known sizes, suggesting that ______blank

", "stem": "

Which choice most logically completes the text?

", "choices": [{"id": "A", "text": "

fluctuations in atmospheric carbon dioxide affected different sauropod lineages differently. 

"}, {"id": "B", "text": "

the evolution of larger body sizes in sauropods did not depend on increased atmospheric carbon dioxide.

"}, {"id": "C", "text": "

atmospheric carbon dioxide was higher when the largest known sauropods lived than it was when the first sauropods appeared.

"}, {"id": "D", "text": "

sauropods probably would not have evolved to such immense sizes if atmospheric carbon dioxide had been even slightly higher.

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer because it presents the conclusion that most logically follows from the text’s discussion of the relationship between atmospheric carbon dioxide and sauropod body size. The text establishes that sauropods evolved to reach enormous sizes, and it notes that some scientists have asserted that the cause of this phenomenon was increased plant production that resulted from increased atmospheric carbon dioxide. The text goes on to state, however, that atmospheric carbon dioxide levels didn’t increase around the time of important periods in sauropods’ evolution of larger body sizes. If significant periods of sauropod evolution toward larger sizes occurred without increased atmospheric carbon dioxide levels, that suggests that the evolution of larger sizes didn’t depend on increased carbon dioxide in the atmosphere. 

Choice A is incorrect because the text doesn’t describe any fluctuations in atmospheric carbon dioxide, so there’s no evidence in the text to support the conclusion that such fluctuations had different effects on different sauropod lineages. All that the text says about atmospheric carbon dioxide levels is that there weren’t increases at particular points that correspond with key moments in sauropod evolution. Choice C is incorrect because the text indicates that there weren’t significant increases in atmospheric carbon dioxide around the time of important periods in sauropods’ evolution toward larger body sizes, not that atmospheric carbon dioxide was higher when the largest sauropods lived than when sauropods first appeared. Choice D is incorrect because the text indicates that atmospheric carbon dioxide levels didn’t increase at important periods in sauropod evolution, not that higher levels would have affected that evolution. The text provides no information about how higher levels of atmospheric carbon dioxide might have affected sauropods. 

"}, {"id": "3f4ab688", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "H", "type": "mc", "stimulus": "

In a research paper, a student criticizes some historians of modern African politics, claiming that they have evaluated Patrice Lumumba, the first prime minister of what is now the Democratic Republic of the Congo, primarily as a symbol rather than in terms of his actions.

", "stem": "

Which quotation from a work by a historian would best illustrate the student’s claim?

", "choices": [{"id": "A", "text": "

“Lumumba is a difficult figure to evaluate due to the starkly conflicting opinions he inspired during his life and continues to inspire today.”

"}, {"id": "B", "text": "

“The available information makes it clear that Lumumba’s political beliefs and values were largely consistent throughout his career.”

"}, {"id": "C", "text": "

“Lumumba’s practical accomplishments can be passed over quickly; it is mainly as the personification of Congolese independence that he warrants scholarly attention.”

"}, {"id": "D", "text": "

“Many questions remain about Lumumba’s ultimate vision for an independent Congo; without new evidence coming to light, these questions are likely to remain unanswered.”

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer because it illustrates the student’s claim about some historians viewing Lumumba primarily as a symbol. This quotation argues that Lumumba “warrants” (or deserves) “scholarly attention” as a symbol and not for his “practical accomplishments”—that is, his actions as prime minister—which “can be passed over quickly,” or dismissed as being of comparatively little importance. Thus, the quotation expresses the view that the student criticizes some historians for holding.

Choice A is incorrect. Although this quotation touches on the difficulty of evaluating Lumumba’s legacy, it doesn’t address how historians of modern African politics view him as a symbol. Choice B is incorrect. While this quotation mentions Lumumba’s political beliefs, it doesn’t discuss historians viewing him as a symbol. Choice D is incorrect. This quotation touches on Lumumba’s vision for his country, but it doesn’t discuss historians viewing him as a symbol.

"}, {"id": "08395130", "domain": "Information and Ideas", "skill": "Inferences", "difficulty": "H", "type": "mc", "stimulus": "

The Hubble Space Telescope (HST) is projected to maintain operation until at least 2030, but it has already revolutionized high-resolution imaging of solar-system bodies in visible and ultraviolet (UV) light wavelengths, notwithstanding that only about 6% of the bodies imaged by the HST are within the solar system. NASA researcher Cindy L. Young and colleagues assert that a new space telescope dedicated exclusively to solar-system observations would permit an extensive survey of minor solar-system bodies and long-term UV observation to discern how solar-system bodies change over time. Young and colleagues’ recommendation therefore implies that the HST ______blank

", "stem": "

Which choice most logically completes the text?

", "choices": [{"id": "A", "text": "

will likely continue to be used primarily to observe objects outside the solar system. 

"}, {"id": "B", "text": "

will no longer be used to observe solar system objects if the telescope recommended by Young and colleagues is deployed. 

"}, {"id": "C", "text": "

can be modified to observe the features of solar system objects that are of interest to Young and colleagues.

"}, {"id": "D", "text": "

lacks the sensors to observe the wavelengths of light needed to discern how solar system bodies change over time.

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. The HST will operate until at least 2030, but it’s only observing stuff inside our solar system 6% of the time. If we could get a different telescope to observe stuff inside our solar system 100% of the time and take more extensive images of certain things, then the HST could continue to be used mainly for observing stuff outside the solar system.

Choice B is incorrect. This inference is too strong to be supported by the text. Even if the new telescope is deployed, the HST might still be used as it’s being used now. Based on the text, the new telescope would just be used for more extensive and long-term imaging of solar system bodies, which doesn’t necessarily overlap with the HST. Choice C is incorrect. This inference isn’t supported. The text never mentions the possibility of modifying the HST, so there is no basis to make this inference. Rather, the researchers suggest using a different telescope to more closely observe certain objects. Choice D is incorrect. This inference is too strong to be supported. The text doesn’t give us enough info to assume that the HST lacks any particular sensors.

"}, {"id": "14189fbb", "domain": "Information and Ideas", "skill": "Central Ideas and Details", "difficulty": "H", "type": "mc", "stimulus": "

Having written the impassioned call to arms “Letter to the Spanish Americans” in 1791, Peruvian intellectual Juan Pablo Viscardo y Guzmán is often considered a forerunner for the independence movements in Latin America. But Viscardo’s role in history would have remained insignificant were it not for Venezuelan revolutionary Francisco de Miranda, who was handed the unpublished letter after Viscardo’s death. Miranda not only helped circulate the letter, but his edits and footnotes to the text position Miranda as a central figure in the text’s creation.

", "stem": "

Which choice best states the main idea of the text?

", "choices": [{"id": "A", "text": "

The original authorship of “Letter to the Spanish Americans” is disputed by contemporary historians.

"}, {"id": "B", "text": "

The majority of the most eloquently stated arguments in “Letter to the Spanish Americans” were written by Miranda.

"}, {"id": "C", "text": "

Miranda played a crucial role in influencing the content and distribution of “Letter to the Spanish Americans.” 

"}, {"id": "D", "text": "

“Letter to the Spanish Americans” persuaded many people in Latin America to pursue national independence.

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. The text describes how Miranda circulated, edited, and added footnotes to “Letter to the Spanish Americans,” and it claims that the letter and its author would have “remained insignificant” if it weren’t for Miranda’s efforts.

Choice A is incorrect. The text only says that Viscardo wrote the letter and that Miranda edited it: it never suggests that the original authorship of the letter is up for debate. Choice B is incorrect. This contradicts the text. The text says that Miranda edited and footnoted the letter, but it identifies Viscardo as the letter’s author. It also never identifies certain arguments as more eloquent than others. Choice D is incorrect. This is outside the scope of the text. The paragraph describes Miranda’s role in the creation and distribution of the letter, but it doesn’t get into the effects of the letter on other people.

"}, {"id": "cef77aa7", "domain": "Information and Ideas", "skill": "Inferences", "difficulty": "H", "type": "mc", "stimulus": "

Geoglyphs are large-scale designs of lines or shapes created in a natural landscape. The Nazca Lines were created in the Nazca Desert in Peru by several Indigenous civilizations over a period of many centuries. Peruvian archaeologist Johny Isla specializes in these geoglyphs. At a German exhibit about the Nazca Lines, he saw an old photograph of a large geoglyph of a whalelike figure and was surprised that he didn’t recognize it. Isla returned to Peru and used a drone to search a wide area, looking for the figure from the air. This approach suggests that Isla thought that if he hadn’t already seen it, the whalelike geoglyph ______blank

", "stem": "

Which choice most logically completes the text?

", "choices": [{"id": "A", "text": "

must represent a species of whale that went extinct before there were any people in Peru.

"}, {"id": "B", "text": "

is actually located in Germany, not Peru, and isn’t part of the Nazca Lines at all.

"}, {"id": "C", "text": "

is probably in a location Isla hadn’t ever come across while on the ground.

"}, {"id": "D", "text": "

was almost certainly created a long time after the other Nazca Lines geoglyphs were created.

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer because it most logically completes the text’s discussion of Johny Isla and the whalelike geoglyph. The text indicates that the German exhibit about the Nazca Lines included a photograph showing a whalelike geoglyph that Isla hadn’t known about before attending the exhibit, even though Isla “specializes in” Nazca Lines geoglyphs. Given his expertise, and his surprise at being unfamiliar with the whale glyph, the text strongly suggests that Isla believed he would have noticed the glyph if he had been to its location. Thus, the text implies that the whalelike geoglyph is likely in a location Isla had not previously been to.   

Choice A is incorrect because the text doesn’t address either the species of whale that the geoglyph is meant to represent or its relationship to the earliest humans in the area that is now Peru. Choice B is incorrect. Although the text indicates that the photograph of the whalelike geoglyph was on display at a “German exhibit,” that exhibit was specifically “about the Nazca Lines,” which the text indicates are located in Peru. Choice D is incorrect. Although the text does indicate that the glyphs were created “over a period of many centuries,” the text doesn’t address when in that period of time any particular glyphs were created.

"}, {"id": "dc3ea63e", "domain": "Information and Ideas", "skill": "Central Ideas and Details", "difficulty": "M", "type": "mc", "stimulus": "

To dye wool, Navajo (Diné) weaver Lillie Taylor uses plants and vegetables from Arizona, where she lives. For example, she achieved the deep reds and browns featured in her 2003 rug In the Path of the Four Seasons by using Arizona dock roots, drying and grinding them before mixing the powder with water to create a dye bath. To intensify the appearance of certain colors, Taylor also sometimes mixes in clay obtained from nearby soil.

", "stem": "

Which choice best states the main idea of the text?

", "choices": [{"id": "A", "text": "

Reds and browns are not commonly featured in most of Taylor’s rugs.

"}, {"id": "B", "text": "

Taylor draws on local resources in the approach she uses to dye wool.

"}, {"id": "C", "text": "

Taylor finds it difficult to locate Arizona dock root in the desert.

"}, {"id": "D", "text": "

In the Path of the Four Seasons is widely acclaimed for its many colors and innovative weaving techniques. 

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. It best states the main idea of the text. The text opens with the statement that Taylor uses local plants and vegetables to dye wool. The rest of the text describes how she does this.

Choice A is incorrect. This doesn’t state the main idea of the text. The text only mentions one rug: In the Path of the Four Seasons, in which reds and browns are featured. It never mentions whether or not these colors are featured in her other rugs. Choice C is incorrect. This doesn’t state the main idea of the text. The text never says that Taylor finds it difficult to locate Arizona dock roots. Choice D is incorrect. This doesn’t state the main idea of the text. The text never says that In the Path of the Four Seasons is widely acclaimed. Rather, it discusses the rug to illustrate the point made earlier in the passage: that Taylor uses local plants and vegetables to dye wool.

"}, {"id": "9c591ff7", "domain": "Information and Ideas", "skill": "Inferences", "difficulty": "H", "type": "mc", "stimulus": "

Some Astyanax mexicanus, a river-dwelling fish found in northeast Mexico, have colonized caves in the region. Although there is little genetic difference between river and cave A. mexicanus and all members of the species can emit the same sounds, biologist Carole Hyacinthe and colleagues found that the context and significance of those sounds vary by location—e.g., the click that river-dwelling A. mexicanus use to signal aggression is used by cave dwellers when foraging—and the acoustic properties of cave fish sounds show some cave-specific variations as well. Hyacinthe and colleagues note that differences in sonic communication could accumulate to the point of inhibiting interbreeding among fish from different locations, suggesting that ______blank

", "stem": "

Which choice most logically completes the text?

", "choices": [{"id": "A", "text": "

although A. mexicanus living in rivers are genetically similar to those living in caves, river fish rely on sonic communication less than cave fish do.

"}, {"id": "B", "text": "

although A. mexicanus is a single species at present, it could be in the process of splitting into distinct populations with different characteristics.

"}, {"id": "C", "text": "

although all A. mexicanus emit sounds, the fish living in rivers produce some sounds that the fish living in caves do not, and vice versa.

"}, {"id": "D", "text": "

although A. mexicanus from different locations can interbreed currently, river fish and cave fish are sufficiently genetically distinct that they can be considered separate species.

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer because it presents the conclusion that most logically follows from the text’s discussion of A. mexicanus. According to the text, A. mexicanus, a river-dwelling fish species, has colonized caves. The fish that live in rivers and those that live in caves show no significant genetic differences and are all capable of making the same sounds. The text indicates, however, that Hyacinthe and colleagues found that sounds that the river fish use in a particular context and for a particular purpose are used in a different context and for a different purpose by the cave fish. Additionally, the sounds made by cave fish show some differences depending on the specific cave the fish inhabit. The text goes on to state that Hyacinthe and colleagues have noted that differences in how the fish use sound to communicate could eventually become so great that they prevent fish from different locations from interbreeding. In other words, the river fish might eventually only breed with other river fish (with whom they share characteristics regarding sonic communication that they do not share with cave fish), while the cave fish might only breed with other cave fish for a similar reason. In context, this observation suggests that even though the fish are a single species right now, they could be in the process of splitting into distinct populations with different characteristics. 

Choice A is incorrect because there is no information in the text suggesting that the river fish are less reliant on sonic communication than the cave fish are. Although the text does indicate that the river fish and cave fish are genetically similar, the text describes both groups as using sonic communication and says nothing to indicate that one group depends on that communication more than the other group does. Choice C is incorrect. The text states that all members of the species can emit the same sounds but that the function and context of sounds differ depending on whether the fish live in rivers or caves, but it does not indicate that river fish produce sounds that cave fish do not or vice versa. Choice D is incorrect because it contradicts the text. The text says that there is little genetic difference between the river fish and the cave fish, not that the river fish and cave fish are so genetically distinct that they can be considered separate species.

"}, {"id": "5d122d45", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "H", "type": "mc", "stimulus": "

Psychologists Dacher Keltner and Jonathan Haidt have argued that experiencing awe—a sensation of reverence and wonder typically brought on by perceiving something grand or powerful—can enable us to feel more connected to others and thereby inspire us to act more altruistically. Keltner, along with Paul K. Piff, Pia Dietze, and colleagues, claims to have found evidence for this effect in a recent study where participants were asked to either gaze up at exceptionally tall trees in a nearby grove (reported to be a universally awe-inspiring experience) or stare at the exterior of a nearby, nondescript building. After one minute, an experimenter deliberately spilled a box of pens nearby.

", "stem": "

Which finding from the researchers’ study, if true, would most strongly support their claim?

", "choices": [{"id": "A", "text": "

Participants who had been looking at the trees helped the experimenter pick up significantly more pens than did participants who had been looking at the building.

"}, {"id": "B", "text": "

Participants who helped the experimenter pick up the pens used a greater number of positive words to describe the trees and the building in a postexperiment survey than did participants who did not help the experimenter.

"}, {"id": "C", "text": "

Participants who did not help the experimenter pick up the pens were significantly more likely to report having experienced a feeling of awe, regardless of whether they looked at the building or the trees.

"}, {"id": "D", "text": "

Participants who had been looking at the building were significantly more likely to notice that the experimenter had dropped the pens than were participants who had been looking at the trees.

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer because it presents a finding that, if true, would most strongly support the researchers’ claim that they found evidence that experiencing awe can make people feel more connected to others and thus more likely to behave altruistically (with beneficial and unselfish concern for others). According to the text, the researchers tested for this effect by first having participants look at either something known to be awe-inspiring (very tall trees) or something ordinary (a plain building) and then purposely spilling pens near the participants. The finding that participants who had looked at the trees helped pick up significantly more pens than did participants who had looked at the building would support the researchers’ claim by demonstrating that the people who had experienced awe behaved more altruistically when the experimenter needed help than the other participants did.

Choice B is incorrect because a finding about helpful participants using positive words to describe the trees and the building after the experiment was over wouldn’t have any bearing on the researchers’ claim that experiencing awe increases altruistic behavior. The text doesn’t address the use of positive words to describe things or suggest any connection between using such words and having experienced awe, so that behavior wouldn’t serve as evidence that experiencing awe played a role in promoting helpful behavior. Choice C is incorrect because a finding that participants who didn’t help the experimenter were significantly more likely than others to report having experienced awe whether they had looked at the building or the trees would weaken the researchers’ claim that experiencing awe increases altruistic behavior by suggesting that the opposite might be true—that experiencing awe is in fact linked to choosing not to act in a way that benefits someone else. Choice D is incorrect because a finding about participants noticing that the experimenter had dropped the pens wouldn’t have any bearing on the researchers’ claim about people behaving altruistically. Being aware of a challenge or problem isn’t necessarily beneficial on its own and isn’t the same as offering help, so the finding wouldn’t support the idea that experiencing awe increases altruistic behavior.

"}, {"id": "742fd8ba", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "M", "type": "mc", "stimulus": "
\n\n\n\n\n7006005004003002001000Metal content(parts per million)without kanamycinwith kanamycinMetal Content of Plants with and without Kanamycin ExposureExperimental conditionzinciron
\n

Many plants lose their leaf color when exposed to kanamycin, an antibiotic produced by some soil microorganisms. Spelman College biologist Mentewab Ayalew and her colleagues hypothesized that plants\u2019 response to kanamycin exposure involves altering their uptake of metals, such as iron and zinc. The researchers grew two groups of seedlings of the plant Arabidopsis thaliana, half of which were exposed to kanamycin and half of which were a control group without exposure to kanamycin, and measured the plants\u2019 metal content five days after germination.

", "stem": "

Which choice best describes data in the graph that support Ayalew and her colleagues’ hypothesis?

", "choices": [{"id": "A", "text": "

The control plants contained higher levels of zinc than iron, but plants exposed to kanamycin contained higher levels of iron than zinc.

"}, {"id": "B", "text": "

Both groups of plants contained more than 200 parts per million of both iron and zinc.

"}, {"id": "C", "text": "

Zinc levels were around 300 parts per million in the control plants but nearly 400 parts per million in the plants exposed to kanamycin.

"}, {"id": "D", "text": "

The plants exposed to kanamycin showed lower levels of iron and zinc than the control plants did. 

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer because it best describes data in the graph supporting Ayalew and her colleagues’ hypothesis that plants’ response to kanamycin exposure involves altering their uptake of metals. The graph compares the metal content of two groups of plants, one with kanamycin exposure and a control group without such exposure. The amount of zinc in plants without kanamycin exposure is around 400 parts per million, while the amount of zinc in plants with kanamycin exposure is lower, at around 300 parts per million. Similarly, the amount of iron in plants without kanamycin exposure is a little over 600 parts per million, while the amount of iron in plants with kanamycin exposure is lower, at a little over 200 parts per million. Thus, the graph shows that plants with kanamycin exposure have significantly lower levels of both iron and zinc than the plants without kanamycin exposure. This is evidence supporting the hypothesis that kanamycin exposure results in plants altering their uptake of metals.

Choice A is incorrect because the graph shows that control plants contained higher levels of iron than zinc, not higher levels of zinc than iron; similarly, the plants exposed to kanamycin contained higher levels of zinc than iron, not higher levels of iron than zinc. Choice B is incorrect. Though the claim that both groups of plants contained more than 200 parts per million of both iron and zinc is supported by the graph, this alone does not state whether plants with kanamycin exposure have a different metal content than plants without kanamycin exposure. Choice C is incorrect. The graph shows that the zinc levels for the control plants (those without kanamycin exposure) were around 400 parts per million, not 300 parts per million, and that the zinc levels for plants with kanamycin exposure were around 300 parts per million, not 400 parts per million.

"}, {"id": "03e5cf33", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "M", "type": "mc", "stimulus": "

Many insects are iridescent, or have colors that appear to shimmer and change when seen from different angles. Scientists have assumed that this feature helps to attract mates but could also attract predators. But biologist Karin Kjernsmo and a team had the idea that the shifting appearance of colors might actually make it harder for other animals to see iridescent insects. To test this idea, the team put beetle forewings on leaves along a forest path and then asked human participants to look for them. Some of the wings were naturally iridescent. Others were painted with a nonchanging color from the iridescent spectrum, such as purple or blue.

", "stem": "

Which finding, if true, would most directly support the team’s idea?

", "choices": [{"id": "A", "text": "

On average, participants found most of the purple wings and blue wings and far fewer of the iridescent wings.

"}, {"id": "B", "text": "

On average, participants found the iridescent wings faster than they found the purple wings or blue wings.

"}, {"id": "C", "text": "

Some participants reported that the purple wings were easier to see than the blue wings.

"}, {"id": "D", "text": "

Some participants successfully found all of the wings on the leaves.

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer because it presents the finding that, if true, would most strongly support the research team’s idea about the effect of iridescence, or colors that appear to shimmer and change. The text indicates that although some scientists have assumed that iridescence could attract predators, Kjernsmo’s team wondered if iridescent insects might be harder for other animals to see. The team tested this idea by asking human participants to look for both iridescent beetle wings and beetle wings that weren’t iridescent but that had been painted colors such as purple or blue. If participants located most of the purple or blue wings but far fewer of the iridescent wings, that finding would support the team’s idea since it would suggest that noniridescent wings are easier to see than iridescent wings.

Choice B is incorrect because if participants located the iridescent wings more quickly than the purple or blue wings, that finding would weaken the team’s idea, not support the team’s idea, since it would suggest that the iridescent wings were easier to see than the noniridescent wings. Choice C is incorrect because finding that some participants believed that the purple wings were easier to see than the blue wings would be irrelevant to the team’s idea. The purple and blue wings were both noniridescent, so any difference in how easy those two colors were to see would have nothing to do with the idea that iridescent insects are harder to see than noniridescent insects. Choice D is incorrect because if some participants found all the wings, that wouldn’t support the team’s idea that iridescent insects may be harder to see than noniridescent insects. If anything, this finding might weaken the team’s idea since it could suggest that iridescence had no effect on how difficult the wings were to see.  

"}, {"id": "156ff681", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "H", "type": "mc", "stimulus": "

Many governments that regularly transfer money to individuals—to provide supplemental incomes for senior citizens, for example—have long done so electronically, but other countries typically have distributed physical money and have only recently developed electronic transfer infrastructure. Researchers studied the introduction of an electronic transfer system in one such location and found that recipients of electronic transfers consumed a different array of foods than recipients of physical transfers of the same amount did. One potential explanation for this result is that individuals conceive of and allocate funds in physical money differently than they conceive of and allocate funds in electronic form. 

", "stem": "

Which finding from the study, if true, would most directly weaken the potential explanation?

", "choices": [{"id": "A", "text": "

Recipients of electronic transfers typically spent their funds at a slower rate than recipients of physical transfers did. 

"}, {"id": "B", "text": "

Nearly every recipient of an electronic transfer withdrew the entire amount in physical money shortly after receiving the transfer.

"}, {"id": "C", "text": "

Recipients of physical transfers tended to purchase food about as frequently as recipients of electronic transfers did. 

"}, {"id": "D", "text": "

Some recipients of physical transfers received small amounts of money relatively frequently, while others received large amounts relatively infrequently.

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. This would weaken the explanation. If the recipients of electronic money immediately withdrew it all as physical money, then both kinds of recipients ended up spending physical money on food. So there must be some other explanation why those who initially received electronic money ate different kinds of food.

Choice A is incorrect. This wouldn’t weaken the explanation. If anything, it actually supports it: it demonstrates that recipients of electronic money and recipients of physical money have different spending habits. Choice C is incorrect. This wouldn’t weaken the explanation. The explanation we’re testing this choice against is about the way that people might “conceive of and allocate” physical and electronic funds differently. This choice only focuses on the timing, not what they spend the money on. Choice D is incorrect. This would have no impact on the explanation. It doesn’t tell us anything about possible differences between the spending habits of those who spend physical money and those who spend money electronically.

"}, {"id": "8545ccfe", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "H", "type": "mc", "stimulus": "

Icebergs generally appear to be mostly white or blue, depending on how the ice reflects sunlight. Ice with air bubbles trapped in it looks white because much of the light reflects off the bubbles. Ice without air bubbles usually looks blue because the light travels deep into the ice and only a little of it is reflected. However, some icebergs in the sea around Antarctica appear to be green. One team of scientists hypothesized that this phenomenon is the result of yellow-tinted dissolved organic carbon in Antarctic waters mixing with blue ice to produce the color green.

", "stem": "

Which finding, if true, would most directly weaken the team’s hypothesis?

", "choices": [{"id": "A", "text": "

White ice doesn’t change color when mixed with dissolved organic carbon due to the air bubbles in the ice.

"}, {"id": "B", "text": "

Dissolved organic carbon has a stronger yellow color in Antarctic waters than it does in other places.

"}, {"id": "C", "text": "

Blue icebergs and green icebergs are rarely found near each other.

"}, {"id": "D", "text": "

Blue icebergs and green icebergs contain similarly small traces of dissolved organic carbon.

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer because it presents a finding that, if true, would weaken the scientists’ hypothesis about icebergs that appear to be green. The text indicates that most icebergs are either mostly white or blue in color but that some icebergs in Antarctica appear to be green. The text goes on to say that the scientists hypothesized that this green color occurs when yellow-tinted dissolved organic carbon in ocean waters mixes with blue ice. A finding that both blue icebergs and green icebergs contain similarly small traces of dissolved organic carbon would suggest that something other than yellow-tinted organic carbon causes some icebergs’ green color, since the blue icebergs that contain yellow-tinted organic carbon remained blue instead of turning green.

Choice A is incorrect because, according to the text, the scientists’ hypothesis was that blue icebergs, not white ones, change color when their ice mixes with yellow-tinted dissolved organic carbon. A finding that white ice, because of its air bubbles, doesn’t change color when it’s mixed with dissolved organic carbon would therefore have no bearing on the scientists’ hypothesis. Choice B is incorrect because the text focuses only on Antarctic icebergs that appear to be green. It doesn’t indicate that icebergs in locations other than Antarctica have been found to have a green hue. A finding that dissolved organic carbon has a stronger yellow color in Antarctic waters than in other places would therefore have no bearing on the scientists’ hypothesis that green color in icebergs in Antarctica is caused by yellow-tinted dissolved organic carbon mixing with blue ice. Choice C is incorrect because, according to the text, the scientists’ hypothesis was that blue icebergs turn green when their ice mixes with yellow-tinted dissolved organic carbon in the sea around them. If that’s correct, one would expect blue icebergs and green icebergs to be located at a distance from each other since all blue icebergs in an area where the waters contain yellow-tinted dissolved organic carbon would take on a green hue. A finding that blue icebergs and green icebergs are rarely found near each other would therefore strengthen, not weaken, the researchers’ hypothesis.

"}, {"id": "40578580", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "E", "type": "mc", "stimulus": "

Many scientists have believed that giraffes are solitary creatures, preferring to spend their time alone instead of with others. But observations of giraffes and their behavior in recent years has suggested that these animals may be more social than we once thought. For example, scientists Zoe Muller and Stephen Harris claim that giraffes may even help each other care for one another’s newborns.

", "stem": "

Which finding, if true, would most directly support Muller and Harris’s  conclusion?

", "choices": [{"id": "A", "text": "

Female giraffes have been observed feeding young giraffes that aren’t their direct offspring.

"}, {"id": "B", "text": "

Confrontations between a younger and an older male giraffe are frequently observed.

"}, {"id": "C", "text": "

Some female giraffes have been observed sniffing and licking their newborn offspring.

"}, {"id": "D", "text": "

Giraffes are able to make sounds but are rarely observed communicating with others.

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. If female giraffes feed nonoffspring young, that’s direct evidence that \"giraffes may even help each other care for one another’s newborns.\"

Choice B is incorrect. Confrontations between males doesn’t tell us anything about whether giraffes help each other care for newborns. Choice C is incorrect. While this option does mention newborn offspring, it only discusses a mother’s behavior toward her own child, not another giraffe’s child. Choice D is incorrect. Whether or not giraffes are observed communicating with each other doesn’t tell us anything about whether they help each other care for newborns.

"}, {"id": "a9ac31e4", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "E", "type": "mc", "stimulus": "
\n\n\n\n\n50403020100Area (square km)GlacierArea of Three Glaciers in the2016 Swiss Glacier Inventory Gorner Fiescher Unteraar
\n

To monitor changes to glaciers in Switzerland, the government periodically measures them for features like total area of ice and mean ice thickness, which are then reported in the Swiss Glacier Inventory. These measurements can be used to compare the glaciers. For example, the Gorner glacier had ______blank

", "stem": "

Which choice most effectively uses data from the graph to complete the example?

", "choices": [{"id": "A", "text": "

a larger area than either the Fiescher glacier or the Unteraar glacier.

"}, {"id": "B", "text": "

a smaller area than the Fiescher glacier but a larger area than the Unteraar glacier.

"}, {"id": "C", "text": "

a smaller area than either the Fiescher glacier or the Unteraar glacier.

"}, {"id": "D", "text": "

a larger area than the Fiescher glacier but a smaller area than the Unteraar glacier.

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. The claim is that measurements such as total area can be used to compare glaciers. The graph shows us the area measurements for three glaciers. Of those, Gorner has the largest area.

Choice B is incorrect. This choice misreads the graph. The graph shows that Gorner has the largest area of the three. Choice C is incorrect. This choice misreads the graph. The graph shows that Gorner has the largest area of the three. Choice D is incorrect. This choice misreads the graph. The graph shows that Gorner has the largest area of the three.

"}, {"id": "e946a32e", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "H", "type": "mc", "stimulus": "

Boldly mixing elements of poetry, fiction, drama, philosophy, and manifesto, Puerto Rican writer Giannina Braschi creates cross-genre literature that explores themes such as immigration and independence. Her works have inspired responses from individuals across different fields and in a wide range of formats, from musical compositions and a comic book to architecture and furniture design. In an essay, a student asserts that the production of these diverse creations by others is reflective of Braschi’s own approach to crafting literature.

", "stem": "

Which quotation from a scholarly review of Braschi’s work best supports the student’s claim?

", "choices": [{"id": "A", "text": "

“Braschi is the focus of a 2020 collection of essays in which fifteen scholars from seven different countries delved into the linguistic and structural patterns of her writings.”

"}, {"id": "B", "text": "

“Braschi’s eagerness to push boundaries and blend genres within literature invites us to consider how other art forms might also engage with literature.”

"}, {"id": "C", "text": "

“Before settling in New York City, where she would go on to become a college professor, Braschi studied both literature and philosophy in several cities around the world.”

"}, {"id": "D", "text": "

“In addition to her creative literary works, Braschi has produced academic pieces analyzing writings by Miguel de Cervantes, Federico García Lorca, and other authors.”

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer because it presents the quotation that best supports the student’s claim about Braschi. By describing how Braschi’s blending of genres invites her audience to think about how other art forms could also engage with literature, the quotation supports the idea that the diversity of responses to Braschi’s work reflects Braschi’s own approach to creating literature.

Choice A is incorrect because the quotation describes scholars from different countries writing essays about Braschi’s use of language in her writings; it doesn’t address how Braschi’s creation of cross-genre literature inspires diverse types of responses, which is the claim the student makes. Choice C is incorrect because the quotation focuses on the fact that Braschi studied in several different cities, which doesn’t address the student’s claim that Braschi’s creation of cross-genre literature inspires diverse types of responses. Choice D is incorrect because the quotation lists some of the authors who Braschi has written academic works about, which is irrelevant to the student’s claim that Braschi’s creation of cross-genre literature inspires diverse types of responses. 

"}, {"id": "df34b586", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "E", "type": "mc", "stimulus": "
\n\n\n\n\n\n\n\n\n\n\n\n\n60,00050,00040,00030,00020,00010,0000Machines sold1903190819131918Singer Sewing Machine Salesin Four Countries, 1903\u20131918Year New Zealand Australia the Philippines Turkey
\n

By the early 1900s, the Singer Corporation, a US sewing machine manufacturer founded in 1851, began to see rapidly increasing sales abroad, particularly in Russia, Germany, and the United Kingdom. These markets were responsible for the bulk of Singer\u2019s overseas sales, but demand for the company\u2019s machines in other countries also grew significantly in the early twentieth century. For instance, sales of their sewing machines in ______blank

", "stem": "

Which choice most effectively uses data from the graph to complete the example?

", "choices": [{"id": "A", "text": "

the Philippines increased dramatically from 1908 to 1918.

"}, {"id": "B", "text": "

New Zealand were largely consistent from 1903 to 1918.

"}, {"id": "C", "text": "

Australia increased steadily from 1903 to 1918.

"}, {"id": "D", "text": "

Turkey declined substantially from 1913 to 1918.

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer because it most effectively uses data from the graph to complete the example. According to the graph, fewer than 10,000 sewing machines were sold in the Philippines in both 1903 and 1908, but nearly 30,000 were sold in 1913 and around 45,000 were sold in 1918. This increase illustrates the statement in the text that demand for Singer sewing machines grew significantly in the early twentieth century in overseas countries other than Russia, Germany, and the United Kingdom.

Choice B is incorrect because consistent sales of Singer sewing machines in New Zealand from 1903 to 1918 do not indicate that demand for the product increased but rather that demand remained relatively the same. Choice C is incorrect because it does not accurately describe the data in the graph. Although sales in Australia did increase somewhat between 1903 and 1908, there was very little change between 1908 and 1913, and then sales declined between 1913 and 1918. The data for Australia, then, do not show a steady increase from 1903 to 1918. Choice D is incorrect because declining sales of Singer sewing machines in Turkey from 1913 to 1918 do not point to an increase in demand for the product but rather to a decline in demand.

"}, {"id": "dc87adf4", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "H", "type": "mc", "stimulus": "

Barchester Towers is an 1857 novel by Anthony Trollope. In the novel, Trollope’s portrayal of Dr. Proudie underscores the character’s exaggerated sense of his own abilities: ______blank

", "stem": "

Which quotation from Barchester Towers most effectively illustrates the claim?

", "choices": [{"id": "A", "text": "

“It must not…be taken as proved that Dr. Proudie was a man of great mental powers, or even of much capacity for business, for such qualities had not been required in him.”

"}, {"id": "B", "text": "

“[Dr. Proudie] was comparatively young, and had, as he fondly flattered himself, been selected as possessing such gifts, natural and acquired, as must be sure to recommend him to a yet higher notice.”

"}, {"id": "C", "text": "

“[Dr. Proudie’s] residence in the metropolis, rendered necessary by duties thus entrusted to him, his high connexions, and the peculiar talents and nature of the man, recommended him to persons in power.”

"}, {"id": "D", "text": "

“[Dr. Proudie] was certainly possessed of sufficient tact to answer the purpose for which he was required without making himself troublesome.”

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. In this quotation, Dr. Proudie is described as \"fondly flatter[ing] himself\" that he has gifts that \"must be sure to recommend him to a yet higher notice.\" In other words, he expects his skills to push him to greater fame and success. This implies an exaggerated sense of his own abilities, which matches the claim we’re trying to support.

Choice A is incorrect. This quotation doesn’t describe Proudie’s view of himself, nor does it paint him in an especially flattering light. Instead, by saying his mental powers and business skill are not \"proved,\" it implies that he is actually dim-witted and bad at business. Choice C is incorrect. This choice describes Proudie’s closeness to power and importance, but it doesn’t show what Proudie thinks of himself. Proudie is not describing himself or his abilities here. The narrator is. Choice D is incorrect. While this quotation offers Proudie very mild praise, it doesn’t show what Proudie thinks of himself or his own abilities, which is what the claim focuses on.

"}, {"id": "3bfcb73b", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "H", "type": "mc", "stimulus": "

An archaeological team led by Piotr Bieli\u0144ski and Sultan al-Bakri found remnants of a 4,000-year-old Bronze Age board game at a site in Oman. Little is left of the game except a stone board, which is carved with a grid and has places to hold game pieces. Some scholars claim that the game was largely played by traders.

", "stem": "

Which finding, if true, would most directly support the scholars’ claim?

", "choices": [{"id": "A", "text": "

Other examples of the game dating to the same period have been found in the remains of several homes in the region, including in one home that may have belonged to a trader.

"}, {"id": "B", "text": "

Similar games have been found in other sites dating to the same period that were connected to the site in Oman via trade routes.

"}, {"id": "C", "text": "

The other known examples of the game dating to the same period have been found along routes that seem to have been used primarily by traders at the time. 

"}, {"id": "D", "text": "

Remnants of other goods have been found at the site in Oman that probably also reached the location through trade.

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer because it presents a finding that, if true, would most directly support the scholars’ claim about the board game. The text explains that the remains of a 4,000-year-old board game were found in Oman. The text then states that scholars claim this board game was played mostly by traders. If the other known examples of this board game from the same time period were discovered along routes that seem to have been used primarily by traders, this finding would directly support the scholars’ claim because it suggests that the game was largely played by traders who brought it with them for entertainment as they traveled.

Choice A is incorrect because this finding would suggest only that a single trader may have possessed examples of the board game, perhaps for the purpose of trading or selling the game to residents of Oman. For this reason, the finding wouldn’t directly support the scholars’ claim that the majority of the game’s players were traders. Choice B is incorrect because this finding doesn’t mention the board game at all, referring only to similar games found at other sites, and would therefore provide no direct support for the scholars’ claim about the board game. Choice D is incorrect because this finding doesn’t mention the board game at all, referring only to the remains of other goods found at the site in Oman, and would therefore provide no direct support for the scholars’ claim about the board game.

"}, {"id": "53c6c179", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "H", "type": "mc", "stimulus": "

\n\n\n\n\n\n\n\n\n\n\n\n\n35302520151050Median marriage age19001910192019301940195019601970198019902000Median Ages of First Marriage for Menand Women in the United States andin England and Wales, 1900\u20132000Years Women (England and Wales) Men (United States) Women (United States) Men (England and Wales)

\n

A sociology student is reading an essay on the median age of first marriage in Western countries throughout the twentieth century. The author of the essay cites factors common to these countries that the author believes caused an increase in the median age of first marriage, such as new technologies that shortened the time needed for domestic chores, making two-person households less necessary and living alone more viable. The student asserts that beyond these factors there must be additional ones specific to particular Western countries that influenced the increase of age at first marriage.

", "stem": "

Which choice most effectively uses data from the graph that support the student’s assertion?

", "choices": [{"id": "A", "text": "

Between 1970 and 2000, the median age of first marriage rose more sharply for men in England and Wales than it did for men in the United States.

"}, {"id": "B", "text": "

In England and Wales, the median age of first marriage was consistently higher for men than for women between 1900 and 2000, but this was not always the case in the United States.

"}, {"id": "C", "text": "

The median age of first marriage for men in England and Wales was lower in 1970 than in 1950 or 1990.

"}, {"id": "D", "text": "

Between 1900 and 2000, the median age of first marriage for women in England and Wales was consistently higher than for women in the United States, as was the case for men.

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. The student concluded that country-specific factors influence changes to median age of first marriage. This choice describes a time period when the rate of change differed between countries, suggesting that country-specific factors may have played a role in these changes.

Choice B is incorrect. This choice misreads the graph. The median age of first marriage was consistently higher for men than for women in the United States during the time period depicted. Choice C is incorrect. The student concluded that country-specific factors influence changes to median age of first marriage. However, this choice doesn’t provide any contrasts between countries and thus doesn’t support the idea of country-specific factors influencing median age of first marriage. Choice D is incorrect. The students’ conclusion is about changes that occurred during the 20th century. This choice provides broad information about the century as a whole, so it doesn’t give insight into how median age at first marriage changed over time.

"}, {"id": "55688b3c", "domain": "Information and Ideas", "skill": "Inferences", "difficulty": "M", "type": "mc", "stimulus": "

Dutch painters in the sixteenth and seventeenth centuries often showed tables filled with large wheels of cheese or carved shards of butter. Some art historians, noting that dairy products were a major component of the Dutch diet, interpret these depictions as reflections of everyday Dutch eating habits. However, a group of researchers recently reviewed hundreds of food-related paintings and found that lemons—which could only be acquired in the Netherlands at great cost, since they had to be imported from warmer climates—feature in Dutch paintings of the period more than three times as frequently as dairy products do, thereby casting doubt on the idea that ______blank

", "stem": "

Which choice most logically completes the text?

", "choices": [{"id": "A", "text": "

dairy products were a more significant component of the Dutch diet of the period than lemons were.

"}, {"id": "B", "text": "

food was a more popular subject among Dutch painters than it was among painters from other countries at the time. 

"}, {"id": "C", "text": "

depictions of food in Dutch paintings of the period should be taken as realistic representations of Dutch eating habits.

"}, {"id": "D", "text": "

Dutch painters of the period may have depicted foods for symbolic reasons rather than to show what Dutch people typically ate.

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. The text tells us that lemons—an expensive imported product—feature in Dutch paintings of the period more frequently than dairy products do. Since it’s unlikely lemons were eaten more often than dairy, this fact casts doubt on the theory that these paintings realistically depicted Dutch diets.

Choice A is incorrect. In fact, the text suggests the opposite: it says that dairy products were a \"major component of the Dutch diet,\" while lemons were an expensive import item, so we can infer that lemons were eaten much more rarely than dairy products. Choice B is incorrect. The passage doesn’t mention painters from other countries, so there’s no basis to make this inference. Choice D is incorrect. In fact, the text suggests that Dutch painters do have reasons for depicting foods other than to show what Dutch people typically ate. For example, lemons in a painting could indicate wealth or prosperity.

"}, {"id": "df91532e", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "H", "type": "mc", "stimulus": "

In the “language nest” model of education, Indigenous children learn the language of their people by using it as the medium of instruction and socialization at pre-K or elementary levels. In their 2016 study of a school in an Anishinaabe community in Ontario, Canada, scholars Lindsay Morcom and Stephanie Roy (who are Anishinaabe themselves) found that the model not only imparted fluency in the Anishinaabe language but also enhanced students’ pride in Anishinaabe culture overall. Given these positive effects, Morcom and Roy predict that the model increases the probability that as adults, former students of the school will transmit the language to younger generations in their community.

", "stem": "

Which finding, if true, would most strongly support the researchers’ prediction?

", "choices": [{"id": "A", "text": "

Anishinaabe adults who didn’t attend the school feel roughly the same degree of cultural pride as the former students of the school feel.

"}, {"id": "B", "text": "

After transferring to the school, new students experience an increase in both fluency and academic performance overall.

"}, {"id": "C", "text": "

As adults, former students of the school are just as likely to continue living in their community as individuals who didn’t attend the school.

"}, {"id": "D", "text": "

As they complete secondary and higher education, former students of the school experience no loss of fluency or cultural pride.

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer because it presents a finding that, if true, would support the researchers’ prediction about the language nest model of education. The text states that Morcom and Roy studied the effects of the language nest model of education on students at an Anishinaabe school, and they found that the model—which is used with students during pre-K or elementary school—increased students’ fluency in the Anishinaabe language and pride in Anishinaabe culture. The researchers predicted that the students’ positive early experiences with the Anishinaabe language would lead them to be more likely to later share the language with younger generations. If former students maintain full fluency and cultural pride after finishing secondary and higher education, it follows that they would be both able and motivated to share what they know with others; this would likely result in a higher probability of transmitting the language to younger generations, as the researchers predict.

Choice A is incorrect because finding that Anishinaabe adults who didn’t attend the school feel approximately the same degree of cultural pride as those adults who did attend wouldn’t support the researchers’ prediction that former students will be more likely to share their knowledge with younger generations. This finding would identify a similarity between the groups rather than a factor that might make former students more likely than other adults to transmit the language to younger people. Choice B is incorrect because finding that new students experience increased performance in language fluency and academics would suggest that the school has a positive effect on students when they attended but wouldn’t reveal anything about those students’ later actions as adults (such as their likelihood of sharing their knowledge with younger generations). Choice C is incorrect because finding that Anishinaabe adults who attended the school are equally likely to stay in the community as adults who didn’t attend the school wouldn’t support the researchers’ prediction that former students will be more likely to share their knowledge with younger generations. This finding would identify a similarity between the groups rather than a factor that might make former students more likely than other adults to transmit the language to younger people.

"}, {"id": "81af81d4", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "M", "type": "mc", "stimulus": "

“Often Rebuked, Yet Always Back Returning” is an 1846 poem by Emily Brontë. The poem conveys the speaker’s determination to experience the countryside around her: ______blank

", "stem": "

Which quotation from the poem most effectively illustrates the claim?

", "choices": [{"id": "A", "text": "

“Often rebuked, yet always back returning / To those first feelings that were born with me, / And leaving busy chase of wealth and learning / For idle dreams of things which cannot be.”

"}, {"id": "B", "text": "

“I’ll walk, but not in old heroic traces, / And not in paths of high morality, / And not among the half-distinguished faces, / The clouded forms of long-past history.”

"}, {"id": "C", "text": "

“I’ll walk where my own nature would be leading: / It vexes me to choose another guide: / Where the grey flocks in ferny glens are feeding; / Where the wild wind blows on the mountain side.”

"}, {"id": "D", "text": "

“To-day, I will seek not the shadowy region; / Its unsustaining vastness waxes drear; / And visions rising, legion after legion, / Bring the unreal world too strangely near.”

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer because it presents the quotation that best illustrates the claim that the speaker is determined to experience the countryside around her. In the quotation, the speaker makes it clear that she plans to walk somewhere based on her own wishes (“where my own nature would be leading”) rather than follow anything else (“another guide”), and that she’ll walk “in ferny glens” alongside the mountain. 

Choice A is incorrect because this quotation suggests that the speaker wants to avoid pursuing money and education (“busy chase of wealth and learning”) and instead return to some earlier interests (her “first feelings”); the quotation doesn’t address her determination to experience the countryside. Choice B is incorrect because the speaker is describing the circumstances under which she won’t walk, which doesn’t address her determination to experience the countryside. Choice D is incorrect because rather than conveying her determination to experience the countryside, the speaker is explaining a particular thing she won’t do (“seek not the shadowy region”).

"}, {"id": "8584f3ce", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "H", "type": "mc", "stimulus": "

When digging for clams, their primary food, sea otters damage the roots of eelgrass plants growing on the seafloor. Near Vancouver Island in Canada, the otter population is large and well established, yet the eelgrass meadows are healthier than those found elsewhere off Canada’s coast. To explain this, conservation scientist Erin Foster and colleagues compared the Vancouver Island meadows to meadows where otters are absent or were reintroduced only recently. Finding that the Vancouver Island meadows have a more diverse gene pool than the others do, Foster hypothesized that damage to eelgrass roots increases the plant’s rate of sexual reproduction; this, in turn, boosts genetic diversity, which benefits the meadow’s health overall.

", "stem": "

Which finding, if true, would most directly undermine Foster’s hypothesis?

", "choices": [{"id": "A", "text": "

At some sites in the study, eelgrass meadows are found near otter populations that are small and have only recently been reintroduced.

"}, {"id": "B", "text": "

At several sites not included in the study, there are large, well-established sea otter populations but no eelgrass meadows.

"}, {"id": "C", "text": "

At several sites not included in the study, eelgrass meadows’ health correlates negatively with the length of residence and size of otter populations.

"}, {"id": "D", "text": "

At some sites in the study, the health of plants unrelated to eelgrass correlates negatively with the length of residence and size of otter populations.

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer because it presents a finding that, if true, would weaken Foster’s hypothesis that damage to eelgrass roots improves the health of eelgrass meadows by boosting genetic diversity. The text indicates that sea otters damage eelgrass roots but that eelgrass meadows near Vancouver Island, where there’s a large otter population, are comparatively healthy. When Foster and her colleagues compared the Vancouver Island eelgrass meadows to those that don’t have established otter populations, the researchers found that the Vancouver Island meadows are more genetically diverse than the other meadows are. This finding led Foster to hypothesize that damage to the eelgrass roots encourages eelgrass reproduction, thereby improving genetic diversity and the health of the meadows. If, however, other meadows not included in the study are less healthy the larger the local otter population is and the longer the otters have been in residence, that would suggest that damage to the eelgrass roots, which would be expected to increase with the size and residential duration of the otter population, isn’t leading meadows to be healthier. Such a finding would therefore weaken Foster’s hypothesis. 

Choice A is incorrect because finding that small, recently introduced otter populations are near other eelgrass meadows in the study wouldn’t weaken Foster’s hypothesis. If otter populations were small and only recently established, they wouldn’t be expected to have caused much damage to eelgrass roots, so even if those eelgrass meadows were less healthy than the Vancouver Island meadows, that wouldn’t undermine Foster’s hypothesis. In fact, it would be consistent with Foster’s hypothesis since it would suggest that the greater damage caused by larger, more established otter populations is associated with healthier meadows. Choice B is incorrect because the existence of areas with otters but without eelgrass meadows wouldn’t reveal anything about whether the damage that otters cause to eelgrass roots ultimately benefits eelgrass meadows. Choice D is incorrect because the health of plants other than eelgrass would have no bearing on Foster’s hypothesis that damage to eelgrass roots leads to greater genetic diversity and meadow health. It would be possible for otters to have a negative effect on other plants while nevertheless improving the health of eelgrass meadows by damaging eelgrass roots. 

"}, {"id": "c95995bc", "domain": "Information and Ideas", "skill": "Inferences", "difficulty": "M", "type": "mc", "stimulus": "

Colonized by Spain in the 1600s, New Mexico is home to a dialect of Spanish that differs significantly from dialects spoken in Spain’s other former colonies in the Americas. Most notably, the New Mexican dialect retains older features of the language that other dialects lost in later centuries. But why would it have done so? New Mexico was so distant from population centers in Spain’s other colonies that it attracted few colonists after its initial colonization. Geographical isolation in turn would have limited the exposure of New Mexican colonists to changes occurring to Spanish grammar and vocabulary elsewhere in the empire. Thus, the present-day uniqueness of the New Mexican dialect suggests the extent to which ______blank

", "stem": "

Which choice most logically completes the text?

", "choices": [{"id": "A", "text": "

a language can protect itself from being influenced by other languages.

"}, {"id": "B", "text": "

the grammar and vocabulary of any given language change from one generation to the next. 

"}, {"id": "C", "text": "

geographical isolation can influence how a language develops.

"}, {"id": "D", "text": "

speakers of one dialect of a language can understand speakers of another dialect of that language.

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer because it is the choice that most logically completes the text. The text mentions a dialect of Spanish spoken in New Mexico, which was colonized by Spain in the 1600s. The text then states that the New Mexican dialect differs greatly from other Spanish dialects in that it still has characteristics of an older Spanish that other dialects eventually lost. After asking why this might be, the text points out that the New Mexico colony was distant from Spain’s other colonies, making it less attractive to colonists after the initial colonization. This geographic isolation limited the colony’s exposure to other Spanish colonists who would have otherwise introduced the changes to the Spanish language that occurred in their respective colonies. It can therefore be inferred that this isolation is a reason why the New Mexican dialect still has characteristics of an older Spanish, while the Spanish dialects spoken in less isolated areas that have more interaction with speakers of other dialects would lose those characteristics over time. Thus, the most logical completion of the text is that geographical isolation can influence how a language develops.

Choice A is incorrect because the text discusses different dialects of Spanish, not different languages altogether. Choice B is incorrect because the text focuses on how the New Mexican dialect has stayed the same over time in some ways, not on how it has changed from one generation to the next. Choice D is incorrect because though the text discusses how the New Mexican dialect of Spanish is different from others, it does not discuss how speakers of different dialects are able to understand each other.

"}, {"id": "dbbbc5dd", "domain": "Information and Ideas", "skill": "Inferences", "difficulty": "E", "type": "mc", "stimulus": "

Off-off-Broadway theaters emerged in the late 1950s as a rebellion against mainstream Broadway theaters in New York, freeing artists to create productions that were more experimental than typical Broadway shows. One such artist was playwright María Irene Fornés. Working with off-off Broadway theaters enabled Fornés not only to direct her own plays but also to direct them exactly as she intended them to be staged, regardless of how strange the results might have seemed to audiences accustomed to Broadway shows. In this way, Fornés ______blank

", "stem": "

Which choice most logically completes the text?

", "choices": [{"id": "A", "text": "

wrote plays that would have been too expensive to produce if someone else had directed the production.

"}, {"id": "B", "text": "

recognized that staging an off-off-Broadway play was more complicated than staging a Broadway play.

"}, {"id": "C", "text": "

would have been more famous if she had created plays that were mainstream instead of experimental.

"}, {"id": "D", "text": "

illustrates the artistic opportunity offered by off-off Broadway theaters.

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. The text says that off-off-Broadway theaters allowed artists to create more experimental shows, and then discusses how Fornés was free to direct her own “strange” plays however she wanted. This suggests that Fornés exemplifies the artistic freedom of off-off Broadway theaters.

Choice A is incorrect. This inference isn’t supported. The text never discusses the costs of production, so we can’t logically make this claim. Choice B is incorrect. This inference isn’t supported. The text never discusses the complexity of staging plays either on Broadway or off-off Broadway, so there’s no basis to make this inference. Choice C is incorrect. This inference isn’t supported. The text never discusses fame at all, so there’s no basis to make this inference.

"}, {"id": "e1546fd6", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "M", "type": "mc", "stimulus": "

Average Nitrate and Phosphate Concentrations in Seawater after Volcanic Eruption

NutrientSeawater in lava-affected area, 5–45 meters below surfaceSeawater in lava-affected area, 75–125 meters below surfaceSeawater outside of lava-affected area, 5–45 meters below surfaceSeawater outside of lava-affected area, 75–125 meters below surface
Nitrate (micromoles per liter)3.10.4≤0.03less than or equal to 0.03≤0.01less than or equal to 0.01
Phosphate (micromoles per liter)0.170.090.140.06

\n

After a volcanic eruption spilled lava into North Pacific Ocean waters, a dramatic increase of diatoms (a kind of phytoplankton) near the surface occurred. Scientists assumed the diatoms were thriving on nutrients such as phosphate from the lava, but analysis showed these nutrients weren’t present near the surface in forms diatoms can consume. However, there was an abundance of usable nitrate, a nutrient usually found in much deeper water and almost never found in lava. Microbial oceanographer Sonya Dyhrman and colleagues believe that as the lava plunged nearly 300 meters below the surface it dislodged pockets of this nutrient, releasing it to float upward, given that ______blank

", "stem": "

Which choice most effectively uses data from the table to complete the statement?

", "choices": [{"id": "A", "text": "

at 5–45 meters below the surface, the average concentration of phosphate was about the same in the seawater in the lava-affected area as in the seawater outside of the lava-affected area.

"}, {"id": "B", "text": "

for both depth ranges measured, the average concentrations of nitrate were substantially higher in the seawater in the lava-affected area than in the seawater outside of the lava-affected area.

"}, {"id": "C", "text": "

for both depth ranges measured in the seawater in the lava-affected area, the average concentrations of nitrate were substantially higher than the average concentrations of phosphate.

"}, {"id": "D", "text": "

in the seawater outside of the lava-affected area, there was little change in the average concentration of nitrate from 75–125 meters below the surface to 5–45 meters below the surface.

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. The claim is that the lava freed the deep nitrate, allowing it to float upward. The table supports this by showing that there was more nitrate in the lava-affected seawater at various depths above 300 meters (the depth to which the lava plunged) than in unaffected seawater.

Choice A is incorrect. This choice doesn’t complete the statement in a way that supports the claim. The claim is about nitrate, not phosphate. Choice C is incorrect. This choice doesn’t complete the statement in a way that supports the claim. The claim is only about nitrate—the concentrations of phosphate aren’t relevant. Choice D is incorrect. This choice doesn’t complete the statement in a way that supports the claim. It doesn’t say anything about the seawater inside the lava-affected area.

"}, {"id": "8a3ecac6", "domain": "Information and Ideas", "skill": "Inferences", "difficulty": "E", "type": "mc", "stimulus": "

North American gray wolves usually have mixed gray and white fur, but some members of the species have a version of a gene, or gene variant, that gives them a mostly black coat instead. Sarah Cubaynes and her team studied twelve populations of North American gray wolves. They found that the black-furred wolves are more common in areas where outbreaks of distemper virus happen regularly. The team also discovered that the black-furred wolves are more likely to be immune to distemper than the gray-furred wolves are. Taken together, these findings suggest that ______blank

", "stem": "

Which choice most logically completes the text?

", "choices": [{"id": "A", "text": "

North American gray wolves experience more outbreaks of distemper virus than other wolf species do.

"}, {"id": "B", "text": "

the gene variant that results in black fur may be linked to immunity to the distemper virus.

"}, {"id": "C", "text": "

the average life span of gray wolves is likely to increase over time because of a particular gene variant.

"}, {"id": "D", "text": "

gray-furred wolves will soon replace black-furred wolves across North America.

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. The text tells us that the black-furred wolves are more common in areas with regular outbreaks of distemper virus and are more likely to be immune to distemper than the gray-furred wolves. This suggests that the gene variant that results in black fur may be linked to immunity to the distemper virus.

Choice A is incorrect. The text never compares North American gray wolves to other wolf species—in fact, it never discusses other wolf species at all, so there’s no basis for this inference. Choice C is incorrect. The life span of gray wolves is never mentioned in this text, so we have no basis for this inference. Choice D is incorrect. This is too extreme. The text says that \"black-furred wolves are more likely to be immune to distemper than the gray-furred wolves,\" but that alone doesn’t mean that black-furred wolves will replace gray-furred wolves across North America.

"}, {"id": "9391b7cc", "domain": "Information and Ideas", "skill": "Inferences", "difficulty": "H", "type": "mc", "stimulus": "

If some artifacts recovered from excavations of the settlement of Kuulo Kataa, in modern Ghana, date from the thirteenth century CE, that may lend credence to claims that the settlement was founded before or around that time. There is other evidence, however, strongly supporting a fourteenth century CE founding date for Kuulo Kataa. If both the artifact dates and the fourteenth century CE founding date are correct, that would imply that ______blank

", "stem": "

Which choice most logically completes the text?

", "choices": [{"id": "A", "text": "

artifacts from the fourteenth century CE are more commonly recovered than are artifacts from the thirteenth century CE. 

"}, {"id": "B", "text": "

the artifacts originated elsewhere and eventually reached Kuulo Kataa through trade or migration.

"}, {"id": "C", "text": "

Kuulo Kataa was founded by people from a different region than had previously been assumed.

"}, {"id": "D", "text": "

excavations at Kuulo Kataa may have inadvertently damaged some artifacts dating to the fourteenth century CE.

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer because it most logically completes the text’s discussion of artifacts and Kuulo Kataa’s founding date. If it were true both that Kuulo Kataa was founded in the fourteenth century CE and that artifacts found in excavations of the settlement are from the thirteenth century CE, it would be reasonable to conclude that the artifacts weren’t created in the Kuulo Kataa settlement. That would suggest, then, that the artifacts originated somewhere else and eventually reached the settlement through trading or as people migrated.

Choice A is incorrect because the existence of thirteenth-century CE artifacts recovered during excavations of a settlement founded in the fourteenth century CE isn’t logically connected to artifacts from one century being more commonly recovered than artifacts from another century. Rather than suggesting anything about how frequently artifacts from different times are found, the existence of artifacts confirmed as predating the settlement’s founding suggests that those items arrived in Kuulo Kataa during or after its establishment. Choice C is incorrect because the text focuses on time periods and says nothing about which region the founders of Kuulo Kataa have been thought to come from; similarly, the text doesn’t suggest anything about where the thirteenth-century CE artifacts originated other than not from Kuulo Kataa. Therefore, it isn’t logical to conclude that the mere existence of artifacts confirmed as predating the Kuulo Kataa settlement suggests that the founders of the settlement came from a particular region other than one previously assumed. Choice D is incorrect because the existence of artifacts from the thirteenth century CE at a site dated to the fourteenth century CE doesn’t imply that fourteenth-century objects were damaged during excavations. There’s nothing in the text to suggest that any objects were damaged; rather, the existence of artifacts confirmed as predating the settlement’s founding suggests that those items were brought to Kuulo Kataa during or after its establishment. 

"}, {"id": "9452092c", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "H", "type": "mc", "stimulus": "

Effects of Mycorrhizal Fungi on 3 Plant Species

Plant speciesMycorrhizal hostAverage mass of plants grown in soil containing mycorrhizal fungi (in grams)Average mass of plants grown in soil treated to kill fungi (in grams)
Cornyes15.13.8
Marigoldyes10.22.4
Broccolino7.57

\n

Mycorrhizal fungi in soil benefits many plants, substantially increasing the mass of some. A student conducted an experiment to illustrate this effect. The student chose three plant species for the experiment, including two that are mycorrhizal hosts (species known to benefit from mycorrhizal fungi) and one nonmycorrhizal species (a species that doesn’t benefit from and may even be harmed by mycorrhizal fungi). The student then grew several plants from each species both in soil containing mycorrhizal fungi and in soil that had been treated to kill mycorrhizal and other fungi. After several weeks, the student measured the plants’ average mass and was surprised to discover that ______blank

", "stem": "

Which choice most effectively uses data from the table to complete the statement?

", "choices": [{"id": "A", "text": "

broccoli grown in soil containing mycorrhizal fungi had a slightly higher average mass than broccoli grown in soil that had been treated to kill fungi.

"}, {"id": "B", "text": "

corn grown in soil containing mycorrhizal fungi had a higher average mass than broccoli grown in soil containing mycorrhizal fungi.

"}, {"id": "C", "text": "

marigolds grown in soil containing mycorrhizal fungi had a much higher average mass than marigolds grown in soil that had been treated to kill fungi.

"}, {"id": "D", "text": "

corn had the highest average mass of all three species grown in soil that had been treated to kill fungi, while marigolds had the lowest.

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer because it most effectively uses data from the table to complete the statement. The text explains that mycorrhizal hosts are plants that benefit from the presence of mycorrhizal fungi in the soil and that some such plants produce more mass when grown in the presence of these fungi, while for nonmycorrhizal species the fungi either have no effect or may be harmful. The experiment included two mycorrhizal hosts (corn and marigold) and one nonmycorrhizal species (broccoli). Given the claim in the text that nonmycorrhizal species will see either no difference or a decrease in mass when exposed to mycorrhizal fungi, the student would likely have been surprised by the higher average mass for broccoli grown in the presence of the fungi than the broccoli grown in the soil treated to kill fungi.

Choice B is incorrect. Although this choice accurately describes the corn data from the table, the fact that the mycorrhizal host corn is more massive in the presence of the fungi likely fits with what the student expected and would therefore not be surprising. Choice C is incorrect. Although this choice accurately describes the marigold data from the table, the fact that the mycorrhizal host marigold is more massive in the presence of the fungi is likely what the student expected and thus would not be surprising. Choice D is incorrect because it does not accurately represent the data in the table—when grown in soil treated to kill fungi, corn had an average mass of 3.8 g while broccoli had an average mass of 7g—and because making comparisons among the plants in the no-fungi condition, by itself, does not provide a basis to compare the average mass of mycorrhizal hosts and nonmycorrhizal species grown in the presence of the fungi with those grown in the soil treated to kill fungi.

"}, {"id": "2a075bd1", "domain": "Information and Ideas", "skill": "Inferences", "difficulty": "H", "type": "mc", "stimulus": "

Indigenous cultures possess unique knowledge of the medicinal uses of plants. According to a 2021 study, 73 percent of the medicinal uses of plants native to North America are reflected in the vocabulary of a single Indigenous language. However, as more and more Indigenous people exclusively speak a globally dominant language, such as English, their ancestral languages fade from daily use. These facts lend added importance to tribal nations’ efforts to preserve their languages. By ensuring the continued use of Cherokee, Ojibwe, and the hundreds of other Indigenous languages in what is now the United States, tribal nations are also ______blank

", "stem": "

Which choice most logically completes the text?

", "choices": [{"id": "A", "text": "

increasing the number of medicinal plants represented in the vocabularies of Indigenous languages.

"}, {"id": "B", "text": "

transmitting terms for medicinal plants from Indigenous languages to globally dominant languages.

"}, {"id": "C", "text": "

preserving knowledge about the medicinal value of plants native to the tribal nations’ lands.

"}, {"id": "D", "text": "

ensuring that citizens of tribal nations have physical access to medicinal plants.

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer because it most logically completes the text’s discussion of the relationship between Indigenous languages and knowledge of the medicinal uses of plants. The text states that Indigenous cultures possess special knowledge of the medicinal uses of plants, which is reflected in their vocabulary. The text then discusses how tribal nations are working to preserve their languages, whose daily use is declining as globally dominant languages become increasingly dominant in Indigenous communities. Given that the languages of tribal nations in what is now the United States function as repositories of knowledge about plants’ medicinal uses, it logically follows that continued use of those languages will assist with passing on knowledge about the medicinal value of plants native to the tribal nations’ lands.

Choice A is incorrect because the text states that preserving Indigenous languages will increase the knowledge, not the number, of medicinal plants. Choice B is incorrect because the text is concerned with how vocabulary about the medicinal value of plants can be preserved through the continued daily use of Indigenous languages, not with how such vocabulary can be incorporated into globally dominant, non-Indigenous languages. Moreover, the text explains that the exclusive use of globally dominant languages in Indigenous communities comes at an expense to the continued daily use of those communities’ languages. Given this relationship, it is unlikely globally dominant languages would borrow Indigenous vocabulary pertaining to  plants’ medicinal uses. Choice D is incorrect because the text doesn’t discuss physical access to medicinal plants, instead focusing on Indigenous knowledge and language surrounding the medicinal uses of plants.

"}, {"id": "8fbed1cb", "domain": "Information and Ideas", "skill": "Inferences", "difficulty": "M", "type": "mc", "stimulus": "

When the Vinland Map, a map of the world purported to date to the mid-1400s, surfaced in 1957, some scholars believed it demonstrated that European knowledge of the eastern coast of present-day North America predated Christopher Columbus’s 1492 arrival. In 2021, a team including conservators Marie-France Lemay and Paula Zyats and materials scientist Anikó Bezur performed an extensive analysis of the map and the ink used. They found that the ink contains titanium dioxide, a compound that was first introduced in ink manufacturing in the early 1900s. Therefore, the team concluded that ______blank

", "stem": "

Which choice most logically completes the text?

", "choices": [{"id": "A", "text": "

mid-1400s Europeans could not have known about the eastern coast of present-day North America.

"}, {"id": "B", "text": "

the Vinland Map could not have been drawn by mid-1400s mapmakers. 

"}, {"id": "C", "text": "

mapmakers must have used titanium compounds in their ink in the 1400s.

"}, {"id": "D", "text": "

there isn’t enough information to determine when the ink was created.

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer because it most logically completes the text’s discussion of Lemay, Zyats, and Bezur’s 2021 analysis of the Vinland Map. The text indicates that while some scholars have believed that the map was drawn in the mid-1400s, the 2021 analysis showed the presence of the compound titanium dioxide in the ink used to draw the map. The text goes on to say that titanium dioxide wasn’t used to manufacture ink until the early 1900s, which means that ink containing this compound couldn’t have been available to mapmakers in the 1400s. Since mapmakers in the mid-1400s couldn’t have used ink with titanium dioxide, it follows that the Vinland Map couldn’t have been drawn by mid-1400s mapmakers.

Choice A is incorrect because the 2021 finding that the ink used to draw the Vinland Map wasn’t available until the early 1900s doesn’t imply that Europeans in the mid-1400s couldn’t have known about the eastern coast of North America. While this finding suggests that the map couldn’t have been created in the mid-1400s, it doesn’t preclude the possibility that Europeans nevertheless had knowledge—and perhaps even drew other maps that are no longer in existence or are yet to be discovered by researchers—of the eastern coast of present-day North America as early as the mid-1400s. Choice C is incorrect because there’s nothing in the text that suggests that the 2021 discovery of the presence of titanium dioxide in the ink used to draw the Vinland Map caused Lemay, Zyats, and Bezur to question or reach a new conclusion about when mapmakers began using ink containing titanium compounds. Instead, the text indicates that titanium dioxide wasn’t used in ink before the early 1900s. This knowledge led the team to conclude that the map, which was drawn with ink containing titanium dioxide, couldn’t have been created in the mid-1400s. Choice D is incorrect because although the text doesn’t indicate that Lemay, Zyats, and Bezur established an exact date for the creation of the ink that was used to draw the Vinland Map, the text does say that titanium dioxide was introduced in ink manufacturing in the early 1900s. This fact provides enough information to determine that the ink that was used to draw the map was created no earlier than the early 1900s. This finding, in turn, led the team to conclude that the Vinland Map couldn’t have been drawn in the mid-1400s.

"}, {"id": "2592e0de", "domain": "Information and Ideas", "skill": "Central Ideas and Details", "difficulty": "E", "type": "mc", "stimulus": "

Bicycles were first mass-produced in the late nineteenth century throughout Europe and North America, allowing individuals remarkable freedom to travel longer distances quickly and comfortably. This freedom, coupled with the affordability of the vehicle, made the bicycle immensely popular. Individuals were able to live farther from their workplaces, easily visit neighboring towns, and participate in new leisure and sport activities. Bicycling quickly became a popular social endeavor, with enthusiasts forming local cycling clubs to enjoy these newfound activities with others. 

", "stem": "

Which choice best states the main idea of the text?

", "choices": [{"id": "A", "text": "

The widespread adoption of the bicycle in the late nineteenth century provided new opportunities for people. 

"}, {"id": "B", "text": "

The affordability of the bicycle in the late nineteenth century made it the preferred way to travel.

"}, {"id": "C", "text": "

The popularity of the bicycle in the late nineteenth century gave rise to the first cycling clubs.

"}, {"id": "D", "text": "

The mass production of the bicycle in the late nineteenth century made it safer for people to use. 

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. The text discusses how the mass production of bicycles in the late nineteenth century allowed people to travel longer distances, live farther from their workplaces, visit neighboring towns, and participate in new activities and social clubs. All of these are new opportunities that were provided by the widespread adoption of the bicycle.

Choice B is incorrect. The text never says this. It does say that the bicycle was “affordable,” and that the “freedom to travel longer distances quickly and comfortably” made the bicycle “popular,” but it never says that the bicycle was more popular than any other way of traveling (like cars or trains or horses). Choice C is incorrect. This is a detail mentioned in the text, but not the main idea. Cycling clubs are only one of the new opportunities that arose from the popularity of the mass-produced bicycle. A “main idea” should capture more of the information in the text. Choice D is incorrect. The text never says this. It doesn’t mention the safety of the mass-produced bicycle at all.

"}, {"id": "5432d1de", "domain": "Information and Ideas", "skill": "Inferences", "difficulty": "M", "type": "mc", "stimulus": "

It’s common for jazz musicians and fans to refer to certain songs as having “swing,” indicating that the songs provoke a strong feeling, like the impulse to tap one’s foot or dance. The exact acoustic properties that give a song swing, however, have long been thought to be undefinable. To investigate swing, a team led by physicist Corentin Nelias delayed the downbeats and synchronized the offbeats in jazz piano solos and asked jazz musicians to compare the intensity of swing in each modified piece with the intensity of swing in the original piece. They found that participants were more than seven times likelier to characterize the modified songs as having swing than to characterize the original versions as having swing, suggesting that ______blank

", "stem": "

Which choice most logically completes the text?

", "choices": [{"id": "A", "text": "

synchronized offbeats tend to give a song swing regardless of whether downbeats are delayed.

"}, {"id": "B", "text": "

the acoustic properties that give a song swing are not easy for jazz musicians to manipulate.

"}, {"id": "C", "text": "

jazz songs that feature the piano are more likely to have swing than are jazz songs that do not feature the piano.

"}, {"id": "D", "text": "

the timing of downbeats and offbeats may play a crucial role in giving a song swing. 

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. The passage tells us that participants were “more than seven times likelier to characterize the modified songs as having swing than to characterize the original versions as having swing.” Because the modified songs had been changed by altering the timing of the downbeats and offbeats, this suggests that the timing of downbeats and offbeats may play a crucial role in giving a song swing.

Choice A is incorrect. Although the passage mentions that the researchers “synchronized the offbeats” in the modified songs, they also “delayed the downbeats” in those songs. Because we can’t disentangle whether it was the synchronized offbeats, the delayed downbeats, or the combination of both that increased the song’s swing, we don’t have enough information to make this inference. Choice B is incorrect. The passage doesn’t mention whether or not it’s difficult for a jazz musician to give a song swing, so there’s no basis for this inference. Choice C is incorrect. The passage doesn’t compare jazz songs that feature piano to those that don’t, so there’s no basis for this inference.

"}, {"id": "4e9afd7a", "domain": "Information and Ideas", "skill": "Inferences", "difficulty": "M", "type": "mc", "stimulus": "

The Indus River valley civilization flourished in South Asia from 3300 BCE to 1300 BCE. Many examples of the civilization’s writing system exist, but researchers haven’t yet deciphered it or identified which ancient language it represents. Nevertheless, archaeologists have found historical artifacts, such as clay figures and jewelry, that provide information about the civilization’s customs and how its communities were organized. The archaeologists’ findings therefore suggest that ______blank

", "stem": "

Which choice most logically completes the text?

", "choices": [{"id": "A", "text": "

investigating an ancient civilization is easier without knowledge of the civilization’s language.

"}, {"id": "B", "text": "

knowing an ancient civilization’s language isn’t necessary in order to learn details about the civilization.

"}, {"id": "C", "text": "

archaeological research should focus on finding additional artifacts rather than deciphering ancient languages.

"}, {"id": "D", "text": "

examining the civilization’s historical artifacts has resolved the debate about this civilization’s language.

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer because it most logically completes the text’s discussion of the Indus River valley civilization. The text establishes that archaeologists haven’t been able to interpret the Indus River valley civilization’s writing system but have nevertheless acquired information about the civilization through historical artifacts. The fact that archaeologists have been able to learn about the Indus River valley civilization’s customs and community organization from historical artifacts suggests that it isn’t necessary to understand an ancient civilization’s language to learn about the civilization.

Choice A is incorrect because the text doesn’t discuss how easy it is to investigate ancient civilizations with or without knowledge of the civilization’s language; rather, it states that even though researchers have not yet deciphered the language of the Indus River valley civilization, they are still able to learn about it through historical artifacts. Choice C is incorrect because the text doesn’t make any claims as to what the focus of archaeological research should be. Rather, the text discusses how archaeologists have been able to learn about an ancient civilization through historical artifacts despite not understanding the civilization’s language. Choice D is incorrect because the text states that the civilization’s language has not yet been interpreted; it makes no mention of a debate about the language. Instead, the text suggests that examination of the historical artifacts has allowed archaeologists to learn about the civilization but has not aided thus far in deciphering its language. 

"}, {"id": "3882ddf6", "domain": "Information and Ideas", "skill": "Inferences", "difficulty": "M", "type": "mc", "stimulus": "

To investigate the history of plate subduction—when one of Earth’s tectonic plates slides beneath another—Sarah M. Aarons and colleagues compared ancient rocks from the Acasta Gneiss Complex in Canada to modern rocks. Using isotope analysis, the researchers found that Acasta rocks dating to about 4.02 billion years ago (bya) most strongly resemble modern rocks formed in a plume setting (an area in which hot rocks from Earth’s mantle flow upward into the crust). By contrast, they found that Acasta rocks dating to about 3.75 bya and 3.6 bya have an isotope composition that is similar to that of modern rocks formed in a subduction setting. Aarons’s team therefore concluded that ______blank

", "stem": "

Which choice most logically completes the text?

", "choices": [{"id": "A", "text": "

subduction-like processes began occurring in some locations no later than 3.75 bya.

"}, {"id": "B", "text": "

subduction replaced mantle plume formation as the most common geological process by about 4.02 bya.

"}, {"id": "C", "text": "

the majority of the rocks in the Acasta Gneiss Complex formed through subduction.

"}, {"id": "D", "text": "

the rocks in the Acasta Gneiss Complex are of a more recent origin than scientists previously thought.

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. Because researchers found “Acasta rocks dating to about 3.75 bya” were similar to “modern rocks formed in a subduction setting,” we can infer that subduction-like processes must have begun occurring in the Acasta Gneiss Complex by this time.

Choice B is incorrect. We only know about geological processes at the Acasta Gneiss Complex, so we do not have information to make inferences about geological processes in general. Also, notice that the rocks dated to 4.02 bya were found to still be formed in a plume setting, so the transition must have happened after this time. Choice C is incorrect. There’s no mention in the passage of what proportion of the rocks within Acasta Gneiss Complex were formed through subduction, so there’s no basis for this inference. Choice D is incorrect. The passage discusses various rocks in the Acasta Gneiss Complex that are dated to different periods of time, but nothing in the passage suggests that these dates are or were wrong.

"}, {"id": "a44bbd6b", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "H", "type": "mc", "stimulus": "

Several studies of sediment (e.g., dirt, pieces of rock, etc.) in streams have shown an inverse correlation between sediment grain size and downstream distance from the primary sediment source, suggesting that stream length has a sorting effect on sediment. In a study of sediment sampled at more than a dozen sites in Alpine streams, however, geologists Camille Litty and Fritz Schlunegger found that cross-site variations in grain size were not associated with differences in downstream distance, though they did not conclude that downstream distance is irrelevant to grain size. Rather, they concluded that sediment influx in these streams may have been sufficiently spatially diffuse to prevent the typical sorting effect from being observed.

", "stem": "

Which finding about the streams in the study, if true, would most directly support Litty and Schlunegger’s conclusion?

", "choices": [{"id": "A", "text": "

The streams regularly experience portions of their banks collapsing into the water at multiple points upstream of the sampling sites. 

"}, {"id": "B", "text": "

The streams contain several types of sediment that are not typically found in streams where the sorting effect has been demonstrated.

"}, {"id": "C", "text": "

The streams mostly originate from the same source, but their lengths vary considerably due to the different courses they take.

"}, {"id": "D", "text": "

The streams are fed by multiple tributaries that carry significant volumes of sediment and that enter the streams downstream of the sampling sites. 

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. This finding would support the conclusion. If stream banks are collapsing into the water at multiple points, then sediment is getting into the water at those various points. This supports the conclusion that the inflow of sediment is very spread out.

Choice B is incorrect. This finding wouldn’t support the conclusion. The conclusion is about the influx of sediment being “spatially diffuse,” meaning spread out over a large area. The type of sediment wouldn’t have an impact on the conclusions. Choice C is incorrect. This finding wouldn’t support the conclusion. It doesn’t say anything about the influx of sediment being “spatially diffuse” (spread out). Choice D is incorrect. This finding wouldn’t support the conclusion. Any sediment that enters downstream of the sampling sites wouldn’t end up in the samples, so it wouldn’t affect the findings or the conclusion.

"}, {"id": "a2b0fc3b", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "M", "type": "mc", "stimulus": "
\n\n\n\n\n\n\n\n\n\n\n\n\n1009080706050403020100Percent of populationliving in cities197019801990200020102020Urban Population of Algeria, France, Japan, and NigeriaYear Algeria France Japan Nigeria
\n

The share of the world\u2019s population living in cities has increased dramatically since 1970, but this change has not been uniform. France and Japan, for example, were already heavily urbanized in 1970, with 70% or more of the population living in cities. The main contributors to the world\u2019s urbanization since 1970 have been countries like Algeria, whose population went from ______blank

", "stem": "

Which choice most effectively uses data from the graph to complete the assertion?

", "choices": [{"id": "A", "text": "

around 50% urban in 1970 to around 90% urban in 2020. 

"}, {"id": "B", "text": "

less than 40% urban in 1970 to around 90% urban in 2020. 

"}, {"id": "C", "text": "

less than 20% urban in 1970 to more than 50% urban in 2020. 

"}, {"id": "D", "text": "

around 40% urban in 1970 to more than 70% urban in 2020.

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. This choice effectively uses data from the graph to complete the example. The line representing the percent of Algeria’s population living in cities is the black triangle line. According to the graph, it started at 40% in 1970 and reached 70% in 2020. 

Choice A is incorrect. This choice misreads the graph. The line representing the percent of Algeria’s population living in cities is the black triangle line. According to the graph, it started at 40% in 1970 and reached 70% in 2020. Choice B is incorrect. This choice misreads the graph. The line representing the percent of Algeria’s population living in cities is the black triangle line. According to the graph, it started at 40% in 1970 and reached 70% in 2020. Choice C is incorrect. This choice misreads the graph. The line representing the percent of Algeria’s population living in cities is the black triangle line. According to the graph, it started at 40% in 1970 and reached 70% in 2020. 

"}, {"id": "89961e26", "domain": "Information and Ideas", "skill": "Central Ideas and Details", "difficulty": "E", "type": "mc", "stimulus": "

Artist Justin Favela explained that he wanted to reclaim the importance of the piñata as a symbol in Latinx culture. To do so, he created numerous sculptures from strips of tissue paper, which is similar to the material used to create piñatas. In 2017, Favela created an impressive life-size piñata-like sculpture of the Gypsy Rose lowrider car, which was displayed at the Petersen Automotive Museum in Los Angeles, California. The Gypsy Rose lowrider was famously driven by Jesse Valadez, an early president of the Los Angeles Imperials Car Club.

", "stem": "

According to the text, which piece of Favela’s art was on display in the Petersen Automotive Museum in 2017?

", "choices": [{"id": "A", "text": "

A painting of Los Angeles

"}, {"id": "B", "text": "

A sculpture of a lowrider car

"}, {"id": "C", "text": "

A painting of a piñata

"}, {"id": "D", "text": "

A sculpture of Jesse Valadez

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. The text describes Favela’s approach to sculpture, and then describes the lowrider car that he depicted in 2017.

Choice A is incorrect. This isn’t what the text says. The Petersen Automotive Museum is located in Los Angeles, but Favela’s artwork isn’t a painting, and it doesn’t depict L.A. Choice C is incorrect. This isn’t what the text says. Favela makes sculptures similar to piñatas, not paintings of them. Choice D is incorrect. This isn’t what the text says. Jesse Valadez owned the lowrider car that Favela depicted in sculpture.

"}, {"id": "2584bcfb", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "M", "type": "mc", "stimulus": "

Matthew D. Rocklage and team examined whether consumer ratings of movies can predict box office success. The team considered both numeric star ratings and written reviews in their research. To analyze the written reviews, the team measured the emotionality—the degree to which a written review expresses an emotional reaction—of user reviews on a movie rating website, assigning each review an emotionality score. After reviewing this research, a student argues that the emotionality of movie reviews is unrelated to a movie’s success at the box office.

", "stem": "

Which finding, if true, would most directly weaken the student’s conclusion?

", "choices": [{"id": "A", "text": "

Movies that had the highest average emotionality scores received the lowest average star ratings on the movie rating website. 

"}, {"id": "B", "text": "

The average emotionality score of a movie’s reviews was a positive predictor of that movie’s box office earnings. 

"}, {"id": "C", "text": "

More than half of the movies that the team examined received an average star rating of 3 out of 5 stars.

"}, {"id": "D", "text": "

The movies that were most successful at the box office tended to have high average star ratings.

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. This choice weakens the student’s conclusion by suggesting that the emotionality of movie reviews is related to box office success: the higher the emotionality score, the better the movie performs at the box office.

Choice A is incorrect. While this choice does mention emotionality scores, it only connects them to star ratings, not to box office success. Choice C is incorrect. The fact that many movies received an average star rating doesn’t tell us anything about the relationship between emotionality and box office success. Choice D is incorrect. While this choice suggests that star ratings can predict box office success, it doesn’t address the issue of emotionality in written reviews, which is the focus of the student’s conclusion.

"}, {"id": "a59245a1", "domain": "Information and Ideas", "skill": "Central Ideas and Details", "difficulty": "M", "type": "mc", "stimulus": "

The painter María Izquierdo played an important role in the development of twentieth-century Mexican art, but her work has never been well-known in the United States except among art historians. One reason for Izquierdo’s relative obscurity is the enormous popularity of some of her peers. In particular, the painters Frida Kahlo and Diego Rivera have so captivated the interest of US audiences that Izquierdo and other Mexican artists from the period often get overlooked, despite the high quality of their work.

", "stem": "

Which choice best states the main idea of the text?

", "choices": [{"id": "A", "text": "

Izquierdo’s work is not as well-known in the United States as it should be because Kahlo and Rivera draw so much of the public’s attention.

"}, {"id": "B", "text": "

During Izquierdo’s lifetime, her paintings were displayed in galleries in the United States much more frequently than paintings by Kahlo and Rivera were.

"}, {"id": "C", "text": "

Izquierdo painted some of the same subjects that Kahlo and Rivera painted but used different techniques than they used. 

"}, {"id": "D", "text": "

Few of Izquierdo’s works are in galleries today because she produced only a small number of paintings. 

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer because it most accurately states the main idea of the text. The text begins by stating that María Izquierdo was an important figure in the history of twentieth-century Mexican art, but despite her importance, her work hasn’t received widespread recognition in the United States. According to the text, one reason for this is that Frida Kahlo and Diego Rivera are so famous in the US that they overshadow other important Mexican artists, including Izquierdo. Thus, the main idea of the text is that Izquierdo’s work is less well known in the US than it should be because Kahlo and Rivera draw most of the public’s attention.

Choice B is incorrect because the text doesn’t discuss the appearance of Izquierdo’s paintings in galleries in the US during her lifetime, nor does it suggest that her paintings were displayed more frequently than paintings by Kahlo or Rivera were. Instead, the text focuses on the fact that Izquierdo has been overlooked in the US because of Kahlo’s and Rivera’s greater popularity. Choice C is incorrect because the text doesn’t discuss either the subject matter of Izquierdo’s paintings or the techniques she used, nor does it compare these aspects of her paintings with those of Kahlo’s and Rivera’s paintings. Choice D is incorrect because the text doesn’t mention how many of Izquierdo’s paintings appear in galleries today, nor does it state that she produced only a small number of paintings.

"}, {"id": "628e1305", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "E", "type": "mc", "stimulus": "

“Valia” is a 1907 short story by Leonid Andreyev. In the story, the author emphasizes that the setting where the character Valia is reading is nearly silent: ______blank

", "stem": "

Which quotation from “Valia” most effectively illustrates the claim?

", "choices": [{"id": "A", "text": "

“The hand in which he carried his book was getting stiff with cold, but he would not ask his mother to take the book from him.”

"}, {"id": "B", "text": "

“Valia was reading a huge, very huge book, almost half as large as himself.”

"}, {"id": "C", "text": "

“Valia approached the window and examined the toys.”

"}, {"id": "D", "text": "

“Everything in the room was quiet, so quiet that the only thing to be heard was the rustling of the pages he turned.”

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer because this quotation most effectively illustrates the claim that the author emphasizes the near silence of the setting where the character Valia is reading. In the quotation, the author highlights the near silence of the setting by twice using the word “quiet” to describe the room. The author also calls attention to the fact that Valia is reading in a nearly silent setting by noting that the only sound to be heard is that of the pages being turned.

Choice A is incorrect because this quotation suggests that Valia is in a chilly setting that causes his hand to become cold, not that he’s in a nearly silent setting. Choice B is incorrect because this quotation emphasizes the size of the book Valia is reading, not a quality of the setting where he’s reading it. Choice C is incorrect because this quotation describes Valia approaching a window and looking at toys, not reading in a quiet setting.

"}, {"id": "3f236877", "domain": "Information and Ideas", "skill": "Inferences", "difficulty": "H", "type": "mc", "stimulus": "

Ratified by more than 90 countries, the Nagoya Protocol is an international agreement ensuring that Indigenous communities are compensated when their agricultural resources and knowledge of wild plants and animals are utilized by agricultural corporations. However, the protocol has shortcomings. For example, it allows corporations to insist that their agreements with communities to conduct research on the commercial uses of the communities’ resources and knowledge remain confidential. Therefore, some Indigenous advocates express concern that the protocol may have the unintended effect of ______blank

", "stem": "

Which choice most logically completes the text?

", "choices": [{"id": "A", "text": "

diminishing the monetary reward that corporations might derive from their agreements with Indigenous communities.

"}, {"id": "B", "text": "

limiting the research that corporations conduct on the resources of the Indigenous communities with which they have signed agreements.

"}, {"id": "C", "text": "

preventing independent observers from determining whether the agreements guarantee equitable compensation for Indigenous communities.

"}, {"id": "D", "text": "

discouraging Indigenous communities from learning new methods for harvesting plants and animals from their corporate partners.

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer because it most logically completes the argument about an unintended effect of the Nagoya Protocol. The text explains that the Nagoya Protocol is an agreement ensuring that Indigenous communities are compensated when their agricultural resources and knowledge are used by corporations. The text then states that the protocol allows corporations to keep their agreements with Indigenous communities confidential, about which some Indigenous advocates express concern. Choice C, when inserted into the blank, gives a good justification for the advocates’ concern: such secrecy could mean that the public is unable to determine whether participating Indigenous communities were properly compensated under these agreements. 

Choice A is incorrect. The text suggests that because corporations can keep their agreements with Indigenous communities confidential, Indigenous communities, not corporations, might not be compensated fairly. Choice B is incorrect because the text doesn’t suggest that the ability of corporations to keep their agreements with Indigenous communities confidential would place limits on how much research corporations can undertake. Choice D is incorrect because the text doesn’t indicate that Indigenous communities aim to learn new harvesting methods from their corporate partners. Rather, the text suggests that corporations use the knowledge of Indigenous communities for their research.

"}, {"id": "5b74feb9", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "H", "type": "mc", "stimulus": "

Political scientists who favor the traditional view of voter behavior claim that voting in an election does not change a voter’s attitude toward the candidates in that election. Focusing on each US presidential election from 1976 to 1996, Ebonya Washington and Sendhil Mullainathan tested this claim by distinguishing between subjects who had just become old enough to vote (around half of whom actually voted) and otherwise similar subjects who were slightly too young to vote (and thus none of whom voted). Washington and Mullainathan compared the attitudes of the groups of subjects toward the winning candidate two years after each election.

", "stem": "

Which finding from Washington and Mullainathan’s study, if true, would most directly weaken the claim made by people who favor the traditional view of voter behavior?

", "choices": [{"id": "A", "text": "

Subjects’ attitudes toward the winning candidate two years after a given election were strongly predicted by subjects’ general political orientation, regardless of whether subjects were old enough to vote at the time of the election.

"}, {"id": "B", "text": "

Subjects who were not old enough to vote in a given election held significantly more positive attitudes towards the winning candidate two years later than they held at the time of the election.

"}, {"id": "C", "text": "

Subjects who voted in a given election held significantly more polarized attitudes toward the winning candidate two years later than did subjects who were not old enough to vote in that election.

"}, {"id": "D", "text": "

Two years after a given election, subjects who voted and subjects who were not old enough to vote were significantly more likely to express negative attitudes than positive attitudes toward the winning candidate in that election.

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer because it presents a finding that, if true, would weaken the claim made by people who favor the traditional view of voter behavior. According to the text, people who favor that view believe that voting in an election doesn’t change a voter’s attitude toward the candidates in that election. If Washington and Mullainathan found that two years after an election, attitudes toward the winning candidate were significantly more polarized among subjects who had voted than among subjects who had been too young to vote, that would suggest that the act of voting did have an effect on the voters’ attitudes toward the candidates, which would undermine the claim that voting doesn’t change voters’ attitudes.

Choice A is incorrect because a finding about links between subjects’ attitudes and general political orientation, regardless of age and ability to vote, wouldn’t address the presence or absence of changes in attitudes among those subjects who did actually vote. Therefore, the finding wouldn’t have any bearing on the claim that voting in an election doesn’t change a voter’s attitude toward the candidates in that election. Choice B is incorrect because a finding that positive attitudes toward a winning candidate significantly increased in the two years after the election among subjects who had been too young to vote would involve only people who didn’t vote; therefore, the finding wouldn’t have any bearing on the claim that when people do vote, the act of voting doesn’t change their attitudes toward the candidates. Choice D is incorrect because the finding that subjects in both groups were more likely to have negative attitudes than positive attitudes toward the winning candidate two years after an election would reflect all subjects’ attitudes at one particular time whether they voted or not, rather than the presence or absence of a change in voters’ attitudes after voting. Therefore, the finding would neither weaken nor strengthen the claim that voting in an election doesn’t change a voter’s attitude toward the candidates.

"}, {"id": "c2c61e7d", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "H", "type": "mc", "stimulus": "

Researchers hypothesized that a decline in the population of dusky sharks near the mid-Atlantic coast of North America led to a decline in the population of eastern oysters in the region. Dusky sharks do not typically consume eastern oysters but do consume cownose rays, which are the main predators of the oysters.

", "stem": "

Which finding, if true, would most directly support the researchers’ hypothesis?

", "choices": [{"id": "A", "text": "

Declines in the regional abundance of dusky sharks’ prey other than cownose rays are associated with regional declines in dusky shark abundance.

"}, {"id": "B", "text": "

Eastern oyster abundance tends to be greater in areas with both dusky sharks and cownose rays than in areas with only dusky sharks.

"}, {"id": "C", "text": "

Consumption of eastern oysters by cownose rays in the region substantially increased before the regional decline in dusky shark abundance began.

"}, {"id": "D", "text": "

Cownose rays have increased in regional abundance as dusky sharks have decreased in regional abundance.

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer because it presents a finding that, if true, would most directly support the researchers’ hypothesis about the connection between the dusky shark population decline and the eastern oyster population decline. The text indicates that although dusky sharks don’t usually eat eastern oysters, they do consume cownose rays, which are the main predators of eastern oysters. An increase in the abundance of cownose rays in the region in response to a decline in the abundance of dusky sharks would directly support the researchers’ hypothesis: a higher number of cownose rays would consume more eastern oysters, driving down the oyster population.

Choice A is incorrect because a finding that there’s an association between a decline in the regional abundance of some of dusky sharks’ prey and the regional abundance of dusky sharks wouldn’t directly support the researchers’ hypothesis that a decline in dusky sharks has led to a decline in eastern oysters in the region. Although such a finding might help explain why shark abundance has declined, it would reveal nothing about whether the shark decline is related to the oyster decline. Choice B is incorrect because a finding that eastern oyster abundance tends to be greater when dusky sharks and cownose rays are present than when only dusky sharks are present wouldn’t support the researchers’ hypothesis that a decline in dusky sharks has led to a decline in eastern oysters in the region. The text indicates that the sharks prey on the rays, which are the main predators of the oysters; if oyster abundance is found to be greater when rays are present than when rays are absent, that would suggest that rays aren’t keeping oyster abundance down, and thus that a decline in rays’ predators, which would be expected to lead to an increase in the abundance of rays, wouldn’t bring about a decline in oyster abundance as the researchers hypothesize. Choice C is incorrect because a finding that consumption of eastern oysters by cownose rays increased substantially before dusky sharks declined in regional abundance wouldn’t support the researchers’ hypothesis that the decline in dusky sharks has led to a decline in eastern oysters in the region. Such a finding would suggest that some factor other than shark abundance led to an increase in rays’ consumption of oysters and thus to a decrease in oyster abundance, thereby weakening the researchers’ hypothesis. 

"}, {"id": "38e79659", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "E", "type": "mc", "stimulus": "

Attendance and Cost of Hosting for Past Four US World’s Fairs

World’s fairs held in the USCost (in US dollars)Number of visitors
Century 21 Exposition (1962)$47 million9.60 million
HemisFair ’68$156 million6.40 million
1984 World’s Fair$350 million7.35 million
Expo ’74$78 million5.60 million

\n

Huge international exhibitions known as world’s fairs have been held since 1851, but the United States hasn’t hosted one since 1984. Architecture expert Mina Chow argues that this is because some people think the events are too expensive and not popular enough. For example, the 1984 World’s Fair cost $350 million and had only ______blank

", "stem": "

Which choice most effectively uses data from the table to complete the example?

", "choices": [{"id": "A", "text": "

7.35 million visitors.

"}, {"id": "B", "text": "

9.60 million visitors.

"}, {"id": "C", "text": "

6.40 million visitors.

"}, {"id": "D", "text": "

5.60 million visitors.

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer because it most effectively uses data from the table to complete the example of the high cost and low popularity of world’s fairs. The text presents Chow’s argument that the United States hasn’t hosted a world’s fair since 1984 because people think these exhibitions are overly expensive and insufficiently popular. The text then cites the 1984 World’s Fair as an example, noting that it cost $350 million. Since the example should illustrate both high cost and insufficient popularity, the best completion of the example is the information from the table that the 1984 World’s Fair had 7.35 million visitors.

Choice B is incorrect because it misrepresents data from the table. The table indicates that the 1984 World’s Fair, which is the world’s fair used as an example in the text, had 7.35 million, not 9.60 million, visitors. Choice C is incorrect because it misrepresents data from the table. The table indicates that the 1984 World’s Fair, which is the world’s fair used as an example in the text, had 7.35 million, not 6.40 million, visitors. Choice D is incorrect because it misrepresents data from the table. The table indicates that the 1984 World’s Fair, which is the world’s fair used as an example in the text, had 7.35 million, not 5.60 million, visitors. 

"}, {"id": "825dc766", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "H", "type": "mc", "stimulus": "

King Lear is a circa 1606 play by William Shakespeare. In the play, the character of King Lear attempts to test his three daughters’ devotion to him. He later expresses regret for his actions, as is evident when he ______blank

", "stem": "

Which choice most effectively uses a quotation from King Lear to illustrate the claim?

", "choices": [{"id": "A", "text": "

says of himself, “I am a man / more sinned against than sinning.”

"}, {"id": "B", "text": "

says during a growing storm, “This tempest will not give me leave to ponder / On things would hurt me more.”

"}, {"id": "C", "text": "

says to himself while striking his head, “Beat at this gate that let thy folly in / And thy dear judgement out!”

"}, {"id": "D", "text": "

says of himself, “I will do such things— / What they are yet, I know not; but they shall be / The terrors of the earth!”

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer because it most effectively uses a quotation from King Lear to illustrate the claim that King Lear expresses regret for his actions. In the quotation, Lear describes striking himself on the head—the same act he’s engaged in as he speaks, and one that suggests he’s deeply upset with himself. Referring to himself in the second person (with “thy”), the character exclaims “Beat at this gate that let thy folly in / And thy dear judgement out!” Lear refers metaphorically to his own mind as a gate that has allowed folly, or poor judgement, to enter and good judgement to escape. This suggests that Lear regrets his attempts to test his three daughters’ devotion to him, regarding those attempts as examples of the folly that has entered the gate of his mind.

Choice A is incorrect because this quotation doesn’t express King Lear’s sense of regret over his own actions; instead, it expresses his belief that the harm that others have done to him (or the extent to which they have “sinned against” him) outweighs whatever harm he himself has caused by “sinning.” Choice B is incorrect because this quotation doesn’t express King Lear’s sense of regret over his own actions; instead, it expresses his thoughts about an approaching storm (“this tempest”), which he believes “will not give [him] leave to ponder,” or time to consider, the harm that he will continue to experience (“things” that “would hurt [him] more”). Choice D is incorrect because this quotation expresses King Lear’s vow to commit terrible actions (or “things” that “shall be / The terrors of the earth”) in the future, not his regret over actions that he’s already taken.

"}, {"id": "0240d11c", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "H", "type": "mc", "stimulus": "

In the twentieth century, ethnographers made a concerted effort to collect Mexican American folklore, but they did not always agree about that folklore’s origins. Scholars such as Aurelio Espinosa claimed that Mexican American folklore derived largely from the folklore of Spain, which ruled Mexico and what is now the southwestern United States from the sixteenth to early nineteenth centuries. Scholars such as Américo Paredes, by contrast, argued that while some Spanish influence is undeniable, Mexican American folklore is mainly the product of the ongoing interactions of various cultures in Mexico and the United States.

", "stem": "

Which finding, if true, would most directly support Paredes’s argument?

", "choices": [{"id": "A", "text": "

The folklore that the ethnographers collected included several songs written in the form of a décima, a type of poem originating in late sixteenth-century Spain. 

"}, {"id": "B", "text": "

Much of the folklore that the ethnographers collected had similar elements from region to region. 

"}, {"id": "C", "text": "

Most of the folklore that the ethnographers collected was previously unknown to scholars. 

"}, {"id": "D", "text": "

Most of the folklore that the ethnographers collected consisted of corridos—ballads about history and social life—of a clearly recent origin. 

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer because it presents a finding that, if true, would support Paredes’s argument that Mexican-American folklore is mostly the result of cultural interactions in Mexico and the United States rather than an adaptation of Spanish folklore. The text describes a disagreement among scholars about whether Mexican-American folklore mostly derived from the folklore of Spain or originated in Mexico and the United States as cultures there have interacted. The latter view is the argument that Paredes puts forward. If Mexican-American folklore collected in the twentieth century mostly consists of ballads about history and social life that originated recently, then that would support Paredes’s argument, since it would suggest that the folklore mostly arose after Spanish rule ended in the early nineteenth century and that the folklore reflects cultural interactions in Mexico and the United States rather than traditions from Spain. 

Choice A is incorrect because the inclusion of songs influenced by sixteenth-century Spanish poetry among Mexican-American folklore collected in the twentieth century would not support Paredes’s view that the folklore was the result of cultural interactions in Mexico and the United States rather than an offshoot of Spanish folklore. If anything, the presence of such songs among the folklore collected in the twentieth century would weaken Paredes’s argument, since it would reflect the influence of Spanish culture on the folklore. Choice B is incorrect because the mere presence of similarities in Mexican-American folklore across regions would not be sufficient to draw a conclusion about where the folklore originated, let alone to support Paredes’s argument that the folklore reflects cultural interactions in Mexico and the United States. In fact, since Paredes argued that Mexican-American folklore is the product of various cultures interacting in Mexico and the United States, he would likely expect there to be regional variations in folklore as different cultures have interacted in different places. Choice C is incorrect because scholars’ previous ignorance of the folklore would have no bearing on Paredes’s argument that Mexican-American folklore mostly reflects cultural interactions in Mexico and the United States. The folklore’s origins are independent of scholars’ knowledge of the folklore. 

"}, {"id": "25290c8d", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "M", "type": "mc", "stimulus": "

“On Virtue” is a 1766 poem by Phillis Wheatley. Wheatley addresses the poem directly to the quality of virtue, imploring it to assist her in reaching a future goal: ______blank

", "stem": "

Which quotation from “On Virtue” most effectively illustrates the claim?

", "choices": [{"id": "A", "text": "

“Attend me, Virtue, thro’ my youthful years! / O leave me not to the false joys of time! / But guide my steps to endless life and bliss.”

"}, {"id": "B", "text": "

“I cease to wonder, and no more attempt / Thine height t’explore, or fathom thy profound.”

"}, {"id": "C", "text": "

“O thou bright jewel in my aim I strive / To comprehend thee. Thine own words declare / Wisdom is higher than a fool can reach.”

"}, {"id": "D", "text": "

“But, O my soul, sink not into despair, / Virtue is near thee, and with gentle hand / Would now embrace thee, hovers o’er thine head.”

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer because it most effectively illustrates the claim that Wheatley addresses her poem \"On Virtue\" to the quality of virtue, imploring it to assist her in reaching a future goal. In the quotation, Wheatley begs virtue to accompany her, or \"attend [her],\" through her youth and to \"guide [her] steps to\" the future goal of \"endless life and bliss.\"

Choice B is incorrect because this quotation suggests the difficulty of fully comprehending virtue. Rather than asking virtue for help, Wheatley presents it as a quality that is impossible to entirely understand because it is so grand and deep. Choice C is incorrect because this quotation describes Wheatley’s effort to comprehend virtue despite virtue itself declaring that such wisdom is beyond her grasp, or \"higher than a fool can reach.\" Choice D is incorrect because rather than asking virtue for help in this quotation, Wheatley urges herself to \"sink not into despair\" because virtue is always nearby.

"}, {"id": "4d3e3c52", "domain": "Information and Ideas", "skill": "Central Ideas and Details", "difficulty": "H", "type": "mc", "stimulus": "

In a paper about p-i-n planar perovskite solar cells (one of several perovskite cell architectures designed to collect and store solar power), Lyndsey McMillon-Brown et al. describe a method for fabricating the cell’s electronic transport layer (ETL) using a spray coating. Conventional ETL fabrication is accomplished using a solution of nanoparticles. The process can result in a loss of up to 80% of the solution, increasing the cost of manufacturing at scale—an issue that may be obviated by spray coating fabrication, which the researchers describe as “highly reproducible, concise, and practical.”

", "stem": "

What does the text most strongly suggest about conventional ETL fabrication?

", "choices": [{"id": "A", "text": "

It is less suitable for manufacturing large volumes of planar p-i-n perovskite solar cells than an alternative fabrication method may be.

"}, {"id": "B", "text": "

It is more expensive when manufacturing at scale than are processes for fabricating ETLs used in other perovskite solar cell architectures.

"}, {"id": "C", "text": "

It typically entails a greater loss of nanoparticle solution than do other established approaches for ETL fabrication.

"}, {"id": "D", "text": "

It is somewhat imprecise and therefore limits the potential effectiveness of p-i-n planar perovskite solar cells at capturing and storing solar power.

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. Conventional solar cell fabrication increases “the cost of manufacturing at scale,” but spray coating might get rid of that problem.

Choice B is incorrect. This is not completely supported by the text. While it’s true that conventional ETL fabrication is expensive at scale, there’s nothing in the text that mentions other perovskite solar cell architectures. Choice C is incorrect. This choice does not match the text. Only one conventional method of ETL fabrication is described, so we can’t compare the solution loss in this method to that of other conventional methods. Choice D is incorrect. This choice isn’t supported by the text. The text never suggests that the effectiveness of solar cells changes based on their method of fabrication.

"}, {"id": "d1b8a9ad", "domain": "Information and Ideas", "skill": "Central Ideas and Details", "difficulty": "H", "type": "mc", "stimulus": "

Disco remains one of the most ridiculed popular music genres of the late twentieth century. But as scholars have argued, the genre is far less superficial than many people believe. Take the case of disco icon Donna Summer: she may have been associated with popular songs about love and heartbreak (subjects hardly unique to disco, by the way), but like many Black women singers before her, much of her music also reflects concerns about community and identity. These concerns are present in many of the genre’s greatest songs, and they generally don’t require much digging to reveal.

", "stem": "

What does the text most strongly suggest about the disco genre?

", "choices": [{"id": "A", "text": "

It has been unjustly ignored by most scholars despite the importance of the themes addressed by many of the genre’s songs.

"}, {"id": "B", "text": "

It evolved over time from a superficial genre focused on romance to a genre focused on more serious concerns.

"}, {"id": "C", "text": "

It has been unfairly dismissed for the inclusion of subject matter that is also found in other musical genres.

"}, {"id": "D", "text": "

It gave rise to a Black women’s musical tradition that has endured even though the genre itself faded in the late twentieth century.

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. The text argues that disco is \"far less superficial\" than its popular perception might indicate, and that love and heartbreak are \"subjects hardly unique to disco.\"

Choice A is incorrect. This choice conflicts with the text, which says that scholars argue that disco \"is far less superficial than many people believe.\" Choice B is incorrect. This choice says the opposite of what the text suggests. The writer argues that the genre is not as superficial as commonly believed, but that it always reflected \"concerns about community and identity.\" Choice D is incorrect. The text doesn’t support this choice. There’s nothing in the text about disco giving rise to an enduring Black women’s musical tradition.

"}, {"id": "02848335", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "H", "type": "mc", "stimulus": "
\n\n\n\n\n181614121086420Power conversion efficiency (%)lowest performinghighest performingPower Conversion Efficiency of Lowest and Highest PerformingSpin-coated and Spray-coatedElectron Transport LayersThicknessspray coatingspin coating
\n

Perovskite solar cells convert light into electricity more efficiently than earlier kinds of solar cells, and manufacturing advances have recently made them commercially attractive. One limitation of the cells, however, has to do with their electron transport layer (ETL), through which absorbed electrons must pass. Often the ETL is applied through a process called spin coating, but such ETLs are fairly inefficient at converting input power to output power. Andr\u00e9 Taylor and colleagues tested a novel spray coating method for applying the ETL. The team produced ETLs of various thicknesses and concluded that spray coating holds promise for improving the power conversion efficiency of ETLs in perovskite solar cells.

", "stem": "

Which choice best describes data from the graph that support Taylor and colleagues’ conclusion?

", "choices": [{"id": "A", "text": "

Both the ETL applied through spin coating and the ETL applied through spray coating showed a power conversion efficiency greater than 10% at their lowest performing thickness. 

"}, {"id": "B", "text": "

The lowest performing ETL applied through spray coating had a higher power conversion efficiency than the highest performing ETL applied through spin coating. 

"}, {"id": "C", "text": "

The highest performing ETL applied through spray coating showed a power conversion efficiency of approximately 13%, while the highest performing ETL applied through spin coating showed a power conversion efficiency of approximately 11%.

"}, {"id": "D", "text": "

There was a substantial difference in power conversion efficiency between the lowest and highest performing ETLs applied through spray coating.

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer because it describes data from the graph that support Taylor and colleagues’ conclusion that spray coating holds promise for improving the power conversion efficiency of ETLs in perovskite solar cells. The text explains that perovskite solar cells’ efficiency at converting light into electricity is diminished by their electron transport layer (ETL), which is applied through spin coating, but that Taylor’s team devised a new spray coating method for applying the ETL that improves its power conversion efficiency. The graph displays data on the power conversion efficiency of solar cells in tests conducted by Taylor’s team, with bars for both the highest- and lowest-performing ETLs in two data categories: spray coating and spin coating. According to the graph, the lowest-performing ETL applied through spray coating had a power conversion efficiency of between 14% and 16%, while the highest-performing ETL applied through spin coating had a power conversion efficiency of less than 14%. These data confirm that ETLs applied through novel spray coating are more efficient than those applied though traditional spin coating. Thus, the data support Taylor and colleagues’ conclusion about spray coating’s potential value.

Choice A is incorrect. Although this claim correctly describes the data in the graph by stating that both the lowest-performing ETL applied through spin coating and the lowest-performing ETL applied through spray coating had a power conversion efficiency greater than 10%, this relationship in the data doesn’t support or relate to Taylor and colleagues’ conclusion that spray coating promises greater efficiency for solar cells than traditional spin coating does. Choice C is incorrect. This claim does address the greater power conversion efficiency of the highest-performing ETL applied through spray coating, compared with the highest-performing ETL applied through spin coating. However, it also incorrectly cites the value for the efficiency of the highest-performing ETL applied through spray coating as approximately 13%, instead of a value between 14% and 16%, and the value for the efficiency of the highest-performing ETL applied through spin coating as approximately 11%, instead of a value between 12% and 14%, as shown in the graph. Choice D is incorrect because Taylor and colleagues’ conclusion is based on the difference in the power conversion efficiency of ETLs applied through spray coating and that of ETLs applied through spin coating, not on the difference between the highest- and lowest-performing ETLs applied through just spray coating.

"}, {"id": "95dbdf51", "domain": "Information and Ideas", "skill": "Inferences", "difficulty": "H", "type": "mc", "stimulus": "

Laura Mulvey has theorized that in narrative film, shots issuing from a protagonist’s point of view compel viewers to identify with the character. Such identification is heightened by “invisible editing,” or editing so inconspicuous that it renders cuts between shots almost unnoticeable. Conversely, Mulvey proposes that conspicuous editing or an absence of point-of-view shots would induce a more critical stance toward a protagonist. Consider, for example, the attic scene in Alfred Hitchcock’s The Birds, a conspicuously edited sequence of tens of shots, few of which correspond to the protagonist’s point of view. According to Mulvey’s logic, this scene should affect viewers by ______blank

", "stem": "

Which choice most logically completes the text?

", "choices": [{"id": "A", "text": "

obscuring their awareness of the high degree of artifice involved in constructing the montage.

"}, {"id": "B", "text": "

lessening their identification with the protagonist, if not alienating them from the character altogether.

"}, {"id": "C", "text": "

compelling them to identify with the film’s director, whose proxy is the camera, and not with the protagonist. 

"}, {"id": "D", "text": "

diverting their attention away from the film’s content and toward its stylistic attributes.

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. We’re told that point-of-view shots and “invisible editing” make audiences identify with a character. We’re also told that obvious editing and a lack of point-of-view shots have the opposite effect. Since the sequence in The Birds falls into this second category, it should have the effect of reducing the audience’s connection with the protagonist.

Choice A is incorrect. The passage doesn’t mention viewers’ awareness of artifice (i.e., camera trickery) in films, so there’s no basis for this inference. Choice C is incorrect. The passage doesn’t mention the director at all, so there’s no basis for this inference. Choice D is incorrect. The passage doesn’t discuss whether a film’s “stylistic attributes” may distract viewers from the film’s story, so there’s no basis for this inference.

"}, {"id": "55df0275", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "H", "type": "mc", "stimulus": "

Ablation Rates for Three Elements in Cosmic Dust, by Dust Source

ElementSPCASTHTCOCC
iron20%28%90%98%
potassium44%74%97%100%
sodium45%75%99%100%

\n

Earth’s atmosphere is bombarded by cosmic dust originating from several sources: short-period comets (SPCs), particles from the asteroid belt (ASTs), Halley-type comets (HTCs), and Oort cloud comets (OCCs). Some of the dust’s material vaporizes in the atmosphere in a process called ablation, and the faster the particles move, the higher the rate of ablation. Astrophysicist Juan Diego Carrillo-Sánchez led a team that calculated average ablation rates for elements in the dust (such as iron and potassium) and showed that material in slower-moving SPC or AST dust has a lower rate than the same material in faster-moving HTC or OCC dust. For example, whereas the average ablation rate for iron from AST dust is 28%, the average rate for ______blank 

", "stem": "

Which choice most effectively uses data from the table to complete the example?

", "choices": [{"id": "A", "text": "

iron from SPC dust is 20%.

"}, {"id": "B", "text": "

sodium from OCC dust is 100%.

"}, {"id": "C", "text": "

iron from HTC dust is 90%.

"}, {"id": "D", "text": "

sodium from AST dust is 75%.

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer because it most effectively completes the example regarding the ablation rate of iron. The table shows the ablation rates for three elements—iron, potassium, and sodium—found in cosmic dust that comes from one of four sources. The text says that the ablation rate for a given element in slower-moving SPC and AST dust was lower than the ablation rate for that same element in faster-moving HTC or OCC dust. The text then presents the first part of an example of this pattern, describing an ablation rate of 28% for iron in AST dust. The information that iron from HTC dust had an ablation rate of 90% is therefore the most effective way to complete this example—the comparison of a relatively low ablation rate for iron in slower-moving AST dust with a relatively high ablation rate for iron in faster-moving HTC dust illustrates the tendency of ablation rates for a given element to be lower in slower-moving dust than in faster-moving dust.

Choice A is incorrect because the text indicates that SPC dust, like AST dust, moves relatively slowly; a comparison of the ablation rates of iron from two slower-moving dust sources could not be an example of the difference between ablation rates in slower-moving dust and faster-moving dust, which is the pattern that the example is supposed to illustrate. Choice B is incorrect because the example in the text is supposed to illustrate the difference in the ablation rates of the same element from slower-moving dust and faster-moving dust, and the first part of the example provides data about the ablation rate of iron, which means the second part of the example must also be about the ablation rate of iron, not the ablation rate of sodium. Choice D is incorrect because the example in the text is supposed to illustrate the difference in the ablation rates of the same element from slower-moving dust and faster-moving dust, and the first part of the example provides data about the ablation rate of iron, which means the second part of the example must also be about the ablation rate of iron, not the ablation rate of sodium. Additionally, any ablation rate from AST dust would be ineffective in this example since AST dust is referenced in the first part of the example and thus additional data focused on AST dust would not illustrate a variation across dust types.

"}, {"id": "66bef967", "domain": "Information and Ideas", "skill": "Central Ideas and Details", "difficulty": "M", "type": "mc", "stimulus": "

Choctaw/Cherokee artist Jeffrey Gibson turns punching bags used by boxers into art by decorating them with beadwork and elements of Native dressmaking. These elements include leather fringe and jingles, the metal cones that cover the dresses worn in the jingle dance, a women’s dance of the Ojibwe people. Thus, Gibson combines an object commonly associated with masculinity (a punching bag) with art forms traditionally practiced by women in most Native communities (beadwork and dressmaking). In this way, he rejects the division of male and female gender roles.

", "stem": "

Which choice best describes Gibson’s approach to art, as presented in the text?

", "choices": [{"id": "A", "text": "

He draws from traditional Native art forms to create his original works.

"}, {"id": "B", "text": "

He has been influenced by Native and non-Native artists equally.

"}, {"id": "C", "text": "

He finds inspiration from boxing in designing the dresses he makes.

"}, {"id": "D", "text": "

He rejects expectations about color and pattern when incorporating beadwork.

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer because it most accurately describes Gibson’s approach to art. As the text explains, Gibson, who is Cherokee and Choctaw, transforms punching bags into art pieces by applying (or attaching) to them beadwork and elements of Native dressmaking, including leather fringe and the jingles of the jingle dress. The text goes on to say that in most Native communities, the art forms of beadwork and dressmaking are traditionally practiced by women. Therefore, Gibson’s approach to art consists of creating original works by drawing from traditional Native art forms.

Choice B is incorrect. Because Gibson incorporates Native art forms into his own original artwork, it can be inferred that he has been influenced by other Native artists, but the text never suggests that non-Native artists have influenced him. Choice C is incorrect because the text doesn’t indicate that Gibson designs dresses influenced by boxing but instead that he turns punching bags, which are used in boxing, into works of art by applying elements of Native dressmaking to them. Choice D is incorrect. Although Gibson does incorporate beadwork into his art, the text never mentions the colors or patterns that he uses or suggests that his art defies the expectations that people might have about color and pattern in beadwork.

"}, {"id": "1703403b", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "E", "type": "mc", "stimulus": "
\n\n\n\n\n\n\n\n\n\n\n\n\n14121086420Average rainfall (inches)MayJuneJulyAugustSeptemberAverage Monthly Rainfall inSelect Puerto Rican Citiesfrom 1981 to 2010Month Rinc\u00f3n Isabela San Sebasti\u00e1n Ponce
\n

A student is presenting average monthly rainfall totals in various Puerto Rican cities for a science class. During the presentation, the student notes that in September ______blank

", "stem": "

Which choice most effectively uses data from the graph to complete the statement?

", "choices": [{"id": "A", "text": "

Rincón’s average rainfall is greater than that of Isabela, San Sebastián, and Ponce.

"}, {"id": "B", "text": "

Rincón and Ponce have an average rainfall of about 5 inches, and Isabela and San Sebastián have an average rainfall of about 10 inches.

"}, {"id": "C", "text": "

Rincón, Ponce, and Isabela each have an average rainfall below 8 inches, but San Sebastián’s average rainfall that month is greater than 8 inches.

"}, {"id": "D", "text": "

Rincón has a similar average rainfall to Isabela, and Ponce has a similar average rainfall to San Sebastián.

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer because it most effectively uses data from the graph to complete the statement about average rainfall in September in select Puerto Rican cities. The graph shows that between 1981 and 2010 Rincón, Ponce, and Isabela all had an average rainfall during the month of September of about 6 inches, and San Sebastián had an average rainfall of nearly 11 inches. Describing the average September rainfall of Rincón, Ponce, and Isabela as below 8 inches and the average September rainfall of San Sebastián as greater than 8 inches therefore offers an accurate description of the data in the graph and most effectively completes the statement.

Choice A is incorrect because it offers an inaccurate interpretation of the data in the graph. The graph shows that in September, Rincón, Isabela, and Ponce all have an average rainfall of about 6 inches, and San Sebastián has an average rainfall of nearly 11 inches. Therefore, Rincón’s average rainfall is the same as, not greater than, that of Isabela and Ponce, and it is below, not greater than, that of San Sebastián. Choice B is incorrect because it inaccurately describes the data in the graph. In September, Rincón and Ponce have an average rainfall of about 6 inches, not 5 inches; Isabela has an average rainfall of about 6 inches, not 10 inches; and San Sebastián has an average rainfall of nearly 11 inches, not 10 inches. Choice D is incorrect because although the graph shows a similar average rainfall (about 6 inches) for Rincón and Isabela in September, it doesn’t show that Ponce has a similar average rainfall to San Sebastián during this month. In September, Ponce’s average rainfall is about 6 inches, whereas San Sebastián’s average rainfall is nearly 11 inches.

"}, {"id": "cbecb873", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "M", "type": "mc", "stimulus": "

Body Length, Filter Time, and Lunges per Dive for Four Whale Species

Whale speciesTypical adult body length (meters)Average time to filter all engulfed water (seconds)Average number of lunges per dive deeper than 50 meters
fin18–2231.303.95
humpback11–1717.126.28
minke7–108.887.48
blue24–3460.274.02

\n

Some whale species practice lunge feeding, in which they lunge toward prey with their mouths open at wide angles, collect the prey and the surrounding water, and then filter out the water through baleen plates in their mouths. Although the volume of water engulfed increases with whales’ body length, the surface area of whales’ baleen plates, which influences the rate at which water can be filtered, does not increase with body length to the same degree, which helps explain why ______blank

", "stem": "

Which choice most effectively uses data from the table to complete the statement?

", "choices": [{"id": "A", "text": "

minke whales and humpback whales show similar average filter times.

"}, {"id": "B", "text": "

humpback whales show an average of 6.28 lunges per dive.

"}, {"id": "C", "text": "

fin whales show a longer average filter time than minke whales do. 

"}, {"id": "D", "text": "

blue whales show the longest average filter time and the highest average number of lunges per dive. 

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. To support the claim, we need to show that longer whales take more time to filter all the water they engulf than shorter whales do. This choice accurately reflects that a longer whale (the fin whale) takes more time to filter engulfed water (31.30 seconds on average) compared to a shorter whale (the minke whale, which only took 8.88 seconds on average).

Choice A is incorrect. The table shows that minke whales take an average of 8.88 seconds to filter engulfed water, while humpback whales take an average of 17.12 seconds to complete the same task. Choice B is incorrect. This choice doesn’t reflect the claim about baleen plates. The claim explains why whales of differing lengths take different amounts of time to filter engulfed water. This choice doesn’t compare whales of different lengths, and it focuses on the number of lunges, which isn’t shown to be relevant to filter time. Choice D is incorrect. The table shows that blue whales average 4.02 lunges per dive, which is not the highest average among the whales in the table.

"}, {"id": "80fd9454", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "H", "type": "mc", "stimulus": "

Percentage of Available Eggs Eaten by Cane Toad Tadpoles

Amphibian species (common name)Percentage of eggs eatenNative to AustraliaProduces bufadienolide
Little red tree frog1%yesno
Cane toad90%noyes
Short-footed frog7%yesno
Striped burrowing frog10%yesno
Dainty green tree frog1%yesno

\n

Native to Latin America, the cane toad was introduced to Australia in the 1930s. In recent decades, tadpoles in the Australian population have been shown to consume eggs of their own species. A 2022 study showed that when presented with cane toad eggs as well as eggs of native Australian amphibians, cane toad tadpoles disproportionately consumed eggs of their own species. This behavior results from their attraction to bufadienolide, a chemical produced by the eggs of cane toads but not by the eggs of native amphibians. However, using data from this study, a student wishes to argue that the presence of bufadienolide doesn’t entirely explain the cane toad tadpoles’ preference for certain eggs over others.

", "stem": "

Which choice best describes data from the table that support the student’s argument?

", "choices": [{"id": "A", "text": "

The tadpoles consumed a higher percentage of the striped burrowing frog eggs than they did of the eggs of the dainty green tree frog.

"}, {"id": "B", "text": "

The tadpoles left a certain percentage of the eggs of each of the five species unharmed, thus ultimately allowing them to hatch. 

"}, {"id": "C", "text": "

The tadpoles consumed a lower percentage of the short-footed frog eggs than they did of the eggs of their own species.

"}, {"id": "D", "text": "

The tadpoles consumed the same percentage of the dainty green tree frog eggs as they did of the little red tree frog eggs. 

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer because it most effectively uses data from the table to support the student’s argument about the role of bufadienolide in the egg preferences of cane toad tadpoles. For each of five amphibian species included in the 2022 study, the table gives the percentage of available eggs that the cane toad tadpoles ate. According to the table, the tadpoles ate 10% of striped burrowing frog eggs and 1% of dainty green tree frog eggs, which suggests a preference for striped burrowing frog eggs over dainty green tree frog eggs. The table also indicates that neither of these species’ eggs produces bufadienolide. Thus, these data suggest that something other than the presence or absence of bufadienolide is needed to adequately explain the tadpoles’ egg preferences.

Choice B is incorrect. Although the table shows that for each of the five amphibian species, the cane toad tadpoles ate less than 100% of that species’ eggs, which demonstrates that the tadpoles did indeed leave some eggs for each species unharmed, this fact alone is irrelevant to the tadpoles’ preferences for some species’ eggs over other species’ eggs. Choice C is incorrect. Although the table indicates that the cane toad tadpoles ate 90% of the cane toad eggs and 7% of the short-footed frog eggs, which suggests that they prefer cane toad eggs over short-footed frog eggs, the table also indicates that cane toad eggs produce bufadienolide, whereas short-footed frog eggs do not. Therefore, these data are not sufficient to exclude that bufadienolide alone could explain the tadpoles’ preference for some species’ eggs over other species’ eggs. Choice D is incorrect. Although the table shows that for both dainty green tree frog eggs and little red tree frog eggs, the cane toad tadpoles ate 1% of those species’ eggs, it also indicates that neither produces bufadienolide. Thus, these data alone don’t indicate bufadienolide’s role in the tadpoles’ egg preferences.

"}, {"id": "c4bee178", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "E", "type": "mc", "stimulus": "

Moons of Dwarf Planets

Dwarf planet nameNumber of moonsName of moons
Haumea2Hi‘iaka, Namaka
Ceres0N/A
Makemake1MK 2
Eris1Dysnomia
Pluto5Charon, Nix, Kerberos, Styx, Hydra

\n

Like Earth, some dwarf planets in the solar system have exactly one moon. Two examples of such dwarf planets are ______blank

", "stem": "

Which choice most effectively uses data from the table to complete the statement?

", "choices": [{"id": "A", "text": "

Eris and Makemake.

"}, {"id": "B", "text": "

Haumea and Eris.

"}, {"id": "C", "text": "

Pluto and Haumea.

"}, {"id": "D", "text": "

Makemake and Ceres.

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer because it most effectively uses data from the table to complete the statement about dwarf planets that have exactly one moon. The table lists several dwarf planets in one column and the number of moons that each of those dwarf planets has in another column. The text states that some dwarf planets have exactly one moon and indicates that there are two examples. Only two dwarf planets in the table have exactly one moon: Eris and Makemake.

Choice B is incorrect. According to the table, Eris has exactly one moon, but Haumea has two moons. Choice C is incorrect. According to the table, Haumea has two moons, and Pluto has five moons. Thus, they are not examples of dwarf planets with exactly one moon. Choice D is incorrect because while the table indicates that Makemake has exactly one moon, the table shows that Ceres has no moons at all.

"}, {"id": "63e7799d", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "H", "type": "mc", "stimulus": "

In vertical inheritance, parents pass genes to their offspring, but in horizontal transfer (HT), one species, often bacteria, passes genetic material to an unrelated species. In a 2022 study, herpetologist Atsushi Kurabayashi and his team investigated HT in multicellular organisms—namely, snakes and frogs in Madagascar. The team detected BovB—a gene transmitted vertically in snakes—in many frog species. The apparent direction of gene transfer seems counterintuitive because frogs usually don’t survive encounters with snakes and so wouldn’t be able to transmit the newly acquired gene to offspring, but the team concluded that BovB is indeed transmitted from snakes to frogs, either directly or indirectly, via HT.

", "stem": "

Which finding, if true, would most directly support the team’s conclusion?

", "choices": [{"id": "A", "text": "

BovB can be transmitted across frog species through HT.

"}, {"id": "B", "text": "

Parasites known to feed on species of snakes and frogs in which the BovB gene occurs also carry BovB. 

"}, {"id": "C", "text": "

BovB cannot be reliably transmitted from a snake species to bacteria that are usually encountered by frog species.

"}, {"id": "D", "text": "

Frog species with BovB show few discernible advantages as compared with frog species that do not carry BovB.

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. If there are parasites that feed on both snakes and frogs, they could carry BovB from snakes to frogs. HT could occur “indirectly” through those encounters, which frogs are more likely to survive than snake encounters.

Choice A is incorrect. The team’s conclusion specifically argues that BovB is transmitted from snakes to frogs via HT, and this choice doesn’t mention snakes. Choice C is incorrect. The team argues that BovB is transmitted from snakes to frogs via HT, and this answer choice discusses a scenario in which the gene is not transmitted. Choice D is incorrect. Whether or not frog species with BovB are advantaged isn’t relevant to the team’s conclusion about how the gene is transmitted.

"}, {"id": "0dba14e6", "domain": "Information and Ideas", "skill": "Inferences", "difficulty": "H", "type": "mc", "stimulus": "

The increased integration of digital technologies throughout the process of book creation in the late 20th and early 21st centuries lowered the costs of book production, but those decreased costs have been most significant in the manufacturing and distribution process, which occurs after the authoring, editing, and design of the book are complete. This suggests that in the late 20th and early 21st centuries, ______blank

", "stem": "

Which choice most logically completes the text?

", "choices": [{"id": "A", "text": "

digital technologies made it easier than it had been previously for authors to write very long works and get them published.

"}, {"id": "B", "text": "

customers generally expected the cost of books to decline relative to the cost of other consumer goods.

"}, {"id": "C", "text": "

publishers increased the variety of their offerings by printing more unique titles but also printed fewer copies of each title.

"}, {"id": "D", "text": "

the costs of writing, editing, and designing a book were less affected by the technologies used than were the costs of manufacturing and distributing a book.

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer because it presents the conclusion that most logically follows from the text’s discussion of how digital technologies affected the process of book creation. The text explains that in the late 20th and early 21st centuries digital technologies lowered book production costs most significantly in manufacturing and distribution. The text goes on to point out that authoring, editing, and book design are distinct steps in the process that occur before manufacturing and distribution. Because the savings connected to digital technologies have been most significant in manufacturing and distribution, it’s reasonable to infer that those technologies had less of an effect on writing, editing, and designing books. 

Choice A is incorrect because the text focuses on lowered book production costs that occur after authoring has taken place; there’s no indication in the text whether digital technologies made writing and publishing lengthy books easier. Choice B is incorrect. Although it’s logical to conclude that customers would expect the cost of books to decline if production costs have declined, the text doesn’t address customer expectations for the cost of books or any other consumer goods. Choice C is incorrect because the text focuses broadly on how digital technologies have affected the cost of the publishing process; it doesn’t address the kinds of books being published or how many copies are printed.

"}, {"id": "860803dd", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "H", "type": "mc", "stimulus": "

Biologist Valentina Gómez-Bahamón and her team have investigated two subspecies of the fork-tailed flycatcher bird that live in the same region in Colombia, but one subspecies migrates south for part of the year, and the other doesn’t. The researchers found that, due to slight differences in feather shape, the feathers of migratory forked-tailed flycatcher males make a sound during flight that is higher pitched than that made by the feathers of nonmigratory males. The researchers hypothesize that fork-tailed flycatcher females are attracted to the specific sound made by the males of their own subspecies, and that over time the females’ preference will drive further genetic and anatomical divergence between the subspecies.

", "stem": "

Which finding, if true, would most directly support Gómez-Bahamón and her team’s hypothesis?

", "choices": [{"id": "A", "text": "

The feathers located on the wings of the migratory fork-tailed flycatchers have a narrower shape than those of the nonmigratory birds, which allows them to fly long distances.

"}, {"id": "B", "text": "

Over several generations, the sound made by the feathers of migratory male fork-tailed flycatchers grows progressively higher pitched relative to that made by the feathers of nonmigratory males.

"}, {"id": "C", "text": "

Fork-tailed flycatchers communicate different messages to each other depending on whether their feathers create high-pitched or low-pitched sounds.  

"}, {"id": "D", "text": "

The breeding habits of the migratory and nonmigratory fork-tailed flycatchers remained generally the same over several generations. 

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer because it presents a finding that, if true, would most directly support Gómez-Bahamón and her team’s hypothesis about fork-tailed flycatchers. The text indicates that although two subspecies of the birds live in the same region, the tail feathers of the migrating males make a higher-pitched sound than the tail feathers of the nonmigrating males do. Gómez-Bahamón and her team hypothesize that female fork-tailed flycatchers are attracted to the particular sound made by the tail feathers of males of their own subspecies, which will bring about additional “genetic and anatomical divergence” between the two subspecies. If it were found that the pitch generated by the tail feathers of migrating males is getting higher over successive generations, it would indicate that the shape of the migrating subspecies’ tail feathers is diverging further from that of the nonmigrating subspecies. And if females continue to prefer the sounds of the males of their own subspecies, the females of the migrating subspecies will become acclimated to increasingly higher pitches over subsequent generations, causing further divergence between the subspecies. Thus, if it were found that migrating males’ tail feathers were producing higher pitches over time, that would support the researchers’ hypothesis.

Choice A is incorrect because the researchers’ hypothesis is that female flycatchers prefer the sounds produced by the tail feathers of males of their own subspecies, which will lead to further divergence between the two subspecies. This finding is about the shape of wing feathers and how that affects long-distance flight, whereas the hypothesis is about the shape of tail feathers and how that relates to female mate preference. Choice C is incorrect because the researchers’ hypothesis is that female flycatchers prefer the sounds produced by the tail feathers of males of their own subspecies, which will lead to further divergence between the two subspecies. This finding focuses on how the tail feather sounds communicate different messages, which doesn’t address differences between the subspecies or female preferences. Choice D is incorrect because the researchers’ hypothesis is that female flycatchers prefer the sounds produced by the tail feathers of males of their own subspecies, which will lead to further divergence between the two subspecies. The finding that breeding habits haven’t changed for either subspecies does not, by itself, suggest anything about female preferences or divergence between the two subspecies.

"}, {"id": "04bcb7a9", "domain": "Information and Ideas", "skill": "Central Ideas and Details", "difficulty": "E", "type": "mc", "stimulus": "

Xin Wang and colleagues have discovered the earliest known example of a flower bud in a 164-million-year-old plant fossil in China. The researchers have named the new species Florigerminis jurassica. They believe that the discovery pushes the emergence of flowering plants, or angiosperms, back to the Jurassic period, which occurred between 145 million and 201 million years ago.

", "stem": "

According to the text, how old was the fossil that Wang and colleagues discovered?

", "choices": [{"id": "A", "text": "

150 million years old

"}, {"id": "B", "text": "

145 million years old

"}, {"id": "C", "text": "

164 million years old

"}, {"id": "D", "text": "

201 million years old

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer because it gives the age for the fossil discovered by Wang and colleagues that is directly supported by the text. According to the text, Xin Wang and colleagues discovered a 164-million-year-old plant fossil. This plant fossil included a flower bud, which the researchers believe provides evidence that flowering plants emerged in the Jurassic period, which falls between 145 million and 201 million years ago.

Choice A is incorrect because the text states that Wang and colleagues discovered a 164-million-year-old flowering plant fossil in China, not one that is 150 million years old. Although 150 million years ago would fall within the Jurassic period, according to the text it isn’t the age of the discovered fossil. Choice B is incorrect because the text states that Wang and colleagues discovered a 164-million-year-old flowering plant fossil in China, not one that is 145 million years old. Although 145 million years ago would fall at the end of the Jurassic period, according to the text it isn’t the age of the discovered fossil. Choice D is incorrect because the text states that Wang and colleagues discovered a 164-million-year-old flowering plant fossil in China, not one that is 201 million years old. Although 201 million years ago would fall at the beginning of the Jurassic period, according to the text it isn’t the age of the discovered fossil.

"}, {"id": "12030076", "domain": "Information and Ideas", "skill": "Central Ideas and Details", "difficulty": "M", "type": "mc", "stimulus": "

NASA’s Aspera mission, led by Carlos Vargas, will investigate the circumgalactic medium (CGM), the huge swaths of low-density gas that fill and surround galaxies. Specifically, the team will focus on portions of the gas that exist in a “warm-hot” phase: these portions haven’t previously been observable but are thought to fuel new star formation and hold most of the mass that makes up a galaxy. Using a telescope capable of revealing these parts of the CGM, the Aspera mission should help answer long-standing questions about how galaxies emerge, change, and even interact.

", "stem": "

Which choice best states the main idea of the text?

", "choices": [{"id": "A", "text": "

As the leader of NASA’s Aspera mission, Vargas will be the first person to investigate the makeup of the CGM.

"}, {"id": "B", "text": "

Although galaxies that are surrounded by the CGM have been studied, researchers have been unable to directly observe low-density gas in the CGM in the “warm-hot” phase.

"}, {"id": "C", "text": "

Researchers don’t yet have a complete understanding of the process of galaxy evolution but have raised the possibility that galaxies interact with each other at times.

"}, {"id": "D", "text": "

The Aspera mission is expected to produce the first direct observations of CGM gas in the “warm-hot” phase, which likely has an important role in the evolution of galaxies.

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer because it most accurately states the main idea of the text. The text begins by mentioning NASA’s Aspera mission, which will investigate the low-density gas that makes up the circumgalactic medium (CGM). According to the text, this mission will focus on a portion of the CGM’s gas that exists in a “warm-hot” phase; this “warm-hot” gas has not been previously observed, but it is thought to make up most of the mass of galaxies and play a part in star formation. Finally, the text mentions a telescope capable of examining this previously unobservable “warm-hot” gas: the Aspera mission will use this telescope in the hope of answering questions about galaxy formation and change. Therefore, the main idea of the text is that the Aspera mission is likely to produce the first direct observations of CGM gas in the “warm-hot” phase, which likely has an important role in the evolution of galaxies.

Choice A is incorrect. Although this choice mentions the Aspera mission, names its leader, and generally states the mission’s purpose, it does not reference the “warm-hot” gas or fully convey the reason why the Aspera mission is significant. Choice B is incorrect. Although this choice mentions the “warm-hot” gas that makes up a portion of the CGM, it does not reference the Aspera mission or describe its importance. The text also does not mention that galaxies surrounded by the CGM have been studied. Choice C is incorrect. Although this choice describes a problem related to the CGM that researchers have been attempting to solve and presents the speculation of those researchers, it does not mention the Aspera mission or describe its purpose.

"}, {"id": "99fdf71c", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "M", "type": "mc", "stimulus": "

“When Dawn Comes to the City” is a 1922 poem by Claude McKay, who immigrated to the United States from the island nation of Jamaica as an adult. The poem conveys McKay’s contrasting feelings about New York City—his adopted home in the US—and his home country: ______blank

", "stem": "

Which quotation from “When Dawn Comes to the City” most effectively illustrates the claim?

", "choices": [{"id": "A", "text": "

“A lonely newsboy hurries by, / Humming a recent ditty; / Red streaks strike through the gray of the sky, / The dawn comes to the city [New York City].”

"}, {"id": "B", "text": "

“Dark figures start for work; / I watch them sadly shuffle on, / ’Tis dawn, dawn in New York. / But I would be on the island of the sea, / In the heart of the island of the sea.”

"}, {"id": "C", "text": "

“And the shaggy Nannie goat is calling, calling, calling / From her little trampled corner of the long wide lea / That stretches to the waters of the hill-stream falling / Sheer upon the flat rocks joyously!”

"}, {"id": "D", "text": "

“The tired cars go grumbling by, / The moaning, groaning cars, / And the old milk carts go rumbling by / Under the same dull stars.”

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer because it presents a quotation illustrating the claim that the poem conveys McKay’s contrasting feelings about New York City and Jamaica. McKay first presents a somewhat negative view of New York City, describing watching “dark figures” who “sadly shuffle” to work at dawn, and then indicates that he would instead like to be “in the heart of the island of the sea.”

Choice A is incorrect because the quotation focuses on a description of only one place (New York City, with its “lonely newsboy” and “red streaks” in the sky at dawn) rather than on different feelings about two places. Choice C is incorrect because the quotation focuses on a description of only one place (which isn’t named) rather than on McKay’s different feelings about two places. Choice D is incorrect because though McKay presents a negative image of an unnamed place with “tired cars” that grumble, moan, and groan, and “old milk carts“ that rumble by under “dull stars,” the quotation focuses on McKay’s feelings about only one place rather than on different feelings about two places.

"}, {"id": "e2829dd7", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "M", "type": "mc", "stimulus": "
\n\n\n\n\n\n\n\n\n\n\n\n\n1,5001,0005000Number of beam breaks-410243852668094108122136150Number of Infrared Beam Breaks by Mice Treated with CNO or Saline, by SexMinutes from treatment females with saline males with saline males with CNO females with CNO
\n

To investigate the influence of certain estrogen-responsive neurons on energy expenditure, biologist Stephanie Correa et al. treated female and male mice with either saline solution or clozapine-N4-oxide (CNO), which activates the neurons. Monitoring the activity levels of the mice by measuring how frequently the animals broke infrared beams crossing their enclosures, Correa et al. found that the mice in their study showed sex-specific differences in response to neuron activation: ______blank

", "stem": "

Which choice most effectively uses data from the graph to complete the assertion?

", "choices": [{"id": "A", "text": "

the four groups of mice differed greatly in their activity levels before treatment but showed identical activity levels at the end of the monitoring period. 

"}, {"id": "B", "text": "

saline-treated females showed substantially more activity at certain points in the monitoring period than saline-treated males did. 

"}, {"id": "C", "text": "

CNO-treated females showed more activity relative to saline-treated females than CNO-treated males showed relative to saline-treated males. 

"}, {"id": "D", "text": "

CNO-treated females showed a substantial increase and then decline in activity over the monitoring period, whereas CNO-treated males showed a substantial decline in activity followed by a steep increase.

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. The graph shows that the CNO-treated females were way more active than the CNO-treated males, while the saline-treated males and females (the control groups) had very similar activity levels. This supports the claim that there were sex-specific differences in the mice’s response to neuron activation.

Choice A is incorrect. This choice misreads the graph. All four groups of mice started at nearly the same activity level before treatment (see how all four points are very close together at -4 minutes, meaning four minutes before treatment). Choice B is incorrect. This choice doesn’t complete the assertion. The assertion is about the mice’s response to neuron activation, so we need to include the data about the CNO-treated females and males. Choice D is incorrect. This choice misreads the graph. The line for the CNO-treated males does not show a “substantial decline” until around 122 minutes, and there is no “steep increase” afterward.

"}, {"id": "194dd448", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "M", "type": "mc", "stimulus": "

“John of God, the Water-Carrier” is a 1913 short story by María Cristina Mena. In the story, the narrator presents John as being a hard worker who is fully dedicated to his job as water carrier, or aguador: ______blank

", "stem": "

Which quotation from “John of God, the Water-Carrier” most effectively illustrates the claim?

", "choices": [{"id": "A", "text": "

“Very happy, he would jog home, the heavy silver pieces in his leather pockets making a discreet and dulcet ‘trink-trak’ between his jugs and his body.”

"}, {"id": "B", "text": "

“He learned that the city aguador may not blow his whistle to halt the traffic while he gravely crosses the street, but must wait for the passing of many vehicles, some with horses and some outlandishly without.”

"}, {"id": "C", "text": "

“From early morn to the fall of the afternoon he would go from fountain to fountain and from portal to portal, his lean body so accustomed to bending that he never thought of straightening it, his head bowed as if in prayer.”

"}, {"id": "D", "text": "

“When his first jugs had worn out—the sweet-scented, porous red clay becomes perforated in time—he had buried them to their necks in the corner where he slept, and they were now his treasury.”

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer because it most effectively illustrates the claim in the text that John is hard-working and dedicated to his job. In the quotation, John is portrayed as spending “early morn to the fall of the afternoon” working hard as a water carrier. John is also described as “so accustomed to bending” while doing his work “that he never thought of straightening” his body, instead remaining deeply focused on his work. These details portray John as a dedicated worker.

Choice A is incorrect because this quotation portrays John as happy about heading home after being paid. It doesn’t showcase John being hard at work. Choice B is incorrect because this quotation doesn’t pertain to John’s commitment to his work; it describes difficulties the traffic in the city causes John in the performance of his work. Choice D is incorrect because this quotation doesn’t pertain to John’s commitment to his work; it discusses what John does with his worn-out water jugs.

"}, {"id": "08b28c1a", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "E", "type": "mc", "stimulus": "

A researcher conducted an experiment inspired by studies suggesting that people may benefit from feeling frightened in certain circumstances, such as when watching scary movies or visiting haunted attractions. The researcher recruited several participants and had them walk through a local haunted house attraction. Immediately after exiting the attraction, each participant completed a survey about their experience. Based on the survey responses, the researcher claims that feeling frightened in controlled situations can boost a person’s mood and confidence.

", "stem": "

Which quotation from a participant would best illustrate the researcher’s claim?

", "choices": [{"id": "A", "text": "

“After I came out of the haunted house, I felt very accomplished and less stressed.”

"}, {"id": "B", "text": "

“My friends kept laughing as we were walking through the haunted house.”

"}, {"id": "C", "text": "

“The haunted house was scary at first, but I knew everyone was just acting, so I felt less scared after a few minutes.”

"}, {"id": "D", "text": "

“The sense of relief I felt at the end of the haunted house was similar to the feelings I have when I finish a scary movie.”

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. This choice illustrates both “feeling frightened in controlled situations” (the haunted house) and the benefit of a boosted mood (“less stressed”) and confidence (“very accomplished”).

Choice B is incorrect. This choice isn’t the best illustration of the claim. While laughing may indicate a good mood, this choice provides no evidence of “feeling frightened” or boosted confidence. Another choice provides better evidence. Choice C is incorrect. This choice isn’t the best illustration of the claim. This choice demonstrates “feeling frightened” in a controlled environment, but it doesn’t provide strong evidence of boosted mood or confidence. Another choice provides better evidence. Choice D is incorrect. This choice isn’t the best illustration of the claim. While a “sense of relief” could be interpreted as a boosted mood, this choice doesn’t provide direct evidence of “feeling frightened” or of increased confidence. This choice simply suggests that haunted houses and scary movies have a similar effect. Another choice provides better evidence for the researcher’s claim.

"}, {"id": "a13c1c66", "domain": "Information and Ideas", "skill": "Inferences", "difficulty": "H", "type": "mc", "stimulus": "

Many animals, including humans, must sleep, and sleep is known to have a role in everything from healing injuries to encoding information in long-term memory. But some scientists claim that, from an evolutionary standpoint, deep sleep for hours at a time leaves an animal so vulnerable that the known benefits of sleeping seem insufficient to explain why it became so widespread in the animal kingdom. These scientists therefore imply that ______blank

", "stem": "

Which choice most logically completes the text?

", "choices": [{"id": "A", "text": "

prolonged deep sleep is likely advantageous in ways that have yet to be discovered.

"}, {"id": "B", "text": "

most traits perform functions that are hard to understand from an evolutionary standpoint.

"}, {"id": "C", "text": "

it is more important to understand how widespread prolonged deep sleep is than to understand its function.

"}, {"id": "D", "text": "

many traits that provide significant benefits for an animal also likely pose risks to that animal.

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. It most logically completes the text. The text says that some scientists can’t explain why prolonged deep sleep is so widespread, given that the known benefits of sleep don’t seem to make up for how vulnerable it leaves an animal. This suggests that prolonged deep sleep probably has unknown evolutionary benefits that make up for the vulnerability.    

Choice B is incorrect. It doesn’t logically complete the text. The text only discusses the benefits and risks of one trait: sleep. So there’s no basis for an inference about “most traits.” Choice C is incorrect. It doesn’t logically complete the text. The text says that it is already known that prolonged deep sleep is widespread in the animal kingdom. Rather, what some scientists can’t explain is WHY prolonged deep sleep is so widespread, given that the known benefits of sleep don’t seem to make up for how vulnerable it leaves an animal. Choice D is incorrect. It doesn’t logically complete the text. The text only discusses the benefits and risks of one trait: sleep. So there’s no basis for an inference about “many traits.”

"}, {"id": "350e2336", "domain": "Information and Ideas", "skill": "Inferences", "difficulty": "M", "type": "mc", "stimulus": "

The Haitian Declaration of Independence was issued in 1804, bringing to an end the revolution against colonial France that began in 1791. Written in French, which was not the first language of most Haitians but which was used throughout Europe as the language of international diplomacy, the declaration notes that Haiti will not bring rebellion to other Caribbean nations, promises to respect the sovereignty of its neighbors—widely understood as a reassurance to the United States—and sets up Haiti as an example for future struggles against colonizers (an implicit reference to the many colonies then found in the Americas). So even though the declaration is explicitly addressed to the Haitian people, it’s reasonable to conclude that ______blank

", "stem": "

Which choice most logically completes the text?

", "choices": [{"id": "A", "text": "

aspects of the declaration were modeled on similar documents from other countries.

"}, {"id": "B", "text": "

the French government may have been surprised by the declaration.

"}, {"id": "C", "text": "

many Haitian people opposed the revolution and the declaration.

"}, {"id": "D", "text": "

the declaration actually had several intended audiences.

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. The passage tells us that the declaration was written in a language important to European diplomacy but not most Haitians, states that the declaration included \"a reassurance to the United States,\" and made implicit references to colonies in the Americas. Because of the messages within the declaration that were largely irrelevant to the Haitian people, we can assume that the Haitian people were not the only audience for this document.

Choice A is incorrect. There’s no mention in the passage of similar documents in other countries, so there’s no basis for this inference. Choice B is incorrect. Although there’s an implicit reference to European governments when the passage discusses how the declaration was written in French, \"which was used throughout Europe as the language of international diplomacy,\" there is no discussion of the French government’s response to the declaration. Therefore, there’s no basis for this inference. Choice C is incorrect. The passage doesn’t mention the popularity of the revolution and declaration among the Haitian people, so there’s no basis for this inference.

"}, {"id": "c6b470bb", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "M", "type": "mc", "stimulus": "

“Odalie” is an 1899 short story by Alice Dunbar-Nelson. In the story, a young woman named Odalie attends the annual Mardi Gras carnival in New Orleans, where she lives with her guardian Tante Louise. Dunbar-Nelson portrays Odalie as eager to escape the monotony of her everyday life: ______blank

", "stem": "

Which quotation from “Odalie” most effectively illustrates the claim?

", "choices": [{"id": "A", "text": "

“Mardi Gras was a tiresome day, after all, she sighed, and Tante Louise agreed with her for once.”

"}, {"id": "B", "text": "

“In the old French house on Royal Street, with its quaint windows and Spanish courtyard green and cool, and made musical by the plashing of the fountain and the trill of caged birds, lived Odalie in convent-like seclusion.”

"}, {"id": "C", "text": "

“When one is shut up in a great French house with a grim sleepy tante and no companions of one’s own age, life becomes a dull thing, and one is ready for any new sensation.”

"}, {"id": "D", "text": "

“It was Mardi Gras day at last, and early through her window Odalie could hear the jingle of folly bells on the [participants’] costumes, the tinkle of music, and the echoing strains of songs.”

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer because it most effectively uses a quotation from “Odalie” to illustrate the claim that Odalie is eager to escape the monotony, or tedious lack of variety, of her everyday life. In the quotation, Odalie describes feeling “shut up” and complains that she has “no companions” except for her “sleepy tante.” Odalie goes on to say that, as a result, her life is “dull” and she is “ready for any new sensation,” meaning she wants a change. This suggests that Odalie wishes to get away from her monotonous everyday life.

Choice A is incorrect. Although this quotation includes the word “tiresome,” which means dull, it does so to suggest Odalie’s negative feelings about Mardi Gras, which is a once-a-year celebration, not her feelings about her everyday life. This quotation therefore doesn’t express that Odalie’s everyday life is monotonous or that she wishes to escape. Choice B is incorrect. Although this quotation ends by saying that Odalie lives in seclusion, or isolation, it doesn’t express that Odalie’s everyday life is monotonous or that she wishes to escape. Instead, it describes the pleasant qualities of the house Odalie lives in, saying that it has “quaint windows” and a “green and cool” courtyard that is “made musical” by the sounds of a fountain and pet birds. Choice D is incorrect because this quotation describes the lively sounds of a Mardi Gras celebration that Odalie hears through her window, not the monotony of Odalie’s everyday life or her wish to escape.

"}, {"id": "f8befe75", "domain": "Information and Ideas", "skill": "Central Ideas and Details", "difficulty": "M", "type": "mc", "stimulus": "

Many intellectual histories of the Black Power movement of the 1960s and 1970s rely heavily on essays and other explicitly ideological works as primary sources, a tendency that can overrepresent the perspectives of a small number of thinkers, most of whom were male. Historian Ashley D. Farmer has shown that expanding the array of primary sources to encompass more types of print material—including political cartoons, advertisements, and artwork—leads to a much better understanding of the movement and the crucial and diverse roles that Black women played in shaping it. 

", "stem": "

Which choice best describes the main idea of the text?

", "choices": [{"id": "A", "text": "

Farmer’s methods and research have enriched the historical understanding of the Black Power movement and Black women’s contributions to it.

"}, {"id": "B", "text": "

Before Farmer’s research, historians had largely ignored the intellectual dimensions of the Black Power movement. 

"}, {"id": "C", "text": "

Other historians of the Black Power movement have criticized Farmer’s use of unconventional primary sources. 

"}, {"id": "D", "text": "

The figures in the Black Power movement whom historians tend to cite would have agreed with Farmer’s conclusions about women’s roles in the movement.

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. It best describes the main idea of the text. The text starts by saying that historians of the Black Power movement are too reliant on openly ideological works, which were written mostly by men, as sources. The text then describes Farmer’s research: she has shown that including other kinds of sources leads to a better understanding of the Black Power movement and the role Black women played in it.

Choice B is incorrect. This doesn’t describe the main idea of the text. In fact, it conflicts with the text. The text says that historians have relied on \"essays and other explicitly ideological works,\" which suggests that they have studied at least some of the intellectual dimensions of the Black Power movement. Choice C is incorrect. This doesn’t describe the main idea of the text. The text never mentions how other historians of the Black Power movement view Farmer’s use of unconventional sources. In fact, the text itself argues in favor of Farmer’s research, claiming that it has led to a \"much better understanding of the movement.\" Choice D is incorrect. This doesn’t describe the main idea of the text. The text never mentions what any figures in the Black Power movement thought about women’s roles in the movement.

"}, {"id": "ccf414c9", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "M", "type": "mc", "stimulus": "

E-book Sales as a Percentage of Total Unit Sales in All Book Formats for a Large US Trade Publisher, by Genre, 2006, 2011, 2016

Genre200620112016
science fiction and fantasy0.627.736.7
cookbooks02.910.5
travel guides05.524.6
romance0.340.656.2

\n

E-books became an increasingly popular means of reading in the United States in the 2000s and 2010s, though that popularity was concentrated in titles that, like those in most fiction genres, are meant to be read straight through from beginning to end. For books in nonfiction genres that do not tell stories and require the reader to flip back and forth through a volume, e-books were significantly less commercially successful. This can be seen by comparing ______blank

", "stem": "

Which choice most effectively uses data from the table to illustrate the claim?

", "choices": [{"id": "A", "text": "

the percentage of 2016 cookbook sales that were e-books with the percentage of 2016 science fiction and fantasy sales that were e-books.

"}, {"id": "B", "text": "

the percentage of 2006 romance sales that were e-books with the percentage of 2016 romance sales that were e-books.

"}, {"id": "C", "text": "

the percentage of 2006 romance sales that were e-books with the 2006 science fiction and fantasy sales that were e-books.

"}, {"id": "D", "text": "

the percentage of 2011 travel guide sales that were e-books with the percentage of 2016 travel guide sales that were e-books.

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer because it uses data from the table to effectively support the claim that book genres that typically require the reader to start at the beginning of the story and read straight through are more commercially successful as e-books than other genres. For each of three years, the table presents four book genres and the percentage of total sales for each genre in e-book format. Cookbooks, a nonfiction genre, do not require the reader to read straight through. According to the table, 10.5 percent of total cookbook sales in 2016 were in the e-book format. The 2016 percentage of e-book sales was 36.7 percent in the science fiction and fantasy genre, which are typically stories read straight through from start to finish. The higher percentage of total sales of the story-based e-books in 2016 supports the claim in the text.

Choice B is incorrect because it compares the e-book sales of romance books in 2006 to those in 2016. Romance books are meant to be read straight through from start to finish. The text claims that books that are not stories and do not require reading straight through are not as commercially successful in e-book format as those that do. As this choice is only comparing e-book sales for one genre, it does not support the claim. Choice C is incorrect because both science fiction and fantasy and romance novels are fiction books meant to be read straight through from beginning to end. The text claims that books that are not stories and do not require reading straight through are less commercially successful in e-book format than those that do. As this choice does not compare e-book sales of story genres to e-book sales in genres that are not stories, it does not support the claim. Choice D is incorrect. Although the data in the table show that the travel guide e-books made up a greater percentage of total sales in 2016 than in 2011, this doesn’t illustrate the claim in the text that e-books in nonfiction genres not meant to be read straight through are less commercially successful. The claim cannot be supported without comparing the percentage of e-book sales between fiction and nonfiction book genres from the table. 

"}, {"id": "f942646f", "domain": "Information and Ideas", "skill": "Inferences", "difficulty": "H", "type": "mc", "stimulus": "

Researchers Suchithra Rajendran and Maximilian Popfinger modeled varying levels of passenger redistribution from short-haul flights (flights of 50 to 210 minutes, from takeoff to landing) to high-speed rail trips. Planes travel faster than trains, but air travel typically requires 3 hours of lead time for security, baggage handling, and boarding that rail travel doesn’t, so short-haul routes take similar amounts of time by air and by rail. However, the model suggests that as rail passenger volumes approach current capacity limits, long lead times emerge. Therefore, for rail to remain a viable alternative to short-haul flights, ______blank

", "stem": "

Which choice most logically completes the text?

", "choices": [{"id": "A", "text": "

rail systems should offer fewer long-haul routes and airlines should offer more long-haul routes.

"}, {"id": "B", "text": "

rail systems may need to schedule additional trains for these routes.

"}, {"id": "C", "text": "

security, baggage handling, and boarding procedures used by airlines may need to be implemented for rail systems.

"}, {"id": "D", "text": "

passengers who travel by rail for these routes will need to accept that lead times will be similar to those for air travel.

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. Air travel usually requires much more “lead time” than train travel, so short flights end up taking the same amount of time as a train trip to the same destination. But train travel starts to need more “lead time” when the trains approach their capacity limits. This suggests that train companies should add more trains for these routes if they want to encourage travelers to take a train instead of a plane.

Choice A is incorrect. This inference isn’t supported. The text never discusses “long-haul routes” for either air travel or rail travel, so there is no basis to make this inference. Choice C is incorrect. This inference isn’t supported. The text only mentions these procedures to explain why the “lead time” is so long for air travel. It never suggests that trains need to start implementing these procedures too. Choice D is incorrect. This inference isn’t supported. The goal is to make sure that trains “remain a viable alternative” to short flights, which suggests that anything that makes train travel take longer should be avoided.

"}, {"id": "3f05e40f", "domain": "Information and Ideas", "skill": "Central Ideas and Details", "difficulty": "M", "type": "mc", "stimulus": "

In many of his sculptures, artist Richard Hunt uses broad forms rather than extreme accuracy to hint at specific people or ideas. In his first major work, Arachne (1956), Hunt constructed the mythical character Arachne, a weaver who was changed into a spider, by welding bits of steel together into something that, although vaguely human, is strange and machine-like. And his large bronze sculpture The Light of Truth (2021) commemorates activist and journalist Ida B. Wells using mainly flowing, curved pieces of metal that create stylized flame.

", "stem": "

Which choice best states the text’s main idea about Hunt?

", "choices": [{"id": "A", "text": "

He often depicts the subjects of his sculptures using an unrealistic style.

"}, {"id": "B", "text": "

He uses different kinds of materials depending on what kind of sculpture he plans to create.

"}, {"id": "C", "text": "

He tends to base his art on important historical figures rather than on fictional characters.

"}, {"id": "D", "text": "

He has altered his approach to sculpture over time, and his works have become increasingly abstract.

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer because it most accurately states the main idea of the text. According to the text, many of Richard Hunt’s sculptures “use broad forms rather than extreme accuracy”—in other words, they are more abstract than realistic. To illustrate Hunt’s abstract approach, the text characterizes his sculpture of Arachne as “vaguely human” and his work in honor of Ida B. Wells as “using mainly flowing, curved pieces of metal that create stylized flame.” Thus, the main idea is that Hunt often depicts the subjects of his sculptures using an unrealistic style.

Choice B is incorrect. Although the text indicates that one of Hunt’s sculptures is made of steel and another of bronze, there is no mention of why he chose these materials. Choice C is incorrect because the text says nothing about how Hunt chose the subjects for his sculptures. Furthermore, of the two examples provided in the text, only Ida B. Wells is an important historical figure; Arachne is a “mythical character.” Choice D is incorrect because the text says nothing about how Hunt’s style changed over time. In fact, although the two examples of Hunt’s work discussed in the text were created 65 years apart, they are both described as heavily stylized rather than realistic, which may suggest that some aspects of Hunt’s style haven’t changed over that time.

"}, {"id": "4a85fea6", "domain": "Information and Ideas", "skill": "Inferences", "difficulty": "M", "type": "mc", "stimulus": "

Euphorbia esula (leafy spurge) is a Eurasian plant that has become invasive in North America, where it displaces native vegetation and sickens cattle. E. esula can be controlled with chemical herbicides, but that approach can also kill harmless plants nearby. Recent research on introducing engineered DNA into plant species to inhibit their reproduction may offer a path toward exclusively targeting E. esula, consequently ______blank

", "stem": "

Which choice most logically completes the text?

", "choices": [{"id": "A", "text": "

making individual E. esula plants more susceptible to existing chemical herbicides.

"}, {"id": "B", "text": "

enhancing the ecological benefits of E. esula in North America.

"}, {"id": "C", "text": "

enabling cattle to consume E. esula without becoming sick.

"}, {"id": "D", "text": "

reducing invasive E. esula numbers without harming other organisms.

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer because it presents the conclusion that most logically follows from the text’s discussion of leafy spurge and engineered DNA. The text establishes that using chemical herbicides to control leafy spurge in North America can also harm other plants nearby. The text then indicates that it might be possible to use engineered DNA to prevent plants from reproducing, which would be useful for “exclusively targeting” leafy spurge. If it’s possible to exclusively target leafy spurge with engineered DNA—meaning that only leafy spurge is affected by the engineered DNA—and prevent the plant from reproducing, then leafy spurge numbers could be reduced “without harming other organisms.”

Choice A is incorrect because the text raises the possibility of using engineered DNA to prevent leafy spurge from reproducing, not to make individual leafy spurge plants more vulnerable to chemical herbicides that already exist. Choice B is incorrect because the text doesn’t describe any ecological benefits of leafy spurge in North America; instead, the text is focused on using engineered DNA to prevent leafy spurge from reproducing and thereby reduce its numbers. The only ecological effects of leafy spurge in North America that are described in the text are harmful. Choice C is incorrect because the text describes the possibility of using engineered DNA to prevent leafy spurge from reproducing; it doesn’t offer a way to enable cattle to eat leafy spurge without becoming sick. 

"}, {"id": "de0a5b4e", "domain": "Information and Ideas", "skill": "Central Ideas and Details", "difficulty": "E", "type": "mc", "stimulus": "

In 2022, researchers rediscovered ancient indigenous glyphs, or drawings, on the walls of a cave in Alabama. The cave’s ceiling was only a few feet high, affording no position from which the glyphs, being as wide as ten feet, could be viewed or photographed in their entirety. However, the researchers used a technique called photogrammetry to assemble numerous photos of the walls into a 3D model. They then worked with representatives of tribes originally from the region, including the Chickasaw Nation, to understand the significance of the animal and humanoid figures adorning the cave.

", "stem": "

According to the text, what challenge did the researchers have to overcome to examine the glyphs?

", "choices": [{"id": "A", "text": "

The cave was so remote that the researchers couldn’t easily reach it.

"}, {"id": "B", "text": "

Some of the glyphs were so faint that they couldn’t be photographed.

"}, {"id": "C", "text": "

The researchers were unable to create a 3D model of the cave.

"}, {"id": "D", "text": "

The cave’s dimensions prevented the researchers from fully viewing the glyphs.

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. The text describes the very low ceiling of the cave, making it impossible to photograph the very wide glyphs all at once.

Choice A is incorrect. The text doesn’t say this. It never suggests that the cave was remote or difficult to access, just that the cave itself was difficult to photograph well. Choice B is incorrect. The text doesn’t say this. The glyphs were so wide that they couldn’t be photographed completely. Choice C is incorrect. The text states the opposite of this. The researchers “used a technique called photogrammetry to assemble numerous photos of the walls into a 3D model.”

"}, {"id": "16025337", "domain": "Information and Ideas", "skill": "Central Ideas and Details", "difficulty": "H", "type": "mc", "stimulus": "

The following text is adapted from William Shakespeare’s 1609 poem “Sonnet 27.” The poem is addressed to a close friend as if he were physically present.

\n

Weary with toil, I [hurry] to my bed,

\n

The dear repose for limbs with travel tired;

\n

But then begins a journey in my head

\n

To work my mind, when body’s work’s expired:

\n

For then my thoughts—from far where I abide—

\n

[Begin] a zealous pilgrimage to thee,

\n

And keep my drooping eyelids open wide,

", "stem": "

What is the main idea of the text?

", "choices": [{"id": "A", "text": "

The speaker is asleep and dreaming about traveling to see the friend.

"}, {"id": "B", "text": "

The speaker is planning an upcoming trip to the friend’s house. 

"}, {"id": "C", "text": "

The speaker is too fatigued to continue a discussion with the friend.

"}, {"id": "D", "text": "

The speaker is thinking about the friend instead of immediately falling asleep.

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer it most accurately states the main idea of the text. The speaker describes going to bed for “repose” (rest) but finding that his thoughts are focused on the friend the speaker is addressing, and the thoughts are keeping the speaker awake.

Choice A is incorrect because the speaker isn’t asleep; the thoughts about the friend are keeping the speaker awake. Choice B is incorrect because the speaker isn’t talking about taking a literal trip; rather, the speaker uses the metaphor of a journey to describe internal thoughts. Choice C is incorrect because the speaker isn’t having a discussion with the friend.

"}, {"id": "20583752", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "H", "type": "mc", "stimulus": "

“The Poet Walt Whitman” is an 1887 essay by José Martí, a Cuban author and political activist, originally written in Spanish. In the essay, Martí explores the value of literature, arguing that a society’s spiritual well-being depends on the character of its literary culture: ______blank

", "stem": "

Which quotation from a translation of “The Poet Walt Whitman” most effectively illustrates the claim?

", "choices": [{"id": "A", "text": "

“Poetry, which brings together or separates, which fortifies or brings anguish, which shores up or demolishes souls, which gives or robs men of faith and vigor, is more necessary to a people than industry itself, for industry provides them with a means of subsistence, while literature gives them the desire and strength for life.”

"}, {"id": "B", "text": "

“Every society brings to literature its own form of expression, and the history of the nations can be told with greater truth by the stages of literature than by chronicles and decades.”

"}, {"id": "C", "text": "

“Where will a race of men go when they have lost the habit of thinking with faith about the scope and meaning of their actions? The best among them, those who consecrate Nature with their sacred desire for the future, will lose, in a sordid and painful annihilation, all stimulus to alleviate the ugliness of humanity.”

"}, {"id": "D", "text": "

“Listen to the song of this hardworking and satisfied nation; listen to Walt Whitman. The exercise of himself exalts him to majesty, tolerance exalts him to justice, and order to joy.”

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer because it most effectively illustrates the claim that Martí argues that a society’s spiritual well-being depends on the character of its literary culture. In the quotation, Martí asserts that poetry is “more necessary to a people than industry itself” and that it has the power to provide people with “faith and vigor.” He also adds that literature gives people “the desire and strength for life.” Therefore, this quotation shows that Martí believes that literature is a societal necessity because it uplifts people and nourishes their spiritual well-being.

Choice B is incorrect. Although this quotation emphasizes the importance of literature, it focuses on how the nature of a society is reflected in that society’s literature rather than on literature’s value for people’s spiritual well-being. Choice C is incorrect. Although this quotation involves an element of spirituality, it doesn’t discuss literature. The quotation instead focuses on humanity’s actions. Choice D is incorrect because this quotation mainly focuses on the importance of Walt Whitman rather than on the value of literature in general.

"}, {"id": "659c6c1d", "domain": "Information and Ideas", "skill": "Central Ideas and Details", "difficulty": "M", "type": "mc", "stimulus": "

The following text is adapted from Robert Louis Stevenson’s 1883 novel Treasure Island. Bill is a sailor staying at the Admiral Benbow, an inn run by the narrator’s parents.

\n

Every day when [Bill] came back from his stroll he would ask if any seafaring men had gone by along the road. At first we thought it was the want of company of his own kind that made him ask this question, but at last we began to see he was desirous to avoid them. When a seaman did [stay] at the Admiral Benbow (as now and then some did) he would look in at him through the curtained door before he entered the parlour; and he was always sure to be as silent as a mouse when any such was present.

", "stem": "

According to the text, why does Bill regularly ask about “seafaring men”?

", "choices": [{"id": "A", "text": "

He’s hoping to find an old friend and fellow sailor.

"}, {"id": "B", "text": "

He’s trying to secure a job as part of the crew on a new ship.

"}, {"id": "C", "text": "

He isn’t sure that other guests at the inn will be welcoming of sailors.

"}, {"id": "D", "text": "

He doesn’t want to encounter any other sailor unexpectedly.

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. The narrator says that, at first, they thought Bill asked regularly about other seafarers because he wanted their company, but eventually they realized that Bill actually wanted to avoid them.

Choice A is incorrect. This isn’t the reason the text gives for why Bill regularly asks about “seafaring men.” The narrator says that, at first, they thought Bill asked regularly about other seafarers because he wanted their company, but eventually they realized that Bill wanted to avoid them. Choice B is incorrect. This isn’t the reason the text gives for why Bill regularly asks about “seafaring men.” The narrator says that, at first, they thought Bill asked regularly about other seafarers because he wanted their company, but eventually they realized that Bill wanted to avoid them. Choice C is incorrect. This isn’t the reason the text gives for why Bill regularly asks about “seafaring men.” The narrator says that, at first, they thought Bill asked regularly about other seafarers because he wanted their company, but eventually they realized that Bill wanted to avoid them.

"}, {"id": "db2da2bf", "domain": "Information and Ideas", "skill": "Central Ideas and Details", "difficulty": "H", "type": "mc", "stimulus": "

In 2019, 20 previously unknown moons were confirmed to be orbiting Saturn. Three of the moons have prograde orbits (orbiting in the direction the planet spins), and the other 17 have retrograde orbits (orbiting in the opposite direction of the planet’s spin). All but one of the 20 moons are thought to be remnants of bodies that orbited Saturn until they broke apart in collisions. Although the one exceptional moon orbits in the same direction as the planet’s spin, its orbit is highly eccentric compared to the rest, which may suggest that it has a different origin than the other 19 moons.

", "stem": "

Based on the text, which choice best describes the moon with the eccentric orbit?

", "choices": [{"id": "A", "text": "

It doesn’t have a retrograde orbit, but it likely has the same origin as the moons with retrograde orbits.

"}, {"id": "B", "text": "

Its orbit is so tilted with respect to the other moons’ orbits that it’s neither prograde nor retrograde.

"}, {"id": "C", "text": "

It has a prograde orbit that is likely the result of having collided with another body orbiting Saturn. 

"}, {"id": "D", "text": "

It has a prograde orbit and may not be a remnant of an earlier body that orbited Saturn.

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer because it most accurately describes the moon with the eccentric orbit. The text indicates that three of the 20 newly discovered moons have prograde orbits, meaning that they orbit Saturn in the same direction as the planet’s spin, while the other 17 moons have retrograde orbits, meaning that they orbit Saturn in the opposite direction of the planet’s spin. The text then states that 19 of the 20 moons appear to be the remains of earlier bodies that orbited Saturn but were broken apart in collisions. The one exception is a moon that orbits Saturn in the same direction as the planet’s spin, meaning that the exceptional moon’s orbit is prograde. The text goes on to state that the exceptional moon’s orbit is so eccentric that the moon may have formed through a different process than the other 19 moons. The moon with the eccentric orbit, therefore, has a prograde orbit and may not be a remnant of an earlier body that orbited Saturn.

Choice A is incorrect because nothing in the text supports the idea that the moon with the eccentric orbit likely has the same origin as the moons with retrograde orbits. Although it’s true that the moon has a prograde orbit (and thus doesn’t have a retrograde orbit), the only information the text provides about the moon’s origin is that it may be different than the origin of the other 19 moons. Choice B is incorrect because the text states that the moon in question orbits Saturn in the same direction as the planet’s spin, meaning that the moon’s orbit is prograde, not that its orbit is neither prograde nor retrograde. Choice C is incorrect because the text merely notes that the moon in question has a prograde orbit without giving any indication of what likely caused that orbit.

"}, {"id": "39de2206", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "M", "type": "mc", "stimulus": "

The Post Office is a 1912 play by Rabindranath Tagore, originally written in Bengali. The character Amal is a young boy who imagines that the people he sees passing the window of his home are carefree even when engaged in work or chores, as is evident when he says to the daughter of a flower seller, ______blank

", "stem": "

Which quotation from The Post Office most effectively illustrates the claim?

", "choices": [{"id": "A", "text": "

“I see, you don’t wish to stop; I don’t care to stay on here either.”

"}, {"id": "B", "text": "

“Oh, flower gathering? That is why your feet seem so glad and your anklets jingle so merrily as you walk.”

"}, {"id": "C", "text": "

“I’ll pay when I grow up—before I leave to look for work out on the other side of that stream there.”

"}, {"id": "D", "text": "

“Wish I could be out too. Then I would pick some flowers for you from the very topmost branches right out of sight.”

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer because it most effectively illustrates the claim that Amal imagines the people he sees are carefree even when engaged in work. In the quotation, Amal observes that the flower seller’s daughter is “flower gathering,” or working, as the text indicates. Moreover, Amal notes that the daughter’s feet “seem so glad” and her “anklets jingle so merrily,” suggesting that Amal believes that the flower seller’s daughter is cheerful.

Choice A is incorrect because the quotation makes no observation about the cheerful mood of the flower seller’s daughter. Choice C is incorrect because the quotation discusses how Amal envisions his future, not the feelings of the flower seller’s daughter. Choice D is incorrect because the quotation discusses Amal’s wishes, not the feelings of the flower seller’s daughter.

"}, {"id": "d5c2a4d4", "domain": "Information and Ideas", "skill": "Central Ideas and Details", "difficulty": "M", "type": "mc", "stimulus": "

The following text is adapted from Guy de Maupassant’s nineteenth-century short story “The Trip of Le Horla” (translated by Albert M. C. McMaster, A. E. Henderson, Mme. Quesada, et al.). The narrator is part of a group traveling in a hot-air balloon at night.

\n
\n

The earth no longer seems to exist, it is buried in milky vapors that resemble a sea. We are now alone in space with the moon, which looks like another balloon travelling opposite us; and our balloon, which shines in the air, appears like another, larger moon, a world wandering in the sky amid the stars, through infinity. We no longer speak, think nor live; we float along through space in delicious inertia. The air which is bearing us up has made of us all beings which resemble itself, silent, joyous, irresponsible beings, peculiarly alert, although motionless.

\n
", "stem": "

Which choice best states the main idea of the text?

", "choices": [{"id": "A", "text": "

The narrator feels a growing sense of isolation even though his companions are nearby during the balloon ride.

"}, {"id": "B", "text": "

The narrator and his companions are completely absorbed in the change in perspective they gain while riding in the balloon.

"}, {"id": "C", "text": "

The narrator and his companions are troubled by the disorienting effects of the altitude while riding in the balloon.

"}, {"id": "D", "text": "

The narrator is pleasantly surprised by his companions’ unrestrained enthusiasm about the sensation of riding in the balloon.

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer because it most accurately states the main idea of the text. The narrator describes the view he and his companions have from the balloon: the earth lies beneath \"milky vapors,\" and the balloon itself looks like another moon. The narrator goes on to explain how the people riding in the balloon are affected by the ride, explaining that they are immersed in the experience: floating along in \"delicious inertia,\" or inactivity, like \"silent, joyous, irresponsible beings.\" Thus, the main idea is that the narrator and his companions are completely absorbed in the change in perspective they gain while riding in the balloon.

Choice A is incorrect because the narrator never describes himself as feeling isolated from his companions; instead, he characterizes riding in the balloon as an experience he is sharing with them. And although he does imply a sense of isolation, it is isolation from those on the ground, as when he says of himself and his companions, \"We are now alone.\" Choice C is incorrect because the narrator doesn’t suggest that he or his companions are troubled by the effects of the balloon ride. Instead, he describes himself and his companions as \"joyous\" and the experience of floating in the balloon as \"delicious.\" Choice D is incorrect because nothing in the text suggests that the narrator is surprised by his companions’ response to the balloon ride. In fact, the text indicates that the narrator and his companions are having the same experience: they’re described as \"silent\" and \"motionless,\" rather than as having unrestrained enthusiasm.

"}, {"id": "cf7491c1", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "M", "type": "mc", "stimulus": "

Characteristics of Five Recently Discovered Gas Exoplanets

Exoplanet designationMass (Jupiters)Radius (Jupiters)Orbital period (days)Distance from the Sun (parsecs)
TOI-640 b0.881.7715.003340
TOI-1601 b0.991.2395.331336
TOI-628 b6.331.0603.409178
TOI-1478 b0.851.06010.180153
TOI-1333 b2.371.3964.720200

\n

“Hot Jupiters” are gas planets that have a mass of at least 0.25 Jupiters (meaning that their mass is at least 25% of that of Jupiter) and an orbital period of less than 10 days (meaning that they complete one orbit around their star in less than 10 days), while “warm Jupiters” are gas planets that meet the same mass criterion but have orbital periods of more than 10 days. In 2021, Michigan State University astronomer Joseph Rodriguez and colleagues announced the discovery of five new gas exoplanets and asserted that four are hot Jupiters and one is a warm Jupiter.

", "stem": "

Which choice best describes data from the table that support Rodriguez and colleagues’ assertion?

", "choices": [{"id": "A", "text": "

None of the planets have an orbital period of more than 10 days, and TOI-628 b has a mass of 6.33 Jupiters. 

"}, {"id": "B", "text": "

TOI-1478 b has an orbital period of 153 days, and the masses of all the planets range from 0.85 to 6.33 Jupiters. 

"}, {"id": "C", "text": "

All the planets have a radius between 1.060 and 1.771 Jupiters, and only TOI-1333 b has an orbital period of more than 10 days. 

"}, {"id": "D", "text": "

Each of the planets has a mass greater than 0.25 Jupiters, and all except for TOI-1478 b have an orbital period of less than 10 days.

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer because it accurately describes data from the table that support Rodriguez and colleagues’ assertion about the classifications of the five new gas exoplanets. The text describes two categories of gas planets: hot Jupiters, which have a mass of at least 0.25 Jupiters and an orbital period of less than 10 days, and warm Jupiters, which have the same mass characteristic but have orbital periods of more than 10 days. According to the table, four of the gas exoplanets discovered by Rodriguez and colleagues have a mass of at least 0.25 Jupiters and an orbital period of less than 10 days, while one of the planets has a mass of at least 0.25 Jupiters and an orbital period of more than 10 days. These data therefore support Rodriguez and colleagues’ assertion that four of the new exoplanets are hot Jupiters and one is a warm Jupiter.

Choice A is incorrect because it doesn’t accurately describe the data from the table. Although the table shows that TOI-628 b has a mass equivalent to 6.33 Jupiters, the table also shows that one of the planets—TOI-1478 b—does indeed have an orbital period of more than 10 days. Choice B is incorrect because it doesn’t accurately describe the data from the table. Although the table does show that the masses of the five planets range from 0.85 to 6.33 Jupiters, the table also shows that TOI-1478 b has an orbital period of 10.180 days, not 153 days. Choice C is incorrect. According to the table, TOI-1333 b has an orbital period of only 4.720 days, not more than 10 days. Additionally, although the table does show that all the planets have a radius between 1.060 and 1.771 Jupiters, the text indicates that a planet may be classified as a hot Jupiter or a warm Jupiter based on its mass and orbital period, not on its radius, making the information about the range of the five planets’ radius values irrelevant.

"}, {"id": "df37c087", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "H", "type": "mc", "stimulus": "
\n\n\n\n\n550500450400350300250200150100500Weight (grams)RobotWeight of Three Aerial Robots Ultra-Fast Robot Hand Permanent Magnet Hand Yale Model T
\n

Aerial robots vary considerably in their holding force; the Ultra-Fast Robot Hand, for example, has a holding force of 56 newtons, more than twice that of the Permanent Magnet Hand and more than four times that of the Yale Model T. Since an aerial robot must lift its own weight along with its cargo, engineer Jiawei Meng and colleagues used a ratio of each robot\u2019s holding force to the robot\u2019s weight to calculate payload capacity, with higher ratios corresponding to greater capacity, concluding that the Ultra-Fast Robot Hand has a higher payload capacity than the Yale Model T.

", "stem": "

Which choice best describes data in the graph that support Meng and colleagues’ conclusion?

", "choices": [{"id": "A", "text": "

The Ultra-Fast Robot Hand and the Yale Model T each weigh more than 450 grams.

"}, {"id": "B", "text": "

The Ultra-Fast Robot Hand and the Yale Model T each weigh more than the Permanent Magnet Hand does.

"}, {"id": "C", "text": "

The Yale Model T has a lower holding force than the Permanent Magnet Hand despite weighing more.

"}, {"id": "D", "text": "

The Ultra-Fast Robot Hand weighs only slightly more than the Yale Model T does.

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer because it describes data in the graph that support Meng and colleagues’ conclusion that the Ultra-Fast Robot Hand has a higher payload capacity than the Yale Model T. According to the text, payload capacity is calculated by using a ratio of a robot’s holding force to the robot’s weight, and higher ratios indicate a greater payload capacity. The Ultra-Fast Robot Hand has a holding force of 56 newtons, four times greater than that of the Yale Model T. Additionally, the graph shows that the Ultra-Fast Robot Hand has a weight of approximately 500 grams, slightly more than the Yale Model T’s weight of approximately 480 grams. Therefore, the Ultra-Fast Robot Hand has a higher ratio of holding force to weight than the Yale Model T. Since higher ratios correspond to greater payload capacity, the information from the graph indicating that the Ultra-Fast Robot Hand weighs only slightly more than the Yale Model T combined with the information in the text ultimately supports the conclusion that the Ultra-Fast Robot Hand has a higher payload capacity than the Yale Model T.

Choice A is incorrect. Although, according to the graph, it’s true that both the Ultra-Fast Robot Hand and the Yale Model T weigh more than 450 grams, this statement doesn’t support Meng and colleagues’ conclusion that the Ultra-Fast Robot Hand has a higher payload capacity than the Yale Model T. This statement emphasizes a similarity, not a distinction, between the two robots. Choice B is incorrect. Although, according to the graph, it’s true that the Ultra-Fast Robot Hand and the Yale Model T both weigh more than the Permanent Magnet Hand does, this statement doesn’t support Meng and colleagues’ conclusion that the Ultra-Fast Robot Hand has a higher payload capacity than the Yale Model T. This statement emphasizes a similarity, not a distinction, between the Ultra-Fast Robot Hand and the Yale Model T. Furthermore, the comparison to the Permanent Magnet Hand is irrelevant to the claim about the relative ratios and payload capacities of the Ultra-Fast Robot Hand and the Yale Model T. Choice C is incorrect. Although the text states that the Yale Model T has a lower holding force than the Permanent Magnet Hand, the graph provides no information about holding force. Moreover,  information about the Permanent Magnet Hand is irrelevant to the conclusion by Meng and colleagues, which only concerns the Ultra-Fast Robot Hand and the Yale Model T.

