PSAT Math Practice Test Questions

A. (6,1)

B. (5,4)

C. (3,3)

D. (2,2)

7- A football team won exactly \(80\%\) of the games it played during the last session. Which of the following could be the total number of games the team played last season?

A. 49

B. 35

C. 12

D. 32

8- If \(x\) is greater than 0 and less than 1, which of the following is true?

A. \(x<\sqrt {(x^2+1)}<\sqrt{(x^2 )}+1\)

B. \(x<\sqrt {(x^2 )}+1<\sqrt {(x^2+1)}\)

C. \((\sqrt {(x^{2} + 1)}< x <\sqrt {(x^{2} ) }+ 1\)

D. \(\sqrt {(x^{2} )}+1< \sqrt{(x^{2}+1) }< x\)

9- If \(x\) is directly proportional to the square of \(y\), and \(y=2\) when \(x=12\), then when \(x=75 y=\)?

A. \(\frac{1}{5}\)

B. 1

C. 5

D. 12

10- Jack earns $616 for his first 44 hours of work in a week and is then paid 1.5 times his regular hourly rate for any additional hours. This week, Jack needs $826 to pay his rent, bills, and other expenses. How many hours must he work to make enough money this week?

A. 40

B. 48

C. 53

D. 54

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- C
\(x+4y=10\)
\(5x+10y=20\)
Multiply the top equation by -5 then,
\(-5x-20y=-50\)
\(5x+10y=20\)
Add two equations
\(-10y=-30→y=3 \) plug in the value of y into the first equation
\(x+4y=10→x+4(3)=10→x+12=10\)
Subtract 12 from both sides of the equation. Then:
\(x+12=10→x=-2\)

3- A
\(6b=5a\sqrt3→b= \frac{5a\sqrt3}{6}\)
\(Therefore:\)
\(\frac{2b\sqrt3}{4a}=\frac{2× \frac{5a\sqrt3}{6}×\sqrt3}{4a}=\frac{2×5a×3}{4×6a}=\frac{5}{4}\)

4- D
\( \frac{2}{5} ×25= \frac{50}{5} =10\)

5- D
The slop of line A is:
\(\frac{y_{2} – y_{1}}{x_{2} – x_{1}} = \frac{3-2}{4-3}=1 \)
Parallel lines have the same slope and only choice \(D (y=x)\) has slope of 1.

6- A

Line AB is the best fit line.
Then, point (6,1) is the farthest from line AB.

7- B
Choices \(A, C\) and \(D\) are incorrect because \(80\%\) of each of the numbers is a non-whole number.
\(49, 80 \% \ of \ 49 = 0.80×49=39.2\)
\(35, 80 \% \ of \ 35=0.80×35=28\)
\(12, 80 \% \ of \ 12=0.80×12=9.6\)
\(32, 80 \% \ of \ 32=0.80×32=25.6\)

8- A
Let \(x\) be equal to 0.5, then: \(x = 0.5\)
\(\sqrt{(x^2+1)}=\sqrt{(0.5^2+1)}=\sqrt{1.25}≈1.12\)
\(\sqrt{(x^2 )+1}=\sqrt{(0.5^2 )}+1=0.5+1=1.5\)
Then, option A is correct.
\(x<\sqrt{(x^2+1)}<\sqrt{(x^2 )}+1\)

9- C
\(x\) is directly proportional to the square of \(y\). Then:
\(x=cy^2\)
\(12=c(2)^2→12=4c→c=\frac{12}{4}=3\)
The relationship between \(x\) and y is:
\(x=3y^2\)
\(x=75\)
\(75= 3y^2 →y^2 = \frac{75}{3} = 25→y=5\)

10- D
The amount of money that jack earns for one hour:
\(\frac{$616}{44} =$14\)
Number of additional hours that he work to make enough money is:
\(\frac{$826-$616}{1.5×$14}=10\)Number of total hours is: \(44 + 10 = 54\)

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.

How to use PSAT Math Practice Test Questions as real practice

PSAT Math Practice Test Questions works best when it is used as a short, focused study session rather than a quick click-through activity. The goal is not simply to finish the questions. The goal is to notice which skills feel automatic, which skills still need review, and which mistakes happen when you rush.

Start with a clean piece of scratch paper. For each item, answer the questions under realistic conditions, then review every missed problem before retaking a similar set. If you get something wrong, do not immediately move on. Write the correct step, circle the part that caused the mistake, and try one similar item before continuing. That small correction habit is what turns an online practice test into lasting math improvement.

A three-round study routine

This routine is simple, but it solves a common problem: students often practice only until an answer looks familiar. Real readiness means you can solve a fresh problem without hints, explain the first step, and check whether the final answer is reasonable.

What to write down while you practice

Keep a tiny mistake log next to the activity. You only need three columns: the topic, the mistake, and the correction. For example, a student might write “fractions,” “forgot common denominator,” and “rewrite both fractions before adding.” A log like that is more useful than a long list of scores because it tells you exactly what to review next.

• If the mistake is a fact or formula, review it before the next round.
• If the mistake is a setup error, copy one worked example and label each step.
• If the mistake is from rushing, slow down and require written work for the next five items.
• If the same mistake appears twice, stop and review that topic before continuing.

When you are ready to move on

You are ready for the next topic when you can get several items correct in a row and explain why the method works. A score by itself is helpful, but it is not the whole story. You should also be able to describe the rule, formula, or pattern that the activity is testing.

For test preparation, come back to PSAT Math Practice Test Questions after a day or two and try a fresh round. If the skill still feels easy after a short break, it is much more likely to stay with you during a quiz, unit test, or standardized test. If it feels shaky, that is useful information too: it tells you exactly where to spend your next study session.

Study tips for parents and teachers

When using this page with a student, ask for the reasoning before the answer. Questions such as “What is the first step?”, “Why did you choose that operation?”, and “How can you check it?” help students build mathematical language. That matters because many test questions measure more than calculation; they also measure whether the student can read the problem, choose a method, and explain a result.

Short sessions are usually best. Ten to fifteen minutes of careful practice can be more productive than a long session full of guessing. End by naming one skill that improved and one skill to review next time. That keeps practice positive, specific, and easy to continue.