Mathematics Knowledge
15 questions · 23 minutes · AFQT
What's covered
Straight math — algebra, geometry, number properties — with no story wrapped around it. Roughly high-school level. The other AFQT math section, and the more memorization-friendly of the two.
Order of operations
PEMDAS: parentheses, exponents, multiplication and division left to right, addition and subtraction left to right.
Exponent rules
xᵃ · xᵇ = xᵃ⁺ᵇ. xᵃ ÷ xᵇ = xᵃ⁻ᵇ. (xᵃ)ᵇ = xᵃᵇ. x⁰ = 1. x⁻ᵃ = 1/xᵃ. These four rules cover most exponent questions on the test.
Algebra
Solve linear equations by undoing operations in reverse. FOIL for multiplying binomials: (x+2)(x+3) = x² + 5x + 6. Factor trinomials by finding two numbers that multiply to the constant and add to the middle coefficient. Recognize the difference of squares: x² − 9 = (x+3)(x−3), so x² − 9 = 0 has two roots, +3 and −3.
Geometry formulas
Area: rectangle lw, triangle ½bh, circle πr², trapezoid ½(b₁+b₂)h. Perimeter: rectangle 2(l+w), circle 2πr or πd. Volume: box lwh, cylinder πr²h, sphere 4/3πr³.
Angles and triangles
Triangle angles sum to 180°, quadrilaterals to 360°, an n-sided polygon to (n−2)×180°. Pythagorean theorem a² + b² = c², with the common triples 3-4-5, 5-12-13, and 8-15-17 worth memorizing.
Coordinate geometry
Slope = (y₂−y₁)/(x₂−x₁). Slope-intercept form y = mx + b, where m is slope and b is the y-intercept.
Number properties
Primes: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 — 2 is the only even one, and 1 is not prime. Know squares through 12² and their roots. Absolute value is distance from zero, so |x| = 5 gives two answers.
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