Questions and Answers by Content Skills https://goo.gl/MkMD29 PSAT 2013-2014 Questions and Answers by Content Skills https://goo.gl/MkMD29

Number and Operations [*18*], [*30*], [*36*] [*18*], [*30*], [*36*] Class of 2015-Problems which < 40% of the students answered correctly… [*18*], [*30*], [*36*] Class of 2016-Problems which < 40% of the students answered correctly… [*18*], [*30*], [*36*]

Difficulty: EASY (3 out of 9) Process Skill: Reasoning [1] If n - 3 is an even integer, which of the following could be the value of n? A. -3 B. -2 C. 0 D. 4 E. 6

A. -3 Difficulty: EASY (3 out of 9) Process Skill: Reasoning [1] If n - 3 is an even integer, which of the following could be the value of n? A. -3 B. -2 C. 0 D. 4 E. 6

Difficulty: EASY (2 out of 9) Process Skill: Reasoning [2] A rate of ½ mile per minute is equal to a rate of how many miles per hour? A. 20 B. 30 C. 40 D. 60 E. 120

B. 30 Difficulty: EASY (2 out of 9) Process Skill: Reasoning [2] A rate of ½ mile per minute is equal to a rate of how many miles per hour? A. 20 B. 30 C. 40 D. 60 E. 120

Difficulty: EASY (3 out of 9) Process Skill: Representation [5] Which of the following numbers is between 5/8 and 11/16? A. 0.3 B. 0.5 C. 0.62 D. 0.67 E. 0.75

D. 0.67 Difficulty: EASY (3 out of 9) Process Skill: Representation [5] Which of the following numbers is between 5/8 and 11/16? A. 0.3 B. 0.5 C. 0.62 D. 0.67 E. 0.75

Difficulty: MEDIUM (6 out of 9) Process Skill: Reasoning [14] Of 60 customers at a convenience store one morning, 18 bought milk, 23 bought candy, and 26 bought a newspaper. Each of these customers bought at least one of these items and none of those who bought milk bought either of the other two items. How many of the 60 customers bought both candy and a newspaper? A. 2 B. 7 C. 10 D. 16 E. 18

B. 7 Difficulty: MEDIUM (6 out of 9) Process Skill: Reasoning [14] Of 60 customers at a convenience store one morning, 18 bought milk, 23 bought candy, and 26 bought a newspaper. Each of these customers bought at least one of these items and none of those who bought milk bought either of the other two items. How many of the 60 customers bought both candy and a newspaper? A. 2 B. 7 C. 10 D. 16 E. 18

Difficulty: HARD (8 out of 9) Process Skill: Reasoning [*18*] How many positive 4-digit integers are divisible by 5 and have their hundreds digit equal to 8? A. 90 B. 120 C. 180 D. 190 E. 200

C. 180 Difficulty: HARD (8 out of 9) Process Skill: Reasoning [*18*] How many positive 4-digit integers are divisible by 5 and have their hundreds digit equal to 8? A. 90 B. 120 C. 180 D. 190 E. 200

Difficulty: EASY (3 out of 9) Process Skill: Communication [23] On a number line, the distance between the number n and 0 is the same as the distance between n2 and 0. Which of the following could be the value of n? A. -2 B. -1 C. -12 D. 2 E. 3

B. -1 Difficulty: EASY (3 out of 9) Process Skill: Communication [23] On a number line, the distance between the number n and 0 is the same as the distance between n2 and 0. Which of the following could be the value of n? A. -2 B. -1 C. -12 D. 2 E. 3

Difficulty: MEDIUM (5 out of 9) Process Skill: Problem Solving [*30*] As a car salesman, each week Ted earns $250 plus 1 percent of the selling price of each of the cars he sells. One week he sold three cars with selling prices of $15,000, $22,500, and $25,000. How much money, in dollars, did Ted earn that week as a car salesman?

