PSAT 8/9 Math Practice Tests

Question 1

1. A snowplow clears a road at a constant rate of 60 meters every 4 minutes. At this rate, how many meters of road does the snowplow clear in 7 minutes? (A) 67 (B) 105 (C) 420 (D) 28

Question 2

1. 4x + 9 = 37 What value of x is the solution to the given equation? (A) 7 (B) 11.5 (C) 28 (D) 9.25

Question 3

A coordinate plane with x from -1 to 9 and y from -1 to 6, grid lines every 1 unit. A straight line crosses the y-axis at (0, 4) and the x-axis at (8, 0); it passes through (2, 3), (4, 2), and (6, 1).

1. The graph of the linear function f is shown. What is the value of f(4)? (A) 4 (B) 8 (C) 0 (D) 2

Question 4

1. (3x^2 + 5x - 4) + (2x^2 - 7x + 6) Which expression is equivalent to the given expression? (A) 5x^2 + 12x + 2 (B) 5x^4 - 2x^2 + 2 (C) 5x^2 - 2x + 2 (D) 5x^2 - 2x - 10

Question 5

1. A school chess club has 40 members. Of these members, 15 are in ninth grade. What percent of the club’s members are in ninth grade? (Disregard the % sign when entering your answer. For example, if your answer is 20%, enter 20.) (type your answer)

Question 6

1. At a garden center, shrubs cost $9 each and flats of flowers cost $6 each. The equation 9s + 6f = 120 represents buying s shrubs and f flats of flowers for a total of $120. If a customer bought 4 shrubs, how many flats of flowers did the customer buy? (type your answer)

Question 7

1. A pottery studio uses the equation C = 12h + 30 to find the total cost C, in dollars, for a customer who uses a pottery wheel for h hours. What is the best interpretation of 12 in this context? (A) The cost for each hour of using a pottery wheel is $12. (B) The customer uses the pottery wheel for 12 hours. (C) The total cost of using a pottery wheel for 1 hour is $12. (D) The fixed fee charged to each customer is $12.

Question 8

1. A rectangular dog run has a length that is 3 times its width. The perimeter of the dog run is 64 feet. What is the area, in square feet, of the dog run? (A) 768 (B) 256 (C) 192 (D) 24

Question 9

A dot plot titled Seeds Sprouted per Tray, with a number line from 3 to 11 labeled Number of seeds sprouted. Dots: 4 has 3 dots, 5 has 4 dots, 6 has 2 dots, 7 has 3 dots, 8 has 0 dots, 9 has 2 dots, and 10 has 1 dot. There are 15 dots in all.

1. The dot plot shows the number of seeds that sprouted in each of 15 planting trays. What is the median number of seeds that sprouted per tray? (A) 5 (B) 6 (C) 6.2 (D) 7

Question 10

1. 2x + y = 14 x - y = 1 The solution to the given system of equations is (x, y). What is the value of y? (A) 5 (B) 9 (C) 6 (D) 4

Question 11

1. f(x) = 4(3)^x For the given function f, what is the value of f(3)? (A) 108 (B) 1,728 (C) 36 (D) 324

Question 12

Triangle ABC with A at the lower left, C at the lower right, and B at the top, closer to C. The angle at A is labeled x degrees, the angle at B is labeled 2x degrees, and the angle at C is labeled 60 degrees.

1. In triangle ABC shown, the measure of angle A is x^°, the measure of angle B is 2x^°, and the measure of angle C is 60^°. What is the value of x? (type your answer)

Question 13

1. (x - 3)^2 = 49 What is the positive solution to the given equation? (type your answer)

Question 14

1. The table shows the after-school activity chosen by each of 110 eighth- and ninth-grade students. If one of the ninth-grade students is selected at random, what is the probability that the student chose chess? (A) (13)/(55) (B) (13)/(24) (C) (13)/(25) (D) (11)/(30)

Question 15

1. At a county fair, Rosa pays $8 to enter and $3 for each ride. She can spend at most $50 in all. Which inequality represents the possible numbers of rides, r, that Rosa can go on? (A) 8r + 3 ≤ 50 (B) 8 + 3r ≤ 50 (C) 8 + 3r ≥ 50 (D) 3(8 + r) ≤ 50

Question 16

1. The table shows three values of x and their corresponding values of y. There is a linear relationship between x and y. Which equation represents this relationship? (A) y = 3x + 11 (B) y = 9x - 7 (C) y = 5x + 1 (D) y = 3x + 5

