ASVAB Mathematics Knowledge
Sample Questions
Practice original high-school mathematics questions covering algebra,
geometry, fractions, exponents, roots, equations, inequalities, functions, ratios,
and other core Mathematics Knowledge skills.
Mathematics Knowledge (MK) Practice
Mathematics Knowledge focuses on high-school math principles rather than long real-world word problems. Solve each problem carefully and select the best answer.
You can also practice with ASVAB sample questions and Arithmetic Reasoning sample questions.
When multiplying powers with the same base, add the exponents: 2⁴ × 2³ = 2⁷ = 128.
Since 12 × 12 = 144, √144 = 12.
Subtract 5 from both sides: 3x = 15. Then divide by 3: x = 5.
Add 6 to both sides: 2x > 14. Divide by 2: x > 7.
The numbers 2 and 3 multiply to 6 and add to 5, so x² + 5x + 6 = (x + 2)(x + 3).
Factor the numerator: a² − 25 = (a − 5)(a + 5). Cancel a − 5 to get a + 5.
Convert 3/4 to 6/8. Then 6/8 + 5/8 = 11/8 = 1 3/8.
First 8 − 5 = 3. Then 3² = 9. Multiply 3 × 9 = 27, and add 6 to get 33.
Divide both terms by 14: 42:14 = 3:1.
Convert 35% to 0.35 and multiply: 0.35 × 240 = 84.
Area of a triangle = 1/2 × base × height = 1/2 × 12 × 7 = 42 square inches.
Circumference = πd = 3.14 × 10 = 31.4 cm.
Use a² + b² = c²: 6² + 8² = 36 + 64 = 100, so c = 10.
Volume = length × width × height = 6 × 4 × 3 = 72 cubic units.
Supplementary angles total 180°. So 180° − 68° = 112°.
Slope = (11 − 3) ÷ (6 − 2) = 8 ÷ 4 = 2.
Multiply the terms: x² − 2x + 4x − 8 = x² + 2x − 8.
Substitute 4: f(4) = 2(4²) − 3 = 2(16) − 3 = 29.
Add the equations: 2x = 16, so x = 8.
A negative exponent means take the reciprocal: x⁻³ = 1/x³.