Difficulty: MEDIUM (5 out of 9) Process Skill: Problem Solving [*30*] As a car salesman, each week Ted earns $250 plus 1 percent of the selling price of each of the cars he sells. One week he sold three cars with selling prices of $15,000, $22,500, and $25,000. How much money, in dollars, did Ted earn that week as a car salesman? Grid in 875.

Difficulty: MEDIUM (5 out of 9) Process Skill: Communication [32] The first term of the sequence above is 27, and each term after the first is equal to ⅓ of the proceeding term. What is the 6th term of the sequence?

Difficulty: MEDIUM (5 out of 9) Process Skill: Communication [32] The first term of the sequence above is 27, and each term after the first is equal to ⅓ of the proceeding term. What is the 6th term of the sequence? Grid in 1/9 or .111.

Difficulty: MEDIUM (7 out of 9) Process Skill: Reasoning [*36*] If x and y are two different numbers selected from the integers from 500 to 1000, inclusive, what is the greatest possible value for (x + y)/(x - y)?

Grid in 1999. Difficulty: MEDIUM (7 out of 9) Process Skill: Reasoning [*36*] If x and y are two different numbers selected from the integers from 500 to 1000, inclusive, what is the greatest possible value for (x + y)/(x - y)? Grid in 1999.

Algebra and Functions [*9*], [*20*], [*25*], [*27*], [*34*], [*38*] Class of 2015-Problems which < 40% of the students answered correctly… [*9*], [*20*], [*25*], [*27*], [*34*], [*38*] Class of 2016-Problems which < 40% of the students answered correctly… [*9*], 11, [*20*], [*25*], [*27*], [*34*], [*38*]

Difficulty: EASY (2 out of 9) Process Skill: Reasoning [3] If 15k + 5 = 80, what is the value of 3k + 1? A. 16 B. 10 C. 8 D. 5 E. 4

A. 16 Difficulty: EASY (2 out of 9) Process Skill: Reasoning [3] If 15k + 5 = 80, what is the value of 3k + 1? A. 16 B. 10 C. 8 D. 5 E. 4

Difficulty: EASY (3 out of 9) Process Skill: Reasoning [6] If x and y are positive integers such that x + y = 8 and x - y > 5, what is the value of x? A. 1 B. 2 C. 4 D. 6 E. 7

E. 7 Difficulty: EASY (3 out of 9) Process Skill: Reasoning [6] If x and y are positive integers such that x + y = 8 and x - y > 5, what is the value of x? A. 1 B. 2 C. 4 D. 6 E. 7

Difficulty: MEDIUM (4 out of 9) Process Skill: Problem Solving P(k) = k3- 20k2+ 300k - 500 [7] A manufacturer estimates that if k units of a certain tool are produced and sold, the total profit will be P dollars, where P is defined above as a function of k. Based on this estimate, the total profit of producing and selling 30 such tools will be which of the following? A. $17,500 B. $26,000 C. $35,500 D. $44,000 E. $53,500

Difficulty: MEDIUM (4 out of 9) Process Skill: Problem Solving P(k) = k3- 20k2+ 300k - 500 [7] A manufacturer estimates that if k units of a certain tool are produced and sold, the total profit will be P dollars, where P is defined above as a function of k. Based on this estimate, the total profit of producing and selling 30 such tools will be which of the following? A. $17,500 B. $26,000 C. $35,500 D. $44,000 E. $53,500

Difficulty: MEDIUM (5 out of 9) Process Skill: Representation [*9*] Kelly paid $60 last month to her health club and visited the club at least once that month. If she visited the club x times last month, what was her cost per visit, in dollars, in terms of x? A. x B. 6 + x C. 60x D. x/60 E. 60/x

E. 60/x Difficulty: MEDIUM (5 out of 9) Process Skill: Representation [*9*] Kelly paid $60 last month to her health club and visited the club at least once that month. If she visited the club x times last month, what was her cost per visit, in dollars, in terms of x? A. x B. 6 + x C. 60x D. x/60 E. 60/x

