ASVAB CHEAT SHEET: Math (AFQT)

AFQT Formula & Weight

`` AFQT = AR + MK + 2(VE) where VE = WK + PC ``

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→ Study AR + MK after securing WK + PC

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AR: Arithmetic Reasoning (Word Problems)

High-Yield Problem Types

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AR Test Strategy

• Read the question first — identify what you're solving for

• Set up the equation on paper before calculating

• Check with real numbers if you have time

• Estimate answer range — eliminate extremes before computing

• No penalty for guessing — always answer

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MK: Mathematics Knowledge (Facts & Formulas)

Priority Topics (by frequency)

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Pythagorean Triples (Memorize)

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→ Recognize instantly on exams; saves calculation time

Order of Operations

PEMDAS: Parentheses → Exponents → Multiply/Divide (left-to-right) → Add/Subtract (left-to-right)

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Number Operations (No-Calculator)

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Algebra (40% of MK)

Solving Linear Equations

Get variables on one side; numbers on the other

Simplify; divide by coefficient

Example: 3x + 5 = 20 → 3x = 15 → x = 5

Factoring

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Inequalities

Solve like equations; flip inequality sign only if multiply/divide by negative

Example: −2x > 10 → x < −5

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Geometry

Area & Perimeter

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Component	Weight	Priority
Arithmetic Reasoning (AR)	1×	AFQT #3
Math Knowledge (MK)	1×	AFQT #4
Word Knowledge (WK)	2× (via VE)	AFQT #1
Paragraph Comprehension (PC)	2× (via VE)	AFQT #2
Type	Setup Cue	Formula/Process
Distance/Rate/Time	"traveled," "speed," "hours"	D = RT
Percent	"% of," "discount," "markup"	Part = % × Whole
Ratio	"ratio of," "for every," "parts"	Set up proportion: a/b = x/y
Work Rate	"workers," "hours," "jobs"	Rate × Time = Work; combine rates
Simple Interest	"borrowed," "annually," "years"	I = PRT (P=principal, R=rate, T=time)
Profit/Loss	"cost," "sells for," "markup"	Profit = Revenue − Cost
Topic	Weight	Key Formulas & Rules
Algebra	~40%	FOIL: (a+b)(c+d) = ac+ad+bc+bd; Quadratic: ax²+bx+c=0 → x=(-b±√(b²-4ac))/2a
Exponents	~20%	a^m × a^n = a^(m+n); (a^m)^n = a^(mn); a^0 = 1; a^(-n) = 1/a^n
Geometry	~25%	Area: circle πr², triangle ½bh, rectangle lw; Volume: box lwh, cylinder πr²h; Pythagorean: a² + b² = c²
Fractions/Decimals/Percent	~15%	a/b × c/d = ac/bd; Convert: % ÷ 100 = decimal; 0.5 = 50% = 1/2
Ratio	Multiples
3-4-5	6-8-10, 9-12-15, 12-16-20
5-12-13	10-24-26
8-15-17	16-30-34
Operation	Rule	Example
Fraction + Fraction	Find common denominator	1/3 + 1/4 = 4/12 + 3/12 = 7/12
Fraction × Fraction	Multiply across; simplify	2/3 × 3/4 = 6/12 = 1/2
Fraction ÷ Fraction	Multiply by reciprocal	2/3 ÷ 1/4 = 2/3 × 4/1 = 8/3
Negative × Negative	Result is positive	(−3) × (−2) = 6
Negative × Positive	Result is negative	(−3) × 2 = −6
Percent Increase	New = Old × (1 + %/100)	50 increased by 20% → 50 × 1.2 = 60
Percent Decrease	New = Old × (1 − %/100)	50 decreased by 20% → 50 × 0.8 = 40
Pattern	Form	Example
Difference of Squares	a² − b² = (a+b)(a−b)	x² − 9 = (x+3)(x−3)
Trinomial	ax² + bx + c	x² + 5x + 6 = (x+2)(x+3)
Shape	Area	Perimeter
Rectangle	lw	2l + 2w
Triangle	½bh	a + b + c