ASVAB Math Cheat Sheet: Every Formula, Flowchart & Shortcut for AR + MK

The ASVAB does not give you a formula sheet or a calculator. This AR + MK cheat sheet collects the formulas, shortcuts, and decision steps that move your AFQT score fastest — drill the formulas and practice mental math until it is automatic.

AR vs. MK: Know Your Enemy

Before you memorize a single formula, understand the battlefield. These two subtests look similar but fight differently.

Arithmetic Reasoning: The Formula Arsenal

AR is all word problems. The math itself isn't hard — the challenge is translating English into equations. Here's every formula you'll need, organized by problem type.

Percentages & Percent Change

These show up on almost every AR section. Drill them until they're automatic.

• Finding a percent: Part = Percent × Whole → or rearranged: Percent = (Part ÷ Whole) × 100
• Percent change: ((New − Old) ÷ Old) × 100
• Discount price: Original Price × (1 − Discount%)
• Tax/markup price: Original Price × (1 + Rate%)

Quick example: A $80 jacket is 25% off. Price = $80 × (1 − 0.25) = $80 × 0.75 = $60.

Ratios & Proportions

If you see "for every" or "per" in a word problem, you're in ratio territory.

• Proportion setup: a/b = c/d
• Cross multiply to solve: a × d = b × c

Quick example: If 3 widgets cost $12, how much do 7 cost? → 3/12 = 7/x → 3x = 84 → x = $28.

Distance, Rate & Time

The king of AR word problems. If something is moving, this is your formula.

• Core formula: Distance = Rate × Time (d = rt)
• Rearranged for rate: r = d ÷ t
• Rearranged for time: t = d ÷ r

Quick example: You drive 180 miles at 60 mph. Time = 180 ÷ 60 = 3 hours.

Work Rate Problems

"Person A can do a job in X hours, Person B in Y hours. How long together?" This formula handles it.

• Combined work rate: 1/t₁ + 1/t₂ = 1/T

Quick example: Alex paints a room in 4 hours, Jamie in 6 hours. Together: 1/4 + 1/6 = 3/12 + 2/12 = 5/12. T = 12/5 = 2.4 hours.

Simple Interest & Money

• Simple interest: I = P × r × t (Principal × rate × time)
• Total amount: A = P + I or A = P(1 + rt)
• Profit: Profit = Revenue − Cost
• Average (Mean): Mean = Sum of all values ÷ Number of values

Flowchart: How to Attack Any AR Word Problem

Don't stare at a word problem wondering where to start. Follow this decision path every single time — it works whether the problem is about money, distance, or paint cans. Start with the question, choose the problem family, then check units before you answer.

Mathematics Knowledge: The Formula Vault

MK strips away the word problem wrapper and tests you on raw math. You either know the formula or you don't. No partial credit for vibes.

Algebra Essentials

• Slope-intercept form: y = mx + b (m = slope, b = y-intercept)
• Slope formula: m = (y₂ − y₁) ÷ (x₂ − x₁)
• Quadratic formula: x = (−b ± √(b² − 4ac)) ÷ 2a
• FOIL method: (a+b)(c+d) = ac + ad + bc + bd
• Difference of squares: a² − b² = (a+b)(a−b)

Exponent Rules

These are free points if you memorize the patterns.

• xᵃ × xᵇ = x^(a+b) — multiplying same base? Add exponents.
• (xᵃ)ᵇ = x^(a×b) — power of a power? Multiply exponents.
• xᵃ ÷ xᵇ = x^(a−b) — dividing same base? Subtract exponents.
• x⁰ = 1 — anything to the zero power equals 1 (except 0⁰).
• x⁻ⁿ = 1/xⁿ — negative exponent? Flip it to a fraction.

Geometry: Areas

• Rectangle: A = length × width
• Triangle: A = ½ × base × height
• Circle: A = πr²
• Trapezoid: A = ½(b₁ + b₂) × h
• Parallelogram: A = base × height

Geometry: Perimeters & Circumference

• Rectangle perimeter: P = 2l + 2w
• Triangle perimeter: P = a + b + c (sum of all sides)
• Circle circumference: C = 2πr or C = πd

Geometry: Volumes

• Rectangular solid (box): V = l × w × h
• Cylinder: V = πr²h
• Sphere: V = (4/3)πr³
• Cone: V = (1/3)πr²h

Geometry: Angles & Triangles

• Pythagorean theorem: a² + b² = c² (right triangles only — c is the hypotenuse)
• Common Pythagorean triples: 3-4-5, 5-12-13, 8-15-17 (and their multiples: 6-8-10, 9-12-15)
• Angles in a triangle: always sum to 180°
• Angles in a quadrilateral: always sum to 360°
• Supplementary angles: sum to 180°
• Complementary angles: sum to 90°
• Vertical angles: always equal

Flowchart: Which Geometry Formula Do I Need?

Geometry questions give you a shape and ask you to find something. This flowchart gets you to the right formula in seconds — match the shape to what the problem asks you to find.

Mnemonics That Stick

Formulas are useless if you can't recall them under pressure. These memory tricks lock them in.

More Memory Hacks

• d = rt → "Dirt" — Distance = Rate × Time. Think of it as a dirt road you're driving down.
• Pythagorean Theorem → "a² + b² = c² ... A Bug plus a Bee = a Cat squared" — silly, but it sticks.
• Area of a circle → "Apple pies are round" = A = πr² (A pie are squared).
• Circumference → "Cherry pies delight" = C = πd.

Beat the Clock: Time Management

Before you calculate, identify the trap: units, percentages, ratios, or rate and time. Most ASVAB math misses come from choosing the wrong setup, not from hard arithmetic. For example, a car travels 180 miles in 3 hours and the answer choices are in miles per hour — that is a rate-time setup, so use distance = rate × time and solve for rate.

5 Rapid-Fire Test Day Tips

1. Always answer every question. The ASVAB has NO penalty for guessing. A blank answer is a guaranteed zero — a guess has at least a 25% chance. Never leave a question unanswered.
2. Eliminate two wrong answers first. If you can knock out two choices, your guess odds jump from 25% to 50%. Look for answers that are obviously too large, too small, or have the wrong sign.
3. Plug in answer choices. On MK algebra problems, sometimes it's faster to plug each answer choice into the equation and see which one works rather than solving from scratch.
4. Estimate before you calculate. Round numbers to make quick mental math. If the answer choices are $47, $52, $98, and $112, and your estimate lands around $50, you've already narrowed it to two choices.
5. Watch your units. The #1 AR careless mistake: calculating correctly but in the wrong unit. If the question asks for feet and you solved in inches, you'll pick the wrong answer with total confidence.

The math sections are where disciplined prep pays off the fastest. You've got the formulas. Now put in the reps.