"}, {"id": "5d6ab069", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "M", "type": "mc", "stimulus": "

Jan Gimsa, Robert Sleigh, and Ulrike Gimsa have hypothesized that the sail-like structure running down the back of the dinosaur Spinosaurus aegyptiacus improved the animal’s success in underwater pursuits of prey species capable of making quick, evasive movements. To evaluate their hypothesis, a second team of researchers constructed two battery-powered mechanical models of S. aegyptiacus, one with a sail and one without, and subjected the models to a series of identical tests in a water-filled tank.

", "stem": "

Which finding from the model tests, if true, would most strongly support Gimsa and colleagues’ hypothesis?

", "choices": [{"id": "A", "text": "

The model with a sail took significantly less time to complete a sharp turn while submerged than the model without a sail did.

"}, {"id": "B", "text": "

The model with a sail displaced significantly more water while submerged than the model without a sail did.

"}, {"id": "C", "text": "

The model with a sail had significantly less battery power remaining after completing the tests than the model without a sail did. 

"}, {"id": "D", "text": "

The model with a sail took significantly longer to travel a specified distance while submerged than the model without a sail did.

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. This finding would most strongly support the hypothesis. The hypothesis is that the sail improved the dinosaur’s ability to chase quick, evasive prey. This finding suggests that the sail helped the dinosaur make sharp turns more quickly, which supports that hypothesis. 

Choice B is incorrect. This finding wouldn’t necessarily support the hypothesis. The hypothesis is that the sail improved the dinosaur’s ability to chase quick, evasive prey. It’s unclear how the sail displacing more water would relate to that hypothesis—it doesn’t seem to be relevant. Choice C is incorrect. This finding wouldn’t necessarily support the hypothesis. The hypothesis is that the sail improved the dinosaur’s ability to chase quick, evasive prey. It’s unclear how the difference in battery power between the models would relate to that hypothesis—it doesn’t seem to be relevant. Choice D is incorrect. This finding would actually weaken the hypothesis. The hypothesis is that the sail improved the dinosaur’s ability to chase quick, evasive prey. This finding suggests that the sail slowed the dinosaur down—which would probably make it worse at catching quick, evasive prey. 

"}, {"id": "6675c5c3", "domain": "Information and Ideas", "skill": "Central Ideas and Details", "difficulty": "E", "type": "mc", "stimulus": "

The following text is from Shyam Selvadurai’s 1994 novel Funny Boy. The seven-year-old narrator lives with his family in Sri Lanka. Radha Aunty is the narrator’s aunt.

\n

Radha Aunty, who was the youngest in my father’s family, had left for America four years ago when I was three, and I could not remember what she looked like. I went into the corridor to look at the family photographs that were hung there. But all the pictures were old ones, taken when Radha Aunty was a baby or young girl. Try as I might, I couldn’t get an idea of what she looked like now. My imagination, however, was quick to fill in this void.

\n

©1994 by Shyam Selvadurai. 

", "stem": "

According to the text, why does the narrator consult some family photographs?

", "choices": [{"id": "A", "text": "

He wants to use the photographs as inspiration for a story he is writing. 

"}, {"id": "B", "text": "

He is curious about how his father dressed a long time ago. 

"}, {"id": "C", "text": "

He hopes the photographs will help him recall what his aunt looked like.  

"}, {"id": "D", "text": "

He wants to remind his aunt of an event that is shown in an old photograph. 

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. The text states that the narrator couldn’t remember what his Radha Aunty looked like, so he went to look at the family photographs she was in.

Choice A is incorrect. There’s no mention of any story that the narrator is writing. Rather, we’re told that the narrator couldn’t remember what his aunt looked like, so he went to look at the family photographs she was in. Choice B is incorrect. The text doesn’t mention how the narrator’s father dressed. Rather, we’re told that the narrator couldn’t remember what his aunt looked like, so he went to look at the family photographs she was in. Choice D is incorrect. The text doesn’t mention any events shown in the photographs. Rather, we’re told that the narrator couldn’t remember what his aunt looked like, so he went to look at the family photographs she was in.

"}, {"id": "0dccbf17", "domain": "Information and Ideas", "skill": "Inferences", "difficulty": "H", "type": "mc", "stimulus": "

Henry Ossawa Tanner’s 1893 painting The Banjo Lesson, which depicts an elderly man teaching a boy to play the banjo, is regarded as a landmark in the history of works by Black artists in the United States. Scholars should be cautious when ascribing political or ideological values to the painting, however: beliefs and assumptions that are commonly held now may have been unfamiliar to Tanner and his contemporaries, and vice versa. Scholars who forget this fact when discussing The Banjo Lesson therefore ______blank

", "stem": "

Which choice most logically completes the text?

", "choices": [{"id": "A", "text": "

risk judging Tanner’s painting by standards that may not be historically appropriate.

"}, {"id": "B", "text": "

tend to conflate Tanner’s political views with those of his contemporaries. 

"}, {"id": "C", "text": "

forgo analyzing Tanner’s painting in favor of analyzing his political activity.

"}, {"id": "D", "text": "

wrongly assume that Tanner’s painting was intended as a critique of his fellow artists. 

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. It most logically completes the text. The text argues that Tanner and his contemporaries may have been unfamiliar with modern beliefs and values. This suggests that scholars who attribute those modern values to Tanner’s painting are risking judging the painting by standards that are not historically accurate.  

Choice B is incorrect. It doesn’t logically complete the text. The text argues that Tanner AND his contemporaries may have been unfamiliar with modern views. It never suggests that Tanner’s views were different from his contemporaries’ views.  Choice C is incorrect. It doesn’t logically complete the text. The text never suggests that scholars should analyze Tanner’s political activity instead of his painting. Rather, the text argues that Tanner and his contemporaries may have been unfamiliar with modern beliefs and values. Choice D is incorrect. It doesn’t logically complete the text. The text never suggests that Tanner wanted to critique his contemporaries with his painting. Rather, the text argues that Tanner AND his contemporaries may have been unfamiliar with modern beliefs and values. 

"}, {"id": "37e15265", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "H", "type": "mc", "stimulus": "

“The Young Girl” is a 1920 short story by Katherine Mansfield. In the story, the narrator takes an unnamed seventeen-year-old girl and her younger brother out for a meal. In describing the teenager, Mansfield frequently contrasts the character’s pleasant appearance with her unpleasant attitude, as when Mansfield writes of the teenager, ______blank

", "stem": "

Which quotation from “The Young Girl” most effectively illustrates the claim?

", "choices": [{"id": "A", "text": "

“I heard her murmur, ‘I can’t bear flowers on a table.’ They had evidently been giving her intense pain, for she positively closed her eyes as I moved them away.”

"}, {"id": "B", "text": "

“While we waited she took out a little, gold powder-box with a mirror in the lid, shook the poor little puff as though she loathed it, and dabbed her lovely nose.”

"}, {"id": "C", "text": "

“I saw, after that, she couldn’t stand this place a moment longer, and, indeed, she jumped up and turned away while I went through the vulgar act of paying for the tea.”

"}, {"id": "D", "text": "

“She didn’t even take her gloves off. She lowered her eyes and drummed on the table. When a faint violin sounded she winced and bit her lip again. Silence.”

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer because it most effectively illustrates the claim in the text that in describing the teenaged girl, Mansfield contrasts the character’s pleasant appearance with her unpleasant attitude. In the quotation, Mansfield describes the teenager as having a “lovely nose” (a compliment about her appearance) but also as treating her makeup puff “as though she loathed it” (a judgment suggesting her unpleasant attitude).

Choice A is incorrect because the teenager′s reaction to the flowers doesn’t make it clear that she has an unpleasant attitude, and nothing in the quotation indicates that any part of her appearance is pleasant. Choice C is incorrect because the quotation suggests that the teenager has an unpleasant attitude (being upset with the location and leaving the table before the narrator has paid for the meal) but doesn’t give any indication that she has a pleasant appearance. Choice D is incorrect because the quotation suggests that the teenager may have an unpleasant attitude (lowering her eyes, wincing, and sitting in silence) but doesn’t give any indication that any part of her appearance is pleasant.

"}, {"id": "f9c4bdab", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "H", "type": "mc", "stimulus": "

A student is writing a paper about One Night in Miami..., a 2020 film directed by Regina King and written by Kemp Powers. Powers adapted the film’s screenplay from his 2013 play, which he wrote after learning about a 1964 meeting that took place in Miami, Florida, between four prominent figures of the Civil Rights movement: Malcolm X, Muhammad Ali, Jim Brown, and Sam Cooke. The student claims that although Powers was inspired by this meeting, the film is best understood not as a precise retelling of historical events but rather as a largely imagined but informed representation of them.

", "stem": "

Which quotation from an article about One Night in Miami... would be the most effective evidence for the student to include in support of this claim?

", "choices": [{"id": "A", "text": "

“When Powers learned of the meeting, he initially planned to write a much longer work about its four famous participants rather than focusing on the meeting itself.”

"}, {"id": "B", "text": "

“One Night in Miami... received numerous awards and nominations, including an Academy Award nomination for Powers for Best Adapted Screenplay.”

"}, {"id": "C", "text": "

“Powers has described One Night in Miami... as the story of four friends encouraging and supporting one another while engaged in a crucial political debate about how best to achieve equality for Black people in the United States.”

"}, {"id": "D", "text": "

“Powers could find only the most superficial historical details about the meeting, so he read extensively about the four individuals and their thinking at the time in an effort to portray what might have happened between them.”

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer because it provides a quotation that effectively supports the student’s claim about the film One Night in Miami…. The quotation states that in researching the play on which the film was based, Kemp Powers only found superficial details about what actually happened during the 1964 meeting in Miami between four leading Civil Rights leaders, meaning that there is very little information about the meeting in the historical record. In the absence of greater details, it wouldn’t have been possible for the film to be a precise retelling of the historical events it depicts. The quotation explains that to compensate for this lack of information about the meeting, Powers did extensive research into the four figures and how they thought at the time in order to speculate in an informed way about what they might have said or what might have occurred between them. Therefore, the quotation effectively supports the claim that the film is best understood not as a precise retelling of a historical event but as a deeply informed imaginative rendering of that event. 

Choice A is incorrect. Although the quotation discusses how on learning about the 1964 meeting in Miami, Powers was inspired to write a play and, later, to adapt it into a screenplay, it doesn’t discuss Powers’s approach to representing what had occurred in the meeting. Instead, it states that Powers didn’t initially plan to write a story only “focusing on the meeting itself” but rather had considered writing a “much longer” and more expansive work about the meeting’s four participants. Choice B is incorrect because the quotation doesn’t discuss Powers’s approach to representing historical events in his play and in the film; instead, the quotation focuses on the film’s positive critical reception by mentioning that it received numerous awards and nominations. Choice C is incorrect. Although the quotation references historical events that are discussed directly in the play and film by explaining how the four historical figures featured in the story engage in political debates about contemporary issues, it doesn’t specify to what extent Powers’s representation of what occurred during the 1964 meeting in Miami is a factual retelling of what happened and how much is an imaginative rendering of what might have happened. Rather, the quotation focuses on Powers’s description of the film’s basic premise and how the characters engage with the historical context of its setting.

"}, {"id": "25893fc7", "domain": "Information and Ideas", "skill": "Inferences", "difficulty": "E", "type": "mc", "stimulus": "

In many cultures, a handshake can create trust between people. Engineer João Avelino and his team are designing a robot to shake hands with a human in order to improve human-robot interactions. The robot hand adjusts its movements and pressure to better imitate the feel of a human hand. The researchers want the robot’s handshake to feel realistic because ______blank

", "stem": "

Which choice most logically completes the text?

", "choices": [{"id": "A", "text": "

lifelike handshakes may make people more comfortable interacting with robots.

"}, {"id": "B", "text": "

it’s easier to program a robot to perform handshakes than it is to program a robot to perform some other types of greetings.

"}, {"id": "C", "text": "

people are less likely to interact with robots that don’t look like humans.

"}, {"id": "D", "text": "

the robot in the researchers’ study may have uses other than interacting with humans.

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. The text says that handshakes create trust, and that the engineers’ goal is to “improve human-robot interactions.” This suggests that they want the robot’s handshake to feel real because they want humans to trust the robot.

Choice B is incorrect. This inference isn’t supported. The text never discusses any other types of greetings, so there is no basis to make this inference. Choice C is incorrect. This inference isn’t supported. The text never discusses the appearance of this robot or any other robots, so there is no basis to make this inference. Choice D is incorrect. This inference isn’t supported. The text never discusses any uses for the robot other than interacting with humans, so there is no basis to make this inference.

"}, {"id": "2df730d0", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "M", "type": "mc", "stimulus": "

\n\n\n\n\n\n\n\n\n\n\n\n\n9080706050403020100Percent of newly installedturbines20112012201320142015201620172018201920202021Rotor Diameters of Newly Installed Wind Turbines in the United States, 2011\u20132021Year >130 meters <100 meters 100\u2013115 meters 115\u2013130 meters

\n

All other things being equal, the larger a wind turbine\u2019s rotor diameter (the diameter of the imaginary circle swept by the turbine\u2019s rotating blades), the greater amount of energy the turbine can generate. In a research paper on wind power, a student claims that in the United States, the amount of energy generated per newly installed turbine increased substantially between 2011 and 2021.

", "stem": "

Which choice best describes data in the graph that support the student’s claim? 

", "choices": [{"id": "A", "text": "

The percentage of newly installed turbines with rotor diameters greater than 130 meters increased every year between 2011 and 2021. 

"}, {"id": "B", "text": "

In 2011, nearly 80% of turbines installed had rotor diameters of less than 100 meters, whereas only a little more than 20% of turbines installed that year had rotor diameters of 100–115 meters. 

"}, {"id": "C", "text": "

No turbines installed in 2011 had rotor diameters greater than 115 meters, whereas the majority of turbines installed in 2021 had rotor diameters greater than 130 meters.

"}, {"id": "D", "text": "

Most turbines installed in 2011 had rotor diameters of less than 100 meters, whereas most turbines installed in 2021 had rotor diameters of at least 115 meters. 

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. The text tells us that turbines with larger rotor diameters produce more energy, so if rotor diameters have generally gotten larger between 2011 and 2021, then turbines created in 2021 should produce more energy than those created in 2011.

Choice A is incorrect. This choice misreads the graph. The percentage of newly installed turbines with rotor diameters greater than 130 meters didn’t show any visible increase until 2018. Choice B is incorrect. This choice doesn’t justify the claim. The claim is about increasing energy output from 2011 to 2021, but this choice only discusses 2011, so it can’t show evidence of change over time. Choice C is incorrect. This choice misreads the graph. In 2021, only about 25% of turbines installed in 2021 had rotor diameters greater than 130 meters.

"}, {"id": "5632ffb4", "domain": "Information and Ideas", "skill": "Inferences", "difficulty": "H", "type": "mc", "stimulus": "

In a study of the cognitive abilities of white-faced capuchin monkeys (Cebus imitator), researchers neglected to control for the physical difficulty of the tasks they used to evaluate the monkeys. The cognitive abilities of monkeys given problems requiring little dexterity, such as sliding a panel to retrieve food, were judged by the same criteria as were those of monkeys given physically demanding problems, such as unscrewing a bottle and inserting a straw. The results of the study, therefore, ______blank

", "stem": "

Which choice most logically completes the text?

", "choices": [{"id": "A", "text": "

could suggest that there are differences in cognitive ability among the monkeys even though such differences may not actually exist.

"}, {"id": "B", "text": "

are useful for identifying tasks that the monkeys lack the cognitive capacity to perform but not for identifying tasks that the monkeys can perform. 

"}, {"id": "C", "text": "

should not be taken as indicative of the cognitive abilities of any monkey species other than C. imitator.

"}, {"id": "D", "text": "

reveal more about the monkeys’ cognitive abilities when solving artificial problems than when solving problems encountered in the wild.

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer because it presents the conclusion that most logically follows from the text’s discussion of the study of capuchin monkeys’ cognitive abilities. The text explains that the study failed to distinguish between outcomes for the tasks performed by the capuchin monkeys, such that simpler tasks requiring less dexterity, or skill, were judged by the same criteria as tasks that demanded more dexterity. Because the study didn’t account for this discrepancy, the researchers might have assumed that observed differences in performance were due to the abilities of the monkeys rather than the complexity of the tasks. In other words, the results may suggest cognitive differences among the monkeys even though such differences may not really exist.

Choice B is incorrect because the text focuses on the fact that the tasks assigned to the capuchin monkeys in the study varied in difficulty and that the variety wasn’t taken into consideration. The text doesn’t suggest that the capuchin monkeys couldn’t perform certain tasks, just that some tasks were more difficult to do. Choice C is incorrect because the text doesn’t suggest that the study’s results are indicative of the abilities of capuchin monkeys but not of other monkey species; in fact, the text suggests that the results may not even be an accurate reflection of capuchin monkeys’ abilities. Choice D is incorrect because the text doesn’t indicate that the researchers compared results for artificial tasks with those for tasks encountered in the wild, although the tasks described in the text—sliding a panel and putting a straw in a bottle—are presumably artificial.

"}, {"id": "5d453dcc", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "M", "type": "mc", "stimulus": "
\n\n\n\n\n1009080706050403020100Probability of voting (%)1234567Voters\u2019 Political Orientation, Level of Political Information, and Probability of VotingVoters\u2019 political orientation (1 = strong Democrat/liberal; 4 = independent; 7 = strong Republican/conservative) low information high information
\n

Economists Kerwin Kofi Charles and Melvin Stephens Jr. investigated a variety of factors that influence voter turnout in the United States. Using survey data that revealed whether respondents voted in national elections and how knowledgeable respondents are about politics, Charles and Stephens claim that the likelihood of voting is driven in part by potential voters\u2019 confidence in their assessments of candidates\u2014essentially, the more informed voters are about politics, the more confident they are at evaluating whether candidates share their views, and thus the more likely they are to vote.

", "stem": "

Which choice best describes data in the graph that support Charles and Stephens’s claim?

", "choices": [{"id": "A", "text": "

At each point on the political orientation scale, high-information voters were more likely than low-information voters to vote. 

"}, {"id": "B", "text": "

Only low-information voters who identify as independents had a voting probability below 50%. 

"}, {"id": "C", "text": "

The closer that low-information voters are to the ends of the political orientation scale, the more likely they were to vote. 

"}, {"id": "D", "text": "

High-information voters were more likely to identify as strong Democrats or strong Republicans than low-information voters were.

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer because it uses data from the graph to effectively support Charles and Stephens’s claim about how level of information affects voters. The graph shows the probability of voting for both high- and low-information voters in seven categories of political orientation. Charles and Stephens claim that “the more informed voters are about politics…the more likely they are to vote.” This statement correctly asserts that the graph shows a higher probability of voting for high-information voters than for low-information voters at each of the seven political orientations. Thus, this statement accurately cites data from the graph that support Charles and Stephens’s claim about how level of information affects voters.

Choice B is incorrect. Although this statement is correct that the only probability in the graph below 50% is for low-information voters categorized as independent (orientation 4), the claim in question is about the relative likelihood that low- and high-information voters will vote, and without some reference to high-information voters, this statement cannot help support such a comparison. Choice C is incorrect. Although this statement is correct that the highest probabilities of voting for low-information voters are at the ends of the orientation scale (1 and 7), the claim in question is about the relative likelihood that low- and high-information voters will vote, and without some reference to high-information voters, this statement cannot help support such a comparison. Choice D is incorrect because the graph does not give any information about how many people are represented in any of the categories, so this statement is not based on data from the graph. Furthermore, even if we did have this information, the claim is about how level of information affects voters’ probability of voting, not whether they’re likely to strongly identify with a particular political party.

"}, {"id": "b32c4b3a", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "H", "type": "mc", "stimulus": "

The Intertropical Convergence Zone (ITCZ), a band of clouds that encircles Earth in the tropics and is a major rainfall source, shifts position in response to temperature variations across Earth’s hemispheres. Data from Huagapo Cave in Peru suggest the ITCZ shifted south during the Little Ice Age (circa 1300–1850), but a shift as far into South America as Huagapo should have led to dry conditions in Central America, which is inconsistent with climate models. To resolve the issue, geologist Yemane Asmerom and colleagues collected data from Yok Balum Cave in Central America and compared them with the Huagapo data. They concluded that during the Little Ice Age, the ITCZ may have expanded northward and southward rather than simply shifted.

", "stem": "

Which finding from Asmerom and colleagues’ study, if true, would most directly support their conclusion? 

", "choices": [{"id": "A", "text": "

Neither the Yok Balum data nor the Huagapo data show significant local variations in temperature during the Little Ice Age. 

"}, {"id": "B", "text": "

Both the Yok Balum data and the Huagapo data show increased temperatures and prolonged dry conditions during the Little Ice Age. 

"}, {"id": "C", "text": "

The Yok Balum data show prolonged dry conditions during the same portions of the Little Ice Age in which the Huagapo data show heightened levels of rainfall. 

"}, {"id": "D", "text": "

The Yok Balum data and the Huagapo data show strongly correlated patterns of high rainfall during the Little Ice Age.

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer because it presents a finding that, if true, would support Asmerom and colleagues’ conclusion that the ITCZ may have expanded northward and southward rather than shifting south during the Little Ice Age. The text indicates that the ITCZ, a band of clouds in the tropics that is a significant rainfall source, can change position. Data from Peru’s Huagapo Cave suggest that the ITCZ shifted south during the Little Ice Age. But according to the text, if the ITCZ moved into South America in that way, then Central America should have been drier than climate models suggest it was. In other words, rainfall should have been reduced in Central America because the ITCZ, a significant rainfall source, had shifted into South America, but climate models do not show such a reduction in Central America. The text goes on to say that Asmerom and colleagues tried to resolve this apparent conflict by collecting data from Yok Balum cave in Central America and comparing them with data from Huagapo, which led the researchers to conclude that the ITCZ may have expanded both northward and southward rather than simply shifting south. If it is true that Yok Balum in Central America and Huagapo in South America show strongly correlated patterns of high rainfall during the Little Ice Age, such a finding would support Asmerom and colleagues’ conclusion by suggesting that the two areas were affected by the same rainfall source, and thus that the ITCZ may have expanded rather than shifted. 

Choice A is incorrect because there is no information in the text about how, if at all, the ITCZ affects temperature in areas where it is located. Rather, the text states that temperature variations across Earth’s hemispheres can shift the position of the ITCZ. Finding that neither Yok Balum nor Huagapo data show evidence of significant local variations in temperature during the Little Ice Age would have no clear bearing on Asmerom and colleagues’ claim. Choice B is incorrect because finding that both Yok Balum and Huagapo experienced prolonged dry conditions during the Little Ice Age would not support Asmerom and colleagues’ conclusion that the ITCZ, a major source of rainfall, may have expanded northward and southward rather than simply shifting south. Dry conditions in both locations would suggest that the ITCZ did not cover either location. Additionally, finding that temperatures were elevated in both locations would have no clear bearing on Asmerom and colleagues’ conclusion, since there is no information in the text that indicates how, if at all, the ITCZ affects temperature. Choice C is incorrect because finding that Yok Balum experienced prolonged dry conditions at the same time that Huagapo experienced high rainfall would weaken Asmerom and colleagues’ conclusion, not strengthen it. Such a finding would suggest that the ITCZ shifted south and left Central America dry rather than expanding both northward and southward. 

"}, {"id": "d102706f", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "H", "type": "mc", "stimulus": "

Estimates of Tyrannosaurid Bite Force

StudyYearEstimation methodApproximate bite force (newtons)
Cost et al.2019muscular and skeletal modeling35,000–63,000
Gignac and Erickson2017tooth-bone interaction analysis8,000–34,000
Meers2002body-mass scaling183,000–235,000
Bates and Falkingham2012muscular and skeletal modeling35,000–57,000

\n

The largest tyrannosaurids—the family of carnivorous dinosaurs that includes Tarbosaurus, Albertosaurus, and, most famously, Tyrannosaurus rex—are thought to have had the strongest bites of any land animals in Earth’s history. Determining the bite force of extinct animals can be difficult, however, and paleontologists Paul Barrett and Emily Rayfield have suggested that an estimate of dinosaur bite force may be significantly influenced by the methodology used in generating that estimate.

", "stem": "

Which choice best describes data from the table that support Barrett and Rayfield’s suggestion?

", "choices": [{"id": "A", "text": "

The study by Meers used body-mass scaling and produced the lowest estimated maximum bite force, while the study by Cost et al. used muscular and skeletal modeling and produced the highest estimated maximum.

"}, {"id": "B", "text": "

In their study, Gignac and Erickson used tooth-bone interaction analysis to produce an estimated bite force range with a minimum of 8,000 newtons and a maximum of 34,000 newtons.

"}, {"id": "C", "text": "

The bite force estimates produced by Bates and Falkingham and by Cost et al. were similar to each other, while the estimates produced by Meers and by Gignac and Erickson each differed substantially from any other estimate. 

"}, {"id": "D", "text": "

The estimated maximum bite force produced by Cost et al. exceeded the estimated maximum produced by Bates and Falkingham, even though both groups of researchers used the same method to generate their estimates.

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer because it accurately describes data from the table that support Barrett and Rayfield’s suggestion about bite force estimates. According to the text, Barrett and Rayfield believe that estimates of dinosaur bite force may be strongly influenced by the methods used to produce them—that is, that different methods may produce significantly different results. The table shows that the studies by Bates and Falkingham and by Cost et al. used the same estimation method (muscular and skeletal modeling) and produced similar bite force estimates (approximately 35,000–57,000 newtons and 35,000–63,000 newtons, respectively). The study by Meers, however, used body-mass scaling and produced a much higher bite force estimate (183,000–235,000 newtons), while the study by Gignac and Erickson used tooth-bone interaction analysis and produced a much lower bite force estimate (8,000–34,000 newtons). The fact that one method produced similar estimates in two different studies and that two different methods used in other studies produced substantially different estimates supports the idea that dinosaur bite force estimates are significantly influenced by the methodology used to produce them.

Choice A is incorrect because it inaccurately describes data from the table. The table does show that the studies by Meers and by Cost et al. used different estimation methods and produced very different ranges of estimated dinosaur bite force, which would support Barrett and Rayfield’s suggestion that different methodologies may produce significantly different estimates. However, the table doesn’t show that the study by Meers produced the lowest estimated maximum bite force while the study by Cost et al. produced the highest. In fact, the study by Meers estimated a maximum bite force of approximately 235,000 newtons, which is the highest of all the estimated maximums. Choice B is incorrect. Although the data from Gignac and Ericson’s study are accurately described, a single set of findings from one study using only one methodology can’t show that different methodologies may produce significantly different dinosaur bite force estimates, as Barrett and Rayfield suggest. Choice D is incorrect. Although the table shows that the maximum bite force estimated by Cost et al. was higher than that estimated by Bates and Falkingham, the difference is relatively small; in fact, both teams estimated a minimum bite force of approximately 35,000 newtons and a maximum bite force close to approximately 60,000 newtons. Because these findings demonstrate that a single methodology (muscular and skeletal modeling) produced similar overall results in two studies, the findings don’t support Barrett and Rayfield’s suggestion that different methodologies may produce significantly different dinosaur bite force estimates.

"}, {"id": "2ef8e367", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "M", "type": "mc", "stimulus": "

“To You” is an 1856 poem by Walt Whitman. In the poem, Whitman suggests that he deeply understands the reader, whom he addresses directly, writing, ______blank

", "stem": "

Which quotation from “To You” most effectively illustrates the claim?

", "choices": [{"id": "A", "text": "

“Your true soul and body appear before me.”

"}, {"id": "B", "text": "

“Whoever you are, now I place my hand upon you, that you be my poem.”

"}, {"id": "C", "text": "

“I should have made my way straight to you long ago.”

"}, {"id": "D", "text": "

“Whoever you are, I fear you are walking the walks of dreams.”

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer because it most directly illustrates the text’s claim about Whitman’s poem, “To You.” The text says that in this poem, Whitman suggests that he deeply understands the poem’s reader. This quotation says that the reader’s “true soul and body appear before” Whitman, thereby asserting that he can see the reader as the reader truly is, suggesting that he deeply understands the reader.

Choice B is incorrect because this quotation describes Whitman making the reader the subject of the poem (“you be my poem”), not Whitman deeply understanding the reader. Choice C is incorrect because instead of suggesting that Whitman deeply understands the reader, it emphasizes Whitman’s regret at not having addressed the reader sooner. Choice D is incorrect. Although this quotation shows Whitman directly addressing the reader and expressing concern about the reader, it doesn’t illustrate the idea that Whitman suggests that he deeply understands the reader. The quotation is simply expressing concern about the reader, which doesn’t necessarily imply deep understanding of the reader. 

"}, {"id": "1b9b29f1", "domain": "Information and Ideas", "skill": "Inferences", "difficulty": "H", "type": "mc", "stimulus": "

A team of biologists led by Jae-Hoon Jung, Antonio D. Barbosa, and Stephanie Hutin investigated the mechanism that allows Arabidopsis thaliana (thale cress) plants to accelerate flowering at high temperatures. They replaced the protein ELF3 in the plants with a similar protein found in another species (stiff brome) that, unlike A. thaliana, displays no acceleration in flowering with increased temperature. A comparison of unmodified A. thaliana plants with the altered plants showed no difference in flowering at 22° Celsius, but at 27° Celsius, the unmodified plants exhibited accelerated flowering while the altered ones did not, which suggests that ______blank

", "stem": "

Which choice most logically completes the text?

", "choices": [{"id": "A", "text": "

temperature-sensitive accelerated flowering is unique to A. thaliana.

"}, {"id": "B", "text": "

A. thaliana increases ELF3 production as temperatures rise.

"}, {"id": "C", "text": "

ELF3 enables A. thaliana to respond to increased temperatures.

"}, {"id": "D", "text": "

temperatures of at least 22° Celsius are required for A. thaliana to flower.

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer because it most logically completes the text’s discussion of accelerated flowering in A. thaliana plants. The text indicates that A. thaliana plants show accelerated flowering at high temperatures. To investigate the mechanism for this accelerated flowering, biologists replaced the ELF3 protein in one group of A. thaliana plants with a similar protein found in another plant species that doesn’t show accelerated flowering. The team then compared these modified plants to A. thaliana plants that retained their original ELF3 protein. The text states that the two samples of plants showed no difference in flowering at 22° Celsius, but at 27° Celsius the unaltered plants with ELF3 showed accelerated flowering while the plants without ELF3 didn’t. If accelerated flowering at the higher temperature occurred in the A. thaliana plants with ELF3 but not in the plants without the protein, then ELF3 likely enables A. thaliana to respond to increased temperatures.

Choice A is incorrect because the text doesn’t mention whether any plants other than A. thaliana and stiff brome show temperature-sensitive flowering, so there is no support for the idea that this type of flowering is unique to A. thaliana. Choice B is incorrect because the text discusses the effects of ELF3 and not the production of it. There’s nothing in the text to suggest that the amount of ELF3 in A. thaliana varies with temperature. Choice D is incorrect. While the text states that there was no difference in the flowering of modified and unmodified A. thaliana plants at 22° Celsius, there’s no suggestion that A. thaliana only begins to flower at 22° Celsius; the text doesn’t mention a specific temperature threshold required for A. thaliana flowering.

"}, {"id": "61228830", "domain": "Information and Ideas", "skill": "Inferences", "difficulty": "H", "type": "mc", "stimulus": "

A heliograph is a semaphore device used for sending optical communications—usually in the form of Morse code—by reflecting flashes of sunlight off a mirror. Heliographs were used for rapid communication across expansive distances for military, surveying, and forestry purposes during the late nineteenth and early twentieth centuries, but they were largely effective only during the daytime, and the range of the device depended on factors such as the opacity of the air and line of sight. Therefore, heliographs were eventually replaced by technology that ______blank

", "stem": "

Which choice most logically completes the text?

", "choices": [{"id": "A", "text": "

worked on similar principles but was easier to produce and maintain. 

"}, {"id": "B", "text": "

was not so constrained by environmental circumstances.

"}, {"id": "C", "text": "

could be used for more than military, surveying, or forestry purposes.

"}, {"id": "D", "text": "

enabled communication that didn’t require knowledge of Morse code.

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. The passage explains that heliographs “were largely effective only during the daytime” and that “the range of the device depended on factors such as the opacity of the air and line of sight.” These constraints would have greatly limited the use of the heliograph, so we can infer that this would have been a reason to replace it with new technology.

Choice A is incorrect. The passage doesn’t discuss the production and maintenance of heliographs, so there’s no basis for this inference. Choice C is incorrect. The passage doesn’t mention any “other purposes” that a heliograph wouldn’t work for, so there’s no basis for this inference. Choice D is incorrect. The passage doesn’t mention knowledge of Morse code as a particular problem with the use of heliographs, so there’s no basis for this inference.

"}, {"id": "ad680167", "domain": "Information and Ideas", "skill": "Central Ideas and Details", "difficulty": "M", "type": "mc", "stimulus": "

The recovery of a 1,000-year-old Chinese shipwreck in the Java Sea near present-day Indonesia has yielded a treasure trove of artifacts, including thousands of small ceramic bowls. Using a portable X-ray fluorescence analyzer tool, Lisa Niziolek and her team were able to detect the chemical composition of these bowls without damaging them. By comparing the chemical signatures of the bowls with those of the materials still at old Chinese kiln sites, Niziolek and her team can pinpoint which Chinese kilns likely produced the ceramic bowls.

", "stem": "

Which choice best states the main idea of the text?

", "choices": [{"id": "A", "text": "

Because of a new technology, researchers can locate and recover more shipwrecks than they could in the past.

"}, {"id": "B", "text": "

Researchers have been able to identify the location of a number of Chinese kilns in operation 1,000 years ago.

"}, {"id": "C", "text": "

With the help of a special tool, researchers have determined the likely origin of bowls recovered from a shipwreck.

"}, {"id": "D", "text": "

Before the invention of portable X-ray fluorescence, researchers needed to take a small piece out of an artifact to analyze its components.

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer because it most accurately states the main idea of the text. According to the text, thousands of ceramic bowls were found in a recovered Chinese shipwreck. The text goes on to say that Niziolek and her team used a special tool, a portable X-ray fluorescence analyzer, to determine the bowls’ chemical signatures. Comparing these chemical signatures with the chemical signatures of materials they had collected from old Chinese kiln sites, the text says, allowed the researchers to identify which kilns had produced the bowls. In other words, the researchers determined the bowls’ origin.

Choice A is incorrect. Although the text indicates that the researchers used technology in the form of a portable X-ray fluorescence analyzer, it doesn’t specifically state that this technology is new. In addition, the text says that Niziolek and her team used the tool to determine the chemical composition of bowls that were found in a Chinese shipwreck, not to locate and recover the shipwreck itself. There’s no indication in the text that a new technology can help researchers locate and recover shipwrecks. Choice B is incorrect because the text indicates that the researchers collected materials from old kiln sites for chemical comparison with the ceramic bowls, which means that the researchers must have already known the location of those kiln sites. Rather than identifying the location of the kilns, the researchers determined which kilns in operation 1,000 years ago had likely produced the bowls that were found in the shipwreck.\n Choice D is incorrect. Although the text says that using a portable X-ray fluorescence analyzer tool enabled Niziolek and her team to analyze artifacts in the form of ceramic bowls without damaging them, the text doesn’t discuss how researchers analyzed artifacts before this tool was invented. Moreover, the point that the bowls were left undamaged isn’t the text’s main idea. Rather, it’s a detail that’s provided to develop the main idea, which is that the researchers used a special tool to determine where the bowls had been produced.

"}, {"id": "af9e3240", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "H", "type": "mc", "stimulus": "

Electra is a circa 420–410 BCE play by Sophocles, translated in 1870 by R.C. Jebb. Electra, who is in mourning for her dead father and her long-absent brother, is aware of the intensity of her grief but believes it to be justified: ______blank

", "stem": "

Which quotation from Electra most effectively illustrates the claim?

", "choices": [{"id": "A", "text": "

“O thou pure sunlight, and thou air, earth’s canopy, how often have ye heard the strains of my lament, the wild blows dealt against this bleeding breast, when dark night fails!”

"}, {"id": "B", "text": "

“Send to me my brother; for I have no more the strength to bear up alone against the load of grief that weighs me down.”

"}, {"id": "C", "text": "

“I know my own passion, it escapes me not; but, seeing that the causes are so dire, will never curb these frenzied plaints, while life is in me.” 

"}, {"id": "D", "text": "

“But never will I cease from dirge and sore lament, while I look on the trembling rays of the bright stars, or on this light of day.”

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. Electra states that she “knows her own passion,” which shows that she’s aware of the intensity of her grief. But she also claims that the “causes are so dire”—meaning the reasons for her grief are so awful—that she can’t let it go, which shows that she believes her grief is justified.

Choice A is incorrect. This quotation doesn’t show that Electra believes her grief is justified. It shows that Electra is aware of its intensity, but it doesn’t suggest that she believes she has a legitimate reason for feeling that way. Choice B is incorrect. This quotation doesn’t show that Electra believes her grief is justified. It shows that Electra is aware of its intensity, but it doesn’t suggest that she believes she has a legitimate reason for feeling that way. Choice D is incorrect. This quotation doesn’t show that Electra believes her grief is justified. It shows that Electra is aware of the intensity of her grief, but it doesn’t suggest that she has a legitimate reason for feeling that way.

"}, {"id": "787729be", "domain": "Information and Ideas", "skill": "Inferences", "difficulty": "E", "type": "mc", "stimulus": "

Martin Dan\u010dák, Wewin Tjiasmanto, and colleagues have identified a new carnivorous plant species (Nepenthes pudica) in Indonesia. Like other carnivorous plants, N. pudica has pitfall traps, or pitchers, that capture prey, but unlike others, the pitchers of N. pudica are located underground. The researchers unearthed the new species on fairly dry ridges with surfaces that host few other plants and animals. Therefore, the researchers hypothesize that the N. pudica species likely ______blank

", "stem": "

Which choice most logically completes the text?

", "choices": [{"id": "A", "text": "

represents one of many undiscovered carnivorous plant species in the region.

"}, {"id": "B", "text": "

formed pitchers early in development to absorb more moisture.

"}, {"id": "C", "text": "

is buried by nearby animals as they forage along the ridges for food.

"}, {"id": "D", "text": "

evolved to have underground traps to access more prey than would surface traps.

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. The text says that N.pudica’s prey-catching pitchers are underground. It also says that the ridges where N. pudica lives don’t have many plants and animals on the surface. This suggests that N. pudica evolved underground pitchers in order to catch more prey.

Choice A is incorrect. This inference isn’t supported. The text never mentions the possibility of other undiscovered carnivorous plant species in Indonesia, so there’s no basis to make this inference. Choice B is incorrect. This inference isn’t supported. The text does say that the ridges where N. pudica lives are dry, but it also says that the purpose of carnivorous plant pitchers is to capture prey. It never suggests that these pitchers also absorb moisture, so there’s no basis to make this inference. Choice C is incorrect. This inference isn’t supported. The text never suggests that N. pudica’s underground pitcher can catch animals on the surface, so there’s no basis to make this inference.

"}, {"id": "e441da80", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "E", "type": "mc", "stimulus": "
\n\n\n\n\n\n\n\n\n\n\n\n\n1,7501,5001,2501,0007505002500Number of articles2010201120122013201420152016201720182019Investigative ArticlesPublished in the Albuquerque Journalfrom 2010 to 2019 Total
\n

Investigative journalists research and report about fraud, corruption, public hazards, and more. The graph shows the number of investigative articles published in the Albuquerque Journal newspaper from 2010 to 2019. According to an analyst, although the number of investigative articles published in this newspaper has varied significantly over the period shown,\u00a0the number overall has fallen since 2010.

", "stem": "

Which choice most effectively uses data from the graph to justify the underlined claim?

", "choices": [{"id": "A", "text": "

The newspaper published approximately 1,000 investigative articles in 2010 and approximately 500 in 2019.

"}, {"id": "B", "text": "

The smallest annual number of investigative articles published in the newspaper during the period shown is approximately 1,600 in 2013. 

"}, {"id": "C", "text": "

The greatest annual number of investigative articles published in the newspaper during the period shown is approximately 1,000 in 2017. 

"}, {"id": "D", "text": "

The newspaper published approximately 1,000 investigative articles in 2010 and approximately 1,600 in 2013.

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. By comparing the number of investigative articles in 2010 to the number in 2019, we can see that the number has fallen overall.

Choice B is incorrect. This choice misreads the graph. The 1,600 articles published in 2013 was the largest annual number of investigative articles published during the period. Also, notice that the claim focuses on an overall change, while this choice just focuses on one year. We can’t determine an overall increase or decrease by looking at just one year. Choice C is incorrect. The 1,000 articles published in 2017 wasn’t the largest number published during the period. Also, notice that the claim focuses on an overall change, while this choice just focuses on one year. We can’t determine an overall increase or decrease by looking at just one year. Choice D is incorrect. This choice doesn’t justify the claim. The claim is about a decrease in articles published between 2010 and 2019. This data shows an increase in articles published over a different period (2010-2013).

"}, {"id": "575e67df", "domain": "Information and Ideas", "skill": "Inferences", "difficulty": "M", "type": "mc", "stimulus": "

By running computer simulations of the development of our solar system, André Izidoro, Rajdeep Dasgupta, and colleagues concluded that the Sun may have been surrounded by three giant dust rings before the planets started to form. The researchers suggest that the materials in the innermost ring became the four planets closest to the Sun, the materials in the middle ring produced the rest of the planets, and the materials in the outermost ring created the asteroids and other small bodies in the region beyond Neptune. In one simulation, the researchers delayed the initial formation of the middle ring, causing oversized super-Earths to begin developing from the innermost ring. The researchers therefore hypothesize that ______blank

", "stem": "

Which choice most logically completes the text?

", "choices": [{"id": "A", "text": "

the middle ring formed earlier in the solar system’s development than the initial simulations suggested. 

"}, {"id": "B", "text": "

the timing of the initial formation of the middle ring played an important role in determining the eventual size of Earth.

"}, {"id": "C", "text": "

if the formation of the outermost ring had occurred earlier in a simulation, all the planets would have become super-Earths.

"}, {"id": "D", "text": "

the innermost ring actually formed into all the planets in our solar system, not just the four closest to the Sun.

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer because it most logically follows from the text’s discussion of André Izidoro, Rajdeep Dasgupta, and colleagues’ computer simulations of our solar system’s development. The text begins by stating that the simulations led the researchers to conclude that the solar system likely formed from three giant dust rings that encircled the Sun. The text explains that the four inner planets, including Earth, formed from the innermost ring and that the remaining planets formed from the middle ring. It then explains that in one simulation, the researchers delayed the formation of the middle ring—that is, they tested to see what would happen if the middle ring had formed later than it actually did. They found that doing so affected the size of the innermost planets, resulting in oversized super-Earths, planets that are much larger than Earth. Since the delayed timing had the effect of changing the size of Earth in the simulation relative to Earth’s real size, it’s reasonable to conclude that the timing of the middle ring’s formation was important in determining Earth’s eventual size. 

Choice A is incorrect. Although the text explains that when the researchers delayed the formation of the middle ring in one simulation, the size of the innermost planets was affected (which suggests that the middle ring likely formed earlier than it did in this simulation), the text doesn’t indicate that this was an initial simulation—that is, a simulation that was conducted before other simulations. Moreover, the text makes no reference to the specific results of any other simulations; therefore, there is no basis for comparing any conclusions based on the simulation in which the middle ring’s formation was delayed with conclusions based on other simulations. Choice C is incorrect because the text discusses how altering the timing of the formation of the middle ring, not the outermost ring, affected the four innermost planets’ eventual size in the researchers’ simulation; therefore, the simulation offers no basis for a conclusion about how the outermost ring’s formation affected the size of the planets. Choice D is incorrect because there is nothing in the text to suggest that the innermost ring produced all the solar system’s planets. Rather, the text states that the simulations showed that the innermost planets formed from the innermost ring and that the remaining planets formed from the middle ring.  

"}, {"id": "1d08c7ee", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "M", "type": "mc", "stimulus": "

Pulitzer Prize–winning writer Héctor Tobar has built a multifaceted career as both a journalist and an author of short stories and novels. In an essay about Tobar’s work, a student claims that Tobar blends his areas of expertise by applying journalism techniques to his creation of works of fiction.

", "stem": "

Which quotation from a literary critic best supports the student’s claim?

", "choices": [{"id": "A", "text": "

“For one novel, an imagined account of a real person’s global travels, Tobar approached his subject like a reporter, interviewing people the man had met along the way and researching the man’s own writings.”

"}, {"id": "B", "text": "

“Tobar got his start as a volunteer for El Tecolote, a community newspaper in San Francisco, and wrote for newspapers for years before earning a degree in creative writing and starting to publish works of fiction.”

"}, {"id": "C", "text": "

“Many of Tobar’s notable nonfiction articles are marked by the writer’s use of techniques usually associated with fiction, such as complex narrative structures and the incorporation of symbolism.”

"}, {"id": "D", "text": "

“The protagonist of Tobar’s third novel is a man who wants to be a novelist and keeps notes about interesting people he encounters so he can use them when developing characters for his stories.”

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. The example of Tobar approaching his subject “like a reporter,” including conducting “interviews” and “research,” shows Tobar applying journalism techniques to his fiction-writing.

Choice B is incorrect. This choice doesn’t support the claim. It tells us about Tobar’s initial career as a journalist, but it doesn’t say anything about him “applying journalism techniques” to his fiction-writing. Choice C is incorrect. This choice doesn’t support the claim. It tells us that Tobar applied fiction techniques to his nonfiction writing, but we’re looking for evidence of the other way around: that Tobar applied journalism techniques to his fiction-writing. Choice D is incorrect. This choice doesn’t support the claim. It tells us that a character in one of Tobar’s novels applied a journalism technique to his fiction-writing, but it doesn’t tell us that Tobar did that himself.

"}, {"id": "adbcbce0", "domain": "Information and Ideas", "skill": "Central Ideas and Details", "difficulty": "M", "type": "mc", "stimulus": "

The following text is adapted from Christina Rossetti’s 1881 poem “Monna Innominata 2.”

\n

I wish I could remember that first day,

\n

 First hour, first moment of your meeting me,

\n

 If bright or dim the season, it might be

\n

Summer or Winter for [all] I can say;

\n

So unrecorded did it slip away,

\n

 So blind was I to see and to foresee,

\n

 So dull to mark the budding of my tree

\n

That would not blossom yet for many a May.

", "stem": "

Which choice best states the main idea of the text?

", "choices": [{"id": "A", "text": "

The speaker celebrates how the passage of time has strengthened a relationship that once seemed unimportant. 

"}, {"id": "B", "text": "

Because the speaker did not anticipate how important a relationship would become, she cannot recall how the relationship began, which she regrets. 

"}, {"id": "C", "text": "

As the anniversary of the beginning of an important relationship approaches, the speaker feels conflicted about how best to commemorate it.

"}, {"id": "D", "text": "

After years of neglecting a once valuable relationship, the speaker worries it may be too late for her to salvage the relationship. 

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. The speaker says that they wish they could remember when they first met someone, but they can’t remember the meeting at all, because they didn’t know at the time that the relationship would \"blossom\" later on.

Choice A is incorrect. The speaker does say that the relationship has \"blossomed\" over time, but only briefly at the end—and they don’t really \"celebrate\" that fact. Rather, the text has a more regretful tone: it’s about how the speaker can’t remember first meeting this person, and they wish they could. Choice C is incorrect. The speaker doesn’t mention an anniversary—in fact, the speaker can’t remember when they met the person they’re talking about. Choice D is incorrect. The speaker doesn’t say that they neglected the relationship. In fact, the speaker suggests that the relationship has become very important to them—that’s why the speaker wishes that they could remember their first meeting.

"}, {"id": "6536183b", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "H", "type": "mc", "stimulus": "

In the mountains of Brazil, Barbacenia tomentosa and Barbacenia macrantha—two plants in the Velloziaceae family—establish themselves on soilless, nutrient-poor patches of quartzite rock. Plant ecologists Anna Abrahão and Patricia de Britto Costa used microscopic analysis to determine that the roots of B. tomentosa and B. macrantha, which grow directly into the quartzite, have clusters of fine hairs near the root tip; further analysis indicated that these hairs secrete both malic and citric acids. The researchers hypothesize that the plants depend on dissolving underlying rock with these acids, as the process not only creates channels for continued growth but also releases phosphates that provide the vital nutrient phosphorus.

", "stem": "

Which finding, if true, would most directly support the researchers’ hypothesis?

", "choices": [{"id": "A", "text": "

Other species in the Velloziaceae family are found in terrains with more soil but have root structures similar to those of B. tomentosa and B. macrantha.

"}, {"id": "B", "text": "

Though B. tomentosa and B. macrantha both secrete citric and malic acids, each species produces the acids in different proportions.

"}, {"id": "C", "text": "

The roots of B. tomentosa and B. macrantha carve new entry points into rocks even when cracks in the surface are readily available.

"}, {"id": "D", "text": "

B. tomentosa and B. macrantha thrive even when transferred to the surfaces of rocks that do not contain phosphates.

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer because it presents a finding that, if true, would support the researchers’ hypothesis about the plants’ dependence on dissolving rock. The text indicates that the roots of the two plant species grow directly into quartzite rock, where hairs on the roots secrete acids that dissolve the rock. The researchers hypothesize that the plants depend on this process because dissolving rock opens spaces for the roots to grow and releases phosphates that provide the plants with phosphorous, a vital nutrient. If the plants carry out this process of dissolving rock even when the rock already has spaces into which the roots could grow, that would support the researchers’ hypothesis because it suggests that the plants are getting some advantage—such as access to phosphorous—from the action of dissolving rock. If the plants don’t benefit from dissolving rock, they would be expected to grow in the cracks that already exist, as doing so would mean that the plants don’t have to spend energy creating and secreting acids; if, however, the plants create new entry points by dissolving rock even when cracks already exist, that would support the hypothesis that they depend on dissolving rock for some benefit.

Choice A is incorrect because the existence of soil-inhabiting members of the Velloziaceae family with similar root structures to those of the two species discussed in the text wouldn’t support the researchers’ hypothesis that the species discussed in the text depend on dissolving rock. If other such members exist, that might suggest that the root structures can serve more functions than secreting acids to dissolve rock (since dissolving rock may not be necessary for plants living in soil), but that wouldn’t suggest anything about whether the species discussed in the text benefit from dissolving rock. Choice B is incorrect because differences in the proportions of citric and malic acid secreted by the two species would be irrelevant to the hypothesis that the plants depend on dissolving rock. There’s no information in the text to suggest that the proportion of each acid has any bearing on the process of dissolving rock or on any benefits the plants might receive from that process. Choice D is incorrect because if the two species thrive on rocks without phosphates, that would weaken the researchers’ hypothesis that the plants depend on dissolving rock partly because dissolving rock gives them access to phosphates. If the plants can survive on rocks without getting a vital nutrient by dissolving those rocks, then either the nutrient isn’t actually vital for those plants or they can get the nutrient in some way other than by dissolving rocks.

"}, {"id": "08ff903e", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "E", "type": "mc", "stimulus": "

A museum curator is writing a biographical statement about Trinidadian-born Chinese dancer, choreographer, and teacher Dai Ailian for a new exhibit on Chinese dance. The curator claims that some of the pieces Dai created shortly after arriving in mainland China in 1941, such as the solo dance Yao Drum, reflect a desire to represent the dances of local communities Dai visited during her travels through China.

", "stem": "

Which quotation from a work by a dance historian would be the most effective evidence for the curator to include in support of this claim?

", "choices": [{"id": "A", "text": "

“There is no sound or music accompanying Dai’s movements in Yao Drum, aside from the sounds of drumsticks beating against a drum and against each other.”

"}, {"id": "B", "text": "

“Unlike some of the works Dai created in the early 1940s, Yao Drum does not feature a narrative structure, humorous elements, or references to real-life events.”

"}, {"id": "C", "text": "

“Yao Drum was inspired by a ceremonial dance Dai witnessed during her time performing field research among the Yao people in the province of Guizhou in 1941 or 1942.” 

"}, {"id": "D", "text": "

“Yao Drum is notable for its intense physicality, with Dai performing sharp jumps, swift turns, and dramatic sweeps of her legs through the air as she moves in circles on the stage.”

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. This choice clearly states that Yao Drum was inspired by a ceremonial dance of the Yao people. This directly supports the curator’s claim that some of Dai’s pieces “represent the dances of local communities” she visited.

Choice A is incorrect. This choice discusses the sound and music in Yao Drum, but it doesn’t connect these elements to “the dances of local communities,” which is the focus of the claim. Choice B is incorrect. This choice doesn’t mention the dances of local communities, but instead discusses how Yao Drum is different from some of Dai’s earlier works. Choice D is incorrect. This choice describes the choreography of Yao Drum, but it doesn’t connect these elements to “the dances of local communities,” which is the focus of the claim.

"}, {"id": "47f2cddd", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "E", "type": "mc", "stimulus": "

“The Rock and the Sea” is an 1893 poem by Charlotte Perkins Gilman. In the poem, a rock is portrayed as intending to confront and restrain the sea: ______blank

", "stem": "

Which quotation from “The Rock and the Sea” most effectively illustrates the claim?

", "choices": [{"id": "A", "text": "

“I am the Rock. Black midnight falls; / The terrible breakers rise like walls; / With curling lips and gleaming teeth / They plunge and tear at my bones beneath.”

"}, {"id": "B", "text": "

“I am the Sea. I hold the land / As one holds an apple in his hand, / Hold it fast with sleepless eyes, / Watching the continents sink and rise.”

"}, {"id": "C", "text": "

“I am the Rock, presumptuous Sea! / I am set to encounter thee. / Angry and loud or gentle and still, / I am set here to limit thy power, and I will!”

"}, {"id": "D", "text": "

“I am the Sea. The earth I sway; / Granite to me is potter’s clay; / Under the touch of my careless waves / It rises in turrets and sinks in caves.”

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. This quotation focuses on the rock, which yells at the sea and announces its intent to “limit [the sea’s] power.” This matches the idea of confrontation and restraint in the claim we’re trying to support.

Choice A is incorrect. This choice doesn’t illustrate the claim. While this quotation does focus on the rock, it suggests that the rock fears the sea. It lacks the sense of boldness and strength implied by the phrase “confront and restrain the sea.” Choice B is incorrect. This choice doesn’t illustrate the claim. This quotation focuses on the sea, not the rock. Choice D is incorrect. This choice doesn’t illustrate the claim. This quotation focuses on the sea, not the rock.

"}, {"id": "dd349efc", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "M", "type": "mc", "stimulus": "

Participants’ Evaluation of the Likelihood That Robots Can Work Effectively in Different Occupations

OccupationSomewhat or very unlikely (%)Neutral (%)Somewhat or very likely (%)
television news anchor24967
teacher371647
firefighter62930
surgeon74916
tour guide10882

\n

Rows in table may not add up to 100 due to rounding.

\n

Georgia Tech roboticists De’Aira Bryant and Ayanna Howard, along with ethicist Jason Borenstein, were interested in people’s perceptions of robots’ competence. They recruited participants and asked them how likely they think it is that a robot could do the work required in various occupations. Participants’ evaluations varied widely depending on which occupation was being considered; for example, ______blank

", "stem": "

Which choice most effectively uses data from the table to complete the example?

", "choices": [{"id": "A", "text": "

47% of participants believe that it is somewhat or very likely that a robot could work effectively as a teacher, but 37% of respondents believe that it is somewhat or very unlikely that a robot could do so. 

"}, {"id": "B", "text": "

9% of participants were neutral about whether a robot could work effectively as a television news anchor, which is the same percent of participants who were neutral when asked about a robot working as a surgeon.

"}, {"id": "C", "text": "

82% of participants believe that it is somewhat or very likely that a robot could work effectively as a tour guide, but only 16% believe that it is somewhat or very likely that a robot could work as a surgeon.

"}, {"id": "D", "text": "

62% of participants believe that it is somewhat or very unlikely that a robot could work effectively as a firefighter. 

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer because it effectively uses data from the table to complete the example of variations in participants’ evaluations. The table shows participants’ evaluations of the likelihood that robots could work effectively in different occupations. The text asserts that participants’ evaluations varied widely depending on the occupation being considered and introduces an example supporting that assertion. The data from the table showing that 82% of participants believe that it is somewhat or very likely that a robot could work effectively as a tour guide but only 16% of participants believe that it is somewhat or very likely that a robot could work effectively as a surgeon illustrate this assertion: those data show participants’ views changing substantially with the occupation being considered.  

Choice A is incorrect because it does not describe data that illustrate the assertion that participants’ evaluations varied widely depending on which occupation was being considered. Although this choice accurately describes data in the table, data about participants’ responses when considering a single occupation—teaching—could not be an example of people’s views changing substantially depending on the occupation being considered. Choice B is incorrect because it identifies a similarity in participants’ responses when considering two different occupations, but the assertion that the example is intended to illustrate is that participants’ evaluations varied widely depending on the occupation being considered. Although this choice accurately describes data in the table, those data do not illustrate the assertion in the text. Choice D is incorrect because it does not describe data that illustrate the assertion that participants’ evaluations varied widely depending on which occupation was being considered. Although this choice accurately describes data in the table, data showing participants’ evaluation of just one occupation could not be an example of participants’ evaluations changing depending on the occupation under evaluation. 

"}, {"id": "b7f79059", "domain": "Information and Ideas", "skill": "Central Ideas and Details", "difficulty": "M", "type": "mc", "stimulus": "

The following text is from Ezra Pound’s 1909 poem “Hymn III,” based on the work of Marcantonio Flaminio.

\n

As a fragile and lovely flower unfolds its gleaming
 foliage on the breast of the fostering earth, if
 the dew and the rain draw it forth;
So doth my tender mind flourish, if it be fed with the
 sweet dew of the fostering spirit,
Lacking this, it beginneth straightway to languish,
 even as a floweret born upon dry earth, if the
 dew and the rain tend it not.

", "stem": "

Based on the text, in what way is the human mind like a flower?

", "choices": [{"id": "A", "text": "

It becomes increasingly vigorous with the passage of time.

"}, {"id": "B", "text": "

It draws strength from changes in the weather.

"}, {"id": "C", "text": "

 It requires proper nourishment in order to thrive.

"}, {"id": "D", "text": "

It perseveres despite challenging circumstances.

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer because it presents a description of how the human mind is like a flower that is directly supported by the text. The text compares the needs of a “fragile and lovely flower” to those of the speaker’s “tender mind”: both need to be fed if they’re going to survive. Without such feeding, they’ll “beginneth straightway to languish,” or weaken. Thus, the text suggests that the human mind is like a flower in that they both need proper nourishment in order to thrive.

Choice A is incorrect because the text doesn’t address the passage of time or describe either the human mind or a flower as becoming increasingly vigorous. Choice B is incorrect because the text doesn’t suggest that human minds or flowers draw strength from changes in weather. The references to rain in the text pertain to a flower’s need for water rather than the general effects of changing weather. Choice D is incorrect because the text doesn’t suggest that the human mind or a flower will persist regardless of challenging circumstances. In fact, the text indicates that they’ll both languish right away if not given what they need.

"}, {"id": "b5e9f3c2", "domain": "Information and Ideas", "skill": "Inferences", "difficulty": "H", "type": "mc", "stimulus": "

Ancestral Puebloans, the civilization from which present-day Pueblo tribes descended, emerged as early as 1500 B.C.E. in an area of what is now the southwestern United States and dispersed suddenly in the late 1200s C.E., abandoning established villages with systems for farming crops and turkeys. Recent analysis comparing turkey remains at Mesa Verde, one such village in southern Colorado, to samples from modern turkey populations in the Rio Grande Valley of north central New Mexico determined that the latter birds descended in part from turkeys cultivated at Mesa Verde, with shared genetic markers appearing only after 1280. Thus, researchers concluded that ______blank

", "stem": "

Which choice most logically completes the text?

", "choices": [{"id": "A", "text": "

conditions of the terrains in the Rio Grande Valley and Mesa Verde had greater similarities in the past than they do today.

"}, {"id": "B", "text": "

some Ancestral Puebloans migrated to the Rio Grande Valley in the late 1200s and carried farming practices with them.

"}, {"id": "C", "text": "

Indigenous peoples living in the Rio Grande Valley primarily planted crops and did not cultivate turkeys before 1280.

"}, {"id": "D", "text": "

the Ancestral Puebloans of Mesa Verde likely adopted the farming practices of Indigenous peoples living in other regions.

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer because it presents the conclusion that most logically follows from the text’s discussion of Ancestral Puebloans’ migration to the Rio Grande Valley. The text states that in the late 1200s C.E., the Ancestral Puebloan civilization abandoned villages in its original homeland, which included the Mesa Verde site. The text goes on to say that recent genetic analysis has demonstrated that the modern turkey population in the Rio Grande Valley descends partly from the ancient turkeys raised at Mesa Verde, and that the genetic markers shared by the two turkey populations first appeared at Mesa Verde only after 1280 C.E. Therefore, it can reasonably be concluded that some Ancestral Puebloans migrated to the Rio Grande Valley in the late 1200s and carried their agricultural practices—including the farming of turkeys—to their new home.

Choice A is incorrect because the text never compares the condition of the Rio Grande Valley’s terrain to that of Mesa Verde’s terrain, either in the present or in the past. Choice C is incorrect. Although genetic analysis has demonstrated that the modern turkey population in the Rio Grande valley descended in part from the turkey population raised by the Ancestral Puebloans of Mesa Verde before their migration to the valley in 1280, this finding doesn’t eliminate the possibility that Indigenous peoples living in the valley before 1280 might also have farmed turkeys. Choice D is incorrect. The text doesn’t consider the possibility that before their migration to the Rio Grande Valley after 1280, the Ancestral Puebloans of Mesa Verde might have adopted turkey farming from an outside Indigenous civilization in another region; instead, the text provides evidence suggesting that the Ancestral Puebloans brought turkey farming to another region—the Rio Grande Valley—after 1280.

"}, {"id": "5eda42a3", "domain": "Information and Ideas", "skill": "Central Ideas and Details", "difficulty": "H", "type": "mc", "stimulus": "

The following text is from Maggie Pogue Johnson’s 1910 poem “Poet of Our Race.” In this poem, the speaker is addressing Paul Laurence Dunbar, a Black author.

Thou, with stroke of mighty pen,
 Hast told of joy and mirth,
And read the hearts and souls of men
 As cradled from their birth.

The language of the flowers,
 Thou hast read them all,
And e’en the little brook
 Responded to thy call.

", "stem": "

Which choice best states the main purpose of the text?

", "choices": [{"id": "A", "text": "

To praise a certain writer for being especially perceptive regarding people and nature

"}, {"id": "B", "text": "

To establish that a certain writer has read extensively about a variety of topics

"}, {"id": "C", "text": "

To call attention to a certain writer’s careful and elaborately detailed writing process

"}, {"id": "D", "text": "

To recount fond memories of an afternoon spent in nature with a certain writer

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer because it most accurately states the main purpose of the text. In the first part of the text, the speaker addresses Paul Laurence Dunbar’s ability to understand people (he has “read the hearts and souls of men” and written of their “joy and mirth”). In the second part of the text, the speaker describes Dunbar’s thorough understanding of the natural world (he has read “the language of the flowers” and engaged with “the little brook”). Thus, the text mainly praises Dunbar for being especially perceptive about people and nature. 

Choice B is incorrect because the speaker describes Dunbar as having read the “hearts and souls of men” and the “language of flowers” to convey Dunbar’s ability to comprehend people and nature, not to suggest that Dunbar has literally read any of these things or has read a great deal about them. Choice C is incorrect because the text notes how well Dunbar has made sense of the topics he’s written about but doesn’t address any specific parts of Dunbar’s writing process beyond the suggestion that he used a pen. Choice D is incorrect because the text focuses on Dunbar’s understanding of people and nature as expressed in his writing. Nothing in the text suggests that the speaker is recalling a particular afternoon actually spent in nature with Dunbar; even if there had been a shared experience, the text isn’t focused on reminiscing.

"}, {"id": "4f9f8ea6", "domain": "Information and Ideas", "skill": "Inferences", "difficulty": "H", "type": "mc", "stimulus": "

Birds of many species ingest foods containing carotenoids, pigmented molecules that are converted into feather coloration. Coloration tends to be especially saturated in male birds’ feathers, and because carotenoids also confer health benefits, the deeply saturated colors generally serve to communicate what is known as an honest signal of a bird’s overall fitness to potential mates. However, ornithologist Allison J. Shultz and others have found that males in several species of the tanager genus Ramphocelus use microstructures in their feathers to manipulate light, creating the appearance of deeper saturation without the birds necessarily having to maintain a carotenoid-rich diet. These findings suggest that ______blank

", "stem": "

Which choice most logically completes the text?

", "choices": [{"id": "A", "text": "

individual male tanagers can engage in honest signaling without relying on carotenoid consumption.

"}, {"id": "B", "text": "

feather microstructures may be less effective than deeply saturated feathers for signaling overall fitness.

"}, {"id": "C", "text": "

scientists have yet to determine why tanagers have a preference for mates with colorful appearances.

"}, {"id": "D", "text": "

a male tanager’s appearance may function as a dishonest signal of the individual’s overall fitness.

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer because it most logically completes the text’s discussion of Shultz’s finding about male tanagers. The text explains that because carotenoids both contribute to deeply saturated feathers and offer health benefits, having deeply saturated feathers is usually “an honest signal” (a true indication) that a bird is generally fit. However, Shultz and others have found that certain male tanagers can appear to have deeply saturated feathers even if they haven’t consumed a diet rich in carotenoids, thanks to microstructures in their feathers that manipulate light. If those birds aren’t necessarily eating carotenoid-rich diets, they may actually be less fit than other birds that appear to have similarly saturated feathers; this suggests that a male tanager’s appearance may function as a dishonest signal, or a false indication, of the bird’s overall fitness. 

Choice A is incorrect because Shultz’s finding suggests that some tanagers can signal fitness without consuming the carotenoids that contribute to fitness, thereby making those signals dishonest, not that tanagers can give honest signals of their fitness without consuming carotenoids. Choice B is incorrect because Shultz’s finding suggests that the microstructures in certain tanagers’ feathers can give a dishonest signal of fitness, not that the microstructures are less effective than actual pigmentation for signaling fitness. Whether the signal of fitness is honest or dishonest has no bearing on how effective the signal is: a signal is effective if potential mates behave as though it’s true, regardless of whether it’s actually true. Since there’s no information in the text about how potential mates respond to the dishonest signals of some tanagers, there’s no support for the idea that the dishonest signals are less effective than the honest signals. Choice C is incorrect because Shultz’s finding suggests that certain male tanagers may appear to be fitter than they actually are, not that scientists haven’t determined why tanagers prefer mates with colorful appearances. 

"}, {"id": "2c06139b", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "H", "type": "mc", "stimulus": "

Tadpole Body Mass and Toxin Production after Three Weeks in Ponds

Population densityAverage tadpole body mass (milligrams)Average number of distinct bufadienolide toxins per tadpoleAverage amount of bufadienolide per tadpole (nanograms)Average bufadienolide concentration (nanograms per milligram of tadpole body mass)
High193.8722.695,815.51374.22
Medium254.5621.655,525.72230.10
Low258.9722.084,664.99171.43

\n

Ecologist Veronika Bókony and colleagues investigated within-species competition among common toads (Bufo bufo), a species that secretes various unpleasant-tasting toxins called bufadienolides in response to threats. The researchers tested B. bufo tadpoles’ responses to different levels of competition by creating ponds with different tadpole population densities but a fixed amount of food. Based on analysis of the tadpoles after three weeks, the researchers concluded that increased competition drove bufadienolide production at the expense of growth.

", "stem": "

Which choice uses data from the table to most effectively support the researchers’ conclusion?

", "choices": [{"id": "A", "text": "

The difference in average tadpole body mass was small between the low and medium population density conditions and substantially larger between the low and high population density conditions.

"}, {"id": "B", "text": "

Tadpoles in the low and medium population density conditions had substantially lower average bufadienolide concentrations but had greater average body masses than those in the high population density condition.

"}, {"id": "C", "text": "

Tadpoles in the high population density condition displayed a relatively modest increase in the average amount of bufadienolide but roughly double the average bufadienolide concentration compared to those in the low population density condition.

"}, {"id": "D", "text": "

Tadpoles produced approximately the same number of different bufadienolide toxins per individual across the population density conditions, but average tadpole body mass decreased as population density increased.

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. This data shows that the tadpoles in the high-density pond (meaning those with the most competition) didn’t grow as big as the other two groups but produced more bufadienolide.

Choice A is incorrect. This doesn’t fully support the conclusion. It doesn’t include any data about bufadienolide production. Choice C is incorrect. This doesn’t fully support the conclusion. It doesn’t include any data about growth. Choice D is incorrect. This doesn’t fully support the conclusion. It doesn’t demonstrate that the tadpoles in the high-density pond produced more bufadienolide overall. The fact that they didn’t produce more kinds of bufadienolide isn’t relevant to the conclusion.

"}, {"id": "01c1d9ee", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "H", "type": "mc", "stimulus": "

Swahili Speakers in Three African Countries

CountryApproximate number of speakers (in millions)Estimated % of population
Democratic Republic of the Congo2225
Kenya55100
Tanzania61100

\n

Swahili is estimated to be the first language of up to 15 million people worldwide. It’s also an officially recognized language in Tanzania, Kenya, and the Democratic Republic of the Congo, which means these countries use Swahili in government documents and proceedings. But even in countries where almost everyone speaks Swahili, for many it isn’t their first language but is instead their second, third, or even fourth language.

", "stem": "

Which choice most effectively uses data from the table to support the underlined claim?

", "choices": [{"id": "A", "text": "

Tanzania has approximately 61 million Swahili speakers, which is much more than the estimated total number of people worldwide for whom Swahili is their first language.

"}, {"id": "B", "text": "

Tanzania is estimated to have at most 15 million Swahili speakers, while the country’s total population is approximately 61 million people.

"}, {"id": "C", "text": "

Approximately 100 percent of the people who speak Swahili as their first language live in Kenya, which has a total population of approximately 55 million people.

"}, {"id": "D", "text": "

Approximately 100 percent of Kenya’s population speaks Swahili, while only about 25 percent of the Democratic Republic of the Congo’s population speaks Swahili.

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer because it most effectively uses data from the table to support the underlined claim. The text indicates that Swahili is the first language of up to 15 million people worldwide. The text goes on to claim, in the underlined portion, that even in countries where nearly everyone speaks Swahili, many of the language’s speakers don’t have Swahili as their first language. The table indicates that 61 million people in Tanzania, which amounts to 100 percent of the population, speak Swahili. If 61 million people in Tanzania speak Swahili, but only 15 million people worldwide have Swahili as their first language, that means there are many people in Tanzania who speak Swahili as a language other than their first language. This information about Swahili speakers in Tanzania therefore supports the claim that many Swahili speakers in countries where nearly everyone speaks Swahili speak it as a language other than their first language (such as their second, third, or fourth language). 

Choice B is incorrect because it doesn’t accurately describe information in the table. According to the table, Tanzania has 61 million Swahili speakers, not at most 15 million Swahili speakers. Additionally, the table indicates that 100 percent of Tanzania’s population speak Swahili, which means that the number of Swahili speakers in the country and the country’s total population should be the same, not that they should differ by such a large amount. Choice C is incorrect because there’s no information in the table or the text that indicates where people who speak Swahili as their first language live. Although Kenya’s total population can be inferred from the table—if Kenya has 55 million Swahili speakers and 100% of Kenya’s population speak Swahili, then Kenya must have a population of 55 million people—nothing suggests that all the people who speak Swahili as their first language live in a single country, let alone that they all live in Kenya. Choice D is incorrect. Although the table does indicate that 100 percent of Kenya’s population and 25 percent of the Democratic Republic of the Congo’s population speak Swahili, this comparison is irrelevant to the claim that Swahili isn’t the first language of many of its speakers even in countries where almost everyone speaks Swahili. On its own, a difference in the proportions of the population who speak Swahili cannot reveal whether those Swahili speakers have Swahili as their first language or a subsequent language. 

"}, {"id": "26ee16ba", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "E", "type": "mc", "stimulus": "

Hip-hop pedagogy is a form of teaching that’s gaining popularity across school subjects. It involves incorporating hip-hop and rap music into lessons as well as using hip-hop elements when teaching other subject matters. For example, Quan Neloms’s students look for college-level vocabulary and historical events in rap songs. Researchers claim that in addition to developing students’ social justice awareness, hip-hop pedagogy encourages student success by raising students’ interest and engagement.

", "stem": "

Which finding, if true, would most strongly support the underlined claim?

", "choices": [{"id": "A", "text": "

Students tend to be more enthusiastic about rap music than they are about hip-hop music.

"}, {"id": "B", "text": "

Students who are highly interested in social justice issues typically don’t sign up for courses that incorporate hip-hop and rap music.

"}, {"id": "C", "text": "

Educators report that they enjoy teaching courses that involve hip-hop and rap music more than teaching courses that don’t.

"}, {"id": "D", "text": "

Courses that incorporate hip-hop and rap music are among the courses with the highest enrollment and attendance rates.

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. Enrollment and attendance are logical ways to measure whether students are interested and engaged. High enrollment and attendance suggests a high level of interest and engagement.

Choice A is incorrect. This choice doesn’t support the claim. Students’ preferences between hip-hop and rap aren’t relevant to the claim, which is focused on whether or not students like classes that use hip-hop pedagogy (which includes the educational use of both hip-hop and rap). Choice B is incorrect. This choice doesn’t support the claim. While the first part of the sentence discusses social justice, the underlined claim focuses on student success, which is unrelated. Choice C is incorrect. This choice doesn’t support the claim. This tells us about teacher enjoyment, which isn’t relevant to a claim about student interest and engagement.

"}, {"id": "f2250478", "domain": "Information and Ideas", "skill": "Inferences", "difficulty": "H", "type": "mc", "stimulus": "

Among social animals that care for their young, such as chickens, macaque monkeys, and humans, newborns appear to show an innate attraction to faces and face-like stimuli. Elisabetta Versace and her colleagues used an image of three black dots arranged in the shape of eyes and a nose or mouth to test whether this trait also occurs in Testudo tortoises, which live alone and do not engage in parental care. They found that tortoise hatchlings showed a significant preference for the image, suggesting that ______blank

", "stem": "

Which choice most logically completes the text?

", "choices": [{"id": "A", "text": "

face-like stimuli are likely perceived as harmless by newborns of social species that practice parental care but as threatening by newborns of solitary species without parental care.

"}, {"id": "B", "text": "

researchers should not assume that an innate attraction to face-like stimuli is necessarily an adaptation related to social interaction or parental care.

"}, {"id": "C", "text": "

researchers can assume that the attraction to face-like stimuli that is seen in social species that practice parental care is learned rather than innate.

"}, {"id": "D", "text": "

newly hatched Testudo tortoises show a stronger preference for face-like stimuli than adult Testudo tortoises do. 

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer because it presents the conclusion that most logically follows from the text’s discussion of the study by Versace and colleagues. The text indicates that newborn animals of some species are attracted to faces and to stimuli that resemble faces. These species, the text says, share two characteristics: they’re social and they practice parental care, meaning that parents care for their young. The text goes on to describe Versace and colleagues’ experiment, which showed that Testudo tortoises, which aren’t social and don’t practice parental care, were attracted to a stimulus that resembles a face. Since Versace and colleagues have shown that a species that isn’t social and doesn’t practice parental care nevertheless has the innate characteristic of being attracted to face-like stimuli, it follows that this characteristic shouldn’t be assumed to be an adaptation related to social interaction or parental care.

Choice A is incorrect because the text indicates that the tortoise hatchlings, which are solitary and don’t practice parental care, were attracted to the face-like stimuli, not that they perceived the stimuli as threatening. Choice C is incorrect because the phenomenon discussed in the text is an attraction to faces and face-like stimuli on the part of newborn animals, which can’t show any learned characteristics since they were just born. Additionally, the text tells us that the tortoises Versace and colleagues studied aren’t social and don’t practice parental care, so any findings about those tortoises wouldn’t be relevant to the question of whether an attraction to faces in social species that practice parental care is innate or learned. Choice D is incorrect because the text gives no indication that adult tortoises were tested on face-like stimuli and, if adults were in fact tested, no information about how they responded is provided. Since no information about adult tortoises’ responses is provided, no conclusion comparing those responses to the responses of newly hatched tortoises can be supported.

"}, {"id": "0b96fa93", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "E", "type": "mc", "stimulus": "

Maximum Height of Maple Trees When Fully Grown

Tree typeMaximum height (feet)Native to North America
Sugar maple75yes
Silver maple70yes
Red maple60yes
Japanese maple25no
Norway maple50no

\n

For a school project, a forestry student needs to recommend a maple tree that is native to North America and won’t grow more than 60 feet in height. Based on the characteristics of five common maple trees, she has decided to select a ______blank

", "stem": "

Which choice most effectively uses data from the table to complete the text?

", "choices": [{"id": "A", "text": "

silver maple.

"}, {"id": "B", "text": "

sugar maple.

"}, {"id": "C", "text": "

red maple.

"}, {"id": "D", "text": "

Norway maple.

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer because it most effectively uses data from the table to complete the statement about the forestry student’s project. The table shows five types of maple trees, each tree’s maximum height, and whether each tree is native to North America. The text indicates that the student needs to recommend a maple tree that’s native to North America and won’t reach a height greater than 60 feet. The red maple is the only tree listed in the table that meets these criteria: its maximum height is 60 feet—meaning that it won’t grow higher than 60 feet—and it’s native to North America.

Choice A is incorrect because the text states that the student needs to recommend a tree that’s native to North America and won’t grow higher than 60 feet, but the table shows that the maximum height of the silver maple is 70 feet. Choice B is incorrect because the text states that the student needs to recommend a tree that’s native to North America and won’t grow higher than 60 feet, but the table shows that the maximum height of the sugar maple is 75 feet. Choice D is incorrect because the text states that the student needs to recommend a tree that’s native to North America and won’t grow higher than 60 feet, but the table shows that the Norway maple isn’t native to North America. 

"}, {"id": "6e0e0de1", "domain": "Information and Ideas", "skill": "Inferences", "difficulty": "H", "type": "mc", "stimulus": "

Aerogels are highly porous foams consisting mainly of tiny air pockets within a solidified gel. These lightweight materials are often applied to spacecraft and other equipment required to withstand extreme conditions, as they provide excellent insulation despite typically being brittle and eventually fracturing due to degradation from repeated exposure to high heat. Now, Xiangfeng Duan of the University of California, Los Angeles, and colleagues have developed an aerogel with uniquely flexible properties. Unlike earlier aerogels, Duan’s team’s material contracts rather than expands when heated and fully recovers after compressing to just 5% of its original volume, suggesting that ______blank

", "stem": "

Which choice most logically completes the text?

", "choices": [{"id": "A", "text": "

the aerogel’s remarkable flexibility results from its higher proportion of air pockets to solidified gel as compared to other aerogels.

"}, {"id": "B", "text": "

the aerogel’s overall strength is greater than that of other insulators but its ability to withstand exposure to intense heat is lower.

"}, {"id": "C", "text": "

the aerogel will be more effective as an insulator for uses that involve gradual temperature shifts than for those that involve rapid heat increases.

"}, {"id": "D", "text": "

the aerogel will be less prone to the structural weakness that ultimately causes most other aerogels to break down with use.

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer because it most logically completes the text’s discussion of aerogels. The text states that aerogels—highly porous foams—offer \"excellent insulation\" but typically break down after prolonged exposure to high heat. However, according to the text, Duan and colleagues developed an aerogel that \"contracts rather than expands when heated\" and recovers its original volume after this contraction. Thus, it is logical to conclude that Duan’s team’s aerogel material will be less prone to the structural weakness that caused earlier aerogels to break down.

Choice A is incorrect. Although the text indicates that aerogels consist \"mainly of tiny air pockets within a solidified gel,\" it doesn’t mention the number or proportion of air pockets to solidified gel in typical aerogels or in the aerogel developed by Duan’s team. Choice B is incorrect because the text suggests that the aerogel developed by Duan’s team has a higher, not a lower, ability to withstand exposure to intense heat due to its contraction and subsequent recovery. Choice C is incorrect. Although the text discusses temperature tolerances of aerogels and says that they offer \"excellent insulation despite typically being brittle and eventually fracturing,\" it doesn’t discuss how different rates of temperature change can affect aerogels.

"}, {"id": "493c46bc", "domain": "Information and Ideas", "skill": "Inferences", "difficulty": "E", "type": "mc", "stimulus": "

In the South Pacific, New Caledonian crows use two different kinds of stick tools. One tool is complex. The crows shape a stick from a rare plant into a hook. The other tool is basic. The crows find a stick without a hook on the ground. The hooked tool is harder to get but is much better than the basic tool at removing prey from holes. When studying New Caledonian crows, ecologist Barbara Klump found that they hold the hooked tools in their claws when not using them, or they carefully put them in a safe place. The crows don’t do the same with the basic tools. This suggests to Klump that the ______blank

", "stem": "

Which choice most logically completes the text?

", "choices": [{"id": "A", "text": "

hooked stick tools are more valuable to the crows than the stick tools without hooks.

"}, {"id": "B", "text": "

hooked stick tools are easier for most of the crows to hold than the stick tools without hooks.

"}, {"id": "C", "text": "

crows prefer to share their hooked stick tools but don’t share the stick tools without hooks.

"}, {"id": "D", "text": "

crows realize that both kinds of stick tools are less effective than their claws are at removing prey from holes.

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer because it most logically completes the text’s discussion of the two types of stick tools used by New Caledonian crows. The text indicates that the more effective type of tool has a hook that the crows make themselves, while the other type of tool is simply a stick without a hook that the crows find and don’t shape in any way. According to the text, Klump found that the crows keep hooked tools—but not the tools without hooks—in their grasp or in safe places when they aren’t using the tools. If the hooked tools are more effective than the tools without hooks are and the crows are more protective of the hooked tools than they are of the tools without hooks, it’s reasonable to conclude that the hooked tools are more valuable to the crows than the tools without hooks are.

Choice B is incorrect because the text gives no indication of how easy it is for the crows to hold either the hooked tools or the tools without hooks. The text does state that crows hold the hooked tools and not the tools without hooks when the tools aren’t in use. However, the text also indicates that the hooked tools require work from the crows to make and are more useful for helping the crows catch prey than the tools without hooks are. This context suggests that the crows hold the hooked tools because they’re more valuable to the crows than the tools without hooks are, not because the hooked tools are easier to hold. Choice C is incorrect because the text makes no mention of the crows sharing tools. Additionally, the text indicates that when the crows aren’t using the hooked tools, they either grasp the tools or store them safely, which suggests that the crows try to maintain possession of the hooked tools, not that crows prefer to share those tools. Choice D is incorrect because the text says nothing about the crows using their claws to remove prey from holes, so there’s no evidence that the crows perceive the stick tools to be less effective than their claws are.

"}, {"id": "1db1a9a6", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "M", "type": "mc", "stimulus": "
\n\n\n\n\n454035302520151050Yield (pounds per acre)201720182019Cantaloupe YieldYearcontrolnitrogen fertilizer
\n

To test the effects of a nitrogen fertilizer on cantaloupe production, researchers grew cantaloupe plants and harvested their fruit over three years. In each year, half the plants were grown using a nitrogen fertilizer, and the other half were grown using a control fertilizer that contained no nitrogen. The researchers concluded that the nitrogen fertilizer increases cantaloupe yield.

", "stem": "

Which choice best describes data in the graph that support the researchers’ conclusion?

", "choices": [{"id": "A", "text": "

In every year of the experiment, plants treated with the nitrogen fertilizer had a yield of at least 30 pounds per acre.

"}, {"id": "B", "text": "

In every year of the experiment, plants treated with the nitrogen fertilizer had a greater yield than did plants treated with the control fertilizer. 

"}, {"id": "C", "text": "

The 2018 yield for plants treated with the control fertilizer was greater than was the 2019 yield for plants treated with the nitrogen fertilizer. 

"}, {"id": "D", "text": "

The yield for plants treated with the nitrogen fertilizer increased from 2017 to 2018. 

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer because it describes data from the graph that support the researchers’ conclusion that using nitrogen fertilizer increases cantaloupe production. The bar graph shows the cantaloupe yield for plants grown with nitrogen fertilizer and for those grown with a control fertilizer (without nitrogen) for three consecutive years (2017–2019). For each year in the graph, the yield for the nitrogen group is greater than the yield for the control group. In pounds per acre, the value in 2017 for the nitrogen-group yield is greater than 30 while the control-group yield is less than 25; in 2018 the nitrogen-group yield is greater than 40 while the control-group yield is less than 35; and in 2019 the nitrogen-group yield is greater than 25 while the control-group yield is less than 20. Thus, these data from the graph strongly support the conclusion that using nitrogen fertilizer increases cantaloupe yield.

Choice A is incorrect because the bar graph shows that in 2019 the nitrogen group had a yield below 30 pounds per acre. Choice C is incorrect. Although this choice accurately describes data in the bar graph—in 2018, the control-group yield is greater than 30 pounds per acre, and in 2019 the nitrogen-group yield is less than 30 pounds per acre—a claim that the control-group yield exceeds that of the nitrogen group strongly conflicts with the researchers’ conclusion that nitrogen fertilizer produces larger yields. Choice D is incorrect. Although it is true that the bar graph shows a higher yield for the nitrogen group in 2018 than in 2017, without the control to compare against, it is impossible to know whether the increase is due to the fertilizer and not, for example, more favorable weather in 2018 than in 2017. 

"}, {"id": "16a4a83b", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "M", "type": "mc", "stimulus": "

An Ideal Husband is an 1895 play by Oscar Wilde. In the play, which is a satire, Wilde suggests that a character named Lady Gertrude Chiltern is perceived as both extremely virtuous and unforgiving, as is evident when another character says ______blank

", "stem": "

Which quotation from An Ideal Husband most effectively illustrates the claim?

", "choices": [{"id": "A", "text": "

“Lady Chiltern is a woman of the very highest principles, I am glad to say. I am a little too old now, myself, to trouble about setting a good example, but I always admire people who do.”

"}, {"id": "B", "text": "

“Do you know, [Lady Chiltern], I don’t mind your talking morality a bit. Morality is simply the attitude we adopt towards people whom we personally dislike.”

"}, {"id": "C", "text": "

“[Lady Chiltern] does not know what weakness or temptation is. I am of clay like other men. She stands apart as good women do—pitiless in her perfection—cold and stern and without mercy.”

"}, {"id": "D", "text": "

“Lady Chiltern, you are a sensible woman, the most sensible woman in London, the most sensible woman I know.”

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer because it most effectively uses a quotation to illustrate the claim that Lady Gertrude Chiltern is perceived as “both extremely virtuous and unforgiving.” In the quotation, a man describes Lady Chiltern as someone who “does not know what weakness or temptation is.” In other words, the man regards her as someone who is strong and adheres to a strict definition of moral perfection. However, he ironically suggests that this definition excludes mercy and forgiveness—qualities that are also thought of as virtues; according to him, Lady Chiltern is “pitiless in her perfection—cold and stern and without mercy.” This description supports the idea that Lady Chiltern is perceived by others as virtuous as well as unforgiving.

Choice A is incorrect. The quotation supports the claim that Lady Chiltern is perceived as virtuous, in that it describes her as “a woman of the very highest principles.” However, it doesn’t characterize her as unforgiving or being perceived as such. Choice B is incorrect. The quotation suggests that Lady Chiltern is concerned with morality, but it suggests that her interest in discussing it is fundamentally hypocritical and functions as a means by which to judge others. However, the quotation doesn’t address the question of whether Lady Chiltern is unmerciful to those who seek forgiveness for harm they have caused. Choice D is incorrect because it doesn’t address either Lady Chiltern’s perceived virtuousness or her perceived lack of forgiveness; instead, it expresses the belief that she is sensible.

"}, {"id": "0b696a0c", "domain": "Information and Ideas", "skill": "Central Ideas and Details", "difficulty": "E", "type": "mc", "stimulus": "

NASA’s Cassini probe has detected an unusual wobble in the rotation of Mimas, Saturn’s smallest moon. Using a computer model to study Mimas’s gravitational interactions with Saturn and tidal forces, geophysicist Alyssa Rhoden and colleagues have proposed that this wobble could be due to a liquid ocean moving beneath the moon’s icy surface. The researchers believe other moons should be examined to see if they too might have oceans hidden beneath their surfaces.

", "stem": "

Which choice best states the main idea of the text?

", "choices": [{"id": "A", "text": "

Rhoden and colleagues were the first to confirm that several of Saturn’s moons contain hidden oceans.

"}, {"id": "B", "text": "

Research has failed to identify signs that there is an ocean hidden beneath the surface of Mimas.

"}, {"id": "C", "text": "

Rhoden and colleagues created a new computer model that identifies moons with hidden oceans without needing to analyze the moons’ rotation. 

"}, {"id": "D", "text": "

Research has revealed that an oddity in the rotation of Mimas could be explained by an ocean hidden beneath its surface.

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. The study isn’t definitive, but it says that Mimas’s wobbly rotation could be explained by the hidden ocean.

Choice A is incorrect. This choice goes too far beyond the information in the text. Rhoden’s team proposed that one moon of Saturn could have a liquid ocean beneath its surface, and that other moons should also be examined, but no one has confirmed anything. Choice B is incorrect. This choice conflicts with the text. Research has  identified at least one sign—the unusual wobble in Mimas’s rotation—that might be due to a hidden ocean beneath its surface. Choice C is incorrect. This choice doesn’t reflect the text. The computer model studies “gravitational interactions,” which seem to account for the wobbly rotation of Mimas.

"}, {"id": "37a49687", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "E", "type": "mc", "stimulus": "

\n\n\n\n\n\n\n\n\n\n\n\n\n403020100Number of individual young fishWinterSpringFallNumber of Young Fish Collected at Mangrove Sites in the Egyptian Red Sea During Three Seasons of 2010Season Common silver-biddy Red Sea goatfish Milkfish

\n

Mangroves are trees or bushes that grow on the coastlines of seas and rivers. Areas with mangroves are great places for young fish since they help keep these fish fed and protected while they grow. To study the importance of mangroves to young fish, researchers Mohamed A.Abu El-Regal and Nesreen K. Ibrahim collected and identified young fish from three different mangrove sites in the Egyptian Red Sea. They collected fish in the winter, spring, and autumn of 2010, collecting a total of 269 fish from 21 different species. For some species, more fish were collected in the winter than the other two seasons, for instance: ______blank

", "stem": "

Which choice most effectively uses the data in the graph to complete the example?

", "choices": [{"id": "A", "text": "

more common silver-biddy and milkfish were collected in the winter than in either of the other two seasons.

"}, {"id": "B", "text": "

the common silver-biddy was collected more frequently than the other two species in all three seasons.

"}, {"id": "C", "text": "

in the spring, researchers collected more Red Sea goldfish than they collected from the other two species.

"}, {"id": "D", "text": "

in the fall, researchers collected 10 common silver-biddy but collected no milkfish or Red Sea goatfish.

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. The claim is about which fish were collected more in winter than in other seasons. By comparing the number of common silver-biddy and milkfish collected in each season, we can see that more of these fish were collected in winter than in any other season.

Choice B is incorrect. The claim is about which fish were collected more in winter than in other seasons. This statement compares collections across the three species of fish, rather than comparing collections of individual types of fish across seasons. Choice C is incorrect. The claim is about which fish were collected more in winter than in other seasons. This statement is about spring, rather than winter. Choice D is incorrect. The claim is about which fish were collected more in winter than in other seasons. This statement is about fall, rather than winter, fish collections.

"}, {"id": "0113152f", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "E", "type": "mc", "stimulus": "

American fashion designer Patrick Kelly was known for his love of colorful buttons. Many of his signature dresses feature bold assortments of buttons throughout the garment. In a paper, a fashion design student claims that Kelly’s use of buttons as decoration was inspired by his childhood observations of the styles and actions of the women in his family.

", "stem": "

Which quotation from a work by a historian would be the most effective evidence for the student to include in support of this claim?

", "choices": [{"id": "A", "text": "

“Although some of the assortments of buttons appear to be mismatched pieces scattered randomly throughout Kelly’s dresses, his most famous designs feature carefully crafted patterns of matching buttons.”

"}, {"id": "B", "text": "

“Many of Kelly’s contemporaries were inspired by his designs to incorporate buttons, as well as zippers and snaps, as decorative items in their work.” 

"}, {"id": "C", "text": "

“Kelly’s grandmother, who would repair clothing when he was a child, frequently added mismatched buttons to the clothes to draw attention away from any flaws in the garments.”

"}, {"id": "D", "text": "

“Kelly was destined to be a designer from a young age: he learned how to sew clothing from his aunt Bertha, and his love of drawing was developed by his mother.”

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. This quotation draws a direct connection between the use of buttons and Kelly’s stylish female relatives.

Choice A is incorrect. This choice mentions Kelly’s use of buttons, but it doesn’t connect that design choice to the influence of women in Kelly’s family. Choice B is incorrect. This choice discusses how other designers were inspired by Kelly, which doesn’t provide evidence that Kelly was inspired by his family. Choice D is incorrect. While this choice does refer to fashionable women in Kelly’s family, it doesn’t connect their influence to Kelly’s use of buttons.

"}, {"id": "3a1f02b0", "domain": "Information and Ideas", "skill": "Central Ideas and Details", "difficulty": "E", "type": "mc", "stimulus": "

The following text is adapted from Frances Hodgson Burnett’s 1911 novel The Secret Garden. Mary, a young girl, recently found an overgrown hidden garden.

\n

Mary was an odd, determined little person, and now she had something interesting to be determined about, she was very much absorbed, indeed. She worked and dug and pulled up weeds steadily, only becoming more pleased with her work every hour instead of tiring of it. It seemed to her like a fascinating sort of play.

", "stem": "

Which choice best states the main idea of the text?

", "choices": [{"id": "A", "text": "

Mary hides in the garden to avoid doing her chores.

"}, {"id": "B", "text": "

Mary is getting bored with pulling up so many weeds in the garden.

"}, {"id": "C", "text": "

Mary is clearing out the garden to create a space to play.

"}, {"id": "D", "text": "

Mary feels very satisfied when she’s taking care of the garden.

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer because it most accurately states the main idea of the text. The text describes Mary’s activities in an overgrown hidden garden, saying that she was “very much absorbed” and was “only becoming more pleased with her work every hour” rather than getting tired of it. She also thinks of garden activities as a “fascinating sort of play.” Thus, the main idea of the text is that Mary feels very satisfied when taking care of the garden.

Choice A is incorrect because the text never makes any mention of Mary’s chores. Choice B is incorrect because the text indicates that Mary finds pulling up weeds to be fascinating, not boring. Choice C is incorrect because Mary thinks of garden activities in and of themselves as play, not as something necessary to do to create a space to play.

"}, {"id": "f38b40ac", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "E", "type": "mc", "stimulus": "

In addition to her technical skill and daring feats, American stunt pilot Bessie Coleman was also known for dazzling the crowds that came to watch her air shows in the 1920s with her exuberant personality. During her career, she was careful and purposeful about how she crafted her public persona. An aviation researcher has claimed that Coleman intentionally defied social norms of the time by how she chose to present herself to the public.

", "stem": "

Which quotation from an article about Coleman would most directly support the aviation researcher’s claim?

", "choices": [{"id": "A", "text": "

“For her air shows, Coleman frequently used the Curtiss JN-4, or ‘Jenny,’ which at that time was one of the most well-known types of planes.”

"}, {"id": "B", "text": "

“While Coleman was beloved by spectators for her charisma, she had a more complicated relationship with her managers and staff, who at times found her behavior too impulsive and demanding.”

"}, {"id": "C", "text": "

“Coleman once considered leaving her career as a stunt pilot to focus her efforts on giving speeches, which she felt would better support her public image.” 

"}, {"id": "D", "text": "

“Although female pilots were typically expected to wear traditional but impractical attire that included dresses or skirts, photographs of Coleman show her wearing pants and leather jackets.”

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. This choice supports the claim of Coleman’s intentional defiance of social norms: female pilots were expected to wear skirts, but Coleman wore pants and leather jackets instead.

Choice A is incorrect. Coleman flew a well-known, common plane, which would not have defied social norms among pilots. Choice B is incorrect. Her complicated relationship with managers and staff would not have been a component of Coleman’s public persona. This choice also fails to mention any “social norms of the time.” Choice C is incorrect. While this quotation suggests that Coleman was careful and purposeful about her public image, it doesn’t directly mention anything about “social norms of the time.”

"}, {"id": "89f71526", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "E", "type": "mc", "stimulus": "

\n\n\n\n\n3.53.02.52.01.51.00.50Deformation rate(centimeters per month)AlcedoMauleFernandinaPacayaSierra NegraDeformation Rate of Five Volcanoesvolcano

\n

When magma moves underneath a volcano, it causes the surface of the volcano to change. This is known as deformation. Researchers recently calculated the amount of deformation occurring each month for five volcanoes in Latin America. Although Sierra Negra experienced a lot of deformation, its deformation rate was still lower than that of ______blank

", "stem": "

Which choice most effectively uses data from the graph to complete the statement?

", "choices": [{"id": "A", "text": "

Alcedo.

"}, {"id": "B", "text": "

Pacaya.

"}, {"id": "C", "text": "

Fernandina.

"}, {"id": "D", "text": "

Maule.

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. Pacaya had a deformation rate of almost 3.5 centimeters per month, while Sierra Negra had a deformation rate of less than 3 centimeters per month. Therefore, Sierra Negra’s deformation rate was lower than Pacaya’s.

Choice A is incorrect. Alcedo has a lower rate of deformation than Sierra Negra. Choice C is incorrect. Fernandina has a lower rate of deformation than Sierra Negra. Choice D is incorrect. Maule has a lower rate of deformation than Sierra Negra.

"}, {"id": "7f293254", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "H", "type": "mc", "stimulus": "

Art collectives, like the United States- and Vietnam-based collective The Propeller Group or Cuba’s Los Carpinteros, are groups of artists who agree to work together: perhaps for stylistic reasons, or to advance certain shared political ideals, or to help mitigate the costs of supplies and studio space. Regardless of the reasons, art collectives usually involve some collaboration among the artists. Based on a recent series of interviews with various art collectives, an arts journalist claims that this can be difficult for artists who are often used to having sole control over their work.

", "stem": "

Which quotation from the interviews best illustrates the journalist’s claim?

", "choices": [{"id": "A", "text": "

“The first collective I joined included many amazingly talented artists, and we enjoyed each other’s company, but because we had a hard time sharing credit and responsibility for our work, the collective didn’t last.” 

"}, {"id": "B", "text": "

“We work together, but that doesn’t mean that individual projects are equally the work of all of us. Many of our projects are primarily the responsibility of whoever originally proposed the work to the group.”

"}, {"id": "C", "text": "

“Having worked as a member of a collective for several years, it’s sometimes hard to recall what it was like to work alone without the collective’s support. But that support encourages my individual expression rather than limits it.”

"}, {"id": "D", "text": "

“Sometimes an artist from outside the collective will choose to collaborate with us on a project, but all of those projects fit within the larger themes of the work the collective does on its own.”

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer because it presents the quotation that best illustrates the journalist’s claim. By indicating that a collective didn’t continue because it was hard to share credit and responsibilities within the group even though the company was enjoyable, the quotation shows that working collaboratively can be difficult for artists who are used to having complete control over their work.

Choice B is incorrect because the quotation indicates that members of a collective are able to collaborate together and have agreed on a fair way to manage their responsibilities; this doesn’t demonstrate the challenge of sharing control among members of a collective. Choice C is incorrect because the quotation highlights the support and encouragement of individual expression an artist experiences due to working in a collective; these positive aspects don’t demonstrate the challenge of sharing control among members of a collective. Choice D is incorrect because the quotation doesn’t address any challenges of sharing control among members of a collective; it simply indicates that artists sometimes choose to work with collectives without having to be a member. Therefore, the quotation doesn’t illustrate the journalist’s claim. 

"}, {"id": "3ae2638c", "domain": "Information and Ideas", "skill": "Inferences", "difficulty": "M", "type": "mc", "stimulus": "

In documents called judicial opinions, judges explain the reasoning behind their legal rulings, and in those explanations they sometimes cite and discuss historical and contemporary philosophers. Legal scholar and philosopher Anita L. Allen argues that while judges are naturally inclined to mention philosophers whose views align with their own positions, the strongest judicial opinions consider and rebut potential objections; discussing philosophers whose views conflict with judges’ views could therefore ______blank

", "stem": "

Which choice most logically completes the text?

", "choices": [{"id": "A", "text": "

allow judges to craft judicial opinions without needing to consult philosophical works.

"}, {"id": "B", "text": "

help judges improve the arguments they put forward in their judicial opinions.

"}, {"id": "C", "text": "

make judicial opinions more comprehensible to readers without legal or philosophical training.

"}, {"id": "D", "text": "

bring judicial opinions in line with views that are broadly held among philosophers.

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer because it most logically completes the text’s discussion of Anita Allen’s argument about judges citing philosophers in their judicial opinions. The text indicates that judges sometimes cite philosophers when writing their judicial opinions and that, according to Allen, judges tend to cite philosophers whose views are in agreement with those of the judges themselves. Allen claims, however, that the best judicial opinions consider potential objections and rebut them, which suggests that judges may be able to strengthen their opinions by including discussions of philosophers with views contrary to their own.  

Choice A is incorrect because Allen’s claim is that judges could improve their judicial opinions by citing philosophers who disagree with the views expressed in the opinions, which would necessarily require judges to consult philosophical works. Choice C is incorrect because there’s no discussion in the text about making judicial opinions more easily understood by any particular group of readers. The focus of the text is on Allen’s claim that judicial opinions could be strengthened by the inclusion of discussions of philosophers whose views disagree with those of the judges authoring the opinions. Choice D is incorrect because the text presents Allen’s argument that discussing philosophers whose views judges disagree with could strengthen judicial opinions, not that doing so could bring those opinions into line with views that are popular among philosophers. 

"}, {"id": "23a7038f", "domain": "Information and Ideas", "skill": "Central Ideas and Details", "difficulty": "E", "type": "mc", "stimulus": "

Shimmering is a collective defense behavior that researchers have observed in giant honeybee colonies. When shimmering, different groups of bees flip their bodies up and down in what looks like waves. This defense is initiated when hornets hover near a colony, serving to deter the hornets from approaching the bees. Researchers hypothesize that this behavior is a specialized defense response to hornets, as it is not observed when other, larger predators approach the colony. 

", "stem": "

Which choice best states the main idea of the text?

", "choices": [{"id": "A", "text": "

Researchers are unsure how giant honeybees defend against predators larger than hornets. 

"}, {"id": "B", "text": "

Researchers think that shimmering in giant honeybees is a specific defense against hornets. 

"}, {"id": "C", "text": "

Hornets are known to be the main predator of giant honeybees. 

"}, {"id": "D", "text": "

Several different species of insects use shimmering to defend against hornets. 

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. The text describes a study about how giant honeybees use shimmering to defend against hornets, but not other predators. The researchers conclude that shimmering could be a specialized defense response to hornets.

Choice A is incorrect. The text says that giant honeybees don’t appear to use shimmering against other, larger predators. However, it never suggests that researchers don’t know which other defenses giant honeybees do use for those predators. Choice C is incorrect. The text says that hornets are one predator of giant honeybees, but it doesn’t say that hornets are the main predator of giant honeybees. This choice also fails to mention “shimmering,” which is a major focus of the text. Choice D is incorrect. The text only discusses the shimmering of giant honeybees—it doesn’t discuss other insects’ defense responses at all.

"}, {"id": "7a895def", "domain": "Information and Ideas", "skill": "Inferences", "difficulty": "E", "type": "mc", "stimulus": "

Georgia Douglas Johnson wrote many plays in the 1920s and 1930s. At the time, professional theater companies rarely put on plays by Black women, so few of Johnson’s plays made it to the stage. Only a small number of her plays were published in her lifetime. But that doesn’t mean that Johnson never learned what other people thought of her plays. Johnson hosted weekly get-togethers for fellow Black writers and artists in her Washington, D.C., home. Attendees would read and discuss one another’s work, including Johnson’s own. These gatherings could therefore serve as ______blank

", "stem": "

Which choice most logically completes the text?

", "choices": [{"id": "A", "text": "

an occasion for professional theater companies to put on plays. 

"}, {"id": "B", "text": "

an opportunity for Johnson to get feedback on her plays. 

"}, {"id": "C", "text": "

a way for Johnson to learn about plays that were produced in other cities.

"}, {"id": "D", "text": "

subject matter for future plays by Johnson. 

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. The passage tells us that attendees at Johnson’s get-togethers \"would read and discuss one another’s work.\" This suggests that the gatherings could provide an opportunity for Johnson to get feedback on her plays. Notice how the text foreshadows this conclusion by the mention of Johnson learning \"what other people thought of her plays.\"

Choice A is incorrect. The passage doesn’t mention theater companies attending the get-togethers, so there is no basis for this inference. Choice C is incorrect. The passage doesn’t mention learning about plays from other cities, so there is no basis for this inference. Choice D is incorrect. The passage doesn’t mention Johnson using the get-togethers as inspiration for future plays, so there is no basis for this inference.

"}, {"id": "5cf5c0d3", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "H", "type": "mc", "stimulus": "

Credited Film Output of James Young Deer, Dark Cloud, Edwin Carewe, and Lillian St. Cyr

IndividualYears activeNumber of films known and commonly credited
James Young Deer1909–192433 (actor), 35 (director), 10 (writer)
Dark Cloud1910–192035 (actor), 1 (writer)
Edwin Carewe1912–193447 (actor), 58 (director), 20 (producer), 4 (writer)
Lillian St. Cyr (Red Wing)1908–192166 (actor)

\n

Some researchers studying Indigenous actors and filmmakers in the United States have turned their attention to the early days of cinema, particularly the 1910s and 1920s, when people like James Young Deer, Dark Cloud, Edwin Carewe, and Lillian St. Cyr (known professionally as Red Wing) were involved in one way or another with numerous films. In fact, so many films and associated records for this era have been lost that counts of those four figures’ output should be taken as bare minimums rather than totals; it’s entirely possible, for example, that ______blank

", "stem": "

Which choice most effectively uses data from the table to complete the example?

", "choices": [{"id": "A", "text": "

Dark Cloud acted in significantly fewer films than did Lillian St. Cyr, who is credited with 66 performances.

"}, {"id": "B", "text": "

Edwin Carewe’s 47 credited acting roles includes only films made after 1934.

"}, {"id": "C", "text": "

Lillian St. Cyr acted in far more than 66 films and Edwin Carewe directed more than 58. 

"}, {"id": "D", "text": "

James Young Deer actually directed 33 films and acted in only 10.

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer because it uses data from the table to effectively exemplify the idea that the film outputs of the four individuals included in the table should be considered bare minimums—that is, that we should assume that the individuals actually had higher outputs than those recorded. The table presents the years during which the individuals were active and the number of known films the individuals are credited in. The table indicates that Lillian St. Cyr has 66 film credits as an actor and that Edwin Carewe has 58 film credits as a director; it follows that if some films and records for the era were lost, it’s possible that Lillian St. Cyr acted in far more than 66 films and that Edwin Carewe directed more than 58 films.

Choice A is incorrect because it doesn’t effectively exemplify the idea that the film outputs of the four individuals included in the table should be considered bare minimums. Rather than addressing the idea that the individuals likely had higher outputs than those presented in the table, this choice simply compares data from the table to make the point that Dark Cloud has fewer credited acting roles than Lillian St. Cyr (35 and 66, respectively). Choice B is incorrect because it misrepresents data from the table, even though it may exemplify the idea that the film outputs of the four individuals included in the table should be considered bare minimums by implying that Edwin Carewe acted in more than 47 films. The table indicates that Edwin Carewe was active from 1912 to 1934, meaning that his 47 credited acting roles were in films made before or during 1934, not after that time. Choice D is incorrect because it doesn’t effectively exemplify the idea that the film outputs of the four individuals included in the table should be considered bare minimums. Instead of addressing the idea that the individuals likely had higher outputs than those recorded, this choice suggests that James Young Deer actually acted in and directed fewer films than presented in the table (only 33 known films as a director instead of 35, and only 10 known films as an actor instead of 33).

"}, {"id": "f3f444bc", "domain": "Information and Ideas", "skill": "Inferences", "difficulty": "M", "type": "mc", "stimulus": "

Many mosquito repellents contain natural components that work by activating multiple odor receptors on mosquitoes’ antennae. As the insects develop resistance, new repellents are needed. Ke Dong and her team found that EBF, a molecular component of a chrysanthemum-flower extract, can repel mosquitoes by activating just one odor receptor—and this receptor, Or31, is present in all mosquito species known to carry diseases. Therefore, the researchers suggest that in developing new repellents, it would be most useful to ______blank

", "stem": "

Which choice most logically completes the text?

", "choices": [{"id": "A", "text": "

identify molecular components similar to EBF that target the activation of Or31 receptors.

"}, {"id": "B", "text": "

investigate alternative methods for extracting EBF molecules from chrysanthemums.

"}, {"id": "C", "text": "

verify the precise locations of Or31 and other odor receptors on mosquitoes’ antennae.

"}, {"id": "D", "text": "

determine the maximum number of different odor receptors that can be activated by a single molecule.

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer because it most logically completes the text’s discussion of mosquito repellents. The text begins by explaining that many repellents work by using natural components to active multiple odor receptors on mosquitoes’ antennae, and that new repellents must be created whenever mosquitoes become resistant to older ones. The text then highlights a research team’s discovery that EBF, a molecular component of a chrysanthemum-flower extract, can repel mosquitoes by activating a single odor receptor, Or31, that is shared by all species of mosquitoes known to carry diseases. The text suggests that compared to the repellents mentioned earlier, a repellent that acts on the Or31 receptor would be more effective: by noting that all mosquito species known to carry diseases share the Or31 receptor, the text suggests that the Or31 receptor may be unique in this respect, meaning that a repellent such as EBF that acts on it would be more effective since it works on a single receptor shared by all mosquito species that carry diseases, rather than a combination of receptors that is not shared by all species. Once mosquitoes become resistant to EBF, it would therefore make sense for researchers to look for other molecular components similar to EBF that target the activation of Or31 receptors, since a single such component could also repel all disease-carrying mosquitoes.

Choice B is incorrect because nothing in the text suggests that EBF molecules are difficult to extract from chrysanthemums and that investigating alternative extraction methods would therefore be useful for developing efficient and effective mosquito repellents. Rather, the text suggests that researchers developing new mosquito repellents should aim to identify molecular components similar to EBF, since that component targets the Or31 odor receptor shared by all species of mosquitoes known to carry diseases. Choice C is incorrect because nothing in the text suggests that researchers are unaware of the precise location of Or31 and other odor receptors in mosquitoes’ antennae or that knowing this information would be useful for developing efficient and effective mosquito repellents. Rather, the text suggests that researchers developing new mosquito repellents should aim to identify molecular components similar to EBF, which targets the Or31 odor receptor. Choice D is incorrect because it doesn’t logically follow that the discovery of one odor receptor shared by all disease-bearing mosquitoes should lead to further research into which repellents might activate the greatest number of odor receptors. Rather, the text suggests that researchers developing new mosquito repellents should instead search for additional molecular components that, like EBF, activate the one odor receptor that is known to be shared by all disease-bearing mosquitoes.

"}, {"id": "9aa5efc4", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "M", "type": "mc", "stimulus": "

Born in 1891 to a Quechua-speaking family in the Andes Mountains of Peru, Martín Chambi is today considered to be one of the most renowned figures of Latin American photography. In a paper for an art history class, a student claims that Chambi’s photographs have considerable ethnographic value—in his work, Chambi was able to capture diverse elements of Peruvian society, representing his subjects with both dignity and authenticity.

", "stem": "

Which finding, if true, would most directly support the student’s claim?

", "choices": [{"id": "A", "text": "

Chambi took many commissioned portraits of wealthy Peruvians, but he also produced hundreds of images carefully documenting the peoples, sites, and customs of Indigenous communities of the Andes.

"}, {"id": "B", "text": "

Chambi’s photographs demonstrate a high level of technical skill, as seen in his strategic use of illumination to create dramatic light and shadow contrasts.   

"}, {"id": "C", "text": "

During his lifetime, Chambi was known and celebrated both within and outside his native Peru, as his work was published in places like Argentina, Spain, and Mexico.

"}, {"id": "D", "text": "

Some of the peoples and places Chambi photographed had long been popular subjects for Peruvian photographers.

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer because it presents a finding that, if true, would support the claim about Chambi’s photographs. The text describes a student advancing the claim that Chambi’s photographs “have considerable ethnographic value”—meaning that they are valuable as records of cultures—and that they “capture diverse elements of Peruvian society” in a respectful way. If it’s true that Chambi carefully photographed people from a range of different communities in Peru as well as photographed the customs and sites of different communities, that would lend support to the claim that the photographs have ethnographic value as depictions of diverse elements of society in Peru. 

Choice B is incorrect because the student’s claim is that Chambi’s photographs have considerable ethnographic value because they depict diverse elements of Peruvian society; the student doesn’t claim anything about the technical skill demonstrated in the photographs. Choice C is incorrect because neither Chambi’s reputation nor the locations where his photographs may have been published would be relevant to the student’s claim that his photographs are valuable as an ethnographic record of Peru’s diverse society. Choice D is incorrect because the popularity among other photographers of the people and places that Chambi photographed would be irrelevant to the student’s claim that Chambi’s photographs are valuable as an ethnographic record of Peru’s diverse society. 

"}, {"id": "b2e54b50", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "H", "type": "mc", "stimulus": "

Correlations Between Congestion Ratings and Features of the Crowd in Raters’ Immediate Vicinity

Crowd featureBefore obstacleAfter obstacleOverall
Density0.85920.73080.7447
Velocity−0.9357negative 0.9357−0.9518negative 0.9518−0.8587negative 0.8587

\n

Researcher Xiaolu Jia and colleagues monitored individuals’ velocity and the surrounding crowd density as a group of study participants walked through a space and navigated around an obstacle. Participants rated how congested it seemed before the obstacle, after the obstacle, and overall, and the researchers correlated those ratings with velocity and density. (Correlations range from −1negative 1 to 1, with greater distance from 0 indicating greater strength). The researchers concluded that the correlations with velocity are stronger than those with density.

", "stem": "

Which choice best describes data from the table that support the researchers’ conclusion?

", "choices": [{"id": "A", "text": "

The correlation between congestion ratings before the obstacle and density is further from 0 than the correlation between overall congestion rating and velocity is.

"}, {"id": "B", "text": "

The correlation between congestion ratings before the obstacle and velocity is further from 0 than the correlation between congestion overall and velocity is.

"}, {"id": "C", "text": "

For each of the three ratings, the correlation with velocity is negative while the correlation with density is positive.

"}, {"id": "D", "text": "

For each of the three ratings, correlations with velocity are further from 0 than the corresponding correlations with density are.

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. The text tells us that the farther the correlation is from 0, the “stronger” it is (doesn’t matter if it’s negative or positive). The table shows that the correlations with velocity are farther from zero than the correlations with density, which supports the conclusion that the correlations with velocity are stronger.

Choice A is incorrect. This choice doesn’t support the conclusion. It makes an “apples to oranges” comparison by comparing density and velocity correlations across features instead of comparing them for each feature. Choice B is incorrect. This choice doesn’t support the conclusion. It doesn’t include the density correlations for comparison. Choice C is incorrect. This choice doesn’t support the conclusion. The text tells us that the farther the correlation is from 0, the “stronger” it is: it doesn’t matter for “strength” whether it’s negative or positive.

"}, {"id": "8af28416", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "E", "type": "mc", "stimulus": "
\n\n\n\n\n2,8002,6002,4002,2002,0001,8001,6001,4001,2001,0008006004002000Number of organic farmsCaliforniaWisconsinNew YorkPennsylvaniaIowaWashingtonUS States with the Greatest Number of Organic Farms in 2016State
\n

Organic farming is a method of growing food that tries to reduce environmental harm by using natural forms of pest control and avoiding fertilizers made with synthetic materials. Organic farms are still a small fraction of the total farms in the United States, but they have been becoming more popular. According to the US Department of Agriculture, in 2016 California had between 2,600 and 2,800 organic farms and ______blank

", "stem": "

Which choice most effectively uses data from the graph to complete the text?

", "choices": [{"id": "A", "text": "

Washington had between 600 and 800 organic farms.

"}, {"id": "B", "text": "

New York had fewer than 800 organic farms.

"}, {"id": "C", "text": "

Wisconsin and Iowa each had between 1,200 and 1,400 organic farms.

"}, {"id": "D", "text": "

Pennsylvania had more than 1,200 organic farms.

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer because it uses data from the graph to accurately complete the text. The graph shows the number of organic farms located in each of six US states in 2016: between 2,600 and 2,800 in California; between 1,200 and 1,400 in Wisconsin; between 1,000 and 1,200 in New York; approximately 800 in Pennsylvania; and between 600 and 800 in both Iowa and Washington. The last sentence of the text provides information about the number of organic farms in 2016, first describing the number in California. The best completion of the sentence is the choice that accurately describes the number of organic farms in 2016 in another state, which the assertion that Washington had between 600 and 800 organic farms provides.

Choice B is incorrect because it doesn’t accurately reflect the data from the graph. The graph indicates that there were between 1,000 and 1,200 organic farms in New York, not fewer than 800 organic farms. Choice C is incorrect because it doesn’t accurately reflect the data from the graph. While the graph indicates that there were between 1,200 and 1,400 organic farms in Wisconsin in 2016, there were only between 600 and 800 in Iowa. Choice D is incorrect because it doesn’t accurately reflect the data from the graph. The graph indicates that in 2016 there were approximately 800 organic farms in Pennsylvania, not more than 1,200. 

"}, {"id": "145da981", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "E", "type": "mc", "stimulus": "

Effect of Paywall Introduction on Newspaper Companies’ Revenues

NewspaperTotal revenue change ($ in thousands)Percentage change (%)Newspaper size
Los Angeles Times93,96612.5large
The New York Times235,78820large
The Denver Post−3,765negative 3,765−1negative 1small
Sun Sentinel−24,899negative 24,899−11.9negative 11.9small
Chicago Tribune94,49219large

\n

Digital paywalls restrict access to online content to those with a paid subscription. In an investigation of the effect of paywalls on newspaper company revenues for print and digital subscriptions and advertising, Doug J. Chung and colleagues compared actual outcomes (with a paywall) to control estimates (without a paywall). The researchers concluded that introducing a paywall is generally more beneficial for larger newspapers, which have high circulation and tend to offer a substantial amount of unique online content.

", "stem": "

Which choice best describes data from the table that support Chung and colleagues’ conclusion?

", "choices": [{"id": "A", "text": "

The Chicago Tribune and the Los Angeles Times had similar total revenue changes, but the Los Angeles Times had a smaller percentage change.

"}, {"id": "B", "text": "

The Los Angeles Times had a 12.5% revenue change, while the Chicago Tribune had a 19% revenue change.

"}, {"id": "C", "text": "

The New York Times had a 20% revenue change, while the Denver Post had a −1%negative 1% revenue change.

"}, {"id": "D", "text": "

The Denver Post had only a −1%negative 1% revenue change, which was the smallest percentage change of the selected companies.

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. The conclusion is that paywalls are more beneficial for large newspapers. This data supports that conclusion by comparing the revenue increase of a large newspaper to the revenue decrease of a small newspaper.

Choice A is incorrect. This choice doesn’t support the conclusion. It doesn’t include any small newspapers for comparison. Choice B is incorrect. This choice doesn’t support the conclusion. It doesn’t include any small newspapers for comparison. Choice D is incorrect. This choice doesn’t support the conclusion. It doesn’t include any large newspapers for comparison.

"}, {"id": "014b3394", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "H", "type": "mc", "stimulus": "

Average Number and Duration of Torpor Bouts and Arousal Episodes for Alaska Marmots and Arctic Ground Squirrels, 2008–2011

FeatureAlaska marmotsArctic ground squirrels
torpor bouts1210.5
duration per bout13.81 days16.77 days
arousal episodes119.5
duration per episode21.2 hours14.2 hours

\n

When hibernating, Alaska marmots and Arctic ground squirrels enter a state called torpor, which minimizes the energy their bodies need to function. Often a hibernating animal will temporarily come out of torpor (called an arousal episode) and its metabolic rate will rise, burning more of the precious energy the animal needs to survive the winter. Alaska marmots hibernate in groups and therefore burn less energy keeping warm during these episodes than they would if they were alone. A researcher hypothesized that because Arctic ground squirrels hibernate alone, they would likely exhibit longer bouts of torpor and shorter arousal episodes than Alaska marmots.

", "stem": "

Which choice best describes data from the table that support the researcher’s hypothesis?

", "choices": [{"id": "A", "text": "

The Alaska marmots’ arousal episodes lasted for days, while the Arctic ground squirrels’ arousal episodes lasted less than a day.

"}, {"id": "B", "text": "

The Alaska marmots and the Arctic ground squirrels both maintained torpor for several consecutive days per bout, on average.

"}, {"id": "C", "text": "

The Alaska marmots had shorter torpor bouts and longer arousal episodes than the Arctic ground squirrels did.

"}, {"id": "D", "text": "

The Alaska marmots had more torpor bouts than arousal episodes, but their arousal episodes were much shorter than their torpor bouts. 

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer because it describes data from the table that support the researcher’s hypothesis. According to the text, the researcher hypothesized that Arctic ground squirrels would exhibit longer torpor bouts and shorter arousal episodes than Alaska marmots do—or, put the other way, that the marmots would show shorter torpor bouts and longer arousal episodes than the ground squirrels do. The table shows data about torpor bouts and arousal episodes for the two species from 2008 to 2011. According to the table, the average duration of torpor bouts was 13.81 days for Alaska marmots, shorter than the average of 16.77 days for Arctic ground squirrels, and the average duration of arousal episodes was 21.2 hours for Alaska marmots, longer than the average of 14.2 hours for Arctic ground squirrels. Thus, the table supports the researcher’s hypothesis by showing that Alaska marmots had shorter bouts of torpor and longer arousal episodes than Arctic ground squirrels did.

Choice A is incorrect because it inaccurately describes data from the table and doesn’t support the researcher’s hypothesis. The table shows that the average duration of arousal episodes was less than a day for both Alaska marmots (21.2 hours) and Arctic ground squirrels (14.2 hours). Additionally, information about arousal episodes for Alaska marmots and Arctic ground squirrels isn’t sufficient to support a hypothesis involving comparisons of both arousal episodes and torpor bouts for those animals. Choice B is incorrect because it doesn’t support the researcher’s hypothesis, which involves comparisons of arousal episodes as well as torpor bouts for Alaska marmots and Arctic ground squirrels. Noting that both animals had torpor bouts lasting several days, on average, doesn’t address arousal episodes at all, nor does it reveal how the animals’ torpor bouts compared. Choice D is incorrect because it doesn’t support the researcher’s hypothesis. Although the table does show that Alaska marmots had more torpor bouts (12) than arousal episodes (11) and that their arousal episodes were much shorter than their torpor bouts (21.2 hours and 13.81 days, respectively), comparing data across only Alaska marmot behaviors isn’t sufficient to support a hypothesis about torpor and arousal behaviors of both Alaska marmots and Arctic ground squirrels.

"}, {"id": "7921b86b", "domain": "Information and Ideas", "skill": "Central Ideas and Details", "difficulty": "E", "type": "mc", "stimulus": "

Oluwaseyi Moejoh cofounded U-recycle Initiative Africa when she was only a teenager. Moejoh and her team founded the organization to teach young people how their actions affect the environment and why recycling is important. For example, the organization put on an exhibit of art made using recycled materials. 

", "stem": "

According to the text, what is one reason Moejoh and others founded U-recycle Initiative Africa? 

", "choices": [{"id": "A", "text": "

To bring attention to overlooked African artists

"}, {"id": "B", "text": "

To teach young people why recycling is important

"}, {"id": "C", "text": "

To help adults gain important outdoor skills

"}, {"id": "D", "text": "

To give teenagers advice about starting businesses

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer because it describes a reason that Moejoh and team founded U-recycle Initiative Africa. The text mentions two reasons the initiative was founded: to teach young people about how they affect the environment and to teach them “why recycling is important.” Thus, teaching the importance of recycling to young people accurately describes a motivation that the text cites as a reason for the initiative’s founding.

Choice A is incorrect. Although art is mentioned in the text, there are no details about artists or whether they are being overlooked. Choice C is incorrect because the text is explicitly about young people and their relationship to the environment and recycling. There is no mention of adults or outdoor skills. Choice D is incorrect. Although the text discusses young people, which likely includes teenagers, there is no mention of starting businesses.

"}, {"id": "46e45728", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "E", "type": "mc", "stimulus": "

Daily Distance Traveled by Adult Mountain Lions in Three Seasons

SeasonKilometers per day traveled by adult femalesKilometers per day traveled by adult males
cold-dry9.2815.81
monsoon12.6418.93
hot-dry12.4818.87

\n

Wildlife researcher Dana L. Karelus and her colleagues tracked the movements of female and male adult mountain lions over three seasons: the cold-dry season, the hot-dry season, and the monsoon season. They found that the least amount of travel per day occurred in ______blank

", "stem": "

Which choice most effectively uses data from the table to complete the statement?

", "choices": [{"id": "A", "text": "

the cold-dry season for both females and males.

"}, {"id": "B", "text": "

the cold-dry season for females and the hot-dry season for males.

"}, {"id": "C", "text": "

the hot-dry season for females and the monsoon season for males.

"}, {"id": "D", "text": "

the monsoon season for both females and males. 

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. Females only traveled 9.28 km per day in the cold-dry season, versus 12.64 and 12.48 km per day in the monsoon and hot-dry seasons, respectively. Males only traveled 15.81 km per day per day in the cold-dry season, versus 18.93 and 18.87 km per day in the monsoon and hot-dry seasons, respectively. So, the cold-dry season was the season where both males and females had the least daily travel.

Choice B is incorrect. Although females traveled least in the cold-dry season, males didn’t travel least in the hot-dry season. Instead, they traveled less per day in the cold-dry season as well. Choice C is incorrect. Females had less daily travel in the cold-dry season than in the hot-dry season (9.28 versus 12.48 km per day), and males had less daily travel in the cold-dry season than in the monsoon season (15.81 versus 18.93 km per day). Choice D is incorrect. In fact, both females and males traveled the most kilometers per day in the monsoon season.

"}, {"id": "9c407117", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "H", "type": "mc", "stimulus": "

A student performs an experiment testing her hypothesis that a slightly acidic soil environment is more beneficial for the growth of the plant Brassica rapa parachinensis (a vegetable commonly known as choy sum) than a neutral soil environment. She plants sixteen seeds of choy sum in a mixture of equal amounts of coffee grounds (which are highly acidic) and potting soil and another sixteen seeds in potting soil without coffee grounds as the control for the experiment. The two groups of seeds were exposed to the same growing conditions and monitored for three weeks.

", "stem": "

Which finding, if true, would most directly weaken the student’s hypothesis?

", "choices": [{"id": "A", "text": "

The choy sum planted in the soil without coffee grounds were significantly taller at the end of the experiment than the choy sum planted in the mixture of soil and coffee grounds.

"}, {"id": "B", "text": "

The choy sum grown in the soil without coffee grounds weighed significantly less at the end of the experiment than the choy sum grown in the mixture of soil and coffee grounds.

"}, {"id": "C", "text": "

The choy sum seeds planted in the soil without coffee grounds sprouted significantly later in the experiment than did the seeds planted in the mixture of soil and coffee grounds.

"}, {"id": "D", "text": "

Significantly fewer of the choy sum seeds planted in the soil without coffee grounds sprouted plants than did the seeds planted in the mixture of soil and coffee grounds.

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer because it describes an experimental outcome that would most directly weaken the student’s hypothesis. According to the text, the student hypothesizes that Brassica rapa parachinensis (choy sum) will benefit more from acidic soil than it will from neutral soil. The text then explains that the student planted 16 choy sum seeds in potting soil with coffee grounds added to increase acidity and another 16 seeds in soil without coffee grounds as a control (a group identical to the experimental group except for the experimental modification being tested). If the hypothesis were correct, the plants in the more acidic soil-and-coffee-grounds mixture would grow faster than those in the control group. However, choice A proposes a scenario in which the plants in soil without coffee grounds were “significantly taller” than those in the more acidic mixture—an outcome that weakens the hypothesis that higher acidity is beneficial to the plants’ growth.

Choice B is incorrect. If the choy sum planted in the neutral soil produced less plant matter and therefore weighed less than the choy sum planted in the acidic soil-and-coffee-grounds mixture, this finding would strengthen the student’s hypothesis, not weaken it. Choice C is incorrect. If seeds planted in neutral soil (without coffee grounds) sprouted significantly later than seeds planted in the acidic soil-and-coffee-grounds mixture, this finding would strengthen, not weaken, the student’s hypothesis that acidic soil benefits choy sum. Choice D is incorrect. If seeds planted in the neutral soil (without coffee grounds) sprouted significantly fewer plants than seeds planted in the acidic soil-and-coffee-grounds mixture did, this finding would strengthen, not weaken, the student’s hypothesis that choy sum benefits from acidic soil.

"}, {"id": "84136d69", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "M", "type": "mc", "stimulus": "

Five of the Responses to Survey about Actions to Conserve Energy

ActionAction categoryPercentage of respondents selecting action (%)
Use efficient cars/hybridsefficiency2.8
Change thermostat settingcurtailment6.3
Use bike or public transportation instead of carcurtailment12.9
Use efficient light bulbsefficiency3.6
Turn off lightscurtailment19.6

\n

In a survey of public perceptions of energy use, researcher Shahzeen Attari and her team asked respondents to name the most effective action ordinary people can take to conserve energy. The team categorized each action as either an efficiency or a curtailment and found that respondents tended to name curtailments more often than they did efficiencies. For example, 19.6% of respondents stated that the most effective way to conserve energy is to turn off the lights, while only ______blank

", "stem": "

Which choice most effectively uses data from the table to complete the text?

", "choices": [{"id": "A", "text": "

6.3% of respondents said it was most effective to use efficient cars or hybrids.

"}, {"id": "B", "text": "

2.8% of respondents said it was most effective to change the thermostat setting.

"}, {"id": "C", "text": "

12.9% of respondents said it was most effective to use a bike or public transportation.

"}, {"id": "D", "text": "

3.6% of respondents said it was most effective to use efficient light bulbs.

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer because it most effectively uses data from the table to complete the text’s discussion of Attari and her team’s survey results. The text states that the team asked respondents to identify the most effective action people can take to save energy, with the team classifying each action as either an efficiency or a curtailment. According to the text, respondents named curtailments more often than they did efficiencies. The text then offers an example that begins by citing a curtailment, turning off the lights, that was selected by a relatively high percentage of respondents (19.6%). Given that the example is presented in support of the idea that more respondents selected curtailments than efficiencies, the most effective way to complete the example is by citing an efficiency, using efficient light bulbs, that was selected by a relatively low percentage of respondents (only 3.6%).

Choice A is incorrect because it inaccurately describes data in the table. The data indicate that 6.3% of respondents said the most effective action was to change the thermostat setting, not to use efficient cars or hybrids. Choice B is incorrect because it inaccurately describes data in the table. The data indicate that 2.8% of respondents said the most effective action was to use efficient cars/hybrids, not to change the thermostat setting. Choice C is incorrect because it mentions a curtailment (using a bike or public transportation) and not an efficiency. The text states that a research team asked respondents to identify the most effective action people can take to save energy, with the team classifying each action as either an efficiency or a curtailment. According to the text, respondents named curtailments more often than they did efficiencies. The text then offers an example that begins by citing a curtailment, turning off the lights, that was selected by a relatively high percentage of respondents (19.6%). Given that the example is presented in support of the idea that more people selected curtailments than efficiencies, the most effective way to complete the example is not by referring to another curtailment but rather by referring to an efficiency that was selected by a relatively low percentage of respondents.

"}, {"id": "95146ebb", "domain": "Information and Ideas", "skill": "Central Ideas and Details", "difficulty": "M", "type": "mc", "stimulus": "

The ice melted on a Norwegian mountain during a particularly warm summer in 2019, revealing a 1,700-year-old sandal to a mountaineer looking for artifacts. The sandal would normally have degraded quickly, but it was instead well preserved for centuries by the surrounding ice. According to archaeologist Espen Finstad and his team, the sandal, like those worn by imperial Romans, wouldn’t have offered any protection from the cold in the mountains, so some kind of insulation, like fabric or animal skin, would have needed to be worn on the feet with the sandal.

", "stem": "

What does the text indicate about the discovery of the sandal?

", "choices": [{"id": "A", "text": "

Temperatures contributed to both protecting and revealing the sandal.

"}, {"id": "B", "text": "

The discovery revealed that the Roman Empire had more influence on Norway than archaeologists previously assumed.

"}, {"id": "C", "text": "

Archaeologists would have found the sandal eventually without help from the general public.

"}, {"id": "D", "text": "

The sandal would have degraded if it hadn’t been removed from the ice.

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. A \"particularly warm summer\" revealed the sandal, and centuries of ice kept it \"well preserved.\"

Choice B is incorrect. This choice doesn’t reflect the information in the text. The sandal is similar to Roman sandals, but there is no indication that it was a result of Roman influence. Choice C is incorrect. The text doesn’t support this choice. We don’t have enough information to know whether or not archaeologists would have found the sandal without people like the treasure-hunting mountaineer. Choice D is incorrect. The text says the opposite of this choice. The sandal was preserved by the ice for centuries.

"}, {"id": "9077be25", "domain": "Information and Ideas", "skill": "Inferences", "difficulty": "E", "type": "mc", "stimulus": "

Alice Guy-Blaché directed hundreds of films between 1896 and 1920. She wanted audiences to feel like they were watching real people on screen. She would encourage actors in her films to behave naturally. Guy-Blaché even hung a large sign reading “Be Natural” in the studio where she made her films. At the time, films lacked sound, so actors needed to rely solely on their bodies and facial expressions to convey emotions. As a result, actors tended to highly exaggerate their actions and expressions. The style of acting in Guy-Blaché’s films was therefore ______blank

", "stem": "

Which choice most logically completes the text?

", "choices": [{"id": "A", "text": "

copied by many of Guy-Blaché’s peers.

"}, {"id": "B", "text": "

familiar to actors who had worked on other directors’ films. 

"}, {"id": "C", "text": "

very unusual for the period. 

"}, {"id": "D", "text": "

better than film acting today.

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. The text tells us that “actors tended to highly exaggerate their actions and expressions” in films produced from 1896 to 1920. This suggests that the natural style of acting in Guy-Blaché’s films was very unusual for the time.

Choice A is incorrect. The text never discusses any other directors copying the style of acting found in Guy-Blaché’s films, and in fact suggests the opposite—that it was unusual for directors to suggest this style of acting at the time. Choice B is incorrect. The text never discusses actors’ familiarity with the style of acting found in Guy-Blaché’s films, so there isn’t much basis for this inference. But since the text tells us that other films of the period used a highly exaggerated form of acting, we might predict that the natural style in Guy-Blachés films would have been unfamiliar to these actors. Choice D is incorrect. The text never discusses film acting today, so there’s no basis for this inference.

"}, {"id": "f27559d4", "domain": "Information and Ideas", "skill": "Inferences", "difficulty": "H", "type": "mc", "stimulus": "

Volunteering, or giving time for a community service for free, is a valuable form of civic engagement because helping in a community is also good for society as a whole. In a survey of youths in the United States, most young people said that they believe volunteering is a way to help people on an individual level. Meanwhile, only 6% of the youths said that they think volunteering is a way to help fix problems in society overall. These replies suggest that ______blank

", "stem": "

Which choice most logically completes the text?

", "choices": [{"id": "A", "text": "

many young people think they can volunteer only within their own communities.

"}, {"id": "B", "text": "

volunteering may be even more helpful than many young people think it is.

"}, {"id": "C", "text": "

volunteering can help society overall more than it can help individual people.

"}, {"id": "D", "text": "

many young people may not know how to find ways to volunteer their time.

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer because it most logically completes the text’s discussion of volunteering. The text asserts that volunteering benefits both the community in which one volunteers and society as a whole. It then states that in a survey of young people, a majority of respondents said that volunteering helps individuals, but only 6% of respondents said that volunteering helps society as a whole. If volunteering does in fact help society as a whole, as the text says, but only 6% of young people believe it does, then it’s reasonable to conclude that volunteering is more helpful than many young people think it is. 

Choice A is incorrect because the text discusses young people’s beliefs about the benefits of volunteering, not where young people believe they are able to volunteer. Nothing in the text suggests that many young people believe they are only able to volunteer in their own communities. Choice C is incorrect. Although the text indicates that volunteering is beneficial for society as a whole, nothing in the text suggests that volunteering can benefit society more than it can benefit individual people. The text doesn’t compare the benefits to society with the benefits to individuals. Choice D is incorrect because the text discusses young people’s beliefs about the benefits of volunteering, not how to find volunteering opportunities. There’s nothing in the text to suggest that many young people don’t know how to volunteer. 

"}, {"id": "d1539546", "domain": "Information and Ideas", "skill": "Inferences", "difficulty": "H", "type": "mc", "stimulus": "

Tides can deposit large quantities of dead vegetation within a salt marsh, smothering healthy plants and leaving a salt panne—a depression devoid of plants that tends to trap standing water—in the marsh’s interior. Ecologist Kathryn Beheshti and colleagues found that burrowing crabs living within these pannes improve drainage by loosening the soil, leading the pannes to shrink as marsh plants move back in. At salt marsh edges, however, crab-induced soil loosening can promote marsh loss by accelerating erosion, suggesting that the burrowing action of crabs ______blank    

", "stem": "

Which choice most logically completes the text?

", "choices": [{"id": "A", "text": "

can be beneficial to marshes with small pannes but can be harmful to marshes with large pannes.

"}, {"id": "B", "text": "

may promote increases in marsh plants or decreases in marsh plants, depending on the crabs’ location.

"}, {"id": "C", "text": "

tends to be more heavily concentrated in areas of marsh interiors with standing water than at marsh edges.

"}, {"id": "D", "text": "

varies in intensity depending on the size of the panne relative to the size of the surrounding marsh.

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. The text says that crab burrowing in the pannes enables plants to grow there again. It also says that crab burrowing at the edges of the marsh speeds up marsh loss. This suggests that burrowing crabs can either help or hurt marshes, depending on where they’re located.

Choice A is incorrect. This inference isn’t supported. The text never discusses pannes of different sizes. Choice C is incorrect. This inference isn’t supported. The text never suggests that crabs do more burrowing in the pannes (the areas with standing water) than they do at the edges. Rather, the text says that the burrowing that happens in the pannes is beneficial, while the burrowing that happens at the edges is harmful. Choice D is incorrect. This inference isn’t supported. The text never discusses the intensity of crab burrowing, nor does it discuss the size of the panne relative to the size of the marsh.

"}, {"id": "faaf484f", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "E", "type": "mc", "stimulus": "

Percent of Residents of City Areas in Favor of Adding More Bike Paths

City AreaPercent of area’s residents in favor of adding more bike paths
North East12%
North Central26%
North West46%
South West88%
South Central33%

\n

A city’s Parks and Recreation department is interested in providing residents with more opportunities for bicycling in their neighborhoods. They’re considering adding more bike paths and conducted a survey to understand where demand for more bike paths is highest. The survey indicated the highest level of demand, with 88 percent of the residents interested in adding more bike paths, is in the city’s ______blank

", "stem": "

Which choice most effectively uses data from the table to complete the statement?

", "choices": [{"id": "A", "text": "

South West area.

"}, {"id": "B", "text": "

South Central area.

"}, {"id": "C", "text": "

North East area.

"}, {"id": "D", "text": "

North Central area.

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer because it most effectively uses data from the table to complete the statement about the bike path survey. The table presents the percent of residents from five city areas who are in favor of adding more bike paths. With 88 percent of residents in favor of adding bike paths, the city’s South West area has the highest level of demand. 

Choice B is incorrect because, according to the data in the table, 33 percent of residents in the South Central area of the city are in favor of additional bike paths. The area of the city that has 88 percent of its surveyed residents in favor of additional bike paths will best complete the statement. Choice C is incorrect because, according to the data in the table, 12 percent of residents in the North East area of the city are in favor of additional bike paths. The area of the city that has 88 percent of its surveyed residents in favor of additional bike paths will best complete the statement. Choice D is incorrect because, according to the data in the table, 26 percent of residents in the North Central area of the city are in favor of additional bike paths. The area of the city that has 88 percent of its surveyed residents in favor of additional bike paths will best complete the statement.

"}, {"id": "df9c5a1d", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "H", "type": "mc", "stimulus": "

Juvenile Plants Found Growing on Bare Ground and in Patches of Vegetation for Five Species

SpeciesBare groundPatches of vegetationTotalPercent found in patches of vegetation
T. moroderi9132259.1%
T. libanitis8312020359.1%
H. syriacim9510620152.7%
H. squamatum21832153959.6%
H. stoechas11122352.2%

\n

Alicia Montesinos-Navarro, Isabelle Storer, and Rocío Perez-Barrales recently examined several plots within a diverse plant community in southeast Spain. The researchers calculated that if individual plants were randomly distributed on this particular landscape, only about 15% would be with other plants in patches of vegetation. They counted the number of juvenile plants of five species growing in patches of vegetation and the number growing alone on bare ground and compared those numbers to what would be expected if the plants were randomly distributed. Based on these results, they claim that plants of these species that grow in close proximity to other plants gain an advantage at an early developmental stage.

", "stem": "

Which choice best describes data from the table that support the researchers’ claim?

", "choices": [{"id": "A", "text": "

For all five species, less than 75% of juvenile plants were growing in patches of vegetation.

"}, {"id": "B", "text": "

The species with the greatest number of juvenile plants growing in patches of vegetation was H. stoechas.

"}, {"id": "C", "text": "

For T. libanitis and T. moroderi, the percentage of juvenile plants growing in patches of vegetation was less than what would be expected if plants were randomly distributed.

"}, {"id": "D", "text": "

For each species, the percentage of juvenile plants growing in patches of vegetation was substantially higher than what would be expected if plants were randomly distributed.

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer because it provides the most direct support from the table for the claim that the plants growing in close proximity to other plants gained an advantage at an early developmental stage. The table shows the total number of juvenile plants from five species that were found growing on bare ground and in patches of vegetation as well as the percentage of the total number of each species that were growing in patches of vegetation. For each of the five species, more than 50% of the juvenile plants were growing in patches of vegetation. The text notes, however, that a random distribution of plants across the landscape should result in only about 15% of the plants being found in patches of vegetation. In other words, for each of the five species, the percentage of juvenile plants found growing in patches of vegetation was substantially higher than could be explained by chance alone. This finding supports the claim in the text: if plants growing in patches are overrepresented among plants that have survived to the juvenile stage, as the data show they are, then it suggests that it’s advantageous for plants at an early stage of development to grow in patches of vegetation.  

Choice A is incorrect because the statement that less than 75% of juvenile plants were found growing in patches of vegetation, while true, doesn’t clearly support the claim that the plants growing in close proximity to other plants gained an advantage at an early developmental stage. Saying that less than 75% of plants were found in patches doesn’t indicate how the percentage growing in patches compares with the percentage that would be expected to grow in patches on the basis of chance alone, which is the information necessary to evaluate whether the claim in the text has support in the table. Put another way, if the percentage of plants found growing in patches was 15% or less, it would be true that less than 75% were found in patches, but the data would in fact weaken the claim in the text, not strengthen it, since the data would show that growing in patches wasn’t advantageous. Choice B is incorrect because only 12 plants of this species were found growing in patches, which was the lowest number of any species, not the greatest number. Additionally, even if it were true that this species had the greatest number of plants growing in patches, the finding would be irrelevant to the claim that plants of all five species gained an advantage by growing in close proximity to other plants. Choice C is incorrect because 59.1% of the plants of these species were found growing in patches, which is a far greater percentage, not a lower percentage, than what would be expected if plants were randomly distributed (around 15%). Additionally, if it were true that the percentage of plants growing in patches was lower for these species than what would be expected from chance alone, that finding would weaken, not strengthen, the claim that growing in patches is advantageous. 

"}, {"id": "1d0b5bf4", "domain": "Information and Ideas", "skill": "Inferences", "difficulty": "E", "type": "mc", "stimulus": "

To create the poems in her 2017 collection One Last Word, poet Nikki Grimes used a writing method called the golden shovel. This method often involves choosing a line from an existing poem and then using each word from that line as the last word of each line in a new poem. Grimes wanted the poems in One Last Word to honor important Black poets of the past, so she chose lines by poets such as Langston Hughes and Georgia Douglas Johnson. Writing in this way can be challenging and might seem as though it would produce awkward poems. However, reviewers praised One Last Word as a beautiful and powerful tribute to the poets who inspired it. This reaction suggests that ______blank

", "stem": "

Which choice most logically completes the text?

", "choices": [{"id": "A", "text": "

most reviewers didn’t understand Grimes’s goal for One Last Word.

"}, {"id": "B", "text": "

Grimes successfully used the golden shovel method to achieve her goal for One Last Word.

"}, {"id": "C", "text": "

Langston Hughes and Georgia Douglas Johnson are two of Grimes’s favorite poets.

"}, {"id": "D", "text": "

Grimes inspired many other writers to create poems using the golden shovel method.

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer because it most logically completes the text’s discussion of Nikki Grimes’s poetry collection One Last Word. The text explains that Grimes used a writing method called the golden shovel to create the poems in her book. According to the text, the method involves basing a new poem on a line from an existing poem. The text then mentions Langston Hughes and Georgia Douglas Johnson as examples of important Black poets whose lines of poetry form the basis of Grimes’s poems. The text goes on to say that this writing method is difficult and that the resulting poems can be awkward, but reviewers have positively reviewed Grimes’s book. If the reviewers of One Last Word specifically note that the work is a “beautiful and powerful tribute to the poets who inspired it,” then they must have appreciated how Grimes used the golden shovel method to pay tribute to other poets. This suggests that Grimes was successful in using the golden shovel method to achieve her goal of honoring Black poets in her book.

Choice A is incorrect because the reaction suggests that most reviewers did understand Grimes’s goal for her book. According to the text, the reviewers noted that the poems in her book were a “beautiful and powerful tribute to the poets who inspired it.” Earlier, the text claims that Grimes intended the poems “to honor important Black poets of the past,” so in their praise of her book, the reviewers clearly indicated that they understood Grimes’s goal. Choice C is incorrect. Although it’s likely that Grimes sought to honor Hughes and Johnson in her book of poetry because they’re among her favorite poets, this fact isn’t suggested by the reviewers’ positive reaction to her book. Instead, the reaction suggests that Grimes was successful in her use of the golden shovel method. Choice D is incorrect because the text doesn’t discuss whether other writers were inspired by Grimes to use the golden shovel method in their poetry. The text mentions the poets Hughes and Johnson as examples of poets honored in Grimes’s book and describes reviewers’ positive reception of her book, but it doesn’t detail Grimes’s impact on other writers.

"}, {"id": "dc47c2ac", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "M", "type": "mc", "stimulus": "

Although most songbirds build open, cupped nests, some species build domed nests with roofs that provide much more protection. Many ecologists have assumed that domed nests would provide protection from weather conditions and thus would allow species that build them to have larger geographic ranges than species that build open nests do. To evaluate this assumption, a research team led by evolutionary biologist Iliana Medina analyzed data for over 3,000 species of songbirds.

", "stem": "

Which finding from Medina and her colleagues’ study, if true, would most directly challenge the assumption in the underlined sentence?

", "choices": [{"id": "A", "text": "

Species that build open nests tend to have higher extinction rates than species that build domed nests.

"}, {"id": "B", "text": "

Species that build open nests tend to be smaller in size than species that build domed nests.

"}, {"id": "C", "text": "

Species that build open nests tend to use fewer materials to build their nests than species that build domed nests do.

"}, {"id": "D", "text": "

Species that build open nests tend to have larger ranges than species that build domed nests.

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer because it presents a finding that, if true, would challenge the assumption that many ecologists have made about the connection between the building of domed nests and geographic range in songbirds. The text says that many ecologists have assumed that since domed nests provide protection from weather conditions, songbird species that build such nests should be able to have larger geographic ranges than songbird species that build open nests do. If Medina and her colleagues found that species that build open nests tend to have larger geographic ranges than species that build domed nests do, their finding would show the opposite of what the ecologists have assumed. It would therefore challenge the ecologists’ assumption.

Choice A is incorrect because nothing in the text suggests that there’s a relationship between songbird species’ extinction rates and their geographic ranges. The finding that species that build open nests tend to have higher extinction rates than species that build domed nests do would therefore have no clear bearing on the ecologists’ assumption that domed nests allow species that build them to have larger geographic ranges than those of species that build open nests. Choice B is incorrect because nothing in the text suggests that there’s a relationship between songbird species’ sizes and their geographic ranges. The finding that species that build open nests tend to be smaller in size than species that build domed nests are would therefore have no clear bearing on the ecologists’ assumption that domed nests allow species that build them to have larger geographic ranges than those of species that build open nests. Choice C is incorrect because although the text indicates that many ecologists have assumed that there’s a connection between how songbird species build their nests and the species’ geographic ranges, the text says that this assumption is based on the shape of the nests—that is, whether the nests are domed or open—not the number of materials used. The finding that species that build open nests tend to use fewer materials to build their nests than species that build domed nests do would therefore have no clear bearing on the ecologists’ assumption that domed nests allow species that build them to have larger geographic ranges than those of species that build open nests.

"}, {"id": "7fdba7ad", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "E", "type": "mc", "stimulus": "

The Milky Way galaxy is composed of millions of stars in a relatively flat structure containing a thin disk and a thick disk. Based on computer simulations and analysis of data on the brightness, position, and chemical composition of about 250,000 stars in the thick disk (collected from two telescopes, one in China and one orbiting in space), astrophysicists Maosheng Xiang and Hans-Walter Rix claim that the thick disk of the Milky Way formed in two distinct phases rather than a single one.

", "stem": "

Which finding, if true, would most directly support the researchers’ claim?

", "choices": [{"id": "A", "text": "

The telescopes used by the researchers have detected stars of similar ages in galaxies other than the Milky Way.

"}, {"id": "B", "text": "

There’s an age difference of about 2 billion years between certain stars in the thick disk.

"}, {"id": "C", "text": "

The thin disk contains about twice as many stars that can be seen from Earth as the thick disk does.

"}, {"id": "D", "text": "

The stars in the Milky Way tend to have very similar chemical compositions.

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. A consistent age difference of 2 billion years between certain stars within the thick disk would support the claim that the thick disk formed in two phases instead of one, with the second phase beginning 2 billion years after the first phase.

Choice A is incorrect. This choice doesn’t support the claim. The researchers base their claim on their study of stars inside the thick disk of the Milky Way. This choice makes a comparison to stars in other galaxies, which isn’t relevant. Choice C is incorrect. This choice doesn’t support the claim. The researchers base their claim on their study of stars inside the thick disk. This choice makes a comparison to the thin disk, which isn’t relevant. Choice D is incorrect. This choice doesn’t support the claim. It’s too general. The claim is specifically about the thick disk.

"}, {"id": "485962a6", "domain": "Information and Ideas", "skill": "Inferences", "difficulty": "M", "type": "mc", "stimulus": "

Astronomers investigated the Arabia Terra region of Mars because it appears to contain irregularly shaped craters that may have been caused by massive volcanic explosions. In their investigations of Arabia Terra, the researchers found remnants of ash deposits in an amount and thickness that would result from a massive volcanic eruption. However, erosion and past resurfacing events could have modified the surface of the planet. Therefore, ______blank

", "stem": "

Which choice most logically completes the text?

", "choices": [{"id": "A", "text": "

the current makeup of the Arabia Terra region might not accurately reflect the volcanic activity of Mars’s past.

"}, {"id": "B", "text": "

eruptions from Mars’s volcanoes were likely not as massive as astronomers previously believed.

"}, {"id": "C", "text": "

ash was most likely expelled from multiple different volcanoes on Mars’s surface.

"}, {"id": "D", "text": "

the craters found in the Arabia Terra region were necessarily created by events other than volcanic eruptions.

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer because it presents the conclusion that most logically follows from the text’s discussion of the Arabia Terra region of Mars. According to the text, there are craters in Arabia Terra that could be the result of volcanic activity, and researchers have found evidence of ash deposits consistent with a large eruption. The text goes on to note, however, that erosion and other events could have altered the surface of Mars. This observation suggests that current conditions on Mars’s surface are not necessarily a reliable guide to past events—some signs of past events could have been transformed or erased entirely—and thus the current makeup of Arabia Terra may not accurately reflect past volcanic activity. 

Choice B is incorrect because the text suggests only that past events could have changed Mars’s surface such that its current appearance isn’t a reliable guide to past activity, not that it’s likely that past eruptions were not as massive as astronomers previously believed. Nothing in the text supports a conclusion about the likely size of past eruptions. Choice C is incorrect because the observation that resurfacing events could have changed the appearance of Mars doesn’t imply that the ash discussed in the text likely came from multiple volcanoes. Although it’s possible that the ash came from different volcanoes, there’s no information in the text supporting a conclusion about how likely that possibility is. Choice D is incorrect because nothing in the text suggests that the Arabia Terra craters had to have been created by something other than volcanic eruptions. Although the text does suggest that the evidence consistent with volcanic eruptions shouldn’t be taken as definitive proof of past eruptions, that doesn’t mean that the craters couldn’t have been created by eruptions, only that we can’t be certain they were. 

"}, {"id": "d2e0cba5", "domain": "Information and Ideas", "skill": "Central Ideas and Details", "difficulty": "H", "type": "mc", "stimulus": "

In a study of new technology adoption, Davit Marikyan et al. examined negative disconfirmation (which occurs when experiences fall short of one’s expectations) to determine whether it could lead to positive outcomes for users. The team focused on established users of  “smart home” technology, which presents inherent utilization challenges but tends to attract users with high expectations, often leading to feelings of dissonance. The researchers found that many users employed cognitive mechanisms to mitigate those feelings, ultimately reversing their initial sense of disappointment.

", "stem": "

Which choice best states the main idea of the text?

", "choices": [{"id": "A", "text": "

Research suggests that most users of smart home technology will not achieve a feeling of satisfaction given the utilization challenges of such technology.

"}, {"id": "B", "text": "

Although most smart home technology is aimed at meeting or exceeding users’ high expectations, those expectations in general remain poorly understood.

"}, {"id": "C", "text": "

Research suggests that users with high expectations for a new technology can feel content with that technology even after experiencing negative disconfirmation.

"}, {"id": "D", "text": "

Although negative disconfirmation has often been studied, little is known about the cognitive mechanisms shaping users’ reactions to it in the context of new technology adoption.

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. The passage begins by describing the study, and concludes with its results: \"many users employed cognitive mechanisms to mitigate those feelings [of negative disconfirmation].\"

Choice A is incorrect. This is the opposite of what the text claims. Rather, the researchers found that \"many users\" reversed \"their initial sense of disappointment.\" Choice B is incorrect. This choice doesn’t reflect the text. What the expectations of smart home tech users are is not discussed. Choice D is incorrect. This choice doesn’t reflect the text. How often these topics have been studied is not mentioned.

"}, {"id": "bcbcc43f", "domain": "Information and Ideas", "skill": "Inferences", "difficulty": "M", "type": "mc", "stimulus": "

The ancient Sumerian civilization formed around 4000 BCE between two large rivers in an area that is now Iraq and Syria. The extremely hot and sunny weather in that area helped crops grow very quickly, but it also made it hard to keep the crops from drying up and dying. So, the Sumerians used water from the rivers in their farming. That method worked so well that they often could harvest even more crops than they needed in a season. As a result, the Sumerians ______blank

", "stem": "

Which choice most logically completes the text?

", "choices": [{"id": "A", "text": "

harvested crops only on the hottest days of each season.

"}, {"id": "B", "text": "

found ways to shield their crops from the sun.

"}, {"id": "C", "text": "

did not begin farming until long after 4000 BCE.

"}, {"id": "D", "text": "

were able to store extra crops for later use.

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer because it presents the conclusion that most logically completes the text’s discussion of Sumerian civilization and crop growth. The text mentions the hot, sunny weather in the area where the Sumerians lived, which made crops grow quickly but also made it difficult to keep them alive. The Sumerians solved this problem by using river water for their farming—as a result, they often harvested more crops than were needed in a season. It follows that the Sumerians must have needed to find something to do with the surplus crops—that is, they stored the extra crops for later use.

Choice A is incorrect because it doesn’t logically follow that a surplus in crops would lead the Sumerians to choose only certain days of the season to harvest. Nor is there any indication in the text that the Sumerians improved their farming methods with the goal of reducing the time spent farming. Choice B is incorrect because the text doesn’t suggest that the Sumerians tried to shield their crops from the sun: in fact, the text indicates that the sunny weather helped crops grow very quickly and that the Sumerians used river water to allow crops to be exposed to the sun without dying. Choice C is incorrect. Having a surplus of crops wouldn’t have caused the Sumerians to begin farming until long after 4000 BCE: in fact, since the text indicates that the Sumerian civilization formed around 4000 BCE and farming was a part of that civilization, the statement that Sumerians only began farming long after 4000 BCE isn’t supported by the text.

"}, {"id": "cf3acc50", "domain": "Information and Ideas", "skill": "Inferences", "difficulty": "H", "type": "mc", "stimulus": "

Compiled in the late 1500s largely through the efforts of Indigenous scribes, Cantares Mexicanos is the most important collection of poetry in Classical Nahuatl, the principal language of the Aztec Empire. The poems portray Aztec society before the occupation of the empire by the army of Spain, and marginal notes in Cantares Mexicanos indicate that much of the collection’s content predates the initial invasion. Nonetheless, some of the poems contain inarguable references to beliefs and customs common in Spain during this era. Thus, some scholars have concluded that ______blank

", "stem": "

Which choice most logically completes the text?

", "choices": [{"id": "A", "text": "

while its content largely predates the invasion, Cantares Mexicanos also contains additions made after the invasion.

"}, {"id": "B", "text": "

although those who compiled Cantares Mexicanos were fluent in Nahuatl, they had limited knowledge of the Spanish language.

"}, {"id": "C", "text": "

before the invasion by Spain, the poets of the Aztec Empire borrowed from the literary traditions of other societies.

"}, {"id": "D", "text": "

the references to beliefs and customs in Spain should be attributed to a coincidental resemblance between the societies of Spain and the Aztec Empire.

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer because it most logically completes the text. The text explains that the Cantares Mexicanos contains poems about the Aztec Empire from before the Spanish invasion. Furthermore, it indicates that notes in the collection attest that some of these poems predate the Spanish invasion, while some customs depicted are likely Spanish in origin. The implication is that some poems were composed before the invasion but the references to Spanish customs could have come about only after the invasion, and thus that the collection includes content that predates the invasion and also content from after the invasion.

Choice B is incorrect because the text clearly indicates that the collection is in Nahuatl, not Spanish, so the compilers’ unfamiliarity with Spanish is irrelevant to whether the collection contains material composed after the Spanish invasion. Choice C is incorrect because the text mentions only the Aztec Empire and Spain: there is no information about the relationship of Aztec literature to any traditions other than its own or Spain’s. Choice D is incorrect because the text states that some of the poems make “inarguable references” to common Spanish customs, which conflicts with the idea that these references can reasonably be attributed to mere coincidence.

"}, {"id": "7254379e", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "E", "type": "mc", "stimulus": "

Some residents in a neighborhood in Atlanta recently founded a community garden inside a local park. The residents agreed to volunteer to take care of the garden together. Students at a local high school surveyed some of the volunteers as part of a project to understand the impact of the new garden. The students concluded that the new garden benefited the community overall by fostering connections and relationships between the volunteers and other residents of the neighborhood who weren’t volunteering at the garden. 

", "stem": "

Which quotation from a survey respondent would best illustrate the students’ conclusion?

", "choices": [{"id": "A", "text": "

“Our first challenge was deciding what plants would be most suitable to the climate and soil here in Atlanta. We needed plants that could survive the hot and humid summers.”

"}, {"id": "B", "text": "

“We’re lucky to have a few expert gardeners living in the neighborhood. Some volunteers and I have gone to them a few times with questions, and they’ve been eager to help us and to learn more about the project.”

"}, {"id": "C", "text": "

“I love getting the opportunity to be outside and around nature, especially on days when the weather is nice.”

"}, {"id": "D", "text": "

“My favorite thing about the garden is the feeling of pride I get when I walk by each day. As I see the plants growing, I feel good knowing I had a small part in creating this beautiful space in the neighborhood.”

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. This choice shows how volunteers have been interacting with nonvolunteer neighbors and benefiting from their gardening expertise: proof of the connections enabled by the garden.

Choice A is incorrect. This volunteer describes the challenges of developing the garden, which isn’t connected to the conclusion about the garden fostering connections between volunteers and neighbors. Choice C is incorrect. While the volunteer expresses enthusiasm for the garden, they don’t mention any interactions with other people, which is what the students need to show for their conclusion. Choice D is incorrect. The respondent enjoys and takes pride in the garden, but they don’t mention interacting with neighbors or other volunteers.

"}, {"id": "23e2421a", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "M", "type": "mc", "stimulus": "

\n\n\n\n\n600550500450400350300250200150100500Number of suggestionsadditiveneither additive nor subtractivesubtractiveinvalidSuggestions for Improving a Universitysuggestion type

\n

Gabrielle Adams and colleagues reviewed suggestions for improving a university that had been submitted to the university\u2019s president. They coded each suggestion as additive (the idea suggested adding something new to the university), subtractive (the idea suggested removing something from the university), neither additive nor subtractive, or invalid (the idea was not comprehensible). The data illustrated people\u2019s tendency to overlook the possibility of removing things to achieve improvements: ______blank

", "stem": "

Which choice most effectively uses data in the graph to complete the statement?

", "choices": [{"id": "A", "text": "

around 175 suggestions were coded as neither additive nor subtractive, whereas around 575 suggestions were coded as additive. 

"}, {"id": "B", "text": "

more than 350 suggestions were coded as invalid, whereas fewer than 100 suggestions were coded as subtractive. 

"}, {"id": "C", "text": "

fewer than 100 suggestions were coded as subtractive, whereas more than 550 suggestions were coded as additive. 

"}, {"id": "D", "text": "

around 575 suggestions were coded as additive, whereas around 175 suggestions were coded as subtractive. 

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. This choice shows that people suggested removing things to achieve improvements a lot less often than they suggested adding things, which supports the claim that people tend not to think of removing things as a likely way to improve the university.

Choice A is incorrect. This choice doesn’t support the claim. We are looking to prove that people suggested subtractive means of achieving improvements less often than other means, but this choice doesn’t address how often people made subtractive suggestions. Choice B is incorrect. This choice doesn’t support the claim. Invalid responses were incomprehensible, so we can’t compare what they were suggesting to what was being suggested in subtractive responses. Choice D is incorrect. This choice misreads the graph. Fewer than 100 suggestions were coded as subtractive. 175 is the approximate number of suggestions coded as “neither additive or subtractive.”

"}, {"id": "9abc3ba5", "domain": "Information and Ideas", "skill": "Inferences", "difficulty": "H", "type": "mc", "stimulus": "

“Gestures” in painting are typically thought of as bold, expressive brushstrokes. In the 1970s, American painter Jack Whitten built a 12-foot (3.7-meter) tool he named the “developer” to apply paint to an entire canvas in one motion, resulting in his series of “slab” paintings from that decade.  Whitten described this process as making an entire painting in “one gesture,” signaling a clear departure from the prevalence of gestures in his work from the 1960s. Some art historians claim this shift represents “removing gesture” from the process. Therefore, regardless of whether using the developer constitutes a gesture, both Whitten and these art historians likely agree that ______blank

", "stem": "

Which choice most logically completes the text?

", "choices": [{"id": "A", "text": "

any tool that a painter uses to create an artwork is capable of creating gestures.

"}, {"id": "B", "text": "

Whitten’s work from the 1960s exhibits many more gestures than his work from the 1970s does.

"}, {"id": "C", "text": "

Whitten became less interested in exploring the role of gesture in his work as his career progressed.

"}, {"id": "D", "text": "

Whitten’s work from the 1960s is much more realistic than his work from the 1970s is.

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. \u200b\u200bWhitten thinks the tool made “one gesture” paintings, while historians think the tool “removed gesture” from the process completely. But putting that debate aside, both Whitten and the historians would agree that the paintings he made with the tool in the ’70s have way fewer gestures than his paintings from the ’60s, in which gestures are “prevalent,” meaning widely and extensively present.

Choice A is incorrect. This inference isn’t supported. The text only discusses the “developer”—it never mentions other tools. Choice C is incorrect. This inference isn’t supported. If anything, the text suggests the opposite: that Whitten became more interested in exploring the role of gesture in his work as his career progressed, as his earlier paintings had many gestures, and his ’70s paintings only had “one gesture.” Choice D is incorrect. This inference isn’t supported. The text never discusses the “realism” of Whitten’s art.

"}, {"id": "5ff1ba73", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "E", "type": "mc", "stimulus": "

Guilds in French Cities in the Late Eighteenth Century

CityDateInhabitantsNumber of guildsInhabitants per guild
Paris1766600,0001334,511
Bordeaux176280,000491,633
Rouen177574,000112661
Lyon1789143,000721,986

\n

Guilds—local associations of artisans and merchants in the same industry—were widespread in France from the medieval period until the late eighteenth century. But guilds were much more numerous relative to the population in some cities than in others: for example, ______blank

", "stem": "

Which choice most effectively uses data from the table to complete the statement?

", "choices": [{"id": "A", "text": "

there were 49 guilds in Bordeaux but 72 guilds in Lyon despite the two cities having nearly equal numbers of inhabitants.

"}, {"id": "B", "text": "

Lyon had far fewer inhabitants than Paris did but had many more guilds. 

"}, {"id": "C", "text": "

there was one guild for every 661 inhabitants in Rouen but one guild for every 4,511 inhabitants in Paris. 

"}, {"id": "D", "text": "

Paris had 133 guilds and 600,000 inhabitants, or one guild for every 4,511 inhabitants. 

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. The claim we’re trying to prove is that guilds were much more numerous relative to population in some cities than others. This choice describes the guilds per number of inhabitants in two cities (Rouen and Paris), showing significant differences between guilds relative to population in these cities.

Choice A is incorrect. This choice misreads the table. Bordeaux had 80,000 inhabitants, according to the table, while Lyon had 143,000, so it isn’t correct to say that they had \"nearly equal numbers of inhabitants.\" Lyon had almost twice as many inhabitants. Choice B is incorrect. This choice misreads the table. Although Lyon did have fewer inhabitants than Paris, it didn’t have more guilds—Paris had 133 guilds versus Lyon’s 72. Choice D is incorrect. This choice doesn’t support the claim. To show that guilds were more numerous relative to population in some cities than others, we would need to compare at least two cities, and this choice only mentions one.

"}, {"id": "94978129", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "M", "type": "mc", "stimulus": "

Approximate Rates of Speech and Information Conveyed for Five Languages

LanguageRate of speech (syllables per second)Rate of information conveyed (bits per second)
Serbian7.239.1
Spanish7.742.0
Vietnamese5.342.5
Thai4.733.8
Hungarian5.934.6

\n

A group of researchers working in Europe, Asia, and Oceania conducted a study to determine how quickly different Eurasian languages are typically spoken (in syllables per second) and how much information they can effectively convey (in bits per second). They found that, although languages vary widely in the speed at which they are spoken, the amount of information languages can effectively convey tends to vary much less. Thus, they claim that two languages with very different spoken rates can nonetheless convey the same amount of information in a given amount of time. 

", "stem": "

Which choice best describes data from the table that support the researchers’ claim?

", "choices": [{"id": "A", "text": "

Among the five languages in the table, Thai and Hungarian have the lowest rates of speech and the lowest rates of information conveyed.

"}, {"id": "B", "text": "

Vietnamese conveys information at approximately the same rate as Spanish despite being spoken at a slower rate.

"}, {"id": "C", "text": "

Among the five languages in the table, the language that is spoken the fastest is also the language that conveys information the fastest.

"}, {"id": "D", "text": "

Serbian and Spanish are spoken at approximately the same rate, but Serbian conveys information faster than Spanish does.

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer because it provides the most direct support from the table for the claim that two languages can convey similar amounts of information even if they’re spoken at different rates. The table shows the approximate rates at which five languages are spoken and the rates at which those five languages convey information. Vietnamese is spoken at around 5.3 syllables per second, whereas Spanish is spoken at around 7.7 syllables per second, but the two languages convey information at very similar rates: Vietnamese at a rate of around 42.5 bits per second and Spanish at a rate of around 42.0 bits per second. Thus, the description of Vietnamese conveying information at around the same rate that Spanish does despite being spoken more slowly supports the claim in the text that languages can convey the same amount of information even if spoken at different rates. 

Choice A is incorrect because it isn’t true that Thai and Hungarian have the lowest rates of speech of the five languages shown. According to the table, Hungarian is spoken at around 5.9 syllables per second, which is faster than Vietnamese (5.3 syllables per second). Additionally, even if this statement were true, the assertion that two languages are spoken the slowest and convey information the slowest wouldn’t support the claim that languages can convey the same amount of information even if they’re spoken at different rates. Choice C is incorrect because it isn’t true that the fastest-spoken language (Spanish, at 7.7 syllables per second) also conveys information the fastest: Spanish conveys information at 42.0 bits per second, which is slower than the 42.5 bits-per-second rate at which Vietnamese conveys information. Additionally, even if this statement were true, the assertion that the language spoken the fastest also conveys information the fastest has no bearing on the claim that languages can convey the same amount of information even if they’re spoken at different rates. Choice D is incorrect because it isn’t true that Serbian conveys information faster than Spanish does. According to the table, Serbian conveys information at a rate of around 39.1 bits per second, which is slower than the 42.0 bits-per-second rate at which Spanish conveys information. 

"}, {"id": "b4cda84d", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "M", "type": "mc", "stimulus": "

In 1967 the US Congress created the Corporation for Public Broadcasting, which in turn created National Public Radio (NPR). NPR began producing and distributing high-quality news and cultural programming to affiliate stations across the United States in 1971. In a research paper, a student claims that the Corporation for Public Broadcasting and NPR were inspired by the British Broadcasting System (BBC), which had been established in the 1920s.

", "stem": "

Which quotation from a work by a historian would be the most effective evidence for the student to include in support of this claim?

", "choices": [{"id": "A", "text": "

“Although the BBC had begun as a private corporation, politicians successfully argued to make it a public company because they believed a public broadcaster could help build national unity in the aftermath of World War I.”

"}, {"id": "B", "text": "

“For many decades, the BBC had no competition since it held Britain’s only broadcasting license, whereas in the United States, the Corporation for Public Broadcasting launched NPR in a broadcasting market already filled with competitors.”

"}, {"id": "C", "text": "

“Congress’s embrace of publicly funded broadcasting reflected a common belief among US politicians that the role of government was not only to ensure people’s safety and liberty but also to enrich people’s lives in other ways.”

"}, {"id": "D", "text": "

“The goal of the BBC was to support British democracy by promoting an informed citizenry, and US legislators believed that ensuring access to high-quality programming could do the same for democracy in the United States.”

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer because this quotation would be the most effective evidence to include in support of the claim that the Corporation for Public Broadcasting and NPR were inspired by the British Broadcasting System (BBC). The quotation states that the goal of the BBC was to support British democracy and that US legislators believed high-quality programming could accomplish the same goal for democracy in the United States. In other words, US legislators looked to the BBC as a model, taking direct inspiration from it when they created the Corporation for Public Broadcasting, which in turn created NPR.

Choice A is incorrect because this quotation provides historical information about the BBC, not information about the inspiration for the creation of the Corporation for Public Broadcasting and NPR. This quotation, therefore, is irrelevant to the student’s claim that the BBC inspired the creation of the Corporation for Public Broadcasting, which in turn created NPR. Choice B is incorrect because this quotation contrasts the lack of competition faced by the BBC with the substantial competition faced by NPR, which has no bearing on the student’s claim that the Corporation for Public Broadcasting and NPR were inspired by the BBC. Choice C is incorrect because this quotation focuses on a common belief among US politicians that inspired Congress’s embrace of publicly funded broadcasting. The quotation doesn’t say anything about the BBC and therefore doesn’t support the claim that the BBC inspired Congress to create the Corporation for Public Broadcasting, which in turn created NPR.

"}, {"id": "5b4829d2", "domain": "Information and Ideas", "skill": "Inferences", "difficulty": "E", "type": "mc", "stimulus": "

Researchers wanted to study how consumers’ reactions to an ad may be affected by other ads. The researchers began by showing study participants an ad for a product, with some seeing a less detailed ad and others seeing a more detailed one. Then, all participants viewed the same second ad for a store and shared their opinion of the store based on this second ad. Participants who had first seen an ad less detailed than the second ad had a higher opinion of the store than the participants who had first seen a more detailed ad. The researchers concluded that reactions to an ad may be affected by ______blank

", "stem": "

Which choice most logically completes the text?

", "choices": [{"id": "A", "text": "

the number of people who viewed the ad.

"}, {"id": "B", "text": "

the length of time viewing previous ads. 

"}, {"id": "C", "text": "

the amount of detail viewed in previous ads.

"}, {"id": "D", "text": "

the time of day that the ad is viewed.

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. The passage tells us that participants who had seen a less detailed ad for a product beforehand had a higher opinion of the store than those who had seen a more detailed ad. This suggests that reactions to an ad may be affected by the amount of detail viewed in previous ads.

Choice A is incorrect. The passage doesn’t mention the number of people who viewed the ad, so there’s no basis for this inference. Choice B is incorrect. The passage doesn’t mention the length of time viewing previous ads, so there’s no basis for this inference. Choice D is incorrect. The passage doesn’t mention the time of day that the ad is viewed, so there’s no basis for this inference.

"}, {"id": "7ffae38a", "domain": "Information and Ideas", "skill": "Central Ideas and Details", "difficulty": "M", "type": "mc", "stimulus": "

The following text is adapted from Jack London’s 1903 novel The Call of the Wild. Buck is a sled dog living with John Thornton in Yukon, Canada.

\n

Thornton alone held [Buck]. The rest of mankind was as nothing. Chance travellers might praise or pet him; but he was cold under it all, and from a too demonstrative man he would get up and walk away. When Thornton’s partners, Hans and Pete, arrived on the long-expected raft, Buck refused to notice them till he learned they were close to Thornton; after that he tolerated them in a passive sort of way, accepting favors from them as though he favored them by accepting.

", "stem": "

Which choice best states the main idea of the text?

", "choices": [{"id": "A", "text": "

Buck has become less social since he began living with Thornton.

"}, {"id": "B", "text": "

Buck mistrusts humans and does his best to avoid them.

"}, {"id": "C", "text": "

Buck has been especially well liked by most of Thornton’s friends.

"}, {"id": "D", "text": "

Buck holds Thornton in higher regard than any other person.

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer because it most accurately states the main idea of the text. After establishing that Buck views most people “as nothing,” the text explains that Buck won’t acknowledge people other than Thornton unless they appear friendly toward Thornton, and even then he’s only reluctantly accepting. Thus, the text focuses on the idea that Thornton has a special status in Buck’s mind, with Buck holding him in higher regard than other people.

Choice A is incorrect because the text conveys that Buck isn’t social with people other than Thornton but doesn’t address Buck’s life or temperament before he lived with Thornton. Choice B is incorrect because the text conveys that Buck doesn’t really care about people other than Thornton and is aloof toward them. However, there’s no indication that Buck mistrusts and avoids people generally; indeed, he accepts Thornton, who is a human. Choice C is incorrect because the text refers to random travelers praising and petting Buck and Thornton’s partners giving Buck favors, but there’s no indication that any of these people are Thornton’s friends or that they have a particular fondness for Buck.

"}, {"id": "409058ee", "domain": "Information and Ideas", "skill": "Central Ideas and Details", "difficulty": "M", "type": "mc", "stimulus": "

To protect themselves when being attacked, hagfish—jawless marine animals that resemble eels—will release large quantities of slimy, mucus-like threads. Because these threads are unusually strong and elastic, scientist Atsuko Negishi and her colleagues have been trying to recreate them in a lab as an eco-friendly alternative to petroleum-based fibers that are often used in fabrics. The researchers want to reproduce the threads in the lab because farming hagfish for their slime would be expensive and potentially harmful to the hagfish.

", "stem": "

Which choice best states the text’s main idea?

", "choices": [{"id": "A", "text": "

The slimy threads that hagfish release might help researchers create a new kind of fabric.

"}, {"id": "B", "text": "

Hagfish have inspired researchers to develop a new petroleum-based fabric.

"}, {"id": "C", "text": "

Hagfish are not well suited to being raised in captivity.

"}, {"id": "D", "text": "

The ability of hagfish to slime their attackers compensates for their being jawless.

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. The text first describes hagfish slime and its properties, then it transitions to talking about the possibilities of using lab-made equivalents to use in eco-friendly fabrics.

Choice B is incorrect. The text says the opposite of this choice. The researchers are developing an alternative to petroleum-based fabric. Choice C is incorrect. This choice is too narrow to be the main point of the text. Only one line describes how farming would be “potentially harmful” to the hagfish. Choice D is incorrect. This choice isn’t supported by the text. We don’t know from the text whether being jawless makes the hagfish more vulnerable.

"}, {"id": "7c9a65bb", "domain": "Information and Ideas", "skill": "Central Ideas and Details", "difficulty": "H", "type": "mc", "stimulus": "

Optical tweezers are specialized scientific tools—particularly useful in biology and medicine—that use high-powered beams of light to trap and manipulate minuscule particles for study. Use of the tool has led to several scientific and medical breakthroughs over the last few decades, but the particles are often under prolonged exposure to the intense heat of the light beams. To overcome the risk of overheating, and thereby damage, researchers sometimes attach nano-sized glass beads to particles, allowing the light to focus on the beads instead of the particles.

", "stem": "

Based on the text, what is one advantage of attaching glass beads to particles when using optical tweezers?

", "choices": [{"id": "A", "text": "

It decreases the time it takes for the optical tweezers to locate and capture the particles.

"}, {"id": "B", "text": "

It facilitates the maneuvering of particles without directly heating the particles themselves.

"}, {"id": "C", "text": "

It allows researchers to use weaker light beams to manipulate particles.

"}, {"id": "D", "text": "

It adds a material to which particles can transfer any heat absorbed from the optical tweezers’ light beam.

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. The text says that the glass beads get the \"focus\" of the light beams so that the particles don’t overheat. From this, we can infer that the beads allow the particles to be manipulated without being directly heated by the light beams.

Choice A is incorrect. The text never says that attaching the glass beads saves time in any way. Choice C is incorrect. The text never says that attaching the glass beads allows researchers to use weaker light beams. Choice D is incorrect. The text doesn’t say that the particles can transfer heat to the glass beads—rather, it says the heat from the light focuses on the glass beads instead of the particles.

"}, {"id": "299c5303", "domain": "Information and Ideas", "skill": "Inferences", "difficulty": "M", "type": "mc", "stimulus": "

As the name suggests, dramaturges originated in theater, where they continue to serve a variety of functions: conducting historical research for directors, compiling character biographies for actors, and perhaps most importantly, helping writers of plays and musicals to hone the works’ stories and characters. Performance scholar Susan Manning observes that many choreographers, like playwrights and musical theater writers, are concerned with storytelling and characterization. In fact, some choreographers describe the dances they create as expressions of narrative through movement; it is therefore unsurprising that ______blank

", "stem": "

Which choice most logically completes the text?

", "choices": [{"id": "A", "text": "

dramaturges can have a profound impact on the artistic direction of plays and musicals.

"}, {"id": "B", "text": "

choreographers developing dances with narrative elements frequently engage dramaturges to assist in refining those elements.

"}, {"id": "C", "text": "

dances by choreographers who incorporate narrative elements are more accessible to audiences than dances by choreographers who do not.

"}, {"id": "D", "text": "

some directors and actors rely too heavily on dramaturges to complete certain research tasks.

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. Dramaturges help playwrights with storytelling and characterization. Choreographers often tell stories through dance, so they are also concerned with storytelling and characterization. This suggests that the fact that choreographers seek the help of dramaturges with the storytelling aspects of their dances should be “unsurprising.”

Choice A is incorrect. This inference isn’t supported. The beginning of the text does imply that this is true, but the end is leading to a conclusion about how choreographers use dramaturges. Choice C is incorrect. This inference isn’t supported. The text never mentions dances by choreographers who don’t incorporate narrative elements. Choice D is incorrect. This inference isn’t supported. The text mentions in passing that directors use dramaturges to conduct research, but it never suggests that directors and actors are too reliant on them. Also, the text is leading to a conclusion about how choreographers use dramaturges.

"}, {"id": "378c66d5", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "H", "type": "mc", "stimulus": "

A member of the Otomi, an Indigenous people in Central Mexico, Octavio Medellín immigrated to the United States as a child, and his sculpture bears the impress of traditions on both sides of the border: US-based modernist sculpture, Mexican modernist painting, Otomi art, and the ancient sculpture of other Mexican Indigenous peoples, including the Maya. In his 1950 masterpiece History of Mexico, Medellín fuses these influences into a style so idiosyncratic that it resists efforts to view his work through the lens of nationality or cultural identity. Artists, he insisted, should strive for individual expression, even as they draw inspiration from their heritage and the communities where they live and work.

", "stem": "

Which quotation from an art critic most directly challenges the underlined claim in the text?

", "choices": [{"id": "A", "text": "

“Although a number of ancient Indigenous artistic traditions pictured human forms in profile, the forms populating the surface of A History of Mexico suggest a specifically Maya influence.”

"}, {"id": "B", "text": "

“In A History of Mexico, the synthesis of ancient and modernist traditions functions as a stylistic parallel to the work’s subject matter: a survey of centuries of Mexican history.”

"}, {"id": "C", "text": "

“Many critics focus on Indigenous influences in A History of Mexico and other key works by Medellín to the exclusion of influences from non-Indigenous art.”

"}, {"id": "D", "text": "

“While A History of Mexico features modernist motifs, it relies primarily on angular human forms in profile—a staple of Maya sculpture—and thus invites classification as Indigenous art.”

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. This critic challenges the claim by arguing that A History of Mexico is not so idiosyncratic (unique) as to resist classification because its use of Maya-style human profiles actually “invites classification as Indigenous art.” Therefore, according to this critic, the work can be viewed, at least partially, through a lens of national or cultural identity.

Choice A is incorrect. While it describes the Maya influence on a particular aspect of A History of Mexico, this quotation doesn’t push back on Medellín’s “idiosyncratic” (unique) style, nor does it try to categorize the entire work into a single cultural tradition. Choice B is incorrect. This choice doesn’t directly challenge the underlined claim, but rather supports it. It suggests that the work effectively blends a variety of artistic products to create a single work that can’t be defined by any one tradition. Instead, the work recalls many centuries of history and culture all at once. Choice C is incorrect. This choice supports rather than challenges the underlined claim. The quotation argues that other critics focus too much on Indigenous influences on the artwork instead of viewing all of the influences equally—that they should instead be viewing the work as an idiosyncratic whole instead of through one or two narrow cultural lenses.

"}, {"id": "b62cb782", "domain": "Information and Ideas", "skill": "Central Ideas and Details", "difficulty": "M", "type": "mc", "stimulus": "

Culinary anthropologist Vertamae Smart-Grosvenor may be known for her decades of work in national public television and radio, but her book Vibration Cooking: or, the Travel Notes of a Geechee Girl is likely her most influential project. The 1970 book, whose title refers to Smart-Grosvenor’s roots in the Low Country of South Carolina, was unusual for its time. It combined memoir, recipes, travel writing, and social commentary and challenged notions about conventions of food and cooking. Long admired by many, the book and its author have shaped contemporary approaches to writing about cuisine.

", "stem": "

Which choice best describes the main idea of the text?

", "choices": [{"id": "A", "text": "

Smart-Grosvenor’s unconventional book Vibration Cooking: or, the Travel Notes of a Geechee Girl is an important contribution to food writing.

"}, {"id": "B", "text": "

Smart-Grosvenor held many different positions over her life, including reporter and food writer.

