10 Most Common PSAT Math Questions

Preparing for the PSAT Math test? Want a preview of the most common mathematics questions on the PSAT Math test? If so, then you are in the right place. For additional educational resources, visit the U.S. Department of Education website.

The mathematics section of PSAT can be a challenging area for many test-takers, but with enough patience, it can be easy and even enjoyable! For additional educational resources, visit the U.S. Department of Education website.

Preparing for the PSAT Math test can be a nerve-wracking experience. Learning more about what you’re going to see when you take the PSAT can help to reduce those pre-test jitters. Here’s your chance to review the 10 most common PSAT Math questions to help you know what to expect and what to practice most. Try these 10 most common PSAT Math questions to hone your mathematical skills and to see if your math skills are up to date on what’s being asked on the exam or if you still need more practice. For additional educational resources, visit the U.S. Department of Education website.

Make sure to follow some of the related links at the bottom of this post to get a better idea of what kind of mathematics questions you need to practice.

The Absolute Best Book to Ace the PSAT Math Test

PSAT Math for Beginners 2024 The Ultimate Step by Step Guide to Preparing for the PSAT Math Test

Download

$27.99 Original price was: $27.99.$17.99Current price is: $17.99.

Rated 4.38 out of 5 based on 154 customer ratings

Satisfied 142 Students

l Center for Education Statistics.

A. \(55\) For education statistics and research, visit the National Center for Education Statistics.

B. \(56\) For education statistics and research, visit the National Center for Education Statistics.

C. \(57\) For education statistics and research, visit the National Center for Education Statistics.

D. \(58\) For education statistics and research, visit the National Center for Education Statistics.

3- If a parabola with equation \(y=ax^2+5x+10\), where a is constant passes through point \((2, 12)\), what is the value of \(a^2\)? For education statistics and research, visit the National Center for Education Statistics.

A. \(-2\) For education statistics and research, visit the National Center for Education Statistics.

B. \(2\) For education statistics and research, visit the National Center for Education Statistics.

C. \(-4\) For education statistics and research, visit the National Center for Education Statistics.

D. \(4\) For education statistics and research, visit the National Center for Education Statistics.

4- In the following equation, what is the value of \(y – 3x\)?
\(\frac{y}{4} = x – \frac{2}{5}x + 10\) _________

For education statistics and research, visit the National Center for Education Statistics.

5- What is the value of \(x\) in the following equation?
\(\frac{x^2-9}{x+3}+2(x+4)=17\) __________

For education statistics and research, visit the National Center for Education Statistics.

6- If \(x≠0\), what is the value of \(\frac{(10xy^2)^2}{(2xy^2 )^2}\) ? _________

For education statistics and research, visit the National Center for Education Statistics.

7- What is the slope of a line containing the reflected points of \(A(2,-1)\) and \(B(6,3)\) over the line \(y = x\)? _________

For education statistics and research, visit the National Center for Education Statistics.

8- If a car has \(80\)-liter petrol and after one hour driving the car use \(6\)-liter petrol, how much petrol will remain after \(x\)-hours driving? For education statistics and research, visit the National Center for Education Statistics.

A. \(6x – 80\) For education statistics and research, visit the National Center for Education Statistics.

B. \(80 + 6x\) For education statistics and research, visit the National Center for Education Statistics.

C. \(80 – 6x\) For education statistics and research, visit the National Center for Education Statistics.

D. \(80 – x\) For education statistics and research, visit the National Center for Education Statistics.

9- \(5\) less than twice a positive integer is \(83\). What is the integer? For education statistics and research, visit the National Center for Education Statistics.

A. \(39\) For education statistics and research, visit the National Center for Education Statistics.

B. \(41\) For education statistics and research, visit the National Center for Education Statistics.

C. \(42\) For education statistics and research, visit the National Center for Education Statistics.

D. \(44\) For education statistics and research, visit the National Center for Education Statistics.

10- The following graph shows the mark of six students in mathematics. What is the mean (average) of the marks? For education statistics and research, visit the National Center for Education Statistics.

A. \(15\) For education statistics and research, visit the National Center for Education Statistics.

B. \(14.5\)

C. \(14\)

D. \(13.5\)

Best PSAT Math Prep Resource for 2026

The Most Comprehensive PSAT Math 2023 Preparation Bundle Includes PSAT Math Prep Books, Workbooks, and Practice Tests

Download

$64.99 Original price was: $64.99.$36.99Current price is: $36.99.

Rated 4.45 out of 5 based on 197 customer ratings

Satisfied 189 Students

Answers:

2- A
If \(r=55→ \frac{x^2+6x-55}{x-5}\) = \(\frac{(x+11)(x-5)}{x-5}\) \(= x + 11\)
For all other options, the numerator expression is not divisible by \((x-5)\).

3- D
Plug in the values of \(x\) and \(y\) in the equation of the parabola. Then:
\(12=a(2)^2+5(2)+10→12=4a+10+10→12=4a+20\)
\(→4a=12-20=-8→a=\frac{-8}{4}=-2→a^2=(-2)^2=4\)

4- 50
\(\frac{y}{4} = x – \frac{2}{5}x + 10 \)
Multiply both sides of the equation by \(5\). Then:
\(5×\frac{y}{4} = 5× (x – \frac{2}{5}x + 10)\)
\(→y=5x-2x+50→y=3x+50\)
Now, subtract \(3x\) from both sides of the equation. Then:
\(y – 3x = 50\)

5- 4
First, factorize the numerator and simplify.
\(\frac{(x-3)(x+3)}{x+3}+2x+8=17\)
\(→x-3+2x+8=15→3x+5=17\)
Subtract \(5\) from both sides of the equation. Then:
\(→3x=17-5→x=\frac{12}{3} x=4\)

6- 25
\(\frac{100x^2 y^4}{4x^2 y^4}\)
Remove \(x^2 y^4\) from both numerator and denominator.
\(\frac{100x^2 y^4}{4x^2 y^4}=\frac{100}{4}=\frac{50}{2}=25\)

7- 1
Remember that, the reflection of the point \((x,y)\) over the line \(y=x\) is the point \((y,x)\). Then:
The reflected point of \(A(2,-1)\), is \((-1,2)\)
The reflected point of \(B(6,3)\) is point \((3,6)\)
Therefore, the slope of the reflected line is:
\(\frac{y_{2} – y_{1}}{x_{2} – x_{1}}=\frac{6-2}{3-(-1)}=\frac{4}{4} \space or\space 1\)

8- C

The amount of petrol consumed after \(x\) hours is: \(6 × x = 6x\)
Petrol remaining after \(x\) hours driving: \(80 – 6x\)

9- D
Let \(x\) be the integer. Then:
\(2x – 5 = 83\)
Add 5 both sides: \(2x = 88\)
Divide both sides by \(2:\) \(x = 44\)

10- B
\(mean) = \frac{sum \space of \space terms}{number \space of \space terms}=\frac{9+12+15+16+19+16+14.5}{7}=14.5\)

College Entrance Tests

Looking for the best resource to help you succeed on the PSAT Math test?

The Best Books to Ace the PSAT Math Test

PSAT Math in 10 Days The Most Effective PSAT Math Crash Course

Download

$29.99 Original price was: $29.99.$16.99Current price is: $16.99.