Difficulty: MEDIUM (4 out of 9) Process Skill: Representation [10] If xa = 2, what is the value of x3a? A. 4 B. 6 C. 8 D. 9 E. 12

C. 8 Difficulty: MEDIUM (4 out of 9) Process Skill: Representation [10] If xa = 2, what is the value of x3a? A. 4 B. 6 C. 8 D. 9 E. 12

Difficulty: MEDIUM (5 out of 9) Process Skill: Problem Solving |2x + y| > 5 [11] Which of the following points in the xy-plane satisfies the inequality above? A. (-3, -2) B. (-3, 4) C. (0, 0) D. (4, -4) E. (7, -10)

Difficulty: MEDIUM (5 out of 9) Process Skill: Problem Solving |2x + y| > 5 [11] Which of the following points in the xy-plane satisfies the inequality above? A. (-3, -2) B. (-3, 4) C. (0, 0) D. (4, -4) E. (7, -10)

Difficulty: MEDIUM (4 out of 9) Process Skill: Problem Solving [12] Gino bought 4 pounds of apples and 2.5 pounds of peaches for a total of $8.40. If the apples cost $1.20 per pound, the cost of the peaches per pound was how much greater than the cost of the apples per pound? A. $0.24 B. $0.27 C. $0.30 D. $0.35 E. $0.44

Difficulty: MEDIUM (4 out of 9) Process Skill: Problem Solving [12] Gino bought 4 pounds of apples and 2.5 pounds of peaches for a total of $8.40. If the apples cost $1.20 per pound, the cost of the peaches per pound was how much greater than the cost of the apples per pound? A. $0.24 B. $0.27 C. $0.30 D. $0.35 E. $0.44

Difficulty: HARD (9 out of 9) Process Skill: Reasoning [*20*] If x + 1/x > y - 1/y, which of the following could be true? x > y x < y x = y [A] I only [B] II only [C] I and III only [D] II and III only [E] I, II, and III

Difficulty: HARD (9 out of 9) Process Skill: Reasoning [*20*] If x + 1/x > y - 1/y, which of the following could be true? x > y x < y x = y [A] I only [B] II only [C] I and III only [D] II and III only [E] I, II, and III

Difficulty: EASY (1 out of 9) Process Skill: Problem Solving [21] If x = -2 and y = -1, what is the value of 6x - 5y? A. -16 B. -7 C. 7 D. 11 E. 17

E. 17 Difficulty: EASY (1 out of 9) Process Skill: Problem Solving [21] If x = -2 and y = -1, what is the value of 6x - 5y? A. -16 B. -7 C. 7 D. 11 E. 17

Geometry and Measurement Class of 2015-Problems which < 40% of the students answered correctly… 17, 19, 28, 35, 37 Class of 2016-Problems which < 40% of the students answered correctly… 8, 13, 17, 19, 28, 35, 37

Difficulty: EASY (3 out of 9) Process Skill: Communication [4] In the xy-plane above, point M(3, 4) is the midpoint of line segment AB. What is the y-coordinate of point B? A. 5 B. 6 C. 7 D. 8 E. 9

Difficulty: EASY (3 out of 9) Process Skill: Communication [4] In the xy-plane above, point M(3, 4) is the midpoint of line segment AB. What is the y-coordinate of point B? A. 5 B. 6 C. 7 D. 8 E. 9

Difficulty: MEDIUM (4 out of 9) Process Skill: Problem Solving [8] If a diameter of a circle has length 18 inches, what is the area, in square inches, of the circle? A. 9π B. 18π C. 36π D. 81π E. 324π

D. 81π Difficulty: MEDIUM (4 out of 9) Process Skill: Problem Solving [8] If a diameter of a circle has length 18 inches, what is the area, in square inches, of the circle? A. 9π B. 18π C. 36π D. 81π E. 324π

Difficulty: MEDIUM (5 out of 9) Process Skill: Connections [13] In the figure above l || k and m || n. Which of the following expressions shows x in terms of y and z? A. y - z B. y + z C. y + z/2 D. 90 - y - z E. 180 - y - z