"}, {"id": "C", "text": "

Smart-Grosvenor’s groundbreaking book Vibration Cooking: or, the Travel Notes of a Geechee Girl didn’t receive the praise it deserved when it was first published in 1970.

"}, {"id": "D", "text": "

Smart-Grosvenor was a talented chef whose work inspired many people to start cooking for themselves.

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer because it most accurately states the main idea of the text. The text describes the book Vibration Cooking: or, the Travel Notes of a Geechee Girl as Smart-Grosvenor’s “most influential project” and as “unusual for its time.” The text also notes that the book and author have influenced contemporary approaches to writing about food and cooking. Therefore, the text mainly conveys that Vibration Cooking: or, the Travel Notes of a Geechee Girl is an unconventional and important contribution to food writing.

Choice B is incorrect. Although the text mentions that Smart-Grosvenor worked in national public television and radio and was a food writer, these details aren’t the main focus. Rather than focusing on Smart-Grosvenor’s various jobs, the text focuses specifically on one specific book she wrote. Choice C is incorrect. Although the text suggests that Vibration Cooking: or, the Travel Notes of a Geechee Girl was groundbreaking, it doesn’t suggest that the book didn’t receive praise when it was published. In fact, the text states that the book is “long admired.” Choice D is incorrect because the text states that Smart-Grosvenor was a culinary anthropologist and that her book influenced later approaches to food writing but doesn’t indicate that Smart-Grosvenor or her book influenced people to begin cooking for themselves.

"}, {"id": "dc5edbf6", "domain": "Information and Ideas", "skill": "Central Ideas and Details", "difficulty": "E", "type": "mc", "stimulus": "

Microplastics are pieces of plastic that are smaller than a grain of rice. These small plastics can be found in large quantities in ocean waters. Ecologist Jessica Reichert and her team are studying the role reef-building corals have in capturing microplastics from ocean waters. Through research, her team has found that these corals may be storing up to 20 million kilograms of microplastics each year in their skeletons and tissues.  

", "stem": "

Which choice best states the main idea of the text?

", "choices": [{"id": "A", "text": "

Ecologists are interested in learning more about how certain corals build large reefs.

"}, {"id": "B", "text": "

Questions remain around the impact certain corals have on ocean ecosystems.   

"}, {"id": "C", "text": "

Microplastics are small pieces of plastic that can be found in ocean waters.

"}, {"id": "D", "text": "

Ecologists predict that corals store large amounts of microplastics from ocean waters.

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. The text describes a study about how reef-building corals capture microplastics from ocean waters, which found that these corals are storing 20 million kilograms of microplastics in their skeletons and tissues.

Choice A is incorrect. While the researchers are studying “reef-building corals,” the focus of their study isn’t how the corals build the reefs. Rather, they’re studying how corals may be storing microplastics from ocean waters. Choice B is incorrect. The text doesn’t mention any unanswered questions about the impact of corals on ocean ecosystems—rather, the study assesses one interaction between corals and microplastics. Choice C is incorrect. The text does say this, but it’s a detail—not the main idea. The main idea of the text is about the study that found that corals may be storing microplastics from ocean waters in their skeletons and tissues.

"}, {"id": "5105ca38", "domain": "Information and Ideas", "skill": "Inferences", "difficulty": "M", "type": "mc", "stimulus": "

Several artworks found among the ruins of the ancient Roman city of Pompeii depict a female figure fishing with a cupid nearby. Some scholars have asserted that the figure is the goddess Venus, since she is known to have been linked with cupids in Roman culture, but University of Leicester archaeologist Carla Brain suggests that cupids may have also been associated with fishing generally. The fact that a cupid is shown near the female figure, therefore, ______blank

", "stem": "

Which choice most logically completes the text?

", "choices": [{"id": "A", "text": "

is not conclusive evidence that the figure is Venus.

"}, {"id": "B", "text": "

suggests that Venus was often depicted fishing.

"}, {"id": "C", "text": "

eliminates the possibility that the figure is Venus. 

"}, {"id": "D", "text": "

would be difficult to account for if the figure is not Venus. 

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer because it presents the conclusion that most logically completes the text’s discussion about the significance of the cupid found at Pompeii. The text indicates that the cupid is near a statue of a female figure who is fishing, and it goes on to indicate that because Venus is associated with cupids, some scholars believe the female figure to be the goddess Venus. But the text then says that, according to archaeologist Carla Brain, cupids may have also been associated with the activity of fishing, which, if true, would suggest that the mere appearance of a cupid near a female figure engaged in fishing does not indicate with certainty that the figure is Venus (that is, the cupid might be associated with fishing, and the figure might be anyone at all).

Choice B is incorrect because the text says nothing about how often Venus was depicted fishing in Roman art: it only implies that in certain instances a female figure may or may not be Venus. Choice C is incorrect because Carla Brain’s proposed explanation for the presence of the cupids makes no reference to the female figure, and so the possibility that the figure in the artworks is in fact Venus cannot be definitively eliminated. Choice D is incorrect because there is nothing in the text to suggest that the only reasonable way to interpret the figure is as Venus.

"}, {"id": "d8758c3b", "domain": "Information and Ideas", "skill": "Central Ideas and Details", "difficulty": "E", "type": "mc", "stimulus": "

Psychologists wanted to test how young children think about rewards and fairness. In an experiment, two teachers handed out rewards while children (ages four to six) watched. The teachers gave out the same number of rewards, but one of them counted the rewards out loud. The children were then asked who was fairer. 73% chose the teacher who counted. The psychologists think that counting showed the children that the teacher wanted to be fair. The children may have believed that the teacher who did not count did not care about fairness.

", "stem": "

Which choice best states the main idea of the text?

", "choices": [{"id": "A", "text": "

Psychologists think children cannot understand the concept of fairness until they are six years old. 

"}, {"id": "B", "text": "

An experiment found that counting out loud is the best way to teach mathematical concepts to children. 

"}, {"id": "C", "text": "

Psychologists think young children expect to be rewarded when the children show that they care about fairness. 

"}, {"id": "D", "text": "

An experiment showed that the way rewards are given out may affect whether young children think the situation is fair.

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. The text describes a study assessing how children think of rewards and fairness and its results. It concludes that the children in the study may have thought that a teacher who counted out loud when giving rewards cared more about fairness than a teacher who did not count out loud.

Choice A is incorrect. The children in the study are described as being “four to six,” and the text doesn’t mention any differences among the different ages. Choice B is incorrect. The experiment wasn’t about teaching math—rather, it was about how counting out loud affected the children’s perception of fairness. Choice C is incorrect. The experiment doesn’t focus on whether the children care about fairness, and the text never mentions the children’s expectations of being rewarded.

"}, {"id": "22b3da87", "domain": "Information and Ideas", "skill": "Inferences", "difficulty": "H", "type": "mc", "stimulus": "

During the Bourbon Restoration in France (1814–1830), the right to vote required in part that a person paid at least 300 francs in direct taxes to the government. The four most common taxes (the quatre vieilles) were levied on real estate (both land and buildings); the doors and windows in taxpayer homes; the rental values of homes; and the businesses of artisans and merchants. (Foreign investments were either exempt from taxation or taxed lightly.) Although relatively few people paid the tax on real estate, it was the main means of voter qualification and accounted for over two-thirds of government receipts during this period, suggesting that during the Bourbon Restoration ______blank

", "stem": "

Which choice most logically completes the text?

", "choices": [{"id": "A", "text": "

those people who had the right to vote most likely had substantial holdings of French real estate.

"}, {"id": "B", "text": "

the voting habits of French artisans and merchants were effective in reducing tax burdens on businesses.

"}, {"id": "C", "text": "

the number of doors and windows in French residences was kept to a minimum but increased after 1830.

"}, {"id": "D", "text": "

French people with significant foreign investments were unlikely to have the right to vote.

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. We’re told that people needed to pay “at least 300 francs in direct taxes” to be able to vote. We’re also told that, while “relatively few people paid the tax on real estate,” real estate taxes were both the main way people qualified to vote and the main source of revenue for the government. Based on this, we can infer that those who did qualify to vote likely had significant French real estate holdings.

Choice B is incorrect. The passage doesn’t mention the voting habits of artisans and merchants nor any reduction in tax burdens on businesses, so there’s no basis for this inference. Choice C is incorrect. Although we know that doors and windows were taxed during the Bourbon Restoration, we don’t have enough information to infer if doors and windows increased after this time. Choice D is incorrect. Although we know that foreign investments were only minimally taxed, we don’t have enough information to determine if those with significant foreign investments were unlikely to have voting rights. For example, it’s possible that those with significant foreign investments were likely to also be people with significant domestic investments which they did pay taxes on, so we don’t have the information necessary to make this inference.

"}, {"id": "303537cf", "domain": "Information and Ideas", "skill": "Central Ideas and Details", "difficulty": "H", "type": "mc", "stimulus": "

The following text is adapted from Lewis Carroll’s 1889 satirical novel Sylvie and Bruno. A crowd has gathered outside a room belonging to the Warden, an official who reports to the Lord Chancellor.

\n

One man, who was more excited than the rest, flung his hat high into the air, and shouted (as well as I could make out) “Who roar for the Sub-Warden?” Everybody roared, but whether it was for the Sub-Warden, or not, did not clearly appear: some were shouting “Bread!” and some “Taxes!”, but no one seemed to know what it was they really wanted.

\n

All this I saw from the open window of the Warden’s breakfast-saloon, looking across the shoulder of the Lord Chancellor.

\n

“What can it all mean?” he kept repeating to himself. “I never heard such shouting before—and at this time of the morning, too! And with such unanimity!”

", "stem": "

Based on the text, how does the Lord Chancellor respond to the crowd?

", "choices": [{"id": "A", "text": "

He asks about the meaning of the crowd’s shouting, even though he claims to know what the crowd wants.

"}, {"id": "B", "text": "

He indicates a desire to speak to the crowd, even though the crowd has asked to speak to the Sub-Warden.

"}, {"id": "C", "text": "

He expresses sympathy for the crowd’s demands, even though the crowd’s shouting annoys him.

"}, {"id": "D", "text": "

He describes the crowd as being united, even though the crowd clearly appears otherwise.

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer because it presents a statement about how the Lord Chancellor responds to the crowd that is supported by the text. The text indicates that the people in the crowd are roaring and shouting “Bread!” or “Taxes!” and presents them as not knowing what they really want. The Lord Chancellor’s response is to ask what their shouting means but also to observe that they’re shouting with “unanimity,” or total agreement. Clearly, this isn’t the case, which supports the statement that the Lord Chancellor describes the crowd as being united even though it’s not. 

Choice A is incorrect because it isn’t supported by the text. Although the text indicates that the Lord Chancellor asks about the meaning of the crowd’s shouting, it doesn’t suggest that he knows what the crowd really wants. Choice B is incorrect because the text doesn’t suggest that the Lord Chancellor wants to speak to the crowd. Furthermore, the text doesn’t indicate that the crowd wants to hear from the Sub-Warden. Although the crowd roars when asked “Who roar for the Sub-Warden?” it’s unclear what the roaring means. Choice C is incorrect because the text doesn’t suggest that the Lord Chancellor knows of or sympathizes with the crowd’s demands. In addition, the text doesn’t indicate that the crowd’s shouting annoys the Lord Chancellor, just that it causes him to keep repeating “What can it all mean?”  

"}, {"id": "bcf2f169", "domain": "Information and Ideas", "skill": "Inferences", "difficulty": "M", "type": "mc", "stimulus": "

Ana Castillo’s 1986 novel The Mixquiahuala Letters is a story told entirely through expressive letters from the narrator to her friend—letters that Castillo suggests could be read in several different orders. As they began reading it in class, some students remarked that they found the novel’s letter format daunting and its treatment of gender relations old-fashioned. The professor, however, pointed out that the novel is written in modern-sounding language and addresses issues that still matter today, suggesting that The Mixquiahuala Letters ______blank

", "stem": "

Which choice most logically completes the text?

", "choices": [{"id": "A", "text": "

has more to say about gender relations than other novels from the same period.

"}, {"id": "B", "text": "

is more relevant to contemporary audiences than it may seem at first.

"}, {"id": "C", "text": "

is easier to read than many contemporary novels that focus on friendship.

"}, {"id": "D", "text": "

is best understood after multiple readings in different orders.

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer because it most logically completes the text’s discussion of Ana Castillo’s 1986 novel The Mixquiahuala Letters. The text states that the novel consists entirely of letters from the narrator to her friend—a format that some students reading the novel in a class found intimidating. According to the text, those students also found the novel’s treatment of gender to be old-fashioned. In response to the students’ concerns, their professor emphasized the novel’s relevance: it’s written in modern-sounding language and addresses issues that still matter. This, in turn, suggests that The Mixquiahuala Letters is more relevant to contemporary audiences than it may initially seem.

Choice A is incorrect because the professor’s response to the students only mentions The Mixquiahuala Letters: it doesn’t compare the novel to others from the same period. Choice C is incorrect because nothing in the professor’s response to the students compares The Mixquiahuala Letters to contemporary novels about friendship. Choice D is incorrect because the professor’s response to the students doesn’t address the idea of reading the novel’s letters multiple times and in different orders.

"}, {"id": "35ec767c", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "H", "type": "mc", "stimulus": "

Corn-Related Vocabulary in Various Southeastern Languages

Language familyWord (language)English translationProposed origin in vocabulary of the Totozoquean language family
Muskogeantanchi’ (Chickasaw); tanchi (Choctaw); vce (Muscogee, pronounced “uh-chi”)cornno
Iroquoianse-lu (Cherokee)cornno
Caddoan-k’as- (Caddo)dried cornyes
Chitimachak’asma (Chitimacha)cornyes

\n

In Caddo, a language from what is now the US Southeast, vocabulary pertaining to corn cultivation resembles equivalent vocabulary in the Totozoquean language family in Mexico. This resemblance is perhaps attributable to cultural contact: such words could have entered Caddo through the intermediary of the neighboring but unrelated Chitimacha language, concurrent with the dissemination of corn itself from Mexico into the Southeast after 700 CE. That the vocabulary pertaining to domestic crops accompanies them as they diffuse into new regions is an established phenomenon globally. Crops may also be decoupled from vocabulary altogether: corn cultivation became ubiquitous among the Southeastern tribes, yet ______blank

", "stem": "

Which choice most effectively uses data from the table to complete the statement?

", "choices": [{"id": "A", "text": "

the origins of vocabulary pertaining to the crop vary across languages in the region, with the words for corn in Cherokee and the Muskogean languages showing no demonstrable relationship to Totozoquean vocabulary.

"}, {"id": "B", "text": "

the region is linguistically diverse, being home not only to Chitimacha and Caddo, but also to the Muskogean language family (including Chickasaw, Choctaw, and Muscogee) and to one Iroquoian language (Cherokee).

"}, {"id": "C", "text": "

corn-related vocabulary underwent changes when entering other, unrelated languages, as can be seen by the divergence of the Caddo word from the Chitimacha word it originated in.

"}, {"id": "D", "text": "

words for corn in the languages of the Muskogean family evolved from a common root, with the Muscogee word having lost certain consonant sounds still present in the Chickasaw and Choctaw words.

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. The table provides evidence that the words for corn in the Cherokee and Muskogean languages appear unrelated to those in Caddo language, which is described as closely related to the Totozoquean language family. This supports the claim that corn cultivation spread across the Southeast without necessarily spreading Totozoquean vocabulary along with it.

Choice B is incorrect. This choice emphasizes the diversity of Southeastern languages in general, but we’re specifically looking for information about words associated with corn. Choice C is incorrect. This choice shows how words for corn can change and evolve, but we’re looking for an example that shows how some words for corn can be completely unrelated. Choice D is incorrect. This choice shows words for corn that share a common root, but we’re looking for an example that shows how some words for corn can be unrelated.

"}, {"id": "0e3b4967", "domain": "Information and Ideas", "skill": "Central Ideas and Details", "difficulty": "E", "type": "mc", "stimulus": "

Scrapbooks of saved fabric pieces were commonly kept by women in the nineteenth-century United States, but few are as meticulously detailed as Hannah Ditzler Alspaugh’s work. Alongside each piece of fabric, Alspaugh recorded intimate memories, such as dressmaking with her sister. Additionally, she listed the prices and how she used the fabric. Historians note that by representing fifty years of changing textures, patterns, and dress styles, the scrapbook is a record of nineteenth-century textiles and dressmaking as well as Alspaugh’s life.

", "stem": "

Which choice best states the main idea of the text?

", "choices": [{"id": "A", "text": "

Alspaugh inspired other women to save pieces of fabric in scrapbooks and provide historical records of nineteenth-century fashions in the United States.

"}, {"id": "B", "text": "

Historians rely on fabric scrapbooks to understand how fashions changed throughout the nineteenth-century United States.

"}, {"id": "C", "text": "

Fabric scrapbooks were a popular hobby for many women in the nineteenth-century United States.

"}, {"id": "D", "text": "

Alspaugh’s scrapbook provides a detailed account of her life and historical record of fashion trends in the nineteenth-century United States.

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is correct. The text describes how Alspaugh’s scrapbook is both a record of her life and a historical record of nineteenth-century textiles and dressmaking.

Choice A is incorrect. The text says that it was common for American women to keep scrapbooks of fabric pieces in the nineteenth century, and it says that Alspaugh was one of these women. However, it never says that other women were inspired by Alspaugh. Choice B is incorrect. This is too general and too strong. The text says that Alspaugh’s scrapbook is a historical record of nineteenth-century textiles and dressmaking, but it never says that historians rely on such scrapbooks in general to understand how fashions changed throughout that time period. This choice also fails to even mention Alspaugh, who is the real focus of the text. Choice C is incorrect. The text does say this, but it’s a detail—not the main idea. The text is mainly about one woman’s scrapbook (Alspaugh’s), and this choice doesn’t even mention her.

"}, {"id": "24c1b7e4", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "H", "type": "mc", "stimulus": "

Percentage Point Changes in US Federal Outlays Relative to GDP by Congressional Status

PeriodCongressional statusChange in total outlaysChange in nondefense outlaysChange in defense outlays
1981–1988divided−0.4−1.30.9
1975–1976divided2.73.0−0.3
1977–1980undivided0.30.6−0.3
1964–1968undivided1.91.40.5
1969–1974divided−1.82.1−3.9

\n

Economist Steve H. Hanke has shown that divided US Congresses—which occur when one party holds the majority in the House of Representatives and another holds the majority in the Senate—tend to accompany reductions in total federal outlays (spending) relative to gross domestic product (GDP), which Hanke interprets to reflect decreases in government size. Hanke calculated the percentage point change in total outlays (encompassing nondefense and defense outlays) for consecutive US Congresses. Hanke has pointed to his calculations as evidence that a divided Congress may be a “necessary but not sufficient condition” for a decrease in government size to occur.

", "stem": "

Which choice best describes data from the table that support the underlined claim?

", "choices": [{"id": "A", "text": "

The periods of undivided Congresses were associated with increases in nondefense outlays, whereas all the periods of divided Congresses except one were associated with reductions in defense outlays.

"}, {"id": "B", "text": "

All the periods of divided Congresses were associated with reductions in total outlays, although two periods were also associated with increases in nondefense outlays.

"}, {"id": "C", "text": "

The periods of undivided Congresses were associated with increases in total outlays, whereas all the periods of divided Congresses were associated with reductions in either nondefense outlays or defense outlays.

"}, {"id": "D", "text": "

All the periods of divided Congresses except one were associated with reductions in total outlays, whereas the periods of undivided Congresses were associated with increases in total outlays.

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. The claim is that divided Congresses are necessary but insufficient—that is, we need divide Congresses, but they are not enough—to decrease government size, as measured by total federal outlays. This choice accurately expresses the supporting data from the “change in total outlays” part of the graph. Within the data set, divided Congresses sometimes decreased total outlays, but undivided ones never did.

Choice A is incorrect. The claim is only about government size, as measured by total federal outlays—defense and nondefense outlays aren’t relevant. Choice B is incorrect. The claim is only about government size as measured by total federal outlays—nondefense outlays aren’t relevant. Choice C is incorrect. The claim is only about government size as measured by total federal outlays—specific information about defense or nondefense outlays isn’t relevant.

"}, {"id": "fbb84fb0", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "M", "type": "mc", "stimulus": "

Hedda Gabler is an 1890 play by Henrik Ibsen. As a woman in the Victorian era, Hedda, the play’s central character, is unable to freely determine her own future. Instead, she seeks to influence another person’s fate, as is evident when she says to another character, ______blank

", "stem": "

Which quotation from a translation of Hedda Gabler most effectively illustrates the claim?

", "choices": [{"id": "A", "text": "

“Then what in heaven’s name would you have me do with myself?”

"}, {"id": "B", "text": "

“I want for once in my life to have power to mould a human destiny.”

"}, {"id": "C", "text": "

“Then I, poor creature, have no sort of power over you?”

"}, {"id": "D", "text": "

“Faithful to your principles, now and for ever! Ah, that is how a man should be!”

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer because it most effectively illustrates the claim in the text that Hedda seeks to influence another character’s fate. In the quotation, Hedda says that she wants “to have power to mould a human destiny,” or shape a person’s fate, just as the text indicates. Additionally, the phrase “for once in my life” suggests that Hedda feels that she has never been able to shape anyone’s life, including her own, supporting the text’s assertion that she “is unable to freely determine her own future.”

Choice A is incorrect because this quotation shows Hedda being uncertain about what to do with her own life, not wanting to influence another person’s fate. Choice C is incorrect because while this quotation shows Hedda’s interest in finding out whether she has any power over another character, it doesn’t clearly show that she wants to influence that person’s fate. In this quotation, Hedda seems to have inferred or concluded (“then”) that she doesn’t have any influence over the person to whom she’s speaking, and she’s asking that person to confirm her lack of influence. Choice D is incorrect because this quotation expresses Hedda’s belief that a man should be true to his principles, not her desire to influence another person’s fate. 

"}, {"id": "73d457b6", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "M", "type": "mc", "stimulus": "

In the 1970s, a roughly 60,000-year-old piece of hyena bone marked with nine notches was discovered at a site in western France once inhabited by Neanderthals. Although many believe that only modern humans developed systems for notating numbers, one archaeologist asserts that this artifact may be a sign that Neanderthals also recorded numerical information. The notches on the bone are unevenly spaced but approximately parallel, and microscopic analysis reveals that they were made with a single stone tool; according to the archaeologist, this suggests that the notches were all made at one time by one individual as a means of counting something.

", "stem": "

Which finding, if true, would most directly weaken the underlined claim?

", "choices": [{"id": "A", "text": "

Parallel lines are a common feature in modern humans’ early systems for recording numerical information.

"}, {"id": "B", "text": "

More than nine approximately parallel notches made with a different stone tool are present on another artifact found at a site in western France.

"}, {"id": "C", "text": "

It would have taken careful effort to make evenly spaced lines on bone with the stone tools typically used by Neanderthals.

"}, {"id": "D", "text": "

Decorative art discovered at another Neanderthal site in western France primarily features patterns of unevenly spaced parallel lines.

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. The archeologist bases their claim on the fact that the hyena bone features unevenly spaced parallel notches. But if unevenly spaced parallel lines were found on \"decorative art\" at another Neanderthal site, it would suggest that the hyena bone is probably decorative art as well—not a counting tool.

Choice A is incorrect. This choice doesn’t weaken the underlined claim. If anything, it might actually strengthen the claim: assuming we can make an inference about Neanderthals using a fact about early humans, it provides more support for the idea that the person who made the notches was counting something. Choice B is incorrect. This choice doesn’t weaken the underlined claim. The fact that another artifact had parallel notches made with a different stone tool doesn’t tell us anything about the use of either artifact. For all we know, they could both have been used for counting. Choice C is incorrect. This choice doesn’t weaken the underlined claim. The fact that it took effort to make the lines doesn’t tell us anything about what the lines were for.

"}, {"id": "56f477fb", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "H", "type": "mc", "stimulus": "

Distribution of Ecosystem Services Affected by Invasive Species by Service Type

Region (Overall)Provisioning (75%)Regulating (21%)Cultural (4%)
West73%27%0%
North88%12%0%
South79%14%7%
East83%6%11%
Central33%67%0%

\n

To assess the impact of invasive species on ecosystems in Africa, Benis N. Egoh and colleagues reviewed government reports from those nations about how invasive species are undermining ecosystem services (aspects of the ecosystem on which residents depend). The services were sorted into three categories: provisioning (material resources from the ecosystem), regulating (natural processes such as cleaning the air or water), and cultural (nonmaterial benefits of ecosystems). Egoh and her team assert that countries in each region reported effects on provisioning services and that provisioning services represent the majority of the reported services.

", "stem": "

Which choice best describes data from the table that support Egoh and colleagues’ assertion?

", "choices": [{"id": "A", "text": "

Provisioning services represent 73% of the services reported for the West region and 33% of those for the Central region, but they represent 75% of the services reported overall.

"}, {"id": "B", "text": "

None of the percentages shown for provisioning services are lower than 33%, and the overall percentage shown for provisioning services is 75%.

"}, {"id": "C", "text": "

Provisioning services are shown for each region, while no cultural services are shown for some regions.

"}, {"id": "D", "text": "

The greatest percentage shown for provisioning services is 88% for the North region, and the least shown for provisioning services is 33% for the Central region.

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. The finding that all the regions reported at least some effects on provisioning services supports the first part of the assertion. And the fact that provisioning services comprise 75% of the reported services overall supports the second part of the assertion.

Choice A is incorrect. This choice doesn’t fully support the assertion. It doesn’t include the finding that all the regions (not just Central and West) reported at least some effects on provisioning services. Choice C is incorrect. This choice doesn’t fully support the assertion. It doesn’t demonstrate that provisioning services represent the majority of the reported services overall. Choice D is incorrect. This choice doesn’t fully support the assertion. It doesn’t demonstrate that provisioning services represent the majority of the reported services overall.

"}, {"id": "cac82f9b", "domain": "Information and Ideas", "skill": "Inferences", "difficulty": "M", "type": "mc", "stimulus": "

Biologist Natacha Bodenhausen and colleagues analyzed the naturally occurring bacterial communities associated with leaves and roots of wild Arabidopsis thaliana, a small flowering plant. The researchers found many of the same bacterial genera in both the plants’ leaves and roots. To explain this, the researchers pointed to the general proximity of A. thaliana leaves to the ground and noted that rain splashing off soil could bring soil-based bacteria into contact with the leaves. Alternatively, the researchers noted that wind, which may be a source of bacteria in the aboveground portion of plants, could also bring bacteria to the soil and roots. Either explanation suggests that ______blank

", "stem": "

Which choice most logically completes the text?

", "choices": [{"id": "A", "text": "

bacteria carried by wind are typically less beneficial to A. thaliana than soil-based bacteria are.

"}, {"id": "B", "text": "

some bacteria in A. thaliana leaves and roots may share a common source.

"}, {"id": "C", "text": "

many bacteria in A. thaliana leaves may have been deposited by means other than rain.

"}, {"id": "D", "text": "

A. thaliana leaves and roots are especially vulnerable to harmful bacteria.

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. Both explanations suggest that the bacteria come from the same place: either they come from the ground and make their way to the leaves, or they come from above the ground and make their way to the roots.

Choice A is incorrect. This inference isn’t supported. The text never discusses any benefits of any kind of bacteria. Choice C is incorrect. This conflicts with the text. One of the theories is that the bacteria in the leaves were deposited by rain splashing off soil. Choice D is incorrect. This inference isn’t supported. The text only discusses “naturally occurring” bacteria. It never mentions either the harms or benefits of these bacteria.

"}, {"id": "783d1388", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "H", "type": "mc", "stimulus": "

The Souls of Black Folk is a 1903 book by W.E.B. Du Bois. In the book, Du Bois suggests that upon hearing Black folk songs, he felt an intuitive and sometimes unexpected sense of cultural recognition: ______blank

\n", "stem": "\n

Which quotation from The Souls of Black Folk most effectively illustrates the claim?

", "choices": [{"id": "A", "text": "

“[Black folk music] still remains as the singular spiritual heritage of the nation and the greatest gift of the Negro people.”

"}, {"id": "B", "text": "

“Ever since I was a child these songs have stirred me strangely. They came out of the South unknown to me, one by one, and yet at once I knew them as of me and of mine.”

"}, {"id": "C", "text": "

“Caricature has sought again to spoil the quaint beauty of the music, and has filled the air with many debased melodies which vulgar ears scarce know from the real. But the true Negro folk-song still lives in the hearts of those who have heard them truly sung and in the hearts of the Negro people.”

"}, {"id": "D", "text": "

“The songs are indeed the siftings of centuries; the music is far more ancient than the words, and in it we can trace here and there signs of development.”

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer because the quotation from The Souls of Black Folk illustrates the claim that Du Bois felt a sense of cultural recognition when he heard Black folk songs. In the quotation, Du Bois explains that for his entire life, Black folk songs “stirred [him] strangely.” Even though they originated in the South, a region he wasn’t familiar with, he knew the songs “as of me and of mine.” That is, he identified strongly with them and associated them with his community. Therefore, Du Bois felt an intuitive sense of cultural recognition when he heard Black folk songs. 

Choice A is incorrect. Although the quotation considers the cultural and spiritual value of Black folk music, it doesn’t establish that this music inspired in Du Bois a sense of cultural recognition. Choice C is incorrect because this quotation addresses the cultural survival of Black folk songs despite attempts to caricature, or parody, them, not Du Bois’s sense of cultural connection to them. Choice D is incorrect because the quotation indicates that the Black folk songs and music are old, “the siftings of centuries,” instead of addressing how Du Bois felt when he heard the songs.

"}, {"id": "af125459", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "E", "type": "mc", "stimulus": "

Number and Origin of Clamshell Tools Found at Different Depths below the Surface in Neanderthal Cave

Depth of tools found below surface in cave (meters)Clamshells that Neanderthals collected from the beachClamshells that Neanderthals harvested from the seafloor
2–370
3–49933
4–520
5–6187
6–710

\n

Two kinds of clamshell tools used by Neanderthals were dug up in a cave on the western coast of Italy. Archaeologist Paola Villa and her colleagues studied the tools and determined that Neanderthals either collected clams that had washed onto the beach or harvested clams from the seafloor and then sharpened the shells to make tools. The highest number of tools made from clamshells that were collected from the beach was found at a depth of ______blank

", "stem": "

Which choice most effectively uses data from the table to complete the text?

", "choices": [{"id": "A", "text": "

5–6 meters below the surface.

"}, {"id": "B", "text": "

4–5 meters below the surface. 

"}, {"id": "C", "text": "

3–4 meters below the surface.

"}, {"id": "D", "text": "

6–7 meters below the surface.

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer because it most effectively uses data from the table to complete the statement about the depth at which the highest number of tools made from clamshells that Neanderthals collected from the beach was found. The table presents the depths at which Neanderthal clamshell tools were found, and, for each depth, the number of those tools made from clamshells that washed up on the beach and the number made from clamshells harvested from the seafloor. The table indicates that the highest number made from clamshells collected from the beach was 99 and that these tools were found at a depth of 3–4 meters.

Choice A is incorrect because the table indicates that 18 tools made from clamshells collected from the beach were found at a depth of 5–6 meters, which is fewer than the 99 tools found at a depth of 3–4 meters. Choice B is incorrect because the table indicates that 2 tools made from clamshells collected from the beach were found at a depth of 4–5 meters, which is fewer than the 99 tools found at a depth of 3–4 meters. Choice D is incorrect because the table indicates that 1 tool made from clamshells collected from the beach was found at a depth of 6–7 meters, which is fewer than the 99 tools found at a depth of 3–4 meters.

"}, {"id": "0045c234", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "H", "type": "mc", "stimulus": "

Given that stars and planets initially form from the same gas and dust in space, some astronomers have posited that host stars (such as the Sun) and their planets (such as those in our solar system) are composed of the same materials, with the planets containing equal or smaller quantities of the materials that make up the host star. This idea is also supported by evidence that rocky planets in our solar system are composed of some of the same materials as the Sun.

", "stem": "

Which finding, if true, would most directly weaken the astronomers’ claim?

", "choices": [{"id": "A", "text": "

Most stars are made of hydrogen and helium, but when cooled they are revealed to contain small amounts of iron and silicate.

"}, {"id": "B", "text": "

A nearby host star is observed to contain the same proportion of hydrogen and helium as that of the Sun.

"}, {"id": "C", "text": "

Evidence emerges that the amount of iron in some rocky planets is considerably higher than the amount in their host star.

"}, {"id": "D", "text": "

The method for determining the composition of rocky planets is discovered to be less effective when used to analyze other kinds of planets.

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer because it presents a finding that, if true, would weaken the astronomers’ claim about the makeup of host stars and their planets. The text explains that because stars and planets begin forming from the same gas and dust, astronomers believe planets should be composed of the same materials as their host stars, but in equal or smaller quantities. The finding that the amount of iron in some rocky planets is much higher than the amount in their host star would weaken the astronomers’ claim because it would show that some planets contain the same material as their host star, but in higher quantities.

Choice A is incorrect because a finding only about the makeup of stars, whether they’ve cooled or not, would provide no information about the makeup of planets. Thus, it wouldn’t have any bearing on the claim that planets and their host stars are composed of the same materials in differing quantities. Choice B is incorrect because a finding about two host stars having similar proportions of certain materials wouldn’t provide any information about the makeup of planets. Thus, it wouldn’t be relevant to the claim that planets and their host stars are composed of the same materials in differing quantities. Choice D is incorrect because the text indicates that the astronomers’ claim is based on a fact—that stars and planets begin forming from the same gas and dust in space—which would remain true regardless of the effectiveness of a method for analysis of compositions. The text does cite analysis of rocky planets in our solar system and the Sun, but only as a single piece of evidence that is consistent with the claim and not as the source of the claim; the finding that the method used for that analysis is less effective in other scenarios wouldn’t weaken a claim that’s based on knowledge of how stars and planets initially form.

"}, {"id": "a3fb5e77", "domain": "Information and Ideas", "skill": "Central Ideas and Details", "difficulty": "H", "type": "mc", "stimulus": "

Some animal-behavior studies involve observing wild animals in their natural habitat, and some involve capturing wild animals and observing them in a laboratory. Each approach has advantages over the other. In wild studies, researchers can more easily presume that the animals are behaving normally, and in lab studies, researchers can more easily control factors that might affect the results. But if, for example, the results from a wild study and a lab study of Western scrub-jays (Aphelocoma californica) contradict each other, one or both of the studies must have failed to account for some factor that was relevant to the birds’ behavior.

", "stem": "

Which choice best states the main idea of the text?

", "choices": [{"id": "A", "text": "

When the results of a natural-habitat study and those from a lab study of a wild animal such as the Western scrub-jay conflict, the study in the natural habitat is more likely than the lab study to have accurate results.

"}, {"id": "B", "text": "

Studying wild animals such as the Western scrub-jay in both their natural habitat and lab settings is likely to yield conflicting results that researchers cannot fully resolve.

"}, {"id": "C", "text": "

Wild animals such as the Western scrub-jay can be effectively studied in their natural habitat and in the lab, but each approach has drawbacks that could affect the accuracy of the findings.

"}, {"id": "D", "text": "

Differing results between natural-habitat and lab studies of wild animals such as the Western scrub-jay are a strong indication that both of the studies had design flaws that affected the accuracy of their results.

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer because it most accurately states the main idea of the text. The text begins by explaining that wild animals can be studied in their natural habitat or in a laboratory setting, with each setting offering unique advantages to researchers. The text then highlights an instance in which Western scrub-jays were studied in both settings but with conflicting results, indicating that one or both studies may have failed to account for the disadvantages of its research setting. Thus, the main idea of the text is that while wild animals can be effectively studied in natural or lab settings, there are drawbacks to each that need to be considered to ensure accurate results.

Choice A is incorrect because the text does not position one study setting (natural or lab) as superior to the other; rather, the text states that each one has advantages over the other. Choice B is incorrect. The text provides a hypothetical example of two studies in different environments with conflicting results, but this single example cannot be extrapolated to a general claim about the likelihood that results of studies in different environments will conflict. Additionally, the text does not assert anything about how researchers can or cannot resolve conflicting study results. Choice D is incorrect because the text does not state that discrepancies between natural-habitat and lab-based animal behavior studies are due to both of the designs being flawed. Rather, the text states that the conflict in results can be the consequence of one or both of the studies having failed to account for some factor. 

"}, {"id": "87023f34", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "M", "type": "mc", "stimulus": "

“Ghosts of the Old Year” is an early 1900s poem by James Weldon Johnson. In the poem, the speaker describes experiencing an ongoing cycle of anticipation followed by regretful reflection: ______blank

", "stem": "

Which quotation from “Ghosts of the Old Year” most effectively illustrates the claim?

", "choices": [{"id": "A", "text": "

“What does this brazen tongue declare, / That falling on the midnight air / Brings to my heart a sense of care / Akin to fright?”

"}, {"id": "B", "text": "

“The snow has ceased its fluttering flight, / The wind sunk to a whisper light, / An ominous stillness fills the night, / A pause—a hush.”

"}, {"id": "C", "text": "

“It tells of many a squandered day, / Of slighted gems and treasured clay, / Of precious stores not laid away, / Of fields unreaped.”

"}, {"id": "D", "text": "

“And so the years go swiftly by, / Each, coming, brings ambitions high, / And each, departing, leaves a sigh / Linked to the past.”

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer because it presents the quotation that most effectively illustrates the claim that the speaker of the poem describes experiencing an ongoing cycle of anticipation followed by regretful reflection. In this quotation, the speaker notes that as years go by, “Each, coming”—that is, each new year as it comes—“brings ambitions high.” In other words, the speaker begins each new year with large goals. But the speaker goes on to say that as each year ends (“each, departing”), it “leaves a sigh / Linked to the past.” A sigh is an expression of longing or regret, so in the context of the whole quotation, this portion suggests that at the end of each year, the speaker regretfully reflects on not having achieved the ambitions formed at the beginning of the year. The phrases “the years go swiftly by,” “Each, coming,” and “each, departing” indicate that this experience happens over and over again: the speaker experiences a cycle of anticipation followed by regretful reflection. 

Choice A is incorrect because this quotation does not describe an ongoing cycle of anticipation followed by regretful reflection. Instead, the speaker describes experiencing a sensation similar to fright as a result of something that has occurred at midnight. Specifically, the speaker has heard a “brazen tongue,” a figurative way of saying that the speaker has heard the clang of a bronze bell being rung. Choice B is incorrect because although this quotation does convey a sense of anticipation through its reference to “ominous stillness,” there is no suggestion of regretful reflection or any indication that the speaker is describing an ongoing cycle of anticipation followed by such reflection. Instead, the speaker is describing a particular moment when a winter storm appears to have momentarily calmed. Choice C is incorrect because although this quotation does convey a sense of regret (“many a squandered day”), nothing in the quotation suggests an ongoing cycle of anticipation followed by regret. Instead, the speaker is simply lamenting wasted time and opportunities. 

"}, {"id": "4fc9a13a", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "H", "type": "mc", "stimulus": "

The novelist Toni Morrison was the first Black woman to work as an editor at the publishing company Random House, from 1967 to 1983. A scholar asserts that one of Morrison’s likely aims during her time as an editor was to strengthen the presence of Black writers on the list of Random House’s published authors.

", "stem": "

Which finding, if true, would most strongly support the scholar’s claim?

", "choices": [{"id": "A", "text": "

The percentage of authors published by Random House who were Black rose in the early 1970s and stabilized throughout the decade.

"}, {"id": "B", "text": "

Black authors who were interviewed in the 1980s and 1990s were highly likely to cite Toni Morrison’s novels as a principal influence on their work.

"}, {"id": "C", "text": "

The novels written by Toni Morrison that were published after 1983 sold significantly more copies and received wider critical acclaim than the novels she wrote that were published before 1983.

"}, {"id": "D", "text": "

Works that were edited by Toni Morrison during her time at Random House displayed stylistic characteristics that distinguished them from works that were not edited by Morrison.

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer because it presents a finding that, if true, would support the scholar’s claim about Toni Morrison’s likely goal of strengthening the presence of Black writers on Random House’s list of published authors. The text explains that Morrison was the first Black woman to be an editor for Random House and that she was an editor there from 1967 to 1983. If it were true that Random House published a higher percentage of works by Black authors throughout the 1970s—during most of Morrison’s time working there—than it had previously published, that would suggest that Morrison may have made a deliberate effort to strengthen the presence of Black authors on the list of Random House’s published authors, thus supporting the scholar’s claim.

Choice B is incorrect because the scholar’s claim is about Morrison’s work as an editor at a publishing company and her likely effort to strengthen the presence of Black writers on that company’s list of published authors. It might be true that Black authors interviewed in the 1980s and 1990s often cited Morrison’s novels as an influence on their work, but that finding would simply suggest something about how those authors approached their work; it wouldn’t show that Morrison intended to increase the number of Black writers among the published authors specifically at Random House. Choice C is incorrect because the scholar’s claim is about Morrison’s work as an editor at a publishing company, not about her work as a novelist. Therefore, a finding that Morrison’s novels published after 1983 sold more copies and were more widely acclaimed than her earlier novels would have no bearing on the claim that as an editor Morrison made an effort to ensure that more Black writers were present on Random House’s list of published authors. Choice D is incorrect. Although the text discusses Morrison’s work as an editor at Random House, the scholar’s claim focuses on Morrison’s likely effort in that role to increase the number of Black writers present on Random House’s list of published authors, not on the influence she may have had on the content of the works she edited. Without knowing whether Morrison’s stylistic influence led to more publications or if Morrison applied her influence specifically to works by Black writers, the finding that works edited by Morrison could be identified by stylistic characteristics would have no bearing on the claim that Morrison intended to strengthen the presence of Black writers among the published authors at Random House.

"}, {"id": "cae97f58", "domain": "Information and Ideas", "skill": "Inferences", "difficulty": "H", "type": "mc", "stimulus": "

Mosses can struggle in harsh desert conditions because these plants require enough sunlight for photosynthesis but not so much that they risk drying out. Researchers Jenna Ekwealor and Kirsten M. Fisher found several species of Syntrichia caninervis, a type of desert moss, growing under quartz crystals in California’s Mojave Desert. To evaluate whether these semitransparent rocks benefited the moss, the researchers compared the shoot tissue, a measure of plant growth, of S. caninervis when growing on the soil surface versus when the moss was growing under the quartz rocks. They found that the shoot tissue was 62% longer for moss growing under the quartz as compared to moss on the soil surface, suggesting that ______blank

", "stem": "

Which choice most logically completes the text?

", "choices": [{"id": "A", "text": "

S. caninervis is one of the few types of moss that can survive under semitransparent rocks.

"}, {"id": "B", "text": "

quartz crystals do not transmit the necessary sunlight for photosynthesis in S. caninervis.

"}, {"id": "C", "text": "

S. caninervis growing under quartz crystals experience lower light intensity and are thus able to retain more moisture.

"}, {"id": "D", "text": "

quartz crystals are capable of supporting S. caninervis growth if the crystals are not too thin.

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer because  it most logically completes the text. The text explains that while desert moss species need sufficient sunlight for photosynthesis, exposure to sunlight can also affect the plants negatively by drying them out. Ekwealor and Fisher’s team found specimens of S. caninervis moss growing under quartz crystals that were semitransparent, allowing some but not all sunlight to pass through them, and the shoot tissue of these specimens was longer than that of S. caninervis specimens found growing on the surface that were unprotected by such crystals. Since, as the text explains, the length of shoot tissue is an indicator of plant growth, and since greater exposure to sunlight results in greater loss of moisture, it can be inferred that S. caninervis growing under quartz crystals experience lower light intensity and are thus able to retain more moisture.

Choice A is incorrect because the text doesn’t mention another moss species besides S. caninervis or discuss whether other such species are able to grow under transparent crystals, as S. caninervis is. Choice B is incorrect because, as the text explains, specimens of S. caninervis were found growing under quartz crystals and exhibited more plant growth than specimens growing on the soil surface. This wouldn’t have been the case if the crystals transmitted insufficient light for the moss’s photosynthesis. Choice D is incorrect. The text contrasts the growth of S. caninervis specimens found beneath semitransparent quartz crystals with that of specimens found on the soil surface absent such crystals, but it doesn’t make a comparison among specimens growing beneath crystals of different degrees of thickness or consider how the relative thickness of the crystals affects the growth of the moss.

"}, {"id": "8391a002", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "H", "type": "mc", "stimulus": "

Black beans (Phaseolus vulgaris) are a nutritionally dense food, but they are difficult to digest in part because of their high levels of soluble fiber and compounds like raffinose. They also contain antinutrients like tannins and trypsin inhibitors, which interfere with the body’s ability to extract nutrients from foods. In a research article, Marisela Granito and Glenda Álvarez from Simón Bolívar University in Venezuela claim that inducing fermentation of black beans using lactic acid bacteria improves the digestibility of the beans and makes them more nutritious.

", "stem": "

Which finding from Granito and Álvarez’s research, if true, would most directly support their claim?

", "choices": [{"id": "A", "text": "

When cooked, fermented beans contained significantly more trypsin inhibitors and tannins but significantly less soluble fiber and raffinose than nonfermented beans. 

"}, {"id": "B", "text": "

Fermented beans contained significantly less soluble fiber and raffinose than nonfermented beans, and when cooked, the fermented beans also displayed a significant reduction in trypsin inhibitors and tannins.

"}, {"id": "C", "text": "

When the fermented beans were analyzed, they were found to contain two microorganisms, Lactobacillus casei and Lactobacillus plantarum, that are theorized to increase the amount of nitrogen absorbed by the gut after eating beans. 

"}, {"id": "D", "text": "

Both fermented and nonfermented black beans contained significantly fewer trypsin inhibitors and tannins after being cooked at high pressure. 

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer because it presents a finding that would best support Granito and Álvarez’s claim that fermenting black beans makes them easier to digest and more nutritious. The text indicates that high levels of soluble fiber and raffinose in black beans make the beans hard to digest and that tannins and trypsin inhibitors make it harder for the body to extract nutrients from the beans. If it were found that fermenting the beans significantly reduces their levels of soluble fiber, raffinose, trypsin inhibitors, and tannins when cooked, this would directly support the claim that fermentation improves the digestibility of the beans and makes them more nutritious.

Choice A is incorrect because the text indicates that trypsin inhibitors and tannins interfere with the body’s ability to extract nutrients from black beans; if fermentation and cooking were found to increase these antinutrients, fermented beans would likely be less nutritious than unfermented ones, not more nutritious (as Granito and Álvarez claim). Choice C is incorrect because the text doesn’t address the idea that greater nitrogen absorption in the gut has an effect on a food’s digestibility or level of nutrition, so the discovery of the presence of microorganisms that may increase nitrogen absorption wouldn’t provide relevant support for the claim that fermentation makes black beans easier to digest and more nutritious. Choice D is incorrect because Granito and Álvarez’s claim focuses on the effect of fermenting black beans, but the finding that nonfermented black beans also have fewer trypsin inhibitors and tannins when cooked at high pressure would suggest that the role of the cooking method could be significant when it comes to nutrition; further, the finding wouldn’t address the beans’ digestibility.

"}, {"id": "ab94d40a", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "E", "type": "mc", "stimulus": "

Time Participants Spent Reading about Five London Museums

Museum NameRankingPercentage of total time spent reading about museum by participants provided with rankingPercentage of total time spent reading about museum by participants not provided with ranking
British Museum13618
National Gallery22120
Tate Modern41617
Victoria and Albert Museum51423
Natural History Museum31322

\n

Researchers recently conducted an experiment to understand how we use rankings to make decisions. They created a fictitious travel website describing five museums in London. Then, they invited two groups of participants, who had never visited the museums, to review the site and select the museum they would be most likely to visit. Meanwhile, the researchers tracked the amount of time each participant spent reading about each museum. For one group, the website ranked each museum, titling the page “The Top 5 Museums in London.” For the other group, the museums and their descriptions were not ranked. The researchers concluded that when reviewing ranked lists, we tend to focus on the top-ranked option. 

", "stem": "

Which choice best describes data in the table that support the researchers’ conclusion?

", "choices": [{"id": "A", "text": "

Participants who were not provided with a ranking of the museums spent roughly equal amounts of time reading about each museum.

"}, {"id": "B", "text": "

Participants who were provided with a ranking of the museums spent disproportionately more time reading about the British museum.

"}, {"id": "C", "text": "

Participants who were provided with a ranking of the museums spent the least amount of time reading about the Natural History Museum.

"}, {"id": "D", "text": "

Participants who were not provided with a ranking of the museums spent the most time reading about the Victoria and Albert Museum.

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. By looking at the top-ranked option, we can see that people provided with ranked lists spent more time reading about the British Museum than reading about other museums (36% of the time versus 21% for the second-ranked option).

Choice A is incorrect. The claim is about people with ranked lists, and these data are about those with unranked lists. Choice C is incorrect. The claim is about people with ranked lists looking at the top-ranked option, and these data are about the third-ranked option. Choice D is incorrect. The claim is about people with ranked lists, and these data are about those with unranked lists.

"}, {"id": "835545cd", "domain": "Information and Ideas", "skill": "Central Ideas and Details", "difficulty": "M", "type": "mc", "stimulus": "

The following text is adapted from Charles W. Chesnutt’s 1901 novel The Marrow of Tradition.

\n

Mrs. Ochiltree was a woman of strong individuality, whose comments upon her acquaintance[s], present or absent, were marked by a frankness at times no less than startling. This characteristic caused her to be more or less avoided. Mrs. Ochiltree was aware of this sentiment on the part of her acquaintance[s], and rather exulted in it.

", "stem": "

Based on the text, what is true about Mrs. Ochiltree’s acquaintances?

", "choices": [{"id": "A", "text": "

They try to refrain from discussing topics that would upset Mrs. Ochiltree. 

"}, {"id": "B", "text": "

They are unable to spend as much time with Mrs. Ochiltree as she would like.

"}, {"id": "C", "text": "

They are too preoccupied with their own concerns to speak with Mrs. Ochiltree.

"}, {"id": "D", "text": "

They are likely offended by what Mrs. Ochiltree has said about them.

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer because it presents a statement about Mrs. Ochiltree’s acquaintances that is supported by the text. The text indicates that Mrs. Ochiltree makes comments about her acquaintances that are frank, or direct and blunt, and sometimes startling. It also states that because of this behavior, the acquaintances tend to avoid Mrs. Ochiltree. Together, these details suggest that the acquaintances choose not to be around Mrs. Ochiltree because they are offended by the things she has said about them.

Choice A is incorrect because the text doesn’t suggest that Mrs. Ochiltree’s acquaintances avoid discussing topics that would upset Mrs. Ochiltree; instead, it states that they avoid being around Mrs. Ochiltree at all. Choice B is incorrect because the text makes it clear that Mrs. Ochiltree knows her acquaintances often avoid her and is pleased about it (she “rather exulted in it”), not that she wants to spend more time with them. Choice C is incorrect because the text doesn’t suggest that Mrs. Ochiltree’s acquaintances don’t speak with Mrs. Ochiltree because they are too focused on their own concerns, but rather because they don’t like the frank comments she makes. 

"}, {"id": "a842db60", "domain": "Information and Ideas", "skill": "Central Ideas and Details", "difficulty": "E", "type": "mc", "stimulus": "

To make her art more widely available, graphic artist Elizabeth Catlett turned to linocuts. In linocut printing, an artist carves an image into a sheet of linoleum to create a stamp that is used to mass-produce prints. In the linocut series The Black Woman (1946–1947), Catlett depicts the everyday experiences of Black women alongside the achievements of well-known Black women. This pairing invites the viewer to draw connections among the women. The linocut process enabled Catlett’s work to reach a wide audience and supported her aim to unite Black women through her art.

", "stem": "

According to the text, what is significant about Catlett’s use of linocut printing?

", "choices": [{"id": "A", "text": "

Linocut printing involved using materials that were readily available to Catlett. 

"}, {"id": "B", "text": "

Linocut printing helped Catlett use art to connect people, especially Black women.

"}, {"id": "C", "text": "

Catlett became commercially successful once she started using linocut printing. 

"}, {"id": "D", "text": "

Catlett was one of the first Black artists to use linocut printing.

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. The last sentence states that the linocut process “supported her [Catlett’s] aim to unite Black women through her art.”

Choice A is incorrect. The text briefly describes the linocut printing process but doesn’t discuss the availability of the materials used in the process. Choice C is incorrect. The text says that the linocut process “enabled Catlett’s work to reach a wide audience,” but that doesn’t mean that linocuts made her “commercially successful.” In other words, we don’t know how much money she made off her linocuts—we only know that more people were able to see her work. Choice D is incorrect. The text says that Catlett depicted Black women in her linocuts, but not that she was one of the first Black artists to use linocut printing.

"}, {"id": "c384987b", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "E", "type": "mc", "stimulus": "

Scientists have long believed that giraffes are mostly silent and communicate only visually with one another. But biologist Angela Stöger and her team analyzed hundreds of hours of recordings of giraffes in three European zoos and found that giraffes make a very low-pitched humming sound. The researchers claim that the giraffes use these sounds to communicate when it’s not possible for them to signal one another visually.

", "stem": "

Which finding, if true, would most directly support Stöger and her team’s claim? 

", "choices": [{"id": "A", "text": "

Giraffes have an excellent sense of vision and can see in color. 

"}, {"id": "B", "text": "

The giraffes only produced the humming sounds at night when they couldn’t see one another.

"}, {"id": "C", "text": "

Wild giraffes have never been recorded making humming sounds.  

"}, {"id": "D", "text": "

Researchers observed other animals in European zoos humming. 

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer because it presents a finding that, if true, would support Stöger and her team’s claim that giraffes use humming to communicate when they cannot signal to one another visually. The text indicates that scientists have long thought that giraffes produce little sound and exclusively rely on visual signals to communicate with one another. The text goes on to say, however, that Stöger and her team have recorded giraffes in three European zoos making a low-pitched humming sound, which the team claims the giraffes use to communicate when they cannot see each other. If the giraffes produced these sounds when visual communication was impossible and never produced them otherwise, that would support Stöger and her team’s claim about the circumstance in which giraffes make the sound. 

Choice A is incorrect because finding that giraffes have excellent vision and can see in color would have no bearing on Stöger and her team’s claim that giraffes produce a low-pitched humming noise to communicate when they cannot communicate visually. As presented in the text, Stöger and her team’s claim is restricted to circumstances in which giraffes cannot signal one another visually; if the giraffes are unable to signal visually, their sense of vision is irrelevant to their communication. Choice C is incorrect because finding that wild giraffes have never been recorded making humming noises would not support Stöger and her team’s claim about the function of the humming noise that the researchers recorded from the giraffes in European zoos. The text provides no information about whether researchers have even attempted to record low-pitched humming in wild giraffes, so nothing can be concluded about the implications of the lack of such recordings. Choice D is incorrect because finding that other animals in European zoos had been observed humming would not support Stöger and her team’s claim, since it would not indicate anything about why giraffes produce humming sounds. Different species could produce similar sounds for different purposes, so scientists could not conclude anything about the function of giraffe humming from a finding that some other animals in zoos also hum. 

"}, {"id": "a66f9b8d", "domain": "Information and Ideas", "skill": "Central Ideas and Details", "difficulty": "M", "type": "mc", "stimulus": "

Cats can judge unseen people’s positions in space by the sound of their voices and thus react with surprise when the same person calls to them from two different locations in a short span of time. Saho Takagi and colleagues reached this conclusion by measuring cats’ levels of surprise based on their ear and head movements while the cats heard recordings of their owners’ voices from two speakers spaced far apart. Cats exhibited a low level of surprise when owners’ voices were played twice from the same speaker, but they showed a high level of surprise when the voice was played once each from the two different speakers.

", "stem": "

According to the text, how did the researchers determine the level of surprise displayed by the cats in the study?

", "choices": [{"id": "A", "text": "

They watched how each cat moved its ears and head.

"}, {"id": "B", "text": "

They examined how each cat reacted to the voice of a stranger.

"}, {"id": "C", "text": "

They studied how each cat physically interacted with its owner.

"}, {"id": "D", "text": "

They tracked how each cat moved around the room.

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer because it explains how the researchers determined the level of surprise displayed by the cats in the study. The text states that Saho Takagi and colleagues played recordings of the voice of each cat’s owner and measured how surprised the cat was by the recording based on how it moved its ears and head.

Choice B is incorrect because, as the text explains, the recordings played for each cat in the study were of the voice of the cat’s owner, not a stranger’s voice. Choice C is incorrect because the text explains that during the study, the cats didn’t interact directly with their owners; instead, the cats listened to recordings of their owners’ voices. Choice D is incorrect because the text doesn’t indicate that the researchers monitored the cats’ movement around the room in which the study was conducted.

"}, {"id": "1e85caa9", "domain": "Information and Ideas", "skill": "Central Ideas and Details", "difficulty": "E", "type": "mc", "stimulus": "

The following text is from Edith Nesbit’s 1902 novel Five Children and It. Five young siblings have just moved with their parents from London to a house in the countryside that they call the White House.

\n
\n

It was not really a pretty house at all; it was quite ordinary, and mother thought it was rather inconvenient, and was quite annoyed at there being no shelves, to speak of, and hardly a cupboard in the place. Father used to say that the ironwork on the roof and coping was like an architect’s nightmare. But the house was deep in the country, with no other house in sight, and the children had been in London for two years, without so much as once going to the seaside even for a day by an excursion train, and so the White House seemed to them a sort of Fairy Palace set down in an Earthly Paradise.

\n
", "stem": "

Which choice best states the main idea of the text?

", "choices": [{"id": "A", "text": "

Although their parents believe the house has several drawbacks, the children are enchanted by it.

"}, {"id": "B", "text": "

The children don’t like the house nearly as much as their parents do.

"}, {"id": "C", "text": "

Each member of the family admires a different characteristic of the house.

"}, {"id": "D", "text": "

The house is beautiful and well built, but the children miss their old home in London.

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. The text lists complaints about the house made by the mother and father, but then it says that the children thought the house was a \"Fairy Palace\" and \"Earthly Paradise.\"

Choice B is incorrect. The text states the opposite of this. It describes how the mother and father dislike the house and says the children think the house seems like paradise. Choice C is incorrect. This isn’t what the text says. Only the children are said to admire the house; mother and father both complain about the house. Choice D is incorrect. The text states the opposite of this. It tells us the house was ugly and poorly built (\"an architect’s nightmare\") and suggests the children were tired of London.

"}, {"id": "124fdcd7", "domain": "Information and Ideas", "skill": "Command of Evidence", "difficulty": "H", "type": "mc", "stimulus": "

Many archaeologists will tell you that categorizing excavated fragments of pottery by style, period, and what objects they belong to relies not only on standard criteria, but also on instinct developed over years of practice. In a recent study, however, researchers trained a deep-learning computer model on thousands of images of pottery fragments and found that it could categorize them as accurately as a team of expert archaeologists. Some archaeologists have expressed concern that they might be replaced by such computer models, but the researchers claim that outcome is highly unlikely.

", "stem": "

Which finding, if true, would most directly support the researchers’ claim?

", "choices": [{"id": "A", "text": "

In the researchers’ study, the model was able to categorize the pottery fragments much more quickly than the archaeologists could. 

"}, {"id": "B", "text": "

In the researchers’ study, neither the model nor the archeologists were able to accurately categorize all the pottery fragments that were presented.

"}, {"id": "C", "text": "

A survey of archaeologists showed that categorizing pottery fragments limits the amount of time they can dedicate to other important tasks that only human experts can do.

"}, {"id": "D", "text": "

A survey of archaeologists showed that few of them received dedicated training in how to properly categorize pottery fragments.

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer because it presents a finding that, if true, would support the researchers’ claim that archaeologists are unlikely to be replaced by certain computer models. The text explains that although archaeologists hold that categorizing pottery fragments relies on both objective criteria and instinct developed through direct experience, researchers have found that a computer model can categorize the fragments with the same degree of accuracy as the humans can—a finding that has caused some archaeologists to worry that their own work won’t be needed any longer. If survey results indicate that categorizing pottery fragments limits the amount of time archaeologists can dedicate to other important tasks that only human experts can do, that would mean that computer models aren’t able to do all of the important things archaeologists do, thus supporting the researchers’ claim that computer models are unlikely to replace human archaeologists.

Choice A is incorrect because if it were true that the computer model could categorize the pottery fragments much more quickly than the archaeologists could, that would weaken the researchers’ claim that archaeologists are unlikely to be replaced by certain computer models, since it would demonstrate that the models could conduct the archaeologists’ work not only with equal accuracy but also at a faster pace. Choice B is incorrect because the inability of both the computer model and the archaeologists to accurately categorize all of the pottery fragments presented wouldn’t support the researchers’ claim that archaeologists are unlikely to be replaced by certain computer models. The text indicates that some archaeologists are worried because the computer model’s accuracy is equal to their own, and that could be the case whether both were perfectly accurate or were unable to achieve complete accuracy. Choice D is incorrect because survey results showing that few archaeologists received special training in properly categorizing pottery fragments wouldn’t support the researchers’ claim that archaeologists are unlikely to be replaced by certain computer models. The amount of special training in categorizing pottery fragments that archaeologists have received has no direct bearing on whether computer models’ success at categorizing fragments will lead to the models replacing the archaeologists. 

"}, {"id": "03701ef3", "domain": "Information and Ideas", "skill": "Inferences", "difficulty": "H", "type": "mc", "stimulus": "

To better understand the burrowing habits of Alpheus bellulus (the tiger pistol shrimp), some studies have used resin casting to obtain precise measurements of the shrimps’ burrows. Resin casting involves completely filling an empty burrow with a liquid plastic that hardens to create a three-dimensional model; however, recovering the model inevitably requires destroying the burrow. In their 2022 study, Miyu Umehara and colleagues discovered that an x-ray computed tomography (CT) scanner can accurately record a burrow’s measurements both at a moment in time and throughout the entire burrow-building process, something that’s impossible with resin casting because ______blank

", "stem": "

Which choice most logically completes the text?

", "choices": [{"id": "A", "text": "

it can only be used on burrows below a certain size.

"}, {"id": "B", "text": "

it does not allow for multiple castings of the same burrow over time.

"}, {"id": "C", "text": "

the casting process takes more time than A. bellulus takes to construct a burrow.

"}, {"id": "D", "text": "

the process of recovering the model distorts the resin’s shape.

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. Since resin casting “inevitably requires destroying the burrow,” it would be impossible to make multiple castings of the same burrow over time.

Choice A is incorrect. The passage doesn’t discuss size requirements for completing resin casting, so there’s no basis for this inference. Choice C is incorrect. The passage never mentions how long the casting process takes nor how long A. bellulus takes to construct a borrow, so there’s no basis for this inference. Choice D is incorrect. The passage never states that recovering the model distorts the resin’s shape, only that it destroys the burrow. Therefore, there’s no basis for this inference.

"}, {"id": "b1fab3e1", "domain": "Information and Ideas", "skill": "Inferences", "difficulty": "M", "type": "mc", "stimulus": "

Violins made by Antonio Stradivari and other craftspeople in the sixteenth to eighteenth centuries in Cremona, Italy, produce a sound that is considered superior to that of modern stringed instruments. Some experts have claimed that the type of wood used to create Cremonese violins is responsible for their prized sound, but modern and Cremonese violins are made of the same kinds of wood: maple and spruce. New analysis, however, has revealed unique indications that the wood in the older violins was chemically treated by the makers, leading researchers to suggest that ______blank

", "stem": "

Which choice most logically completes the text?

", "choices": [{"id": "A", "text": "

Cremonese violins probably were not considered superior to other instruments at the time they were made. 

"}, {"id": "B", "text": "

the sound quality of Cremonese violins results in part from a method the craftspeople used to alter the wood.

"}, {"id": "C", "text": "

if modern violins were made of a wood other than maple or spruce, they likely would sound as good as Cremonese violins.

"}, {"id": "D", "text": "

the current process of making violins is the same process that was used centuries ago by Cremonese craftspeople.

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer because it most logically completes the text’s discussion of the sound quality of Cremonese and modern violins. The text states that violins made in Cremona in the sixteenth to eighteenth centuries sound superior to modern violins. It then indicates that some experts attribute the difference to different woods being used to make these violins, but both Cremonese and modern violins are made of the same woods (maple and spruce); thus this cannot account for the difference. The text then says that recent analysis suggests the wood in Cremonese violins was chemically treated by the craftspeople who made them, thereby providing an alternate explanation for the sound differences: the chemical alteration that is present in the Cremonese violins but absent from the modern ones.

Choice A is incorrect because the text does not discuss how the sound quality of Cremonese violins compares with the sound quality of other instruments made during the sixteenth to eighteenth centuries. Instead it focuses on how the sound of the Cremonese violins compares with that of modern violins. Choice C is incorrect. The text states that there are differences in sound quality between the Cremonese and modern violins, and that both types of violin are made with maple or spruce. Thus the type of wood alone does not determine a violin’s sound quality. Furthermore, even if the type of wood alone could account for differences in sound quality, the text makes no mention of other woods, so there is no basis to judge how modern violins would sound if they were made using woods besides maple and spruce. Choice D is incorrect because the text states that there is evidence that Cremonese craftspeople chemically treated the wood used in Cremonese violins. This evidence is attributed to “new analysis,” which strongly suggests that this process was unknown to modern violin makers before that analysis. If the chemical treatment was unknown until recently, the manufacturing process for modern violins must differ with respect to the previously unknown practice of chemically treating the wood.

"}, {"id": "84b5125b", "domain": "Craft and Structure", "skill": "Words in Context", "difficulty": "E", "type": "mc", "stimulus": "

Artist Marilyn Dingle’s intricate, coiled baskets are ______blank sweetgrass and palmetto palm. Following a Gullah technique that originated in West Africa, Dingle skillfully winds a thin palm frond around a bunch of sweetgrass with the help of a “sewing bone” to create the basket’s signature look that no factory can reproduce.

", "stem": "

Which choice completes the text with the most logical and precise word or phrase?

", "choices": [{"id": "A", "text": "

indicated by

"}, {"id": "B", "text": "

handmade from

"}, {"id": "C", "text": "

represented by

"}, {"id": "D", "text": "

collected with

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer because it most logically completes the text’s discussion of Marilyn Dingle’s baskets. In this context, to say that Dingle’s baskets are “handmade from” particular plants means that Dingle creates baskets herself using those plants but without using machines. The text says that Dingle “skillfully winds” parts of palmetto palm plants around sweetgrass plants to make baskets with an appearance that “no factory can reproduce.” This context suggests that Dingle’s baskets are handmade from sweetgrass and palmetto palm. 

Choice A is incorrect because the text describes how Dingle uses sweetgrass and palmetto palm to create her baskets, not how her baskets are “indicated by,” or signified by, sweetgrass and palmetto palm. Choice C is incorrect. Although Dingle’s baskets are described as being made using sweetgrass and palm, there’s nothing in the text to suggest that the baskets are “represented by,” or exemplified or portrayed by, sweetgrass and palmetto palm. Instead, the focus of the text is on Dingle’s use of sweetgrass and palmetto palm and the impossibility of replicating the appearance of her baskets using machines. Choice D is incorrect because there’s nothing in the text to suggest that Dingle’s baskets are “collected with,” or brought together in a group with, sweetgrass and palmetto palm. Instead, the text describes how Dingle uses those plants to make her baskets.

"}, {"id": "359902ae", "domain": "Craft and Structure", "skill": "Words in Context", "difficulty": "M", "type": "mc", "stimulus": "

The following text is adapted from Nathaniel Hawthorne’s 1837 story “Dr. Heidegger’s Experiment.” The main character, a physician, is experimenting with rehydrating a dried flower.

\n
\n

At first [the rose] lay lightly on the surface of the fluid, appearing to imbibe none of its moisture. Soon, however, a singular change began to be visible. The crushed and dried petals stirred and assumed a deepening tinge of crimson, as if the flower were reviving from a deathlike slumber.

\n
", "stem": "

As used in the text, what does the phrase “a singular” most nearly mean?

", "choices": [{"id": "A", "text": "

A lonely

"}, {"id": "B", "text": "

A disagreeable

"}, {"id": "C", "text": "

An acceptable

"}, {"id": "D", "text": "

An extraordinary

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer because as used in the text, “singular” most nearly means extraordinary. The text portrays an experiment in which a character rehydrates a dried rose by infusing it with moisture. After prolonged contact with the liquid, the rose begins to absorb it, undergoing an exceptional transformation: its color deepens, its previously “crushed and dried” petals shift, and the entire flower revives “from a deathlike slumber.” In other words, an extraordinary change is visible in the flower.

Choice A is incorrect. Although in some contexts “singular” can mean of or relating to an individual or to a single instance of something, this usage doesn’t imply loneliness or an otherwise unsatisfactory condition of isolation. Moreover, the text doesn’t attribute such a condition to the rose. Choice B is incorrect. Although “singular” has several related meanings, none of them relate to being disagreeable or unpleasant. Moreover, the text doesn’t portray the change undergone by the rose as necessarily disagreeable. Choice C is incorrect because “singular” means extraordinary, not acceptable. The change is portrayed as striking, not barely satisfactory.

"}, {"id": "22a41819", "domain": "Craft and Structure", "skill": "Words in Context", "difficulty": "H", "type": "mc", "stimulus": "

Rejecting the premise that the literary magazine Ebony and Topaz (1927) should present a unified vision of Black American identity, editor Charles S. Johnson fostered his contributors’ diverse perspectives by promoting their authorial autonomy. Johnson’s self-effacement diverged from the editorial stances of W.E.B. Du Bois and Alain Locke, whose decisions for their publications were more ______blank.

", "stem": "

Which choice completes the text with the most logical and precise word or phrase?

", "choices": [{"id": "A", "text": "

proficient

"}, {"id": "B", "text": "

dogmatic

"}, {"id": "C", "text": "

ambiguous

"}, {"id": "D", "text": "

unpretentious

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. A person who is \"dogmatic\" believes strongly that their principles and opinions are true. Because Du Bois and Locke are implied to have one \"unified vision\" of Black American identity that they prioritize over the \"diverse perspectives\" of different writers, they can be described as dogmatic.

Choice A is incorrect. \"Proficient\" means \"skilled.\" Du Bois and Locke are contrasted with Johnson, but nothing in the text suggests that Johnson was not skilled at making editorial decisions. Based on the text, the three editors just have different styles; they’re not necessarily more or less skilled. Choice C is incorrect. \"Ambiguous\" means \"unclear\" or \"open to multiple interpretations.\" However, it’s actually Johnson who encouraged multiple interpretations (\"diverse perspectives\"). Since Du Bois and Locke are said to \"diverge\" from Johnson, we can assume that the views they published were not ambiguous, but instead clear and firm (a \"unified vision\"). Choice D is incorrect. \"Unpretentious\" means \"not trying to impress others with greater skill or importance than is actually possessed.\" Du Bois and Locke are contrasted with Johnson, but nothing in the text suggests that Johnson is pretentious (trying to impress others).

"}, {"id": "ca50de52", "domain": "Craft and Structure", "skill": "Text Structure and Purpose", "difficulty": "H", "type": "mc", "stimulus": "

“How lifelike are they?” Many computer animators prioritize this question as they strive to create ever more realistic environments and lighting. Generally, while characters in computer-animated films appear highly exaggerated, environments and lighting are carefully engineered to mimic reality. But some animators, such as Pixar’s Sanjay Patel, are focused on a different question. Rather than asking first whether the environments and lighting they’re creating are convincingly lifelike, Patel and others are asking whether these elements reflect their films’ unique stories.

", "stem": "

Which choice best describes the function of the underlined question in the text as a whole?

", "choices": [{"id": "A", "text": "

It reflects a primary goal that many computer animators have for certain components of the animations they produce.

"}, {"id": "B", "text": "

It represents a concern of computer animators who are more interested in creating unique backgrounds and lighting effects than realistic ones.

"}, {"id": "C", "text": "

It conveys the uncertainty among many computer animators about how to create realistic animations using current technology.

"}, {"id": "D", "text": "

It illustrates a reaction that audiences typically have to the appearance of characters created by computer animators.

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer because it most accurately describes the function of the underlined question in the text as a whole. The text begins with the underlined question, “How lifelike are they?” The text then explains that many computer animators pose this question about the environments and lighting that they create for animated films, striving for realistic animation of those components even if the characters themselves aren’t portrayed in realistic terms. The focus of the text then shifts to describe how some animators strive to create environments and lighting that reflect the film’s unique stories rather than making them appear realistic. Therefore, the function of the underlined question is to reflect a primary goal that many computer animators have for certain components of the animations they produce.

Choice B is incorrect because, as the text makes clear, the underlined question is one posed by computer animators who wish to create realistic backgrounds and lighting effects, not by those who, instead, wish to create effects that reflect films’ unique stories and aren’t necessarily realistic; this latter group of animators is discussed later in the text. Choice C is incorrect. As the text explains, many computer animators strive for realistic environments and lighting, while others do not; this difference of approach relates to whether these components should be realistic, not to how realism can be achieved using current technology, and the text never suggests that animators are uncertain how to achieve it. Choice D is incorrect because the underlined question pertains to the perspective of computer animators, not the audience, and the text never considers audience’s reactions to characters in animated films.

"}, {"id": "82cb7dda", "domain": "Craft and Structure", "skill": "Text Structure and Purpose", "difficulty": "H", "type": "mc", "stimulus": "

The field of study called affective neuroscience seeks instinctive, physiological causes for feelings such as pleasure or displeasure. Because these sensations are linked to a chemical component (for example, the release of the neurotransmitter dopamine in the brain when one receives or expects a reward), they can be said to have a partly physiological basis. These processes have been described in mammals, but Jingnan Huang and his colleagues have recently observed that some behaviors of honeybees (such as foraging) are also motivated by a dopamine-based signaling process.

", "stem": "

What choice best describes the main purpose of the text?

", "choices": [{"id": "A", "text": "

It describes an experimental method of measuring the strength of physiological responses in humans.

"}, {"id": "B", "text": "

It illustrates processes by which certain insects can express how they are feeling.

"}, {"id": "C", "text": "

It summarizes a finding suggesting that some mechanisms in the brains of certain insects resemble mechanisms in mammalian brains.

"}, {"id": "D", "text": "

It presents research showing that certain insects and mammals behave similarly when there is a possibility of a reward for their actions.

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer because it most accurately describes the main purpose of the text, which is to summarize a finding suggesting that some mechanisms in the brains of certain insects resemble mechanisms in mammalian brains. The text begins by explaining that feelings such as pleasure and displeasure are linked to chemical processes in the brain, such as the release of dopamine when one receives a reward. The text then indicates that such processes have been seen in mammals but that researchers have recently observed similar processes involving dopamine in honeybees. Taken together, this information serves to sum up the discovery that some mechanisms in the brains of certain insects may resemble mechanisms linked to feelings such as pleasure and displeasure in mammals.

Choice A is incorrect because the text doesn’t describe any experiments or experimental methods. Instead, the text describes a phenomenon that has been observed in mammals and then presents the recent observations of Huang and colleagues that this phenomenon is also seen in honeybees. Choice B is incorrect because there’s nothing in the text to suggest that certain insects can express how they’re feeling through particular processes. The text does indicate that certain honeybee behaviors such as foraging are linked to dopamine, but it doesn’t suggest that these behaviors enable honeybees to communicate feelings or sensations. Choice D is incorrect because the text presents research showing that certain honeybee behaviors such as foraging are linked to dopamine and therefore may be motivated by similar mechanisms to those in mammalian brains, not that honeybees and mammals behave similarly when there is the possibility of reward for their actions.

"}, {"id": "e35d481c", "domain": "Craft and Structure", "skill": "Words in Context", "difficulty": "H", "type": "mc", "stimulus": "

Some economic historians ______blank that late nineteenth- and early twentieth-century households in the United States experienced an economy of scale when it came to food purchases—they assumed that large households spent less on food per person than did small households. Economist Trevon Logan showed, however, that a close look at the available data disproves this supposition.

", "stem": "

Which choice completes the text with the most logical and precise word or phrase?

", "choices": [{"id": "A", "text": "

surmised

"}, {"id": "B", "text": "

contrived

"}, {"id": "C", "text": "

questioned

"}, {"id": "D", "text": "

regretted

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer because it most logically completes the text’s discussion of late nineteenth- and early twentieth-century household food purchases. In this context, “surmised” means formed an idea or assumption with little evidence. The text explains that certain economic historians “assumed” that large and small households spent different amounts on food per person, but that another economist found this supposition to be false based on evidence from available data. This context suggests that the economic historians made an incorrect assumption without enough consideration of evidence.

Choice B is incorrect. In this context, “contrived” would mean brought about or created through trickery. Nothing in the text suggests that the economic historians were deliberately trying to trick people with a claim about food purchasing behaviors in late nineteenth- and early twentieth-century households; the text simply suggests that they made an assumption about those behaviors that another historian believes isn’t supported by the available data. Choice C is incorrect because the text indicates that it’s Logan and not the economic historians who “questioned,” or doubted, the assumption that large and small households in the late nineteenth and early twentieth centuries spent different amounts on food per person; the economic historians are the ones who made that assumption to begin with. Choice D is incorrect because nothing in the text suggests that some economic historians “regretted,” or felt sad or remorseful about, the food purchasing behaviors of late nineteenth- and early twentieth-century households. The text focuses on the idea that the economic historians made an assumption about those behaviors that may not be supported by available data, not on the historians’ emotional response to what households did in the past.

"}, {"id": "45a109a3", "domain": "Craft and Structure", "skill": "Words in Context", "difficulty": "E", "type": "mc", "stimulus": "

The following text is from Bram Stoker’s 1897 novel Dracula. The narrator is being driven in a carriage through a remote region at night.

\n
\n

The baying of the wolves sounded nearer and nearer, as though they were closing round on us from every side. I grew dreadfully afraid, and the horses shared my fear. The driver, however, was not in the least disturbed; he kept turning his head to left and right, but I could not see anything through the darkness.

\n
", "stem": "

As used in the text, what does the word “disturbed” most nearly mean?

", "choices": [{"id": "A", "text": "

Disorganized

"}, {"id": "B", "text": "

Alarmed

"}, {"id": "C", "text": "

Offended

"}, {"id": "D", "text": "

Interrupted

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer because as used in the text, “disturbed” most nearly means alarmed. The text portrays the narrator traveling in a carriage as wolves howl in the surrounding darkness. The text contrasts the reaction of both the narrator and the horses pulling the carriage with that of the driver of the carriage: the narrator and horses are “dreadfully afraid,” but the driver is “not in the least disturbed.” In other words, the driver is not alarmed by the wolves nearby.

Choice A is incorrect. Although in some contexts, “disturbed” can mean disorganized, the text doesn’t portray a character acting in a disorganized manner; instead, the driver continues to drive the carriage, even though the horses pulling it are alarmed. Choice C is incorrect. Although in some contexts, “disturbed” can mean offended, the text doesn’t portray one character feeling offended, or upset, by another’s actions; instead, it contrasts the fear felt by the narrator with another character’s lack of fear. Choice D is incorrect. Although in some contexts, “disturbed” can mean interrupted, the text doesn’t portray an action being interrupted; indeed, the travel depicted in the scene continues despite the threat of the wolves outside the carriage.

"}, {"id": "5e57efec", "domain": "Craft and Structure", "skill": "Words in Context", "difficulty": "H", "type": "mc", "stimulus": "

Economist Marco Castillo and colleagues showed that nuisance costs—the time and effort people must spend to make donations—reduce charitable giving. Charities can mitigate this effect by compensating donors for nuisance costs, but those costs, though variable, are largely ______blank donation size, so charities that compensate donors will likely favor attracting a few large donors over many small donors.

", "stem": "

Which choice completes the text with the most logical and precise word or phrase?

", "choices": [{"id": "A", "text": "

supplemental to

"}, {"id": "B", "text": "

predictive of

"}, {"id": "C", "text": "

independent of

"}, {"id": "D", "text": "

subsumed in

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. We’re told that charities that pay donors back for nuisance costs will attract a few large donors instead of many small donors. This suggests that nuisance costs are not linked to donation size.

Choice A is incorrect. This doesn’t fit the logic of the text. If nuisance costs are supplemental to (meaning in addition to) donation size, that wouldn’t result in charities that compensate donors for those costs attracting a few large donors over many small donors. Choice B is incorrect. This doesn’t fit the logic of the text. If nuisance costs can predict donation size, that wouldn’t necessarily result in charities that compensate donors for those costs attracting a few large donors over many small donors. Choice D is incorrect. This doesn’t fit the logic of the text. If nuisance costs are subsumed in (meaning included in) donation size, that wouldn’t result in charities that compensate donors for those costs attracting a few large donors over many small donors.

"}, {"id": "c966ad55", "domain": "Craft and Structure", "skill": "Text Structure and Purpose", "difficulty": "E", "type": "mc", "stimulus": "

The following text is from Srimati Svarna Kumari Devi’s 1894 novel The Fatal Garland (translated by A. Christina Albers in 1910). Shakti is walking near a riverbank that she visited frequently during her childhood.

\n
\n

She crossed the woods she knew so well. The trees seemed to extend their branches like welcoming arms. They greeted her as an old friend. Soon she reached the river-side.

\n
", "stem": "

Which choice best describes the function of the underlined portion in the text as a whole? 

", "choices": [{"id": "A", "text": "

It suggests that Shakti feels uncomfortable near the river.

"}, {"id": "B", "text": "

It indicates that Shakti has lost her sense of direction in the woods.

"}, {"id": "C", "text": "

It emphasizes Shakti’s sense of belonging in the landscape.

"}, {"id": "D", "text": "

It conveys Shakti’s appreciation for her long-term friendships. 

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer because it most accurately describes how the underlined sentence functions in the text as a whole. The first sentence of the text states that Shakti knows the woods she is walking in well. The next sentence, which is underlined, emphasizes Shakti’s familiarity with, and sense of security within, the woods by describing how the tree branches are friendly and “welcoming,” as they are depicted as extending open arms to her. The remainder of the text also shows that Shakti is comfortable and content in the woods by describing her as “an old friend” of the trees. Thus, the function of the underlined portion is to emphasize Shakti’s sense of belonging in the wooded landscape that she visits.

Choice A is incorrect because the text and underlined portion suggest that Shakti is comfortable, not uncomfortable, in her surroundings: the trees around her are described as welcoming and reassuring. Moreover, the underlined portion discusses Shakti’s feelings in the forest, not the river, since she hasn’t reached the river yet. Choice B is incorrect because the text and underlined portion emphasize Shakti’s familiarity with the woods. The trees are inviting, and she feels like “an old friend” to the woods, so she isn’t lost or confused there. Choice D is incorrect because the third sentence uses the phrase “as an old friend” figuratively in reference to Shakti’s sense of familiarity with the landscape, not in reference to her long-standing friendships with other people, and the text and underlined portion never discuss her feelings about such friendships.

"}, {"id": "757077f9", "domain": "Craft and Structure", "skill": "Words in Context", "difficulty": "M", "type": "mc", "stimulus": "

During a 2014 archaeological dig in Spain, Vicente Lull and his team uncovered the skeleton of a woman from El Algar, an Early Bronze Age society, buried with valuable objects signaling a high position of power. This finding may persuade researchers who have argued that Bronze Age societies were ruled by men to ______blank that women may have also held leadership roles.

", "stem": "

Which choice completes the text with the most logical and precise word or phrase?

", "choices": [{"id": "A", "text": "

waive

"}, {"id": "B", "text": "

concede

"}, {"id": "C", "text": "

refute

"}, {"id": "D", "text": "

require

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer because it most logically completes the text’s discussion of the significance of the 2014 archaeological finding at El Algar. In this context, “concede” means to admit something is true after first resisting that admission. The text indicates that some researchers believe “Bronze Age societies were ruled by men.” But the Bronze Age burial of a woman at El Algar included “valuable objects signaling a high position of power,” which would raise the possibility that “women may have also held leadership roles.” Thus, the text is calling into question the notion that only men were leaders in these societies and speculating that people holding this view may reconsider their opinion.

Choice A is incorrect because “waive” means to refrain from insisting that something, such as a right or a requirement, be observed; the word isn’t used, however, in contexts where someone acknowledges that an opinion they hold may be invalid, as is the case in the text. Choice C is incorrect. According to the text, the finding from the El Algar burial site undermines the view that Bronze Age societies were exclusively ruled by men. However, “refute” means to demonstrate that something is false and would not make sense in context. Lull and team’s finding supports the view that women may have also held leadership roles, not that they did not participate in such roles. Choice D is incorrect because in this context, “require” means to demand or specify as mandatory. However, it would not make sense for contemporary researchers to demand that Bronze Age “women may have also held leadership roles.”

"}, {"id": "b13378c8", "domain": "Craft and Structure", "skill": "Text Structure and Purpose", "difficulty": "M", "type": "mc", "stimulus": "

Early in the Great Migration of 1910–1970, which involved the mass migration of Black people from the southern to the northern United States, political activist and Chicago Defender writer Fannie Barrier Williams was instrumental in helping other Black women establish themselves in the North. Many women hoped for better employment opportunities in the North because, in the South, they faced much competition for domestic employment and men tended to get agricultural work. To aid with this transition, Barrier Williams helped secure job placement in the North for many women before they even began their journey.

", "stem": "

Which choice best states the main purpose of the text?

", "choices": [{"id": "A", "text": "

To introduce and illustrate Barrier Williams’s integral role in supporting other Black women as their circumstances changed during part of the Great Migration

"}, {"id": "B", "text": "

To establish that Barrier Williams used her professional connections to arrange employment for other Black women, including jobs with the Chicago Defender

"}, {"id": "C", "text": "

To demonstrate that the factors that motivated the start of the Great Migration were different for Black women than they were for Black men

"}, {"id": "D", "text": "

To provide an overview of the employment challenges faced by Black women in the agricultural and domestic spheres in the southern United States

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer because it most accurately describes the text’s purpose, which is to discuss the important role Barrier Williams played in supporting many other Black women as they relocated to the northern United States during the early years of the Great Migration. After introducing Barrier Williams, the text describes how she helped find jobs for other Black women, who in many cases relocated in search of better employment prospects than the South could offer at the time. The text indicates that by doing so, she eased these women’s transition as their circumstances changed.

Choice B is incorrect. Although the text mentions Barrier Williams’s work as a political activist and writer for the Chicago Defender, it doesn’t discuss any professional connections she made in these roles or indicate that she used any such connections in her work to secure employment for other Black women. Choice C is incorrect. Although the text discusses a factor that caused many women to relocate during the Great Migration, their difficulty finding employment in the South, the text doesn’t indicate that this factor motivated the start of the Great Migration. Moreover, the text doesn’t discuss the factors that motivated Black men to migrate. Choice D is incorrect. Although the text mentions the difficult employment prospects for Black women in the domestic and agricultural sectors in the South during the Great Migration, the text’s main purpose isn’t to provide an overview of the employment challenges Black women faced in these sectors. Rather, it provides this information to show that Barrier Williams played a crucial role in supporting many Black women who relocated to the North by helping them achieve one of their main goals, securing a job.

"}, {"id": "97e5bf55", "domain": "Craft and Structure", "skill": "Cross-Text Connections", "difficulty": "H", "type": "mc", "stimulus": "

Text 1

\n

In 1916, H. Dugdale Sykes disputed claims that The Two Noble Kinsmen was coauthored by William Shakespeare and John Fletcher. Sykes felt Fletcher’s contributions to the play were obvious—Fletcher had a distinct style in his other plays, so much so that lines with that style were considered sufficient evidence of Fletcher’s authorship. But for the lines not deemed to be by Fletcher, Sykes felt that their depiction of women indicated that their author was not Shakespeare but Philip Massinger.

\n

Text 2

\n

Scholars have accepted The Two Noble Kinsmen as coauthored by Shakespeare since the 1970s: it appears in all major one-volume editions of Shakespeare’s complete works. Though scholars disagree about who wrote what exactly, it is generally held that on the basis of style, Shakespeare wrote all of the first act and most of the last, while John Fletcher authored most of the three middle acts.

", "stem": "

Based on the texts, both Sykes in Text 1 and the scholars in Text 2 would most likely agree with which statement?

", "choices": [{"id": "A", "text": "

John Fletcher’s writing has a unique, readily identifiable style.

"}, {"id": "B", "text": "

The women characters in John Fletcher’s plays are similar to the women characters in Philip Massinger’s plays.

"}, {"id": "C", "text": "

The Two Noble Kinsmen belongs in one-volume compilations of Shakespeare’s complete plays.

"}, {"id": "D", "text": "

Philip Massinger’s style in the first and last acts of The Two Noble Kinsmen is an homage to Shakespeare’s style.

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. Text 1 states that Sykes felt Fletcher’s contributions to the play were obvious because he had a distinct style in his other plays. Text 2 states that scholars generally agree “on the basis of style” that Fletcher wrote most of the three middle acts. Both texts imply that Fletcher’s writing has a unique, readily identifiable style that can be used to distinguish his work from others.

Choice B is incorrect. While Text 1 refers to the women in Massinger plays, neither text compares the women of Fletcher’s plays to the women of Massinger’s plays. Text 2 doesn’t mention Massinger at all. Choice C is incorrect. Text 1 states that Sykes disputed that Shakespeare coauthored the play, and implied that it was coauthored by Fletcher and Massinger instead. Sykes, therefore, would disagree that The Two Noble Kinsmen belongs in a Shakespeare compilation. Choice D is incorrect. Text 1 doesn’t suggest that Massinger was inspired by Shakespeare, and Text 2 doesn’t mention Massinger at all.

"}, {"id": "d4a8f7cb", "domain": "Craft and Structure", "skill": "Words in Context", "difficulty": "E", "type": "mc", "stimulus": "

Dance choreographer Jawole Willa Jo Zollar aims to give people the opportunity to be ______blank her creative process. For example, live performances of her dance HairStories, which debuted in 2001, featured videos of people across the United States talking about their hair and audience members sharing pictures of their interesting hairstyles.

", "stem": "

Which choice completes the text with the most logical and precise word or phrase?

", "choices": [{"id": "A", "text": "

nervous about

"}, {"id": "B", "text": "

completed by

"}, {"id": "C", "text": "

delayed by

"}, {"id": "D", "text": "

involved in

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. “Involved in” means “playing an active role in.” This fits the context clues describing how Zollar includes the audience in her shows by incorporating their stories and pictures.

Choice A is incorrect. “Nervous” means “worried or anxious about.” Nothing in the text suggests that people would be nervous about Zollar’s creative process. Choice B is incorrect. “Completed by” means “made whole by.” It doesn’t make sense to say that Zollar’s shows would make her audience complete. Choice C is incorrect. “Delayed by” means “made late by.” Nothing in the text suggests that people would be delayed by Zollar’s creative process.

"}, {"id": "84ece3f6", "domain": "Craft and Structure", "skill": "Words in Context", "difficulty": "M", "type": "mc", "stimulus": "

The following text is adapted from Nathaniel Hawthorne’s 1844 short story “Drowne’s Wooden Image.” Drowne, a young man, is carving a wooden figure to decorate the front of a ship.

\n

Day by day, the work assumed greater precision, and settled its irregular and misty outline into distincter grace and beauty. The general design was now obvious to the common eye.

", "stem": "

As used in the text, what does the word “assumed” most nearly mean?

", "choices": [{"id": "A", "text": "

Acquired

"}, {"id": "B", "text": "

Acknowledged

"}, {"id": "C", "text": "

Imitated

"}, {"id": "D", "text": "

Speculated

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer because as used in the text, “assumed” most nearly means acquired, or came to possess. The text portrays a character named Drowne carving a figure out of wood. At first “irregular and misty,” or haphazard and indistinct, the figure’s outline gradually showed “distincter grace and beauty” until the general design of the carved object “was now obvious to the common eye,” or plainly recognizable to anyone. In other words, as Drowne continued to carve, the wooden object came to possess, or acquired, greater precision, changing from an indistinct outline or shape into a graceful, beautiful, and clearly recognizable form.

Choice B is incorrect. Although in some contexts “assumed” can mean acknowledged, or recognized, it doesn’t have that meaning in this context because an inanimate object like the wooden figure can’t acknowledge its own precision. Choice C is incorrect because there’s nothing in the text to suggest that the wooden figure merely imitated, or mimicked, precision. Rather, the text suggests that as Drowne carved his wooden figure, it gradually became more precise. Choice D is incorrect. Although in some contexts “assumed” can mean speculated, or supposed based on incomplete information, it doesn’t have that meaning in this context because an inanimate object like the wooden figure can’t speculate about its own precision.

"}, {"id": "d4732483", "domain": "Craft and Structure", "skill": "Text Structure and Purpose", "difficulty": "H", "type": "mc", "stimulus": "

Studying late nineteenth- and early twentieth-century artifacts from an agricultural and domestic site in Texas, archaeologist Ayana O. Flewellen found that Black women employed as farm workers utilized hook-and-eye closures to fasten their clothes at the waist, giving themselves a silhouette similar to the one that was popular in contemporary fashion and typically achieved through more restrictive garments such as corsets. Flewellen argues that this sartorial practice shows that these women balanced hegemonic ideals of femininity with the requirements of their physically demanding occupation.

", "stem": "

Which choice best states the main purpose of the text?

", "choices": [{"id": "A", "text": "

To describe an unexpected discovery that altered a researcher’s view of how rapidly fashions among Black female farmworkers in late nineteenth- and early twentieth-century Texas changed during the period

"}, {"id": "B", "text": "

To discuss research that investigated the ways in which Black female farmworkers in late nineteenth- and early twentieth-century Texas used fashion practices to resist traditional gender ideals

"}, {"id": "C", "text": "

To evaluate a scholarly work that offers explanations for the impact of urban fashion ideals on Black female farmworkers in late nineteenth- and early twentieth-century Texas

"}, {"id": "D", "text": "

To summarize the findings of a study that explored factors influencing a fashion practice among Black female farmworkers in late nineteenth- and early twentieth-century Texas

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. The text provides an overview of a scholarly work discussing the fashion practices of Black female farmworkers in late 19th- and early 20th-century Texas, and how these practices were influenced by both the fashion ideals of the time and the demands of farmwork.

Choice A is incorrect. The text never discusses the rate of fashion change among Black female farmworkers. The text also never categorizes Flewellen’s findings as \"unexpected.\" Choice B is incorrect. The text actually explains that Black female farmworkers were trying to achieve traditional feminine ideals, not resist them. Choice C is incorrect. The text doesn’t evaluate a scholarly work but rather simply describes it. Furthermore, the text is focused on \"agricultural and domestic\" fashion, not urban fashion as this choice suggests.

"}, {"id": "e818241b", "domain": "Craft and Structure", "skill": "Text Structure and Purpose", "difficulty": "H", "type": "mc", "stimulus": "

Astronomers are confident that the star Betelgeuse will eventually consume all the helium in its core and explode in a supernova. They are much less confident, however, about when this will happen, since that depends on internal characteristics of Betelgeuse that are largely unknown. Astrophysicist Sarafina El-Badry Nance and colleagues recently investigated whether acoustic waves in the star could be used to determine internal stellar states but concluded that this method could not sufficiently reveal Betelgeuse’s internal characteristics to allow its evolutionary state to be firmly fixed.

", "stem": "

Which choice best describes the function of the second sentence in the overall structure of the text?

", "choices": [{"id": "A", "text": "

It describes a serious limitation of the method used by Nance and colleagues. 

"}, {"id": "B", "text": "

It presents the central finding reported by Nance and colleagues. 

"}, {"id": "C", "text": "

It identifies the problem that Nance and colleagues attempted to solve but did not.

"}, {"id": "D", "text": "

It explains how the work of Nance and colleagues was received by others in the field. 

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer because it best describes how the second sentence functions in the text as a whole. The first sentence establishes something astronomers believe with some certainty: that Betelgeuse will explode in a supernova. The second sentence then introduces a problem: astronomers aren’t certain when Betelgeuse will explode because they don’t have enough information about the star’s internal characteristics. Finally, the third sentence indicates that researcher Sarafina El-Badry Nance and colleagues investigated a possible method of obtaining the necessary information about Betelgeuse’s internal characteristics, though they found that the method wouldn’t be sufficient. Thus, the function of the second sentence is to identify the problem that Nance and colleagues attempted to solve but didn’t.

Choice A is incorrect because the second sentence introduces the general problem Nance and colleagues hoped to solve, not a serious limitation of how Nance and colleagues tried to solve it. It is the third sentence that introduces Nance and colleagues, but no serious limitation of their approach to studying a method of determining internal stellar states is described. Choice B is incorrect because the second sentence introduces the general problem Nance and colleagues hoped to solve, not the central finding they ultimately reported. It is the third sentence that presents Nance and colleagues’ conclusion that a potential method for determining internal stellar states would be insufficient. Choice D is incorrect because the second sentence doesn’t indicate how other astronomers or astrophysicists responded to the work done by Nance and colleagues; the text doesn’t address this information at all.

"}, {"id": "236fee8e", "domain": "Craft and Structure", "skill": "Text Structure and Purpose", "difficulty": "M", "type": "mc", "stimulus": "

Archeological excavation of Market Street Chinatown, a nineteenth-century Chinese American community in San Jose, California, provided the first evidence that Asian food products were imported to the United States in the 1800s: bones from a freshwater fish species native to Southeast Asia. Jinshanzhuang—Hong Kong–based import/export firms—likely coordinated the fish’s transport from Chinese-operated fisheries in Vietnam and Malaysia to North American markets. This route reveals the (often overlooked) multinational dimensions of the trade networks linking Chinese diaspora communities.

", "stem": "

Which choice best describes the function of the underlined sentence in the text as a whole?

", "choices": [{"id": "A", "text": "

It explains why efforts to determine the country of origin of the items mentioned in the previous sentence remain inconclusive.

"}, {"id": "B", "text": "

It provides information that helps support a claim about a discovery’s significance that is presented in the following sentence.

"}, {"id": "C", "text": "

It traces the steps that were taken to locate and recover the objects that are described in the previous sentence.

"}, {"id": "D", "text": "

It outlines a hypothesis that additional evidence discussed in the following sentence casts some doubt on.

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. The underlined sentence provides information about import/export firms, showing how Chinese communities across the world were connected by trade routes.

Choice A is incorrect. The underlined sentence never suggests that the countries of origin of the fish are in question—in fact, it tells us exactly where they came from. Choice C is incorrect. The passage never describes the steps taken to discover the fish bones described in the previous sentence. Choice D is incorrect. The underlined sentence doesn’t outline a hypothesis but instead provides evidence. And the following sentence agrees with the underlined sentence, so we could eliminate this choice just for saying that the following sentence \"casts some doubt on\" the underlined one—partly wrong is all wrong.

"}, {"id": "97ab5669", "domain": "Craft and Structure", "skill": "Words in Context", "difficulty": "E", "type": "mc", "stimulus": "

Former astronaut Ellen Ochoa says that although she doesn’t have a definite idea of when it might happen, she ______blank that humans will someday need to be able to live in other environments than those found on Earth. This conjecture informs her interest in future research missions to the moon.

", "stem": "

Which choice completes the text with the most logical and precise word or phrase?

", "choices": [{"id": "A", "text": "

demands

"}, {"id": "B", "text": "

speculates

"}, {"id": "C", "text": "

doubts

"}, {"id": "D", "text": "

establishes

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer because it most logically completes the text’s discussion of Ochoa’s prediction that humans will one day need to live in places other than Earth. As used in this context, “speculates” would mean puts forward an idea without firm evidence. The text states that Ochoa “doesn’t have a definite idea” about when humans might need to live in other environments and characterizes Ochoa’s prediction as a “conjecture,” or a conclusion presented without convincing evidence. This context indicates that Ochoa speculates when she makes this prediction. 

Choice A is incorrect because saying that Ochoa “demands,” or insists or requires, that humans will one day need to live in other environments than Earth’s would not make sense in context. The text indicates that she’s unsure about the timing but hypothesizes that it will someday happen. Choice C is incorrect because  saying that Ochoa “doubts,” or questions or disbelieves, that humans will one day need to live in other environments than Earth’s would not make sense in context. The text indicates that although Ochoa is unsure about the timing, she hypothesizes that humans will need to live in places other than Earth and encourages research into future travel to the moon. Choice D is incorrect because  saying that Ochoa “establishes,” or proves, that humans will one day need to live in other environments than Earth’s would not make sense in context. Rather than stating that Ochoa discusses her idea with certainty and supports it with evidence, the text indicates that Ochoa is unsure about when humans might need to live in other environments.

"}, {"id": "02fd3da7", "domain": "Craft and Structure", "skill": "Cross-Text Connections", "difficulty": "E", "type": "mc", "stimulus": "

Text 1

\n

Public policy researcher Anthony Fowler studied the history of elections in Australia, a country that requires citizens to vote. Fowler argues that requiring citizens to vote leads to a significant increase in voters who would otherwise not have the time or motivation to vote. Thus, election results in countries that require citizens to vote better reflect the preferences of the country as a whole. 

\n

 

\n

Text 2

\n

Governments in democratic countries function better when more people vote. However, forcing people to vote may have negative consequences. Shane P. Singh and Jason Roy studied what happens when a country requires its citizens to vote. They found that when people feel forced to vote, they tend to spend less time looking for information about their choices when voting. As a result, votes from these voters may not reflect their actual preferences.

", "stem": "

Based on the texts, how would Singh and Roy (Text 2) most likely respond to the research discussed in Text 1?

", "choices": [{"id": "A", "text": "

Only countries of a certain population size should implement mandatory voting.

"}, {"id": "B", "text": "

People who are forced to vote are likely to become politically engaged in other ways, such as volunteering or running for office.

"}, {"id": "C", "text": "

Requiring people to vote does not necessarily lead to election outcomes that better represent the preferences of the country as a whole.

"}, {"id": "D", "text": "

Countries that require voting must also make the process of voting easier for their citizens.

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. Text 1 claims that mandatory voting results in elections that \"better reflect the preferences of the country.\" Singh and Roy disagree. They claim that more voters doesn’t equal more quality votes—instead, they argue that forced voting may lead to less-informed votes that \"may not reflect [voters’] actual preferences.\"

Choice A is incorrect. Neither text mentions the population size of countries that require voting, or how that might affect election outcomes. Choice B is incorrect. Neither text discusses the effects of mandatory voting on other forms of political engagement. Choice D is incorrect. Neither text discusses the ease or difficulty of the voting process in countries that require voting.

"}, {"id": "06b96bfc", "domain": "Craft and Structure", "skill": "Words in Context", "difficulty": "E", "type": "mc", "stimulus": "

A musician and member of the Quechua of Peru, Renata Flores Rivera was eager to promote the Quechua language in her music, but she was ______blank speaking it. She met this challenge by asking her grandmother, a native speaker of Quechua, to help her pronounce words in her song lyrics and also by taking classes in the language.

", "stem": "

Which choice completes the text with the most logical and precise word or phrase?

", "choices": [{"id": "A", "text": "

prepared for

"}, {"id": "B", "text": "

inexperienced with

"}, {"id": "C", "text": "

skilled in

"}, {"id": "D", "text": "

excited about

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer because it most logically completes the text’s discussion of Renata Flores Rivera’s use of Quechua in her music. In this context, “inexperienced with” means not accustomed to. The text indicates that Flores Rivera wanted to promote the Quechua language in her music and overcame a challenge by seeking help with pronunciation from her grandmother and by taking language classes. This context conveys the idea that Flores Rivera was not sufficiently familiar with Quechua to use it in her music without help. Thus, she was inexperienced with speaking the language, which she addressed by seeking help.

Choice A is incorrect because describing Flores Rivera as “prepared for”—or ready for—speaking Quechua wouldn’t make sense in context. The text indicates that speaking Quechua presented a challenge, but if she were ready to speak the language, then there would be no challenge. Choice C is incorrect because describing Flores Rivera as “skilled in”—meaning good at or capable of—speaking Quechua wouldn’t make sense in context. The text indicates that speaking Quechua presented a challenge, but if she were capable of speaking the language, then there would be no challenge. Choice D is incorrect. Flores Rivera was likely “excited about”—or thrilled or delighted with—speaking Quechua, but this wouldn’t make sense in context. The text indicates that speaking Quechua presented a challenge, but if she were delighted with speaking the language, then there would be no challenge.

"}, {"id": "93665100", "domain": "Craft and Structure", "skill": "Words in Context", "difficulty": "H", "type": "mc", "stimulus": "

Seminole/Muscogee director Sterlin Harjo ______blank television’s tendency to situate Native characters in the distant past: this rejection is evident in his series Reservation Dogs, which revolves around teenagers who dress in contemporary styles and whose dialogue is laced with current slang.

", "stem": "

Which choice completes the text with the most logical and precise word or phrase?

", "choices": [{"id": "A", "text": "

repudiates

"}, {"id": "B", "text": "

proclaims

"}, {"id": "C", "text": "

foretells

"}, {"id": "D", "text": "

recants

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer because it most logically completes the text’s discussion of Sterlin Harjo’s approach to representing Native characters on television. As used in this context, “repudiates” means rejects or refuses to have anything to do with. The text indicates that television shows tend to depict Native characters as living long ago, but that Harjo’s series Reservation Dogs focuses on Native teenagers in the present day, representing a “rejection” of the typical approach to depicting Native characters. This context thus indicates that Harjo repudiates television’s general tendency regarding Native characters. 

Choice B is incorrect because the text describes Harjo’s “rejection” of the typical approach to representing Native characters on television, so it wouldn’t make sense to say that Harjo “proclaims,” or declares or affirms, television’s general tendency regarding Native characters. Harjo is described as refusing to follow the pattern of depicting Native characters in the distant past, not as proclaiming that pattern. Choice C is incorrect because the text describes television’s tendency to represent Native characters in the distant past as something that is already occurring, not as something that Harjo “foretells,” or predicts will happen in the future. The text is focused on Harjo’s “rejection” of this pattern, not on any predictions he may have about it. Choice D is incorrect because saying that Harjo “recants” something would mean that he withdraws a previously held belief, and it wouldn’t make sense to say that Harjo recants television’s tendency to represent Native characters as living in the past. No beliefs previously held by Harjo are mentioned. Additionally, a tendency isn’t a belief and thus isn’t something that can be recanted.

"}, {"id": "0f040c50", "domain": "Craft and Structure", "skill": "Words in Context", "difficulty": "E", "type": "mc", "stimulus": "

The following text is from Yann Martel’s 2001 novel Life of Pi. The narrator’s family owned a zoo when he was a child. 

\n
\n

It was a huge zoo, spread over numberless acres, big enough to require a train to explore it, though it seemed to get smaller as I grew older, train included. 

\n
\n

©2001 by Yann Martel

", "stem": "

As used in the text, what does the word “spread” most nearly mean?

", "choices": [{"id": "A", "text": "

Hidden

"}, {"id": "B", "text": "

Discussed

"}, {"id": "C", "text": "

Extended

"}, {"id": "D", "text": "

Coated

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer because as used in the text, “spread” most nearly means extended. The text states that the zoo is “huge,” that it covers “numberless acres,” and that it is large enough that a train is needed to explore it. Thus, the text’s emphasis on the zoo’s size suggests that the zoo extended, or stretched, over a large area of land.

Choice A is incorrect because if the zoo covers “numberless acres,” then it could not reasonably be described as hidden, or concealed from view. Choice B is incorrect because there is nothing in the text to suggest that the zoo was discussed, or talked about. Rather, the text focuses on the zoo’s large size. Choice D is incorrect. Although in some contexts “spread” can mean coated, it doesn’t have that meaning in this context because to coat something means to apply a thin layer of a liquid substance, such as oil or paint, to a surface. Therefore, it would not be accurate to say that the zoo coated the acres on which it sits.  

"}, {"id": "e1d5d5df", "domain": "Craft and Structure", "skill": "Words in Context", "difficulty": "E", "type": "mc", "stimulus": "

According to botanists, a viburnum plant experiencing insect damage may develop erineum—a discolored, felty growth—on its leaf blades. A ______blank viburnum plant, on the other hand, will have leaves with smooth surfaces and uniformly green coloration.

", "stem": "

Which choice completes the text with the most logical and precise word or phrase?

", "choices": [{"id": "A", "text": "

struggling

"}, {"id": "B", "text": "

beneficial

"}, {"id": "C", "text": "

simple

"}, {"id": "D", "text": "

healthy

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer because it most logically completes the text’s discussion of damage to viburnum plants. In this context, “healthy” would mean not distressed or diseased. The text states that insect damage may cause viburnum plants to be discolored and have abnormal growths. In the next sentence, the phrase “on the other hand” indicates a contrast with the description of plants suffering from damage. Thus, the context contrasts the appearance of healthy, undamaged plants with the appearance of damaged plants.

Choice A is incorrect because in this context, “struggling” would mean working against difficulties. The text first describes viburnum plants experiencing damage by insects, and the phrase “on the other hand” then establishes a contrast with that description. It wouldn’t make sense to contrast struggling viburnum plants with those being damaged by insects, because in both cases the plants would be experiencing difficulties. Choice B is incorrect because in this context, “beneficial” would mean producing good or helpful effects. The text doesn’t discuss how viburnum plants affect other things or suggest that the plants are helpful in some way; rather, it focuses on how viburnum plants are affected by certain conditions. Choice C is incorrect because in this context “simple” would mean plain or uncomplicated. The text doesn’t discuss whether certain viburnum plants are complicated or uncomplicated; rather, it focuses on how viburnum plants are affected by certain conditions.

"}, {"id": "9e501aaf", "domain": "Craft and Structure", "skill": "Words in Context", "difficulty": "E", "type": "mc", "stimulus": "

Research conducted by planetary scientist Katarina Miljkovic suggests that the Moon’s surface may not accurately ______blank early impact events. When the Moon was still forming, its surface was softer, and asteroid or meteoroid impacts would have left less of an impression; thus, evidence of early impacts may no longer be present.

", "stem": "

Which choice completes the text with the most logical and precise word or phrase?

", "choices": [{"id": "A", "text": "

reflect

"}, {"id": "B", "text": "

receive

"}, {"id": "C", "text": "

evaluate

"}, {"id": "D", "text": "

mimic

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer because it most logically completes the text’s discussion of the Moon’s surface. In this context, “reflect” means show or make apparent. The text states that because the surface of the Moon was softer when the Moon was still forming than it is now, early asteroid and meteoroid impacts “would have left less of an impression” and, as a result, evidence of them may no longer exist. This context supports the idea that the surface of the Moon may not accurately show signs of early impact events.

Choice B is incorrect because it wouldn’t make sense to say that the surface of the Moon may not accurately “receive,” or acquire or experience, early impacts from asteroids or meteoroids. The text indicates that the impacts have already occurred, and it isn’t clear how the Moon’s surface could be accurate or inaccurate in experiencing them. Choice C is incorrect because it wouldn’t make sense to say that the surface of the Moon may not accurately “evaluate,” or determine the significance or condition of, early impacts from asteroids or meteoroids, since that would suggest that it’s possible for the Moon’s surface to make a decision of any kind. Choice D is incorrect. In this context, “mimic” would mean to deliberately simulate or closely imitate something. It wouldn’t make sense to say that the surface of the Moon may not accurately mimic early asteroid and meteoroid impacts, since that would suggest that it’s possible for the Moon to deliberately imitate something. 

"}, {"id": "9cdcd902", "domain": "Craft and Structure", "skill": "Words in Context", "difficulty": "E", "type": "mc", "stimulus": "

Charles “Teenie” Harris was a photographer for the Pittsburgh Courier from 1936 to 1975. During his career he took over 70,000 photographs documenting everyday life in Pittsburgh’s Black communities. The Carnegie Museum of Art maintains thousands of his photographs, carefully ______blank them so that audiences can continue to view them well into the future. 

", "stem": "

Which choice completes the text with the most logical and precise word or phrase?

", "choices": [{"id": "A", "text": "

replacing

"}, {"id": "B", "text": "

inventing

"}, {"id": "C", "text": "

preserving

"}, {"id": "D", "text": "

counting

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. \"Preserving\" means \"maintaining\" or \"keeping in good condition,\" so preserving the photographs means that audiences should be able to view them for a long time.

Choice A is incorrect. \"Replacing\" means \"putting something new in place of\" the photographs. Replacing the photos will make it so that audiences can’t view them at all. Choice B is incorrect. \"Inventing\" means \"creating a new idea, process, or thing.\" The museum can’t invent photographs that already exist. Choice D is incorrect. Counting the photographs will not help audiences view them well into the future.

"}, {"id": "e459076b", "domain": "Craft and Structure", "skill": "Words in Context", "difficulty": "H", "type": "mc", "stimulus": "

The following text is adapted from George Eliot’s 1871–72 novel Middlemarch.

\n
\n

[Mr. Brooke] had travelled in his younger years, and was held in this part of the country to have contracted a too rambling habit of mind. Mr. Brooke’s conclusions were as difficult to predict as the weather.

\n
", "stem": "

As used in the text, what does the word “contracted” most nearly mean?

", "choices": [{"id": "A", "text": "

Restricted

"}, {"id": "B", "text": "

Described

"}, {"id": "C", "text": "

Developed

"}, {"id": "D", "text": "

Settled

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer because as used in the text, “contracted” most nearly means developed. The text explains that Mr. Brooke has a “too rambling habit of mind,” which the text likens to a disease, saying he is thought to have contracted it. To contract a disease means to acquire or develop a disease. In other words, the text indicates that Mr. Brooke is believed to have acquired, or developed, the habit of mind described in the text.

Choice A is incorrect. Although “contracted” can mean limited or restricted in some contexts, here Mr. Brooke is said to draw unpredictable conclusions, suggesting that he exhibits this “too rambling habit of mind,” not that it has been somehow limited or restricted. Choice B is incorrect. Although the text describes Mr. Brooke’s habit of mind, nothing suggests that those are his descriptions or, indeed, that he described his habit of mind at all. Choice D is incorrect because settled means calmed or mitigated, but here Mr. Brooke is said to draw unpredictable conclusions, suggesting that he exhibits this “too rambling habit of mind,” not that it has been somehow calmed or mitigated.

"}, {"id": "4974b053", "domain": "Craft and Structure", "skill": "Words in Context", "difficulty": "M", "type": "mc", "stimulus": "

Although science fiction was dominated mostly by white male authors when Octavia Butler, a Black woman, began writing, she did not view the genre as ______blank: Butler broke into the field with the publication of several short stories and her 1976 novel Patternmaster, and she later became the first science fiction writer to win a prestigious MacArthur Fellowship.

", "stem": "

Which choice completes the text with the most logical and precise word or phrase?

", "choices": [{"id": "A", "text": "

legitimate

"}, {"id": "B", "text": "

impenetrable

"}, {"id": "C", "text": "

compelling

"}, {"id": "D", "text": "

indecipherable

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer because it most logically completes the discussion of Octavia Butler’s career. In this context, “impenetrable” means impossible to enter. The text indicates that the field of science fiction was dominated by white males when Butler, a Black woman, started writing, but she published several science fiction short stories and a novel and later won a prestigious award; that is, Butler pursued science fiction writing and had success. This context suggests that Butler didn’t view the genre as impossible to enter.

Choice A is incorrect. In this context, “legitimate” would mean genuinely good or valid. Nothing in the text suggests that Butler didn’t think the science fiction genre was good or valid; in fact, it indicates that she pursued and made a successful career of publishing work in that field. Choice C is incorrect. In this context, “compelling” would mean attracting or demanding attention. The text indicates that Butler chose to write science fiction, so it wouldn’t make sense to say that she didn’t see the field as drawing her attention. Choice D is incorrect. To say that Butler didn’t consider science fiction “indecipherable,” or impossible to understand, would suggest that Butler did understand it. However, the text doesn’t address Butler’s ability to interpret works in the genre; rather, it focuses on Butler’s successful pursuit of writing science fiction.

"}, {"id": "105ea6de", "domain": "Craft and Structure", "skill": "Cross-Text Connections", "difficulty": "H", "type": "mc", "stimulus": "

Text 1

\n

Growth in the use of novel nanohybrids—materials created from the conjugation of multiple distinct nanomaterials, such as iron oxide and gold nanomaterials conjugated for use in magnetic imaging—has outpaced studies of nanohybrids’ environmental risks. Unfortunately, risk evaluations based on nanohybrids’ constituents are not reliable: conjugation may alter constituents’ physiochemical properties such that innocuous nanomaterials form a nanohybrid that is anything but.

\n

Text 2

\n

The potential for enhanced toxicity of nanohybrids relative to the toxicity of constituent nanomaterials has drawn deserved attention, but the effects of nanomaterial conjugation vary by case. For instance, it was recently shown that a nanohybrid of silicon dioxide and zinc oxide preserved the desired optical transparency of zinc oxide nanoparticles while mitigating the nanoparticles’ potential to damage DNA.

", "stem": "

Based on the texts, how would the author of Text 2 most likely respond to the assertion in the underlined portion of Text 1?

", "choices": [{"id": "A", "text": "

By concurring that the risk described in Text 1 should be evaluated but emphasizing that the risk is more than offset by the potential benefits of nanomaterial conjugation

"}, {"id": "B", "text": "

By arguing that the situation described in Text 1 may not be representative but conceding that the effects of nanomaterial conjugation are harder to predict than researchers had expected

"}, {"id": "C", "text": "

By denying that the circumstance described in Text 1 is likely to occur but acknowledging that many aspects of nanomaterial conjugation are still poorly understood

"}, {"id": "D", "text": "

By agreeing that the possibility described in Text 1 is a cause for concern but pointing out that nanomaterial conjugation does not inevitably produce that result

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. The author of Text 2 acknowledges that nanohybrids may be more toxic than their constituent parts, but also provides an example of a nanohybrid that has reduced toxicity compared to its components: silicon dioxide and zinc oxide together have all the benefits of zinc oxide nanoparticles without any of the DNA harm zinc oxide has on its own.

Choice A is incorrect. While the author of Text 2 gives an example of a nanohybrid that isn’t as toxic as its constituent parts, they don’t argue that the benefit outweighs the risk. They merely argue that “the effects of nanomaterial conjugation vary by case.” Choice B is incorrect. The author of Text 2 states that the effects of nanomaterial conjugation “vary by case,” and that the attention that their potential toxicity has drawn is warranted. If the situation in Text 1 weren’t representative, then there would be less attention to the potential danger of these materials. Furthermore, neither passage suggests that researchers had expected that they could predict the effects of nanomaterial conjugation. Choice C is incorrect. The author of Text 2 agrees that the potential toxicity of nanohybrids “has drawn deserved attention,” so they aren’t denying the problem.

"}, {"id": "2903a041", "domain": "Craft and Structure", "skill": "Text Structure and Purpose", "difficulty": "M", "type": "mc", "stimulus": "

Using NASA’s powerful James Webb Space Telescope (JWST), Mercedes López-Morales and colleagues measured the wavelengths of light traveling through the atmosphere of WASP-39b, an exoplanet, or planet outside our solar system. Different molecules absorb different wavelengths of light, and the wavelength measurements showed the presence of carbon dioxide (CO\u2082) in WASP-39b’s atmosphere. This finding not only offers the first decisive evidence of CO\u2082 in the atmosphere of an exoplanet but also illustrates the potential for future scientific breakthroughs held by the JWST.

", "stem": "

Which choice best describes the overall structure of the text?

", "choices": [{"id": "A", "text": "

It discusses a method used by some researchers, then states why an alternative method is superior to it.

"}, {"id": "B", "text": "

It describes how researchers made a scientific discovery, then explains the importance of that discovery.

"}, {"id": "C", "text": "

It outlines the steps taken in a scientific study, then presents a hypothesis based on that study.

"}, {"id": "D", "text": "

It examines how a group of scientists reached a conclusion, then shows how other scientists have challenged that conclusion.

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. The text begins by describing how the researchers used the JWST to detect CO\u2082 in WASP-39b’s atmosphere. Then the text discusses the significance of this finding, both as the first evidence of CO\u2082 in an exoplanet’s atmosphere and as an illustration of the JWST’s potential for making new discoveries in general.

Choice A is incorrect. The text doesn’t compare two different methods, but rather focuses on one study that used the JWST. Choice C is incorrect. The text doesn’t present a hypothesis, but rather reports on the findings of a study. Choice D is incorrect. The text doesn’t mention any scientists challenging the conclusion reached by López-Morales and colleagues.

"}, {"id": "066a3295", "domain": "Craft and Structure", "skill": "Text Structure and Purpose", "difficulty": "E", "type": "mc", "stimulus": "

Researchers have found a nearly 164,000-year-old molar from a member of the archaic human species known as Denisovans in a cave in Laos, suggesting that Denisovans lived in a wider range of environments than indicated by earlier evidence. Before the discovery, Denisovans were thought to have lived only at high altitudes in relatively cold climates in what are now Russia and China, but the discovery of the tooth in Laos suggests that they may have lived at low altitudes in relatively warm climates in Southeast Asia as well.

", "stem": "

Which choice best states the function of the underlined portion in the text as a whole?

", "choices": [{"id": "A", "text": "

It dismisses as untrue the research presented in the previous sentence.

"}, {"id": "B", "text": "

It defines a term used in the description that follows in the rest of the sentence.

"}, {"id": "C", "text": "

It emphasizes the main goal of the research introduced in the previous sentence.

"}, {"id": "D", "text": "

It provides context that clarifies the significance of the information that follows in the rest of the sentence.

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. The text describes how a new discovery expands our understanding of Denisovans. The underlined portion describes what we used to believe about Denisovans, which helps the reader understand the significance of the discovery of the molar: it suggests that they lived in more places than we’d previously thought.

Choice A is incorrect. The underlined portion doesn’t do this. Instead, it explains what we used to believe about Denisovans before the discovery—it doesn’t dismiss the new discovery as false. Choice B is incorrect. The underlined portion doesn’t do this. No term is defined here. Choice C is incorrect. The underlined portion doesn’t do this. The text never tells us what the “goal” of the research was, just what its discovery was.

"}, {"id": "ac9a3a26", "domain": "Craft and Structure", "skill": "Text Structure and Purpose", "difficulty": "H", "type": "mc", "stimulus": "

According to historian Vicki L. Ruiz, Mexican American women made crucial contributions to the labor movement during World War II. At the time, food processing companies entered into contracts to supply United States armed forces with canned goods. Increased production quotas conferred greater bargaining power on the companies’ employees, many of whom were Mexican American women: employees insisted on more favorable benefits, and employers, who were anxious to fulfill the contracts, complied. Thus, labor activism became a platform for Mexican American women to assert their agency.

", "stem": "

Which choice best describes the function of the underlined portion in the text as a whole?

", "choices": [{"id": "A", "text": "

It elaborates on a claim about labor relations in a particular industry made earlier in the text.

"}, {"id": "B", "text": "

It offers an example of a trend in the World War II–era economy discussed earlier in the text.

"}, {"id": "C", "text": "

It notes a possible exception to the historical narrative of labor activism sketched earlier in the text.

"}, {"id": "D", "text": "

It provides further details about the identities of the workers discussed earlier in the text.

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer because it best describes how the underlined portion functions in the text as a whole. The text says that the increased production quotas of food processing companies during World War II enabled employees to make better bargains in exchange for their labor. The underlined portion presents an example of this increased bargaining power: employees requested more favorable benefits, and employers complied because they were under pressure to fulfill the demanding terms of their contracts. Thus, the underlined portion of the text elaborates on a claim about labor relations in a particular industry (food processing) made earlier in the text.

Choice B is incorrect because there is no indication in the text that the economic factors that influenced food processing also influenced other parts of the economy; thus, the bargaining described in the underlined portion of the text cannot be called an example of a trend. Choice C is incorrect because the underlined portion supports the historical narrative of labor activism in food processing that is sketched in the text, instead of noting an exception to that narrative. Choice D is incorrect because while the underlined portion does discuss the demands that workers made in exchange for their labor, it does not discuss the identities of the workers.

"}, {"id": "03c9f327", "domain": "Craft and Structure", "skill": "Text Structure and Purpose", "difficulty": "H", "type": "mc", "stimulus": "

The following text is from Charlotte Brontë’s 1847 novel Jane Eyre. Jane, the narrator, works as a governess at Thornfield Hall.

\n

I went on with my day’s business tranquilly; but ever and anon vague suggestions kept wandering across my brain of reasons why I should quit Thornfield; and I kept involuntarily framing advertisements and pondering conjectures about new situations: these thoughts I did not think to check; they might germinate and bear fruit if they could.

", "stem": "

Which choice best states the main purpose of the text?

", "choices": [{"id": "A", "text": "

To convey a contrast between Jane’s outward calmness and internal restlessness

"}, {"id": "B", "text": "

To emphasize Jane’s loyalty to the people she works for at Thornfield Hall

"}, {"id": "C", "text": "

To demonstrate that Jane finds her situation both challenging and deeply fulfilling

"}, {"id": "D", "text": "

To describe Jane’s determination to secure employment outside of Thornfield Hall

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer because it most accurately describes the main purpose of the text, which is to show that while Jane calmly goes about her daily tasks, she is experiencing internal agitation about possibly seeking a new job. At the start of the text, Jane says, “I went on with my day’s business tranquilly,” indicating that she is outwardly calm. This outward calmness is then contrasted with her intense internal restlessness, as Jane says that thoughts of leaving her job keep running through her mind, that she is “involuntarily framing advertisements” (meaning that she can’t stop herself from thinking up potential listings for jobs), and that she often wonders what new “situations” (or jobs) would be like. 

Choice B is incorrect because the text gives no indication of Jane’s feelings, either positive or negative, about the people she works for at Thornfield Hall. And rather than emphasizing that Jane feels particularly loyal to her employers, the text focuses on her constant consideration of leaving her job. Choice C is incorrect because the text gives no indication that Jane finds her current situation fulfilling, or satisfying. Given that much of the text is focused on Jane’s thoughts about possibly leaving her job for a new one, it might be the case that she finds her situation challenging, but there is no evidence in the text that Jane also finds that situation satisfying—she says nothing positive about her current job at all, in fact. Choice D is incorrect because the text describes Jane as wondering about getting a new job, not as determined to definitely do so. Jane keeps thinking about reasons why she “should” quit her current job (indicating that she hasn’t yet decided to) and imagining possible new situations she could find, but she says at the end of the text that these thoughts “might germinate and bear fruit if they could,” meaning that the thoughts haven’t yet led to a decision—that Jane isn’t yet determined to get a new job somewhere else.

"}, {"id": "e3f05561", "domain": "Craft and Structure", "skill": "Words in Context", "difficulty": "E", "type": "mc", "stimulus": "

In the 1970s, video cameras became increasingly affordable for ordinary consumers and gave Ulysses Jenkins and other artists capabilities that were previously unavailable except to television broadcasters. Jenkins recognized and took full advantage of this ______blank access to powerful technology to create groundbreaking works of video art, such as Mass of Images (1978).

", "stem": "

Which choice completes the text with the most logical and precise word or phrase?

", "choices": [{"id": "A", "text": "

newfound

"}, {"id": "B", "text": "

delicate

"}, {"id": "C", "text": "

inevitable

"}, {"id": "D", "text": "

habitual

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer because it most logically completes the text’s discussion of Ulysses Jenkins’s video art. As used in this context, “newfound” means recently discovered or established. The text indicates that in the 1970s, video cameras became cheaper and therefore more widely available than they had been in the past. The text goes on to say that this development provided Jenkins and other artists with capabilities that they previously didn’t have. As a result, Jenkins began producing groundbreaking works of video art. This context supports the idea that Jenkins took advantage of newfound access to video cameras.

Choice B is incorrect because “delicate” means fine in texture or structure or easily broken, neither of which would make sense in this context. The text doesn’t focus on describing what video art looks like or whether it’s breakable. Choice C is incorrect because “inevitable” means impossible to avoid, which wouldn’t make sense in this context. The text doesn’t discuss the likelihood of artists, or anyone else, gaining access to video cameras. Choice D is incorrect because “habitual” means doing something regularly or repeatedly. Although the text does suggest that Jenkins created multiple pieces of video art, its focus is on the fact that video cameras had only just become widely available to artists in the 1970s. Jenkins’s ability to take advantage of video cameras to make art was therefore newfound, not habitual, at the time.

"}, {"id": "c4737d6a", "domain": "Craft and Structure", "skill": "Cross-Text Connections", "difficulty": "H", "type": "mc", "stimulus": "

Text 1

\n

Africa’s Sahara region—once a lush ecosystem—began to dry out about 8,000 years ago. A change in Earth’s orbit that affected climate has been posited as a cause of desertification, but archaeologist David Wright also attributes the shift to Neolithic peoples. He cites their adoption of pastoralism as a factor in the region drying out: the pastoralists’ livestock depleted vegetation, prompting the events that created the Sahara Desert.

\n

Text 2

\n

Research by Chris Brierley et al. challenges the idea that Neolithic peoples contributed to the Sahara’s desertification. Using a climate-vegetation model, the team concluded that the end of the region’s humid period occurred 500 years earlier than previously assumed. The timing suggests that Neolithic peoples didn’t exacerbate aridity in the region but, in fact, may have helped delay environmental changes with practices (e.g., selective grazing) that preserved vegetation.

", "stem": "

Based on the texts, how would Chris Brierley (Text 2) most likely respond to the discussion in Text 1?

", "choices": [{"id": "A", "text": "

By pointing out that given the revised timeline for the end of the Sahara’s humid period, the Neolithic peoples’ mode of subsistence likely didn’t cause the region’s desertification

"}, {"id": "B", "text": "

By claiming that pastoralism was only one of many behaviors the Neolithic peoples took part in that may have contributed to the Sahara’s changing climate

"}, {"id": "C", "text": "

By insisting that pastoralism can have both beneficial and deleterious effects on a region’s vegetation and climate

"}, {"id": "D", "text": "

By asserting that more research needs to be conducted into factors that likely contributed to the desertification of the Sahara region

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. Brierley et al.’s research directly challenges Wright’s claim that pastoralism turned the Sahara into a desert, suggesting that, in a Sahara that turned arid 500 years earlier than previously thought, pastoral practices may have actually “preserved vegetation” rather than depleting it.

Choice B is incorrect. Brierley et al.’s research actually disputes the idea that any Neolithic peoples’ behaviors, including pastoralism, could have contributed to the Sahara’s changing climate. In fact, their research implies that the Neolithic peoples’ practices did not “exacerbate aridity” (i.e., make things worse), but may have slowed environmental changes. Choice C is incorrect. Brierley et al.’s research does not acknowledge that pastoralism can have deleterious (i.e., negative) effects on a region’s vegetation and climate. It only describes one possible beneficial effect: preserving vegetation through practices like selective grazing. Choice D is incorrect. Brierley et al.’s research does not call for more research into factors that likely contributed to the desertification of the Sahara region.

"}, {"id": "47598085", "domain": "Craft and Structure", "skill": "Text Structure and Purpose", "difficulty": "M", "type": "mc", "stimulus": "

Yawn contagion occurs when one individual yawns in response to another’s yawn. Studies of this behavior in primates have focused on populations in captivity, but biologist Elisabetta Palagi and her colleagues have shown that it can occur in wild primate populations as well. In their study, which focused on a wild population of gelada monkeys (Theropithecus gelada) in Ethiopia, the researchers further reported that yawn contagion most commonly occurred in males and across different social groups instead of within a single social group.

", "stem": "

Which choice best describes the function of the first sentence in the text as a whole?

", "choices": [{"id": "A", "text": "

It defines a phenomenon that is discussed in the text.

"}, {"id": "B", "text": "

It introduces a problem that is examined in the text.

"}, {"id": "C", "text": "

It makes a claim that is challenged in the text.

"}, {"id": "D", "text": "

It presents a hypothesis that is evaluated in the text.

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer because it most accurately describes how the first sentence functions in the text as a whole. The first sentence introduces what yawn contagion is, explaining that it occurs when an individual yawns in response to the yawn of another individual. The text goes on to describe Elisabetta Palagi and her colleagues’ study of this phenomenon in a wild population of gelada monkeys. According to the text, the study showed that wild primate populations experience yawn contagion and that the behavior occurs most commonly in male monkeys and across social groups. Thus, the function of the first sentence is to define the phenomenon of yawn contagion that is discussed in the text.

Choice B is incorrect. Although the first sentence introduces the text’s discussion of yawn contagion, it doesn’t present this behavior, or anything else, as a problem. Choice C is incorrect because the first sentence doesn’t present a claim but instead explains what yawn contagion is. Moreover, the text doesn’t challenge anything; it’s an informative text that describes the findings of a research study about yawning in wild primate populations. Choice D is incorrect. Although the text describes a scientific study, and most scientific studies are guided by a hypothesis, the text doesn’t say what Palagi and her colleagues’ hypothesis was; the text discusses their findings instead.

"}, {"id": "a87c3925", "domain": "Craft and Structure", "skill": "Cross-Text Connections", "difficulty": "H", "type": "mc", "stimulus": "

Text 1

\n

Soy sauce, made from fermented soybeans, is noted for its umami flavor. Umami—one of the five basic tastes along with sweet, bitter, salty, and sour—was formally classified when its taste receptors were discovered in the 2000s. In 2007, to define the pure umami flavor scientists Rie Ishii and Michael O’Mahony used broths made from shiitake mushrooms and kombu seaweed, and two panels of Japanese and US judges closely agreed on a description of the taste.

\n

 

\n

Text 2

\n

A 2022 experiment by Manon Jünger et al. led to a greater understanding of soy sauce’s flavor profile. The team initially presented a mixture of compounds with low molecular weights to taste testers who found it was not as salty or bitter as real soy sauce. Further analysis of soy sauce identified proteins, including dipeptides, that enhanced umami flavor and also contributed to saltiness. The team then made a mix of 50 chemical compounds that re-created soy sauce’s flavor.

", "stem": "

Based on the texts, if Ishii and O’Mahony (Text 1) and Jünger et al. (Text 2) were aware of the findings of both experiments, they would most likely agree with which statement?

", "choices": [{"id": "A", "text": "

On average, the diets of people in the United States tend to have fewer foods that contain certain dipeptides than the diets of people in Japan have.

"}, {"id": "B", "text": "

Chemical compounds that activate both the umami and salty taste receptors tend to have a higher molecular weight than those that only activate umami taste receptors.

"}, {"id": "C", "text": "

Fermentation introduces proteins responsible for the increase of umami flavor in soy sauce, and those proteins also increase the perception of saltiness.

"}, {"id": "D", "text": "

The broths in the 2007 experiment most likely did not have a substantial amount of the dipeptides that played a key part in the 2022 experiment.

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. Ishii and O’Mahony were trying to isolate the pure umami flavor, while Jünger was trying to recreate soy sauce, which has a mix of flavors that includes umami. Accordingly, the broths from Text 1 are not described as having any soy sauce in them—just “shiitake mushrooms and kombu seaweed.” So they probably don’t have as much of the dipeptides described in Text 2, which were found to be a key part of soy sauce’s umami-ness and its saltiness.

Choice A is incorrect. Neither text supports this. Neither text gets into the diets of people in the United States, nor the diets of people in Japan. Choice B is incorrect. Neither text supports this. Text 2 does talk about the molecular weights of chemical compounds, but there isn’t enough information provided about molecular weights in Text 1 to make an inference about what the scientists in Text 1 would say. Choice C is incorrect. Neither text supports this. Text 1 briefly mentions that soy sauce is “made from fermented soybeans,” but it never claims that fermentation is responsible for its flavor in any way. And Text 2 never mentions fermentation at all.

"}, {"id": "4a2b2535", "domain": "Craft and Structure", "skill": "Words in Context", "difficulty": "E", "type": "mc", "stimulus": "

A brief book review cannot fully convey the ______blank of Olga Tokarczuk’s novel The Books of Jacob, with its enormous cast of characters, its complicated, wandering plot, and its page numbers that count backward (beginning at 965 and ending at 1).

", "stem": "

Which choice completes the text with the most logical and precise word or phrase?

", "choices": [{"id": "A", "text": "

accuracy

"}, {"id": "B", "text": "

inactivity

"}, {"id": "C", "text": "

complexity

"}, {"id": "D", "text": "

restraint

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer because it most logically completes the text’s discussion of Olga Tokarczuk’s novel The Books of Jacob. As used in this context, “complexity” means having many complicated parts that when taken as a whole are difficult to follow or explain. The text indicates that The Books of Jacob has a large cast of characters, a complicated and wandering plot (that is, a plot that is difficult to follow), and reverse page numbering. Together, these features make up a novel that’s challenging to read and summarize. This context supports the idea that a brief book review can’t do justice to the novel’s complexity.

Choice A is incorrect. Although the word “accuracy,” or being free from error or falsehood, can sometimes be used to describe a novel, the text doesn’t discuss whether Tokarczuk’s novel has this quality. Instead, the text describes the novel as having a large cast of characters, a difficult-to-follow plot, and reverse page numbering. These features suggest complexity, not accuracy. Choice B is incorrect because “inactivity” means being in a state of idleness or doing nothing, neither of which would make sense in this context. The text describes Tokarczuk’s novel, and although it’s possible the novel could portray its characters as inactive, it wouldn’t make sense to describe the novel itself as such. Choice D is incorrect because in this context “restraint” would mean holding back or showing self-control, and the text doesn’t indicate that Tokarczuk’s novel has either of these qualities. In fact, the features of the novel that the text describes, such as a large cast of characters, a complicated and wandering plot, and reverse page numbering, suggest excess and complexity, not restraint.

"}, {"id": "b0f7541b", "domain": "Craft and Structure", "skill": "Text Structure and Purpose", "difficulty": "H", "type": "mc", "stimulus": "

The following text is adapted from Herman Melville’s 1857 novel The Confidence-Man. Humphry Davy was a prominent British chemist and inventor.

\n
\n

Years ago, a grave American savant, being in London, observed at an evening party there, a certain coxcombical fellow, as he thought, an absurd ribbon in his lapel, and full of smart [banter], whisking about to the admiration of as many as were disposed to admire. Great was the savant’s disdain; but, chancing ere long to find himself in a corner with the jackanapes, got into conversation with him, when he was somewhat ill-prepared for the good sense of the jackanapes, but was altogether thrown aback, upon subsequently being [informed that he was] no less a personage than Sir Humphry Davy.

\n
", "stem": "

Which choice best states the main purpose of the text?

", "choices": [{"id": "A", "text": "

It portrays the thoughts of a character who is embarrassed about his own behavior.

"}, {"id": "B", "text": "

It presents an account of a misunderstanding.

"}, {"id": "C", "text": "

It offers a short history of how a person came to be famous.

"}, {"id": "D", "text": "

It explains why one character dislikes another.

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. The text tells a story of a first impression that turned out to be wrong: a serious American savant was dismissive of a goofy-looking, wisecracking guest at a British party, and then was shocked to learn that the guest was actually a prominent British chemist and inventor.

Choice A is incorrect. This is too strong and too narrow. Only at the very end is the savant \"thrown aback\" by the fact that the man was Sir Humphry Davy—he’s not \"embarrassed about his own behavior.\" Choice C is incorrect. This isn’t the main purpose. The text never provides the history of how Sir Humphry Davy came to be famous. Nor does it provide any history for the American savant. Choice D is incorrect. This is too narrow. It doesn’t include the second half of the text, where the savant gets into a conversation with the man and then finds out that the man is Sir Humphry Davy.

"}, {"id": "8d802289", "domain": "Craft and Structure", "skill": "Cross-Text Connections", "difficulty": "E", "type": "mc", "stimulus": "

Text 1

\n

Dance choreographer Alvin Ailey’s deep admiration for jazz music can most clearly be felt in the rhythms and beats his works were set to. Ailey collaborated with some of the greatest jazz legends, like Charles Mingus, Charlie Parker, and perhaps his favorite, Duke Ellington. With his choice of music, Ailey helped bring jazz to life for his audiences.

\n

 

\n

Text 2

\n

Jazz is present throughout Ailey’s work, but it’s most visible in Ailey’s approach to choreography. Ailey often incorporated improvisation, a signature characteristic of jazz music, in his work. When managing his dance company, Ailey rarely forced his dancers to an exact set of specific moves. Instead, he encouraged his dancers to let their own skills and experiences shape their performances, as jazz musicians do.

", "stem": "

Based on the texts, both authors would most likely agree with which statement?

", "choices": [{"id": "A", "text": "

Dancers who worked with Ailey greatly appreciated his supportive approach as a choreographer.

"}, {"id": "B", "text": "

Ailey’s work was strongly influenced by jazz.

"}, {"id": "C", "text": "

Audiences were mostly unfamiliar with the jazz music in Ailey’s works.

"}, {"id": "D", "text": "

Ailey blended multiple genres of music together when choreographing dance pieces.

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. Author 1 states that Ailey had a “deep admiration for jazz music” and that he “helped bring jazz to life for his audiences.” Author 2 states that “Jazz is present throughout Ailey’s work.” While the authors name different aspects of Ailey’s work as the most influenced by jazz, they agree that jazz was a strong influence. 

Choice A is incorrect. This isn’t something that either text claims. Neither text mentions how Ailey’s dancers felt about his approach as a choreographer, so we have no evidence that either author would agree with this. Choice C is incorrect. This isn’t something that either text claims. Neither text mentions how familiar audiences were with any aspect of Ailey’s works, so we have no evidence that either author would agree with this. Choice D is incorrect. This isn’t something that either text claims. Neither text mentions any genre of music other than jazz, so we have no evidence that either author would agree with this.

"}, {"id": "7bf79a90", "domain": "Craft and Structure", "skill": "Cross-Text Connections", "difficulty": "M", "type": "mc", "stimulus": "

Text 1

\n

Microbes are tiny organisms in the soil, water, and air all around us. They thrive even in very harsh conditions. That’s why Noah Fierer and colleagues were surprised when soil samples they collected from an extremely cold, dry area in Antarctica didn’t seem to contain any life. The finding doesn’t prove that there are no microbes in that area, but the team says it does suggest that the environment severely restricts microbes’ survival.

\n

 

\n

Text 2

\n

Microbes are found in virtually every environment on Earth. So it’s unlikely they would be completely absent from Fierer’s team’s study site, no matter how extreme the environment is. There were probably so few organisms in the samples that current technology couldn’t detect them. But since a spoonful of typical soil elsewhere might contain billions of microbes, the presence of so few in the Antarctic soil samples would show how challenging the conditions are.

", "stem": "

Based on the texts, Fierer’s team and the author of Text 2 would most likely agree with which statement about microbes?

", "choices": [{"id": "A", "text": "

Most microbes are better able to survive in environments with extremely dry conditions than in environments with harsh temperatures.

"}, {"id": "B", "text": "

A much higher number of microbes would probably be found if another sample of soil were taken from the Antarctic study site.

"}, {"id": "C", "text": "

Microbes are likely difficult to detect in the soil at the Antarctic study site because they tend to be smaller than microbes found in typical soil elsewhere.

"}, {"id": "D", "text": "

Most microbes are probably unable to withstand the soil conditions at the Antarctic study site.

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer because it presents a statement about microbes with which Fierer’s team (Text 1) and the author of Text 2 would most likely agree. Text 1 states that microbes usually thrive in very harsh conditions, and so Fierer’s team was surprised when samples collected from an extremely cold and dry area of Antarctica didn’t appear to contain any life. Fierer’s team says that though this doesn’t conclusively prove there are no microbes in the area, it suggests that microbes would have a notably difficult time surviving in the environment. The author of Text 2 says it’s unlikely that there would be no microbes at all in the Antarctic study site from which Fierer’s team retrieved soil samples and that there may have been hard-to-detect microbes in the samples. However, the presence of only a few microbes in the Antarctic samples rather than the billions found in a typical soil sample (which would presumably be much easier to detect) would illustrate conditions in the Antarctic soil that make it difficult for microbes to thrive. Since Fierer’s team says that the seeming absence of microbes in the Antarctic samples suggests an unusually harsh environment and the author of Text 2 says that even if there are a few undetectable microbes in the samples, the relatively tiny number of microbes would also suggest an unusually harsh environment, then Fierer’s team and the author of Text 2 would most likely agree that most microbes are unable to withstand the soil conditions at the Antarctic study site.

Choice A is incorrect. The samples taken by Fierer’s team were from an area of Antarctica that is described in part as extremely dry, and these samples didn’t appear to have any life. Therefore, even though these samples also came from an extremely cold area, Fierer’s team wouldn’t argue based on the evidence available that microbes were better able to survive in dry conditions than in areas with harsh temperatures. Moreover, the author of Text 2 says that microbes are found in virtually every environment on Earth but doesn’t compare dry environments and harsh environments. Choice B is incorrect. Nothing in Text 1 indicates that another collection of samples from the Antarctic study site might yield different results from the samples already taken by Fierer’s team. The author of Text 2 does state that microbes are found in virtually every environment on Earth and suggests that new technology may be better able to detect so few microbes in a soil sample, but the author of Text 2 concludes that the unusual absence of microbes in the Antarctic samples is evidence of the harsh Antarctic environment. Therefore, there is no reason to believe that the author of Text 2 thinks that another sample drawn from that same harsh environment would yield a much higher number of microbes. Choice C is incorrect. The author of Text 2 does speculate that there may have been so few microbes in the Antarctic samples that current technology couldn’t detect them, but the author doesn’t speculate that this is due to the size of the microbes. Moreover, nothing that Fierer’s team says suggests that they are speculating that their samples might have microbes that are smaller than microbes in typical soil samples.

"}, {"id": "9ccf463e", "domain": "Craft and Structure", "skill": "Words in Context", "difficulty": "E", "type": "mc", "stimulus": "

The following text is from Nella Larsen’s 1928 novel Quicksand.

\n
\n

The trees in their spring beauty sent through her restive mind a sharp thrill of pleasure. Seductive, charming, and beckoning as cities were, they had not this easy unhuman loveliness.

\n
", "stem": "

As used in the text, what does the word “beckoning” most nearly mean?

", "choices": [{"id": "A", "text": "

Demanding

"}, {"id": "B", "text": "

Signaling

"}, {"id": "C", "text": "

Inviting

"}, {"id": "D", "text": "

Shifting

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer because as used in the text, “beckoning” most nearly means “inviting,” or attractive. The text portrays a woman who is looking at “trees in their spring beauty.” She compares them to cities, which have their own pleasures even if they do not have the “easy unhuman loveliness” of trees: she thinks of cities as “seductive” and “charming,” both adjectives that signify something that is enticing, or attractive. Therefore, cities that are seductive and charming would also be described as inviting people closer to them.

Choice A is incorrect because there is no indication in this context that cities are “demanding,” or requiring effort. Choice B is incorrect. Though “signaling,” or communicating something, might be considered a key feature of the act of “beckoning,” in the context here, “beckoning” suggests that cities have attractive qualities that naturally draw people to them. Such attractive qualities are not described by the word “signaling” alone. Therefore, “signaling” is an incorrect answer because it is insufficiently precise. Choice D is incorrect because there is no reason to think in this context that the cities are “shifting,” or changing shape.

"}, {"id": "835d1ae6", "domain": "Craft and Structure", "skill": "Cross-Text Connections", "difficulty": "E", "type": "mc", "stimulus": "

Text 1

\n

Historians studying pre-Inca Peru have looked to ceramic vessels to understand daily life among the Moche people. These mold-made sculptures present plants, animals, and human faces in precise ways—vessels representing human faces are so detailed that scholars have interpreted facial markings to represent scars and other skin irregularities. Some historians have even used these objects to identify potential skin diseases that may have afflicted people at the time.

\n

 

\n

Text 2

\n

Art historian and archaeologist Lisa Trever has argued that the interpretation of Moche “portrait” vessels as hyper-realistic portrayals of identifiable people may inadvertently disregard the creativity of the objects’ creators. Moche ceramic vessels, Trever argues, are artworks in which sculptors could free their imagination, using realistic objects and people around them as inspiration to explore more abstract concepts.

", "stem": "

Based on the texts, what would Lisa Trever (Text 2) most likely say about the interpretation presented in the underlined portion of Text 1?

", "choices": [{"id": "A", "text": "

Depictions of human faces are significantly more realistic than depictions of plants and other animals are.

"}, {"id": "B", "text": "

It is likely that some depictions of human faces with extensive markings are intended to portray the same historical individual.

"}, {"id": "C", "text": "

Some vessels may have been damaged during their excavation and thus provide little insight into Moche culture.

"}, {"id": "D", "text": "

Markings on depictions of human faces are not necessarily intended to portray particular details about the physical appearance of individuals.

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. Trever thinks that the “hyper-realistic portrayal of identifiable people” interpretation ignores the sculptors’ imagination and creativity. We can infer that Trevor thinks the facial markings on the sculptures may not have represented real skin blemishes on real people.

Choice A is incorrect. The text gives us no reason to think that Trever would respond to the underlined interpretation in this way. Neither text compares the depictions of human faces to the depictions of plants or animals, so we have no basis to draw this conclusion. Choice B is incorrect. The text gives us no reason to think that Trever would respond to the underlined interpretation in this way. There’s nothing in either text about multiple depictions representing the same person, so we have no basis to draw this conclusion. Choice C is incorrect. The text gives us no reason to think that Trever would respond to the underlined interpretation in this way. Neither text mentions the state of the vessels (damaged or intact), so we have no basis to draw this conclusion.

"}, {"id": "ca47273b", "domain": "Craft and Structure", "skill": "Words in Context", "difficulty": "E", "type": "mc", "stimulus": "

Biologist Jane Edgeloe and colleagues have located what is believed to be the largest individual plant in the world in the Shark Bay area of Australia. The plant is a type of seagrass called Posidonia australis, and it ______blank approximately 200 square kilometers.

", "stem": "

Which choice completes the text with the most logical and precise word or phrase?

", "choices": [{"id": "A", "text": "

acknowledges

"}, {"id": "B", "text": "

produces

"}, {"id": "C", "text": "

spans

"}, {"id": "D", "text": "

advances

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. “Spans” means “extends over a distance of” or “encompasses.” Since we’re talking about the world’s largest plant, it makes sense to say that it “spans” about 200 square kilometers.

Choice A is incorrect. “Acknowledges” means “recognizes” or “admits the truth of.” Either way, it doesn’t make sense here: a plant can’t “acknowledge” a distance. Choice B is incorrect. “Produces” can mean “makes,” “causes,” or “presents.” But none of those definitions make sense here: a plant can’t make, cause, or present a distance. Choice D is incorrect. This doesn’t fit the logic of the text. “Advances” means “moves forward” or “progresses.” But the plant isn’t necessarily moving forward. Rather, the text suggests that it already covers a distance of 200 square kilometers.

"}, {"id": "69a6d050", "domain": "Craft and Structure", "skill": "Words in Context", "difficulty": "E", "type": "mc", "stimulus": "

In the early 1800s, the Cherokee scholar Sequoyah created the first script, or writing system, for an Indigenous language in the United States. Because it represented the sounds of spoken Cherokee so accurately, his script was easy to learn and thus quickly achieved ______blank use: by 1830, over 90 percent of the Cherokee people could read and write it.

", "stem": "

Which choice completes the text with the most logical and precise word or phrase?

", "choices": [{"id": "A", "text": "

widespread

"}, {"id": "B", "text": "

careful

"}, {"id": "C", "text": "

unintended

"}, {"id": "D", "text": "

infrequent

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer because it most logically completes the text’s discussion of the writing system created by Sequoyah. In this context, “widespread” means widely accepted or practiced. The text indicates that because Sequoyah’s script accurately represented the spoken sounds of the Cherokee language and was easy to learn, nearly all Cherokee people were able to read and write it soon after it was created. This context demonstrates that the script was widely used by the Cherokee people.

Choice B is incorrect. In this context, “careful” would mean exercised with care and attentive concern. Although the work of creating a writing system likely involved great care, the text indicates that the system was “easy to learn,” which conflicts with the idea that using this system requires a noteworthy amount of care. Choice C is incorrect because in this context “unintended” means not deliberate. The idea that using Sequoyah’s script was unintentional conflicts directly with the claim that it was easy to learn and used by “over 90% of the Cherokee people” by 1830. In fact, because one had to learn this system, it’s not clear how one could use it unintentionally. Choice D is incorrect because in this context “infrequent” means rare or not occurring often, which conflicts directly with the claim that “over 90% of the Cherokee people” were using Sequoyah’s script by 1830.

"}, {"id": "81da17d3", "domain": "Craft and Structure", "skill": "Cross-Text Connections", "difficulty": "E", "type": "mc", "stimulus": "

Text 1

\n

Italian painters in the 1500s rarely depicted themselves in their work. Even more rare were self-portrait paintings that portrayed the artist as a painter. At the time, painting was not yet respected as a profession, so painters mostly chose to emphasize other qualities in their self-portraits, like their intellect or social status. In the city of Bologna, the first artist to depict themself painting was a man named Annibale Carracci. A painting of his from around 1585 shows Carracci in front of an easel holding a palette. 

\n

 

\n

Text 2

\n

In their self-portraits, Bolognese artists typically avoided referring to the act of painting until the mid-1600s. However, Lavinia Fontana’s 1577 painting, Self-Portrait at the Keyboard, stands out as the earliest example of such a work by an artist from Bologna. Although the artist is depicted playing music, in the background, one can spot a painting easel by a window.

", "stem": "

Based on the texts, how would the author of Text 2 most likely respond to the underlined claim in Text 1?

", "choices": [{"id": "A", "text": "

Carracci and Fontana were among the most well-respected painters in Bologna at the time.

"}, {"id": "B", "text": "

The depiction of Fontana in Self-Portrait at the Keyboard was intended to underscore the artist’s creativity.

"}, {"id": "C", "text": "

Fontana likely inspired the reference to an easel and palette in Carracci’s painting.

"}, {"id": "D", "text": "

Self-Portrait at the Keyboard was painted earlier than Carracci’s painting and also refers to the artist’s craft.

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. The author of Text 2 states that Fontana’s painting, which depicts a painting easel in the background, was made in 1577, eight years before Carracci’s painting. Therefore, they might argue that Caracci was not “the first artist” to depict themself as a painter.

Choice A is incorrect. The texts don’t support this choice. Neither text mentions the reputation or status of either Carracci or Fontana. Choice B is incorrect. The author of Text 2 does not comment on the intention or meaning of Fontana’s self-depiction in Self-Portrait at the Keyboard. This choice also holds little connection to the underlined claim. Choice C is incorrect. The texts don’t support this choice. The author of Text 2 does not suggest any inspirational relationship between Fontana and Carracci. The author of Text 2 is concerned with showing that Fontana’s painting is the earliest example of an artist referring to painting in their self-portrait, but makes no mention of her influence on others.

"}, {"id": "e41dfaab", "domain": "Craft and Structure", "skill": "Words in Context", "difficulty": "E", "type": "mc", "stimulus": "

In 1929 the Atlantic Monthly published several articles based on newly discovered letters allegedly exchanged between President Abraham Lincoln and a woman named Ann Rutledge. Historians were unable to ______blank the authenticity of the letters, however, and quickly dismissed them as a hoax.

", "stem": "

Which choice completes the text with the most logical and precise word or phrase?

", "choices": [{"id": "A", "text": "

validate

"}, {"id": "B", "text": "

interpret

"}, {"id": "C", "text": "

relate

"}, {"id": "D", "text": "

accommodate

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer because it most logically completes the text’s discussion of letters allegedly exchanged between President Lincoln and Rutledge. In this context, “validate” means to confirm that something is real or correct. According to the text, it was alleged, or claimed, that the newly discovered letters had been written by Lincoln and Rutledge. The text also indicates that historians ultimately decided the letters were a hoax, or fraudulent. This context suggests that the historians couldn’t confirm that the letters were authentic.

Choice B is incorrect. The text focuses on the authenticity of the letters, which were claimed to have been written by Lincoln and Rutledge and were then quickly dismissed as fraudulent by historians. Rather than conveying that the historians simply weren’t able to “interpret,” or explain in an understandable way, the letters’ authenticity, the text suggests that the historians decided the letters lacked authenticity altogether. Choice C is incorrect. The text states that the historians quickly dismissed the letters claimed to have been written by Lincoln and Rutledge as fraudulent; this suggests that rather than being unable to “relate,” or tell others about, the letters’ authenticity, the historians were able to share what they’d decided about the letters. Choice D is incorrect because it wouldn’t make sense to suggest that the historians couldn’t “accommodate,” or give consideration to, the authenticity of the letters claimed to have been written by Lincoln and Rutledge; the text states that the historians decided that the letters were fraudulent, which indicates that they did consider whether the letters were authentic.

"}, {"id": "e13171c4", "domain": "Craft and Structure", "skill": "Text Structure and Purpose", "difficulty": "E", "type": "mc", "stimulus": "

Historians Tiya Miles and Roy E. Finkenbine have both documented the assistance Indigenous peoples gave to Black freedom seekers leaving the South before the US Civil War. Much of the historical evidence of this help comes from Indigenous oral traditions and from autobiographies written by the freedom seekers. One such narrative is Jermain Loguen’s autobiography, which tells about how Neshnabé (Potawatomi) villagers offered him food, lodging, and directions during his 1835 journey from Tennessee to Canada.

", "stem": "

Which choice best describes the function of the underlined sentence?

", "choices": [{"id": "A", "text": "

It provides an example of an autobiography that describes help given by an Indigenous people to a Black freedom seeker.

"}, {"id": "B", "text": "

It shows why Loguen decided to write in great detail about his experiences traveling from Tennessee to Canada in his autobiography.

"}, {"id": "C", "text": "

It argues that autobiographies are particularly important sources of information about geography in the United States before the Civil War.

"}, {"id": "D", "text": "

It suggests that most historians believe that Neshnabé villagers were more successful in assisting freedom seekers than other people were.

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. The previous sentence broadly mentions \"autobiographies written by the freedom seekers.\" This sentence identifies Loguen’s autobiography as a specific example.

Choice B is incorrect. The sentence never explains why Loguen chose to write about his experiences. Choice C is incorrect. The previous sentence identifies autobiographies as useful sources of historical information about a specific topic, but not for \"information about geography.\" The underlined sentence provides details of one autobiography as an example of a source of information about that specific topic (interactions between Indigenous people and Black freedom seekers). Choice D is incorrect. The text never discusses other specific people who helped freedom seekers, and therefore can’t make a comparison between the Neshnabé and anyone else.

"}, {"id": "4d1a9c0d", "domain": "Craft and Structure", "skill": "Words in Context", "difficulty": "E", "type": "mc", "stimulus": "

Following the principles of community-based participatory research, tribal nations and research institutions are equal partners in health studies conducted on reservations. A collaboration between the Crow Tribe and Montana State University ­­­­______blank this model: tribal citizens worked alongside scientists to design the methodology and continue to assist in data collection.

", "stem": "

Which choice completes the text with the most logical and precise word or phrase?

", "choices": [{"id": "A", "text": "

circumvents

"}, {"id": "B", "text": "

eclipses

"}, {"id": "C", "text": "

fabricates

"}, {"id": "D", "text": "

exemplifies

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer because it most logically completes the text’s discussion of the collaboration between the Crow Tribe and Montana State University. As used in this context, “exemplifies” means demonstrates. The text conveys how the Crow Tribe–Montana State University collaboration serves to illustrate the model of community-based participatory research introduced earlier in the text and expanded on later in the text. 

Choice A is incorrect because referring to “circumvents,” or avoids, wouldn’t make sense in context. The text suggests that the Crow Tribe–Montana State University collaboration serves as an example of the principles of community-based participatory research, not that the collaboration evades this model. Choice B is incorrect because referring to “eclipses,” or overshadows, wouldn’t make sense in context. The text describes the Crow Tribe–Montana State University collaboration as an equal partnership, which indicates that it’s an example of the community-based participatory research model, not that it overshadows the model. Choice C is incorrect because saying that the collaboration “fabricates,” or creates, the model wouldn’t make sense in context. The text indicates that the Crow Tribe–Montana State University collaboration serves as an example of the model, not that it created the model. 

"}, {"id": "5effa190", "domain": "Craft and Structure", "skill": "Words in Context", "difficulty": "E", "type": "mc", "stimulus": "

The process of mechanically recycling plastics is often considered ______blank because of the environmental impact and the loss of material quality that often occurs. But chemist Takunda Chazovachii has helped develop a cleaner process of chemical recycling that converts superabsorbent polymers from diapers into a desirable reusable adhesive.

", "stem": "

Which choice completes the text with the most logical and precise word or phrase?

", "choices": [{"id": "A", "text": "

resilient

"}, {"id": "B", "text": "

inadequate

"}, {"id": "C", "text": "

dynamic

"}, {"id": "D", "text": "

satisfactory

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer because it most logically completes the text’s discussion about recycling plastics. In this context, “inadequate” means not satisfactory. The text indicates that the mechanical plastic-recycling process affects the environment and causes “the loss of material quality.” The text contrasts that with Chazovachii’s chemical plastic-recycling process, which is cleaner and produces a desirable product. The text’s emphasis on the negative aspects of mechanical recycling suggests that it is inadequate in terms of environmental impact and the quality of the material the process yields.

Choice A is incorrect because in this context “resilient” would mean able to withstand difficulty and the text does not characterize the plastic-recycling process as having this quality or describe any difficulties that these processes might need to overcome. Choice C is incorrect because in this context “dynamic” would mean constantly changing. Although the text suggests that there have been changes in the field of recycling, as is the case with the advent of Chazovachii’s chemical recycling process, there is nothing to suggest that the mechanical process itself has changed or is prone to change. Choice D is incorrect because in this context “satisfactory” would mean acceptable but not perfect. The text mentions only shortcomings of the mechanical process (environmental effects and lower material quality), so the text more strongly supports a negative view of this process and provides no evidence that it would be considered satisfactory.

"}, {"id": "f3fac04f", "domain": "Craft and Structure", "skill": "Words in Context", "difficulty": "E", "type": "mc", "stimulus": "

Bioluminescent beetles called fireflies may seem to create flashes of light randomly, but each species of firefly actually has its own special series of repeated flashes and pauses. These unique ______blank allow fireflies of the same species to find each other.

", "stem": "

Which choice completes the text with the most logical and precise word or phrase?

", "choices": [{"id": "A", "text": "

quantities 

"}, {"id": "B", "text": "

decorations

"}, {"id": "C", "text": "

patterns

"}, {"id": "D", "text": "

agreements

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer because it most logically completes the text’s discussion of the flashes created by fireflies. In this context, “patterns” means distinct and predictable sequences. The text indicates that although the flashes that fireflies produce appear to occur randomly—that is, without any particular sequence or rhythm—each species actually produces its own special series of flashes and pauses. Indeed, these series of flashes are so unique that fireflies can use them to find other members of their species. Therefore, this context supports the idea that fireflies produce flashes in distinct and recognizable patterns.

Choice A is incorrect because “quantities” means certain amounts or numbers of something. Although the text discusses how different firefly species produce flashes and pauses in unique sequences that help other members of their species to find them, it doesn’t mention the number of flashes that are used in these sequences. Choice B is incorrect because in this context, “decorations” would mean things that make an object more beautiful. Although it may be reasonable to say that firefly flashes are beautiful, the text focuses on the fact that fireflies use these unique sequences of flashes to find other members of their own species, not that the flashes make fireflies more beautiful. Choice D is incorrect because in this context, “agreements” would refer to deals that individuals have discussed and come to a consensus about. Since fireflies aren’t capable of making such agreements, it wouldn’t make sense to use this word to refer to the signals they send each other with their flashes.

"}, {"id": "d6c77ae5", "domain": "Craft and Structure", "skill": "Cross-Text Connections", "difficulty": "H", "type": "mc", "stimulus": "

 

Text 1

\n

Astronomer Mark Holland and colleagues examined four white dwarfs—small, dense remnants of past stars—in order to determine the composition of exoplanets that used to orbit those stars. Studying wavelengths of light in the white dwarf atmospheres, the team reported that traces of elements such as lithium and sodium support the presence of exoplanets with continental crusts similar to Earth’s.

\n\n

 

Text 2

\n

Past studies of white dwarf atmospheres have concluded that certain exoplanets had continental crusts. Geologist Keith Putirka and astronomer Siyi Xu argue that those studies unduly emphasize atmospheric traces of lithium and other individual elements as signifiers of the types of rock found on Earth. The studies don’t adequately account for different minerals made up of various ratios of those elements, and the possibility of rock types not found on Earth that contain those minerals.

", "stem": "

Based on the texts, how would Putirka and Xu (Text 2) most likely characterize the conclusion presented in Text 1?

", "choices": [{"id": "A", "text": "

As unexpected, because it was widely believed at the time that white dwarf exoplanets lack continental crusts

"}, {"id": "B", "text": "

As premature, because researchers have only just begun trying to determine what kinds of crusts white dwarf exoplanets had

"}, {"id": "C", "text": "

As questionable, because it rests on an incomplete consideration of potential sources of the elements detected in white dwarf atmospheres

"}, {"id": "D", "text": "

As puzzling, because it’s unusual to successfully detect lithium and sodium when analyzing wavelengths of light in white dwarf atmospheres

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer because it reflects how Putirka and Xu (Text 2) would likely characterize the conclusion presented in Text 1. Text 1 discusses a study by Mark Holland and colleagues in which they detected traces of lithium and sodium in the atmospheres of four white dwarf stars. The team claims that this supports the idea that exoplanets with continental crusts like Earth’s once orbited these stars. Text 2 introduces Putirka and Xu, who indicate that sodium and lithium are present in several different minerals and that some of those minerals might exist in types of rock that are not found on Earth. Therefore, Putirka and Xu would likely describe the conclusion in Text 1 as questionable because it does not consider that lithium and sodium are also found in rocks that are not like Earth’s continental crust.

Choice A is incorrect because the texts do not indicate how widely held any of the viewpoints described are. Choice B is incorrect because neither text discusses how new this area of study is. Choice D is incorrect because neither text discusses how likely lithium and sodium are to be detected by analyzing wavelengths of light. 

"}, {"id": "6d5ddea4", "domain": "Craft and Structure", "skill": "Words in Context", "difficulty": "E", "type": "mc", "stimulus": "

According to Potawatomi ecologist Robin Wall Kimmerer, the Indigenous method of harvesting Hierochloe odorata, or sweetgrass, by snapping the plant off at the root actually ______blank wild populations: it may seem counterintuitive, she says, but this method of removal allows new sweetgrass plants to repopulate the space, with an overall increase in number and vigor.

", "stem": "

Which choice completes the text with the most logical and precise word or phrase?

", "choices": [{"id": "A", "text": "

selects

"}, {"id": "B", "text": "

originates

"}, {"id": "C", "text": "

conditions

"}, {"id": "D", "text": "

replenishes

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer because it most logically completes the text’s discussion of the Indigenous method of harvesting Hierochloe odorata. As used in this context, “replenishes” means helps increase the population or helps it recover. The text explains that although snapping off a wild plant at the root might seem detrimental to the wild population, it actually helps Hierochloe odorata, increasing both their “number and vigor.” This context conveys the idea that even though it seems counterintuitive, the Indigenous method of harvesting Hierochloe odorata actually replenishes the wild population.

Choice A is incorrect. Although a harvesting method could be used to select for certain traits in plants, it’s not clear what it would mean for a harvesting method to select “wild populations” of plants. Choice B is incorrect because as used in this context, “originates” means creates. The text doesn’t address the origin of Hierochloe odorata, but rather how the Indigenous harvesting method affects it. Choice C is incorrect because in this context, “conditions” means to influence someone or something to behave in a certain way, and the text doesn’t suggest the new plants that replace the harvested ones differ in any meaningful way, or in any way that could be the result of conditioning.

"}, {"id": "df46a2ee", "domain": "Craft and Structure", "skill": "Text Structure and Purpose", "difficulty": "M", "type": "mc", "stimulus": "

The following text is from Joseph Conrad’s 1907 novel The Secret Agent: A Simple Tale. Mr. Verloc is navigating the London streets on his way to a meeting.

\n

Before reaching Knightsbridge, Mr. Verloc took a turn to the left out of the busy main thoroughfare, uproarious with the traffic of swaying omnibuses and trotting vans, in the almost silent, swift flow of hansoms [horse-drawn carriages]. Under his hat, worn with a slight backward tilt, his hair had been carefully brushed into respectful sleekness; for his business was with an Embassy. And Mr. Verloc, steady like a rock—a soft kind of rock—marched now along a street which could with every propriety be described as private.

", "stem": "

Which choice best describes the function of the underlined phrase in the text as a whole?

", "choices": [{"id": "A", "text": "

It qualifies an earlier description of Mr. Verloc.

"}, {"id": "B", "text": "

It emphasizes an internal struggle Mr. Verloc experiences. 

"}, {"id": "C", "text": "

It contrasts Mr. Verloc with his surroundings.

"}, {"id": "D", "text": "

It reveals a private opinion Mr. Verloc holds. 

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. The underline phrase qualifies (meaning adds limits or conditions to) the description of Mr. Verloc as “steady like a rock,” adding that he is a “soft” rock.

Choice B is incorrect. In fact, the passage never mentions Mr. Verloc experiencing any internal struggles. Choice C is incorrect. The underlined phrase doesn’t contrast Mr. Verloc with his surroundings, but is instead modifying the description of him as a rock. Choice D is incorrect. The underlined phrase doesn’t reveal a private opinion Mr. Verloc holds: instead, it further describes his character for the reader.

"}, {"id": "5a278f24", "domain": "Craft and Structure", "skill": "Words in Context", "difficulty": "M", "type": "mc", "stimulus": "

The work of molecular biophysicist Enrique M. De La Cruz is known for ______blank traditional boundaries between academic disciplines. The university laboratory that De La Cruz runs includes engineers, biologists, chemists, and physicists, and the research the lab produces makes use of insights and techniques from all those fields.

", "stem": "

Which choice completes the text with the most logical and precise word or phrase?

", "choices": [{"id": "A", "text": "

epitomizing

"}, {"id": "B", "text": "

transcending

"}, {"id": "C", "text": "

anticipating

"}, {"id": "D", "text": "

reinforcing

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. Based on the text, we’re looking for a word that means something similar to \"mak[ing] use of insights and techniques from all those fields.\" \"Transcending\" means \"going beyond,\" so \"transcending traditional boundaries\" would mean crossing into all those various fields of research, which is exactly the meaning we want.

Choice A is incorrect. This isn’t a logical word choice. Based on the text, we’re looking for a word that means something similar to \"mak[ing] use of insights and techniques from all those fields.\" To \"epitomize\" means to \"be a perfect example of,\" so \"epitomizing traditional boundaries\" would mean the opposite of what we want: keeping the fields of research separate. Choice C is incorrect. This isn’t a logical word choice. Based on the text, we’re looking for a word that means something similar to \"mak[ing] use of insights and techniques from all those fields.\" \"Anticipating\" means \"expecting\" or \"waiting for,\" and would result in a confusing sentence with an unclear meaning. Choice D is incorrect. This isn’t a logical word choice. Based on the text, we’re looking for a word that means something similar to \"mak[ing] use of insights and techniques from all those fields.\" \"Reinforcing traditional boundaries\" would mean the opposite: keeping the fields of research separate.

"}, {"id": "76e4c51d", "domain": "Craft and Structure", "skill": "Words in Context", "difficulty": "H", "type": "mc", "stimulus": "

The güiro, a musical instrument traditionally made from a dried and hollowed gourd, is thought to have originated with the Taíno people of Puerto Rico. Players use a wooden stick to scrape along ridges cut into the side of the gourd, creating sounds that are highly ______blank: the sounds produced by güiros can differ based on the distance between the ridges, the types of strokes the player uses, and the thickness of the gourd.

", "stem": "

Which choice completes the text with the most logical and precise word or phrase?

", "choices": [{"id": "A", "text": "

overlooked

"}, {"id": "B", "text": "

powerful

"}, {"id": "C", "text": "

routine

"}, {"id": "D", "text": "

variable

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer because it most logically completes the text’s discussion of the sounds made by güiros. In this context, “variable” means able to change. The text begins by explaining that güiros are instruments made out of hollowed gourds with ridges cut into their sides and that players scrape the ridges with wooden sticks to produce sounds. The text goes on to say that güiros’ sounds can change depending on gourd thickness, the distance between ridges, and the types of strokes the player uses, thus supporting the idea that the sounds created by these instruments are variable.

Choice A is incorrect because “overlooked” means not being seen or noticed, and there is nothing in the text to suggest that the sounds produced by güiros are overlooked or not noticed. Choice B is incorrect because in this context, “powerful” would mean having a great ability to produce an effect. While it’s possible that the sounds produced by güiros have a strong effect on listeners, the text doesn’t discuss this aspect of their sounds. Choice C is incorrect because “routine” means usual and unvarying, and there is nothing in the text to suggest that the sounds produced by güiros are unvarying. In fact, the text describes how the sounds produced by güiros can differ based on several factors. 

"}, {"id": "a2835734", "domain": "Craft and Structure", "skill": "Words in Context", "difficulty": "E", "type": "mc", "stimulus": "

Visual artist Gabriela Alemán states that the bold colors of comics, pop art, and Latinx culture have always fascinated her. This passion for the rich history and colors of her Latinx community translates into the ______blank artworks she produces.

", "stem": "

Which choice completes the text with the most logical and precise word or phrase?

", "choices": [{"id": "A", "text": "

vivid

"}, {"id": "B", "text": "

unknown

"}, {"id": "C", "text": "

definite

"}, {"id": "D", "text": "

reserved

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. \"Vivid\" can mean \"colorful\" or \"bright-colored.\" This definition fits the context clues about Alemán’s fascination with and passion for bold colors.

Choice B is incorrect. This doesn’t fit the logic of the text. Nothing in the text indicates that Alemán’s artworks are \"unknown.\" Choice C is incorrect. This doesn’t fit the logic of the text. \"Definite\" means \"certain\" or \"decided.\" It wouldn’t make sense to describe artwork as \"definite.\" Choice D is incorrect. This doesn’t fit the logic of the text. \"Reserved\" can either mean \"slow to reveal emotions\" or \"booked.\" But the clues suggest that Alemán’s artworks are boldly colorful—almost the opposite of \"reserved.\"

"}, {"id": "ff97fd53", "domain": "Craft and Structure", "skill": "Text Structure and Purpose", "difficulty": "M", "type": "mc", "stimulus": "

In 1973, poet Miguel Algarín started inviting other writers who, like him, were Nuyorican—a term for New Yorkers of Puerto Rican heritage—to gather in his apartment to present their work. The gatherings were so well attended that Algarín soon had to rent space in a cafe to accommodate them. Thus, the Nuyorican Poets Cafe was born. Moving to a permanent location in 1981, the Nuyorican Poets Cafe expanded its original scope beyond the written word, hosting art exhibitions and musical performances as well. Half a century since its inception, it continues to foster emerging Nuyorican talent.

", "stem": "

Which choice best describes the overall purpose of the text?

", "choices": [{"id": "A", "text": "

To explain what motivated Algarín to found the Nuyorican Poets Cafe

"}, {"id": "B", "text": "

To situate the Nuyorican Poets Cafe within the cultural life of New York as a whole

"}, {"id": "C", "text": "

To discuss why the Nuyorican Poets Cafe expanded its scope to include art and music

"}, {"id": "D", "text": "

To provide an overview of the founding and mission of the Nuyorican Poets Cafe

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. The text presents a brief history of the Nuyorican Poets Cafe, from how it got started in the ’70s, to its expansion in the ’80s, to its ongoing mission today.

Choice A is incorrect. This isn’t the overall purpose. The text never mentions Algarín’s motivations. Choice B is incorrect. This isn’t the overall purpose. The text never discusses the cultural life of New York as a whole. Choice C is incorrect. This is too narrow. One sentence mentions that the Nuyorican Poets Cafe expanded its scope to include art and music, but this is only one point in the broader history of the Nuyorican Poets Cafe, which is the overall focus of the text.

"}, {"id": "c61a7c4a", "domain": "Craft and Structure", "skill": "Text Structure and Purpose", "difficulty": "H", "type": "mc", "stimulus": "

Some studies have suggested that posture can influence cognition, but we should not overstate this phenomenon. A case in point: In a 2014 study, Megan O’Brien and Alaa Ahmed had subjects stand or sit while making risky simulated economic decisions. Standing is more physically unstable and cognitively demanding than sitting; accordingly, O’Brien and Ahmed hypothesized that standing subjects would display more risk aversion during the decision-making tasks than sitting subjects did, since they would want to avoid further feelings of discomfort and complicated risk evaluations. But O’Brien and Ahmed actually found no difference in the groups’ performance. 

", "stem": "

Which choice best states the main purpose of the text?

", "choices": [{"id": "A", "text": "

It argues that research findings about the effects of posture on cognition are often misunderstood, as in the case of O’Brien and Ahmed’s study.

"}, {"id": "B", "text": "

It presents the study by O’Brien and Ahmed to critique the methods and results reported in previous studies of the effects of posture on cognition. 

"}, {"id": "C", "text": "

It explains a significant problem in the emerging understanding of posture’s effects on cognition and how O’Brien and Ahmed tried to solve that problem. 

"}, {"id": "D", "text": "

It discusses the study by O’Brien and Ahmed to illustrate why caution is needed when making claims about the effects of posture on cognition. 

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer because it most accurately describes the main purpose of the text. The text notes that although some studies have suggested that posture may have an effect on cognition, this phenomenon should not be overstated. In other words, the text begins by urging caution and restraint when discussing the effects of posture on cognition, implying that even though some studies have shown posture to affect cognition, we should not assume that posture always affects cognition or does so in a strong way. The text goes on to discuss O’Brien and Ahmed’s study as a \"case in point\" (that is, as an example of the point made previously). According to the text, O’Brien and Ahmed hypothesized that since standing is more cognitively demanding than sitting, standing subjects in their experiment would respond differently to decision-making tasks than sitting subjects would, which would show an effect of posture on cognition. What the researchers actually found, however, was that the standing and sitting subjects performed the same—posture did not affect cognition. By presenting a circumstance in which posture does not appear to affect cognition, the discussion of O’Brien and Ahmed’s study shows why it is important not to overstate the phenomenon. The purpose of the text, therefore, is to discuss O’Brien and Ahmed’s study to illustrate why caution is needed when making claims about posture’s effects on cognition.

Choice A is incorrect because the text discusses O’Brien and Ahmed’s study as an example of why caution is needed when discussing posture’s effects on cognition, not as an example of how research findings related to posture and cognition are often misunderstood. Although the text does warn against misunderstanding the scope of the relationship between posture and cognition that has been reported in some previous studies, O’Brien and Ahmed’s study is not one of those studies, and there is no suggestion that anyone has misunderstood O’Brien and Ahmed’s findings. Choice B is incorrect because the text makes no mention of the methods used in previous studies of the effects of posture on cognition. Although the text does urge caution when discussing posture’s effects on cognition, it does not critique the results of studies that suggested that posture can affect cognition. Instead, the text suggests that such results should not be exaggerated or taken too broadly. Choice C is incorrect because although the text implies that overstating posture’s effects on cognition would be a problem, nothing in the text suggests that O’Brien and Ahmed share that view or that they attempted to solve that problem. O’Brien and Ahmed are presented as hypothesizing that posture would affect cognition in their study, not as trying to resolve the problem the text describes.

"}, {"id": "acb852e7", "domain": "Craft and Structure", "skill": "Text Structure and Purpose", "difficulty": "M", "type": "mc", "stimulus": "

The following text is from the 1923 poem “Black Finger” by Angelina Weld Grimké, a Black American writer. A cypress is a type of evergreen tree.

\n\n

I have just seen a most beautiful thing,
Slim and still,
 Against a gold, gold sky,
 A straight black cypress,
Sensitive,
Exquisite,
A black finger
Pointing upwards.
Why, beautiful still finger, are you black?
And why are you pointing upwards?

", "stem": "

Which choice best describes the overall structure of the text?

", "choices": [{"id": "A", "text": "

The speaker assesses a natural phenomenon, then questions the accuracy of her assessment.

"}, {"id": "B", "text": "

The speaker describes a distinctive sight in nature, then ponders what meaning to attribute to that sight.

"}, {"id": "C", "text": "

The speaker presents an outdoor scene, then considers a human behavior occurring within that scene.

"}, {"id": "D", "text": "

The speaker examines her surroundings, then speculates about their influence on her emotional state.

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer because it most accurately describes the overall structure of the text. First, the speaker describes observing a “most beautiful” sight: a tree (“black cypress”) standing out from the golden sky behind it, looking like a person’s finger “pointing upwards” and appearing “sensitive” and “exquisite.” Then the speaker wonders about the image’s meaning, asking why the finger is black and why it’s pointing upward. Thus, the text moves from the speaker’s description of a distinctive sight in nature to her pondering about what meaning to attribute to that sight.

Choice A is incorrect because the speaker assesses a natural sight—a “black cypress” tree standing “against a gold, gold sky” like a pointed finger—but doesn’t question the accuracy of her own assessment. Although she wonders why the finger, which is really a tree, is black and why it’s pointing, the speaker doesn’t suggest that her belief that the tree resembles a finger is wrong. Choice C is incorrect. Although the speaker describes seeing a “black cypress” tree standing “against a gold, gold sky” like a pointed finger, she wonders about that natural image (asking why the finger, which is really a tree, is black and why it’s pointing) and doesn’t give any indication that any people are present in the scene. Choice D is incorrect. Although the speaker examines and wonders about one thing in her surroundings—a “black cypress” tree standing “against a gold, gold sky” like a pointed finger—she doesn’t address her own emotional state or consider how it’s affected by her surroundings.

"}, {"id": "98364791", "domain": "Craft and Structure", "skill": "Words in Context", "difficulty": "H", "type": "mc", "stimulus": "

In studying the use of external stimuli to reduce the itching sensation caused by an allergic histamine response, Louise Ward and colleagues found that while harmless applications of vibration or warming can provide a temporary distraction, such ______blank stimuli actually offer less relief than a stimulus that seems less benign, like a mild electric shock.

", "stem": "

Which choice completes the text with the most logical and precise word or phrase?

", "choices": [{"id": "A", "text": "

deceptive

"}, {"id": "B", "text": "

innocuous

"}, {"id": "C", "text": "

novel

"}, {"id": "D", "text": "

impractical

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer because it most logically completes the text’s discussion of Ward and colleagues’ findings. As used in this context, “innocuous” means mild or unharmful. The text describes the vibration and warming that Ward and colleagues used to alleviate itching as “harmless applications” and goes on to contrast these applications with another stimulus that actually offers more relief even though it seems to be stronger and “less benign.” This context conveys the idea that vibration and warming were innocuous stimuli. 

Choice A is incorrect because the text focuses on a distinction between harmless stimuli and those that seem to be less benign. Nothing in the text suggests that any of the treatments are “deceptive,” or misleading; indeed, even the less effective ones are described as offering some relief. Choice C is incorrect because the text focuses on the amount of relief from itching offered by harmless stimuli and those that seem to be less benign. The text doesn’t suggest that any of these stimuli are “novel,” or original and new; heat, vibration, and electricity aren’t new inventions. Choice D is incorrect because it wouldn’t make sense to describe an application of vibration or warming as “impractical,” or not suitable for use. The text indicates that these harmless applications are useful in that they offer at least some temporary relief.

"}, {"id": "aa5897b8", "domain": "Craft and Structure", "skill": "Text Structure and Purpose", "difficulty": "H", "type": "mc", "stimulus": "

In Jane Austen’s novel Mansfield Park, an almost imperceptible smile from potential suitor Henry Crawford causes the protagonist Fanny Price to blush; her embarrassment grows when she suspects that he is aware of it. This moment—in which Fanny not only infers Henry’s mental state through his gestures, but also infers that he is drawing inferences about her mental state—illustrates what literary scholar George Butte calls “deep intersubjectivity,” a technique for representing interactions between consciousnesses through which Austen’s novels derive much of their social and psychological drama.

", "stem": "

Which choice best describes the function of the underlined sentence in the text as a whole?

", "choices": [{"id": "A", "text": "

It states a claim about Austen’s skill at representing psychological complexity that is reinforced by an example presented in the following sentence. 

"}, {"id": "B", "text": "

It advances an interpretation of an Austen protagonist who is contrasted with protagonists from other Austen novels cited in the following sentence. 

"}, {"id": "C", "text": "

It describes a recurring theme in Austen’s novels that is the focus of a literary scholar’s analysis summarized in the following sentence. 

"}, {"id": "D", "text": "

It provides a synopsis of an interaction in an Austen novel that illustrates a literary concept discussed in the following sentence. 

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. The underlined sentence provides a concrete example to ground readers’ understanding of the “deep intersubjectivity” described in the next sentence as central to Austen’s work.

