PSAT Math Practice Test Questions 2025

Last Updated on February 19, 2025

PSAT Math Practice Test Questions 2025—No Calculator is permitted. The test will consist of 17 Questions, and you will have 25 minutes to complete it. The Math sections on the PSAT are Sections 3 and 4. Section 3 contains 13 multiple-choice questions and 4 grid-in questions.

Although we’ll show you which mathematical concepts are most important for the PSAT, this PSAT Math Practice Test relies on your knowledge of basic math concepts. If you’re a little rusty, this test is for you. Review the math basics you’ll need to know before you continue.

PSAT Math Practice Test Questions No Calculator

Since these basic concepts appear in ways you’re probably not used to from math class, you need to prepare yourself with a set of test-specific problem-solving skills designed to help you solve PSAT Math problems.

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NMSQT/PSAT 10 Math Test No Calculator

NMSQT/PSAT 10 Math Test

Math Test – No Calculator
25 MINUTES, 17 QUESTIONS

For questions 1–13, solve each problem, choose the best answer from the choices provided, and fill in the corresponding circle on your answer sheet. For questions 14–17, solve the problem and enter your answer in the grid on the answer sheet. Please refer to the directions before question 14 on how to enter your answers in the grid. You may use any available space in your test booklet for scratch work.

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1)

Which of the following functions is represented in the graph above?

A) y = (x – 3)²

B) y = (x + 3)²

C) y = x – 3

D) y = x² + 3

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2) If b < 0, which of the following could be the graph of y = 3x + b?

A) A

B) B

C) C

D) D

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3) If $\frac{x^{2} - 4x + 3} {3}$ = 2(x – 1), what is one possible value of x ?

A) 3

B) 5

C) 6

D) 9

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4) From January of 1993 to January of 1999, the median income of U.S. households rose from 49,000 to 57,000. If this trend had continued linearly, which of the following equations could have been used to predict the median income, in thousands, in the United States x years after January 1999 ?

A) I = 49 + 8x

B) I = 57 + 8x

C) I = 57 + $frac{4} {3}x$

D) I = 49 + $frac{4} {3}x$

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5) If $\frac{3(z + 3)} {4}$ - $\frac{2(z - 2)} {3} = 2$ what is the value of z ?

A) -19

B) 13

C) 19

D) 41

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6)

Medical researchers measured the populations of bacteria in a petri dish after treatment with the new antibiotic as well as in a petri dish that was untreated. The graph above plots the populations of bacteria in both dishes. Which of the following expressions shows the difference in population between the treated petri dish and the control dish t hours after treatment?

A) 5,000(0.95)^t – 4,000(0.9)^t

B) 4,000(0.95)^t – 5,000(0.9)^t

C) 5,000(0.9)^t – 4,000(0.95)^t

D) 5,000(1.1)^t – 4,000(1.05)^t

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7) If $\frac{a^3}{\sqrt{ab}} = b$ and ab > 0, which of the following statements must

A) a = b³

B) a⁵ = b³

C) a² = b²

D) a² = b

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8) At the farmer’s market, a bag of apples and 3 cartons of strawberries cost $18 total. If a bag of apples costs 50% more than a carton of strawberries, how much does a bag of apples cost?

A) $4.00

B) $4.50

C) $5.13

D) $6.00

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9) The number of visitors, V, a website receives doubles every 3 months. If 6 months ago the website received 24,500 visitors, how many visitors, in thousands, will it receive t years from now?

A) V = 24.5(2^4t)

B) V = 98(2^t)

C) V = 98(2^4t)

D) V = 98(1^4t)

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10) At a store the cost of a shirt and two pairs of equally priced socks is $24, and the cost for three of the same shirt and two pairs of the same socks is $32. What is the cost of the shirt and one pair of socks?

A) 4

B) 10

C) 14

D) 56

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11) David is a criminology student and wants to determine the effect of several population parameters on the murder rate in a city. He collects data from hundreds of U.S. cities and determines that the number of murders can be approximated with a formula: M = P , $\frac{51 - I \sqrt{L}}{25}$ in which P is the population in thousands, I is the median income, and L is the literacy rate expressed as a decimal. Which of the following expresses I in terms of M, P, and L ?

A) $\frac{1}{\sqrt{L}} (51 - \frac{25M} {P}$

B) $\frac{1}{\sqrt{L}} \frac{25M} {P} - 49$

C) $\frac{M} {P} - \frac{51} {25} + \sqrt{L}$

D) $\sqrt{L} ( 51 - \frac{25M} {P}$

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12) The radius of circle O (not shown) is 4, and the radian measure of central angle AOB is between If $\frac{3 \pi}{4}$ and $\frac{5 \pi}{4}$ . Which of the following could be the length of the arc AB ?

A) 3π

B) 4π

C) 5π

D) 8π

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13) The value of John’s baseball card collection decreases exponentially over time, and the value of his silver collection increases exponentially over time. If the value of John’s two collections combined t years from now is given by the function $v = 500(1.05)^t + 600(0.95)^{\frac{t}{2}}$ , which of the following statements must be true?

A) John’s silver collection is more valuable currently than his baseball collection.

B) The value of John’s silver collection changes at a faster rate than the value of John’s baseball card collection.

C) John’s baseball card collection decreases in value by 10% every six months.

D) The total value of the two collections remains constant over time.

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14) If f(x) = 3x and g(x) = x – 3, what is the value of f(4) – g(2) ?

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15) There are 8 more males in Sara’s class than females. If $\frac{3}{5}$ of the students are male, how many students are in Sara’s class?

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16) For positive integers c and d, the value of c is at least 3 times the value of d. If the difference between c and d is no more than 8, what is the largest possible value of d ?

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17) The distance an object in motion travels is given by the following equation: Displacement = V_it + 0.5at², in which V_i, a, and t represent initial velocity, acceleration, and time, respectively. The final velocity of the object is calculated with the equation V_f = V_i + at. How long does an object travel, in seconds, if it has a displacement of 22 meters, an initial velocity of 15 meters per seconds, and a final velocity of 5 meters per second?

Your score is

See also:

PSAT 10 Reading Practice Test

PSAT 10 Writing and Language Practice Test

PSAT 10 Math Practice Test