Difficulty: MEDIUM (5 out of 9) Process Skill: Connections [13] In the figure above l || k and m || n. Which of the following expressions shows x in terms of y and z? A. y - z B. y + z C. y + z/2 D. 90 - y - z E. 180 - y - z

Difficulty: HARD (7 out of 9) Process Skill: Problem Solving [*17*] In the figure above, PQR has a height of 12. The triangle is to be completely divided into smaller, congruent non-overlapping triangles, each similar to PQR and each with a height of 4. How many smaller triangles will be there? A. 6 B. 9 C. 12 D. 15 E. 18

Difficulty: HARD (7 out of 9) Process Skill: Problem Solving [*17*] In the figure above, PQR has a height of 12. The triangle is to be completely divided into smaller, congruent non-overlapping triangles, each similar to PQR and each with a height of 4. How many smaller triangles will be there? A. 6 B. 9 C. 12 D. 15 E. 18

Difficulty: HARD (8 out of 9) Process Skill: Connections [*19*] If x is an integer such that 2 < x < 8, and a triangle has sides of length 2, 7, and x, how many possible values are there for x? A. One B. Two C. Three D. Four E. Five

B. Two Difficulty: HARD (8 out of 9) Process Skill: Connections [*19*] If x is an integer such that 2 < x < 8, and a triangle has sides of length 2, 7, and x, how many possible values are there for x? A. One B. Two C. Three D. Four E. Five

Difficulty: EASY (2 out of 9) Process Skill: Connections [22] In the figure above, l and m intersect at a point. What is the value of x? A. 40 B. 50 C. 60 D. 70 E. 80

Difficulty: EASY (2 out of 9) Process Skill: Connections [22] In the figure above, l and m intersect at a point. What is the value of x? A. 40 B. 50 C. 60 D. 70 E. 80

Difficulty: MEDIUM (4 out of 9) Process Skill: Problem Solving [24] In the figure above, BD || AE and AB || ED. What is the area of the square FBCE? A. 9 B. 12 C. 16 D. 20 E. 25

Difficulty: MEDIUM (4 out of 9) Process Skill: Problem Solving [24] In the figure above, BD || AE and AB || ED. What is the area of the square FBCE? A. 9 B. 12 C. 16 D. 20 E. 25

Difficulty: HARD (8 out of 9) Process Skill: Connections [*28*] The figure below shows a solid formed by joining the bases of two square pyramids to opposite faces of a cube. If each edge of the solid has length 5 inches, what is the total surface area, in square inches, of this solid? A. 100 + 25√3 (approximately 143.3) B. 100 + 50√3 (approximately 186.6) C.150 + 25√3 (approximately 193.3) D. 200 E.150 + 50√3 (approximately 236.6)

Difficulty: HARD (8 out of 9) Process Skill: Connections [*28*] The figure below shows a solid formed by joining the bases of two square pyramids to opposite faces of a cube. If each edge of the solid has length 5 inches, what is the total surface area, in square inches, of this solid? A. 100 + 25√3 (approximately 143.3) B. 100 + 50√3 (approximately 186.6) C.150 + 25√3 (approximately 193.3) D. 200 E.150 + 50√3 (approximately 236.6)

Difficulty: EASY (3 out of 9) Process Skill: Connections [31] The lengths of the sides of a triangle are 10, x, and x. If the perimeter of the triangle is 24, what is the value of x?

Grid in 7. Difficulty: EASY (3 out of 9) Process Skill: Connections [31] The lengths of the sides of a triangle are 10, x, and x. If the perimeter of the triangle is 24, what is the value of x? Grid in 7.

Difficulty: HARD (7 out of 9) Process Skill: Communication [*35*] A fan is made by gluing tissue paper to seven bamboo sticks that are joined at one point. The figures above show the nearly closed fan at the left and the fully opened fan on the right. When fully opened, the fan forms a semicircle. If the fan is opened to56of the full semicircle and the angles formed between consecutive bamboo sticks are equal, what is the degree measure of one of these angles?