Choice A is incorrect. There is no evaluation made of Austen’s skill in this sentence, and no examples are given in the following sentence. This choice essentially flips the paragraph: it’s this first sentence that provides an example. Choice B is incorrect. There are no other Austen protagonists mentioned in this passage, so this couldn’t be the answer. Choice C is incorrect. The underlined sentence doesn’t identify any “recurring theme,” but instead simply describes one interaction from one book. This interaction exemplifies the literary technique of “deep intersubjectivity” that is introduced in the next sentence.

"}, {"id": "a4ca92fd", "domain": "Craft and Structure", "skill": "Words in Context", "difficulty": "E", "type": "mc", "stimulus": "

Beginning in the 1950s, Navajo Nation legislator Annie Dodge Wauneka continuously worked to promote public health; this ______blank effort involved traveling throughout the vast Navajo homeland and writing a medical dictionary for speakers of Diné bizaad, the Navajo language.

", "stem": "

Which choice completes the text with the most logical and precise word or phrase?

", "choices": [{"id": "A", "text": "

impartial

"}, {"id": "B", "text": "

offhand

"}, {"id": "C", "text": "

persistent

"}, {"id": "D", "text": "

mandatory

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer because it most logically completes the text’s discussion of Annie Dodge Wauneka’s work as a Navajo Nation legislator. As used in this context, “persistent” means existing continuously. The text states that Wauneka “continuously worked to promote public health,” traveling extensively and authoring a medical dictionary; this indicates that Wauneka’s effort was persistent.

Choice A is incorrect because describing Wauneka’s effort related to public health as “impartial,” or not partial or biased and treating all things equally, wouldn’t make sense in context. The text suggests that Wauneka’s continuous work was partial in one way, as she focused specifically on promoting public health throughout the Navajo homeland and to speakers of the Navajo language. Choice B is incorrect because the text emphasizes that Wauneka’s effort to promote public health as a Navajo Nation legislator was continuous and extensive, involving wide travels and the authoring of a medical dictionary. Because this work clearly involved care and dedication, it wouldn’t make sense to describe it as “offhand,” or casual and informal. Choice D is incorrect because nothing in the text suggests that Wauneka’s effort to promote public health was “mandatory,” or required by law or rule, even though Wauneka was a Navajo Nation legislator. Rather than suggesting that Wauneka’s effort was required for any reason, the text emphasizes the continuous and extensive nature of her work.

"}, {"id": "8de51658", "domain": "Craft and Structure", "skill": "Cross-Text Connections", "difficulty": "M", "type": "mc", "stimulus": "

Text 1

\n

The idea that time moves in only one direction is instinctively understood, yet it puzzles physicists. According to the second law of thermodynamics, at a macroscopic level some processes of heat transfer are irreversible due to the production of entropy—after a transfer we cannot rewind time and place molecules back exactly where they were before, just as we cannot unbreak dropped eggs. But laws of physics at a microscopic or quantum level hold that those processes should be reversible.

\n

 

\n

Text 2

\n

In 2015, physicists Tiago Batalhão et al. performed an experiment in which they confirmed the irreversibility of thermodynamic processes at a quantum level, producing entropy by applying a rapidly oscillating magnetic field to a system of carbon-13 atoms in liquid chloroform. But the experiment “does not pinpoint ... what causes [irreversibility] at the microscopic level,” coauthor Mauro Paternostro said.

", "stem": "

Based on the texts, what would the author of Text 1 most likely say about the experiment described in Text 2?

", "choices": [{"id": "A", "text": "

It would suggest an interesting direction for future research were it not the case that two of the physicists who conducted the experiment disagree on the significance of its findings.

"}, {"id": "B", "text": "

It provides empirical evidence that the current understanding of an aspect of physics at a microscopic level must be incomplete.

"}, {"id": "C", "text": "

It is consistent with the current understanding of physics at a microscopic level but not at a macroscopic level.

"}, {"id": "D", "text": "

It supports a claim about an isolated system of atoms in a laboratory, but that claim should not be extrapolated to a general claim about the universe.

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. Author 1 describes the puzzle that physicists still can’t solve: at a microscopic level, the “laws of physics” suggest that we should be able to reverse processes that are not reversible at a macroscopic level (and, maybe, turn back time!). The experiment confirmed that those processes are not reversible even on the microscopic level, but it didn’t explain why. This supports Author 1’s point that physicists still don’t fully understand how things work at a microscopic level—maybe the laws need to be revised.

Choice A is incorrect. We can’t infer that the author of Text 1 would respond this way to the experiment. Text 2 does name two of the physicists involved in the experiment, but it never suggests that they disagree on anything. Choice C is incorrect. This is the opposite of what the experiment suggests. The experiment confirmed that the macroscopic-level law (“these things can’t be reversed—like time”) was still true on the microscopic level—meaning it supports the current understanding of physics at a macroscopic level. Choice D is incorrect. We can’t infer that the author of Text 1 would respond this way to the experiment. Neither text makes this distinction between laboratory findings and the way the universe works in general.

"}, {"id": "e0656211", "domain": "Craft and Structure", "skill": "Words in Context", "difficulty": "M", "type": "mc", "stimulus": "

In Nature Poem (2017), Kumeyaay poet Tommy Pico portrays his ______blank the natural world by honoring the centrality of nature within his tribe’s traditional beliefs while simultaneously expressing his distaste for being in wilderness settings himself.

", "stem": "

Which choice completes the text with the most logical and precise word or phrase?

", "choices": [{"id": "A", "text": "

responsiveness to

"}, {"id": "B", "text": "

ambivalence toward

"}, {"id": "C", "text": "

renunciation of

"}, {"id": "D", "text": "

mastery over

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer because it most logically completes the text’s description of how Pico feels about the natural world. In this context, to say that Pico portrays his “ambivalence toward” nature would mean that he portrays his mixed feelings about nature. The text explains that Pico “honors the centrality of nature” and also makes it clear that he doesn’t enjoy being in nature. This context suggests that Pico feels ambivalence toward nature.

Choice A is incorrect because saying that Pico portrays his “responsiveness to” nature would mean that he portrays himself as quick to react to nature, which isn’t supported by the text. Instead, the text focuses on Pico’s mixed feelings toward nature, describing him as both honoring nature’s role in his tribe’s beliefs and expressing his personal dislike for being in nature. Choice C is incorrect because saying that Pico portrays his “renunciation of” nature would mean that he portrays himself as rejecting nature, which isn’t supported by the text. The text conveys that Pico demonstrates both positive and negative responses toward nature, not that he’s giving it up completely. Choice D is incorrect because saying that Pico portrays his “mastery over” nature would mean that he portrays himself as having control over nature, which isn’t supported by the text. The text focuses on Pico’s mixed feelings about nature; nothing in the text suggests that Pico feels mastery over nature.

"}, {"id": "9421ed62", "domain": "Craft and Structure", "skill": "Text Structure and Purpose", "difficulty": "E", "type": "mc", "stimulus": "

In 2007, computer scientist Luis von Ahn was working on converting printed books into a digital format. He found that some words were distorted enough that digital scanners couldn’t recognize them, but most humans could easily read them. Based on that finding, von Ahn invented a simple security test to keep automated “bots” out of websites. The first version of the reCAPTCHA test asked users to type one known word and one of the many words scanners couldn’t recognize. Correct answers proved the users were humans and added data to the book-digitizing project.

", "stem": "

Which choice best states the main purpose of the text?

", "choices": [{"id": "A", "text": "

To discuss von Ahn’s invention of reCAPTCHA

"}, {"id": "B", "text": "

To explain how digital scanners work

"}, {"id": "C", "text": "

To call attention to von Ahn’s book-digitizing project

"}, {"id": "D", "text": "

To indicate how popular reCAPTCHA is

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer because it most accurately states the main purpose of the text. After providing a brief introduction to computer scientist Luis von Ahn, the text focuses on discussing how von Ahn’s digitization work led to the invention of a digital security test known as reCAPTCHA.

Choice B is incorrect because the text doesn’t address how digital scanners work. Choice C is incorrect. Although the text mentions von Ahn’s book-digitizing project, that information is provided as a detail, not as the main purpose of the text. Choice D is incorrect because the text doesn’t provide any indication of reCAPTCHA’s popularity; instead, it describes reCAPTCHA’s origin.

"}, {"id": "7d84fe2b", "domain": "Craft and Structure", "skill": "Words in Context", "difficulty": "E", "type": "mc", "stimulus": "

Particle physicists like Ayana Holloway Arce and Aida El-Khadra spend much of their time ______blank what is invisible to the naked eye: using sophisticated technology, they closely examine the behavior of subatomic particles, the smallest detectable parts of matter.

", "stem": "

Which choice completes the text with the most logical and precise word or phrase?

", "choices": [{"id": "A", "text": "

selecting

"}, {"id": "B", "text": "

inspecting

"}, {"id": "C", "text": "

creating

"}, {"id": "D", "text": "

deciding

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer because it most logically completes the text’s discussion of the work of particle physicists. In this context, “inspecting” means viewing closely in order to examine. The text indicates that as particle physicists, Arce and El-Khadra’s work involves using advanced technology to “closely examine” subatomic particles. In other words, they use technology to inspect small parts of matter that can’t be seen by the naked eye.

Choice A is incorrect because nothing in the text suggests that Arce and El-Khadra spend time “selecting,” or choosing, subatomic particles for some purpose; the text simply states that the particle physicists use advanced technology to see and study the behavior of those tiny parts of matter. Choice C is incorrect because nothing in the text suggests that Arce and El-Khadra spend time “creating” subatomic particles, or bringing them into existence; the text simply states that the particle physicists use advanced technology to see and study the behavior of those tiny parts of matter. Choice D is incorrect. In this context, “deciding” would mean making a final choice or judgment about something. It wouldn’t make sense to say that particle physicists get to choose what is and isn’t visible to the naked eye, especially when the text presents it as fact that subatomic particles are “the smallest detectable parts of matter” and would therefore be invisible. The text focuses on Arce and El-Khadra’s close observation of those particles, not on any decisions they might make. 

"}, {"id": "d2eb1df1", "domain": "Craft and Structure", "skill": "Words in Context", "difficulty": "E", "type": "mc", "stimulus": "

In recommending Bao Phi’s collection Sông I Sing, a librarian noted that pieces by the spoken-word poet don’t lose their ______blank nature when printed: the language has the same pleasant musical quality on the page as it does when performed by Phi.

", "stem": "

Which choice completes the text with the most logical and precise word or phrase?

", "choices": [{"id": "A", "text": "

scholarly

"}, {"id": "B", "text": "

melodic

"}, {"id": "C", "text": "

jarring

"}, {"id": "D", "text": "

personal

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. Based on the text, we’re looking for a word that means something similar to “pleasant musical quality.” That’s exactly what “melodic” means.

Choice A is incorrect. This isn’t a logical word choice. Based on the text, we’re looking for a word that means something similar to “pleasant musical quality.” “Scholarly” would suggest something that is academic or well-researched, which doesn’t match the meaning we’re looking for. Choice C is incorrect. This isn’t a logical word choice. Based on the text, we’re looking for a word that means something similar to “pleasant musical quality.” “Jarring” would suggest the opposite: something unpleasant or discordant. Choice D is incorrect. This isn’t a logical word choice. Based on the text, we’re looking for a word that means something similar to “pleasant musical quality.” “Personal” would suggest something that is expressive or intimate, which doesn’t match the meaning we’re looking for.

"}, {"id": "d72b325e", "domain": "Craft and Structure", "skill": "Cross-text Connections", "difficulty": "H", "type": "mc", "stimulus": "

Text 1

\n

What factors influence the abundance of species in a given ecological community? Some theorists have argued that historical diversity is a major driver of how diverse an ecological community eventually becomes: differences in community diversity across otherwise similar habitats, in this view, are strongly affected by the number of species living in those habitats at earlier times. 

\n

Text 2

\n

In 2010, a group of researchers including biologist Carla Cáceres created artificial pools in a New York forest. They stocked some pools with a diverse mix of zooplankton species and others with a single zooplankton species and allowed the pool communities to develop naturally thereafter. Over the course of four years, Cáceres and colleagues periodically measured the species diversity of the pools, finding—contrary to their expectations—that by the end of the study there was little to no difference in the pools’ species diversity. 

", "stem": "

Based on the texts, how would Cáceres and colleagues (Text 2) most likely describe the view of the theorists presented in Text 1?

", "choices": [{"id": "A", "text": "

It is largely correct, but it requires a minor refinement in light of the research team’s results.

"}, {"id": "B", "text": "

It is not compelling as a theory regardless of any experimental data collected by the research team.

"}, {"id": "C", "text": "

It may seem plausible, but it is not supported by the research team’s findings. 

"}, {"id": "D", "text": "

It probably holds true only in conditions like those in the research team’s study.

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. This is how Cáceres and co. would most likely describe the view presented in Text 1. The view in Text 1 is that historical diversity affects how diverse an ecological community eventually becomes. But Cáceres and co. did not get this result: they found no difference in eventual diversity between a zooplankton pool that started out diverse and a zooplankton pool that started out with only a single species.

Choice A is incorrect. Cáceres and co. would probably not describe the view presented in Text 1 this way. The view in Text 1 is that historical diversity affects how diverse an ecological community eventually becomes. Cáceres and co’s findings directly undermine this view: they found no difference in eventual diversity between a zooplankton pool that started out diverse and a zooplankton pool that started out with only a single species. Choice B is incorrect. Cáceres and co. would probably not describe the view presented in Text 1 this way. Their experiment was designed to test this hypothesis, and their findings were \"contrary to their expectations.\" In other words, before the study, they predicted the theory was correct. Choice D is incorrect. Cáceres and co. would not describe the view presented in Text 1 this way. Their research finding directly undermines the view presented in Text 1: so it definitely doesn’t hold true in conditions like those in the study.

"}, {"id": "cb526866", "domain": "Craft and Structure", "skill": "Words in Context", "difficulty": "E", "type": "mc", "stimulus": "

The recent discovery of a carved wooden figure dating to around 2,000 years ago in a ditch in England was truly surprising. Wooden objects ______blank survive for so long due to their high susceptibility to rot, but archaeologists suspect layers of sediment in the ditch preserved the figure by creating an oxygen-free environment.

", "stem": "

Which choice completes the text with the most logical and precise word or phrase?

", "choices": [{"id": "A", "text": "

sturdily

"}, {"id": "B", "text": "

carelessly

"}, {"id": "C", "text": "

rarely

"}, {"id": "D", "text": "

simply

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer because it most logically completes the text’s discussion of the discovery of a carved wooden figure dating to around 2,000 years ago. In this context, “rarely” means infrequently. The text states that the discovery of the figure was “truly surprising” and notes that wooden objects are highly prone to rot. This context conveys the idea that wooden objects infrequently survive for as long as the carved figure has survived.

Choice A is incorrect because “sturdily” means strongly, which wouldn’t make sense in context. If wooden objects in general could strongly survive for long periods of time, then the discovery of a wooden figure that’s around 2,000 years old wouldn’t be surprising. Choice B is incorrect because “carelessly” means accidentally. The text conveys the idea that wooden objects in general don’t survive for very long because they rot, not that wooden objects in general accidentally survive despite this. Choice D is incorrect because the text conveys the idea that wooden objects in general don’t survive for very long because they rot, not that wooden objects in general “simply,” or merely, survive for long periods of time. If wooden objects in general could merely survive for as long as the figure has survived, then the discovery of the figure wouldn’t have been surprising.

"}, {"id": "83687083", "domain": "Craft and Structure", "skill": "Words in Context", "difficulty": "E", "type": "mc", "stimulus": "

Due to their often strange images, highly experimental syntax, and opaque subject matter, many of John Ashbery’s poems can be quite difficult to ______blank and thus are the object of heated debate among scholars.

", "stem": "

Which choice completes the text with the most logical and precise word or phrase?

", "choices": [{"id": "A", "text": "

delegate

"}, {"id": "B", "text": "

compose

"}, {"id": "C", "text": "

interpret

"}, {"id": "D", "text": "

renounce

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer because it most logically completes the text’s discussion of John Ashbery’s poems. As used in this context, “interpret” would mean decipher the meaning of. The text indicates that Ashbery’s poems have many unusual features, that it’s difficult to tell what exactly the poems’ subject matter is, and that scholars strongly disagree about the poems. This context conveys the idea that it’s difficult to interpret Ashbery’s poems. 

Choice A is incorrect because “delegate” means to assign someone as a representative of another person or to entrust something to someone else, neither of which would make sense in context. The text is focused only on the difficulty that readers have interpreting Ashbery’s poems due to their many unusual features; it doesn’t suggest anything about the poems being difficult to delegate. Choice B is incorrect because describing Ashbery’s poems as difficult to “compose,” or put together or produce, would make sense only if the text were about Ashbery’s experience of writing the poems. It could be true that it was difficult for Ashbery to compose his poems, but the text doesn’t address this; it instead discusses how readers interpret and engage with the poems. Choice D is incorrect because describing Ashbery’s poems as being difficult to “renounce,” or give up or refuse, wouldn’t make sense in context. The text focuses on the idea that features of Ashbery’s poems are odd or unclear and have caused heated scholarly debate. This context suggests that the poems are difficult to interpret, not that the poems are difficult to renounce.

"}, {"id": "637d0878", "domain": "Craft and Structure", "skill": "Words in Context", "difficulty": "E", "type": "mc", "stimulus": "

The Appalachian Trail is a hiking path in the eastern United States. Much of the 2,000 mile trail passes through wilderness areas. In order to ______blank those areas, the United States Congress passed the National Trails System Act in 1968, ensuring that the trail would not be sold or commercially developed.

", "stem": "

Which choice completes the text with the most logical and precise word or phrase?

", "choices": [{"id": "A", "text": "

borrow

"}, {"id": "B", "text": "

postpone

"}, {"id": "C", "text": "

protect

"}, {"id": "D", "text": "

decorate

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. \"Protect\" means \"preserve\" or \"keep safe from.\" By ensuring that the wilderness areas along the Appalachian Trail can’t be sold or developed, the National Trails System Act protects them.

Choice A is incorrect. \"Borrow\" means \"to take something with intent to return it.\" The text doesn’t say anything about taking and returning the wilderness that surrounds the Appalachian Trail. Choice B is incorrect. \"Postpone\" means \"to put off until later.\" Nothing in the passage suggests that Congress wants to \"postpone\" the wilderness areas (and that doesn’t make sense anyway—they can postpone doing something to the wilderness areas, but they can’t postpone the areas themselves). Choice D is incorrect. \"Decorate\" means \"to adorn\" or \"add extra items or pictures to make more attractive.\" No details in the text suggest that Congress wishes to make the trail fancier or more attractive.

"}, {"id": "39857700", "domain": "Craft and Structure", "skill": "Text Structure and Purpose", "difficulty": "H", "type": "mc", "stimulus": "

The following text is from Edith Wharton’s 1905 novel The House of Mirth. Lily Bart and a companion are walking through a park.

\n

Lily had no real intimacy with nature, but she had a passion for the appropriate and could be keenly sensitive to a scene which was the fitting background of her own sensations. The landscape outspread below her seemed an enlargement of her present mood, and she found something of herself in its calmness, its breadth, its long free reaches. On the nearer slopes the sugar-maples wavered like pyres of light; lower down was a massing of grey orchards, and here and there the lingering green of an oak-grove.

", "stem": "

Which choice best describes the function of the underlined sentence in the text as a whole?

", "choices": [{"id": "A", "text": "

It creates a detailed image of the physical setting of the scene.

"}, {"id": "B", "text": "

It establishes that a character is experiencing an internal conflict.

"}, {"id": "C", "text": "

It makes an assertion that the next sentence then expands on.

"}, {"id": "D", "text": "

It illustrates an idea that is introduced in the previous sentence.

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer because it best describes how the underlined sentence functions in the text as a whole. The first sentence of the text establishes that Lily can be “keenly sensitive to” scenes that serve as a “fitting background” for her feelings—that is, she’s very aware of when a setting seems to reflect her mood. The next sentence, which is underlined, then demonstrates this awareness: Lily views the landscape she’s in as a large-scale reflection of her current mood, identifying with elements such as its calmness. Thus, the function of the underlined sentence is to illustrate an idea introduced in the previous sentence.

Choice A is incorrect because the underlined sentence describes the scene only in very general terms, referring to its calmness, breadth, and long stretches of land. It’s the next sentence that adds specific details about colors, light, and various trees nearby. Choice B is incorrect because nothing in the underlined sentence suggests that Lily is experiencing an internal conflict. In fact, the sentence indicates that Lily thinks the landscape reflects her own feeling of calmness. Choice C is incorrect because the only assertion in the underlined sentence is that Lily feels that broad aspects of the landscape, such as its calmness, reflect her current mood, and that assertion isn’t expanded on in the next sentence. Instead, the next sentence describes specific details of the scene without connecting them to Lily’s feelings.

"}, {"id": "e929fe98", "domain": "Craft and Structure", "skill": "Text Structure and Purpose", "difficulty": "E", "type": "mc", "stimulus": "

Composer Florence Price won first place for her score Symphony in E Minor at the 1932 Wanamaker Foundation Awards. The piece was performed the following year by the Chicago Symphony Orchestra, a significant recognition of its quality. Price continued to compose many musical pieces throughout her career, blending traditional Black spirituals with classical European Romantic musical traditions. In recent years, Price’s concertos and symphonies have been performed and recorded by several major orchestras, further preserving her work for others to enjoy.

", "stem": "

Which choice best states the main purpose of the text?

", "choices": [{"id": "A", "text": "

To provide examples of Price’s importance as a composer

"}, {"id": "B", "text": "

To argue that more major orchestras should perform Price’s compositions

"}, {"id": "C", "text": "

To describe the musical styles that inspired many of Price’s symphonies

"}, {"id": "D", "text": "

To compare Price’s scores with those of classical European composers

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. The text provides an overview of Florence Price’s importance by describing her success at the 1932 Wanamaker Foundation Awards, her blending of Black spirituals and classical European Romantic musical traditions, and the recent performances and recordings of her concertos and symphonies by major orchestras.

Choice B is incorrect. The text does mention that Price’s compositions have been performed and recorded by major orchestras, but it doesn’t argue that more orchestras should do so. Choice C is incorrect. The text does mention the blending of Black spirituals and classical European Romantic musical traditions, but only briefly, as part of a broader overview of Price’s career. Choice D is incorrect. The text mentions Price’s blending of Black spirituals with classical European Romantic musical traditions, but it doesn’t directly compare Price’s scores with those of classical European composers.

"}, {"id": "2aaee77f", "domain": "Craft and Structure", "skill": "Text Structure and Purpose", "difficulty": "E", "type": "mc", "stimulus": "

Some bird species don’t raise their own chicks. Instead, adult females lay their eggs in other nests, next to another bird species’ own eggs. Female cuckoos have been seen quickly laying eggs in the nests of other bird species when those birds are out looking for food. After the eggs hatch, the noncuckoo parents will typically raise the cuckoo chicks as if they were their own offspring, even if the cuckoos look very different from the other chicks.

", "stem": "

Which choice best describes the function of the underlined sentence in the text as a whole?

", "choices": [{"id": "A", "text": "

It introduces a physical feature of female cuckoos that is described later in the text.

"}, {"id": "B", "text": "

It describes the appearance of the cuckoo nests mentioned earlier in the text.

"}, {"id": "C", "text": "

It offers a detail about how female cuckoos carry out the behavior discussed in the text.

"}, {"id": "D", "text": "

It explains how other birds react to the female cuckoo behavior discussed in the text.

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer because it best describes how the underlined sentence functions in the text as a whole. The first two sentences establish that birds of some species don’t raise their own young; instead, they lay their eggs in the nests of birds of other species. The underlined sentence then states that female cuckoo birds engage in this behavior, having been observed specifically laying their eggs in other nests while the other birds are out finding food. According to the text, the cuckoo chicks are then raised by the other birds. Thus, the underlined sentence provides a particular detail about how female cuckoos carry out the behavior of laying eggs for other birds to raise.

Choice A is incorrect. Rather than mentioning a physical feature of female cuckoos, the underlined sentence introduces a specific behavior of female cuckoos: laying eggs in the nests of birds of other species when the other birds are away. The only reference to physical features is the last sentence’s general mention of cuckoo chicks looking different from chicks of other species. Choice B is incorrect because the underlined sentence refers to the nests of birds other than cuckoos and doesn’t describe how any nests look, cuckoo or otherwise. Instead, the sentence addresses how female cuckoos use other birds’ nests. Choice D is incorrect because the underlined sentence describes only female cuckoo behavior (laying eggs in the nests of birds of other species when the other birds are away); it’s the last sentence of the text that addresses the other birds’ reaction, indicating that those birds usually raise the cuckoo chicks once they’ve hatched. 

"}, {"id": "54804e10", "domain": "Craft and Structure", "skill": "Words in Context", "difficulty": "H", "type": "mc", "stimulus": "

While scholars believe many Mesoamerican cities influenced each other, direct evidence of such influence is difficult to ascertain. However, recent excavations in a sector of Tikal (Guatemala) unearthed a citadel that shows ______blank Teotihuacán (Mexico) architecture—including a near replica of a famed Teotihuacán temple—providing tangible evidence of outside influence in portions of Tikal.

", "stem": "

Which choice completes the text with the most logical and precise word or phrase?

", "choices": [{"id": "A", "text": "

refinements of

"}, {"id": "B", "text": "

precursors of

"}, {"id": "C", "text": "

commonalities with

"}, {"id": "D", "text": "

animosities toward

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer because it most logically completes the text’s discussion of architectural influences among Mesoamerican cities. In this context, “commonalities with” means similarities to or shared attributes with. The text indicates that a recently discovered citadel in Tikal includes a close imitation of a famous temple in Teotihuacán (another Mesoamerican city) and other evidence of Teotihuacán influence, which suggests that the citadel possesses features that resemble architectural features found in Teotihuacán. This context thus indicates that the Tikal citadel shows commonalities with Teotihuacán architecture.

Choice A is incorrect because there’s nothing in the text that suggests that the Tikal citadel shows “refinements of,” or improvements on, Teotihuacán architecture. Although the text suggests that the architecture of Teotihuacán influenced the architecture of the Tikal citadel, and although it’s possible that later architectural designs could make improvements on earlier designs, the text doesn’t discuss whether, in imitating Teotihuacán architecture, the Tikal citadel’s builders improved on it. Choice B is incorrect because describing the citadel in Tikal as showing “precursors of” Teotihuacán architecture—or features that preceded and foreshadowed those of Teotihuacán architecture—would imply the opposite of what the text suggests about the relationship between the architecture found in Tikal and Teotihuacán. The text claims that the discovery of similarities between the Tikal citadel and the architecture of Teotihuacán, including a replica of a temple in Teotihuacán, provides evidence of outside influences on Tikal architecture. If the Tikal citadel was influenced by Teotihuacán architecture, then the Teotihuacán architecture must predate the citadel, not the other way around. In this context, therefore, it wouldn’t make sense to say that the Tikal citadel shows precursors of Teotihuacán architecture. Choice D is incorrect because the text discusses how the citadel in Tikal indicates the influence of Teotihuacán architecture, which implies that the makers of the Tikal citadel likely admired aspects of Teotihuacán architecture enough to imitate it. Thus, there’s no reason to think that the Tikal citadel provides evidence of the Tikal people’s “animosities toward,” or feelings of strong dislike or hostility toward, Teotihuacán architecture. 

"}, {"id": "4480fae9", "domain": "Craft and Structure", "skill": "Words in Context", "difficulty": "E", "type": "mc", "stimulus": "

The following text is adapted from Sui Sin Far’s 1912 short story “Mrs. Spring Fragrance.” Mr. and Mrs. Spring Fragrance immigrated to the United States from China.

\n
\n

Mrs. Spring Fragrance was unaware that Mr. Spring Fragrance, tired with the day’s business, had thrown himself down on the bamboo settee on the veranda, and that although his eyes were engaged in scanning the pages of the Chinese World, his ears could not help receiving the words which were borne to him through the open window.

\n
", "stem": "

As used in the text, what does the word “receiving” most nearly mean?

", "choices": [{"id": "A", "text": "

Denying

"}, {"id": "B", "text": "

Entering

"}, {"id": "C", "text": "

Carrying

"}, {"id": "D", "text": "

Hearing

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer because as used in the text, “receiving” most nearly means hearing, or perceiving sound. The text describes Mr. Spring Fragrance as he reads a newspaper, focusing on his eyes and ears. While his eyes look at the newspaper, he is unwillingly distracted by words coming through a nearby open window (that is, “his ears could not help receiving the words”). The words are being perceived specifically by his ears and not his eyes, and ears are the organs of sense with which one hears, so therefore Mr. Spring Fragrance is hearing the words through the open window.

Choice A is incorrect because there is no indication in the text that Mr. Spring Fragrance is denying, or refusing the truth of, the words coming to him through the window. He is merely distracted by them. Choice B is incorrect because it wouldn’t make sense to say that Mr. Spring Fragrance’s ears couldn’t help entering, or coming into, the words coming to him through the window. Instead, the text indicates that the opposite occurs: that is, when Mr. Spring Fragrance hears the words, they enter his ears, but his ears don’t enter the words. Choice C is incorrect because it doesn’t make sense in this context to think of Mr. Spring Fragrance as carrying the words coming to him through the window, even though the word “carry” can have a number of different meanings depending on context: for example, he is not lifting them, he is not supporting them, and he is not accepting blame for them (as one “carries the blame” for a mistake).

"}, {"id": "5d2fd27d", "domain": "Craft and Structure", "skill": "Words in Context", "difficulty": "E", "type": "mc", "stimulus": "

While we can infer information about climate activity in Earth’s distant past from physical evidence, we of course cannot observe past climates directly. To study early Earth’s climate in action, we must ______blank that climate using computer models that represent various climate conditions consistent with the physical evidence.

", "stem": "

Which choice completes the text with the most logical and precise word or phrase?

", "choices": [{"id": "A", "text": "

invent

"}, {"id": "B", "text": "

simulate

"}, {"id": "C", "text": "

exaggerate

"}, {"id": "D", "text": "

preserve

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer because it most logically completes the text’s discussion of climate activity in Earth’s distant past. In this context, to “simulate” most nearly means to represent a natural process using computer models. According to the text, understanding Earth’s early climate is difficult because we cannot make direct observations of the distant past. Instead, scientists must create computer models that approximate early climate conditions, based on the physical evidence that those conditions left behind on Earth’s surface. This context supports the idea that computer models simulate Earth’s climate in the distant past.

Choice A is incorrect because scientists use existing physical evidence as a basis for developing computer models that describe what Earth’s actual past climate might have been like. The models are not being used to “invent,” or imagine, a completely fictional climate. Choice C is incorrect because the computer models are being used in an attempt to describe as accurately as possible what Earth’s past climate might have been like. They are not attempting to “exaggerate,” or distort, those features. Choice D is incorrect because the computer models do not “preserve,” or protect from deterioration, Earth’s early climate; instead, they attempt to reproduce the characteristics of that climate, based on the remaining physical evidence of that climate.

"}, {"id": "9aa44886", "domain": "Craft and Structure", "skill": "Words in Context", "difficulty": "M", "type": "mc", "stimulus": "

The following text is from F. Scott Fitzgerald’s 1925 novel The Great Gatsby.

\n
\n

[Jay Gatsby] was balancing himself on the dashboard of his car with that resourcefulness of movement that is so peculiarly American—that comes, I suppose, with the absence of lifting work in youth and, even more, with the formless grace of our nervous, sporadic games. This quality was continually breaking through his punctilious manner in the shape of restlessness.

\n
", "stem": "

As used in the text, what does the word “quality” most nearly mean?

", "choices": [{"id": "A", "text": "

Standard

"}, {"id": "B", "text": "

Prestige

"}, {"id": "C", "text": "

Characteristic

"}, {"id": "D", "text": "

Accomplishment

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. “This quality” refers to Gatsby’s “resourcefulness of movement,” which is described as a characteristic or trait of his. 

Choice A is incorrect. This isn’t what “quality” means in this context. Here, “this quality” refers to Gatsby’s “resourcefulness of movement,” which is described as a characteristic or trait of his. “Standard” is a synonym for a different definition of “quality”: the degree of excellence of something. Choice B is incorrect. This isn’t what “quality” means in this context. Here, “this quality” refers to Gatsby’s “resourcefulness of movement,” which is described as a characteristic or trait of his. “Prestige” would suggest a high status or an admirable reputation, which doesn’t match that description. Choice D is incorrect. This isn’t what “quality” means in this context. Here, “this quality” refers to Gatsby’s “resourcefulness of movement,” which is described as a characteristic or trait of his. “Accomplishment” would suggest an achievement, which doesn’t match that description.   

"}, {"id": "e1befb41", "domain": "Craft and Structure", "skill": "Cross-Text Connections", "difficulty": "M", "type": "mc", "stimulus": "

 

Text 1

\n

In a study of the benefits of having free time, Marissa Sharif found that the reported sense of life satisfaction tended to plateau when participants had two hours of free time per day and actually began to fall when they had five hours of free time per day. After further research, Sharif concluded that this dip in life satisfaction mainly occurred when individuals spent all their free time unproductively, such as by watching TV or playing games.

\n

 

Text 2

\n

Psychologist James Maddux cautions against suggesting an ideal amount of free time. The human desire for both free time and productivity is universal, but Maddux asserts that individuals have unique needs for life satisfaction. Furthermore, he points out that there is no objective definition for what constitutes productivity; reading a book might be considered a productive activity by some, but idleness by others.

", "stem": "

Based on the texts, how would Maddux (Text 2) most likely respond to the conclusion Sharif (Text 1) reached after her further research?

", "choices": [{"id": "A", "text": "

By acknowledging that free time is more likely to enhance life satisfaction when it is spent productively than when it is spent unproductively

"}, {"id": "B", "text": "

By challenging the reasoning in Text 1, as it has not been proved that productivity commonly contributes to individuals’ life satisfaction

"}, {"id": "C", "text": "

By warning against making an overly broad assumption, as there is no clear consensus in distinguishing between productive and unproductive activities

"}, {"id": "D", "text": "

By claiming that the specific activities named in Text 1 are actually examples of productive activities rather than unproductive ones

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer because it characterizes how Maddux would most likely respond to the conclusion Sharif reached after her research. Text 1 describes Sharif’s study of the benefits of free time, saying that the reported sense of satisfaction plateaued at two hours per day and began to decline at five hours per day. Further research led Sharif to conclude that time spent doing tasks she defines as unproductive, such as watching TV or playing games, correlated with a drop in life satisfaction.  However, in Text 2 Maddux says that there is no objective definition of what constitutes productive behavior, giving the example that reading a book might be considered productive by some but unproductive by others. It can be inferred that Maddux would also assert that whether watching TV or playing games is productive or unproductive is a matter of subjective judgment. Thus, Maddux would most likely caution against making an overly broad assumption, as there is no clear consensus in distinguishing between productive and unproductive activities.

Choice A is incorrect because Maddux asserts that individuals have unique needs for life satisfaction: some may want to spend that time productively, others unproductively, and what counts as productive is subjective. Therefore, Maddux would likely not consider it universally true that free time is more likely to enhance life satisfaction when it is spent productively. Choice B is incorrect because the study described in Text 1 concerns whether free time contributes to life satisfaction, not whether productivity contributes to life satisfaction. The dip in life satisfaction that Sharif claims to observe in Text 1 happens only after five hours, and mainly if the time is spent unproductively—that is, two hours of free time spent productively might increase life satisfaction just as much as two hours spent unproductively. Choice D is incorrect because Maddux holds the opinion that whether an activity is productive or unproductive is subjective and depends on the individual; therefore, he would most likely claim that watching TV or playing games might be productive for some and unproductive for others.

"}, {"id": "afd48140", "domain": "Craft and Structure", "skill": "Words in Context", "difficulty": "E", "type": "mc", "stimulus": "

In 1877, 85% of California’s railways were already controlled by the Southern Pacific Railroad. The company further solidified its ______blank in rail access to the state’s Pacific coast when it completed the Sunset Route in 1883: running from Louisiana to Southern California, the route established the first transcontinental rail line across the southern United States. 

", "stem": "

Which choice completes the text with the most logical and precise word or phrase?

", "choices": [{"id": "A", "text": "

dominance

"}, {"id": "B", "text": "

creativity

"}, {"id": "C", "text": "

insignificance

"}, {"id": "D", "text": "

neutrality

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer because it most logically and precisely completes the text’s discussion of the Southern Pacific Railroad. As used in this context, \"dominance\" means the state of being more successful than others. The text states that the Southern Pacific Railroad already controlled 85% of California’s railways in 1877, and that the Sunset Route it constructed in 1883 was the first transcontinental rail line across the southern United States. Therefore, the Southern Pacific Railroad would be more successful than other railroads in the area, and the construction of the Sunset Route would further solidify its dominance in rail access to California’s coast.

Choice B is incorrect. Although the construction of the Sunset Route must have required some creativity, or use of imagination, the word \"creativity\" would not also encompass the fact that the Southern Pacific Railroad already controlled 85% of California’s railways. The text is more focused on the railroad’s control of the field and overall success rather than its imaginative thought processes. Choice C is incorrect because if the Southern Pacific Railroad controlled the majority of California’s railways, it would not make sense to refer to its \"insignificance,\" or the state of being unimportant. Rather, the opposite would be true. Choice D is incorrect because in context it would not make sense to refer to the Southern Pacific Railroad’s \"neutrality,\" or absence of strong opinion on a matter, since no opinions are mentioned. Nor would \"neutrality\" in the sense of impartiality in a conflict be a logical or precise choice since no conflict is explicitly described. There might be an implied conflict between the Southern Pacific Railroad and other railroads doing business in California, but that is not a conflict in which the Southern Pacific Railroad would take an impartial position.

"}, {"id": "b4887dae", "domain": "Craft and Structure", "skill": "Text Structure and Purpose", "difficulty": "H", "type": "mc", "stimulus": "

Mathematician Claude Shannon is widely regarded as a foundational figure in information theory. His most important paper, “A Mathematical Theory of Communication,” published in 1948 when he was employed at Bell Labs, utilized a concept called a “binary digit” (shortened to “bit”) to measure the amount of information in any signal and determine the fastest rate at which information could be transmitted while still being reliably decipherable. Robert Gallagher, one of Shannon’s colleagues, said that the bit was “[Shannon’s] discovery, and from it the whole communications revolution has sprung.”

", "stem": "

Which choice best describes the overall structure of the text?

", "choices": [{"id": "A", "text": "

It presents a theoretical concept, illustrates how the name of the concept has changed, and shows how the name has entered common usage.

"}, {"id": "B", "text": "

It introduces a respected researcher, describes an aspect of his work, and suggests why the work is historically significant.

"}, {"id": "C", "text": "

It names the company where an important mathematician worked, details the mathematician’s career at the company, and provides an example of the recognition he received there.

"}, {"id": "D", "text": "

It mentions a paper, offers a summary of the paper’s findings, and presents a researcher’s commentary on the paper.

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. The text starts with a general statement that introduces Shannon, then describes a specific contribution from one of his papers, then provides a quote that illustrates just how important this contribution was.

Choice A is incorrect. This isn’t the overall structure. The text only mentions very briefly, in parentheses, that “binary digit” was shortened to “bit.” It doesn’t go into detail about this name change, and it doesn’t discuss any “common usage” of the name at all. Choice C is incorrect. This isn’t the overall structure. Shannon’s employment at Bell Labs is only mentioned once, very briefly: the text never goes into detail about his career there, and it never mentions any recognition he received there. Choice D is incorrect. This is too narrow. Overall, the text is about Shannon’s importance in his field, not just this one paper of his.

"}, {"id": "c68ceeff", "domain": "Craft and Structure", "skill": "Cross-Text Connections", "difficulty": "E", "type": "mc", "stimulus": "

Text 1

\n

Today the starchy root cassava is found in many dishes across West Africa, but its rise to popularity was slow. Portuguese traders brought cassava from Brazil to the West African coast in the 1500s. But at this time, people living in the capitals further inland had little contact with coastal communities. Thus, cassava remained relatively unknown to most of the region’s inhabitants until the 1800s.

\n

 

\n

Text 2

\n

Cassava’s slow adoption into the diet of West Africans is mainly due to the nature of the crop itself. If not cooked properly, cassava can be toxic. Knowledge of how to properly prepare cassava needed to spread before the food could grow in popularity. The arrival of formerly enslaved people from Brazil in the 1800s, who brought their knowledge of cassava and its preparation with them, thus directly fueled the spread of this crop.

", "stem": "

Based on the texts, the author of Text 1 and the author of Text 2 would most likely agree with which statement?

", "choices": [{"id": "A", "text": "

Cassava did not become a significant crop in West Africa until long after it was first introduced.

"}, {"id": "B", "text": "

Several of the most commonly grown crops in West Africa are originally from Brazil.

"}, {"id": "C", "text": "

The climate of the West African coast in the 1500s prevented cassava’s spread in the region. 

"}, {"id": "D", "text": "

The most commonly used methods to cook cassava today date to the 1500s.

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. Text 1 states that cassava’s “rise to popularity was slow” in West Africa. Text 2 also describes cassava’s “slow adoption into the diet of West Africans.” While the two texts identify different causes for this slow adoption, both agree that cassava took a long time to catch on.

Choice B is incorrect. This isn’t something that either text claims. Cassava is the only crop discussed in the passages, so we have no basis to draw conclusions about what the authors might say about “several” crops. Choice C is incorrect. This isn’t something that either text claims. Neither text mentions the “climate of the West African coast,” so we have no evidence that either author would agree with this. Choice D is incorrect. This isn’t something that either text claims. The 1500s were when cassava was brought to West Africa, but neither text describes how cassava is cooked, nor do they make any claims about when cooking methods were developed.

"}, {"id": "daaed806", "domain": "Craft and Structure", "skill": "Words in Context", "difficulty": "E", "type": "mc", "stimulus": "

Mônica Lopes-Ferreira and others at Brazil’s Butantan Institute are studying the freshwater stingray species Potamotrygon rex to determine whether biological characteristics such as the rays’ age and sex have ______blank effect on the toxicity of their venom—that is, to see if differences in these traits are associated with considerable variations in venom potency.

", "stem": "

Which choice completes the text with the most logical and precise word or phrase?

", "choices": [{"id": "A", "text": "

a disconcerting

"}, {"id": "B", "text": "

an acceptable

"}, {"id": "C", "text": "

an imperceptible

"}, {"id": "D", "text": "

a substantial

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer because it most logically completes the text’s discussion of the research that Lopes-Ferreira and her colleagues are conducting on the stingray species Potamotrygon rex. As used in this context, “a substantial” effect means an effect that is sizable or noteworthy. The text indicates that the researchers are seeking to determine whether there are “considerable variations” in the potency of stingray venom that are associated with variation in the stingrays’ age and sex. This context suggests that the researchers want to find out whether stingray age and sex have a substantial effect on venom toxicity.

Choice A is incorrect because there’s nothing in the text that suggests that the researchers have been studying whether the stingrays’ age and sex have “a disconcerting,” or an unsettling and disturbing, effect on the stingrays’ venom. The text indicates that the researchers wish to determine if stingray age and sex cause large variations in the toxicity of stingray venom, not if the effect of age and sex is disconcerting. Choice B is incorrect because the text indicates that researchers want to find out whether differences in stingray age and sex produce differences in stingray venom, not that the researchers want to find out whether age and sex have “an acceptable,” or a satisfactory, effect on venom. The text makes no mention of what would make an effect on venom toxicity acceptable and gives no indication that the researchers are interested in that question. Choice C is incorrect because it wouldn’t make sense in context for the researchers to be looking for “an imperceptible,” or an unnoticeable, effect of age and sex on stingray venom. The text says that the researchers are trying to determine if there are “considerable variations” in venom toxicity linked to age and sex, not that the researchers are trying to find effects that they can’t perceive.

"}, {"id": "3e6ad72d", "domain": "Craft and Structure", "skill": "Text Structure and Purpose", "difficulty": "H", "type": "mc", "stimulus": "

A study by a team including finance professor Madhu Veeraraghavan suggests that exposure to sunshine during the workday can lead to overly optimistic behavior. Using data spanning from 1994 to 2010 for a set of US companies, the team compared over 29,000 annual earnings forecasts to the actual earnings later reported by those companies. The team found that the greater the exposure to sunshine at work in the two weeks before a manager submitted an earnings forecast, the more the manager’s forecast exceeded what the company actually earned that year.

", "stem": "

Which choice best states the function of the underlined sentence in the overall structure of the text?

", "choices": [{"id": "A", "text": "

To summarize the results of the team’s analysis

"}, {"id": "B", "text": "

To present a specific example that illustrates the study’s findings

"}, {"id": "C", "text": "

To explain part of the methodology used in the team’s study

"}, {"id": "D", "text": "

To call out a challenge the team faced in conducting its analysis

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer because it best describes how the underlined sentence functions in the text as a whole. The first sentence presents the implications of Veeraraghavan’s team’s study: sunshine exposure during work hours can cause overly optimistic behavior. The underlined sentence then describes the data the team consulted and how they were used (comparing predictions about earnings to what the companies actually earned), and the final sentence presents what the team found in their examination of the data. Thus, the underlined sentence mainly functions to explain part of the methodology used in the team’s study.

Choice A is incorrect because the underlined sentence explains in part how the team conducted their analysis of the effect of sunshine but doesn’t address what the team found; a broad summary is instead given in the other two sentences. Choice B is incorrect because the underlined sentence doesn’t present any specific examples from the team’s comparisons of 29,000 earnings predictions to actual earnings; it simply explains in part how the team conducted their analysis. Choice D is incorrect because the underlined sentence simply explains in part how the team conducted their analysis; the text never mentions any challenges that the team encountered in their study.

"}, {"id": "f3c45b4f", "domain": "Craft and Structure", "skill": "Cross-Text Connections", "difficulty": "H", "type": "mc", "stimulus": "

Text 1

\n

Fossils of the hominin Australopithecus africanus have been found in the Sterkfontein Caves of South Africa, but assigning an age to the fossils is challenging because of the unreliability of dating methods in this context. The geology of Sterkfontein has caused soil layers from different periods to mix, impeding stratigraphic dating, and dates cannot be reliably imputed from those of nearby animal bones since the bones may have been relocated by flooding.

\n

Text 2

\n

Archaeologists used new cosmogenic nuclide dating techniques to reevaluate the ages of A. africanus fossils found in the Sterkfontein Caves. This technique involves analyzing the cosmogenic nucleotides in the breccia—the matrix of rock fragments immediately surrounding the fossils. The researchers assert that this approach avoids the potential for misdating associated with assigning ages based on Sterkfontein’s soil layers or animal bones.

", "stem": "

Based on the texts, how would the researchers in Text 2 most likely respond to the underlined portion in Text 1?

", "choices": [{"id": "A", "text": "

They would emphasize the fact that the A. africanus fossils found in the Sterkfontein Caves may have been corrupted in some way over the years.

"}, {"id": "B", "text": "

They would contend that if analyses of surrounding layers and bones in the Sterkfontein Caves were combined, then the dating of the fossils there would be more accurate. 

"}, {"id": "C", "text": "

They would argue that their techniques are better suited than other methods to the unique challenges posed by the Sterkfontein Caves.

"}, {"id": "D", "text": "

They would claim that cosmogenic nuclide dating is reliable in the context of the Sterkfontein Caves because it is applied to the fossils directly.

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. Text 2 states that the researchers used cosmogenic nuclide dating to \"avoid the potential for misdating\" caused by the geology of Sterkfontein, which Text 1 describes as \"challenging\" and unreliable.

Choice A is incorrect. Neither text suggests that the A. africanus fossils have been \"corrupted,\" but only that traditional dating methods are difficult in Sterkfontein because of floods and soil mixing where the fossils were found. Nothing is implied to have compromised the fossils themselves. Choice B is incorrect. This choice misreads Text 2. Text 2 agrees that stratigraphy and other methods are prone to error in the context of Sterkfontein: there’s a \"potential for misdating\" when evaluating age based on soil layers and bones. Choice D is incorrect. Text 2 does not state that cosmogenic nuclide dating is applied to the fossils directly but rather to the breccia that surrounds them.

"}, {"id": "bdab32fc", "domain": "Craft and Structure", "skill": "Words in Context", "difficulty": "E", "type": "mc", "stimulus": "

Cucurbits, a group of plants that includes squash and melons, relied on mastodons to spread their seeds in the Ice Age. When these animals died out, cucurbits faced extinction in turn, having lost their means of seed dispersal. Around this time, however, the ancestors of Indigenous peoples in North America began raising cucurbits as crops, thus ______blank the plants’ survival.

", "stem": "

Which choice completes the text with the most logical and precise word or phrase?

", "choices": [{"id": "A", "text": "

verifying

"}, {"id": "B", "text": "

multiplying

"}, {"id": "C", "text": "

comforting

"}, {"id": "D", "text": "

ensuring

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer because it most logically completes the text’s discussion of cucurbits. In this context, “ensuring” means guaranteeing, or making sure of, the cucurbits’ survival. The text states that cucurbits faced extinction in the past because their means of seed dispersal disappeared, but the ancestors of Indigenous peoples in North America began farming cucurbits around that same time, so the crops were no longer threatened. Therefore, the context supports the idea that the ancestors of Indigenous peoples in North America helped with ensuring the cucurbits’ survival.

Choice A is incorrect because in this context verifying means making sure that something is accurate. In the text, the ancestors of Indigenous peoples in North America were ensuring the survival, not the accuracy of, the cucurbits. Choice B is incorrect. Although the cucurbit crops themselves were multiplying, or growing in number, as a result of the work of the ancestors of Indigenous peoples in North America, it wouldn’t make sense in context to say that the survival of the plants was multiplying. Choice C is incorrect because according to the text, in raising cucurbits as crops, the ancestors of Indigenous peoples in North America were attempting to help the plants grow and survive; they weren’t attempting to comfort, or free the plants from pain.

"}, {"id": "e8c26398", "domain": "Craft and Structure", "skill": "Words in Context", "difficulty": "M", "type": "mc", "stimulus": "

To develop a method for measuring snow depth with laser beams, NASA physicist Yongxiang Hu relied on ______blank; identifying broad similarities between two seemingly different phenomena, Hu used information about how ants move inside colonies to calculate how the particles of light that make up laser beams travel through snow.

", "stem": "

Which choice completes the text with the most logical and precise word or phrase?

", "choices": [{"id": "A", "text": "

a collaboration

"}, {"id": "B", "text": "

an accessory

"}, {"id": "C", "text": "

a contradiction

"}, {"id": "D", "text": "

an analogy

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. The text after the semicolon tells us that Hu \"identif[ied] broad similarities between two seemingly different phenomena,\" comparing ants with light particles. Since an analogy seeks similarities between seemingly unrelated phenomena, this fits the context perfectly.

Choice A is incorrect. \"A collaboration\" refers to \"an act of working with others,\" but what comes after the semicolon doesn’t describe collaboration with other researchers. Instead, it shows a comparison between two different (but ultimately similar) scientific phenomena. Choice B is incorrect. \"An accessory\" can refer to \"something added to increase attractiveness or usefulness.\" No accessories are described in this text. Choice C is incorrect. \"A contradiction\" means \"a set of ideas or things that are opposed to or inconsistent with each other.\" The text describes how Hu used the similarity between ant and light particle movement to develop his method, so a word that refers to difference would not make sense here.

"}, {"id": "5336f2e4", "domain": "Craft and Structure", "skill": "Text Structure and Purpose", "difficulty": "H", "type": "mc", "stimulus": "

The following text is adapted from Zora Neale Hurston’s 1921 short story “John Redding Goes to Sea.” John is a child who lives in a town in the woods.

\n

Perhaps ten-year-old John was puzzling to the folk there in the Florida woods for he was an imaginative child and fond of day-dreams. The St. John River flowed a scarce three hundred feet from his back door. On its banks at this point grow numerous palms, luxuriant magnolias and bay trees. On the bosom of the stream float millions of delicately colored hyacinths. [John Redding] loved to wander down to the water’s edge, and, casting in dry twigs, watch them sail away down stream to Jacksonville, the sea, the wide world and [he] wanted to follow them.

", "stem": "

Which choice best describes the function of the underlined sentence in the text as a whole?

", "choices": [{"id": "A", "text": "

It provides an extended description of a location that John likes to visit.

"}, {"id": "B", "text": "

It reveals that some residents of John’s town are confused by his behavior.

"}, {"id": "C", "text": "

It illustrates the uniqueness of John’s imagination compared to the imaginations of other children.

"}, {"id": "D", "text": "

It suggests that John longs to experience a larger life outside the Florida woods.

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer because it accurately describes how the underlined sentence functions in the text as a whole. The text establishes that John has a strong imagination and then goes on to describe the St. John River near John’s home in the Florida woods. The underlined sentence depicts John sending twigs sailing down the river while he imagines them reaching “Jacksonville, the sea, the wide world,” where he wishes he could follow. This suggests that John longs to expand his life experiences beyond the Florida woods.

Choice A is incorrect because the second and third sentences of the text provide an extended description of the riverbank where John likes to go, whereas the underlined sentence describes what John does at that location. Choice B is incorrect because the first sentence of the text suggests that John’s behavior “was puzzling” to others around him, whereas the underlined sentence concerns the content of John’s imaginings. Choice C is incorrect because the underlined sentence elaborates on John’s imagination but doesn’t mention any other children to whom John could be compared.

"}, {"id": "6f5fc289", "domain": "Craft and Structure", "skill": "Text Structure and Purpose", "difficulty": "M", "type": "mc", "stimulus": "

The following text is adapted from Charles Dickens’s 1854 novel Hard Times. Coketown is a fictional town in England. 

\n

[Coketown] contained several large streets all very like one another, and many small streets still more like one another, inhabited by people equally like one another, who all went in and out at the same hours, with the same sound upon the same pavements, to do the same work, and to whom every day was the same as yesterday and tomorrow, and every year the counterpart of the last and the next. 

", "stem": "

Which choice best states the main purpose of the text?

", "choices": [{"id": "A", "text": "

To emphasize the uniformity of both the town and the people who live there

"}, {"id": "B", "text": "

To explain the limited work opportunities available to the town’s residents

"}, {"id": "C", "text": "

To reveal how the predictability of the town makes it easy for people lose track of time

"}, {"id": "D", "text": "

To argue that the simplicity of life in the town makes it a pleasant place to live

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. The author describes Coketown as having streets that are all very similar and residents who live similarly and do the same work. This repetition of similarities emphasizes how everything in Coketown is alike.

Choice B is incorrect. While the text mentions that all the residents “do the same work,” it never explains what that work is or why everyone does it. Besides, the idea that they all do the same work is just one of several similarities among the townspeople described in the text. Choice C is incorrect. While the last sentence states that “every day was the same as yesterday and tomorrow, and every year the counterpart of the last and the next,” it never suggests that people actually “lose track of time.” This is also too narrow to be the main idea, since time is just one of many aspects of Coketown that the text describes as always being the same. Choice D is incorrect. The text never mentions whether life is simple in Coketown, and the town sounds as though it’s probably a pretty dull place to live, rather than a pleasant one.

"}, {"id": "7bc05fa2", "domain": "Craft and Structure", "skill": "Words in Context", "difficulty": "H", "type": "mc", "stimulus": "

Whether the reign of a French monarch such as Hugh Capet or Henry I was historically consequential or relatively uneventful, its trajectory was shaped by questions of legitimacy and therefore cannot be understood without a corollary understanding of the factors that allowed the monarch to ______blank his right to hold the throne.

", "stem": "

Which choice completes the text with the most logical and precise word or phrase?

", "choices": [{"id": "A", "text": "

disengage

"}, {"id": "B", "text": "

annotate

"}, {"id": "C", "text": "

buttress

"}, {"id": "D", "text": "

reciprocate

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer because it most logically completes the text’s discussion of the legitimacy of the reigns of French monarchs such as Hugh Capet and Henry I. As used in this context, “buttress” means to strengthen or defend. The text indicates that regardless of whether a French monarch’s reign was significant or uneventful, each monarch faced questions about his right to the throne. The text goes on to say that in order to understand the path of a French monarch’s reign, it’s important to understand what contributed to the monarch’s ability to “hold the throne.” This context suggests that French monarchs such as Hugh Capet and Henry I had to buttress, or defend, their right to be monarch. 

Choice A is incorrect because it wouldn’t make sense in context to discuss factors that enabled a monarch to “disengage,” or withdraw his right to the French throne. The text focuses on an examination of people who reigned as French monarchs, not on people who didn’t choose to rule. Choice B is incorrect because it wouldn’t make sense in context to discuss factors that enabled a monarch to “annotate,” or add notes to or explain, his right to the French throne. Nothing in the text suggests that the monarchs were writing notes about their right to the throne; instead, faced with questions about the legitimacy of their reign, the monarchs defended their right. Choice D is incorrect. Saying that a monarch who is faced with questions about the legitimacy of his reign was able to “reciprocate” his right to the French throne would mean that he either returned his right to the throne or that he responded in kind to the challenge. Neither of these meanings would make sense in context because the text focuses on people who did reign as French monarchs and defended their right to do so.

"}, {"id": "b92c13fa", "domain": "Craft and Structure", "skill": "Words in Context", "difficulty": "E", "type": "mc", "stimulus": "

According to statistician Nassim Nicholas Taleb, the best way to predict the amount of time a nonperishable entity (such as a building or a technology) will continue to exist is to examine how long it has survived so far. In this view, an item’s age is the strongest ______blank how much longer it will last.

", "stem": "

Which choice completes the text with the most logical and precise word or phrase?

", "choices": [{"id": "A", "text": "

uncertainty about

"}, {"id": "B", "text": "

indicator of

"}, {"id": "C", "text": "

motivation for

"}, {"id": "D", "text": "

criticism of

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. “Indicator” means “something that shows or suggests,” which matches Taleb’s argument that an item’s age can suggest how much longer it will last.

Choice A is incorrect. The passage tells us that examining an item’s age is the best way to predict how much longer it will last. Therefore, according to Taleb’s theory, an item’s age should add more certainty about how much longer it will last. Choice C is incorrect. A “motivation” is “a reason for doing.” Items don’t have feelings and motivations, so it wouldn’t make sense to say that their age is a motivation for how much longer they will last. Choice D is incorrect. “Criticism” can mean “describing faults or problems” or “an analysis of an artistic work.” Neither of these definitions makes sense here. An item’s age can’t criticize how much longer it will last.

"}, {"id": "f7c02e89", "domain": "Craft and Structure", "skill": "Cross-Text Connections", "difficulty": "H", "type": "mc", "stimulus": "

 

Text 1

\n

Films and television shows commonly include a long list of credits naming the people involved in a production. Credit sequences may not be exciting, but they generally ensure that everyone’s contributions are duly acknowledged. Because they are highly standardized, film and television credits are also valuable to anyone researching the careers of pioneering cast and crew members who have worked in the mediums.

\n

 

Text 2

\n

Video game scholars face a major challenge in the industry’s failure to consistently credit the artists, designers, and other contributors involved in making video games. Without a reliable record of which people worked on which games, questions about the medium’s development can be difficult to answer, and the accomplishments of all but its best-known innovators can be difficult to trace.

", "stem": "

Based on the texts, how would the author of Text 1 most likely respond to the discussion in Text 2?

", "choices": [{"id": "A", "text": "

By recommending that the scholars mentioned in Text 2 consider employing the methods regularly used by film and television researchers

"}, {"id": "B", "text": "

By pointing out that credits have a different intended purpose in film and television than in the medium addressed by the scholars mentioned in Text 2

"}, {"id": "C", "text": "

By suggesting that the scholars mentioned in Text 2 rely more heavily on credits as a source of information than film and television researchers do

"}, {"id": "D", "text": "

By observing that a widespread practice in film and television largely prevents the kind of problem faced by the scholars mentioned in Text 2

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer because it reflects how the author of Text 1 would most likely respond to Text 2 based on the information provided. Text 2 discusses how the inconsistent use of credits to identify the contributors to video games can pose an obstacle to scholars of the medium, who rely on such credits to answer questions about the medium’s development. Text 1 notes that in film and television, on the other hand, credits are used consistently and are valuable to researchers studying the cast and crew members in these mediums. Since Text 1 asserts how the consistent use of credits benefits scholars of film and television, it can be inferred that this text’s author would respond to the discussion in Text 2 by observing that the kind of problem faced by scholars of video games—the inability to know who contributed to a particular production and how—is, in film and television studies, largely prevented by the widespread practice of credits in these mediums.

Choice A is incorrect. Although Text 1 discusses a method used by film and television researchers—namely, relying on credits to research the careers of cast and crew members—the author doesn’t explicitly recommend that or any other method. Moreover, Text 1 states that films and television shows themselves, not their researchers, regularly use the method of listing credits. Choice B is incorrect. It can be inferred from Text 2 that when video games do feature credits, they have essentially the same function as credits in film and television—namely, to identify the individuals who worked on a particular production. Therefore, it is unlikely that the author of Text 1 would characterize video game credits as differing in purpose from film and television credits. Choice C is incorrect because, as Text 2 explains, credits are not consistently used in video games. Therefore, it is unlikely that the author of Text 1 would argue that scholars of the medium discussed in this text—video games—rely more heavily on credits than scholars of film and television, two mediums where credits consistently appear.

"}, {"id": "82c05b34", "domain": "Craft and Structure", "skill": "Cross-Text Connections", "difficulty": "M", "type": "mc", "stimulus": "

Text 1

\n

The live music festival business is growing in event size and genre variety. With so many consumer options, organizers are finding ways to cement festival attendance as a special experience worth sharing. This phenomenon is linked to the growing “experiential economy,” where many find it gratifying to purchase lived experiences. To ensure a profitable event, venues need to consider the overall consumer experience, not just the band lineup.

\n

Text 2

\n

Music festival appearances are becoming a more important part of musicians’ careers. One factor in this shift is the rising use of streaming services that allow access to huge numbers of songs for a monthly fee, subsequently reducing sales of full-length albums. With this shift in consumer behavior, musicians are increasingly dependent on revenue from live performances.

", "stem": "

Based on the texts, both authors would most likely agree with which statement?

", "choices": [{"id": "A", "text": "

Consumers are more interested in paying subscription fees to stream music than in attending music festivals in person. 

"}, {"id": "B", "text": "

Consumers’ growing interest in purchasing experiences is mostly confined to the music industry. 

"}, {"id": "C", "text": "

Changing consumer behaviors are leading to changes in music-related businesses. 

"}, {"id": "D", "text": "

The rising consumer demand for live music festivals also generates higher demand for music streaming platforms.

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. Both authors mention how consumer behaviors have shifted, and how this affects different aspects of the music industry. Text 1 states that consumers enjoy purchasing “lived experiences,” and that this influences how organizers design music festivals. Text 2 states that consumers are using streaming services more, and that this reduces album sales and increases the importance of live performances for musicians.

Choice A is incorrect. Neither text claims that consumers prefer streaming to festivals, or that these are mutually exclusive options. Text 1 implies that festivals are popular and profitable, and Text 2 never suggests that streaming services diminish the demand for live music. Choice B is incorrect. This choice misreads Text 1, which identifies music festivals as just one example of a broader trend of purchasing “lived experiences.” Text 2 doesn’t mention growing interest in purchasing experiences, in the music industry or otherwise. Choice D is incorrect. Neither text establishes a cause/effect relationship between the demand for festivals and the demand for streaming platforms. Text 1 does not mention streaming platforms at all, and Text 2 does not imply that streaming platforms benefit from the popularity of festivals.

"}, {"id": "849bf8d7", "domain": "Craft and Structure", "skill": "Words in Context", "difficulty": "E", "type": "mc", "stimulus": "

In the mid-nineteenth century, some abolitionist newspapers ______blank westward migration in the United States; by printing a letter that described the easy fortunes and high salaries miners could make in California during the Gold Rush, Frederick Douglass’s newspaper North Star was one such publication that inspired readers to relocate.

", "stem": "

Which choice completes the text with the most logical and precise word or phrase?

", "choices": [{"id": "A", "text": "

stimulated

"}, {"id": "B", "text": "

assigned

"}, {"id": "C", "text": "

opposed

"}, {"id": "D", "text": "

disregarded

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. \"Stimulated\" means \"encouraged interest or increased activity in.\" Because the newspapers discussed the benefits of westward migration and \"inspired readers to relocate,\" we can infer that they encouraged people to move west.

Choice B is incorrect. \"Assigned\" means \"gave a job or duty.\" Newspapers do not have the power to assign people to move west, although they can encourage it. Choice C is incorrect. \"Opposed\" means \"disapproved of.\" We can tell that this isn’t the case, because the newspapers discussed \"the easy fortunes and high salaries miners could make in California\" and \"inspired readers to relocate.\" Choice D is incorrect. \"Disregarded\" means \"ignored.\" If the newspapers are writing about the west and \"inspir[ing] readers to relocate,\" they can’t be ignoring it at the same time.

"}, {"id": "f7d58b53", "domain": "Craft and Structure", "skill": "Words in Context", "difficulty": "E", "type": "mc", "stimulus": "

Like other tribal nations, the Muscogee (Creek) Nation is self-governing; its National Council generates laws regulating aspects of community life such as land use and healthcare, while the principal chief and cabinet officials ______blank those laws by devising policies and administering services in accordance with them.

", "stem": "

Which choice completes the text with the most logical and precise word or phrase?

", "choices": [{"id": "A", "text": "

implement

"}, {"id": "B", "text": "

presume

"}, {"id": "C", "text": "

improvise

"}, {"id": "D", "text": "

mimic

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer because it most logically completes the text’s discussion of self-government among the Muscogee (Creek) Nation. In this context, “implement” means to carry out or put into effect. The text states that the National Council generates laws, while the principal chief and cabinet officials are responsible for “devising policies and administering services in accordance with” those laws. This context suggests that the principal chief and cabinet officials implement the laws: they put the laws into effect by creating policies and administering services that accord with those laws.

Choice B is incorrect because “presume” in this context would mean to assume based on incomplete information, and the text does not suggest that the principal chief and cabinet officials either made assumptions about the content of the laws or had incomplete information about them. Choice C is incorrect because in this context “improvise” would mean to create something without preparation, and the text does not suggest that the principal chief and cabinet officials create policies and administer services without advance preparation. Choice D is incorrect because nothing in the text suggests that the principal chief and cabinet officials “mimic,” or imitate, the laws generated by the National Council. To mimic laws would mean to generate new laws that are imitations of existing laws, but the text indicates that the National Council, not the principal chief and cabinet officials, is responsible for generating laws. Instead of generating laws, the principal chief and cabinet officials put laws into effect by “devising policies and administering services in accordance with” the laws.

"}, {"id": "8b46bb51", "domain": "Craft and Structure", "skill": "Words in Context", "difficulty": "M", "type": "mc", "stimulus": "

A journalist and well-respected art critic of nineteenth-century Britain, Lady Elizabeth Rigby Eastlake did not hesitate to publish reviews that went against popular opinion. One of her most divisive works was an essay questioning the idea of photography as an emerging medium for fine art: in the essay, Eastlake ______blank that the value of photographs was informational rather than creative.

", "stem": "

Which choice completes the text with the most logical and precise word or phrase?

", "choices": [{"id": "A", "text": "

exposed

"}, {"id": "B", "text": "

asserted

"}, {"id": "C", "text": "

discovered

"}, {"id": "D", "text": "

doubted

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. \"Asserted\" means \"stated confidently.\" Eastlake \"did not hesitate to publish reviews going against popular opinion,\" so we can assume that she was confident in sharing her opinions.

Choice A is incorrect. \"Exposed\" means \"made visible by uncovering\" and, when talking about ideas, tends to be used in relation to uncovering the truth. Eastlake was sharing an opinion, not uncovering a truth. Choice C is incorrect. \"Discovered\" means \"found,\" but Eastlake was writing an opinion essay. She was writing her own opinion, not \"discovering\" a new universal truth. Choice D is incorrect. \"Doubted\" means \"didn’t believe in.\" We’re told that Eastlake \"questioned\" the idea that photography could be fine art. Placing \"doubted\" in the blank would actually suggest that Eastlake argued that photos were valuable for creativity and not for information, which is the opposite of what we were told she believes.

"}, {"id": "44cc5f75", "domain": "Craft and Structure", "skill": "Words in Context", "difficulty": "E", "type": "mc", "stimulus": "

Artificially delivering biomolecules to plant cells is an important component of protecting plants from pathogens, but it is difficult to transmit biomolecules through the layers of the plant cell wall. Markita del Carpio Landry and her colleagues have shown that it may be possible to ______blank this problem by transmitting molecules through carbon nanotubes, which can cross cell walls.

", "stem": "

Which choice completes the text with the most logical and precise word or phrase?

", "choices": [{"id": "A", "text": "

conceptualize

"}, {"id": "B", "text": "

neglect

"}, {"id": "C", "text": "

illustrate

"}, {"id": "D", "text": "

overcome

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer because it most logically completes the text’s discussion of delivering biomolecules to plant cells. In this context, “overcome” means to succeed in dealing with an obstacle. The text suggests that although it’s difficult to move biomolecules through plant cell walls, Landry and her colleagues have shown that carbon nanotubes may be useful, since they can cross cell walls. This context conveys that Landry and her colleagues think it’s possible, using carbon nanotubes, to succeed in dealing with the obstacle of transmitting biomolecules to plant cells.

Choice A is incorrect because it wouldn’t make sense in context to say that Landry and her colleagues have shown that it may be possible to “conceptualize,” or form an idea of, the difficulty of transmitting biomolecules through the walls of plant cells. The text presents this difficulty as a known problem that Landry and her colleagues think they may have solved, not as a mysterious occurrence that they have yet to form ideas about. Choice B is incorrect because the text suggests that Landry and her colleagues think it may be possible to successfully deal with the problem of transmitting biomolecules through the walls of plant cells, not that Landry and her colleagues think it may be possible to “neglect,” or simply to disregard and ignore the problem. Choice C is incorrect because it wouldn’t make sense in context to say that Landry and her colleagues have shown that it may be possible to “illustrate,” or demonstrate, the difficulty of transmitting biomolecules through the walls of plant cells by using carbon nanotubes. According to the text, carbon nanotubes allow molecules to be transmitted to plant cells—something that is otherwise difficult to do. The text therefore presents carbon nanotubes as a way of possibly solving a problem, not as a means of demonstrating the problem.

"}, {"id": "aaa3ee7c", "domain": "Craft and Structure", "skill": "Words in Context", "difficulty": "H", "type": "mc", "stimulus": "

Critics have asserted that fine art and fashion rarely ______blank in a world where artists create timeless works for exhibition and designers periodically produce new styles for the public to buy. Luiseño/Shoshone-Bannock beadwork artist and designer Jamie Okuma challenges this view: her work can be seen in the Metropolitan Museum of Art and purchased through her online boutique.

", "stem": "

Which choice completes the text with the most logical and precise word or phrase?

", "choices": [{"id": "A", "text": "

prevail

"}, {"id": "B", "text": "

succumb

"}, {"id": "C", "text": "

diverge

"}, {"id": "D", "text": "

intersect

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer because it most logically completes the text’s discussion about the relationship between fine art and fashion. As used in this context, “intersect” means to connect or overlap. The text indicates that Jamie Okuma challenges the position held by critics because her work can be seen at an art museum and can be bought by the public from her online boutique. The text also presents the critics’ view as being influenced by a perception that fine artists create works that are “timeless” and meant for exhibition, whereas fashion designers periodically produce new styles that are meant for purchase. This context suggests that the critics believe that fine art and fashion tend not to overlap—in other words, that they rarely intersect. 

Choice A is incorrect because it wouldn’t make sense in context to say that critics contend that fine art and fashion rarely “prevail,” or prove to be triumphant or widespread. The text indicates that Okuma is an example of an artist who demonstrates that it’s possible to make fine art that is also available to the public as fashion. Choice B is incorrect because it wouldn’t make sense in context to say that fine art and fashion rarely “succumb,” or surrender. The text establishes that unlike what critics believe, Okuma creates works that are in art museums and available for the public to purchase, suggesting that critics believe fine art and fashion rarely overlap, not that they rarely succumb. Choice C is incorrect because saying that critics believe that fine art and fashion rarely “diverge,” or disagree or move in different directions, wouldn’t make sense in context. The text presents Okuma’s work as both fine art and fashion, thereby undermining what the critics assert. This suggests that the critics believe that fine art and fashion rarely intersect rather than that the two rarely diverge.

"}, {"id": "ea971260", "domain": "Craft and Structure", "skill": "Text Structure and Purpose", "difficulty": "E", "type": "mc", "stimulus": "

The following text is adapted from Louisa May Alcott’s 1869 novel An Old-Fashioned Girl. Polly, a teenager, is visiting her friend Fanny.

\n
\n

Fanny’s friends did not interest Polly much; she was rather afraid of them [because] they seemed so much older and wiser than herself, even those younger in years. They talked about things of which she knew nothing and when Fanny tried to explain, she didn’t find them interesting; indeed, some of them rather shocked and puzzled her.

\n
", "stem": "

Which choice best states the main purpose of the text?

", "choices": [{"id": "A", "text": "

To portray Polly’s reaction to Fanny’s friends

"}, {"id": "B", "text": "

To identify the topics Polly talks about with Fanny’s friends

"}, {"id": "C", "text": "

To explain how Fanny met some of her friends

"}, {"id": "D", "text": "

To illustrate how Fanny’s friends feel about Polly

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer because it most accurately describes the main purpose of the text, which is to show how Polly reacted to some of Fanny’s other friends. The text describes Polly as being frightened of Fanny’s friends because they seemed “much older and wiser” to her and elaborates that they “talked about things of which” Polly was unfamiliar, uninterested, and shocked. Thus, the main purpose of the text is to describe Polly’s impressions of Fanny’s other friends. 

Choice B is incorrect because the text does not provide any of the topics Polly discussed with Fanny’s friends, stating only that Polly found the topics unfamiliar, uninteresting, and shocking. Choice C is incorrect because the text says nothing about how Fanny and her other friends first met. Choice D is incorrect because the focus of the text is on Polly’s feelings about Fanny’s other friends, not on the other friends’ feelings about Polly.

"}, {"id": "975b0602", "domain": "Craft and Structure", "skill": "Text Structure and Purpose", "difficulty": "H", "type": "mc", "stimulus": "

A number of Indigenous politicians have been elected to the United States Congress since 2000 as members of the country’s two established political parties. In Canada and several Latin American countries, on the other hand, Indigenous people have formed their own political parties to advance candidates who will advocate for the interests of their communities. This movement has been particularly successful in Ecuador, where Guadalupe Llori, a member of the Indigenous party known as Pachakutik, was elected president of the National Assembly in 2021.

", "stem": "

Which choice best states the main purpose of the text?

", "choices": [{"id": "A", "text": "

To trace the history of an Indigenous political movement and speculate about its future development

"}, {"id": "B", "text": "

To argue that Indigenous politicians in the United States should form their own political party

"}, {"id": "C", "text": "

To highlight two approaches to achieving political representation for Indigenous people

"}, {"id": "D", "text": "

To consider how Indigenous politicians in the United States have influenced Indigenous politicians in Canada and Latin America

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer because it most accurately describes the main purpose of the text, which is to illustrate two approaches that Indigenous politicians have taken to achieve political representation for their communities. The text begins by explaining that one approach is exemplified by Indigenous politicians in the United States who, in an effort to ensure that the interests of their communities are represented in government, joined preexisting political parties and were subsequently elected to Congress. The text goes on to highlight a second approach adopted by Indigenous leaders in Canada and several Latin American countries: rather than joining established political parties, many Indigenous politicians in these countries have instead formed their own parties to promote candidates for office who support causes that are important to their communities. 

Choice A is incorrect because the text’s focus is on the contrasting approaches adopted by different Indigenous political movements in different countries; thus, it isn’t accurate to say that the text traces the history of one political movement. Moreover, the text only discusses examples from 2000 to 2021, a relatively short period of time; therefore, it provides very little in the way of discussion of larger historical developments, nor does it make any predictions about how these movements might continue to develop in the future. Choice B is incorrect because the text never urges Indigenous politicians in the US to alter their strategy of striving for representation through the established political parties, nor does it suggest that this strategy is inferior to that of Indigenous politicians in Canada and Latin America, who have formed their own parties. In fact, the text notes that both strategies have resulted in the election of Indigenous politicians to national governments. Choice D is incorrect because the text never suggests that Indigenous politicians in the US have influenced those in Canada and Latin America; instead, it stresses how Indigenous politicians’ approach toward achieving representation in the US government has differed from the approach Indigenous politicians have taken to achieve representation in national governments elsewhere in the Americas.

"}, {"id": "2b085bc6", "domain": "Craft and Structure", "skill": "Text Structure and Purpose", "difficulty": "M", "type": "mc", "stimulus": "

The following text is adapted from Paul Laurence Dunbar’s 1902 novel The Sport of the Gods. Joe and some of his family members have recently moved to New York City.

\n
\n

[Joe] was wild with enthusiasm and with a desire to be a part of all that the metropolis meant. In the evening he saw the young fellows passing by dressed in their spruce clothes, and he wondered with a sort of envy where they could be going. Back home there had been no place much worth going to, except church and one or two people’s houses.

\n
", "stem": "

Which choice best states the main purpose of the text?

", "choices": [{"id": "A", "text": "

It illustrates a character’s reaction to a new environment.

"}, {"id": "B", "text": "

It explains why a character has traveled to a city.

"}, {"id": "C", "text": "

It compares a character’s thoughts about an event at two different times of day.

"}, {"id": "D", "text": "

It presents a character feeling regret over leaving home.

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer because it most accurately describes the main purpose of the text. The narrator describes how Joe responds to being in “the metropolis”: he’s excited and “wild with enthusiasm.” He also envies the young fellows who walk by because, dressed as they are, they look as if they have somewhere special to go. The text contrasts this new place with the place Joe comes from, where apparently there wasn’t as much to do. Thus, the main purpose of the text is to illustrate Joe’s reaction to a new environment.

Choice B is incorrect because the text makes no reference to why Joe has moved. The narrator indicates that Joe is enthusiastic about being in a city, but there’s no explanation provided for the move. Choice C is incorrect because the text makes no reference to how Joe thinks about an event. The narrator describes young men passing by in the evening and then recalls places worth going to at home—church and a few people’s houses—but there’s no explicit comparison made nor is a time of day mentioned for these events back home. Choice D is incorrect because the text doesn’t support the idea that Joe feels regret over leaving home. Instead, Joe is described as “wild with enthusiasm” at being in the city. Joe’s home is mentioned, but only to compare it unfavorably with the city.

"}, {"id": "f8ca5766", "domain": "Craft and Structure", "skill": "Words in Context", "difficulty": "E", "type": "mc", "stimulus": "

Nigerian American author Teju Cole’s ______blank his two passions—photography and the written word—culminates in his 2017 book, Blind Spot, which evocatively combines his original photographs from his travels with his poetic prose.

", "stem": "

Which choice completes the text with the most logical and precise word or phrase?

", "choices": [{"id": "A", "text": "

indifference to

"}, {"id": "B", "text": "

enthusiasm for

"}, {"id": "C", "text": "

concern about

"}, {"id": "D", "text": "

surprise at

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer because it most logically completes the text’s discussion of Cole’s book Blind Spot. In this context, “enthusiasm for” means excitement about. The text explains that Blind Spot consists of original photographs as well as poetic prose—two elements that correspond to Cole’s passions, identified in the text, for photography and the written word. This context suggests that Cole’s excitement about photography and writing led him to create a book that successfully combines the two mediums.

Choice A is incorrect because describing Cole as feeling “indifference to” his two passions wouldn’t make sense in context. If Cole is indifferent to his passions, that would mean he doesn’t care about photography or writing—in which case they wouldn’t be his passions at all. Choice C is incorrect because there’s nothing in the text to suggest that Cole feels “concern about,” or uneasiness about, his passions. The text’s use of the word “culminates” indicates that Blind Spot represents a triumphant climax of Cole’s passions, not a work that results from his sense of discomfort with photography and writing. Choice D is incorrect because there’s nothing in the text to suggest that Cole feels “surprise at,” or astonished by, his passions. The text indicates that Cole’s feeling about his passions “culminates” in a book that “evocatively” combines photographs and writing, suggesting that Cole has a long-standing and skillful relationship to his passions, not that he is startled by them.

"}, {"id": "9671d61d", "domain": "Craft and Structure", "skill": "Words in Context", "difficulty": "E", "type": "mc", "stimulus": "

The following text is from Claude McKay’s 1922 poem “Morning Joy.” The speaker is looking out a window and observing a wold, or large area of land.

\n

 

\n
\n

At night the wide and level stretch of wold,

\n

Which at high noon had basked in quiet gold,

\n

Far as the eye could see was ghostly white;

\n

Dark was the night save for the snow’s weird light.

\n

 

\n

I drew the shades far down, crept into bed;

\n

Hearing the cold wind moaning overhead

\n

Through the sad pines, my soul, catching its pain,

\n

Went sorrowing with it across the plain.

\n
", "stem": "

As used in the text, what does the word “drew” most nearly mean?

", "choices": [{"id": "A", "text": "

Pulled

"}, {"id": "B", "text": "

Drained

"}, {"id": "C", "text": "

Inspired

"}, {"id": "D", "text": "

Sketched

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer because as used in the text, “drew” most nearly means pulled. In the text, the speaker stands at a window, looking out on a landscape at night. The speaker then “drew the shades far down, crept into bed.” That is, the speaker pulled down, or lowered, the shades until they were completely shut before going to sleep. 

Choice B is incorrect. Although in some contexts, “drew” can refer to draining or removing liquid, especially water, as when someone draws water from a well, in this context it refers to the speaker pulling down window shades for the night. Choice C is incorrect. In some contexts, “drew” can be used to describe how a person or thing inspires, or elicits, a response from someone, as when a performer draws applause from an audience. But in this context it refers to the speaker pulling down window shades for the night. Choice D is incorrect. Although “drew” has several meanings, including sketched, or illustrated with a pen or pencil, in this context it refers to the speaker pulling down window shades for the night.

"}, {"id": "a06c434d", "domain": "Craft and Structure", "skill": "Words in Context", "difficulty": "H", "type": "mc", "stimulus": "

The work of Kiowa painter T.C. Cannon derives its power in part from the tension among his ______blank influences: classic European portraiture, with its realistic treatment of faces; the American pop art movement, with its vivid colors; and flatstyle, the intertribal painting style that rejects the effect of depth typically achieved through shading and perspective.

", "stem": "

Which choice completes the text with the most logical and precise word or phrase?

", "choices": [{"id": "A", "text": "

complementary

"}, {"id": "B", "text": "

unknown

"}, {"id": "C", "text": "

disparate

"}, {"id": "D", "text": "

interchangeable

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer because it most logically completes the text’s discussion of the artistic styles that have influenced Cannon’s work. As used in this context, “disparate” means distinct or dissimilar. The text indicates that a tension exists among the styles that have influenced Cannon’s work and goes on to describe how those styles differ: classic European portraiture favors realism, American pop art uses vivid colors, and intertribal flatstyle rejects the use of shading and perspective to achieve depth. This context suggests that the styles that have influenced Cannon’s work are disparate. 

Choice A is incorrect because the text indicates that there is a tension among the influences on Cannon’s artwork, so it wouldn’t make sense to say that the influences are “complementary,” or that they complete one another or make up for one another’s deficiencies. Choice B is incorrect because it wouldn’t make sense to characterize Cannon’s influences as “unknown,” or not familiar; it’s clear that the influences are known because the text goes on to list them. Choice D is incorrect because the text indicates that there is a tension among the influences on Cannon’s work, not that they are  “interchangeable,” or capable of being used in one another’s place.

"}, {"id": "c8603ed7", "domain": "Craft and Structure", "skill": "Text Structure and Purpose", "difficulty": "E", "type": "mc", "stimulus": "

San Francisco is known for the colorful murals painted on many of its buildings. The densest collection of murals is found on Balmy Alley in the Mission District neighborhood. In the 1970s, Latina artists painted vivid scenes of community life on walls along this block. As the original murals have faded, later generations of artists have painted new ones over them. As a result, Balmy Alley has become a living showcase of San Francisco’s artistic spirit, with its murals reflecting changes in the cultural life of the city.

", "stem": "

Which choice best states the main purpose of the text?

", "choices": [{"id": "A", "text": "

To compare the Balmy Alley murals to other murals in San Francisco

"}, {"id": "B", "text": "

To offer an overview of the history and importance of the Balmy Alley murals

"}, {"id": "C", "text": "

To urge people to protect the murals of San Francisco from decay

"}, {"id": "D", "text": "

To describe the rise of mural painting in San Francisco beginning in the 1970s

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer because it best states the main purpose of the text. The text begins by briefly stating that San Francisco is known for its murals, then transitions to a discussion of a single collection of murals, which is found on Balmy Alley in the city’s Mission District. The text explains that the murals in this area were originally created in the 1970s, then observes that they have changed over time: as some have faded through the decades, others have been painted in their place. The text ends by emphasizing that these murals are significant because they reflect San Francisco’s artistic spirit and cultural life. Therefore, the text provides an overview of the history and importance of the Balmy Alley murals.

Choice A is incorrect. Although it can be inferred from the text that there are murals in other areas of San Francisco besides Balmy Alley, the text doesn’t specifically discuss murals in other areas or compare the murals of Balmy Alley to those in other areas. Choice C is incorrect. By observing that some of the murals of Balmy Alley have been replaced due to fading, the text implies that murals can decay, but it never urges readers to protect this specific collection of murals—or any murals elsewhere in San Francisco, for that matter. Indeed, by describing the ever-changing murals of Balmy Alley as “a living showcase of San Francisco’s artistic spirit,” the text emphasizes the positive aspects of the fact that the original Balmy Alley murals have faded and been replaced with new murals. Choice D is incorrect because the text doesn’t describe the rise of mural painting in San Francisco generally or note when this occurred. The only historical development of the 1970s mentioned in the text is the origin of the murals in a specific area of the city: Balmy Alley in the Mission District.

"}, {"id": "9c759a09", "domain": "Craft and Structure", "skill": "Text Structure and Purpose", "difficulty": "E", "type": "mc", "stimulus": "

The following text is from Georgia Douglas Johnson’s 1922 poem “Benediction.”

\n

Go forth, my son,
Winged by my heart’s desire!
Great reaches, yet unknown,
Await
For your possession.
I may not, if I would,
Retrace the way with you,
My pilgrimage is through,
But life is calling you!

", "stem": "

Which choice best states the main purpose of the text?

", "choices": [{"id": "A", "text": "

To express hope that a child will have the same accomplishments as his parent did

"}, {"id": "B", "text": "

To suggest that raising a child involves many struggles

"}, {"id": "C", "text": "

To warn a child that he will face many challenges throughout his life

"}, {"id": "D", "text": "

To encourage a child to embrace the experiences life will offer

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer because it accurately states the text’s main purpose. The poem begins with the speaker urging a child to “go forth” with her encouragement (“my heart’s desire”). The speaker goes on to suggest that new experiences (“Great reaches, yet unknown”) lie ahead for the son that “life is calling” him to seek out. Thus, the main purpose is to encourage a child to embrace the experiences available to him in his life.

Choice A is incorrect because the speaker encourages the child to pursue new experiences (“Great reaches”) without knowing exactly what those experiences will be (“yet unknown”) or suggesting that they should match the speaker’s own accomplishments. Choice B is incorrect because the speaker focuses on positive possibilities for her son (“Great reaches, yet unknown”) and her enthusiastic encouragement to embrace those possibilities (“life is calling you!”), while there is no mention of raising a child or associated struggles. Choice C is incorrect because the speaker frames the possibilities for her son in a positive light when she says that “great reaches, yet unknown” are waiting for him, and this positive outlook for the son is consistent throughout the text.

"}, {"id": "5a4b147c", "domain": "Craft and Structure", "skill": "Cross-Text Connections", "difficulty": "E", "type": "mc", "stimulus": "

Text 1

\n

On April 26th, 1777, Sybil Ludington rode 40 miles by horse through Putnam County, New York, to gather up local militia. British forces were burning nearby Danbury, Connecticut, and Ludington wanted to rally rebel troops to meet them. Although she was only 16 years old at the time, her brave feat made Ludington one of the heroes of the American Revolution. Since then, Ludington has been widely celebrated, inspiring postage stamps, statues, and even children’s TV series. 

\n

 

\n

Text 2

\n

Historian Paula D. Hunt researched the life and legacy of Sybil Ludington but found no evidence for her famous ride. Although many articles and books have been written about Ludington, Hunt believes writers may have been inventing details about Ludington as they retold her story. Ludington is revered by Americans today, but there simply isn’t a strong historical record of her heroic ride.

", "stem": "

Based on the texts, both authors would most likely agree with which statement?

", "choices": [{"id": "A", "text": "

Sybil Ludington was crucial to the outcome of the Revolutionary War.

"}, {"id": "B", "text": "

Historians have confirmed which route Sybil Ludington took.

"}, {"id": "C", "text": "

Sybil Ludington was likely not a real person.

"}, {"id": "D", "text": "

Many people have come to admire the story of Sybil Ludington’s ride.

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. Both authors agree that Ludington’s story has been widely celebrated and revered by Americans, even if they disagree on its accuracy. Text 1 states that Ludington has inspired postage stamps, statues, and TV series, and Text 2 states that many articles and books have been written about her. Thus, both authors acknowledge the popularity of Ludington’s story.

Choice A is incorrect. Neither author claims that Ludington had a significant impact on the war. Text 1 doesn’t mention how Ludington’s ride affected the war overall, and Text 2 suggests that Ludington’s ride may have been exaggerated or invented over time. Choice B is incorrect. Neither author claims that Ludington’s route has been verified by historians. Text 1 claims she rode 40 miles through Putnam County, but doesn’t cite any sources for this information, while Text 2 suggests the ride may not have even happened. Choice C is incorrect. This choice misreads text 2. Neither author claims that Ludington was not a real person, only that her ride may not have happened. Both authors seem to treat Ludington as a genuine historical figure.

"}, {"id": "b411eb09", "domain": "Craft and Structure", "skill": "Words in Context", "difficulty": "H", "type": "mc", "stimulus": "

New and interesting research conducted by Suleiman A. Al-Sweedan and Moath Alhaj is inspired by their observation that though there have been many studies of the effect of high altitude on blood chemistry, there is a ______blank studies of the effect on blood chemistry of living in locations below sea level, such as the California towns of Salton City and Seeley.

", "stem": "

Which choice completes the text with the most logical and precise word or phrase?

", "choices": [{"id": "A", "text": "

quarrel about

"}, {"id": "B", "text": "

paucity of

"}, {"id": "C", "text": "

profusion of

"}, {"id": "D", "text": "

verisimilitude in

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer because it most logically and precisely completes the text’s discussion of studies of altitude’s effect on blood chemistry. In this context, “paucity of” means lack of. In describing the inspiration behind Al-Sweedan and Alhaj’s research, the text uses the word “though” to suggest a contrasting relationship between two types of studies: those examining the effect on blood chemistry of living at a high altitude and those examining the effect on blood chemistry of living in locations below sea level. This contrasting relationship and the text’s use of the word “many” provide context suggesting that there are few, if any, examples of the second type of study, whereas there are numerous examples of the first type.

Choice A is incorrect because it wouldn’t make sense in context for there to be a “quarrel about,” or open disagreement about, studies of the effect on blood chemistry of living in locations below sea level. The text’s use of the words “though” and “many” suggests a contrasting relationship in terms of amount between two types of studies: those examining the effect on blood chemistry of living at a high altitude and those examining the effect on blood chemistry of living in locations below sea level. There’s nothing in the text to suggest that the contrast between the two types of studies involves the extent to which researchers broadly agree or disagree about the contents of either type. Choice C is incorrect because it wouldn’t make sense in context for there to be a “profusion of,” or great abundance of, studies of the effect on blood chemistry of living in locations below sea level. The text’s use of the words “though” and “many” suggests a contrasting relationship in terms of amount between two types of studies: those examining the effect on blood chemistry of living at a high altitude and those examining the effect on blood chemistry of living in locations below sea level. Rather than logically completing this contrast, “profusion of” would indicate that the two types of studies are similar in terms of amount, with many examples existing of both types. Choice D is incorrect because it wouldn’t make sense in context for there to be a “verisimilitude in,” or appearance of truth in, studies of the effect on blood chemistry of living in locations below sea level. The text’s use of the words “though” and “many” suggests a contrasting relationship in terms of amount between two types of studies: those examining the effect on blood chemistry of living at a high altitude and those examining the effect on blood chemistry of living in locations below sea level. There’s nothing in the text to suggest that the contrast between the two types of studies involves the extent to which either type of study presents an appearance of truth.

"}, {"id": "8963273a", "domain": "Craft and Structure", "skill": "Text Structure and Purpose", "difficulty": "M", "type": "mc", "stimulus": "

Musician Joni Mitchell, who is also a painter, uses images she creates for her album covers to emphasize ideas expressed in her music. For the cover of her album Turbulent Indigo (1994), Mitchell painted a striking self-portrait that closely resembles Vincent van Gogh’s Self-Portrait with Bandaged Ear (1889). The image calls attention to the album’s title song, in which Mitchell sings about the legacy of the postimpressionist painter. In that song, Mitchell also hints that she feels a strong artistic connection to Van Gogh—an idea that is reinforced by her imagery on the cover.

", "stem": "

Which choice best describes the overall structure of the text?

", "choices": [{"id": "A", "text": "

It presents a claim about Mitchell, then gives an example supporting that claim.

"}, {"id": "B", "text": "

It discusses Van Gogh’s influence on Mitchell, then considers Mitchell’s influence on other artists.

"}, {"id": "C", "text": "

It describes a similarity between two artists, then notes a difference between them.

"}, {"id": "D", "text": "

It describes the songs on Turbulent Indigo, then explains how they relate to the album’s cover.

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer because it accurately describes the organization of the elements within the text. The text begins with the claim that Joni Mitchell’s album covers use images she creates in order to emphasize ideas embedded in her albums. It then goes on to provide an example of how Mitchell’s self-portrait on the cover of Turbulent Indigo resembles a painting by Van Gogh, which the text indicates helps emphasize the strong connection Mitchell feels toward Van Gogh, a connection that is also expressed in the album’s title song.

Choice B is incorrect because there are no references in the text to artists other than Joni Mitchell and Van Gogh. Choice C is incorrect because there is nothing in the text that calls attention to any similarities or differences between Joni Mitchell and Van Gogh. Instead, it mentions that Mitchell feels a strong “artistic connection” to Van Gogh. Choice D is incorrect because the text discusses the cover before referring to any songs, and it only references one song from the album not all the songs.

"}, {"id": "c4900368", "domain": "Craft and Structure", "skill": "Text Structure and Purpose", "difficulty": "M", "type": "mc", "stimulus": "

The following text is from the 1924 poem “Cycle” by D’Arcy McNickle, who was a citizen of the Confederated Salish and Kootenai Tribes.

\n

There shall be new roads wending,
A new beating of the drum—
Men’s eyes shall have fresh seeing,
Grey lives reprise their span—
But under the new sun’s being,
Completing what night began,
There’ll be the same backs bending,
The same sad feet shall drum—
When this night finds its ending
And day shall have come.....

", "stem": "

Which choice best states the main purpose of the text?

", "choices": [{"id": "A", "text": "

To consider how the repetitiveness inherent in human life can be both rewarding and challenging

"}, {"id": "B", "text": "

To question whether activities completed at one time of day are more memorable than those completed at another time of day

"}, {"id": "C", "text": "

To refute the idea that joy is a more commonly experienced emotion than sadness is

"}, {"id": "D", "text": "

To demonstrate how the experiences of individuals relate to the experiences of their communities

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer because it accurately states the main purpose of the text. The text begins by discussing the promise of the future, with positive references to renewal such as “new roads,” “new beating of the drum,” and “fresh seeing.” But with the “new sun,” the text continues, there will still be “the same backs bending” and “the same sad feet” drumming, indicating that these difficulties will follow people into this new day. The poem thus considers both the rewards and challenges associated with the repetitiveness of human life.

Choice B is incorrect because the text doesn’t say anything about how memorable activities are, let alone compare the memorability of activities completed at different times of the day. Choice C is incorrect. Although the text contrasts hope with difficulty, it does not compare the relative frequency of joyful feelings with that of sad feelings. Choice D is incorrect because the text makes no distinction between the experiences of individuals and the experiences of their communities.

"}, {"id": "1ad04ea0", "domain": "Craft and Structure", "skill": "Words in Context", "difficulty": "E", "type": "mc", "stimulus": "

In habitats with limited nutrients, certain fungus species grow on the roots of trees, engaging in mutually beneficial relationships known as ectomycorrhizae: in this symbiotic exchange, the tree provides the fungus with carbon, a nutrient necessary for both species, and the fungus ______blank by enhancing the tree’s ability to absorb nitrogen, another key nutrient, from the soil.

", "stem": "

Which choice completes the text with the most logical and precise word or phrase?

", "choices": [{"id": "A", "text": "

overreacts

"}, {"id": "B", "text": "

reciprocates

"}, {"id": "C", "text": "

retaliates

"}, {"id": "D", "text": "

deviates

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer because it most logically completes the text’s discussion of ectomycorrhizae relationships. In this context, “reciprocates” means responds in kind or degree. The text indicates that the relationship between certain fungi and trees in some habitats is “mutually beneficial” and involves a “symbiotic exchange” in which each organism helps the other access an important nutrient. In other words, each organism provides the same kind of benefit it receives: the tree provides a nutrient (carbon) for the fungus and the fungus reciprocates by helping the tree to absorb more of another nutrient (nitrogen).

Choice A is incorrect because the text emphasizes that the relationship between certain fungi and trees in some habitats involves a “symbiotic exchange” in which each organism helps the other access an important nutrient. Nothing in the text suggests that the fungus “overreacts,” or responds too strongly, by allowing the tree to be better able to absorb a beneficial nutrient. Choice C is incorrect because “retaliates” means responds to a harmful action with a similarly harmful action. The text indicates that the relationship between certain fungi and trees in some habitats is “mutually beneficial” and involves a “symbiotic exchange” in which each organism helps the other, not that the relationship is one in which the organisms harm one another. Choice D is incorrect. In this context, “deviates” would mean departs from an established course or norm. The text explains that the relationship between certain fungi and trees in some habitats involves a “symbiotic exchange” in which each organism helps the other access an important nutrient. Because the relationship involves benefits for both the fungus and the tree, it wouldn’t make sense to say that the fungus deviates by helping the tree be better able to absorb a beneficial nutrient.

"}, {"id": "a68239ed", "domain": "Craft and Structure", "skill": "Text Structure and Purpose", "difficulty": "E", "type": "mc", "stimulus": "

The following text is adapted from Oscar Wilde’s 1897 nonfiction work De Profundis. 

\n
\n

People whose desire is solely for self-realisation never know where they are going. They can’t know. In one sense of the word it is of course necessary to know oneself: that is the first achievement of knowledge. But to recognise that the soul of a man is unknowable, is the ultimate achievement of wisdom. The final mystery is oneself. When one has weighed the sun in the balance, and measured the steps of the moon, and mapped out the seven heavens star by star, there still remains oneself. Who can calculate the orbit of his own soul?

\n
", "stem": "

Which choice best describes the function of the underlined question in the text as a whole?

", "choices": [{"id": "A", "text": "

It reinforces the text’s skepticism about the possibility of truly achieving self-knowledge.

"}, {"id": "B", "text": "

It speculates that some readers will share the doubts expressed in the text about the value of self-knowledge.

"}, {"id": "C", "text": "

It cautions readers that the text’s directions for how to achieve self-knowledge are hard to follow.

"}, {"id": "D", "text": "

It concedes that the definition of self-knowledge advanced in the text is unpopular.

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. The text repeatedly claims that true self-knowledge can’t possibly be achieved, and this rhetorical question emphasizes that point.

Choice B is incorrect. The underlined question doesn’t do this. The text never expresses doubts about the value of self-knowledge—rather, the text expresses doubts about the possibility of achieving self-knowledge. Choice C is incorrect. The underlined question doesn’t do this. The text doesn’t provide directions for how to achieve self-knowledge—rather, it claims that true self-knowledge is impossible to achieve. Choice D is incorrect. The underlined question doesn’t do this. The text doesn’t ever define self-knowledge, and popularity isn’t mentioned in the text at all.

"}, {"id": "479c7e82", "domain": "Craft and Structure", "skill": "Words in Context", "difficulty": "E", "type": "mc", "stimulus": "

Although critics believed that customers would never agree to pay to pick their own produce on farms, such concerns didn’t ______blank Booker T. Whatley’s efforts to promote the practice. Thanks in part to Whatley’s determined advocacy, farms that allow visitors to pick their own apples, pumpkins, and other produce can be found throughout the United States.

", "stem": "

Which choice completes the text with the most logical and precise word or phrase?

", "choices": [{"id": "A", "text": "

enhance

"}, {"id": "B", "text": "

hinder

"}, {"id": "C", "text": "

misrepresent

"}, {"id": "D", "text": "

aggravate

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer because it most logically completes the text’s discussion of Booker T. Whatley. In this context, “hinder” means hold back or obstruct. The text explains that Whatley encouraged farms to allow customers on site to pick their own produce for a fee. He did so despite critics’ concerns that the customers would never pay to do so. This context establishes that the critics’ concerns didn’t hinder Whatley’s efforts to promote the practice.

Choice A is incorrect. The text indicates that critics’ skepticism of the idea that customers would pay to pick their own produce didn’t have some effect on Whatley’s promotion of the practice. The text illustrates this assertion by describing Whatley’s “determined advocacy” for the practice. This context suggests that critics’ concerns didn’t obstruct Whatley’s efforts, not that critics’ concerns didn’t “enhance,” or increase or improve, Whatley’s efforts. Choice C is incorrect because in this context, “misrepresent” would mean portray inaccurately, and the text includes no information relevant to the issue of how Whatley’s efforts were portrayed by critics of the practice of charging customers to pick their own produce. Choice D is incorrect. The text indicates that critics’ skepticism of the idea that customers would pay to pick their own produce didn’t have some effect on Whatley’s promotion of the practice. The text illustrates this assertion by describing Whatley’s “determined advocacy” for the practice. This context suggests that critics’ concerns didn’t obstruct Whatley’s efforts, not that critics’ concerns didn’t “aggravate,” or irritate or make more severe, Whatley’s efforts.

"}, {"id": "74446089", "domain": "Craft and Structure", "skill": "Text Structure and Purpose", "difficulty": "M", "type": "mc", "stimulus": "

For his 1986 album Keyboard Fantasies, Beverly Glenn-Copeland wrote songs grounded in traditional soul and folk music, then accompanied them with futuristic synthesizer arrangements featuring ambient sounds and complex rhythms. The result was so strange, so unprecedented, that the album attracted little attention when first released. In recent years, however, a younger generation of musicians has embraced the stylistic experimentation of Keyboard Fantasies. Alternative R&B musicians Blood Orange and Moses Sumney, among other contemporary recording artists, cite the album as an influence.

", "stem": "

Which choice best describes the function of the underlined sentence in the text as a whole?

", "choices": [{"id": "A", "text": "

It urges contemporary musicians to adopt the unique sound of Keyboard Fantasies.

"}, {"id": "B", "text": "

It responds to criticism of Keyboard Fantasies by some younger musicians.

"}, {"id": "C", "text": "

It offers examples of younger musicians whose work has been impacted by Keyboard Fantasies.

"}, {"id": "D", "text": "

It contrasts Keyboard Fantasies with the recordings of two younger musicians.

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer because it most accurately describes the function of the underlined sentence in the text as a whole. The text’s subject is Beverly Glenn-Copeland’s 1986 album Keyboard Fantasies, notable for its innovative, experimental arrangements. According to the text, the album was not initially admired, but in recent years it has become popular among younger musicians. The underlined portion of the text mentions two of those musicians, Blood Orange and Moses Sumney, who “cite the album as an influence.” Therefore, the underlined portion of the text offers examples of younger musicians whose work has been impacted by Keyboard Fantasies.

Choice A is incorrect because even though the underlined sentence states that Blood Orange and Moses Sumney were influenced by Keyboard Fantasies, it doesn’t say that all other musicians should also embrace the album’s experimental style. Choice B is incorrect. Although the text states that Keyboard Fantasies was not admired on its first release, the text doesn’t present any criticism of the album by younger musicians: it only presents two younger musicians who cite it as an influence. Choice D is incorrect because the underlined sentence doesn’t mention any differences between Keyboard Fantasies and the work of Blood Orange and Moses Sumney.

"}, {"id": "c14daa3c", "domain": "Craft and Structure", "skill": "Words in Context", "difficulty": "H", "type": "mc", "stimulus": "

Close analysis of the painting Girl with a Flute, long attributed to the seventeenth-century Dutch painter Johannes Vermeer, has revealed subtle deviations from the artist’s signature techniques. These variations suggest that the work may be that of a student under Vermeer’s tutelage—potentially ______blank our understanding of Vermeer as a solitary artist.

", "stem": "

Which choice completes the text with the most logical and precise word or phrase?

", "choices": [{"id": "A", "text": "

negating 

"}, {"id": "B", "text": "

prefiguring

"}, {"id": "C", "text": "

entrenching

"}, {"id": "D", "text": "

substantiating

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. \"Negating\" means \"reversing\" or \"making invalid.\" Proving that Vermeer worked with students would reverse the view of him as a solitary artist.

Choice B is incorrect. \"Prefiguring\" means \"being an early indicator of.\" There already existed views of Vermeer as a solitary painter, so a new painting would not be an early indicator of those views. Rather, a painting proving that Vermeer had a student would contradict those earlier views. Choice C is incorrect. \"Entrenching\" means \"solidifying.\" A painting proving that Vermeer had a student would not solidify views of him as solitary, but would rather contradict those views. Choice D is incorrect. \"Substantiating\" means \"supporting with proof.\" A painting proving that Vermeer had a student would not support views of him as solitary, but would rather contradict those views.

"}, {"id": "d3ca5d59", "domain": "Craft and Structure", "skill": "Words in Context", "difficulty": "M", "type": "mc", "stimulus": "

Stephen Hannock’s luminous landscape paintings are appealing to viewers but have elicited little commentary from contemporary critics, a phenomenon that may be due to the very fact that the paintings seem so ______blank. Many critics focus their attention on art that is cryptic or overtly challenging. 

", "stem": "

Which choice completes the text with the most logical and precise word or phrase?

", "choices": [{"id": "A", "text": "

innovative

"}, {"id": "B", "text": "

subversive

"}, {"id": "C", "text": "

profound

"}, {"id": "D", "text": "

accessible

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. When talking about a thing, “accessible” means “easy to understand.” This sets up the contrast in the next sentence, which tells us that critics mostly focus on art that is “cryptic or challenging” (meaning not easy to understand).

Choice A is incorrect. This doesn’t fit the logic of the text. The next sentence tells us that critics focus on art that is mysterious and challenging. If Hannock’s paintings are “innovative” (meaning advanced and original), then critics probably would comment on them. Choice B is incorrect. This doesn’t fit the logic of the text. The next sentence tells us that critics focus on art that is mysterious and challenging. If Hannock’s paintings are “subversive” (meaning disruptive and revolutionary), then critics probably would comment on them. Choice C is incorrect. This doesn’t fit the logic of the text. The next sentence tells us that critics focus on art that is mysterious and challenging. If Hannock’s paintings are “profound” (meaning very deep and insightful), then critics probably would comment on them.

"}, {"id": "0ee67e09", "domain": "Craft and Structure", "skill": "Words in Context", "difficulty": "E", "type": "mc", "stimulus": "

Anthropologist Kristian J. Carlson and colleagues examined the fossilized clavicle and shoulder bones of a 3.6-million-year-old early hominin known as “Little Foot.” They found that these bones were ______blank the clavicle and shoulder bones of modern apes that are frequent climbers, such as gorillas and chimpanzees, suggesting that Little Foot had adapted to life in the trees.

", "stem": "

Which choice completes the text with the most logical and precise word or phrase?

", "choices": [{"id": "A", "text": "

surpassed by

"}, {"id": "B", "text": "

comparable to

"}, {"id": "C", "text": "

independent of

"}, {"id": "D", "text": "

obtained from

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer because it most logically completes the text’s discussion of the fossilized bones of the hominin known as Little Foot. As used in this context, “comparable to” would mean similar to. The text indicates that the relationship between the fossilized clavicle and shoulder bones of Little Foot and the clavicle and shoulder bones of “frequent climbers,” such as chimpanzees and gorillas, suggests that Little Foot had adapted to moving around in trees. This context suggests that the relationship between the fossilized bones of Little Foot and the bones of chimpanzees and gorillas is one of similarity—the Little Foot fossils are likely comparable to the modern ape bones. 

Choice A is incorrect because if the fossilized bones of Little Foot were “surpassed by,” or exceeded by or made inferior to, the bones of modern apes that are frequent climbers, it wouldn’t suggest, as the text says, that Little Foot was adapted to moving around in trees. If anything, learning that Little Foot’s clavicle and shoulder bones were surpassed by those of chimpanzees and gorillas would suggest that Little Foot was poorly adapted to climbing. Choice C is incorrect because if Little Foot’s fossilized clavicle and shoulder bones were “independent of,” or not influenced by or affiliated with, the bones of modern apes that climb often, it wouldn’t suggest, as the text says, that Little Foot was adapted to moving around in trees. Choice D is incorrect because the text indicates that Little Foot’s fossilized bones date to 3.6 million years ago, so they couldn’t have been “obtained from,” or acquired from, the bones of modern apes.   

"}, {"id": "760ee1db", "domain": "Craft and Structure", "skill": "Words in Context", "difficulty": "E", "type": "mc", "stimulus": "

Although the playwrights hoped that their play would be ______blank when performed live, critics generally agreed that the production and performances had the opposite effect, wearying audiences instead of energizing them.

", "stem": "

Which choice completes the text with the most logical and precise word or phrase?

", "choices": [{"id": "A", "text": "

multifaceted

"}, {"id": "B", "text": "

realistic

"}, {"id": "C", "text": "

rousing

"}, {"id": "D", "text": "

subtle

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer because it most logically completes the text’s discussion of the play’s effect on audiences. As used in this context, “rousing” means exciting or energizing. The text indicates that critics found the play to have “the opposite effect” on audiences of what the playwrights hoped for. The critics, the text says, thought the play was wearying rather than energizing to viewers. This context supports the idea that the playwrights hoped live performances of the play would be energizing, or rousing, to audiences.

Choice A is incorrect because there’s no information in the text suggesting that the playwrights hoped live performances of the play would be “multifaceted,” or be varied or have many aspects. The text indicates that critics found the play to be wearying to audiences and that this was the opposite of what the playwrights hoped for. Multifaceted is not the opposite of wearying, but rousing is, which suggests that the playwrights hoped the play would be rousing. Choice B is incorrect because there’s no information in the text suggesting that the playwrights hoped live performances of the play would be “realistic,” or lifelike or sensible. The text says that critics found the play to be wearying to audiences and that this was the opposite of what the playwrights hoped for. Realistic is not the opposite of wearying, but rousing is, which suggests that the playwrights hoped the play would be rousing. Choice D is incorrect because there’s no information in the text suggesting that the playwrights hoped live performances of the play would be subtle, or complex or understated. The text says that critics found the play to be wearying to audiences and that this was the opposite of what the playwrights hoped for. Subtle is not the opposite of wearying, but rousing is, which suggests that the playwrights hoped the play would be rousing. 

"}, {"id": "c5b1afe5", "domain": "Craft and Structure", "skill": "Words in Context", "difficulty": "M", "type": "mc", "stimulus": "

Bicycle sharing systems allow users to rent a bicycle at one location within a city and return it to any other designated location in that city, which can cause serious problems of bicycle supply and user demand within the city’s system. Tohru Ikeguchi uses open-source data and statistical modeling to identify when a high number of users making one-way trips is likely to leave some locations within the system ______blank bicycles and other areas with insufficient supply.

", "stem": "

Which choice completes the text with the most logical and precise word or phrase?

", "choices": [{"id": "A", "text": "

susceptible to

"}, {"id": "B", "text": "

contingent on

"}, {"id": "C", "text": "

saturated with

"}, {"id": "D", "text": "

depleted of

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer because it most logically completes the text’s discussion of Ikeguchi’s model of bicycle supply. In this context, “saturated with” means thoroughly or completely supplied with. The text explains a problem encountered by some bicycle-sharing programs: users can return bicycles to different locations than where the users picked up the bicycles to start, which can result in a mismatch between bicycle supply (that is, where the bicycles are currently located) and user demand (that is, the locations where users are hoping to pick up bicycles). The text goes on to explain that Ikeguchi developed a way to identify when this mismatch is likely to occur. This context suggests that Ikeguchi’s method will show when it is likely that some locations have an insufficient supply and other locations, by implicit contrast, are saturated with bicycles. 

Choice A is incorrect because nothing in the text suggests that some locations are “susceptible to,” or sensitive to or easily influenced by, bicycles. The text describes the phenomenon of bicycles being redistributed away from locations where users want them, not anything about those locations being influenced by the bicycles. Choice B is incorrect because the text describes situations in which some locations have an insufficient supply of bicycles because the bicycles have been relocated elsewhere, which suggests that the other locations have many bicycles, not that the other locations are “contingent on,” or dependent on, the bicycles. Nothing in the text suggests that the locations themselves depend on the bicycles for anything. Choice D is incorrect because it would not make sense in context to say that some locations are “depleted of,” or empty of, bicycles while others have an insufficient supply. The text describes situations in which bicycles have been relocated such that there is a mismatch between bicycle supply and user demand—the bicycles are no longer at the locations where users want to pick them up. This means that some locations do not have enough bicycles, while other locations must have many bicycles, not be depleted of bicycles. \n 

"}, {"id": "84dbd633", "domain": "Craft and Structure", "skill": "Cross-Text Connections", "difficulty": "H", "type": "mc", "stimulus": "

Text 1

\n

The Cretaceous-Paleogene (K-Pg) mass extinction event is usually attributed solely to an asteroid impact near Chicxulub, Mexico. Some scientists argue that volcanic activity was the true cause, as the K-Pg event occurred relatively early in a long period of eruption of the Deccan Traps range that initially produced huge amounts of climate-altering gases. These dissenters note that other mass extinctions have coincided with large volcanic eruptions, while only the K-Pg event lines up with an asteroid strike.

\n

 

\n

Text 2

\n

In a 2020 study, Pincelli Hull and her colleagues analyzed ocean core samples and modeled climate changes around the K-Pg event. The team concluded that Deccan Traps gases did affect global conditions prior to the event, but that the climate returned to normal well before the extinctions began—extinctions that instead closely align with the Chicxulub impact.

", "stem": "

Based on the texts, how would Hull’s team (Text 2) most likely respond to the argument in the underlined portion of Text 1?

", "choices": [{"id": "A", "text": "

By agreeing that the Chicxulub impact changed the climate and that the Deccan Traps eruption caused the K-Pg event

"}, {"id": "B", "text": "

By declaring that the changes in climate caused by the Deccan Traps eruption weren’t the main cause of the K-Pg event

"}, {"id": "C", "text": "

By questioning why those scientists assume that the Chicxulub impact caused the Deccan Traps eruption

"}, {"id": "D", "text": "

By asserting that the Deccan Traps eruption had a more significant effect on global conditions than those scientists claim

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer because it describes how Hull’s team would most likely respond to the argument in the underlined portion of Text 1, which asserts that volcanic activity in the Deccan Traps range led to changes in the climate and caused the K-Pg mass extinction event. According to Text 2, although Hull’s team found that activity in the Deccan Traps did indeed alter the climate before the K-Pg event, the team determined that the climate had returned to normal before mass extinctions began. This finding and the observation that the K-Pg extinctions closely align with the Chicxulub asteroid impact suggest that Hull’s team would likely dispute the claim in the underlined portion of Text 1 and say that the climate changes caused by the Deccan Traps activity were not the main cause of the extinctions.

Choice A is incorrect because Text 2 describes how Hull’s team found that the climate had recovered from the changes brought about by the Deccan Traps activity before the K-Pg event occurred, which suggests that Hull’s team would disagree that the Deccan Traps activity caused the K-Pg event. Additionally, the claim in the underlined portion of Text 1 says nothing about how the Chicxulub impact changed the climate, so while Hull’s team might believe that the impact did in fact change the climate, they could not be said to agree with the claim in Text 1 on this point. Choice C is incorrect because there is no indication in either text that any scientists assume that the Chicxulub impact caused the Deccan Traps activity, so there is no reason to conclude that Hull’s team would question why the scientists referred to in Text 1 make such an assumption. Choice D is incorrect because Text 2 describes how Hull’s team found that the climate had recovered from the changes brought about by the Deccan Traps activity before the K-Pg event occurred, which suggests that Hull’s team would say that the Deccan Traps activity had a less enduring effect on global conditions than the scientists referenced in Text 1 believe, not that the effect on global conditions was more significant than those scientists claim.

"}, {"id": "a2dd51c1", "domain": "Craft and Structure", "skill": "Text Structure and Purpose", "difficulty": "E", "type": "mc", "stimulus": "

In most building demolitions, the building materials are destroyed and sent to landfills. City officials in Portland, Oregon, wanted to reduce this waste. The officials passed a law requiring demolition companies to deconstruct some buildings instead. Deconstruction involves carefully taking buildings apart piece by piece. Damage to the materials is avoided so that they can be reused in new constructions. A 2019 study found that 27 percent of materials from deconstructions in Portland were able to be reused. The remaining materials were processed for recycling instead of going to a landfill.

", "stem": "

Which choice best states the main purpose of the text?

", "choices": [{"id": "A", "text": "

To explain an effort made by the city of Portland to reduce demolition waste and some results of that effort 

"}, {"id": "B", "text": "

To show that popular support for measures that reduce demolition waste has increased since 2019

"}, {"id": "C", "text": "

To argue that building deconstruction is not as effective as other measures at reducing demolition waste

"}, {"id": "D", "text": "

To discuss laws aimed to reduce demolition waste in Portland and compare them to similar laws in other cities 

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. The author first describes a Portland law aimed at reducing demolition waste, and then goes on to explain that 27% of materials from building deconstructions were able to be reused and the rest were recycled.

Choice B is incorrect. The text never discusses the popularity of the law. Choice C is incorrect. The text never compares building deconstruction to other measures designed to reduce demolition waste. Choice D is incorrect. The text never mentions laws in cities other than Portland, Oregon.

"}, {"id": "9d73c9eb", "domain": "Craft and Structure", "skill": "Words in Context", "difficulty": "E", "type": "mc", "stimulus": "

Osage Nation citizen Randy Tinker-Smith produced and directed the ballet Wahzhazhe, which vividly chronicles Osage history and culture. Telling Osage stories through ballet is ______blank choice because two of the foremost ballet dancers of the twentieth century were Osage: sisters Maria and Marjorie Tallchief. 

", "stem": "

Which choice completes the text with the most logical and precise word or phrase?

", "choices": [{"id": "A", "text": "

a suitable

"}, {"id": "B", "text": "

a determined

"}, {"id": "C", "text": "

an arbitrary

"}, {"id": "D", "text": "

an unpredictable

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. “Suitable” means “appropriate for a particular purpose.” Since the text indicates that two of the best ballet dancers of the twentieth century were Osage, we can infer that the author believes that ballet is a very suitable artform for telling Osage stories.

Choice B is incorrect. The text never suggests that Tinker-Smith’s choice was determined. That would imply that Tinker-Smith initially faced some kind of obstacle or opposition, and nothing like that is mentioned in the passage. Choice C is incorrect. The text implies the opposite of this. “Arbitrary” means “based on random choice or whim rather than reason.” But the text does give us a good reason behind the choice to tell Osage stories through ballet: two of the best ballet dancers of the twentieth century were Osage. Choice D is incorrect. The text never suggests that Tinker-Smith’s choice was “unpredictable.” Rather, the fact that two of the best ballet dancers of the twentieth century were Osage makes ballet especially appropriate for telling Osage stories.

"}, {"id": "81a3a607", "domain": "Craft and Structure", "skill": "Words in Context", "difficulty": "M", "type": "mc", "stimulus": "

In the Indigenous intercropping system known as the Three Sisters, maize, squash, and beans form an ______blank web of relations: maize provides the structure on which the bean vines grow; the squash vines cover the soil, discouraging competition from weeds; and the beans aid their two “sisters” by enriching the soil with essential nitrogen.

", "stem": "

Which choice completes the text with the most logical and precise word or phrase?

", "choices": [{"id": "A", "text": "

indecipherable

"}, {"id": "B", "text": "

ornamental

"}, {"id": "C", "text": "

obscure

"}, {"id": "D", "text": "

intricate

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer because it most logically completes the text’s discussion of the Three Sisters intercropping system. As used in this context, “intricate” would mean made up of complexly related elements. The text indicates that in the Three Sisters system, maize, squash, and beans form a “web of relations” in which the crops interact in various ways. The text’s description of these interactions—the bean vines growing on the maize stalks, the squash vines keeping weeds away, and the beans adding nutrients that the maize and squash use—provides context suggesting that this “web of relations” is intricate.

Choice A is incorrect because describing the relationship among the crops in the Three Sisters system as “indecipherable,” or impossible to comprehend, would not make sense in context. Although the text presents the relationship as complex, the text’s description of the role that each crop plays makes it clear that the relationship is well understood, not indecipherable. Choice B is incorrect because the text discusses the practical benefits that each plant in the Three Sisters system provides to other members of the system, showing that the relationship among the crops that make up the system is not “ornamental,” or mainly serving a decorative purpose. Choice C is incorrect because describing the relationship among the crops in the Three Sisters system as “obscure,” or unknown or poorly understood, would not make sense in context. Although the text presents the relationship as complex, the text’s description of the role that each crop plays makes it clear that the relationship is well understood, not obscure. 

"}, {"id": "48e4021d", "domain": "Craft and Structure", "skill": "Text Structure and Purpose", "difficulty": "E", "type": "mc", "stimulus": "

The following text is from Holly Goldberg Sloan’s 2017 novel Short. 

\n
\n

More than two years ago my parents bought a piano from some people who were moving to Utah. Mom and Dad gave it to my brothers and me for Christmas. I had to act really happy because it was such a big present, but I pretty much hated the thing from the second it was carried into the hallway upstairs, which is right next to my bedroom. The piano glared at me. It was like a songbird in a cage. It wanted to be set free.  

\n
\n

©2017 by Holly Goldberg Sloan

", "stem": "

Which choice best states the main purpose of the text?

", "choices": [{"id": "A", "text": "

It explains why the narrator always wanted a piano close to her bedroom. 

"}, {"id": "B", "text": "

It establishes how the narrator feels about the piano.

"}, {"id": "C", "text": "

It suggests that the narrator’s brothers are talented piano players.

"}, {"id": "D", "text": "

It describes the event that led the narrator’s parents to buy a piano.

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer because it best states the main purpose of the text, which is to establish the narrator’s feelings about the piano. The narrator reveals that she “had to act really happy” about the piano even though she “pretty much hated the thing” as soon as it was placed upstairs near her bedroom. The narrator also describes the piano as glaring at her and compares it to a caged bird that wants to be set free. These details establish the narrator’s feelings about the piano, suggesting that it makes her uneasy.

Choice A is incorrect because the text indicates that the narrator hated having the piano upstairs right next to her bedroom, not that she wanted a piano to be close to her bedroom. Choice C is incorrect because the only information provided in the text about the narrator’s brothers is that they were given the piano along with the narrator. Choice D is incorrect because the text does not describe the event that led the narrator’s parents to buy the piano from the people moving to Utah. Instead, the text focuses on the narrator’s feelings about the piano after it was given to her and her brothers.

"}, {"id": "8d579825", "domain": "Craft and Structure", "skill": "Words in Context", "difficulty": "E", "type": "mc", "stimulus": "

The printing of Virginia Woolf’s novels featured a creative ______blank between Woolf and her sister Vanessa Bell: a talented painter, Bell worked closely with Woolf to create original cover art for most of the novels.

", "stem": "

Which choice completes the text with the most logical and precise word or phrase?

", "choices": [{"id": "A", "text": "

rebellion

"}, {"id": "B", "text": "

partnership

"}, {"id": "C", "text": "

discovery

"}, {"id": "D", "text": "

disagreement

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer because it most logically completes the text’s discussion of the cover art of Virginia Woolf’s novels. In this context, “partnership” means collaboration or joint effort. The text states that Woolf’s sister Vanessa Bell was a talented painter and that Bell worked with Woolf to provide the cover art for most of Woolf’s novels. Thus, this context suggests that Woolf and Bell pursued a creative partnership in order to produce several of Woolf’s novels.

Choice A is incorrect because there is no indication that Woolf or Bell were undergoing a “rebellion,” or revolt, against anything in particular. Instead, the text focuses on how they worked together in some aspects of the production of Woolf’s novels. Choice C is incorrect because there is nothing in the text to indicate that Woolf or Bell made a “discovery,” or encountered anything new for the first time as they worked together. The text suggests that Woolf had already written her novels and that Bell then assisted Woolf with the cover art for many of them. Choice D is incorrect because the text implies that Woolf and Bell had a positive relationship. According to the text, the sisters “worked closely” together to produce the cover art for many of Woolf’s novels; the text doesn’t mention whether while working together, Woolf and Bell had a “disagreement,” or conflict.

"}, {"id": "3566120b", "domain": "Craft and Structure", "skill": "Words in Context", "difficulty": "H", "type": "mc", "stimulus": "

The following text is adapted from Oscar Wilde’s 1895 play The Importance of Being Earnest.

\n

CECILY: Have we got to part?

\n

ALGERNON: I am afraid so. It’s a very painful parting.

\n

CECILY: It is always painful to part from people whom one has known for a very brief space of time. The absence of old friends one can endure with equanimity. But even a momentary separation from anyone to whom one has just been introduced is almost unbearable.

", "stem": "

As used in the text, what does the word “endure” most nearly mean?

", "choices": [{"id": "A", "text": "

Regret

"}, {"id": "B", "text": "

Persist

"}, {"id": "C", "text": "

Tolerate

"}, {"id": "D", "text": "

Encourage

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer because as used in the text, “endure” most nearly means tolerate. In the text, Cecily and Algernon discuss parting, or saying goodbye. Cecily remarks on the deep pain of saying goodbye to people whom one has only known briefly and then comments on the equanimity, or calm steadiness, one experiences when separated from old friends. The text sets up an ironic contrast: one can easily tolerate, or put up with, the absence of close friends, but even a very short separation from a new acquaintance is unbearable.

Choice A is incorrect. Nothing in the text suggests that Cecily associates regret, or a feeling of sorrow, with the absence of old friends. Rather, the text sets up an ironic contrast between the feeling of calm steadiness one feels when separated from old friends and the unbearable pain of being separated from new acquaintances. Choice B is incorrect. Although in some contexts “endure” can mean persist, or proceed stubbornly, it doesn’t have that meaning in this context because what is being endured is the absence of old friends. Whereas one can persist despite the absence of someone else, one can’t persist the absence itself. Choice D is incorrect because the text doesn’t convey that Cecily encourages, or urges, old friends to be absent. Although it may be that Cecily prefers new acquaintances to friends she has known for a long time, the text focuses on her feelings as a result of others’ absences, not on her treatment of others.

"}, {"id": "f2c48e47", "domain": "Craft and Structure", "skill": "Text Structure and Purpose", "difficulty": "M", "type": "mc", "stimulus": "

The following text is from Charlotte Perkins Gilman’s 1910 poem “The Earth’s Entail.”

\n

No matter how we cultivate the land,

\n

Taming the forest and the prairie free;

\n

No matter how we irrigate the sand,

\n

Making the desert blossom at command,

\n

 We must always leave the borders of the sea;

\n

 The immeasureable reaches

\n

 Of the windy wave-wet beaches,

\n

The million-mile-long margin of the sea.

", "stem": "

Which choice best describes the overall structure of the text?

", "choices": [{"id": "A", "text": "

The speaker argues against interfering with nature and then gives evidence supporting this interference.

"}, {"id": "B", "text": "

The speaker presents an account of efforts to dominate nature and then cautions that such efforts are only temporary.

"}, {"id": "C", "text": "

The speaker provides examples of an admirable way of approaching nature and then challenges that approach. 

"}, {"id": "D", "text": "

The speaker describes attempts to control nature and then offers a reminder that not all nature is controllable. 

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. This best describes the overall structure of the text. In the first half of the text, the speaker describes our attempts to control nature: cultivating, taming, and irrigating different kinds of land. In the second half, the speaker states that we can never tame the sea or the beach. 

Choice A is incorrect. This doesn’t describe the overall structure of the text. The speaker never argues that we should not interfere with nature. Rather, the speaker says that we are able to tame many different kinds of land, but we are unable to tame the sea or beaches. Choice B is incorrect. This doesn’t describe the overall structure of the text. The speaker never describes our cultivation, taming, and irrigation of land as “temporary.” Rather, the speaker says that we are able to tame many different kinds of land, but we are unable to tame the sea or beaches. Choice C is incorrect. This doesn’t describe the overall structure of the text. The speaker never describes our cultivation, taming, and irrigation of land as an “admirable” approach to nature.” Rather, the speaker says that we are able to tame many different kinds of land, but we are unable to tame the sea or beaches. 

"}, {"id": "bcc91b1e", "domain": "Craft and Structure", "skill": "Words in Context", "difficulty": "E", "type": "mc", "stimulus": "

The spacecraft OSIRIS-REx briefly made contact with the asteroid 101955 Bennu in 2020. NASA scientist Daniella DellaGiustina reports that despite facing the unexpected obstacle of a surface mostly covered in boulders, OSIRIS-REx successfully ______blank a sample of the surface, gathering pieces of it to bring back to Earth.

", "stem": "

Which choice completes the text with the most logical and precise word or phrase?

", "choices": [{"id": "A", "text": "

attached

"}, {"id": "B", "text": "

collected

"}, {"id": "C", "text": "

followed

"}, {"id": "D", "text": "

replaced

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer because it most logically completes the text’s discussion of the OSIRIS-REx spacecraft’s contact with the asteroid 101955 Bennu. In this context, “collected” means acquired and took away. The text indicates that although the boulders on the asteroid’s surface caused some unforeseen problems, OSIRIS-REx was able to gather a sample to return to Earth. This context suggests that OSIRIS-REx successfully collected a sample of 101955 Bennu.

Choice A is incorrect because in this context “attached” means connected or affixed. The text indicates that OSIRIS-REx gathered pieces of 101955 Bennu to bring to Earth; it doesn’t suggest that the spacecraft attached anything to the asteroid. Choice C is incorrect because in this context “followed” means tracked or traveled behind and the text discusses OSIRIS-REx’s brief encounter with 101955 Bennu during which the spacecraft gathered a sample to bring to Earth. The text doesn’t suggest that the spacecraft tracked the sample, and it’s not clear what it would mean for the spacecraft to travel behind the sample it collected. Choice D is incorrect because in this context “replaced” means put back or returned. The text indicates that OSIRIS-REx gathered pieces of 101955 Bennu to bring to Earth but doesn’t suggest that anything was returned to the asteroid.

"}, {"id": "9645f55e", "domain": "Craft and Structure", "skill": "Cross-Text Connections", "difficulty": "E", "type": "mc", "stimulus": "

Text 1

\n

For decades, bluegrass musicians have debated whether their genre should exclude influences from mainstream genres such as rock. Many insist that bluegrass is defined by its adherence to the folk music of the US South, out of which bluegrass emerged. Such “purists,” as they are known, regard the recordings of Bill Monroe, which established the bluegrass sound in the 1940s, as a standard against which the genre should still be measured.

\n

 

\n

Text 2

\n

Bluegrass isn’t simply an extension of folk traditions into the era of recorded music. In reality, Bill Monroe created the bluegrass sound in the 1940s by combining Southern folk music with commercial genres that had arisen only a few decades before, such as jazz and the blues. Since bluegrass has always been a mixed genre, contemporary bluegrass musicians should not be forbidden from incorporating into it influences from rock and other mainstream genres.

", "stem": "

Based on the texts, how would the author of Text 2 most likely regard the perspective of bluegrass purists, as described in Text 1?

", "choices": [{"id": "A", "text": "

As inconsistent, since bluegrass purists themselves enjoy other musical genres

"}, {"id": "B", "text": "

As unrealistic, since bluegrass purists have no way of enforcing their musical preferences

"}, {"id": "C", "text": "

As shortsighted, because bluegrass could enlarge its audience by including influences from mainstream genres

"}, {"id": "D", "text": "

As illogical, because the purists overlook crucial aspects of how the bluegrass sound first originated.

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. According to Author 1, the “purists” argue that bluegrass should stick to its folk music roots. But Author 2 points out that this isn’t how bluegrass emerged: it actually got its sound from a mix of folk, jazz, and blues.

Choice A is incorrect. There’s nothing in Text 2 about what other genres the purists enjoy, so this inference about Author 2’s views isn’t supported. Choice B is incorrect. There’s nothing in Text 2 about whether or how purists can enforce their preferences, so this inference about Author 2’s views isn’t supported. Choice C is incorrect. There’s nothing in Text 2 about the size of bluegrass’s audience, so this inference about Author 2’s views isn’t supported.

"}, {"id": "f1c9d2c1", "domain": "Craft and Structure", "skill": "Cross-Text Connections", "difficulty": "M", "type": "mc", "stimulus": "

Text 1

\n

Stage lighting theorist Adolphe Appia was perhaps the first to argue that light must be considered alongside all the various elements of a stage to create a single, unified performance. Researcher Kelly Bremner, however, has noted that Appia lacked technical expertise in the use of light in the theater. As a result of Appia’s inexperience, Bremner argues, Appia’s theory of light called for lighting practices that weren’t possible until after the advent of electricity around 1881. 

\n

 

\n

Text 2

\n

Adolphe Appia was not an amateur in the practice of lighting. Instead, it is precisely his exposure to lighting techniques at the time that contributed to his theory on the importance of light. When working as an apprentice for a lighting specialist in his youth, Appia observed the use of portable lighting devices that could be operated by hand. This experience developed his understanding of what was possible in the coordination of elements on the stage.

", "stem": "

Based on the texts, how would the author of Text 2 most likely respond to the claim about Appia’s level of technical expertise made by Bremner in Text 1?

", "choices": [{"id": "A", "text": "

Many lighting technicians dismissed Appia’s ideas about light on the stage.

"}, {"id": "B", "text": "

Appia likely gained a level of technical expertise during his time as an apprentice.

"}, {"id": "C", "text": "

Theater practitioners who worked with Appia greatly admired his work.

"}, {"id": "D", "text": "

Appia was unfamiliar with the use of music and sound in theater.

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. The author of Text 2 directly contradicts Bremner’s claim that Appia lacked technical expertise by stating that Appia was “not an amateur in the practice of lighting.” His experience as a lighting specialist’s apprentice would have, the author of Text 2 argues, allowed Appia to “[develop] his understanding of what was possible” with the elements of theatrical design.

Choice A is incorrect. Neither text describes how other lighting technicians responded to Appia’s ideas. Furthermore, this claim isn’t relevant to Bremner’s evaluation of Appia’s technical expertise. Choice C is incorrect. Neither text mentions anything about the opinions of theater practitioners who worked with Appia, so this answer choice does not relate to the claim about Appia’s level of technical expertise made by Bremner in Text 1. Choice D is incorrect. Neither text mentions anything about Appia’s familiarity with or ignorance of the use of music and sound in theater. Both focus on his expertise (or lack thereof) in lighting.

"}, {"id": "31d0bd9a", "domain": "Craft and Structure", "skill": "Words in Context", "difficulty": "E", "type": "mc", "stimulus": "

The parasitic dodder plant increases its reproductive success by flowering at the same time as the host plant it has latched onto. In 2020, Jianqiang Wu and his colleagues determined that the tiny dodder achieves this ______blank with its host by absorbing and utilizing a protein the host produces when it is about to flower.

", "stem": "

Which choice completes the text with the most logical and precise word or phrase?

", "choices": [{"id": "A", "text": "

synchronization

"}, {"id": "B", "text": "

hibernation

"}, {"id": "C", "text": "

prediction

"}, {"id": "D", "text": "

moderation

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer because it most logically completes the text’s discussion of a relationship between the dodder plant and its host plant. As used in this context, “synchronization” means the act of things happening at the same time. The text indicates that the dodder and its host plant flower in unison and that this synchronization occurs because the dodder makes use of a protein produced by the host shortly before flowering.

Choice B is incorrect because referring to “hibernation,” or the state of being dormant or inactive, wouldn’t make sense in context. The text focuses on something the dodder plant actively engages in—making use of a protein and producing flowers. Choice C is incorrect because stating that the dodder plant and its host engage together in “prediction,” or the act of declaring or indicating something in advance, wouldn’t make sense in context. Rather than indicating that the dodder plant and its host plant make a prediction about flowering activity, the text suggests that the host produces a protein as part of its regular flowering process and that the dodder then absorbs and uses that protein to flower at the same time. Choice D is incorrect because referring to “moderation,” or the act of causing something to become less intense or extreme, wouldn’t make sense in context. Although the text states that the dodder plant absorbs and uses a protein made by its host plant, it doesn’t suggest that the dodder lessens the host plant’s flowering activity; the two plants simply flower in unison.

"}, {"id": "dc043599", "domain": "Craft and Structure", "skill": "Cross-Text Connections", "difficulty": "E", "type": "mc", "stimulus": "

Text 1

\n

Most scientists agree that the moon was likely formed after a collision between Earth and a large planet named Theia. This collision likely created a huge debris field, made up of material from both Earth and Theia. Based on models of this event, scientists believe that the moon was formed from this debris over the course of thousands of years.

\n

 

\n

Text 2 

\n

Researchers from NASA’s Ames Research Center used a computer to model how the moon could have formed. Although simulations of the moon’s formation have been done in the past, the team from NASA ran simulations that were much more detailed. They found that the formation of the moon was likely not a slow process that took many years. Instead, it’s probable that the moon’s formation happened immediately after impact, taking just a few hours.

", "stem": "

Which choice best describes a difference in how the author of Text 1 and the author of Text 2 view the evidence for the formation of the moon?

", "choices": [{"id": "A", "text": "

The author of Text 1 argues that the formation of the moon occurred much earlier than the author of Text 2 argues.

"}, {"id": "B", "text": "

The author of Text 1 suggests there is more evidence confirming the existence of Theia than the author of Text 2 suggests.

"}, {"id": "C", "text": "

The author of Text 1 claims that the moon’s surface is more similar to Earth’s surface than the author of Text 2 claims.

"}, {"id": "D", "text": "

The author of Text 1 believes that the moon formed more slowly than the author of Text 2 believes.

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. Text 1 states that the moon was formed from the debris “over the course of thousands of years,” while Text 2 states that the moon’s formation happened “immediately after impact, taking just a few hours.” This shows a clear difference in how the authors view the evidence for the speed of the moon’s formation.

Choice A is incorrect. While Text 2 suggests that the moon formed over “just a few hours” and Text 1 says it took “thousands of years,” neither one mentions when that formation occurred. Choice B is incorrect. While Theia isn’t mentioned in Text 2, neither text describes or disputes evidence of Theia’s existence. Choice C is incorrect. Neither text makes any claims about the similarity or difference between the moon’s surface and Earth’s surface.

"}, {"id": "47955354", "domain": "Craft and Structure", "skill": "Words in Context", "difficulty": "E", "type": "mc", "stimulus": "

Sumerian civilization (which lasted from around 3300 to 2000 BCE) ______blank many concepts that persist into present-day civilizations: for example, the first description of the seven-day week appears in the Sumerian Epic of Gilgamesh.

", "stem": "

Which choice completes the text with the most logical and precise word or phrase?

", "choices": [{"id": "A", "text": "

transformed

"}, {"id": "B", "text": "

introduced

"}, {"id": "C", "text": "

inherited

"}, {"id": "D", "text": "

overlooked

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer because it most logically completes the text’s discussion of the contributions of the Sumerian civilization. In this context, “introduced” means brought into practice or use. The text states that the first reference to a seven-day week appears in the Sumerian Epic of Gilgamesh. The text presents this information about the seven-day week as an example of a concept introduced by the Sumerian civilization that persists into present-day civilizations. 

Choice A is incorrect because nothing in the text suggests that the Sumerian civilization “transformed,” or changed the nature of, concepts that persist into present-day civilizations. Instead, the text’s presentation of a Sumerian literary work that contains the first description of the seven-day week is an example of the phenomenon described in the first half of the sentence, suggesting that the Sumerians invented many concepts that still persist. Choice C is incorrect because the information that a Sumerian literary work includes the first description of the seven-day week suggests that Sumerian civilization may have originated the seven-day week and other concepts that persist into present-day civilizations, not that it “inherited” the concepts, or received them from an ancestral figure or culture. Choice D is incorrect because the information that Sumerian civilization produced the first description of the seven-day week is presented as an example of the phenomenon described in the first half of the sentence, suggesting that Sumerian civilization originated this and other concepts that still persist, not that the Sumerians “overlooked,” or failed to notice or consider, such concepts.

"}, {"id": "a3761c7e", "domain": "Craft and Structure", "skill": "Words in Context", "difficulty": "E", "type": "mc", "stimulus": "

Physicist Joseph Weber performed ______blank work in gravitational wave research in the 1960s and 1970s, conducting key experiments that scientists later used as the basis for their own investigations that led to the first verified detection of a gravitational wave in 2015.

", "stem": "

Which choice completes the text with the most logical and precise word or phrase?

", "choices": [{"id": "A", "text": "

foundational

"}, {"id": "B", "text": "

supplementary

"}, {"id": "C", "text": "

repetitive

"}, {"id": "D", "text": "

ineffective

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer because it most logically completes the text’s discussion of physicist Joseph Webster’s research on gravitational waves. In this context “foundational” means the basis on which something else develops. The text indicates that Webster’s experiments in the 1960s and 1970s were earlier than, and “key” to, the work of later scientists in the field; thus, Webster’s work was foundational to the later scientists’ experiments and the eventual detection of a gravitational wave in 2015.  

Choice B is incorrect because the text does not suggest that Webster’s work was supplementary, or an additional element of an existing, larger project, but rather it was “the basis for” later experiments. Choice C is incorrect because the text does not assert that Webster’s work was repetitive, or involved doing something the same way many times. Rather, the text indicates that Webster’s work formed the basis for later investigations in the field of gravitational wave research.  Choice D is incorrect because the text does not state that Webster’s work was ineffective, or failed to produce the desired outcome. Rather, the text strongly implies that Webster’s work was productive and extremely important to later work in the field of gravitational wave research. 

"}, {"id": "34d7bb25", "domain": "Craft and Structure", "skill": "Text Structure and Purpose", "difficulty": "H", "type": "mc", "stimulus": "

According to Indian economist and sociologist Radhakamal Mukerjee (1889–1968), the Eurocentric concepts that informed early twentieth-century social scientific methods—for example, the idea that all social relations are reducible to struggles between individuals—had little relevance for India. Making the social sciences more responsive to Indians’ needs, Mukerjee argued, required constructing analytical categories informed by India’s cultural and ecological circumstances. Mukerjee thus proposed the communalist “Indian village” as the ideal model on which to base Indian economic and social policy.

", "stem": "

Which choice best describes the overall structure of the text?

", "choices": [{"id": "A", "text": "

The text recounts Mukerjee’s early training in the social scientific disciplines and then lists social policies whose implementation Mukerjee oversaw. 

"}, {"id": "B", "text": "

The text mentions some of Mukerjee’s economic theories and then traces their impact on other Indian social scientists of the twentieth century.

"}, {"id": "C", "text": "

The text presents Mukerjee’s critique of the social sciences and then provides an example of his attempts to address issues he identified in his critique.

"}, {"id": "D", "text": "

The text explains an influential economic theory and then demonstrates how that theory was more important to Mukerjee’s work than other social scientists have acknowledged.  

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. The text does indeed present Mukerjee’s critique of the social sciences—that they were too Eurocentric—and then provides an example of how he attempted to address the issues he identified: by suggesting a social science model based on the Indian village.

Choice A is incorrect. The text doesn’t discuss Mukerjee’s early training or his oversight of the implementation of social policies at all. Choice B is incorrect. The text never discusses any other Indian social scientists. Choice D is incorrect. The text never mentions other social scientists’ responses to Mukerjee’s work.

"}, {"id": "c0e1b70a", "domain": "Craft and Structure", "skill": "Text Structure and Purpose", "difficulty": "M", "type": "mc", "stimulus": "

The following text is adapted from Etsu Inagaki Sugimoto’s 1925 memoir A Daughter of the Samurai. As a young woman, Sugimoto moved from feudal Japan to the United States.

\n
\n

The standards of my own and my adopted country differed so widely in some ways, and my love for both lands was so sincere, that sometimes I had an odd feeling of standing upon a cloud in space, and gazing with measuring eyes upon two separate worlds. At first I was continually trying to explain, by Japanese standards, all the queer things that came every day before my surprised eyes; for no one seemed to know the origin or significance of even the most familiar customs, nor why they existed and were followed.

\n
", "stem": "

Which choice best describes the main purpose of the text?

", "choices": [{"id": "A", "text": "

To convey the narrator’s experience of observing and making sense of differences between two cultures she embraces

"}, {"id": "B", "text": "

To establish the narrator’s hope of forming connections with new companions by sharing customs she learned as a child

"}, {"id": "C", "text": "

To reveal the narrator’s recognition that she is hesitant to ask questions about certain aspects of a culture she is newly encountering 

"}, {"id": "D", "text": "

To emphasize the narrator’s wonder at discovering that the physical distance between two countries is greater than she had expected

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer because it most accurately describes the main purpose of the text. The narrator asserts that she loves both her “own” country (Japan) and her “adopted country” (the United States) even though the two countries differ “widely.” She also indicates that, at first, she would try to explain unfamiliar experiences that she had in the United States using the standards ingrained in her from growing up in Japan. Thus, the main purpose of the text is to convey the narrator’s experience of observing and making sense of the differences between two cultures she embraces.

Choice B is incorrect because the text makes no reference to possible companions. Although the text does indicate that the narrator sometimes used the cultural framework she acquired growing up in Japan to explain some experiences she’s had, there is no suggestion that this was in service of making friends. And although “no one seemed to know” strongly implies that the narrator has interacted with other people in the United States, there is no indication that these conversations involved her discussing Japanese customs. Choice C is incorrect because nothing in the text suggests that the narrator was hesitant to ask questions. In fact, the narrator indicates that “no one seemed to know the origin” of various customs, which provides evidence that, rather than being hesitant, she sought information from several people. Choice D is incorrect because the text makes no reference to the physical distance between Japan and the United States. Although the narrator indicates that the two countries differ “widely” and likens them to “two separate worlds,” these descriptions relate to cultural aspects of the countries and the narrator’s feelings about the two countries, not the physical distance between them.

"}, {"id": "f631132b", "domain": "Craft and Structure", "skill": "Text Structure and Purpose", "difficulty": "M", "type": "mc", "stimulus": "

In the Here and Now Storybook (1921), educator Lucy Sprague Mitchell advanced the then controversial idea that books for very young children should imitate how they use language, since toddlers, who cannot yet grasp narrative or abstract ideas, seek reassurance in verbal repetition and naming. The most enduring example of this idea is Margaret Wise Brown’s 1947 picture book Goodnight Moon, in which a young rabbit names the objects in his room as he drifts off to sleep. Scholars note that the book’s emphasis on repetition, rhythm, and nonsense rhyme speaks directly to Mitchell’s influence. 

", "stem": "

Which choice best describes the overall structure of the text?

", "choices": [{"id": "A", "text": "

The text outlines a debate between two authors of children’s literature and then traces how that debate shaped theories on early childhood education. 

"}, {"id": "B", "text": "

The text summarizes an argument about how children’s literature should be evaluated and then discusses a contrasting view on that subject.

"}, {"id": "C", "text": "

The text lists the literary characteristics that are common to many classics of children’s literature and then indicates the narrative subjects that are most appropriate for young children.

"}, {"id": "D", "text": "

The text presents a philosophy about what material is most suitable for children’s literature and then describes a book influenced by that philosophy.  

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. The text starts by introducing Mitchell’s philosophy about using simple, repetitive language in books for young children. Then it describes a book influenced by that philosophy, Goodnight Moon.

Choice A is incorrect. Although two authors are mentioned in the text, they both agree about the type of language that should be contained in books for young children. Choice B is incorrect. The text never discusses the evaluation of children’s literature. It does provide one view of how children’s books should be written, but never introduces a competing view. Choice C is incorrect. The text doesn’t mention “many classics of children’s literature.” Instead, it describes an educational theory and identifies one example of a famous children’s book that was influenced by that theory.

"}, {"id": "80ebb189", "domain": "Craft and Structure", "skill": "Words in Context", "difficulty": "E", "type": "mc", "stimulus": "

As an architect in Los Angeles in the 1950s, Helen Liu Fong became known for avoiding ______blank designs in her buildings. Instead of using standard shapes and colors, she typically explored innovative forms and daring hues.

", "stem": "

Which choice completes the text with the most logical and precise word or phrase?

", "choices": [{"id": "A", "text": "

creative

"}, {"id": "B", "text": "

bold

"}, {"id": "C", "text": "

traditional

"}, {"id": "D", "text": "

understandable

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer because it most logically completes the text’s discussion of Helen Liu Fong’s architectural designs. In this context, “traditional” means conventional. The text states that rather than use “standard shapes and colors,” Fong pursued “innovative” and “daring” design choices in her work. Fong’s style is depicted as inventive, so it therefore makes sense in this context that she avoided mainstream, traditional designs in her buildings. 

Choice A is incorrect because the text indicates that Fong’s work is innovative and experimental. Thus, Fong’s design choices could reasonably be considered creative, or original. She likely would have pursued creative designs, not avoided them. Choice B is incorrect because the text indicates that Fong used “daring” hues in her designs. Thus, Fong likely would have pursued bold, or brave and vivid design choices; she wouldn’t have avoided them. Choice D is incorrect because the text doesn’t address whether Fong’s designs are understandable, or reasonable or expected. The text focuses on certain characteristics of Fong’s designs, not on how people received or understood them.

"}, {"id": "e7d37666", "domain": "Craft and Structure", "skill": "Words in Context", "difficulty": "H", "type": "mc", "stimulus": "

It is by no means ______blank to recognize the influence of Dutch painter Hieronymus Bosch on Ali Banisadr’s paintings; indeed, Banisadr himself cites Bosch as an inspiration. However, some scholars have suggested that the ancient Mesopotamian poem Epic of Gilgamesh may have had a far greater impact on Banisadr’s work.

", "stem": "

Which choice completes the text with the most logical and precise word or phrase?

", "choices": [{"id": "A", "text": "

substantial

"}, {"id": "B", "text": "

satisfying

"}, {"id": "C", "text": "

unimportant

"}, {"id": "D", "text": "

appropriate

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer because it most logically completes the sentence about the influences on Banisadr’s work. In context, “It is by no means” followed by “unimportant” conveys how it is relevant to recognize Bosch’s influence on Banisadr. The text points out that the artist himself cites Bosch as an inspiration, and then goes on to claim that The Epic of Gilgamesh has had a more significant influence than Bosch. 

Choice A is incorrect because “substantial,” which means weighty or meaningful, incorrectly suggests that it wouldn’t be meaningful to acknowledge Bosch’s influence on Banisadr. The phrase “indeed, Banisadr himself cites Bosch as an inspiration” doesn’t support this suggestion. Choice B is incorrect because “satisfying,” which means pleasing, incorrectly suggests that it wouldn’t be pleasing to acknowledge Bosch’s influence on Banisadr. The phrase “indeed, Banisadr himself cites Bosch as an inspiration” doesn’t support this suggestion. Choice D is incorrect because “appropriate,” which means suitable, incorrectly suggests that it wouldn’t be proper to acknowledge Bosch’s influence on Banisadr. The phrase “indeed, Banisadr himself cites Bosch as an inspiration” doesn’t support this suggestion. 

"}, {"id": "570970cd", "domain": "Craft and Structure", "skill": "Text Structure and Purpose", "difficulty": "H", "type": "mc", "stimulus": "

The following text is adapted from Indian Boyhood, a 1902 memoir by Ohiyesa (Charles A. Eastman), a Santee Dakota writer. In the text, Ohiyesa recalls how the women in his tribe harvested maple syrup during his childhood.

\n

Now the women began to test the trees—moving leisurely among them, axe in hand, and striking a single quick blow, to see if the sap would appear. The trees, like people, have their individual characters; some were ready to yield up their life-blood, while others were more reluctant. Now one of the birchen basins was set under each tree, and a hardwood chip driven deep into the cut which the axe had made. From the corners of this chip—at first drop by drop, then more freely—the sap trickled into the little dishes.

", "stem": "

Which choice best describes the function of the underlined sentence in the text as a whole?

", "choices": [{"id": "A", "text": "

It portrays the range of personality traits displayed by the women as they work.

"}, {"id": "B", "text": "

It foregrounds the beneficial relationship between humans and maple trees.

"}, {"id": "C", "text": "

It demonstrates how human behavior can be influenced by the natural environment.

"}, {"id": "D", "text": "

It elaborates on an aspect of the maple trees that the women evaluate.

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer because it best describes the function of the underlined sentence in the text’s overall portrayal of how the women in Ohiyesa’s tribe harvested maple syrup. The text states that the women used an axe to strike the maple trees in order to find out which ones would produce sap. The underlined sentence compares the trees to people, with the sap described as the trees’ “life-blood.” Some of the trees are ready to give out their sap, while others are unwilling to do so. Using personification, the sentence provides greater detail about the aspect of the maple trees—their potential to give sap—that the women are evaluating.

Choice A is incorrect because the personalities of the women are not discussed in the text. Although the underlined sentence does mention “individual characters,” this reference is not to the women in the text but rather to the maple trees, which the sentence compares to people with individual character traits. Choice B is incorrect because the underlined sentence focuses on the trees’ willingness or refusal to yield sap, not on the beneficial relationship between the women and the trees. Additionally, although the text does suggest that the women and their tribe benefit from the maple trees since the trees allow the women to harvest syrup, there is nothing in the text to suggest that the trees benefit from this relationship in turn. Choice C is incorrect because the underlined sentence is comparing maple trees to humans, not addressing the influence of the natural environment on how the actual humans in the text, the women, behave.

"}, {"id": "eae66bf9", "domain": "Craft and Structure", "skill": "Cross-Text Connections", "difficulty": "M", "type": "mc", "stimulus": "

Text 1

\n

In 2021, a team led by Amir Siraj hypothesized that the Chicxulub impactor—the object that struck the Yucatán Peninsula sixty-six million years ago, precipitating the mass extinction of the dinosaurs—was likely a member of the class of long-period comets. As evidence, Siraj cited the carbonaceous chondritic composition of samples from the Chicxulub impact crater as well as of samples obtained from long-period comet Wild 2 in 2006.

\n

 

\n

Text 2

\n

Although long-period comets contain carbonaceous chondrites, asteroids are similarly rich in these materials. Furthermore, some asteroids are rich in iridium, as Natalia Artemieva points out, whereas long-period comets are not. Given the prevalence of iridium at the crater and, more broadly, in geological layers deposited worldwide following the impact, Artemieva argues that an asteroid is a more plausible candidate for the Chicxulub impactor.

", "stem": "

Based on the texts, how would Artemieva likely respond to Siraj’s hypothesis, as presented in Text 1?

", "choices": [{"id": "A", "text": "

By insisting that it overestimates how representative Wild 2 is of long-period comets as a class

"}, {"id": "B", "text": "

By arguing that it does not account for the amount of iridium found in geological layers dating to the Chicxulub impact

"}, {"id": "C", "text": "

By praising it for connecting the composition of Chicxulub crater samples to the composition of certain asteroids

"}, {"id": "D", "text": "

By concurring that carbonaceous chondrites are prevalent in soil samples from sites distant from the Chicxulub crater

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. Siraj’s hypothesis is that the Chicxulub impactor was a long-period comet. But Artemieva points to the iridium found in the crater and in “geological layers that were deposited worldwide after the impact” as evidence that it was actually an asteroid, not a long-period comet.

Choice A is incorrect. We can’t infer that this is how Artemieva would respond to Siraj’s hypothesis. Text 2 never discusses whether Wild 2 is representative of long-period comets in general. Rather, Text 2 presents Artemieva’s argument that the Chicxulub impactor was an asteroid, not a long-term comet. Choice C is incorrect. We can’t infer that this is how Artemieva would respond to Siraj’s hypothesis. Siraj’s hypothesis doesn’t make this connection: rather, Siraj hypothesizes that the Chicxulub impactor was a long-term comet. Choice D is incorrect. We can’t infer that this is how Artemieva would respond to Siraj’s hypothesis. “Soil samples from sites distant from the Chicxulub crater” is too vague. Only soil samples from sites that are connected to the impact in some way are involved in either hypothesis.

"}, {"id": "a60b0004", "domain": "Craft and Structure", "skill": "Words in Context", "difficulty": "H", "type": "mc", "stimulus": "

Scholarly discussions of gender in Shakespeare’s comedies often celebrate the rebellion of the playwright’s characters against the rigid expectations ______blank by Elizabethan society. Most of the comedies end in marriage, with characters returning to their socially dictated gender roles after previously defying them, but there are some notable exceptions.

", "stem": "

Which choice completes the text with the most logical and precise word or phrase?

", "choices": [{"id": "A", "text": "

interjected

"}, {"id": "B", "text": "

committed

"}, {"id": "C", "text": "

illustrated

"}, {"id": "D", "text": "

prescribed

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer because it most logically completes the text’s discussion of gender roles in Shakespeare’s comedies. As used in this context, “prescribed” would mean laid down as rules. The text indicates that the characters in the comedies often defy gender roles that are “socially dictated” (even if most characters do return to those roles eventually) and that scholars have been very interested in these acts of defiance. This context indicates that what the characters are rebelling against are standards of behavior prescribed by the society of the time.  

Choice A is incorrect because saying that expectations about gender were “interjected,” or suddenly inserted between other things, wouldn’t make sense in context. There’s no suggestion in the text that the issue of gender roles was inserted between other things or was an interruption in a larger discussion. Choice B is incorrect because the text indicates that Shakespeare depicts characters rebelling against expectations about gender that have been “socially dictated,” not expectations that society has “committed,” or carried out, entrusted, or promised. Choice C is incorrect because the text indicates that Shakespeare depicts characters rebelling against expectations about gender that have been “socially dictated,” not expectations that have been “illustrated,” or clarified with examples. Although it’s possible for expectations about gender roles to be illustrated, there’s nothing in the text to indicate that characters in Shakespeare’s comedies rebel against illustrations of gender expectations.

"}, {"id": "03080769", "domain": "Craft and Structure", "skill": "Cross-Text Connections", "difficulty": "M", "type": "mc", "stimulus": "

Text 1

\n

Philosopher G.E. Moore’s most influential work entails the concept of common sense. He asserts that there are certain beliefs that all people, including philosophers, know instinctively to be true, whether or not they profess otherwise: among them, that they have bodies, or that they exist in a world with other objects that have three dimensions. Moore’s careful work on common sense may seem obvious but was in fact groundbreaking.

\n

 

\n

Text 2

\n

External world skepticism is a philosophical stance supposing that we cannot be sure of the existence of anything outside our own minds. During a lecture, G.E. Moore once offered a proof refuting this stance by holding out his hands and saying, “Here is one hand, and here is another.” Many philosophers reflexively reject this proof (Annalisa Coliva called it “an obviously annoying failure”) but have found it a challenge to articulate exactly why the proof fails.

", "stem": "

Based on the texts, how would the author of Text 1 most likely respond to proponents of the philosophical stance outlined in Text 2?

", "choices": [{"id": "A", "text": "

By agreeing with those proponents that Moore’s treatment of positions that contradict his own is fundamentally unserious

"}, {"id": "B", "text": "

By suggesting that an instinctive distaste for Moore’s position is preventing external world skeptics from constructing a sufficiently rigorous refutation of Moore

"}, {"id": "C", "text": "

By arguing that if it is valid to assert that some facts are true based on instinct, it is also valid to assert that some proofs are inadequate based on instinct

"}, {"id": "D", "text": "

By pointing out that Moore would assert that external world skepticism is at odds with other beliefs those proponents must unavoidably hold

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. According to the author of Text 1, Moore’s definition of common sense—things we instinctively know are true—includes the belief that we all “exist in a world with other objects.” The author of Text 1 describes this notion as both “obvious” and “groundbreaking.”  So it’s safe to infer that the author would observe that Moore would respond to external world skeptics by arguing that since everyone instinctively knows that things exist outside of their own minds, then external world skepticism must be wrong.

Choice A is incorrect. We can’t infer that the author of Text 1 would respond this way to external world skeptics. If anything, the author of Text 1 seems to agree with Moore. Choice B is incorrect. We can’t infer that the author of Text 1 would respond this way to external world skeptics. The author of Text 1 never mentions external world skeptics directly, let alone why they have a hard time refuting Moore’s position. Choice C is incorrect. We can’t infer that the author of Text 1 would respond this way to external world skeptics. Text 1’s presentation of Moore’s concept of common sense only includes the idea that some facts are true based on instinct—it doesn’t mention the idea that some proofs are inadequate based on instinct.

"}, {"id": "b0ea8c28", "domain": "Craft and Structure", "skill": "Words in Context", "difficulty": "E", "type": "mc", "stimulus": "

Sueño de Familia is an exhibition of drawings, paintings, and ceramics that explores the artistic heritage of US-based artist Yolanda González. The exhibition ______blank five generations, featuring works by González’s great-grandfather, grandmother, mother, and niece as well as González herself. 

", "stem": "

Which choice completes the text with the most logical and precise word or phrase?

", "choices": [{"id": "A", "text": "

borrows

"}, {"id": "B", "text": "

spans

"}, {"id": "C", "text": "

judges

"}, {"id": "D", "text": "

neglects

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer because it most logically completes the text’s discussion of the Sueño de Familia art exhibition. In this context, “spans” means extends across or covers. The text states that the exhibition explores González’s artistic heritage and features artwork by her great-grandfather, grandmother, mother, and niece. This context conveys the idea that the exhibition spans, or extends across, five generations of González’s family.

Choice A is incorrect because it wouldn’t make sense to say that the exhibition “borrows,” or acquires, five generations of González’s family. The text indicates that the exhibition features artwork by family members from five generations, not that the five generations themselves have been acquired for inclusion in the exhibition. Choice C is incorrect because the text indicates that the purpose of the exhibition is to highlight artwork, not to “judge,” or give an opinion on, five generations of the artist’s family. Choice D is incorrect because the text doesn’t suggest that the exhibition “neglects,” or gives little attention to, five generations of González’s family. On the contrary, the text indicates that the exhibition is dedicated to exploring González’s artistic heritage and therefore designed to bring attention to her family members and their artwork.

"}, {"id": "749f3334", "domain": "Craft and Structure", "skill": "Text Structure and Purpose", "difficulty": "M", "type": "mc", "stimulus": "

The following text is from Charlotte Forten Grimké’s 1888 poem “At Newport.”

\n

Oh, deep delight to watch the gladsome waves
Exultant leap upon the rugged rocks;
Ever repulsed, yet ever rushing on—
Filled with a life that will not know defeat;
To see the glorious hues of sky and sea.
The distant snowy sails, glide spirit like,
Into an unknown world, to feel the sweet
Enchantment of the sea thrill all the soul,
Clearing the clouded brain, making the heart
Leap joyous as it own bright, singing waves!

", "stem": "

Which choice best describes the function of the underlined portion in the text as a whole?

", "choices": [{"id": "A", "text": "

It portrays the surroundings as an imposing and intimidating scene.

"}, {"id": "B", "text": "

It characterizes the sea’s waves as a relentless and enduring force.

"}, {"id": "C", "text": "

It conveys the speaker’s ambivalence about the natural world.

"}, {"id": "D", "text": "

It draws a contrast between the sea’s waves and the speaker’s thoughts.

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer because it most accurately describes how the underlined portion functions in the text as a whole. The text presents the speaker’s experience of viewing the sea. In the underlined portion, the speaker focuses on the idea that the waves hitting rocks on the shore are a relentless and enduring force: they are constantly pushed back (“ever repulsed”) but always return (“ever rushing on”), as though they have an energy that can’t be overcome (“a life that will not know defeat”).

Choice A is incorrect. Although the underlined portion characterizes the waves as a relentless force (always “repulsed” but still “rushing on” and never being defeated), the speaker doesn’t suggest that the surroundings are intimidating. Instead, the speaker presents the scene in a positive way, describing the “deep delight” of the “gladsome,” or cheerful, waves and feeling “the heart / Leap joyous” while viewing the sea. Choice C is incorrect because the underlined portion doesn’t suggest that the speaker is ambivalent, or has mixed feelings about, the natural world. Instead, it presents a single view of one part of the immediate surroundings: the speaker characterizes the sea’s waves as an unstoppable force, since they are constantly pushed back but always return (“ever repulsed, yet ever rushing on”). Choice D is incorrect. Although the text later suggests the speaker’s view of her own thoughts by referring to a “clouded brain” and a heart that leaps joyously, this reference neither occurs within the underlined portion nor establishes a clear contrast with the relentless determination of the waves. The underlined portion addresses only the speaker’s view of the waves and doesn’t suggest what her own thoughts might be.

"}, {"id": "fce80a36", "domain": "Craft and Structure", "skill": "Words in Context", "difficulty": "M", "type": "mc", "stimulus": "

In 2008 a complete set of ancient pessoi (glass game pieces) was uncovered from beneath a paving stone in modern-day Israel. Due to their small size, pessoi were easily misplaced, making a whole set a rare find. This has led some experts to suggest that the set may have been buried intentionally; however, without clear evidence, archaeologists are left to ______blank what happened.

", "stem": "

Which choice completes the text with the most logical and precise word or phrase?

", "choices": [{"id": "A", "text": "

speculate about

"}, {"id": "B", "text": "

dismiss

"}, {"id": "C", "text": "

expand on

"}, {"id": "D", "text": "

catalog

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. \"Speculate\" means \"to form a theory or guess without any clear evidence.\" This makes sense because, due to the lack of \"clear evidence,\" the archaeologists can only guess how the pessoi set might have come to be there.

Choice B is incorrect. \"Dismiss\" can mean \"send away\" or \"treat as unworthy of consideration.\" The text implies that the archaeologists are trying to figure out the truth—they wouldn’t \"dismiss\" what really happened. Choice C is incorrect. \"Expand on\" means \"give more details about,\" but there aren’t any details to give. Without any \"clear evidence,\" the archaeologists can’t give any more details. Choice D is incorrect. \"Catalog\" means \"carefully record\" or \"make a list of.\" However, there’s no \"clear evidence,\" so there’s no real information to \"catalog.\"

"}, {"id": "e4e2aeb3", "domain": "Craft and Structure", "skill": "Cross-Text Connections", "difficulty": "H", "type": "mc", "stimulus": "

Text 1

\n

Like the work of Ralph Ellison before her, Toni Morrison’s novels feature scenes in which characters deliver sermons of such length and verbal dexterity that for a time, the text exchanges the formal parameters of fiction for those of oral literature. Given the many other echoes of Ellison in Morrison’s novels, both in structure and prose style, these scenes suggest Ellison’s direct influence on Morrison.

\n

Text 2

\n

In their destabilizing effect on literary form, the sermons in Morrison’s works recall those in Ellison’s. Yet literature by Black Americans abounds in moments where interpolated speech erodes the division between oral and written forms that literature in English has traditionally observed. Morrison’s use of the sermon is attributable not only to the influence of Ellison but also to a community-wide strategy of resistance to externally imposed literary conventions.

", "stem": "

Based on the texts, how would the author of Text 2 most likely characterize the underlined claim in Text 1?

", "choices": [{"id": "A", "text": "

As failing to consider Ellison’s and Morrison’s equivalent uses of the sermon within the wider cultural context in which they wrote

"}, {"id": "B", "text": "

As misunderstanding the function of sermons in novels by Black American writers other than Ellison and Morrison

"}, {"id": "C", "text": "

As disregarding points of structural and stylistic divergence between the works of Ellison and those of Morrison

"}, {"id": "D", "text": "

As being indebted to the tradition of resisting literary conventions that privilege written forms, such as novels, over sermons and other oral forms

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. The author of Text 2 argues that Morrison’s use of the sermon is not only influenced by Ellison, but also by a “community-wide strategy of resistance” to literary conventions practiced by Black American authors. Ellison, Text 2 alleges, is only one of many influences on Morrison.

Choice B is incorrect. Neither text specifically mentions sermons in works by authors other than Morrison or Ellison, only a tendency towards eroding “the division between oral and written forms” among Black American writers. Choice C is incorrect. Both texts describe similarities between the works of Ellison and Morrison, and neither points out instances of divergence. Text 2 simply suggests that Morrison was influenced by more than just Ellison. Choice D is incorrect. While Text 2 does discuss Morrison’s resistance to certain literary conventions, it’s unclear what it would mean for the underlined claim to be “indebted” to that tradition. This choice recycles language from the text, but not in a way that makes any coherent point.

"}, {"id": "0d402146", "domain": "Craft and Structure", "skill": "Words in Context", "difficulty": "E", "type": "mc", "stimulus": "

US traffic signals didn’t always contain the familiar three lights (red, yellow, and green). Traffic lights only ______blank red and green lights until the three-light traffic signal was developed in the 1920s.

", "stem": "

Which choice completes the text with the most logical and precise word or phrase?

", "choices": [{"id": "A", "text": "

avoided

"}, {"id": "B", "text": "

featured

"}, {"id": "C", "text": "

appreciated

"}, {"id": "D", "text": "

disregarded

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer because it most logically completes the text’s discussion of traffic signals. As used in this context, “featured” means had as a characteristic or part. The text indicates that although US traffic signals have lights of three different colors (red, yellow, and green), this wasn’t the case until the 1920s, when the three-light signal was first developed. Before then, the text suggests, traffic signals had fewer lights (as indicated by the word “only” in the second sentence). This context supports the idea that before the 1920s, traffic signals featured only red and green lights.

Choice A is incorrect because “avoided” means kept away from someone or something or prevented something from occurring, neither of which would make sense in context. The text doesn’t discuss keeping away from someone or something but instead focuses on what US traffic signals look like. The text states that they didn’t have lights of three different colors until the three-light signal was developed in the 1920s. Choice C is incorrect because “appreciated” means admired or increased in value, neither of which would make sense in context. The text focuses solely on the fact that US traffic signals have contained lights of three colors only since the three-light signal was developed in the 1920s. The text doesn’t mention how this characteristic or traffic signals in general are perceived or what their value is. Moreover, the blank portion of the text describes “traffic signals,” which are lifeless objects and therefore unable to admire or increase the value of something. Choice D is incorrect because “disregarded” means ignored or treated something as unworthy of notice, neither of which would make sense in context. The text doesn’t discuss how people react to traffic signals; rather, it addresses the idea that US traffic signals have contained lights of three colors only since the three-light signal was developed in the 1920s. Moreover, the blank portion of the text describes “traffic signals,” which are lifeless objects and therefore unable to ignore or treat something in a particular manner. 

"}, {"id": "e5da61f1", "domain": "Craft and Structure", "skill": "Text Structure and Purpose", "difficulty": "E", "type": "mc", "stimulus": "

The following text is adapted from Charles Chesnutt’s 1899 short story “Mars Jeems’s Nightmare.” The narrator and his wife have recently moved to the southern United States, and Julius is their carriage driver.

\n
\n

Julius [was] very useful when we moved to our new residence. He had a thorough knowledge of the neighborhood, was familiar with the roads and the watercourses, knew the qualities of the various soils and what they would produce, and where the best hunting and fishing were to be had. He was a marvelous hand in the management of horses and dogs.

\n
", "stem": "

Which choice best states the main purpose of the text?

", "choices": [{"id": "A", "text": "

To compare the narrator’s reaction to a new home with his wife’s reaction

"}, {"id": "B", "text": "

To give an example of Julius’s knowledge about soil

"}, {"id": "C", "text": "

To show that the narrator and Julius often hunt and fish together

"}, {"id": "D", "text": "

To explain different ways in which Julius was helpful

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer because it most accurately describes the main purpose of the text, which is to explain different ways in which Julius was helpful. The text begins with the narrator stating that Julius was very helpful to him and his wife when they moved to their new residence. The narrator then provides a list of examples to illustrate Julius’s helpfulness. For instance, the narrator states that Julius was familiar with the neighborhood’s roads, which suggests that he was helpful in navigating them, and that Julius helped manage the horses and dogs. The text’s many examples of Julius’s usefulness reinforce just how helpful he was and in how many different ways.

Choice A is incorrect because the text doesn’t portray either the narrator’s or his wife’s reaction to their new home. Rather, the text focuses on how Julius was useful to the narrator and his wife in their new home. Choice B is incorrect. Although the text states that Julius was knowledgeable about the soil, this is one of several supporting details that illustrate how helpful Julius was. Moreover, the text merely states that Julius was knowledgeable about soil; it doesn’t provide an example of that knowledge. Choice C is incorrect because there’s nothing in the text to suggest the frequency with which the narrator and Julius hunted and fished together. In fact, it’s unclear from the text whether the narrator and Julius hunted and fished together at all. The text merely indicates that Julius knew the best places to hunt and fish—a detail that supports the text’s main purpose by conveying Julius’s usefulness.

"}, {"id": "6a1dc7c5", "domain": "Craft and Structure", "skill": "Cross-Text Connections", "difficulty": "H", "type": "mc", "stimulus": "

Text 1

\n

Virginia Woolf’s 1928 novel Orlando is an oddity within her body of work. Her other major novels consist mainly of scenes of everyday life and describe their characters’ interior states in great detail, whereas Orlando propels itself through a series of fantastical events and considers its characters’ psychology more superficially. Woolf herself sometimes regarded the novel as a minor work, even admitting once that she “began it as a joke.”

\n

 

\n

Text 2

\n

Like Woolf’s other great novels, Orlando portrays how people’s memories inform their experience of the present. Like those works, it examines how people navigate social interactions shaped by gender and social class. Though it is lighter in tone—more entertaining, even—this literary “joke” nonetheless engages seriously with the themes that motivated the four or five other novels by Woolf that have achieved the status of literary classics.

", "stem": "

Based on the texts, how would the author of Text 2 most likely respond to the assessment of Orlando presented in Text 1?

", "choices": [{"id": "A", "text": "

By conceding that Woolf’s talents were best suited to serious novels but asserting that the humor in Orlando is often effective

"}, {"id": "B", "text": "

By agreeing that Orlando is less impressive than certain other novels by Woolf but arguing that it should still be regarded as a classic

"}, {"id": "C", "text": "

By acknowledging that Orlando clearly differs from Woolf’s other major novels but insisting on its centrality to her body of work nonetheless 

"}, {"id": "D", "text": "

By concurring that the reputation of Orlando as a minor work has led readers to overlook this novel but maintaining that the reputation is unearned 

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer because it reflects how the author of Text 2 would most likely respond to the assessment of Orlando in Text 1. Both authors agree that Orlando is unusual for Woolf: Text 1 states that the novel examines its characters’ psychologies more superficially than Woolf’s other novels do, and Text 2 describes it as being lighter in tone. However, while Text 1 calls Orlando an “oddity” and mentions that Woolf “began it as a joke,” Text 2 asserts that Orlando engages the same themes as Woolf’s other great novels. Hence, the author of Text 2 would most likely accept that Orlando differs from Woolf’s other novels but would also insist on its importance in the context of Woolf’s work as a writer.

Choice A is incorrect. Text 2 does suggest that the humor in Orlando is effective. However, there’s nothing in Text 2 to suggest that the author would agree that Woolf’s talents were best suited to serious novels. Rather, the author of Text 2 compares Orlando favorably to other novels by Woolf that are implied to be darker in tone. Choice B is incorrect because the author of Text 2 does not indicate that Orlando is less impressive than Woolf’s other novels, but instead points out that it engages the same themes as other novels by Woolf that are considered classics. Choice D is incorrect because there’s nothing in Text 1 or Text 2 to suggest that readers have generally ignored Orlando because of its reputation.

"}, {"id": "5dce6cab", "domain": "Craft and Structure", "skill": "Words in Context", "difficulty": "H", "type": "mc", "stimulus": "

Given that the conditions in binary star systems should make planetary formation nearly impossible, it’s not surprising that the existence of planets in such systems has lacked ______blank explanation. Roman Rafikov and Kedron Silsbee shed light on the subject when they used modeling to determine a complex set of factors that could support planets’ development.

", "stem": "

Which choice completes the text with the most logical and precise word or phrase?

", "choices": [{"id": "A", "text": "

a discernible

"}, {"id": "B", "text": "

a straightforward

"}, {"id": "C", "text": "

an inconclusive

"}, {"id": "D", "text": "

an unbiased

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer because it most logically completes the text’s description of efforts to explain the existence of planets in binary star systems. As used in this context, describing an explanation as “a straightforward” one would mean that the explanation is direct and uncomplicated. The text asserts that since it should be “nearly impossible” for planets to form in binary star systems, it’s “not surprising” that there isn’t a straightforward explanation for the existence of planets in such systems; the fact that one potential approach involves “complex” factors offers further contextual support for this idea.

Choice A is incorrect because it would not make sense in context to say that there isn’t “a discernible” explanation—meaning an explanation capable of being perceived—for the existence of planets in binary star systems. The text discusses just such an explanation offered by Roman Rafikov and Kedron Silsbee, which indicates that their explanation can be discerned. Choice C is incorrect because the text emphasizes how difficult it is to explain the existence of planets in binary star systems, suggesting that the situation isn’t marked by the lack of “an inconclusive” explanation—an explanation that does not resolve the issue—but rather that if any explanations have been offered, they’ve likely been inconclusive ones. Choice D is incorrect because nothing in the text suggests that there is a lack of “an unbiased,” or impartial and unprejudiced, explanation for the existence of planets in binary star systems. The text indicates that it’s difficult to explain the existence of planets in such systems and it describes one attempt to do so, but there is no evidence that explanations from Roman Rafikov and Kedron Silsbee or others are biased. 

"}, {"id": "f99847ed", "domain": "Craft and Structure", "skill": "Words in Context", "difficulty": "H", "type": "mc", "stimulus": "

For her 2021 art installation Anthem, Wu Tsang joined forces with singer and composer Beverly Glenn-Copeland to produce a piece that critics found truly ______blank: they praised Tsang for creatively transforming a museum rotunda into a dynamic exhibit by projecting filmed images of Glenn-Copeland onto a massive 84-foot curtain and filling the space with the sounds of his and other voices singing.

", "stem": "

Which choice completes the text with the most logical and precise word or phrase?

", "choices": [{"id": "A", "text": "

restrained

"}, {"id": "B", "text": "

inventive

"}, {"id": "C", "text": "

inexplicable

"}, {"id": "D", "text": "

mystifying

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer because it most logically completes the text’s discussion of the art installation Anthem. In this context, “inventive” means characterized by invention and creativity. The text explains that critics’ responses to the installation involved praise for Tsang’s creative transformation of a space into a dynamic exhibit with huge images and lots of sound. This context conveys that the critics found the piece particularly creative.

Choice A is incorrect because the text indicates that critics praised the installation for being dynamic and including huge images and lots of sound, and it wouldn’t make sense to describe such an exhibit as “restrained,” or limited and not extravagant or showy. Choice C is incorrect because it wouldn’t make sense to say that critics found the installation “inexplicable,” or incapable of being explained or interpreted, since the critics were able to explain their praise for the installation’s transformation of a space with huge images and lots of sound. Choice D is incorrect because the text focuses on the idea that critics praised Tsang for creatively transforming a space into a dynamic exhibit, not that they found the installation “mystifying,” or bewildering and hard to understand. Nothing in the text suggests that the critics couldn’t understand the piece.

"}, {"id": "5e101c70", "domain": "Craft and Structure", "skill": "Cross-Text Connections", "difficulty": "H", "type": "mc", "stimulus": "

 

Text 1

\n

Most animals can regenerate some parts of their bodies, such as skin. But when a three-banded panther worm is cut into three pieces, each piece grows into a new worm. Researchers are investigating this feat partly to learn more about humans’ comparatively limited abilities to regenerate, and they’re making exciting progress. An especially promising discovery is that both humans and panther worms have a gene for early growth response (EGR) linked to regeneration.

\n\n

 

Text 2

\n

When Mansi Srivastava and her team reported that panther worms, like humans, possess a gene for EGR, it caused excitement. However, as the team pointed out, the gene likely functions very differently in humans than it does in panther worms. Srivastava has likened EGR to a switch that activates other genes involved in regeneration in panther worms, but how this switch operates in humans remains unclear.

", "stem": "

Based on the texts, what would the author of Text 2 most likely say about Text 1’s characterization of the discovery involving EGR?

", "choices": [{"id": "A", "text": "

It is reasonable given that Srivastava and her team have identified how EGR functions in both humans and panther worms.

"}, {"id": "B", "text": "

It is overly optimistic given additional observations from Srivastava and her team.

"}, {"id": "C", "text": "

It is unexpected given that Srivastava and her team’s findings were generally met with enthusiasm.

"}, {"id": "D", "text": "

It is unfairly dismissive given the progress that Srivastava and her team have reported.

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer because it reflects how the author of Text 2 would most likely respond to Text 1 based on the information provided. Text 1 discusses the discovery of a regeneration-linked gene, EGR, in both three-banded panther worms (which are capable of full regeneration) and humans (who have relatively limited regeneration abilities). Text 1 characterizes this discovery as “especially promising” and a sign of “exciting progress” in understanding human regeneration. The author of Text 2, on the other hand, focuses on the fact that the team that reported the EGR finding pointed out that while EGR’s function in humans isn’t yet known, it’s likely very different from its function in panther worms. Therefore, the author of Text 2 would most likely say that Text 1’s enthusiasm about the EGR discovery is overly optimistic given Srivastava’s team’s observations about EGR in humans.

Choice A is incorrect because the author of Text 2 explains that Srivastava and her team explicitly reported that they haven’t yet identified how EGR functions in humans; therefore, the author of Text 2 wouldn’t say that Text 1’s excitement is reasonable for the stated reason. Instead, the author of Text 2 would likely characterize Text 1’s excitement as premature and overly optimistic. Choice C is incorrect because Text 1 does treat Srivastava’s team’s findings with enthusiasm; it describes the discovery of EGR in both three-banded panther worms and humans as promising and exciting. It would be illogical for the author of Text 2 to say that because most others treat the discovery with enthusiasm, Text 1’s enthusiastic characterization of the discovery is unexpected. Choice D is incorrect because Text 1 isn’t at all dismissive of Srivastava’s team’s findings; instead, Text 1 is optimistic about the EGR discovery, characterizing it as promising and exciting. There’s nothing in Text 2 to suggest that the author of Text 2 would say that Text 1’s praise for the discovery is dismissive, or disdainful. 

"}, {"id": "12d81fc1", "domain": "Craft and Structure", "skill": "Cross-Text Connections", "difficulty": "M", "type": "mc", "stimulus": "

Text 1

\n

Because literacy in Nahuatl script, the writing system of the Aztec Empire, was lost after Spain invaded central Mexico in the 1500s, it is unclear exactly how meaning was encoded in the script’s symbols. Although many scholars had assumed that the symbols signified entire words, linguist Alfonso Lacadena theorized in 2008 that they signified units of language smaller than words: individual syllables.

\n

 

\n

Text 2

\n

The growing consensus among scholars of Nahuatl script is that many of its symbols could signify either words or syllables, depending on syntax and content at any given site within a text. For example, the symbol signifying the word huipil (blouse) in some contexts could signify the syllable “pil” in others, as in the place name “Chipiltepec.” Thus, for the Aztecs, reading required a determination of how such symbols functioned each time they appeared in a text.

", "stem": "

Based on the texts, how would the author of Text 2 most likely characterize Lacadena’s theory, as described in Text 1?

", "choices": [{"id": "A", "text": "

By praising the theory for recognizing that the script’s symbols could represent entire words

"}, {"id": "B", "text": "

By arguing that the theory is overly influenced by the work of earlier scholars 

"}, {"id": "C", "text": "

By approving of the theory’s emphasis on how the script changed over time

"}, {"id": "D", "text": "

By cautioning that the theory overlooks certain important aspects of how the script functioned

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. Lacadena’s theory is that Nahuatl script symbols signified syllables, but the consensus described in Text 2 is that they can signify either symbols or full words, depending on the context. So the author of Text 2 would likely consider Lacadena’s theory too simplistic: it’s missing the importance of the context in determining the meaning of a symbol.

