Compiled by Sarah Thompson
Curriculum Developer | 12 Years in Military Education
Key Math Formulas
You need these math rules for the Arithmetic Reasoning and Mathematics Knowledge subtests. Learn them by heart before test day — you will not get a sheet of math rules or a calculator.
Shape Formulas (Geometry)
Rectangle
Area = length × width
Perimeter = 2(length + width)
Triangle
Area = ½ × base × height
Perimeter = side₁ + side₂ + side₃
Circle
Area = π × r²
Circumference = 2πr or πd
Box (Rectangular Solid)
Volume = length × width × height
Surface Area = 2(lw + lh + wh)
Cylinder
Volume = π × r² × height
Surface Area = 2πr² + 2πrh
Pythagorean Theorem
a² + b² = c²
(right triangles only)
Algebra Formulas
Slope of a Line
m = (y₂ - y₁) / (x₂ - x₁)
Slope-Intercept Form
y = mx + b
m = slope, b = y-intercept
Quadratic Formula
x = (-b ± √(b² - 4ac)) / 2a
Distance Formula
d = √((x₂-x₁)² + (y₂-y₁)²)
Midpoint Formula
M = ((x₁+x₂)/2, (y₁+y₂)/2)
FOIL Method
(a+b)(c+d) = ac + ad + bc + bd
Percentages, Ratios & Word Problems
Percent Formula
Part = Percent × Whole
Percent = Part / Whole × 100
Percent Change
Change = (New - Old) / Old × 100
Simple Interest
I = P × R × T
Principal × Rate × Time
Distance Problems
Distance = Rate × Time
Rate = Distance / Time
Work Problems
1/A + 1/B = 1/Total
A and B are the times each one takes alone
Average (Mean)
Average = Sum of values / Number of values
Key Words to Know
Word Knowledge tests if you know what words mean. Learn these common ASVAB words and what they mean. Learn to figure out words from their parts too: the start (prefix), the end (suffix), and the root.
ASVAB Words That Show Up a Lot
Abate
To get less strong; lessen
Benevolent
Kind and giving; generous
Concise
Brief and to the point
Diligent
Hardworking; keeps at it
Eloquent
Speaks well and makes people agree
Frugal
Careful with money; thrifty
Gregarious
Likes to be with people; outgoing
Hinder
To get in the way of, slow down, or stop
Imminent
About to happen very soon
Meticulous
Very careful about every detail
Pragmatic
Sensible; thinks about what really works
Resilient
Able to bounce back fast
Tenacious
Does not give up; determined
Vigilant
Watchful; on the lookout for danger
Common Word Starts & Ends
Prefixes (Word Starts)
Suffixes (Word Ends)
General Science Key Ideas
The General Science subtest covers biology, chemistry, physics, and Earth science. Focus on these basic ideas.
Biology
- Cell parts: nucleus, mitochondria, cell membrane
- Photosynthesis: CO₂ + H₂O + light → glucose + O₂
- Body systems: blood (circulatory), breathing (respiratory), food (digestive), nerves (nervous)
- Genetics: DNA, genes, strong and hidden (dominant/recessive) traits
- Ecology: food chains, ecosystems, biomes (large living areas)
Chemistry
- Parts of an atom: protons, neutrons, electrons
- Periodic table: groups, periods, what each element is like
- States of matter: solid, liquid, gas, plasma
- Chemical reactions: what goes in (reactants), what comes out (products), balancing
- Acids & bases: pH scale, how they cancel out (neutralization)
Physics
- Newton's Laws: inertia, F=ma, action-reaction
- Energy: moving (kinetic), stored (potential), energy is never lost (conservation)
- Waves: frequency, wavelength, amplitude
- Light: bouncing (reflection), bending (refraction), colors (spectrum)
- Heat: conduction, convection, radiation
Earth Science
- Earth layers: crust, mantle, core
- Plate tectonics (moving land plates): earthquakes, volcanoes
- Weather: fronts, high and low pressure, clouds
- Water cycle: evaporation, condensation, precipitation (rain and snow)
- Solar system: planets, orbits, sun
Electronics Information
Key electricity ideas and formulas for the Electronics Information subtest.
Ohm's Law & Basic Formulas
V = I × R
Voltage = Current × Resistance
P = V × I
Power = Voltage × Current
P = I² × R
Power = Current² × Resistance
Key Electricity Ideas
- Voltage (V): The push behind electricity, measured in volts
- Current (I): How much electricity flows, measured in amperes (amps)
- Resistance (R): What slows the current down, measured in ohms
- Series circuit: Parts in one single path; the current is the same everywhere
- Parallel circuit: Many paths; the voltage is the same on each path
- AC vs DC: Current that switches back and forth (alternating) vs. current that flows one way (direct)
- Capacitor: Stores electrical energy
- Resistor: Holds back how much current flows
Mechanical Comprehension
Key ideas about machines and forces, plus the simple machines you need to know.
Simple Machines
Lever
Fulcrum (pivot point), effort, load. There are three kinds, based on where each part sits.
Pulley
Changes which way you pull. More pulleys = less effort needed.
Inclined Plane (Ramp)
Takes less effort, but you move the load farther.
Wheel & Axle
Bigger wheel = more help from the machine (mechanical advantage).
Screw
A ramp wrapped around a rod.
Wedge
Two ramps back to back, used to split or lift.
Gears & Mechanical Advantage
Gear Ratios
- • The gear you turn (driver) makes the next gear (driven) spin the other way
- • More teeth on the driven gear = slower speed, more turning force (torque)
- • Gear ratio = driven teeth / driver teeth
- • A middle gear (idler) changes the way it spins but not the ratio
Mechanical Advantage
- • MA = Output force / Input force
- • MA > 1 means the force gets bigger
- • The catch: less force means you move it a longer way
- • Efficiency = (Work out / Work in) × 100%
Sample Practice Questions
Test yourself with these real questions from our free AFQT practice quizzes. Each one shows the right answer and why it is right.
Sample question 1
Find the perimeter of the figure shown.
Sample question 2
A grocer mixes 30 pounds of nuts costing $4.50 per pound with some nuts costing $6 per pound. If the mixture costs $5 per pound, how many pounds of the $6 nuts were used?
Sample question 3
Mundane most nearly means:
Study Tips That Work
Before You Study
- Take a practice test to find your weak spots
- Make a study schedule (4-8 weeks is best)
- Study the AFQT subjects first
- Keep all your study things in one place
While You Study
- Study for 25-50 minutes at a time with full focus
- Quiz yourself from memory; do not just read
- Go over new words for 15 minutes each day
- Practice math without a calculator