These 7 PSAT math practice questions focus on Algebra and Advanced Math, two of the four Math domains College Board lists for the PSAT/NMSQT (the others are Problem-Solving and Data Analysis, and Geometry and Trigonometry). Each one is modeled on a real question type from our Digital SAT question banks, with new numbers. The PSAT and SAT use the same Math layout (70 minutes, 44 questions), so these work for both. Try each one before you open the solution.
How to use this page
Give yourself about 95 seconds a question. That is the PSAT pace: College Board splits Math into 2 modules of 35 minutes and 22 questions, about 1 minute 35 seconds each, with questions ordered from easiest to hardest in each module. Write down your answer, then check. If you miss one, the solution names the trap so you can spot it next time.
Algebra
1. (Medium) For the linear function f, b is a constant and f(x) = 4x + b. If f(6) = 30, what is the value of b?
Show solution
Plug in x = 6: 4(6) + b = 30, so 24 + b = 30 and b = 6.
The trap: answering 30 or 24. The question asks for b, the constant.
2. (Medium) In this system, r is a constant, and the system has infinitely many solutions. What is the value of r?
3x + 5y = 12
rx + 20y = 48
Show solution
Infinitely many solutions means the two equations describe the same line. The second equation's y-term is 20y, which is 4 times 5y, and 48 is 4 times 12. So the whole first equation was multiplied by 4, and r = 4(3) = 12.
3. (Hard) In the equation c(x − 3) = −4(x + k), c and k are constants. The equation has exactly one solution. Which statement must be true?
A) c = −4 B) c ≠ −4 C) k = 3 D) k ≠ 3
Show solution
Expand both sides: cx − 3c = −4x − 4k. Move the x terms together: (c + 4)x = 3c − 4k. You can solve for exactly one x only if the coefficient c + 4 is not zero. So c ≠ −4. The answer is B.
The trap: k does not decide how many solutions there are. If c = −4, the equation has either no solution or infinitely many, depending on k.
Algebra word problems
4. (Medium) Two candidates ran for class president. A total of 6,300 votes were cast, and one candidate received twice as many votes as the other. How many votes did the winning candidate receive?
Show solution
Call the loser's votes v. The winner got 2v, so v + 2v = 6,300 and 3v = 6,300. That gives v = 2,100, and the winner got 2(2,100) = 4,200.
The trap: stopping at 2,100, which is the loser's total.
Linear tables, functions and exponential models
5. (Hard) The table shows four values of x and their y-values. There is a linear relationship between x and y. Which equation represents it?
| x | −10 | −4 | 4 | 10 |
|---|---|---|---|---|
| y | 80 | 50 | 10 | −20 |
A) y = −5x + 30 B) y = 5x + 30 C) y = −5x + 80 D) y = −30x + 5
Show solution
Slope: from x = −4 to x = 4, y drops from 50 to 10, so the slope is (10 − 50) ÷ (4 − (−4)) = −40 ÷ 8 = −5. Use (4, 10): 10 = −5(4) + b, so b = 30. The answer is A, y = −5x + 30. Check x = 10: −50 + 30 = −20. It matches.
The trap: C uses the first y-value, 80, as the intercept. The y-intercept is the y-value when x = 0, not when x = −10.
6. (Hard) A scientist runs a program to reduce an invasive beetle population. The function f(x) = 3,500(0.75)x estimates the population x years after 2010. What is the best interpretation of 3,500?
Show solution
At x = 0 (the year 2010), (0.75)0 = 1, so f(0) = 3,500. The 3,500 is the estimated beetle population in 2010, when the program started.
The trap: reading 3,500 as the yearly decrease. The 0.75 controls the decrease: each year the population is 75% of the year before, a 25% drop.
7. (Hard) For a linear function f, f(−9) = 11/3 and f(3) = −1/3. Which equation could define f?
A) f(x) = (2 − x)/3 B) f(x) = (x + 2)/3 C) f(x) = −3x + 2 D) f(x) = (11 − x)/3
Show solution
Slope: (−1/3 − 11/3) ÷ (3 − (−9)) = (−12/3) ÷ 12 = −4 ÷ 12 = −1/3. So f(x) = −x/3 + b. Use f(3) = −1/3: −1 + b = −1/3, so b = 2/3. That gives f(x) = −x/3 + 2/3 = (2 − x)/3, choice A. Check f(−9): (2 + 9)/3 = 11/3. It works.
Desmos shortcut: type each choice and check that it passes through (−9, 11/3) and (3, −1/3).
Want hundreds more like these?
Our question bank has real Digital SAT Math questions sorted by skill and difficulty. The PSAT tests the same skills.
Geometry practice
Students who took the October 2026 PSAT asked about an equilateral triangle inside a circle. We wrote two practice questions on that skill in our October 2026 PSAT recap. For circle rules you can check with Desmos, see our circle geometry guide.
What these questions tell you
If you missed 1, 2 or 4, review linear equations and word problems. They are the fastest points on the test. If you missed 3, 5 or 7, those are Hard items, the kind you see more of in the harder second module. If you missed 6, practice reading what each number in an exponential model means.
New to the test? Read what the PSAT is. Aiming for National Merit? Remember that Reading and Writing counts twice in your Selection Index, so balance math practice with our PSAT Reading and Writing practice questions and the PSAT vocabulary list.
Frequently asked questions
How many math questions are on the PSAT?
44, in 70 minutes, according to College Board.
What math is on the PSAT?
Four domains: Algebra, Advanced Math, Problem-Solving and Data Analysis, and Geometry and Trigonometry.
Can you use a calculator on the PSAT?
Yes. College Board says you can use an acceptable calculator on the entire Math section. Check your school's instructions for test day.
Are PSAT math questions the same as SAT math questions?
They test the same skills in the same format. These practice questions are modeled on real Digital SAT items from our banks.
Sources
- College Board, PSAT/NMSQT Math Section (four domains).
- College Board, How the PSAT/NMSQT Is Structured (70 minutes, 44 questions).
- The Test Advantage Digital SAT question banks (September 2026 and August 2026 Math), the source question types for these reskinned items.
Frequently Asked Questions
How many math questions are on the PSAT?
44 questions in 70 minutes, split into two 35-minute modules, according to College Board.
What math is on the PSAT?
Four domains: Algebra, Advanced Math, Problem-Solving and Data Analysis, and Geometry and Trigonometry.
Can you use a calculator on the PSAT?
Yes. College Board says an acceptable calculator can be used on the entire Math section.
Are PSAT math questions the same as SAT math questions?
They test the same skills in the same format. The practice questions on this page are modeled on real Digital SAT question types.