Choice A is incorrect. This conflicts with Text 1’s description of Lacadena’s theory. Lacadena’s theory is that Nahuatl script symbols signified syllables. Choice B is incorrect. This conflicts with Text 1’s description of Lacadena’s theory. Text 1 states that Lacadena’s theory differed from what earlier scholars believed. Choice C is incorrect. We can’t infer that this is how the author of Text 2 would characterize Lacadena’s theory. Neither text mentions how or even if the script changed over time.

"}, {"id": "e4f312c5", "domain": "Craft and Structure", "skill": "Words in Context", "difficulty": "H", "type": "mc", "stimulus": "

While most animals are incapable of passing somatic mutations—genetic alterations that arise in an organism’s nonreproductive cells—on to their offspring, elkhorn coral (Acropora palmata) presents an intriguing ______blank: in a 2022 study, researchers found that elkhorn coral produced offspring that inherited somatic mutations from a parent.

", "stem": "

Which choice completes the text with the most logical and precise word or phrase?

", "choices": [{"id": "A", "text": "

hypothesis

"}, {"id": "B", "text": "

affinity

"}, {"id": "C", "text": "

anomaly

"}, {"id": "D", "text": "

corroboration

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. An \"anomaly\" is something that deviates from norms or expectations. In this case, the elkhorn coral is an anomaly because it can pass on somatic mutations, whereas most other animals can’t.

Choice A is incorrect. A \"hypothesis\" is \"a theory about something,\" but no theories are provided about elkhorn coral in this text, just facts. Choice B is incorrect. \"Affinity\" represents \"an inclination or liking toward something.\" As genetic mutations tend to occur without any conscious effort, you can’t really have an inclination toward passing on somatic mutations. Choice D is incorrect. \"Corroboration\" means \"evidence to support or prove something.\" Because elkhorn coral do the opposite of what most animals do, they do not provide corroboration of the theory that somatic mutations can’t be passed onto offspring. Rather, they show the opposite.

"}, {"id": "a4f50d30", "domain": "Craft and Structure", "skill": "Words in Context", "difficulty": "E", "type": "mc", "stimulus": "

Scientists previously thought that all electric eels belong to a single species, but a team of researchers led by zoologist C. David de Santana proved this idea wrong by ______blank that there are in fact three distinct species of electric eels. 

", "stem": "

Which choice completes the text with the most logical and precise word or phrase?

", "choices": [{"id": "A", "text": "

pretending

"}, {"id": "B", "text": "

complaining

"}, {"id": "C", "text": "

requiring

"}, {"id": "D", "text": "

demonstrating

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. “Demonstrating” means “showing,” and the text describes how de Santana disproved a previous belief in only one species of electric eel by showing that three electric eel species actually exist.

Choice A is incorrect. Pretending that there are three species of electric eel might be a fun game for marine biologists, but it wouldn’t prove the existence of more than one species. Choice B is incorrect. Complaining won’t prove anything about eels, so de Santana could not have proved wrong the idea of only one species of electric eel by complaining about it. Choice C is incorrect. “Requiring” means “needing.” It wouldn’t make sense to say that de Santana “needed” there to be three distinct species of electric eel.

"}, {"id": "fa7a89f1", "domain": "Craft and Structure", "skill": "Words in Context", "difficulty": "E", "type": "mc", "stimulus": "

Studying how workload affects productivity, Maryam Kouchaki and colleagues found that people who chose to do relatively easy tasks first were less ______blank compared to those who did hard tasks first. Finishing easy tasks gave participants a sense of accomplishment, but those who tackled hard tasks first actually became more skilled and productive workers over time.

", "stem": "

Which choice completes the text with the most logical and precise word or phrase?

", "choices": [{"id": "A", "text": "

secretive

"}, {"id": "B", "text": "

efficient

"}, {"id": "C", "text": "

outgoing

"}, {"id": "D", "text": "

unsympathetic

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer because it most logically completes the text’s discussion about Kouchaki and colleagues’ research into how workload affects productivity. In context, “efficient” means effective or well organized. The text indicates that, according to Kouchaki and colleagues’ research, people who worked on hard tasks first were “more skilled and productive” than those who did easy tasks first. This context conveys the idea that despite their sense of accomplishment, the people who chose to do the easy tasks first were less efficient or productive than those who tackled hard tasks first. 

Choice A is incorrect because there’s nothing in the text to suggest that workers who do easy tasks first are less “secretive,” or uncommunicative or silent, than those who do hard tasks first. Rather, the text suggests that people are less skillful or efficient if they tackle easy tasks before the hard ones. Choice C is incorrect because “outgoing” means openly friendly, which wouldn’t make sense in this context. The text focuses on Kouchaki and colleagues’ research in which people who worked on hard tasks first were “more skilled and productive” than those who did easy tasks first and were therefore less efficient. Choice D is incorrect because there’s nothing in the text to suggest that workers who do easy tasks first are less “unsympathetic,” or insensitive or unkind, than those who do hard tasks first. Rather, the text suggests that people are less skillful or efficient if they tackle easy tasks before the hard ones.

"}, {"id": "e37b9e34", "domain": "Craft and Structure", "skill": "Words in Context", "difficulty": "M", "type": "mc", "stimulus": "

Some researchers believe that the genes that enable groundhogs and certain other mammals to hibernate through the winter by slowing their breathing and heart rates and lowering their body temperature may be ______blank in humans: present yet having essentially no effect on our bodily processes.

", "stem": "

Which choice completes the text with the most logical and precise word or phrase?

", "choices": [{"id": "A", "text": "

decisive

"}, {"id": "B", "text": "

lacking

"}, {"id": "C", "text": "

variable

"}, {"id": "D", "text": "

dormant

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer because it logically completes the text’s discussion about genes related to hibernation. In this context, “dormant” means inactive. The text explains that the same genes that enable certain nonhuman mammal species to hibernate during the winter by altering their bodily processes are also found in our species but have “essentially no effect” on humans’ bodily processes. In other words, these genes don’t function in humans.

Choice A is incorrect because in this context, “decisive” means has the power to affect the outcome of something, but the text states that genes related to hibernation are instead inactive in humans—that is, the genes don’t affect humans’ bodily processes, although they are present in their bodies. Choice B is incorrect because in this context, “lacking” means missing, but the text states that the genes are present in humans, though inactive. Choice C is incorrect because “variable” means characterized by the potential to change, but the text indicates that these genes don’t change in their effect on humans’ bodily processes; instead, the genes are consistently inactive in humans.

"}, {"id": "faa5696c", "domain": "Craft and Structure", "skill": "Words in Context", "difficulty": "E", "type": "mc", "stimulus": "

Arturo A. Schomburg was dedicated to preserving books, art, and other materials from peoples of African descent around the world. To get these items, Schomburg ______blank friends and colleagues, whom he asked to bring back rare and valuable objects from their international travels. Now, Schomburg’s collection is a valuable resource for scholars of Black history and culture.

", "stem": "

Which choice completes the text with the most logical and precise word or phrase?

", "choices": [{"id": "A", "text": "

admired

"}, {"id": "B", "text": "

disagreed with

"}, {"id": "C", "text": "

warned

"}, {"id": "D", "text": "

depended on

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer because it most logically completes the text’s discussion of Arturo A. Schomburg’s collection. In this context, the phrase “depended on” means relied on. The text explains that Schomburg, wanting to preserve “books, art, and other materials” created by peoples of African descent from around the world, built a large collection of these objects. The text also states that in order to obtain these items, Schomburg asked friends and colleagues who were traveling internationally to bring them back for him. This implies that he wouldn’t have been able to create his collection without help. Thus, the context supports the idea that Schomburg relied on, or depended on, friends and colleagues to build his collection.

Choice A is incorrect because “admired” means respected and approved of. Although it’s reasonable to expect that Schomburg respected his friends and colleagues, the text doesn’t discuss any such aspect of their relationships. The text focuses instead on what Schomburg asked his friends and colleagues to do to help build his collection. Choice B is incorrect because “disagreed with” means held an opposing belief, and nothing in the text suggests that Schomburg and his friends or colleagues held opposing views on any subject. In fact, the text strongly implies that Schomburg’s friends and colleagues supported him in his goal of preserving objects of importance for Black history and culture by bringing him such objects from around the world. Choice C is incorrect because “warned” means informed someone in advance about something dangerous, which wouldn’t make sense in this context. Nothing in the text suggests that Schomburg thought his friends and colleagues were in any danger, let alone that he warned them of danger.

"}, {"id": "f0ae0da3", "domain": "Craft and Structure", "skill": "Cross-text Connections", "difficulty": "M", "type": "mc", "stimulus": "

Text 1

\n

When companies in the same industry propose merging with one another, they often claim that the merger will benefit consumers by increasing efficiency and therefore lowering prices. Economist Ying Fan investigated this notion in the context of the United States newspaper market. She modeled a hypothetical merger of Minneapolis-area newspapers and found that subscription prices would rise following a merger.

\n

Text 2

\n

Economists Dario Focarelli and Fabio Panetta have argued that research on the effect of mergers on prices has focused excessively on short-term effects, which tend to be adverse for consumers. Using the case of consumer banking in Italy, they show that over the long term (several years, in their study), the efficiency gains realized by merged companies do result in economic benefits for consumers. 

", "stem": "

Based on the texts, how would Focarelli and Panetta (Text 2) most likely respond to Fan’s findings (Text 1)?

", "choices": [{"id": "A", "text": "

They would recommend that Fan compare the near-term effect of a merger on subscription prices in the Minneapolis area with the effect of a merger in another newspaper market.

"}, {"id": "B", "text": "

They would argue that over the long term the expenses incurred by the merged newspaper company will also increase.

"}, {"id": "C", "text": "

They would encourage Fan to investigate whether the projected effect on subscription prices persists over an extended period.

"}, {"id": "D", "text": "

They would claim that mergers have a different effect on consumer prices in the newspaper industry than in most other industries. 

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer because, based on the information presented in the texts, it represents how Focarelli and Panetta would most likely respond to Fan’s findings. Text 1 indicates that Fan found that a newspaper merger would result in a rise in subscription prices. This rise wouldn’t benefit customers, who would have to pay more for news after a merger. Text 2 presents Focarelli and Panetta’s argument that merger research tends to focus too much on what happens immediately after the merger. Text 2 goes on to describe their finding that mergers can be economically beneficial for consumers over the long term. This suggests that Focarelli and Panetta would encourage Fan to investigate the long-term effect of the hypothetical newspaper merger on subscription prices.

Choice A is incorrect because Text 2 doesn’t indicate that Focarelli and Panetta connect the effects of mergers to specific locations. Instead, Focarelli and Panetta focus on the length of time over which the effects of mergers should be evaluated. Choice B is incorrect because Text 2 indicates that Focarelli and Panetta found that merged companies experience \"efficiency gains\" over the long term, meaning that their expenses go down relative to their output, not that their expenses increase. Choice D is incorrect because there’s no indication in Text 2 that Focarelli and Panetta believe that the newspaper industry is different from any other industry when it comes to the effects of mergers. Although their own research was about consumer banking, Text 2 suggests that they view their conclusions as applicable to mergers in general.

"}, {"id": "54c6128b", "domain": "Craft and Structure", "skill": "Text Structure and Purpose", "difficulty": "M", "type": "mc", "stimulus": "

When ancient oak planks were unearthed during subway construction in Rome, Mauro Bernabei and his team examined the growth rings in the wood to determine where these planks came from. By comparing the growth rings on the planks to records of similar rings in oaks from Europe, the team could trace the wood to the Jura region of France, hundreds of kilometers from Rome. Because timber could only have been transported from distant Jura to Rome by boat, the team’s findings suggest the complexity of Roman trade routes.

", "stem": "

Which choice best describes the function of the underlined sentence in the text as a whole?

", "choices": [{"id": "A", "text": "

It presents a conclusion about Roman trade routes based on the team’s findings. 

"}, {"id": "B", "text": "

It questions how the team was able to conclude that the planks were used to build a boat.

"}, {"id": "C", "text": "

It explains why the planks were made from oak rather than a different kind of wood. 

"}, {"id": "D", "text": "

It describes common methods used in Roman subway construction.

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer because it most accurately describes how the underlined sentence functions in the text as a whole. The first sentence explains that Bernabei and his team studied growth rings to obtain information about the ancient oak planks found during a construction project in Rome. The next sentence presents what the researchers learned: the wood from the planks came from France’s Jura region, which is far from Rome. The underlined sentence then presents the implications of the findings about the planks: the wood must have been brought to Rome by boat, a difficult task that suggests Roman trade routes were complex. Thus, the underlined sentence mainly functions to present a conclusion about Roman trade routes based on the team’s findings.

Choice B is incorrect because the text doesn’t suggest that the team thought the ancient planks were used in the construction of a boat, nor does the underlined sentence question that conclusion. Instead, the text states that the wood could only have been transported from Jura to Rome in a boat. Choice C is incorrect because the underlined sentence simply offers a conclusion drawn from the team’s findings about the likely place of origin of the ancient planks; the text never mentions why oak was chosen for the planks instead of other wood. Choice D is incorrect because neither the underlined sentence nor the text as a whole addresses any methods that Romans used in constructing subways. Instead, the underlined sentence offers a conclusion drawn from the team’s findings about the likely place of origin of the ancient wooden planks discovered.

"}, {"id": "2c50ed1a", "domain": "Craft and Structure", "skill": "Cross-Text Connections", "difficulty": "E", "type": "mc", "stimulus": "

Text 1

\n

Literary scholars have struggled with the vastness of Nigerian writer Wole Soyinka’s collective works of drama (spanning over 20 plays in total). It is best, however, to understand Soyinka’s body of work as a dramatist chronologically. Soyinka’s progression as a playwright can be considered to fall into three periods, with each one representing a particular thematic and stylistic cohesion: the 1960s, the two decades between 1970 and 1990, and lastly, from roughly 1990 onwards. 

\n

 

\n

Text 2 

\n

It is tempting to impose a linear sense of order on the expanse of Wole Soyinka’s body of work as a dramatist. However, critics who have considered Soyinka’s plays to fit neatly into three phases overlook potential commonalities in Soyinka’s work that span across these phases. Additionally, this view may discount significant differences in the styles and content of plays written around the same time. 

", "stem": "

Which choice best describes a difference in how the author of Text 1 and the author of Text 2 view the study of Soyinka’s works of drama?

", "choices": [{"id": "A", "text": "

While the author of Text 1 believes that thinking about Soyinka’s works of theater in phases is useful, the author of Text 2 views such an approach as limiting.

"}, {"id": "B", "text": "

Although the author of Text 1 claims that Soyinka’s style as a dramatist has evolved over time, the author of Text 2 argues that Soyinka’s style has remained consistent throughout his career.

"}, {"id": "C", "text": "

The author of Text 1 considers Soyinka’s plays to showcase his strongest writing, whereas the author of Text 2 believes that Soyinka’s poetry is where he is most skilled.

"}, {"id": "D", "text": "

The author of Text 1 argues that Soyinka’s early plays were his most politically charged, whereas the author of Text 2 claims that Soyinka’s most recent plays are the most politicized.

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. The author of Text 1 states that Soyinka’s progression as a playwright can be considered to fall into three periods, implying that this is a helpful way to understand his works. The author of Text 2, on the other hand, challenges this view and says that it overlooks potential commonalities and differences in Soyinka’s work across what Text 1 calls distinctive stylistic phases.

Choice B is incorrect. This choice overstates the central claim of Text 2. The author of Text 2 argues against the chronological progression supported in Text 1, but does not go so far as to say that Soyinka’s style remained consistent. In fact, Text 2 points out “significant differences in styles and content” among Soyinka’s plays. Choice C is incorrect. Neither of the texts mention Soyinka’s poetry, nor do they rank his dramatic writing relative to his other work. Choice D is incorrect. Neither text discusses the political aspects of Soyinka’s plays, nor do they make any claims about whether they have changed over time.

"}, {"id": "0ed94d4c", "domain": "Craft and Structure", "skill": "Text Structure and Purpose", "difficulty": "E", "type": "mc", "stimulus": "

Jackie Ormes’s Torchy Brown in Dixie to Harlem (1937–38) was the first comic strip by a Black woman to appear in a widely read newspaper. The strip tells the story of Torchy, a young woman who leaves Mississippi to become a performer in New York City. Torchy’s story reflects the experience of the Great Migration (1910–1970), when millions of Black Americans left the South in search of opportunities in other parts of the United States. Torchy Brown thus shows how Ormes used comics to comment humorously on issues affecting Black Americans, which she continued to do throughout her career.

", "stem": "

Which choice best states the main purpose of the text?

", "choices": [{"id": "A", "text": "

To show how Ormes’s Torchy Brown inspired other Black women to write comic strips in the 1930s

"}, {"id": "B", "text": "

To illustrate how the subjects Ormes addressed in her comic strips changed over the course of her career

"}, {"id": "C", "text": "

To give an example of how Ormes presented the experiences of Black Americans in her comic strips 

"}, {"id": "D", "text": "

To claim that several characters in Torchy Brown were based on people that Ormes knew personally 

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. The text describes how Torchy Brown depicted the experiences of a young Black woman experiencing America’s Great Migration. It further states that Ormes continued to use comics throughout her career to humorously comment on important issues impacting Black Americans.

Choice A is incorrect. The text never mentions other Black women comic strip writers. Choice B is incorrect. The text never mentions any changes in the subjects Ormes addressed. Choice D is incorrect. The text never mentions the inspiration for characters in Torchy Brown.

"}, {"id": "79fe7550", "domain": "Craft and Structure", "skill": "Words in Context", "difficulty": "H", "type": "mc", "stimulus": "

Researcher Haesung Jung led a 2020 study showing that individual acts of kindness can ______blank prosocial behavior across a larger group. Jung and her team found that bystanders who witness a helpful act become more likely to offer help to someone else, and in doing so, can inspire still others to act.

", "stem": "

Which choice completes the text with the most logical and precise word or phrase?

", "choices": [{"id": "A", "text": "

require

"}, {"id": "B", "text": "

remember

"}, {"id": "C", "text": "

foster

"}, {"id": "D", "text": "

discourage

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer because it most logically completes the text’s discussion of Jung and her team’s study of acts of kindness. In this context, “foster” means encourage or promote the development of. The text indicates that Jung and her team found that seeing a helpful (or prosocial) act makes a bystander more likely to help someone else, which can in turn inspire additional people to help others. That is, the team showed that single acts of kindness can foster additional prosocial acts across a group.

Choice A is incorrect because nothing in the text suggests that Jung and her team found that single acts of kindness “require,” or depend on or make obligatory, broader prosocial (or helpful) behavior across a group. There’s no suggestion in the text that individual acts of kindness can only occur if other prosocial acts have already occurred, and the text indicates only that an act of kindness can inspire additional helpful acts, not that it necessarily will do so. Choice B is incorrect because the text focuses on a possible direct effect of individual acts of kindness, or single helpful actions, and it wouldn’t make sense to suggest that actions can “remember,” or hold a memory of, something. Choice D is incorrect because the text doesn’t indicate that Jung and her team found that single acts of kindness can “discourage,” or hinder, prosocial (or helpful) behavior across a group. On the contrary, the text states that Jung and her team found that seeing a helpful act makes a bystander more likely to help someone else, which can in turn inspire even more people to help others.

"}, {"id": "0a04cac5", "domain": "Craft and Structure", "skill": "Text Structure and Purpose", "difficulty": "H", "type": "mc", "stimulus": "

The following text is adapted from Jane Austen’s 1814 novel Mansfield Park. The speaker, Tom, is considering staging a play at home with a group of his friends and family.

\n

We mean nothing but a little amusement among ourselves, just to vary the scene, and exercise our powers in something new. We want no audience, no publicity. We may be trusted, I think, in choosing some play most perfectly unexceptionable; and I can conceive no greater harm or danger to any of us in conversing in the elegant written language of some respectable author than in chattering in words of our own.

", "stem": "

Which choice best states the main purpose of the text?

", "choices": [{"id": "A", "text": "

To offer Tom’s assurance that the play will be inoffensive and involve only a small number of people

"}, {"id": "B", "text": "

To clarify that the play will not be performed in the manner Tom had originally intended

"}, {"id": "C", "text": "

To elaborate on the idea that the people around Tom lack the skills to successfully stage a play

"}, {"id": "D", "text": "

To assert that Tom believes the group performing the play will be able to successfully promote it

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer because it most accurately portrays the main purpose of the text. At the beginning of the text, Tom asserts that he and the other people staging the play are doing so only for “a little amusement among ourselves” and aren’t interested in attracting an audience or any attention with the production. Then, Tom promises that the play they chose is modest and appropriate, and he further reasons that using the well-written prose of “some respectable author” is better than using their own words. Overall, the main purpose of the text is to convey Tom’s promise that the play will be inoffensive and involve only a few people.

Choice B is incorrect because the text doesn’t indicate that Tom had earlier intentions for the play’s performance or that anything has changed since the group first decided to stage a play. Instead, the text focuses on how harmless the entire endeavor will be. Choice C is incorrect. Although Tom mentions that using the words of a “respectable author” will be better than using their own words, he never addresses the idea that the people around him generally aren’t skilled enough to stage a play. Choice D is incorrect because in the text Tom specifically says that they “want no audience, no publicity,” which indicates that they don’t plan on promoting the play at all. 

"}, {"id": "1fa751f1", "domain": "Craft and Structure", "skill": "Words in Context", "difficulty": "M", "type": "mc", "stimulus": "

Handedness, a preferential use of either the right or left hand, typically is easy to observe in humans. Because this trait is present but less ______blank in many other animals, animal-behavior researchers often employ tasks specially designed to reveal individual animals’ preferences for a certain hand or paw.

", "stem": "

Which choice completes the text with the most logical and precise word or phrase?

", "choices": [{"id": "A", "text": "

recognizable

"}, {"id": "B", "text": "

intriguing

"}, {"id": "C", "text": "

significant

"}, {"id": "D", "text": "

useful

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer because it most logically completes the text’s discussion about handedness in animals. As used in this context, “recognizable” means apparent or identifiable. The text indicates that handedness is “easy to observe in humans,” but that animal-behavior researchers use special tasks to determine handedness in other animals. This context and the use of “less” before the blank indicate that compared with handedness in humans, handedness in other animals is less recognizable.

Choice B is incorrect because there’s nothing in the text to suggest that handedness is less “intriguing,” or fascinating, in nonhuman animals than it is in humans. The text focuses on how easy it is to observe handedness in humans as compared with other animals; the text doesn’t suggest that handedness is more fascinating in humans.  Choice C is incorrect because there’s nothing in the text to suggest that handedness is less “significant,” or important or meaningful, in nonhuman animals than it is in humans. The text focuses on how easy it is to observe handedness in humans as compared with other animals; the text doesn’t suggest that handedness is more significant in humans. Choice D is incorrect because “useful,” or functional or helpful, wouldn’t make sense in context. The text focuses on the ease with which researchers can determine whether an animal or person is right- or left-handed, not on how useful handedness in nonhuman animals is compared with handedness in humans. 

"}, {"id": "49bbe4d7", "domain": "Craft and Structure", "skill": "Words in Context", "difficulty": "E", "type": "mc", "stimulus": "

For painter Jacob Lawrence, being ______blank was an important part of the artistic process. Because he paid close attention to all the details of his Harlem neighborhood, Lawrence’s artwork captured nuances in the beauty and vitality of the Black experience during the Harlem Renaissance and the Great Migration.

", "stem": "

Which choice completes the text with the most logical and precise word or phrase?

", "choices": [{"id": "A", "text": "

skeptical

"}, {"id": "B", "text": "

observant

"}, {"id": "C", "text": "

critical

"}, {"id": "D", "text": "

confident

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer because it most logically completes the text’s discussion of Jacob Lawrence’s artistic process. In this context, “observant” means watchful and perceptive. The text emphasizes that the “close attention” Lawrence paid to “all the details” of his neighborhood allowed him to reflect subtle elements of “the beauty and vitality of the Black experience” in his artwork. This context indicates that being observant of his surroundings was an important part of Lawrence’s work as an artist.

Choice A is incorrect because the text gives no indication that Lawrence was “skeptical,” or had an attitude of doubt in general or about particular things, let alone that skepticism was important to him as an artist. Rather than indicating that he was skeptical, the text focuses on how Lawrence paid careful attention to everything around him and reflected his observations in his artwork. Choice C is incorrect because the text gives no indication that Lawrence was “critical,” which in this context would mean inclined to criticize harshly or unfairly. Rather than indicating that Lawrence found fault in things, the text suggests that he paid careful attention to everything around him and that his artwork reflects this careful attention. Choice D is incorrect because the text doesn’t suggest that Lawrence was “confident,” or self-assured. Rather than addressing how Lawrence felt about himself and how that feeling affected his artistic process, the text emphasizes the careful attention Lawrence paid to everything around him—attention that allowed him to capture subtle elements of a particular place and time in his artwork.

"}, {"id": "f6d1f735", "domain": "Craft and Structure", "skill": "Words in Context", "difficulty": "E", "type": "mc", "stimulus": "

Researchers have struggled to pinpoint specific causes for hiccups, which happen when a person’s diaphragm contracts ______blank. However, neuroscientist Kimberley Whitehead has found that these uncontrollable contractions may play an important role in helping infants regulate their breathing.

", "stem": "

Which choice completes the text with the most logical and precise word or phrase?

", "choices": [{"id": "A", "text": "

involuntarily

"}, {"id": "B", "text": "

beneficially

"}, {"id": "C", "text": "

strenuously

"}, {"id": "D", "text": "

smoothly

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer because it most logically completes the text’s discussion of diaphragm contractions and hiccups. In this context, “involuntarily” means done without any control, or by reflex. The text explains that when a person’s diaphragm repeatedly contracts and results in hiccups (which may be beneficial for infants), those muscle contractions are “uncontrollable.” This context indicates that the diaphragm contractions occur without the person’s control.

Choice B is incorrect because it wouldn’t support the logical relationship established in the text’s discussion of diaphragm contractions and hiccups. The text indicates that although specific causes for hiccups haven’t been identified, it may be the case that the muscle contractions that occur have an important purpose in infants. It wouldn’t make sense to say that even though the contractions occur “beneficially,” or with a good or helpful effect, they might play a positive role in infants’ breathing regulation. Choice C is incorrect because the text indicates that the diaphragm contractions that result in hiccups are “uncontrollable.” Because those muscle contractions are described as happening automatically and without the person’s control, it wouldn’t make sense to describe them as occurring “strenuously,” or in a way that requires great effort or energy. Choice D is incorrect because the text doesn’t describe the quality of the diaphragm contractions that result in hiccups beyond stating that they are “uncontrollable.” Nothing in the text indicates that those muscle contractions occur “smoothly,” or evenly and continuously.

"}, {"id": "fcc328c6", "domain": "Craft and Structure", "skill": "Text Structure and Purpose", "difficulty": "E", "type": "mc", "stimulus": "

Streams and rivers carry soil and rocks from one location to another. But there is another way for these geological materials to move. Scientists call this process “aeolian transport.” In aeolian transport, winds move small particles of soil or rock over potentially great distances. Geologist Melisa Diaz and her team studied dust in Antarctica to find out if it was moved by aeolian transport. They discovered that the dust matched geological material in Australia. Aeolian transport had carried it from one continent to another, across thousands of miles of open ocean. 

", "stem": "

Which choice best describes the function of the underlined portion in the text as a whole?

", "choices": [{"id": "A", "text": "

It presents Melisa Diaz’s remarks about difficulties that her team encountered.

"}, {"id": "B", "text": "

It introduces a scientific term that is used in the discussion that follows. 

"}, {"id": "C", "text": "

It emphasizes the surprising nature of the findings that are presented.

"}, {"id": "D", "text": "

It explains the difference between two kinds of geological material. 

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer because it most accurately describes the function of the underlined portion in the text as a whole. The first two sentences introduce the idea that soil and rocks can be moved from one location to another by something other than rivers and streams. The underlined sentence then states that the term used by scientists to refer to this process is “aeolian transport.” The discussion that follows explains what aeolian transport is (the movement of small geological materials over potentially great distances by the wind) and describes an example of a study that found that dust particles had been moved by aeolian transport from Australia to Antarctica. Thus, the underlined portion introduces a scientific term that is used in the discussion that follows.

Choice A is incorrect because the underlined portion of the text doesn’t present any remarks from Melisa Diaz, nor does it suggest that Diaz and her team encountered difficulties in their study. Instead, the phrase in quotation marks in the underlined portion simply presents a term that is used by scientists to refer to a specific process discussed in the text. Choice C is incorrect because nothing in either the underlined portion or the text as a whole suggests that the findings of the study presented in the text were surprising or unexpected. In fact, the text suggests that Diaz and her team wanted to see if aeolian transport could explain the appearance of certain geological materials in Antarctica, and their findings did indeed confirm the involvement of aeolian transport. Choice D is incorrect. Although the first sentence of the text mentions soil and rocks, which are two different kinds of geological material, the underlined portion doesn’t refer to these materials, nor does it explain the difference between them. Rather, the underlined portion introduces the scientific term “aeolian transport,” which is used in the discussion that follows. 

"}, {"id": "aa7ae735", "domain": "Craft and Structure", "skill": "Words in Context", "difficulty": "E", "type": "mc", "stimulus": "

The following text is adapted from Mohsin Hamid’s 2017 novel Exit West. Saeed lives with his mother and father.

\n

On cloudless nights after a daytime rain, Saeed’s father would sometimes bring out the telescope, and the family would sip green tea on their balcony, enjoying a breeze, and take turns to look up at objects whose light, often, had been emitted before any of these three viewers had been born—light from other centuries, only now reaching Earth.

\n

©2017 by Mohsin Hamid

", "stem": "

As used in the text, what does the word “reaching” most nearly mean?

", "choices": [{"id": "A", "text": "

Arriving at

"}, {"id": "B", "text": "

Consulting with

"}, {"id": "C", "text": "

Running to

"}, {"id": "D", "text": "

Clinging to

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. The word \"reaching\" in this text means \"to arrive\" at Earth. Before, the light had been traveling across space; now, it had arrived at Earth.

Choice B is incorrect. \"Consulting with\" means \"seeking advice or information from someone.\" Light is not alive, so it can’t consult with Earth. Choice C is incorrect. It’s confusing to say that starlight is \"only now running to Earth,\" both because light doesn’t literally \"run\" and because the text is describing the moment the light touches Earth, not the period of time when it’s traveling to Earth. Choice D is incorrect. This might be tempting, as \"clinging to\" has a connotation of \"sticking to.\" It wouldn’t make sense to say that the light was \"only now\" clinging to Earth.

"}, {"id": "84a7fbca", "domain": "Craft and Structure", "skill": "Words in Context", "difficulty": "E", "type": "mc", "stimulus": "

When Mexican-American archaeologist Zelia Maria Magdalena Nuttall published her 1886 research paper on sculptures found at the ancient Indigenous city of Teotihuacan in present-day Mexico, other researchers readily ______blank her work as groundbreaking; this recognition stemmed from her convincing demonstration that the sculptures were much older than had previously been thought.

", "stem": "

Which choice completes the text with the most logical and precise word or phrase?

", "choices": [{"id": "A", "text": "

acknowledged

"}, {"id": "B", "text": "

ensured

"}, {"id": "C", "text": "

denied

"}, {"id": "D", "text": "

underestimated

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer because it most logically completes the text’s discussion of Nuttall’s 1886 research paper. In this context, “acknowledged” means recognized as having a certain status. The text indicates that other researchers recognized Nuttall’s work as groundbreaking because of its “convincing demonstration” related to the age of the ancient sculptures. In other words, the researchers recognized the groundbreaking status of Nuttall’s work.

Choice B is incorrect because in this context, “ensured” would mean to have guaranteed or made sure something was the case. The text states that other researchers gave Nuttall’s work recognition after it was published, but there’s no indication that they contributed to the work or had any involvement that would have allowed them to make sure the work would be groundbreaking. Choice C is incorrect because the text doesn’t suggest that other researchers “denied,” or refused to admit or accept, that Nuttall’s work was groundbreaking; on the contrary, it indicates that researchers praised the work, recognizing it as groundbreaking due to its “convincing demonstration” related to the age of the ancient sculptures. Choice D is incorrect because the text doesn’t suggest that other researchers “underestimated,” or undervalued, Nuttall’s work; on the contrary, it indicates that researchers praised the work, recognizing it as groundbreaking due to its “convincing demonstration” related to the age of the ancient sculptures.

"}, {"id": "428cd2c1", "domain": "Craft and Structure", "skill": "Words in Context", "difficulty": "E", "type": "mc", "stimulus": "

Some people have speculated that two helmets with attached horns discovered in Denmark in 1942 belonged to Vikings, but scholars have long been skeptical. Archaeologist Helle Vandkilde and colleagues recently provided radiocarbon dates for the helmets, and their findings ______blank scholars’ skepticism: the helmets date to the Nordic Bronze Age, centuries before the Vikings existed.

", "stem": "

Which choice completes the text with the most logical and precise word or phrase?

", "choices": [{"id": "A", "text": "

anticipate

"}, {"id": "B", "text": "

inspect

"}, {"id": "C", "text": "

reveal

"}, {"id": "D", "text": "

justify

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer because it most logically completes the text’s discussion of the helmets found in Denmark. In this context, “justify” means confirm or give reasons for. The text indicates that scholars have long been skeptical about the supposed Viking origin of two helmets found in Denmark. The radiocarbon dating of the helmets conducted by Vandkilde and colleagues demonstrates that the helmets date from the Nordic Bronze Age, making the helmets too old to have belonged to Vikings. This context supports the idea that the scholars’ skepticism is justified.

Choice A is incorrect because “anticipate” means expect or come before, neither of which would make sense in context. The text indicates that scholars have long been skeptical of the idea that the helmets belonged to Vikings. Because the skepticism has existed for a long time, Vandkilde and colleagues’ research couldn’t be said to anticipate it. Instead, the radiocarbon dating results justify or confirm the scholar’s skepticism. Choice B is incorrect because “inspect” means examine or review, which wouldn’t make sense in this context. Research findings are inanimate and therefore unable to inspect scholars’ skepticism. The text focuses on the origin of two helmets, which some people believe belonged to Vikings. Vandkilde and colleagues found that the helmets are from the Nordic Bronze Age and therefore much older than the Vikings. This context suggests that the researchers’ findings justify, not inspect, the scholars’ skepticism. Choice C is incorrect because “reveal” means uncover or report, which wouldn’t make sense in context. The text focuses on the origin of two helmets, which some people believe belonged to Vikings. Vandkilde and colleagues tested the helmets and found that they date to the Nordic Bronze Age and therefore are much older than the Vikings. This context suggests that the researchers’ findings confirm or justify the scholars’ skepticism, which was already known so didn’t need to be revealed.

"}, {"id": "62a18353", "domain": "Craft and Structure", "skill": "Words in Context", "difficulty": "M", "type": "mc", "stimulus": "

The following text is adapted from Zora Neale Hurston’s 1921 short story “John Redding Goes to Sea.” John wants to travel far beyond the village where he lives near his mother, Matty.

\n
\n

[John] had on several occasions attempted to reconcile his mother to the notion, but found it a difficult task. Matty always took refuge in self-pity and tears. Her son’s desires were incomprehensible to her, that was all.

\n
", "stem": "

As used in the text, what does the phrase “reconcile his mother to” most nearly mean?

", "choices": [{"id": "A", "text": "

Get his mother to accept

"}, {"id": "B", "text": "

Get his mother to apologize for

"}, {"id": "C", "text": "

Get his mother to match

"}, {"id": "D", "text": "

Get his mother to reunite with

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. The expression “reconcile to” means “to cause (a person) to accept something difficult or disagreeable.” The text suggests that John wants his mother to accept his desire to travel, even though she doesn’t like that idea.

Choice B is incorrect. This doesn’t make sense. John doesn’t want his mother to apologize for his own desire to travel—he wants her to accept his desire to travel. Choice C is incorrect. The text doesn’t suggest that John wants his mother to match his desire to travel. Rather, he wants her to accept his desire to travel even though she doesn’t like it. Choice D is incorrect. This is tempting, because it seems to pick up on the idea of people “reconciling” after a fight, but it actually doesn’t make sense. The text never suggests that John’s mother was “united with” the idea of him traveling in the past—if anything, it seems like she’s always been against it. Besides, it would be strange to say that a person “reunites with” a notion.

"}, {"id": "4eee64fa", "domain": "Craft and Structure", "skill": "Text Structure and Purpose", "difficulty": "H", "type": "mc", "stimulus": "

Space scientists Anna-Lisa Paul, Stephen M. Elardo, and Robert Ferl planted seeds of Arabidopsis thaliana in samples of lunar regolith—the surface material of the Moon—and, serving as a control group, in terrestrial soil. They found that while all the seeds germinated, the roots of the regolith-grown plants were stunted compared with those in the control group. Moreover, unlike the plants in the control group, the regolith-grown plants exhibited red pigmentation, reduced leaf size, and inhibited growth rates—indicators of stress that were corroborated by postharvest molecular analysis.

", "stem": "

Which choice best states the main purpose of the text?

", "choices": [{"id": "A", "text": "

It describes an experiment that addressed an unresolved question about the extent to which lunar regolith resembles terrestrial soils.

"}, {"id": "B", "text": "

It compares two distinct methods of assessing indicators of stress in plants grown in a simulated lunar environment.

"}, {"id": "C", "text": "

It presents evidence in support of the hypothesis that seed germination in lunar habitats is an unattainable goal.

"}, {"id": "D", "text": "

It discusses the findings of a study that evaluated the effects of exposing a plant species to lunar soil conditions.

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. The text describes an experiment wherein space scientists compared plant growth in terrestrial and lunar soil conditions. It then discusses the findings of the study, including the fact that all the seeds germinated but that the plants grown in lunar soil exhibited signs of stress.

Choice A is incorrect. The text doesn’t address this question, and never describes any specific characteristics of either soil. It merely describes the outcome of an experiment that exposed a plant species to lunar soil conditions. Choice B is incorrect. The text never compares methods of assessing indicators of stress—instead, it simply mentions several stress indicators observed in the study (red pigmentation, reduced leaf size, and inhibited growth rates). Choice C is incorrect. The text doesn’t present any evidence that we could never achieve seed germination in lunar habitats, and in fact states that the seeds in the lunar soil did germinate.

"}, {"id": "c2c26e20", "domain": "Craft and Structure", "skill": "Words in Context", "difficulty": "E", "type": "mc", "stimulus": "

The following text is adapted from Sadakichi Hartmann’s 1894 short story “Magnolia Blossoms.” The narrator is standing on the deck of a boat.

\n
\n

What a night it was! My soul had left its body to lose itself in the wild unrestrained beauty around me—from where it came—and only left a trembling suggestion of its existence within me. The other passengers moved around me like shadows, and again and again my eyes drank in all the glory and wealth of that night.

\n
", "stem": "

As used in the text, what does the word “suggestion” most nearly mean? 

", "choices": [{"id": "A", "text": "

Trace

"}, {"id": "B", "text": "

Opinion

"}, {"id": "C", "text": "

Dispute

"}, {"id": "D", "text": "

Command

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer because as used in the text, “suggestion” most nearly means trace. The text portrays the narrator standing on the deck of a boat, admiring the view of nature afforded by this position: “My soul had left its body to lose itself in the wild unrestrained beauty around me,” says the narrator, “and only left a trembling suggestion of its existence within me.” This intense response to beauty is such that the narrator’s soul seems to disengage from its body, leaving behind only a barely detectible indication of its presence there. In other words, the narrator senses only a trace of soul left in the body.

Choice B is incorrect. Although in some contexts “suggestion” can refer to an implied or indirectly expressed opinion, the text doesn’t portray the narrator expressing an opinion; instead, the narrator is explaining an experience of intense emotion. Choice C is incorrect. While “suggestion” might be used in some contexts to refer to the tactful expression of a differing viewpoint, it doesn’t refer to the dispute or difference of opinion itself. Moreover, the text doesn’t portray a dispute between characters with differing viewpoints. Choice D is incorrect. Although in some contexts, “suggestion” might be used to refer to a politely worded command, the text doesn’t portray a scenario in which someone receives such a command.

"}, {"id": "a70cbc53", "domain": "Craft and Structure", "skill": "Text Structure and Purpose", "difficulty": "H", "type": "mc", "stimulus": "

Raymond Antrobus, an accomplished poet and writer of prose, recently released his debut spoken word poetry album, The First Time I Wore Hearing Aids, in collaboration with producer Ian Brennan. The album contains both autobiographical and reflective pieces combining Antrobus’s spoken words with Brennan’s fragmented audio elements and pieces of music to convey how people who are deaf may experience sound, both its presence and absence. Some critics suggest that the album questions the function of sound in the world, highlighting that the experience of sound is multifaceted.

", "stem": "

Which choice best describes the overall structure of the text?

", "choices": [{"id": "A", "text": "

It introduces a collaborative spoken word poetry project, details the approach taken to produce the work, and then provides an example of critique the album received upon release. 

"}, {"id": "B", "text": "

It mentions a collection of spoken word poems, distinguishes one poem as being an exemplar on the album, and then offers a summary of the subject matter of the whole collection.

"}, {"id": "C", "text": "

It summarizes the efforts to produce a collection of spoken word poems, presents biographies of two people who worked on the album, and speculates about the meaning behind the poetry.

"}, {"id": "D", "text": "

It connects two artists to the same spoken word poetry project, explains the extent of their collaboration on each poem, and then provides an overview of the technique used to produce the work.

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. The text first introduces the album as being a collaboration between Antrobus and Brennan, then describes the approach taken to produce it, then mentions how critics have said that it calls into question the function of sound.

Choice B is incorrect. While the text does mention a collection of spoken word poems, it doesn’t single out one poem as being particularly noteworthy. Additionally, the text doesn’t simply summarize the subject matter—it goes into detail about the content and production of the album. Choice C is incorrect. The text doesn’t provide biographical information about the two artists, and the text doesn’t speculate about the meaning behind the poetry—instead, it relays what some critics have said about the album. Choice D is incorrect. The text doesn’t provide just an overview of the production techniques used but instead goes into more detail about the content and audio elements of the album, as well as critical response to the album.

"}, {"id": "3d658a5a", "domain": "Craft and Structure", "skill": "Words in Context", "difficulty": "H", "type": "mc", "stimulus": "

Some foraging models predict that the distance bees travel when foraging will decline as floral density increases, but biologists Shalene Jha and Claire Kremen showed that bees’ behavior is inconsistent with this prediction if flowers in dense patches are ______blank: bees will forage beyond patches of low species richness to acquire multiple resource types. 

", "stem": "

Which choice completes the text with the most logical and precise word or phrase?

", "choices": [{"id": "A", "text": "

depleted 

"}, {"id": "B", "text": "

homogeneous

"}, {"id": "C", "text": "

immature

"}, {"id": "D", "text": "

dispersed

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer because it most logically completes the text’s discussion of Jha and Kremen’s finding about bees’ foraging behavior. In this context, “homogeneous” means uniform or of the same kind. The text indicates that some models predict that the distance that bees travel when they’re foraging declines as the density of flowers increases. The text goes on to say, however, that Jha and Kremen identified a circumstance in which bees don’t behave this way. Specifically, if bees encounter “patches of low species richness”—that is, patches in which the flowers are largely from the same species—they’ll travel beyond those patches to get varied food resources. This context thus suggests that bees don’t behave as some models predict if the dense patches of flowers the bees encounter are homogeneous. 

Choice A is incorrect because the text indicates that Jha and Kremen found that bees will behave differently than some models predict if the bees encounter flower patches that are not rich in species, not if the flowers are “depleted,” or emptied or reduced in quality or quantity. Although it could be true that bees are likely to leave depleted patches in search of more resources, the text doesn’t indicate that Jha and Kremen investigated that possibility. Choice C is incorrect because there’s no information in the text suggesting that bees will not behave as some models predict if flowers in patches are “immature,” or not fully developed. Instead, the text indicates that Jha and Kremen found that bees will behave contrary to some models’ predictions if the flower patches are not rich in species. Choice D is incorrect because the text indicates that bees’ behavior will be inconsistent with the predictions of some models if the flower patches that the bees encounter are of low species richness, not if the flowers are in patches that are “dispersed,” or widely scattered. Although the text does describe bees as leaving patches that are not rich in species to forage elsewhere, there’s no suggestion that Jha and Kremen found that the distance between dense flower patches affects whether the bees behave as some models predict.

"}, {"id": "cd2ce51f", "domain": "Craft and Structure", "skill": "Words in Context", "difficulty": "M", "type": "mc", "stimulus": "

Like the 1945 play it reimagines—Federico García Lorca’s The House of Bernarda Alba—Marcus Gardley’s 2014 play The House That Will Not Stand prominently features women. In both plays, the all-female cast ______blank an array of female characters, including a strong mother and several daughters dealing with individual struggles.

", "stem": "

Which choice completes the text with the most logical and precise word or phrase?

", "choices": [{"id": "A", "text": "

engulfs

"}, {"id": "B", "text": "

encourages

"}, {"id": "C", "text": "

comprises

"}, {"id": "D", "text": "

provokes

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer because it most logically completes the text’s discussion of Gardley’s play. In this context, “comprises” means constitutes or makes up the totality of, and the text indicates that The House That Will Not Stand had an “all-female cast” that stands in some relationship to “an array of female characters” in the play. Because all cast members are female, the characters must be played by these female cast members; therefore the cast constitutes, or comprises, the collection of characters.

Choice A is incorrect. In this context, “engulfs” would mean encloses or overwhelms, and although it is fairly common to describe an actor as embodying (or personifying realistically) a character, there is nothing in the text to suggest that the cast members enclosed or overwhelmed the characters they played. Choice B is incorrect because in this context, “encourages” would mean inspires with courage or hope. Although the text does mention “a strong mother and several daughters dealing with individual struggles,” which might suggest that there are moments of encouragement among the characters during the play, there is nothing to suggest that the cast members encouraged the characters they portrayed. Choice D is incorrect because, in this context, “provokes” would mean instigates or incites to anger. Nothing in the text addresses provocation or what it might mean for actors to provoke the characters they are playing.

"}, {"id": "17bf10de", "domain": "Craft and Structure", "skill": "Cross-Text Connections", "difficulty": "H", "type": "mc", "stimulus": "

Text 1

\n

Despite its beautiful prose, The Guns of August, Barbara Tuchman’s 1962 analysis of the start of World War I, has certain weaknesses as a work of history. It fails to address events in Eastern Europe just before the outbreak of hostilities, thereby giving the impression that Germany was the war’s principal instigator. Had Tuchman consulted secondary works available to her by scholars such as Luigi Albertini, she would not have neglected the influence of events in Eastern Europe on Germany’s actions.

\n

 

\n

Text 2

\n

Barbara Tuchman’s The Guns of August is an engrossing if dated introduction to World War I. Tuchman’s analysis of primary documents is laudable, but her main thesis that European powers committed themselves to a catastrophic outcome by refusing to deviate from military plans developed prior to the conflict is implausibly reductive.

", "stem": "

Which choice best describes a difference in how the authors of Text 1 and Text 2 view Barbara Tuchman’s The Guns of August?

", "choices": [{"id": "A", "text": "

The author of Text 1 argues that Tuchman should have relied more on the work of other historians, while the author of Text 2 implies that Tuchman’s most interesting claims result from her original research.

"}, {"id": "B", "text": "

The author of Text 1 believes that the scope of Tuchman’s research led her to an incorrect interpretation, while the author of Text 2 believes that Tuchman’s central argument is overly simplistic.

"}, {"id": "C", "text": "

The author of Text 1 asserts that the writing style of The Guns of August makes it worthwhile to read despite any perceived deficiency in Tuchman’s research, while the author of Text 2 focuses exclusively on the weakness of Tuchman’s interpretation of events.

"}, {"id": "D", "text": "

The author of Text 1 claims that Tuchman would agree that World War I was largely due to events in Eastern Europe, while the author of Text 2 maintains that Tuchman would say that Eastern European leaders were not committed to military plans in the same way that other leaders were.

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. Both texts are critical of The Guns of August, but for different reasons: the author of Text 1 argues that Tuchman missed an important factor leading up to the war because she didn’t consult secondary sources, and the author of Text 2 argues that Tuchman’s main thesis is \"reductive,\" which is a close synonym for \"overly simplistic.\"

Choice A is incorrect. This doesn’t accurately describe the difference. This choice’s summary of Text 1 is accurate, but Text 2 never says that Tuchman’s most interesting claims result from her original research. Choice C is incorrect. This doesn’t accurately describe the difference. Text 1 never says that The Guns of August is worthwhile to read despite its research weaknesses. Text 2 does call out a weakness of Tuchman’s interpretation of events, but it also praises her analysis of primary sources. Choice D is incorrect. This doesn’t accurately describe the difference. Text 1 actually says that Tuchman \"fails to address\" the influence of events in Eastern Europe, while Text 2 says that Tuchman’s thesis was that European powers (not Eastern European leaders) were committed to military plans.

"}, {"id": "b4c6cff6", "domain": "Craft and Structure", "skill": "Words in Context", "difficulty": "M", "type": "mc", "stimulus": "

The following text is adapted from Karel \u010capek’s 1920 play R.U.R. (Rossum’s Universal Robots), translated by Paul Selver and Nigel Playfair in 1923. Fabry and Busman are telling Miss Glory why their company manufactures robots.

\n

FABRY: One Robot can replace two and a half workmen. The human machine, Miss Glory, was terribly imperfect. It had to be removed sooner or later.

\n

BUSMAN: It was too expensive.

\n

FABRY: It was not effective. It no longer answers the requirements of modern engineering. Nature has no idea of keeping pace with modern labor. 

", "stem": "

As used in the text, what does the word “answers” most nearly mean?

", "choices": [{"id": "A", "text": "

Explains

"}, {"id": "B", "text": "

Rebuts

"}, {"id": "C", "text": "

Defends

"}, {"id": "D", "text": "

Fulfills

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer because as used in the text, “answers” most nearly means fulfills. In the text, Fabry and Busman claim that the robots manufactured by their company are more efficient than human workers, which they refer to as “the human machine.” Fabry observes that the human machine “no longer answers the requirements of modern engineering.” That is, human workers are incapable of meeting the rigorous needs of modern, industrialized workplaces.

Choice A is incorrect. Although in some contexts “answers” can mean explains, it doesn’t have that meaning in this context because the topic under discussion is human beings’ inability to perform labor efficiently, not their inability to engage in discussion or explanation. Choice B is incorrect. Although in some contexts “answers” can mean rebuts, or proves a claim or argument to be false, it wouldn’t make sense to speak of proving requirements to be false; requirements might or might not be reasonable, but they can’t be verified as truthful or untruthful, as claims or accusations can. Choice C is incorrect. Although in some contexts, “answers” can mean defends against criticism, or justifies, it doesn’t have that meaning in this context because the opinion that Fabry expresses is that human workers can no longer fulfill the requirements of modern workplaces, not that they have ceased to justify those requirements or to defend them against criticism; indeed, there is no suggestion in the text that workers ever defended those requirements. 

"}, {"id": "d8d1ecaa", "domain": "Craft and Structure", "skill": "Words in Context", "difficulty": "M", "type": "mc", "stimulus": "

Business researcher Melanie Brucks and colleagues found that remote video conference meetings may be less conducive to brainstorming than in-person meetings are. The researchers suspect that video meeting participants are focused on staring at the speaker on the screen and don’t allow their eyes or mind to wander as much, which may ultimately ______blank creativity.

", "stem": "

Which choice completes the text with the most logical and precise word or phrase?

", "choices": [{"id": "A", "text": "

recommend

"}, {"id": "B", "text": "

criticize

"}, {"id": "C", "text": "

impede

"}, {"id": "D", "text": "

construct

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. The first sentence tells us that video meetings are “less conducive to” (meaning less good for) brainstorming. This suggests that the video meeting participants’ focus is bad for their creativity. “Impede” means “delay” or “prevent,” which works perfectly in this context.

Choice A is incorrect. This choice is too positive to fit the context. The first sentence tells us that video meetings are “less conducive to” (meaning less good for) brainstorming. This suggests that the video meeting participants’ focus is bad for their creativity. Choice B is incorrect. This choice doesn’t make sense. The participants’ intense focus on the screen is the subject of the missing verb. It wouldn’t make sense to say that their over-focusing “criticizes” their creativity. Choice D is incorrect. “Construct” means “build” or “make,” which is too positive to fit the context. The first sentence tells us that video meetings are “less conducive to” (meaning less good for) brainstorming. This suggests that the video meeting participants’ focus is bad for their creativity.

"}, {"id": "d0198544", "domain": "Craft and Structure", "skill": "Cross-Text Connections", "difficulty": "H", "type": "mc", "stimulus": "

 

Text 1

\n

In 2007, a team led by Alice Storey analyzed a chicken bone found in El Arenal, Chile, dating it to 1321–1407 CE—over a century before Europeans invaded the region, bringing their own chickens. Storey also found that the El Arenal chicken shared a unique genetic mutation with the ancient chicken breeds of the Polynesian Islands in the Pacific. Thus, Polynesian peoples, not later Europeans, probably first introduced chickens to South America.

\n

 

Text 2

\n

An Australian research team weakened the case for a Polynesian origin for the El Arenal chicken by confirming that the mutation identified by Storey has occurred in breeds from around the world. More recently, though, a team led by Agusto Luzuriaga-Neira found that South American chicken breeds and Polynesian breeds share other genetic markers that European breeds lack. Thus, the preponderance of evidence now favors a Polynesian origin.

", "stem": "

Based on the texts, how would the author of Text 2 most likely respond to the underlined claim in Text 1?

", "choices": [{"id": "A", "text": "

By broadly agreeing with the claim but objecting that the timeline it presupposes conflicts with the findings of the genetic analysis conducted by Storey’s team

"}, {"id": "B", "text": "

By faulting the claim for implying that domestic animals couldn’t have been transferred from South America to the Polynesian Islands as well

"}, {"id": "C", "text": "

By critiquing the claim for being based on an assumption that before the European invasion of South America, the chickens of Europe were genetically uniform

"}, {"id": "D", "text": "

By noting that while the claim is persuasive, the findings of Luzuriaga-Neira’s team provide stronger evidence for it than the findings of the genetic analysis conducted by Storey do

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer because it accurately describes how the author of Text 2 would most likely respond to the underlined claim in Text 1. Text 1 indicates that Storey found a genetic mutation in South American chickens from before the European invasion and in Polynesian chickens, which implies that chickens were first brought to South America by Polynesian people. Text 2 explains that the genetic mutation Storey found is in chickens from all over the world, thus undercutting the mutation as evidence of a Polynesian origin. However, Text 2 goes on to say “[m]ore recently” Luzuriaga-Neira and colleagues found multiple genetic markers shared by South American and Polynesian chickens but “that European breeds lack,” which strongly suggests a Polynesian origin for the South American chickens. This indicates that the author of Text 2 believes Luzuriaga-Neira’s evidence for a Polynesian origin is compelling while Storey’s evidence has been undermined. Thus, the author of Text 2 would most likely agree with the underlined statement and believes Luzuriaga-Neira and colleagues’ evidence for the statement is stronger than Storey’s evidence is.

Choice A is incorrect because both texts indicate that chickens were introduced to South America before the arrival of Europeans. Text 1 states that the El Arenal chicken bone dates from “1321–1407 CE—over a century before Europeans invaded the region” and concludes that these chickens were likely brought to South America by Polynesians. While Text 2 is not as explicit about the time period as Text 1 is, nothing in Text 2 undermines the timing of events ascribed to Storey’s account in Text 1. Choice B is incorrect because both texts agree that chickens were first brought to South America by Polynesian peoples (the underlined claim), and nothing in Text 2 suggests that this claim is in any way deficient because the possibility that animals could have been transferred from South America to Polynesia was not explicitly addressed. Choice C is incorrect because the criticism that Text 2 raises about the ideas in Text 1 is specifically about whether the single genetic mutation cited by Storey in fact supports the idea of a Polynesian origin for South American chickens. There is nothing in Text 2 to suggest that the underlined sentence (Storey’s conclusion) is deficient because it is based on an assumption about the genetic uniformity of European chickens. 

"}, {"id": "a2be625e", "domain": "Craft and Structure", "skill": "Text Structure and Purpose", "difficulty": "M", "type": "mc", "stimulus": "

The following text is from Sarah Orne Jewett’s 1899 short story “Martha’s Lady.” Martha is employed by Miss Pyne as a maid.

\n

Miss Pyne sat by the window watching, in her best dress, looking stately and calm; she seldom went out now, and it was almost time for the carriage. Martha was just coming in from the garden with the strawberries, and with more flowers in her apron. It was a bright cool evening in June, the golden robins sang in the elms, and the sun was going down behind the apple-trees at the foot of the garden. The beautiful old house stood wide open to the long-expected guest.

", "stem": "

Which choice best states the main purpose of the text?

", "choices": [{"id": "A", "text": "

To convey the worries brought about by a new guest

"}, {"id": "B", "text": "

To describe how the characters have changed over time

"}, {"id": "C", "text": "

To contrast the activity indoors with the stillness outside

"}, {"id": "D", "text": "

To depict the setting as the characters await a visitor’s arrival 

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer because it most accurately reflects the main purpose of the text. The text portrays Miss Pyne as awaiting the arrival of a carriage while Martha brings strawberries and flowers from the garden into the house. The text also describes the surroundings of the scene, stating that Miss Pyne looks “stately and calm,” the evening is bright and cool, and birds are singing in the garden as the sun sets. Then the last sentence states that the house was “wide open to the long-expected guest,” which strongly suggests that Miss Pyne’s anticipation and Martha’s activities were in preparation for the guest who is expected to arrive in the carriage. Thus, the text depicts the setting and conveys what these characters are doing as they await the arrival of their visitor.

Choice A is incorrect because there is nothing in the text to indicate that the characters feel any worry about the guest’s arrival. The text indicates that the guest was “long-expected,“ but characterizing Miss Pyne as “stately and calm” conflicts with the idea that the characters are worried about the guest. Choice B is incorrect because the text describes a moment in time when two characters are awaiting the arrival of a visitor rather than an extended period over which characters could be seen changing. Choice C is incorrect. Although the text describes the activity indoors (Miss Pyne sitting calmly), it describes a higher level of activity, not stillness, outside (Martha bringing fruit and flowers and birds singing).

"}, {"id": "ab56a107", "domain": "Craft and Structure", "skill": "Cross-Text Connections", "difficulty": "M", "type": "mc", "stimulus": "

 

Text 1

\n

Digital art, the use of digital technology to create or display images, isn’t really art at all. It doesn’t require as much skill as creating physical art. “Painting” with a tablet and stylus is much easier than using paint and a brush: the technology is doing most of the work.

\n

 

Text 2

\n

The painting programs used to create digital art involve more than just pressing a few buttons. In addition to knowing the fundamentals of art, digital artists need to be familiar with sophisticated software. Many artists will start by drawing an image on paper before transforming the piece to a digital format, where they can apply a variety of colors and techniques that would otherwise require many different traditional tools.

", "stem": "

Based on the texts, how would the author of Text 2 most likely respond to the claims of the author of Text 1? 

", "choices": [{"id": "A", "text": "

By arguing that a piece of art created digitally can still be displayed traditionally

"}, {"id": "B", "text": "

By explaining that it’s actually much harder to use a tablet and stylus to create art than to use paint and a brush

"}, {"id": "C", "text": "

By insisting that digital art requires artistic abilities and skill even if it employs less traditional tools

"}, {"id": "D", "text": "

By admitting that most digital artists don’t think fundamental drawing skills are important

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer because it reflects how the author of Text 2 would respond to the claims in Text 1. Both texts address skills needed to produce digital art. Text 1 claims that digital art doesn’t require the same amount of skill as creating physical art and that “the technology is doing most of the work.” Text 2 states that digital art requires “knowing the fundamentals of art” and that many digital artists begin their work on paper and then transfer it to a digital format using “sophisticated software” and “a variety of colors and techniques.” Therefore, the author of Text 2 would most likely insist that digital art requires artistic abilities even if it employs less traditional tools.

Choice A is incorrect because neither text discusses nondigital means of displaying art. Choice B is incorrect because the author of Text 2 doesn’t address whether it’s harder to use a tablet and stylus than it is to use paint and a brush. Text 2 does argue that digital art requires skills that aren’t part of the traditional methods for producing art, but the text doesn’t address relative difficulty. Choice D is incorrect because the author of Text 2 states that digital artists still need to know “the fundamentals of art” and that many digital artists begin their work by drafting on paper before transferring the work to a digital format.

"}, {"id": "f773a56b", "domain": "Craft and Structure", "skill": "Words in Context", "difficulty": "E", "type": "mc", "stimulus": "

As Mexico’s first president from an Indigenous community, Benito Juarez became one of the most ______blank figures in his country’s history: among the many significant accomplishments of his long tenure in office (1858–1872), Juarez consolidated the authority of the national government and advanced the rights of Indigenous peoples.

", "stem": "

Which choice completes the text with the most logical and precise word or phrase?

", "choices": [{"id": "A", "text": "

unpredictable

"}, {"id": "B", "text": "

important

"}, {"id": "C", "text": "

secretive

"}, {"id": "D", "text": "

ordinary

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer because it most logically completes the text’s discussion of Juarez. In this context, “important” means marked by significant work or consequence. The text indicates that Juarez, who was the first president of Mexico from an Indigenous community, became a certain kind of figure in Mexico’s history. It then supports that claim by describing some of the “many significant accomplishments” from Juarez’s long tenure in office. This context conveys that Juarez is a significant and consequential figure in Mexico’s history.

Choice A is incorrect because the text focuses on Juarez’s role as the first president of Mexico from an Indigenous community and on his many major accomplishments during his lengthy time in office; nothing in the text suggests that Juarez was “unpredictable,” or tended to behave in ways that couldn’t be predicted. Choice C is incorrect because nothing in the text suggests that Juarez was a particularly “secretive” figure, or that he tended to keep things private or hidden from others. Instead, the text focuses on things that are known about Juarez: that he was the first president of Mexico from an Indigenous community, that he had a lengthy tenure, and that his many major accomplishments included consolidating the national government’s authority and advancing Indigenous rights. Choice D is incorrect because the text focuses on the idea that Juarez, who was the first president of Mexico from an Indigenous community, had many major accomplishments during his lengthy time in office. Rather than suggesting that Juarez was an “ordinary,” or common and typical, figure in Mexico’s history, this context conveys that Juarez was instead a notable figure.

"}, {"id": "f653b273", "domain": "Craft and Structure", "skill": "Cross-Text Connections", "difficulty": "M", "type": "mc", "stimulus": "

 

Text 1

\n

A tiny, unusual fossil in a piece of 99-million-year-old amber is of the extinct species Oculudentavis khaungraae. The O. khaungraae fossil consists of a rounded skull with a thin snout and a large eye socket. Because these features look like they are avian, or related to birds, researchers initially thought that the fossil might be the smallest avian dinosaur ever found.

\n

 

Text 2

\n

Paleontologists were excited to discover a second small fossil that is similar to the strange O. khaungraae fossil but has part of the lower body along with a birdlike skull. Detailed studies of both fossils revealed several traits that are found in lizards but not in dinosaurs or birds. Therefore, paleontologists think the two creatures were probably unusual lizards, even though the skulls looked avian at first.

", "stem": "

Based on the texts, what would the paleontologists in Text 2 most likely say about the researchers’ initial thought in Text 1?

", "choices": [{"id": "A", "text": "

It is understandable because the fossil does look like it could be related to birds, even though O. khaungraae is probably a lizard.

"}, {"id": "B", "text": "

It is confusing because it isn’t clear what caused the researchers to think that O. khaungraae might be related to birds.

"}, {"id": "C", "text": "

It is flawed because the researchers mistakenly assumed that O. khaungraae must be a lizard.

"}, {"id": "D", "text": "

It is reasonable because the O. khaungraae skull is about the same size as the skull of the second fossil but is shaped differently.

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer because it reflects what the paleontologists in Text 2 would most likely say about what the researchers in Text 1 initially thought. Text 1 focuses on the discovery of a strange fossil consisting of the skull of the extinct species Oculudentavis khaungraae. According to Text 1, the fossil has features that appear to be avian, or related to birds, which led researchers to initially think that the fossil might be a very small avian dinosaur. Text 2 begins by noting the discovery of a second fossil similar to the one discussed in Text 1, then explains that based on detailed studies of both fossils, paleontologists think that the two creatures were probably unusual lizards, even though the skulls appeared avian at first. This suggests that the paleontologists in Text 2 recognize that the fossils do indeed look like they could be related to birds. For this reason, the paleontologists in Text 2 would most likely say that the initial thought of the researchers in Text 1—that the fossil was avian—is understandable, even if the fossil is probably not avian but rather is from a lizard.

Choice B is incorrect because Text 2 indicates that the fossils initially looked avian, so the paleontologists described in Text 2 wouldn’t be confused by the researchers in Text 1 initially thinking that O. khaungraae might be related to birds. The paleontologists would find that initial thought understandable, not confusing. Choice C is incorrect because Text 1 never mentions lizards, so it wouldn’t make sense for the paleontologists in Text 2 to say that the researchers in Text 1 mistakenly assumed that O. khaungraae must be a lizard. Choice D is incorrect. Although the paleontologists in Text 2 might agree that the initial thought of the researchers in Text 1 was reasonable, nothing in Text 2 suggests that the two skulls were shaped differently.

"}, {"id": "5e732e67", "domain": "Craft and Structure", "skill": "Text Structure and Purpose", "difficulty": "E", "type": "mc", "stimulus": "

Many films from the early 1900s have been lost. These losses include several films by the first wave of Black women filmmakers. We know about these lost movies only from small pieces of evidence. For example, an advertisement for Jennie Louise Touissant Welcome’s documentary Doing Their Bit still exists. There’s a reference in a magazine to Tressie Souders’s film A Woman’s Error. And Maria P. Williams’s The Flames of Wrath is mentioned in a letter and a newspaper article, and one image from the movie was discovered in the 1990s.

", "stem": "

Which choice best describes the overall structure of the text?

", "choices": [{"id": "A", "text": "

The text identifies a complex problem, then presents examples of unsuccessful attempts to solve that problem. 

"}, {"id": "B", "text": "

The text summarizes a debate among researchers, then gives reasons for supporting one side in that debate. 

"}, {"id": "C", "text": "

The text describes a general situation, then illustrates that situation with specific examples.

"}, {"id": "D", "text": "

The text discusses several notable individuals, then explains commonly overlooked differences between those individuals. 

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. The first three sentences describe the general situation: these early films have been lost, and we only know about them from small pieces of evidence. The rest of the text offers specific examples of the small pieces of evidence.

Choice A is incorrect. This isn’t the overall structure. The fact that we only know about these lost early films from small pieces of evidence isn’t presented as a “complex problem”—that’s too extreme. And the examples presented are not “unsuccessful attempts” to solve it. If anything, the examples represent a success, because we discovered that these films existed in the first place. Choice B is incorrect. This isn’t the overall structure. There’s no “debate” presented in the text, so there’s no “side” for the text to support. Choice D is incorrect. This isn’t the overall structure. The text doesn’t discuss any “differences” between the filmmakers.

"}, {"id": "14b7dced", "domain": "Craft and Structure", "skill": "Text Structure and Purpose", "difficulty": "M", "type": "mc", "stimulus": "

The following text is from Walt Whitman’s 1860 poem “Calamus 24.”

\n

I HEAR it is charged against me that I seek to destroy institutions;

But really I am neither for nor against institutions

(What indeed have I in common with them?—Or what with the destruction of them?),

Only I will establish in the Mannahatta [Manhattan] and in every city of These States, inland and seaboard,

And in the fields and woods, and above every keel [ship] little or large, that dents the water,

Without edifices, or rules, or trustees, or any argument,

The institution of the dear love of comrades.

", "stem": "

Which choice best describes the overall structure of the text?

", "choices": [{"id": "A", "text": "

The speaker questions an increasingly prevalent attitude, then summarizes his worldview.

"}, {"id": "B", "text": "

The speaker regrets his isolation from others, then predicts a profound change in society.

"}, {"id": "C", "text": "

The speaker concedes his personal shortcomings, then boasts of his many achievements.

"}, {"id": "D", "text": "

The speaker addresses a criticism leveled against him, then announces a grand ambition of his.

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer because it best describes the overall structure of the text. The speaker begins by stating that he has heard that others are accusing him of seeking to destroy institutions. The speaker then addresses this criticism by stating that he is “neither for nor against institutions.” Instead, the speaker states that his ultimate goal is to instill “the institution of the dear love of comrades” everywhere in the country. Therefore, the overall structure of the text is best described as an address of criticism followed by an announcement of a grand ambition.

Choice A is incorrect. While the speaker does address an opinion of him that he believes to be untrue, he doesn’t indicate that this attitude has become increasingly prevalent. The speaker also concludes by explaining his goal for the future rather than his current worldview. Choice B is incorrect because the text doesn’t portray the speaker as isolated or regretful, and the speaker gestures toward a hope for societal change but doesn’t offer an explicit prediction that it will happen. Choice C is incorrect because the speaker addresses a criticism of him that he believes to be false; he doesn’t admit any personal shortcomings. Moreover, the speaker concludes by stating a goal he has rather than showcasing his achievements.

"}, {"id": "3118ca93", "domain": "Craft and Structure", "skill": "Words in Context", "difficulty": "E", "type": "mc", "stimulus": "

The fashion resale market, in which consumers purchase secondhand clothing from stores and online sellers, generated nearly $30 billion globally in 2019. Expecting to see continued growth, some analysts ______blank that revenues will more than double by 2028.

", "stem": "

Which choice completes the text with the most logical and precise word or phrase?

", "choices": [{"id": "A", "text": "

produced

"}, {"id": "B", "text": "

denied

"}, {"id": "C", "text": "

worried

"}, {"id": "D", "text": "

predicted

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer because it most logically completes the text’s discussion of the fashion resale market’s continued growth. As used in this context, “predicted” means forecast, or indicated that something would happen in the future. The text indicates that the fashion resale market made a lot of money in 2019 and that some analysts expected the market to continue to grow. This context suggests that the analysts believed that the fashion resale market was going to make more money than it had already made, with the analysts indicating that revenues would more than double by 2028.

Choice A is incorrect because it wouldn’t make sense in context to say that some analysts “produced,” or manufactured or brought about, the increase in future revenues of the fashion resale market. The analysts themselves couldn’t have brought about the future revenue growth, since, as the text suggests, they were merely in the position of drawing conclusions about future fashion resale market revenue based on 2019 revenue. Choice B is incorrect because the text indicates that some analysts expected the fashion resale market to continue to grow in the future, not that they “denied,” or rejected, this notion. Nothing in the text supports the idea that these analysts thought the revenues wouldn’t grow. Choice C is incorrect because the text indicates that some analysts expected the fashion resale market to continue to grow in the future, not that they “worried,” or felt concerned, that revenue would significantly increase by 2028. Nothing in the text suggests that the analysts felt concerned about the increase; rather, the text suggests that the increase would represent a favorable outcome, since it would mean that the fashion resale market grew to generate even more revenue.

"}, {"id": "21d95d1d", "domain": "Craft and Structure", "skill": "Words in Context", "difficulty": "E", "type": "mc", "stimulus": "

Ofelia Zepeda’s contributions to the field of linguistics are ______blank: her many accomplishments include working as a linguistics professor and bilingual poet, authoring the first Tohono O’odham grammar book, and co-founding the American Indian Language Development Institute.

", "stem": "

Which choice completes the text with the most logical and precise word or phrase?

", "choices": [{"id": "A", "text": "

pragmatic

"}, {"id": "B", "text": "

controversial

"}, {"id": "C", "text": "

extensive

"}, {"id": "D", "text": "

universal

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer because it most logically completes the text’s discussion of how Ofelia Zepeda has contributed to the field of linguistics. As used in this context, “extensive” means having a wide or considerable extent. The text indicates that Zepeda’s many accomplishments in linguistics are varied, including teaching linguistics, writing poetry in more than one language, creating a grammar book, and co-founding a language institute. This context supports the idea that Zepeda’s contributions to the field are extensive.

Choice A is incorrect because the sentence presents Zepeda’s accomplishments as examples to support the claim made in the first part of the sentence. It wouldn’t make sense to say that achievements as a professor, poet and author, and co-founder of a language institute demonstrate that Zepeda’s contributions in her field are “pragmatic,” or related to practical matters and not involving intellectual or artistic matters. Choice B is incorrect because the sentence presents Zepeda’s accomplishments as a professor, poet and author, and co-founder of a language institute as examples to support the claim made in the first part of the sentence. There’s no reason to believe that the positive achievements listed demonstrate that Zepeda’s contributions in her field are “controversial,” or have caused disputes and opposing viewpoints. Choice D is incorrect because in this context, “universal” would mean including or covering everything in a group. The sentence presents Zepeda’s accomplishments as examples to support the claim made in the first part of the sentence, and it wouldn’t make sense to say that these specific achievements—particularly as the author of a grammar book specific to the Tohono O’odham language—demonstrate that Zepeda’s contributions relate to everything in the field of linguistics.

"}, {"id": "56ec23a0", "domain": "Craft and Structure", "skill": "Text Structure and Purpose", "difficulty": "E", "type": "mc", "stimulus": "

Hiroshi Senju is known worldwide for his paintings of waterfalls. These paintings are large and tend not to show the entire waterfall.  Instead, Senju focuses on just the point where the falling water reaches the pool below, keeping the top of the waterfall out of view. While Senju’s paintings are rooted in art movements originating in the United States, the artist uses traditional Japanese techniques and materials that make his work instantly recognizable.

", "stem": "

Which choice best describes the overall structure of the text?

", "choices": [{"id": "A", "text": "

It introduces an artist and then explains some common characteristics of well-known paintings by that artist.

"}, {"id": "B", "text": "

It explains a specific painting technique and then provides examples of artists who use the technique.

"}, {"id": "C", "text": "

It describes a famous painting and then compares it to a lesser-known painting from the same time period. 

"}, {"id": "D", "text": "

It gives an opinion on an artist and then suggests multiple reasons why the artist’s work has been largely overlooked.

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. The first sentence introduces Senju as a famous artist, while the next three sentences describe the defining features of his art, such as it only showing part of the waterfall and its origins in US art movements and Japanese techniques.

Choice B is incorrect. The text doesn’t provide examples of any other artists who use Senju’s techniques. Choice C is incorrect. The text doesn’t describe any single famous painting or make comparisons between paintings. Choice D is incorrect. The text doesn’t provide an opinion on Senju (just facts), nor does it suggest that his art has been overlooked—in fact, it states that he is “known worldwide.”

"}, {"id": "a318c1ef", "domain": "Craft and Structure", "skill": "Words in Context", "difficulty": "E", "type": "mc", "stimulus": "

The Cambrian explosion gets its name from the sudden appearance and rapid diversification of animal remains in the fossil record about 541 million years ago, during the Cambrian period. Some scientists argue that this ______blank change in the fossil record might be because of a shift in many organisms to body types that were more likely to be preserved.

", "stem": "

Which choice completes the text with the most logical and precise word or phrase?

", "choices": [{"id": "A", "text": "

catastrophic

"}, {"id": "B", "text": "

elusive

"}, {"id": "C", "text": "

abrupt

"}, {"id": "D", "text": "

imminent

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer because it most logically and precisely completes the text’s discussion of the fossil record from the Cambrian period. In this context, “abrupt” means sudden. The text explains that the fossil record reflects the unexpected appearance and rapid diversification, or increase in variety, of animal remains during the Cambrian period. This context establishes that these remains’ entry into the fossil record was sudden.

Choice A is incorrect. Although the word “explosion” appears in the name of the event marked by the fossil record change, the text never suggests that the change was “catastrophic,” or disastrous. In context, “explosion” refers to the rapid diversification, or the swift increase in variety, of animal remains in the fossil record—a phenomenon that the text presents in a relatively neutral manner, without commenting on whether it was negative or positive. Choice B is incorrect because the text never suggests that the change toward greater diversification is “elusive,” or difficult to locate, in the fossil record. Rather, the text notes that the change occurred about 541 million years ago, suggesting that scientists have indeed been able to locate it. Choice D is incorrect because it wouldn’t make sense in context to describe the change in the fossil record as “imminent,” or about to occur, since the text indicates that the change already occurred millions of years ago.

"}, {"id": "e56b66e5", "domain": "Craft and Structure", "skill": "Words in Context", "difficulty": "M", "type": "mc", "stimulus": "

Set in a world where science fiction tropes exist as everyday realities, Charles Yu’s 2010 novel How to Live Safely in a Science Fictional Universe traces a time traveler’s quest to find his father. Because the journey at the novel’s center is so ______blank, with the protagonist ricocheting chaotically across time, the reader often wonders whether the pair will ever be reunited.

", "stem": "

Which choice completes the text with the most logical and precise word or phrase?

", "choices": [{"id": "A", "text": "

haphazard

"}, {"id": "B", "text": "

premeditated

"}, {"id": "C", "text": "

inspirational

"}, {"id": "D", "text": "

fruitless

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer because it most logically completes the text’s discussion of Yu’s novel. In this context, “haphazard” means marked by a lack of plan or order. The text indicates that the quest featured in the novel, which involves the protagonist bouncing across time, is chaotic and causes the reader to often wonder what will happen. This context suggests that the protagonist’s journey seems to be marked by a lack of order.

Choice B is incorrect because the text indicates that the journey featured in Yu’s novel involves a character “ricocheting chaotically,” or bouncing in a disordered way, across time and causes the reader to often wonder what will happen. It wouldn’t make sense to say that a chaotic journey seems “premeditated,” or characterized by forethought and planning. Choice C is incorrect because the text doesn’t give any indication that readers regard the journey in Yu’s novel as “inspirational,” or as causing extraordinarily creative or brilliant thoughts or actions; instead, the text focuses on the idea that the protagonist’s journey is chaotic, or disordered, and doesn’t give readers a clear sense of what will happen. Choice D is incorrect. Rather than suggesting that the journey featured in Yu’s novel is “fruitless,” or has an unsuccessful outcome, the text focuses on the idea that while reading about the protagonist’s chaotic movements across time, readers are often unsure of what will happen—that is, they don’t know whether the protagonist will be successful in finding his father.

"}, {"id": "bce627d9", "domain": "Craft and Structure", "skill": "Words in Context", "difficulty": "M", "type": "mc", "stimulus": "

Mineralogical differences are detectable in samples collected from two locations on the near-Earth asteroid Ryugu, but such differences may not indicate substantial compositional variations in the asteroid. Cosmochemist Kazuhide Nagashima and colleagues note that at the small scale of the samples, the distribution of minerals is unlikely to be ______blank.

", "stem": "

Which choice completes the text with the most logical and precise word or phrase?

", "choices": [{"id": "A", "text": "

neglected

"}, {"id": "B", "text": "

redundant

"}, {"id": "C", "text": "

ongoing

"}, {"id": "D", "text": "

uniform

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. The text tells us that the samples are too \"small scale\" to reflect the composition of the asteroid, which probably doesn’t show the same variation on a large scale. This suggests that the mineral composition of the samples are unlikely to be exactly the same from sample to sample.

Choice A is incorrect. \"Neglected\" means \"suffering a lack of proper care\" or \"abandoned,\" which doesn’t work here. The text never suggests that the distribution of minerals in the samples would be neglected, so this statement doesn’t logically follow. Choice B is incorrect. \"Redundant\" means \"not or no longer useful or needed,\" which is too strong. The text doesn’t suggest that the variation between the samples isn’t a useful finding at all—just that we can’t assume that the large-scale composition of the asteroid will show the same variation. But the composition of the samples might be useful for something else. Choice C is incorrect. \"Ongoing\" means \"still in progress,\" which doesn’t make sense: the distribution of minerals in a sample can’t be \"ongoing.\"

"}, {"id": "f83f0aab", "domain": "Craft and Structure", "skill": "Words in Context", "difficulty": "H", "type": "mc", "stimulus": "

Some scientists have suggested that mammals in the Mesozoic era were not a very ______blank group, but paleontologist Zhe-Xi Luo’s research suggests that early mammals living in the shadow of dinosaurs weren’t all ground-dwelling insectivores. Fossils of various plant-eating mammals have been found in China, including species like Vilevolodon diplomylos, which Luo says could glide like a flying squirrel.

", "stem": "

Which choice completes the text with the most logical and precise word or phrase?

", "choices": [{"id": "A", "text": "

predatory

"}, {"id": "B", "text": "

obscure

"}, {"id": "C", "text": "

diverse

"}, {"id": "D", "text": "

localized

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer because it most logically completes the text’s discussion of the kinds of mammals alive during the Mesozoic era. As used in this context, “diverse” means to have a significant amount of variety. The text indicates that some scientists have suggested that Mesozoic mammals can’t be characterized in a certain way, then contrasts the view put forward by those scientists with Luo’s research, which shows that Mesozoic mammals “weren’t all ground-dwelling insectivores” and instead were “various.” This context suggests that some scientists have viewed Mesozoic mammals as being all alike, or not a very diverse group. 

Choice A is incorrect because it wouldn’t make sense to say that some scientists have suggested that Mesozoic mammals weren’t very “predatory,” or that they didn’t prey on other animals, since the text establishes a contrast between what some scientists have suggested and Luo’s research showing that Mesozoic mammals “weren’t all ground-dwelling insectivores.” This context suggests that some scientists have regarded Mesozoic mammals as all being insectivores, or animals that prey on insects, not that some scientists have suggested that Mesozoic mammals didn’t prey on other animals. Choice B is incorrect because it wouldn’t make sense to say that some scientists have suggested that Mesozoic mammals weren’t very “obscure,” or concealed or not well known, since the text establishes a contrast between what some scientists have suggested and Luo’s research showing that Mesozoic mammals were a varied group. There’s no contrast between saying that the mammals weren’t concealed or well known and the mammals being varied. Choice D is incorrect because it wouldn’t make sense to say that some scientists have suggested that Mesozoic mammals weren’t very “localized,” or confined to a particular area, since the text establishes a contrast between what some scientists have suggested and Luo’s research showing that Mesozoic mammals were a varied group. There’s no contrast between saying that the mammals weren’t localized and the mammals being varied. Although the text mentions mammal fossils found in China, nothing in the discussion of Luo’s research addresses the limits of Mesozoic mammal habitats. 

"}, {"id": "d5235d39", "domain": "Craft and Structure", "skill": "Words in Context", "difficulty": "E", "type": "mc", "stimulus": "

The Mule Bone, a 1930 play written by Zora Neale Hurston and Langston Hughes, is perhaps the best-known of the few examples of ______blank in literature. Most writers prefer working alone, and given that working together cost Hurston and Hughes their friendship, it is not hard to see why.

", "stem": "

Which choice completes the text with the most logical and precise word or phrase?

", "choices": [{"id": "A", "text": "

characterization

"}, {"id": "B", "text": "

interpretation

"}, {"id": "C", "text": "

collaboration

"}, {"id": "D", "text": "

commercialization

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer because it logically and precisely completes the text’s discussion of The Mule Bone, a play that Zora Neale Hurston and Langston Hughes wrote together. In this context, “collaboration” means working together with someone to write a literary work. The text indicates that most writers prefer to work alone and that working together destroyed the friendship between Hurston and Hughes. This establishes that The Mule Bone is a relatively rare example of collaboration in literature.

Choice A is incorrect because in this context, “characterization” would mean a literary work’s portrayal of characters’ psychological experiences and motivations, but the text doesn’t discuss characterization in The Mule Bone specifically or in collaborative works more generally. Choice B is incorrect because in this context, “interpretation” would mean the explanation of a literary work’s meaning or significance, but the text doesn’t discuss how readers or critics have interpreted The Mule Bone; instead, the text discusses how the play was written collaboratively and how the writing process affected the two authors. Choice D is incorrect because in this context, “commercialization” would mean writing a literary work in such a way as to ensure its commercial appeal, but the text never discusses commercial appeal as a factor in the writing of The Mule Bone specifically or the writing of collaborative works more generally.

"}, {"id": "1fbf276a", "domain": "Craft and Structure", "skill": "Words in Context", "difficulty": "M", "type": "mc", "stimulus": "

Interruptions in the supply chain for microchips used in personal electronics have challenged an economist’s assertion that retailers can expect robust growth in sales of those devices in the coming months. The delays are unlikely to ______blank her projection entirely but will almost certainly extend its time frame.

", "stem": "

Which choice completes the text with the most logical and precise word or phrase?

", "choices": [{"id": "A", "text": "

dispute

"}, {"id": "B", "text": "

withdraw

"}, {"id": "C", "text": "

underscore

"}, {"id": "D", "text": "

invalidate

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer because it most logically completes the text’s discussion of the economist’s claim about sales of personal electronic devices. In this context, “invalidate” most nearly means nullify or make invalid. The text indicates that interruptions in the supply of microchips for personal electronics “have challenged” the economist’s claim that sales of personal electronics will show strong growth in the coming months. The text goes on to clarify the effect of the delays on the economist’s projection, stating that the delays are very likely to extend the time frame over which the projected growth in sales will occur. This context suggests that the delays are unlikely to invalidate the economist’s projection entirely—the delays will probably alter the time frame of the projection, not nullify it or make it invalid.

Choice A is incorrect because saying that the delays are unlikely to “dispute,” or argue against, the economist’s projection wouldn’t make sense. Since the delays are an inanimate circumstance, they couldn’t argue against a prediction about the sales of personal electronics. Choice B is incorrect because saying that the delays are unlikely to “withdraw,” or remove from consideration, the economist’s projection wouldn’t make sense. Although the economist could withdraw her projection because of the delays, the delays themselves couldn’t withdraw her projection since they’re an inanimate circumstance and thus can’t choose to remove something from consideration. Choice C is incorrect because there’s nothing in the text to suggest that the delays will “underscore,” or emphasize, the economist’s projection. Instead, the text suggests that the delays are likely to extend the time frame of the economist’s projection but not to undermine the projection entirely. 

"}, {"id": "1c6b1fa0", "domain": "Craft and Structure", "skill": "Text Structure and Purpose", "difficulty": "E", "type": "mc", "stimulus": "

In 1801, a Blackfoot chief named Ac Ko Mok Ki drew a finely detailed map of the Upper Missouri region. This work demonstrates a vast amount of topographic knowledge, as the map features specific names of mountains and rivers, as well as the first-known sketch of the drainage network of the Missouri River. The map is especially notable because Ac Ko Mok Ki also included details about the numerous tribes that lived in the area.

", "stem": "

Which choice best describes the function of the underlined sentence in the text as a whole?

", "choices": [{"id": "A", "text": "

It emphasizes Ac Ko Mok Ki’s desire to represent other tribes on the map.

"}, {"id": "B", "text": "

It explains how Ac Ko Mok Ki developed an interest in mapmaking.

"}, {"id": "C", "text": "

It identifies some reasons why the map is impressive.

"}, {"id": "D", "text": "

It details how the map was used for hunting and trading purposes.

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer because it best describes how the underlined sentence functions in the text as a whole. The text presents information about a map drawn by Blackfoot chief Ac Ko Mok Ki in 1801. The underlined sentence states that the map \"demonstrates a vast amount of topographic knowledge\" and mentions that it features the \"specific names of mountains and rivers\" and includes the first-known sketch of the Missouri River’s drainage network. These are all characteristics that indicate that the map was executed with remarkable skill. Thus, the underlined sentence identifies some reasons why the map is impressive.

Choice A is incorrect. Though the sentence after the underlined sentence in the text mentions that Ac Ko Mok Ki included information about other tribes on his map, the underlined sentence itself does not address this topic. Choice B is incorrect because nothing in the underlined sentence indicates how Ac Ko Mok Ki became interested in mapmaking, only that his mapmaking skills are impressive. Choice D is incorrect because though the underlined sentence describes several features of the map, it does not specifically describe how the map was used.

"}, {"id": "f4166aae", "domain": "Craft and Structure", "skill": "Words in Context", "difficulty": "M", "type": "mc", "stimulus": "

In addition to being an accomplished psychologist himself, Francis Cecil Sumner was a ______blank increasing the opportunity for Black students to study psychology, helping to found the psychology department at Howard University, a historically Black university, in 1930.

", "stem": "

Which choice completes the text with the most logical and precise word or phrase?

", "choices": [{"id": "A", "text": "

proponent of

"}, {"id": "B", "text": "

supplement to

"}, {"id": "C", "text": "

beneficiary of

"}, {"id": "D", "text": "

distraction for

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer because it most logically completes the text’s discussion of Francis Cecil Sumner. As used in this context, “proponent of” means supporter of. The text says that Sumner helped to found the psychology department at historically Black Howard University in 1930. This is evidence that Sumner supported increasing the opportunity for Black students to study psychology.

Choice B is incorrect because the phrase “supplement to,” or addition to, wouldn’t make sense in context. The text discusses Sumner’s efforts to increase the number of Black psychology students, but it doesn’t make sense to describe him as an addition to his efforts. Choice C is incorrect because Sumner was already an accomplished psychologist himself when he helped to found the Howard University psychology department. While Black students were the beneficiaries of his efforts—that is, they received help because of his efforts—it wouldn’t make sense in this context to describe Sumner as a “beneficiary of” opportunities, because he was the one doing the helping. Choice D is incorrect because founding a psychology department at Howard University wouldn’t be a “distraction for” Sumner’s aim to increase the opportunity for Black students to study psychology—that is, it wouldn’t be something that draws Sumner’s attention away from that goal, but rather the opposite.

"}, {"id": "9b2fbb2e", "domain": "Craft and Structure", "skill": "Words in Context", "difficulty": "E", "type": "mc", "stimulus": "

Logically, a damaged fossil should provide less information than an intact one, but for paleontologist Brigitte Schoenemann, a broken area on a fossilized trilobite (a crustacean-like creature) ______blank fresh insight, allowing her to view the inner structure of the organism’s eye.

", "stem": "

Which choice completes the text with the most logical and precise word or phrase?

", "choices": [{"id": "A", "text": "

resolved

"}, {"id": "B", "text": "

adjusted

"}, {"id": "C", "text": "

offered

"}, {"id": "D", "text": "

directed

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer because it most logically completes the text’s discussion about how, for Schoenemann, a damaged trilobite fossil was informative. In context, “offered” means provided or gave. The text suggests that although it may seem counterintuitive, a broken fossilized trilobite allowed Schoenemann to observe more details of the trilobite’s eye than an intact fossilized trilobite would. This context conveys the idea that a damaged fossil offered, or provided, fresh insight into the structure of a trilobite’s eye.

Choice A is incorrect because “resolved” means determined or figured out, which wouldn’t make sense in this context. The text focuses on how Schoenemann was able to get more information from a broken fossil than an intact one. Although the damaged fossil may have allowed her to determine certain information, as an inanimate object the fossil isn’t capable of resolving anything. Choice B is incorrect because saying that the broken part of a trilobite fossil “adjusted,” or changed or modified, fresh insight wouldn’t make sense in this context. The text focuses on how Schoenemann was able to get more information from a broken fossil than an intact one. This context suggests that the fossil offered fresh insight, or understanding, not that it adjusted fresh insight. Choice D is incorrect because “directed” means managed or instructed, which wouldn’t make sense in this context. The text focuses on how Schoenemann was able to get more information from a broken fossil than an intact one. This context suggests that the fossil offered fresh insight, or understanding, not that it directed fresh insight.

"}, {"id": "1782cdd7", "domain": "Craft and Structure", "skill": "Text Structure and Purpose", "difficulty": "E", "type": "mc", "stimulus": "

In many agricultural environments, the banks of streams are kept forested to protect water quality, but it’s been unclear what effects these forests may have on stream biodiversity. To investigate the issue, biologist Xingli Giam and colleagues studied an Indonesian oil palm plantation, comparing the species richness of forested streams with that of nonforested streams. Giam and colleagues found that species richness was significantly higher in forested streams, a finding the researchers attribute to the role leaf litter plays in sheltering fish from predators and providing food resources.

", "stem": "

Which choice best states the main purpose of the text?

", "choices": [{"id": "A", "text": "

It discusses research intended to settle a debate about how agricultural yields can be increased without negative effects on water quality.   

"}, {"id": "B", "text": "

It explains the differences between stream-protection strategies used in oil palm plantations and stream-protection strategies used in other kinds of agricultural environments.

"}, {"id": "C", "text": "

It describes findings that challenge a previously held view about how fish that inhabit streams in agricultural environments attempt to avoid predators. 

"}, {"id": "D", "text": "

It presents a study that addresses an unresolved question about the presence of forests along streams in agricultural environments.

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. The author first describes an unresolved question: what effect do bank forests have on stream biodiversity? Then the author presents a study that answers the question: bank forests increase stream biodiversity.

Choice A is incorrect. This isn’t the main purpose of the text. The text never mentions agricultural yields. Choice B is incorrect. This isn’t the main purpose of the text. The text never mentions other kinds of agricultural environments. Choice C is incorrect. This isn’t the main purpose of the text. The text never mentions any previously held view about how fish in these streams try to avoid predators.

"}, {"id": "6d44060a", "domain": "Craft and Structure", "skill": "Text Structure and Purpose", "difficulty": "M", "type": "mc", "stimulus": "

Works of moral philosophy, such as Plato’s Republic or Aristotle’s Nicomachean Ethics, are partly concerned with how to live a morally good life. But philosopher Jonathan Barnes argues that works that present a method of living such a life without also supplying a motive are inherently useful only to those already wishing to be morally good—those with no desire for moral goodness will not choose to follow their rules. However, some works of moral philosophy attempt to describe what constitutes a morally good life while also proposing reasons for living one.

", "stem": "

Which choice best describes the overall structure of the text?

", "choices": [{"id": "A", "text": "

It provides a characterization about a field of thought by noting two works in it and then details a way in which some works in that field are more comprehensive than others.

"}, {"id": "B", "text": "

It mentions two renowned works and then claims that despite their popularity it is impossible for these works to serve the purpose their authors intended.

"}, {"id": "C", "text": "

It summarizes the history of a field of thought by discussing two works and then proposes a topic of further research for specialists in that field.

"}, {"id": "D", "text": "

It describes two influential works and then explains why one is more widely read than the other.

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. The text starts by stating what moral philosophy is concerned with and naming two examples of works in the field. Then it describes a shortcoming of some works in that field (they say how but not why), and finally it states that other works try to avoid that shortcoming (by including both how and why to live a morally good life).

Choice B is incorrect. This is too extreme. The text never mentions whether the two works are popular or not, and it never argues that these works don’t serve their intended purpose of describing how to live a morally good life. Rather, the text claims that works of moral philosophy that don’t include both how and why to be moral are not useful to readers who don’t already want to be moral. Choice C is incorrect. This isn’t the overall structure. The text never discusses the history of moral philosophy at all, and it doesn’t propose any topic for further research. Choice D is incorrect. This isn’t the overall structure. The text never discusses which of the two works is more widely read.

"}, {"id": "590f0ad2", "domain": "Craft and Structure", "skill": "Text Structure and Purpose", "difficulty": "M", "type": "mc", "stimulus": "

Industrial activity is often assumed to be a threat to wildlife, but that isn’t always so. Consider the silver-studded blue butterfly (Plebejus argus): as forest growth has reduced grasslands in northern Germany, many of these butterflies have left meadow habitats and are now thriving in active limestone quarries. In a survey of multiple active quarries and patches of maintained grassland, an ecologist found silver-studded blue butterflies in 100% of the quarries but only 57% of the grassland patches. Moreover, butterfly populations in the quarries were four times larger than those in the meadows.

", "stem": "

Which choice best describes the function of the underlined portion in the text as a whole?

", "choices": [{"id": "A", "text": "

It challenges a common assumption about the species under investigation in the research referred to in the text.

"}, {"id": "B", "text": "

It introduces discussion of a specific example that supports the general claim made in the previous sentence.

"}, {"id": "C", "text": "

It suggests that a certain species should be included in additional studies like the one mentioned later in the text.

"}, {"id": "D", "text": "

It provides a definition for an unfamiliar term that is central to the main argument in the text.

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer because it most accurately describes how the underlined portion functions in the text as a whole. The first sentence presents the general claim that industrial activity is not always a threat to wildlife. The underlined portion of the sentence that follows suggests that the silver-studded blue butterfly is an example of wildlife thriving in areas of industrial activity: active limestone quarries. Thus, the function of the underlined portion is to introduce a specific example in support of the general claim in the previous sentence.

Choice A is incorrect. Although the first sentence indicates that “industrial activity is often assumed” to harm wildlife, in the case of the silver-studded blue butterfly the text mentions neither an assumption about this species nor any challenge to such an assumption. Choice C is incorrect because the text mentions only one study: the “survey.” Additional studies are not mentioned in the text. Choice D is incorrect because neither the underlined portion nor any other portion of the text provides a definition for any of the terms used in the text’s argument.

"}, {"id": "19688783", "domain": "Craft and Structure", "skill": "Text Structure and Purpose", "difficulty": "M", "type": "mc", "stimulus": "

The following text is from Lucy Maud Montgomery’s 1908 novel Anne of Green Gables. Anne, an eleven-year-old girl, has come to live on a farm with a woman named Marilla in Nova Scotia, Canada.

\n
\n

 Anne reveled in the world of color about her.

\n

“Oh, Marilla,” she exclaimed one Saturday morning, coming dancing in with her arms full of gorgeous boughs, “I’m so glad I live in a world where there are Octobers. It would be terrible if we just skipped from September to November, wouldn’t it? Look at these maple branches. Don’t they give you a thrill—several thrills? I’m going to decorate my room with them.”

\n

“Messy things,” said Marilla, whose aesthetic sense was not noticeably developed. “You clutter up your room entirely too much with out-of-doors stuff, Anne. Bedrooms were made to sleep in.”

\n
", "stem": "

Which choice best states the main purpose of the text?

", "choices": [{"id": "A", "text": "

To demonstrate that Anne has a newly developed appreciation of nature

"}, {"id": "B", "text": "

To describe an argument that Anne and Marilla often have

"}, {"id": "C", "text": "

To emphasize Marilla’s disapproval of how Anne has decorated her room

"}, {"id": "D", "text": "

To show that Anne and Marilla have very different personalities

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer because it most accurately describes the main purpose of the text. The text begins by noting that Anne “reveled in the world of color about her”—that is, she takes great delight in colorful things. It then relates a scene when she enthusiastically enters the house with autumn foliage and announces that she will decorate her room with it. The focus of the text then shifts to Marilla, who has an undeveloped “aesthetic sense,” or appreciation of beauty, as can be seen when she dismisses the maple leaves as “messy things” and criticizes Anne for cluttering her room with objects from outside. This episode thus illustrates that Anne and Marilla differ in their appreciation of beauty and, more generally, in their basic character: Anne is exuberant and joyful, while Marilla is stern and critical. Therefore, the purpose of the text is to show that Anne and Marilla have very different personalities.

Choice A is incorrect because the text presents Anne’s appreciation of nature as a basic personality trait, not as a newfound enthusiasm, and never indicates how recently she developed that appreciation. Choice B is incorrect. Although the text portrays Anne and Marilla as having different personalities and attitudes toward natural beauty and home decoration, it doesn’t show them engaging in an argument about this difference or suggest that they often argue about it. Choice C is incorrect. Although the text does indicate that Marilla disapproves of how Anne plans to decorate her room, Marilla’s disapproval is a supporting detail that serves to develop her personality, which the text as a whole contrasts with Anne’s personality.

"}, {"id": "d7dccee7", "domain": "Craft and Structure", "skill": "Words in Context", "difficulty": "M", "type": "mc", "stimulus": "

In a 2019 study, Jeremy Gunawardena and colleagues found that the single-celled protozoan Stentor roeseli not only uses strategies to escape irritating stimuli but also switches strategies when one fails. This evidence of protozoans sophisticatedly “changing their minds” demonstrates that single-celled organisms may not be limited to ______blank behaviors.

", "stem": "

Which choice completes the text with the most logical and precise word or phrase?

", "choices": [{"id": "A", "text": "

aggressive

"}, {"id": "B", "text": "

rudimentary

"}, {"id": "C", "text": "

evolving

"}, {"id": "D", "text": "

advantageous

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer because it most logically completes the text’s discussion of single-celled organism behavior. As used in this context, “rudimentary” means basic or unsophisticated. According to the text, a study of the single-celled protozoan Stentor roeseli showed that the organisms can switch strategies for escaping certain stimuli, “sophisticatedly ‘changing their minds’” and using new strategies should other strategies fail. This context suggests that single-celled organisms may not be limited to behaviors that are basic or rudimentary, since the study showed that single-celled protozoans can respond complexly to irritating stimuli.

Choice A is incorrect because the text doesn’t suggest that single-celled organisms may not be limited to behavior that is “aggressive,” or threatening. Rather, the text suggests that single-celled organisms may not be limited to behaviors that are basic, since the study of Stentor roeseli showed that single-celled protozoans can respond complexly to irritating stimuli. Choice C is incorrect because the text doesn’t suggest that single-celled organisms may not be limited to behavior that is “evolving,” or advancing. Rather, the text suggests that single-celled organisms may not be limited to behaviors that are basic, since the study of Stentor roeseli showed that single-celled protozoans can respond complexly to irritating stimuli. Choice D is incorrect because the text doesn’t suggest that single-celled organisms may not be limited to behavior that is “advantageous,” or helpful. Rather, the text suggests that single-celled organisms may not be limited to behaviors that are basic, since the study of Stentor roeseli showed that single-celled protozoans can respond complexly to irritating stimuli.

"}, {"id": "d69bc408", "domain": "Craft and Structure", "skill": "Text Structure and Purpose", "difficulty": "M", "type": "mc", "stimulus": "

The following text is adapted from Aphra Behn’s 1689 novel The Lucky Mistake. Atlante and Rinaldo are neighbors who have been secretly exchanging letters through Charlot, Atlante’s sister.

\n

[Atlante] gave this letter to Charlot; who immediately ran into the balcony with it, where she still found Rinaldo in a melancholy posture, leaning his head on his hand: She showed him the letter, but was afraid to toss it to him, for fear it might fall to the ground; so he ran and fetched a long cane, which he cleft at one end, and held it while she put the letter into the cleft, and stayed not to hear what he said to it. But never was man so transported with joy, as he was at the reading of this letter; it gives him new wounds; for to the generous, nothing obliges love so much as love.

", "stem": "

Which choice best describes the overall structure of the text?

", "choices": [{"id": "A", "text": "

It describes the delivery of a letter, and then portrays a character’s happiness at reading that letter.

"}, {"id": "B", "text": "

It establishes that a character is desperate to receive a letter, and then explains why another character has not yet written that letter.

"}, {"id": "C", "text": "

It presents a character’s concerns about delivering a letter, and then details the contents of that letter.

"}, {"id": "D", "text": "

It reveals the inspiration behind a character’s letter, and then emphasizes the excitement that another character feels upon receiving that letter.

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer because it most accurately describes the overall structure of the text. The narrator begins by explaining how Charlot carefully delivers Atlante’s letter to Rinaldo, and then relates that Rinaldo feels “transported with joy” after reading the letter. Therefore, the overall structure of the text is best described as a description of the delivery of a letter followed by the portrayal of a character’s happiness after reading the letter.

Choice B is incorrect because the text indicates that the letter has been written; there’s no explanation why another character hasn’t written one. In addition, the text’s description of Rinaldo “in a melancholy posture” suggests that he’s sad and thoughtful, not that he’s desperate to receive the letter. Choice C is incorrect. Although the text states that Charlot won’t toss the letter to Rinaldo because she doesn’t want it to fall, the text doesn’t refer to the contents of the letter. Instead, the text describes how happy Rinaldo feels after reading it. Choice D is incorrect. Although the text does describe Rinaldo’s reaction to the letter, the text doesn’t begin by discussing Atlante’s inspiration for writing the letter. Instead, the text begins by discussing the delivery of the letter. 

"}, {"id": "22105871", "domain": "Craft and Structure", "skill": "Cross-Text Connections", "difficulty": "E", "type": "mc", "stimulus": "

Text 1

\n

In a study of insect behavior, Samadi Galpayage and colleagues presented bumblebees with small wooden balls and observed many of the bees clinging to, rolling, and dragging the objects. The researchers provided no external rewards (such as food) to encourage these interactions. The bees simply appeared to be playing—and for no other reason than because they were having fun.

\n

Text 2

\n

Insects do not have cortexes or other brain areas associated with emotions in humans. Still, Galpayage and her team have shown that bumblebees may engage in play, possibly experiencing some kind of positive emotional state. Other studies have suggested that bees experience negative emotional states (for example, stress), but as Galpayage and her team have acknowledged, emotions in insects, if they do indeed exist, are likely very rudimentary.

", "stem": "

Based on the texts, how would the author of Text 2 most likely respond to the underlined portion of Text 1?

", "choices": [{"id": "A", "text": "

By objecting that the bees were actually experiencing a negative feeling akin to stress rather than a positive feeling

"}, {"id": "B", "text": "

By arguing that some insects other than bumblebees may be capable of experiencing complex emotional states

"}, {"id": "C", "text": "

By pointing out that even humans sometimes struggle to have fun while engaging in play

"}, {"id": "D", "text": "

By noting that if the bees were truly playing, any positive feelings they may have experienced were probably quite basic

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. The author of Text 2 agrees with the author of Text 1 that bumblebees may engage in play and possibly experience some kind of positive emotional state. However, the author of Text 2 also qualifies this claim by stating that emotions in insects, if they do exist, are “likely very rudimentary.”

Choice A is incorrect. While Text 2 states that other studies might indicate “negative emotional states” in bees, it does not contradict the findings from the Galpayage study—that the bees might have been having fun. Choice B is incorrect. The author of Text 2 does not mention or imply that any insects, including bumblebees, are capable of experiencing complex emotional states. The author of Text 2 states that if insects do feel emotions, those emotions are “likely very rudimentary.” Choice C is incorrect. The author of Text 2 does not compare or contrast the behavior or emotions of insects and humans, and neither does the author of Text 1.

"}, {"id": "02e49a0c", "domain": "Craft and Structure", "skill": "Text Structure and Purpose", "difficulty": "E", "type": "mc", "stimulus": "

Genetic studies have led researchers to suggest that turtles are most closely related to the group that includes modern crocodiles. But studies of fossils have suggested instead that turtles are most closely related to other groups, such as the one that contains modern snakes. However, many of the fossil studies have relied on incomplete data sets. For a 2022 investigation, biologist Tiago R. Simões and colleagues examined more than 1,000 reptile fossils collected worldwide. From this large data set, they found clear agreement with the results of the genetic studies.

", "stem": "

Which choice best describes the function of the underlined sentence?

", "choices": [{"id": "A", "text": "

It offers an overview of the tools scientists use to examine fossils.

"}, {"id": "B", "text": "

It describes a limitation of some studies about the origin of turtles.

"}, {"id": "C", "text": "

It summarizes previous research on the evolution of crocodiles.

"}, {"id": "D", "text": "

It criticizes a widely held belief about genetic studies of reptiles.

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. The sentence mentions that some fossil studies have relied on incomplete data sets, suggesting that these studies are limited in what they can tell us about turtles’ origins.

Choice A is incorrect. While the sentence mentions the incompleteness of the data sets studied, it doesn’t mention any tools or techniques used to examine fossils. Choice C is incorrect. The sentence doesn’t mention anything about the evolution of crocodiles. Choice D is incorrect. This sentence doesn’t directly mention or criticize any \"widely held belief,\" and it focuses on a limitation of fossil studies of reptiles, not genetic studies.

"}, {"id": "27d9bb69", "domain": "Craft and Structure", "skill": "Cross-Text Connections", "difficulty": "M", "type": "mc", "stimulus": "

Text 1

\n

Many studies in psychology have shown that people seek out information even when they know in advance that they have no immediate use for it and that they won’t directly benefit from it. Such findings support the consensus view among researchers of curiosity: namely, that curiosity is not instrumental but instead represents a drive to acquire information for its own sake.

\n

Text 2

\n

While acknowledging that acquiring information is a powerful motivator, Rachit Dubey and colleagues ran an experiment to test whether emphasizing the usefulness of scientific information could increase curiosity about it. They found that when research involving rats and fruit flies was presented as having medical applications for humans, participants expressed greater interest in learning about it than when the research was not presented as useful.

", "stem": "

Based on the texts, how would Dubey and colleagues (Text 2) most likely respond to the consensus view discussed in Text 1?

", "choices": [{"id": "A", "text": "

By suggesting that curiosity may not be exclusively motivated by the desire to merely acquire information   

"}, {"id": "B", "text": "

By conceding that people may seek out information that serves no immediate purpose only because they think they can use it later     

"}, {"id": "C", "text": "

By pointing out that it is challenging to determine when information-seeking serves no goal beyond acquiring information

"}, {"id": "D", "text": "

By disputing the idea that curiosity can help explain apparently purposeless information-seeking behaviors

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. The researchers in Text 2 recognize that acquiring information is a powerful motivator, but showed that this motivation can still be affected by other factors, like whether or not the information is expected to be useful or not. This suggests that other desires may play a part in driving people to acquire information.

Choice B is incorrect. The consensus view in Text 1 is that people acquire information regardless of whether they think they can use it later. Dubey and colleagues acknowledge this fact (so they don’t claim people seek out information “only” because it might be useful later). Choice C is incorrect. This choice misreads the results of Dubey and colleagues’ study in Text 2. Neither text discusses the difficulty of determining the motivation for information-seeking. Choice D is incorrect. This choice contradicts Text 2, which starts with Dubey and colleagues “acknowledging that acquiring information is a powerful motivator” (i.e., agreeing that curiosity explains the seeking of apparently purposeless information). The research in Text 2 simply suggests that more than just curiosity can motivate information-seeking behavior when the information has a purpose.

"}, {"id": "c885c38b", "domain": "Craft and Structure", "skill": "Cross-Text Connections", "difficulty": "H", "type": "mc", "stimulus": "

 

Text 1

\n

Conventional wisdom long held that human social systems evolved in stages, beginning with hunter-gatherers forming small bands of members with roughly equal status. The shift to agriculture about 12,000 years ago sparked population growth that led to the emergence of groups with hierarchical structures: associations of clans first, then chiefdoms, and finally, bureaucratic states.

\n

 

Text 2

\n

In a 2021 book, anthropologist David Graeber and archaeologist David Wengrow maintain that humans have always been socially flexible, alternately forming systems based on hierarchy and collective ones with decentralized leadership. The authors point to evidence that as far back as 50,000 years ago some hunter-gatherers adjusted their social structures seasonally, at times dispersing in small groups but also assembling into communities that included esteemed individuals.

", "stem": "

Based on the texts, how would Graeber and Wengrow (Text 2) most likely respond to the “conventional wisdom” presented in Text 1?

", "choices": [{"id": "A", "text": "

By conceding the importance of hierarchical systems but asserting the greater significance of decentralized collective societies

"}, {"id": "B", "text": "

By disputing the idea that developments in social structures have followed a linear progression through distinct stages

"}, {"id": "C", "text": "

By acknowledging that hierarchical roles likely weren’t a part of social systems before the rise of agriculture

"}, {"id": "D", "text": "

By challenging the assumption that groupings of hunter-gatherers were among the earliest forms of social structure

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer because it describes the most likely way that Graeber and Wengrow (Text 2) would respond to the “conventional wisdom” presented in Text 1. According to Text 1, the conventional wisdom about human social systems is that they developed through stages, beginning with hunter-gatherer bands, then moving to clan associations, then chiefdoms, and finally arriving at states with bureaucratic structures. Text 2 indicates that Graeber and Wengrow believe that human social systems have been flexible, shifting between different types of structures, including both hierarchical and collective systems, and that these shifts may have even occurred seasonally. This suggests that Graeber and Wengrow would dispute the idea that developments in social structures have followed a linear progression through distinct stages. 

Choice A is incorrect because nothing in Text 2 suggests that Graeber and Wengrow believe that decentralized collective societies are more significant than hierarchical systems. Text 2 is focused on Graeber and Wengrow’s view that humans have flexibly shifted among various social structures, not on the importance of particular structures relative to others. Choice C is incorrect because Text 2 doesn’t include any information suggesting that Graeber and Wengrow believe that hierarchies didn’t emerge until after the rise of agriculture. In fact, Text 2 indicates that Graeber and Wengrow cite evidence suggesting that some hunter-gatherer groups formed social structures with hierarchical elements (“communities that included esteemed individuals”) 50,000 years ago, long before the rise of agriculture, which Text 1 says occurred around 12,000 years ago. Choice D is incorrect because there’s no information in Text 2 suggesting that Graeber and Wengrow would challenge the assumption that groupings of hunter-gatherers were among the earliest forms of social structure. Although Text 1 does indicate that hunter-gatherer groups are assumed to be the earliest human social system, Text 2 says only that Graeber and Wengrow believe that some hunter-gatherer groups made use of different social structures at different times. Text 2 doesn’t imply that Graeber and Wengrow doubt that hunter-gatherer groups preceded most other social structures.

"}, {"id": "de2c2f57", "domain": "Craft and Structure", "skill": "Cross-Text Connections", "difficulty": "H", "type": "mc", "stimulus": "

Text 1

\n

The fossil record suggests that mammoths went extinct around 11 thousand years (kyr) ago. In a 2021 study of environmental DNA (eDNA)—genetic material shed into the environment by organisms—in the Arctic, Yucheng Wang and colleagues found mammoth eDNA in sedimentary layers formed millennia later, around 4 kyr ago. To account for this discrepancy, Joshua H. Miller and Carl Simpson proposed that arctic temperatures could preserve a mammoth carcass on the surface, allowing it to leach DNA into the environment, for several thousand years.

\n

Text 2

\n

Wang and colleagues concede that eDNA contains DNA from both living organisms and carcasses, but for DNA to leach from remains over several millennia requires that the remains be perpetually on the surface. Scavengers and weathering in the Arctic, however, are likely to break down surface remains well before a thousand years have passed.

", "stem": "

Which choice best describes how Text 1 and Text 2 relate to each other?

", "choices": [{"id": "A", "text": "

Text 1 discusses two approaches to studying mammoth extinction without advocating for either, whereas Text 2 advocates for one approach over the other.

"}, {"id": "B", "text": "

Text 1 presents findings by Wang and colleagues and gives another research team’s attempt to explain those findings, whereas Text 2 provides additional detail that calls that explanation into question.

"}, {"id": "C", "text": "

Text 1 describes Wang and colleagues’ study and a critique of their methodology, whereas Text 2 offers additional details showing that methodology to be sound.

"}, {"id": "D", "text": "

Text 1 argues that new research has undermined the standard view of when mammoths went extinct, whereas Text 2 suggests a way to reconcile the standard view with that new research.

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. Text 1 introduces Wang and colleagues’ study and its surprising results, and then mentions Miller and Simpson’s hypothesis as a possible way to explain them. Text 2, however, challenges Miller and Simpson’s hypothesis by pointing out the difficulties of preserving mammoth carcasses on the surface for thousands of years: “scavengers and weathering” are the additional details that complicate the Miller/Simpson hypothesis.

Choice A is incorrect. Neither text compares two different approaches for studying mammoth extinction. Text 1 describes one study and one hypothesis pertaining to it. Text 2 critiques that hypothesis. Choice C is incorrect. Text 1 does not describe a critique of Wang and colleagues’ methodology, but rather an interpretation of their results by Miller and Simpson. Text 2 does not offer additional details showing that methodology to be sound, but rather casts doubt on the Miller/Simpson explanation. Choice D is incorrect. Both components mentioned here (the new “undermining” research and the theory for reconciling this discovery) are contained in Text 1. Text 2 then shows how the attempt to reconcile the standard view and new research is flawed, and still fails to explain the discrepancy.

"}, {"id": "3f753a8e", "domain": "Craft and Structure", "skill": "Words in Context", "difficulty": "H", "type": "mc", "stimulus": "

Investigating whether shared false visual memories—specific but inaccurate and widely held recollections of images such as product logos—are caused by people’s previous ______blank incorrect renditions of the images, researchers Deepasri Prasad and Wilma Bainbridge found that, in fact, such memories are often not explained by familiarity with erroneous versions of the images.

", "stem": "

Which choice completes the text with the most logical and precise word or phrase?

", "choices": [{"id": "A", "text": "

compliance with

"}, {"id": "B", "text": "

exposure to

"}, {"id": "C", "text": "

criteria for

"}, {"id": "D", "text": "

forfeiture of

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. \"Exposure to\" means \"having contact with.\" It makes sense that Prasad and Bainbridge were investigating whether seeing false versions of images was a cause of false visual memories. Notice how \"exposure to incorrect renditions\" matches the idea of \"familiarity with erroneous versions,\" which appears later in the sentence.

Choice A is incorrect. \"Compliance with\" means \"going along with a command or directive.\" False versions of images can’t give commands or directives, so this doesn’t apply. Choice C is incorrect. \"Criteria\" means \"standards by which to judge something.\" It’s not clear how people would come to have standards for the wrong version of an image in the first place, let alone how those standards would cause them to falsely remember the correct version. In other words, this choice would result in a confusing, unclear sentence. Choice D is incorrect. \"Forfeiture of\" means \"a giving up of something.\" It wouldn’t make sense to say that false memories of an image might be caused by giving up the wrong version of the image.

"}, {"id": "82b7c3b2", "domain": "Craft and Structure", "skill": "Words in Context", "difficulty": "E", "type": "mc", "stimulus": "

The following text is from Booth Tarkington’s 1921 novel Alice Adams.

\n
\n

Mrs. Adams had always been fond of vases, she said, and every year her husband’s Christmas present to her was a vase of one sort or another—whatever the clerk showed him, marked at about twelve or fourteen dollars.

\n
", "stem": "

As used in the text, what does the word “marked” most nearly mean?

", "choices": [{"id": "A", "text": "

Staged

"}, {"id": "B", "text": "

Priced

"}, {"id": "C", "text": "

Stained

"}, {"id": "D", "text": "

Watched

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. The text suggests that Mrs. Adam’s typical Christmas present from her husband was a vase that cost, or was \"priced at,\" about twelve or fourteen dollars.

Choice A is incorrect. This isn’t the meaning of \"marked\" as used here. It wouldn’t make sense to say that a vase was \"staged at twelve or fourteen dollars.\" Choice C is incorrect. This isn’t the meaning of \"marked\" as used here. It wouldn’t make sense to say that a vase was \"stained at twelve or fourteen dollars.\" Choice D is incorrect. This isn’t the meaning of \"marked\" as used here. It wouldn’t make sense to say that a vase was \"watched at twelve or fourteen dollars.\"

"}, {"id": "159ef46d", "domain": "Craft and Structure", "skill": "Cross-Text Connections", "difficulty": "E", "type": "mc", "stimulus": "

Text 1

\n

Although food writing is one of the most widely read genres in the United States, literary scholars have long neglected it. And within this genre, cookbooks attract the least scholarly attention of all, regardless of how well written they may be. This is especially true of works dedicated to regional US cuisines, whose complexity and historical significance are often overlooked.

\n

 

\n

Text 2

\n

With her 1976 cookbook The Taste of Country Cooking, Edna Lewis popularized the refined Southern cooking she had grown up with in Freetown, an all-Black community in Virginia. She also set a new standard for cookbook writing: the recipes and memoir passages interspersing them are written in prose more elegant than that of most novels. Yet despite its inarguable value as a piece of writing, Lewis’s masterpiece has received almost no attention from literary scholars.

", "stem": "

Based on the two texts, how would the author of Text 1 most likely regard the situation presented in the underlined sentence in Text 2?

", "choices": [{"id": "A", "text": "

As typical, because scholars are dismissive of literary works that achieve popularity with the general public

"}, {"id": "B", "text": "

As unsurprising, because scholars tend to overlook the literary value of food writing in general and of regional cookbooks in particular

"}, {"id": "C", "text": "

As justifiable, because Lewis incorporated memoir into The Taste of Country Cooking, thus undermining its status as a cookbook

"}, {"id": "D", "text": "

As inevitable, because The Taste of Country Cooking was marketed to readers of food writing and not to readers of other genres

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. Text 1 states that literary scholars ignore regional cookbooks most of all, even when they have historical significance and are well written. So the author of Text 1 wouldn’t be surprised that scholars ignored Edna Lewis’s cookbook.

Choice A is incorrect. We can’t infer that this is how the author of Text 1 would regard the situation. Text 1 never suggests that scholars are dismissive of popular works in general. Instead, Text 1 says that scholars ignore food writing specifically, despite its popularity—and despite the fact that it can be historically significant and complex. Choice C is incorrect. We can’t infer that this is how the author of Text 1 would regard the situation. Text 1 never suggests that elements of other genres should be kept out of cookbooks. Choice D is incorrect. We can’t infer that this is how the author of Text 1 would regard the situation. Text 1 never discusses how food writing is or should be marketed.

"}, {"id": "e1e89221", "domain": "Craft and Structure", "skill": "Words in Context", "difficulty": "E", "type": "mc", "stimulus": "

The following text is from Frances Hodgson Burnett’s 1911 novel The Secret Garden. Mary, a young girl, is outside trying her new jump rope.

\n
\n

The sun was shining and a little wind was blowing—not a rough wind, but one which came in delightful little gusts and brought a fresh scent of newly turned earth with it. She skipped round the fountain garden, and up one walk and down another.

\n
", "stem": "

As used in the text, what does the word “rough” most nearly mean?

", "choices": [{"id": "A", "text": "

Harsh

"}, {"id": "B", "text": "

Scratchy

"}, {"id": "C", "text": "

Basic

"}, {"id": "D", "text": "

Vague

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer because as used in the text, \"rough\" most nearly means harsh, or forceful and unpleasant. The text describes Mary’s surroundings as she plays: the sun is out and there’s \"a little wind.\" To further illustrate the wind, the narrator contrasts the word \"rough\" with a description of the wind blowing in \"delightful little gusts,\" suggesting that the wind is not unpleasant or harsh at all.

Choice B is incorrect. Although in some contexts \"rough\" objects, or objects with irregular surfaces, can sometimes be scratchy, rough doesn’t mean scratchy in this context. The text explains that the wind is not rough but rather gentle, \"delightful little gusts,\" which suggests that the use of \"rough\" here is referring to the degree of force of the wind. Choice C is incorrect because there’s nothing in the text to suggest that the wind wasn’t \"basic,\" or simple and uncomplicated. Instead, the text describes the wind as blowing not roughly or harshly but in \"delightful little gusts.\" Choice D is incorrect because the word \"vague\" means not clearly expressed or seen. Nothing in the text indicates that the wind was barely noticeable to Mary as she played outside, but rather the text states that it was delightful.

"}, {"id": "b11bb2a3", "domain": "Craft and Structure", "skill": "Words in Context", "difficulty": "E", "type": "mc", "stimulus": "

The following text is adapted from Amy Lowell’s 1912 poem “Summer.”

\n
\n

It is summer, glorious, deep-toned summer,

\n

The very crown of nature’s changing year

\n

When all her surging life is at its full.

\n

To me alone it is a time of pause,

\n

A void and silent space between two worlds,

\n

When inspiration lags, and feeling sleeps,

\n

Gathering strength for efforts yet to come.

\n
", "stem": "

As used in the text, what does the phrase “a void” most nearly mean?

", "choices": [{"id": "A", "text": "

A useless

"}, {"id": "B", "text": "

An empty

"}, {"id": "C", "text": "

A forgotten

"}, {"id": "D", "text": "

An incomplete

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer because as used in the text, a span of time is described as \"a void\" space, which most nearly means an empty or vacant one. In the text, the speaker describes summertime in counterintuitive terms: although nature’s \"surging life is at its full\" during the season, the speaker feels summer to be \"a time of pause, / A void and silent space between two worlds.\" The speaker says further that during summer, \"feeling sleeps / Gathering strength\" for future efforts. Thus, the speaker regards summer as an empty stretch of time, to be followed by a period of greater activity.

Choice A is incorrect. Although the text does present summer as a time of inactivity, it doesn’t characterize that inactivity as useless, or as having no purpose; in fact, the speaker regards summer as a time when \"feeling\" gathers \"strength for efforts yet to come.\" Choice C is incorrect. Although the text characterizes summer as a time \"when inspiration lags, and feeling sleeps,\" it doesn’t discuss the season’s relationship to the speaker’s memory or suggest that summer can easily be forgotten. Choice D is incorrect. In some contexts, \"void\" can mean devoid of, or lacking, a particular element, and such a lack could be conceived of as incompleteness. However, the text doesn’t portray summer as not being complete or whole; instead, it characterizes vacancy or inactivity as being an essential quality of the season, as experienced by the speaker.

"}, {"id": "97360a00", "domain": "Craft and Structure", "skill": "Text Structure and Purpose", "difficulty": "M", "type": "mc", "stimulus": "

The following text is adapted from Gwendolyn Bennett’s 1926 poem “Street Lamps in Early Spring.”

\n

Night wears a garment
All velvet soft, all violet blue... 
And over her face she draws a veil
As shimmering fine as floating dew... 
And here and there
In the black of her hair
The subtle hands of Night
Move slowly with their gem-starred light.

", "stem": "

Which choice best describes the overall structure of the text?

", "choices": [{"id": "A", "text": "

It presents alternating descriptions of night in a rural area and in a city.

"}, {"id": "B", "text": "

It sketches an image of nightfall, then an image of sunrise.

"}, {"id": "C", "text": "

It makes an extended comparison of night to a human being.

"}, {"id": "D", "text": "

It portrays how night changes from one season of the year to the next.

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer because it most accurately describes the overall structure of the text. Throughout the text, the speaker characterizes nighttime as if it were a person who wears clothing (“a garment” that is “velvet soft” and “violet blue”) and a veil “over her face” and who moves her hands “slowly with their gem-starred light” through her dark hair. Thus, the text is structured as an extended comparison of night to a human being.

Choice A is incorrect because the text never mentions any particular location; instead, it focuses on presenting a single description of night as a person with certain clothing and features. Choice B is incorrect because the text doesn’t make any reference to the sun or sunrise; instead, it focuses on presenting a single image of night as a person with certain clothing and features. Choice D is incorrect. Rather than describing how nighttime changes seasonally (or in any other way), the text presents a single image of night as a person with certain clothing and features.

"}, {"id": "9c35759f", "domain": "Craft and Structure", "skill": "Words in Context", "difficulty": "M", "type": "mc", "stimulus": "

Novelist N. K. Jemisin declines to ______blank the conventions of the science fiction genre in which she writes, and she has suggested that her readers appreciate her work precisely because of this willingness to thwart expectations and avoid formulaic plots and themes.

", "stem": "

Which choice completes the text with the most logical and precise word or phrase?

", "choices": [{"id": "A", "text": "

question

"}, {"id": "B", "text": "

react to

"}, {"id": "C", "text": "

perceive

"}, {"id": "D", "text": "

conform to

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer because it most logically completes the text’s discussion of Jemisin’s writing. In this context, “conform to” means to act in accordance with something. The text suggests that in her science fiction writing, Jemisin’s willingness to go against expectations and not use plots and themes that seem to follow a formula reflects how she treats the standard practices of the genre. This context conveys that Jemisin chooses not to act in accordance with those conventions.

Choice A is incorrect. In this context, “question” would mean doubt or object to. The text indicates that Jemisin is willing to go against expectations and not use formulaic plots and themes in her science fiction writing, suggesting that she may actually object to those conventions of the genre, not that she chooses not to question them. Choice B is incorrect because the text indicates that in her science fiction writing, Jemisin is willing to go against expectations and not use formulaic plots and themes. Rather than suggesting that Jemisin chooses not to “react to,” or act in response to, the standard practices of the genre, this context suggests that she is acting in response to such conventions by deliberately avoiding them. Choice C is incorrect. In this context, “perceive” would mean become aware of or understand. The text indicates that in her science fiction writing, Jemisin is willing to go against expectations and not use formulaic plots and themes. This context conveys that Jemisin is aware of and deliberately avoids those conventions of the genre, not that she chooses not to be aware of them.

"}, {"id": "6a1194e8", "domain": "Craft and Structure", "skill": "Words in Context", "difficulty": "M", "type": "mc", "stimulus": "

Rydra Wong, the protagonist of Samuel R. Delany’s 1966 novel Babel-17, is a poet, an occupation which, in Delany’s work, is not ______blank: nearly a dozen of the characters that populate his novels are poets or writers.

", "stem": "

Which choice completes the text with the most logical and precise word or phrase?

", "choices": [{"id": "A", "text": "

infallible

"}, {"id": "B", "text": "

atypical

"}, {"id": "C", "text": "

lucrative

"}, {"id": "D", "text": "

tedious

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer because it most logically completes the text’s discussion of Samuel R. Delany’s character Rydra Wong. As used in this context, “atypical” would mean unrepresentative or not common. The text indicates that Wong is one of “nearly a dozen” characters in Delany’s novels who are poets or writers. This context conveys that being a poet isn’t an atypical occupation for a character in one of Delany’s works.  

Choice A is incorrect because “infallible” means to be accurate or without fault, which wouldn’t make sense in context. The text focuses on the fact that Delany has written many characters who are poets and writers. This context suggests that the occupation isn’t atypical for Delany, not that the occupation isn’t infallible, or problematic. Choice C is incorrect because “lucrative” means to be profitable, which wouldn’t make sense in context. If writing poet characters weren’t profitable, it wouldn’t be logical to explain this by citing that Delany gave many of his characters the same occupation. Choice D is incorrect because “tedious” means to be boring, which wouldn’t make sense in context. The text focuses on the fact that Delany has written many characters who are poets and writers. This context suggests that the occupation isn’t atypical for Delany, not that the occupation isn’t tedious.

"}, {"id": "4fa7e50e", "domain": "Craft and Structure", "skill": "Words in Context", "difficulty": "H", "type": "mc", "stimulus": "

According to a US tax policy expert, state taxes are ______blank other factors when considering an interstate move. Even significant differences in state taxation have almost no effect on most people’s decisions, while differences in employment opportunities, housing availability, and climate are strong influences.

", "stem": "

Which choice completes the text with the most logical and precise word or phrase?

", "choices": [{"id": "A", "text": "

consistent with

"}, {"id": "B", "text": "

representative of

"}, {"id": "C", "text": "

overshadowed by

"}, {"id": "D", "text": "

irrelevant to

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer because it most logically completes the text’s discussion of the factors that influence peoples’ decisions to move to a different state. As used in this context, “overshadowed by” means to be surpassed by or caused to seem less important than other factors affecting a move. The text indicates that, according to a US tax policy expert, when people think about an interstate move, state taxes have little effect on their decisions, while employment opportunities, housing availability, and climate have a very strong effect. This context suggests that people consider these other factors to be more important than state taxes. 

Choice A is incorrect because the text indicates that state taxes aren’t as important a consideration as other factors when people are thinking of moving to another state. The context doesn’t suggest that state taxes are “consistent with,” or in agreement with these other factors. Choice B is incorrect because it wouldn’t make sense in context to say that state taxes are “representative of,” or typical of, other factors. Taxes aren’t an example of employment opportunities, housing availability, and climate, which are the other factors listed in the text. Choice D is incorrect because it wouldn’t make sense in context to say that state taxes are “irrelevant to,” or unconnected or unimportant to other factors. State taxes are irrelevant to peoples’ decisions, not to other factors. In other words, although the text suggests that state taxes may be irrelevant to people considering a move to another state, the other factors mentioned in the text, such as employment opportunities, are unable to have an opinion about state taxes. Furthermore, the text indicates that significant differences in state taxes have almost no effect on peoples’ choices to move, but they aren’t completely unimportant.

"}, {"id": "aa7fc89b", "domain": "Craft and Structure", "skill": "Text Structure and Purpose", "difficulty": "M", "type": "mc", "stimulus": "

The following text is adapted from Susan Glaspell’s 1912 short story “‘Out There.’” An elderly shop owner is looking at a picture that he recently acquired and hopes to sell.

\n

It did seem that the picture failed to fit in with the rest of the shop. A persuasive young fellow who claimed he was closing out his stock let the old man have it for what he called a song. It was only a little out-of-the-way store which subsisted chiefly on the framing of pictures. The old man looked around at his views of the city, his pictures of cats and dogs, his flaming bits of landscape. “Don’t belong in here,” he fumed.

\n

And yet the old man was secretly proud of his acquisition. There was a hidden dignity in his scowling as he shuffled about pondering the least ridiculous place for the picture.

", "stem": "

Which choice best states the main purpose of the text?

", "choices": [{"id": "A", "text": "

To reveal the shop owner’s conflicted feelings about the new picture

"}, {"id": "B", "text": "

To convey the shop owner’s resentment of the person he got the new picture from

"}, {"id": "C", "text": "

To describe the items that the shop owner most highly prizes

"}, {"id": "D", "text": "

To explain differences between the new picture and other pictures in the shop

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer because it most accurately describes the main purpose of the text. The text begins by stating that the new picture “failed to fit in” with the other items that the shop owner has. The text goes on to illustrate that point by describing the other pictures the shop owner has, indicating that the shop owner is fuming because he doesn’t think the new picture belongs in the store. In the second paragraph, however, the text indicates that the shop owner is “secretly proud of his acquisition.” The main purpose of the text is thus to reveal the shop owner’s conflicted feelings about the new picture.

Choice B is incorrect because the text doesn’t suggest that the shop owner resents the young man who sold him the new picture; in fact, the text gives no indication of the owner’s feelings about the young man at all. Choice C is incorrect. Although the text indicates that the new picture is different from the other items in the shop, there’s no suggestion that the shop owner prizes either the new picture or the pictures of the city, pets, and landscapes more than he prizes any other items. Choice D is incorrect because the text doesn’t describe what the new picture looks like; rather, the text identifies some of the other kinds of images that the shop owner has and states that they’re different from the new picture without explaining how they’re different. 

"}, {"id": "aad56f2b", "domain": "Craft and Structure", "skill": "Words in Context", "difficulty": "E", "type": "mc", "stimulus": "

As a young photographer in the 1950s, William Klein ______blank the conventions of photography by creating images that were high contrast and included blurred and distorted elements—features generally seen as flaws. So unorthodox was Klein’s work that he had difficulty finding a publisher for his now-iconic 1956 photo book Life is Good & Good for You in New York.

", "stem": "

Which choice completes the text with the most logical and precise word or phrase?

", "choices": [{"id": "A", "text": "

reviewed

"}, {"id": "B", "text": "

defied

"}, {"id": "C", "text": "

respected

"}, {"id": "D", "text": "

prevented

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. \"Defied\" means \"resisted\" or \"deliberately disobeyed,\" which matches the way Klein broke from the conventions of photography in his time by including features that were generally seen as flaws.

Choice A is incorrect. \"Reviewed\" means \"analyzed\" or \"evaluated,\" but that doesn’t really fit the context here. Klein isn’t directly providing any thoughtful examination of the conventions of photography: he’s just breaking all the rules. Choice C is incorrect. \"Respected\" can mean \"admired\" or \"followed\" (as in the case of conventions). It’s clear that Klein didn’t respect conventions, given his use of photographic features that were generally considered \"flaws.\" Choice D is incorrect. \"Prevented\" means \"stopped,\" and Klein did not stop the conventions—they still existed. Instead, he made images that were seen as \"flawed\" under those conventions.

"}, {"id": "48555763", "domain": "Craft and Structure", "skill": "Text Structure and Purpose", "difficulty": "M", "type": "mc", "stimulus": "

The following text is from Herman Melville’s 1854 novel The Lightning-rod Man.

\n\n

The stranger still stood in the exact middle of the cottage, where he had first planted himself. His singularity impelled a closer scrutiny. A lean, gloomy figure. Hair dark and lank, mattedly streaked over his brow. His sunken pitfalls of eyes were ringed by indigo halos, and played with an innocuous sort of lightning: the gleam without the bolt. The whole man was dripping. He stood in a puddle on the bare oak floor: his strange walking-stick vertically resting at his side.

", "stem": "

Which choice best states the function of the underlined sentence in the overall structure of the text?

", "choices": [{"id": "A", "text": "

It elaborates on the previous sentence’s description of the character.

"}, {"id": "B", "text": "

It introduces the setting that is described in the sentences that follow.

"}, {"id": "C", "text": "

It establishes a contrast with the description in the previous sentence.

"}, {"id": "D", "text": "

It sets up the character description presented in the sentences that follow.

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. This best states the function of the underlined sentence. The sentence basically says: “He stood out, so I looked more closely at him.” Then the rest of the text describes him in detail.  

Choice A is incorrect. This doesn’t state the function of the underlined sentence. The previous sentence basically says: “He was still standing in the middle of the cottage”—it doesn’t include any description of the character himself.  Choice B is incorrect. This doesn’t state the function of the underlined sentence. The following sentences describe the character, not the setting. Choice C is incorrect. This doesn’t state the function of the underlined sentence. The underlined sentence basically says: “He stood out, so I looked more closely at him.” The previous sentence basically says: “He was still standing in the middle of the cottage.” There’s no contrast between these two sentences. 

"}, {"id": "e7247766", "domain": "Craft and Structure", "skill": "Text Structure and Purpose", "difficulty": "M", "type": "mc", "stimulus": "

Horizontal gene transfer occurs when an organism of one species acquires genetic material from an organism of another species through nonreproductive means. The genetic material can then be transferred “vertically” in the second species—that is, through reproductive inheritance. Scientist Atma Ivancevic and her team have hypothesized infection by invertebrate parasites as a mechanism of horizontal gene transfer between vertebrate species: while feeding, a parasite could acquire a gene from one host, then relocate to a host from a different vertebrate species and transfer the gene to it in turn.

", "stem": "

Which choice best describes the function of the underlined portion in the text as a whole?

", "choices": [{"id": "A", "text": "

It explains why parasites are less susceptible to horizontal gene transfer than their hosts are.

"}, {"id": "B", "text": "

It clarifies why some genes are more likely to be transferred horizontally than others are.

"}, {"id": "C", "text": "

It contrasts how horizontal gene transfer occurs among vertebrates with how it occurs among invertebrates. 

"}, {"id": "D", "text": "

It describes a means by which horizontal gene transfer might occur among vertebrates.

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. The text defines horizontal gene transfer and then gives one possibility for how it happens in vertebrates (via infection by parasites). The underlined part describes how that mechanism could work.

Choice A is incorrect. The underlined portion doesn’t do this.  Parasites are only described as the mechanism that does the transferring, not the species that gives or receives the genes. Choice B is incorrect. The underlined portion doesn’t do this.  The text never discusses which genes are more likely to be transferred. Choice C is incorrect. The underlined portion doesn’t do this.  The text never discusses how horizontal gene transfer occurs among invertebrates.

"}, {"id": "ae2b3112", "domain": "Craft and Structure", "skill": "Text Structure and Purpose", "difficulty": "M", "type": "mc", "stimulus": "

By combining Indigenous and classical music, Cree composer and cellist Cris Derksen creates works that reflect the diverse cultural landscape of Canada. For her album Orchestral Powwow, Derksen composed new songs in the style of traditional powwow music that were accompanied by classical arrangements played by an orchestra. But where an orchestra would normally follow the directions of a conductor, the musicians on Orchestral Powwow are led by the beat of a powwow drum.

", "stem": "

Which choice best states the main purpose of the text?

", "choices": [{"id": "A", "text": "

To examine how Derksen’s musical compositions blend cultures

"}, {"id": "B", "text": "

To argue that Derksen should be recognized for creating a new style of music

"}, {"id": "C", "text": "

To describe the difficulties Derksen encountered when producing her album

"}, {"id": "D", "text": "

To establish a contrast between Derksen’s classical training and her Cree heritage 

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer because it most accurately describes the main purpose of the text, which is to discuss how Derksen’s compositions incorporate elements from both Indigenous and classical music. After introducing Derksen, the text describes how the songs Derksen composed for her album Orchestral Powwow feature aspects of the two musical traditions. Specifically, the text notes that Derksen wrote songs in the style of traditional powwow music but accompanied them with classical arrangements played by an orchestra that followed the beat of a powwow drum rather than the directions of a conductor. In this way, Derksen’s compositions blend different cultures.

Choice B is incorrect because although the text suggests that Derksen’s songs contain innovative elements since they blend styles from two different musical traditions, it doesn’t discuss whether her compositions constitute a new style of music, let alone whether Derksen should be recognized for creating a new style of music. Choice C is incorrect because the text doesn’t mention any difficulties Derksen encountered when producing her album. Rather, the text describes how the songs on the album exemplify how Derksen combines music from two different cultures.\n Choice D is incorrect because although the text mentions Derksen’s Cree heritage and suggests that she relies on knowledge of both Indigenous and classical music when she composes her songs, it doesn’t discuss her musical training. Additionally, the text is primarily focused on how Derksen combines different cultural traditions, not on contrasting Derksen’s training with her heritage.

"}, {"id": "e7b709fc", "domain": "Craft and Structure", "skill": "Words in Context", "difficulty": "E", "type": "mc", "stimulus": "

Archaeologists studying an ancient amphitheater in Switzerland believe that it dates back to the fourth century CE. Their discoveries of a coin made between 337 and 341 CE and era-appropriate building materials ______blank evidence for this theory.

", "stem": "

Which choice completes the text with the most logical and precise word or phrase?

", "choices": [{"id": "A", "text": "

dismiss

"}, {"id": "B", "text": "

provide

"}, {"id": "C", "text": "

regulate

"}, {"id": "D", "text": "

refuse

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer because it most logically completes the text’s discussion of the archaeologists’ study of the ancient amphitheater in Switzerland. In this context, “provide” means make available or supply. The text states that the archaeologists believe that the amphitheater dates to the fourth century CE. The text goes on to say that the archaeologists discovered a coin made between 337 and 341 CE (that is, made during the fourth century CE) and building materials appropriate to the era in question. This context suggests that these discoveries provide evidence for the archaeologists’ theory about the dating of the amphitheater. 

Choice A is incorrect because the archaeologists’ discoveries are presented as supplying evidence in favor of their theory about the dating of the amphitheater, not something that would “dismiss,” or reject serious consideration of, evidence for that theory. Choice C is incorrect because nothing in the text suggests that the archaeologists’ discoveries would “regulate,” or govern or bring order to, evidence for the archaeologists’ theory about the dating of the amphitheater. The discoveries are presented as supplying evidence for the archaeologists’ theory, not as changing how evidence for the theory is controlled or ordered. Choice D is incorrect because the archaeologists’ discoveries are presented as supplying evidence in favor of their theory about the dating of the amphitheater, not something that would “refuse,” or be unwilling to accept, evidence for the archaeologists’ theory. 

"}, {"id": "94eb800d", "domain": "Craft and Structure", "skill": "Words in Context", "difficulty": "M", "type": "mc", "stimulus": "

For a 2020 exhibition, photographer and neurobiologist Okunola Jeyifous ______blank a series of new images based on a series of alphabet posters from the 1970s known as the “Black ABCs,” which featured Black children from Chicago. Jeyifous photographed the now-adult models and layered the photos over magnified images of the models’ cells, resulting in what he called “micro and macro portraiture.”

", "stem": "

Which choice completes the text with the most logical and precise word or phrase?

", "choices": [{"id": "A", "text": "

validated

"}, {"id": "B", "text": "

created

"}, {"id": "C", "text": "

challenged

"}, {"id": "D", "text": "

restored

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer because it most logically and precisely completes the text’s discussion of Jeyifous’s series of images for the 2020 exhibition. In this context, “created” means produced. The text explains that Jeyifous, a photographer and neurobiologist, photographed adults who had appeared as children in posters from the 1970s, then combined those photographs with magnified images of the adults’ cells—a process that resulted in what he called “micro and macro portraiture.” This context suggests that Jeyifous drew on his dual interests in photography and neurobiology to produce the images for display in the exhibition.

Choice A is incorrect because there’s nothing in the text to suggest that Jeyifous “validated,” or corroborated, the series of images. The text describes Jeyifous’s process for composing the images but doesn’t describe Jeyifous making an effort to evaluate the images for their artistic or scientific legitimacy. Choice C is incorrect because there’s nothing in the text to suggest that Jeyifous “challenged,” or disputed, an aspect of the images; rather, the focus of the text is on the inspiration behind the images and the method Jeyifous used to achieve them. Choice D is incorrect because the text indicates that Jeyifous made the images himself using a combination of photography and magnified pictures of cells, not that he “restored,” or reconditioned, the images from a deteriorated state.

"}, {"id": "7b55e895", "domain": "Craft and Structure", "skill": "Cross-Text Connections", "difficulty": "E", "type": "mc", "stimulus": "

Text 1

\n

Some animal species, like the leopard, can be found in many kinds of areas. On the other hand, tropical mountain bird species tend to be limited in the types of spaces they can call home. This is because many mountain bird species are only able to survive at very specific elevations. Over time, these species have likely become used to living at a specific temperature. Therefore, these species struggle to survive at elevations that are warmer or colder than they are used to.

\n

 

\n

Text 2

\n

A new study reviewed observations of nearly 3,000 bird species to understand why tropical mountain bird species live at specific elevations. They noted that when a mountain bird species was found in an area with many other bird species, it tended to inhabit much smaller geographic areas. It is thus likely that competition for resources with other species, not temperature, limits where these birds can live.

", "stem": "

Based on the texts, both authors would most likely agree with which statement?

", "choices": [{"id": "A", "text": "

Tropical mountain bird species are restricted in where they can live.

"}, {"id": "B", "text": "

Scientists have better tools to observe tropical mountain birds than they did in the past.

"}, {"id": "C", "text": "

Little is known about how tropical mountain birds build their nests.

"}, {"id": "D", "text": "

Tropical mountain bird species that live at high elevations tend to be genetically similar.

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. Both texts state that tropical mountain bird species have limited ranges or habitats, although they disagree on the reason for this. Text 1 claims that temperature is the main factor that determines where these birds can live, while Text 2 claims that competition with other species is the main factor. However, both texts agree that these birds are not able to survive in many kinds of areas.

Choice B is incorrect. Neither text mentions the tools or methods that scientists use to observe these birds, either now or in the past. Choice C is incorrect. Neither text mentions anything about how these birds build their nests. Choice D is incorrect. Neither text provides any information about the genetic similarity of these birds, so we have no evidence that either author would agree with this statement.

"}, {"id": "8bc66f89", "domain": "Craft and Structure", "skill": "Text Structure and Purpose", "difficulty": "M", "type": "mc", "stimulus": "

Part of the Atacama Desert in Peru has surprisingly rich plant life despite receiving almost no rainfall. Moisture from winter fog sustains plants once they’re growing, but the soil’s tough crust makes it hard for seeds to germinate in the first place. Local birds that dig nests in the ground seem to be of help: they churn the soil, exposing buried seeds to moisture and nutrients. Indeed, in 2016 Cristina Rengifo Faiffer found that mounds of soil dug up by birds were far more fertile and supported more seedlings than soil in undisturbed areas.

", "stem": "

Which choice best describes the function of the underlined portion in the text as a whole?

", "choices": [{"id": "A", "text": "

It elaborates on the idea that the top layer of Atacama Desert soil forms a tough crust. 

"}, {"id": "B", "text": "

It describes the process by which seeds are deposited into Atacama Desert soil.

"}, {"id": "C", "text": "

It identifies the reason particular bird species dig nests in Atacama Desert soil.

"}, {"id": "D", "text": "

It explains how certain birds promote seed germination in Atacama Desert soil.

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer because it most accurately describes how the underlined portion functions in the text as a whole. The first two sentences establish a natural phenomenon: there is a richness of plant life found in the Atacama Desert despite the hard soil that makes it challenging for seeds to germinate. The next sentence, which contains the underlined portion, offers a potential explanation for the phenomenon: local birds dig ground nests exposing seeds to moisture and materials in the soil necessary for germination. The last sentence summarizes a study that compared the fertileness of mounds of dirt dug up by birds to mounds that were undisturbed to support the explanation in the underlined portion. Thus, the underlined portion mainly functions to explain how certain birds promote seed germination in the Atacama Desert soil.

Choice A is incorrect because the underlined portion doesn’t address the topic of the soil’s tough crust or its formation. Instead, the text elaborates on the idea that local birds that build ground nests may help seeds germinate in the hard soil. Choice B is incorrect because the underlined portion describes how some birds may support seed germination in Atacama Desert soil but doesn’t describe how the seeds are deposited into the soil before germination begins.  Choice C is incorrect because neither the underlined portion nor the text as a whole identifies a reason that a particular bird species may choose to dig ground nests in the Atacama Desert soil.

"}, {"id": "c106b9f7", "domain": "Craft and Structure", "skill": "Cross-Text Connections", "difficulty": "E", "type": "mc", "stimulus": "

Text 1

\n

American sculptor Edmonia Lewis is best known for her sculptures that represent figures from history and mythology, such as The Death of Cleopatra and Hagar. Although Lewis sculpted other subjects, her career as a sculptor is best represented by the works in which she depicted these historical and mythical themes. 

\n

 

\n

Text 2 

\n

Art historians have typically ignored the many portrait busts Edmonia Lewis created. Lewis likely carved these busts (sculptures of a person’s head) frequently throughout her long career. She is known for her sculptures that represent historical figures, but Lewis likely supported herself financially by carving portrait busts for acquaintances who paid her to represent their features. Thus, Lewis’s portrait busts are a central aspect of her career as a sculptor.

", "stem": "

Based on the texts, both authors would most likely agree with which statement? 

", "choices": [{"id": "A", "text": "

Lewis’s portrait busts have overshadowed her other work.

"}, {"id": "B", "text": "

The Death of Cleopatra is Lewis’s most famous piece.

"}, {"id": "C", "text": "

Sculpting representations of historical figures was a short-lived trend.

"}, {"id": "D", "text": "

Lewis’s works are varied in the subjects they depict.

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. Author 1 acknowledges that Lewis sculpted other subjects besides historical and mythical figures, suggesting a variety of subjects depicted. Author 2 mentions that Lewis carved portrait busts as well as historical sculptures, which also implies variation among Lewis’s subjects.

Choice A is incorrect. Neither text suggests that Lewis’s portrait busts have received more attention or appreciation than her other work. Author 1 briefly mentions her “other works,” but mostly focuses on her historical and mythical works. Author 2 states that art historians have typically ignored her portrait busts, which suggests that they haven’t overshadowed her other work. Choice B is incorrect. Neither text explicitly states that The Death of Cleopatra is Lewis’s most famous piece. Author 1 mentions it as one example of her historical works, but does not single it out as being more important or influential than Hagar. Author 2 does not mention it at all, focusing instead on her portrait busts. Choice C is incorrect. This choice isn’t supported by the texts. Neither text suggests that sculpting historical figures was a trend that faded quickly.

"}, {"id": "6977d22b", "domain": "Craft and Structure", "skill": "Cross-Text Connections", "difficulty": "H", "type": "mc", "stimulus": "

 

Text 1

\n

Ecologists have long wondered how thousands of microscopic phytoplankton species can live together near ocean surfaces competing for the same resources. According to conventional wisdom, one species should emerge after outcompeting the rest. So why do so many species remain? Ecologists’ many efforts to explain this phenomenon still haven’t uncovered a satisfactory explanation.

\n

 

Text 2

\n

Ecologist Michael Behrenfeld and colleagues have connected phytoplankton’s diversity to their microscopic size. Because these organisms are so tiny, they are spaced relatively far apart from each other in ocean water and, moreover, experience that water as a relatively dense substance. This in turn makes it hard for them to move around and interact with one another. Therefore, says Behrenfeld’s team, direct competition among phytoplankton probably happens much less than previously thought.

", "stem": "

Based on the texts, how would Behrenfeld and colleagues (Text 2) most likely respond to the “conventional wisdom” discussed in Text 1?

", "choices": [{"id": "A", "text": "

By arguing that it is based on a misconception about phytoplankton species competing with one another

"}, {"id": "B", "text": "

By asserting that it fails to recognize that routine replenishment of ocean nutrients prevents competition between phytoplankton species 

"}, {"id": "C", "text": "

By suggesting that their own findings help clarify how phytoplankton species are able to compete with larger organisms

"}, {"id": "D", "text": "

By recommending that more ecologists focus their research on how competition among phytoplankton species is increased with water density

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer because based on Text 2, it represents how Behrenfeld and colleagues would most likely respond to the “conventional wisdom” discussed in Text 1. The conventional wisdom cited holds the opinion that when there is species diversity within a phytoplankton population, “one species should emerge after outcompeting the rest”—that is, after being so successful in competing for resources that the other species vanish from the population. However, Text 2 explains that according to Behrenfeld and colleagues, phytoplankton are so small and spaced so far apart in the water that there is “much less” direct competition for resources within phytoplankton populations than scientists had previously thought. 

Choice B is incorrect because Text 2 never discusses whether routine replenishment of ocean nutrients affects competition between phytoplankton species. Choice C is incorrect because the interspecies competition discussed in both texts is specifically between phytoplankton species, and neither text considers whether phytoplankton compete for resources with larger nonphytoplankton species. Choice D is incorrect because according to Text 2, Behrenfeld and colleagues argue that water density decreases, not increases, competition between phytoplankton species.

"}, {"id": "213248f7", "domain": "Craft and Structure", "skill": "Words in Context", "difficulty": "E", "type": "mc", "stimulus": "

The following text is adapted from Lewis Carroll’s 1865 novel Alice’s Adventures in Wonderland.

\n
\n

“The second thing is to find my way into that lovely garden. I think that will be the best plan.” It sounded like an excellent plan, no doubt, and very neatly and simply arranged; the only difficulty was, that Alice had not the smallest idea how to set about it.

\n
", "stem": "

As used in the text, what does the word “simply” most nearly mean?

", "choices": [{"id": "A", "text": "

Faintly

"}, {"id": "B", "text": "

Hastily

"}, {"id": "C", "text": "

Easily

"}, {"id": "D", "text": "

Foolishly

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer because as used in the text, “simply” most nearly means easily, or involving minimal difficulty or effort. The text first provides Alice’s reflections on her plan to gain access to a garden and then offers commentary on her plan by the novel’s narrator. The text indicates that a reason Alice likes her plan despite not being fully thought through is that she nonetheless believes it can be efficiently arranged. In other words, the text indicates that one of the supposed benefits of Alice’s plan is that it can be easily arranged.

Choice A is incorrect because the text describes how Alice’s plan can be arranged, and it wouldn’t make sense to say that it can be arranged “faintly,” or with little strength or not strongly. Instead, the text indicates that the plan can be arranged with little difficulty. Choice B is incorrect. Although in some contexts “simply” can mean quickly, hastily, or hurriedly, the word “hastily” indicates that something is done too quickly. Although it may be true that Alice’s plan was made in haste, the text doesn’t focus on this aspect of her plan. Instead, the text focuses on the plan’s seemingly good qualities, saying that Alice thinks of it as “the best,” and the narrator refers to it as “excellent” and “neatly,” or efficiently, arranged. Choice D is incorrect. Although in some contexts “simply” can mean foolishly, or lacking good sense, it doesn’t have this meaning in this context. Although the text says that Alice doesn’t know how to go about her plan, it begins by presenting her plan in a positive light: Alice describes her plan as “the best,” and the narrator refers to the plan as “excellent” and “neatly,” or efficiently, arranged.

"}, {"id": "6bc0ba75", "domain": "Craft and Structure", "skill": "Text Structure and Purpose", "difficulty": "H", "type": "mc", "stimulus": "

The mimosa tree evolved in East Asia, where the beetle Bruchidius terrenus preys on its seeds. In 1785, mimosa trees were introduced to North America, far from any B. terrenus. But evolutionary links between predators and their prey can persist across centuries and continents. Around 2001, B. terrenus was introduced in southeastern North America near where botanist Shu-Mei Chang and colleagues had been monitoring mimosa trees. Within a year, 93 percent of the trees had been attacked by the beetles. 

", "stem": "

Which choice best describes the function of the third sentence in the overall structure of the text?

", "choices": [{"id": "A", "text": "

It states the hypothesis that Chang and colleagues had set out to investigate using mimosa trees and B. terrenus.

"}, {"id": "B", "text": "

It presents a generalization that is exemplified by the discussion of the mimosa trees and B. terrenus.

"}, {"id": "C", "text": "

It provides context that clarifies why the species mentioned spread to new locations. 

"}, {"id": "D", "text": "

It offers an alternative explanation for the findings of Chang and colleagues. 

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer because it most accurately describes the function of the third sentence within the overall structure of the text. The third sentence makes a generalization, asserting that evolutionary links between predators and prey can persist across great expanses of time and distance. This generalization is exemplified by the text’s discussion of the relationship between mimosa trees and B. terrenus beetles. When mimosa trees were introduced to North America in 1785, no B. terrenus beetles were present, so the relationship between the trees and the beetles that exists in their native East Asia was disrupted. When the beetles were introduced to North America more than 200 years later, however, they quickly attacked mimosa trees, illustrating the generalization that links between predators and prey \"can persist across centuries and continents.\"

Choice A is incorrect because the third sentence doesn’t indicate that Chang and colleagues were investigating any hypothesis. According to the text, Chang and colleagues were simply monitoring mimosa trees when the beetles happened to be introduced to the area. Choice C is incorrect because the third sentence doesn’t discuss any particular species, let alone the species mentioned elsewhere in the text, nor does the sentence explain why species spread to new locations. Choice D is incorrect because the third sentence offers a generalization about the relationship between predators and prey, not an explanation for the findings by Chang and colleagues that’s an \"alternative\" to an explanation presented elsewhere in the text.

"}, {"id": "b4d29611", "domain": "Craft and Structure", "skill": "Text Structure and Purpose", "difficulty": "M", "type": "mc", "stimulus": "

Michelene Pesantubbee, a historian and citizen of the Choctaw Nation, has identified a dilemma inherent to research on the status of women in her tribe during the 1600s and 1700s: the primary sources from that era, travel narratives and other accounts by male European colonizers, underestimate the degree of power conferred on Choctaw women by their traditional roles in political, civic, and ceremonial life. Pesantubbee argues that the Choctaw oral tradition and findings from archaeological sites in the tribe’s homeland supplement the written record by providing crucial insights into those roles.

", "stem": "

Which choice best describes the overall structure of the text?

", "choices": [{"id": "A", "text": "

It details the shortcomings of certain historical sources, then argues that research should avoid those sources altogether.

"}, {"id": "B", "text": "

It describes a problem that arises in research on a particular topic, then sketches a historian’s approach to addressing that problem.

"}, {"id": "C", "text": "

It lists the advantages of a particular research method, then acknowledges a historian’s criticism of that method.

"}, {"id": "D", "text": "

It characterizes a particular topic as especially challenging to research, then suggests a related topic for historians to pursue instead.

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. The text begins by stating a problem with research on the status of Choctaw women in the 1600s and 1700s: written primary sources underestimate the power they had in their traditional roles. Then it presents one historian’s solution: looking to oral tradition and archeological findings for more insight into these roles.

Choice A is incorrect. This isn’t the overall structure. The text never says that research should avoid written primary sources, just that research should also use oral tradition and archeological sites as sources. Choice C is incorrect. This isn’t the overall structure. The text never mentions the advantages of using written primary sources. Choice D is incorrect. This isn’t the overall structure. The text never says that the status of Choctaw women during the 1600s and 1700s is too challenging to research. And it doesn’t mention any other topics to research instead.

"}, {"id": "f6352bd3", "domain": "Craft and Structure", "skill": "Text Structure and Purpose", "difficulty": "M", "type": "mc", "stimulus": "

Many archaeologists assume that large-scale engineering projects in ancient societies required an elite class to plan and direct the necessary labor. However, recent discoveries, such as the excavation of an ancient canal near the Gulf Coast of Alabama, have complicated this picture. Using radiocarbon dating, a team of researchers concluded that the 1.39-kilometer-long canal was most likely constructed between 576 and 650 CE by an Indigenous society that was relatively free of social classes.

", "stem": "

Which choice best describes the overall structure of the text?

", "choices": [{"id": "A", "text": "

It describes a common view among archaeologists, then discusses a recent finding that challenges that view.

"}, {"id": "B", "text": "

It outlines a method used in some archaeological fieldwork, then explains why an alternative method is superior to it.

"}, {"id": "C", "text": "

It presents contradictory conclusions drawn by archaeologists, then evaluates a study that has apparently resolved that contradiction.

"}, {"id": "D", "text": "

It identifies a gap in scientific research, then presents a strategy used by some archaeologists to remedy that gap.

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. The text starts by introducing a common view among archaeologists about the need for an elite class to direct large-scale engineering projects. Then, it discusses the discovery of a large canal most likely built by a society without an elite class, which challenges the first view.

Choice B is incorrect. Although the text discusses carbon dating as an archaeological method, it doesn’t compare it to any other alternative methods. Choice C is incorrect. The study doesn’t resolve any contradictions—rather, it introduces a contradiction to the one view presented at the beginning of the text. Choice D is incorrect. The text never identifies any gaps in scientific research.

"}, {"id": "5fa165f7", "domain": "Craft and Structure", "skill": "Words in Context", "difficulty": "E", "type": "mc", "stimulus": "

In the 1960s, Sam Gilliam, a Black painter from the southern United States, became the first artist to drape painted canvases into flowing shapes. He later explored a different style, ______blank quilt-like paintings inspired by the patchwork quilting tradition of Black communities in the South.

", "stem": "

Which choice completes the text with the most logical and precise word or phrase?

", "choices": [{"id": "A", "text": "

predicting

"}, {"id": "B", "text": "

refusing

"}, {"id": "C", "text": "

hiding

"}, {"id": "D", "text": "

creating

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer because it most logically completes the text’s discussion of Sam Gilliam’s artworks. As used in this context, “creating” means producing or bringing something into existence. The text indicates that Gilliam is an artist who made draped canvases and, later, quilt-like paintings. This context supports the idea that Gilliam explored different styles in his art by creating special types of paintings.

Choice A is incorrect because the text indicates that Gilliam actually explored and pursued the creation of quilt-like paintings; he wasn’t just “predicting,” or declaring in advance, the existence of these paintings. Choice B is incorrect because in this context “refusing” would mean rejecting, and there is nothing in the text to suggest that Gilliam rejected his quilt-like paintings. Instead, the text indicates that he was exploring and pursuing a new art style in these paintings. Choice C is incorrect because in this context “hiding” would mean concealing from view, and there is nothing in the text to suggest that Gilliam attempted to conceal his quilt-like paintings. Instead, the text indicates that he was exploring and pursuing a new art style in these paintings.  

"}, {"id": "571cf537", "domain": "Craft and Structure", "skill": "Words in Context", "difficulty": "H", "type": "mc", "stimulus": "

The author’s claim about the relationship between Neanderthals and Homo sapiens is ______blank, as it fails to account for several recent archaeological discoveries. To be convincing, his argument would need to address recent finds of additional hominid fossils, such as the latest Denisovan specimens and Homo longi.

", "stem": "

Which choice completes the text with the most logical and precise word or phrase?

", "choices": [{"id": "A", "text": "

disorienting

"}, {"id": "B", "text": "

tenuous

"}, {"id": "C", "text": "

nuanced

"}, {"id": "D", "text": "

unoriginal

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer because it most logically completes the text’s discussion of the author’s claim about the relationship between Neanderthals and Homo sapiens. As used in this context, “tenuous” means lacking substance. The end of the first sentence states that the author’s claim didn’t consider certain key pieces of evidence—“recent archaeological discoveries”—and is therefore weak.  

Choice A is incorrect because it wouldn’t make sense in context to refer to the author’s claim as “disorienting,” or confusing. The text suggests that the author’s claim is insubstantial, not that it’s difficult to grasp. Choice C is incorrect because referring to the claim as “nuanced,” or subtle, wouldn’t make sense in context. According to the text, the claim is incomplete because it didn’t consider certain key information about recent archaeological finds; it doesn’t suggest that what’s in the claim lacks precision. Choice D is incorrect because saying that the claim is “unoriginal,” or imitative, wouldn’t make sense in context. The text faults the claim because it doesn’t consider certain key information about recent archaeological finds; it doesn’t suggest that the author’s claim lacks originality.

"}, {"id": "dba9eaf8", "domain": "Craft and Structure", "skill": "Words in Context", "difficulty": "H", "type": "mc", "stimulus": "

Within baleen whale species, some individuals develop an accessory spleen—a seemingly functionless formation of splenetic tissue outside the normal spleen. Given the formation’s greater prevalence among whales known to make deeper dives, some researchers hypothesize that its role isn’t ______blank; rather, the accessory spleen may actively support diving mechanisms.

", "stem": "

Which choice completes the text with the most logical and precise word or phrase?

", "choices": [{"id": "A", "text": "

replicable

"}, {"id": "B", "text": "

predetermined

"}, {"id": "C", "text": "

operative

"}, {"id": "D", "text": "

latent

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer because it most logically completes the text’s discussion of baleen whale accessory spleens. In this context, “latent” means dormant or functionless. The text sets up a contrast between the idea that baleen whale accessory spleens appear not to have a function and the research indicating that the accessory spleen may actually have a role in supporting the whales’ diving mechanisms. This context therefore conveys the idea that the assumption that baleen whale accessory spleens are latent may be incorrect.

Choice A is incorrect because it wouldn’t make sense to say that the role of the accessory spleen is “replicable,” or capable of being reproduced. The text indicates that the role of the accessory spleen seems to have no function, but some researchers think it does have a role; the text doesn’t address whether the role of the accessory spleen could or couldn’t be reproduced. Choice B is incorrect because suggesting that the role of the accessory spleen is “predetermined,” or decided in advance, wouldn’t make sense in context. Although the researchers may agree that the role of the accessory spleen or any other organ hasn’t been determined in advance, the text focuses on the idea that the accessory spleen was thought to have been functionless but may in fact serve an active role for baleen whales. Choice C is incorrect because it’s the opposite of what the context of the text is conveying. The second sentence of the text indicates that baleen whale accessory spleens may not be useless, not that they aren’t “operative,” or functional.

"}, {"id": "a756aa95", "domain": "Craft and Structure", "skill": "Words in Context", "difficulty": "H", "type": "mc", "stimulus": "

The province of Xoconochco was situated on the Pacific coast, hundreds of kilometers southeast of Tenochtitlan, the capital of the Aztec Empire. Because Xoconochco’s location within the empire was so ______blank, cacao and other trade goods produced there could reach the capital only after a long overland journey.

", "stem": "

Which choice completes the text with the most logical and precise word or phrase?

", "choices": [{"id": "A", "text": "

unobtrusive

"}, {"id": "B", "text": "

concealed

"}, {"id": "C", "text": "

approximate

"}, {"id": "D", "text": "

peripheral

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer because it most logically completes the text’s discussion of the location of the province of Xoconochco within the Aztec Empire. As used in this context, “peripheral” means situated toward the outer bounds rather than the center. The text indicates that Xoconochco was located on a coast, hundreds of kilometers away from the capital of the Aztec Empire. The text also states that trade between the province and the capital required “a long overland journey.” This context suggests that Xoconochco was situated toward an edge of the empire’s territory rather than near its center.

Choice A is incorrect because it wouldn’t make sense in context to refer to Xoconochco’s location within the Aztec Empire as “unobtrusive,” or not blatant or undesirably prominent; it’s not clear how a province’s physical location would or wouldn’t be blatant. Instead of focusing on how noticeable Xoconochco’s location was, the text emphasizes the province’s distance from the capital of the empire, pointing out that because of this distance trade between the two required “a long overland journey.” Choice B is incorrect because the text indicates that the province of Xoconochco was located on a coast far from the capital of the Aztec Empire, not that it was “concealed,” or kept out of sight or hidden from view. Nothing in the text suggests that Xoconochco was actually hidden such that people couldn’t see it, and being hidden wouldn’t necessarily result in trade between the province and the capital requiring “a long overland journey.” Choice C is incorrect because to say that Xoconochco’s location within the Aztec Empire was “approximate” would mean that the location either wasn’t precisely correct or was close to some other location. Neither of these meanings would make sense in context because the text indicates that Xoconochco’s location is known and that it was far from the empire’s capital, so there’s no reason to characterize the location as either not precisely correct or close to another location.

"}, {"id": "441e2b9e", "domain": "Craft and Structure", "skill": "Words in Context", "difficulty": "E", "type": "mc", "stimulus": "

Researchers and conservationists stress that biodiversity loss due to invasive species is ______blank. For example, people can take simple steps such as washing their footwear after travel to avoid introducing potentially invasive organisms into new environments.

", "stem": "

Which choice completes the text with the most logical and precise word or phrase?

", "choices": [{"id": "A", "text": "

preventable

"}, {"id": "B", "text": "

undeniable

"}, {"id": "C", "text": "

common

"}, {"id": "D", "text": "

concerning

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer because it most logically completes the text’s discussion of how biodiversity loss due to invasive species can be avoided. As used in this context, “preventable” means able to be stopped or kept from happening. The text indicates that “people can take simple steps” to avoid bringing possible invasive species into new environments. It presents these steps as an example of how biodiversity loss due to invasive species is preventable.

Choice B is incorrect because it wouldn’t make sense to say that a simple step like washing your shoes after traveling is an example of biodiversity loss due to invasive species being “undeniable,” or something that can’t be proved to be wrong. Although the text may suggest that biodiversity loss due to invasive species is something that really happens, the word that completes the text must make the first sentence into an assertion that is illustrated by the second sentence, and the second sentence illustrates the idea that biodiversity loss due to invasive species is preventable, not undeniable. Choice C is incorrect because it wouldn’t make sense to say that a simple step like washing your shoes after traveling is an example of biodiversity loss due to invasive species being “common,” or something that happens regularly. Additionally, the text doesn’t provide any information about how frequently invasive species cause biodiversity loss. Choice D is incorrect because it wouldn’t make sense to say that a simple step like washing your shoes after traveling is an example of biodiversity loss due to invasive species being “concerning,” or something that is troubling or causes worry. Although the text implies that the phenomenon of biodiversity loss due to invasive species is itself a concerning phenomenon, the word that completes the text must make the first sentence into an assertion that is illustrated by the second sentence, and the second sentence illustrates the idea that biodiversity loss due to invasive species is preventable, not concerning.

"}, {"id": "88bb0f6f", "domain": "Craft and Structure", "skill": "Cross-Text Connections", "difficulty": "E", "type": "mc", "stimulus": "

Text 1

\n

A team led by Bernardo Strassburg has found that rewilding farmland (returning the land to its natural state) could help preserve biodiversity and offset carbon emissions. The amount of farmland that would need to be restored, they found, is remarkably low. Rewilding a mere 15% of the world’s current farmland would prevent 60% of expected species extinctions and help absorb nearly 299 gigatons of carbon dioxide—a clear win in the fight against the biodiversity and climate crises.

\n

 

\n

Text 2

\n

While Strassburg’s team’s findings certainly offer encouraging insight into the potential benefits of rewilding, it’s important to consider potential effects on global food supplies. The researchers suggest that to compensate for the loss of food-producing land, remaining farmland would need to produce even more food. Thus, policies focused on rewilding farmland must also address strategies for higher-yield farming.

", "stem": "

Which choice best describes a difference in how the author of Text 1 and the author of Text 2 view Strassburg’s team’s study?

", "choices": [{"id": "A", "text": "

The author of Text 2 approaches the study’s findings with some caution, whereas the author of Text 1 is optimistic about the reported potential environmental benefits.

"}, {"id": "B", "text": "

The author of Text 2 claims that the percentage of farmland identified by Strassburg’s team is too low for rewilding to achieve meaningful results, whereas the author of Text 1 thinks the percentage is sufficient.

"}, {"id": "C", "text": "

The author of Text 2 believes that the results described by Strassburg’s team are achievable in the near future, whereas the author of Text 1 argues that they likely aren’t.

"}, {"id": "D", "text": "

The author of Text 2 focuses on rewilding’s effect on carbon emissions, whereas the author of Text 1 focuses on its effect on biodiversity.

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. Text 1 is extremely positive about Strassburg’s team’s findings, calling the potential results \"a clear win in the fight against the biodiversity and climate crises.\" Text 2 is not as positive, arguing that while the findings point to \"potential benefits,\" we also need to consider the \"potential effects on global food supplies.\"

Choice B is incorrect. This isn’t a difference between the two views. Text 1 does present the 15% number as enough to achieve meaningful results, but that’s not what Text 2 takes issue with: rather, Text 2 argues that we need to consider the effect that rewilding this much farmland would have on food supplies. Choice C is incorrect. This isn’t a difference between the two views. Neither text mentions the timeline for achieving the results described by Strassburg’s team. Choice D is incorrect. This isn’t a difference between the two views. Text 1 focuses on rewilding’s effects on both carbon emissions and biodiversity. Text 2 doesn’t focus on rewilding’s effect on carbon emissions at all. Instead, it focuses on a third factor: global food supplies.

"}, {"id": "35e21b06", "domain": "Craft and Structure", "skill": "Cross-Text Connections", "difficulty": "H", "type": "mc", "stimulus": "

Text 1

\n

Dominique Potvin and colleagues captured five Australian magpies (Gymnorhina tibicen) to test a new design for attaching tracking devices to birds. As the researchers fitted each magpie with a tracker attached by a small harness, they noticed some magpies without trackers pecking at another magpie’s tracker until it broke off. The researchers suggest that this behavior could be evidence of magpies attempting to help another magpie without benefiting themselves.

\n

 

\n

Text 2

\n

It can be tempting to think that animals are deliberately providing help when we see them removing trackers and other equipment from one another, especially when a species is known to exhibit other cooperative behaviors. At the same time, it can be difficult to exclude the possibility that individuals are simply interested in the equipment because of its novelty, curiously pawing or pecking at it until it detaches.

", "stem": "

Based on the texts, how would the author of Text 2 most likely respond to the researchers’ perspective in Text 1 on the behavior of the magpies without trackers?

", "choices": [{"id": "A", "text": "

That behavior might have been due to the novelty of the magpies’ captive setting rather than to the novelty of the tracker.

"}, {"id": "B", "text": "

That behavior likely indicates that the magpies were deliberately attempting to benefit themselves by obtaining the tracker.

"}, {"id": "C", "text": "

That behavior may not be evidence of selflessness in Gymnorhina tibicen because not all the captured magpies demonstrated it.

"}, {"id": "D", "text": "

That behavior might be adequately explained without suggesting that the magpies were attempting to assist the other magpie.

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer because it reflects how the author of Text 2 would most likely respond to the researchers’ perspective in Text 1 on the behavior of the magpies without trackers. According to Text 1, Dominique Potvin and colleagues observed magpies without trackers pecking at a tracker on another magpie until the device fell off. The researchers suggested that the birds might have been attempting to help the other bird, with no benefit to themselves. Text 2 generally discusses scenarios in which animals have been observed removing trackers from each other. The text cautions that it shouldn’t be assumed that these animals are helping one another deliberately, since they might simply be pecking at trackers out of curiosity, causing them to fall off eventually. Therefore, the author of Text 2 would most likely respond to Potvin and colleagues’ perspective in Text 1 by saying that the behavior of the magpies without trackers could be adequately explained without suggesting that they were attempting to assist the other magpie.

Choice A is incorrect because Text 2 never discusses the novelty, or the newness and unusual quality, of the captive settings in which animals have been observed to remove trackers from other animals, nor does it suggest that such novelty might account for this behavior. Instead, the text suggests that it’s the novelty of the tracking equipment itself that might cause the behavior: interested in the trackers because they’re unusual, animals might paw or peck at them until they fall off. Choice B is incorrect because Text 2 never suggests that when animals remove trackers from other animals, they do so because they wish to obtain the trackers for themselves. Instead, Text 2 argues that animals paw or peck at trackers because they are merely curious about them. Choice C is incorrect because Text 2 doesn’t argue that when captured animals are observed removing trackers from each other, their behavior should be regarded as selfless only if all of them participate in it. Instead, the text argues that the behavior may not be selfless at all and may instead be attributed to animals’ curiosity about the new and unusual trackers.

"}, {"id": "9b01bcf4", "domain": "Craft and Structure", "skill": "Text Structure and Purpose", "difficulty": "H", "type": "mc", "stimulus": "

The 1967 release of Harold Cruse’s book The Crisis of the Negro Intellectual isolated him from almost all other scholars and activists of the American Civil Rights Movement—though many of those thinkers disagreed with each other, he nonetheless found ways to disagree with them all. He thought that activists who believed that Black people such as himself should culturally assimilate were naïve. But he also sharply criticized Black nationalists such as Marcus Garvey who wanted to establish independent, self-contained Black economies and societies, even though Cruse himself identified as a Black nationalist.

", "stem": "

Which choice best describes the function of the underlined sentence in the text as a whole?

", "choices": [{"id": "A", "text": "

It describes a direction that Cruse felt the Civil Rights Movement ought to take.

"}, {"id": "B", "text": "

It indicates that Cruse’s reputation as a persistent antagonist of other scholars is undeserved.

"}, {"id": "C", "text": "

It describes a controversy that Cruse’s work caused within the Black nationalist movement.

"}, {"id": "D", "text": "

It helps explain Cruse’s position with respect to the community of civil rights thinkers.

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. The text as a whole claims that Cruse disagreed with virtually all other Civil Rights scholars and activists. The underlined sentence describes one way that Cruse both did and didn’t fit in with those thinkers: he criticized Black nationalists, even though he identified as one.

Choice A is incorrect. The underlined sentence doesn’t do this. It describes Cruse’s criticisms—it never mentions what Cruse did want the movement to do instead. Choice B is incorrect. This conflicts with the text, which argues that Cruse did disagree with almost all other scholars of the Civil Rights Movement. Choice C is incorrect. This is a step too far. The text never says that Cruse’s work caused controversy within the Black nationalist movement.

"}, {"id": "f52cc78c", "domain": "Craft and Structure", "skill": "Cross-Text Connections", "difficulty": "M", "type": "mc", "stimulus": "

Text 1

\n

Polar bears sustain themselves primarily by hunting seals on the Arctic sea ice, but rising ocean temperatures are causing the ice to diminish, raising concerns about polar bear population declines as these large predators’ seal-hunting habitats continue to shrink. A 2020 study examining polar bear populations across the Arctic concluded that populations affected by sea-ice loss are at great risk of extinction by the end of the twenty-first century.

\n

Text 2

\n

Monitoring carried out by researchers from the Norwegian Polar Institute shows that the polar bear population on the Arctic archipelago of Svalbard remains stable and well nourished despite rapidly declining sea ice in recent years. The researchers attribute this population’s resilience in part to a shift in feeding strategies: in addition to hunting seals, the Svalbard polar bears have begun relying on a diet of reindeer meat and birds’ eggs.

", "stem": "

Based on the texts, how would the researchers in Text 2 most likely respond to the conclusion presented in the underlined portion of Text 1?

", "choices": [{"id": "A", "text": "

By noting that it neglects the possibility of some polar bear populations adapting to changes in their environment

"}, {"id": "B", "text": "

By suggesting that it is likely incorrect about the rates at which warming ocean temperatures have caused sea ice to melt in the Arctic

"}, {"id": "C", "text": "

By asserting that it overlooks polar bear populations that have not yet been affected by loss of seal-hunting habitats

"}, {"id": "D", "text": "

By arguing that it fails to account for polar bears’ reliance on a single seal-hunting strategy

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. Text 2 describes how the Svalbard polar bears have adapted to the loss of sea ice by diversifying their diet and feeding on reindeer and seabird eggs, resulting in a “stable and well nourished” population despite environmental challenges. This counters the underlined claim that polar bears facing a loss of sea ice are at “great risk of extinction” by the end of the century.

Choice B is incorrect. Text 2 does not challenge the fact that sea ice is rapidly declining in the Arctic due to warming ocean temperatures. In fact, it states that the Svalbard polar bears have faced “rapidly declining sea ice in recent years.” Choice C is incorrect. The claim in Text 1 is specific to polar bear populations affected by the loss of seal hunting habitats, so unaffected populations are irrelevant to the claim. Also, Text 2 doesn’t mention any polar bear populations that haven’t yet been affected by loss of seal hunting habitats. It focuses on a population that has been affected by sea-ice loss but has managed to survive and thrive nevertheless. Choice D is incorrect. Text 2 doesn’t imply that polar bears rely on a single seal-hunting strategy. In fact, the researcher in Text 2 would say that Text 1 fails to account for polar bears’ ability to develop other hunting strategies and food sources.

"}, {"id": "8634bf4a", "domain": "Craft and Structure", "skill": "Words in Context", "difficulty": "M", "type": "mc", "stimulus": "

Diego Velázquez was the leading artist in the court of King Philip IV of Spain during the seventeenth century, but his influence was hardly ______blank Spain: realist and impressionist painters around the world employed his techniques and echoed elements of his style.

", "stem": "

Which choice completes the text with the most logical and precise word or phrase?

", "choices": [{"id": "A", "text": "

derived from

"}, {"id": "B", "text": "

recognized in

"}, {"id": "C", "text": "

confined to

"}, {"id": "D", "text": "

repressed by

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer because it most logically completes the discussion of the artist Diego Velázquez’s influence outside Spain. As used in this context, “confined to” means restricted to. The text says that Velázquez was the leading artist in the Spanish court during the seventeenth century, but it also notes that other painters around the world were influenced by his techniques and style. Thus, Velázquez’s influence was hardly (or almost not) confined to, or restricted to, Spain.

Choice A is incorrect because if Velázquez was a leading artist in Spain, it doesn’t make logical sense to claim that his influence was hardly (or almost not) derived from, or obtained from, Spain. Moreover, the other painters around the world who employed Velázquez’s techniques would by definition be influenced by Spanish style. Choice B is incorrect because if Velázquez was a leading artist in the court of King Philip IV of Spain, then his influence must have been widely recognized, or acknowledged, rather than being hardly (or almost not) recognized. Choice D is incorrect because the text gives no indication that deliberately limiting Velázquez’s influence outside Spain was ever considered by anyone. Thus, even if it is true that his influence was not repressed, or restrained, it doesn’t make logical sense to say so in this context.

"}, {"id": "e8fb0744", "domain": "Craft and Structure", "skill": "Words in Context", "difficulty": "H", "type": "mc", "stimulus": "

As an undergraduate researcher in anthropology, Jennifer C. Chen contributed to a groundbreaking study challenging the accepted view that among prehistoric peoples, female participation in hunting was ______blank. The research team’s review of data from late Pleistocene and early Holocene burials in the Americas revealed that, in fact, as many as half of the hunters in those populations were female.

", "stem": "

Which choice completes the text with the most logical and precise word or phrase?

", "choices": [{"id": "A", "text": "

inevitable

"}, {"id": "B", "text": "

satisfactory

"}, {"id": "C", "text": "

negligible

"}, {"id": "D", "text": "

commonplace

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer because it most logically completes the text’s discussion of the study of female participation in hunting among prehistoric peoples. In this context, “negligible” means not significant enough to be worth considering. The text says that the study challenged the accepted view of female participation in hunting among prehistoric peoples. The text goes on to say that the researchers found that “in fact, as many as half” the hunters in the groups studied were female. The phrase “in fact” establishes a contrast indicating that the finding that as many as half the hunters were female differs from the accepted view. This context suggests, then, that the accepted view is that female participation in hunting was negligible. 

Choice A is incorrect because the text indicates that the study challenged the accepted view by showing that as many as half of hunters among prehistoric peoples were female, which suggests that the accepted view is that female participation was low, not that female participation was “inevitable,” or unavoidable. Nothing in the text suggests that the accepted view is that prehistoric peoples could not avoid female participation in hunting. Choice B is incorrect because nothing in the text suggests that the accepted view of female participation in hunting among prehistoric peoples is that such participation was “satisfactory,” or sufficient to meet a requirement or demand. There is no information in the text about any demands or requirements regarding female participation in hunting, let alone any information about how much female participation in hunting would be enough to satisfy those demands or requirements. Instead, the text indicates that the study challenged the accepted view by showing that as many as half the hunters in the groups studied were female, suggesting that the accepted view is that female participation in hunting was low. Choice D is incorrect because the text indicates that the study challenged the accepted view by showing that as many as half of hunters among the prehistoric peoples studied were female, which suggests that the accepted view is that female participation was low, not that female participation was “commonplace,” or ordinary or unremarkable. Although the study under discussion suggests that female participation may have been commonplace, that study is presented as challenging the accepted view, not as reinforcing the accepted view. 

"}, {"id": "c843d63c", "domain": "Craft and Structure", "skill": "Words in Context", "difficulty": "M", "type": "mc", "stimulus": "

The artisans of the Igun Eronmwon guild in Benin City, Nigeria, typically ______blank the bronze- and brass-casting techniques that have been passed down through their families since the thirteenth century, but they don’t strictly observe every tradition; for example, guild members now use air-conditioning motors instead of handheld bellows to help heat their forges.

