ASVAB Mathematics Knowledge Practice Test
Updated October 27, 2026
Mathematics Knowledge (MK) tests math concepts directly, rather than through word problems: algebra, exponents and roots, fractions, and geometry. It’s one of the four AFQT tests, with 15 scored questions on the CAT-ASVAB, and no calculator is allowed. Try the free questions below.
What Mathematics Knowledge covers
- Number concepts: factors, primes, fractions, decimals and order of operations
- Algebra: solving equations and inequalities, simplifying expressions, factoring
- Exponents and square roots
- Geometry: angles, perimeter, area, volume and the Pythagorean theorem
Free Mathematics Knowledge practice questions
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Solve for x: 3x + 5 = 26Answer: CSubtract 5: 3x = 21. Divide by 3: x = 7.
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What is 2⁵?Answer: D2⁵ = 2 × 2 × 2 × 2 × 2 = 32.
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What is the area of a triangle with a base of 10 inches and a height of 6 inches?Answer: BArea of a triangle = ½ × base × height = ½ × 10 × 6 = 30 square inches.
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Two angles of a triangle measure 50° and 65°. What is the third angle?Answer: BThe angles of a triangle add up to 180°: 180 − 50 − 65 = 65°.
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Simplify: 3(x + 4) − 2xAnswer: ADistribute: 3x + 12 − 2x = x + 12.
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Which number is prime?Answer: C29 has no factors other than 1 and itself. 21 = 3 × 7, 27 = 3 × 9 and 33 = 3 × 11.
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What is √144 + √25?Answer: B√144 = 12 and √25 = 5, so the sum is 17.
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Solve for x: 2(x − 3) = 14Answer: DDivide by 2: x − 3 = 7. Add 3: x = 10.
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What is the area of a circle with a radius of 5? (Use π ≈ 3.14.)Answer: CArea = πr² = 3.14 × 25 = 78.5.
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Which is equal to x² · x³?Answer: AWhen multiplying powers with the same base, add the exponents: x² · x³ = x⁵.
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What is the least common multiple of 6 and 8?Answer: CMultiples of 6: 6, 12, 18, 24. Multiples of 8: 8, 16, 24. The smallest shared multiple is 24.
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Two angles are supplementary. One measures 115°. What does the other measure?Answer: BSupplementary angles add up to 180°: 180 − 115 = 65°.
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Solve: x² = 49Answer: CBoth 7² and (−7)² equal 49, so x = 7 or x = −7.
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What is 0.25 written as a fraction in lowest terms?Answer: A0.25 = 25/100, which simplifies to 1/4.
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The volume of a cube with sides of 3 inches is:Answer: CVolume of a cube = side³ = 3 × 3 × 3 = 27 cubic inches.
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If 3x − y = 10 and y = 2, what is x?Answer: BSubstitute y = 2: 3x − 2 = 10, so 3x = 12 and x = 4.
Pair this with Arithmetic Reasoning practice, the other AFQT math test.
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