MK vs. AR: What's the Difference?
The ASVAB has two math sections. Arithmetic Reasoning (AR) tests applied math through word problems. Mathematics Knowledge (MK) tests your knowledge of math concepts directly — no story, just equations, expressions, and geometric figures.
MK has 16 questions on the CAT-ASVAB and 25 on the paper version. Questions cover algebra, number theory, and geometry. No calculators are permitted.
Like AR, MK feeds into your AFQT and several line score composites (ST, EL, CO, FA). Strong MK scores are especially important for Air Force Electronic (E) and Army Skilled Technical (ST) composites.
Algebra — The Biggest Category
At least half of MK questions involve algebra. You need to be comfortable with:
Solving Linear Equations
Isolate the variable by performing the same operation on both sides.
Example: 3x − 7 = 14 → 3x = 21 → x = 7
Systems of Equations
Two equations, two unknowns. Use substitution or elimination.
Example: x + y = 10 and x − y = 4 → Add both: 2x = 14 → x = 7 → y = 3
Factoring Quadratics
Know how to factor expressions like x² + 5x + 6 = (x + 2)(x + 3).
The FOIL method in reverse: find two numbers that multiply to C and add to B in ax² + bx + c.
Inequalities
Solve like equations, but flip the inequality sign when multiplying or dividing by a negative number.
−2x > 8 → x < −4 (sign flips)
Exponents and Roots
Rules to memorize:
- a^m × a^n = a^(m+n)
- a^m ÷ a^n = a^(m−n)
- (a^m)^n = a^(mn)
- a^0 = 1
- a^(−n) = 1/a^n
- √(a × b) = √a × √b
Know perfect squares through 15² = 225 and perfect cubes through 5³ = 125.
Number Theory
Factors and Multiples
A factor of N divides into N evenly. A multiple of N is N times an integer.
GCF (Greatest Common Factor): largest factor shared by two numbers. LCM (Least Common Multiple): smallest multiple shared by two numbers.
Prime Numbers
Primes up to 50 you should know: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47.
Note: 1 is NOT prime.
Order of Operations (PEMDAS)
Parentheses → Exponents → Multiplication/Division (left to right) → Addition/Subtraction (left to right)
Example: 3 + 4 × 2² = 3 + 4 × 4 = 3 + 16 = 19 (not 56)
Absolute Value
|x| = distance from zero. Always non-negative. |−7| = 7.
Geometry
Angles
- Complementary angles: sum to 90°
- Supplementary angles: sum to 180°
- Vertical angles (opposite when two lines cross): equal
- Triangle angles: always sum to 180°
Triangles
- Pythagorean theorem: a² + b² = c² (right triangles only)
- Common right triangle sets: 3-4-5, 5-12-13, 8-15-17
- Area = ½ × base × height
- Equilateral: all sides equal, all angles 60°
- Isosceles: two equal sides, two equal base angles
Circles
- Circumference = 2πr = πd
- Area = πr²
- Remember: π ≈ 3.14
Quadrilaterals
- Rectangle area: l × w; perimeter: 2(l + w)
- Square area: s²; perimeter: 4s
- Parallelogram area: base × height
- Trapezoid area: ½ × (b₁ + b₂) × h
Probability and Statistics Basics
Occasionally tested:
- Probability = favorable outcomes ÷ total outcomes
- Mean = sum ÷ count
- Median = middle value when sorted
- Mode = most frequent value
Study Tips for MK
Unlike vocabulary, math skills don't fade as quickly between study sessions — but they do require active problem-solving, not passive review. Reading a formula is not the same as being able to apply it under time pressure.
- Drill one topic per day — factoring one day, exponents the next. Don't mix topics until you're confident in each.
- Do problems without a calculator — you won't have one on test day. Build mental math speed for multiplication tables and basic operations.
- Khan Academy has free video lessons for every MK topic, plus practice sets. Use it for any concept you can't work through from a formula sheet alone.
- Focus on algebra first — it makes up the largest share of MK questions and transfers directly to AR word problems.
Use our MK section drills to practice under timed conditions and see exactly which concept areas need the most work.