", "stem": "

Which choice completes the text with the most logical and precise word or phrase?

", "choices": [{"id": "A", "text": "

experiment with

"}, {"id": "B", "text": "

adhere to

"}, {"id": "C", "text": "

improve on

"}, {"id": "D", "text": "

grapple with

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer because it most logically completes the text’s discussion of bronze- and brass-casting techniques used by the Igun Eronmwon guild. In this context “adhere to” would mean to act in accordance with. The text states that although members of the Igun Eronmwon guild typically do something with techniques that have been passed down since the thirteenth century, they “don’t strictly observe every tradition.” By establishing a contrast with not always following traditions, the context suggests that guild members do typically adhere to traditional techniques.

Choice A is incorrect because in this context “experiment with” would mean to do something new with. Although using motors rather than manual bellows is presented as a new approach, the text establishes a contrast between what the guild members typically do with techniques that have been passed down over centuries and the idea that the members “don’t strictly observe every tradition.” The phrase “experiment with” wouldn’t support the contrast because regularly trying new things with the techniques would be an example of not strictly following all traditions. Choice C is incorrect because in this context “improve on” would mean to make better. Although using motors rather than manual bellows might be an improved approach, the text establishes a contrast between what the guild members typically do with techniques that have been passed down over centuries and the idea that the members “don’t strictly observe every tradition.” The phrase “improve on” wouldn’t support the contrast because regularly making changes to the techniques would be an example of not strictly following all traditions. Choice D is incorrect because in this context “grapple with” would mean to try hard to solve a difficult problem. Although bronze- and brass-casting are likely challenging tasks, nothing in the text suggests that the guild members have any particular difficulties with the techniques passed down since the thirteenth century. 

"}, {"id": "afec1a70", "domain": "Expression of Ideas", "skill": "Rhetorical Synthesis", "difficulty": "H", "type": "mc", "stimulus": "

While researching a topic, a student has taken the following notes:

\n", "stem": "

The student wants to present the primary aim of the research study. Which choice most effectively uses relevant information from the notes to accomplish this goal?

", "choices": [{"id": "A", "text": "

Bhosale’s team wanted to better understand the mechanics behind bird nests’ uniquely flexible yet cohesive structural properties.

"}, {"id": "B", "text": "

The researchers used laboratory models that simulated the arrangement of flexible sticks and analyzed the points where sticks touched one another.

"}, {"id": "C", "text": "

After analyzing the points where sticks touched, the researchers found that the structures became stiffer when pressure was applied.

"}, {"id": "D", "text": "

As analyzed by Bhosale’s team, bird nests are uniquely flexible yet cohesive engineered structures.

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. It describes the reason Bhosale’s team wanted to study the structures of bird nests—that is to say, the study’s primary aim.

Choice B is incorrect. This choice doesn’t present the primary aim of the research study. It describes how the study worked, but not why it was done. Choice C is incorrect. This choice doesn’t present the primary aim of the research study. It describes a result of the experiment, but not why it was carried out. Choice D is incorrect. This choice doesn’t present the primary aim of the research study.

"}, {"id": "660d50dc", "domain": "Expression of Ideas", "skill": "Transitions", "difficulty": "E", "type": "mc", "stimulus": "

Samuel Coleridge-Taylor was a prominent classical music composer from England who toured the US three times in the early 1900s. The child of a West African father and an English mother, Coleridge-Taylor emphasized his mixed-race ancestry. For example, he referred to himself as Anglo-African. ______blank he incorporated the sounds of traditional African music into his classical music compositions.

", "stem": "

Which choice completes the text with the most logical transition?

", "choices": [{"id": "A", "text": "

In addition,

"}, {"id": "B", "text": "

Actually,

"}, {"id": "C", "text": "

However,

"}, {"id": "D", "text": "

Regardless,

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. “In addition” logically signals that the detail in this sentence—that Coleridge-Taylor included traditional African music in his classical compositions—adds to the information in the previous sentence. Specifically, the previous sentence indicates one way in which Coleridge-Taylor emphasized his mixed-race ancestry, and the claim that follows indicates a second, additional way.

Choice B is incorrect because “actually” illogically signals that the detail in this sentence is surprising in light of the information in the previous sentence. Instead, the detail adds to the information, indicating a second, additional way in which Coleridge-Taylor emphasized his mixed-race ancestry. Choice C is incorrect because “however” illogically signals that the detail in this sentence contrasts with the information in the previous sentence. Instead, the detail adds to the information, indicating a second, additional way in which Coleridge-Taylor emphasized his mixed-race ancestry. Choice D is incorrect because “regardless” illogically signals that the detail in this sentence is true despite the information in the previous sentence. Instead, the detail adds to the information, indicating a second, additional way in which Coleridge-Taylor emphasized his mixed-race ancestry.

"}, {"id": "4d2736f0", "domain": "Expression of Ideas", "skill": "Transitions", "difficulty": "H", "type": "mc", "stimulus": "

In her poetry collection Thomas and Beulah, Rita Dove interweaves the titular characters’ personal stories with broader historical narratives. She places Thomas’s journey from the American South to the Midwest in the early 1900s within the larger context of the Great Migration. ______blank Dove sets events from Beulah’s personal life against the backdrop of the US Civil Rights Movement.

", "stem": "

Which choice completes the text with the most logical transition?

", "choices": [{"id": "A", "text": "

Specifically,

"}, {"id": "B", "text": "

Thus,

"}, {"id": "C", "text": "

Regardless,

"}, {"id": "D", "text": "

Similarly,

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. “Similarly” logically signals that the information in the sentence—that Dove situates Beulah’s life in the context of the US Civil Rights Movement—is similar to the previous information about Thomas and the Great Migration. Both sentences support the first sentence’s claim that Dove portrays her characters in the context of broader historical narratives. 

Choice A is incorrect because “specifically” illogically signals that the information about Beulah in this sentence provides specific details elaborating on the previous information about Thomas. Instead, it’s similar to the previous information about Thomas. Choice B is incorrect because “thus” illogically signals that the information about Beulah in this sentence is a result or consequence of the previous information about Thomas. Instead, it’s similar to the previous information about Thomas. Choice C is incorrect because “regardless” illogically signals that the information about Beulah in this sentence is true despite the previous information about Thomas. Instead, it’s similar to the previous information about Thomas.

"}, {"id": "39ccb463", "domain": "Expression of Ideas", "skill": "Rhetorical Synthesis", "difficulty": "H", "type": "mc", "stimulus": "

While researching a topic, a student has taken the following notes:

\n", "stem": "

The student wants to introduce Cathryn Halverson’s book to an audience already familiar with the Atlantic Monthly. Which choice most effectively uses relevant information from the notes to accomplish this goal?

", "choices": [{"id": "A", "text": "

Cathryn Halverson’s Faraway Women and the “Atlantic Monthly”  discusses female authors whose autobiographies appeared in the magazine in the early 1900s.

"}, {"id": "B", "text": "

A magazine called the Atlantic Monthly, referred to in Cathryn Halverson’s book title, was first published in 1857.

"}, {"id": "C", "text": "

Faraway Women and the “Atlantic Monthly”  features contributors to the Atlantic Monthly, first published in 1857 as a magazine focusing on politics, art, and literature. 

"}, {"id": "D", "text": "

An author discussed by Cathryn Halverson is Juanita Harrison, whose autobiography appeared in the Atlantic Monthly in the early 1900s.

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. The sentence effectively introduces Cathryn Halverson’s book to an audience already familiar with the Atlantic Monthly, noting the title of Halverson’s book and describing its content without providing background information about the Atlantic Monthly.

Choice B is incorrect. The sentence introduces the Atlantic Monthly and mentions that it’s referred to in Cathryn Halverson’s book title; it doesn’t effectively introduce Halverson’s book. Choice C is incorrect. The sentence assumes that the audience is unfamiliar with the Atlantic Monthly, providing background information about the magazine; it doesn’t effectively introduce Halverson’s book to an audience already familiar with the Atlantic Monthly. Choice D is incorrect. While the sentence assumes that the audience is familiar with the Atlantic Monthly, it doesn’t effectively introduce Cathryn Halverson’s book.

"}, {"id": "b46e0c8a", "domain": "Expression of Ideas", "skill": "Rhetorical Synthesis", "difficulty": "M", "type": "mc", "stimulus": "

While researching a topic, a student has taken the following notes:

\n", "stem": "

The student wants to present the study to an audience already familiar with environmental DNA. Which choice most effectively uses relevant information from the notes to accomplish this goal?

", "choices": [{"id": "A", "text": "

Sara Oyler-McCance’s researchers analyzed eDNA in water samples from the Florida Everglades for evidence of invasive constrictor snakes, which are difficult to observe.

"}, {"id": "B", "text": "

An analysis of eDNA can detect the presence of invasive species that are difficult to observe, such as constrictor snakes.

"}, {"id": "C", "text": "

Researchers found Burmese python eDNA, or environmental DNA, in water samples; eDNA is the DNA in released cellular materials, such as shed skin cells.

"}, {"id": "D", "text": "

Sara Oyler-McCance’s researchers analyzed environmental DNA (eDNA)—that is, DNA from cellular materials released by organisms—in water samples from the Florida Everglades.

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. This choice presents the study in a way that assumes the audience is already familiar with eDNA.

Choice B is incorrect. This choice doesn’t present the study. It only states a general fact about eDNA analysis. Choice C is incorrect. This choice isn’t suited for an audience already familiar with eDNA. A familiar audience wouldn’t need to have the term defined or explained. Choice D is incorrect. This choice isn’t suited for an audience already familiar with eDNA. A familiar audience wouldn’t need to have the term defined or explained. It also doesn’t present the study.

"}, {"id": "48d0bb34", "domain": "Expression of Ideas", "skill": "Rhetorical Synthesis", "difficulty": "M", "type": "mc", "stimulus": "

While researching a topic, a student has taken the following notes:

\n", "stem": "

The student wants to describe the rocking chair to an audience unfamiliar with Sam Maloof. Which choice most effectively uses relevant information from the notes to accomplish this goal?

", "choices": [{"id": "A", "text": "

With its sleek, contoured armrests and seat, the walnut rocking chair in Boston’s Museum of Fine Arts is just one piece of furniture created by American woodworker Sam Maloof.

"}, {"id": "B", "text": "

Sam Maloof was born in 1916 and died in 2009, and during his life, he made a chair that you can see if you visit the Museum of Fine Arts in Boston.

"}, {"id": "C", "text": "

Furniture designer Sam Maloof was a recipient of one of the John D. and Catherine T. MacArthur Foundation’s “genius grants.”

"}, {"id": "D", "text": "

The rocking chair is made from walnut, and it has been shaped such that its armrests and seat are sleek and contoured.

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. The sentence effectively describes the rocking chair to an audience unfamiliar with Sam Maloof, noting its sleek, contoured armrests and seat and explaining that Sam Maloof (the walnut chair’s creator) was an American woodworker.

Choice B is incorrect. While the sentence explains who Sam Maloof was and mentions a chair, it doesn’t describe the chair. Choice C is incorrect. While the sentence explains who Sam Maloof was, it doesn’t describe the rocking chair. Choice D is incorrect. While the sentence describes the rocking chair, it doesn’t explain who Sam Maloof was.

"}, {"id": "aa7e10d0", "domain": "Expression of Ideas", "skill": "Rhetorical Synthesis", "difficulty": "M", "type": "mc", "stimulus": "

While researching a topic, a student has taken the following notes:

\n", "stem": "

The student wants to present the study and its findings. Which choice most effectively uses relevant information from the notes to accomplish this goal?

", "choices": [{"id": "A", "text": "

A study led by Arelee Estefanía Muñoz-Hernández identified a total of 74 Orchidaceae species in the temperate forests of Oaxaca, Mexico. 

"}, {"id": "B", "text": "

There are orchids in many environments, but there are 74 Orchidaceae species in Oaxaca, Mexico.

"}, {"id": "C", "text": "

Oaxaca, Mexico, is home to temperate forests containing 74 Orchidaceae species.

"}, {"id": "D", "text": "

Arelee Estefanía Muñoz-Hernández and her team wanted to know how many different Orchidaceae species are present in the forests of Oaxaca, Mexico, so they conducted a study to collect orchids.

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. This choice most effectively presents the study and its findings. It opens with the study and names its lead researcher, then tells us its finding: that they identified 74 Orchidaceae species in the temperate forests of Oaxaca, Mexico. 

Choice B is incorrect. This choice doesn’t include the study’s findings, so it fails to achieve the goal. It doesn’t mention that there was a study at all.  Choice C is incorrect. This choice doesn’t present the study, so it fails to achieve the goal. It doesn’t mention that there was a study at all.  Choice D is incorrect. This choice doesn’t include the study’s findings, so it fails to achieve the goal.

"}, {"id": "264e7415", "domain": "Expression of Ideas", "skill": "Rhetorical Synthesis", "difficulty": "E", "type": "mc", "stimulus": "

While researching a topic, a student has taken the following notes:

\n", "stem": "

The student wants to emphasize the distance covered by the Philadelphia and Lancaster Turnpike. Which choice most effectively uses relevant information from the notes to accomplish this goal?

", "choices": [{"id": "A", "text": "

The sixty-two-mile-long Philadelphia and Lancaster Turnpike connected the Pennsylvania cities of Philadelphia and Lancaster.

"}, {"id": "B", "text": "

The Philadelphia and Lancaster Turnpike was the first private turnpike in the United States.

"}, {"id": "C", "text": "

The Philadelphia and Lancaster Turnpike, which connected two Pennsylvania cities, was built between 1792 and 1794.

"}, {"id": "D", "text": "

A historic Pennsylvania road, the Philadelphia and Lancaster Turnpike was completed in 1794.

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. The sentence emphasizes the distance covered by the Philadelphia and Lancaster Turnpike, noting that the turnpike, which connected the two Pennsylvania cities in its name, was sixty-two miles long.

Choice B is incorrect. The sentence emphasizes the significance of the turnpike; it doesn’t emphasize the distance that the turnpike covered. Choice C is incorrect. While the sentence mentions that the turnpike connected two Pennsylvania cities, it doesn’t emphasize the specific distance covered by the turnpike. Choice D is incorrect. The sentence emphasizes when the turnpike was built; it doesn’t emphasize the distance that the turnpike covered.

"}, {"id": "e3edc138", "domain": "Expression of Ideas", "skill": "Transitions", "difficulty": "H", "type": "mc", "stimulus": "

In a heated debate in biogeography, the field is divided between dispersalists and vicariancists. ______blank there are those who argue that dispersal is the most crucial determining factor in a species’ distribution, and those who insist that vicariance (separation due to geographic barriers) is. Biogeographer Isabel Sanmartín counts herself among neither.

", "stem": "

Which choice completes the text with the most logical transition?

", "choices": [{"id": "A", "text": "

Furthermore,

"}, {"id": "B", "text": "

By contrast,

"}, {"id": "C", "text": "

Similarly,

"}, {"id": "D", "text": "

That is,

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. “That is” logically signals that this sentence clarifies the terms of the scientific debate introduced in the previous sentence by explaining the difference between dispersalists and vicariancists.

Choice A is incorrect because “furthermore” illogically signals that the information in this sentence is merely additional to (and separate from) the information in the previous sentence about the scientific debate. Instead, the information about dispersalists and vicariancists clarifies the terms of that debate. Choice B is incorrect because “by contrast” illogically signals that the information in this sentence contrasts with the information in the previous sentence about the scientific debate. Instead, the information about dispersalists and vicariancists clarifies the terms of that debate. Choice C is incorrect because “similarly” illogically signals that the information in this sentence is merely similar to the information in the previous sentence about the scientific debate. Instead, the information about dispersalists and vicariancists clarifies the terms of that debate.

"}, {"id": "a40c7aa3", "domain": "Expression of Ideas", "skill": "Transitions", "difficulty": "M", "type": "mc", "stimulus": "

Most of the planets that have been discovered outside our solar system orbit G-type stars, like our Sun. In 2014, ______blank researchers identified a planet orbiting KELT-9, a B-type star more than twice as massive and nearly twice as hot as the Sun. Called KELT-9b, it is one of the hottest planets ever discovered.

", "stem": "

Which choice completes the text with the most logical transition?

", "choices": [{"id": "A", "text": "

likewise,

"}, {"id": "B", "text": "

however,

"}, {"id": "C", "text": "

therefore,

"}, {"id": "D", "text": "

for example,

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. The word “however” logically signals that the information in this sentence about the planet KELT-9b—that it orbits a B-type star—contrasts with the previous information about planets discovered outside our solar system. Most of these planets orbit G-type stars, not B-type stars.

Choice A is incorrect because “likewise” illogically signals that the information about the planet KELT-9b is similar to the previous information about most planets outside our solar system. Instead, it contrasts with that information. Choice C is incorrect because “therefore” illogically signals that the information about the planet KELT-9b is a result of the previous information about most planets outside our solar system. Instead, it contrasts with that information. Choice D is incorrect because “for example” illogically signals that the information about the planet KELT-9b is an example of the previous information about most planets outside our solar system. Instead, it contrasts with that information.

"}, {"id": "00221c00", "domain": "Expression of Ideas", "skill": "Transitions", "difficulty": "H", "type": "mc", "stimulus": "

In 1815, while in exile in Jamaica, Venezuelan revolutionary Simón Bolívar penned a letter praising England’s republican government and expressing hope that Latin American nations seeking independence from Spain might achieve something similar. The letter was addressed to a local merchant, Henry Cullen; ______blank though, Bolívar’s goal was to persuade political leaders from England and Europe to support his cause.

", "stem": "

Which choice completes the text with the most logical transition?

", "choices": [{"id": "A", "text": "

additionally,

"}, {"id": "B", "text": "

ultimately,

"}, {"id": "C", "text": "

accordingly,

"}, {"id": "D", "text": "

consequently,

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. “Ultimately” means “in the long run” or “at the highest level.” Although Bolívar wrote to a local merchant, his ultimate goal was to send a message to political leaders in Europe. Therefore, “ultimately” fits perfectly in this context.

Choice A is incorrect. This choice uses a transition that indicates the addition of an agreeing idea. However, the second part of the sentence actually disagrees with the first part. Bolívar addressed the letter to Cullen, but he was really sending a message to someone else. Notice how the contrast word “though” also acts as a transition between these ideas. Choice C is incorrect. This choice uses a cause-and-effect transition. Bolívar’s writing of the letter to Cullen would not cause him to have a goal of persuading European powers to support him. Choice D is incorrect. This choice uses a cause-and-effect transition. Bolívar’s writing of the letter to Cullen would not cause him to have a goal of persuading European powers to support him.

"}, {"id": "af89fa02", "domain": "Expression of Ideas", "skill": "Transitions", "difficulty": "M", "type": "mc", "stimulus": "

The Babylonian king Hammurabi achieved much during his forty-year reign. He conquered all of Mesopotamia and built Babylon into one of the most powerful cities of the ancient world. Today, ______blank he is mainly remembered for a code of laws inscribed on a seven-foot-tall block of stone: the Code of Hammurabi.

", "stem": "

Which choice completes the text with the most logical transition?

", "choices": [{"id": "A", "text": "

therefore,

"}, {"id": "B", "text": "

likewise,

"}, {"id": "C", "text": "

however,

"}, {"id": "D", "text": "

for instance,

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. “However” logically signals that the information in this sentence—that Hammurabi is mainly remembered for just a single achievement, the Code of Hammurabi—is contrary to what might be assumed from the previous information about Hammurabi’s many achievements. 

Choice A is incorrect because “therefore” illogically signals that the information in this sentence is a result of the previous information about Hammurabi’s many achievements. Instead, this sentence makes a point that is contrary to what might be assumed from the previous information. Choice B is incorrect because “likewise” illogically signals that the information in this sentence is similar to the previous information about Hammurabi’s many achievements. Instead, this sentence makes a point that is contrary to what might be assumed from the previous information. Choice D is incorrect because “for instance” illogically signals that this sentence exemplifies the previous information about Hammurabi’s many achievements. Instead, this sentence makes a point that is contrary to what might be assumed from the previous information.

"}, {"id": "16631d34", "domain": "Expression of Ideas", "skill": "Rhetorical Synthesis", "difficulty": "H", "type": "mc", "stimulus": "

While researching a topic, a student has taken the following notes:

\n", "stem": "

The student wants to explain a disadvantage of relying on audio features to predict a song’s popularity. Which choice most effectively uses relevant information from the notes to accomplish this goal?

", "choices": [{"id": "A", "text": "

Many popularity-predicting algorithms are based on a song’s audio features, such as loudness and pitch intervals.

"}, {"id": "B", "text": "

Algorithms based on audio features may misidentify the main features of a song with varying acoustic traits, making such algorithms less reliable predictors of popularity than those based on fixed traits.

"}, {"id": "C", "text": "

Audio features describe acoustic traits such as pitch intervals, which may vary within a song, whereas descriptive tags describe fixed traits such as genre, which are reliable predictors of popularity.

"}, {"id": "D", "text": "

The MSD’s descriptive tags are reliable predictors of a song’s popularity, as the traits they describe are fixed.

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. This choice uses relevant information from the notes to explain a disadvantage of relying on audio features to predict a song’s popularity—namely, that it may misidentify features of certain songs. It also contrasts audio features with descriptive tags, which are more reliable predictors.

Choice A is incorrect. This choice only states a fact about the algorithms without evaluating their reliability or accuracy. Choice C is incorrect. This choice only describes the difference between audio features and descriptive tags without indicating why this difference matters for predicting popularity. Choice D is incorrect. This choice only mentions descriptive tags, which are not the focus of the student’s rhetorical goal.

"}, {"id": "e2693197", "domain": "Expression of Ideas", "skill": "Rhetorical Synthesis", "difficulty": "E", "type": "mc", "stimulus": "

While researching a topic, a student has taken the following notes:

\n", "stem": "

The student wants to describe how fabric is used in Assertion of Will. Which choice most effectively uses relevant information from the notes to accomplish this goal?

", "choices": [{"id": "A", "text": "

In Assertion of Will, the figures’ clothing is made of fabric pieces stitched to the painting’s canvas.

"}, {"id": "B", "text": "

The exhibition Oracles of the Pink Universe featured artworks by artist Simphiwe Ndzube.

"}, {"id": "C", "text": "

Depicting three standing, clothed figures, Assertion of Will is a painting by Simphiwe Ndzube.

"}, {"id": "D", "text": "

Simphiwe Ndzube’s Assertion of Will was one of eight artworks exhibited in Oracles of the Pink Universe at the Denver Museum of Art.

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. This choice directly describes how fabric is used in Assertion of Will, by explaining that the fabric pieces are part of the painting itself. 

Choice B is incorrect. This choice provides contextual information about the exhibition, but it doesn’t mention anything about the painting or the fabric. Choice C is incorrect. This choice mentions that the figures are clothed, but it doesn’t explain how the fabric is integrated into the painting. Choice D is incorrect. This choice provides contextual information about the painting, but it doesn’t mention anything about the fabric or how it is used. 

"}, {"id": "601b9d18", "domain": "Expression of Ideas", "skill": "Transitions", "difficulty": "M", "type": "mc", "stimulus": "

Some members of the US Supreme Court have resisted calls to televise the court’s oral arguments, concerned that the participants would be tempted to perform for the cameras (and thus lower the quality of the discourse). ______blank the justices worry that most viewers would not even watch the full deliberations, only short clips that could be misinterpreted and mischaracterized.

", "stem": "

Which choice completes the text with the most logical transition?

", "choices": [{"id": "A", "text": "

However,

"}, {"id": "B", "text": "

Additionally,

"}, {"id": "C", "text": "

In comparison,

"}, {"id": "D", "text": "

For example,

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. “Additionally” logically signals that the claim in this sentence—that some Supreme Court justices worry that viewers (of televised court arguments) would watch only short, misleading clips—adds to the information in the previous sentence. Specifically, the previous sentence indicates one concern raised by those opposed to televising the court’s oral arguments, and the claim that follows indicates a second, additional concern.

Choice A is incorrect because “however” illogically signals that the claim in this sentence contrasts with the information in the previous sentence. Instead, the claim adds to the information, indicating a second, additional concern that some Supreme Court justices have about televising the court’s arguments. Choice C is incorrect because “in comparison” illogically signals that the claim in this sentence is being compared to the information in the previous sentence. Instead, the claim adds to the information, indicating a second, additional concern that some Supreme Court justices have about televising the court’s arguments. Choice D is incorrect because “for example” illogically signals that the claim in this sentence exemplifies the information in the previous sentence. Instead, the claim adds to the information, indicating a second, additional concern that some Supreme Court justices have about televising the court’s arguments.

"}, {"id": "ec3d7605", "domain": "Expression of Ideas", "skill": "Transitions", "difficulty": "M", "type": "mc", "stimulus": "

Award-winning travel writer Linda Watanabe McFerrin considers the background research she conducts on destinations featured in her travel books to be its own reward. ______blank McFerrin admits to finding the research phase of her work just as fascinating and engaging as exploring a location in person.

", "stem": "

Which choice completes the text with the most logical transition?

", "choices": [{"id": "A", "text": "

By contrast,

"}, {"id": "B", "text": "

Likewise,

"}, {"id": "C", "text": "

Besides,

"}, {"id": "D", "text": "

In fact,

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. “In fact” logically signals that the information in this sentence—that McFerrin finds the research phase of her work to be just as fascinating as travel—emphasizes and elaborates on the previous sentence’s point that McFerrin regards background research as a rewarding activity.

Choice A is incorrect because “by contrast” illogically signals that the information in this sentence contrasts with the previous sentence’s point about McFerrin’s attitude toward background research. Instead, it emphasizes and elaborates on that point. Choice B is incorrect because “likewise” illogically signals that this sentence merely adds a second, similar point to the previous sentence’s point about McFerrin’s attitude toward background research. Instead, it emphasizes and elaborates on that point. Choice C is incorrect because “besides” illogically signals that this sentence provides a separate point in addition to, or apart from, the previous sentence’s point about McFerrin’s attitude toward background research. Instead, it emphasizes and elaborates on that point. 

"}, {"id": "a819d8b6", "domain": "Expression of Ideas", "skill": "Transitions", "difficulty": "M", "type": "mc", "stimulus": "

In 1873, Spanish scientist Santiago Ramón y Cajal observed that brain fibers have distinct boundaries with clear end points, a finding that went against earlier assumptions about the brain. ______blank scientists had assumed that the brain was a continuous web of fused fibers, not a vast network of distinct, individual cells. 

", "stem": "

Which choice completes the text with the most logical transition?

", "choices": [{"id": "A", "text": "

However,

"}, {"id": "B", "text": "

Previously,

"}, {"id": "C", "text": "

As a result,

"}, {"id": "D", "text": "

Likewise,

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. “Previously” logically signals that the fused fiber theory came before Ramón y Cajal’s discovery.

Choice A is incorrect. “However” illogically signals that the fused fiber theory in this sentence contrasts with the information in the previous sentence. While this theory does contrast with Ramón y Cajal’s discovery, the previous sentence concludes by stating that his discovery went against prior assumptions about the brain. The fact that the fused fiber theory was one of those earlier assumptions makes “however” an illogical choice. Choice C is incorrect because “as a result” illogically signals that the fused fiber theory in this sentence was a result of the discovery in the previous sentence. Instead, the fused fiber theory came before Ramón y Cajal’s discovery. Choice D is incorrect because “likewise” illogically signals that the fused fiber theory in this sentence was similar to the discovery in the previous sentence. Instead, the fused fiber theory, which came before Ramón y Cajal’s discovery, was very different from it.

"}, {"id": "84e108cf", "domain": "Expression of Ideas", "skill": "Rhetorical Synthesis", "difficulty": "M", "type": "mc", "stimulus": "

While researching a topic, a student has taken the following notes:

\n", "stem": "

The student wants to explain an advantage of the new platinum catalyst developed by Jianbo Tang and his colleagues. Which choice most effectively uses relevant information from the notes to accomplish this goal?

", "choices": [{"id": "A", "text": "

Researcher Jianbo Tang and his colleagues created a platinum catalyst that combines platinum, a rare and expensive metal, with liquid gallium.

"}, {"id": "B", "text": "

Like other platinum catalysts, the new platinum catalyst requires a particular amount of the metal to be effective. 

"}, {"id": "C", "text": "

Platinum is a rare and expensive metal that is used as a catalyst for chemical reactions; however, platinum catalysts typically require a large amount of platinum to be effective.

"}, {"id": "D", "text": "

While still highly effective, the new platinum catalyst requires far less of the rare and expensive metal than do other platinum catalysts.

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. The sentence explains an advantage of Tang and his colleagues’ platinum catalyst, noting that it requires far less platinum (which is rare and expensive) than other platinum catalysts do.

Choice A is incorrect. The sentence describes the platinum catalyst that Tang and his colleagues created; it doesn’t explain an advantage of their platinum catalyst. Choice B is incorrect. The sentence emphasizes a similarity between the new platinum catalyst and other platinum catalysts; it doesn’t explain an advantage of the new platinum catalyst. Choice C is incorrect. The sentence connects the metal platinum to the functioning of platinum catalysts, noting that large amounts of platinum are typically required for platinum catalysts to be effective; it doesn’t explain an advantage of Tang and his colleagues’ platinum catalyst.

"}, {"id": "326017ce", "domain": "Expression of Ideas", "skill": "Transitions", "difficulty": "M", "type": "mc", "stimulus": "

For years, biologists have experimented with using grime-eating bacteria rather than harsh chemicals to clean artworks, and results have been impressive overall. ______blank these bacterial strains—which can metabolize centuries’ worth of oil, glue, dirt, and other surface impurities without creating harmful byproducts—have proven more effective than traditional chemical cleaning methods.

", "stem": "

Which choice completes the text with the most logical transition?

", "choices": [{"id": "A", "text": "

However,

"}, {"id": "B", "text": "

In many cases,

"}, {"id": "C", "text": "

As a result,

"}, {"id": "D", "text": "

Additionally,

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. The first sentence makes the claim that using grime-eating bacteria has led to “impressive results.” This sentence supports that claim by describing the specific findings of the biologists’ experimentation. The transition “in many cases” fits the context perfectly.

Choice A is incorrect. This choice uses a disagreement transition. But this sentence actually agrees with the previous sentence. Both claim that grime-eating bacteria are better at cleaning artworks than chemicals. Choice C is incorrect. This choice uses a cause-and-effect transition, which doesn’t make sense in context. The fact that the results of the experimentation have been impressive overall doesn’t cause the bacteria to have proven more effective. Choice D is incorrect. This choice uses a transition that indicates the addition of a new idea. But this sentence doesn’t introduce a new idea. Instead, it elaborates on the same idea laid out in the previous sentence by describing the “impressive results” in more detail.

"}, {"id": "c78620ba", "domain": "Expression of Ideas", "skill": "Transitions", "difficulty": "E", "type": "mc", "stimulus": "

In 1968, US Congressman John Conyers introduced a bill to establish a national holiday in honor of Dr. Martin Luther King Jr. The bill didn’t make it to a vote, but Conyers was determined. He teamed up with Shirley Chisholm, the first Black woman to be elected to Congress, and they resubmitted the bill every session for the next fifteen years. ______blank in 1983, the bill passed.

", "stem": "

Which choice completes the text with the most logical transition?

", "choices": [{"id": "A", "text": "

Instead,

"}, {"id": "B", "text": "

Likewise,

"}, {"id": "C", "text": "

Finally,

"}, {"id": "D", "text": "

Additionally,

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. “Finally” logically signals that the bill passing—following many attempts between 1968 and 1983—is the final, concluding event in the sequence described in the previous sentences. 

Choice A is incorrect because “instead” illogically signals that the bill passing is an alternative to one of the events described in the previous sentences. Instead, it is the final event in the sequence. Choice B is incorrect because “likewise” illogically signals that the bill passing is similar to one of the events described in the previous sentences. Instead, it is the final event in the sequence. Choice D is incorrect because “additionally” illogically signals that the bill passing is merely another event described along with the events of the previous sentences. Instead, it is the final, concluding event in the sequence.

"}, {"id": "20733eac", "domain": "Expression of Ideas", "skill": "Transitions", "difficulty": "E", "type": "mc", "stimulus": "

It has long been thought that humans first crossed a land bridge into the Americas approximately 13,000 years ago. ______blank based on radiocarbon dating of samples uncovered in Mexico, a research team recently suggested that humans may have arrived more than 30,000 years ago—much earlier than previously thought.

", "stem": "

Which choice completes the text with the most logical transition?

", "choices": [{"id": "A", "text": "

As a result,

"}, {"id": "B", "text": "

Similarly,

"}, {"id": "C", "text": "

However,

"}, {"id": "D", "text": "

In conclusion, 

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. “However” logically signals that the theory discussed in this sentence—that humans may have arrived in the Americas over 30,000 years ago—contrasts with the previously discussed theory that humans arrived around 13,000 years ago.

Choice A is incorrect because “as a result” illogically signals that the theory in this sentence is the result of the theory discussed in the previous sentence. Instead, this theory contrasts with the previous one. Choice B is incorrect because “similarly” illogically signals that the theory in this sentence is similar to the theory discussed in the previous sentence. Instead, this theory contrasts with the previous one. Choice D is incorrect because “in conclusion” illogically signals that the theory in this sentence concludes or summarizes the discussion of the previous theory. Instead, this theory contrasts with the previous one.

"}, {"id": "ca4ff52d", "domain": "Expression of Ideas", "skill": "Rhetorical Synthesis", "difficulty": "E", "type": "mc", "stimulus": "

While researching a topic, a student has taken the following notes:

\n", "stem": "

The student wants to emphasize a difference between the two muslins. Which choice most effectively uses relevant information from the notes to accomplish this goal?

", "choices": [{"id": "A", "text": "

Dhaka muslin is a handmade fabric with an extremely fine weave, while sheeting muslin is machine made with a coarse weave.

"}, {"id": "B", "text": "

Dhaka muslin and sheeting muslin are two different types of woven cotton fabrics.

"}, {"id": "C", "text": "

Muslins can be used in a variety of ways, from making luxury clothing to upholstering furniture and creating backdrops for theater sets.

"}, {"id": "D", "text": "

Sheeting muslin is machine made, has a coarse weave, and is used for furniture and theater sets.

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. The difference between the two different kinds of muslin is emphasized.

Choice B is incorrect. This choice lists two kinds of muslins, but does not say how they are different from one another. Choice C is incorrect. This choice does not emphasize a difference between the two muslins. Choice D is incorrect. This choice does not emphasize a difference between the two muslins. It only describes sheeting muslin.

"}, {"id": "6c9df5d1", "domain": "Expression of Ideas", "skill": "Rhetorical Synthesis", "difficulty": "H", "type": "mc", "stimulus": "

While researching a topic, a student has taken the following notes:

\n", "stem": "

The student wants to emphasize a difference between the two books. Which choice most effectively uses relevant information from the notes to accomplish this goal?

", "choices": [{"id": "A", "text": "

Although both are powerful works of literature that contributed to new legislation, Equiano’s book is an autobiography, while Sinclair’s is fictional.

"}, {"id": "B", "text": "

They may have written about different topics, but Equiano and Sinclair both influenced readers.

"}, {"id": "C", "text": "

The 1807 Slave Trade Act resulted in part from a book by Equiano, while the 1906 Pure Food and Drug Act resulted in part from a book by Sinclair. 

"}, {"id": "D", "text": "

The Interesting Narrative of the Life of Olaudah Equiano and The Jungle are two works of literature that contributed to new legislation (concerning the slave trade and food safety, respectively). 

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. This choice emphasizes a difference between the two books by using relevant information from the notes to contrast their genres. 

Choice B is incorrect. This choice mentions a difference between the books (their different topics), but it emphasizes a similarity between the books (their influence on readers). Choice C is incorrect. This choice provides information about the books that reflects both a similarity (both resulted in new laws) and a difference (the specific laws that resulted), without emphasizing either. Choice D is incorrect. This choice doesn’t emphasize a difference between the two books. Instead, it emphasizes a similarity.

"}, {"id": "f07570bb", "domain": "Expression of Ideas", "skill": "Transitions", "difficulty": "E", "type": "mc", "stimulus": "

Researchers believe that pieces of hull found off Oregon’s coast are from a Spanish cargo ship that was lost in 1697. Stories passed down among the area’s Confederated Tribes of Siletz Indians support this belief. ______blank Siletz stories describe how blocks of beeswax, an item the ship had been carrying, began washing ashore after the ship was lost. 

", "stem": "

Which choice completes the text with the most logical transition?

", "choices": [{"id": "A", "text": "

For this reason,

"}, {"id": "B", "text": "

For example,

"}, {"id": "C", "text": "

However,

"}, {"id": "D", "text": "

Likewise,

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. “For example” logically signals that the Siletz beeswax stories mentioned in this sentence are examples consistent with the previous claim that Siletz stories support the shipwreck theory.

Choice A is incorrect because “for this reason” illogically signals that the Siletz stories about the beeswax were caused by the previous claim that Siletz stories support the shipwreck theory. Instead, the beeswax stories are examples consistent with the claim. Choice C is incorrect because “however” illogically signals that the Siletz stories about the beeswax contrast with the previous claim that Siletz stories support the shipwreck theory. Instead, the beeswax stories are examples consistent with the claim. Choice D is incorrect because “likewise” illogically signals that the Siletz stories about the beeswax are similar to the previous claim that Siletz stories support the shipwreck theory. Instead, the beeswax stories are examples consistent with the claim.

"}, {"id": "221ecf0f", "domain": "Expression of Ideas", "skill": "Transitions", "difficulty": "M", "type": "mc", "stimulus": "

Alexander Lawrence Posey (1873–1908) varied his focus and tone depending on the genre in which he was writing. In his poetry, he used heartfelt language to evoke the beauty and peacefulness of his natural surroundings; in his journalism, ______blank he employed humor and satire to comment on political issues affecting his Muskogee Creek community.

", "stem": "

Which choice completes the text with the most logical transition?

", "choices": [{"id": "A", "text": "

that is,

"}, {"id": "B", "text": "

granted,

"}, {"id": "C", "text": "

similarly,

"}, {"id": "D", "text": "

by contrast,

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. This sentence compares two examples of Posey’s tone: the “heartfelt language” he used in his poetry versus the “humor and satire” he used in his journalism. We know from these descriptions and from the claim in the previous sentence that the two tones are very different from each other. So the transition “by contrast” fits the context perfectly.

Choice A is incorrect. This choice uses a transition that indicates a restatement of the same idea in other words. But the text isn’t restating the first example here. Instead, it’s offering a second, totally different example. Choice B is incorrect. This choice uses a transition that means “admittedly.” But the text isn’t admitting or conceding anything here. Instead, these two examples work together to support the claim made in the first sentence. Choice C is incorrect. This choice uses a transition that indicates the addition of an agreeing idea. But these two examples are intentionally very different from each other, so “similarly” doesn’t make sense here.

"}, {"id": "296801d2", "domain": "Expression of Ideas", "skill": "Rhetorical Synthesis", "difficulty": "E", "type": "mc", "stimulus": "

While researching a topic, a student has taken the following notes:

\n", "stem": "

The student wants to specify who may have first populated the Azores, according to the 2015 study. Which choice most effectively uses relevant information from the notes to accomplish this goal?

", "choices": [{"id": "A", "text": "

Historians have long believed that the first humans to populate the Azores, a group of islands about 870 miles off the coast of Portugal, arrived in the fifteenth century.

"}, {"id": "B", "text": "

Portuguese mariners may not have been the first humans to populate the Azores.

"}, {"id": "C", "text": "

In their 2015 study, the researchers found a genetic connection between house mice in the Azores and those in Scandinavia.

"}, {"id": "D", "text": "

According to a 2015 study, the first humans to populate the Azores may have been Vikings from Scandinavia, not mariners from Portugal as previously believed.

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. This choice effectively specifies who may have first populated the Azores, according to the 2015 study: the Vikings. 

Choice A is incorrect. This choice doesn’t effectively specify who may have first populated the Azores, according to the 2015 study. It only mentions the historical belief that the Portuguese were first. The 2015 study drew a different conclusion. Choice B is incorrect. This choice casts doubt on the Portuguese claim but doesn’t name the group of people who may have arrived before the Portuguese. Choice C is incorrect. This choice mentions the evidence that the researchers found but not the conclusion they drew from it. It doesn’t name the possible group of people who may have arrived before the Portuguese.

"}, {"id": "92fe0ed7", "domain": "Expression of Ideas", "skill": "Transitions", "difficulty": "E", "type": "mc", "stimulus": "

Geoscientists have long considered Hawaii’s Mauna Loa volcano to be Earth’s largest shield volcano by volume, measuring approximately 74,000 cubic kilometers. ______blank according to a 2020 study by local geoscientist Michael Garcia, Hawaii’s P\u016bh\u0101honu shield volcano is significantly larger, boasting a volume of about 148,000 cubic kilometers.

", "stem": "

Which choice completes the text with the most logical transition?

", "choices": [{"id": "A", "text": "

Secondly,

"}, {"id": "B", "text": "

Consequently,

"}, {"id": "C", "text": "

Moreover,

"}, {"id": "D", "text": "

However,

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. “However” logically signals that this sentence, which indicates that the P\u016bh\u0101honu volcano may be larger than the Mauna Loa volcano, offers a contrast to or refutation of the previous assumption that Mauna Loa is the largest shield volcano.

Choice A is incorrect because “secondly” illogically signals that this sentence merely offers an additional or secondary point concerning the previous assumption that Mauna Loa is the largest shield volcano. Instead, the sentence offers a contrast to or refutation of that assumption. Choice B is incorrect because “consequently” illogically signals that this sentence offers a result or consequence of the previous assumption that Mauna Loa is the largest shield volcano. Instead, the sentence offers a contrast to or refutation of that assumption. Choice C is incorrect because “moreover” illogically signals that this sentence merely adds to the previous assumption that Mauna Loa is the largest shield volcano. Instead, the sentence offers a contrast to or refutation of that assumption.

"}, {"id": "97e2e364", "domain": "Expression of Ideas", "skill": "Transitions", "difficulty": "M", "type": "mc", "stimulus": "

Okot p’Bitek’s poem Song of Lawino (1966) explores postcolonial Ugandan life through the eyes of a woman living in a rural village. With its vibrant imagery, bitingly satiric tone, and dexterous use of traditional Acholi song and phraseology, the poem inspired a generation of East African writers. ______blank those who adopted its style are often referred to as Okot School poets.  

", "stem": "

Which choice completes the text with the most logical transition?

", "choices": [{"id": "A", "text": "

Nevertheless,

"}, {"id": "B", "text": "

Fittingly,

"}, {"id": "C", "text": "

By comparison, 

"}, {"id": "D", "text": "

Instead,

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. “Fittingly” is a transition that means “appropriately” or “suitably,” and it is appropriate that writers who adopted their style from Okot p’Bitek would be known as the Okot School poets.

Choice A is incorrect. This choice uses a disagreement transition. But this sentence is not disagreeing with anything—rather, it’s discussing how it makes sense for those writers who adopted Okot’s style to be known as the Okot School poets. Choice C is incorrect. This choice uses a transition that compares two ideas. But this sentence is not comparing the Okot School poets and their style to Okot’s style. Choice D is incorrect. This choice uses a disagreement transition. But this sentence is not disagreeing with anything—rather, it’s discussing how it makes sense for those writers who adopted Okot’s style to be known as the Okot School poets.

"}, {"id": "01c8c433", "domain": "Expression of Ideas", "skill": "Transitions", "difficulty": "E", "type": "mc", "stimulus": "

Before the 1847 introduction of the US postage stamp, the cost of postage was usually paid by the recipient of a letter rather than the sender, and recipients were not always able or willing to pay promptly. ______blank collecting this fee could be slow and arduous, and heaps of unpaid-for, undeliverable mail piled up in post offices.

", "stem": "

Which choice completes the text with the most logical transition?

", "choices": [{"id": "A", "text": "

Regardless,

"}, {"id": "B", "text": "

On the contrary,

"}, {"id": "C", "text": "

Consequently,

"}, {"id": "D", "text": "

For example,

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. “Consequently” logically signals that the postal problems described in this sentence (slow fee collection, heaps of undeliverable mail) were a consequence of the fee system described in the previous sentence.

Choice A is incorrect because “regardless” illogically signals that the postal problems described in this sentence occurred despite the fee system described in the previous sentence. Instead, they were a consequence of that system. Choice B is incorrect because “on the contrary” illogically signals that the postal problems described in this sentence contrast with the fee system described in the previous sentence. Instead, they were a consequence of that system. Choice D is incorrect because “for example” illogically signals that the postal problems described in this sentence are an example of the fee system described in the previous sentence. Instead, they were a consequence of that system.

"}, {"id": "883493d5", "domain": "Expression of Ideas", "skill": "Rhetorical Synthesis", "difficulty": "M", "type": "mc", "stimulus": "

While researching a topic, a student has taken the following notes:

\n", "stem": "

The student wants to describe the distinctive style of Houser’s sculptures. Which choice most effectively uses relevant information from the notes to accomplish this goal?

", "choices": [{"id": "A", "text": "

A sculptor, illustrator, and painter, Houser developed a distinctive style for portraying Native American figures.

"}, {"id": "B", "text": "

Houser’s sculptures employ abstract, modernist forms to depict Native American figures.

"}, {"id": "C", "text": "

Many other artists have been influenced by the style of Houser’s sculptures.

"}, {"id": "D", "text": "

The sculpture Sacred Rain Arrow is a well-known example of Houser’s style.

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. The sentence describes the distinctive style of Houser’s sculptures, explaining that the sculptures use abstract, modernist forms to depict Native American figures.

Choice A is incorrect. While the sentence indicates that Houser developed a distinctive style for portraying Native American figures, it doesn’t describe this style. Choice C is incorrect. While the sentence states that other artists have been influenced by the style of Houser’s sculptures, it doesn’t describe this style. Choice D is incorrect. While the sentence mentions the name of a sculpture that’s a well-known example of Houser’s style, it doesn’t describe the sculpture’s style.

"}, {"id": "db8fe023", "domain": "Expression of Ideas", "skill": "Transitions", "difficulty": "E", "type": "mc", "stimulus": "

A potter choosing which type of clay to use for a piece considers two key factors: the desired look of the piece and its intended use. ______blank earthenware clay is often used for decorative pieces because of its rustic look. This type of clay is not often used in industrial settings, though, because it is less durable than other clays.

", "stem": "

Which choice completes the text with the most logical transition?

", "choices": [{"id": "A", "text": "

In other words,

"}, {"id": "B", "text": "

Regardless,

"}, {"id": "C", "text": "

In conclusion,

"}, {"id": "D", "text": "

For example,

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. The previous sentence tells us that potters think about the look and use of a piece when selecting clay. This sentence provides a specific example of a type of clay selected for its appearance, so the transition \"for example\" fits perfectly.

Choice A is incorrect. This choice uses a transition that indicates a restatement of the same idea. But this sentence does more than just restate the previous idea. Instead, it provides a more specific example of the idea presented in the first sentence. Choice B is incorrect. This choice uses a disagreement transition. But this sentence actually agrees with the previous sentence. Both sentences suggest that desired look plays a role in the selection of clay types for pottery pieces. Choice C is incorrect. This choice uses a concluding transition. But this sentence doesn’t sum up the previous sentence. Instead, it gives a specific example of the idea presented in the previous sentence.

"}, {"id": "04ad68ca", "domain": "Expression of Ideas", "skill": "Transitions", "difficulty": "E", "type": "mc", "stimulus": "

In Gothic architecture, flying buttresses are large arches that help support a building’s exterior walls. Before the Gothic era, cathedrals’ heavy ceilings had to be supported by thick, short walls, but the invention of flying buttresses eliminated this need. ______blank Gothic cathedrals could be built with thinner, higher walls.

", "stem": "

Which choice completes the text with the most logical transition?

", "choices": [{"id": "A", "text": "

Similarly,

"}, {"id": "B", "text": "

For instance,

"}, {"id": "C", "text": "

Nevertheless,

"}, {"id": "D", "text": "

As a result,

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. “As a result” logically signals that the thinner, higher walls in this sentence were a result of the invention of flying buttresses in the previous sentence.

Choice A is incorrect because “similarly” illogically signals that the thinner, higher walls in this sentence are similar to the invention of flying buttresses in the previous sentence. Instead, the walls were a result of that invention. Choice B is incorrect because “for instance” illogically signals that the thinner, higher walls in this sentence are an example supporting the statement about the invention of flying buttresses in the previous sentence. Instead, the walls were a result of that invention. Choice C is incorrect because “nevertheless” illogically signals that the thinner, higher walls in this sentence occurred despite the invention of flying buttresses in the previous sentence. Instead, the walls were a result of that invention.

"}, {"id": "fc2bcc79", "domain": "Expression of Ideas", "skill": "Transitions", "difficulty": "E", "type": "mc", "stimulus": "

Tyrian purple was a highly prized dye among the Phoenicians (an ancient civilization located in present-day Lebanon). The Phoenicians were famous for using this natural dye to color their clothes a distinctive purple. ______blank the name “Phoenicia” itself, some historians claim, may have originally meant “land of purple.”

", "stem": "

Which choice completes the text with the most logical transition?

", "choices": [{"id": "A", "text": "

In fact,

"}, {"id": "B", "text": "

Regardless,

"}, {"id": "C", "text": "

Lastly,

"}, {"id": "D", "text": "

On the contrary,

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. “In fact” logically signals that the claim in this sentence—Phoenicia being named after the color purple—emphasizes and supports the previous claim that Phoenicians were famous for using purple dye.

Choice B is incorrect because “regardless” illogically signals that the claim about Phoenicia’s name contrasts with the previous claim that Phoenicians were famous for using purple dye. Instead, the naming emphasizes and supports this claim. Choice C is incorrect because “lastly” illogically signals that the claim about Phoenicia’s name is the final step in a process or sequence. Instead, the naming emphasizes and supports the previous claim that Phoenicians were famous for using purple dye. Choice D is incorrect because “on the contrary” illogically signals that the claim about Phoenicia’s name directly opposes the previous claim that Phoenicians were famous for using purple dye. Instead, the naming emphasizes and supports this claim.

"}, {"id": "57bcd0d6", "domain": "Expression of Ideas", "skill": "Transitions", "difficulty": "E", "type": "mc", "stimulus": "

Etched into Peru’s Nazca Desert are line drawings so large that they can only be fully seen from high above. Archaeologists have known of the lines since the 1920s, when a researcher spotted some from a nearby foothill, and they have been studying the markings ever since. ______blank archaeologists’ efforts are aided by drones that capture high-resolution aerial photographs of the lines.

", "stem": "

Which choice completes the text with the most logical transition?

", "choices": [{"id": "A", "text": "

Currently,

"}, {"id": "B", "text": "

In comparison,

"}, {"id": "C", "text": "

Still,

"}, {"id": "D", "text": "

However,

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. “Currently” logically signals that the archaeologists’ use of drones (a current technology) to photograph the lines is the present-day continuation of the ongoing archaeological research described in the previous sentence.

Choice B is incorrect because “in comparison” illogically signals that the action described in this sentence offers a comparison to the ongoing archaeological research described in the previous sentence. Instead, the use of drones is the present-day continuation of that research. Choice C is incorrect because “still” illogically signals that the action described in this sentence occurs despite the ongoing archaeological research described in the previous sentence. Instead, the use of drones is the present-day continuation of that research. Choice D is incorrect because “however” illogically signals that the action described in this sentence occurs either despite or in contrast to the ongoing archaeological research described in the previous sentence. Instead, the use of drones is the present-day continuation of that research.

"}, {"id": "11df9b99", "domain": "Expression of Ideas", "skill": "Transitions", "difficulty": "M", "type": "mc", "stimulus": "

Because an achiral molecule is symmetrical, flipping it yields a structurally identical molecule. A flipped chiral molecule, ______blank can be compared to a glove that has been turned inside out: it produces a structurally inverted molecule rather than an identical one.

", "stem": "

Which choice completes the text with the most logical transition?

", "choices": [{"id": "A", "text": "

in other words,

"}, {"id": "B", "text": "

by contrast,

"}, {"id": "C", "text": "

for example,

"}, {"id": "D", "text": "

similarly,

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. This sentence compares a chiral molecule to an achiral one. It discusses how when a chiral molecule is flipped, it results in something very different than when an achiral molecule is flipped. So the transition \"by contrast\" fits the context perfectly.

Choice A is incorrect. This choice uses a transition that indicates a restatement of the same idea in different words. But this sentence doesn’t restate the same idea as the previous sentence. Instead, it makes a new point about a different type of molecule (chiral instead of achiral). Choice C is incorrect. This choice uses a transition that introduces an example, which doesn’t make sense here. The second sentence isn’t an example of the first sentence’s claim about achiral molecules: it actually introduces an entirely different idea that focuses on chiral molecules. Choice D is incorrect. This choice uses a transition that indicates the addition of an agreeing idea. But this sentence shows a contrast with the first sentence—namely, that a chiral molecule acts very differently from an achiral molecule when flipped.

"}, {"id": "2bf05ae9", "domain": "Expression of Ideas", "skill": "Rhetorical Synthesis", "difficulty": "M", "type": "mc", "stimulus": "

While researching a topic, a student has taken the following notes:

\n", "stem": "

The student wants to emphasize the uniqueness of Taylor’s accomplishment. Which choice most effectively uses relevant information from the notes to accomplish this goal?

", "choices": [{"id": "A", "text": "

Taylor fled to St. Simons Island, which was then occupied by the Union army, for whom she began working.

"}, {"id": "B", "text": "

After escaping slavery, Taylor began working for an all-Black army regiment as a nurse and teacher.

"}, {"id": "C", "text": "

The book Taylor wrote about the time she spent with the regiment is still available to readers in print and online.

"}, {"id": "D", "text": "

Taylor was the only Black woman to publish a Civil War memoir.

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. By indicating that Taylor’s book was the only Civil War memoir published by a Black woman, this sentence emphasizes the uniqueness, or one-of-a-kind nature, of Taylor’s accomplishment.

Choice A is incorrect. While the sentence describes some of Taylor’s accomplishments, it doesn’t emphasize the uniqueness of them. Choice B is incorrect. While the sentence describes some of Taylor’s accomplishments, it doesn’t emphasize that they were unique. Choice C is incorrect. While the sentence provides information about Taylor’s book, it doesn’t emphasize what made the book unique.

"}, {"id": "827afb27", "domain": "Expression of Ideas", "skill": "Transitions", "difficulty": "E", "type": "mc", "stimulus": "

Most conifers (trees belonging to the phylum Coniferophyta) are evergreen. That is, they keep their green leaves or needles year-round. However, not all conifer species are evergreen. Larch trees, ______blank lose their needles every fall.

", "stem": "

Which choice completes the text with the most logical transition?

", "choices": [{"id": "A", "text": "

for instance,

"}, {"id": "B", "text": "

nevertheless,

"}, {"id": "C", "text": "

meanwhile,

"}, {"id": "D", "text": "

in addition,

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. “For instance” logically signals that the information in this sentence—that larch trees lose their needles every fall—is an example supporting the claim in the previous sentence (that not all conifer species keep their leaves or needles year-round). 

Choice B is incorrect because “nevertheless” illogically signals that the information in this sentence is true in spite of the claim about conifer species in the previous sentence. Instead, it’s an example supporting that claim. Choice C is incorrect because “meanwhile” illogically signals that the information in this sentence is separate from (while occurring simultaneously with) the claim about conifer species in the previous sentence. Instead, it’s an example supporting that claim. Choice D is incorrect because “in addition” illogically signals that the information in this sentence is merely an additional fact related to the claim about conifer species in the previous sentence. Instead, it’s an example supporting that claim.

"}, {"id": "8fe4f4ab", "domain": "Expression of Ideas", "skill": "Rhetorical Synthesis", "difficulty": "H", "type": "mc", "stimulus": "

While researching a topic, a student has taken the following notes:

\n", "stem": "

The student wants to explain how the House of Wisdom preserved the world’s knowledge. Which choice most effectively uses relevant information from the notes to accomplish this goal?

", "choices": [{"id": "A", "text": "

The House of Wisdom was known for bringing together knowledge from around the world, including from Greece, India, and China.

"}, {"id": "B", "text": "

Founded in Iraq in the eighth century, the House of Wisdom employed many scholars as translators.

"}, {"id": "C", "text": "

Writings from the Greek philosopher Aristotle and the Indian mathematician Aryabhata were preserved at the House of Wisdom.

"}, {"id": "D", "text": "

The House of Wisdom collected writings from different countries and created paper versions in Arabic to be studied and shared.

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. The sentence explains how the House of Wisdom preserved the world’s knowledge, noting that the library collected, translated, and printed writings from different countries.   

Choice A is incorrect. While the sentence indicates that the House of Wisdom was known for bringing together knowledge from around the world, it doesn’t explain how the library preserved this knowledge. Choice B is incorrect. The sentence makes a generalization about the scholars who were employed by the House of Wisdom; it doesn’t explain how the library preserved the world’s knowledge. Choice C is incorrect. The sentence identifies two authors whose writings were preserved at the House of Wisdom; it doesn’t explain how the library preserved the world’s knowledge.

"}, {"id": "bb275f0d", "domain": "Expression of Ideas", "skill": "Rhetorical Synthesis", "difficulty": "M", "type": "mc", "stimulus": "

While researching a topic, a student has taken the following notes:

\n", "stem": "

The student wants to make and support a generalization about honeybees. Which choice most effectively uses relevant information from the notes to accomplish this goal?

", "choices": [{"id": "A", "text": "

Cities tend to have a wider range of flowering vegetation than do rural areas, which are often dominated by monoculture crops.

"}, {"id": "B", "text": "

In urban areas, over 60 percent of honeybees, on average, will survive a harsh winter, whereas in rural areas, only 40 percent will. 

"}, {"id": "C", "text": "

The strength of honeybees’ immune systems depends on what the bees eat, and a varied diet is more available to bees in an urban area than to those in a rural area.

"}, {"id": "D", "text": "

Honeybees are more likely to thrive in cities than in rural areas because the varied diet available in urban areas strengthens the bees’ immune systems.

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer because the sentence makes and supports a generalization about honeybees. It claims that honeybees living in urban areas are more likely to thrive than rural bees, and it supports the claim with information about the effect of a varied diet on urban bees’ immune systems. 

Choice A is incorrect. While the sentence makes a generalization, it doesn’t mention honeybees. Choice B is incorrect. While the sentence provides data about honeybee survival, it doesn’t make a generalization about honeybees based on this information. Choice C is incorrect. While the sentence makes a generalization about honeybees’ diets and immune systems, it doesn’t provide adequate support for this generalization.

"}, {"id": "30438650", "domain": "Expression of Ideas", "skill": "Transitions", "difficulty": "M", "type": "mc", "stimulus": "

Jhumpa Lahiri’s story collection Interpreter of Maladies features multiple stories about romantic relationships. In “This Blessed House,” newlyweds argue over whether to replace items left by the previous owners of their new home. ______blank in “A Temporary Matter,” a husband and wife attempt to rekindle their relationship during a four-night blackout.

", "stem": "

Which choice completes the text with the most logical transition?

", "choices": [{"id": "A", "text": "

Granted,

"}, {"id": "B", "text": "

For example,

"}, {"id": "C", "text": "

Likewise,

"}, {"id": "D", "text": "

Hence,

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. \"Likewise\" is a transition that indicates the addition of a new but related idea. In this sentence, the author is providing another similar example to that discussed in the previous sentence. Therefore, \"likewise\" works best in this context.

Choice A is incorrect. This choice uses a transition that means \"admittedly.\" But the text isn’t admitting or conceding anything here. Instead, these two examples work together to support the claim made in the first sentence. Choice B is incorrect. This choice uses an exemplification transition, which doesn’t make sense here. The second story is not an example of the story in the previous sentence—it’s another, similar story. And while both stories exemplify the first sentence in the text, the transition we’re looking for isn’t actually connected to that sentence. Choice D is incorrect. This choice uses a cause-and-effect transition, which doesn’t make sense here. The first story didn’t result in the events of the second story.

"}, {"id": "a773f069", "domain": "Expression of Ideas", "skill": "Transitions", "difficulty": "E", "type": "mc", "stimulus": "

Small, flat structures called spatulae are found at the tips of the hairs on a spider’s leg. These spatulae temporarily bond with the atoms of whatever they touch. ______blank spiders are able to cling to and climb almost any surface.

", "stem": "

Which choice completes the text with the most logical transition?

", "choices": [{"id": "A", "text": "

For instance,

"}, {"id": "B", "text": "

However,

"}, {"id": "C", "text": "

Similarly,

"}, {"id": "D", "text": "

As a result,

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. “As a result” logically signals that the claim in this sentence—that spiders can cling to and climb almost any surface—is because of the previous information about the bonding properties of spiders’ spatulae.

Choice A is incorrect because “for instance” illogically signals that the claim in this sentence exemplifies the information in the previous sentences. Instead, the claim is because of the previous information about the bonding properties of spiders’ spatulae. Choice B is incorrect because “however” illogically signals that the claim in this sentence contrasts with the information in the previous sentences. Instead, the claim is because of the previous information about the bonding properties of spiders’ spatulae. Choice C is incorrect because “similarly” illogically signals that the claim in this sentence is similar to, but separate from, the information in the previous sentences. Instead, the claim is because of the previous information about the bonding properties of spiders’ spatulae.

"}, {"id": "6249b173", "domain": "Expression of Ideas", "skill": "Rhetorical Synthesis", "difficulty": "M", "type": "mc", "stimulus": "

While researching a topic, a student has taken the following notes:

\n", "stem": "

The student wants to present the study’s results. Which choice most effectively uses relevant information from the notes to accomplish this goal?

", "choices": [{"id": "A", "text": "

Macaques in the study called out to and gestured more frequently at humans holding food than at empty-handed humans.

"}, {"id": "B", "text": "

In 2018, researchers who had observed macaques in India’s Bandipur National Park calling out to and gesturing at humans designed a study.

"}, {"id": "C", "text": "

The researchers hoped to find out if the macaques were intentionally communicating to try to persuade humans to share their food.

"}, {"id": "D", "text": "

The researchers studied how macaques behaved around both humans holding food and empty-handed humans.

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. This choice presents the study’s results from the last two bullet points.

Choice B is incorrect. This choice describes the background and motivation of the study but not the outcome or findings. Choice C is incorrect. This choice describes the research question or hypothesis of the study but not the evidence or conclusion. Choice D is incorrect. This choice describes the method or design of the study but not the actual results.

"}, {"id": "1b219d14", "domain": "Expression of Ideas", "skill": "Transitions", "difficulty": "E", "type": "mc", "stimulus": "

As a young historian in the 1950s, Alixa Naff began interviewing fellow Arab American immigrants about their experiences straddling two cultures. Over the next few decades, Naff conducted more than 450 such interviews, also known as oral histories. ______blank she collected photographs and other artifacts that represented her subjects’ experiences.

", "stem": "

Which choice completes the text with the most logical transition?

", "choices": [{"id": "A", "text": "

In other words,

"}, {"id": "B", "text": "

On the contrary,

"}, {"id": "C", "text": "

In addition,

"}, {"id": "D", "text": "

Today,

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. \"In addition\" logically signals that Naff’s artifact collecting was separate from, and in addition to, her interviewing.

Choice A is incorrect because \"in other words\" illogically signals that the information about Naff’s artifact collecting restates the previous information about her interviewing. Instead, Naff collected artifacts in addition to conducting interviews. Choice B is incorrect because \"on the contrary\" illogically signals that Naff’s artifact collecting was contrary to her interviewing. Instead, Naff collected artifacts in addition to conducting interviews. Choice D is incorrect because \"today\" illogically signals that Naff’s artifact collecting is occurring in the present day. Instead, this activity occurred in the past, as indicated by the past tense verb \"collected.\"

"}, {"id": "a3204ab0", "domain": "Expression of Ideas", "skill": "Rhetorical Synthesis", "difficulty": "E", "type": "mc", "stimulus": "

While researching a topic, a student has taken the following notes:

\n", "stem": "

The student wants to specify the number of gray wolves in Yellowstone. Which choice most effectively uses relevant information from the notes to accomplish this goal?

", "choices": [{"id": "A", "text": "

Gray wolves were reintroduced into Yellowstone, a national park in the northwest United States, in 1995.

"}, {"id": "B", "text": "

As of 1995, there were gray wolves living in Yellowstone, a national park in the northwest United States.

"}, {"id": "C", "text": "

The carrying capacity of an environment, such as Yellowstone, describes the maximum number of species that the environment can sustain over time.

"}, {"id": "D", "text": "

Yellowstone is a national park that has roughly 100 gray wolves living in it.

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. This choice uses relevant information from the third bullet point to state the approximate number of gray wolves in Yellowstone.

Choice A is incorrect. This choice mentions the year gray wolves in Yellowstone were reintroduced but not how many there are currently. Choice B is incorrect. This choice mentions the year gray wolves in Yellowstone were reintroduced but not how many there are currently. Choice C is incorrect. This choice defines the term carrying capacity but doesn’t connect it to the specific number of gray wolves currently living in Yellowstone.

"}, {"id": "fd24f48f", "domain": "Expression of Ideas", "skill": "Transitions", "difficulty": "M", "type": "mc", "stimulus": "

Before California’s 1911 election to approve a proposition granting women the right to vote, activists across the state sold tea to promote the cause of suffrage. In San Francisco, the Woman’s Suffrage Party sold Equality Tea at local fairs. ______blank in Los Angeles, activist Nancy Tuttle Craig, who ran one of California’s largest grocery store firms, distributed Votes for Women Tea.

", "stem": "

Which choice completes the text with the most logical transition?

", "choices": [{"id": "A", "text": "

For example,

"}, {"id": "B", "text": "

To conclude,

"}, {"id": "C", "text": "

Similarly,

"}, {"id": "D", "text": "

In other words,

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. “Similarly” logically signals that the activity described in this sentence (Nancy Tuttle Craig distributing Votes for Women Tea in her Los Angeles grocery stores) is like the activity described in the previous sentence (the Woman’s Suffrage Party selling Equality Tea at fairs in San Francisco). Together, the two examples support the preceding claim that “activists across the state sold tea to promote the cause of suffrage.”

Choice A is incorrect because “for example” illogically signals that the activity described in this sentence exemplifies the activity described in the previous sentence. Instead, the two activities are similar, and both support the preceding claim about selling tea to promote women’s right to vote. Choice B is incorrect because “to conclude” illogically signals that the activity described in this sentence concludes or summarizes the information in the previous sentences. Instead, the activity is similar to the one described in the previous sentence, and both support the preceding claim about selling tea to promote women’s right to vote. Choice D is incorrect because “in other words” illogically signals that the activity described in this sentence paraphrases the activity described in the previous sentence. Instead, the two activities are similar, and both support the preceding claim about selling tea to promote women’s right to vote.

"}, {"id": "1a8126aa", "domain": "Expression of Ideas", "skill": "Transitions", "difficulty": "M", "type": "mc", "stimulus": "

In 2019, researcher Patricia Jurado Gonzalez and food historian Nawal Nasrallah prepared a stew from a 4,000-year-old recipe found on a Mesopotamian clay tablet. When they tasted the dish, known as pašr\u016btum (“unwinding”), they found that it had a mild taste and inspired a sense of calm. ______blank the researchers, knowing that dishes were sometimes named after their intended effects, theorized that the dish’s name, “unwinding,” referred to its function: to help ancient diners relax.

", "stem": "

Which choice completes the text with the most logical transition?

", "choices": [{"id": "A", "text": "

Therefore,

"}, {"id": "B", "text": "

Alternately,

"}, {"id": "C", "text": "

Nevertheless,

"}, {"id": "D", "text": "

Likewise,

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. \"Therefore\" logically signals that the action described in this sentence—the researchers theorizing that the dish was named for its effect on diners—is a result or consequence of the previous observation that the dish had a calming effect.

Choice B is incorrect because \"alternately\" illogically signals that the action described in this sentence offers an alternative or contrast to the previous observation that the dish had a calming effect. Instead, the action is a result or consequence of that observation. Choice C is incorrect because \"nevertheless\" illogically signals that the action described in this sentence occurs despite the previous observation that the dish had a calming effect. Instead, the action is a result or consequence of that observation. Choice D is incorrect because \"likewise\" illogically signals that this sentence merely adds a second, similar detail to the previous observation that the dish had a calming effect. Instead, this sentence describes an action that is a result or consequence of that observation.

"}, {"id": "63a4fa29", "domain": "Expression of Ideas", "skill": "Rhetorical Synthesis", "difficulty": "M", "type": "mc", "stimulus": "

While researching a topic, a student has taken the following notes:

\n", "stem": "

The student wants to present the Quanhucun study and its conclusions. Which choice most effectively uses relevant information from the notes to accomplish this goal?

", "choices": [{"id": "A", "text": "

As part of a 2013 study of cat domestication, a chemical analysis was conducted on cat bone fragments found in Quanhucun, China.

"}, {"id": "B", "text": "

A 2013 analysis of cat bone fragments found in Quanhucun, China, suggests that cats there may have been domesticated 5,300 years ago. 

"}, {"id": "C", "text": "

In 2013, archaeologists studied what cats in Quanhucun, China, had eaten more than 5,000 years ago.

"}, {"id": "D", "text": "

Cat bone fragments estimated to be 5,300 years old were found in Quanhucun, China, in 2013.

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. The sentence presents the study, describing it as a 2013 analysis of Quanhucun cat bone fragments, and its conclusions, indicating what the analysis suggests about cat domestication in Quanhucun.   

Choice A is incorrect because the sentence focuses on the study’s methodology; it doesn’t present conclusions from the study. Choice C is incorrect. While the sentence provides a general overview of the study, it doesn’t present conclusions from the study. Choice D is incorrect. The sentence describes a finding from the study; it doesn’t present conclusions from the study.

"}, {"id": "0d3ebdce", "domain": "Expression of Ideas", "skill": "Transitions", "difficulty": "E", "type": "mc", "stimulus": "

Neuroscientist Karen Konkoly wanted to determine whether individuals can understand and respond to questions during REM sleep. She first taught volunteers eye movements they would use to respond to basic math problems while asleep (a single left-right eye movement indicated the number one). ______blank she attached electrodes to the volunteers’ faces to record their eye movements during sleep.

", "stem": "

Which choice completes the text with the most logical transition?

", "choices": [{"id": "A", "text": "

Specifically,

"}, {"id": "B", "text": "

Next,

"}, {"id": "C", "text": "

For instance,

"}, {"id": "D", "text": "

In sum, 

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. “Next” logically signals that the action described in this sentence—Konkoly recording participants’ eye movements—is the next step in Konkoly’s experiment.

Choice A is incorrect because “specifically” illogically signals that this sentence specifies or elaborates on an aspect of the action described in the previous sentence. Instead, it describes the next step in Konkoly’s experiment. Choice C is incorrect because “for instance” illogically signals that the action described in this sentence is an example of the action described in the previous sentence. Instead, it is the next step in Konkoly’s experiment. Choice D is incorrect because “in sum” illogically signals that this sentence summarizes or concludes the action described in the previous sentence. Instead, it describes the next step in Konkoly’s experiment.

"}, {"id": "00460c13", "domain": "Expression of Ideas", "skill": "Rhetorical Synthesis", "difficulty": "E", "type": "mc", "stimulus": "

While researching a topic, a student has taken the following notes:

\n", "stem": "

The student wants to identify the setting of Cather’s novel My Ántonia. Which choice most effectively uses relevant information from the notes to accomplish this goal?

", "choices": [{"id": "A", "text": "

My Ántonia is set in Nebraska, where Cather grew up.

"}, {"id": "B", "text": "

Cather, author of My Ántonia, described the experiences of immigrants in her novels. 

"}, {"id": "C", "text": "

Among Cather’s best-known novels are O Pioneers! (1913) and My Ántonia (1918).

"}, {"id": "D", "text": "

Cather attended the University of Nebraska-Lincoln and set some of her novels in Nebraska.

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. This choice directly identifies the setting of Cather’s novel My Ántonia as Nebraska.

Choice B is incorrect. This choice mentions that Cather wrote about immigrants, but it doesn’t indicate where they lived. Choice C is incorrect. This choice mentions that My Ántonia is one of Cather’s best-known novels but doesn’t state where it takes place. Choice D is incorrect. This choice mentions that some of Cather’s novels are set in Nebraska, but it doesn’t specify which ones, so we can’t be certain that My Ántonia is one of them. It also includes irrelevant information about Cather’s education.

"}, {"id": "dd11e5ab", "domain": "Expression of Ideas", "skill": "Rhetorical Synthesis", "difficulty": "M", "type": "mc", "stimulus": "

While researching a topic, a student has taken the following notes:

\n", "stem": "

The student wants to emphasize the thoroughness of Ida Tarbell’s investigation of the Standard Oil Company. Which choice most effectively uses relevant information from the notes to accomplish this goal?

", "choices": [{"id": "A", "text": "

Ida Tarbell not only interviewed Standard Oil executives, oil industry workers, and public officials but also examined thousands of pages of the company’s internal communications.

"}, {"id": "B", "text": "

Ida Tarbell, who investigated the Standard Oil Company, was a muckraker (a journalist who sought to expose corruption in US institutions during the Progressive Era, 1897–1920).

"}, {"id": "C", "text": "

As part of her investigation of the Standard Oil Company, muckraker Ida Tarbell conducted interviews. 

"}, {"id": "D", "text": "

Published in 1904, muckraker Ida Tarbell’s book The History of the Standard Oil Company exposed the company’s unfair business practices. 

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. It describes Tarbell’s investigation and the lengths she went to complete it.

Choice B is incorrect. This choice doesn’t describe how thorough Tarbell was. Instead, it gives a biographical sketch. Choice C is incorrect. This choice doesn’t describe how thorough Tarbell was. Tarbell didn’t only conduct interviews—she also “examined thousands of pages of the company’s internal communications.” Choice D is incorrect. This choice doesn’t describe how thorough Tarbell was. It describes her book but doesn’t include anything about her investigation.

"}, {"id": "74149724", "domain": "Expression of Ideas", "skill": "Rhetorical Synthesis", "difficulty": "M", "type": "mc", "stimulus": "

While researching a topic, a student has taken the following notes:

\n", "stem": "

The student wants to specify the reason the Mayflower Compact was created. Which choice most effectively uses relevant information from the notes to accomplish this goal?

", "choices": [{"id": "A", "text": "

Stating that its signatories wanted to “plant the first colony in the northern parts of Virginia,” the Mayflower Compact was a legal agreement among the pilgrims that immigrated to Plymouth Colony.

"}, {"id": "B", "text": "

Created in 1620, the Mayflower Compact states that the pilgrims wanted to “plant the first colony in the northern parts of Virginia.”

"}, {"id": "C", "text": "

The Mayflower Compact was created to establish a common government among the pilgrims that immigrated to Plymouth Colony.

"}, {"id": "D", "text": "

The Mayflower Compact had 41 signatories, including John Carver, the first governor of Plymouth Colony.

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. The sentence specifies the reason the Mayflower Compact was created, noting that it was created to establish a common government among the pilgrims that immigrated to Plymouth Colony.

Choice A is incorrect. While the sentence provides background information about the Mayflower Compact and notes the signatories’ goal for the colony, it doesn’t specify why the compact was created. Choice B is incorrect. While the sentence provides background information about the Mayflower Compact and notes the signatories’ goal for the colony, it doesn’t specify why the compact was created. Choice D is incorrect. The sentence specifies the number of pilgrims that signed the Mayflower Compact; it doesn’t specify the reason the compact was created.

"}, {"id": "f1d8550e", "domain": "Expression of Ideas", "skill": "Rhetorical Synthesis", "difficulty": "M", "type": "mc", "stimulus": "

While researching a topic, a student has taken the following notes:

\n", "stem": "

The student wants to emphasize the order in which two of Jordan Bennett’s exhibitions were held. Which choice most effectively uses relevant information from the notes to accomplish this goal?  

", "choices": [{"id": "A", "text": "

Jordan Bennett’s 2017 exhibition Wije’wi was followed a year later by his exhibition Ketu’elmita’jik.

"}, {"id": "B", "text": "

Jordan Bennett’s paintings, some of which appeared in 2017 and 2018 exhibitions, pay homage to traditional Mi’Kmaq craftsmanship. 

"}, {"id": "C", "text": "

Mi’Kmaq visual artist Jordan Bennett has displayed his work in over 75 exhibitions, including Wije’wi and Ketu’elmita’jik.

"}, {"id": "D", "text": "

Jordan Bennett’s 2018 exhibition Ketu’elmita’jik was held at the Art Gallery of Nova Scotia; another was held at the Grenfell Art Gallery.

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. The sentence emphasizes the order in which two of Jordan Bennett’s exhibitions were held, indicating that Wije’wi took place in 2017 and Ketu’elmita’jik took place a year later (2018).

Choice B is incorrect. While the sentence mentions that exhibitions of Jordan Bennett’s paintings took place in 2017 and 2018, it doesn’t identify the exhibitions or emphasize the order in which they were held. Choice C is incorrect. While the sentence mentions two of Jordan Bennett’s exhibitions, it doesn’t indicate the order in which they were held. Choice D is incorrect. While the sentence mentions two of Jordan Bennett’s exhibitions and specifies when one of them was held, it doesn’t state when the exhibition at the Grenfell Art Gallery occurred. Thus, the order in which the two exhibitions were held isn’t clearly established in the sentence. 

"}, {"id": "47547d07", "domain": "Expression of Ideas", "skill": "Transitions", "difficulty": "E", "type": "mc", "stimulus": "

In June, female loggerhead sea turtles will swim back to the sandy beaches where they were born to lay eggs of their own. First, the turtle will dig her nest in the sand. ______blank she will lay up to 100 eggs in the nest. Finally, she will cover it all with sand, before returning to the ocean.

", "stem": "

Which choice completes the text with the most logical transition?

", "choices": [{"id": "A", "text": "

By contrast,

"}, {"id": "B", "text": "

Similarly,

"}, {"id": "C", "text": "

Next,

"}, {"id": "D", "text": "

For example,

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. “Next” logically signals that the egg laying in this sentence is the next step in the sequence of events described in the other sentences.

Choice A is incorrect because “by contrast” illogically signals that the egg laying in this sentence contrasts with the nest digging in the previous sentence. Instead, the egg laying follows the nest digging as the next step in the sequence of events. Choice B is incorrect because “similarly” illogically signals that the egg laying in this sentence is similar to the nest digging in the previous sentence. Though the two actions are related, they are not similar. Instead, the egg laying follows the nest digging as the next step in the sequence of events. Choice D is incorrect because “for example” illogically signals that the egg laying in this sentence is an example of the nest digging in the previous sentence. Instead, the egg laying follows the nest digging as the next step in the sequence of events.

"}, {"id": "8e9677e6", "domain": "Expression of Ideas", "skill": "Transitions", "difficulty": "H", "type": "mc", "stimulus": "

In 2009, the Craft and Folk Art Museum in Los Angeles hosted a special exhibition, Sueños/Yume, showcasing the works of local sculptor Dora de Larios. As suggested by the show’s title (sueños and yume mean “dreams” in Spanish and Japanese, respectively), de Larios’s art reflects a mix of cultural influences. ______blank her work is grounded in the artistic traditions of both Mexico and Japan.

", "stem": "

Which choice completes the text with the most logical transition?

", "choices": [{"id": "A", "text": "

In addition,

"}, {"id": "B", "text": "

In contrast,

"}, {"id": "C", "text": "

Specifically,

"}, {"id": "D", "text": "

Therefore,

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. “Specifically” logically signals that this sentence provides specific, precise details elaborating on the previous sentence’s claim that de Larios’s art reflects a mix of cultures. This sentence specifies which cultures the previous sentence is referring to: the artistic traditions of both Mexico and Japan. 

Choice A is incorrect because “in addition” illogically signals that the information in this sentence is a separate point that follows the previous claim about de Larios’s art. Instead, it provides specific details elaborating on that claim. Choice B is incorrect because “in contrast” illogically signals that the information in this sentence contrasts with the previous claim about de Larios’s art. Instead, it provides specific details elaborating on that claim. Choice D is incorrect because “therefore” illogically signals that the information in this sentence is a result of the previous claim about de Larios’s art. Instead, it provides specific details elaborating on that claim.

"}, {"id": "8432a140", "domain": "Expression of Ideas", "skill": "Rhetorical Synthesis", "difficulty": "M", "type": "mc", "stimulus": "

While researching a topic, a student has taken the following notes:

\n", "stem": "

The student wants to introduce the scientist and her field of study to a new audience. Which choice most effectively uses relevant information from the notes to accomplish this goal?

", "choices": [{"id": "A", "text": "

Located in Brazil, the Amazon Reef is one of the largest known coral reefs in the world.

"}, {"id": "B", "text": "

Marine biologist Camille Jazmin Gaynus studies coral reefs, vital underwater ecosystems that provide homes to 25% of all marine species. 

"}, {"id": "C", "text": "

Providing homes to 25% of all marine species, including up to 8,000 species of fish, coral reefs are vital underwater ecosystems and thus of great interest to marine biologists.

"}, {"id": "D", "text": "

As Camille Jazmin Gaynus knows well, coral reefs are vital underwater ecosystems, providing homes to thousands of species of fish.

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. We’re asked to select the sentence that \"introduce[s] the scientist and her field of study.\" This choice introduces scientist Camille Jazmin Gaynus as a marine biologist and explains what marine life she studies.

Choice A is incorrect. This choice doesn’t mention Camille Jazmin Gaynus, so it fails to \"introduce the scientist.\" Choice C is incorrect. This choice doesn’t mention Camille Jazmin Gaynus, so it fails to \"introduce the scientist.\" Choice D is incorrect. This choice mentions Camille Jazmin Gaynus, but it doesn’t identify her as a marine biologist. It says she \"knows well\" about coral reefs, but doesn’t identify her expertise as a \"field of study.\"

"}, {"id": "6e0c60da", "domain": "Expression of Ideas", "skill": "Transitions", "difficulty": "H", "type": "mc", "stimulus": "

When one looks at the dark craggy vistas in Hitoshi Fugo’s evocative photo series, one’s mind might wander off to the cratered surfaces of faraway planets. ______blank it’s the series’ title, Flying Frying Pan, that brings one back to Earth, reminding the viewer that each photo is actually a close-up view of a familiar household object: a frying pan.

", "stem": "

Which choice completes the text with the most logical transition?

", "choices": [{"id": "A", "text": "

Consequently,

"}, {"id": "B", "text": "

Alternatively,

"}, {"id": "C", "text": "

Ultimately,

"}, {"id": "D", "text": "

Additionally,

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. The first sentence describes an experience that the viewer has when they’re looking at the photos: they imagine other planets. This sentence describes an experience that the viewer has afterward: the title reminds them that the photos are of frying pans, bringing them back to reality. “Ultimately” is a transition that means “eventually” or “in the end,” so it fits the context perfectly.

Choice A is incorrect. This choice uses a cause-and-effect transition, which doesn’t make sense here. The viewer imagining other planets when they’re looking at the photos doesn’t cause the title to bring them back to reality. Choice B is incorrect. This choice uses a transition that indicates another option or possibility, which doesn’t make sense here. Rather, the viewer has both experiences: first the viewer imagines that they’re looking at another planet, and then the title reminds them that it’s just a frying pan. Choice D is incorrect. This choice uses a transition that indicates the addition of an agreeing idea. But the viewer’s experience in the second sentence is actually the opposite of the viewer’s experience in the first sentence. In the first sentence, the viewer is imagining that they’re seeing a landscape from another planet. In the second sentence, the viewer is reminded that they’re looking at a frying pan.

"}, {"id": "64e88c58", "domain": "Expression of Ideas", "skill": "Rhetorical Synthesis", "difficulty": "H", "type": "mc", "stimulus": "

While researching a topic, a student has taken the following notes:

\n", "stem": "

The student wants to provide an explanation and an example of Oliveros’s Sonic Meditations. Which choice most effectively uses relevant information from the notes to accomplish this goal?

", "choices": [{"id": "A", "text": "

Sonic Meditations is not music but rather a series of sound-based meditations that consist of instructions; Meditation XVIII, for instance, instructs participants to “listen to a sound until you no longer recognize it.”

"}, {"id": "B", "text": "

In 1971, Oliveros created Sonic Meditations, a series of meditations that consist of instructions for participants to make, imagine, listen to, or remember sounds.

"}, {"id": "C", "text": "

“Walk so silently that the bottoms of your feet become ears” is one example of the instructions found in Oliveros’s Sonic Meditations.

"}, {"id": "D", "text": "

While both meditations consist of instructions, Meditation XVIII instructs participants to “listen,” whereas Meditation V instructs participants to “walk.”

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. It describes what a “Sonic Meditation” is, and then gives an example in the form of Meditation XVIII.

Choice B is incorrect. This choice describes what a “Sonic Meditation” is, but doesn’t give an example of one. Choice C is incorrect. This choice gives an example of a “Sonic Meditation,” but doesn’t explain what the meditations are. Choice D is incorrect. This choice doesn’t describe what a “Sonic Meditation” is.

"}, {"id": "2c61e0b9", "domain": "Expression of Ideas", "skill": "Rhetorical Synthesis", "difficulty": "H", "type": "mc", "stimulus": "

While researching a topic, a student has taken the following notes:

\n", "stem": "

The student wants to make a generalization about the kind of study conducted by Glickman, Brown, and Song. Which choice most effectively uses relevant information from the notes to accomplish this goal?

", "choices": [{"id": "A", "text": "

Based on statistical analysis, Glickman, Brown, and Song claim that John Lennon wrote the verse of “In My Life.”

"}, {"id": "B", "text": "

There is only an 18.9% probability that Paul McCartney wrote the verse for “In My Life”; John Lennon is the more likely author.

"}, {"id": "C", "text": "

It is likely that John Lennon, not Paul McCartney, wrote the verse for “In My Life.”

"}, {"id": "D", "text": "

Researchers have used statistical methods to address questions of authorship within the field of music.

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. The sentence uses information from the notes to make a generalization about the kind of study Glickman, Brown, and Song conducted. Specifically, the sentence indicates that the study was of a kind that used statistical methods to address questions of authorship within the field of music.

Choice A is incorrect because the sentence summarizes the methodology and findings of a particular analysis of a single song; it doesn’t make a generalization about the kind of study conducted. Choice B is incorrect because the sentence mentions the data and conclusion of a particular analysis of a single song; it doesn’t make a generalization about the kind of study conducted. Choice C is incorrect because the sentence focuses on a specific conclusion from a particular analysis of a single song; it doesn’t make a generalization about the kind of study conducted.

"}, {"id": "14037904", "domain": "Expression of Ideas", "skill": "Rhetorical Synthesis", "difficulty": "M", "type": "mc", "stimulus": "

While researching a topic, a student has taken the following notes:

\n", "stem": "

The student wants to emphasize a similarity in how critics responded to Treuer’s book. Which choice most effectively uses relevant information from the notes to accomplish this goal?

", "choices": [{"id": "A", "text": "

Treuer’s book, which was widely reviewed, focuses on Native American history from 1890 to the present.

"}, {"id": "B", "text": "

Dubbed “a monumental achievement” by the Missoulian, Treuer’s book documents over a century of Native American history.

"}, {"id": "C", "text": "

Critics praised Treuer’s book for its compelling narrative, with O, The Oprah Magazine calling it “a marvel of research and storytelling” and The Economist likewise writing that “Treuer’s storytelling skills shine” and that the book is an “elegant handling of [a] complex narrative.”

"}, {"id": "D", "text": "

While the Missoulian focused on the book’s broader achievement, The Economist zeroed in on Treuer’s storytelling skills.

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. The sentence emphasizes a similarity in how critics responded to Treuer’s book, noting that the critics for O, The Oprah Magazine and The Economist both praised the book’s storytelling.

Choice A is incorrect. The sentence provides background information about Treuer’s book; it doesn’t emphasize a similarity in how critics responded to it. Choice B is incorrect. The sentence cites a single critic’s response to Treuer’s book; it doesn’t emphasize a similarity in the responses of multiple critics. Choice D is incorrect. The sentence emphasizes a difference, not a similarity, in how two critics responded to Treuer’s book.

"}, {"id": "6081831f", "domain": "Expression of Ideas", "skill": "Transitions", "difficulty": "E", "type": "mc", "stimulus": "

When Chinese director Chloé Zhao accepted the Oscar in 2021 for her film Nomadland, she made Academy Award history. ______blank only one other woman, Kathryn Bigelow of the United States, had been named best director at the Oscars, making Zhao the second woman and the first Asian woman to win the award.

", "stem": "

Which choice completes the text with the most logical transition?

", "choices": [{"id": "A", "text": "

As a result,

"}, {"id": "B", "text": "

Previously,

"}, {"id": "C", "text": "

However,

"}, {"id": "D", "text": "

Likewise,

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. “Previously” logically signals that the event described in this sentence—Bigelow being named best director—occurred before Zhao’s win. The fact that only one other woman had won the award before puts Zhao’s win in perspective.

Choice A is incorrect because “as a result” illogically signals that the event described in this sentence occurred as a result or consequence of Zhao’s win. Instead, it occurred before Zhao was named best director and puts Zhao’s win in perspective. Choice C is incorrect because “however” illogically signals that the event described in this sentence occurred in spite of or in contrast to Zhao’s win. Instead, it occurred before Zhao was named best director and puts Zhao’s win in perspective. Choice D is incorrect because “likewise” illogically signals that this sentence merely adds a second, similar piece of information to the information about Zhao’s win. Instead, the fact that only one other woman had won the award before puts Zhao’s win in perspective.

"}, {"id": "129089b5", "domain": "Expression of Ideas", "skill": "Transitions", "difficulty": "M", "type": "mc", "stimulus": "

In 1933, the Twentieth Amendment to the US Constitution was ratified. The amendment mandates that presidential inaugurations be held on January 20, approximately ten weeks after the November election. ______blank this amendment requires newly elected US senators and representatives to be sworn into their respective offices on January 3.

", "stem": "

Which choice completes the text with the most logical transition?

", "choices": [{"id": "A", "text": "

Instead,

"}, {"id": "B", "text": "

For instance,

"}, {"id": "C", "text": "

Specifically,

"}, {"id": "D", "text": "

In addition,

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. “In addition” logically signals that the information in this sentence—that the Twentieth Amendment requires newly elected US senators and representatives to be sworn in on January 3—is separate from and additional to the amendment’s mandate concerning presidential inaugurations.

Choice A is incorrect because “instead” illogically signals that the information in the sentence presents an alternative to or substitute for the Twentieth Amendment’s mandate concerning presidential inaugurations. Rather, the sentence presents a separate requirement in addition to that one. Choice B is incorrect because “for instance” illogically signals that the information in the sentence exemplifies the Twentieth Amendment’s mandate concerning presidential inaugurations. Instead, the sentence presents a separate requirement in addition to that one. Choice C is incorrect because “specifically” illogically signals that the sentence provides specific, precise details elaborating on the Twentieth Amendment’s mandate concerning presidential inaugurations. Instead, the sentence presents a separate requirement in addition to that one.

"}, {"id": "f4b63a04", "domain": "Expression of Ideas", "skill": "Rhetorical Synthesis", "difficulty": "E", "type": "mc", "stimulus": "

While researching a topic, a student has taken the following notes: 

\n", "stem": "

The student wants to explain the origin of the species’ name. Which choice most effectively uses relevant information from the notes to accomplish this goal?

", "choices": [{"id": "A", "text": "

Mansourasaurus, a new species discovered in Egypt in 2013, lived approximately 80 million years ago.

"}, {"id": "B", "text": "

A partial dinosaur skeleton found in Egypt’s Dakhla Oasis belonged to a species named Mansourasaurus.

"}, {"id": "C", "text": "

Mansourasaurus, a species that lived approximately 80 million years ago, was discovered in 2013 by Egyptian paleontologist Hesham Sallam and a team of university students.

"}, {"id": "D", "text": "

The new species was named Mansourasaurus to recognize the team that discovered it, a professor and students from Mansoura University.

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. It explains where the dinosaur’s name came from.

Choice A is incorrect. This choice does not explain the origin of the dinosaur’s name. Choice B is incorrect. This choice does not explain the origin of the dinosaur’s name. Choice C is incorrect. This choice does not explain the origin of the dinosaur’s name.

"}, {"id": "af88c47a", "domain": "Expression of Ideas", "skill": "Rhetorical Synthesis", "difficulty": "H", "type": "mc", "stimulus": "

While researching a topic, a student has taken the following notes:

\n", "stem": "

The student wants to begin a narrative about Wong’s award-nominated web series. Which choice most effectively uses relevant information from the notes to accomplish this goal?

", "choices": [{"id": "A", "text": "

In 2012, director and visual effects artist Freddie Wong launched a new action-comedy web series: Video Game High School.

"}, {"id": "B", "text": "

Video Game High School was celebrated for its inventive video game–centric world and high-quality special effects, and it was nominated for a Producer’s Guild Award for Outstanding Digital Series.

"}, {"id": "C", "text": "

Wong, cocreator of the YouTube channel RocketJump, would go on to see his web series be nominated for a Producers Guild Award.

"}, {"id": "D", "text": "

In 2012, Video Game High School premiered on RocketJump; it would later be nominated for an award.

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. This choice introduces Wong and VGHS in an active and specific way, as if to an audience unfamiliar with the series. It also sets up the time and genre of the web series, which are useful ways to introduce the series of events in a narrative.

Choice B is incorrect. This choice isn’t suited for beginning a narrative. A narrative is a story that follows a sequence of events and creates interest and suspense for the reader. This choice jumps to the end, explaining the success of VGHS without explaining what it is. Choice C is incorrect. This choice isn’t suited for beginning a narrative. It doesn’t actually introduce the web series by name. It just jumps to later in the story without sufficient explanation. Choice D is incorrect. This choice is not very effective for beginning a narrative. It doesn’t explain what VGHS is, and it doesn’t mention Wong.

"}, {"id": "d6dec50e", "domain": "Expression of Ideas", "skill": "Rhetorical Synthesis", "difficulty": "M", "type": "mc", "stimulus": "

While researching a topic, a student has taken the following notes:

\n", "stem": "

The student wants to summarize the study. Which choice most effectively uses relevant information from the notes to accomplish this goal?

", "choices": [{"id": "A", "text": "

For a 2019 study, researchers from the UK and Germany collected data on auks’ attempts to land at cliffside nesting sites in different wind conditions.

"}, {"id": "B", "text": "

Emily Shepard and her colleagues wanted to know the extent to which wind affected auks’ success in landing at cliffside nesting sites, so they conducted a study.

"}, {"id": "C", "text": "

Knowing that auks often need multiple attempts to land at their cliffside nesting sites, Emily Shepard studied the birds’ success rate, which was only around 20% in some conditions.

"}, {"id": "D", "text": "

Emily Shepard’s 2019 study of auks’ success in landing at cliffside nesting sites showed that as wind conditions intensified, the birds’ success rate decreased.

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. The sentence effectively summarizes the study, noting who conducted it, when it was conducted, and what its results showed: that auks’ landing success rate decreased as wind conditions intensified.

Choice A is incorrect. While the sentence presents the methodology of the study—that is, the approach taken by the researchers—it fails to summarize the study as a whole. Choice B is incorrect. While the sentence presents the aim, or goal, of the study, it fails to summarize the study as a whole. Choice C is incorrect. While the sentence indicates what Shepard studied, it fails to mention a key factor: the effect of wind. It thus fails to summarize the study as a whole.

"}, {"id": "94cb8720", "domain": "Expression of Ideas", "skill": "Rhetorical Synthesis", "difficulty": "M", "type": "mc", "stimulus": "

While researching a topic, a student has taken the following notes:

\n", "stem": "

The student wants to explain an advantage of the “Women and the Vote” format. Which choice most effectively uses relevant information from the notes to accomplish this goal?

", "choices": [{"id": "A", "text": "

“Women and the Vote” featured a drawing of a Victorian-style house with several rooms, each containing suffrage artifacts.

"}, {"id": "B", "text": "

To access video clips, songs, artwork, and texts, audiences had to first click on an artifact.

"}, {"id": "C", "text": "

The “Women and the Vote” format appealed to audiences because it allowed them to control the experience.   

"}, {"id": "D", "text": "

Using an interactive format, theater students at Radford and Virginia Tech created “Women and the Vote,” a play about woman suffrage activists. 

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. The sentence explains an advantage of the “Women and the Vote” format, noting that the format appealed to audiences because it allowed them to control the experience.

Choice A is incorrect. The sentence describes a digital drawing on the “Women and the Vote” website; it doesn’t explain an advantage of the play’s format. Choice B is incorrect. The sentence explains how audiences interacted with the “Women and the Vote” website; it doesn’t explain an advantage of the play’s format. Choice D is incorrect. While the sentence mentions that “Women and the Vote” had an interactive format, it doesn’t explain what advantage this format might have. 

"}, {"id": "9551ef8b", "domain": "Expression of Ideas", "skill": "Rhetorical Synthesis", "difficulty": "H", "type": "mc", "stimulus": "

While researching a topic, a student has taken the following notes:

\n", "stem": "

The student wants to emphasize a similarity between the two ways a magnificent frigatebird acquires food. Which choice most effectively uses relevant information from the notes to accomplish this goal?

", "choices": [{"id": "A", "text": "

A magnificent frigatebird never dives into the water, instead using its hook-tipped bill to snatch prey from the surface.

"}, {"id": "B", "text": "

Neither of a magnificent frigatebird’s two ways of acquiring food requires the bird to dive into the water.

"}, {"id": "C", "text": "

Of the magnificent frigatebird’s two ways of acquiring food, only one is known as kleptoparasitism.

"}, {"id": "D", "text": "

In addition to snatching prey from the water with its hook-tipped bill, a magnificent frigatebird takes food from other birds by force. 

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. The sentence emphasizes a similarity between the two ways a magnificent frigatebird acquires food, noting that neither way requires the seabird to dive into the water.

Choice A is incorrect. The sentence describes how a magnificent frigatebird captures prey without diving into water; it doesn’t emphasize a similarity between the two ways the seabird acquires food. Choice C is incorrect. The sentence notes the term used to describe one of the two ways that magnificent frigatebirds acquire food; it doesn’t emphasize a similarity between the two ways. Choice D is incorrect. The sentence describes the two ways that a magnificent frigatebird acquires food; it doesn’t emphasize a similarity between the two ways.

"}, {"id": "9502ec65", "domain": "Expression of Ideas", "skill": "Transitions", "difficulty": "H", "type": "mc", "stimulus": "

When soil becomes contaminated by toxic metals, it can be removed from the ground and disposed of in a landfill. ______blank contaminated soil can be detoxified via phytoremediation: plants that can withstand high concentrations of metals absorb the pollutants and store them in their shoots, which are then cut off and safely disposed of, preserving the health of the plants.

", "stem": "

Which choice completes the text with the most logical transition?

", "choices": [{"id": "A", "text": "

Alternatively,

"}, {"id": "B", "text": "

Specifically,

"}, {"id": "C", "text": "

For example,

"}, {"id": "D", "text": "

As a result,

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. “Alternatively” logically signals that the soil decontamination method described in this sentence—removing toxic metals from the soil via phytoremediation—offers an alternative to the previously described method (removing the contaminated soil from the ground).

Choice B is incorrect because “specifically” illogically signals that the soil decontamination method described in this sentence specifies or elaborates on an aspect of the previously described method (removing the contaminated soil from the ground). Instead, phytoremediation is an alternative to that method. Choice C is incorrect because “for example” illogically signals that the soil decontamination method described in this sentence is an example of the previously described method (removing the contaminated soil from the ground). Instead, phytoremediation is an alternative to that method. Choice D is incorrect because “as a result” illogically signals that the soil decontamination method described in this sentence is a result or consequence of the previously described method (removing the contaminated soil from the ground). Instead, phytoremediation is an alternative to that method.

"}, {"id": "2df7b582", "domain": "Expression of Ideas", "skill": "Transitions", "difficulty": "H", "type": "mc", "stimulus": "

Plato believed material objects to be crude representations of unseen ideal forms. In his view, such abstract, nonmaterial forms are the ultimate source of knowledge. Aristotle disagreed, positing that knowledge is best obtained through direct engagement with the material world; ______blank sensory experience of the material is the ultimate source of knowledge.

", "stem": "

Which choice completes the text with the most logical transition?

", "choices": [{"id": "A", "text": "

regardless,

"}, {"id": "B", "text": "

admittedly,

"}, {"id": "C", "text": "

in other words,

"}, {"id": "D", "text": "

meanwhile,

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. “In other words” logically signals that the claim about sensory experience that follows—that sensory experience is the source of knowledge—is a restatement of Aristotle’s theory from earlier in the sentence.

Choice A is incorrect because “regardless” illogically signals that the claim about sensory experience that follows is true in spite of Aristotle’s theory from earlier in the sentence. Instead, this claim is a restatement of his theory. Choice B is incorrect because “admittedly” illogically signals that the claim about sensory experience that follows is an exception to Aristotle’s theory from earlier in the sentence. Instead, this claim is a restatement of his theory. Choice D is incorrect because “meanwhile” illogically signals that the claim about sensory experience that follows is separate from (while occurring simultaneously with) Aristotle’s theory from earlier in the sentence. Instead, this claim is a restatement of his theory.

"}, {"id": "c7e85c0a", "domain": "Expression of Ideas", "skill": "Transitions", "difficulty": "E", "type": "mc", "stimulus": "

The envelope-shaped paper bags common in the US 150 years ago were impractical for carrying goods. ______blank because they were the only paper bags that could be mass-produced, these bags dominated the market. That all changed in the 1870s, when industrial designer Margaret Knight patented a machine to make flat-bottomed, foldable paper bags.

", "stem": "

Which choice completes the text with the most logical transition?

", "choices": [{"id": "A", "text": "

However,

"}, {"id": "B", "text": "

For instance,

"}, {"id": "C", "text": "

Thus,

"}, {"id": "D", "text": "

In other words,

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. “However” logically signals that the information in this sentence—that envelope-shaped bags dominated the market—contrasts with the previous claim that these bags were impractical for carrying goods.

Choice B is incorrect because “for instance” illogically signals that the information in this sentence is an example supporting the previous claim that envelope-shaped bags were impractical for carrying goods. Instead, the sentence contrasts with the previous claim about the bags. Choice C is incorrect because “thus” illogically signals that the information in this sentence is a result of the previous claim that envelope-shaped bags were impractical for carrying goods. Instead, the sentence contrasts with the previous claim about the bags. Choice D is incorrect because “in other words” illogically signals that the information in this sentence is a paraphrase of the previous claim that envelope-shaped bags were impractical for carrying goods. Instead, the sentence contrasts with the previous claim about the bags.

"}, {"id": "1792fa73", "domain": "Expression of Ideas", "skill": "Rhetorical Synthesis", "difficulty": "E", "type": "mc", "stimulus": "

While researching a topic, a student has taken the following notes:

\n", "stem": "

The student wants to emphasize how harsh the conditions can be in the tundra. Which choice most effectively uses relevant information from the notes to accomplish this goal?

", "choices": [{"id": "A", "text": "

Winters in the tundra are especially harsh, with temperatures averaging a frigid −30negative 30 degrees Fahrenheit.

"}, {"id": "B", "text": "

Animals that have adapted to harsh winter conditions can survive tundra winters.

"}, {"id": "C", "text": "

There are around 1,700 different kinds of plants that can live in the tundra, where average temperatures can reach a mild 54 degrees Fahrenheit.

"}, {"id": "D", "text": "

Along with animals that have adapted to the tundra’s conditions, around 1,700 different kinds of plants can live in the tundra.

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. The sentence emphasizes how harsh the conditions in the tundra can be, noting that the winters are especially harsh and describing the average temperatures as “frigid.”

Choice B is incorrect because the sentence explains that some animals can survive harsh tundra winters; it doesn’t emphasize how harsh the conditions can be. Choice C is incorrect because the sentence specifies how many different kinds of plants can live in the tundra; it doesn’t emphasize how harsh the conditions in the tundra can be. Choice D is incorrect because the sentence explains that both plants and animals can survive in the tundra; it doesn’t emphasize how harsh the conditions in the tundra can be.

"}, {"id": "f33f0892", "domain": "Expression of Ideas", "skill": "Transitions", "difficulty": "E", "type": "mc", "stimulus": "

Although novels and poems are considered distinct literary forms, many authors have created hybrid works that incorporate elements of both. Bernardine Evaristo’s The Emperor’s Babe, ______blank is a verse novel, a book-length narrative complete with characters and a plot but conveyed in short, crisp lines of poetry rather than prose.

", "stem": "

Which choice completes the text with the most logical transition?

", "choices": [{"id": "A", "text": "

by contrast,

"}, {"id": "B", "text": "

consequently,

"}, {"id": "C", "text": "

secondly,

"}, {"id": "D", "text": "

for example,

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. “For example” logically signals that the information in this sentence—that The Emperor’s Babe is a novel conveyed in lines of poetry—exemplifies the claim in the previous sentence about hybrid works that incorporate elements of both novels and poems.

Choice A is incorrect because “by contrast” illogically signals that the information in this sentence contrasts with the claim about hybrid works in the previous sentence. Instead, the information demonstrates that Evaristo’s novel is an example of a hybrid work. Choice B is incorrect because “consequently” illogically signals that the information in this sentence is a consequence, or result, of the claim about hybrid works in the previous sentence. Instead, the information demonstrates that Evaristo’s novel is an example of a hybrid work. Choice C is incorrect because “secondly” illogically signals that the information in this sentence is a second, separate claim from the previous sentence’s claim about hybrid works. Instead, the information demonstrates that Evaristo’s novel is an example of a hybrid work.

"}, {"id": "7d56630a", "domain": "Expression of Ideas", "skill": "Transitions", "difficulty": "E", "type": "mc", "stimulus": "

In studying whether jellyfish sleep, researchers Michael Abrams, Claire Bedbrook, and Ravi Nath attempted to answer three questions. ______blank is there a period each day when the pulse rates of jellyfish decline? Second, do jellyfish respond more slowly to stimuli during that period? Finally, if prevented from sleeping, are jellyfish adversely affected?

", "stem": "

Which choice completes the text with the most logical transition?

", "choices": [{"id": "A", "text": "

As a result,

"}, {"id": "B", "text": "

First,

"}, {"id": "C", "text": "

Additionally,

"}, {"id": "D", "text": "

However,

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. “First” logically signals that the question in this sentence—whether there is a daily period during which jellyfish pulse rates decline—is the first in a sequence of three questions the researchers attempted to answer about jellyfish sleep behavior.

Choice A is incorrect because “as a result” illogically signals that the question in this sentence is a result of the three questions the researchers attempted to answer. Instead, it is the first of those three questions. Choice C is incorrect because “additionally” illogically signals that the question in this sentence is an additional question related to the three questions the researchers attempted to answer. Instead, it is the first of those three questions. Choice D is incorrect because “however” illogically signals that the question in this sentence contrasts with the three questions the researchers attempted to answer. Instead, it is the first of those three questions.

"}, {"id": "58281fc4", "domain": "Expression of Ideas", "skill": "Rhetorical Synthesis", "difficulty": "M", "type": "mc", "stimulus": "

While researching a topic, a student has taken the following notes:

\n", "stem": "

The student wants to describe Unwoven Light to an audience unfamiliar with Soo Sunny Park. Which choice most effectively uses relevant information from the notes to accomplish this goal?

", "choices": [{"id": "A", "text": "

Park’s 2013 installation Unwoven Light, which included a chain-link fence and iridescent tiles made from plexiglass, featured light as its primary medium of expression.

"}, {"id": "B", "text": "

Korean American light artist Soo Sunny Park created Unwoven Light in 2013.

"}, {"id": "C", "text": "

The chain-link fence in Soo Sunny Park’s Unwoven Light was fitted with tiles made from iridescent plexiglass.

"}, {"id": "D", "text": "

In Unwoven Light, a 2013 work by Korean American artist Soo Sunny Park, light formed colorful prisms as it passed through a fence Park had fitted with iridescent tiles. 

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. The sentence effectively describes Unwoven Light to an audience unfamiliar with Park, noting that Soo Sunny Park is a Korean American artist and that the 2013 work consists of colorful prisms formed by light passing through iridescent tiles.

Choice A is incorrect. The sentence describes aspects of Unwoven Light but doesn’t mention who Park is; it thus doesn’t effectively describe the work to an audience unfamiliar with Park. Choice B is incorrect. Although the sentence indicates when the work was created and who Park is, it lacks descriptive details and thus doesn’t effectively describe Unwoven Light. Choice C is incorrect. The sentence mentions Park and describes an aspect of Unwoven Light—the chain-link fence—but doesn’t effectively describe the overall work to an audience unfamiliar with the artist.

"}, {"id": "a6155e60", "domain": "Expression of Ideas", "skill": "Transitions", "difficulty": "E", "type": "mc", "stimulus": "

Every chemical compound has a spectroscopic fingerprint, a pattern of reflected light unique to that compound. ______blank upon analyzing the light reflected by the bright regions on the surface of the dwarf planet Ceres, Maria Cristina De Sanctis of Rome’s National Institute of Astrophysics was able to determine that the regions contain large amounts of the compound sodium carbonate.

", "stem": "

Which choice completes the text with the most logical transition?

", "choices": [{"id": "A", "text": "

Regardless,

"}, {"id": "B", "text": "

Meanwhile,

"}, {"id": "C", "text": "

Thus,

"}, {"id": "D", "text": "

In comparison,

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. “Thus” logically signals that the action described in this sentence—the researcher being able to determine the chemical makeup of the planet’s bright regions based on how they reflect light—is a result or consequence of the previous information about spectroscopic fingerprints.

Choice A is incorrect because “regardless” illogically signals that the action described in this sentence occurs despite the previous information about spectroscopic fingerprints. Instead, the finding in this sentence is a result or consequence of that information. Choice B is incorrect because “meanwhile” illogically signals that the action described in this sentence either occurs at the same time as or offers an alternative to the previous information about spectroscopic fingerprints. Instead, the finding in this sentence is a result or consequence of that information. Choice D is incorrect because “in comparison” illogically signals that the action described in this sentence is being compared with the previous information about spectroscopic fingerprints. Instead, the finding in this sentence is a result or consequence of that information.

"}, {"id": "17ec916d", "domain": "Expression of Ideas", "skill": "Rhetorical Synthesis", "difficulty": "M", "type": "mc", "stimulus": "

While researching a topic, a student has taken the following notes:

\n", "stem": "

The student wants to introduce the novel The Holder of the World to an audience already familiar with Bharati Mukherjee. Which choice most effectively uses relevant information from the notes to accomplish this goal? 

", "choices": [{"id": "A", "text": "

Bharati Mukherjee’s settings include both twentieth-century United States and seventeenth-century India.

"}, {"id": "B", "text": "

In addition to her novel The Holder of the World, which was published in 1993, Indian-born author Bharati Mukherjee wrote other novels and short stories.

"}, {"id": "C", "text": "

Bharati Mukherjee’s novel The Holder of the World centers around two women, one living in twentieth-century United States and the other in seventeenth-century India.

"}, {"id": "D", "text": "

The Holder of the World was not the only novel written by Indian-born author Bharati Mukherjee.

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. The sentence effectively introduces The Holder of the World to an audience already familiar with Mukherjee, explaining that the novel centers around two women and mentioning the author without providing any other identifying information.

Choice A is incorrect. The sentence provides a detail about Mukherjee’s settings; it doesn’t introduce, or even mention, the novel. Choice B is incorrect. The sentence provides introductory information about Mukherjee; it doesn’t effectively introduce her novel to an audience already familiar with the author. Choice D is incorrect. The sentence provides introductory information about Mukherjee; it doesn’t effectively introduce her novel to an audience already familiar with the author.

"}, {"id": "24014c3f", "domain": "Expression of Ideas", "skill": "Rhetorical Synthesis", "difficulty": "M", "type": "mc", "stimulus": "

While researching a topic, a student has taken the following notes:

\n", "stem": "

The student wants to emphasize the significance of Ochoa’s discovery. Which choice most effectively uses relevant information from the notes to accomplish this goal?

", "choices": [{"id": "A", "text": "

Ochoa’s 1955 discovery of PNPase proved critical to deciphering the human genetic code, leading to a better understanding of how genetic variations affect human health.

"}, {"id": "B", "text": "

Ochoa first discovered PNPase, an enzyme that he hypothesized contained the genetic blueprints for mRNA, in 1955. 

"}, {"id": "C", "text": "

In 1955, Ochoa discovered the PNPase enzyme, which is involved in both the creation and degradation of mRNA.

"}, {"id": "D", "text": "

Though his discovery of PNPase was critical to deciphering the human genetic code, Ochoa incorrectly hypothesized that the enzyme was the source of mRNA’s genetic blueprints.

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. The sentence emphasizes the significance of Ochoa’s discovery, noting that it proved critical to deciphering the human genetic code, which resulted in a better understanding of how genetic variations affect human health.

Choice B is incorrect. While the sentence explains what Ochoa discovered, it doesn’t emphasize the significance of the discovery. Choice C is incorrect. While the sentence explains what Ochoa discovered, it doesn’t emphasize the significance of the discovery. Choice D is incorrect. While the sentence mentions that Ochoa’s discovery was crucial, it emphasizes Ochoa’s incorrect hypothesis, not the significance of the discovery.

"}, {"id": "3067723b", "domain": "Expression of Ideas", "skill": "Rhetorical Synthesis", "difficulty": "E", "type": "mc", "stimulus": "

While researching a topic, a student has taken the following notes:

\n", "stem": "

The student wants to compare the lengths of the two rail tunnels. Which choice most effectively uses relevant information from the notes to accomplish this goal?

", "choices": [{"id": "A", "text": "

Some of the world’s rail tunnels, including one tunnel that extends from Folkestone, England, to Coquelles, France, are longer than 30 miles.

"}, {"id": "B", "text": "

The Seikan Tunnel is roughly 33 miles long, while the slightly shorter Channel Tunnel is about 31 miles long.

"}, {"id": "C", "text": "

The Seikan Tunnel, which is roughly 33 miles long, connects the Japanese islands of Honshu and Hokkaido.

"}, {"id": "D", "text": "

Both the Seikan Tunnel, which is located in Japan, and the Channel Tunnel, which is located in Europe, are examples of rail tunnels.

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. The sentence compares the lengths of the two rail tunnels, noting that the Channel Tunnel (about 31 miles long) is slightly shorter than the Seikan Tunnel (roughly 33 miles long). 

Choice A is incorrect. The sentence makes a generalization about the length of some rail tunnels; it doesn’t compare the lengths of the two rail tunnels. Choice C is incorrect. The sentence describes a single rail tunnel; it doesn’t compare the lengths of the two rail tunnels. Choice D is incorrect. While the sentence mentions the two rail tunnels, it doesn’t compare their lengths.

"}, {"id": "e2d97f10", "domain": "Expression of Ideas", "skill": "Rhetorical Synthesis", "difficulty": "M", "type": "mc", "stimulus": "

While researching a topic, a student has taken the following notes:

\n", "stem": "

The student wants to present the study and its findings. Which choice most effectively uses relevant information from the notes to accomplish this goal?

", "choices": [{"id": "A", "text": "

In 2021, Chinsamy-Turan studied pterosaur jawbones and was initially unsure if the bones belonged to juveniles or adults. 

"}, {"id": "B", "text": "

Pterosaur jawbones located in the Sahara Desert were the focus of a 2021 study.

"}, {"id": "C", "text": "

In a 2021 study, Chinsamy-Turan used advanced microscope techniques to analyze the jawbones of pterosaurs, flying reptiles that existed millions of years ago.

"}, {"id": "D", "text": "

In a 2021 study, Chinsamy-Turan determined that pterosaur jawbones located in the Sahara Desert had few growth lines relative to the bones of fully grown pterosaurs and thus belonged to juveniles.

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. The sentence presents both the study and its findings, noting the study’s date and the researcher’s name as well as describing what the researcher determined about the jawbones and how she determined it.

Choice A is incorrect. While the sentence describes the study and the researcher’s initial assessment, it doesn’t present the study’s findings. Choice B is incorrect. While the sentence describes the study and its focus, it doesn’t present the study’s findings or the name of the researcher who conducted it. Choice C is incorrect. While the sentence mentions the study’s methodology and provides information about pterosaurs, it doesn’t present the study’s findings.

"}, {"id": "e1b00a70", "domain": "Expression of Ideas", "skill": "Transitions", "difficulty": "M", "type": "mc", "stimulus": "

The more diverse and wide ranging an animal’s behaviors, the larger and more energy demanding the animal’s brain tends to be. ______blank from an evolutionary perspective, animals that perform only basic actions should allocate fewer resources to growing and maintaining brain tissue. The specialized subtypes of ants within colonies provide an opportunity to explore this hypothesis. 

", "stem": "

Which choice completes the text with the most logical transition?

", "choices": [{"id": "A", "text": "

Subsequently,

"}, {"id": "B", "text": "

Besides,

"}, {"id": "C", "text": "

Nevertheless,

"}, {"id": "D", "text": "

Thus,

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. “Thus” logically signals that the claim in this sentence—that animals performing only basic actions should allocate relatively few resources to their brain tissue—is a consequence of the previous sentence’s claim about the energy demands of animal brains (namely, that the more diverse an animal’s behaviors, the more energy its brain needs). 

Choice A is incorrect because “subsequently” illogically signals that the claim in this sentence occurs later in a chronological sequence of events than the previous sentence’s claim about the energy demands of animal brains. Instead, the second claim is a consequence of the first. Choice B is incorrect because “besides” illogically signals that the claim in this sentence provides a separate point in addition to, or apart from, the previous sentence’s claim about the energy demands of animal brains. Instead, the second claim is a consequence of the first. Choice C is incorrect because “nevertheless” illogically signals that the claim in this sentence is true in spite of the previous sentence’s claim about the energy demands of animal brains. Instead, the second claim is a consequence of the first.

"}, {"id": "bce57278", "domain": "Expression of Ideas", "skill": "Rhetorical Synthesis", "difficulty": "M", "type": "mc", "stimulus": "

While researching a topic, a student has taken the following notes:

\n", "stem": "

The student wants to explain the goal of Brook Farm using a quotation from George Ripley. Which choice most effectively uses relevant information from the notes to accomplish this goal?

", "choices": [{"id": "A", "text": "

In a letter, writer George Ripley explained his goal to “guarantee the highest mental freedom.”

"}, {"id": "B", "text": "

Utopias, such as Brook Farm, founded by George Ripley in 1841, were based on a specific set of principles intended to create a perfect society.

"}, {"id": "C", "text": "

Founded by George Ripley near Boston, Massachusetts, Brook Farm was part of a trend in the 1800s, when reformers in the United States built utopias.

"}, {"id": "D", "text": "

Established in 1841, Brook Farm was a utopian community created to “guarantee the highest mental freedom, by providing all with labor... [and] the fruits of their industry,” according to founder George Ripley.

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. This choice explains the goal of Brook Farm—to provide mental freedom to all by engaging individuals in labor suited to their interests—using a quotation from George Ripley.

Choice A is incorrect. This choice only mentions part of Ripley’s goal, and it doesn’t mention Brook Farm at all. Choice B is incorrect. This choice defines what a utopia is but doesn’t use Ripley’s words to describe his vision for Brook Farm. Choice C is incorrect. This choice provides some background information about Brook Farm, but it doesn’t explain its goals or include Ripley’s words.

"}, {"id": "2b89bfe5", "domain": "Expression of Ideas", "skill": "Rhetorical Synthesis", "difficulty": "M", "type": "mc", "stimulus": "

While researching a topic, a student has taken the following notes:

\n", "stem": "

The student wants to emphasize how hot the Sun is relative to nearby stars. Which choice most effectively uses relevant information from the notes to accomplish this goal?

", "choices": [{"id": "A", "text": "

At around 9,800°F, which classifies it as a G star, the Sun is hotter than most but not all of the stars within 10 parsecs of it.

"}, {"id": "B", "text": "

Astronomer Todd Henry determined that the Sun, at around 9,800°F, is a G star, and several other stars within a 10-parsec range are A or F stars.

"}, {"id": "C", "text": "

Of the 357 stars within ten parsecs of the Sun, 327 are classified as K or M stars, with surface temperatures under 8,900°F.

"}, {"id": "D", "text": "

While most of the stars within 10 parsecs of the Sun are classified as K, M, A, or F stars, the Sun is classified as a G star due to its surface temperature of 9,800°F.

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. Noting that the Sun (9,800°F) is hotter than most stars within 10 parsecs of it, the sentence emphasizes how hot the Sun is relative to nearby stars.

Choice B is incorrect. The sentence explains that astronomer Todd Henry determined the classifications for the Sun and several other stars nearby; it doesn’t emphasize how hot the Sun is relative to nearby stars. Choice C is incorrect. The sentence explains that the majority of stars near the Sun are classified as K or M stars; it doesn’t indicate the Sun’s temperature or emphasize how hot it is relative to nearby stars. Choice D is incorrect. While the sentence indicates that the Sun is classified differently than most nearby stars due to its surface temperature, it doesn’t emphasize how hot the Sun is relative to nearby stars.

"}, {"id": "54c1b2dd", "domain": "Expression of Ideas", "skill": "Rhetorical Synthesis", "difficulty": "M", "type": "mc", "stimulus": "

While researching a topic, a student has taken the following notes:

\n", "stem": "

The student wants to emphasize a similarity between the two paintings. Which choice most effectively uses relevant information from the notes to accomplish this goal?

", "choices": [{"id": "A", "text": "

Monkman, a Cree artist, finished his painting in 2019; Leutze, a German American artist, completed his in 1851. 

"}, {"id": "B", "text": "

Although Monkman’s painting was inspired by Leutze’s, the people and actions the two paintings portray are very different.

"}, {"id": "C", "text": "

Leutze’s and Monkman’s paintings are both huge, measuring 149 × 255 inches and 132 × 264 inches, respectively.

"}, {"id": "D", "text": "

Leutze’s painting depicts Revolutionary War soldiers, while Monkman’s depicts Indigenous people and refugees.

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. The sentence emphasizes a similarity between the two paintings, noting that Leutze’s painting (which measures 149 × 255 inches) and Monkman’s painting (which measures 132 × 264 inches) are both very large.

Choice A is incorrect. The sentence mentions that Monkman’s painting was completed in 2019 and Leutze’s was completed in 1851; it doesn’t emphasize a similarity between the two paintings. Choice B is incorrect. While the sentence acknowledges that one painting was inspired by the other, it emphasizes differences between the two paintings; it doesn’t emphasize a similarity between them. Choice D is incorrect. The sentence mentions a difference between the two paintings; it doesn’t emphasize a similarity between them.

"}, {"id": "5fa51c86", "domain": "Expression of Ideas", "skill": "Rhetorical Synthesis", "difficulty": "H", "type": "mc", "stimulus": "

While researching a topic, a student has taken the following notes:

\n", "stem": "

The student wants to emphasize the relative sizes of the two capitals’ populations. Which choice most effectively uses information from the given sentences to emphasize the relative sizes of the two capitals’ populations?

", "choices": [{"id": "A", "text": "

Mongolia’s capital is Ulaanbaatar, which has 907,802 people, and Vietnam’s capital is Hanoi, which has 7,781,631 people.

"}, {"id": "B", "text": "

Comparing Vietnam and Mongolia, 7,781,631 is 8.14 percent of Vietnam’s population, and 907,802 is 31.98 percent of Mongolia’s.

"}, {"id": "C", "text": "

Even though Hanoi (population 7,781,631) is larger than Ulaanbaatar (population 907,802), Ulaanbaatar accounts for more of its country’s population.

"}, {"id": "D", "text": "

The populations of the capitals of Mongolia and Vietnam are 907,802 (Ulaanbaatar) and 7,781,631 (Hanoi), respectively.

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. The sentence emphasizes the relative sizes of the capital cities’ populations, noting that even though Hanoi has more people overall, Ulaanbaatar accounts for a larger percentage of the people in its country.

Choice A is incorrect. While the sentence indicates the population size of each capital, it fails to emphasize their sizes relative to each other or to their countries’ overall population sizes. Choice B is incorrect. The sentence emphasizes the population sizes of the two countries; it fails to mention the capitals. Choice D is incorrect. While the sentence indicates the population size of each capital, it fails to emphasize their sizes relative to each other or to their countries’ overall population sizes.

"}, {"id": "08be6347", "domain": "Expression of Ideas", "skill": "Transitions", "difficulty": "M", "type": "mc", "stimulus": "

In his 1925 book The Morphology of Landscape, US geographer Carl Sauer challenged prevailing views about how natural landscapes influence human cultures. ______blank Sauer argued that instead of being shaped entirely by their natural surroundings, cultures play an active role in their own development by virtue of their interactions with the environment.

", "stem": "

Which choice completes the text with the most logical transition?

", "choices": [{"id": "A", "text": "

Similarly,

"}, {"id": "B", "text": "

Finally,

"}, {"id": "C", "text": "

Therefore,

"}, {"id": "D", "text": "

Specifically,

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. “Specifically” logically signals that the information in this sentence about Sauer’s argument—that, according to Sauer, cultures play a role in their own development, as opposed to being shaped solely by natural surroundings—provides specific, precise details elaborating on the more general information in the previous sentence about how Sauer challenged prevailing views about how natural landscapes influence human cultures.

Choice A is incorrect because “similarly” illogically signals that the information in this sentence about Sauer’s argument is similar to, but separate from, the more general information in the previous sentence. Instead, it provides specific, precise details elaborating on that information. Choice B is incorrect because “finally” illogically signals that the information in this sentence about Sauer’s argument indicates a last step in a process or a concluding summary. Instead, it provides specific, precise details elaborating on the general information in the previous sentence. Choice C is incorrect because “therefore” illogically signals that the information in this sentence about Sauer’s argument is a result of the more general information in the previous sentence. Instead, it provides specific, precise details elaborating on that information.

"}, {"id": "5d3177aa", "domain": "Expression of Ideas", "skill": "Rhetorical Synthesis", "difficulty": "M", "type": "mc", "stimulus": "

While researching a topic, a student has taken the following notes:

\n", "stem": "

The student wants to present the significance of the Hart-Celler Act to an audience unfamiliar with the history of US immigration. Which choice most effectively uses relevant information from the notes to accomplish this goal?

", "choices": [{"id": "A", "text": "

Almost 70% of slots were reserved for immigrants from Great Britain, Ireland, and Germany at the time the Hart-Celler Act was proposed.

"}, {"id": "B", "text": "

Prior to the Hart-Celler Act, new immigration quotas were based on how many people from each country lived in the US in 1890.

"}, {"id": "C", "text": "

The quota system in place in the early 1960s was abolished by the 1965 Hart-Celler Act. 

"}, {"id": "D", "text": "

The 1965 Hart-Celler Act abolished the national-origins quota system, which favored immigrants from northern Europe.

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. The sentence presents the significance of the Hart-Celler Act to an audience unfamiliar with the history of US immigration, noting that the 1965 act abolished the national-origins quota system and explaining why that mattered, historically: because the old quota system had favored immigrants from northern Europe.

Choice A is incorrect. The sentence describes an aspect of immigration policy at the time the Hart-Celler Act was proposed; it doesn’t present the significance of the Hart-Celler Act to an audience unfamiliar with the history of US immigration. Choice B is incorrect. The sentence describes an aspect of immigration policy before the Hart-Celler Act; it doesn’t describe or present the significance of the act to an audience unfamiliar with the history of US immigration. Choice C is incorrect. While the sentence indicates that the Hart-Celler Act abolished the old quota system, it doesn’t explain the act or the quota system to an audience unfamiliar with the history of US immigration.

"}, {"id": "7c9d0e38", "domain": "Expression of Ideas", "skill": "Rhetorical Synthesis", "difficulty": "M", "type": "mc", "stimulus": "

While researching a topic, a student has taken the following notes:

\n", "stem": "

The student wants to emphasize the different orders in which Australia’s invertebrate animals are classified. Which choice most effectively uses relevant information from the notes to accomplish this goal?

", "choices": [{"id": "A", "text": "

In Australia, 28,200 species are estimated to be beetles and weevils, both classified as invertebrates of the order Coleoptera.

"}, {"id": "B", "text": "

Among Australia’s many invertebrates, sawflies, wasps, bees, and ants belong to the order Hymenoptera, while beetles and weevils belong to the order Coleoptera.

"}, {"id": "C", "text": "

Many sawflies, wasps, bees, and ants of the order Hymenoptera are threatened by some of Australia’s invasive bird and fish species.

"}, {"id": "D", "text": "

The order Hymenoptera is estimated to make up 14,800 of Australia’s 200,000 animal species.

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. The sentence emphasizes the different orders that Australia’s invertebrates belong to, specifying that sawflies, wasps, bees, and ants belong to the order Hymenoptera, whereas beetles and weevils belong to the order Coleoptera.

Choice A is incorrect. The sentence only mentions one order, Coleoptera; it doesn’t emphasize the different orders that Australia’s invertebrates belong to. Choice C is incorrect. The sentence only mentions one order, Hymenoptera; it doesn’t emphasize the different orders that Australia’s invertebrates belong to. Choice D is incorrect. The sentence only mentions one order, Hymenoptera; it doesn’t emphasize the different orders that Australia’s invertebrates belong to.

"}, {"id": "ff3865b3", "domain": "Expression of Ideas", "skill": "Rhetorical Synthesis", "difficulty": "E", "type": "mc", "stimulus": "

While researching a topic, a student has taken the following notes:

\n", "stem": "

The student wants to describe the wok’s shape. Which choice most effectively uses relevant information from the notes to accomplish this goal?

", "choices": [{"id": "A", "text": "

Grace Young’s 2004 book, The Breath of a Wok, traces the history of the cooking pan.

"}, {"id": "B", "text": "

Able to cook food evenly and contain oil splatters, the wok is the subject of Grace Young’s 2004 book.

"}, {"id": "C", "text": "

A wok is a cooking pan with a round, wide base and high, angled sides.

"}, {"id": "D", "text": "

The design of a wok, a type of cooking pan that originated in China during the Han dynasty, helps the pan cook food evenly and contain oil splatters.

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. It summarizes the information that describes the wok’s shape from the second and third bullet points.

Choice A is incorrect. This choice doesn’t describe the shape of a wok. Choice B is incorrect. This choice doesn’t describe the shape of a wok, just some of its features. Choice D is incorrect. This choice doesn’t describe the shape of a wok, only some of its benefits or functions.

"}, {"id": "f1631638", "domain": "Expression of Ideas", "skill": "Rhetorical Synthesis", "difficulty": "M", "type": "mc", "stimulus": "

While researching a topic, a student has taken the following notes:

\n", "stem": "

The student wants to emphasize a difference between the two portraits. Which choice most effectively uses relevant information from the notes to accomplish this goal?

", "choices": [{"id": "A", "text": "

The portraits, or artistic representations, of Luis Jimenez and Rudolfo Anaya were both completed by Enriquez in the early 2000s.

"}, {"id": "B", "text": "

Enriquez has completed portraits of numerous Mexican Americans, including sculptor Luis Jimenez and writer Rudolfo Anaya. 

"}, {"id": "C", "text": "

While both are by Enriquez, the 2003 portrait of Luis Jimenez is a painting, and the 2016 portrait of Rudolfo Anaya is a drawing. 

"}, {"id": "D", "text": "

Luis Jimenez was a Mexican American sculptor, and Rudolfo Anaya was a Mexican American writer.

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. The sentence emphasizes a difference between the portraits, noting that one is a painting and the other is a drawing.

Choice A is incorrect. The sentence emphasizes a similarity between the two portraits rather than a difference. Choice B is incorrect. The sentence makes a generalization about Enriquez’s portraits; it doesn’t emphasize a difference between the portraits of Jimenez and Anaya. Choice D is incorrect. While the sentence notes a difference between Jimenez and Anaya, it doesn’t emphasize a difference between, or even mention, their portraits.

"}, {"id": "fdd9a360", "domain": "Expression of Ideas", "skill": "Rhetorical Synthesis", "difficulty": "H", "type": "mc", "stimulus": "

While researching a topic, a student has taken the following notes:

\n", "stem": "

The student wants to use a quotation to emphasize a potential problem with the wood-wide web theory. Which choice most effectively uses relevant information from the notes to accomplish this goal?

", "choices": [{"id": "A", "text": "

Describing trees as “super-cooperators,” Simard first suggested that trees can exchange resources with one another in 1997.

"}, {"id": "B", "text": "

In “The Decay of the Wood-Wide Web?,” Karst and colleagues note that common mycorrhizal networks “have captured the interest of broad audiences.”

"}, {"id": "C", "text": "

After evaluating dozens of CMN studies, Karst and colleagues expressed concern that recent claims about common mycorrhizal networks are “disconnected from evidence.”

"}, {"id": "D", "text": "

Despite the concerns expressed in the 2022 study “The Decay of the Wood-Wide Web?,” the wood-wide web theory remains popular.

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. This choice uses a quotation to convey the authors’ criticism and challenge to the wood-wide web theory due to an absence of evidence.

Choice A is incorrect. This choice doesn’t emphasize a potential problem with the wood-wide web theory. It uses a quotation to introduce the theory and its originator. It doesn’t mention any criticism or challenge to the theory. Choice B is incorrect. This choice uses a quotation, but it doesn’t emphasize a potential problem with the wood-wide web theory. It uses a quotation to describe the appeal and interest of the theory, but it doesn’t indicate why the authors are concerned or what evidence they have. Choice D is incorrect. This choice doesn’t use a quotation at all. It paraphrases the main idea of the 2022 study, but it doesn’t include any specific words or phrases from the notes. It also doesn’t emphasize a potential problem with the theory, but rather its popularity.

"}, {"id": "1b94a80a", "domain": "Expression of Ideas", "skill": "Rhetorical Synthesis", "difficulty": "M", "type": "mc", "stimulus": "

While researching a topic, a student has taken the following notes:

\n", "stem": "

The student wants to emphasize how Romney wool differs from Merino and Rambouillet wool. Which choice most effectively uses relevant information from the notes to accomplish this goal?

", "choices": [{"id": "A", "text": "

Romney wool is just one of the many kinds of wools, each originating from a different breed of sheep.

"}, {"id": "B", "text": "

Sheep wool varies from breed to breed, so Romney wool will be different than other kinds of wool.

"}, {"id": "C", "text": "

The fine wool produced by Merino and Rambouillet sheep is used for apparel, whereas the thicker wool of Romney sheep is used in rugs and blankets.

"}, {"id": "D", "text": "

Wool is an economically important fiber—especially in Australia—that can be used to make apparel or even rugs and blankets.

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. This choice most effectively emphasizes how Romney wool differs from Merino and Rambouillet wool. It describes the difference in thickness and the difference in what they’re used for. 

Choice A is incorrect. This choice doesn’t emphasize how Romney wool differs from Merino and Rambouillet wool. It doesn’t mention Merino or Rambouillet wool at all. Choice B is incorrect. This choice doesn’t emphasize how Romney wool differs from Merino and Rambouillet wool. It doesn’t mention Merino or Rambouillet wool at all. Choice D is incorrect. This choice doesn’t emphasize how Romney wool differs from Merino and Rambouillet wool. It doesn’t mention Romney, Merino or Rambouillet wool at all. 

"}, {"id": "88308a39", "domain": "Expression of Ideas", "skill": "Rhetorical Synthesis", "difficulty": "M", "type": "mc", "stimulus": "

While researching a topic, a student has taken the following notes:

\n", "stem": "

The student wants to emphasize a similarity between the two books by Shaun Tan. Which choice most effectively uses relevant information from the notes to accomplish this goal?

", "choices": [{"id": "A", "text": "

Shaun Tan’s book Tales from Outer Suburbia, which describes surreal events occurring in otherwise ordinary places, contains fewer short stories than Tales from the Inner City does.

"}, {"id": "B", "text": "

Tales from Outer Suburbia was published in 2008, and Tales from the Inner City was published in 2018.

"}, {"id": "C", "text": "

Unlike Tales from the Inner City, Shaun Tan’s book Tales from Outer Suburbia is set in suburban neighborhoods.

"}, {"id": "D", "text": "

Shaun Tan’s books Tales from Outer Suburbia and Tales from the Inner City both describe surreal events occurring in otherwise ordinary places.

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. The sentence uses “both” to emphasize a thematic similarity between Tan’s two books, noting that both Tales from Outer Suburbia and Tales from the Inner City describe surreal events occurring in otherwise ordinary places.

Choice A is incorrect. The sentence emphasizes a difference (one contains fewer stories than the other), not a similarity, between the two books. Choice B is incorrect. The sentence indicates that Tan’s books were published ten years apart; it doesn’t emphasize a similarity between the two books. Choice C is incorrect. The sentence uses “unlike” to emphasize a difference between Tales from Outer Suburbia and Tales from the Inner City; it doesn’t emphasize a similarity between the two books.

"}, {"id": "0fab0c90", "domain": "Expression of Ideas", "skill": "Rhetorical Synthesis", "difficulty": "H", "type": "mc", "stimulus": "

While researching a topic, a student has taken the following notes:

\n", "stem": "

The student wants to emphasize the duration and purpose of Cohen’s and Rodrigues’s work. Which choice most effectively uses relevant information from the notes to accomplish this goal?

", "choices": [{"id": "A", "text": "

At the Gullah Museums in Hilton Head Island and Georgetown, South Carolina, visitors can learn more about the Gullah people who have lived in the region for centuries.

"}, {"id": "B", "text": "

Louise Miller Cohen and Vermelle Rodrigues have worked to preserve the culture of the Gullah people, who have lived in the United States since the 18th century.

"}, {"id": "C", "text": "

Since 2003, Louise Miller Cohen and Vermelle Rodrigues have worked to preserve Gullah culture through their museums.

"}, {"id": "D", "text": "

Influenced by the traditions of West and Central Africa, Gullah culture developed in parts of the southeastern United States in the 18th century.

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. The sentence emphasizes both the duration (the length of time) and the purpose of Cohen’s and Rodrigues’s work by noting that the women have been working since 2003 to preserve Gullah culture. 

Choice A is incorrect. While the sentence emphasizes what visitors to Cohen’s and Rodrigues’s museums can learn, it doesn’t mention the duration or purpose of the women’s work. Choice B is incorrect. While the sentence emphasizes the purpose of Cohen’s and Rodrigues’s work, it doesn’t mention the duration of that work (the length of time the women have been working to preserve Gullah culture). Choice D is incorrect. While the sentence emphasizes where and when Gullah culture developed, it doesn’t mention the duration or purpose of Cohen’s and Rodrigues’s work.

"}, {"id": "00e0170f", "domain": "Expression of Ideas", "skill": "Transitions", "difficulty": "H", "type": "mc", "stimulus": "

Magnetic levitation (maglev) trains are suspended above a track by powerful electromagnets, reducing friction and thus allowing for much faster speeds. Though maglev advocates in the US have long imagined these trains crisscrossing the country, their dream remains unrealized. ______blank of the handful of maglev trains currently in operation, all are in Asia.

", "stem": "

Which choice completes the text with the most logical transition?

", "choices": [{"id": "A", "text": "

In fact,

"}, {"id": "B", "text": "

To that end,

"}, {"id": "C", "text": "

Nevertheless,

"}, {"id": "D", "text": "

That said,

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. This sentence emphasizes just how far maglev advocates’ dreams are from coming true. “In fact” is a transition used to emphasize the truth of a statement that modifies the previous statement and therefore fits perfectly in this context.

Choice B is incorrect. This choice uses a cause-and-effect transition, which doesn’t make sense here. Maglev advocates’ dream remaining unrealized would not cause there to be only a few maglev trains, all located in Asia. Choice C is incorrect. This choice uses a disagreement transition, which doesn’t make sense here. In fact, this sentence agrees with the previous sentence—both talk about how maglev trains are far from becoming common in the US. Choice D is incorrect. This choice uses a disagreement transition, which doesn’t make sense here. In fact, this sentence agrees with the previous sentence—both talk about how maglev trains are far from becoming common in the US.

"}, {"id": "56cad44a", "domain": "Expression of Ideas", "skill": "Rhetorical Synthesis", "difficulty": "M", "type": "mc", "stimulus": "

While researching a topic, a student has taken the following notes:

\n", "stem": "

The student wants to emphasize a difference between surface-dwelling and cave-dwelling tetras. Which choice most effectively uses relevant information from the notes to accomplish this goal?

", "choices": [{"id": "A", "text": "

Surface-dwelling and cave-dwelling tetras may belong to the same species, but they are quite different.

"}, {"id": "B", "text": "

Cave-dwelling tetras can no longer see but use sensory receptors on their skulls to navigate.

"}, {"id": "C", "text": "

Mexican tetras are a fish species with two distinct populations: surface-dwelling tetras and cave-dwelling tetras.

"}, {"id": "D", "text": "

Surface-dwelling tetras can see, whereas cave-dwelling tetras cannot.

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. The sentence emphasizes a difference between surface-dwelling and cave-dwelling tetras, noting that while surface-dwelling tetras can see, cave-dwelling tetras can’t.

Choice A is incorrect. While the sentence notes that surface-dwelling and cave-dwelling tetras are different, it doesn’t emphasize any difference between the two populations of tetras. Choice B is incorrect because the sentence explains that cave-dwelling tetras use sensory receptors on their skulls to navigate; it doesn’t emphasize a difference between surface-dwelling and cave-dwelling tetras. Choice C is incorrect. While the sentence notes that there are two different populations of Mexican tetras, it doesn’t emphasize any difference between the two populations.

"}, {"id": "c071eca2", "domain": "Expression of Ideas", "skill": "Transitions", "difficulty": "H", "type": "mc", "stimulus": "

Iraqi artist Nazik Al-Malaika, celebrated as the first Arabic poet to write in free verse, didn’t reject traditional forms entirely; her poem “Elegy for a Woman of No Importance” consists of two ten-line stanzas and a standard number of syllables. Even in this superficially traditional work, ______blank Al-Malaika was breaking new ground by memorializing an anonymous woman rather than a famous man.

", "stem": "

Which choice completes the text with the most logical transition?

", "choices": [{"id": "A", "text": "

therefore,

"}, {"id": "B", "text": "

in fact,

"}, {"id": "C", "text": "

moreover,

"}, {"id": "D", "text": "

though,

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. The first sentence tells us that Al-Malaika sometimes used \"traditional forms\". The second tells us that even when she used traditional forms, Al-Malaika was \"breaking new ground\". To connect these ideas, we need a contrast word like \"but.\" \"Though\" is a contrast word similar to \"but.\"

Choice A is incorrect. This isn’t a logical transition. The first sentence tells us that Al-Malaika sometimes used \"traditional forms\". The second tells us that even when she used traditional forms, Al-Malaika was \"breaking new ground\". To connect these ideas, we need a contrast word like \"but.\" \"Therefore\" doesn’t show contrast; it shows cause and effect. Choice B is incorrect. This isn’t a logical transition. The first sentence tells us that Al-Malaika sometimes used \"traditional forms\". The second tells us that even when she used traditional forms, Al-Malaika was \"breaking new ground\". To connect these ideas, we need a contrast word like \"but.\" \"In fact\" is a phrase that usually emphasizes the truth of the previous statement. Choice C is incorrect. This isn’t a logical transition. The first sentence tells us that Al-Malaika sometimes used \"traditional forms\". The second tells us that even when she used traditional forms, Al-Malaika was \"breaking new ground\". To connect these ideas, we need a contrast word like \"but.\" \"Moreover\" doesn’t show contrast—it introduces additional information that continues or supports the previous idea.

"}, {"id": "176edca6", "domain": "Expression of Ideas", "skill": "Transitions", "difficulty": "H", "type": "mc", "stimulus": "

A 2017 study of sign language learners tested the role of iconicity—the similarity of a sign to the thing it represents—in language acquisition. The study found that the greater the iconicity of a sign, the more likely it was to have been learned. ______blank the correlation between acquisition and iconicity was lower than that between acquisition and another factor studied: sign frequency.

", "stem": "

Which choice completes the text with the most logical transition?

", "choices": [{"id": "A", "text": "

In fact,

"}, {"id": "B", "text": "

In other words,

"}, {"id": "C", "text": "

Granted,

"}, {"id": "D", "text": "

As a result,

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. “Granted” logically signals that the following information—that iconicity is not as highly correlated with acquisition as sign frequency—is true in spite of the information about the correlation between iconicity and acquisition in the previous sentence.

Choice A is incorrect because “in fact” illogically signals that the sentence that follows either emphasizes or refutes the information in the previous sentence regarding the correlation between iconicity and acquisition. Instead, the sentence that follows provides additional information that is true in spite of the preceding information; it neither emphasizes nor refutes that information. Choice B is incorrect because “in other words” illogically signals that the sentence that follows is a restatement of the information in the previous sentence; instead, the sentence that follows provides additional information that is true in spite of the preceding information. Choice D is incorrect because “as a result” illogically signals that the sentence that follows is a result of the information in the previous sentence regarding the correlation between iconicity and acquisition; instead, the sentence that follows is true in spite of the preceding information.

"}, {"id": "10cd0327", "domain": "Expression of Ideas", "skill": "Rhetorical Synthesis", "difficulty": "H", "type": "mc", "stimulus": "

While researching a topic, a student has taken the following notes:

\n", "stem": "

The student wants to present the study’s findings to an audience already familiar with thermal inversions. Which choice most effectively uses relevant information from the notes to accomplish this goal?

", "choices": [{"id": "A", "text": "

Heat-absorbing metals may reside in a planet’s upper atmosphere.

"}, {"id": "B", "text": "

The team studied thermal inversions in twenty-five gas giants, which are largely composed of helium and hydrogen.

"}, {"id": "C", "text": "

Researchers found that gas giants featuring a thermal inversion were likely to contain heat-absorbing metals, which may reside in the planets’ upper atmospheres.

"}, {"id": "D", "text": "

Gas giants were likely to contain heat-absorbing metals when they featured a layer of atmosphere warmer than the layer beneath it, researchers found; this phenomenon is known as a thermal inversion.

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. It describes the study’s findings in a way that assumes the audience is already familiar with thermal inversions.

Choice A is incorrect. This choice doesn’t fully describe the findings of the study, because it doesn’t include anything about thermal inversions. Choice B is incorrect. This choice doesn’t describe the study’s findings. Choice D is incorrect. This choice isn’t suited for an audience already familiar with thermal inversion. A familiar audience wouldn’t need to have the term defined.

"}, {"id": "388b45aa", "domain": "Expression of Ideas", "skill": "Transitions", "difficulty": "M", "type": "mc", "stimulus": "

Establishing Coordinated Universal Time (UTC) is no easy task. Each month, readings of a single second from atomic clocks around the world are taken and sent to the International Bureau of Weights and Measures (BIPM) in France. ______blank BIPM metrologists perform the meticulous work of assembling these minutely disparate readings into a globally shared time standard.

", "stem": "

Which choice completes the text with the most logical transition?

", "choices": [{"id": "A", "text": "

There,

"}, {"id": "B", "text": "

In particular,

"}, {"id": "C", "text": "

For example,

"}, {"id": "D", "text": "

Conversely,

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. \"There\" indicates that the work of calculating Coordinated Universal Time takes place at the International Bureau of Weights and Measures in France. Because \"there\" indicates a location, it fits the context perfectly.

Choice B is incorrect. This choice uses an exemplification transition, which doesn’t make sense here. This sentence is describing where the work of coordinating Coordinated Universal Time takes place, not giving an example of the work described in the previous sentence. Choice C is incorrect. This choice uses an exemplification transition, which doesn’t make sense here. This sentence is describing where the work of coordinating Coordinated Universal Time takes place, not giving an example of the work described in the previous sentence. Choice D is incorrect. This choice uses a disagreement transition. But this sentence doesn’t disagree with the previous sentence. They both describe the work involved in calculating Coordinated Universal Time.

"}, {"id": "4b376902", "domain": "Expression of Ideas", "skill": "Rhetorical Synthesis", "difficulty": "E", "type": "mc", "stimulus": "

While researching a topic, a student has taken the following notes:

\n", "stem": "

The student wants to explain an advantage of microprobes. Which choice most effectively uses relevant information from the notes to accomplish this goal?

", "choices": [{"id": "A", "text": "

Despite being heavy, NASA’s rovers can land successfully on the surface of Mars.

"}, {"id": "B", "text": "

Microprobes, which weigh as little as 50 milligrams, could explore areas of Mars that are inaccessible to NASA’s heavy, wheeled rovers.

"}, {"id": "C", "text": "

NASA currently uses its rovers on Mars, but microprobes have been proposed as an alternative.

"}, {"id": "D", "text": "

Though they are different sizes, both microprobes and rovers can be used to explore the surface of Mars.

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. The sentence explains an advantage of microprobes, noting that because microprobes weigh as little as 50 milligrams, they can explore areas inaccessible to rovers.

Choice A is incorrect. The sentence indicates that rovers can land successfully on Mars despite their weight; it doesn’t explain an advantage of microprobes. Choice C is incorrect. While the sentence mentions that microprobes have been proposed as an alternative to rovers, it doesn’t explain an advantage of microprobes. Choice D is incorrect. The sentence emphasizes a similarity between microprobes and rovers; it doesn’t explain an advantage of microprobes.

"}, {"id": "dede8260", "domain": "Expression of Ideas", "skill": "Rhetorical Synthesis", "difficulty": "M", "type": "mc", "stimulus": "

While researching a topic, a student has taken the following notes:

\n", "stem": "

The student wants to emphasize the study’s methodology. Which choice most effectively uses relevant information from the notes to accomplish this goal?

", "choices": [{"id": "A", "text": "

The student policies of 132 medical schools can be found online, according to research by Terry Kind.

"}, {"id": "B", "text": "

To find out how many medical schools have guidelines about student social media use, Terry Kind and her team examined the student policies of 132 medical schools.

"}, {"id": "C", "text": "

Out of 132 medical schools, only thirteen had student policies that mentioned social media, and only five specified what use was acceptable. 

"}, {"id": "D", "text": "

Terry Kind and her team wanted to know how many medical schools have student social media policies in place about protecting patient confidentiality. 

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. The sentence effectively emphasizes Kind’s methodology: examining the student policies of 132 medical schools for guidelines about student social media use.

Choice A is incorrect. The sentence specifies how many medical schools’ student policies are available online; it doesn’t emphasize the study’s methodology. Choice C is incorrect. The sentence emphasizes the study’s results, not the study’s methodology. Choice D is incorrect. The sentence emphasizes the aim of the study, not the study’s methodology.

"}, {"id": "81315093", "domain": "Expression of Ideas", "skill": "Rhetorical Synthesis", "difficulty": "M", "type": "mc", "stimulus": "

While researching a topic, a student has taken the following notes:

\n", "stem": "

The student wants to make a generalization about ultramarathons. Which choice most effectively uses relevant information from the notes to accomplish this goal?

", "choices": [{"id": "A", "text": "

Examples of ultramarathons include the 37.3-mile Kepler Challenge in New Zealand and the 261-mile Spreelauf in Germany.

"}, {"id": "B", "text": "

A marathon is 26.2 miles long, but the Spreelauf ultramarathon, at 261 miles, is far longer.

"}, {"id": "C", "text": "

Ultramarathons range widely in length, from a few dozen miles to a few hundred.

"}, {"id": "D", "text": "

While the Kepler Challenge is a one-day ultramarathon, the Spreelauf is a six-day ultramarathon.

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. This is the only choice that makes a generalization about ultramarathons.

Choice A is incorrect. This choice gives specific examples of ultramarathons but doesn’t say anything about them as a category. Choice B is incorrect. This choice compares marathons in general to one specific ultramarathon but doesn’t say anything about ultramarathons as a category. Choice D is incorrect. This choice contrasts two specific ultramarathons but doesn’t say anything about them as a category.

"}, {"id": "1773fa73", "domain": "Expression of Ideas", "skill": "Rhetorical Synthesis", "difficulty": "H", "type": "mc", "stimulus": "

While researching a topic, a student has taken the following notes:

\n", "stem": "

The student wants to provide an overview of the matsutake commodity chain. Which choice most effectively uses relevant information from the notes to accomplish this goal?

", "choices": [{"id": "A", "text": "

The contemporary matsutake commodity chain has its origins in the 1980s when, according to Tsing, “the scarcity of matsutake in Japan first became clear.”

"}, {"id": "B", "text": "

Commodity chains include the linked production and purchase of commodities, such as the matsutake mushroom, on the world market.

"}, {"id": "C", "text": "

Decades after the Japanese import of matsutake began, a commodity chain now links matsutake pickers in Oregon with wealthy consumers of the costly mushrooms in Japan.

"}, {"id": "D", "text": "

Wealthy consumers who buy the costly mushrooms in Japan are at one end of the matsutake commodity chain.

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. The sentence provides an overview of the matsutake commodity chain, connecting the Oregon mushroom pickers at one end to the Japanese consumers at the other.

Choice A is incorrect. While the sentence mentions the matsutake commodity chain, it focuses only on its origins; it does not provide an overview. Choice B is incorrect. The sentence provides a general definition of commodity chains, not an overview of the matsutake chain. Choice D is incorrect. While the sentence mentions the matsutake commodity chain, it focuses only on one end of the chain (the consumers); it does not provide an overview.

"}, {"id": "6b5bc97d", "domain": "Expression of Ideas", "skill": "Rhetorical Synthesis", "difficulty": "E", "type": "mc", "stimulus": "

While researching a topic, a student has taken the following notes: 

\n", "stem": "

The student wants to specify the location of Ctesiphon. Which choice most effectively uses relevant information from the notes to accomplish this goal?

", "choices": [{"id": "A", "text": "

The Sasanian Empire began in AD 224 and ended in AD 651.

"}, {"id": "B", "text": "

The capital of the Sasanian Empire, which spanned 1.4 million square miles, was Ctesiphon.

"}, {"id": "C", "text": "

The Sasanians controlled an area of 1.4 million square miles, including present-day Iran and Iraq.

"}, {"id": "D", "text": "

Ctesiphon, the capital of the Sasanian Empire, was located near present-day Baghdad, Iraq.

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. The sentence specifies the location of Ctesiphon, noting that it was located near present-day Baghdad, Iraq.

Choice A is incorrect because the sentence explains when the Sasanian Empire began and ended; it doesn’t specify the location of Ctesiphon. Choice B is incorrect because the sentence emphasizes that Ctesiphon was the capital of the Sasanian Empire; it doesn’t specify Ctesiphon’s location. Choice C is incorrect because it emphasizes the size of the Sasanian Empire; it doesn’t specify the location of Ctesiphon.

"}, {"id": "5b8b69a2", "domain": "Expression of Ideas", "skill": "Rhetorical Synthesis", "difficulty": "H", "type": "mc", "stimulus": "

While researching a topic, a student has taken the following notes:

\n", "stem": "

The student wants to summarize the kelp highway hypothesis. Which choice most effectively uses relevant information from the notes to accomplish this goal?

", "choices": [{"id": "A", "text": "

Pacific Ocean islands and coastlines likely contained “a rich mix of marine, estuarine, riverine, and terrestrial resources” such as seaweeds, fish, and birds, according to researchers.

"}, {"id": "B", "text": "

One argument about how humans first arrived in the Americas is the kelp highway hypothesis proposed by Jon Erlandson and colleagues.

"}, {"id": "C", "text": "

Humans may have first arrived in the Americas by sea, traveling between Pacific Ocean islands and coastlines and subsisting on a variety of resources.

"}, {"id": "D", "text": "

As glaciers melted and sea levels rose, many Pacific Ocean islands and coastal zones were submerged.

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. This choice summarizes the main idea of the kelp highway hypothesis, providing a high-level overview of how the hypothesis explains human migration to the Americas.

Choice A is incorrect. This choice describes one aspect of the proposed scenario but doesn’t discuss human migration, which is the main focus of the kelp highway hypothesis. Choice B is incorrect. This choice introduces the kelp highway hypothesis but doesn’t explain what it entails. Choice D is incorrect. This choice describes one element of the proposed scenario but doesn’t discuss human migration, which is the main focus of the kelp highway hypothesis.

"}, {"id": "49fe306b", "domain": "Expression of Ideas", "skill": "Rhetorical Synthesis", "difficulty": "M", "type": "mc", "stimulus": "

While researching a topic, a student has taken the following notes:

\n", "stem": "

The student wants to explain the origin of the Perseid meteor shower’s name. Which choice most effectively uses relevant information from the notes to accomplish this goal?

", "choices": [{"id": "A", "text": "

The Perseid meteor shower is named for the constellation Perseus, the location of the meteor shower’s radiant.

"}, {"id": "B", "text": "

A meteor shower’s name may be linked to a single spot in the sky.

"}, {"id": "C", "text": "

The Perseid meteor shower, which has a radiant, is visible in the northern hemisphere in July and August.

"}, {"id": "D", "text": "

From Earth, all the meteors in a meteor shower appear to originate from a radiant, such as the one within Perseus.

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. The sentence explains the origin of the Perseid meteor shower’s name: the constellation Perseus, where the meteor shower’s radiant is located.

Choice B is incorrect. The sentence makes a claim about meteor shower names in general; it doesn’t explain the origin of the Perseid meteor shower’s name specifically. Choice C is incorrect. The sentence indicates when and where the Perseid meteor shower is visible; it doesn’t explain the origin of the meteor shower’s name. Choice D is incorrect. The sentence discusses meteor showers in general; it doesn’t explain the origin of the Perseid meteor shower’s name.

"}, {"id": "5888712f", "domain": "Expression of Ideas", "skill": "Rhetorical Synthesis", "difficulty": "M", "type": "mc", "stimulus": "

While researching a topic, a student has taken the following notes:

\n", "stem": "

The student wants to contrast the emissivity of reflective metal fibers with that of silicon carbide fibers. Which choice most effectively uses relevant information from the notes to accomplish this goal?

", "choices": [{"id": "A", "text": "

The ability of reflective metal fibers and silicon carbide fibers to emit heat was determined by an analysis of each material’s emissivity.

"}, {"id": "B", "text": "

The amount of heat a material absorbs is equal to the amount it emits, as evidenced in Abebe’s analyses.

"}, {"id": "C", "text": "

Though the reflective metal fibers and silicon carbide fibers had different rates of emissivity, Abebe planned to use both in a garment.

"}, {"id": "D", "text": "

Whereas the reflective metal fibers had an emissivity of just 0.02, the silicon carbide fibers absorbed large amounts of heat, resulting in an emissivity of 0.74.

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. The sentence uses “whereas” to contrast the emissivities of the two fibers, noting that the emissivity of the reflective metal fibers was just 0.02, far lower than that of the silicon carbide fibers (0.74).

Choice A is incorrect. The sentence emphasizes the ability of reflective metal fibers and silicon carbide fibers to emit heat; it doesn’t contrast the emissivities of the two fibers. Choice B is incorrect. The sentence states a law of thermodynamics: the amount of heat a material absorbs is equal to the amount it emits. The sentence doesn’t contrast the emissivity of reflective metal fibers with that of silicon carbide fibers. Choice C is incorrect. While the sentence includes a generalization about the emissivities of reflective metal fibers and silicon carbide fibers, it emphasizes Abebe’s plans for their use in a garment; it doesn’t contrast the emissivities of the two fibers.

"}, {"id": "0acc26b2", "domain": "Expression of Ideas", "skill": "Rhetorical Synthesis", "difficulty": "H", "type": "mc", "stimulus": "

While researching a topic, a student has taken the following notes:

\n", "stem": "

The student wants to make and support a generalization about the orbits of comets. Which choice most effectively uses relevant information from the notes to accomplish these goals? 

", "choices": [{"id": "A", "text": "

Astronomers estimate that the number of comets orbiting the Sun is in the billions; the comets’ orbits may change over time.

"}, {"id": "B", "text": "

Like Uranus, Jupiter, and Mars, billions of comets orbit the Sun.

"}, {"id": "C", "text": "

One example of a comet is 81P/Wild, whose orbit around the Sun once lay between Uranus’s and Jupiter’s orbits but is now positioned between those of Jupiter and Mars.

"}, {"id": "D", "text": "

A comet’s orbit around the Sun may change over time: the orbit of comet 81P/Wild once lay between the orbits of Uranus and Jupiter but is now positioned between those of Jupiter and Mars.

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. The sentence makes a generalization—that a comet’s orbit around the Sun may change over time—and supports the generalization with the example of the orbit of comet 81P/Wild, which once lay between the orbits of Uranus and Jupiter but is now positioned between the orbits of Jupiter and Mars.

Choice A is incorrect. The sentence emphasizes the number of comets orbiting the Sun and makes a generalization about their orbits, but it doesn’t support the generalization with an example. Choice B is incorrect. The sentence makes a generalization about comets and compares them to the planets Uranus, Jupiter, and Mars; it doesn’t make and support a generalization about comets’ orbits. Choice C is incorrect. While the sentence provides an example of a comet whose orbit has changed, it doesn’t make a generalization about the orbits of comets.

"}, {"id": "1c6e1d55", "domain": "Expression of Ideas", "skill": "Transitions", "difficulty": "H", "type": "mc", "stimulus": "

Historically, most conductors of major orchestras and opera companies have been European men, but a new, more diverse generation of artists is stepping up to the podium. Mexico’s Alondra de la Parra took over as conductor for the Queensland Symphony Orchestra in 2017, ______blank and Colombia’s Lina Gonzalez-Granados did the same for the Los Angeles Opera in 2022.

", "stem": "

Which choice completes the text with the most logical transition?

", "choices": [{"id": "A", "text": "

in addition,

"}, {"id": "B", "text": "

lastly,

"}, {"id": "C", "text": "

granted,

"}, {"id": "D", "text": "

for instance,

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. “For instance” logically signals that the details in this sentence—that Mexican conductor Alondra de la Parra and Colombian conductor Lina Gonzalez-Granados took new conducting positions—are examples supporting the previous claim about the new generation of artists.

Choice A is incorrect because “in addition” illogically signals that the details in this sentence about de la Parra and Gonzalez-Granados are merely additional facts related to the previous claim about the new generation of artists. Instead, they are examples supporting that claim. Choice B is incorrect because “lastly” illogically signals that the details in this sentence about de la Parra and Gonzalez-Granados are the last step or a concluding summary of the previous claim about the new generation of artists. Instead, they are examples supporting that claim. Choice C is incorrect because “granted” illogically signals that the details in this sentence about de la Parra and Gonzalez-Granados are exceptions to the previous claim about the new generation of artists. Instead, they are examples supporting that claim.

"}, {"id": "8622320e", "domain": "Expression of Ideas", "skill": "Transitions", "difficulty": "M", "type": "mc", "stimulus": "

Earth’s auroras—colorful displays of light seen above the northern and southern poles—result, broadly speaking, from the Sun’s activity. ______blank the Sun releases charged particles that are captured by Earth’s magnetic field and channeled toward the poles. These particles then collide with atoms in the atmosphere, causing the atoms to emit auroral light.

", "stem": "

Which choice completes the text with the most logical transition?

", "choices": [{"id": "A", "text": "

Specifically,

"}, {"id": "B", "text": "

Similarly,

"}, {"id": "C", "text": "

Nevertheless,

"}, {"id": "D", "text": "

Hence,

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. “Specifically” logically signals that the information in this sentence—that the Sun releases charged particles that later collide with atoms, resulting in auroral light—provides specific, precise details about how auroras result from the Sun’s activity. 

Choice B is incorrect because “similarly” illogically signals that the information in this sentence is similar to the general information about auroras in the previous sentence. Instead, this sentence provides specific, precise details about how auroras form. Choice C is incorrect because “nevertheless” illogically signals that the information in this sentence is despite the general information about auroras in the previous sentence. Instead, this sentence provides specific, precise details about how auroras form. Choice D is incorrect because “hence” illogically signals that the information in this sentence is a result of the general information about auroras in the previous sentence. Instead, this sentence provides specific, precise details about how auroras form.

"}, {"id": "04397a63", "domain": "Expression of Ideas", "skill": "Rhetorical Synthesis", "difficulty": "M", "type": "mc", "stimulus": "

While researching a topic, a student has taken the following notes:

\n", "stem": "

The student wants to present the influence theory to an audience unfamiliar with the Haudenosaunee Confederacy. Which choice most effectively uses relevant information from the notes to accomplish this goal?

", "choices": [{"id": "A", "text": "

Historian Bruce Johansen believes that the Great Law of Peace was very influential.

"}, {"id": "B", "text": "

The influence theory is supported by the fact that Benjamin Franklin and Thomas Jefferson both studied the Haudenosaunee Confederacy.

"}, {"id": "C", "text": "

The influence theory holds that the principles of the Great Law of Peace, a centuries-old agreement binding six Native nations in the northeastern US, influenced the US Constitution.

"}, {"id": "D", "text": "

Native people, including the members of the Haudenosaunee Confederacy, influenced the founding of the US in many different ways.

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. The sentence effectively presents the influence theory to an audience unfamiliar with the Haudenosaunee Confederacy, explaining the theory’s position that the Great Law of Peace influenced the US Constitution while avoiding mention of the Haudenosaunee Confederacy itself.

Choice A is incorrect. The sentence broadly emphasizes Johansen’s ideas about the Great Law of Peace; it doesn’t identify the influence theory or effectively present it. Choice B is incorrect. The sentence emphasizes one fact that supports the influence theory; it doesn’t effectively present the theory to an audience unfamiliar with the Haudenosaunee Confederacy. Choice D is incorrect. The sentence makes a broad generalization about Native people’s influence on the founding of the US; it doesn’t effectively present the influence theory.

"}, {"id": "164a32e7", "domain": "Expression of Ideas", "skill": "Rhetorical Synthesis", "difficulty": "M", "type": "mc", "stimulus": "

While researching a topic, a student has taken the following notes:

\n", "stem": "

The student wants to emphasize Claude McKay’s accomplishments before moving to Harlem. Which choice most effectively uses relevant information from the notes to accomplish this goal?

", "choices": [{"id": "A", "text": "

Jamaican American writer Claude McKay is the author of works such as Songs of Jamaica (1912), Constab Ballads (1912), Harlem Shadows (1922), and Home to Harlem (1928).

"}, {"id": "B", "text": "

Although he is best known as a Harlem Renaissance writer, Claude McKay had published two acclaimed poetry collections in 1912 while living in Jamaica: Songs of Jamaica and Constab Ballads.

"}, {"id": "C", "text": "

In 1914, Claude McKay moved to Harlem, where he would become known as a poet and novelist of the Harlem Renaissance (a literary and cultural movement of the 1920s and 1930s).

"}, {"id": "D", "text": "

Before moving to Harlem, Claude McKay—author of the poetry collection Harlem Shadows (1922) and the novel Home to Harlem (1928)—lived in Jamaica.

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. This choice contrasts McKay’s fame as a Harlem Renaissance writer with his earlier achievements as a Jamaican poet, and it names the two collections he published before moving to Harlem.

Choice A is incorrect. This choice doesn’t emphasize McKay’s accomplishments before moving to Harlem. It lists some of his works but doesn’t distinguish between those he wrote in Jamaica and those he wrote in Harlem. Choice C is incorrect. This choice doesn’t emphasize McKay’s accomplishments before moving to Harlem. It only mentions the year he moved and what he would become known for afterwards. Choice D is incorrect. This choice doesn’t emphasize McKay’s accomplishments before moving to Harlem. It mentions that he lived in Jamaica, but it doesn’t name any of the works he published there.

"}, {"id": "fbffb352", "domain": "Expression of Ideas", "skill": "Rhetorical Synthesis", "difficulty": "E", "type": "mc", "stimulus": "

While researching a topic, a student has taken the following notes:

\n", "stem": "

The student wants to emphasize a similarity between the Laas Geel paintings and the Dhagah Nabi Galay paintings. Which choice most effectively uses relevant information from the notes to accomplish this goal?

", "choices": [{"id": "A", "text": "

The earliest examples of writing in East Africa are thought to be featured in the paintings at the Dhagah Nabi Galay caves in Somaliland.

"}, {"id": "B", "text": "

The paintings at the Dhagah Nabi Galay caves feature examples of writing, while those at the Laas Geel caves feature humans and animals.

"}, {"id": "C", "text": "

In Somaliland, the paintings in the Laas Geel caves feature human figures and animals.

"}, {"id": "D", "text": "

The Laas Geel paintings and the Dhagah Nabi Galay paintings are both examples of ancient rock art found in Somaliland.

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. This choice compares the Laas Geel paintings and the Dhagah Nabi Galay paintings to one another and emphasizes what they have in common: they are both ancient rock art found in the same region.

Choice A is incorrect. This choice only mentions the Dhagah Nabi Galay paintings. It doesn’t compare them to the Laas Geel paintings. Choice B is incorrect. This choice doesn’t emphasize a similarity between the two paintings. Instead, it emphasizes a difference: the type of content they depict. Choice C is incorrect. This choice only mentions the Laas Geel paintings. It doesn’t compare them to the Dhagah Nabi Galay paintings.

"}, {"id": "9f1a0d91", "domain": "Expression of Ideas", "skill": "Transitions", "difficulty": "H", "type": "mc", "stimulus": "

“Tulip mania”—the rapid rise and sudden fall of the price of tulip bulbs in seventeenth-century Amsterdam—is often cited as an example of the perils of rampant market speculation. However, recent research has demonstrated that the episode was neither as frenzied nor as disastrous as has been thought. The popular myth surrounding it, ______blank should be regarded with some skepticism.

", "stem": "

Which choice completes the text with the most logical transition?

", "choices": [{"id": "A", "text": "

for example,

"}, {"id": "B", "text": "

by contrast,

"}, {"id": "C", "text": "

nevertheless,

"}, {"id": "D", "text": "

therefore,

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. This sentence is arguing that new evidence contradicting popular beliefs about “tulip mania” should cast doubt on those beliefs. “Therefore” is a cause-and-effect transition, which fits perfectly in this context.

Choice A is incorrect. This choice uses an exemplification transition, which doesn’t make sense here. Skepticism about the popular beliefs is not an example of recent evidence contradicting those beliefs—rather, skepticism is an effect of that recent evidence. Choice B is incorrect. This choice uses a disagreement transition. But this sentence doesn’t disagree with the previous sentence. Instead, it connects a cause from the previous sentence (new evidence that tulip mania was not as disastrous as thought) to an effect (that we should look with skepticism upon the myth about its disastrousness). Choice C is incorrect. This choice uses a disagreement transition. But this sentence doesn’t disagree with the previous sentence. Instead, it connects a cause from the previous sentence (new evidence that tulip mania was not as disastrous as thought) to an effect (that we should look with skepticism upon the myth about its disastrousness).

"}, {"id": "17e49403", "domain": "Expression of Ideas", "skill": "Transitions", "difficulty": "M", "type": "mc", "stimulus": "

When, in the 1800s, geologists first realized that much of Earth had once been covered by great sheets of ice, some theorized that the phenomenon was cyclical, occurring at regular intervals. Each Ice Age is so destructive, though, that it largely erases the geological evidence of its predecessor. ______blank geologists were unable to confirm the theory of cyclical Ice Ages until the 1960s.

", "stem": "

Which choice completes the text with the most logical transition?

", "choices": [{"id": "A", "text": "

Hence,

"}, {"id": "B", "text": "

Moreover,

"}, {"id": "C", "text": "

Nevertheless,

"}, {"id": "D", "text": "

Next,

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. “Hence” logically signals that the information in this sentence—that geologists couldn’t confirm the theory of cyclical Ice Ages until the 1960s—is a consequence of the previous information about the destructiveness of each Ice Age and the erasure of necessary geological evidence.  

Choice B is incorrect because “moreover” illogically signals that the information in this sentence is merely additional to the previous information about the destructiveness of each Ice Age. Instead, the sentence  identifies a specific consequence of that information. Choice C is incorrect because “nevertheless” illogically signals that the information in this sentence is true despite the previous information about the destructiveness of each Ice Age. Instead, the sentence identifies a specific consequence of that information. Choice D is incorrect because “next” illogically signals that the information in this sentence is the next step in a process. Instead, the sentence identifies a specific consequence of the previous information.

"}, {"id": "5222ffab", "domain": "Expression of Ideas", "skill": "Rhetorical Synthesis", "difficulty": "H", "type": "mc", "stimulus": "

While researching a topic, a student has taken the following notes:

\n", "stem": "

The student wants to summarize the study’s findings. Which choice most effectively uses relevant information from the notes to accomplish this goal?

", "choices": [{"id": "A", "text": "

To arrive at these findings, which describe dual methods of processing smells in the piriform cortex, Padmanabhan and Chen devised a study using mathematical models.

"}, {"id": "B", "text": "

Padmanabhan and Chen showed that olfactory information is captured by cells in the piriform cortex, where the perception of odor forms.

"}, {"id": "C", "text": "

Using mathematical models, Padmanabhan and Chen devised a study to better understand the workings of the brain’s olfactory system.

"}, {"id": "D", "text": "

According to Padmanabhan and Chen, the brain can toggle between capturing olfactory information at a given moment and tracking changes in that information over time.

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. The sentence effectively summarizes the study’s findings, explaining what Padmanabhan and Chen found: that the brain can toggle between one method of processing smells (capturing information at a given moment) and another (tracking changes in information over time). 

Choice A is incorrect. While the sentence mentions findings, it mainly focuses on Padmanabhan and Chen’s methodology. It doesn’t effectively summarize the study’s findings. Choice B is incorrect. The sentence notes a fact about the olfactory system—that the perception of odor forms in the piriform cortex—but doesn’t summarize the findings of Padmanabhan and Chen’s study. Choice C is incorrect. The sentence presents the goal of Padmanabhan and Chen’s study; it doesn’t summarize the study’s findings.

"}, {"id": "7aac173e", "domain": "Expression of Ideas", "skill": "Rhetorical Synthesis", "difficulty": "M", "type": "mc", "stimulus": "

While researching a topic, a student has taken the following notes:

\n", "stem": "

The student wants to specify why historians believe Abele designed most of Duke’s campus buildings. Which choice most effectively uses relevant information from the notes to accomplish this goal?

", "choices": [{"id": "A", "text": "

Given that most of the buildings on Duke’s campus feature architectural styles that Abele had studied in Europe, historians believe Abele is the one who designed them.

"}, {"id": "B", "text": "

Though Abele wasn’t formally credited at the time, historians believe he designed most of the buildings on Duke’s campus.

"}, {"id": "C", "text": "

Most of Duke’s campus buildings, which were designed by a firm Abele worked for, were designed in the Gregorian and neo-Gothic architectural styles.

"}, {"id": "D", "text": "

Abele, an architect who studied Gregorian and neo-Gothic architecture in Europe, is believed to have designed most of the buildings on Duke’s campus.

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. The sentence specifies why historians believe Abele designed most of Duke’s campus buildings, noting that most of the buildings feature architectural styles that Abele had studied.

Choice B is incorrect. While the sentence explains that historians believe Abele designed most of Duke’s campus buildings, it doesn’t specify why historians hold that belief. Choice C is incorrect because the sentence emphasizes the architectural styles of Duke’s campus buildings; it doesn’t specify why historians believe Abele designed the buildings. Choice D is incorrect. While the sentence explains that Abele is believed to have designed most of the buildings on Duke’s campus, it doesn’t specify why historians believe that he designed the buildings.

"}, {"id": "3dcc7140", "domain": "Expression of Ideas", "skill": "Rhetorical Synthesis", "difficulty": "H", "type": "mc", "stimulus": "

While researching a topic, a student has taken the following notes:

\n", "stem": "

The student wants to make and support a generalization about nissologists’ definition of an island. Which choice most effectively uses relevant information from the notes to accomplish these goals?

", "choices": [{"id": "A", "text": "

The definition of an island as any piece of land surrounded by water is supported by some nissologists, scientists who study islands.

"}, {"id": "B", "text": "

Multiple counts of Sweden’s islands have been based on different definitions of an island.

"}, {"id": "C", "text": "

Based on a recent count, Sweden has a relatively small number of islands with at least 50 permanent residents.

"}, {"id": "D", "text": "

Nissologists’ different definitions can result in huge disparities in counts of islands, as the example of Sweden shows.

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. The sentence makes a generalization about nissologists’ definition of an island—specifically, that the use of one definition rather than another can result in huge disparities in the number of islands counted—and supports that generalization by citing Sweden as an example.

Choice A is incorrect. The sentence introduces one definition of an island to an audience unfamiliar with nissologists; it doesn’t make a generalization about nissologists’ definition of an island. Choice B is incorrect. While the sentence synthesizes information from the notes about counts of Sweden’s islands, it doesn’t make and support a generalization about nissologists’ definition of an island. Choice C is incorrect. The sentence makes an inference about islands in Sweden; it doesn’t mention nissologists’ definition of an island or make a generalization about it. 

"}, {"id": "b7571c0a", "domain": "Expression of Ideas", "skill": "Transitions", "difficulty": "E", "type": "mc", "stimulus": "

Practical movie effects, such as the use of actual locations in a film, provide a more realistic visual experience than computer-generated imagery (CGI) does, but giving audiences the “real thing” can be prohibitively expensive. ______blank many filmmakers use a blended approach, employing practical effects whenever possible and CGI elements as necessary to control costs.

", "stem": "

Which choice completes the text with the most logical transition?

", "choices": [{"id": "A", "text": "

Similarly,

"}, {"id": "B", "text": "

For this reason,

"}, {"id": "C", "text": "

Furthermore,

"}, {"id": "D", "text": "

In other words,

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. The first sentence tells us that practical effects are more realistic but also more expensive than CGI. The second sentence tells us that many filmmakers use both kinds of effects, balancing realism with cost. To connect these ideas, we need a cause-and-effect transition, like “therefore.” “For this reason” has the same meaning as “therefore.” .

Choice A is incorrect. This isn’t a logical transition. The first sentence tells us that practical effects are more realistic but also more expensive than CGI. The second sentence tells us that many filmmakers use both kinds of effects, balancing realism with cost. To connect these ideas, we need a cause-and-effect transition, like “therefore.” “Similarly” doesn’t show cause and effect: it shows the addition of another agreeing idea. Choice C is incorrect. This isn’t a logical transition. The first sentence tells us that practical effects are more realistic but also more expensive than CGI. The second sentence tells us that many filmmakers use both kinds of effects, balancing realism with cost. To connect these ideas, we need a cause-and-effect transition, like “therefore.” “Furthermore” doesn’t show cause and effect: it shows the addition of another agreeing idea. Choice D is incorrect. This isn’t a logical transition. The first sentence tells us that practical effects are more realistic but also more expensive than CGI. The second sentence tells us that many filmmakers use both kinds of effects, balancing realism with cost. To connect these ideas, we need a cause-and-effect transition, like “therefore.” “In other words” doesn’t show cause and effect: it shows a restatement of the same idea in different words. 

"}, {"id": "d54e16ee", "domain": "Expression of Ideas", "skill": "Transitions", "difficulty": "M", "type": "mc", "stimulus": "

Originally coined by economist Joan Robinson to refer to markets with multiple sellers of a product but only one buyer, the term “monopsony” can also refer to markets where demand for labor is limited. In a product monopsony, the single buyer can force sellers to lower their prices. ______blank in a labor monopsony, employers can force workers to accept lower wages.

", "stem": "

Which choice completes the text with the most logical transition?

", "choices": [{"id": "A", "text": "

Earlier,

"}, {"id": "B", "text": "

Instead,

"}, {"id": "C", "text": "

Similarly,

"}, {"id": "D", "text": "

In particular,

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. “Similarly” logically signals that the information in this sentence about a labor monopsony is similar to the information in the previous sentence about a product monopsony. In both types of markets, one party (an employer or a buyer) has the power to force another party (a worker or seller) to accept less money (for labor or products).  

Choice A is incorrect because “earlier” illogically signals that the information in this sentence about a labor monopsony occurs earlier (in a chronological sequence) than the information about a product monopsony. Instead, it is similar to the information about a product monopsony. Choice B is incorrect because “instead” illogically signals that the information in this sentence about a labor monopsony is an alternative to the previous information about a product monopsony. Instead, it is similar to the information about a product monopsony.  Choice D is incorrect because “in particular” illogically signals that the information in this sentence about a labor monopsony provides specific details elaborating on the previous information about a product monopsony. Instead, it is similar to the information about a product monopsony.

"}, {"id": "a1ca7ec4", "domain": "Expression of Ideas", "skill": "Rhetorical Synthesis", "difficulty": "M", "type": "mc", "stimulus": "

While researching a topic, a student has taken the following notes:

\n", "stem": "

The student wants to introduce the artist’s 1983 poetry collection. Which choice most effectively uses relevant information from the notes to accomplish this goal?

", "choices": [{"id": "A", "text": "

Before she published the books Precario/Precarious (1983) and Instan (2002), Cecilia Vicuña exhibited visual art at the Museo Nacional de Bellas Artes in Santiago, Chile.

"}, {"id": "B", "text": "

Cecilia Vicuña is a true multidisciplinary artist whose works include numerous poetry collections and visual art exhibitions.

"}, {"id": "C", "text": "

Published in 1983 by Tanam Press, Precario/Precarious is a collection of poetry by the multidisciplinary artist Cecilia Vicuña.

"}, {"id": "D", "text": "

In 1971, Cecilia Vicuña exhibited her first solo art exhibition, Pinturas, poemas y explicaciones, in Chile, her country of birth.

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. The sentence effectively introduces the poetry collection Precario/Precarious, noting that it is a collection by Vicuña that was published in 1983 by Tanam Press.

Choice A is incorrect. While the sentence mentions the 1983 poetry collection Precario/Precarious, it focuses mainly on Vicuña’s visual art. Choice B is incorrect. The sentence doesn’t introduce the 1983 poetry collection Precario/Precarious; instead, it introduces Vicuña. Choice D is incorrect. The sentence emphasizes the location of Vicuña’s 1971 exhibition Pinturas, poemas y explicaciones; it doesn’t introduce the 1983 poetry collection Precario/Precarious..

"}, {"id": "47e238be", "domain": "Expression of Ideas", "skill": "Transitions", "difficulty": "H", "type": "mc", "stimulus": "

Seismologists Kaiqing Yuan and Barbara Romanowicz have proposed that the magma fueling Iceland’s more than 30 active volcano systems emerges from deep within Earth. The great depths involved—nearly 3,000 km—mark Iceland’s volcanoes as extreme outliers; ______blank many of Earth’s volcanoes are fed by shallow pockets of magma found less than 15 km below the surface.

", "stem": "

Which choice completes the text with the most logical transition?

", "choices": [{"id": "A", "text": "

indeed,

"}, {"id": "B", "text": "

nevertheless,

"}, {"id": "C", "text": "

in addition,

"}, {"id": "D", "text": "

consequently,

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. The second part of the sentence says that many volcanoes use shallow pockets of magma. This is an elaboration of the same underlying idea from the first part of the sentence, which says that the super deep magma of Icelandic volcanoes’ makes them outliers. “Indeed” is a transition used for elaborating on the same idea, so it fits the context perfectly.

Choice B is incorrect. This choice uses a disagreement transition. But these two parts of the sentence agree with each other, so “nevertheless” doesn’t make sense. Choice C is incorrect. This choice uses a transition that indicates the addition of a new idea. But the second part of the sentence isn’t adding a new idea: it’s elaborating on the same idea expressed in the first part of the sentence. Choice D is incorrect. This choice uses a cause-and-effect transition, which doesn’t make sense here. The fact that Iceland’s deep-magma volcanoes are outliers doesn’t cause many other volcanoes to get fed by shallow pockets of magma.

"}, {"id": "d7c5388f", "domain": "Expression of Ideas", "skill": "Rhetorical Synthesis", "difficulty": "M", "type": "mc", "stimulus": "

While researching a topic, a student has taken the following notes:

\n", "stem": "

The student wants to emphasize a difference between C-type and S-type asteroids. Which choice most effectively uses relevant information from the notes to accomplish this goal? 

", "choices": [{"id": "A", "text": "

Planetary scientists classify asteroids into types, two of which are the C-type and the S-type.

"}, {"id": "B", "text": "

Planetary scientists consider an asteroid’s composition (such as whether the asteroid is composed mainly of silicate minerals or carbon) when classifying it.

"}, {"id": "C", "text": "

Roughly 17 percent of known asteroids are classified as S-type asteroids; another percentage is classified as C-type asteroids. 

"}, {"id": "D", "text": "

C-type asteroids are mainly composed of carbon, whereas S-type asteroids are primarily made up of silicate minerals.

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. The sentence emphasizes a difference between C-type and S-type asteroids, noting that C-type asteroids are mainly composed of carbon, while S-type asteroids are mainly composed of silicate minerals.