Question 17

1. 4x^2 - 25 Which expression is equivalent to the given expression? (A) (2x - 5)(2x + 5) (B) (2x - 5)^2 (C) (4x - 5)(x + 5) (D) 2(2x^2 - 25)

Question 18

Scatterplot of hours in course (x, 0 to 11) versus typing speed in words per minute (y, 40 to 100). Points: (1, 59), (2, 53), (3, 56), (4, 72), (5, 66), (6, 79), (7, 72), (8, 88), (9, 81), (10, 85). The line of best fit y = 4x + 50 is drawn; points at x = 1, 4, 6, and 8 are above the line and the other 6 points are below it.

1. The scatterplot shows the number of hours x that each of 10 students spent in a typing course and each student’s typing speed y, in words per minute. A line of best fit, y = 4x + 50, is also shown. For how many of the 10 students is the actual typing speed greater than the speed predicted by the line of best fit? (A) 6 (B) 10 (C) 5 (D) 4

Question 19

1. At a café, 3 bagels and 2 juices cost a total of $7.50, and 1 bagel and 4 juices cost a total of $10.00. Each bagel has the same price, and each juice has the same price. What is the price, in dollars, of one juice? (type your answer)

Question 20

1. 3x + 4y = 10 6x + ay = 20 In the given system of equations, a is a constant. If the system has infinitely many solutions, what is the value of a? (type your answer)

Question 21

1. The function h(t) = -5(t - 3)^2 + 50 gives the height, in meters, of a model rocket t seconds after it is launched. According to the function, what is the maximum height, in meters, of the model rocket? (A) 3 (B) 45 (C) 50 (D) 5

Question 22

A right triangle. A vertical segment labeled 24 represents the platform; a horizontal segment labeled 70 represents the ground from the base of the platform; the right angle is at the base of the platform. The slanted segment from the top of the platform to the end of the ground segment is labeled zip line. Lengths are in meters.

1. A straight zip line runs from the top of a platform to a point on level ground, as shown. The platform is 24 meters tall and stands straight up from the ground, and the zip line reaches the ground 70 meters from the base of the platform. What is the length, in meters, of the zip line? (A) 94 (B) 74 (C) 46 (D) sqrt4,324

Question 1

1. A ceramics studio uses 750 grams of clay to make each mug (1 kilogram = 1,000 grams). How many kilograms of clay does the studio need to make 36 mugs? (A) 270 (B) 2.7 (C) 27 (D) 27,000

Question 2

1. 3(x - 4) = 2x + 5 What is the solution to the given equation? (A) 17 (B) 9 (C) -7 (D) 7

Question 3

1. For the linear function f, f(2) = 11 and f(6) = 23. What is the value of f(10)? (A) 55 (B) 41 (C) 29 (D) 35

Question 4

1. (2x + 3)(x - 4) Which expression is equivalent to the given expression? (A) 2x^2 - 12 (B) 2x^2 - 5x - 12 (C) 2x^2 + 5x - 12 (D) 2x^2 - 11x - 12

Question 5

1. The solar panels on a school produced 3,200 kilowatt-hours of electricity in March and 4,000 kilowatt-hours in April. The amount produced in April was p% of the amount produced in March. What is the value of p? (type your answer)

Question 6

1. In the xy-plane, a line has the equation 3x - 4y = 24. What is the slope of the line? (type your answer)

Question 7

1. Dana traveled a total of 36 kilometers in 5 hours. She walked part of the time at 4 kilometers per hour and cycled the rest of the time at 12 kilometers per hour. How many hours did Dana spend cycling? (A) 3 (B) 2 (C) 9 (D) 2.25

Question 8

1. The mean of Jordan’s first 6 quiz scores is 84. After Jordan takes a seventh quiz, the mean of all 7 quiz scores is 85. What is Jordan’s score on the seventh quiz? (A) 85 (B) 86 (C) 90 (D) 91

Question 9

Two horizontal parallel lines: line AB on top (A at left, B at right) and line CD below (C at left, D at right). A slanted line rises from lower left to upper right and crosses both. At the lower intersection, the angle between the slanted line and the part of line CD toward D (above line CD, to the right of the slanted line) is labeled (3x + 10) degrees. At the upper intersection, the angle between the slanted line and the part of line AB toward A (below line AB, to the left of the slanted line) is labeled (5x - 30) degrees. The two labeled angles are alternate interior angles.

