Top 10 HSPT Math Practice Questions

HSPT mathematics is split between the Quantitative section, which tests number reasoning and comparisons, and the Mathematics section, which tests arithmetic, algebra and geometry. These ten questions are drawn from both, each with a worked answer, so weak areas show up quickly.

Help your students start their HSPT Math test prep journey right now with these sample HSPT Math questions.

The Absolute Best Book to Ace the HSPT Math Test

HSPT Math for Beginners 2026 The Ultimate Step by Step Guide to Preparing for the HSPT Math Test

Download

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

Rated 4.48 out of 5 based on 180 customer ratings

Satisfied 172 Students

, Right triangle ABC has two legs of lengths 9 cm (AB) and 12 cm (AC). What is the length of the third side (BC)?

A. 6 cm

B. 8 cm

C. 14 cm

D. 15 cm

8- If \(40\%\) of a class are girls, and \(25\%\) of girls play tennis, what percent of the class plays tennis?

A. \(10\%\)

B. \(15\%\)

C. \(20\%\)

D. \(40\%\)

9- The area of a circle is less than \(36 π\). Which of the following can be the circumference of the circle?

A. \(10 π\)

B. \(12 π\)

C. \(24 π\)

D. \(36 π\)

10- Which of the following values for \(x\) and \(y\) satisfy the following system of equations?
\(\begin{cases}x+4y=10 \\ 5x+10y=10\end{cases}\)

A. \( x=3,y=2\)

B. \( x=2,y−3\)

C. \(x=−6,y=4\)

D. \( x=4,y=−2\)

Best HSPT Math Prep Resource for 2026

Answers:

2- A
The sum of supplement angles is \(180\). Let \(x\) be that angle. Therefore, \(x+9x =180,10x=180\), divide both sides by \(10: x=18\)

3- C
The average speed of John is: \(150÷6=25\) km, The average speed of Alice is: \(160÷4=40\) km. Write the ratio and simplify. \(25∶40 ⇒ 5:8\)

4- C
\($7×10=$70\), Petrol use: \(10×2=20\) liters. Petrol cost: \(20×$1=$20\)
Money earned: \($70-$20=$50\)

5- C
average \(=\frac{sum \ of \ terms}{number \ of \ terms}=\frac{12+ 13+7+21+22}{5} = \frac{75}{5} =15\)

6- C
Let \(x\) be the original price. If the price of the sofa is decreased by \(15\%\) to $476, then: \(85\%\) of \(x=476 ⇒ 0.85x=476 ⇒ x=476÷0.85=560\)

7- D
Use Pythagorean Theorem: \(a^2+b^2=c^2, 9^2+12^2= c^2 ⇒ 81+144=c^2⇒ 225=c^2⇒c=15\)

8- A
The percent of girls playing tennis is: \(40\%×25\% =0.40×0.25=0.10=10\%\)

9- A
The area of the circle is less than \(12 π\). Use the formula for the area of a circle. Area \(=πr^2 ⇒ \)
\(36 π> πr^2⇒ 36>r^2⇒ r<6\). The radius of the circle is less than 6. Let’s put 6 for the radius. Now, use the circumference formula: Circumference \(=2πr=2π (6)=12 π\)
Since the radius of the circle is less than \(6\). Then, the circumference of the circle must be less than \(12 π\). Only choice A is less than \(12 π\).

10- C
\(\begin{cases}x+4y=10 \\ 5x+10y=10\end{cases}\rightarrow\) Multiply the top equation by \(-5\) then,
\(\begin{cases}-5x-20y=-50 \\ 5x+10y=10\end{cases}\rightarrow\) Add two equations
\(-10y=-40→y=4\), plug in the value of \(y\) into the first equation
\(x+4y=10→x+4(4)=10→x+16=10\)
Subtract 16 from both sides of the equation. Then: \(x+16=10→x=-6\)

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

The Only Resource Your student Will Ever Need to ace the HSPT Math Test

More from Effortless Math for HSPT Test …

Would you like to take a closer look at the HSPT math test?

Then join us in the Overview of the HSPT Mathematics Test.

HSPT math test day is approaching, and you do not know what to do.

Do not miss our test day tips !: HSPT Math-Test Day Tips.

Do you need more practice to get the desired score on the HSPT math test?

HSPT Math Practice Test Questions will be a good resource for you to practice more.

The Best Books to Ace the HSPT Test

HSPT Math Comprehensive Prep Bundle Everything You Need to Ace the HSPT Math Test

Download

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

Rated 4.46 out of 5 based on 74 customer ratings

Satisfied 66 Students

Have any questions about the HSPT Test?

Write your questions about the HSPT or any other topics below and we’ll reply!