Choice A is incorrect. The sentence states that C-type and S-type are two types of asteroids, but it doesn’t emphasize a difference between them. Choice B is incorrect because it doesn’t directly mention C-type or S-type asteroids. Choice C is incorrect. While the sentence mentions that 17 percent of known asteroids are S-type asteroids, it doesn’t identify the percentage of asteroids that are C-type. Therefore, the sentence doesn’t emphasize a difference between the two types.

"}, {"id": "dd087f31", "domain": "Expression of Ideas", "skill": "Transitions", "difficulty": "E", "type": "mc", "stimulus": "

Chimamanda Ngozi Adichie’s 2013 novel Americanah chronicles the divergent experiences of Ifemelu and Obinze, a young Nigerian couple, after high school. Ifemelu moves to the United States to attend a prestigious university. ______blank Obinze travels to London, hoping to start a career there. However, frustrated with the lack of opportunities, he soon returns to Nigeria.

", "stem": "

Which choice completes the text with the most logical transition?

", "choices": [{"id": "A", "text": "

Meanwhile,

"}, {"id": "B", "text": "

Nevertheless,

"}, {"id": "C", "text": "

Secondly,

"}, {"id": "D", "text": "

In fact,

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. “Meanwhile” logically signals that the action described in this sentence (Obinze’s move to London to pursue a career) is simultaneous with the action described in the previous sentence (Ifemelu’s move to the United States). The first sentence establishes that the actions take place around the same time, referring to the characters’ “divergent experiences” following high school.  

Choice B is incorrect because “nevertheless” illogically signals that the information in this sentence about Obinze’s move to London is true despite the previous information about Ifemelu’s move to the United States. Instead, as the first sentence establishes, Obinze’s move and Ifemelu’s move are related, parallel experiences that occur around the same time. Choice C is incorrect because “secondly” illogically signals that the information in this sentence is a second point or reason separate from the previous information about Ifemelu’s move to the United States. Instead, as the first sentence establishes, Obinze’s move and Ifemelu’s move are related, parallel experiences that occur around the same time. Choice D is incorrect because “in fact” illogically signals that the information in this sentence emphasizes, modifies, or contradicts the previous information about Ifemelu’s move to the United States. Instead, as the first sentence establishes, Obinze’s move and Ifemelu’s move are related, parallel experiences that occur around the same time. 

"}, {"id": "622a351d", "domain": "Expression of Ideas", "skill": "Rhetorical Synthesis", "difficulty": "H", "type": "mc", "stimulus": "

While researching a topic, a student has taken the following notes:

\n", "stem": "

The student wants to make and support a generalization about the Alta conflict. Which choice most effectively uses relevant information from the notes to accomplish this goal?

", "choices": [{"id": "A", "text": "

During the Alta conflict, Sámi activists staged protests to block the construction of a dam on the Alta River in Norway that would disrupt local fishing and reindeer herding.

"}, {"id": "B", "text": "

Although the dam that the Sámi activists had protested was ultimately built, the Alta conflict had a lasting impact.

"}, {"id": "C", "text": "

Sámi rights to lands, waters, and resources received international attention and legal protections as a result of the Alta conflict.

"}, {"id": "D", "text": "

The Alta conflict had a lasting impact, resulting in international attention and legal protections for Sámi rights to lands, waters, and resources.

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. It makes a generalization—the conflict had a lasting impact—and then supports it with evidence—the attention and protections were results of the conflict.

Choice A is incorrect. This choice doesn’t make a generalization about the conflict. It describes a specific event from the conflict. Choice B is incorrect. This choice makes a generalization about the Alta conflict, but doesn’t support it. Choice C is incorrect. This choice makes a statement about the aftermath of the conflict, but doesn’t support it. The statement is also a little too specific to be a generalization.

"}, {"id": "0c13dea9", "domain": "Expression of Ideas", "skill": "Transitions", "difficulty": "M", "type": "mc", "stimulus": "

The chemical trimethylamine N-oxide not only gives fish their fishy smell but also protects them from crushing hydrostatic pressure in deep waters. Trimethylamine N-oxide strengthens the bonds between water molecules in a fish’s body. ______blank these water molecules maintain their linked structure at extreme depths, thus preventing pressure-related damage.

", "stem": "

Which choice completes the text with the most logical transition?

", "choices": [{"id": "A", "text": "

Nevertheless,

"}, {"id": "B", "text": "

As a result,

"}, {"id": "C", "text": "

However,

"}, {"id": "D", "text": "

For instance,

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. “As a result” indicates that water molecules maintaining their linked structure at high pressures is caused by the strengthening of these water molecules by trimethylamine N-oxide. So the transition “as a result” fits the context perfectly.

Choice A is incorrect. This choice uses a disagreement transition. But this sentence doesn’t disagree with the previous one—rather, it’s describing an effect of the phenomenon described in the previous sentence. Choice C is incorrect. This choice uses a disagreement transition. But this sentence doesn’t disagree with the previous one; it actually expands on the previous sentence by describing an effect of the strengthened molecules. Choice D is incorrect. This choice uses an exemplification transition, which doesn’t make sense here. The second sentence doesn’t provide an example or instance of the idea in the previous sentence. Instead, it explores the effects of the previous idea in more depth.

"}, {"id": "4fde4454", "domain": "Expression of Ideas", "skill": "Transitions", "difficulty": "M", "type": "mc", "stimulus": "

One poll taken after the first 1960 presidential debate suggested that John Kennedy lost badly: only 21 percent of those who listened on the radio rated him the winner. ______blank the debate was ultimately considered a victory for the telegenic young senator, who rated higher than his opponent, Vice President Richard Nixon, among those watching on the new medium of television.  

", "stem": "

Which choice completes the text with the most logical transition?

", "choices": [{"id": "A", "text": "

In other words,

"}, {"id": "B", "text": "

Therefore,

"}, {"id": "C", "text": "

Likewise,

"}, {"id": "D", "text": "

Nevertheless,

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. “Nevertheless” logically signals that the claim in this sentence—that the telegenic Kennedy was ultimately considered the winner of the debate—is true despite the previous information about the poll of radio listeners.

Choice A is incorrect because “in other words” illogically signals that the claim in this sentence is a paraphrase of the previous information about the poll of radio listeners. Instead, Kennedy was ultimately considered the winner despite what that poll suggested about his performance. Choice B is incorrect because “therefore” illogically signals that the claim in this sentence is a result of the previous information about the poll of radio listeners. Instead, Kennedy was ultimately considered the winner despite what that poll suggested about his performance. Choice C is incorrect because “likewise” illogically signals that the claim in this sentence is similar to the previous information about the poll of radio listeners. Instead, Kennedy was ultimately considered the winner despite what that poll suggested about his performance.

"}, {"id": "34e1124f", "domain": "Expression of Ideas", "skill": "Rhetorical Synthesis", "difficulty": "M", "type": "mc", "stimulus": "

While researching a topic, a student has taken the following notes:

\n", "stem": "

The student wants to provide an explanation and an example of Aeolian landforms. Which choice most effectively uses relevant information from the notes to accomplish this goal?

", "choices": [{"id": "A", "text": "

Aeolian landforms are created by different wind-based processes; for example, some are created by wind erosion.

"}, {"id": "B", "text": "

Aeolian landforms—landforms created by the wind—include the mushroom rock, a rock formation in which the wind erodes the base of the rock faster than the top.

"}, {"id": "C", "text": "

Erosion, transportation, and deposition are three examples of how the wind can create Aeolian landforms and mushroom rocks.

"}, {"id": "D", "text": "

A mushroom rock is a rock formation that owes its shape to the wind, a natural force associated with Aeolus in Greek mythology.

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. The sentence provides an explanation and an example of Aeolian landforms, explaining that they are landforms created by wind and offering the mushroom rock as an example.

Choice A is incorrect. The sentence explains that Aeolian landforms are created by wind but does not provide an example of any specific Aeolian landforms. Rather, the example it provides is of a wind-based process. Choice C is incorrect. While the sentence provides a partial explanation of Aeolian landforms, noting that they are created by the wind, it does not effectively provide an example. The sentence seems to indicate that mushroom rocks, rather than being an example of Aeolian landforms, are distinct from them. Choice D is incorrect. While the sentence provides an explanation of a mushroom rock, which is a specific example of an Aeolian landform, it doesn’t provide an explanation of Aeolian landforms in general.

"}, {"id": "7fd39a42", "domain": "Expression of Ideas", "skill": "Rhetorical Synthesis", "difficulty": "M", "type": "mc", "stimulus": "

While researching a topic, a student has taken the following notes:

\n", "stem": "

The student wants to emphasize the location of the first synchrotron built to provide synchrotron light. Which choice most effectively uses relevant information from the notes to accomplish this goal?

", "choices": [{"id": "A", "text": "

Tantalus, the first synchrotron created for the purpose of providing synchrotron light, was built in 1968.

"}, {"id": "B", "text": "

Circular particle accelerators known as synchrotrons radiate energy in the form of light, and this light is an ideal tool for researchers investigating the structure of matter.

"}, {"id": "C", "text": "

The first synchrotron created for the purpose of providing synchrotron light, Tantalus, was housed near the University of Wisconsin–Madison.

"}, {"id": "D", "text": "

Synchrotron light is among the brightest light ever produced, making it an ideal tool for researchers investigating the structure of matter.

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. After identifying Tantalus as the first synchrotron built to provide light, the sentence emphasizes its location.

Choice A is incorrect. While the sentence identifies Tantalus as the first synchrotron built to provide light, it doesn’t emphasize (or mention) its location. Choice B is incorrect. The sentence describes synchrotrons and how researchers use them; it doesn’t emphasize (or mention) the location of Tantalus. Choice D is incorrect. The sentence describes synchrotron light and how researchers use it; the sentence doesn’t emphasize (or mention) the location of Tantalus.

"}, {"id": "96a86bce", "domain": "Expression of Ideas", "skill": "Rhetorical Synthesis", "difficulty": "H", "type": "mc", "stimulus": "

While researching a topic, a student has taken the following notes:

\n", "stem": "

The student wants to present Tan’s research to an audience unfamiliar with Angkor Wat. Which choice most effectively uses relevant information from the notes to accomplish this goal?

", "choices": [{"id": "A", "text": "

Tan photographed Angkor Wat’s plaster walls and then applied decorrelation stretch analysis to the photographs.

"}, {"id": "B", "text": "

Decorrelation stretch analysis is a novel digital imaging technique that Tan used to enhance the contrast between colors in a photograph.

"}, {"id": "C", "text": "

Using a novel digital imaging technique, Tan revealed hundreds of images hidden on the walls of Angkor Wat, a Cambodian temple.

"}, {"id": "D", "text": "

Built to honor a Hindu god before becoming a Buddhist temple, Cambodia’s Angkor Wat concealed hundreds of images on its plaster walls. 

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. The sentence effectively presents Tan’s research to an audience unfamiliar with Angkor Wat, explaining the results of the research and identifying Angkor Wat as a temple in Cambodia.

Choice A is incorrect. While the sentence presents Tan’s research, it fails to explain what Angkor Wat is for an audience unfamiliar with the temple. Choice B is incorrect. The sentence emphasizes the role that decorrelation stretch analysis played in Tan’s research; it doesn’t present the research, which would require specifying where it was conducted. Choice D is incorrect. While the sentence explains what Angkor Wat is, it fails to present Tan’s research.

"}, {"id": "db3ad406", "domain": "Expression of Ideas", "skill": "Rhetorical Synthesis", "difficulty": "H", "type": "mc", "stimulus": "

While researching a topic, a student has taken the following notes:

\n", "stem": "

The student wants to explain what a quenched galaxy is. Which choice most effectively uses relevant information from the notes to accomplish this goal?

", "choices": [{"id": "A", "text": "

Before quenching, a starburst galaxy will form stars at a rapid rate.

"}, {"id": "B", "text": "

When it becomes quenched, a starburst galaxy enters the poststarburst phase.

"}, {"id": "C", "text": "

Having entered the poststarburst phase, a quenched galaxy is one that no longer forms stars.

"}, {"id": "D", "text": "

A starburst galaxy will lose star-forming gas and eventually become quenched.

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. This choice defines a quenched galaxy as “one that no longer forms stars.”

Choice A is incorrect. This choice only describes what happens before quenching. Choice B is incorrect. This choice only describes what happens after quenching. Choice D is incorrect. This choice only describes what causes quenching.

"}, {"id": "973632d2", "domain": "Expression of Ideas", "skill": "Rhetorical Synthesis", "difficulty": "H", "type": "mc", "stimulus": "

While researching a topic, a student has taken the following notes:

\n", "stem": "

The student wants to emphasize the aim of the research study. Which choice most effectively uses relevant information from the notes to accomplish this goal?

", "choices": [{"id": "A", "text": "

Thomas Rogers and F. Leland Russell, researchers at Wichita State University, wanted to know if woodland expansion is related to changes in climate.

"}, {"id": "B", "text": "

Thanks to the work done by Thomas Rogers and F. Leland Russell, we now know that droughts may have played a role in woodland expansion.

"}, {"id": "C", "text": "

Wichita State University researchers have determined that tree population growth was associated with dry intervals.

"}, {"id": "D", "text": "

Thomas Rogers and F. Leland Russell analyzed core samples from oak trees on a site that was not wooded in the past, indexing the age of the trees with historical climate data.

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. The sentence effectively emphasizes the aim, or goal, of the research study (in other words, what the researchers hoped to learn from the study): Rogers and Russell wanted to know if woodland expansion is related to changes in climate.

Choice B is incorrect. The sentence emphasizes the researchers’ findings; it doesn’t emphasize the aim of the study. Choice C is incorrect. The sentence emphasizes the results of the study; it doesn’t emphasize the aim. Choice D is incorrect. The sentence emphasizes the methodology of the study; it doesn’t emphasize the aim.

"}, {"id": "f114cbf0", "domain": "Expression of Ideas", "skill": "Transitions", "difficulty": "M", "type": "mc", "stimulus": "

A firefly uses specialized muscles to draw oxygen into its lower abdomen through narrow tubes, triggering a chemical reaction whereby the oxygen combines with chemicals in the firefly’s abdomen to produce a glow. ______blank when the firefly stops drawing in oxygen, the reaction—and the glow—cease.

", "stem": "

Which choice completes the text with the most logical transition?

", "choices": [{"id": "A", "text": "

For instance,

"}, {"id": "B", "text": "

By contrast,

"}, {"id": "C", "text": "

Specifically,

"}, {"id": "D", "text": "

In conclusion,

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. “By contrast” logically signals that the information in this sentence—that a firefly’s glow ceases when it stops drawing in oxygen—contrasts with the previous sentence’s discussion of the processes that cause a firefly to begin to glow.

Choice A is incorrect because “for instance” illogically signals that the information in the sentence exemplifies the previous sentence’s discussion of how a firefly begins to glow. Instead, it contrasts with the previous sentence’s discussion. Choice C is incorrect because “specifically” illogically signals that the information in the sentence provides specific details elaborating on the previous sentence’s discussion of how a firefly begins to glow. Instead, it contrasts with the previous sentence’s discussion. Choice D is incorrect because “in conclusion” illogically signals that the information in the sentence sums up the previous sentence’s discussion of how a firefly begins to glow. Instead, it contrasts with the previous sentence’s discussion. 

"}, {"id": "b7c404d1", "domain": "Expression of Ideas", "skill": "Transitions", "difficulty": "M", "type": "mc", "stimulus": "

With her room-sized installation The Interstitium, Iranian American artist Laleh Mehran succeeded in creating a space that felt, as intended, both “familiar and distant.” ______blank with a video screen placed at the far end of the coal slag-encrusted room, her installation was reminiscent of a typical movie theater—albeit one found in a subterranean coal mine.

", "stem": "

Which choice completes the text with the most logical transition?

", "choices": [{"id": "A", "text": "

Next,

"}, {"id": "B", "text": "

Nevertheless,

"}, {"id": "C", "text": "

Indeed,

"}, {"id": "D", "text": "

Instead,

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. \"Indeed\" logically signals that the information in this sentence—that Laleh Mehran’s installation resembled both a typical movie theater and a coal mine—supports the previous sentence’s claim that the space Mehran created felt both \"familiar and distant.\"

Choice A is incorrect because \"next\" illogically signals that the description of Laleh Mehran’s installation in this sentence is the next step in a process. Rather, it supports the previous sentence’s claim about Mehran’s installation. Choice B is incorrect because \"nevertheless\" illogically signals that the information in this sentence is true despite the claim about Laleh Mehran’s installation in the previous sentence. Rather, it supports that claim. Choice D is incorrect because \"instead\" illogically signals that this sentence presents an alternative to the previous sentence’s claim about Laleh Mehran’s installation. Rather, it supports that claim.

"}, {"id": "d9d314d9", "domain": "Expression of Ideas", "skill": "Rhetorical Synthesis", "difficulty": "M", "type": "mc", "stimulus": "

While researching a topic, a student has taken the following notes:

\n", "stem": "

The student wants to emphasize the fossil’s significance. Which choice most effectively uses relevant information from the notes to accomplish this goal?

", "choices": [{"id": "A", "text": "

Canadian paleobiologist Natalia Rybczynski’s fossil has the skull and teeth of a seal, which, like sea lions and walruses, is a pinniped.

"}, {"id": "B", "text": "

Pinnipeds are descended from four-legged, land-dwelling carnivores; a fossil that resembles both was recently found.

"}, {"id": "C", "text": "

Having four legs but the skull and teeth of a seal, the rare fossil illustrates an early stage in the evolution of pinnipeds from their land-dwelling ancestors.

"}, {"id": "D", "text": "

A “transitional fossil” was recently found by paleobiologist Natalia Rybczynski.

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. The sentence effectively emphasizes the fossil’s significance, explaining that the fossil is rare and illustrates an early stage in the evolution of pinnipeds from their land-dwelling ancestors.

Choice A is incorrect. The sentence describes the fossil Rybczynski found; it doesn’t emphasize the fossil’s significance. Choice B is incorrect. The sentence mentions that a fossil resembling both pinnipeds and their ancestors was found; it doesn’t emphasize the fossil’s significance. Choice D is incorrect. The sentence notes a term used to describe the fossil Rybczynski found; it doesn’t emphasize the fossil’s significance. 

"}, {"id": "ad729337", "domain": "Expression of Ideas", "skill": "Transitions", "difficulty": "H", "type": "mc", "stimulus": "

With its clichéd imagery of suburban lawns and power lines, John Ashbery’s 2004 poem “Ignorance of the Law Is No Excuse” may seem barren terrain for critical analysis. ______blank cultural critic Lauren Berlant finds fertile ground in just its first two stanzas, devoting most of a book chapter to deciphering the “weight of the default space” Ashbery creates in this poem.

", "stem": "

Which choice completes the text with the most logical transition?

", "choices": [{"id": "A", "text": "

Likewise,

"}, {"id": "B", "text": "

Nonetheless,

"}, {"id": "C", "text": "

In turn,

"}, {"id": "D", "text": "

That is,

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. “Nonetheless” is a transition that indicates disagreement. The first sentence describes the unlikelihood of finding much for critical analysis in Ashbery’s poem (“barren terrain”), while the second sentence describes how Berlant did in fact find much to analyze in Ashbery’s poem (“fertile ground”), so the transition “nonetheless” fits perfectly.

Choice A is incorrect. This choice uses a transition that indicates the addition of a new but similar idea, which doesn’t make sense here. The idea in this sentence directly contradicts the idea in the previous sentence. Choice C is incorrect. This choice uses a cause-and-effect transition, which doesn’t make sense in this context—a poem seemingly having little opportunity for critical analysis would not cause someone to write an extensive critical analysis (in fact, we might expect the opposite). Choice D is incorrect. This choice uses a transition that indicates a restatement of the same idea in other words. But the text isn’t restating the first idea here. Instead, it’s offering a contradiction to the idea expressed in the first sentence.

"}, {"id": "ce282575", "domain": "Expression of Ideas", "skill": "Rhetorical Synthesis", "difficulty": "M", "type": "mc", "stimulus": "

While researching a topic, a student has taken the following notes:

\n", "stem": "

The student wants to contrast the purposes of the two maps in The Hobbit. Which choice most effectively uses relevant information from the notes to accomplish this goal?

", "choices": [{"id": "A", "text": "

The Hobbit’s opening map introduces readers to the fictional world they are about to enter, while the closing map allows them to reconstruct the story they have just read.

"}, {"id": "B", "text": "

The Hobbit, a novel published by J.R.R. Tolkien in 1937, features a reproduction of a map that the characters use on their quest, as well as a map that appears at the end of the novel.

"}, {"id": "C", "text": "

The Hobbit’s two maps, one opening and one closing the novel, each serve a purpose for readers.

"}, {"id": "D", "text": "

In 1937, author J.R.R. Tolkien published The Hobbit, a novel featuring both an opening and a closing map.

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. The sentence contrasts the purposes of the two maps in The Hobbit, noting that the opening map introduces readers to the book’s fictional world, while the closing map helps readers reconstruct the story. The word “while” helps signal a contrast between the purposes of the maps. 

Choice B is incorrect. While the sentence mentions the two maps, it doesn’t contrast the maps’ purposes. Choice C is incorrect. While the sentence mentions the two maps and notes that each has a purpose, it doesn’t specify what those purposes are or how they contrast. Choice D is incorrect. While the sentence mentions the two maps, it doesn’t contrast the maps’ purposes.

"}, {"id": "0ee64efc", "domain": "Expression of Ideas", "skill": "Transitions", "difficulty": "E", "type": "mc", "stimulus": "

In the 1850s, William Still was instrumental in helping nearly 1,000 people escape from slavery, earning him the moniker “the Father of the Underground Railroad.” ______blank despite the fame of his contributions during his lifetime, Still is discussed far less today than other prominent Black abolitionists from his era, such as Frederick Douglass and Harriet Tubman.   

", "stem": "

Which choice completes the text with the most logical transition?

", "choices": [{"id": "A", "text": "

For example,

"}, {"id": "B", "text": "

However,

"}, {"id": "C", "text": "

Specifically,

"}, {"id": "D", "text": "

Similarly,

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. \"However\" is used to indicate a contrast between two ideas. The first sentence describes how Still used to be famous. This sentence describes how Still is not very famous today, so the transition \"however\" fits perfectly.

Choice A is incorrect. This choice uses a transition that introduces an example. But the second sentence doesn’t provide a specific example of Still’s famous contributions to the Underground Railroad. Instead, it changes the subject to how his fame has faded over time. Choice C is incorrect. This choice uses a transition that introduces an example or continuation of a previous idea. But the second sentence doesn’t provide a specific example of Still’s famous contributions to the Underground Railroad. Instead, it changes the subject to how his fame has faded over time. Choice D is incorrect. This choice uses a transition that indicates the agreement between two ideas. But this sentence shows a contrast with the first sentence—namely, that Still used to be very famous but now isn’t very famous.

"}, {"id": "b8eec031", "domain": "Expression of Ideas", "skill": "Transitions", "difficulty": "M", "type": "mc", "stimulus": "

Researchers Helena Mihaljevi\u0107-Brandt, Lucía Santamaría, and Marco Tullney report that while mathematicians may have traditionally worked alone, evidence points to a shift in the opposite direction. ______blank mathematicians are choosing to collaborate with their peers—a trend illustrated by a rise in the number of mathematics publications credited to multiple authors.

", "stem": "

Which choice completes the text with the most logical transition?

", "choices": [{"id": "A", "text": "

Similarly,

"}, {"id": "B", "text": "

For this reason,

"}, {"id": "C", "text": "

Furthermore,

"}, {"id": "D", "text": "

Increasingly,

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. “Increasingly” logically signals that the claim in this sentence—that mathematicians are collaborating with their peers—marks a change relative to what was traditionally done. As the previous sentence explains, while mathematicians may have traditionally worked alone, evidence points to a shift in the opposite direction. The claim describes the shift: a rise in collaboration.

Choice A is incorrect because “similarly” illogically signals that the claim in this sentence is similar to, but separate from, the previous claim about the shift away from mathematicians working alone. Instead, the claim about the rise in collaboration elaborates on the previous claim, describing the shift. Choice B is incorrect because “for this reason” illogically signals that the claim in this sentence is caused by the previous claim about the shift away from mathematicians working alone. Instead, the claim about the rise in collaboration elaborates on the previous claim, describing the shift. Choice C is incorrect because “furthermore” illogically signals that the claim in this sentence is in addition to the previous claim about the shift away from mathematicians working alone. Instead, the claim about the rise in collaboration elaborates on the previous claim, describing the shift.

"}, {"id": "9e34720b", "domain": "Expression of Ideas", "skill": "Transitions", "difficulty": "M", "type": "mc", "stimulus": "

Although those who migrated to California in 1849 dreamed of finding gold nuggets in streambeds, the state’s richest deposits were buried deeply in rock, beyond the reach of individual prospectors. ______blank by 1852, many had given up their fortune-hunting dreams and gone to work for one of the large companies capable of managing California’s complex mining operations.  

", "stem": "

Which choice completes the text with the most logical transition?

", "choices": [{"id": "A", "text": "

Furthermore,

"}, {"id": "B", "text": "

Still,

"}, {"id": "C", "text": "

Consequently,

"}, {"id": "D", "text": "

Next,

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. “Consequently” logically signals that the information in this sentence—that many individual gold prospectors gave up their fortune-hunting dreams and became employees of mining companies—is a result or consequence of the previous information about the inaccessibility of the state’s gold deposits. 

Choice A is incorrect because “furthermore” illogically signals that the information in this sentence merely adds to the previous information about the inaccessibility of the state’s gold deposits. Instead, it’s a result or consequence of that information. Choice B is incorrect because “still” illogically signals that the information in this sentence offers a contrast or exception to the previous information about the inaccessibility of the state’s gold deposits. Instead, it’s a result or consequence of that information. Choice D is incorrect because “next” illogically signals that the information in this sentence is the next step in a process. Instead, it’s a result or consequence of the previous information about the inaccessibility of the state’s gold deposits.

"}, {"id": "63c73b50", "domain": "Expression of Ideas", "skill": "Transitions", "difficulty": "E", "type": "mc", "stimulus": "

In 2018, Kurt Luther and Vikram Mohanty created the web-based tool Civil War Photo Sleuth (CWPS). A user uploading an unknown Civil War soldier’s photograph to CWPS first tags the photo with all known information. ______blank CWPS’s facial-recognition software analyzes twenty-seven different physical features and looks for matches to tagged images already in the database.

", "stem": "

Which choice completes the text with the most logical transition?

", "choices": [{"id": "A", "text": "

Then, 

"}, {"id": "B", "text": "

In fact,

"}, {"id": "C", "text": "

Likewise,

"}, {"id": "D", "text": "

For example, 

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. “Then” indicates that the events in this sentence took place after the events in the previous sentence. Only after users upload images of unknown soldiers can those images be analyzed.

Choice B is incorrect. This transition is used to emphasize the truth of a statement that modifies the previous statement. But this sentence doesn’t modify the step described in the previous statement: instead, it introduces an entirely new step in the process. So “in fact” wouldn’t make sense here. Choice C is incorrect. This choice uses a transition that indicates the addition of a new but related idea, which doesn’t make sense here. Analyzing the physical features in the uploaded photographs isn’t a similar idea, but rather the next step in the process. Choice D is incorrect. This choice uses an exemplification transition, which doesn’t make sense here. Analyzing physical features is not an example of uploading and tagging an image.

"}, {"id": "3831f2d7", "domain": "Expression of Ideas", "skill": "Transitions", "difficulty": "E", "type": "mc", "stimulus": "

Arkansas aviator Louise Thaden was already a record breaker when she won the inaugural National Women’s Air Derby, a race from California to Ohio, in August of 1929. ______blank in December of 1928, Thaden had set an aviation record when she reached an altitude of 20,269 feet in a Travel Air biplane.

", "stem": "

Which choice completes the text with the most logical transition?

", "choices": [{"id": "A", "text": "

Earlier,

"}, {"id": "B", "text": "

However,

"}, {"id": "C", "text": "

Next,

"}, {"id": "D", "text": "

As a result,

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. This choice uses a transition that indicates a shift back in time. Since the first sentence talks about Thaden’s race win in 1929 and the second shifts back to talking about her record in 1928, this makes the most sense here.

Choice B is incorrect. This choice uses a disagreement transition. But this sentence actually agrees with and expands on the previous sentence by describing the earlier record that Thaden had \"already\" held. Choice C is incorrect. This choice uses a transition that indicates a shift forward in time, which doesn’t make sense here. A record in 1928 didn’t come after Thaden’s race win in 1929. Choice D is incorrect. This choice uses a cause-and-effect transition, which doesn’t make sense in this context—an event in 1929 can’t cause something in 1928.

"}, {"id": "1469d23a", "domain": "Expression of Ideas", "skill": "Rhetorical Synthesis", "difficulty": "M", "type": "mc", "stimulus": "

While researching a topic, a student has taken the following notes:

\n", "stem": "

The student wants to describe Adnan’s December from My Window to an audience already familiar with leporellos. Which choice most effectively uses relevant information from the notes to accomplish this goal?

", "choices": [{"id": "A", "text": "

Featuring a panoramic landscape, the 1993 work is one of Adnan’s many leporellos, which are accordion-style folded books that when expanded reveal the artist’s work.

"}, {"id": "B", "text": "

When expanded, Adnan’s 1993 leporello December from My Window reveals a panoramic landscape painted in ink and watercolor.

"}, {"id": "C", "text": "

Known for making many other accordion-style folded books called leporellos, Adnan created December from My Window in 1993.

"}, {"id": "D", "text": "

A leporello, such as Adnan’s December from My Window, is folded accordion style, and due to its zigzag shape it is able to stand on its own when fully expanded. 

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. This choice describes Adnan’s December from My Window in a way that assumes the audience is already familiar with leporellos and focuses on the specific features of the work—its content and medium.

Choice A is incorrect. This choice isn’t suited for an audience already familiar with leporellos. A familiar audience wouldn’t need to have the term defined or explained. Choice C is incorrect. This choice doesn’t describe Adnan’s December from My Window. It mentions the year and the type of work but not the content or the medium. In addition, it provides a simple definition of leporellos, making this an inappropriate choice for an audience already familiar with leporellos. Choice D is incorrect. This choice isn’t suited for an audience already familiar with leporellos. A familiar audience wouldn’t need to have the term defined.

"}, {"id": "2b5e0731", "domain": "Expression of Ideas", "skill": "Transitions", "difficulty": "E", "type": "mc", "stimulus": "

With darkness falling, a mother elephant loses sight of her calf and wants to make sure it is safe. ______blank she releases an infrasonic call for the calf to hear. Infrasonic sound is below the range of human hearing, but many animals can hear these sounds from several miles away.

", "stem": "

Which choice completes the text with the most logical transition?

", "choices": [{"id": "A", "text": "

For example,

"}, {"id": "B", "text": "

For this reason,

"}, {"id": "C", "text": "

Nowadays,

"}, {"id": "D", "text": "

Similarly,

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. \"For this reason\" is a cause-and-effect transition. The cause in this case is that the mother elephant wants to know that her calf is safe, so the effect is that she lets out an infrasonic call for the calf to hear. Therefore, \"for this reason\" fits perfectly in this context.

Choice A is incorrect. This choice uses a transition that introduces an example of a previous idea. But the second sentence doesn’t provide an example of the events described in the first sentence. Instead, it describes what happens next: the mother elephant calls for her calf. Choice C is incorrect. This choice uses a transition that indicates a shift from the past to the current time, which doesn’t make sense here. Both sentences use the present tense, as they’re describing the same time period. Choice D is incorrect. This choice uses a transition that indicates commonality or agreement between two ideas. But this sentence isn’t similar to the events in the first sentence. Instead, it describes the events that happen next.

"}, {"id": "3ea7372e", "domain": "Expression of Ideas", "skill": "Rhetorical Synthesis", "difficulty": "M", "type": "mc", "stimulus": "

While researching a topic, a student has taken the following notes:

\n", "stem": "

The student wants to emphasize a difference between the MexiCali Biennial and traditional biennials. Which choice most effectively uses relevant information from the notes to accomplish this goal?

", "choices": [{"id": "A", "text": "

In 2006, artists Ed Gomez and Luis Hernandez founded the MexiCali Biennial, which has taken place in 2006, 2009–10, 2013, and 2018–20.

"}, {"id": "B", "text": "

Unlike traditional biennials, the MexiCali Biennial hosts exhibitions in different venues on an uneven schedule.

"}, {"id": "C", "text": "

The term biennial traditionally refers to an art exhibition that takes place every two years in a single location, not to exhibitions hosted at a variety of times and venues.

"}, {"id": "D", "text": "

Biennial exhibitions have been held in New York, Berlin, and Venice but also on both sides of the US-Mexico border.

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. The sentence effectively emphasizes a difference between the MexiCali Biennial and traditional biennials, stating that the MexiCali Biennial is unlike traditional biennials because it hosts exhibitions in different venues on an uneven schedule.

Choice A is incorrect. The sentence indicates who founded the MexiCali Biennial and the years this biennial has taken place; it doesn’t emphasize a difference between the MexiCali Biennial and traditional biennials. Choice C is incorrect. While the sentence clarifies the traditional meaning of biennial with language that could apply to the MexiCali Biennial, it doesn’t mention the MexiCali Biennial by name. Therefore, the sentence doesn’t effectively emphasize a difference between the MexiCali Biennial and traditional biennials. Choice D is incorrect. The sentence notes locations where various biennial exhibitions have been held; it doesn’t emphasize a difference between the MexiCali Biennial and traditional biennials.

"}, {"id": "1c36e3e1", "domain": "Expression of Ideas", "skill": "Transitions", "difficulty": "E", "type": "mc", "stimulus": "

The number of dark spots that appear on the Sun, known as sunspots, can vary greatly. For example, there were about 180 sunspots in November 2001. ______blank there were only about 2 sunspots in December 2008.

\n

 

", "stem": "

Which choice completes the text with the most logical transition?

", "choices": [{"id": "A", "text": "

 In other words,

"}, {"id": "B", "text": "

Similarly,

"}, {"id": "C", "text": "

Therefore,

"}, {"id": "D", "text": "

By comparison,

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. The first sentence claims that the number of sunspots can vary greatly. To support this claim, the next two sentences compare two examples: one time when there were 180 sunspots and one time when there were only 2 sunspots. So the transition “by comparison” fits perfectly.

Choice A is incorrect. This choice uses a transition that indicates a restatement of the same idea, which doesn’t make sense here. This sentence doesn’t restate the first example—it describes a totally different example. Choice B is incorrect. This choice uses a transition that indicates the addition of a similar idea, which doesn’t make sense here. This sentence describes a second example that is very different from the first example. Choice C is incorrect. This choice uses a cause-and-effect transition, which doesn’t make sense here. The first example didn’t result in the second example.

"}, {"id": "8d1ddd1b", "domain": "Expression of Ideas", "skill": "Rhetorical Synthesis", "difficulty": "H", "type": "mc", "stimulus": "

While researching a topic, a student has taken the following notes:

\n", "stem": "

The student wants to present the study and its methodology. Which choice most effectively uses relevant information from the notes to accomplish this goal?

", "choices": [{"id": "A", "text": "

A study revealed that ducklings, which expend up to 62.8% less energy when swimming in a line behind their mother, also experience 158% less drag.

"}, {"id": "B", "text": "

Seeking to understand how ducklings swimming in a line behind their mother save energy, Zhiming Yuan used computer simulations to study the effect of the mother duck’s wake.

"}, {"id": "C", "text": "

Zhiming Yuan studied the physics behind the fact that by being pushed in a forward direction by waves, ducklings save energy.

"}, {"id": "D", "text": "

Naval architect Zhiming Yuan discovered that ducklings are pushed in a forward direction by the waves of their mother’s wake, reducing the effect of drag by 158%.

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. The sentence presents both the study and its methodology (that is, the researcher’s approach to the problem), explaining that Yuan used computer simulations to study the effect of the mother duck’s wake on the ducklings’ energy expenditure.

Choice A is incorrect. The sentence describes the findings of Yuan’s study; it doesn’t present the study and its methodology. Choice C is incorrect. While the sentence provides general information about Yuan’s study, it doesn’t present the study’s methodology. Choice D is incorrect. The sentence describes the findings of Yuan’s study; it doesn’t present the study and its methodology. 

"}, {"id": "82ec9628", "domain": "Expression of Ideas", "skill": "Transitions", "difficulty": "M", "type": "mc", "stimulus": "

Archaeologist Sue Brunning explains why the seventh-century ship burial site at Sutton Hoo in England was likely the tomb of a king. First, the gold artifacts inside the ship suggest that the person buried with them was a wealthy and respected leader. ______blank the massive effort required to bury the ship would likely only have been undertaken for a king.

", "stem": "

Which choice completes the text with the most logical transition?

", "choices": [{"id": "A", "text": "

Instead,

"}, {"id": "B", "text": "

Still,

"}, {"id": "C", "text": "

Specifically,

"}, {"id": "D", "text": "

Second,

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. “Second” logically signals that the information in this sentence—that the effort to bury the ship would likely only have been made for a king—joins the information in the previous sentence (“first…”) in supporting Brunning’s claim that the burial site was likely the tomb of a king.

Choice A is incorrect because “instead” illogically signals that the information in this sentence presents an alternative or substitute to the previous information about the gold artifacts inside the ship. Rather, this sentence presents a second piece of information that supports Brunning’s claim. Choice B is incorrect because “still” illogically signals that the information in this sentence exists in contrast to or despite the previous information about the gold artifacts inside the ship. Instead, this sentence presents a second piece of information that supports Brunning’s claim. Choice C is incorrect because “specifically” illogically signals that the information in this sentence specifies or elaborates on the previous information about the gold artifacts inside the ship. Instead, this sentence presents a second piece of information that supports Brunning’s claim.

"}, {"id": "ba263620", "domain": "Expression of Ideas", "skill": "Rhetorical Synthesis", "difficulty": "E", "type": "mc", "stimulus": "

While researching a topic, a student has taken the following notes:

\n", "stem": "

The student wants to emphasize a similarity between Beard’s invention and Jones’s invention. Which choice most effectively uses relevant information from the notes to accomplish this goal?

", "choices": [{"id": "A", "text": "

Beard’s automatic coupler and Jones’s mobile refrigeration system both improved on existing designs.

"}, {"id": "B", "text": "

In 1897, Beard invented an automatic coupler, which made the job of connecting train cars safer.

"}, {"id": "C", "text": "

Beard’s invention made the job of connecting train cars safer, whereas Jones’s invention enabled food transport trucks to carry perishables farther. 

"}, {"id": "D", "text": "

Jones’s mobile refrigeration system, which he invented in 1938, made it possible for food transport trucks to carry perishable foods farther.

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. It compares Beard’s and Jones’s inventions to one another, and emphasizes what they have in common.

Choice B is incorrect. This choice doesn’t emphasize a similarity. It only mentions Beard’s invention. It doesn’t compare it to Jones’s invention. Choice C is incorrect. This choice doesn’t emphasize a similarity between the two inventions. Instead, it emphasizes a difference. Choice D is incorrect. This choice doesn’t emphasize a similarity. It only mentions Jones’s invention. It doesn’t compare it to Beard’s invention.

"}, {"id": "4f2710ab", "domain": "Expression of Ideas", "skill": "Transitions", "difficulty": "E", "type": "mc", "stimulus": "

Organisms have evolved a number of surprising adaptations to ensure their survival in adverse conditions. Tadpole shrimp (Triops longicaudatus) embryos, ______blank can pause development for over ten years during extended periods of drought.

", "stem": "

Which choice completes the text with the most logical transition?

", "choices": [{"id": "A", "text": "

in contrast,

"}, {"id": "B", "text": "

for example,

"}, {"id": "C", "text": "

meanwhile,

"}, {"id": "D", "text": "

consequently,

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. “For example” logically signals that the information in this sentence—that tadpole shrimp embryos can pause development during extended periods of drought—exemplifies the previous sentence’s claim that organisms have evolved surprising adaptations to survive in adverse conditions.  

Choice A is incorrect because “in contrast” illogically signals that the information in this sentence contrasts with the claim about organisms in the previous sentence. Instead, it exemplifies this claim. Choice C is incorrect because “meanwhile” illogically signals that the information in this sentence is separate from (while occurring simultaneously with) the claim about organisms in the previous sentence. Instead, it exemplifies this claim. Choice D is incorrect because “consequently” illogically signals that the information in this sentence is a consequence, or result, of the claim about organisms in the previous sentence. Instead, it exemplifies this claim. 

"}, {"id": "480ade7e", "domain": "Expression of Ideas", "skill": "Transitions", "difficulty": "H", "type": "mc", "stimulus": "

In response to adverse environmental conditions, many plants produce abscisic acid (ABA), a stress hormone. ABA triggers a slowdown in the biological processes of most plants. ______blank when the mustard plant Schrenkiella parvula produces ABA in response to an environmental stressor, the hormone triggers accelerated growth.  

", "stem": "

Which choice completes the text with the most logical transition?

", "choices": [{"id": "A", "text": "

Moreover,

"}, {"id": "B", "text": "

In contrast,

"}, {"id": "C", "text": "

For example,

"}, {"id": "D", "text": "

Thus,

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. “In contrast” logically signals that the information in this sentence—that ABA triggers accelerated growth in the mustard plant Schrenkiella parvula—contrasts with the previous information about ABA triggering a slowdown in most plants’ biological processes.

Choice A is incorrect because “moreover” illogically signals that the information in this sentence about the mustard plant merely adds to the previous information about the effects of ABA. Instead, it contrasts with that information. Choice C is incorrect because “for example” illogically signals that the information in this sentence about the mustard plant provides an example consistent with the previous information about the effects of ABA. Instead, it contrasts with that information.  Choice D is incorrect because “thus” illogically signals that the information in this sentence about the mustard plant is a consequence, or result, of the previous information about the effects of ABA. Instead, it contrasts with that information. 

"}, {"id": "34a5ba1c", "domain": "Expression of Ideas", "skill": "Transitions", "difficulty": "E", "type": "mc", "stimulus": "

By 1936, Spanish Romani dancer Carmen Amaya was known all over Spain for her powerful style of flamenco dancing. However, in July of that year, the outbreak of the Spanish Civil War made it difficult for her to perform in her home country. ______blank Amaya left Spain to perform abroad, dancing for audiences across North and South America.

", "stem": "

Which choice completes the text with the most logical transition?

", "choices": [{"id": "A", "text": "

In comparison,

"}, {"id": "B", "text": "

As a result,

"}, {"id": "C", "text": "

First of all,

"}, {"id": "D", "text": "

For example,

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. “As a result” logically signals that the information in this sentence about Amaya leaving Spain to perform abroad is a result of the previous information about the Spanish Civil War.

Choice A is incorrect because “in comparison” illogically signals that the information in this sentence is being compared to the previous information about the Spanish Civil War. Instead, Amaya leaving Spain is a result of that war. Choice C is incorrect because “first of all” illogically signals that the information in this sentence is the beginning of a sequence of events. Instead, Amaya leaving Spain is a result of the event (the outbreak of war) described in the previous sentence. Choice D is incorrect because “for example” illogically signals that the information in this sentence is an example supporting the previous statement about the Spanish Civil War. Instead, Amaya leaving Spain is a result of that war.

"}, {"id": "c34d6bff", "domain": "Expression of Ideas", "skill": "Rhetorical Synthesis", "difficulty": "H", "type": "mc", "stimulus": "

While researching a topic, a student has taken the following notes:

\n", "stem": "

The student wants to compare the two women’s contributions to the March on Washington. Which choice most effectively uses relevant information from the notes to accomplish this goal?

", "choices": [{"id": "A", "text": "

Hedgeman and Bates contributed to the march in different ways; Bates, for example, delivered a brief but memorable address.

"}, {"id": "B", "text": "

Hedgeman worked in politics and helped organize the march, while Bates was a journalist and school desegregation advocate.

"}, {"id": "C", "text": "

Although Hedgeman worked behind the scenes to make sure a woman speaker was included, Bates was the sole woman to speak at the march.

"}, {"id": "D", "text": "

Many African American women, including Bates and Hedgeman, fought for civil rights, but only one spoke at the march.

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. The sentence compares the two women’s contributions to the march: Hedgeman worked behind the scenes to make sure a woman speaker was included, whereas Bates actually spoke at the event. 

Choice A is incorrect. While it acknowledges that the two women both contributed to the march, it doesn’t indicate what Hedgeman did, so no comparison is made. Choice B is incorrect. While the sentence provides information about the two women, it doesn’t mention anything about Bates’s contribution to the march. Choice D is incorrect. While the sentence indicates that the two women both fought for civil rights, it doesn’t compare their individual contributions to the march.

"}, {"id": "ac8eb085", "domain": "Expression of Ideas", "skill": "Transitions", "difficulty": "E", "type": "mc", "stimulus": "

“O2 Arena,” an award-winning science fiction story by Nigerian author Oghenechovwe Donald Ekpeki, takes place in an alternate version of Nigeria where breathable air is a rare commodity that is owned and sold by companies. ______blank people must purchase it with currency called O2 credits.

", "stem": "

Which choice completes the text with the most logical transition?

", "choices": [{"id": "A", "text": "

As a result,

"}, {"id": "B", "text": "

In any case,

"}, {"id": "C", "text": "

Nevertheless,

"}, {"id": "D", "text": "

Earlier,

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. The second sentence describes a consequence of the system laid out in the first sentence: because air is owned and sold by companies in this world, people have to buy it.

Choice B is incorrect. This choice uses a transition that means “no matter what happens” or “whatever the situation is,” which doesn’t make sense here. There’s only one situation described in the text: a fictional world in which companies own all the breathable air, forcing people to buy it. Choice C is incorrect. This choice uses a disagreement transition. But this sentence doesn’t disagree with the previous sentence. They both describe the same fictional situation. Choice D is incorrect. This choice uses a transition that indicates a shift back in time, which doesn’t make sense here. Both sentences use the present tense, as they’re describing the same fictional time period.

"}, {"id": "37957752", "domain": "Expression of Ideas", "skill": "Transitions", "difficulty": "E", "type": "mc", "stimulus": "

As biologist Terrie Williams has documented, deep dives present a challenge for seals and other marine mammals. A seal must exert enough energy to propel itself hundreds of meters downward, while keeping its heart rate low enough that it doesn’t run out of oxygen while underwater. ______blank a seal moves its flippers as little as possible on a deep dive, gliding to conserve energy.

", "stem": "

Which choice completes the text with the most logical transition?

", "choices": [{"id": "A", "text": "

In the first place,

"}, {"id": "B", "text": "

On the other hand,

"}, {"id": "C", "text": "

For this reason,

"}, {"id": "D", "text": "

In comparison,

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. “For this reason” logically signals that the behavior described in this sentence is a consequence of the information about seals in the previous sentence. That is, a seal moves its flippers as little as possible during a deep dive because it needs to keep its heart rate low enough that it does not run out of oxygen. 

Choice A is incorrect because “in the first place” illogically signals that this sentence is the first point in a discussion. Instead, the sentence describes a behavior that is a consequence of the previous information about seals.  Choice B is incorrect because “on the other hand” illogically signals that the behavior described in this sentence contrasts with the previous information about seals. Instead, it is a consequence of that information. Choice D is incorrect because “in comparison” illogically signals that the behavior described in this sentence is being compared to the previous information about seals. Instead, it is a consequence of that information. 

"}, {"id": "2b5f4bdc", "domain": "Expression of Ideas", "skill": "Transitions", "difficulty": "M", "type": "mc", "stimulus": "

In the early 1900s, Jovita Idár fought injustice on both sides of the Mexico–United States border. As a reporter for the Texas newspaper La Crónica, she voiced support for the Mexican people’s revolt against authoritarian rule. ______blank she founded the League of Mexican Women, a group that advocated for the rights of Mexican Americans.

", "stem": "

Which choice completes the text with the most logical transition?

", "choices": [{"id": "A", "text": "

Additionally,

"}, {"id": "B", "text": "

In conclusion,

"}, {"id": "C", "text": "

For example,

"}, {"id": "D", "text": "

Rather,

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer because “additionally” logically signals that the information in this sentence—that Idár founded the League of Mexican Women—is another instance of Idár fighting injustice, this time advocating for the rights of Mexican Americans.

Choice B is incorrect because “in conclusion” illogically signals that the information in this sentence sums up or concludes the discussion of Idár’s support for the Mexican people’s revolt. Instead, the founding of the League of Mexican Women is a separate instance of Idár fighting injustice. Choice C is incorrect because “for example” illogically signals that the information in this sentence is an example of how, as a newspaper reporter, Idár voiced support for the Mexican people’s revolt. Instead, the founding of the League of Mexican Women is a separate instance of Idár fighting injustice, this time in support of Mexican Americans. Choice D is incorrect because “rather” illogically signals that the information in this sentence offers a contrast or exception to the previous information about Idár’s support for the Mexican people’s revolt. Instead, the founding of the League of Mexican Women is a separate instance of Idár fighting injustice.

"}, {"id": "90117366", "domain": "Expression of Ideas", "skill": "Transitions", "difficulty": "E", "type": "mc", "stimulus": "

To explore how blinking affects social interactions, Dutch researchers observed interactions between human speakers and “listeners” (animated human faces on a screen). The researchers found that when the listeners blinked slowly, the speakers tended to talk for less time. ______blank quicker blinks were associated with longer talking times.

", "stem": "

Which choice completes the text with the most logical transition?

", "choices": [{"id": "A", "text": "

For example,

"}, {"id": "B", "text": "

Specifically,

"}, {"id": "C", "text": "

Firstly,

"}, {"id": "D", "text": "

By contrast,

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. “By contrast” logically signals that the finding described in this sentence contrasts with the finding described in the previous sentence. That is, quicker blinks were associated with longer talking times, whereas slower blinks were associated with shorter talking times. 

Choice A is incorrect because “for example” illogically signals that the finding described in this sentence is an example of the finding described in the previous sentence. Instead, it contrasts with that finding. Choice B is incorrect because “specifically” illogically signals that this sentence provides specific, precise details about the finding described in the previous sentence. Instead, it presents information that contrasts with that finding. Choice C is incorrect because “firstly” illogically signals that the finding described in this sentence is a first point or occurs first in a chronological sequence of events. Instead, it contrasts with the finding described in the previous sentence. 

"}, {"id": "ed80971c", "domain": "Expression of Ideas", "skill": "Rhetorical Synthesis", "difficulty": "M", "type": "mc", "stimulus": "

While researching a topic, a student has taken the following notes:

\n", "stem": "

The student wants to emphasize how long the museum has existed. Which choice most effectively uses relevant information from the notes to accomplish this goal?

", "choices": [{"id": "A", "text": "

The Pueblo of Zuni is home to the A:shiwi A:wan Museum and Heritage Center, which was founded by tribal members.

"}, {"id": "B", "text": "

The A:shiwi A:wan Museum and Heritage Center has served the Pueblo of Zuni since 1992.

"}, {"id": "C", "text": "

According to its website, the A:shiwi A:wan Museum and Heritage Center (founded in the 1990s) works to “emphasize A:shiwi ways of knowing.”

"}, {"id": "D", "text": "

Knowledge has been one of the central themes of the A:shiwi A:wan Museum and Heritage Center from its founding.

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. This choice effectively uses information from the notes to emphasize how long the museum has existed. It says that the museum has existed since 1992.

Choice A is incorrect. This choice doesn’t emphasize how long the museum has existed. It doesn’t say when the museum was founded. Choice C is incorrect. This choice doesn’t emphasize how long the museum has existed. It doesn’t say the exact date of the museum’s founding. Rather, it emphasizes the museum’s mission. Choice D is incorrect. This choice doesn’t emphasize how long the museum has existed. It doesn’t say when the museum was founded. 

"}, {"id": "13f36b03", "domain": "Expression of Ideas", "skill": "Rhetorical Synthesis", "difficulty": "E", "type": "mc", "stimulus": "

While researching a topic, a student has taken the following notes:

\n", "stem": "

The student wants to provide an explanation and example of “flauna.” Which choice most effectively uses relevant information from the notes to accomplish this goal?

", "choices": [{"id": "A", "text": "

The term “flauna,” used by Los Angeles-based painter Jon Ching, is a combination of the words “flora” and “fauna.”

"}, {"id": "B", "text": "

Jon Ching uses the term “flauna,” a combination of the words “flora” and “fauna,” to describe the subjects of his surreal paintings: plant-animal hybrids such as a parrot with leaves for feathers.

"}, {"id": "C", "text": "

Jon Ching, who created Nectar, refers to the subjects of his paintings as “flauna.”

"}, {"id": "D", "text": "

The subjects of Nectar and Primaveral are types of “flauna,” a term that the paintings’ creator, Jon Ching, uses when describing his surreal artworks.

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer because it provides both an explanation and an example of “flauna.” The sentence explains that flauna, a combination of the words “flora” and “fauna,” is a term used by Jon Ching to describe the plant-animal hybrids in his paintings. The sentence also mentions an example of Ching’s flauna: a parrot with leaves for feathers. 

Choice A is incorrect. While the sentence partially explains what “flauna” is, it doesn’t provide a full explanation or specific example of Ching’s flauna. Choice C is incorrect. While the sentence partially explains what “flauna” is and includes a title of a Ching painting, it doesn’t provide a full explanation or specific example of Ching’s flauna. Choice D is incorrect. While the sentence partially explains what “flauna” is and includes the titles of two Ching paintings, it doesn’t provide a full explanation of Ching’s flauna.

"}, {"id": "52b31d7b", "domain": "Expression of Ideas", "skill": "Transitions", "difficulty": "M", "type": "mc", "stimulus": "

In November 1934, Amrita Sher-Gil was living in what must have seemed like the ideal city for a young artist: Paris. She was studying firsthand the color-saturated style of France’s modernist masters and beginning to make a name for herself as a painter. ______blank Sher-Gil longed to return to her childhood home of India; only there, she believed, could her art truly flourish.

", "stem": "

Which choice completes the text with the most logical transition?

", "choices": [{"id": "A", "text": "

Still,

"}, {"id": "B", "text": "

Therefore,

"}, {"id": "C", "text": "

Indeed,

"}, {"id": "D", "text": "

Furthermore,

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. “Still” logically signals that the information about Sher-Gil in this sentence—that she longed to leave Paris and return to India—contrasts with what one would expect after reading about Sher-Gil’s experiences in Paris in the previous sentences. 

Choice B is incorrect because “therefore” illogically signals that the information about Sher-Gil in this sentence is a result or consequence of the descriptions in the previous sentences. Instead, this information contrasts with what one would expect after reading about Sher-Gil’s experiences in Paris. Choice C is incorrect because “indeed” illogically signals that the information about Sher-Gil in this sentence offers additional emphasis in support of the descriptions in the previous sentences. Instead, this information contrasts with what one would expect after reading about Sher-Gil’s experiences in Paris. Choice D is incorrect because “furthermore” illogically signals that the information about Sher-Gil in this sentence offers additional support for or confirmation of the descriptions in the previous sentences. Instead, this information contrasts with what one would expect after reading about Sher-Gil’s experiences in Paris.

"}, {"id": "a86c0b1b", "domain": "Expression of Ideas", "skill": "Rhetorical Synthesis", "difficulty": "M", "type": "mc", "stimulus": "

While researching a topic, a student has taken the following notes:

\n", "stem": "

The student wants to specify the reason the Pleiades’ appearance changed. Which choice most effectively uses relevant information from the notes to accomplish this goal?

", "choices": [{"id": "A", "text": "

Ancient Native American and Australian Aboriginal cultures described the Pleiades, which was referred to in Greek mythology as the Seven Sisters, as having seven stars.

"}, {"id": "B", "text": "

Although once referred to as the Seven Sisters, the Pleiades appears to have only six stars today.

"}, {"id": "C", "text": "

In the time since ancient cultures described the Pleiades as having seven stars, two of the cluster’s stars have moved so close together that they now appear as one.

"}, {"id": "D", "text": "

The Pleiades has seven stars, but two are so close together that they appear to be a single star.

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. The sentence specifies the reason the Pleiades’ appearance changed, noting that two of the cluster’s stars have moved so close together that they now appear as one star.

Choice A is incorrect. The sentence specifies how ancient Native American and Australian Aboriginal cultures described the Pleiades; it doesn’t specify the reason the Pleiades’ appearance changed. Choice B is incorrect. The sentence describes the appearance of the Pleiades today; it doesn’t specify the reason the Pleiades’ appearance changed. Choice D is incorrect. The sentence explains why two of the Pleiades’ stars appear to be a single star; it doesn’t specify the reason the Pleiades’ appearance changed.

"}, {"id": "eaded344", "domain": "Expression of Ideas", "skill": "Rhetorical Synthesis", "difficulty": "E", "type": "mc", "stimulus": "

While researching a topic, a student has taken the following notes:

\n", "stem": "

The student wants to introduce Kahlo to an audience unfamiliar with the artist. Which choice most effectively uses relevant information from the notes to accomplish this goal?

", "choices": [{"id": "A", "text": "

Known for being vivid and richly symbolic, Frida Kahlo’s self-portraits include The Two Fridas (1939).

"}, {"id": "B", "text": "

The 1939 painting The Two Fridas is one example of a self-portrait by Frida Kahlo.

"}, {"id": "C", "text": "

One painting by Frida Kahlo features two versions of herself, with one version wearing a European-style dress and the other a traditional Tehuana dress.

"}, {"id": "D", "text": "

One of the most influential artists of the twentieth century, Mexican painter Frida Kahlo is best known for her self-portraits, which are vivid and richly symbolic.

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. By identifying Kahlo as an influential artist from Mexico, and by describing the work she’s best known for, this choice provides the background information necessary to introduce Kahlo to an unfamiliar audience.

Choice A is incorrect. This choice doesn’t effectively introduce Kahlo. It doesn’t include any background information about who Kahlo is or where she’s from. It simply identifies one of her paintings. Choice B is incorrect. This choice doesn’t effectively introduce Kahlo. It doesn’t include any background information about who Kahlo is or where she’s from. It simply identifies one of her paintings. Choice C is incorrect. This choice doesn’t effectively introduce Kahlo. It doesn’t include any background information about who Kahlo is or where she’s from. Instead, it describes one of her paintings in detail.

"}, {"id": "86b78078", "domain": "Expression of Ideas", "skill": "Rhetorical Synthesis", "difficulty": "M", "type": "mc", "stimulus": "

While researching a topic, a student has taken the following notes:

\n", "stem": "

The student wants to introduce Samuel Selvon and his novel The Lonely Londoners to a new audience. Which choice most effectively uses relevant information from the notes to accomplish this goal?

", "choices": [{"id": "A", "text": "

In 1956, Trinidadian author Samuel Selvon published one of his most celebrated novels, The Lonely Londoners, which is about a group of men who emigrate from the Caribbean to Great Britain after World War II.

"}, {"id": "B", "text": "

Samuel Selvon wrote the novel Moses Ascending after he wrote The Lonely Londoners. 

"}, {"id": "C", "text": "

The Lonely Londoners, a celebrated novel that was published in 1956, depicts post–World War II Caribbean migration from the perspective of a Trinidadian author.

"}, {"id": "D", "text": "

Some of the characters who appear in Samuel Selvon’s Moses Ascending also appear in The Lonely Londoners.

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. By noting that Selvon is a Trinidadian author and indicating that The Lonely Londoners, published in 1956, is about a group of men who emigrate from the Caribbean to Great Britain after World War II, the sentence effectively introduces Samuel Selvon and his novel to a new audience.

Choice B is incorrect. The sentence indicates the order in which two of Selvon’s novels were written; it doesn’t introduce Samuel Selvon and The Lonely Londoners to a new audience. Choice C is incorrect. While the sentence describes the novel The Lonely Londoners, it doesn’t mention its author, Samuel Selvon, by name and thus doesn’t effectively introduce him to a new audience. Choice D is incorrect. The sentence indicates that two of Selvon’s novels include the same characters; it doesn’t introduce Samuel Selvon and The Lonely Londoners to a new audience.

"}, {"id": "4f9ee1dc", "domain": "Expression of Ideas", "skill": "Rhetorical Synthesis", "difficulty": "M", "type": "mc", "stimulus": "

While researching a topic, a student has taken the following notes:

\n", "stem": "

The student wants to emphasize a similarity between the two sea turtle species. Which choice most effectively uses relevant information from the notes to accomplish this goal?

", "choices": [{"id": "A", "text": "

Among the seven species of sea turtle is the olive ridley sea turtle, which can be found in the Atlantic Ocean.

"}, {"id": "B", "text": "

The Kemp’s ridley sea turtle is referred to as Lepidochelys kempii, while the olive ridley sea turtle is referred to as Lepidochelys olivacea.

"}, {"id": "C", "text": "

Both the Kemp’s ridley sea turtle and the olive ridley sea turtle can be found in the Atlantic Ocean.

"}, {"id": "D", "text": "

The Kemp’s ridley sea turtle (Lepidochelys kempii) and the olive ridley sea turtle (Lepidochelys olivacea) are different species.

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. The sentence emphasizes a similarity between the two sea turtle species: both can be found in the Atlantic Ocean.

Choice A is incorrect. The sentence indicates that the olive ridley sea turtle is one of seven species of sea turtle; it fails to mention the Kemp’s ridley sea turtle. Choice B is incorrect. The sentence emphasizes a difference between the two sea turtle species rather than a similarity. Choice D is incorrect. The sentence emphasizes a difference between the two sea turtle species rather than a similarity.

"}, {"id": "2bda9edb", "domain": "Expression of Ideas", "skill": "Transitions", "difficulty": "E", "type": "mc", "stimulus": "

In 1885, Chinese-born California resident Mary Tape became a hero of the Asian American civil rights movement. In January of that year, she won an antidiscrimination case in the California Supreme Court. ______blank in April, she wrote an open letter criticizing her local board of education for discrimination. Both actions are remembered today as historic stands against racism.

", "stem": "

Which choice completes the text with the most logical transition?

", "choices": [{"id": "A", "text": "

Later,

"}, {"id": "B", "text": "

For instance,

"}, {"id": "C", "text": "

In other words,

"}, {"id": "D", "text": "

Rather,

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. “Later” logically signals that the letter-writing discussed in this sentence occurred later in a chronological sequence of events than did the antidiscrimination case discussed in the previous sentence.

Choice B is incorrect because “for instance” illogically signals that the letter-writing discussed in this sentence is an example of the antidiscrimination case discussed in the previous sentence. Instead, the letter-writing is an event that occurred after the court case. Choice C is incorrect because “in other words” illogically signals that the letter-writing discussed in this sentence is a paraphrase or restatement of the antidiscrimination case discussed in the previous sentence. Instead, the letter-writing is an event that occurred after the court case. Choice D is incorrect because “rather” illogically signals that the letter-writing discussed in this sentence is an alternative to the antidiscrimination case discussed in the previous sentence. Instead, the letter-writing is an event that occurred after the court case.

"}, {"id": "e3484c07", "domain": "Expression of Ideas", "skill": "Rhetorical Synthesis", "difficulty": "E", "type": "mc", "stimulus": "

While researching a topic, a student has taken the following notes:

\n", "stem": "

The student wants to emphasize a difference between the behavior of jellyfish and that of black dragonfish. Which choice most effectively uses relevant information from the notes to accomplish this goal?

", "choices": [{"id": "A", "text": "

Both jellyfish and black dragonfish are organisms that emit light, which is produced by chemical reactions in these organisms’ cells.

"}, {"id": "B", "text": "

Black dragonfish emit a steady red light, which helps them locate prey in deep waters.

"}, {"id": "C", "text": "

Bioluminescence, the emission of light by living organisms, results from chemical reactions in organisms’ cells. 

"}, {"id": "D", "text": "

Jellyfish emit light to startle predators, whereas black dragonfish do so to locate prey.

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. The sentence emphasizes a difference between the behavior of jellyfish and that of black dragonfish, noting that jellyfish and black dragonfish emit light as part of different behaviors (protection and predation, respectively).

Choice A is incorrect. The sentence emphasizes a similarity between jellyfish and black dragonfish; it doesn’t emphasize a difference between the behavior of the two animals. Choice B is incorrect. The sentence emphasizes the type of bioluminescence exhibited by black dragonfish, noting that it’s used in predation; it doesn’t emphasize a difference between the behavior of the two animals. Choice C is incorrect. The sentence defines bioluminescence and explains how it works; the sentence doesn’t mention either animal or emphasize a difference between them.

"}, {"id": "fc95a352", "domain": "Expression of Ideas", "skill": "Transitions", "difficulty": "H", "type": "mc", "stimulus": "

When designing costumes for film, American artist Suttirat Larlarb typically custom fits the garments to each actor. ______blank for the film Sunshine, in which astronauts must reignite a dying Sun, she designed a golden spacesuit and had a factory reproduce it in a few standard sizes; lacking a tailor-made quality, the final creations reflected the ungainliness of actual spacesuits.

", "stem": "

Which choice completes the text with the most logical transition?

", "choices": [{"id": "A", "text": "

Nevertheless,

"}, {"id": "B", "text": "

Thus,

"}, {"id": "C", "text": "

Likewise,

"}, {"id": "D", "text": "

Moreover,

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. “Nevertheless” logically signals that the information in this sentence—that the spacesuits Suttirat Larlarb designed for the film Sunshine were made in standard sizes in a factory—presents a notable exception to Larlarb’s typical approach of custom-fitting garments to actors, which is described in the previous sentence. 

Choice B is incorrect because “thus” illogically signals that the information in this sentence is a result or consequence of the previous information about Larlarb’s typical approach of custom-fitting garments to actors. Instead, it presents a notable exception to Larlarb’s typical approach. Choice C is incorrect because “likewise” illogically signals that the information in this sentence is similar to the previous information about Larlarb’s typical approach of custom-fitting garments to actors. Instead, it presents a notable exception to Larlarb’s typical approach. Choice D is incorrect because “moreover” illogically signals that the information in this sentence merely adds to the previous information about Larlarb’s typical approach of custom-fitting garments to actors. Instead, it presents a notable exception to Larlarb’s typical approach. 

"}, {"id": "5a5e22b5", "domain": "Expression of Ideas", "skill": "Rhetorical Synthesis", "difficulty": "M", "type": "mc", "stimulus": "

While researching a topic, a student has taken the following notes:

\n", "stem": "

The student wants to present LIGO’s aim and methodology. Which choice most effectively uses relevant information from the notes to accomplish this goal?

", "choices": [{"id": "A", "text": "

In 2015, LIGO’s massive interferometers detected a powerful ripple that originated in deep space and eventually passed through Earth.

"}, {"id": "B", "text": "

Though the physics study LIGO began in 2002, its massive interferometers didn’t detect a gravitational wave until 2015.

"}, {"id": "C", "text": "

To achieve its aims, LIGO uses a pair of massive interferometers that are thousands of miles apart.

"}, {"id": "D", "text": "

A physics study designed to detect and analyze gravitational waves, LIGO uses a pair of massive interferometers that are thousands of miles apart.

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. The sentence effectively presents the LIGO study’s aim, noting that it is designed to detect and analyze gravitational waves, and its methodology (it uses two interferometers to detect the waves).

Choice A is incorrect. The sentence describes a finding from the LIGO study; it doesn’t effectively present the study’s aim or its methodology. Choice B is incorrect. The sentence provides background information about the LIGO study’s timeline; it doesn’t effectively present the study’s aim or its methodology. Choice C is incorrect. The sentence touches on LIGO’s methodology, noting that it uses two interferometers, but doesn’t indicate what the study’s aims are. 

"}, {"id": "bc56170b", "domain": "Expression of Ideas", "skill": "Rhetorical Synthesis", "difficulty": "M", "type": "mc", "stimulus": "

While researching a topic, a student has taken the following notes:

\n", "stem": "

The student wants to emphasize the aim of the research study. Which choice most effectively uses relevant information from the notes to accomplish this goal?

", "choices": [{"id": "A", "text": "

As it orbited the Moon, the Kaguya satellite collected data that was later analyzed by cosmochemist Kentaro Terada.

"}, {"id": "B", "text": "

Before 2008, Kentaro Terada wondered if the Moon was receiving some of its oxygen from Earth.

"}, {"id": "C", "text": "

Cosmochemist Kentaro Terada set out to determine whether some of the Moon’s oxygen was coming from Earth.

"}, {"id": "D", "text": "

Kentaro Terada’s study determined that Earth is sending a small amount of oxygen to the Moon.

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. The sentence emphasizes the aim, or goal, of the research study, noting what Terada set out to do: determine whether some of the Moon’s oxygen was coming from Earth.

Choice A is incorrect. The sentence focuses on how the Kaguya satellite collected data; it doesn’t emphasize the aim of the research study. Choice B is incorrect. While the sentence mentions what Terada was curious about before conducting the research study, it doesn’t emphasize his study’s aim. Choice D is incorrect. The sentence presents the research study’s conclusion; it doesn’t emphasize the study’s aim.

"}, {"id": "d7f31e68", "domain": "Expression of Ideas", "skill": "Rhetorical Synthesis", "difficulty": "E", "type": "mc", "stimulus": "

While researching a topic, a student has taken the following notes: 

\n", "stem": "

The student wants to emphasize Wu’s most well-known achievement. Which choice most effectively uses relevant information from the notes to accomplish this goal?

", "choices": [{"id": "A", "text": "

Annie Wu, who has won multiple national flute competitions, has also combined flute playing and beatboxing.

"}, {"id": "B", "text": "

Among her many achievements, prominent American flutist Annie Wu graduated from the New England Conservatory and has won multiple national flute competitions.

"}, {"id": "C", "text": "

Annie Wu is best known for a 2011 YouTube video performance of Three Beats for Beatbox Flute that has been viewed over two million times.

"}, {"id": "D", "text": "

Composer Greg Pattillo’s original work Three Beats for Beatbox Flute combines flute playing and beatboxing.

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. This describes the achievement for which Wu is best known.

Choice A is incorrect. This choice doesn’t emphasize Wu’s most well-known achievement. It mentions some of her general achievements, but not the one for which she is “best known.” Choice B is incorrect. This choice doesn’t emphasize Wu’s most well-known achievement—it describes several of her achievements equally. Choice D is incorrect. This choice doesn’t emphasize Wu’s most well-known achievement. It describes a piece of music featured in her most well-known achievement.

"}, {"id": "6351062d", "domain": "Expression of Ideas", "skill": "Rhetorical Synthesis", "difficulty": "M", "type": "mc", "stimulus": "

While researching a topic, a student has taken the following notes:

\n", "stem": "

The student wants to emphasize the decline in unique apple varieties in the US and specify why this decline occurred. Which choice most effectively uses relevant information from the notes to accomplish these goals?

", "choices": [{"id": "A", "text": "

The Lost Apple Project is dedicated to finding some of the apple varieties lost following a shift in agricultural practices in the mid-1900s.

"}, {"id": "B", "text": "

While over 14,000 apple varieties were grown in the US in the late 1890s, only 15 unique varieties make up most of the apples sold today.

"}, {"id": "C", "text": "

Since the rise of industrial agriculture, US farmers have mainly grown the same few unique apple varieties, resulting in the loss of thousands of varieties less suitable for commercial growth.

"}, {"id": "D", "text": "

As industrial agriculture rose to prominence in the mid-1900s, the number of crops selected for cultivation decreased dramatically.

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. The sentence emphasizes the decline in unique apple varieties in the US and specifies why this decline occurred, noting that thousands of apple varieties were lost because US farmers started mainly growing the same few unique varieties.

Choice A is incorrect. The sentence introduces the Lost Apple Project; it doesn’t emphasize the decline in unique apple varieties in the US and specify why this decline occurred. Choice B is incorrect. While the sentence emphasizes the decline in unique apple varieties in the US, it doesn’t explain why this decline occurred. Choice D is incorrect. The sentence emphasizes the general decline of crop varieties in the mid-1900s; it doesn’t emphasize the specific decline in unique apple varieties in the US.

"}, {"id": "5bb7dc03", "domain": "Expression of Ideas", "skill": "Rhetorical Synthesis", "difficulty": "M", "type": "mc", "stimulus": "

While researching a topic, a student has taken the following notes:

\n", "stem": "

The student wants to emphasize a difference in the origins of the two words. Which choice most effectively uses relevant information from the notes to accomplish this goal?

", "choices": [{"id": "A", "text": "

“Guerdon,” the final word of the 2008 Scripps National Spelling Bee, is of Anglo-French origin, while the following year’s final word, “Laodicean,” derives from ancient Greek.

"}, {"id": "B", "text": "

In 2008, Sameer Mishra won the Scripps National Spelling Bee by correctly spelling the word “guerdon”; however, the following year, Kavya Shivashankar won based on spelling the word “Laodicean.”

"}, {"id": "C", "text": "

Kavya Shivashankar won the 2009 Scripps National Spelling Bee by correctly spelling “Laodicean,” which derives from the ancient Greek word “Laodíkeia.”

"}, {"id": "D", "text": "

The Scripps National Spelling Bee uses words from diverse linguistic origins, such as “guerdon” and “Laodicean.”

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. Noting that “guerdon” is of Anglo-French origin and “Laodicean” is of ancient Greek origin, the sentence uses “while” to emphasize a difference in the origins of the two words.

Choice B is incorrect. While the sentence emphasizes two words used in the Scripps National Spelling Bee, it doesn’t emphasize (or mention) the words’ linguistic origins. Choice C is incorrect. While the sentence specifies the linguistic origin of one word used in the Scripps National Spelling Bee, it doesn’t mention the other word or emphasize a difference in the two words’ origins. Choice D is incorrect. While the sentence makes a generalization about words used in the Scripps National Spelling Bee, it doesn’t emphasize a difference in the words’ origins.

"}, {"id": "9e2d4ef7", "domain": "Expression of Ideas", "skill": "Rhetorical Synthesis", "difficulty": "M", "type": "mc", "stimulus": "

While researching a topic, a student has taken the following notes:

\n", "stem": "

The student wants to introduce Paradise to an audience unfamiliar with the novel and its author. Which choice most effectively uses relevant information from the notes to accomplish this goal?

", "choices": [{"id": "A", "text": "

Abdulrazak Gurnah, who wrote Paradise and later was awarded the Nobel Prize in Literature, was born in Zanzibar in East Africa and currently lives in the United Kingdom. 

"}, {"id": "B", "text": "

Many readers have singled out Abdulrazak Gurnah’s 1994 book Paradise, a historical novel about colonial East Africa, for praise. 

"}, {"id": "C", "text": "

A much-praised historical novel about colonial East Africa, Paradise (1994) was written by Abdulrazak Gurnah, winner of the 2021 Nobel Prize in Literature.

"}, {"id": "D", "text": "

Paradise is a historical novel about events that occurred in colonial East Africa, Abdulrazak Gurnah’s homeland.

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. The sentence effectively introduces Paradise to an audience unfamiliar with the novel and its author, describing Paradise as a historical novel about colonial East Africa and its author as the winner of the 2021 Nobel Prize in Literature. 

Choice A is incorrect. While the sentence introduces Abdulrazak Gurnah to an audience unfamiliar with the author, it doesn’t effectively introduce Paradise. Choice B is incorrect. While the sentence provides background information about Paradise, it doesn’t effectively introduce the novel to an audience unfamiliar with its author. Choice D is incorrect. While the sentence provides background information about Paradise, it doesn’t effectively introduce the novel to an audience unfamiliar with its author.

"}, {"id": "87d8a2ff", "domain": "Expression of Ideas", "skill": "Transitions", "difficulty": "E", "type": "mc", "stimulus": "

During a 2021 launch, Rocket Labs’ Electron rocket experienced an unexpected failure: its second-stage booster shut down suddenly after ignition. ______blank instead of downplaying the incident, Rocket Labs’ CEO publicly acknowledged what happened and apologized for the loss of the rocket’s payload, which had consisted of two satellites.

", "stem": "

Which choice completes the text with the most logical transition?

", "choices": [{"id": "A", "text": "

Afterward,

"}, {"id": "B", "text": "

Additionally,

"}, {"id": "C", "text": "

Indeed,

"}, {"id": "D", "text": "

Similarly,

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. “Afterward” logically signals that the events described in this sentence—the CEO’s public acknowledgment and apology—occurred after the rocket booster’s failure and are part of a chronological sequence of events.

Choice B is incorrect because “additionally” illogically signals that the events described in this sentence merely occurred in addition to the rocket booster’s failure. Instead, they occurred after the rocket booster’s failure and are part of a chronological sequence of events. Choice C is incorrect because “indeed” illogically signals that the events described in this sentence emphasize or strengthen a statement made in the previous sentence. Instead, they occurred after the rocket booster’s failure and are part of a chronological sequence of events. Choice D is incorrect because “similarly” illogically signals that the events described in this sentence are similar to the rocket booster’s failure. Instead, they occurred after the rocket booster’s failure and are part of a chronological sequence of events.

"}, {"id": "94f4eecb", "domain": "Expression of Ideas", "skill": "Rhetorical Synthesis", "difficulty": "M", "type": "mc", "stimulus": "

While researching a topic, a student has taken the following notes:

\n", "stem": "

The student wants to emphasize the role a misconception played in the naming of a place. Which choice most effectively uses relevant information from the notes to accomplish this goal?

", "choices": [{"id": "A", "text": "

The novel Las sergas de Esplandián featured a fictional island known as California.

"}, {"id": "B", "text": "

To the south of the US state of California lies Baja California (“Lower California”), originally called California after a fictional place. 

"}, {"id": "C", "text": "

In the sixteenth century, Spanish explorers learned of a peninsula off the west coast of Mexico and called it California. 

"}, {"id": "D", "text": "

Thinking it was an island, Spanish explorers called a peninsula California after an island in a popular novel.

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. The sentence emphasizes the role a misconception played in the naming of a place, explaining that Spanish explorers mistook a peninsula for an island and, as a result, named the peninsula after a fictional island, California.

Choice A is incorrect. The sentence mentions a novel that featured a fictional island, California; it doesn’t emphasize the role a misconception played in the naming of a place. Choice B is incorrect. The sentence notes that Baja California was originally named after a fictional place; it doesn’t emphasize the role a misconception—specifically, the Spanish explorers’ mistaken belief that the peninsula was an island—played in the naming of a place. Choice C is incorrect. The sentence indicates when Spanish explorers learned of the peninsula they called California; it doesn’t emphasize the role a misconception played in the naming of a place.

"}, {"id": "99183985", "domain": "Expression of Ideas", "skill": "Rhetorical Synthesis", "difficulty": "M", "type": "mc", "stimulus": "

While researching a topic, a student has taken the following notes:

\n", "stem": "

The student wants to explain an advantage of the infilling technique. Which choice most effectively uses relevant information from the notes to accomplish this goal?

", "choices": [{"id": "A", "text": "

To remove carvings from sandstone arches in Utah’s Arches National Park, power grinding is not always feasible.

"}, {"id": "B", "text": "

Filling in carvings with ground sandstone and a bonding agent is less invasive than smoothing them away with a power grinder, which can greatly alter or damage the sandstone arches.

"}, {"id": "C", "text": "

Park rangers can use a power grinding technique to smooth away carvings or fill them in with ground sandstone and a bonding agent.

"}, {"id": "D", "text": "

As methods for removing carvings from sandstone, power grinding and infilling differ in their level of invasiveness.

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. The sentence effectively explains an advantage of infilling: it’s less invasive than using a power grinder.

Choice A is incorrect. The sentence identifies a disadvantage of power grinding; it doesn’t explain an advantage of infilling. Choice C is incorrect. The sentence identifies the two techniques park rangers use; it doesn’t explain an advantage of infilling. Choice D is incorrect. The sentence indicates that power grinding and infilling are different in one aspect; it fails to explain an advantage of infilling.

"}, {"id": "4154a7a3", "domain": "Expression of Ideas", "skill": "Transitions", "difficulty": "E", "type": "mc", "stimulus": "

In 1891, dancer and choreographer Loie Fuller first performed her celebrated Serpentine Dance, artfully twirling her long, flowing skirt to create striking visual effects. ______blank in 1896, cinema pioneers Auguste and Louis Lumière made a groundbreaking short film of Fuller’s dance. 

", "stem": "

Which choice completes the text with the most logical transition?

", "choices": [{"id": "A", "text": "

However,

"}, {"id": "B", "text": "

In conclusion,

"}, {"id": "C", "text": "

Later,

"}, {"id": "D", "text": "

In other words, 

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. “Later” logically signals that the event discussed in this sentence—the creation of the short film featuring Fuller’s dance—is a related event that occurred after the event discussed in the previous sentence (the 1891 debut of the dance).

Choice A is incorrect because “however” illogically signals that the information in this sentence contrasts with the information in the previous sentence. Instead, the creation of the short film is a related event that followed the event discussed in the previous sentence. Choice B is incorrect because “in conclusion” illogically signals that the information in this sentence concludes or summarizes the information in the previous sentence. Instead, the creation of the short film is a related event that followed the event discussed in the previous sentence. Choice D is incorrect because “in other words” illogically signals that the information in this sentence is a paraphrase or restatement of the information in the previous sentence. Instead, the creation of the short film is a related event that followed the event discussed in the previous sentence.

"}, {"id": "9c78f702", "domain": "Expression of Ideas", "skill": "Transitions", "difficulty": "E", "type": "mc", "stimulus": "

Phytoplankton play a crucial role in the ocean’s uptake of carbon from the atmosphere. When alive, these tiny marine organisms absorb atmospheric carbon via photosynthesis. ______blank after they die, the phytoplankton sink to the seafloor, where the carbon in their cells gets stored in sediment, preventing it from cycling back into the atmosphere.

", "stem": "

Which choice completes the text with the most logical transition?

", "choices": [{"id": "A", "text": "

Specifically,

"}, {"id": "B", "text": "

By contrast,

"}, {"id": "C", "text": "

Nevertheless,

"}, {"id": "D", "text": "

Then,

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. “Then” logically signals that the event described in this sentence—carbon in phytoplankton cells being trapped in sediment after the organisms have died—occurs later in a chronological sequence than the event described in the previous sentence (phytoplankton absorbing carbon while alive).

Choice A is incorrect because “specifically” illogically signals that the information that follows provides specific, precise details elaborating on the previous information about what phytoplankton do when alive. Instead, this sentence explains what happens after phytoplankton die—a later step in the chronological sequence of events. Choice B is incorrect because “by contrast” illogically signals that the information that follows contrasts with the previous information about what phytoplankton do when alive. Instead, this sentence explains what happens after phytoplankton die—a later step in the chronological sequence of events. There is no contrast: in both life and death, phytoplankton contribute to the ocean’s carbon uptake. Choice C is incorrect because “nevertheless” illogically signals that the information that follows is in spite of the previous information about what phytoplankton do when alive. Instead, this sentence explains what happens after phytoplankton die—a later step in the chronological sequence of events. There is no contrast: in both life and death, phytoplankton contribute to the ocean’s carbon uptake.

"}, {"id": "d3898d32", "domain": "Expression of Ideas", "skill": "Transitions", "difficulty": "E", "type": "mc", "stimulus": "

Riley Black—the author of critically acclaimed books such as My Beloved Brontosaurus (2013)—is best known for writing about dinosaurs, but she has also conducted hands-on fieldwork. ______blank her fieldwork has included paleontological digs in Utah, Montana, and Wyoming, and her dinosaur fossil discoveries can be seen at places such as the Carnegie Museum of Natural History.

", "stem": "

Which choice completes the text with the most logical transition?

", "choices": [{"id": "A", "text": "

Regardless, 

"}, {"id": "B", "text": "

Subsequently,

"}, {"id": "C", "text": "

Specifically, 

"}, {"id": "D", "text": "

Conversely,

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. The second sentence provides more specific information about the fieldwork mentioned in the first sentence—that the paleontological digs took place in Utah, Montana, and Wyoming. Therefore, “specifically” fits perfectly in this context.

Choice A is incorrect. This choice uses a disagreement transition. But this sentence doesn’t disagree with the previous sentence. Rather, this sentence agrees with and elaborates on the last sentence by providing more specifics about the fieldwork Black does. Choice B is incorrect. This choice uses a transition that indicates that an event took place after another event. But the two sentences are not describing different events—instead, this sentence gives more details about the fieldwork discussed in the first sentence. Choice D is incorrect. This choice uses a disagreement transition. But this sentence doesn’t disagree with the previous sentence. Rather, this sentence agrees with and elaborates on the last sentence by providing more specifics about the fieldwork Black does.

"}, {"id": "ecb31049", "domain": "Expression of Ideas", "skill": "Transitions", "difficulty": "H", "type": "mc", "stimulus": "

The Sun and other stars are powered by nuclear fusion reactions, in which two atoms collide to form a single heavier atom, releasing energy. Scientists have long believed that fusion has the potential to meet humanity’s clean energy needs. ______blank prior to December 2022, no fusion reaction in a laboratory setting had ever generated a net energy gain.

", "stem": "

Which choice completes the text with the most logical transition?

", "choices": [{"id": "A", "text": "

For this reason,

"}, {"id": "B", "text": "

Moreover,

"}, {"id": "C", "text": "

Specifically,

"}, {"id": "D", "text": "

That said,

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. Scientists believe in fusion’s potential as an energy source, but have struggled to actually make it work—in other words, there is a contradiction between scientists’ beliefs and their reality. “That said” is a disagreement transition that works perfectly in this context.

Choice A is incorrect. This choice uses a cause-and-effect transition, which doesn’t make sense here. Scientists not being able to generate extra energy from lab fusion reactions isn’t an effect of them believing in fusion’s potential. Choice B is incorrect. This transition indicates the addition of another supporting point. But this sentence is not adding a supporting point to the previous sentence—scientists not being able to successfully generate energy from fusion isn’t another point in favor of fusion meeting humanity’s clean energy needs. Choice C is incorrect. This choice uses a transition that introduces or elaborates on a particular example. But this sentence doesn’t give an example of scientists’ belief in fusion’s potential to meet humanity’s clean energy needs—in fact, it contrasts that optimistic belief with the reality of past failures to successfully employ fusion for energy production.

"}, {"id": "eea351c4", "domain": "Expression of Ideas", "skill": "Transitions", "difficulty": "M", "type": "mc", "stimulus": "

“Wishcycling”—putting nonrecyclable items into recycling bins under the mistaken belief that those items can be recycled—ultimately does more harm than good. Nonrecyclable items, such as greasy pizza boxes, can contaminate recyclable materials, rendering entire batches unusable. ______blank nonrecyclable products can damage recycling plants’ machinery. 

", "stem": "

Which choice completes the text with the most logical transition?

", "choices": [{"id": "A", "text": "

Fittingly, 

"}, {"id": "B", "text": "

On the contrary,

"}, {"id": "C", "text": "

Moreover,

"}, {"id": "D", "text": "

Nevertheless,

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. The first sentence tells us that “wishcycling” is harmful, the previous sentence gives us an example, and this sentence gives us another example. So “moreover”—a transition that indicates the addition of another supporting point—fits perfectly here.

Choice A is incorrect. This choice uses a transition that means “appropriately” or “suitably,” which doesn’t make sense in context. This sentence adds another example of how “wishcycling” is harmful, so we’re looking for an addition transition. Choice B is incorrect. This choice uses a disagreement transition. But this sentence actually agrees with the previous sentence. Both provide examples of how “wishcycling” is harmful. Choice D is incorrect. This choice uses a disagreement transition. But this sentence actually agrees with the previous sentence. Both provide examples of how “wishcycling” is harmful.

"}, {"id": "0205e563", "domain": "Expression of Ideas", "skill": "Transitions", "difficulty": "M", "type": "mc", "stimulus": "

At two weeks old, the time their critical socialization period begins, wolves can smell but cannot yet see or hear. Domesticated dogs, ______blank can see, hear, and smell by the end of two weeks. This relative lack of sensory input may help explain why wolves behave so differently around humans than dogs do: from a very young age, wolves are more wary and less exploratory.

", "stem": "

Which choice completes the text with the most logical transition?

", "choices": [{"id": "A", "text": "

in other words,

"}, {"id": "B", "text": "

for instance,

"}, {"id": "C", "text": "

by contrast,

"}, {"id": "D", "text": "

accordingly,

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. “By contrast” logically signals that the information in this sentence—that dogs can see, hear, and smell by the end of two weeks—contrasts with the preceding information (that wolves can smell but not see or hear at the same age).

Choice A is incorrect because “in other words” illogically signals that the information about domesticated dogs in this sentence paraphrases the information about wolves in the previous sentence. Instead, the information about dogs contrasts with what came before. Choice B is incorrect because “for instance” illogically signals that the information about domesticated dogs in this sentence exemplifies the information about wolves in the previous sentence. Instead, the information about dogs contrasts with what came before. Choice D is incorrect because “accordingly” illogically signals that the information about domesticated dogs in this sentence is in accordance with, or results from, the information about wolves in the previous sentence. Instead, the information about dogs contrasts with what came before.

"}, {"id": "efc19153", "domain": "Expression of Ideas", "skill": "Rhetorical Synthesis", "difficulty": "M", "type": "mc", "stimulus": "

While researching a topic, a student has taken the following notes:

\n", "stem": "

The student wants to make and support a generalization about the effect of redesigning a city flag. Which choice most effectively uses relevant information from the notes to accomplish this goal?

", "choices": [{"id": "A", "text": "

Over one hundred US cities have redesigned their flags, including Pocatello, whose flag had been named the most poorly designed flag in North America.

"}, {"id": "B", "text": "

Pocatello is just one of over one hundred US cities that have redesigned their flags.

"}, {"id": "C", "text": "

After it was named the most poorly designed flag in North America, the flag of Pocatello was redesigned to better represent the city’s geography and civic priorities.

"}, {"id": "D", "text": "

Redesigning a poorly designed city flag can create a meaningful symbol of civic pride, as was the case when Pocatello redesigned its original flag to better represent its geography and civic priorities. 

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. The sentence makes and supports a generalization about the effect of redesigning a city flag, noting that redesigning a city flag can create a meaningful symbol of civic pride, as was the case when the city of Pocatello redesigned its flag.

Choice A is incorrect because the sentence explains that many US cities have redesigned their flags and provides an example; it doesn’t make and support a generalization about the effect of redesigning a city flag. Choice B is incorrect because the sentence provides an example of a city that redesigned its flag; it doesn’t make and support a generalization about the effect of redesigning a city flag. Choice C is incorrect because the sentence emphasizes why the flag of Pocatello was redesigned; it doesn’t make and support a generalization about the effect of redesigning a city flag.

"}, {"id": "eae29760", "domain": "Expression of Ideas", "skill": "Rhetorical Synthesis", "difficulty": "E", "type": "mc", "stimulus": "

While researching a topic, a student has taken the following notes:

\n", "stem": "

The student wants to explain an advantage of the Hanke-Henry calendar. Which choice most effectively uses relevant information from the notes to accomplish this goal?

", "choices": [{"id": "A", "text": "

The Gregorian calendar has 365 days, which is one day longer than the Hanke-Henry permanent calendar.

"}, {"id": "B", "text": "

Adopting the Hanke-Henry permanent calendar would help solve a problem with the Gregorian calendar.

"}, {"id": "C", "text": "

Designed so calendar dates would occur on the same day of the week each year, the Hanke-Henry calendar supports more predictable scheduling than does the Gregorian calendar.

"}, {"id": "D", "text": "

The Hanke-Henry permanent calendar was developed as an alternative to the Gregorian calendar, which is currently the most-used calendar in the world.

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. The sentence explains an advantage of the Hanke-Henry calendar, noting that it supports more predictable scheduling than does the Gregorian calendar and describing how it does so (by having calendar dates occur on the same day each year).

Choice A is incorrect. The sentence compares the number of days in the Gregorian and Hanke-Henry calendars; it doesn’t explain an advantage of the Hanke-Henry calendar. Choice B is incorrect. While the sentence refers to a possible reason to adopt the Hanke-Henry calendar—that doing so would help solve a problem with the Gregorian calendar—it doesn’t identify the problem or the solution and thus doesn’t explain the advantage of the Hanke-Henry calendar. Choice D is incorrect. The sentence describes the origins of the Hanke-Henry calendar; it doesn’t explain an advantage of it.

"}, {"id": "835b101b", "domain": "Expression of Ideas", "skill": "Rhetorical Synthesis", "difficulty": "M", "type": "mc", "stimulus": "

While researching a topic, a student has taken the following notes:

\n", "stem": "

The student wants to contrast Minnesota’s definition of a lake with Wisconsin’s. Which choice most effectively uses relevant information from the notes to accomplish this goal?

", "choices": [{"id": "A", "text": "

Wisconsin, which doesn’t take size into account in defining a lake, claims that it has over 15,000 lakes.

"}, {"id": "B", "text": "

Because its definition of a lake is different from Minnesota’s, it is unclear how many lakes Wisconsin really has.

"}, {"id": "C", "text": "

According to Minnesota’s definition of a lake—an inland body of water of at least 10 acres—Wisconsin has about 6,000 lakes.

"}, {"id": "D", "text": "

Minnesota’s definition of a lake—an inland body of water of at least 10 acres—is more restrictive than Wisconsin’s, which doesn’t take size into account.

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. The sentence contrasts Minnesota’s definition of a lake with Wisconsin’s, explaining that Minnesota’s definition (which takes size into account) is more restrictive than Wisconsin’s definition (which doesn’t).

Choice A is incorrect. While the sentence notes that Wisconsin’s definition of a lake doesn’t take size into account, it doesn’t contrast Minnesota’s definition with Wisconsin’s. Choice B is incorrect. The sentence states that Wisconsin’s definition of a lake is different from Minnesota’s, but it doesn’t clarify how they differ. In other words, it doesn’t contrast Minnesota’s definition with Wisconsin’s. Choice C is incorrect. The sentence indicates how many lakes Wisconsin has according to Minnesota’s definition of a lake, but it doesn’t clarify how the states’ definitions differ. In other words, it doesn’t contrast Minnesota’s definition with Wisconsin’s.

"}, {"id": "39d1a519", "domain": "Expression of Ideas", "skill": "Transitions", "difficulty": "M", "type": "mc", "stimulus": "

To discover which fruit varieties were grown in Italy’s Umbria region before the introduction of industrial farming, botanist Isabella Dalla Ragione often turns to centuries-old lists of cooking ingredients. ______blank she analyzes Renaissance paintings of Umbria, as they can provide accurate representations of fruits that were grown there long ago.

", "stem": "

Which choice completes the text with the most logical transition?

", "choices": [{"id": "A", "text": "

In sum,

"}, {"id": "B", "text": "

Instead,

"}, {"id": "C", "text": "

Thus,

"}, {"id": "D", "text": "

Additionally,

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. “Additionally” logically signals that the painting analysis discussed in this sentence is an additional part of the botany research discussed in the previous sentence. That is, to research which fruits Umbrians grew in the past, the botanist analyzes old paintings in addition to looking at old lists of ingredients. 

Choice A is incorrect because “in sum” illogically signals that the painting analysis discussed in this sentence is a concluding summary of the botany research discussed in the previous sentence. Instead, the painting analysis is an additional part of that research. Choice B is incorrect because “instead” illogically signals that the painting analysis discussed in this sentence is an alternative to the botany research discussed in the previous sentence. Rather, the painting analysis is an additional part of that research. Choice C is incorrect because “thus” illogically signals that the painting analysis discussed in this sentence is a result of the botany research discussed in the previous sentence. Instead, the painting analysis is an additional part of that research.

"}, {"id": "aec8d3e8", "domain": "Expression of Ideas", "skill": "Rhetorical Synthesis", "difficulty": "M", "type": "mc", "stimulus": "

While researching a topic, a student has taken the following notes:

\n", "stem": "

The student wants to emphasize a difference between baking soda and baking powder. Which choice most effectively uses relevant information from the notes to accomplish this goal?

", "choices": [{"id": "A", "text": "

To make batters rise, bakers use chemical leavening agents such as baking soda and baking powder.

"}, {"id": "B", "text": "

Baking soda and baking powder are chemical leavening agents that, when mixed with other ingredients, cause carbon dioxide to be released within a batter.

"}, {"id": "C", "text": "

Baking soda is pure sodium bicarbonate, and honey is a type of acidic ingredient.

"}, {"id": "D", "text": "

To produce carbon dioxide within a liquid batter, baking soda needs to be mixed with an acidic ingredient, whereas baking powder does not.

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. The sentence emphasizes a difference between baking soda and baking powder, noting that baking soda needs to be mixed with an acidic ingredient to produce carbon dioxide but baking powder doesn’t.

Choice A is incorrect. The sentence focuses on what bakers use to make batters rise; it doesn’t emphasize a difference between baking soda and baking powder. Choice B is incorrect. The sentence provides a general description of baking soda and baking powder; it doesn’t emphasize a difference between them. Choice C is incorrect. The sentence explains what baking soda and honey are; it doesn’t emphasize a difference between baking soda and baking powder.

"}, {"id": "6916c8e5", "domain": "Expression of Ideas", "skill": "Transitions", "difficulty": "E", "type": "mc", "stimulus": "

Laetitia Ky’s hair is her art. Inspired by hairstyles from various African tribes, the Ivorian artist uses wire and thread to sculpt her hair into all kinds of shapes. ______blank she once made her hair into the shape of the continent of Africa—including the island of Madagascar!

", "stem": "

Which choice completes the text with the most logical transition?

", "choices": [{"id": "A", "text": "

Soon,

"}, {"id": "B", "text": "

Elsewhere,

"}, {"id": "C", "text": "

For example,

"}, {"id": "D", "text": "

However,

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. “For example” logically signals that the following information about Ky—that she once shaped her hair to look like Africa—is an example supporting the previous statement that she makes different shapes with her hair.

Choice A is incorrect because “soon” illogically signals that the event described in this sentence occurred soon after the statement about Ky making different shapes with her hair. Instead, the sentence provides an example of one of these shapes. Choice B is incorrect because “elsewhere” illogically signals that the event described in this sentence occurred in a different place than the statement about Ky making different shapes with her hair. Instead, the sentence provides an example of one of these shapes. Choice D is incorrect because “however” illogically signals that the information in this sentence contrasts with the statement that Ky makes different shapes with her hair. Instead, the sentence provides an example of one of these shapes.

"}, {"id": "56b000d0", "domain": "Expression of Ideas", "skill": "Rhetorical Synthesis", "difficulty": "H", "type": "mc", "stimulus": "

While researching a topic, a student has taken the following notes:

\n", "stem": "

The student wants to emphasize the aim of the research study. Which choice most effectively uses relevant information from the notes to accomplish this goal?

", "choices": [{"id": "A", "text": "

Researchers wanted to know which factors influence lizard egg clutch size because such factors have been well studied in birds but not in lizards.

"}, {"id": "B", "text": "

After they obtained data for over 3,900 lizard species, researchers determined that larger clutch size was associated with environments in higher latitudes that have more seasonal change.

"}, {"id": "C", "text": "

We now know that lizards in higher-latitude environments may lay larger clutches to take advantage of shorter windows of favorable conditions.

"}, {"id": "D", "text": "

Researchers obtained clutch-size and habitat data for over 3,900 lizard species and analyzed the data with statistical models.

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. The sentence emphasizes the aim of the research study by highlighting what the researchers conducting the study wanted to know—specifically, which factors influence clutch size among lizards.

Choice B is incorrect because the sentence emphasizes what researchers determined at the end of the study, not what the study’s aim was. Choice C is incorrect because the sentence emphasizes a finding from the research study, not the aim of the study. Choice D is incorrect because the sentence emphasizes the research study’s methodology, not its aim.

"}, {"id": "92dec236", "domain": "Expression of Ideas", "skill": "Rhetorical Synthesis", "difficulty": "M", "type": "mc", "stimulus": "

While researching a topic, a student has taken the following notes:

\n", "stem": "

The student wants to emphasize a similarity between the two works. Which choice most effectively uses relevant information from the notes to accomplish this goal?

", "choices": [{"id": "A", "text": "

Erasure (2008) uses discarded objects such as audiocassette tapes and magnets; Home Grown (2009), however, includes pushpins, plastic plates and forks, and wood.

"}, {"id": "B", "text": "

Tubbs’s work, which often features discarded objects, has been shown both within the United States and abroad. 

"}, {"id": "C", "text": "

Like many of Tubbs’s sculptures, both Erasure and Home Grown include discarded objects: Erasure uses audiocassette tapes, and Home Grown uses plastic forks.

"}, {"id": "D", "text": "

Tubbs completed Erasure in 2008 and Home Grown in 2009.

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. This choice most effectively emphasizes \"a similarity\" by identifying a trait the works share: \"both Erasure and Home Grown include discarded objects.\"

Choice A is incorrect. This choice doesn’t \"emphasize a similarity.\" Instead, this choice shows how the materials used in the two works are different. Notice the use of the contrast word \"however.\" Choice B is incorrect. This choice doesn’t \"emphasize a similarity between the two works.\" While it says that Tubbs’s work \"often features discarded objects,\" it doesn’t provide details about the two works in question. Choice D is incorrect. This choice doesn’t \"emphasize a similarity.\" Instead, this choice shows how the works were produced at different times.

"}, {"id": "de55ec71", "domain": "Standard English Conventions", "skill": "Boundaries", "difficulty": "E", "type": "mc", "stimulus": "

Generations of mystery and horror ______blank have been influenced by the dark, gothic stories of celebrated American author Edgar Allan Poe (1809–1849).

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

writers

"}, {"id": "B", "text": "

writers,

"}, {"id": "C", "text": "

writers—

"}, {"id": "D", "text": "

writers;

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. The convention being tested is punctuation between a subject and a verb. When, as in this case, a subject (“Generations of mystery and horror writers”) is immediately followed by a verb (“have been influenced”), no punctuation is needed.

Choice B is incorrect because no punctuation is needed between the subject and the verb. Choice C is incorrect because no punctuation is needed between the subject and the verb. Choice D is incorrect because no punctuation is needed between the subject and the verb.

"}, {"id": "e38b3e4f", "domain": "Standard English Conventions", "skill": "Form, Structure, and Sense", "difficulty": "E", "type": "mc", "stimulus": "

The radiation that ______blank during the decay of radioactive atomic nuclei is known as gamma radiation.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

occurs

"}, {"id": "B", "text": "

have occurred

"}, {"id": "C", "text": "

occur

"}, {"id": "D", "text": "

are occurring

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. The convention being tested is subject-verb agreement. The singular verb \"occurs\" agrees in number with the singular subject \"radiation.\"

Choice B is incorrect because the plural verb \"have occurred\" doesn’t agree in number with the singular subject \"radiation.\" Choice C is incorrect because the plural verb \"occur\" doesn’t agree in number with the singular subject \"radiation.\" Choice D is incorrect because the plural verb \"are occurring\" doesn’t agree in number with the singular subject \"radiation.\"

"}, {"id": "89fbc3eb", "domain": "Standard English Conventions", "skill": "Boundaries", "difficulty": "M", "type": "mc", "stimulus": "

The Mission 66 initiative, which was approved by Congress in 1956, represented a major investment in the infrastructure of overburdened national ______blank it prioritized physical improvements to the parks’ roads, utilities, employee housing, and visitor facilities while also establishing educational programming for the public.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

parks and

"}, {"id": "B", "text": "

parks

"}, {"id": "C", "text": "

parks;

"}, {"id": "D", "text": "

parks,

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. The convention being tested is the coordination of main clauses within a sentence. This choice uses a semicolon to correctly join the first main clause (“The Mission…parks”) and the second main clause that begins with “it.”

Choice A is incorrect. When coordinating two longer main clauses such as these, it’s conventional to use a comma before the coordinating conjunction. Choice B is incorrect because it results in a run-on sentence. The two main clauses are fused without punctuation and/or a conjunction. Choice D is incorrect because it results in a comma splice. Without a conjunction following it, a comma can’t be used in this way to join two main clauses.

"}, {"id": "960dec02", "domain": "Standard English Conventions", "skill": "Boundaries", "difficulty": "H", "type": "mc", "stimulus": "

A recent study tracked the number of bee species present in twenty-seven New York apple orchards over a ten-year period. ______blank found that when wild growth near an orchard was cleared, the number of different bee species visiting the orchard decreased. 

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

Entomologist Heather Grab:

"}, {"id": "B", "text": "

Entomologist, Heather Grab,

"}, {"id": "C", "text": "

Entomologist Heather Grab

"}, {"id": "D", "text": "

Entomologist Heather Grab,

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. The convention being tested is punctuation use between a name and title and between a subject and a verb. No punctuation is needed between the proper noun “Heather Grab” and “entomologist,” the title that describes Grab. Additionally, no punctuation is needed between the sentence’s subject (“Entomologist Heather Grab”) and the main verb (“found”) that indicates what Grab did.

Choice A is incorrect because no punctuation is needed between the subject and the verb. Choice B is incorrect because no punctuation is needed. Setting the entomologist’s name off with commas suggests that it could be removed without affecting the coherence of the sentence, which isn’t the case. Choice D is incorrect because no punctuation is needed between the subject and the verb.

"}, {"id": "37e5c794", "domain": "Standard English Conventions", "skill": "Form, Structure, and Sense", "difficulty": "H", "type": "mc", "stimulus": "

Despite being cheap, versatile, and easy to produce, ______blank they are made from nonrenewable petroleum, and most do not biodegrade in landfills.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

there are two problems associated with commercial plastics:

"}, {"id": "B", "text": "

two problems are associated with commercial plastics:

"}, {"id": "C", "text": "

commercial plastics’ two associated problems are that

"}, {"id": "D", "text": "

commercial plastics have two associated problems:

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. The convention being tested is subject-modifier placement. This choice ensures that the modifying phrase “despite being cheap, versatile, and easy to produce” appears immediately before the noun it modifies, “commercial plastics,” clearly establishing that the commercial plastics—and not another noun in the sentence—are being described as cheap, versatile, and easy to produce. 

Choice A is incorrect because it results in a dangling modifier. The placement of the function word “there” immediately after the modifying phrase illogically and confusingly suggests that “there” is cheap, versatile, and easy to produce. Choice B is incorrect because it results in a dangling modifier. The placement of the noun “two problems” immediately after the modifying phrase illogically suggests that the “problems” are cheap, versatile, and easy to produce. Choice C is incorrect because it results in a dangling modifier. The placement of the noun phrase “commercial plastics’ two associated problems” immediately after the modifying phrase illogically suggests that the “problems” are cheap, versatile, and easy to produce.

"}, {"id": "6f08641e", "domain": "Standard English Conventions", "skill": "Form, Structure, and Sense", "difficulty": "M", "type": "mc", "stimulus": "

On April 5, 1977, Kitty Cone and 150 other disability rights activists entered a San Francisco federal building. After pleading for years—to no effect—for the passage of key antidiscrimination legislation, ______blank until their demands were addressed. Finally, on April 28, the legislation was signed.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

pressure on lawmakers increased when the activists staged a sit-in protest

"}, {"id": "B", "text": "

a sit-in protest staged by the activists increased pressure on lawmakers

"}, {"id": "C", "text": "

lawmakers came under increased pressure when the activists staged a sit-in protest

"}, {"id": "D", "text": "

the activists increased pressure on lawmakers by staging a sit-in protest

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. The convention being tested is subject-modifier placement. This choice makes the noun phrase “the activists” the subject of the sentence and places it immediately after the modifying phrase “after...legislation.” In doing so, this choice clearly establishes that the activists—and not another noun in the sentence—were pleading for the passage of antidiscrimination legislation.

Choice A is incorrect because it results in a dangling modifier. The placement of the noun phrase “pressure on lawmakers” immediately after the modifying phrase illogically suggests that the “pressure” was pleading for the passage of antidiscrimination legislation. Choice B is incorrect because it results in a dangling modifier. The placement of the noun phrase “a sit-in protest” immediately after the modifying phrase illogically suggests that the “protest” was pleading for the passage of antidiscrimination legislation. Choice C is incorrect because it results in a dangling modifier. The placement of the noun phrase “lawmakers” immediately after the modifying phrase suggests that “lawmakers” were pleading for the passage of antidiscrimination legislation. While it’s possible for lawmakers to plead for the passage of legislation, the context strongly suggests that it’s the activists who pleaded for years for the passage of antidiscrimination legislation.

"}, {"id": "3580533b", "domain": "Standard English Conventions", "skill": "Form, Structure, and Sense", "difficulty": "E", "type": "mc", "stimulus": "

In recent years, economists around the world have created new tools that quantify the overall well-being of a country’s citizens. Economists in India, for example, use an Ease of Living Index. This tool ______blank economic potential, sustainability, and citizens’ quality of life.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

measures

"}, {"id": "B", "text": "

had measured

"}, {"id": "C", "text": "

would have measured

"}, {"id": "D", "text": "

will have been measuring

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. The previous sentence tells us how economists in India \"use\" a certain tool, while this sentence describes general facts about that tool. To express general facts (and also to match the simple present tense of \"use\"), we should use the simple present tense form \"measures.\"

Choice B is incorrect. This choice uses the past perfect tense, but the previous sentence tells us that the tool is currently used to measure things, so the past tense doesn’t make sense for this verb. Choice C is incorrect. This choice uses the future perfect conditional tense, but the previous sentence tells us that the tool is currently used to measure things, so the future tense doesn’t make sense for this verb. Choice D is incorrect. This choice uses the future perfect continuous tense, but the previous sentence tells us that the tool is currently used to measure things, so the future tense doesn’t make sense for this verb.

"}, {"id": "74ce2f05", "domain": "Standard English Conventions", "skill": "Boundaries", "difficulty": "M", "type": "mc", "stimulus": "

A study led by scientist Rebecca Kirby at the University of Wisconsin–Madison found that black bears that eat human food before hibernation have increased levels of a rare carbon isotope, ______blank due to the higher 13C levels in corn and cane sugar. Bears with these elevated levels were also found to have much shorter hibernation periods on average.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

carbon-13, (13C)

"}, {"id": "B", "text": "

carbon-13 (13C)

"}, {"id": "C", "text": "

carbon-13, (13C),

"}, {"id": "D", "text": "

carbon-13 (13C),

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. The convention being tested is the punctuation of a supplementary element within a sentence. The comma after “(13C)” pairs with the comma after “isotope” to separate the supplementary element “carbon-13 (13C)” from the rest of the sentence. This supplementary element defines the “rare carbon isotope,” and the pair of commas indicates that this element could be removed without affecting the grammatical coherence of the sentence.

Choice A is incorrect because it fails to use appropriate punctuation to separate the supplementary element “carbon-13 (13C)” from the rest of the sentence. Choice B is incorrect because it fails to use appropriate punctuation to separate the supplementary element “carbon-13 (13C)” from the rest of the sentence. Choice C is incorrect because it fails to use appropriate punctuation to separate the supplementary element “carbon-13 (13C)” from the rest of the sentence. The comma after “carbon-13” isn’t necessary because the parentheses around “13C” already separate this element from the rest of the sentence.

"}, {"id": "adf210e7", "domain": "Standard English Conventions", "skill": "Boundaries", "difficulty": "H", "type": "mc", "stimulus": "

The haiku-like poems of Tomas Tranströmer, which present nature- and dream-influenced images in crisp, spare language, have earned the Swedish poet praise from leading contemporary ______blank them Nigerian American essayist and novelist Teju Cole, who has written that Tranströmer’s works “contain a luminous simplicity.”

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

writers. Among 

"}, {"id": "B", "text": "

writers among 

"}, {"id": "C", "text": "

writers; among 

"}, {"id": "D", "text": "

writers, among 

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. The convention being tested is punctuation use between a main clause and a supplementary phrase. This choice correctly uses a comma to mark the boundary between the main clause (“The haiku-like…writers”) and the supplementary phrase (“among…Cole”) that specifies a contemporary writer who has praised Tomas Tranströmer’s haiku-like poems. 

Choice A is incorrect because it results in a rhetorically unacceptable sentence fragment beginning with “among.” Choice B is incorrect because it fails to mark the boundary between the main clause and the supplementary phrase with appropriate punctuation. Choice C is incorrect because a semicolon can’t be used in this way to join the main clause (“The haiku-like…writers”) and the supplementary phrase (“among…Cole”). 

"}, {"id": "b7363ba2", "domain": "Standard English Conventions", "skill": "Form, Structure, and Sense", "difficulty": "E", "type": "mc", "stimulus": "

Mathematician and meteorologist Edward Lorenz used the metaphor of the “butterfly effect” to explain how seemingly minor events can have major impacts on future weather. According to Lorenz’s metaphor, the wind from a butterfly flapping ______blank in Brazil might eventually grow into a storm elsewhere across the globe.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

its wings

"}, {"id": "B", "text": "

its wings’

"}, {"id": "C", "text": "

it’s wing’s

"}, {"id": "D", "text": "

it’s wings’

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. The conventions being tested are the use of possessive determiners and plural nouns. The singular possessive determiner \"its\" and the plural noun \"wings\" correctly indicate that the butterfly has multiple wings.

Choice B is incorrect because the context requires the plural noun \"wings,\" not the plural possessive noun \"wings’.\" Choice C is incorrect because the context requires the singular possessive determiner \"its\" and the plural noun \"wings,\" not the contraction \"it’s\" and the singular possessive noun \"wing’s.\" Choice D is incorrect because the context requires the singular possessive determiner \"its\" and the plural noun \"wings,\" not the contraction \"it’s\" and the plural possessive noun \"wings’.\"

"}, {"id": "1ee7b429", "domain": "Standard English Conventions", "skill": "Form, Structure, and Sense", "difficulty": "M", "type": "mc", "stimulus": "

Bonnie Buratti of NASA’s Jet Propulsion Laboratory ______blank data about Saturn’s rings collected by the Cassini spacecraft when she made an interesting discovery: the tiny moons embedded between and within Saturn’s rings are shaped by the buildup of ring material on the moons’ surfaces.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

studies 

"}, {"id": "B", "text": "

has been studying

"}, {"id": "C", "text": "

will study

"}, {"id": "D", "text": "

was studying

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. The convention being tested is the use of verbs to express tense in a sentence. In this choice, the past progressive tense verb “was studying” is consistent with the other past tense verbs (e.g., “made” and “collected”) used to describe Buratti’s discovery. Further, the past progressive tense correctly indicates that an ongoing action in the past was occurring (she was studying) at the same time that another event occurred in the past (she made an interesting discovery). 

Choice A is incorrect because the present tense verb “studies” isn’t consistent with the past tense verbs used to describe Buratti’s discovery. Choice B is incorrect because the present perfect progressive tense verb “has been studying” isn’t consistent with the past tense verbs used to describe Buratti’s discovery. Choice C is incorrect because the future tense verb “will study” isn’t consistent with the past tense verbs used to describe Buratti’s discovery.

"}, {"id": "333b2b65", "domain": "Standard English Conventions", "skill": "Boundaries", "difficulty": "E", "type": "mc", "stimulus": "

While one requires oxygen and one does ______blank and anaerobic respiration are both forms of cellular respiration—that is, they are processes by which cells break down glucose to use as energy.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

not aerobic

"}, {"id": "B", "text": "

 not. Aerobic

"}, {"id": "C", "text": "

not, aerobic

"}, {"id": "D", "text": "

 not; aerobic

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. A comma is the appropriate way to link the dependent clause “While...not” and the independent clause that follows.

Choice A is incorrect. This choice creates a run-on sentence error. “While...not” is a dependent clause, which must be separated from the independent clause that follows with some sort of punctuation. Choice B is incorrect. This choice creates a sentence fragment. “While one requires oxygen and one does not” isn’t an independent clause, so it can’t stand alone as a complete sentence. Choice D is incorrect. This choice creates a punctuation error. “While one requires oxygen and one does not” isn’t an independent clause, so it can’t be linked to the clause that follows with a semicolon.

"}, {"id": "aaa1907f", "domain": "Standard English Conventions", "skill": "Boundaries", "difficulty": "H", "type": "mc", "stimulus": "

To serve local families during the Great Depression, innovative New York City librarian Pura Belpré offered storytelling in both English and Spanish, an uncommon ______blank celebrated el Día de los Tres Reyes Magos, an important community holiday; and put on puppet shows dramatizing Puerto Rican folktales.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

practice, at the time

"}, {"id": "B", "text": "

practice at the time;

"}, {"id": "C", "text": "

practice, at the time,

"}, {"id": "D", "text": "

practice at the time,

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. The convention being tested is the punctuation of elements in a complex series. It’s conventional to use a semicolon to separate items in a complex series with internal punctuation, and in this choice, the semicolon after \"time\" is conventionally used to separate the first item (\"offered…time\") and the second (\"celebrated…holiday\") in the series of activities that librarian Pura Belpré offered. Moreover, the semicolon after \"time\" matches the semicolon used later to separate the second item (\"celebrated...holiday\") and the third (\"and...folktales\") in the series.

Choice A is incorrect because it fails to use appropriate punctuation to separate the first item and the second item in the complex series. Furthermore, a comma isn’t needed between the noun \"practice\" and the prepositional phrase \"at the time\" because the prepositional phrase is essential to the full meaning of the phrase \"an uncommon practice at the time.\" Choice C is incorrect because a comma after \"time\" doesn’t match the semicolon used later to separate the second (\"celebrated...holiday\") and third (\"and...folktales\") items in the series. Furthermore, a comma isn’t needed between the noun \"practice\" and the prepositional phrase \"at the time\" because the prepositional phrase is essential to the full meaning of the phrase \"an uncommon practice at the time.\" Choice D is incorrect because a comma after \"time\" doesn’t match the semicolon used later to separate the second (\"celebrated...holiday\") and third (\"and...folktales\") items in the series.

"}, {"id": "7f48b098", "domain": "Standard English Conventions", "skill": "Boundaries", "difficulty": "M", "type": "mc", "stimulus": "

Photosynthesis, the mechanism by which plants use sunlight to turn carbon dioxide and water into ______blank is fueled in part by an enzyme called Photosystem II that harvests energy-giving electrons from water molecules.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

nutrients

"}, {"id": "B", "text": "

nutrients and

"}, {"id": "C", "text": "

nutrients,

"}, {"id": "D", "text": "

nutrients—

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. The convention being tested is the punctuation of a supplementary element within a sentence. The comma after “nutrients” pairs with the comma after “photosynthesis” to separate the supplementary element “the mechanism by which plants use sunlight to turn carbon dioxide and water into nutrients” from the rest of the sentence. This supplementary element functions to define the term “photosynthesis,” and the pair of commas indicates that this element could be removed without affecting the grammatical coherence of the sentence.

Choice A is incorrect because it fails to use appropriate punctuation to separate the supplementary element from the rest of the sentence. Choice B is incorrect because a conjunction can’t be paired with a comma in this way to separate the supplementary element from the rest of the sentence. Choice D is incorrect because a dash can’t be paired with a comma in this way to separate the supplementary element from the rest of the sentence.

"}, {"id": "148be4da", "domain": "Standard English Conventions", "skill": "Boundaries", "difficulty": "E", "type": "mc", "stimulus": "

Human-made (synthetic) fibers used in clothes and many other consumer products are more durable than most natural plant ______blank the manufacture of synthetic fibers requires toxic chemical solvents that can pollute air and water.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

fibers,

"}, {"id": "B", "text": "

fibers but

"}, {"id": "C", "text": "

fibers

"}, {"id": "D", "text": "

fibers, but

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. The convention being tested is the coordination of main clauses within a sentence. This choice correctly uses a comma and the coordinating conjunction “but” to join the first main clause (“Human-made...fibers”) and the second main clause (“the manufacture...water”).

Choice A is incorrect because it results in a comma splice. Without a conjunction following it, a comma can’t be used in this way to join two main clauses. Choice B is incorrect because when coordinating two longer main clauses such as these, it’s conventional to use a comma before the coordinating conjunction. Choice C is incorrect because it results in a run-on sentence. The two main clauses are fused without punctuation and/or a conjunction. 

"}, {"id": "0f39b19c", "domain": "Standard English Conventions", "skill": "Boundaries", "difficulty": "M", "type": "mc", "stimulus": "

After a spate of illnesses as a child, Wilma Rudolph was told she might never walk again. Defying all odds, Rudolph didn’t just walk, she ______blank the 1960 Summer Olympics in Rome, she won both the 100- and 200-meter dashes and clinched first place for her team in the 4x100-meter relay, becoming the first US woman to win three gold medals in a single Olympics.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

ran—fast—during

"}, {"id": "B", "text": "

ran—fast during

"}, {"id": "C", "text": "

ran—fast, during

"}, {"id": "D", "text": "

ran—fast. During

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. The convention being tested is punctuation use between sentences. In this choice, the period is used correctly to mark the boundary between one sentence (“Defying…fast”) and another sentence that begins with a supplementary phrase (“During…Olympics”).

Choice A is incorrect. When a dash is present in a sentence (“ran—fast”), it’s not conventional to use another dash (“fast—during”) to mark the boundary between sentences because it creates a potentially confusing sentence. In this context, a period, semicolon, or colon would be clear and more conventional. Choice B is incorrect because it results in a run-on sentence. The sentences (“Defying…fast”) and (“during…Olympics”) are fused without punctuation and/or a conjunction. Choice C is incorrect because it results in a comma splice. A comma can’t be used in this way to mark the boundary between sentences.

"}, {"id": "f0864217", "domain": "Standard English Conventions", "skill": "Form, Structure, and Sense", "difficulty": "H", "type": "mc", "stimulus": "

Rabinal Achí is a precolonial Maya dance drama performed annually in Rabinal, a town in the Guatemalan highlands. Based on events that occurred when Rabinal was a city-state ruled by a king, ______blank had once been an ally of the king but was later captured while leading an invading force against him.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

Rabinal Achí tells the story of K’iche’ Achí, a military leader who

"}, {"id": "B", "text": "

K’iche’ Achí, the military leader in the story of Rabinal Achí,

"}, {"id": "C", "text": "

the military leader whose story is told in Rabinal Achí, K’iche’ Achí, 

"}, {"id": "D", "text": "

there was a military leader, K’iche’ Achí, who in Rabinal Achí

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. The modifier “Based on events…by a king,” is describing the drama “Rabinal Achí.” Modifiers need to be next to the subjects they describe, so “Rabinal Achí” needs to be the first word after the comma. 

Choice B is incorrect. This doesn’t complete the text in a way that conforms to the conventions of Standard English. The modifier “Based on events…by a king,” is describing the drama “Rabinal Achí.” Modifiers need to be next to the subjects they describe, so “Rabinal Achí” needs to be the first word after the comma. Choice C is incorrect. This doesn’t complete the text in a way that conforms to the conventions of Standard English. The modifier “Based on events…by a king,” is describing the drama “Rabinal Achí.” Modifiers need to be next to the subjects they describe, so “Rabinal Achí” needs to be the first word after the comma. Choice D is incorrect. This doesn’t complete the text in a way that conforms to the conventions of Standard English. The modifier “Based on events…by a king,” is describing the drama “Rabinal Achí.” Modifiers need to be next to the subjects they describe, so “Rabinal Achí” needs to be the first word after the comma. 

"}, {"id": "c91ef0f0", "domain": "Standard English Conventions", "skill": "Form, Structure, and Sense", "difficulty": "H", "type": "mc", "stimulus": "

During the American Civil War, Thomas Morris Chester braved the front lines as a war correspondent for the Philadelphia Press. Amplifying the voices and experiences of Black soldiers ______blank of particular importance to Chester, who later became an activist and lawyer during the postwar Reconstruction period.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

were

"}, {"id": "B", "text": "

have been

"}, {"id": "C", "text": "

are

"}, {"id": "D", "text": "

was

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. The convention being tested is subject-verb agreement. The singular verb \"was\" agrees in number with the singular subject \"amplifying.\" Gerunds such as \"amplifying\" are always singular.

Choice A is incorrect because the plural verb \"were\" doesn’t agree in number with the singular subject \"amplifying.\" Choice B is incorrect because the plural verb \"have been\" doesn’t agree in number with the singular subject \"amplifying.\" Choice C is incorrect because the plural verb \"are\" doesn’t agree in number with the singular subject \"amplifying.\"

"}, {"id": "7b419faf", "domain": "Standard English Conventions", "skill": "Form, Structure, and Sense", "difficulty": "E", "type": "mc", "stimulus": "

In 1903, environmentalist John Muir guided President Theodore Roosevelt on a scenic, sprawling trip through California’s Yosemite Valley. Upon returning from the three-day excursion, Roosevelt ______blank to conserve the nation’s wilderness areas, a vow he upheld for his remaining six years in office.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

is vowing

"}, {"id": "B", "text": "

vowed

"}, {"id": "C", "text": "

will vow

"}, {"id": "D", "text": "

vows

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. The convention being tested is the use of verbs to express tense in a sentence. In this choice, the past tense verb “vowed” is consistent with the other past tense verbs (“guided” and “upheld”) used to narrate the events surrounding President Roosevelt’s decision to conserve the nation’s wilderness areas.

Choice A is incorrect because the present progressive tense verb “is vowing” isn’t consistent with the past tense verbs used to narrate the events surrounding President Roosevelt’s decision to conserve the nation’s wilderness areas. Choice C is incorrect because the future tense verb “will vow” isn’t consistent with the past tense verbs used to narrate the events surrounding President Roosevelt’s decision to conserve the nation’s wilderness areas. Choice D is incorrect because the simple present tense verb “vows” isn’t consistent with the past tense verbs used to narrate the events surrounding President Roosevelt’s decision to conserve the nation’s wilderness areas.

"}, {"id": "29c9be28", "domain": "Standard English Conventions", "skill": "Form, Structure, and Sense", "difficulty": "E", "type": "mc", "stimulus": "

To survive when water is scarce, embryos inside African turquoise killifish eggs ______blank a dormant state known as diapause. In this state, embryonic development is paused for as long as two years—longer than the life span of an adult killifish.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

enter

"}, {"id": "B", "text": "

to enter

"}, {"id": "C", "text": "

having entered

"}, {"id": "D", "text": "

entering

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. The convention being tested is finite and nonfinite verb forms within a sentence. A main clause requires a finite verb to perform the action of the subject (in this case, “embryos”), and this choice supplies the clause with the finite present tense verb “enter” to indicate how the embryos achieve diapause.

Choice B is incorrect because the nonfinite to-infinitive “to enter” doesn’t supply the main clause with a finite verb. Choice C is incorrect because the nonfinite participle “having entered” doesn’t supply the main clause with a finite verb. Choice D is incorrect because the nonfinite participle “entering” doesn’t supply the main clause with a finite verb.

"}, {"id": "983d33fa", "domain": "Standard English Conventions", "skill": "Form, Structure, and Sense", "difficulty": "E", "type": "mc", "stimulus": "

In 1637, the price of tulips skyrocketed in Amsterdam, with single bulbs of rare varieties selling for up to the equivalent of $200,000 in today’s US dollars. Some historians ______blank that this “tulip mania” was the first historical instance of an asset bubble, which occurs when investors drive prices to highs not supported by actual demand.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

claiming

"}, {"id": "B", "text": "

claim

"}, {"id": "C", "text": "

having claimed

"}, {"id": "D", "text": "

to claim

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. The convention being tested is the use of finite and nonfinite verb forms within a sentence. A main clause requires a finite verb to perform the action of the subject (in this case, “some historians”), and this choice supplies the finite present tense verb “claim” to indicate what some historians do. 

Choice A is incorrect because the nonfinite participle “claiming” doesn’t supply the main clause with a finite verb. Choice C is incorrect because the nonfinite participle “having claimed” doesn’t supply the main clause with a finite verb. Choice D is incorrect because the nonfinite to-infinitive “to claim” doesn’t supply the main clause with a finite verb.

"}, {"id": "6e193b19", "domain": "Standard English Conventions", "skill": "Form, Structure, and Sense", "difficulty": "M", "type": "mc", "stimulus": "

Professional American football player Fred Cox invented one of the world’s most popular toys. In the 1970s, he came up with the idea for the Nerf football, which ______blank of the harder and heavier regulation football.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

were a smaller, foam version

"}, {"id": "B", "text": "

are smaller, foam versions

"}, {"id": "C", "text": "

were smaller, foam versions

"}, {"id": "D", "text": "

is a smaller, foam version

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. The convention being tested is subject-verb agreement and agreement between nouns. The singular verb “is” and the singular noun “version” both agree in number with the relative pronoun “which.” In this context, “which” functions as a singular subject because it refers to the singular noun “the Nerf football.”

Choice A is incorrect because the plural verb “were” doesn’t agree in number with the singular noun phrase “the Nerf football” that it’s modifying. Choice B is incorrect because the plural verb “are” and the plural noun “versions” don’t agree in number with the singular noun phrase “the Nerf football” that they’re modifying. Choice C is incorrect because the plural verb “were” and the plural noun “versions” don’t agree in number with the singular noun phrase “the Nerf football” that they’re modifying.

"}, {"id": "52b61716", "domain": "Standard English Conventions", "skill": "Form, Structure, and Sense", "difficulty": "E", "type": "mc", "stimulus": "

Formed in 1967 to foster political and economic stability within the Asia-Pacific region, the Association of Southeast Asian Nations was originally made up of five members: Thailand, the Philippines, Singapore, Malaysia, and Indonesia. By the end of the 1990s, the organization ______blank its initial membership.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

has doubled

"}, {"id": "B", "text": "

had doubled

"}, {"id": "C", "text": "

doubles

"}, {"id": "D", "text": "

will double

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. The convention being tested is the use of verbs to express tense. In this choice, the past perfect verb “had doubled” properly indicates that the doubling of the organization’s initial membership occurred during a specific period before the present (between the organization’s founding in 1967 and the end of the 1990s). 

Choice A is incorrect because the present perfect verb “has doubled” doesn’t indicate that the organization’s doubling of its initial membership occurred during a specific period in the past. Choice C is incorrect because the present tense verb “doubles” doesn’t indicate that the organization’s doubling of its initial membership occurred during a specific period in the past. Choice D is incorrect because the future tense verb “will double” doesn’t indicate that the organization’s doubling of its initial membership occurred during a specific period in the past.

"}, {"id": "96c720af", "domain": "Standard English Conventions", "skill": "Form, Structure, and Sense", "difficulty": "E", "type": "mc", "stimulus": "

Atoms in a synchrotron, a type of circular particle accelerator, travel faster and faster until they ______blank a desired energy level, at which point they are diverted to collide with a target, smashing the atoms.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

will reach

"}, {"id": "B", "text": "

reach

"}, {"id": "C", "text": "

had reached

"}, {"id": "D", "text": "

are reaching

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. The convention being tested is the use of verbs to express tense in a sentence. In this choice, the present tense verb “reach” is consistent with the present tense verbs “travel” and “are diverted” used to describe how atoms move through the synchrotron.

Choice A is incorrect because the future tense verb “will reach” is inconsistent with the present tense verbs used to describe how atoms move through the synchrotron. Though the atoms’ movement is a recurring action and “will reach” can also be used to indicate a habitual or recurring action, it creates a logical inconsistency in this sentence when paired with the present tense verbs “travel” and “are diverted.” Choice C is incorrect because the past perfect tense verb “had reached” is inconsistent with the present tense verbs used to describe how atoms move through the synchrotron. Choice D is incorrect because the present progressive tense verb “are reaching” is inconsistent with the present tense verbs used to describe how atoms move through the synchrotron. While both verbs occur in the present, the present progressive tense suggests that the action is currently in progress. This creates a logical inconsistency when paired with the present tense verbs “travel” and “are diverted,” which offer a general description of the tendencies of the atoms’ movement, rather than a description of an action that is currently in progress.

"}, {"id": "dbd78791", "domain": "Standard English Conventions", "skill": "Form, Structure, and Sense", "difficulty": "E", "type": "mc", "stimulus": "

Led by Syrian American astronomer Shadia Habbal, the Solar Wind Sherpas are an intrepid team of scientists who travel the globe to study solar winds, the streams of particles emanating from the Sun that are only visible from certain locations during a total solar eclipse. When such an eclipse is imminent, the Sherpas pack up their telescopes and ______blank ready.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

get

"}, {"id": "B", "text": "

had gotten

"}, {"id": "C", "text": "

got

"}, {"id": "D", "text": "

were getting

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. The convention being tested is the use of verbs to express tense in a sentence. In this choice, the present tense verb “get” is consistent with the other present tense verbs (“are,” “travel,” and “pack”) used to describe the Sherpas and their activities.

Choice B is incorrect. The past perfect verb “had gotten” isn’t consistent with the other present tense verbs used to describe the Sherpas and their activities. Choice C is incorrect. The past tense verb “got” isn’t consistent with the other present tense verbs used to describe the Sherpas and their activities. Choice D is incorrect. The past progressive verb “were getting” isn’t consistent with the other present tense verbs used to describe the Sherpas and their activities.

"}, {"id": "9091458d", "domain": "Standard English Conventions", "skill": "Boundaries", "difficulty": "E", "type": "mc", "stimulus": "

Emperor penguins don’t waddle out of the ocean. They launch themselves at such a high speed that they travel up to two meters before landing. How ______blank A layer of microbubbles on their plumage reduces friction as the penguins speed to the surface.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

they are able to move so fast!

"}, {"id": "B", "text": "

 are they able to move so fast.

"}, {"id": "C", "text": "

they are able to move so fast.

"}, {"id": "D", "text": "

are they able to move so fast?

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. The convention being tested is end-of-sentence punctuation. This choice correctly uses a question mark to punctuate the interrogative sentence “how are they able to move so fast?” The interrogative sentence asks a direct question, and the next sentence answers it.

Choice A is incorrect because the context requires an interrogative sentence. The exclamative sentence “how they are able to move so fast!” emphasizes the penguin’s high rate of speed, but it doesn’t set up the next sentence’s explanation of how the penguins achieve such speeds. Choice B is incorrect because a period can’t be used in this way to punctuate an interrogative sentence. Choice C is incorrect because the context requires an interrogative sentence. The exclamative sentence “how they are able to move so fast” emphasizes the penguin’s high rate of speed, but it doesn’t set up the next sentence’s explanation of how the penguins achieve such speeds.\n 

"}, {"id": "ac5536c1", "domain": "Standard English Conventions", "skill": "Boundaries", "difficulty": "M", "type": "mc", "stimulus": "

Beatrix Potter is perhaps best known for writing and illustrating children’s books such as The Tale of Peter Rabbit (1902), but she also dedicated herself to mycology, the study of ______blank more than 350 paintings of the fungal species she observed in nature and submitting her research on spore germination to the Linnean Society of London.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

fungi; producing

"}, {"id": "B", "text": "

fungi. Producing

"}, {"id": "C", "text": "

fungi producing

"}, {"id": "D", "text": "

fungi, producing

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. The convention being tested is punctuation use between two supplementary phrases following the coordinate clause (“but she…mycology”). This choice correctly uses a comma to mark the boundary between the supplementary noun phrase (“the study of fungi”) that defines the term “mycology” and the supplementary participial phrase (“producing...London”) that provides additional information about the extent to which Potter dedicated herself to mycology.

Choice A is incorrect because a semicolon can’t be used in this way to join two supplementary phrases following a coordinate clause. Choice B is incorrect because it results in a rhetorically unacceptable sentence fragment beginning with “producing.” Choice C is incorrect. The lack of punctuation results in a sentence that illogically suggests that the study of fungi is producing more than 350 paintings.

"}, {"id": "77bf77cd", "domain": "Standard English Conventions", "skill": "Form, Structure, and Sense", "difficulty": "E", "type": "mc", "stimulus": "

Farouk El-Baz, a geologist and space scientist, ______blank part of the team that selected the lunar landing sites for the Apollo program during the 1960s and 1970s. 

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

are

"}, {"id": "B", "text": "

was

"}, {"id": "C", "text": "

have been

"}, {"id": "D", "text": "

were

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. The convention being tested is subject-verb agreement. The singular verb \"was\" agrees in number with the singular subject \"Farouk El-Baz.\"

Choice A is incorrect because the plural verb \"are\" doesn’t agree in number with the singular subject \"Farouk El-Baz.\" Choice C is incorrect because the plural verb \"have been\" doesn’t agree in number with the singular subject \"Farouk El-Baz.\" Choice D is incorrect because the plural verb \"were\" doesn’t agree in number with the singular subject \"Farouk El-Baz.\"

"}, {"id": "ea0aa676", "domain": "Standard English Conventions", "skill": "Form, Structure, and Sense", "difficulty": "H", "type": "mc", "stimulus": "

In the 1970s, Janaki Ammal, a prominent botanist, emerged as a powerful voice in India’s environmental conservation movement. Her exhaustive chromosomal survey of plants in Silent Valley, a pristine tropical forest in Kerala, India, that is home to nearly 1,000 species of native flora (many of which are endangered), ______blank instrumental in the government’s decision to preserve the forest.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

are

"}, {"id": "B", "text": "

were

"}, {"id": "C", "text": "

have been

"}, {"id": "D", "text": "

was

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. The subject \"survey\" is singular, and so is the verb \"was.\"

Choice A is incorrect. The subject \"survey\" is singular, but the verb \"are\" is plural. Choice B is incorrect. The subject \"survey\" is singular, but the verb \"were\" is plural. Choice C is incorrect. The subject \"survey\" is singular, but the verb \"have been\" is plural.

"}, {"id": "83898524", "domain": "Standard English Conventions", "skill": "Boundaries", "difficulty": "H", "type": "mc", "stimulus": "

In addition to advocating for South America’s independence in two political treatises, the Cartagena Manifesto and the Letter from Jamaica, Simón Bolívar personally led armies against the Spanish, liberating three South American territories—New Granada (present-day Colombia and Panama), Venezuela, and Quito (present-day ______blank from colonial rule.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

Ecuador,)

"}, {"id": "B", "text": "

Ecuador)

"}, {"id": "C", "text": "

Ecuador),

"}, {"id": "D", "text": "

Ecuador)—

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. The convention being tested is the punctuation of a supplementary element within a sentence. The dash after “Ecuador” and the closing parenthesis pairs with the dash after “territories” to separate the supplementary element (“New…Ecuador”) from the rest of the sentence. The supplementary element specifies the three South American territories that Simón Bolívar liberated, and the pair of dashes indicates that this element could be removed without affecting the grammatical coherence of the sentence.

Choice A is incorrect because it fails to use appropriate punctuation to separate the supplementary element from the rest of the sentence. Furthermore, punctuation isn’t needed between “Ecuador” and the closing parenthesis. Choice B is incorrect because it fails to use appropriate punctuation to separate the supplementary element from the rest of the sentence. Choice C is incorrect because a comma can’t be paired with a dash to separate the supplementary element from the rest of the sentence.

"}, {"id": "fba5d8d1", "domain": "Standard English Conventions", "skill": "Boundaries", "difficulty": "H", "type": "mc", "stimulus": "

In a 2016 study, Eastern Washington University psychologist Amani El-Alayli found that, among the study participants who experienced frisson (a physiological response akin to goosebumps or getting the chills) while listening to music, there was one personality trait that they scored particularly ______blank openness to experience.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

high. On

"}, {"id": "B", "text": "

high on;

"}, {"id": "C", "text": "

high on

"}, {"id": "D", "text": "

high on:

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. The convention being tested is punctuation use between a main clause and a supplementary phrase. In this choice, a colon is correctly used to mark the boundary between the main clause (\"there...on\") and the supplementary phrase (\"openness to experience\") and to introduce the information that identifies which personality trait participants scored especially high on.

Choice A is incorrect because it results in a rhetorically unacceptable sentence fragment beginning with \"on\" and separates a necessary preposition from the clause beginning with \"there.\" Choice B is incorrect because a semicolon can’t be used in this way to join the main clause (\"there...on\") and the supplementary phrase (\"openness to experience\"). A semicolon is conventionally used to join two main clauses, whereas a colon is conventionally used to introduce an element that explains or amplifies the information in the preceding clause, making the colon the better choice in this context. Choice C is incorrect because it fails to mark the boundary between the main clause (\"there...on\") and the supplementary phrase (\"openness to experience\").

"}, {"id": "57998dd3", "domain": "Standard English Conventions", "skill": "Form, Structure, and Sense", "difficulty": "E", "type": "mc", "stimulus": "

Obsidian is a kind of volcanic glass formed when lava cools so quickly that the atoms inside it cannot arrange themselves in a crystalline structure. You ______blank more about obsidian’s structure, which is classified as amorphous, in a later chapter.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

had learned

"}, {"id": "B", "text": "

had been learning

"}, {"id": "C", "text": "

will learn

"}, {"id": "D", "text": "

have learned

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. The convention being tested is the use of verbs to express tense in a sentence. In this choice, the future tense verb “will learn,” used in conjunction with the phrase “in a later chapter,” correctly indicates that “you” (the reader) are going to learn about obsidian’s structure at some point in the future.

Choice A is incorrect because the past perfect verb “had learned” doesn’t indicate that the subject is going to learn about obsidian’s structure in the future. Choice B is incorrect because the past perfect progressive verb “had been learning” doesn’t indicate that the subject is going to learn about obsidian’s structure in the future. Choice D is incorrect because the present perfect verb “have learned” doesn’t indicate that the subject is going to learn about obsidian’s structure in the future.

"}, {"id": "dc645172", "domain": "Standard English Conventions", "skill": "Form, Structure, and Sense", "difficulty": "H", "type": "mc", "stimulus": "

The artistic talents of Barbara Chase-Riboud, most known for her 1979 historical novel Sally Hemings and the conversation it inspired, ______blank limited to the realm of prose: she first excelled in sculpture, where her affinity for bronze—a material she described as “timeless” due to its use across eras and cultures—became part of her artistic identity.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

hasn’t been

"}, {"id": "B", "text": "

wasn’t

"}, {"id": "C", "text": "

isn’t

"}, {"id": "D", "text": "

aren’t

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. The subject \"talents\" is plural, and so is the verb \"aren’t\": \"the artistic talents…aren’t limited.\"

Choice A is incorrect. The subject \"talents\" is plural, but the verb \"hasn’t been\" is singular. Choice B is incorrect. The subject \"talents\" is plural, but the verb \"wasn’t\" is singular. Choice C is incorrect. The subject \"talents\" is plural, but the verb \"isn’t\" is singular.

"}, {"id": "6fece68e", "domain": "Standard English Conventions", "skill": "Boundaries", "difficulty": "E", "type": "mc", "stimulus": "

Emperor Ashoka ruled the Maurya Empire in South Asia from roughly 270 to 232 BCE. He is known for enforcing a moral code called the Law of Piety, which established the sanctity of animal ______blank the just treatment of the elderly, and the abolition of the slave trade.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

life

"}, {"id": "B", "text": "

life;

"}, {"id": "C", "text": "

life:

"}, {"id": "D", "text": "

life,

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. Notice that \"the sanctity of animal life\" is the first item in a list of three things. We must use a comma to separate the first two items in the list, just as a comma is used to separate \"the just treatment of the elderly\" and \"the abolition of the slave trade.\"

Choice A is incorrect. This choice creates a punctuation error. Notice that \"the sanctity of animal life\" is the first item in a list of three things. To appropriately format the list, we need punctuation to separate each item. Choice B is incorrect. This choice creates a punctuation error. Notice that \"the sanctity of animal life\" is the first item in a list of three things. While semicolons are sometimes used to separate list items, this list uses commas to separate the other list items, and lists must use the same punctuation throughout. Choice C is incorrect. This choice creates a punctuation error. Notice that \"the sanctity of animal life\" is the first item in a list of three things. While colons can be used to introduce lists, they can’t be used to separate items within a list.

"}, {"id": "886dc9f9", "domain": "Standard English Conventions", "skill": "Boundaries", "difficulty": "H", "type": "mc", "stimulus": "

On July 23, 1854, a clipper ship called the Flying Cloud entered San Francisco ______blank left New York Harbor under the guidance of Captain Josiah Perkins Creesy and his wife, navigator Eleanor Creesy, a mere 89 days and 8 hours earlier, the celebrated ship set a record that would stand for 135 years.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

Bay and having

"}, {"id": "B", "text": "

Bay. Having

"}, {"id": "C", "text": "

Bay, having

"}, {"id": "D", "text": "

Bay having

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. The convention being tested is punctuation use between sentences. In this choice, the period after “Bay” is used correctly to mark the boundary between one sentence (“On…Bay”) and another sentence that begins with a supplementary phrase (“Having…years”). Here, the supplementary phrase beginning with “having” modifies the subject of the second sentence, “the celebrated ship.”

Choice A is incorrect. Without a comma preceding it, the conjunction “and” can’t be used in this way to join sentences. Choice C is incorrect because it results in a comma splice. A comma can’t be used in this way to join two sentences. Choice D is incorrect because it results in a run-on sentence. The sentences (“On…Bay” and “having…years”) are fused without punctuation and/or a conjunction.

"}, {"id": "166efaa2", "domain": "Standard English Conventions", "skill": "Form, Structure, and Sense", "difficulty": "E", "type": "mc", "stimulus": "

Public-awareness campaigns about the need to reduce single-use plastics can be successful, says researcher Kim Borg of Monash University in Australia, when these campaigns give consumers a choice: for example, Japan achieved a 40 percent reduction in plastic-bag use after cashiers were instructed to ask customers whether ______blank wanted a bag.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

they

"}, {"id": "B", "text": "

one

"}, {"id": "C", "text": "

you

"}, {"id": "D", "text": "

it

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. The convention being tested is pronoun–antecedent agreement. The plural pronoun “they” agrees in number with the plural antecedent “customers.”

Choice B is incorrect because the singular pronoun “one” doesn’t agree in number with the plural antecedent “customers.” Choice C is incorrect because the second person pronoun “you” isn’t conventional as a substitute for “customers.” It suggests that the audience (“you”) is the customer. Choice D is incorrect because the singular pronoun “it” doesn’t agree in number with the plural antecedent “customers.”

"}, {"id": "59a246dc", "domain": "Standard English Conventions", "skill": "Boundaries", "difficulty": "H", "type": "mc", "stimulus": "

When external forces are applied to common glass made from silicates, energy builds up around minuscule defects in the material, resulting in fractures. Recently, engineer Erkka Frankberg of Tampere University in Finland used the chemical ______blank to make a glassy solid that can withstand higher strain than silicate glass can before fracturing.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

compound, aluminum oxide

"}, {"id": "B", "text": "

compound aluminum oxide,

"}, {"id": "C", "text": "

compound, aluminum oxide,

"}, {"id": "D", "text": "

compound aluminum oxide

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. The convention being tested is the use of punctuation around noun phrases. No punctuation is needed because the noun phrase “aluminum oxide” is a restrictive appositive, meaning that it provides essential identifying information about the noun phrase before it, “the chemical compound,” and thus doesn’t require punctuation around it.

Choice A is incorrect because no punctuation is needed. Choice B is incorrect because no punctuation is needed. Choice C is incorrect because the noun phrase “aluminum oxide” is a restrictive appositive. Setting the phrase off with punctuation suggests that it could be removed without affecting the coherence of the sentence, which isn’t the case.

"}, {"id": "db4e3819", "domain": "Standard English Conventions", "skill": "Form, Structure, and Sense", "difficulty": "E", "type": "mc", "stimulus": "

Midway through her 1968 jazz album A Monastic Trio, Alice Coltrane switches instruments, swapping the piano for the harp. With the same fluid style that Coltrane was famous for on piano, she ______blank her fingers across the harp strings and creates a radiant sound.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

sweep

"}, {"id": "B", "text": "

are sweeping

"}, {"id": "C", "text": "

were sweeping

"}, {"id": "D", "text": "

sweeps

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. The convention being tested is subject-verb agreement. The singular verb \"sweeps\" agrees in number with the singular subject \"she,\" which refers to Alice Coltrane.

Choice A is incorrect because the plural verb \"sweep\" doesn’t agree in number with the singular subject \"she.\" Choice B is incorrect because the plural verb \"are sweeping\" doesn’t agree in number with the singular subject \"she.\" Choice C is incorrect because the plural verb \"were sweeping\" doesn’t agree in number with the singular subject \"she.\"

"}, {"id": "6ea8c23f", "domain": "Standard English Conventions", "skill": "Boundaries", "difficulty": "H", "type": "mc", "stimulus": "

In 2018, a team of researchers led by Dr. Caitlin Whalen compiled every available measurement of ocean mixing rates from the past two decades. With this novel data set, the team was able to determine how current-driven mixing varies across ______blank and what impact it has on the distribution of heat and nutrients in the ocean.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

regions,

"}, {"id": "B", "text": "

regions:

"}, {"id": "C", "text": "

regions;

"}, {"id": "D", "text": "

regions

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. The convention being tested is punctuation between coordinates in a sentence. The two elements \"how…regions\" and \"what…ocean\" work together as coordinates to complete the description of what the team was able to determine. Because there are only two coordinates in this case (as opposed to a series of three or more), no punctuation is needed between them.

Choice A is incorrect because no punctuation is needed between the coordinates \"how…regions\" and \"what…ocean.\" Choice B is incorrect because no punctuation is needed between the coordinates \"how…regions\" and \"what…ocean.\" Choice C is incorrect because no punctuation is needed between the coordinates \"how…regions\" and \"what…ocean.\"

"}, {"id": "aab74a3b", "domain": "Standard English Conventions", "skill": "Boundaries", "difficulty": "H", "type": "mc", "stimulus": "

Researcher Lin Zhi developed a process for increasing the tensile strength—measured in gigapascals, or GPa—of silkworm ______blank dissolving and reweaving the silk in a solution of iron metal ions, zinc, and sugar, Zhi increased the amount of force required to stretch it from approximately 0.5 GPa to 2 GPa.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

silk, by

"}, {"id": "B", "text": "

silk by

"}, {"id": "C", "text": "

silk and by

"}, {"id": "D", "text": "

silk. By

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. The independent clauses \"researcher Lin Zhi…silk\" and \"by dissolving…2 GPa\" can be grammatically separated by a period. They can stand alone as sentences, and this is the only choice that lets them do that.

Choice A is incorrect. This choice results in a grammar error called a comma splice. \"Researcher Lin Zhi…silk\" and \"by dissolving…2 GPa\" are both independent clauses. They need to either be separated with punctuation like a period or a semicolon, or they need to be connected by a comma and a coordinating conjunction like \"and.\" A comma alone isn’t enough. Choice B is incorrect. This choice results in a grammar error called a run-on sentence. \"Researcher Lin Zhi…silk\" and \"by dissolving…2 GPa\" are both independent clauses. They need to either be separated with punctuation like a period or a semicolon, or they need to be connected by a comma and a coordinating conjunction like \"and.\" Choice C is incorrect. This choice results in a grammar error called a run-on sentence. \"Researcher Lin Zhi…silk\" and \"by dissolving…2 GPa\" are both independent clauses. The coordinating conjunction \"and\" isn’t enough to link them by itself. We need a comma, too.

"}, {"id": "1724dac2", "domain": "Standard English Conventions", "skill": "Boundaries", "difficulty": "E", "type": "mc", "stimulus": "

A subseasonal weather forecast attempts to predict weather conditions three to four weeks in ______blank its predictions are therefore more short-term than those of the seasonal forecast, which attempts to predict the weather more than a month in advance.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

advance,

"}, {"id": "B", "text": "

advance

"}, {"id": "C", "text": "

advance;

"}, {"id": "D", "text": "

advance and

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. The clause “A subseasonal…advance” and the clause “its predictions…forecast” are both independent clauses, so using a semicolon to separate them is grammatically correct. 

Choice A is incorrect. This choice creates a run-on sentence error. The clause “A subseasonal…advance” and the clause “its predictions…forecast” are both independent clauses, so a comma is not enough to separate them. Choice B is incorrect. This choice creates a run-on sentence error. The clause “A subseasonal…advance” and the clause “its predictions…forecast” are both independent clauses, so they need to be separated with specific punctuation (a period, a semi-colon, a colon, a dash, or a comma + a coordinating conjunction). Choice D is incorrect. This choice creates a run-on sentence error. The clause “A subseasonal…advance” and the clause “its predictions…forecast” are both independent clauses, so the word “and” by itself is not enough to separate them. There would need to be a comma before “and” for this choice to work. 

"}, {"id": "512f0ac9", "domain": "Standard English Conventions", "skill": "Form, Structure, and Sense", "difficulty": "H", "type": "mc", "stimulus": "

Working from an earlier discovery of Charpentier’s, chemists Emmanuelle Charpentier and Jennifer Doudna—winners of the 2020 Nobel Prize in Chemistry—re-created and then reprogrammed the so-called “genetic scissors” of a species of DNA-cleaving bacteria ______blank a tool that is revolutionizing the field of gene technology.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

to forge

"}, {"id": "B", "text": "

forging

"}, {"id": "C", "text": "

forged

"}, {"id": "D", "text": "

and forging

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. The convention being tested is the use of finite and nonfinite verb forms within a sentence. The nonfinite to-infinitive “to forge” is correctly used to form a nonfinite (infinitive) clause that explains why the chemists re-created and reprogrammed the DNA-cleaving bacteria.

Choice B is incorrect. Without a comma separating the main clause (“chemists...bacteria”) from the participle “forging,” this choice illogically suggests that the bacteria are forging a tool, which doesn’t make sense. Choice C is incorrect. Without a coordinating conjunction such as “and” placed before it, the finite past tense verb “forged” can’t be used in this way to describe the chemists’ actions. Choice D is incorrect. If read as a finite verb, the present progressive verb “forging” isn’t consistent with the past tense verbs used in this sentence to describe the actions of the chemists. If read as a nonfinite verb, the participle “forging” can’t be used in this way because there is no following main clause for it to modify.  

"}, {"id": "a9e5b788", "domain": "Standard English Conventions", "skill": "Boundaries", "difficulty": "H", "type": "mc", "stimulus": "

In discussing Mary Shelley’s 1818 epistolary novel Frankenstein, literary theorist Gayatri Spivak directs the reader’s attention to the character of Margaret Saville. As Spivak points out, Saville is not the protagonist of Shelley’s ______blank as the recipient of the letters that frame the book’s narrative, she’s the “occasion” of it.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

novel

"}, {"id": "B", "text": "

novel,

"}, {"id": "C", "text": "

novel; rather,

"}, {"id": "D", "text": "

novel, rather,

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. The convention being tested is the coordination of main clauses within a sentence. This choice correctly uses a semicolon to join a main clause (“Saville...novel”) and a second main clause (“she’s...it”) preceded by supplementary elements (“rather...narrative”).

Choice A is incorrect because it results in a run-on sentence. The two main clauses are fused without punctuation and/or a conjunction. Choice B is incorrect because it results in a comma splice. Without a conjunction following it, a comma can’t be used in this way to join two main clauses. Choice D is incorrect because it results in a comma splice. Without a conjunction following it, the comma after “novel” can’t be used in this way to join the two main clauses.

"}, {"id": "cdbbbf94", "domain": "Standard English Conventions", "skill": "Boundaries", "difficulty": "M", "type": "mc", "stimulus": "

As British scientist Peter Whibberley has observed, “the Earth is not a very good timekeeper.” Earth’s slightly irregular rotation rate means that measurements of time must be periodically adjusted. Specifically, an extra “leap second” (the 86,401st second of the day) is ______blank time based on the planet’s rotation lags a full nine-tenths of a second behind time kept by precise atomic clocks.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

added, whenever

"}, {"id": "B", "text": "

added; whenever

"}, {"id": "C", "text": "

added. Whenever

"}, {"id": "D", "text": "

added whenever

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. The convention being tested is punctuation between a verb and a preposition. When, as in this case, a verb (“is added”) is immediately followed by a preposition (“whenever”), no punctuation is needed.

Choice A is incorrect because no punctuation is needed between the verb and the preposition. Choice B is incorrect because no punctuation is needed between the verb and the preposition. Choice C is incorrect because no punctuation is needed between the verb and the preposition.

"}, {"id": "d47bb0a4", "domain": "Standard English Conventions", "skill": "Form, Structure, and Sense", "difficulty": "E", "type": "mc", "stimulus": "

Objects ranging from the Kikkoman soy sauce bottle to the Yamaha VMAX motorcycle to the Komachi bullet train ______blank designed by twentieth-century industrial designer Kenji Ekuan.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

was

"}, {"id": "B", "text": "

is

"}, {"id": "C", "text": "

has been

"}, {"id": "D", "text": "

were

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. The convention being tested is subject-verb agreement. The plural verb \"were\" agrees in number with the plural subject \"objects.\"

Choice A is incorrect because the singular verb \"was\" doesn’t agree in number with the plural subject \"objects.\" Choice B is incorrect because the singular verb \"is\" doesn’t agree in number with the plural subject \"objects.\" Choice C is incorrect because the singular verb \"has been\" doesn’t agree in number with the plural subject \"objects.\"

"}, {"id": "e3b72630", "domain": "Standard English Conventions", "skill": "Form, Structure, and Sense", "difficulty": "E", "type": "mc", "stimulus": "

In the historical novel The Surrender Tree, Cuban American author Margarita Engle uses poetry rather than prose ______blank the true story of Cuban folk hero Rosa La Bayamesa.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

tells

"}, {"id": "B", "text": "

told

"}, {"id": "C", "text": "

is telling

"}, {"id": "D", "text": "

to tell

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. The convention being tested is the use of finite and nonfinite verb forms within a sentence. The nonfinite to-infinitive “to tell” is correctly used to form a nonfinite (infinitive) clause that explains the reason Engle uses poetry in her novel.

Choice A is incorrect because the finite present tense verb “tells” can’t be used in this way to explain the reason that Engle uses poetry in her novel. Choice B is incorrect because the finite past tense verb “told” can’t be used in this way to explain the reason that Engle uses poetry in her novel. Choice C is incorrect because the finite present progressive tense verb “is telling” can’t be used in this way to explain the reason that Engle uses poetry in her novel. 

"}, {"id": "d2b81427", "domain": "Standard English Conventions", "skill": "Form, Structure, and Sense", "difficulty": "H", "type": "mc", "stimulus": "

In assessing the films of Japanese director Akira Kurosawa, ______blank have missed his equally deep engagement with Japanese artistic traditions such as Noh theater.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

many critics have focused on Kurosawa’s use of Western literary sources but 

"}, {"id": "B", "text": "

Kurosawa’s use of Western literary sources has been the focus of many critics, who

"}, {"id": "C", "text": "

there are many critics who have focused on Kurosawa’s use of Western literary sources, but they

"}, {"id": "D", "text": "

the focus of many critics has been on Kurosawa’s use of Western literary sources; they

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. The convention being tested is subject-modifier placement. This choice makes the noun phrase “many critics” the subject of the sentence and places it immediately after the modifying phrase “in assessing…Kurosawa.” In doing so, this choice clearly establishes that it is the critics—and not another noun in the sentence—who assess Kurosawa’s films.

Choice B is incorrect because it results in a dangling modifier. The placement of the noun phrase “Kurosawa’s…sources” immediately after the modifying phrase illogically suggests that his use of Western literary sources is what assesses Kurosawa’s films. Choice C is incorrect because it results in a dangling modifier. The placement of the function word “there” immediately after the modifying phrase illogically suggests that “there” is what assesses Kurosawa’s films. Choice D is incorrect because it results in a dangling modifier. The placement of the noun phrase “the focus…critics” immediately after the modifying phrase illogically suggests that the critics’ focus is what assesses Kurosawa’s films.

"}, {"id": "a1e0c981", "domain": "Standard English Conventions", "skill": "Boundaries", "difficulty": "E", "type": "mc", "stimulus": "

In her book The Woman Warrior: Memoirs of a Girlhood Among Ghosts, author Maxine Hong Kingston examines themes ______blank childhood, womanhood, and Chinese American identity by intertwining autobiography and mythology.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

of:

"}, {"id": "B", "text": "

 of

"}, {"id": "C", "text": "

of—

"}, {"id": "D", "text": "

of,

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. “Themes of childhood” is one noun phrase, with “themes of” implicitly carrying over to the other items on the list (“themes of childhood, [themes of] womanhood, and [themes of] Chinese American identity”).  

Choice A is incorrect. This choice inappropriately breaks up the introduction of a list. Also, “In her book…themes of” is not an independent clause, thanks to the dangling “of” at the end, so it can’t precede a colon. Choice C is incorrect. This choice inappropriately breaks up the introduction of a list. Also, “In her book…themes of” is not an independent clause, thanks to the dangling “of” at the end, so it can’t precede a single dash. Choice D is incorrect. This choice inappropriately breaks up the introduction of a list. “Themes of” implicitly carries over to each item on the list (“themes of childhood, [themes of] womanhood, and [themes of] Chinese American identity”), so we don’t want to use a comma to separate it. 

"}, {"id": "b35cefb7", "domain": "Standard English Conventions", "skill": "Boundaries", "difficulty": "E", "type": "mc", "stimulus": "

The fine, powdery substance that covers the Moon’s surface is called regolith. Because regolith is both readily available and high in oxygen ______blank scientists have wondered whether it could be used as a potential source of oxygen for future lunar settlements.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

content and

"}, {"id": "B", "text": "

content,

"}, {"id": "C", "text": "

content

"}, {"id": "D", "text": "

content, and

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. The convention being tested is punctuation between a subordinate clause and a main clause. This choice correctly uses a comma to mark the boundary between the subordinate clause (“Because...content”) and the main clause (“scientists...settlements”).

Choice A is incorrect. Joining the subordinate clause (“Because...content”) and the clause that follows (“scientists...settlements”) with the conjunction “and” results in an ungrammatical sentence that lacks a main clause. Choice C is incorrect because it fails to mark the boundary between the subordinate clause and the main clause with appropriate punctuation. Choice D is incorrect. Joining the subordinate clause (“Because...content”) and the clause that follows (“scientists...settlements”) with a comma and the conjunction “and” results in an ungrammatical sentence that lacks a main clause.

"}, {"id": "e76e74e8", "domain": "Standard English Conventions", "skill": "Boundaries", "difficulty": "H", "type": "mc", "stimulus": "

Over twenty years ago, in a landmark experiment in the psychology of choice, professor Sheena Iyengar set up a jam-tasting booth at a grocery store. The number of jams available for tasting ______blank some shoppers had twenty-four different options, others only six. Interestingly, the shoppers with fewer jams to choose from purchased more jam.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

varied:

"}, {"id": "B", "text": "

varied, 

"}, {"id": "C", "text": "

varied, while

"}, {"id": "D", "text": "

varied while

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. The convention being tested is the use of a colon within a sentence. In this choice, the colon is used in a conventional way to introduce the following description of how the number of jams available varied. 

Choice B is incorrect because it creates a comma splice. A comma can’t be used in this way to join two main clauses (“the number…varied” and “some…six”). Choice C is incorrect because it results in an illogical and confusing sentence. Using the conjunction “while” to join the main clause (“the number…varied”) with the following clause’s description of the number of jams available suggests that the variation in the number of jams is in contrast to some shoppers having twenty-four options. Choice D is incorrect because it results in an illogical and confusing sentence. Using “while” in this way suggests that the number of jams available varied during the time in which some shoppers had twenty-four options and others had six. The sentence makes clear, however, that what follows “varied” is a description of the variation, not a separate, simultaneous occurrence.

"}, {"id": "b74f676f", "domain": "Standard English Conventions", "skill": "Form, Structure, and Sense", "difficulty": "M", "type": "mc", "stimulus": "

Classical composer Florence Price’s 1927 move to Chicago marked a turning point in her career. It was there that Price premiered her First Symphony—a piece that was praised for blending traditional Romantic motifs with aspects of Black folk music—and ______blank supportive relationships with other Black artists.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

developing

"}, {"id": "B", "text": "

developed

"}, {"id": "C", "text": "

to develop

"}, {"id": "D", "text": "

having developed

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. The missing verb is part of the same clause as the verb \"premiered,\" and \"Price\" is the subject of both. So we need the past-tense form \"developed\" in order to match \"premiered.\"

Choice A is incorrect. This choice creates a verb form error. The missing verb is part of the same clause as the verb \"premiered,\" and \"Price\" is the subject of both. So we need the past-tense form \"developed\" in order to match \"premiered.\" Choice C is incorrect. This choice creates a verb form error. The missing verb is part of the same clause as the verb \"premiered,\" and \"Price\" is the subject of both. So we need the past-tense form \"developed\" in order to match \"premiered.\" Choice D is incorrect. This choice creates a verb form error. The missing verb is part of the same clause as the verb \"premiered,\" and \"Price\" is the subject of both. So we need the past-tense form \"developed\" in order to match \"premiered.\"

"}, {"id": "3a35ddd1", "domain": "Standard English Conventions", "skill": "Form, Structure, and Sense", "difficulty": "E", "type": "mc", "stimulus": "

Like other amphibians, the wood frog (Rana sylvatica) is unable to generate its own heat, so during periods of subfreezing temperatures, it ______blank by producing large amounts of glucose, a sugar that helps prevent damaging ice from forming inside its cells.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

had survived

"}, {"id": "B", "text": "

survived

"}, {"id": "C", "text": "

would survive

"}, {"id": "D", "text": "

survives

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. The convention being tested is the use of verbs to express tense. In this choice, the present tense verb “survives” correctly indicates that the wood frog regularly survives subfreezing temperatures by producing large amounts of glucose.

Choice A is incorrect because the past perfect verb “had survived” doesn’t indicate that the wood frog regularly survives subfreezing temperatures by producing large amounts of glucose. Choice B is incorrect because the past tense verb “survived” doesn’t indicate that the wood frog regularly survives subfreezing temperatures by producing large amounts of glucose. Choice C is incorrect because the conditional verb “would survive” doesn’t indicate that the wood frog regularly survives subfreezing temperatures by producing large amounts of glucose.

"}, {"id": "69f031ab", "domain": "Standard English Conventions", "skill": "Form, Structure, and Sense", "difficulty": "E", "type": "mc", "stimulus": "

While exploring Nevada’s Gypsum Cave in 1930, Seneca and Abenaki archaeologist Bertha Parker made her most famous discovery: the skull of a now-extinct ground sloth (Nothrotheriops shastensis) alongside human-made tools. Parker’s crucial finding was the first ______blank humans in North America as far back as 10,000 years ago.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

places

"}, {"id": "B", "text": "

placed

"}, {"id": "C", "text": "

place

"}, {"id": "D", "text": "

to place

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. The object for the verb \"was\" is \"first,\" and \"to place\" is acting as a modifier for \"first.\" What was the finding? It was \"the first.\" The first to do what? The first \"to place humans in North America\" 10,000 years ago. When a verb serves as a modifier within a noun phrase, it must be nonfinite (i.e., not conjugated to a specific subject). The infinitive form \"to place\" is the only nonfinite option among the choices that makes sense in context.

Choice A is incorrect. The object for the verb \"was\" is \"first,\" and \"places\" is acting as a modifier for \"first.\" What was the thing that Parker’s finding did? What was it the first to do? Place humans in North America 10,000 years ago. When a verb acts as a modifier, it must be nonfinite (i.e., not conjugated to a specific subject), but \"places\" is a finite form of the verb. Choice B is incorrect. The object for the verb \"was\" is \"first,\" and \"placed\" is acting to modify \"first.\" What was it that Parker’s finding was the first to do? Place humans in North America 10,000 years ago. When a verb acts as a modifier, it must be nonfinite (i.e., not conjugated to a specific subject), but \"placed\" is a finite form. \"Placed\" can also be a past participle, but that wouldn’t make sense here because the meaning of \"the first placed humans\" would be unclear. Choice C is incorrect. The object for the verb \"was\" is \"first,\" and \"place\" is modifying \"first.\" What was the thing that Parker’s finding did? What was it the first to do? Place humans in North America. When a verb acts as a modifier, it must be nonfinite (i.e., not conjugated to a specific subject), but \"place\" is a finite form of the verb. Additionally, \"place\" can’t serve as a noun here, because it results in an illogical sentence (the \"finding\" wasn’t \"the first place\").

"}, {"id": "083a35dc", "domain": "Standard English Conventions", "skill": "Boundaries", "difficulty": "M", "type": "mc", "stimulus": "

Po’Pay was a Tewa leader from Ohkay Owingeh, a pueblo located about twenty-five miles north of present-day Santa Fe, New Mexico. He was instrumental in organizing the Pueblo Revolt of ______blank as a result of his leadership, the Spanish colonizers were expelled from the region for a time.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

1680

"}, {"id": "B", "text": "

1680 and

"}, {"id": "C", "text": "

1680,

"}, {"id": "D", "text": "

1680, and

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. The convention being tested is the coordination of main clauses within a sentence. This choice correctly uses a comma and the coordinating conjunction “and” to join the first main clause (“He…1680”) and the second main clause (“as…time”).

Choice A is incorrect because it results in a run-on sentence. The two main clauses are fused without punctuation and/or a conjunction. Choice B is incorrect because when coordinating two longer main clauses such as these, it’s conventional to use a comma before the coordinating conjunction. Choice C is incorrect because it results in a comma splice. Without a conjunction following it, a comma can’t be used in this way to join two main clauses.

"}, {"id": "aab78b25", "domain": "Standard English Conventions", "skill": "Boundaries", "difficulty": "E", "type": "mc", "stimulus": "

Psychophysicist Howard Moskowitz was hired by a soda company to determine how much artificial sweetener ______blank After conducting consumer taste tests, he found that no such ideal existed: participants expressed a wide range of preferences for different blends of sweetener, carbonization, and flavoring.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

do most people prefer in a diet drink? 

"}, {"id": "B", "text": "

do most people prefer in a diet drink.

"}, {"id": "C", "text": "

most people prefer in a diet drink?

"}, {"id": "D", "text": "

most people prefer in a diet drink.

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. This sentence is a statement: “Moskowitz was hired by a soda company to determine how much artificial sweetener most people prefer in a diet drink.” So a period is the most appropriate punctuation mark.  

Choice A is incorrect. This doesn’t complete the text in a way that conforms to the conventions of Standard English. This sentence is not a question—it’s a statement. So a question mark is not the appropriate punctuation. Choice B is incorrect. This doesn’t complete the text in a way that conforms to the conventions of Standard English. We already have the verbs “was hired…to determine” in this sentence. The verb “do” is not needed and results in a confusing, ungrammatical sentence. Choice C is incorrect. This doesn’t complete the text in a way that conforms to the conventions of Standard English. This sentence is not a question—it’s a statement. So a question mark is not the appropriate punctuation. 

"}, {"id": "145d5ca7", "domain": "Standard English Conventions", "skill": "Boundaries", "difficulty": "M", "type": "mc", "stimulus": "

Gathering accurate data on water flow in the United States is challenging because of the country’s millions of miles of ______blank the volume and speed of water at any given location can vary drastically over time.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

waterways and the fact that,

"}, {"id": "B", "text": "

waterways, and the fact that,

"}, {"id": "C", "text": "

waterways, and, the fact that

"}, {"id": "D", "text": "

waterways and the fact that

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. The convention being tested is punctuation within two coordinated noun phrases. When, as in this case, a noun phrase (“the country’s millions of miles of waterways”) is coordinated with another noun phrase (“the fact”) followed by an integrated relative clause (“that the volume...time”), no punctuation is needed.

Choice A is incorrect because no punctuation is needed. Choice B is incorrect because no punctuation is needed. Choice C is incorrect because no punctuation is needed.

"}, {"id": "843f92af", "domain": "Standard English Conventions", "skill": "Form, Structure, and Sense", "difficulty": "E", "type": "mc", "stimulus": "

The sun never sets during the Arctic summer in the Far North. In response, reindeer in this region must change their sleep habits. Instead of resting when it gets dark, they rest when they need ______blank their food.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

digest

"}, {"id": "B", "text": "

will digest

"}, {"id": "C", "text": "

to digest

"}, {"id": "D", "text": "

digesting

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. The convention being tested is the use of nonfinite verb forms within a sentence. Working together with the finite verb \"need,\" the nonfinite to-infinitive verb \"to digest\" is correctly used to form a subordinate clause that describes what the reindeer need.

Choice A is incorrect because the verb \"digest\" (in either its finite or nonfinite form) can’t be used in this way with the finite verb \"need.\" Choice B is incorrect because the finite verb \"will digest\" can’t be used in this way with the finite verb \"need.\" Choice D is incorrect because the nonfinite participle \"digesting\" can’t be used in this way with the finite verb \"need.\"

"}, {"id": "430d929a", "domain": "Standard English Conventions", "skill": "Form, Structure, and Sense", "difficulty": "E", "type": "mc", "stimulus": "

British scientists James Watson and Francis Crick won the Nobel Prize in part for their 1953 paper announcing the double helix structure of DNA, but it is misleading to say that Watson and Crick discovered the double helix. ______blank findings were based on a famous X-ray image of DNA fibers, “Photo 51,” developed by X-ray crystallographer Rosalind Franklin and her graduate student Raymond Gosling.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

They’re

"}, {"id": "B", "text": "

It’s

"}, {"id": "C", "text": "

Their

"}, {"id": "D", "text": "

Its

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. The convention being tested is the use of possessive determiners. The plural possessive determiner “their” agrees in number with the plural conjoined noun phrase “Watson and Crick” and thus indicates that the findings were those of Watson and Crick.

Choice A is incorrect because “they’re” is the contraction for “they are,” not a possessive determiner. Choice B is incorrect because “it’s” is the contraction for “it is” or “it has,” not a possessive determiner. Choice D is incorrect because the singular possessive determiner “its” doesn’t agree in number with the plural conjoined noun phrase “Watson and Crick.”

"}, {"id": "be34a3df", "domain": "Standard English Conventions", "skill": "Boundaries", "difficulty": "M", "type": "mc", "stimulus": "

In 2008, two years after the death of science fiction writer Octavia Butler, the Huntington Library in ______blank received a collection of more than 8,000 items, including Butler’s private notes, research materials, manuscripts, photos, and drawings. Today, the Octavia E. Butler Collection is one of the most researched archives at the library.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

California,

"}, {"id": "B", "text": "

California:

"}, {"id": "C", "text": "

California—

"}, {"id": "D", "text": "

California

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. No punctuation should separate the subject of the sentence (“the Huntington Library in California”) from its verb (“received”).

Choice A is incorrect. No punctuation should separate the subject of the sentence (“the Huntington Library in California”) from its verb (“received”). Choice B is incorrect. No punctuation should separate the subject of the sentence (“the Huntington Library in California”) from its verb (“received”). Choice C is incorrect. No punctuation should separate the subject of the sentence (“the Huntington Library in California”) from its verb (“received”).

"}, {"id": "1f8cd95f", "domain": "Standard English Conventions", "skill": "Form, Structure, and Sense", "difficulty": "M", "type": "mc", "stimulus": "

In the 1950s, a man named Joseph McVicker was struggling to keep his business afloat when his sister-in-law Kay Zufall advised him to repurpose the company’s product, a nontoxic, clay-like substance for removing soot from wallpaper, as a modeling putty for kids. In addition, Zufall ______blank selling the product under a child-friendly name: Play-Doh.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

suggested

"}, {"id": "B", "text": "

suggests

"}, {"id": "C", "text": "

had suggested

"}, {"id": "D", "text": "

was suggesting

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. The convention being tested is the use of verbs to express tense. In this choice, the simple past tense verb “suggested” properly indicates that Zufall offered her suggestion for the product’s name in the past. This verb tense is consistent with the previous sentence’s use of a simple past tense verb (“advised”) to describe Zufall’s advice to McVicker in the 1950s.

Choice B is incorrect because the present tense verb “suggests” doesn’t indicate that Zufall offered her suggestion in the past. Choice C is incorrect because the past perfect verb “had suggested” isn’t consistent with the previous sentence’s use of the simple past tense verb “advised” to describe Zufall’s advice to McVicker. Choice D is incorrect because the past progressive verb “was suggesting” isn’t consistent with the previous sentence’s use of the simple past tense verb “advised” to describe Zufall’s advice to McVicker. 

"}, {"id": "73a6603c", "domain": "Standard English Conventions", "skill": "Boundaries", "difficulty": "H", "type": "mc", "stimulus": "

On sunny days, dark rooftops absorb solar energy and convert it to unwanted heat, raising the surrounding air ______blank a light-colored covering to an existing dark roof, either by attaching prefabricated reflective sheets or spraying on a paint-like coating, helps combat this effect. 

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

temperature; by adding

"}, {"id": "B", "text": "

temperature, adding

"}, {"id": "C", "text": "

temperature. Adding

"}, {"id": "D", "text": "

temperature by adding

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. The convention being tested is punctuation use between sentences. In this choice, the period is used correctly to mark the boundary between the first sentence (“On…temperature”) and the second sentence (“Adding…effect”). The gerund phrase beginning with “adding” is the subject of the second sentence, and the verb phrase “helps combat this effect” describes what adding a light-colored covering can do. 

Choice A is incorrect because a semicolon can’t be used in this way to join the sentence “On...temperature” and the supplementary phrases that follow. Doing so leaves the verb phrase “helps combat” without a subject and thus results in a grammatically unconventional sentence. Choice B is incorrect because it results in a comma splice. A comma can’t be used in this way to mark the boundary between sentences. Choice D is incorrect. This choice results in a confusing and illogical sentence that suggests that adding a light-colored covering to an existing dark roof raises the temperature of the surrounding air. Furthermore, it creates ambiguity by leaving the verb phrase “helps combat” without a subject (so it isn’t clear what helps combat the effect).

"}, {"id": "70ced8dc", "domain": "Standard English Conventions", "skill": "Boundaries", "difficulty": "E", "type": "mc", "stimulus": "

Typically, underlines, scribbles, and notes left in the margins by a former owner lower a book’s ______blank when the former owner is a famous poet like Walt Whitman, such markings, known as marginalia, can be a gold mine to literary scholars.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

value, but

"}, {"id": "B", "text": "

value

"}, {"id": "C", "text": "

value, 

"}, {"id": "D", "text": "

value but

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. The convention being tested is the coordination of independent clauses within a sentence. An independent clause is a phrase containing a subject and a verb that can stand on its own as a sentence. This choice uses a comma and the coordinating conjunction “but” to join the first independent clause (“underlines…lower a book’s value”) and the second independent clause (“such markings…can be a gold mine to scholars”) to create a compound sentence.

Choice B is incorrect because it results in a run-on sentence. The two independent clauses are fused without punctuation and/or a conjunction. Choice C is incorrect because it results in a comma splice. A comma can’t be used in this way to mark the boundary between two independent clauses. Choice D is incorrect because a comma is needed to mark the boundary between two coordinated independent clauses.

"}, {"id": "3bceeb93", "domain": "Standard English Conventions", "skill": "Form, Structure, and Sense", "difficulty": "H", "type": "mc", "stimulus": "

When they were first discovered in Australia in 1798, duck-billed, beaver-tailed platypuses so defied categorization that one scientist assigned them the name Ornithorhynchus paradoxus: “paradoxical bird-snout.” The animal, which lays eggs but also nurses ______blank young with milk, has since been classified as belonging to the monotremes group.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

they’re

"}, {"id": "B", "text": "

their

"}, {"id": "C", "text": "

its

"}, {"id": "D", "text": "

it’s

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. The singular possessive pronoun \"its\" agrees with the singular antecedent \"the animal\" and indicates that the \"young\" belong to it.

Choice A is incorrect. This choice creates a pronoun-antecedent agreement error. \"They’re\" is a contraction of \"they are,\" a plural pronoun and verb, but the antecedent \"the animal\" is singular. Also, we don’t need the extra verb \"are\" — we already have a main verb in this clause, so adding \"are\" would be confusing and ungrammatical. Choice B is incorrect. This choice creates a pronoun-antecedent agreement error. \"Their\" is a plural pronoun, but the subject of the sentence is \"the animal,\" a singular noun. Choice D is incorrect. This choice creates a confusing and ungrammatical sentence. \"It’s\" is a contraction for \"it is.\" We already have the verb \"nurses\" in this clause, so we shouldn’t add the verb \"is.\"

"}, {"id": "8a3998f1", "domain": "Standard English Conventions", "skill": "Boundaries", "difficulty": "E", "type": "mc", "stimulus": "

After the United Kingdom began rolling out taxes equivalent to a few cents on single-use plastic grocery bags in 2011, plastic-bag consumption decreased by up to ninety ______blank taxes are subject to what economists call the “rebound effect”: as the change became normalized, plastic-bag use started to creep back up.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

percent, such

"}, {"id": "B", "text": "

percent and such

"}, {"id": "C", "text": "

percent. Such

"}, {"id": "D", "text": "

percent such

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. The convention being tested is punctuation use between sentences. In this choice, the period after “percent” is used correctly to mark the boundary between one sentence (“After…percent”) and another (“Such…up”).

Choice A is incorrect because it results in a comma splice. A comma can’t be used in this way to mark the boundary between sentences. Choice B is incorrect. Without a comma preceding it, the conjunction “and” can’t be used in this way to join sentences. Choice D is incorrect because it results in a run-on sentence. The sentences (“After…percent” and “Such…up”) are fused without punctuation and/or a conjunction.

"}, {"id": "dab8b8ee", "domain": "Standard English Conventions", "skill": "Form, Structure, and Sense", "difficulty": "H", "type": "mc", "stimulus": "

Known as Earth’s “living skin,” biocrusts are thin layers of soil held together by surface-dwelling microorganisms such as fungi, lichens, and cyanobacteria. Fortifying soil in arid ecosystems against erosion, ______blank

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

a recent study’s estimate is that these crusts reduce global dust emissions by 60 percent each year. 

"}, {"id": "B", "text": "

an estimated 60 percent reduction in global dust emissions each year is due to these crusts, according to a recent study.

"}, {"id": "C", "text": "

these crusts reduce global dust emissions by an estimated 60 percent each year, according to a recent study.

"}, {"id": "D", "text": "

a recent study has estimated that these crusts reduce global dust emissions by 60 percent each year.

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. The subject of the modifier \"fortifying soil in arid ecosystems against erosion\" is \"biocrusts.\" Subject-modifier placement requires a modifier and its subject to be next to each other, so \"biocrusts\" or some variant meaning \"biocrusts\" (in this case, \"these crusts\") must begin the missing clause.

Choice A is incorrect. Modifiers and their subjects must go next to each other. The subject of the modifier \"fortifying soil in arid ecosystems against erosion\" is \"biocrusts,\" not \"a recent study’s estimate.\" Choice B is incorrect. Modifiers and their subjects must go next to each other. The subject of the modifier \"fortifying soil in arid ecosystems against erosion\" is \"biocrusts,\" not \"an estimated 60 percent reduction.\" Choice D is incorrect. Modifiers and their subjects must go next to each other. The subject of the modifier \"fortifying soil in arid ecosystems against erosion\" is \"biocrusts,\" not \"a recent study.\"

"}, {"id": "4bed4658", "domain": "Standard English Conventions", "skill": "Form, Structure, and Sense", "difficulty": "E", "type": "mc", "stimulus": "

In order to prevent nonnative fish species from moving freely between the Mediterranean and Red Seas, marine biologist Bella Galil has proposed that a saline lock system be installed along the Suez Canal in Egypt’s Great Bitter Lakes. The lock would increase the salinity of the lakes and ______blank a natural barrier of water most marine creatures would be unable to cross.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

creates

"}, {"id": "B", "text": "

create

"}, {"id": "C", "text": "

creating

"}, {"id": "D", "text": "

created

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. The convention being tested is the use of non-finite (untensed) verb forms in a sentence. The modal “would,” which indicates the future from a perspective in the past, should be accompanied by a non-finite plain form verb. In this choice, the non-finite plain form verb “create” is used correctly in conjunction with the non-finite plain form verb “increase” to describe what the lock would do.\n 

Choice A is incorrect because the finite present tense verb “creates” can’t be used in this way with the modal “would” to describe what the lock would do. Choice C is incorrect because the present participle “creating” can’t be used in this way with the modal “would” to describe what the lock would do. Choice D is incorrect because the finite past tense verb “created” can’t be used in this way with the modal “would” to describe what the lock would do.

"}, {"id": "96953201", "domain": "Standard English Conventions", "skill": "Boundaries", "difficulty": "E", "type": "mc", "stimulus": "

In her two major series “Memory Test” and “Autobiography,” painter Howardena Pindell explored themes ______blank healing, self-discovery, and memory by cutting and sewing back together pieces of canvas and inserting personal artifacts, such as postcards, into some of the paintings.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

of

"}, {"id": "B", "text": "

of,

"}, {"id": "C", "text": "

of—

"}, {"id": "D", "text": "

of:

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. The convention being tested is punctuation between a preposition and its complement. No punctuation is needed between the preposition “of” and its complement, the noun phrase “healing, self-discovery, and memory.”

Choice B is incorrect because no punctuation is needed between a preposition and its complement. Choice C is incorrect because no punctuation is needed between a preposition and its complement. Choice D is incorrect because no punctuation is needed between a preposition and its complement. 