Grid in 25. Difficulty: HARD (7 out of 9) Process Skill: Communication [*35*] A fan is made by gluing tissue paper to seven bamboo sticks that are joined at one point. The figures above show the nearly closed fan at the left and the fully opened fan on the right. When fully opened, the fan forms a semicircle. If the fan is opened to56of the full semicircle and the angles formed between consecutive bamboo sticks are equal, what is the degree measure of one of these angles? Grid in 25.

Difficulty: HARD (8 out of 9) Process Skill: Connections [*37*] The four points A(-2, n), B(-1, 2n), C(4, k), and D(3, 1) lie in the xy-coordinate plane. If AB and CD are opposite sides of parallelogram ABCD and 2 < n < 4, what is one possible value of k?

Difficulty: HARD (8 out of 9) Process Skill: Connections [*37*] The four points A(-2, n), B(-1, 2n), C(4, k), and D(3, 1) lie in the xy-coordinate plane. If AB and CD are opposite sides of parallelogram ABCD and 2 < n < 4, what is one possible value of k? 3 < x < 5

Data, Statistics, and Probability Class of 2015-Problems which < 40% of the students answered correctly… [*15*], [*16*], [*33*] Class of 2016-Problems which < 40% of the students answered correctly… [*15*], [*16*], [*33*]

Difficulty: MEDIUM (6 out of 9) Process Skill: Problem Solving List 1: 2, 3, 4, 5, 6, 7 List 2: 1, 2, 3, 6, 6, 8 [*15*] If, in the lists above, x is inserted in List 1 and 2x is inserted in List 2, then the new lists will have equal medians. What is the value of x? A. 2 B. 3 C. 4 D. 5 E. 6

A. 2 Difficulty: MEDIUM (6 out of 9) Process Skill: Problem Solving List 1: 2, 3, 4, 5, 6, 7 List 2: 1, 2, 3, 6, 6, 8 [*15*] If, in the lists above, x is inserted in List 1 and 2x is inserted in List 2, then the new lists will have equal medians. What is the value of x? A. 2 B. 3 C. 4 D. 5 E. 6

Difficulty: HARD (7 out of 9) Process Skill: Problem Solving [*16*] The line graph above shows the number of students in the computer lab during seven periods on one school day. Each of the students in the computer lab during lunch was also in the lab during two of the other periods. What is the maximum number of different students who could have been in the computer lab on that day? A. 156 B. 148 C. 132 D. 124 E. 116

Difficulty: HARD (7 out of 9) Process Skill: Problem Solving [*16*] The line graph above shows the number of students in the computer lab during seven periods on one school day. Each of the students in the computer lab during lunch was also in the lab during two of the other periods. What is the maximum number of different students who could have been in the computer lab on that day? A. 156 B. 148 C. 132 D. 124 E. 116

Difficulty: MEDIUM (5 out of 9) Process Skill: Problem Solving [26] Each of 25 students was shown the same photograph of a person and was then asked to estimate the person was born. The graph above shows the estimates. What percent of the students estimated a year of birth before 1992? A. 24% B. 32% C. 44% D. 56% E. 76%

Difficulty: MEDIUM (5 out of 9) Process Skill: Problem Solving [26] Each of 25 students was shown the same photograph of a person and was then asked to estimate the person was born. The graph above shows the estimates. What percent of the students estimated a year of birth before 1992? A. 24% B. 32% C. 44% D. 56% E. 76%

Difficulty: MEDIUM (5 out of 9) Process Skill: Problem Solving [*33*] In a survey, 120 college students each indicated their major, and the results are shown in the pictogram above. If a student from the group is chosen at random, what is the probability that the student is a history major?

Difficulty: MEDIUM (5 out of 9) Process Skill: Problem Solving [*33*] In a survey, 120 college students each indicated their major, and the results are shown in the pictogram above. If a student from the group is chosen at random, what is the probability that the student is a history major? ⅜ or .375