1. In the figure, line AB is parallel to line CD, and a third line intersects both of them. What is the value of x? (A) 20 (B) 25 (C) 70 (D) 110

Question 10

1. The function P(t) = 1,200(0.9)^t estimates the number of fish in a lake t years after a survey was taken. Which statement best describes how the estimated number of fish changes according to the function? (A) It increases by 90% each year. (B) It decreases by 90% each year. (C) It decreases by 10% each year. (D) It decreases by 0.9 fish each year.

Question 11

1. 5 - 2x < -9 Which of the following values of x is a solution to the given inequality? (A) -7 (B) 6 (C) 7 (D) 8

Question 12

1. 2x^2 - 7x - 15 = 0 What is the positive solution to the given equation? (type your answer)

Question 13

1. A rectangular box has inside dimensions of 10 inches by 8 inches by 6 inches. The box is to be filled completely with identical cubes that each have an edge length of 2 inches. How many cubes are needed to fill the box? (type your answer)

Question 14

1. The table shows the preferred class type and preferred time of day of each of 150 members of a fitness center. If a member who does not prefer yoga is selected at random, what is the probability that the member prefers the evening? (A) (3)/(5) (B) (2)/(5) (C) (3)/(4) (D) (8)/(15)

Question 15

A coordinate plane with x from -2 to 7 and y from -4 to 6, grid lines every 1 unit. A straight line falls from left to right, passing through the labeled points (0, 4) and (4, -2); it crosses the x-axis between x = 2 and x = 3.

1. The graph of the linear function f is shown in the xy-plane. Which equation defines f? (A) f(x) = -(2)/(3)x + 4 (B) f(x) = -(3)/(2)x + 4 (C) f(x) = (3)/(2)x + 4 (D) f(x) = 4x - (3)/(2)

Question 16

A coordinate plane with x from -1 to 7 and y from -5 to 6. An upward-opening parabola crosses the x-axis at the labeled points (1, 0) and (5, 0); its lowest point is the labeled point (3, -4).

1. The graph of y = f(x), where f is a quadratic function, is shown. Which of the following could define f? (A) f(x) = (x + 1)(x + 5) (B) f(x) = (x - 3)^2 + 4 (C) f(x) = (x - 1)(x - 5) (D) f(x) = (x + 3)^2 - 4

Question 17

1. Tank A contains 480 liters of water and is being drained at a constant rate of 12 liters per minute. At the same time, Tank B contains 60 liters of water and is being filled at a constant rate of 18 liters per minute. After how many minutes will the two tanks contain the same amount of water? (A) 70 (B) 35 (C) 14 (D) 18

Question 18

Scatterplot of days after planting (x, 0 to 32) versus height in centimeters (y, 0 to 90). Points: (5, 21), (8, 31), (10, 32), (13, 43), (15, 48), (18, 52), (20, 59), (23, 64), (25, 71), (28, 76), (30, 81). The line of best fit y = 2.4x + 10 passes close to all of the points.

1. The scatterplot shows the height y, in centimeters, of a sunflower plant x days after it was planted. A line of best fit for the data, y = 2.4x + 10, is also shown. Based on the line of best fit, which of the following is closest to the predicted increase in the plant’s height, in centimeters, for every increase of 5 days? (A) 12 (B) 2.4 (C) 22 (D) 0.48

Question 19

1. 2x + 3y = 23 3x + 2y = 22 If (x, y) is the solution to the given system of equations, what is the value of x + y? (type your answer)

Question 20

1. (x + 5)^2 = x^2 + kx + 25 In the given equation, k is a constant. The equation is true for all values of x. What is the value of k? (type your answer)

Question 21

A coordinate plane with x from -4 to 6 and y from -1 to 9, grid lines every 1 unit. Segment RS joins point R at (-3, 2) and point S at (5, 8).

1. Points R(-3, 2) and S(5, 8) are shown in the xy-plane. What is the distance between points R and S? (A) 14 (B) 100 (C) 6 (D) 10

Question 22

1. A school band is holding a car wash to raise at least $600. The band charges $12 to wash an SUV and $8 to wash a car. So far, the band has washed 30 SUVs. What is the least number of cars the band must wash to reach its goal? (A) 75 (B) 30 (C) 20 (D) 50