"}, {"id": "8f6d6ae6", "domain": "Standard English Conventions", "skill": "Boundaries", "difficulty": "M", "type": "mc", "stimulus": "

Archaeologists have estimated that the pre-Columbian Native American city of Cahokia, located across the Mississippi River from modern-day St. Louis, Missouri, had as many as 20,000 inhabitants in the year 1150 ______blank it one of the largest cities in North America at the time.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

CE making

"}, {"id": "B", "text": "

CE. Making

"}, {"id": "C", "text": "

CE, making

"}, {"id": "D", "text": "

CE; making

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. The phrase “making…at the time” provides additional information about Cahokia that’s not required for the sentence to make sense or function grammatically. As a nonessential supplement, this phrase should be separated from the rest of the sentence with a comma.

Choice A is incorrect. This choice results in a run-on sentence. The nonessential descriptive aside “making…at the time” needs to be separated from the rest of the sentence with a comma. Choice B is incorrect. This choice results in a sentence fragment. “Making…at the time” doesn’t have a subject and can’t stand on its own as a sentence. Thus, it can’t be separated from the rest of the sentence with a period. Choice D is incorrect. This choice results in a punctuation error. “Making…at the time” doesn’t have a subject and can’t stand on its own as an independent clause. Since a semicolon can only link two independent clauses, using one here creates an error.

"}, {"id": "26c8c88c", "domain": "Standard English Conventions", "skill": "Boundaries", "difficulty": "E", "type": "mc", "stimulus": "

About 70,000 meteorites have been found on Earth. Although most meteorites are fragments of ______blank hundred have been identified as being from the Moon or Mars.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

asteroids. Several

"}, {"id": "B", "text": "

asteroids, several

"}, {"id": "C", "text": "

asteroids; several

"}, {"id": "D", "text": "

asteroids: several

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. This choice uses a comma to correctly separate the dependent clause \"although…asteroids\" from the independent clause \"several hundred have been…Mars.\"

Choice A is incorrect. This choice results in a sentence fragment. \"Although…asteroids\" is a dependent clause. It can’t stand on its own as a sentence, which means it can’t end in a period. Choice C is incorrect. This choice results in a punctuation error. \"Although…asteroids\" is a dependent clause and can’t be joined to the independent clause \"several hundred have been…Mars\" with a semicolon. A semicolon can only join two independent clauses. Choice D is incorrect. This choice creates a punctuation error. A colon can only come after an independent clause, but \"although…asteroids\" is a dependent clause.

"}, {"id": "c06af4d8", "domain": "Standard English Conventions", "skill": "Boundaries", "difficulty": "H", "type": "mc", "stimulus": "

Sociologist Alton Okinaka sits on the review board tasked with adding new sites to the Hawai‘i Register of Historic Places, which includes Pi‘ilanihale Heiau and the ‘\u014cpaeka‘a Road Bridge. Okinaka doesn’t make such decisions ______blank all historical designations must be approved by a group of nine other experts from the fields of architecture, archaeology, history, and Hawaiian culture.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

single-handedly, however;

"}, {"id": "B", "text": "

single-handedly; however,

"}, {"id": "C", "text": "

single-handedly, however,

"}, {"id": "D", "text": "

single-handedly however

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. The convention being tested is the punctuation of a supplementary word or phrase between two main clauses. This choice correctly uses a comma to separate the supplementary adverb “however” from the preceding main clause (“Okinaka doesn’t…single-handedly”) and a semicolon to join the next main clause (“all…culture”) to the rest of the sentence. Further, placing the semicolon after “however” correctly indicates that the information in the preceding main clause (Okinaka doesn’t make such decisions single-handedly) is contrary to what might be assumed from the information in the previous sentence (Okinaka sits on the review board that adds new sites to the Hawaii Register of Historic Places).

Choice B is incorrect because placing the semicolon after “single-handedly” and the comma after “however” illogically indicates that the information in the next main clause (all historical designations must be approved by a group of experts) is contrary to the information in the previous clause (Okinaka doesn’t make such decisions single-handedly). Choice C is incorrect because it results in a comma splice. Commas can’t be used in this way to punctuate a supplementary word or phrase between two main clauses. Choice D is incorrect because it results in a run-on sentence. The two main clauses are fused without punctuation and/or a conjunction.

"}, {"id": "f4fd123c", "domain": "Standard English Conventions", "skill": "Form, Structure, and Sense", "difficulty": "E", "type": "mc", "stimulus": "

The African Games Co-production Market, one of over 180 annual international conferences supporting video game development, ______blank the growth of the African gaming industry by helping start-up studios in Africa find partners.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

promote

"}, {"id": "B", "text": "

are promoting

"}, {"id": "C", "text": "

promotes

"}, {"id": "D", "text": "

have promoted

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. The subject of the sentence is “The African Games Co-production Market.” That’s one market, so it’s a singular noun, which means it needs a singular verb. “Promotes” is the only singular verb among the choices. 

Choice A is incorrect. This choice creates a subject-verb agreement error. The subject “The African Games Co-production Market” is singular, but the verb “promote” is plural. Choice B is incorrect. This choice creates a subject-verb agreement error. The subject “The African Games Co-production Market” is singular, but the verb “are promoting” is plural. Choice D is incorrect. This choice creates a subject-verb agreement error. The subject “The African Games Co-production Market” is singular, but the verb “have promoted” is plural.

"}, {"id": "60713427", "domain": "Standard English Conventions", "skill": "Boundaries", "difficulty": "E", "type": "mc", "stimulus": "

Polyphenols are organic compounds ______blank among their many roles, provide pigment that helps protect plants against ultraviolet radiation from sunlight.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

that—

"}, {"id": "B", "text": "

that;

"}, {"id": "C", "text": "

that,

"}, {"id": "D", "text": "

that:

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. The convention being tested is the punctuation of a supplementary element within a sentence. The comma after “that” pairs with the comma after “roles” to separate the supplementary element “among their many roles” from the rest of the sentence. This supplementary element functions to clarify that polyphenols have many roles, and the pair of commas indicates that this element could be removed without affecting the grammatical coherence of the sentence.

Choice A is incorrect because a dash can’t be paired with a comma to separate the supplementary element from the rest of the sentence. Choice B is incorrect because a semicolon can’t be paired with a comma to separate the supplementary element from the rest of the sentence. Choice D is incorrect because a colon can’t be paired with a comma to separate the supplementary element from the rest of the sentence.

"}, {"id": "7f1df833", "domain": "Standard English Conventions", "skill": "Form, Structure, and Sense", "difficulty": "M", "type": "mc", "stimulus": "

In 1966, Emmett Ashford became the first African American to umpire a Major League Baseball game. His energetic gestures announcing when a player had struck out and his habit of barreling after a hit ball to see if it would land out of ______blank transform the traditionally solemn umpire role into a dynamic one.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

bounds helped

"}, {"id": "B", "text": "

bounds, helping

"}, {"id": "C", "text": "

bounds that helped

"}, {"id": "D", "text": "

bounds to help

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. The convention being tested is finite verb use in a main clause. A main clause requires a finite verb to perform the action of the subject (in this case, Ashford’s “gestures” and “habit”), and this choice supplies the finite past tense verb “helped” to indicate what Ashford’s gestures and habit helped accomplish.

Choice B is incorrect because the non-finite participle “helping” doesn’t supply the main clause with a finite verb. Choice C is incorrect because the relative clause “that helped” doesn’t supply the main clause with a finite verb. Choice D is incorrect because the non-finite to-infinitive “to help” doesn’t supply the main clause with a finite verb.

"}, {"id": "2ee50d41", "domain": "Standard English Conventions", "skill": "Form, Structure, and Sense", "difficulty": "E", "type": "mc", "stimulus": "

The classic children’s board game Chutes and Ladders is a version of an ancient Nepalese game, Paramapada Sopanapata. In both games, players encounter “good” or “bad” spaces while traveling along a path; landing on one of the good spaces ______blank a player to skip ahead and arrive closer to the end goal.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

allows

"}, {"id": "B", "text": "

are allowing

"}, {"id": "C", "text": "

have allowed

"}, {"id": "D", "text": "

allow

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. The convention being tested is subject–verb agreement. The singular verb “allows” agrees in number with the singular subject “landing.”

Choice B is incorrect because the plural verb “are allowing” doesn’t agree in number with the singular subject “landing.” Choice C is incorrect because the plural verb “have allowed” doesn’t agree in number with the singular subject “landing.” Choice D is incorrect because the plural verb “allow” doesn’t agree in number with the singular subject “landing.”

"}, {"id": "15d6d837", "domain": "Standard English Conventions", "skill": "Form, Structure, and Sense", "difficulty": "E", "type": "mc", "stimulus": "

Literary agents estimate that more than half of all nonfiction books credited to a celebrity or other public figure are in fact written by ghostwriters, professional authors who are paid to write other ______blank but whose names never appear on book covers.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

people’s stories

"}, {"id": "B", "text": "

peoples story’s

"}, {"id": "C", "text": "

peoples stories

"}, {"id": "D", "text": "

people’s story’s

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. The convention being tested is the use of plural and possessive nouns. The plural possessive noun “people’s” and the plural noun “stories” correctly indicate that there are multiple stories from multiple people. 

Choice B is incorrect because the context requires the plural possessive noun “people’s” and the plural noun “stories,” not the plural noun “peoples” and the singular possessive noun “story’s.” Choice C is incorrect because the context requires the plural possessive noun “people’s,” not the plural noun “peoples.” Choice D is incorrect because the context requires the plural noun “stories,” not the singular possessive noun “story’s.”

"}, {"id": "59209b6d", "domain": "Standard English Conventions", "skill": "Form, Structure, and Sense", "difficulty": "M", "type": "mc", "stimulus": "

Based on genetic evidence, archaeologists have generally agreed that reindeer domestication began in the eleventh century CE. However, since uncovering fragments of a 2,000-year-old reindeer training harness in northern Siberia, ______blank may have begun much earlier.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

researcher Robert Losey has argued that domestication 

"}, {"id": "B", "text": "

researcher Robert Losey’s argument is that domestication

"}, {"id": "C", "text": "

domestication, researcher Robert Losey has argued,

"}, {"id": "D", "text": "

the argument researcher Robert Losey has made is that domestication

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. The convention being tested is subject-modifier placement. This choice makes the noun phrase “researcher Robert Losey” the subject of the sentence and places it immediately after the modifying phrase “since…Siberia.” In doing so, this choice clearly establishes that researcher Robert Losey—and not another noun in the sentence—is who uncovered fragments of a 2,000-year-old reindeer training harness in northern Siberia.

Choice B is incorrect because it results in a dangling modifier. The placement of the noun phrase “researcher Robert Losey’s argument” immediately after the modifying phrase illogically suggests that the “argument” is what uncovered fragments of a 2,000-year-old reindeer training harness in northern Siberia. Choice C is incorrect because it results in a dangling modifier. The placement of the noun “domestication” immediately after the modifying phrase illogically suggests that “domestication” is what uncovered fragments of a 2,000-year-old reindeer training harness in northern Siberia. Choice D is incorrect because it results in a dangling modifier. The placement of the noun phrase “the argument” immediately after the modifying phrase illogically suggests that the “argument” is what uncovered fragments of a 2,000-year-old reindeer training harness in northern Siberia.

"}, {"id": "2b512e65", "domain": "Standard English Conventions", "skill": "Boundaries", "difficulty": "M", "type": "mc", "stimulus": "

Eli Eisenberg, a genetics expert at Tel Aviv University in Israel, recently discovered that ______blank have a special genetic ability called RNA editing that confers evolutionary advantages.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

cephalopods, ocean dwellers that include the squid, the octopus, and the cuttlefish

"}, {"id": "B", "text": "

cephalopods—ocean dwellers—that include the squid, the octopus, and the cuttlefish,

"}, {"id": "C", "text": "

cephalopods, ocean dwellers that include: the squid, the octopus, and the cuttlefish,

"}, {"id": "D", "text": "

cephalopods—ocean dwellers that include the squid, the octopus, and the cuttlefish—

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. The convention being tested is the punctuation of a supplementary element within a sentence. In this choice, the dash after “cephalopods” pairs with the dash after “cuttlefish” to clearly separate the supplementary element “ocean dwellers that include the squid, the octopus, and the cuttlefish” from the rest of the sentence. This supplementary element functions to explain what cephalopds are, and the pair of dashes indicates that this element could be removed without affecting the grammatical coherence of the sentence.

Choice A is incorrect because it fails to use appropriate punctuation to separate the supplementary element that explains what cephalopods are from the rest of the sentence. Choice B is incorrect because it fails to use appropriate punctuation to separate the supplementary element that explains what cephalopods are from the rest of the sentence. Choice C is incorrect because it fails to use appropriate punctuation to separate the supplementary element that explains what cephalopods are from the rest of the sentence.

"}, {"id": "856b495d", "domain": "Standard English Conventions", "skill": "Form, Structure, and Sense", "difficulty": "E", "type": "mc", "stimulus": "

In the early twentieth century, Joseph Kekuku and other Hawaiian ______blank in the mainland United States to the bright and lilting sound of the k\u012bk\u0101 kila, or Hawaiian steel guitar. The instrument soon became a fixture in American blues and country music.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

musicians introduced audiences

"}, {"id": "B", "text": "

musicians’ introduced audiences’

"}, {"id": "C", "text": "

musician’s introduced audience’s

"}, {"id": "D", "text": "

musicians’ introduced audiences

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. The convention being tested is the use of plural nouns. The plural nouns \"musicians\" and \"audiences\" correctly indicate that there were multiple musicians introducing the music to multiple audiences.

Choice B is incorrect because the context requires the plural nouns \"musicians\" and \"audiences,\" not the plural possessive nouns \"musicians’\" and \"audiences’.\" Choice C is incorrect because the context requires the plural nouns \"musicians\" and \"audiences,\" not the singular possessive nouns \"musician’s\" and \"audience’s.\" Choice D is incorrect because the context requires the plural noun \"musicians,\" not the plural possessive noun \"musicians’.\"

"}, {"id": "870ae7ec", "domain": "Standard English Conventions", "skill": "Boundaries", "difficulty": "M", "type": "mc", "stimulus": "

Detroit natives Timothy Paule and Nicole Lindsey have combined their two passions, Detroit and beekeeping, to improve the health of their city’s flowers and other vegetation. In 2017, the couple converted a vacant lot in the city into an ______blank in the years that followed they acquired nine additional lots and established more than 35 hives.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

apiary,

"}, {"id": "B", "text": "

apiary, and

"}, {"id": "C", "text": "

apiary and

"}, {"id": "D", "text": "

apiary 

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. Both clauses in this sentence could stand alone as complete sentences, which means they are both independent clauses. This choice uses a comma plus a coordinating conjunction to link them together, which is one of the correct ways to link two independent clauses. 

Choice A is incorrect. This choice results in a run-on sentence error. Both clauses in this sentence could stand alone as complete sentences, which means they are both independent clauses. A comma by itself is not enough punctuation to link two independent clauses. Choice C is incorrect. This choice results in a run-on sentence error. Both clauses in this sentence could stand alone as complete sentences, which means they are both independent clauses. Independent clauses can only be linked in a few ways, including with a comma plus a coordinating conjunction. This choice uses the coordinating conjunction “and,” but it is missing the comma beforehand. Choice D is incorrect. This choice results in a run-on sentence error. Both clauses in this sentence could stand alone as complete sentences, which means they are both independent clauses. Independent clauses need to have certain kinds of punctuation marks between them. This choice doesn’t use any punctuation between the two clauses. 

"}, {"id": "fcaff694", "domain": "Standard English Conventions", "skill": "Boundaries", "difficulty": "M", "type": "mc", "stimulus": "

The city of Pompeii, which was buried in ash following the eruption of Mount Vesuvius in 79 CE, continues to be studied by archaeologists. Unfortunately, as ______blank attest, archaeological excavations have disrupted ash deposits at the site, causing valuable information about the eruption to be lost.    

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

researchers, Roberto Scandone and Christopher Kilburn,

"}, {"id": "B", "text": "

researchers, Roberto Scandone and Christopher Kilburn

"}, {"id": "C", "text": "

researchers Roberto Scandone and Christopher Kilburn

"}, {"id": "D", "text": "

researchers Roberto Scandone, and Christopher Kilburn

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. The convention being tested is the punctuation of a restrictive coordinated noun phrase. No punctuation is needed within or around the coordinated noun phrase “researchers Roberto Scandone and Christopher Kilburn” because it would create an illogical separation between the noun “researchers” and the coordinated noun phrase “Roberto Scandone and Christopher Kilburn.”

Choice A is incorrect because no punctuation is needed. Placing a pair of commas around the coordinated noun phrase “Roberto Scandone and Christopher Kilburn” creates an illogical separation between the noun “researchers” and the aforementioned coordinated noun phrase. In this case, it illogically suggests that researchers in general bear the specific names Roberto Scandone and Christopher Kilburn. Choice B is incorrect because no punctuation is needed between the noun “researchers” and the coordinated noun phrase “Roberto Scandone and Christopher Kilburn.” Choice D is incorrect because no punctuation is needed within the coordinated noun phrase “Roberto Scandone and Christopher Kilburn.”

"}, {"id": "0fe5ce68", "domain": "Standard English Conventions", "skill": "Form, Structure, and Sense", "difficulty": "H", "type": "mc", "stimulus": "

Ten of William Shakespeare’s plays are classified as histories. Although each one of these plays, which include Henry V and Richard III, ______blank on a single historical figure (specifically, an English king), some, such as Henry VI Part One and Henry VI Part Two, feature different episodes from the same monarch’s life.     

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

focuses

"}, {"id": "B", "text": "

focus

"}, {"id": "C", "text": "

are focused

"}, {"id": "D", "text": "

were focused

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. The convention being tested is subject-verb agreement. The singular verb \"focuses\" agrees in number with the singular subject \"each one of these plays,\" which refers to each play individually.

Choice B is incorrect because the plural verb \"focus\" doesn’t agree in number with the singular subject \"each one of these plays.\" Choice C is incorrect because the plural verb \"are focused\" doesn’t agree in number with the singular subject \"each one of these plays.\" Choice D is incorrect because the plural verb \"were focused\" doesn’t agree in number with the singular subject \"each one of these plays.\"

"}, {"id": "790fc366", "domain": "Standard English Conventions", "skill": "Boundaries", "difficulty": "H", "type": "mc", "stimulus": "

Using satellite remote sensing, Dr. Catherine Nakalembe, director of NASA’s Harvest Africa initiative, gathers important data on crop health. Nakalembe doesn’t just compile the ______blank she also shares her findings with African farmers, enabling them to make data-driven decisions about managing critical food crops.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

information, though;

"}, {"id": "B", "text": "

information, though,

"}, {"id": "C", "text": "

information; though

"}, {"id": "D", "text": "

information though,

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. This choice uses a semicolon to join two independent clauses (\"Nakalembe doesn’t just…though\" and \"she also shares...\"). This choice also appropriately includes \"though\" in the first clause, where it logically belongs.

Choice B is incorrect. This choice results in a grammar error called a comma splice. It incorrectly joins two independent clauses with only a comma instead of a comma and a coordinating conjunction like \"and\" or \"but.\" \"Though\" is a transition word, but it’s not a coordinating conjunction. Choice C is incorrect. This choice results in a punctuation error. A semicolon can only be used to link two independent clauses. However, if \"though\" is included in the second clause, it turns the second clause into a dependent clause, so a semicolon can’t be used after \"information.\" Choice D is incorrect. This choice results in a grammar error called a comma splice. It incorrectly joins two independent clauses with only a comma instead of a comma and a coordinating conjunction like \"and\" or \"but.\"

"}, {"id": "62120607", "domain": "Standard English Conventions", "skill": "Boundaries", "difficulty": "H", "type": "mc", "stimulus": "

From afar, African American fiber artist Bisa Butler’s portraits look like paintings, their depictions of human faces, bodies, and clothing so intricate that it seems only a fine brush could have rendered them. When viewed up close, however, the portraits reveal themselves to be ______blank stitching barely visible among the thousands of pieces of printed, microcut fabric.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

quilts, and the

"}, {"id": "B", "text": "

quilts, the

"}, {"id": "C", "text": "

quilts; the

"}, {"id": "D", "text": "

quilts. The

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. The convention being tested is punctuation use between a main clause and a supplementary phrase. This choice correctly uses a comma to mark the boundary between the main clause (“the portraits...quilts”) and the supplementary noun phrase (“the stitching...fabric”) that provides a further description of how the portraits can be identified as quilts.

Choice A is incorrect. A comma and the conjunction “and” can’t be used in this way to join a main clause and a supplementary noun phrase. Choice C is incorrect because a semicolon can’t be used in this way to join a main clause and a supplementary noun phrase. Choice D is incorrect because it results in a rhetorically unacceptable sentence fragment beginning with “the stitching.”

"}, {"id": "2bb7416a", "domain": "Standard English Conventions", "skill": "Boundaries", "difficulty": "H", "type": "mc", "stimulus": "

In paleontology, the term “Elvis taxon” gets applied to a newly identified living species that was once presumed to be extinct. Like an Elvis impersonator who might bear a striking resemblance to the late musical icon Elvis Presley himself, an Elvis taxon is not the real thing, ______blank is a misidentified look-alike.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

however but it

"}, {"id": "B", "text": "

however it

"}, {"id": "C", "text": "

however, it

"}, {"id": "D", "text": "

however. It

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. The clause “Like an Elvis impersonator…real thing” and the clause “it is…look-alike” are both independent clauses, so making them into two separate sentences is grammatically correct. 

Choice A is incorrect. This choice creates a run-on sentence error. The clause “Like an Elvis impersonator…real thing” and the clause “it is…look-alike” are both independent clauses, so they need to be separated with at least a comma + a coordinating conjunction. This choice provides the coordinating conjunction “but,” but it’s missing a comma. Choice B is incorrect. This choice creates a run-on sentence error. The clause “Like an Elvis impersonator…real thing” and the clause “it is…look-alike” are both independent clauses, so they need to be separated with a semicolon, a colon, a dash, a period, or a comma + a coordinating conjunction. Choice C is incorrect. This choice creates a run-on sentence error. The clause “Like an Elvis impersonator…real thing” and the clause “it is…look-alike” are both independent clauses, so they need to be separated with at least a comma + a coordinating conjunction. This choice provides a comma, but it’s missing a coordinating conjunction.

"}, {"id": "97b62fab", "domain": "Standard English Conventions", "skill": "Form, Structure, and Sense", "difficulty": "E", "type": "mc", "stimulus": "

Smaller than poppy seeds, tardigrades are tiny, but they are tough. These minuscule animals can survive for thirty years without food or water, and ______blank can withstand extreme temperatures as low as minus 328 degrees and as high as 304 degrees Fahrenheit.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

that

"}, {"id": "B", "text": "

it

"}, {"id": "C", "text": "

they

"}, {"id": "D", "text": "

he

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. The convention being tested is pronoun-antecedent agreement. The plural pronoun \"they\" agrees in number with the plural antecedent \"animals,\" which refers to tardigrades.

Choice A is incorrect because the singular pronoun \"that\" doesn’t agree in number with the plural antecedent \"animals.\" Choice B is incorrect because the singular pronoun \"it\" doesn’t agree in number with the plural antecedent \"animals.\" Choice D is incorrect because the singular pronoun \"he\" doesn’t agree in number with the plural antecedent \"animals.\"

"}, {"id": "89ab0d46", "domain": "Standard English Conventions", "skill": "Boundaries", "difficulty": "E", "type": "mc", "stimulus": "

After the printing press was introduced in 1440, handwritten manuscripts from Europe’s medieval period were often destroyed and the paper used for other purposes. In one instance, pages ______blank a collection of Norse tales dating to 1270 were discovered lining a bishop’s miter (hat).

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

from:

"}, {"id": "B", "text": "

from,

"}, {"id": "C", "text": "

from

"}, {"id": "D", "text": "

from—

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. The word “from” introduces a prepositional phrase that modifies the noun “pages” and provides essential information about their origin. No additional punctuation is needed after “from” in this context.

Choice A is incorrect. This choice results in a punctuation error, illogically separating the preposition “from” from the rest of the prepositional phrase with a colon. Also, a colon can only follow an independent clause, but what comes before the blank could not stand on its own as a complete sentence. Choice B is incorrect. This choice results in a punctuation error, illogically separating the preposition “from” from the rest of the prepositional phrase with a comma. Choice D is incorrect. This choice results in a punctuation error, illogically separating the preposition “from” from the rest of the prepositional phrase with a dash.

"}, {"id": "b0a525be", "domain": "Standard English Conventions", "skill": "Boundaries", "difficulty": "M", "type": "mc", "stimulus": "

Santa Clara Pueblo artist Roxanne Swentzell’s sculpture Mud Woman Rolls On consists of five human figures made of clay and plant fiber and arranged in descending size; each figure holds the smaller one in front of it. The arrangement of the figures, according to ______blank represents her idea that “we all come from the Earth, generation after generation.”

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

Swentzell

"}, {"id": "B", "text": "

Swentzell,

"}, {"id": "C", "text": "

Swentzell:

"}, {"id": "D", "text": "

Swentzell—

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. The phrase “according to Swentzell” is an aside that interrupts the flow of the sentence, so it needs to be separated from the sentence with a pair of matching punctuation marks: two commas, two dashes, or a pair of parentheses. We already have a comma before “according,” so we must add a comma after “Swentzell.” .

Choice A is incorrect. This choice creates a punctuation error. The phrase “according to Swentzell” is an aside that interrupts the flow of the sentence, so it needs to be separated from the sentence with a pair of matching punctuation marks: one before and one after the phrase. Choice C is incorrect. This choice creates a punctuation error. “The arrangement of the figures, according to Swentzell” is not an independent clause, so it can’t come before a colon. Choice D is incorrect. This choice creates a punctuation error. The phrase “according to Swentzell” is an aside that interrupts the flow of the sentence, so it needs to be separated from the sentence with a pair of matching punctuation marks. We already have a comma at the beginning, so we have to use another comma here to match. We can’t just switch to a dash! .

"}, {"id": "eef91a50", "domain": "Standard English Conventions", "skill": "Boundaries", "difficulty": "M", "type": "mc", "stimulus": "

Nine months before Rosa Parks made history by refusing to comply with the segregated seating policy on a Montgomery, Alabama, bus, a fifteen-year-old Montgomery girl named Claudette Colvin was arrested for the same ______blank to some historians, Colvin’s arrest led to Parks’s action and eventually to the desegregation of Montgomery’s bus system.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

offense. According

"}, {"id": "B", "text": "

offense, according

"}, {"id": "C", "text": "

offense according

"}, {"id": "D", "text": "

offense and according

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. “Nine months…offense” and “according to…system” are both independent clauses. Separating them with a period and turning them into their own sentences is the only grammatically correct choice among the provided options.

Choice B is incorrect. This choice results in a comma splice error, which is a punctuation error that occurs when two independent clauses are joined by only a comma. “Nine months…offense” and “according to…system” are both independent clauses, so they need to be either joined by a semicolon, joined by a comma and a coordinating conjunction, or separated by a period. Choice C is incorrect. This choice results in a run-on sentence, which occurs when two independent clauses are joined without punctuation. “Nine months…offense” and “according to…system” are both independent clauses, so they need to be either joined by a semicolon, joined by a comma and a coordinating conjunction, or separated by a period. Choice D is incorrect. This choice results in a run-on sentence, which occurs when two independent clauses are joined without punctuation. “Nine months…offense” and “according to…system” are independent clauses, so we would need to put a comma before the coordinating conjunction “and” to join them properly.

"}, {"id": "01a32c84", "domain": "Standard English Conventions", "skill": "Boundaries", "difficulty": "M", "type": "mc", "stimulus": "

The first computerized spreadsheet, Dan Bricklin’s VisiCalc, improved financial recordkeeping not only by providing users with an easy means of adjusting data in spreadsheets but also by automatically updating all calculations that were dependent on these ______blank to VisiCalc’s release, changing a paper spreadsheet often required redoing the entire sheet by hand, a process that could take days.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

adjustments prior

"}, {"id": "B", "text": "

adjustments, prior 

"}, {"id": "C", "text": "

adjustments. Prior

"}, {"id": "D", "text": "

adjustments and prior

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. The convention being tested is punctuation use between sentences. In this choice, the period is used correctly to mark the boundary between the first sentence (“The...adjustments”) and the second sentence (“Prior...days”). Because the adverbial phrase beginning with “prior” indicates when changing a spreadsheet required redoing the sheet by hand, that phrase belongs with the second sentence. 

Choice A is incorrect because it results in a run-on sentence. Two sentences are fused without punctuation and/or a conjunction. Choice B is incorrect because it results in a comma splice. A comma can’t be used in this way to mark the boundary between sentences. Choice D is incorrect. Without a comma preceding it, the conjunction “and” can’t be used in this way to join the sentences.

"}, {"id": "548f4956", "domain": "Standard English Conventions", "skill": "Boundaries", "difficulty": "M", "type": "mc", "stimulus": "

It is generally true that technological change is a linear process, in which once-useful technologies are replaced by new and better ______blank the reawakening of interest in the steam engine (from advocates of carbon-neutral rail travel) reminds us that ostensibly obsolete technologies may be brought back into service to address society’s changing needs.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

ones, even so; 

"}, {"id": "B", "text": "

ones even so, 

"}, {"id": "C", "text": "

ones; even so, 

"}, {"id": "D", "text": "

ones, even so, 

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. The convention being tested is the coordination of main clauses within a sentence. This choice uses a semicolon in a conventional way to join the first main clause (“It is…ones”) and the second main clause  (“even so…needs”). Furthermore, the placement of the semicolon after “ones” indicates that the supplementary phrase “even so” modifies the following clause (“the reawakening...needs”), resulting in the most logical and grammatically complete sentence. With this punctuation, the sentence logically indicates that the recent interest in an old technology like steam engines is despite the fact that technological change typically seeks out new technologies.

Choice A is incorrect because it results in a confusing and illogical sentence. Placing the semicolon after “so” indicates that the supplementary element “even so” modifies the first clause of the sentence, which doesn’t make sense in this context. Choice B is incorrect because it results in a run-on sentence. It fails to mark the boundary between the two main clauses with appropriate punctuation. Choice D is incorrect because it results in a comma splice. Without a conjunction following it, a comma can’t be used in this way to join the two main clauses of the sentence.

"}, {"id": "2c84f96a", "domain": "Standard English Conventions", "skill": "Boundaries", "difficulty": "M", "type": "mc", "stimulus": "

In 2017, artists Isabel and Ruben Toledo redesigned the costumes and sets for The Miami City Ballet’s production of The ______blank to reviewers, the Toledos’ designs helped infuse the production with elements of Miami’s Latin American culture.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

Nutcracker according, 

"}, {"id": "B", "text": "

Nutcracker, according 

"}, {"id": "C", "text": "

Nutcracker according 

"}, {"id": "D", "text": "

Nutcracker. According 

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. The convention being tested is punctuation use between sentences. In this choice, the period is used correctly to mark the boundary between one sentence (“In 2017...Nutcracker”) and another (“According...culture”). The supplementary element “according to reviewers” modifies the main clause of the second sentence (“the Toledos’...culture”).

Choice A is incorrect because it results in a run-on sentence. The sentences are fused without punctuation and/or a conjunction. Furthermore, no punctuation is needed within the supplementary element “according to reviewers.” Choice B is incorrect because it results in a comma splice. A comma can’t be used in this way to mark the boundary between sentences. Choice C is incorrect because it results in a run-on sentence. The sentences are fused without punctuation and/or a conjunction.

"}, {"id": "dd6a0326", "domain": "Standard English Conventions", "skill": "Form, Structure, and Sense", "difficulty": "M", "type": "mc", "stimulus": "

African American Percy Julian was a scientist and entrepreneur whose work helped people around the world to see. Named in 1999 as one of the greatest achievements by a US chemist in the past hundred years, ______blank led to the first mass-produced treatment for glaucoma.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

Julian synthesized the alkaloid physostigmine in 1935; it 

"}, {"id": "B", "text": "

in 1935 Julian synthesized the alkaloid physostigmine, which

"}, {"id": "C", "text": "

Julian’s 1935 synthesis of the alkaloid physostigmine

"}, {"id": "D", "text": "

the alkaloid physostigmine was synthesized by Julian in 1935 and

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. The convention being tested is subject-modifier placement. This choice makes the noun phrase “Julian’s 1935 synthesis” the subject of the sentence and places it immediately after the modifying phrase “named…years.” In doing so, this choice clearly establishes that Julian’s 1935 synthesis of the alkaloid physostigmine—and not another noun in the sentence—was named in 1999 as one of the greatest achievements by a US chemist in the past hundred years.  

Choice A is incorrect because it results in a dangling modifier. The placement of the noun “Julian” immediately after the modifying phrase illogically suggests that Julian himself was named as one of the greatest achievements by a US chemist in the past hundred years. Choice B is incorrect because it results in a dangling modifier. The placement of the prepositional phrase “in 1935” immediately after the modifying phrase illogically and confusingly suggests that “in 1935” was named as one of the greatest achievements by a US chemist in the past hundred years. Choice D is incorrect because it results in a dangling modifier. The placement of the noun phrase “the alkaloid physostigmine” immediately after the modifying phrase illogically and confusingly suggests that the alkaloid physostigmine itself (not the synthesis of it) was named as one of the greatest achievements by a US chemist in the past hundred years.

"}, {"id": "4ba99a6f", "domain": "Standard English Conventions", "skill": "Boundaries", "difficulty": "M", "type": "mc", "stimulus": "

Seneca sculptor Marie Watt’s blanket art comes in a range of shapes and sizes. In 2004, Watt sewed strips of blankets together to craft a 10-by-13-inch ______blank in 2014, she arranged folded blankets into two large stacks and then cast them in bronze, creating two curving 18-foot-tall blue-bronze pillars.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

sampler later,

"}, {"id": "B", "text": "

sampler; 

"}, {"id": "C", "text": "

sampler, 

"}, {"id": "D", "text": "

sampler, later,

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. The convention being tested is the coordination of main clauses within a sentence. This choice uses a semicolon in a conventional way to join the first main clause (“In 2004…sampler”) and the second main clause (“in 2014…pillars”).

Choice A is incorrect because it results in a comma splice. Without a conjunction following it, a comma can’t be used in this way to join two main clauses. The word “later” is an adverb and cannot be used to join two main clauses unless it is preceded by a conjunction. Choice C is incorrect because it results in a comma splice. Without a conjunction following it, a comma can’t be used in this way to join two main clauses. Choice D is incorrect because it results in a comma splice. Without a conjunction following it, a comma can’t be used in this way to join two main clauses. The word “later” is an adverb and cannot be used to join two main clauses unless it is preceded by a conjunction.

"}, {"id": "ce81d0b7", "domain": "Standard English Conventions", "skill": "Boundaries", "difficulty": "E", "type": "mc", "stimulus": "

The life spans of rockfish vary greatly by species. For instance, the colorful calico rockfish (Sebastes dalli) can survive for a little over a ______blank the rougheye rockfish (Sebastes aleutianus) boasts a maximum life span of about two centuries.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

decade: while

"}, {"id": "B", "text": "

decade. While

"}, {"id": "C", "text": "

decade; while

"}, {"id": "D", "text": "

decade, while

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. The convention being tested is punctuation between a main clause and a subordinate clause. This choice correctly uses a comma to mark the boundary between the main clause (“the colorful…decade”) and the subordinate clause (“while…centuries”) that provides contrasting information about the life span of rougheye rockfish. 

Choice A is incorrect because a colon can’t be used in this way to join a main clause and a subordinate clause. Choice B is incorrect because it results in a rhetorically unacceptable sentence fragment beginning with “while.” Choice C is incorrect because a semicolon can’t be used in this way to join a main clause and a subordinate clause. 

"}, {"id": "db24ecc9", "domain": "Standard English Conventions", "skill": "Boundaries", "difficulty": "H", "type": "mc", "stimulus": "

The Arctic-Alpine Botanic Garden in Norway and the Jardim Botânico of Rio de Janeiro in Brazil are two of many botanical gardens around the world dedicated to growing diverse plant ______blank fostering scientific research; and educating the public about plant conservation.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

species, both native and nonnative,

"}, {"id": "B", "text": "

species, both native and nonnative;

"}, {"id": "C", "text": "

species; both native and nonnative,

"}, {"id": "D", "text": "

species both native and nonnative,

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. The convention being tested is the punctuation of items in a complex series (a series including internal punctuation). The semicolon after “nonnative” is correctly used to separate the first item (“growing diverse plant species, both native and nonnative”) and the second item (“fostering scientific research”) in the series of things that botanical gardens are dedicated to. Further, the comma after “species” is correctly used to separate the noun phrase “diverse plant species” and the supplementary phrase “both native and nonnative” that modifies it.

Choice A is incorrect because a comma (specifically, the comma after “nonnative”) can’t be used in this way to separate items in a complex series. Choice C is incorrect because a semicolon can’t be used in this way to separate the noun phrase “diverse plant species” and the supplementary phrase “both native and nonnative” that modifies it. Further, a comma can’t be used in this way to separate items in a complex series. Choice D is incorrect because it fails to use appropriate punctuation to separate the noun phrase “diverse plant species” and the supplementary phrase “both native and nonnative” that modifies it. Further, a comma can’t be used in this way to separate items in a complex series.

"}, {"id": "35360da9", "domain": "Standard English Conventions", "skill": "Form, Structure, and Sense", "difficulty": "E", "type": "mc", "stimulus": "

The US Geological Survey wants to map every human-made structure in the United States, and it is asking volunteers to help. Cassie Tammy Wang and Ashish D’Souza are just two of the many volunteer map editors who ______blank to the project since it began in 2012.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

contribute

"}, {"id": "B", "text": "

will contribute

"}, {"id": "C", "text": "

have contributed

"}, {"id": "D", "text": "

will be contributing

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. The convention being tested is the use of verbs to express tense in a sentence. In this choice, the present perfect tense verb “have contributed,” used in conjunction with the phrase “since it began in 2012,” correctly indicates that map editors have contributed in the past and continue to do so in the present.

Choice A is incorrect because the present tense verb “contribute” is inconsistent with the phrase “since it began in 2012,” which suggests that the contributions occurred in the past and continue into the present. Choice B is incorrect because the future tense verb “will contribute” is inconsistent with the phrase “since it began in 2012,” which suggests that the contributions occurred in the past and continue into the present. Choice D is incorrect because the future tense verb “will be contributing” is inconsistent with the phrase “since it began in 2012,” which suggests that the contributions occurred in the past and continue into the present.

"}, {"id": "0fa289a7", "domain": "Standard English Conventions", "skill": "Boundaries", "difficulty": "H", "type": "mc", "stimulus": "

In 1955, Indian Bengali filmmaker Satyajit Ray released his first movie, Pather ______blank quiet black-and-white drama about a family in rural India, Ray’s film was quite different from the loud, colorful action-romance movies that were popular at the time.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

Panchali a

"}, {"id": "B", "text": "

Panchali, which was a

"}, {"id": "C", "text": "

Panchali, a

"}, {"id": "D", "text": "

Panchali. A

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. The convention being tested is punctuation use between sentences. In this choice, the period is used correctly to mark the boundary between one sentence (\"In…Panchali\") and another (\"A quiet…time\"). The phrase beginning with \"a quiet\" modifies the subject of the next sentence, \"Ray’s film.\"

Choice A is incorrect because it results in a run-on sentence. The sentences are fused without punctuation and/or a conjunction. Choice B is incorrect because it results in a comma splice. A comma can’t be used in this way to mark the boundary between sentences. Choice C is incorrect because it results in a comma splice. A comma can’t be used in this way to mark the boundary between sentences.

"}, {"id": "684b8bd2", "domain": "Standard English Conventions", "skill": "Form, Structure, and Sense", "difficulty": "M", "type": "mc", "stimulus": "

Far from being modern inventions, ______blank more than 5,000 years ago.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

Sumerians in ancient Mesopotamia used drinking straws

"}, {"id": "B", "text": "

drinking straws were used by Sumerians in ancient Mesopotamia

"}, {"id": "C", "text": "

the use of drinking straws by Sumerians in ancient Mesopotamia happened

"}, {"id": "D", "text": "

ancient Mesopotamia was home to Sumerians who used drinking straws

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. Modifiers and their subjects must go next to each other. The modifier “far from being modern inventions” must be describing “drinking straws,” because those are the only possible inventions in this sentence.

Choice A is incorrect. Modifiers and their subjects must go next to each other. The modifier “far from being modern inventions” can’t be describing “Sumerians,” because they are a group of people, not an invention. Choice C is incorrect. Modifiers and their subjects must go next to each other. The modifier “far from being modern inventions” can’t be describing “the use of drinking straws,” because it is not “the use” of drinking straws that is an invention—it is the drinking straws themselves. Choice D is incorrect. Modifiers and their subjects must go next to each other. The modifier “far from being modern inventions” can’t be describing “Ancient Mesopotamia,” because that is a place, not an invention.

"}, {"id": "f30a478e", "domain": "Standard English Conventions", "skill": "Boundaries", "difficulty": "H", "type": "mc", "stimulus": "

A study published by Rice University geoscientist Ming Tang in 2019 offers a new explanation for the origin of Earth’s ______blank structures called arcs, towering ridges that form when a dense oceanic plate subducts under a less dense continental plate, melts in the mantle below, and then rises and bursts through the continental crust above.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

continents geological

"}, {"id": "B", "text": "

continents: geological

"}, {"id": "C", "text": "

continents; geological

"}, {"id": "D", "text": "

continents. Geological

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. The convention being tested is punctuation use between a main clause and a supplementary phrase. In this choice, a colon is correctly used to mark the boundary between the main clause (“A study…continents”) and the supplementary phrase (“geological…above”) and to introduce the following explanation of the origin of Earth’s continents.

Choice A is incorrect because it fails to mark the boundary between the main clause (“A study…continents”) and the supplementary phrase (“geological…above”) with appropriate punctuation. Choice C is incorrect because a semicolon can’t be used in this way to join the main clause (“A study…continents”) and the supplementary phrase (“geological…above”). A semicolon is conventionally used to join two main clauses, whereas a colon is conventionally used to introduce an element that explains or amplifies the information in the preceding clause, making it the better choice in this context. Choice D is incorrect because it results in a rhetorically unacceptable sentence fragment beginning with “geological.”

"}, {"id": "67667d72", "domain": "Standard English Conventions", "skill": "Boundaries", "difficulty": "M", "type": "mc", "stimulus": "

Humans were long thought to have begun occupying the Peruvian settlement of Machu Picchu between 1440 and 1450 CE. However, a team led by anthropologist Dr. Richard Burger used accelerator mass spectrometry to uncover evidence that it was occupied ______blank 1420 CE, according to Burger, humans were likely inhabiting the area.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

earlier. In

"}, {"id": "B", "text": "

earlier, in

"}, {"id": "C", "text": "

earlier, which in

"}, {"id": "D", "text": "

earlier in

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. The convention being tested is punctuation use between sentences. In this choice, the period is used correctly to mark the boundary between one sentence (“However...earlier”) and another (“In...area”). The supplementary phrase “in 1420 CE” modifies “humans,” the subject of the third sentence.

Choice B is incorrect because it results in a comma splice. A comma can’t be used in this way to mark the boundary between sentences. Choice C is incorrect because it results in a comma splice. A comma can’t be used in this way to mark the boundary between sentences. Moreover, the subordinating conjunction “which” creates a confusing and illogical sentence that suggests that the supplementary phrase beginning with “in” modifies the previous information (“However...earlier”) rather than the information that follows. Choice D is incorrect because it results in a run-on sentence. The sentences (“However...earlier” and “in...area”) are fused without punctuation and/or a conjunction.

"}, {"id": "dd428136", "domain": "Standard English Conventions", "skill": "Form, Structure, and Sense", "difficulty": "M", "type": "mc", "stimulus": "

Cheng Dang and her colleagues at the University of Washington recently ran simulations to determine the extent to which individual snow ______blank affect the amount of light reflecting off a snowy surface.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

grain’s physical properties’

"}, {"id": "B", "text": "

grains’ physical properties

"}, {"id": "C", "text": "

grains’ physical property’s

"}, {"id": "D", "text": "

grains physical properties

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. The convention being tested is the use of plural and possessive nouns. The plural possessive noun “grains’” and the plural noun “properties” correctly indicate that the simulations involved multiple snow grains and that those snow grains had several properties.

Choice A is incorrect because the context requires the plural possessive noun “grains’” and the plural noun “properties,” not the singular possessive noun “grain’s” and the plural possessive noun “properties’.” Choice C is incorrect because the context requires the plural noun “properties,” not the singular possessive noun “property’s.” Choice D is incorrect because the context requires the plural possessive noun “grains’,” not the plural noun “grains.”

"}, {"id": "04bfd364", "domain": "Standard English Conventions", "skill": "Boundaries", "difficulty": "E", "type": "mc", "stimulus": "

The intense pressure found in the deep ocean can affect the structure of proteins in fish’s cells, distorting the proteins’ shape. The chemical trimethylamine N-oxide (TMAO) counters this effect, ensuring that proteins retain their original ______blank is found in high concentrations in the cells of the deepest-dwelling fish.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

configurations. TMAO

"}, {"id": "B", "text": "

configurations TMAO

"}, {"id": "C", "text": "

configurations, TMAO

"}, {"id": "D", "text": "

configurations and TMAO

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. The convention being tested is punctuation use between sentences. In this choice, the period after “configurations” is used correctly to mark the boundary between one sentence (“The intense…configurations”) and another (“TMAO…fish”). The supplementary phrase (“ensuring…configurations”) modifies the main clause of the first sentence (“The chemical…effect”), and “TMAO” is the subject of the second sentence.

Choice B is incorrect because it results in a run-on sentence. The sentences  (“The intense…configurations” and “TMAO…fish”) are fused without punctuation and/or a conjunction. Choice C is incorrect because it results in a comma splice. A comma can’t be used in this way to mark the boundary between sentences. Choice D is incorrect. Without a comma preceding it, the conjunction “and” can’t be used in this way to join sentences.

"}, {"id": "ea8f4658", "domain": "Standard English Conventions", "skill": "Boundaries", "difficulty": "E", "type": "mc", "stimulus": "

When particles are suspended in liquid (like pollen in a water glass), they will zigzag randomly through the liquid and collide with one another in perpetuity. This type of random, continuous ______blank is known as Brownian motion, can be observed throughout the natural world.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

movement: which

"}, {"id": "B", "text": "

movement, which

"}, {"id": "C", "text": "

movement which

"}, {"id": "D", "text": "

movement. Which

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. This choice correctly uses commas to set off the nonessential relative clause \"which is known as Brownian motion\" that provides extra information about the \"random, continuous movement\" that isn’t necessary for the function of the sentence.

Choice A is incorrect. This choice results in a punctuation error. The relative clause \"which is known as Brownian motion\" is a nonessential supplement. Nonessential supplements need to be set apart from the rest of the sentence with a pair of commas, dashes, or parentheses, so we can’t use a colon here. Also, notice that colons can only come after an independent clause, which isn’t the case here. Choice C is incorrect. This choice results in a punctuation error. The relative clause \"which is known as Brownian motion\" is a nonessential supplement, so it should be separated from the rest of the sentence by a pair of matching punctuation marks. We already have a comma after \"motion,\" so we need to add a comma before \"which.\" This choice is missing that comma. Choice D is incorrect. This choice results in a sentence fragment. \"This type of random, continuous movement\" is not an independent clause and can’t stand alone as a full sentence, so we can’t put a period here.

"}, {"id": "775f3eb9", "domain": "Standard English Conventions", "skill": "Form, Structure, and Sense", "difficulty": "E", "type": "mc", "stimulus": "

In his groundbreaking book Bengali Harlem and the Lost Histories of South Asian America, Vivek Bald uses newspaper articles, census records, ships’ logs, and memoirs to tell the ______blank who made New York City their home in the early twentieth century.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

story’s of the South Asian immigrants

"}, {"id": "B", "text": "

story’s of the South Asian immigrants’

"}, {"id": "C", "text": "

stories of the South Asian immigrants

"}, {"id": "D", "text": "

stories’ of the South Asian immigrant’s

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. The convention being tested is the use of plural and possessive nouns. The plural nouns “stories” and “immigrants” correctly indicate that the memoir tells multiple stories of multiple immigrants.

Choice A is incorrect because the context requires the plural noun “stories,” not the singular possessive noun “story’s.” Choice B is incorrect because the context requires the plural nouns “stories” and “immigrants,” not the singular possessive noun “story’s” and the plural possessive noun “immigrants’.” Choice D is incorrect because the context requires the plural nouns “stories” and “immigrants,” not the plural possessive noun “stories’” and the singular possessive noun “immigrant’s.”

"}, {"id": "b6560e5a", "domain": "Standard English Conventions", "skill": "Boundaries", "difficulty": "M", "type": "mc", "stimulus": "

Materials scientist Marie-Agathe Charpagne and her colleagues believed they could improve on the multicomponent alloy NiCoCr, an equal-proportions mixture of nickel (Ni), cobalt (Co), and chromium (Cr), by replacing chromium with ruthenium ______blank the alloy that resulted, NiCoRu, turned out to be an unsuitable replacement for NiCoCr.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

(Ru)

"}, {"id": "B", "text": "

(Ru) but

"}, {"id": "C", "text": "

(Ru),

"}, {"id": "D", "text": "

(Ru), but

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. The convention being tested is the coordination of main clauses. This choice correctly uses a comma and the coordinating conjunction “but” to join the first main clause (“Materials…Ru”) and the second main clause (“the alloy…NiCoCr”).

Choice A is incorrect because it results in a run-on sentence. The two main clauses are fused without punctuation and/or a conjunction. Choice B is incorrect because when coordinating two longer main clauses such as these, it’s conventional to use a comma before the coordinating conjunction. Choice C is incorrect because it results in a comma splice. Without a conjunction following it, a comma can’t be used in this way to join two main clauses. 

"}, {"id": "5b8f9cf2", "domain": "Standard English Conventions", "skill": "Form, Structure, and Sense", "difficulty": "H", "type": "mc", "stimulus": "

In the canon of North African literature, Moroccan author Driss Chraïbi’s 1954 novel The Simple Past (Le Passé simple) looms large. A coming-of-age story, a social meditation, and a sober gaze into the dark maw of French colonialism, ______blank interrogates systemic power with memorable intensity.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

Morocco gained its independence two years before the publication of Chraïbi’s debut novel, which

"}, {"id": "B", "text": "

Chraïbi’s debut novel, published two years before Morocco gained its independence,

"}, {"id": "C", "text": "

Chraïbi wrote a debut novel that, published two years before Morocco gained its independence,

"}, {"id": "D", "text": "

published two years before Morocco gained its independence, Chraïbi wrote a debut novel that

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. Subject-modifier placement requires a modifier and its subject to be next to each other. The subject of the modifier \"a coming-of-age story…colonialism\" is Chraïbi’s novel The Simple Past, so the subject \"Chraïbi’s debut novel\" fits perfectly after this introductory modifying phrase.

Choice A is incorrect. Modifiers and their subjects must go next to each other. The introductory modifier \"a coming-of-age story…colonialism\" is describing Chraïbi’s novel, not Morocco. However, this choice places Morocco directly next to that modifier. Choice C is incorrect. Modifiers and their subjects must go next to each other. The introductory modifier \"a coming-of-age story…colonialism\" all describes Chraïbi’s novel, not Chraïbi himself. However, this choice places Chraïbi directly next to that modifier. Choice D is incorrect. Modifiers and their subjects must go next to each other. The modifier \"a coming-of-age story…\" is describing Chraïbi’s novel, so that needs to be the subject immediately after the modifier. This choice adds another modifier that describes Chraïbi’s novel, but then puts \"Chraïbi\" himself—not the novel—right after that modifier, which doesn’t make sense. Chraïbi wasn’t \"published two years before\" Moroccan independence; his novel The Simple Past was.

"}, {"id": "b5b74c3f", "domain": "Standard English Conventions", "skill": "Form, Structure, and Sense", "difficulty": "E", "type": "mc", "stimulus": "

When writing The Other Black Girl (2021), novelist Zakiya Dalila Harris drew on her own experiences working at a publishing office. The award-winning book is Harris’s first novel, but her writing ______blank honored before. At the age of twelve, she entered a contest to have a story published in American Girl magazine—and won.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

were

"}, {"id": "B", "text": "

have been

"}, {"id": "C", "text": "

has been

"}, {"id": "D", "text": "

are

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. The convention being tested is subject-verb agreement. The singular verb “has been” agrees in number with the singular subject “writing.”

Choice A is incorrect because the plural verb “were” doesn’t agree in number with the singular subject “writing.” Choice B is incorrect because the plural verb “have been” doesn’t agree in number with the singular subject “writing.” Choice D is incorrect because the plural verb “are” doesn’t agree in number with the singular subject “writing.”

"}, {"id": "432b1ede", "domain": "Standard English Conventions", "skill": "Boundaries", "difficulty": "M", "type": "mc", "stimulus": "

The forty-seven geothermal springs of Arkansas’ Hot Springs National Park are sourced via a process known as natural groundwater recharge, in which rainwater percolates downward through the earth—in this case, the porous rocks of the hills around Hot ______blank collect in a subterranean basin.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

Springs to

"}, {"id": "B", "text": "

Springs: to

"}, {"id": "C", "text": "

Springs—to

"}, {"id": "D", "text": "

Springs, to

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. The convention being tested is the punctuation of a supplementary element within a sentence. The dash after “Springs” pairs with the dash after “earth” to separate the supplementary element “in this case, the porous rocks of the hills around Hot Springs” from the rest of the sentence.

Choice A is incorrect because it fails to use appropriate punctuation to separate the supplementary element from the rest of the sentence. Choice B is incorrect because a colon can’t be paired with a dash in this way to separate the supplementary element from the rest of the sentence. Choice D is incorrect because a comma can’t be paired with a dash in this way to separate the supplementary element from the rest of the sentence.

"}, {"id": "c21df211", "domain": "Standard English Conventions", "skill": "Boundaries", "difficulty": "E", "type": "mc", "stimulus": "

In 1959, the film industry debuted Smell-O-Vision. Theaters were fitted with specialized vents that emitted odors at specific points in a ______blank as the scent of roses when roses appeared in a scene. Smell-O-Vision failed to impress, however, with one reviewer declaring it “briefly weird and not very interesting.”

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

movie such

"}, {"id": "B", "text": "

movie; such

"}, {"id": "C", "text": "

movie. Such

"}, {"id": "D", "text": "

movie, such

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. The comma appropriately separates the nonessential descriptive aside \"such as…scene\" from the independent clause \"Theaters were…movie.\" Since the descriptive example of roses isn’t necessary for the sentence to function, it needs to be set off with punctuation.

Choice A is incorrect. This choice results in a run-on sentence. Since the example of roses isn’t necessary for the sentence to function, the descriptive aside \"such as…scene\" needs to be separated from the preceding independent clause with some sort of punctuation. Choice B is incorrect. This choice creates a punctuation error. A semicolon can only be used to separate two independent clauses, but \"such…scene\" is not an independent clause and couldn’t stand on its own as a sentence. Choice C is incorrect. This choice results in a sentence fragment. The descriptive aside \"Such…scene\" is not an independent clause and can’t stand on its own as a sentence.

"}, {"id": "50445680", "domain": "Standard English Conventions", "skill": "Form, Structure, and Sense", "difficulty": "E", "type": "mc", "stimulus": "

In winter, the diets of Japanese macaques, also known as snow monkeys, are influenced more by food availability than by food preference. Although the monkeys prefer to eat vegetation and land-dwelling invertebrates, those food sources may become unavailable because of extensive snow and ice cover, ______blank the monkeys to hunt for marine animals in any streams that have not frozen over.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

forces

"}, {"id": "B", "text": "

to force

"}, {"id": "C", "text": "

forcing

"}, {"id": "D", "text": "

forced

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. The convention being tested is the use of finite and nonfinite verb forms within a sentence. The nonfinite present participle “forcing” is correctly used to form a participial phrase that supplements the main clause “those...cover,” describing the effects on monkeys of the lack of food sources.

Choice A is incorrect because the finite present tense verb “forces” can’t be used in this way to supplement the main clause (“those...cover”). Choice B is incorrect. While the nonfinite to-infinitive “to force” could be used to form a subordinate clause that supplements the main clause (“those...cover”), to-infinitives conventionally express purpose, and nothing in the sentence suggests that the food sources become unavailable for the purpose of forcing monkeys to hunt marine animals. Choice D is incorrect because the finite past tense verb “forced” can’t be used in this way to supplement the main clause (“those...cover”).

"}, {"id": "267a13e2", "domain": "Standard English Conventions", "skill": "Boundaries", "difficulty": "M", "type": "mc", "stimulus": "

In 2010, archaeologist Noel Hidalgo Tan was visiting the twelfth-century temple of Angkor Wat in Cambodia when he noticed markings of red paint on the temple ______blank the help of digital imaging techniques, he discovered the markings to be part of an elaborate mural containing over 200 paintings.   

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

walls, with

"}, {"id": "B", "text": "

walls with 

"}, {"id": "C", "text": "

walls so with 

"}, {"id": "D", "text": "

walls. With

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. The convention being tested is punctuation use between sentences. In this choice, the period after “walls” is used correctly to mark the boundary between the first sentence (“In...walls”) and the second sentence (“With…techniques”), which starts with a supplementary phrase.

Choice A is incorrect because it results in a comma splice. A comma can’t be used in this way to mark the boundary between sentences. Choice B is incorrect because it results in a run-on sentence. The sentences (“In...walls” and “with...paintings”) are fused without punctuation and/or a conjunction. Choice C is incorrect. Without a comma preceding it, the conjunction “so” can’t be used in this way to join sentences.

"}, {"id": "403d7bb5", "domain": "Standard English Conventions", "skill": "Boundaries", "difficulty": "M", "type": "mc", "stimulus": "

According to Naomi Nakayama of the University of Edinburgh, the reason seeds from a dying dandelion appear to float in the air while ______blank is that their porous plumes enhance drag, allowing the seeds to stay airborne long enough for the wind to disperse them throughout the surrounding area.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

falling,

"}, {"id": "B", "text": "

falling:

"}, {"id": "C", "text": "

falling;

"}, {"id": "D", "text": "

falling

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. The word “falling” occurs in the middle of a clause and isn’t part of a supplement, so we don’t need any punctuation after it. We can see this more clearly if we simplify the rest of the sentence: “The reason seeds appear to float while falling is that their plumes enhance drag.” .

Choice A is incorrect. This doesn’t complete the text in a way that conforms to the conventions of Standard English. The word “falling” occurs in the middle of a clause and isn’t part of a supplement, so we don’t need any punctuation after it. We can see this more clearly if we simplify the sentence: “The reason seeds appear to float while falling is that their plumes enhance drag.” . Choice B is incorrect. This doesn’t complete the text in a way that conforms to the conventions of Standard English. The word “falling” occurs in the middle of a clause and isn’t part of a supplement, so we don’t need any punctuation after it. We can see this more clearly if we simplify the sentence: “The reason seeds appear to float while falling is that their plumes enhance drag.” . Choice C is incorrect. This doesn’t complete the text in a way that conforms to the conventions of Standard English. The word “falling” occurs in the middle of a clause and isn’t part of a supplement, so we don’t need any punctuation after it. We can see this more clearly if we simplify the sentence: “The reason seeds appear to float while falling is that their plumes enhance drag.” .

"}, {"id": "de3dd17d", "domain": "Standard English Conventions", "skill": "Form, Structure, and Sense", "difficulty": "H", "type": "mc", "stimulus": "

Planetary scientist Briony Horgan and her colleagues have determined that as much as 25 percent of the sand on Mars is composed of impact spherules. These spherical bits of glass form when asteroids collide with the planet, ejecting bits of molten rock into the atmosphere that, after cooling and solidifying into glass, ______blank back onto Mars’s surface.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

to rain

"}, {"id": "B", "text": "

raining

"}, {"id": "C", "text": "

having rained

"}, {"id": "D", "text": "

rain

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. \"That…[rain] back onto Mars’s surface\" is a relative clause that describes the \"bits of molten rock.\" Forming the clause requires a conjugated, finite verb, and this is the only choice that provides that.

Choice A is incorrect. \"To rain\" is an infinitive and can’t serve as the main verb of a clause. A conjugated verb is needed here to form the main verb of the relative clause \"that…[rain] back onto Mars’s surface,\" which describes the \"bits of molten rock.\" Choice B is incorrect. \"Raining\" is a present participle and, on its own, can’t serve as the main verb of a clause. A conjugated verb is needed here to form the main verb of the relative clause \"that…[rain] back onto Mars’s surface,\" which describes the \"bits of molten rock.\" Choice C is incorrect. \"Having rained\" is a perfect participle and can’t serve as the main verb of a clause. A conjugated verb is needed here to form the main verb of the relative clause \"that…[rain] back onto Mars’s surface,\" which describes the \"bits of molten rock.\"

"}, {"id": "6b49f5f1", "domain": "Standard English Conventions", "skill": "Boundaries", "difficulty": "M", "type": "mc", "stimulus": "

In 1727, dramatist Lewis Theobald presented a new play, Double Falsehood, at a London theater. Theobald claimed that his drama was based on a little-known play by William Shakespeare, Cardenio. Many, including poet Alexander Pope, were ______blank historians have determined that Shakespeare’s company did perform a play called Cardenio in 1613.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

skeptical but

"}, {"id": "B", "text": "

skeptical, but

"}, {"id": "C", "text": "

skeptical,

"}, {"id": "D", "text": "

skeptical

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. There are two independent clauses in the sentence, each with a subject and a verb: \"many...were skeptical\" and \"historians have determined….\" These clauses can be grammatically joined by a comma and the coordinating conjunction \"but.\"

Choice A is incorrect. This choice results in a run-on sentence, which occurs when two independent clauses are joined without punctuation. Two independent clauses can’t be joined by just the coordinating conjunction \"but.\" A comma would also be required. Choice C is incorrect. This choice creates a punctuation error called a comma splice. This sentence contains two independent clauses (\"Many…were skeptical\" and \"historians have determined…\"). A comma alone can’t join two independent clauses. That requires a comma and a coordinating conjunction. Choice D is incorrect. This choice results in a run-on sentence, which occurs when two independent clauses are joined without punctuation. This sentence contains two independent clauses (\"Many…were skeptical\" and \"historians have determined…\"), which need to be either joined by a semicolon, joined by a comma and a coordinating conjunction, or separated by a period.

"}, {"id": "2dd1b8bf", "domain": "Standard English Conventions", "skill": "Form, Structure, and Sense", "difficulty": "H", "type": "mc", "stimulus": "

Compared to that of alumina glass, ______blank silica glass atoms are so far apart that they are unable to re-form bonds after being separated.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

silica glass is at a significant disadvantage due to its more dispersed atomic arrangement:

"}, {"id": "B", "text": "

silica glass has a more dispersed atomic arrangement, resulting in a significant disadvantage:

"}, {"id": "C", "text": "

a significant disadvantage of silica glass is that its atomic arrangement is more dispersed:

"}, {"id": "D", "text": "

silica glass’s atomic arrangement is more dispersed, resulting in a significant disadvantage:

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. The convention being tested is subject-modifier placement. This choice makes “silica glass’s atomic arrangement” the subject of the sentence and places it immediately after the modifying phrase “compared to that of alumina glass.” In doing so, this choice clearly establishes that silica glass’s atomic arrangement—and not another noun in the sentence—is being compared to the atomic arrangement (“that”) of alumina glass.

Choice A is incorrect because it results in a dangling modifier. The placement of the noun phrase “silica glass” immediately after the modifying phrase illogically suggests that silica glass itself (rather than its atomic arrangement) is being compared to alumina glass’s atomic arrangement. Choice B is incorrect because it results in a dangling modifier. The placement of the noun phrase “silica glass” immediately after the modifying phrase illogically suggests that silica glass itself (rather than its atomic arrangement) is being compared to alumina glass’s atomic arrangement. Choice C is incorrect because it results in a dangling modifier. The placement of the noun phrase “a significant disadvantage” immediately after the modifying phrase illogically suggests that “a significant disadvantage” is being compared to alumina glass’s atomic arrangement.

"}, {"id": "577b09fa", "domain": "Standard English Conventions", "skill": "Boundaries", "difficulty": "E", "type": "mc", "stimulus": "

Robin Wall Kimmerer of the Citizen Potawatomi Nation is a bryologist, a plant scientist who specializes in mosses. To Kimmerer, mosses are Earth’s most adaptable plants: they can clone ______blank enter a dormant state in times of drought, and grow in areas that don’t have soil.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

themselves;

"}, {"id": "B", "text": "

themselves,

"}, {"id": "C", "text": "

themselves. And

"}, {"id": "D", "text": "

themselves

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. The convention being tested is the punctuation of items in a series. The comma after “themselves” is used conventionally to separate the first item (“they can clone themselves”) and the second item (“enter a dormant state in times of drought”) in the series of things mosses can do. 

Choice A is incorrect because a semicolon can’t be used in this way to separate items in a simple series such as this. Choice C is incorrect because it results in a rhetorically unacceptable sentence fragment beginning with “And enter.” Choice D is incorrect because it fails to use appropriate punctuation to separate the first and second items in the series.

"}, {"id": "59094d87", "domain": "Standard English Conventions", "skill": "Boundaries", "difficulty": "H", "type": "mc", "stimulus": "

The Tantaquidgeon Museum in Uncasville, Connecticut, was founded in 1931 with the goal of showcasing the culture and history of the Mohegan ______blank today, nearly a century later, it is the oldest Native-owned and -operated museum in the country.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

Tribe, and

"}, {"id": "B", "text": "

Tribe

"}, {"id": "C", "text": "

Tribe and

"}, {"id": "D", "text": "

Tribe,

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. This choice uses a comma and a coordinating conjunction (“and”) to join two independent clauses (“The Tantaquidgeon…Tribe” and “Today…country”).

Choice B is incorrect. This choice results in a grammar error known as a run-on sentence. The clauses before and after “Tribe” are both independent, so they need to be separated with some sort of punctuation. Choice C is incorrect. This choice results in a grammar error known as a run-on sentence. The clauses before and after “and” are both independent, so they can’t be linked with just a conjunction. A comma would also be required. Choice D is incorrect. This choice results in a grammar error called a comma splice. The clauses before and after “Tribe” are both independent, so they can’t be linked with just a comma. A coordinating conjunction like “and” or “but” would also be required.

"}, {"id": "0ff8477b", "domain": "Standard English Conventions", "skill": "Form, Structure, and Sense", "difficulty": "E", "type": "mc", "stimulus": "

Food and the sensation of taste are central to Monique Truong’s novels. In The Book of Salt, for example, the exiled character of Bình connects to his native Saigon through the food he prepares, while in Bitter in the Mouth, the character of Linda ______blank a form of synesthesia whereby the words she hears evoke tastes.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

experienced

"}, {"id": "B", "text": "

had experienced

"}, {"id": "C", "text": "

experiences

"}, {"id": "D", "text": "

will be experiencing

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. The convention being tested is the use of verbs to express tense. In this choice, the present tense verb “experiences” is consistent with the other present tense verbs (e.g., “connects” and “prepares”) used to describe the events in Truong’s novels. Furthermore, it’s conventional to use the present tense when discussing a literary work.

Choice A is incorrect because the past tense verb “experienced” isn’t consistent with the other present tense verbs used to describe the events in Truong’s novels. Choice B is incorrect because the past perfect tense verb “had experienced” isn’t consistent with the other present tense verbs used to describe the events in Truong’s novels. Choice D is incorrect because the future progressive tense verb “will be experiencing” isn’t consistent with the other present tense verbs used to describe the events in Truong’s novels.

"}, {"id": "b260c65a", "domain": "Standard English Conventions", "skill": "Form, Structure, and Sense", "difficulty": "E", "type": "mc", "stimulus": "

Earth is not a perfect sphere. Due to the ______blank gravitational pull, Earth bulges out on the sides closest to and farthest from the Moon. This distorting pull is known as a tidal force, and it is responsible for the changes in water levels that are called high and low tides.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

Moon’s

"}, {"id": "B", "text": "

Moons

"}, {"id": "C", "text": "

Moons’

"}, {"id": "D", "text": "

Moon

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. The convention being tested is the use of possessive nouns. The singular possessive noun \"Moon’s\" correctly indicates that there is only one Moon, and it has a gravitational pull.

Choice B is incorrect because the context requires the singular possessive noun \"Moon’s,\" not the plural noun \"Moons.\" Choice C is incorrect because the context requires the singular possessive noun \"Moon’s,\" not the plural possessive noun \"Moons’.\" Choice D is incorrect because the context requires the singular possessive noun \"Moon’s,\" not the singular noun \"Moon.\"

"}, {"id": "9f737b2a", "domain": "Standard English Conventions", "skill": "Form, Structure, and Sense", "difficulty": "M", "type": "mc", "stimulus": "

In Death Valley National Park’s Racetrack Playa, a flat, dry lakebed, are 162 rocks—some weighing less than a pound but others almost 700 pounds—that move periodically from place to place, seemingly of their own volition. Racetrack-like trails in the ______blank mysterious migration.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

playas sediment mark the rock’s

"}, {"id": "B", "text": "

playa’s sediment mark the rocks

"}, {"id": "C", "text": "

playa’s sediment mark the rocks’

"}, {"id": "D", "text": "

playas’ sediment mark the rocks’ 

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. The convention being tested is the use of plural and possessive nouns. The singular possessive noun “playa’s” and the plural possessive noun “rocks’” correctly indicate that the sediment is that of one playa (the Racetrack Playa) and that there are multiple rocks that have mysteriously migrated across the sediment.

Choice A is incorrect because the context requires the singular possessive noun “playa’s” and the plural possessive noun “rocks’,” not the plural noun “playas” and the singular possessive noun “rock’s.” Choice B is incorrect because the context requires the plural possessive noun “rocks’,” not the plural noun “rocks.” Choice D is incorrect because the context requires the singular possessive noun “playa’s,” not the plural possessive noun “playas’.” 

"}, {"id": "c52652c9", "domain": "Standard English Conventions", "skill": "Form, Structure, and Sense", "difficulty": "M", "type": "mc", "stimulus": "

The human brain is primed to recognize faces—so much so that, due to a perceptual tendency called pareidolia, ______blank will even find faces in clouds, wooden doors, pieces of fruit, and other faceless inanimate objects. Researcher Susan Magsamen has focused her work on better understanding this everyday phenomenon.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

she

"}, {"id": "B", "text": "

they

"}, {"id": "C", "text": "

it

"}, {"id": "D", "text": "

those

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. \"It\" is a singular pronoun used to stand in for objects. Since the antecedent in this case is the singular noun phrase \"the human brain,\" \"it\" is a perfect pronoun to use here.

Choice A is incorrect. Although \"she\" is a singular pronoun, it is reserved for people and animals, not objects like \"the human brain.\" Choice B is incorrect. \"They\" is a plural pronoun, but we need a singular pronoun to represent the antecedent \"the human brain.\" Choice D is incorrect. \"Those\" is a plural pronoun, but we need a singular pronoun to represent the antecedent \"the human brain.\"

"}, {"id": "ba8ebf49", "domain": "Standard English Conventions", "skill": "Boundaries", "difficulty": "H", "type": "mc", "stimulus": "

The poem Beowulf begins with the word “hwæt,” which is an Old English ______blank as “hark!” or “listen!” in some versions, the word was playfully rendered as “bro!” by Maria Dahvana Headley in her 2020 translation of the poem.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

exclamation, translated

"}, {"id": "B", "text": "

exclamation and translated

"}, {"id": "C", "text": "

exclamation translated

"}, {"id": "D", "text": "

exclamation. Translated

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. The convention being tested is punctuation use between sentences. In this choice, the period is used correctly to mark the boundary between one sentence (\"The poem…exclamation\") and another sentence that begins with a supplementary element (\"Translated…poem\"). The supplementary element \"translated as ‘hark!’ or ‘listen!’ in some versions\" modifies the subject of the second sentence, \"the word\" (referring to hwæt).

Choice A is incorrect because it results in a comma splice after \"exclamation.\" A comma can’t be used in this way to mark the boundary between sentences. Choice B is incorrect. Without a comma preceding it, the conjunction \"and\" can’t be used in this way to join sentences. Choice C is incorrect because it results in a comma splice after \"versions.\" A comma can’t be used in this way to mark the boundary between sentences.

"}, {"id": "188f7e3c", "domain": "Standard English Conventions", "skill": "Form, Structure, and Sense", "difficulty": "H", "type": "mc", "stimulus": "

In 2016, engineer Vanessa Galvez oversaw the installation of 164 bioswales, vegetated channels designed to absorb and divert stormwater, along the streets of Queens, New York. By reducing the runoff flowing into city sewers, ______blank

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

the mitigation of both street flooding and the resulting pollution of nearby waterways has been achieved by bioswales.

"}, {"id": "B", "text": "

the bioswales have mitigated both street flooding and the resulting pollution of nearby waterways.

"}, {"id": "C", "text": "

the bioswales’ mitigation of both street flooding and the resulting pollution of nearby waterways has been achieved.

"}, {"id": "D", "text": "

both street flooding and the resulting pollution of nearby waterways have been mitigated by bioswales.

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. The convention being tested is subject-modifier placement. This choice makes the noun phrase “the bioswales” the subject of the sentence and places it immediately after the modifying phrase “By reducing…sewers.” In doing so, this choice clearly establishes that the bioswales—and not another noun in the sentence—are reducing runoff flowing into city sewers.

Choice A is incorrect because it results in a dangling modifier. The placement of the noun phrase “the mitigation…waterways” immediately after the modifying phrase results in unclear modification. The resulting sentence makes it hard to determine what is responsible for “reducing the runoff”: the bioswales or some other noun in the sentence. Choice C is incorrect because it results in a dangling modifier. The placement of the noun phrase “the bioswales’ mitigation…waterways”  immediately after the modifying phrase results in unclear modification. The resulting sentence makes it hard to determine what is responsible for “reducing the runoff”: the bioswales or some other noun in the sentence. Choice D is incorrect because it results in a dangling modifier. The placement of the noun phrase “street flooding and the resulting pollution” immediately after the modifying phrase illogically suggests that the “flooding and pollution” are reducing runoff flowing into city sewers.

"}, {"id": "36944347", "domain": "Standard English Conventions", "skill": "Form, Structure, and Sense", "difficulty": "M", "type": "mc", "stimulus": "

Official measurements of the Mississippi River’s length vary: according to the US Geologic Survey, the river is 2,300 miles long, whereas the Environmental Protection Agency records its length as 2,320 miles. This disparity can be explained in part by the fact that rivers such as the Mississippi expand and contract as ______blank sediment.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

they accumulate

"}, {"id": "B", "text": "

one accumulates

"}, {"id": "C", "text": "

it accumulates

"}, {"id": "D", "text": "

we accumulate

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. The noun that goes with \"expand and contract\" is \"rivers,\" a plural noun. \"They\" is a third-person plural pronoun, so it can correctly stand in for \"rivers.\"

Choice B is incorrect. This choice creates a pronoun-antecedent agreement error. \"One\" is a singular pronoun, but the noun that goes with \"expand and contract\" is \"rivers,\" a plural noun. Choice C is incorrect. This choice creates a pronoun-antecedent agreement error. \"It\" is a singular pronoun, but the noun that goes with \"expand and contract\" is \"rivers,\" a plural noun. Choice D is incorrect. This choice creates a pronoun-antecedent agreement error. The noun that goes with \"expand and contract\" is the plural noun \"rivers.\" Rivers are not people, so \"we\" can’t be used to stand in for it.

"}, {"id": "a466679a", "domain": "Standard English Conventions", "skill": "Boundaries", "difficulty": "E", "type": "mc", "stimulus": "

In 1976, the Inuit rock group Sikumiut recorded the album People of the Ice. Though only their first record, it shows a band already skilled at the difficult task of making music that sounds easy and fun. On songs like “Utirumavunga,” Lucassie Koperqualuk’s guitar riffs effortlessly ______blank Charlie Adams’s delightfully catchy vocal melodies.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

blend, with

"}, {"id": "B", "text": "

blend. With

"}, {"id": "C", "text": "

blend; with

"}, {"id": "D", "text": "

blend with

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. The convention being tested is punctuation between a verb and a prepositional phrase. No punctuation is needed between the verb “blend” and the prepositional phrase “with Charlie Adams’s delightfully catchy vocal melodies.” The prepositional phrase completes the idea of the sentence, explaining with what Koperqualuk’s guitar riffs blend.

Choice A is incorrect because no punctuation is needed between the verb and the prepositional phrase.  Choice B is incorrect because no punctuation is needed between the verb and the prepositional phrase.  Choice C is incorrect because no punctuation is needed between the verb and the prepositional phrase.  

"}, {"id": "a8fa749a", "domain": "Standard English Conventions", "skill": "Boundaries", "difficulty": "H", "type": "mc", "stimulus": "

Nigerian author Buchi Emecheta’s celebrated literary oeuvre includes The Joys of Motherhood, a novel about the changing roles of women in 1950s ______blank a television play about the private struggles of a newlywed couple in Nigeria; and Head Above Water, her autobiography.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

Lagos, A Kind of Marriage,

"}, {"id": "B", "text": "

Lagos; A Kind of Marriage,

"}, {"id": "C", "text": "

Lagos, A Kind of Marriage:

"}, {"id": "D", "text": "

Lagos; A Kind of Marriage

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. The convention being tested is the punctuation of items in a complex series (a series including internal punctuation). In this choice, the semicolon after “Lagos” is conventionally used to separate the first item (“The Joys…Lagos”) and the second item (“A Kind…Nigeria”) in the series. Further, the comma after “Marriage” correctly separates the title “A Kind of Marriage” from the supplementary phrase (“a television…Nigeria”) that describes it.

Choice A is incorrect because the comma after “Lagos” doesn’t match the semicolon used later in the series to separate the second item (“A Kind…Nigeria”) from the third item (“and…autobiography”). Choice C is incorrect because the comma after “Lagos” doesn’t match the semicolon used later in the series to separate the second item (“A Kind…Nigeria”) from the third item (“and…autobiography”). Additionally, a colon can’t be used in this way to separate the title “A Kind of Marriage” from the supplementary phrase (“a television…Nigeria”) that describes it. Choice D is incorrect because it fails to use appropriate punctuation to separate the title “A Kind of Marriage” from the supplementary phrase (“a television…Nigeria”) that describes it.

"}, {"id": "898f182c", "domain": "Standard English Conventions", "skill": "Form, Structure, and Sense", "difficulty": "E", "type": "mc", "stimulus": "

Richard Spikes was a prolific African American inventor known for his contributions to automotive engineering. Between 1907 and 1946, he patented many inventions, ______blank an automobile turn signal, a safety brake, and—most famously—the first automatic gearshift.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

included

"}, {"id": "B", "text": "

includes

"}, {"id": "C", "text": "

including

"}, {"id": "D", "text": "

will include

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. The convention being tested is the use of nonfinite verb forms within a sentence. The nonfinite present participle \"including\" is correctly used to form a participial phrase that supplements the main clause \"he patented many inventions,\" listing several of Spikes’s patented inventions.

Choice A is incorrect because the finite past tense verb \"included\" can’t be used in this way to supplement the main clause \"he patented many inventions.\" Choice B is incorrect because the finite present tense verb \"includes\" can’t be used in this way to supplement the main clause \"he patented many inventions.\" Choice D is incorrect because the finite future tense verb \"will include\" can’t be used in this way to supplement the main clause \"he patented many inventions.\"

"}, {"id": "6e5bf3a8", "domain": "Standard English Conventions", "skill": "Form, Structure, and Sense", "difficulty": "E", "type": "mc", "stimulus": "

Even though bats prefer very sweet nectar, the plants that attract them have evolved to produce nectar that is only moderately sweet. A recent study ______blank why: making sugar is energy-intensive, and it is more advantageous for plants to make a large amount of low-sugar nectar than a small amount of high-sugar nectar.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

explains

"}, {"id": "B", "text": "

explaining

"}, {"id": "C", "text": "

having explained

"}, {"id": "D", "text": "

to explain

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. The convention being tested is the use of finite and nonfinite verb forms within a sentence. A main clause requires a finite verb to perform the action of the subject (in this case, “a recent study”), and this choice supplies the finite present tense verb “explains” to indicate that the study explains why plants that attract bats have evolved to produce moderately sweet nectar. 

Choice B is incorrect because the nonfinite participle “explaining” doesn’t supply the main clause with a finite verb. Choice C is incorrect because the nonfinite participle “having explained” doesn’t supply the main clause with a finite verb. Choice D is incorrect because the nonfinite to-infinitive “to explain” doesn’t supply the main clause with a finite verb.

"}, {"id": "84658166", "domain": "Standard English Conventions", "skill": "Boundaries", "difficulty": "H", "type": "mc", "stimulus": "

In 1943, in the midst of World War II, mathematics professor Grace Hopper was recruited by the US military to help the war effort by solving complex equations. Hopper’s subsequent career would involve more than just ______blank as a pioneering computer programmer, Hopper would help usher in the digital age.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

equations, though:

"}, {"id": "B", "text": "

equations, though,

"}, {"id": "C", "text": "

equations. Though,

"}, {"id": "D", "text": "

equations though

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. The convention being tested is the use of punctuation to mark boundaries between supplements and clauses. The comma after “equations” is used to separate the independent clause (“Hopper’s…equation”) from the supplementary adverb phrase “though.” The colon after “though” is used to mark the boundary between the clause ending with “though” and the following clause (“as…age”). A colon used in this way introduces information that illustrates or explains information that has come before it. In this case, the colon after “though” introduces the following explanation of how Hopper’s subsequent career would involve more than just solving equations: she would become a pioneering computer programmer.

Choice B is incorrect because it results in a comma splice. A comma can’t be used in this way to join two independent clauses (“Hopper’s…though” and “as…age”) such as these. Choice C is incorrect because it results in an illogical sequence of sentences. Placing the period after “equations” and beginning the next sentence with “Though” illogically suggests that the following information (that Hopper would help usher in the digital age) is contrary to the information in the previous sentence (Hopper’s subsequent career would involve more than just solving equations). Instead, the information that follows supports the information from the previous sentence by explaining how her work and influence extended beyond solely solving equations. Choice D is incorrect because it results in a run-on sentence. The two independent clauses (“Hopper’s…though” and “as…age”) are fused without punctuation.

"}, {"id": "7c48a6dd", "domain": "Standard English Conventions", "skill": "Form, Structure, and Sense", "difficulty": "E", "type": "mc", "stimulus": "

In the late 1960s, inspired in part by the sight of laundry hanging on a clothesline, African American abstract painter Sam Gilliam began to create his iconic “Drape” paintings. He applied bold, saturated hues to large canvases and ______blank them from ceilings or walls, causing the drooping fabric to cascade in dramatic loops and curves.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

to have suspended

"}, {"id": "B", "text": "

suspending

"}, {"id": "C", "text": "

to suspend

"}, {"id": "D", "text": "

suspended

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. The past tense of \"suspended\" matches the past tense of \"applied,\" which has the same subject (\"he\") and takes place in the same context: \"He applied…and [he] suspended.\"

Choice A is incorrect. The perfect infinitive \"to have suspended\" doesn’t match the past tense of \"applied,\" and it can’t serve as a verb on its own. These are both verbs with the same subject and in the same context, so there’s no need to shift tenses. Choice B is incorrect. The present participle \"suspending\" doesn’t match the past tense of \"applied,\" and it can’t serve as a verb on its own. These are both verbs with the same subject and in the same context, so there’s no need to shift tenses. Choice C is incorrect. The infinitive \"to suspend\" doesn’t match the past tense of \"applied,\" and it can’t serve as a verb on its own. These are both verbs with the same subject and in the same context, so there’s no need to shift tenses.

"}, {"id": "5cc85f01", "domain": "Standard English Conventions", "skill": "Boundaries", "difficulty": "M", "type": "mc", "stimulus": "

A conceptual artist and designer embraced by both the art world and the fashion ______blank Mary Ping was chosen to curate the exhibition Front Row: Chinese American Designers for the Museum of Chinese in America.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

world

"}, {"id": "B", "text": "

world:

"}, {"id": "C", "text": "

world;

"}, {"id": "D", "text": "

world,

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. The convention being tested is punctuation between a supplementary phrase and a main clause. This choice correctly uses a comma to mark the boundary between the supplementary phrase (“A conceptual artist…world”), which describes Mary Ping, and the main clause (“Mary…America”).

Choice A is incorrect because it fails to mark the boundary between the supplementary phrase (“A conceptual artist…world”) and the main clause (“Mary…America”) with appropriate punctuation. Choice B is incorrect because a colon can’t be used in this way to join the supplementary phrase (“A conceptual artist…world”) and the main clause (“Mary…America”). In this context, the colon incorrectly suggests that the information in the supplementary phrase is an explanation or amplification of the information in the main clause (Mary Ping being chosen to curate the exhibition), which isn’t the case. Choice C is incorrect because a semicolon can’t be used in this way to join the supplementary phrase (“A conceptual artist…world”) and the main clause (“Mary…America”). Semicolons are conventionally used to separate two main clauses or to separate items in a complex series.

"}, {"id": "8d53e7a0", "domain": "Standard English Conventions", "skill": "Form, Structure, and Sense", "difficulty": "M", "type": "mc", "stimulus": "

Slam poet Elizabeth Acevedo’s debut novel The Poet X, winner of the 2018 National Book Award for Young People’s Literature, is composed of ______blank protagonist, fifteen-year-old Xiomara Batista.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

poems putatively written by the novel’s

"}, {"id": "B", "text": "

poem’s putatively written by the novel’s 

"}, {"id": "C", "text": "

poem’s putatively written by the novels’

"}, {"id": "D", "text": "

poems putatively written by the novels’

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. Nothing belongs to the “poems” in the sentence, so it should not be possessive—just a simple plural noun. The protagonist does belong to the novel—it’s the protagonist of the novel—so “novel” needs to be a singular possessive noun.

Choice B is incorrect. This doesn’t complete the text in a way that conforms to the conventions of Standard English. This choice uses the singular possessive “poem’s,” but the text indicates that it should be the simple plural “poems”: there is more than one poem, and nothing belongs to the poems. Choice C is incorrect. This doesn’t complete the text in a way that conforms to the conventions of Standard English. This choice uses the singular possessive “poem’s,” but the text indicates that it should be the simple plural “poems”: there is more than one poem, and nothing belongs to the poems. This choice also uses the plural possessive “novels’,” which is incorrect because there is only one novel. Choice D is incorrect. This doesn’t complete the text in a way that conforms to the conventions of Standard English. This choice uses the plural possessive “novels’,” which is incorrect because there is only one novel, so it should be the singular possessive “novel’s.” .

"}, {"id": "cabe71d4", "domain": "Standard English Conventions", "skill": "Boundaries", "difficulty": "E", "type": "mc", "stimulus": "

Both Sona Charaipotra, an Indian American, and Dhonielle Clayton, an African American, grew up frustrated by the lack of diverse characters in books for young people. In 2011, these two writers joined forces to found CAKE Literary, a book packaging ______blank specializes in the creation and promotion of stories told from diverse perspectives for children and young adults.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

company,

"}, {"id": "B", "text": "

company that

"}, {"id": "C", "text": "

company

"}, {"id": "D", "text": "

company, that

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. The convention being tested is the use and punctuation of an integrated relative clause. This choice correctly uses the relative pronoun “that” and no punctuation to create an integrated relative clause that provides essential information about the noun phrase (“a book packaging company”) that it modifies.

Choice A is incorrect because it doesn’t use a relative pronoun to link the verb phrase beginning with “specializes” to the noun phrase that it modifies (“a book packaging company”). Choice C is incorrect because it doesn’t use a relative pronoun to link the verb phrase beginning with “specializes” to the noun phrase that it modifies (“a book packaging company”). Choice D is incorrect because no punctuation is needed between the integrated relative clause beginning with “that specializes” and the noun phrase that it modifies (“a book packaging company”).

"}, {"id": "61160f0a", "domain": "Standard English Conventions", "skill": "Form, Structure, and Sense", "difficulty": "H", "type": "mc", "stimulus": "

Author Madeline L’Engle, ______blank to create a suspenseful tone that draws the reader in, begins her novel A Wrinkle in Time with descriptions of “wraithlike shadows” and “the frenzied lashing of the wind.”

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

looked

"}, {"id": "B", "text": "

looks

"}, {"id": "C", "text": "

is looking

"}, {"id": "D", "text": "

looking

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. The convention being tested is the use of verb forms within a sentence. The nonfinite present participle verb “looking” is correctly used to form a subordinate clause that describes the intent behind how L’Engle begins her novel.

Choice A is incorrect because the finite past tense verb “looked” can’t be used in this way to form a subordinate clause. Choice B is incorrect because the finite present tense verb “looks” can’t be used in this way to form a subordinate clause. Choice C is incorrect because the finite present progressive tense verb “is looking” can’t be used in this way to form a subordinate clause.

"}, {"id": "7b950fc2", "domain": "Standard English Conventions", "skill": "Boundaries", "difficulty": "E", "type": "mc", "stimulus": "

In 2000, Nora de Hoyos Comstock, herself an owner of a successful consulting firm, sought to increase Latina representation in corporate ______blank founded Las Comadres para las Americas, an international community that for over two decades has served as a resource and information network for Latina business professionals.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

settings she

"}, {"id": "B", "text": "

settings, she

"}, {"id": "C", "text": "

settings and she

"}, {"id": "D", "text": "

settings. She

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. It appropriately uses a period to mark the end of one independent clause (\"In 2000…settings\") and the start of another (\"She founded…professionals\").

Choice A is incorrect. This choice results in a run-on sentence error. Both the clause before the blank (\"In 2000…settings\") and the clause after the blank (\"she…professionals\") are independent clauses, so they need to be separated by punctuation. Choice B is incorrect. This choice results in a comma splice error. It incorrectly joins two independent clauses with just a comma. Linking two independent clauses with a comma also requires the use of a coordinating conjunction (like for, and, nor, but, or, yet, or so). Choice C is incorrect. This choice results in a run-on sentence, an error caused when two independent clauses are joined without punctuation or appropriate conjunctions. Since both the clause before the blank (\"In 2000…settings\") and the clause after the blank (\"she…professionals\") are independent, a comma would be required in addition to the coordinating conjunction \"and.\"

"}, {"id": "75f49353", "domain": "Standard English Conventions", "skill": "Form, Structure, and Sense", "difficulty": "M", "type": "mc", "stimulus": "

The Progressive Era in the United States witnessed the rise of numerous Black women’s clubs, local organizations that advocated for racial and gender equality. Among the clubs’ leaders ______blank Josephine St. Pierre Ruffin, founder of the Women’s Era Club of Boston.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

was

"}, {"id": "B", "text": "

were

"}, {"id": "C", "text": "

are

"}, {"id": "D", "text": "

have been

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. The convention being tested here is subject-verb agreement. The singular verb “was” agrees in number with the singular subject “Josephine St. Pierre Ruffin.”

Choice B is incorrect because the plural verb “were” doesn’t agree in number with the singular subject “Josephine St. Pierre Ruffin.” Choice C is incorrect because the plural verb “are” doesn’t agree in number with the singular subject “Josephine St. Pierre Ruffin.” Choice D is incorrect because the plural verb “have been” doesn’t agree in number with the singular subject “Josephine St. Pierre Ruffin.”

"}, {"id": "1b97cce9", "domain": "Standard English Conventions", "skill": "Boundaries", "difficulty": "H", "type": "mc", "stimulus": "

Hegra is an archaeological site in present-day Saudi Arabia and was the second largest city of the Nabataean Kingdom (fourth century BCE to first century CE). Archaeologist Laila Nehmé recently traveled to Hegra to study its ancient ______blank into the rocky outcrops of a vast desert, these burial chambers seem to blend seamlessly with nature.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

tombs. Built

"}, {"id": "B", "text": "

tombs, built

"}, {"id": "C", "text": "

tombs and built

"}, {"id": "D", "text": "

tombs built

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. The convention being tested is punctuation use between sentences. In this choice, the period after “tombs” is used correctly to mark the boundary between one sentence (“Archaeologist...tombs”) and another (“Built...nature”).

Choice B is incorrect because it results in a comma splice. A comma can’t be used in this way to mark the boundary between sentences. Choice C is incorrect. Without a comma preceding it, the conjunction “and” can’t be used in this way to join the two sentences. Choice D is incorrect because it results in a run-on sentence. The sentences (“Archaeologist...tombs” and “Built...nature”) are fused without punctuation and/or a conjunction.

"}, {"id": "fff4c7f4", "domain": "Standard English Conventions", "skill": "Form, Structure, and Sense", "difficulty": "E", "type": "mc", "stimulus": "

American poet Emily Dickinson wrote many of her poems on scraps of paper, but she also took steps to collect these works. From 1858 to around 1864, for example, she copied more than 800 of ______blank into forty homemade booklets (known as fascicles).

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

them

"}, {"id": "B", "text": "

this

"}, {"id": "C", "text": "

that

"}, {"id": "D", "text": "

it

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. The pronoun \"them\" agrees with the plural antecedents \"poems\" and \"works.\"

Choice B is incorrect. \"This\" is a singular pronoun, but its antecedents, \"poems\" and \"works,\" are plural. Choice C is incorrect. \"That\" is a singular pronoun, but its antecedents, \"poems\" and \"works,\" are plural. Choice D is incorrect. \"It\" is a singular pronoun, but its antecedents, \"poems\" and \"works,\" are plural.

"}, {"id": "40c3589d", "domain": "Standard English Conventions", "skill": "Boundaries", "difficulty": "M", "type": "mc", "stimulus": "

Luci Tapahonso is the inaugural poet laureate of the Navajo Nation. Her book Sáanii Dahataal/The Women Are Singing—a combination of fiction and memoir, poetry and ______blank serves as a testament to her versatility as a writer.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

prose;

"}, {"id": "B", "text": "

prose

"}, {"id": "C", "text": "

prose,

"}, {"id": "D", "text": "

prose—

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. “A combination of fiction and memoir, poetry and prose” is a nonessential supplement, so it needs to be set off from the rest of the sentence with a pair of matching punctuation marks. We already have a dash at the beginning of the supplement, so we need to add a dash at the end of the supplement to match. 

Choice A is incorrect. This doesn’t complete the text in a way that conforms to the conventions of Standard English. “A combination of fiction and memoir, poetry and prose” is a nonessential supplement, so it needs to be set off from the rest of the sentence with a pair of matching punctuation marks. We already have a dash at the beginning of the supplement, so we need to add a dash at the end of the supplement to match. Choice B is incorrect. This doesn’t complete the text in a way that conforms to the conventions of Standard English. “A combination of fiction and memoir, poetry and prose” is a nonessential supplement, so it needs to be set off from the rest of the sentence with a pair of matching punctuation marks. We already have a dash at the beginning of the supplement, so we need to add a dash at the end of the supplement to match. Choice C is incorrect. This doesn’t complete the text in a way that conforms to the conventions of Standard English. “A combination of fiction and memoir, poetry and prose” is a nonessential supplement, so it needs to be set off from the rest of the sentence with a pair of matching punctuation marks. We already have a dash at the beginning of the supplement, so we need to add a dash at the end of the supplement to match. 

"}, {"id": "b15724fc", "domain": "Standard English Conventions", "skill": "Boundaries", "difficulty": "H", "type": "mc", "stimulus": "

American writer Edwidge Danticat, who emigrated from Haiti in 1981, has won acclaim for her powerful short stories, novels, and ______blank her lyrical yet unflinching depictions of her native country’s turbulent history, writer Robert Antoni has compared Danticat to Nobel Prize–winning novelist Toni Morrison.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English? 

", "choices": [{"id": "A", "text": "

essays, praising

"}, {"id": "B", "text": "

essays and praising

"}, {"id": "C", "text": "

essays praising

"}, {"id": "D", "text": "

essays. Praising

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. The convention being tested is punctuation use between sentences. In this choice, the period after “essays” is used correctly to mark the boundary between one sentence (“American…essays”) and another (“praising…Morrison”). The participial phrase beginning with “Praising” modifies the subject of the second sentence, “writer Robert Antoni.”

Choice A is incorrect because it results in a comma splice. A comma can’t be used in this way to mark the boundary between sentences. Choice B is incorrect. Without a comma preceding it, the conjunction “and” can’t be used in this way to join sentences. Choice C is incorrect because it results in a run-on sentence. The sentences (“American…essays” and “Praising…Morrison”) are fused without punctuation and/or a conjunction.

"}, {"id": "c5d39bc7", "domain": "Standard English Conventions", "skill": "Form, Structure, and Sense", "difficulty": "E", "type": "mc", "stimulus": "

Scientists believe that, unlike most other species of barnacle, turtle barnacles (Chelonibia testudinari) can dissolve the cement-like secretions they use to attach ______blank to a sea turtle shell, enabling the barnacles to move short distances across the shell’s surface.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

it

"}, {"id": "B", "text": "

themselves

"}, {"id": "C", "text": "

 them

"}, {"id": "D", "text": "

itself

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. The convention being tested is pronoun-antecedent agreement. The plural reflexive pronoun “themselves” agrees in number with the plural antecedent “turtle barnacles,” correctly indicating what is attached to a sea turtle shell.  

Choice A is incorrect because the singular pronoun “it” doesn’t agree in number with the plural antecedent “turtle barnacles.” Choice C is incorrect because it results in an unclear and confusing sentence. In this context, it’s unclear what the plural pronoun “them” refers to. Choice D is incorrect because the singular reflexive pronoun “itself” doesn’t agree in number with the plural antecedent “turtle barnacles.”

"}, {"id": "e2759b92", "domain": "Standard English Conventions", "skill": "Form, Structure, and Sense", "difficulty": "E", "type": "mc", "stimulus": "

Occupying a significant part of modern-day Nigeria, the Kingdom of Benin was one of the major powers in West Africa between the thirteenth and nineteenth centuries. It ______blank ruled by Oba Ewuare I from 1440 to 1473.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

is

"}, {"id": "B", "text": "

will be

"}, {"id": "C", "text": "

has been

"}, {"id": "D", "text": "

was

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. The convention being tested is the use of verbs to express tense in a sentence. In this choice, the past tense verb “was ruled” correctly indicates that Oba Ewuare I ruled the Kingdom of Benin in the distant past (from 1440 to 1473). This past tense verb choice is consistent with the other past tense verb (“was”) used to describe the Kingdom of Benin.

Choice A is incorrect because the present tense verb “is ruled” doesn’t indicate that Oba Ewuare I ruled the Kingdom of Benin in the distant past. Choice B is incorrect because the future tense verb “will be ruled” doesn’t indicate that Oba Ewuare I ruled the Kingdom of Benin in the distant past. Choice C is incorrect because the present perfect tense verb “has been ruled” doesn’t indicate that Oba Ewuare I ruled the Kingdom of Benin in the distant past.

"}, {"id": "594b4a94", "domain": "Standard English Conventions", "skill": "Boundaries", "difficulty": "H", "type": "mc", "stimulus": "

The field of geological oceanography owes much to American ______blank Marie Tharp, a pioneering oceanographic cartographer whose detailed topographical maps of the ocean floor and its multiple rift valleys helped garner acceptance for the theories of plate tectonics and continental drift.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

geologist,

"}, {"id": "B", "text": "

geologist

"}, {"id": "C", "text": "

geologist;

"}, {"id": "D", "text": "

geologist:

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. “Marie tharp” is essential information that completes the first clause — the first clause doesn’t function without it. So we don’t want to separate it with punctuation. 

Choice A is incorrect. This choice creates a punctuation error. “The field of geological oceanography owes much to American geologist” is unclear: which geologist are we talking about? We need the “Marie Tharp” for clarity, which means it’s essential information and should not be separated by a comma. Choice C is incorrect. This choice creates a punctuation error. “The field of geological oceanography owes much to American geologist” is unclear: which geologist are we talking about? We need the “Marie Tharp” for clarity, which means it’s essential information and should not be separated by a semicolon. Choice D is incorrect. This choice creates a punctuation error. “The field of geological oceanography owes much to American geologist” is unclear: which geologist are we talking about? We need the “Marie Tharp” for clarity, which means it’s essential information and should not be separated by a colon. 

"}, {"id": "2fd05c15", "domain": "Standard English Conventions", "skill": "Boundaries", "difficulty": "H", "type": "mc", "stimulus": "

In crafting her fantasy fiction, Nigerian-born British author Helen Oyeyemi has drawn inspiration from the classic nineteenth-century fairy tales of the Brothers Grimm. Her 2014 novel Boy, Snow, Bird, for instance, is a complex retelling of the story of Snow White, while her 2019 novel ______blank offers a delicious twist on the classic tale of Hansel and Gretel.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

­­Gingerbread—

"}, {"id": "B", "text": "

­­Gingerbread,

"}, {"id": "C", "text": "

Gingerbread

"}, {"id": "D", "text": "

­­Gingerbread:

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. The convention being tested is punctuation between a subject and a verb. When, as in this case, a subject (“her 2019 novel Gingerbread”) is immediately followed by a verb (“offers”), no punctuation is needed.

Choice A is incorrect because no punctuation is needed between the subject and the verb. Choice B is incorrect because no punctuation is needed between the subject and the verb. Choice D is incorrect because no punctuation is needed between the subject and the verb.

"}, {"id": "175df826", "domain": "Standard English Conventions", "skill": "Form, Structure, and Sense", "difficulty": "E", "type": "mc", "stimulus": "

In the 2011 documentary The Barber of Birmingham, civil rights activist James Armstrong recounts how his barbershop in Birmingham, Alabama, ______blank as a political hub for members of the Black community during the 1950s.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

serving

"}, {"id": "B", "text": "

having served

"}, {"id": "C", "text": "

served

"}, {"id": "D", "text": "

to serve

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. The convention being tested is the use of verb forms within a sentence. Relative clauses, such as the one beginning with \"how,\" require a finite (tensed) verb, a verb that can function as the main verb of a clause. This choice correctly supplies the clause with the finite past tense verb \"served.\"

Choice A is incorrect because it results in an ungrammatical sentence. The nonfinite participle \"serving\" doesn’t supply the clause with a finite verb. Choice B is incorrect because it results in an ungrammatical sentence. The nonfinite participle \"having served\" doesn’t supply the clause with a finite verb. Choice D is incorrect because it results in an ungrammatical sentence. The nonfinite to-infinitive \"to serve\" doesn’t supply the clause with a finite verb.

"}, {"id": "c8540a5b", "domain": "Standard English Conventions", "skill": "Boundaries", "difficulty": "M", "type": "mc", "stimulus": "

Swedish scientists Eva Engvall and Peter Perlmann developed a method for measuring the concentration of different proteins in a biological sample. Their ______blank ELISA (enzyme-linked immunosorbent assay), is used to detect and measure proteins that indicate the presence of certain diseases.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

method (called

"}, {"id": "B", "text": "

method—called

"}, {"id": "C", "text": "

method, called

"}, {"id": "D", "text": "

method called

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. The convention being tested is the punctuation of a supplementary element within a sentence. The comma after “method” pairs with the comma after the closing parenthesis to separate the supplementary element “called ELISA (enzyme-linked immunosorbent assay)” from the rest of the sentence. This supplementary element functions to identify the name of Engvall and Perlmann’s method, and the pair of commas indicates that this element could be removed without affecting the grammatical coherence of the sentence.

Choice A is incorrect because an opening parenthesis can’t be paired with a comma to separate the supplementary element from the rest of the sentence. Choice B is incorrect because a dash can’t be paired with a comma to separate the supplementary element from the rest of the sentence. Choice D is incorrect because it fails to use appropriate punctuation to separate the supplementary element from the rest of the sentence.

"}, {"id": "e15c50b2", "domain": "Standard English Conventions", "skill": "Boundaries", "difficulty": "E", "type": "mc", "stimulus": "

A standard Argo float, a type of autonomous robot, measures temperature and salinity in the upper regions of ice-free oceans. More advanced floats can measure a wider range of ______blank and monitor seasonal ice zones.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

variables: travel to greater depths

"}, {"id": "B", "text": "

variables, travel to greater depths,

"}, {"id": "C", "text": "

variables travel to greater depths,

"}, {"id": "D", "text": "

variables, travel to greater depths;

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. The convention being tested is the punctuation of items in a series. The comma after “variables” is used conventionally to separate the first and second items in the series, and the comma after “depths” is used conventionally to separate the second and third items.

Choice A is incorrect because a colon can’t be used in this way to separate items in a simple series. Choice C is incorrect because a comma is needed after “variables” to separate the first and second items in the series. Choice D is incorrect because a semicolon can’t be used in this way to separate items in a simple series.

"}, {"id": "988c78eb", "domain": "Standard English Conventions", "skill": "Form, Structure, and Sense", "difficulty": "E", "type": "mc", "stimulus": "

Former First Lady of the United States Eleanor Roosevelt and Indian activist and educator Hansa Mehta were instrumental in drafting the United Nations’ Universal Declaration of Human Rights, a document that ______blank the basic freedoms to which all people are entitled.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

have outlined

"}, {"id": "B", "text": "

were outlining

"}, {"id": "C", "text": "

outlines

"}, {"id": "D", "text": "

outline

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. The convention being tested is subject-verb agreement. The singular verb “outlines” agrees in number with the singular subject “document.”

Choice A is incorrect because the plural verb “have outlined” doesn’t agree in number with the singular subject “document.” Choice B is incorrect because the plural verb “were outlining” doesn’t agree in number with the singular subject “document.” Choice D is incorrect because the plural verb “outline” doesn’t agree in number with the singular subject “document.” 

"}, {"id": "96499989", "domain": "Standard English Conventions", "skill": "Boundaries", "difficulty": "E", "type": "mc", "stimulus": "

Fans of science fiction will ______blank multiple references to classic sci-fi stories in Janelle Monáe’s song lyrics, including her recurring nods to the plot of the 1927 sci-fi film Metropolis.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

appreciate the

"}, {"id": "B", "text": "

appreciate. The

"}, {"id": "C", "text": "

appreciate, the

"}, {"id": "D", "text": "

appreciate: the

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. The convention being tested here is punctuation between a verb and object. No punctuation is needed between the verb (\"appreciate\") and its object (\"the multiple references...\"). The object helps complete the idea of the verb—in this case, it explains what fans of science fiction will appreciate—and any punctuation between the two results in an ungrammatical sentence.

Choice B is incorrect because no punctuation is needed between the verb and its object. Choice C is incorrect because no punctuation is needed between the verb and its object. Choice D is incorrect because no punctuation is needed between the verb and its object.

"}, {"id": "fdb16e20", "domain": "Standard English Conventions", "skill": "Boundaries", "difficulty": "H", "type": "mc", "stimulus": "

Quantum particles of light—photons—provide an unhackable means of transmitting encryption keys over networks, as attempts to observe particles in quantum states will invariably alter the particles ______blank dismantle any information they transmit.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

and in the process,

"}, {"id": "B", "text": "

and, in the process,

"}, {"id": "C", "text": "

and in the process—

"}, {"id": "D", "text": "

and, in the process

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. This choice uses paired punctuation in the form of two commas to set off the nonessential phrase \"in the process.\"

Choice A is incorrect. The phrase \"in the process\" is a nonessential element and needs to be set off with paired punctuation. We need a comma after \"and\" to match the one after \"process.\" Choice C is incorrect. The phrase \"in the process\" is a nonessential element and needs to be set off with paired punctuation, so we would need a dash after \"and\" to match the one following \"process.\" Choice D is incorrect. The phrase \"in the process\" is a nonessential element and needs to be set off with paired punctuation. We would need a comma after \"process\" to match the one following \"and.\"

"}, {"id": "4565a53c", "domain": "Standard English Conventions", "skill": "Boundaries", "difficulty": "E", "type": "mc", "stimulus": "

Lucía Michel of the University of Chile observed that alkaline soils contain an insoluble form of iron that blueberry plants cannot absorb, thus inhibiting blueberry growth. If these plants were grown in alkaline soil alongside grasses that aid in iron solubilization, ______blank Michel was determined to find out.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

could the blueberries thrive. 

"}, {"id": "B", "text": "

the blueberries could thrive. 

"}, {"id": "C", "text": "

the blueberries could thrive?

"}, {"id": "D", "text": "

could the blueberries thrive?

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. The convention being tested is end-of-sentence punctuation. This choice correctly uses a question mark to punctuate the interrogative clause “could the blueberries thrive,” which asks a direct question at the end of the sentence.

Choice A is incorrect because a period can’t be used in this way to punctuate an interrogative clause, such as “could the blueberries thrive,” at the end of a sentence. Choice B is incorrect because the context requires an interrogative clause. The declarative clause “the blueberries could thrive” incorrectly indicates that it was known that the blueberries could thrive in alkaline soil, whereas Michel had yet to find this out. Choice C is incorrect because a question mark can’t be used in this way to punctuate a declarative clause, such as “the blueberries could thrive,” at the end of a sentence.

"}, {"id": "7a0d9031", "domain": "Standard English Conventions", "skill": "Form, Structure, and Sense", "difficulty": "M", "type": "mc", "stimulus": "

In many of her landscape paintings from the 1970s and 1980s, Lebanese American artist Etel Adnan worked to capture the essence of California’s fog-shrouded Mount Tamalpais region through abstraction, using splotches of color to represent the area’s features. Interestingly, the triangle representing the mountain itself ______blank among the few defined figures in her paintings.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

are

"}, {"id": "B", "text": "

have been 

"}, {"id": "C", "text": "

were

"}, {"id": "D", "text": "

is

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. The convention being tested is subject–verb agreement. The singular verb “is” agrees in number with the singular subject “the triangle.”

Choice A is incorrect because the plural verb “are” doesn’t agree in number with the singular subject “the triangle.” Choice B is incorrect because the plural verb “have been” doesn’t agree in number with the singular subject “the triangle.” Choice C is incorrect because the plural verb “were” doesn’t agree in number with the singular subject “the triangle.”

"}, {"id": "91fbd59d", "domain": "Standard English Conventions", "skill": "Boundaries", "difficulty": "E", "type": "mc", "stimulus": "

Award-winning cinematographer James Wong Howe was known for his innovative filming techniques. While filming a boxing match for the movie Body and Soul ______blank Howe had a handheld camera operator wear roller skates. This allowed the operator to move smoothly around actors in a boxing ring, creating an immersive experience for viewers.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

(1947), and

"}, {"id": "B", "text": "

(1947),

"}, {"id": "C", "text": "

(1947) and

"}, {"id": "D", "text": "

(1947)

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. The convention being tested is punctuation between a supplementary element and a main clause. This choice correctly uses a comma to mark the boundary between the supplementary phrase (“While...1947”), which indicates when the action occurred, and the main clause (“Howe had a handheld camera operator wear roller skates”).

Choice A is incorrect because a comma paired with the conjunction “and” can’t be used in this way to mark the boundary between the supplementary element (“While…1947”) and the main clause (“Howe…skates”). Choice C is incorrect because the conjunction “and” can’t be used in this way to join the supplementary element (“While…1947”) and the main clause (“Howe…skates”). Choice D is incorrect because it fails to mark the boundary between the supplementary element and the main clause with appropriate punctuation.

"}, {"id": "d46ac7e7", "domain": "Standard English Conventions", "skill": "Form, Structure, and Sense", "difficulty": "H", "type": "mc", "stimulus": "

A second-generation Japanese American, Wataru Misaka ______blank in World War II (1941-45) and won two amateur national basketball championships at the University of Utah when he joined the New York Knicks for the 1947-48 season, becoming the first non-white basketball player in the US’s top professional league.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

already served

"}, {"id": "B", "text": "

was already serving

"}, {"id": "C", "text": "

already serves

"}, {"id": "D", "text": "

had already served

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. Misaka served in World War II before he joined the New York Knicks in 1947. To show that a past occurrence took place before another past occurrence, we need to use “had” + the past tense form of the verb. This is called the past perfect tense.

Choice A is incorrect. Misaka served in World War II before he joined the Knicks. Both events are in the past, but his service in World War II happened earlier, so we need a verb that makes it clear that his service (and the two national championships) had ended by the time he joined the Knicks. Choice B is incorrect. “Was already serving” forms the continuous past tense, which we use when we’re showing a past action that was ongoing. Misaka served in World War II before he joined the Knicks. Both events are in the past, but they’re not happening at the same time, so we shouldn’t use the continuous past tense here. Choice C is incorrect. Misaka served in World War II in the past, so we shouldn’t use the present tense “serves.”

"}, {"id": "b1e8b87f", "domain": "Standard English Conventions", "skill": "Boundaries", "difficulty": "E", "type": "mc", "stimulus": "

Winding through the ice atop Norway’s Jotunheim Mountains is the Lendbreen pass, an ancient route that was used by hunters, farmers, traders, and travelers in the Middle Ages before eventually falling into disuse. Recently, archeologists have ______blank knives, horseshoes, wool tunics, and thousands of other artifacts from the icy pass.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

unearthed:

"}, {"id": "B", "text": "

unearthed,

"}, {"id": "C", "text": "

unearthed—

"}, {"id": "D", "text": "

unearthed

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. No punctuation should separate the verb \"unearthed\" and its objects (i.e, what was \"unearthed\"): \"knives, horseshoes, wool tunics, and thousands of other artifacts.\"

Choice A is incorrect. This choice creates a punctuation error, separating the verb \"unearthed\" from its objects (i.e, what was \"unearthed\") with a colon. Choice B is incorrect. This choice creates a punctuation error, separating the verb \"unearthed\" from its objects (i.e, what was \"unearthed\") with a comma. Choice C is incorrect. This choice creates a punctuation error, separating the verb \"unearthed\" from its objects (i.e, what was \"unearthed\") with a dash.

"}, {"id": "3595a991", "domain": "Standard English Conventions", "skill": "Form, Structure, and Sense", "difficulty": "M", "type": "mc", "stimulus": "

In 1930, Japanese American artist Chiura Obata depicted the natural beauty of Yosemite National Park in two memorable woodcuts: Evening at Carl Inn and Lake Basin in the High Sierra. In 2019, ______blank exhibited alongside 150 of Obata’s other works in a single-artist show at the Smithsonian American Art Museum.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

it was

"}, {"id": "B", "text": "

they were

"}, {"id": "C", "text": "

this was

"}, {"id": "D", "text": "

some were

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. The convention being tested is pronoun–antecedent agreement. The plural pronoun “they” agrees in number with the plural antecedent “woodcuts” and clearly identifies what was exhibited at the Smithsonian American Art Museum.

Choice A is incorrect because the singular pronoun “it” doesn’t agree in number with the plural antecedent “woodcuts.” Choice C is incorrect because the singular pronoun “this” doesn’t agree in number with the plural antecedent “woodcuts.” Choice D is incorrect because the plural pronoun “some” is illogical in this context (referring to “some” of two woodcuts).

"}, {"id": "1ee4485c", "domain": "Standard English Conventions", "skill": "Boundaries", "difficulty": "H", "type": "mc", "stimulus": "

Journalists have dubbed Gil Scott-Heron the “godfather of rap,” a title that has appeared in hundreds of articles about him since the 1990s. Scott-Heron himself resisted the godfather ______blank feeling that it didn’t encapsulate his devotion to the broader African American blues music tradition as well as “bluesologist,” the moniker he preferred.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

nickname, however

"}, {"id": "B", "text": "

nickname, however;

"}, {"id": "C", "text": "

nickname, however,

"}, {"id": "D", "text": "

nickname; however,

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. The convention being tested is punctuation use between a main clause and two supplementary elements. In this choice, the commas after “nickname” and “however” are correctly used to separate the supplementary adverb “however” from the main clause (“Scott-Heron…nickname”) on one side and the supplementary participial phrase (“feeling…bluesologist”) on the other.

Choice A is incorrect because it fails to mark the boundary between the supplementary adverb “however” and the supplementary phrase (“feeling…bluesologist”). Choice B is incorrect because a semicolon can’t be used in this way to join the supplementary adverb “however” and the supplementary phrase (“feeling…bluesologist”). Choice D is incorrect because a semicolon can’t be used in this way to join the main clause (“Scott-Heron…nickname”) and the supplementary word and phrase (“however” and “feeling…bluesologist”). Moreover, placing the semicolon after “nickname” illogically signals that the following information (Scott-Heron’s feeling that the nickname didn’t encapsulate his devotion to the blues tradition) is contrary to the information in the previous clause (Scott-Heron’s resistance to the nickname).

"}, {"id": "31362d2d", "domain": "Standard English Conventions", "skill": "Form, Structure, and Sense", "difficulty": "E", "type": "mc", "stimulus": "

If simple sugars such as ribose and glycolaldehyde ______blank Earth from elsewhere and survived impact—a possibility astrophysicist Nicolle Zellner outlined in a 2020 study—the sugars could have reacted with other molecules that were already present on the planet to form the nucleotides that are the structural components of RNA and DNA.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

reach

"}, {"id": "B", "text": "

had reached

"}, {"id": "C", "text": "

will reach

"}, {"id": "D", "text": "

are reaching

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. The convention being tested is the use of verbs to express tense. In this choice, the past perfect verb “had reached” is used correctly to describe a past action that was completed before another action in the past. Specifically, in this hypothetical scenario about the origins of RNA and DNA on Earth, the simple sugars had to have reached Earth before they could react with other molecules on the planet.

Choice A is incorrect because the present tense verb “reach” doesn’t indicate that the simple sugars reached Earth before reacting with other molecules on the planet. Choice C is incorrect because the future tense verb “will reach” doesn’t indicate that the simple sugars reached Earth before reacting with other molecules on the planet. Choice D is incorrect because the present progressive verb “are reaching” doesn’t indicate that the simple sugars reached Earth before reacting with other molecules on the planet.

"}, {"id": "d2cf0e11", "domain": "Standard English Conventions", "skill": "Form, Structure, and Sense", "difficulty": "M", "type": "mc", "stimulus": "

Inventor John Friedman created a prototype of the first flexible straw by inserting a screw into a paper straw and, using dental floss, binding the straw tightly around the ______blank When the floss and screw were removed, the resulting corrugations in the paper allowed the straw to bend easily over the edge of a glass.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

screw’s thread’s.

"}, {"id": "B", "text": "

screws’ threads.

"}, {"id": "C", "text": "

screw’s threads.

"}, {"id": "D", "text": "

screws threads’.

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. The convention being tested is the use of plural and possessive nouns. The singular possessive noun “screw’s” and the plural noun “threads” correctly indicate that there is only one screw and it has multiple threads.

Choice A is incorrect because the context requires the plural noun “threads,” not the singular possessive noun “thread’s.” Choice B is incorrect because the context requires the singular possessive noun “screw’s,” not the plural possessive noun “screws’.” Choice D is incorrect because the context requires the singular possessive noun “screw’s” and the plural noun “threads,” not the plural noun “screws” or the plural possessive noun “threads.’”

"}, {"id": "1d971f75", "domain": "Standard English Conventions", "skill": "Form, Structure, and Sense", "difficulty": "E", "type": "mc", "stimulus": "

Photographer Ansel Adams’s landscape portraits are iconic pieces of American art. However, many of the ______blank of landscapes were intended not as art but as marketing; a concessions company at Yosemite National Park had hired Adams to take pictures of the park for restaurant menus and brochures.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

photographer’s early photo’s

"}, {"id": "B", "text": "

photographers early photo’s

"}, {"id": "C", "text": "

photographer’s early photos

"}, {"id": "D", "text": "

photographers early photos

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. There’s only one photographer (Adams), and the photos are his, so the singular possessive \"photographer’s\" is correct. There’s more than one photo, and nothing belongs to the photos, so the simple plural \"photos\" is correct.

Choice A is incorrect. This choice uses the singular possessive \"photo’s,\" which isn’t correct. There’s more than one photo, and they don’t possess anything, so the noun should be the simple plural \"photos.\" Choice B is incorrect. This choice uses the simple plural \"photographers\" and the singular possessive \"photo’s,\" which aren’t correct. There’s only one photographer (Adams) and there’s more than one photo. Choice D is incorrect. This choice uses the simple plural \"photographers,\" which isn’t correct. There’s only one photographer (Adams).

"}, {"id": "f40ca576", "domain": "Standard English Conventions", "skill": "Form, Structure, and Sense", "difficulty": "E", "type": "mc", "stimulus": "

Each year in the fall, when the weather starts to cool in the northern hemisphere, millions of North American monarch butterflies journey south. Searching for food and warmer habitats, they ______blank thousands of miles—from as far north as Canada all the way down to Mexico—on this annual migration.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

flew

"}, {"id": "B", "text": "

were flying

"}, {"id": "C", "text": "

had flown

"}, {"id": "D", "text": "

fly

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. The convention being tested is the use of verbs to express tense. In this choice, the present tense verb “fly” is consistent with the other present tense verb ( “journey”) used to describe the butterflies’ yearly migration. Together, these simple present tense verbs correctly indicate that the migration is a current, yearly occurrence.

Choice A is incorrect. The simple past tense verb “flew” isn’t consistent with the other present tense verb used to describe the butterflies’ yearly migration. Choice B is incorrect. The past progressive tense verb “were flying” isn’t consistent with the other present tense verb used to describe the butterflies’ yearly migration. Choice C is incorrect. The past perfect tense verb “had flown” isn’t consistent with the other present tense verb used to describe the butterflies’ yearly migration.

"}, {"id": "c101fc44", "domain": "Standard English Conventions", "skill": "Boundaries", "difficulty": "M", "type": "mc", "stimulus": "

How do scientists determine what foods were eaten by extinct hominins such as Neanderthals? In the past, researchers were limited to studying the marks found on the fossilized teeth of skeletons, but in 2017 a team led by Laura Weyrich of the Australian Centre for Ancient DNA tried something ______blank the DNA found in Neanderthals’ fossilized dental plaque.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

new: sequencing

"}, {"id": "B", "text": "

new; sequencing

"}, {"id": "C", "text": "

new, sequencing:

"}, {"id": "D", "text": "

new. Sequencing

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. “A team…tried something new” is an independent clause leading to an explanation of what the new thing was. A colon can only be used at the end of an independent clause, and typically introduces further explanation that expands upon the first clause, which makes a colon the perfect choice here.

Choice B is incorrect. This choice results in a punctuation error. “Sequencing…dental plaque” can’t stand on its own as a sentence, and so it can’t be linked to the independent clause “a team…tried something new” with a semicolon. Only two independent clauses can be connected in this way. Choice C is incorrect. This choice results in a punctuation error. If “sequencing” is included in the first clause, it can no longer stand on its own as a complete idea. Since a colon can only come at the end of an independent clause, using one in this way creates an error. Choice D is incorrect. This choice results in a sentence fragment. “Sequencing…dental plaque” can’t stand on its own as a sentence.

"}, {"id": "0bcb4417", "domain": "Standard English Conventions", "skill": "Form, Structure, and Sense", "difficulty": "M", "type": "mc", "stimulus": "

Oglala Lakota poet Layli Long Soldier’s star quilt poems offer an unusually open-ended reading experience. With ______blank eight panels of text stitched together in the shape of a traditional eight-pointed Lakota star quilt, the poems present viewers with a seemingly infinite number of ways to read them.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

their

"}, {"id": "B", "text": "

it’s

"}, {"id": "C", "text": "

they’re

"}, {"id": "D", "text": "

its

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. The convention being tested is the use of possessive determiners. The plural possessive determiner \"their\" agrees in number with the plural noun \"the poems,\" thus indicating that the poems had eight panels of text stitched together in the shape of a traditional eight-pointed Lakota star quilt.

Choice B is incorrect because \"it’s\" is the contraction for \"it is\" or \"it has,\" not a possessive determiner. Choice C is incorrect because \"they’re\" is the contraction for \"they are,\" not a possessive determiner. Choice D is incorrect because\u202fthe singular possessive determiner \"its\" doesn’t agree in number with the plural noun \"the poems.\"

"}, {"id": "dddfa043", "domain": "Standard English Conventions", "skill": "Boundaries", "difficulty": "E", "type": "mc", "stimulus": "

Before the Erie Canal was completed in 1825, transporting goods by wagon between New York City and the Midwest took up to forty-five days and cost one hundred dollars per ton. By linking the Hudson River to Lake ______blank canal reduced transport time to nine days and cut costs to six dollars per ton.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

Erie; the

"}, {"id": "B", "text": "

Erie (the

"}, {"id": "C", "text": "

Erie, the

"}, {"id": "D", "text": "

Erie: the

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. The convention being tested is punctuation between a supplementary phrase and a main clause. This choice correctly uses a comma to mark the boundary between the introductory supplementary phrase (“By linking the Hudson River to Lake Erie”), which identifies how the canal reduced transport time, and the main clause (“the canal reduced transport time to nine days and cut costs to six dollars per ton”).

Choice A is incorrect because a semicolon can’t be used in this way to mark the boundary between a supplementary phrase (“By…Erie”) and the main clause (“the canal...ton”). Choice B is incorrect because an open parenthesis can’t be used in this way to mark the boundary between a supplementary phrase (“By…Erie”) and the main clause (“the canal...ton”). Choice D is incorrect because a colon can’t be used in this way to mark the boundary between an introductory supplementary phrase (“By…Erie”) and the main clause (“the canal...ton”).

"}, {"id": "be37d4ae", "domain": "Standard English Conventions", "skill": "Boundaries", "difficulty": "H", "type": "mc", "stimulus": "

During the English neoclassical period (1660–1789), many writers imitated the epic poetry and satires of ancient Greece and Rome. They were not the first in England to adopt the literary modes of classical ______blank some of the most prominent figures of the earlier Renaissance period were also influenced by ancient Greek and Roman literature.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

antiquity, however

"}, {"id": "B", "text": "

antiquity, however,

"}, {"id": "C", "text": "

antiquity, however;

"}, {"id": "D", "text": "

antiquity; however,

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. The convention being tested is the punctuation of a supplementary phrase following a clause. This choice uses a comma to separate the supplementary adverb phrase “however” from the independent clause it modifies (“They …antiquity”) and uses a semicolon to join the first independent clause (“They …antiquity”) and the second independent clause (“some…literature”). Further, placing the semicolon after “however” indicates that the information in the clause that this part of (that neoclassical writers were not the first to adopt classical literary modes) is contrary to what might be assumed from the information in the previous sentence (that the neoclassical writers were unique in imitating classical epic poetry and satires).

Choice A is incorrect because it fails to mark the boundary after “however” between the two independent clauses with appropriate punctuation. Choice B is incorrect because the comma after “however” can’t be used in this way to mark the boundary between the two independent clauses. Choice D is incorrect because placing the semicolon after “antiquity” illogically indicates that the information in the clause that this part of (that prominent Renaissance figures were also influenced by classical literature) is contrary to the information in the previous clause (that neoclassical writers were not the first to adopt classical literary modes).

"}, {"id": "c8607bdf", "domain": "Standard English Conventions", "skill": "Form, Structure, and Sense", "difficulty": "M", "type": "mc", "stimulus": "

“Praise Song for the Day,” Elizabeth Alexander’s 2009 inaugural poem, asserts that “We cross dirt roads and highways…to see what’s on the other side.” Alexander’s use of “we” ______blank Americans’ collective efforts and shared desire to seek new opportunity.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

evokes

"}, {"id": "B", "text": "

are evoking

"}, {"id": "C", "text": "

have evoked

"}, {"id": "D", "text": "

evoke

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. The convention being tested is subject-verb agreement. The singular verb \"evokes\" agrees in number with the singular subject \"Alexander’s use.\"

Choice B is incorrect because the plural verb \"are evoking\" doesn’t agree in number with the singular subject \"Alexander’s use.\" Choice C is incorrect because the plural verb \"have evoked\" doesn’t agree in number with the singular subject \"Alexander’s use.\" Choice D is incorrect because the plural verb \"evoke\" doesn’t agree in number with the singular subject \"Alexander’s use.\"

"}, {"id": "5aae2475", "domain": "Standard English Conventions", "skill": "Boundaries", "difficulty": "H", "type": "mc", "stimulus": "

Stomata, tiny pore structures in a leaf that absorb gases needed for plant growth, open when guard cells surrounding each pore swell with water. In a pivotal 2007 article, plant cell ______blank showed that lipid molecules called phosphatidylinositol phosphates are responsible for signaling guard cells to open stomata.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

biologist, Yuree Lee

"}, {"id": "B", "text": "

biologist Yuree Lee,

"}, {"id": "C", "text": "

biologist Yuree Lee

"}, {"id": "D", "text": "

biologist, Yuree Lee,

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. The convention being tested is the use of punctuation between titles and proper nouns. No punctuation is needed to offset the proper noun “Yuree Lee” form the title “plant cell biologist” that describes Lee.

Choice A is incorrect because no punctuation is needed. Choice B is incorrect because no punctuation is needed. Choice D is incorrect because no punctuation is needed around the proper noun “Yuree Lee.” Setting the phrase off with punctuation suggests that it could be removed without affecting the coherence of the sentence, which isn’t the case.

"}, {"id": "db2e480a", "domain": "Standard English Conventions", "skill": "Form, Structure, and Sense", "difficulty": "M", "type": "mc", "stimulus": "

By the time Hawaiian king Kamehameha III ______blank the throne, the number of longhorn cattle, first introduced to the islands in 1793, had drastically increased, and so too had the need for paniolo (Hawaiian cowboys) to manage the wild herds that then roamed throughout the volcanic terrain.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

ascended

"}, {"id": "B", "text": "

will ascend

"}, {"id": "C", "text": "

ascends

"}, {"id": "D", "text": "

is ascending

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. \"Ascended\" is in the simple past tense. Since Kamehameha became king in the past, this makes the most sense.

Choice B is incorrect. \"Will ascend\" is in the future tense, but we wouldn’t know about Kamehameha III’s ascent if it hadn’t happened yet. The information in the sentence, as well as the tense of other verbs, tells us that the events described happened in the past. Choice C is incorrect. \"Ascends\" is in the simple present tense. However, the information in the sentence, as well as the tense of other verbs, tells us that the events described happened in the past. Choice D is incorrect. \"Is ascending\" is in the continuous present tense, which we use to show that something is ongoing, but this doesn’t make sense here—the information in the sentence, as well as the tense of other verbs, tells us that the events described happened in the past.

"}, {"id": "4c9a2aee", "domain": "Standard English Conventions", "skill": "Form, Structure, and Sense", "difficulty": "E", "type": "mc", "stimulus": "

Wanda Diaz-Merced is an astrophysicist who lost her sight when she was young. Diaz-Merced’s condition inspired her to develop software that can translate scientific data into sound. Sound-based tools ______blank scientists to detect subtle patterns in data. Such patterns may not be evident in traditional graphs.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

has enabled

"}, {"id": "B", "text": "

enable

"}, {"id": "C", "text": "

is enabling  

"}, {"id": "D", "text": "

enables

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. The convention being tested is subject-verb agreement. The plural verb \"enable\" agrees in number with the plural subject \"sound-based tools.\"

Choice A is incorrect because the singular verb \"has enabled\" doesn’t agree in number with the plural subject \"sound-based tools.\" Choice C is incorrect because the singular verb \"is enabling\" doesn’t agree in number with the plural subject \"sound-based tools.\" Choice D is incorrect because the singular verb \"enables\" doesn’t agree in number with the plural subject \"sound-based tools.\"

"}, {"id": "a30567fd", "domain": "Standard English Conventions", "skill": "Form, Structure, and Sense", "difficulty": "M", "type": "mc", "stimulus": "

Nuh\u0101d al-\u1e24add\u0101d, known as Fairuz, was one of the most beloved Lebanese singers of the twentieth century. Her broad singing repertoire—which included traditional forms, such as the Arabic qasida and maqam, alongside modern pop and jazz styles—lent Fairuz a timeless, cross-generational appeal, ______blank her the moniker “the soul of Lebanon.”

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

earned

"}, {"id": "B", "text": "

had earned

"}, {"id": "C", "text": "

earning

"}, {"id": "D", "text": "

earn

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. The word \"earning\" is being used to introduce an additional modifying phrase, which describes how Fairuz’s repertoire lent her cross-generational appeal. When a verb ends in -ing and doesn’t have a helper verb like \"is\" before it, it can be used to modify a noun or verb. This is appropriate here.

Choice A is incorrect. The underlined verb is being used to introduce additional descriptive information, which is set off from the rest of the sentence by a comma. Because there is no subject here, a finite form of the verb (like \"earned\") creates an error. We need another form of the verb that doesn’t require a subject and can introduce descriptive information. Choice B is incorrect. The underlined verb is being used to introduce additional descriptive information, which is set off from the rest of the sentence by a comma. Because there is no subject here, a finite form of the verb (like \"had earned\") creates an error. We need another form of the verb that doesn’t require a subject and can introduce descriptive information. Choice D is incorrect. The underlined verb is being used to introduce additional descriptive information, which is set off from the rest of the sentence by a comma. Because there is no subject here, a finite form of the verb (like \"earn\") creates an error. We need another form of the verb that doesn’t require a subject and can introduce descriptive information.

"}, {"id": "329255db", "domain": "Standard English Conventions", "skill": "Form, Structure, and Sense", "difficulty": "H", "type": "mc", "stimulus": "

Bengali author Toru Dutt’s A Sheaf Gleaned in French Fields (1876), a volume of English translations of French poems, ______blank scholars’ understanding of the transnational and multilingual contexts in which Dutt lived and worked.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

has enhanced

"}, {"id": "B", "text": "

are enhancing

"}, {"id": "C", "text": "

have enhanced

"}, {"id": "D", "text": "

enhance

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. The convention being tested is subject-verb agreement. The singular verb “has enhanced” agrees in number with the singular subject “A Sheaf Gleaned in French Fields,” which is the title of a book of poems.

Choice B is incorrect because the plural verb “are enhancing” doesn’t agree in number with the singular subject “A Sheaf Gleaned in French Fields.” Choice C is incorrect because the plural verb “have enhanced” doesn’t agree in number with the singular subject “A Sheaf Gleaned in French Fields.” Choice D is incorrect because the plural verb “enhance” doesn’t agree in number with the singular subject “A Sheaf Gleaned in French Fields.”

"}, {"id": "603755a5", "domain": "Standard English Conventions", "skill": "Boundaries", "difficulty": "E", "type": "mc", "stimulus": "

In 1959, marine biologist Dr. Albert Jones founded the Underwater Adventure Seekers, a scuba diving ______blank that is the oldest club for Black divers in the United States and that has helped thousands of diving enthusiasts become certified in the field.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

club

"}, {"id": "B", "text": "

club,

"}, {"id": "C", "text": "

club—

"}, {"id": "D", "text": "

club, and

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. “That is…field” is an essential supplement, so we should not use punctuation to separate it from “scuba diving club.” .

Choice B is incorrect. This choice creates a punctuation error. “That is…field” is an essential supplement, so we should not use a comma (or any kind of punctuation) to separate it from “scuba diving club.” . Choice C is incorrect. This choice creates a punctuation error. “That is…field” is an essential supplement, so we should not use a dash (or any kind of punctuation) to separate it from “scuba diving club.” . Choice D is incorrect. This choice creates a run-on sentence. It makes “that is…United States” into an awkward independent clause, but it also makes “that has…field” into its own awkward independent clause without the correct punctuation separating it. 

"}, {"id": "ad046778", "domain": "Standard English Conventions", "skill": "Boundaries", "difficulty": "M", "type": "mc", "stimulus": "

To humans, it does not appear that the golden orb-weaver spider uses camouflage to capture its ______blank the brightly colored arachnid seems to wait conspicuously in the center of its large circular web for insects to approach. Researcher Po Peng of the University of Melbourne has explained that the spider’s distinctive coloration may in fact be part of its appeal.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

prey, rather,

"}, {"id": "B", "text": "

prey rather,

"}, {"id": "C", "text": "

prey, rather;

"}, {"id": "D", "text": "

prey; rather,

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. The convention being tested is the coordination of main clauses within a sentence. The semicolon is correctly used to join the first main clause (“To humans…prey”) and the second main clause (“rather…approach”). Further, the comma after the adverb “rather” is correctly used to separate the adverb from the main clause (“the brightly…approach”) it modifies, logically indicating that the information in this clause (how the spider’s behavior appears to humans) is contrary to the information in the previous clause (how the spider’s behavior does not appear to humans).

Choice A is incorrect because it results in a comma splice. Without a conjunction following it, a comma can’t be used in this way to join two main clauses. Choice B is incorrect because it results in a run-on sentence. The two main clauses are fused without appropriate punctuation and/or a conjunction. Choice C is incorrect. Placing the comma between the first main clause “To humans…prey” and the adverb “rather” illogically indicates that the information in the first main clause is contrary to what came before, which doesn’t make sense in this context.

"}, {"id": "7ce4ee13", "domain": "Standard English Conventions", "skill": "Boundaries", "difficulty": "H", "type": "mc", "stimulus": "

After immigrating from Mexico and obtaining U.S. citizenship, Octaviano Ambrosio Larrazolo entered politics, earning a reputation for being a fervent defender of Hispanic civil rights. In 1919 Larrazolo was elected governor of ______blank in 1928 he became the nation’s first Hispanic U.S. Senator. 

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

New Mexico and

"}, {"id": "B", "text": "

New Mexico,

"}, {"id": "C", "text": "

New Mexico, and

"}, {"id": "D", "text": "

New Mexico

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. The convention being tested is the coordination of main clauses within a sentence. This choice correctly uses a comma and the coordinating conjunction \"and\" to join the first main clause (\"In 1919 Larrazolo was elected governor of New Mexico\") and the second main clause (\"in 1928 he became the nation’s first Hispanic US Senator\").

Choice A is incorrect because when coordinating two longer main clauses such as these, it’s conventional to use a comma before the coordinating conjunction. Choice B is incorrect because it results in a comma splice. Without a conjunction following it, a comma can’t be used in this way to join two main clauses. Choice D is incorrect because it results in a run-on sentence. The two main clauses are fused without punctuation and/or a conjunction.

"}, {"id": "0a114526", "domain": "Standard English Conventions", "skill": "Boundaries", "difficulty": "H", "type": "mc", "stimulus": "

In 1937, Chinese American screen actor Anna May Wong, who had portrayed numerous villains and secondary characters but never a heroine, finally got a starring role in Paramount Pictures’ Daughter of Shanghai, a film that ______blank “expanded the range of possibilities for Asian images on screen.”

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

critic, Stina Chyn, claims

"}, {"id": "B", "text": "

critic, Stina Chyn, claims,

"}, {"id": "C", "text": "

critic Stina Chyn claims

"}, {"id": "D", "text": "

critic Stina Chyn, claims,

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. The conventions being tested are punctuation use between titles and proper nouns and between verbs and integrated quotations. No punctuation is needed to set off the proper noun “Stina Chyn” from the title that describes Chyn, “critic.” Because “Stina Chyn” is essential information identifying the “critic,” no punctuation is necessary. Further, no punctuation is needed between the verb “claims” and the following quotation because the quotation is integrated into the structure of the sentence.

Choice A is incorrect because no punctuation is needed before or after the proper noun “Stina Chyn.” Setting the critic’s name off with commas suggests that it could be removed without affecting the coherence of the sentence, which isn’t the case. Choice B is incorrect because no punctuation is needed before or after the proper noun “Stina Chyn.” Setting the critic’s name off with commas suggests that it could be removed without affecting the coherence of the sentence, which isn’t the case. Additionally, no punctuation is needed between “claims” and the integrated quotation. Choice D is incorrect because no punctuation is needed between the verb “claims” and its subject, “critic Stina Chyn.” Additionally, no punctuation is needed between the verb “claims” and the integrated quotation.

"}, {"id": "42cc9236", "domain": "Standard English Conventions", "skill": "Form, Structure, and Sense", "difficulty": "E", "type": "mc", "stimulus": "

If you try on one of artist Nick Cave’s signature Soundsuits, you can expect to swish, rustle, or clang every time you move. Cave makes his suits out of found objects, everything from ceramic birds to broken record players. He carefully considers the sound an object makes before using ______blank in a suit.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

this

"}, {"id": "B", "text": "

that

"}, {"id": "C", "text": "

these

"}, {"id": "D", "text": "

it

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. The convention being tested here is pronoun-antecedent agreement. The singular pronoun \"it\" agrees in number with the singular antecedent \"object.\"

Choice A is incorrect. The singular pronoun \"this\" is used to refer to a specific thing, but here there is no specific object being referred to. Instead, the sentence is referring back to a hypothetical object that Cave might use in a Soundsuit. Choice B is incorrect. The singular pronoun \"that\" is used to refer to a specific thing, but here there is no specific object being referred to. Instead, the sentence is referring back to a hypothetical object that Cave might use in a Soundsuit. Choice C is incorrect because the plural pronoun \"these\" doesn’t agree in number with the singular antecedent \"object.\"

"}, {"id": "81ac953e", "domain": "Standard English Conventions", "skill": "Form, Structure, and Sense", "difficulty": "E", "type": "mc", "stimulus": "

In 1899, Swedish chemist Svante Arrhenius developed an equation to answer a long-standing question: why do chemical reactions speed up at higher temperatures? The Arrhenius equation, named for its creator, ______blank an important concept in modern chemistry.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

have remained

"}, {"id": "B", "text": "

remain

"}, {"id": "C", "text": "

remains

"}, {"id": "D", "text": "

are remaining

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. This choice uses the singular verb \"remains\" to match the singular subject \"equation.\"

Choice A is incorrect. The singular noun \"equation\" doesn’t match with the plural verb conjugation \"have remained.\" Choice B is incorrect. The singular noun \"equation\" doesn’t match with the plural verb conjugation \"remain.\" Choice D is incorrect. The singular noun \"equation\" doesn’t match with the plural verb conjugation \"are remaining.\"

"}, {"id": "50801257", "domain": "Standard English Conventions", "skill": "Form, Structure, and Sense", "difficulty": "H", "type": "mc", "stimulus": "

In 1994, almost 200 years after the death of Wang Zhenyi, the International Astronomical ______blank the contributions of the barrier-breaking 18th-century astronomer and author of “Dispute of the Procession of the Equinoxes,” naming a crater on Venus after her.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

Union would finally acknowledge

"}, {"id": "B", "text": "

Union to finally acknowledge

"}, {"id": "C", "text": "

Union, having finally acknowledged

"}, {"id": "D", "text": "

Union, finally acknowledging

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. It’s the only choice that offers a form of the verb “acknowledge” that can go with the subject “International Astronomical Union” to make a complete sentence. This might seem like an odd use of “would,” but when speaking from a point of view in the past, we can actually use “would” to express something that happened later. That’s the case here: 200 years after Wang Zhenyi’s death, the IAU would finally acknowledge her contributions.

Choice B is incorrect. This choice creates a sentence fragment. There’s no main verb elsewhere in the sentence, so we need a form of the verb “acknowledge” that can go with the subject “the International Astronomical Union” and serve as that main verb. “To acknowledge” can’t do that. Choice C is incorrect. This choice creates a sentence fragment. There’s no main verb elsewhere in the sentence, so we need a form of the verb “acknowledge” that can go with the subject “the International Astronomical Union” and serve as that main verb. “Having acknowledged” can’t do that. Choice D is incorrect. This choice creates a sentence fragment. There’s no main verb elsewhere in the sentence, so we need a form of the verb “acknowledge” that can go with the subject “the International Astronomical Union” and serve as that main verb. The “-ing” form can’t do that.

"}, {"id": "1f39ab8b", "domain": "Standard English Conventions", "skill": "Boundaries", "difficulty": "E", "type": "mc", "stimulus": "

In the novel Things Fall Apart by Chinua Achebe, Okonkwo is a leader of Umuofia (a fictional Nigerian clan) and takes pride in his culture’s traditions. However, when the arrival of European missionaries brings changes to Umuofia, the novel asks a central question: How ______blank

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

Umuofia’s traditions will be affected.

"}, {"id": "B", "text": "

will Umuofia’s traditions be affected.

"}, {"id": "C", "text": "

Umuofia’s traditions will be affected?

"}, {"id": "D", "text": "

will Umuofia’s traditions be affected?

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. The clause before the colon tells us that the novel “asks a question,” so the clause after the colon should be in the conventional form of a question: with the verb before the subject, and a question mark at the end. 

Choice A is incorrect. This choice ends the sentence with a period, which isn’t right. The clause before the colon tells us that the novel “asks a question,” so the clause after the colon should be that question. Choice B is incorrect. This choice ends the sentence with a period, which isn’t right. The clause before the colon tells us that the novel “asks a question,” so the clause after the colon should be that question. In Standard English, questions place the verb before the subject and end with a question mark. Choice C is incorrect. This choice doesn’t conform to the conventions of Standard English. In Standard English, questions place the verb before the subject.

"}, {"id": "a14eef71", "domain": "Standard English Conventions", "skill": "Form, Structure, and Sense", "difficulty": "H", "type": "mc", "stimulus": "

In 2015, a team led by materials scientists Anirudha Sumant and Diana Berman succeeded in reducing the coefficient of friction (COF) between two surfaces to the lowest possible level—superlubricity. A nearly frictionless (and, as its name suggests, extremely slippery) state, ______blank

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

when their COF drops below 0.01, two surfaces reach superlubricity.

"}, {"id": "B", "text": "

two surfaces, when their COF drops below 0.01, reach superlubricity.

"}, {"id": "C", "text": "

reaching superlubricity occurs when two surfaces’ COF drops below 0.01.

"}, {"id": "D", "text": "

superlubricity is reached when two surfaces’ COF drops below 0.01.

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. The subject of the modifier “a nearly frictionless state” is “superlubricity.” Subject-modifier placement requires a modifier and its subject to be next to one another, so “superlubricity” must be the first word in the missing clause.

Choice A is incorrect. This choice creates a subject-modifier placement error. The subject of the modifier “a nearly frictionless state” is “superlubricity.” Subject-modifier placement requires a modifier and its subject to be next to one another, so “superlubricity” must be the first word in the missing clause. Choice B is incorrect. This choice creates a subject-modifier placement error. The subject of the modifier “a nearly frictionless state” is “superlubricity.” Subject-modifier placement requires a modifier and its subject to be next to one another, so “superlubricity” must be the first word in the missing clause. Choice C is incorrect. This choice creates a subject-modifier placement error. The subject of the modifier “a nearly frictionless state” is “superlubricity.” Subject-modifier placement requires a modifier and its subject to be next to one another, so “superlubricity” must be the first word in the missing clause.

"}, {"id": "f868d438", "domain": "Standard English Conventions", "skill": "Boundaries", "difficulty": "H", "type": "mc", "stimulus": "

In 2018, the innovative works of Congolese sculptor and architect Bodys Isek ______blank were featured in City Dreams, a solo exhibition at New York’s Museum of Modern Art.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

Kingelez;

"}, {"id": "B", "text": "

Kingelez,

"}, {"id": "C", "text": "

Kingelez

"}, {"id": "D", "text": "

Kingelez:

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. The convention being tested is punctuation between a subject and a verb. No punctuation is needed when the subject of a sentence is immediately followed by a main verb. In this case, the sentence’s subject (“the innovative works of Congolese sculptor and architect Bodys Isek Kingelez”) is followed by the main verb “were featured,” and no punctuation should come between them.

Choice A is incorrect because no punctuation is needed between the subject and the verb. Choice B is incorrect because no punctuation is needed between the subject and the verb. Choice D is incorrect because no punctuation is needed between the subject and the verb.

"}, {"id": "6d4b2e1e", "domain": "Standard English Conventions", "skill": "Boundaries", "difficulty": "H", "type": "mc", "stimulus": "

The 1977 play And the Soul Shall Dance depicts two Japanese American farming families in Depression-era Southern California. Critics have noted the way pioneering ______blank compares the experiences of issei (Japanese nationals who emigrated to America) and nisei (their American-born children).

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

playwright, Wakako Yamauchi,

"}, {"id": "B", "text": "

playwright, Wakako Yamauchi

"}, {"id": "C", "text": "

playwright Wakako Yamauchi,

"}, {"id": "D", "text": "

playwright Wakako Yamauchi

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. The convention being tested is the use of punctuation between titles and proper nouns. No punctuation is needed to set off the proper noun \"Wakako Yamauchi\" from the title that describes Yamauchi, \"pioneering playwright.\" Because \"Wakako Yamauchi\" is essential information identifying the \"pioneering playwright,\" no punctuation is necessary.

Choice A is incorrect because no punctuation is needed before or after the proper noun \"Wakako Yamauchi.\" Setting the playwright’s name off with commas suggests that it could be removed without affecting the coherence of the sentence, which isn’t the case. Choice B is incorrect because no punctuation is needed between the title \"pioneering playwright\" and the proper noun \"Wakako Yamauchi.\" Choice C is incorrect because no punctuation is needed between the proper noun \"Wakako Yamauchi\" and the verb \"compares.\"

"}, {"id": "b85c19ed", "domain": "Standard English Conventions", "skill": "Form, Structure, and Sense", "difficulty": "M", "type": "mc", "stimulus": "

The violins handmade in the seventeeth century by Italian craftsman Antonio Stradivari have been celebrated as some of the finest in the world. In close collaboration with musicians, Stradivari introduced changes to the shape of a traditional violin, flattening some of the instrument’s curves and making ______blank lighter overall.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

those

"}, {"id": "B", "text": "

one

"}, {"id": "C", "text": "

them

"}, {"id": "D", "text": "

it

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. The convention being tested is pronoun–antecedent agreement. The singular pronoun “it” agrees in number with the singular antecedent “violin” and thus indicates that the traditional violin (and not its curves) was made lighter.

Choice A is incorrect because the plural pronoun “those” doesn’t agree in number with the singular antecedent “violin.” Choice B is incorrect because the singular pronoun “one” is ambiguous in this context; the resulting sentence leaves unclear what Stradivari made lighter. Choice C is incorrect because the plural pronoun “them” doesn’t agree in number with the singular antecedent “violin.”

"}, {"id": "109d5bbb", "domain": "Standard English Conventions", "skill": "Boundaries", "difficulty": "H", "type": "mc", "stimulus": "

With some 16,000 in attendance, the Second World Black and African Festival of Arts and ______blank or FESTAC ‘77, as the event was more commonly known—became the largest pan-African event on record. FESTAC drew people from around the world to Lagos, Nigeria, for a monthlong celebration of Black and African art, scholarship, and activism.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

Culture:

"}, {"id": "B", "text": "

Culture—

"}, {"id": "C", "text": "

Culture,

"}, {"id": "D", "text": "

Culture

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. The text uses a dash to introduce a nonessential element that explains the acronym FESTAC. The dash matches the dash that comes after “known,” ending the descriptive aside.

Choice A is incorrect. A colon can only come after an independent clause, which isn’t the case here. Choice C is incorrect. While punctuation is required to set off “or FESTAC…known” from the rest of the sentence, nonessential elements must be separated from the sentence with matching punctuation. Since a dash appears on the other side of the element, we can’t use a comma here. Choice D is incorrect. The descriptive aside “or FESTAC…known” is a nonessential element that must be separated with punctuation from the rest of the sentence. This choice fails to add the necessary punctuation before the nonessential element.

"}, {"id": "56770dda", "domain": "Standard English Conventions", "skill": "Form, Structure, and Sense", "difficulty": "E", "type": "mc", "stimulus": "

In his 1963 exhibition Exposition of Music—Electronic Television, Korean American artist Nam June Paik showed how television images could be manipulated to express an artist’s perspective. Today, Paik ______blank considered the first video artist.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

will be

"}, {"id": "B", "text": "

had been

"}, {"id": "C", "text": "

was

"}, {"id": "D", "text": "

is

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. The convention being tested is the use of verbs to express tense. In this choice, the present tense verb “is,” used in conjunction with the word “today,” correctly indicates that Paik is currently considered the first video artist.

Choice A is incorrect because the future-indicating verb “will be” doesn’t indicate that Paik is currently considered the first video artist. Choice B is incorrect because the past perfect tense verb “had been” doesn’t indicate that Paik is currently considered the first video artist. Choice C is incorrect because the past tense verb “was” doesn’t indicate that Paik is currently considered the first video artist.

"}, {"id": "d073983d", "domain": "Standard English Conventions", "skill": "Form, Structure, and Sense", "difficulty": "M", "type": "mc", "stimulus": "

Known for her massive photorealistic paintings of African American figures floating or swimming in pools, Calida Garcia ______blank was the logical choice to design the book cover for Ta-Nehisi Coates’s The Water Dancer, a novel about an African American man who can travel great distances through water.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

Rawles—

"}, {"id": "B", "text": "

Rawles:

"}, {"id": "C", "text": "

Rawles,

"}, {"id": "D", "text": "

Rawles

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. The convention being tested is punctuation between a subject and a verb. When, as in this case, a subject (“Calida Garcia Rawles”) is immediately followed by a verb (“was”), no punctuation is needed.

Choice A is incorrect because no punctuation is needed between the subject and the verb. Choice B is incorrect because no punctuation is needed between the subject and the verb. Choice C is incorrect because no punctuation is needed between the subject and the verb.

"}, {"id": "c468db1c", "domain": "Standard English Conventions", "skill": "Boundaries", "difficulty": "H", "type": "mc", "stimulus": "

A group of ecologists led by Axel Mithöfer at the Max Planck Institute for Chemical Ecology in Germany examined the defensive responses of two varieties of the sweet potato ______blank TN57, which is known for its insect resistance, and TN66, which is much more susceptible to pests.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

plant. 

"}, {"id": "B", "text": "

plant;

"}, {"id": "C", "text": "

plant 

"}, {"id": "D", "text": "

plant:

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. The convention being tested is punctuation use between a main clause and a supplementary phrase. In this choice, a colon is correctly used to mark the boundary between the main clause (“A group…plant”) and the supplementary element (“TN57…pests”) and to introduce the following elaboration on the specific varieties of sweet potato plants that were examined.

Choice A is incorrect because it results in a rhetorically unacceptable sentence fragment beginning with “TN57.”  Choice B is incorrect because a semicolon can’t be used in this way to join the main clause (“A group…plant”) and the supplementary element (“TN57…pests”). A semicolon is conventionally used to join two main clauses, whereas a colon is conventionally used to introduce an element that explains or amplifies the information in the preceding clause. Choice C is incorrect because it fails to mark the boundary between the main clause (“A group...plant”) and the supplementary element (“TN57...pests”) with appropriate punctuation.

"}, {"id": "8a9d2f4e", "domain": "Standard English Conventions", "skill": "Form, Structure, and Sense", "difficulty": "H", "type": "mc", "stimulus": "

Researchers studying the “terra-cotta army,” the thousands of life-size statues of warriors found interred near the tomb of Emperor Qin Shi Huang of China, were shocked to realize that the shape of each statue’s ears, like the shape of each person’s ears, ______blank unique.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

are

"}, {"id": "B", "text": "

 is

"}, {"id": "C", "text": "

were

"}, {"id": "D", "text": "

have been

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. The convention being tested is subject–verb agreement. because the singular verb “is” agrees in number with the singular subject “the shape.”

Choice A is incorrect because the plural verb “are” doesn’t agree in number with the singular subject “the shape.” Choice C is incorrect because the plural verb “were” doesn’t agree in number with the singular subject “the shape.” Choice D is incorrect because the plural verb “have been” doesn’t agree in number with the singular subject “the shape.”

"}, {"id": "576b2c70", "domain": "Standard English Conventions", "skill": "Form, Structure, and Sense", "difficulty": "E", "type": "mc", "stimulus": "

A member of the Cherokee Nation, Mary Golda Ross is renowned for her contributions to NASA’s Planetary Flight Handbook, which ______blank detailed mathematical guidance for missions to Mars and Venus.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

provided

"}, {"id": "B", "text": "

having provided

"}, {"id": "C", "text": "

to provide

"}, {"id": "D", "text": "

providing

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. The convention being tested is the use of finite verbs in a relative clause. Relative clauses, such as the one beginning with “which,” require a finite verb, a verb that can function as the main verb of a clause. This choice correctly supplies the clause with the finite past tense verb “provided.”

Choice B is incorrect because the non-finite participle “having provided” doesn’t supply the clause with a finite verb. Choice C is incorrect because the non-finite to-infinitive “to provide” doesn’t supply the clause with a finite verb. Choice D is incorrect because the non-finite participle “providing” doesn’t supply the clause with a finite verb.

"}, {"id": "dfbf5d33", "domain": "Standard English Conventions", "skill": "Form, Structure, and Sense", "difficulty": "H", "type": "mc", "stimulus": "

In 1453, English King Henry VI became unfit to rule after falling gravely ill. As a result, Parliament appointed Richard, Third Duke of York, who had a strong claim to the English throne, to rule as Lord Protector. Upon recovering two years later, ______blank forcing an angered Richard from the royal court and precipitating a series of battles later known as the Wars of the Roses.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

Henry resumed his reign,

"}, {"id": "B", "text": "

the reign of Henry resumed,

"}, {"id": "C", "text": "

Henry’s reign resumed,

"}, {"id": "D", "text": "

it was Henry who resumed his reign, 

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. The convention being tested is subject-modifier placement. This choice ensures that the introductory phrase “upon recovering two years later” appears immediately before the noun it modifies (“Henry”), clearly establishing that Henry recovered two years later.

Choice B is incorrect because it results in a dangling modifier. The placement of the noun phrase “the reign of Henry” immediately after the introductory phrase illogically suggests that the reign of Henry recovered two years later. Choice C is incorrect because it results in a dangling modifier. The placement of the noun phrase “Henry’s reign” immediately after the introductory phrase illogically suggests that Henry’s reign recovered two years later. Choice D is incorrect because it results in a dangling modifier. The placement of the function word “it” immediately after the introductory phrase illogically suggests that “it” recovered two years later.

"}, {"id": "f2eaaf5d", "domain": "Standard English Conventions", "skill": "Boundaries", "difficulty": "E", "type": "mc", "stimulus": "

At eight paragraphs long, the preamble to the constitution of ______blank country in Western Asia—is much longer than the one-paragraph preamble to the United States Constitution.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

Bahrain—a 

"}, {"id": "B", "text": "

Bahrain, a

"}, {"id": "C", "text": "

Bahrain a

"}, {"id": "D", "text": "

Bahrain: a

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. The convention being tested is the punctuation of a supplementary element within a sentence. The dash after “Bahrain” pairs with the dash after “Asia” to separate the supplementary element “a country in Western Asia” from the rest of the sentence. 

Choice B is incorrect because a comma can’t be paired with a dash in this way to separate the supplementary element from the rest of the sentence. Choice C is incorrect because it fails to use appropriate punctuation to separate the supplementary element from the rest of the sentence. Choice D is incorrect because a colon can’t be paired with a dash in this way to separate the supplementary element from the rest of the sentence.

"}, {"id": "ec08463d", "domain": "Standard English Conventions", "skill": "Form, Structure, and Sense", "difficulty": "E", "type": "mc", "stimulus": "

Botanists recognize over fifty different species of sunflower. One species, the silverleaf sunflower, ______blank both an early-flowering ecotype that tends to grow in coastal areas and a late-flowering ecotype that grows inland.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

having included

"}, {"id": "B", "text": "

including

"}, {"id": "C", "text": "

to include

"}, {"id": "D", "text": "

includes

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. This verb needs to function as the main verb in the sentence, with the subject “one species,” so it needs to be conjugated. This choice gives us the singular present tense “includes,” which is the only conjugated form of the verb among the choices. 

Choice A is incorrect. This doesn’t complete the text in a way that conforms to the conventions of Standard English. This verb needs to function as the main verb in the sentence, with the subject “one species,” so it needs to be conjugated. “Having included” is a participle form of the verb: it’s not conjugated and doesn’t function like a normal verb. Choice B is incorrect. This doesn’t complete the text in a way that conforms to the conventions of Standard English. This verb needs to function as the main verb in the sentence, with the subject “one species,” so it needs to be conjugated. “Including” is the gerund form of the verb: it’s not conjugated and doesn’t function like a normal verb. Choice C is incorrect. This doesn’t complete the text in a way that conforms to the conventions of Standard English. This verb needs to function as the main verb in the sentence, with the subject “one species,” so it needs to be conjugated. “To include” is the infinitive form of the verb: it’s not conjugated. 

"}, {"id": "4a90a978", "domain": "Standard English Conventions", "skill": "Form, Structure, and Sense", "difficulty": "E", "type": "mc", "stimulus": "

In 1990, California native and researcher Ellen Ochoa left her position as chief of the Intelligent Systems Technology Branch at a NASA research center ______blank the space agency’s astronaut training program.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

to join

"}, {"id": "B", "text": "

is joining

"}, {"id": "C", "text": "

joined

"}, {"id": "D", "text": "

joins

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. The convention being tested is the use of nonfinite verb forms in a sentence. The nonfinite to-infinitive verb \"to join\" is correctly used to form a subordinate clause that expresses why Ochoa left her position (to join the training program).

Choice B is incorrect because the finite verb \"is joining\" can’t be used in this way to indicate Ochoa’s action of joining the training program. A conjunction such as \"and\" would be needed to coordinate \"is joining\" with the previous finite verb, \"left.\" Choice C is incorrect because the finite verb \"joined\" can’t be used in this way to indicate Ochoa’s action of joining the training program. A conjunction such as \"and\" would be needed to coordinate \"joined\" with the previous finite verb, \"left.\" Choice D is incorrect because the finite verb \"joins\" can’t be used in this way to indicate Ochoa’s action of joining the training program. A conjunction such as \"and\" would be needed to coordinate \"joins\" with the previous finite verb, \"left.\"

"}, {"id": "59e41600", "domain": "Standard English Conventions", "skill": "Form, Structure, and Sense", "difficulty": "E", "type": "mc", "stimulus": "

Why are Rome’s famous concrete structures, such as the Colosseum, still standing after 2,000-plus years, when modern concrete may not even last for fifty? Scientists ______blank that the secret to Roman concrete’s durability was its unique blend of ingredients, which included volcanic ash and seawater.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

explain

"}, {"id": "B", "text": "

having explained

"}, {"id": "C", "text": "

explaining

"}, {"id": "D", "text": "

to explain

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. The convention being tested is the use of verb forms within a sentence. The main clause of a sentence requires a finite (tensed) verb, and this choice supplies the finite present tense verb “explain” to indicate what the scientists do.

Choice B is incorrect because it results in an ungrammatical sentence. The nonfinite participle “having explained” doesn’t supply the main clause with a finite verb. Choice C is incorrect because it results in an ungrammatical sentence. The nonfinite participle “explaining” doesn’t supply the main clause with a finite verb. Choice D is incorrect because it results in an ungrammatical sentence. The nonfinite to-infinitive “to explain” doesn’t supply the main clause with a finite verb.

"}, {"id": "d75d57a0", "domain": "Standard English Conventions", "skill": "Boundaries", "difficulty": "E", "type": "mc", "stimulus": "

While many video game creators strive to make their graphics ever more ______blank others look to the past, developing titles with visuals inspired by the “8-bit” games of the 1980s and 1990s. (The term “8-bit” refers to a console whose processor could only handle eight bits of data at once.)

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

lifelike but

"}, {"id": "B", "text": "

lifelike

"}, {"id": "C", "text": "

lifelike,

"}, {"id": "D", "text": "

lifelike, but

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. The convention being tested is punctuation between a subordinate clause and a main clause. This choice correctly uses a comma to mark the boundary between the subordinate clause (“While…lifelike”) and the main clause (“others look to the past”).

Choice A is incorrect because it results in an incomplete sentence with no main clause. Choice B is incorrect because it fails to mark the boundary between the subordinate clause (“While…lifelike”) and the main clause (“others…past”). Choice D is incorrect because it results in an incomplete sentence with no main clause.

"}, {"id": "a427a52c", "domain": "Standard English Conventions", "skill": "Boundaries", "difficulty": "M", "type": "mc", "stimulus": "

The Lion Light system, developed by Kenyan inventor Richard Turere, consists of LED lights installed around the perimeter of livestock pastures. Powered with ______blank the blinking LEDs keep lions away at night, thus protecting the livestock without risking harm to the endangered lions.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

energy collected, by solar panels, during the day

"}, {"id": "B", "text": "

energy collected by solar panels during the day

"}, {"id": "C", "text": "

energy collected by solar panels during the day,

"}, {"id": "D", "text": "

energy, collected by solar panels during the day,

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. The convention being tested is punctuation between a supplementary phrase and a main clause. This choice correctly uses a comma to mark the boundary between the supplementary phrase (“powered…day”), which describes how the LEDs are powered, and the main clause (“the blinking…night”).

Choice A is incorrect because it fails to mark the boundary between the supplementary phrase and the main clause with appropriate punctuation. Furthermore, placing commas around the phrase “by solar panels” suggests that it could be removed without affecting the coherence of the sentence, which isn’t the case. Choice B is incorrect because it fails to mark the boundary between the supplementary phrase and the main clause with appropriate punctuation. Choice D is incorrect. Placing commas around the phrase “collected by solar panels during the day″ suggests that it could be removed without affecting the coherence of the sentence, which isn’t the case.

"}, {"id": "3daf126e", "domain": "Standard English Conventions", "skill": "Form, Structure, and Sense", "difficulty": "H", "type": "mc", "stimulus": "

A model created by biologist Luis Valente predicts that the rate of speciation—the rate at which new species form—on an isolated island located approximately 5,000 kilometers from the nearest mainland ______blank triple the rate of speciation on an island only 500 kilometers from the mainland.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

being

"}, {"id": "B", "text": "

to be

"}, {"id": "C", "text": "

to have been

"}, {"id": "D", "text": "

will be

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. The convention being tested is finite and nonfinite verb forms within a sentence. Relative clauses, such as the one beginning with “that,” require a finite verb, a verb that can function as the main verb of a clause. This choice correctly supplies the clause with the finite future tense verb “will be.” 

Choice A is incorrect because the nonfinite participle “being” doesn’t supply the clause with a finite verb. Choice B is incorrect because the nonfinite to-infinitive “to be” doesn’t supply the clause with a finite verb. Choice C is incorrect because the nonfinite to-infinitive “to have been” doesn’t supply the clause with a finite verb.

"}, {"id": "975eda7c", "domain": "Standard English Conventions", "skill": "Form, Structure, and Sense", "difficulty": "E", "type": "mc", "stimulus": "

For thousands of years, people in the Americas ______blank the bottle gourd, a large bitter fruit with a thick rind, to make bottles, other types of containers, and even musical instruments. Oddly, there is no evidence that any type of bottle gourd is native to the Western Hemisphere; either the fruit or its seeds must have somehow been carried from Asia or Africa.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

to use

"}, {"id": "B", "text": "

have used

"}, {"id": "C", "text": "

having used

"}, {"id": "D", "text": "

using

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. The convention being tested is finite and nonfinite verb forms within a sentence. A main clause requires a finite verb to perform the action of the subject (in this case, “people in the Americas”), and this choice supplies the finite past perfect tense verb “have used” to indicate what people in the Americas used the gourd for. 

Choice A is incorrect because the nonfinite to-infinitive “to use” doesn’t supply the main clause with a finite verb. Choice C is incorrect because the nonfinite participle “having used” doesn’t supply the main clause with a finite verb. Choice D is incorrect because the nonfinite participle “using” doesn’t supply the main clause with a finite verb.

"}, {"id": "c04e9136", "domain": "Standard English Conventions", "skill": "Boundaries", "difficulty": "M", "type": "mc", "stimulus": "

The 2022 Nobel Prize in Chemistry was awarded to three pioneers in the field of click chemistry: two-time Nobel laureate Barry Sharpless, who coined the term “click chemistry” in 1998; Carolyn Bertozzi, founder of the Bertozzi Group at ______blank and Morten Meldal, a professor at the University of Copenhagen in Denmark. 

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

Stanford

"}, {"id": "B", "text": "

Stanford,

"}, {"id": "C", "text": "

Stanford:

"}, {"id": "D", "text": "

Stanford;

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. This choice correctly uses a semicolon to punctuate a complex list (which is made up of items that have commas in them).

Choice A is incorrect. This is a complex list, indicated by the semicolon between \"1998\" and \"Carolyn Bertozzi.\" What comes after the blank is a separate list item, so punctuation is needed after \"Stanford.\" Choice B is incorrect. This is a complex list, indicated by the semicolon between \"1998\" and \"Carolyn Bertozzi.\" The items in this list have internal punctuation in the form of commas and must therefore be separated by semicolons to avoid confusion. Choice C is incorrect. This is a complex list, indicated by the semicolon between \"1998\" and \"Carolyn Bertozzi.\" Colons aren’t used to separate items in a list.

"}, {"id": "588887b9", "domain": "Standard English Conventions", "skill": "Form, Structure, and Sense", "difficulty": "E", "type": "mc", "stimulus": "

In 1881, French chemist Camille Faure redesigned the rechargeable lead-acid battery. Faure’s design greatly increased the amount of electricity that the original battery, which the French physicist Gaston Planté ______blank fifteen years earlier, could hold.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

is inventing

"}, {"id": "B", "text": "

will invent

"}, {"id": "C", "text": "

invents

"}, {"id": "D", "text": "

had invented

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. Faure redesigned the battery in 1881, and the original battery was invented “fifteen years earlier.” Notice that this is the only choice in the past tense. To indicate that a past occurrence took place before another past occurrence, we need to use “had” + the past tense form of the verb. This is called the “past perfect” tense.

Choice A is incorrect. This choice creates a tense error. Planté invented the original battery in the past, so we shouldn’t use the present tense “is inventing.” Choice B is incorrect. This choice creates a tense error. Planté invented the original battery in the past, so we shouldn’t use the future tense “will invent.” Choice C is incorrect. This choice creates a tense error. Planté invented the original battery in the past, so we shouldn’t use the present tense “invents.”

"}, {"id": "fe41f258", "domain": "Standard English Conventions", "skill": "Boundaries", "difficulty": "M", "type": "mc", "stimulus": "

In ancient Greece, an Epicurean was a follower of Epicurus, a philosopher whose beliefs revolved around the pursuit of pleasure. Epicurus defined pleasure as “the absence of pain in the body and of trouble in the ______blank that all life’s virtues derived from this absence.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

soul,” positing

"}, {"id": "B", "text": "

soul”: positing 

"}, {"id": "C", "text": "

soul”; positing

"}, {"id": "D", "text": "

soul.” Positing 

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. The convention being tested is punctuation use between a main clause and a participial phrase. This choice correctly uses a comma to mark the boundary between the main clause (“Epicurus…‘soul’”) and the participial phrase (“positing…absence”) that provides additional information about how Epicurus defined pleasure.

Choice B is incorrect because a colon can’t be used in this way to join a main clause and a participial phrase. Choice C is incorrect because a semicolon can’t be used in this way to join a main clause and a participial phrase. Choice D is incorrect because it results in a rhetorically unacceptable sentence fragment beginning with “positing.”

"}, {"id": "9902d2de", "domain": "Standard English Conventions", "skill": "Boundaries", "difficulty": "E", "type": "mc", "stimulus": "

The Alvarez theory, developed in 1980 by physicist Luis Walter Alvarez and his geologist son Walter Alvarez, maintained that the secondary effects of an asteroid impact caused many dinosaurs and other animals to die ______blank it left unexplored the question of whether unrelated volcanic activity might have also contributed to the mass extinctions.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

out but

"}, {"id": "B", "text": "

out, but

"}, {"id": "C", "text": "

out

"}, {"id": "D", "text": "

out, 

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. The convention being tested is the coordination of main clauses within a sentence. This choice correctly uses a comma and the coordinating conjunction “but” to join the first main clause (“the Alvarez…out”) and the second main clause (“it left…extinctions”).

Choice A is incorrect because when coordinating two longer main clauses such as these, it’s conventional to use a comma before the coordinating conjunction. Choice C is incorrect because it results in a run-on sentence. The two main clauses are fused without punctuation and/or a conjunction. Choice D is incorrect because it results in a comma splice. Without a conjunction following it, a comma can’t be used in this way to join two main clauses.

"}, {"id": "cd2443c0", "domain": "Standard English Conventions", "skill": "Form, Structure, and Sense", "difficulty": "M", "type": "mc", "stimulus": "

A pioneer in the field of taphonomy (the study of how organic remains become fossils), ______blank may be just as prevalent in the fossil record as those of thick-shelled organisms.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

fossils of thin-shelled organisms, Anna Behrensmeyer demonstrated in a 2005 analysis,

"}, {"id": "B", "text": "

Anna Behrensmeyer demonstrated in a 2005 analysis that fossils of thin-shelled organisms

"}, {"id": "C", "text": "

it was demonstrated in a 2005 analysis by Anna Behrensmeyer that fossils of thin-shelled organisms

"}, {"id": "D", "text": "

a 2005 analysis—by Anna Behrensmeyer—demonstrated that fossils of thin-shelled organisms

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. The convention being tested is subject-modifier placement. This choice makes the noun phrase “Anna Behrensmeyer” the subject of the sentence and places it immediately after the modifying phrase “a pioneer…fossils.” In doing so, this choice clearly establishes that Anna Behrensmeyer—and not another noun in the sentence—is a pioneer in the field of taphonomy.

Choice A is incorrect because it results in a dangling modifier. The placement of the noun phrase “fossils of thin-shelled organisms” immediately after the modifying phrase illogically suggests that the “fossils” are a pioneer in the field of taphonomy. Choice C is incorrect because it results in a dangling modifier. The placement of the pronoun “it” immediately after the modifying phrase illogically suggests that “it” is a pioneer in the field of taphonomy. Choice D is incorrect because it results in a dangling modifier. The placement of the noun phrase “a 2005 analysis” immediately after the modifying phrase illogically suggests that “a 2005 analysis” is a pioneer in the field of taphonomy. 

"}, {"id": "e44db0a0", "domain": "Standard English Conventions", "skill": "Form, Structure, and Sense", "difficulty": "M", "type": "mc", "stimulus": "

Because a cycle of lunar phases ______blank 29.5 days to complete, it’s possible to observe two full moons in a single month, one at the beginning and one at the end. 

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

are taking

"}, {"id": "B", "text": "

have taken

"}, {"id": "C", "text": "

take

"}, {"id": "D", "text": "

takes

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. The convention being tested is subject-verb agreement. The singular verb \"takes\" agrees in number with the singular subject \"a cycle of lunar phases.\"

Choice A is incorrect because the plural verb \"are taking\" doesn’t agree in number with the singular subject \"a cycle of lunar phases.\" Choice B is incorrect because the plural verb \"have taken\" doesn’t agree in number with the singular subject \"a cycle of lunar phases.\" Choice C is incorrect because the plural verb \"take\" doesn’t agree in number with the singular subject \"a cycle of lunar phases.\"

"}, {"id": "96e5da01", "domain": "Standard English Conventions", "skill": "Form, Structure, and Sense", "difficulty": "E", "type": "mc", "stimulus": "

The alga species Chlorella vulgaris is very efficient at making oxygen. For this reason, scientists are currently exploring ways to use this species in space. C. vulgaris might be used, for example, to build future biological air exchange systems that ______blank oxygen for astronauts. 

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

are producing

"}, {"id": "B", "text": "

produced

"}, {"id": "C", "text": "

produce

"}, {"id": "D", "text": "

have produced

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. The convention being tested is the use of verbs to express tense. Simple present tense verbs can be used to describe actions that tend to occur, including in a hypothetical or future scenario. In this case, the simple present tense verb “produce” indicates what the air exchange systems might be able to do in the future (produce oxygen for astronauts).

Choice A is incorrect. The present progressive tense verb “are producing” suggests that the oxygen is currently being produced, not that it might be produced in the future. Choice B is incorrect because the past tense verb “produced” suggests that the oxygen was produced in the past, not that it might be produced in the future. Choice D is incorrect because the present perfect tense verb “have produced” suggests that the oxygen has been produced from a point in the past up to the present, not that it might be produced in the future.

"}, {"id": "2c4cd76d", "domain": "Standard English Conventions", "skill": "Boundaries", "difficulty": "H", "type": "mc", "stimulus": "

Researchers studying magnetosensation have determined why some soil-dwelling roundworms in the Southern Hemisphere move in the opposite direction of Earth’s magnetic field when searching for ______blank in the Northern Hemisphere, the magnetic field points down, into the ground, but in the Southern Hemisphere, it points up, toward the surface and away from worms’ food sources.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

food:

"}, {"id": "B", "text": "

food,

"}, {"id": "C", "text": "

food while

"}, {"id": "D", "text": "

food

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. The convention being tested is colon use within a sentence. A colon used in this way introduces information that illustrates or explains information that has come before it. In this case, the colon introduces the following explanation of why some roundworms in the Southern Hemisphere move in the opposite direction of Earth’s magnetic field.

Choice B is incorrect because it results in a comma splice. A comma can’t be used in this way to join two long independent clauses (“Researchers…food” and “in…sources”) such as these. Choice C is incorrect because it results in a run-on sentence. The two clauses (“Researchers…food” and “in…sources”) are fused without punctuation. Furthermore, the conjunction “while” fails to indicate that what follows is an explanation of why some roundworms in the Southern Hemisphere move in the opposite direction of Earth’s magnetic field. Choice D is incorrect because it results in a run-on sentence. The two clauses (“Researchers…food” and “in…sources”) are fused without punctuation and/or a conjunction.

"}, {"id": "12bd5b75", "domain": "Standard English Conventions", "skill": "Form, Structure, and Sense", "difficulty": "E", "type": "mc", "stimulus": "

With its towering, six-spired exterior of granitelike quartz monzonite, the Salt Lake Temple is one of the most instantly recognizable structures in the state of Utah. However, many people do not know that ______blank built over the course of forty years, with construction beginning in 1853 and ending in 1893.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

it was

"}, {"id": "B", "text": "

one was

"}, {"id": "C", "text": "

they were

"}, {"id": "D", "text": "

both were

"}], "answerId": "A", "acceptedAnswers": [], "rationale": "

Choice A is the best answer. The convention being tested is pronoun-antecedent agreement. The singular pronoun \"it\" agrees in number with the singular antecedent \"the Salt Lake Temple.\"

Choice B is incorrect because the singular pronoun \"one\" is ambiguous in this context; the resulting sentence leaves unclear whether there is only one Salt Lake temple or multiple. Choice C is incorrect because the plural pronoun \"they\" doesn’t agree in number with the singular antecedent \"the Salt Lake Temple.\" Choice D is incorrect because the plural pronoun \"both\" doesn’t agree in number with the singular antecedent \"the Salt Lake Temple.\"

"}, {"id": "3ed5ebb4", "domain": "Standard English Conventions", "skill": "Boundaries", "difficulty": "M", "type": "mc", "stimulus": "

In her analysis of Edith Wharton’s The House of Mirth (1905), scholar Candace Waid observes that the novel depicts the upper classes of New York society as “consumed by the appetite of a soulless ______blank an apt assessment given that The House of Mirth is set during the Gilded Age, a period marked by rapid industrialization, economic greed, and widening wealth disparities.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

materialism”; and

"}, {"id": "B", "text": "

materialism” and 

"}, {"id": "C", "text": "

materialism,”

"}, {"id": "D", "text": "

materialism”

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. The convention being tested is punctuation between a main clause and a supplementary noun phrase. This choice correctly uses a comma to mark the boundary between the main clause (“scholar…materialism”) and the supplementary noun phrase (“an apt assessment”) that describes Waid’s observation about how The House of Mirth depicts the upper classes of New York society.

Choice A is incorrect because a semicolon and the conjunction “and” can’t be used in this way to mark the boundary between a main clause and a supplementary noun phrase. Choice B is incorrect. Joining the main clause (“scholar…materialism”) and the following noun phrase with the conjunction “and” results in a confusing and illogical sentence that suggests that the novel depicts the upper classes of New York society as “an apt assessment,” which doesn’t make sense in this context. Choice D is incorrect because it fails to mark the boundary between the main clause and the supplementary noun phrase with appropriate punctuation.

"}, {"id": "67614549", "domain": "Standard English Conventions", "skill": "Form, Structure, and Sense", "difficulty": "M", "type": "mc", "stimulus": "

After winning the 1860 presidential election, Abraham Lincoln appointed Edward Bates, Salmon P. Chase, and William H. Seward to his cabinet. Lincoln’s decision was surprising, since each of these men had run against him, but historians have praised it, noting that Lincoln ______blank his rivals’ diverse talents to strengthen his administration.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

has leveraged

"}, {"id": "B", "text": "

is leveraging

"}, {"id": "C", "text": "

will leverage

"}, {"id": "D", "text": "

leveraged

"}], "answerId": "D", "acceptedAnswers": [], "rationale": "

Choice D is the best answer. The subject of the verb is “Lincoln,” and the first sentence tells us that we’re talking about something that Abraham Lincoln did in 1860. So the simple past tense “leveraged” fits the logic of the text.

Choice A is incorrect. This choice creates a tense issue. “Has leveraged” is the present perfect tense, which is used for an action that began in the past and continues into the present. Lincoln started leveraging his rivals’ talents in 1860—it’s definitely not still happening today. So the present perfect tense isn’t appropriate. Choice B is incorrect. This choice creates a tense issue. “Is leveraging” is the present tense, but Lincoln leveraged his rivals’ talents in 1860, so the present tense isn’t appropriate. Choice C is incorrect. This choice creates a tense issue. “Will leverage” is the future tense, but Lincoln leveraged his rivals’ talents in 1860, so the future tense isn’t appropriate.

"}, {"id": "78b88c04", "domain": "Standard English Conventions", "skill": "Boundaries", "difficulty": "H", "type": "mc", "stimulus": "

Joshua Hinson, director of the language revitalization program of the Chickasaw Nation in Oklahoma, helped produce the world’s first Indigenous-language instructional app, Chickasaw ______blank Chickasaw TV, in 2010; and a Rosetta Stone language course in Chickasaw, in 2015.

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

Basic; in 2009, an online television network;

"}, {"id": "B", "text": "

Basic; in 2009, an online television network,

"}, {"id": "C", "text": "

Basic, in 2009; an online television network,

"}, {"id": "D", "text": "

Basic, in 2009, an online television network, 

"}], "answerId": "C", "acceptedAnswers": [], "rationale": "

Choice C is the best answer. The convention being tested is the punctuation of items in a complex series. It’s conventional to use a semicolon to separate items in a complex series with internal punctuation, and in this choice, the semicolon after “2009” is conventionally used to separate the first item (“the world’s…2009”) and the second item (“an online…2010”) in the series of things that Hinson helped create. Further, the comma after “Basic” correctly pairs with the comma after “app,” and the comma after “network” correctly pairs with the comma after “TV” to set off the supplemental elements (“Chickasaw Basic” and “Chickasaw TV”) that provide the names of the app and the TV network, respectively. Altogether, the punctuation in this choice results in a sentence that clearly indicates that Hinson helped make a language app in 2009, an online TV network in 2010, and a language course in 2015.  

Choice A is incorrect because it fails to punctuate the complex series in a way that makes clear that Hinson helped make a language app in 2009, an online TV network in 2010, and a language course in 2015. Choice B is incorrect because it fails to punctuate the complex series in a way that makes clear that Hinson helped make a language app in 2009, an online TV network in 2010, and a language course in 2015. Choice D is incorrect because the comma after “2009” doesn’t match the semicolon used to separate the second and third items in the complex series.

"}, {"id": "bd11fe93", "domain": "Standard English Conventions", "skill": "Form, Structure, and Sense", "difficulty": "E", "type": "mc", "stimulus": "

Dr. Rocío Paola Caballero-Gill is a paleoceanographer. This means that Dr. Caballero-Gill doesn’t just study oceans as they are today. She uses chemistry and fossil evidence ______blank oceans as they were in the past. 

", "stem": "

Which choice completes the text so that it conforms to the conventions of Standard English?

", "choices": [{"id": "A", "text": "

has studied

"}, {"id": "B", "text": "

to study

"}, {"id": "C", "text": "

studied

"}, {"id": "D", "text": "

studies

"}], "answerId": "B", "acceptedAnswers": [], "rationale": "

Choice B is the best answer. The convention being tested is the use of verb forms within a sentence. The nonfinite to-infinitive verb “to study” is correctly used to form a subordinate clause that indicates what Dr. Caballero-Gill uses chemistry and fossil evidence for (to study oceans as they were in the past).

Choice A is incorrect because it results in an ungrammatical sentence. The finite verb “has studied” can’t be used in this way to form a subordinate clause that indicates what Dr. Caballero-Gill uses the evidence for. Choice C is incorrect because it results in an ungrammatical sentence. The finite verb “studied” can’t be used in this way to form a subordinate clause that indicates what Dr. Caballero-Gill uses the evidence for. Choice D is incorrect because it results in an ungrammatical sentence. The finite verb “studies” can’t be used in this way to form a subordinate clause that indicates what Dr. Caballero-Gill uses the evidence for.

"}]}