PSAT 10 Math Practice: 10 Free Questions with Answers

Practice 10 free PSAT 10 math questions, then check the worked answers below. This independent Effortless Math sample covers circles, systems of equations, radicals, fractions, slope, data, percents, proportional relationships and rates.

Use this short set to find skills to review. It is not an official College Board test, a full-length digital simulation or a scaled-score predictor.

Current PSAT 10 math format

College Board describes the digital PSAT 10 Math section as 44 questions in two modules of 22 questions, with 35 minutes per module—70 minutes in total. It includes multiple-choice and student-produced responses, and an acceptable calculator is permitted throughout the Math section.

The four domains are Algebra, Advanced Math, Problem-Solving and Data Analysis, and Geometry and Trigonometry. See College Board’s PSAT 10 Math overview for the official scope. For full-length digital practice, use College Board’s official practice options, including Bluebook.

Try these 10 PSAT 10 math questions

Write your choices and working before opening the answers. On your first attempt, focus on setting up the problem correctly rather than racing through it. These are the article’s existing public sample questions.

1- The area of a circle is \(64π\). What is the circumference of the circle?

A. \(8π\)

B. \(16π\)

C. \(32π\)

D. \(64π\)

2- Which of the following values for \(x\) and \(y\) satisfy the following system of equations?
\(x+4y=10\)
\(5x+10y=20\)

A. \(x=3,y=2\)

B. \(x=2,y=-3\)

C. \(x=-2,y=3\)

D. \(x=3,y=-2\)

3- If \(a ≠ 0\) and \(6b=5a\sqrt{3}\), then what is the value of \(\frac{2b \sqrt{3}}{4a}\) ?

A. \(\frac{5}{4}\)

B. \(\frac{5}{4}a\)

C. \(2a\)

D. \(2a\sqrt{3}\)

4- If a gas tank can hold 25 gallons, how many gallons does it contain when it is \( \frac{2}{5} \) full?

A. 50

B. 125

C. 62.5

D. 10

5- In the \(xy\)-plane, the point \((4,3)\) and \((3,2)\) are on line \(A\). Which of the following equations of lines is parallel to line \(A\)?

A. \(y = 3x\)

B. \(y = \frac{x}{2}\)

C. \(y = 2x\)

D. \(y = x\)

6- In the following graph, which data point is farthest from the line of best fit (not shown)?

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 season. 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

Worked answers

Show all 10 answers and explanations

1. B: 16π. From πr² = 64π, the radius is r = 8. The circumference is 2πr = 16π.

2. C: x = −2, y = 3. Multiply x + 4y = 10 by 5 to get 5x + 20y = 50. Subtract 5x + 10y = 20, giving 10y = 30, so y = 3. Then x + 12 = 10, so x = −2. Both original equations check.

3. A: 5/4. Since b = (5a√3)/6, substitute that expression into (2b√3)/(4a). The numerator becomes (2 × 5a × 3)/6 = 5a. Dividing by 4a gives 5/4. The condition a ≠ 0 allows cancellation.

4. D: 10 gallons. Calculate (2/5) × 25 = 10.

5. D: y = x. Line A has slope (3 − 2)/(4 − 3) = 1. A parallel line must also have slope 1; among the choices, y = x does.

6. A: (6,1). Most points follow an upward trend. The point (6,1) lies well below that trend, farther from the approximate best-fit line than the other listed points.

7. B: 35 games. A team must win a whole number of games. Since 80% = 4/5, the total must be divisible by 5. Only 35 qualifies, and 0.8 × 35 = 28 wins.

8. A. Because x > 0, √(x²) = x. Also, x² < x² + 1 < (x + 1)²: the second inequality follows from 2x > 0. Taking square roots gives x < √(x² + 1) < x + 1, which is choice A.

9. C: 5. Write x = ky². Using x = 12 and y = 2 gives k = 3. Then 75 = 3y², so y² = 25. Both y = 5 and y = −5 satisfy that equation, but only 5 appears among the answer choices.

10. D: 54 hours. The regular rate is 616 ÷ 44 = 14 dollars per hour, so the additional-hours rate is 1.5 × 14 = 21 dollars per hour. Jack needs 826 − 616 = 210 more dollars, requiring 210 ÷ 21 = 10 additional hours. Total: 44 + 10 = 54 hours.

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Plan your next review

Group missed questions by the skill behind them: circles (1), linear equations and slope (2 and 5), radicals (3 and 8), fractions and percents (4 and 7), data (6), proportional relationships (9), or rates (10). Record the setup error or unfamiliar rule, review that topic, and try a similar problem later without looking at the solution.

Continue with the existing public resource paths:

• Open the PSAT 10 Math Hub for matching lessons and review tools.
• Start PSAT 10 Math practice to explore the site’s broader practice collection.

A correct-answer count here identifies review needs; it does not convert into an official PSAT 10 score. Use official practice and its scoring guidance for that purpose.

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