PSAT Math Practice Test Questions

Try 10 free PSAT Math practice questions, then check the worked answers below. This is a short mixed-skill set from Effortless Math, not a full-length test or an official College Board assessment.

10 sample PSAT Math practice questions

Write your answer and reasoning on scratch paper before checking the solutions. The set covers circles, equations, radicals, ratios, slope, scatterplots and rates; it does not cover every tested skill.

Question 1

The area of a circle is 64π square units. What is its circumference?

1. 8π
2. 16π
3. 32π
4. 64π

Question 2

Which values of x and y satisfy both equations: x + 4y = 10 and 5x + 10y = 20?

1. x = 3, y = 2
2. x = 2, y = −3
3. x = −2, y = 3
4. x = 3, y = −2

Question 3

If a ≠ 0 and 6b = 5a√3, what is (2b√3)/(4a)?

1. 5/4
2. (5/4)a
3. 2a
4. 2a√3

Question 4

A gas tank holds 25 gallons. How many gallons does it contain when it is 2/5 full?

1. 50
2. 125
3. 62.5
4. 10

Question 5

In the xy-plane, (4, 3) and (3, 2) lie on line A. Which line is parallel to line A?

1. y = 3x
2. y = x/2
3. y = 2x
4. y = x

Question 6

In this scatterplot, which listed point is farthest from the line of best fit (not shown)?

1. (6, 1)
2. (5, 4)
3. (3, 3)
4. (2, 2)

Question 7

A football team won exactly 80% of its games last season. Which could be the total number of games it played?

1. 49
2. 35
3. 12
4. 32

Question 8

If 0 < x < 1, which inequality is true?

1. x < √(x² + 1) < √(x²) + 1
2. x < √(x²) + 1 < √(x² + 1)
3. √(x² + 1) < x < √(x²) + 1
4. √(x²) + 1 < √(x² + 1) < x

Question 9

For positive y, x is directly proportional to y². When y = 2, x = 12. What is y when x = 75?

1. 1/5
2. 1
3. 5
4. 12

Question 10

Jack earns $616 for his first 44 hours of work in a week, then 1.5 times his regular hourly rate for additional hours. He needs $826 this week. How many hours must he work to earn that amount?

1. 40
2. 48
3. 53
4. 54

Worked answers

Question 1: B — 16π

The area formula gives πr² = 64π, so r² = 64 and r = 8. Circumference = 2πr = 2π × 8 = 16π.

Question 2: C — x = −2, y = 3

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

Question 3: A — 5/4

From 6b = 5a√3, b = (5a√3)/6. Substituting gives (2 × 5a√3 × √3)/(6 × 4a) = 30a/(24a) = 5/4. Cancelling a is valid because a ≠ 0.

Question 4: D — 10 gallons

Take 2/5 of the capacity: (2/5) × 25 = 10 gallons.

Question 5: D — y = x

The slope of line A is (3 − 2)/(4 − 3) = 1. Parallel lines have the same slope; y = x also has slope 1.

Question 6: A — (6, 1)

The other listed points follow the rising pattern. The point (6, 1) lies well below the fitted line.

Question 7: B — 35 games

Since 80% = 4/5, the number of games must be a multiple of 5 for the number of wins to be whole. Only 35 works: (4/5) × 35 = 28 wins.

Question 8: A — x < √(x² + 1) < √(x²) + 1

Because x is positive, √(x²) = x. First, x² < x² + 1, so x < √(x² + 1). Also, (x + 1)² = x² + 2x + 1 > x² + 1. Both sides are positive, so √(x² + 1) < x + 1. Together these prove A for every 0 < x < 1; checking only one value would not prove the whole interval.

Question 9: C — 5

Write x = cy². Then 12 = c × 2², giving c = 3. At x = 75, y² = 75/3 = 25. Since the question specifies positive y, y = 5. Without that condition, −5 would also satisfy the relationship.

Question 10: D — 54 hours

Regular rate: $616 ÷ 44 = $14 per hour. Overtime rate: 1.5 × $14 = $21 per hour. He needs $826 − $616 = $210 more, which requires $210 ÷ $21 = 10 overtime hours. Total: 44 + 10 = 54 hours.

Choose your next practice

If a question was difficult, review that skill before attempting another mixed set. Use the PSAT Math worksheet collection for focused practice, or the PSAT hub linked below to find lessons and formulas.

For a full-length digital rehearsal, use College Board’s official Bluebook practice options. The current PSAT/NMSQT Math section has 44 questions in two 35-minute modules, includes multiple-choice and student-produced responses, and permits a calculator throughout. This 10-question article is skill practice, not a timed simulation or a PSAT score predictor.

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