Mathematics Knowledge (MK)
Mathematics Knowledge (MK) is the second math AFQT subtest. It tests high-school math concepts and procedures — you need to know the rules and apply them quickly, with no formula sheet provided.
Practise Mathematics Knowledge freeAlready know what's on it and still stuck? How to improve your Mathematics Knowledge score.
What's on it
Algebra (solving linear equations and inequalities, simplifying and evaluating expressions, factoring, basic quadratics); geometry (perimeter, area, volume, angles, circles, and the Pythagorean theorem); number properties (primes, factors, GCF/LCM, order of operations, integer sign rules); exponents, roots and scientific notation; and basic probability.
Memorize the core formulas
You can't look them up. Rectangle area = length × width; triangle area = ½ × base × height; circle area = πr² and circumference = 2πr; rectangular-prism volume = l × w × h; cylinder volume = πr²h; Pythagorean theorem a² + b² = c². A triangle's interior angles sum to 180°.
Exponent and order-of-operations traps
Same base: multiply → add exponents (2³ × 2² = 2⁵ = 32, not 2⁶); divide → subtract; power of a power → multiply. x⁰ = 1 and a negative exponent means the reciprocal. Follow PEMDAS carefully — this is where careless points are lost.
Test-day strategy
Simplify fully before choosing an answer. When an equation is awkward, substitute the answer choices back in. Draw the shape for any geometry question.
Key takeaways
- One of the 4 AFQT subtests.
- Algebra and geometry dominate — know the area/volume/Pythagoras formulas cold.
- Exponent rules and PEMDAS are the most common trap areas.
Start a free Mathematics Knowledge practice set — timed, with a worked explanation after every question.
Go to Mathematics Knowledge practiceFree sample Mathematics Knowledge questions
A few sample questions with worked answers. Our free Mathematics Knowledge practice set has 199 questions in total — every one with a full explanation.
- A.x = 2 or x = 10
- B.x = -4 or x = -5
- C.x = 1 or x = 20
- D.x = 4 or x = 5 ✓
- A.6
- B.9
- C.23
- D.8 ✓
- A.14(pi) ✓
- B.49(pi)
- C.28(pi)
- D.7(pi)
- A.3.5
- B.5 ✓
- C.7
- D.25
- A.20 ✓
- B.24
- C.35
- D.44
Mathematics Knowledge cheat sheet
The formulas and facts worth memorising for this subtest. See all ASVAB cheat sheets →
- PEMDAS: brackets, exponents, × & ÷, then + & −
- Same base: multiply → ADD exponents; divide → SUBTRACT; power of a power → MULTIPLY
- x^0 = 1; x^(−n) = 1 / x^n; x^(1/2) = √x
- Difference of squares: a² − b² = (a − b)(a + b)
- Slope = (y₂ − y₁) ÷ (x₂ − x₁)
- Isolate the variable with inverse operations on both sides
- Rectangle area = l × w; triangle area = ½ × base × height
- Circle: area = πr², circumference = 2πr
- Box volume = l × w × h; cylinder = πr²h
- Pythagoras: a² + b² = c²
- Angles: triangle = 180°, straight line = 180°, full circle = 360°
- Prime = only factors 1 and itself; GCF = largest shared factor; LCM = smallest shared multiple