Mathematics Knowledge (MK)

25% of the AFQT · blueprint AFQT = AR + MK + 2×VE (WK+PC), per officialasvab.com (2026)

Short answer

Mathematics Knowledge is an AFQT subtest counted once in the formula. It tests high-school algebra and geometry directly — solving linear equations and inequalities, exponents and roots, factoring and expanding, order of operations, number properties (primes, factors, LCM/GCF), angles, triangles, circles, area, perimeter and volume. On paper it is 25 questions in 24 minutes, under a minute each.

Why it matters

MK is the most "study-able" subtest: a finite list of rules, no reading trap. Weak MK usually means forgotten formulas, which the planner can fix fast.

Key concepts

Algebra: isolate the variable; do the same thing to both sides; flip the inequality when multiplying by a negative.
Exponents: a^m·a^n = a^(m+n); (a^m)^n = a^(mn); a^0 = 1; negative exponent = reciprocal.
Factoring: x² + 5x + 6 = (x+2)(x+3); difference of squares a² − b² = (a−b)(a+b).
Geometry: triangle angles sum to 180°; area = ½bh; circle area πr², circumference 2πr; rectangle volume lwh; Pythagorean theorem a² + b² = c².
Number properties: even/odd rules, prime numbers, LCM/GCF, divisibility.

Common mistakes

Forgetting to distribute a negative sign.
Using diameter where the formula needs the radius.

Worked example

Solve 3(x − 4) = 2x + 1: 3x − 12 = 2x + 1 → x = 13.

Original practice questions

Mathematics Knowledge (MK)Difficulty 2/5

Solve for x: 3(x − 4) = 2x + 1

A11
B13
C−13
D5

Show answer and rationale

Correct: B. Distribute: 3x − 12 = 2x + 1. Subtract 2x: x − 12 = 1. Add 12: x = 13.

D — 5 results from forgetting to distribute the 3 to −4.
A — 11 results from writing the right side as 2x − 1 instead of 2x + 1.
C — −13 reverses the sign in the final step.

Mathematics Knowledge (MK)Difficulty 2/5

What is (2³)² × 2⁻²?

Show answer and rationale

Correct: C. Power of a power multiplies exponents: (2³)² = 2⁶ = 64. Multiplying by 2⁻² subtracts 2 from the exponent: 2⁴ = 16.

B — 8 = 2³, missing the square.
D — 32 = 2⁵.
A — 64 = 2⁶, ignoring the 2⁻² factor.

Mathematics Knowledge (MK)Difficulty 2/5

A right triangle has legs of 6 and 8. What is the length of the hypotenuse?

Show answer and rationale

Correct: D. Pythagorean theorem: 6² + 8² = 36 + 64 = 100; √100 = 10.

A — 12 is not √100.
B — 14 is the sum of the legs, not the hypotenuse.
C — 48 is the product of the legs.

All 5 Mathematics Knowledge (MK) questions →

Tools for this topic

ASVAB / AFQT score explorer — Enter the AFQT percentile from your official score report to see your category (I–V) and what the percentile means against the national reference group; optionally add your AR, MK, PC and WK standard scores to see how the four AFQT subtests compare.

2 flashcards for Mathematics Knowledge (MK)

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Blueprint-mapped questions with full rationales for every choice.

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Primary references

Understanding ASVAB Scores — AFQT computation, percentiles, categories, standard scores — Official ASVAB (U.S. Department of Defense) · government · retrieved 2026-09-21, verified 2026-09-21
What to Expect — CAT-ASVAB and paper-and-pencil subtests, counts and time limits — Official ASVAB (U.S. Department of Defense) · government · retrieved 2026-09-21, verified 2026-09-21

Last reviewed: 2026-09-21Next review by: 2026-12-20Draft — pending editorial reviewHow we verify facts