Compiled by Sarah Thompson
Curriculum Developer | 12 Years in Military Education
Essential Math Formulas
These formulas are essential for the Arithmetic Reasoning and Mathematics Knowledge subtests. Memorize them before test day — you won't have access to a formula sheet or calculator.
Geometry Formulas
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
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 individual times
Average (Mean)
Average = Sum of values / Number of values
Essential Vocabulary
Word Knowledge tests your vocabulary directly. Learn these common ASVAB words, their meanings, and how to identify them using prefixes, suffixes, and roots.
High-Frequency ASVAB Words
Abate
To reduce in intensity; lessen
Benevolent
Kind, generous, charitable
Concise
Brief and to the point
Diligent
Hardworking, persistent
Eloquent
Fluent and persuasive in speech
Frugal
Economical, thrifty
Gregarious
Sociable, outgoing
Hinder
To obstruct, delay, or prevent
Imminent
About to happen; impending
Meticulous
Extremely careful and precise
Pragmatic
Practical, realistic
Resilient
Able to recover quickly
Tenacious
Persistent, determined
Vigilant
Watchful, alert to danger
Common Prefixes & Suffixes
Prefixes
Suffixes
General Science Key Concepts
The General Science subtest covers biology, chemistry, physics, and earth science. Focus on these fundamental concepts.
Biology
- Cell structure: nucleus, mitochondria, cell membrane
- Photosynthesis: CO₂ + H₂O + light → glucose + O₂
- Human body systems: circulatory, respiratory, digestive, nervous
- Genetics: DNA, genes, dominant/recessive traits
- Ecology: food chains, ecosystems, biomes
Chemistry
- Atomic structure: protons, neutrons, electrons
- Periodic table: groups, periods, element properties
- States of matter: solid, liquid, gas, plasma
- Chemical reactions: reactants, products, balancing
- Acids & bases: pH scale, neutralization
Physics
- Newton's Laws: inertia, F=ma, action-reaction
- Energy: kinetic, potential, conservation
- Waves: frequency, wavelength, amplitude
- Light: reflection, refraction, spectrum
- Heat: conduction, convection, radiation
Earth Science
- Earth layers: crust, mantle, core
- Plate tectonics: earthquakes, volcanoes
- Weather: fronts, pressure systems, clouds
- Water cycle: evaporation, condensation, precipitation
- Solar system: planets, orbits, sun
Electronics Information
Essential electrical concepts 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 Electrical Concepts
- Voltage (V): Electrical pressure, measured in volts
- Current (I): Flow of electrons, measured in amperes
- Resistance (R): Opposition to current, measured in ohms
- Series circuit: Components in single path, current same everywhere
- Parallel circuit: Multiple paths, voltage same across branches
- AC vs DC: Alternating vs direct current
- Capacitor: Stores electrical energy
- Resistor: Limits current flow
Mechanical Comprehension
Key mechanical principles and simple machines you'll need to understand.
Simple Machines
Lever
Fulcrum, effort, load. Three classes based on position.
Pulley
Changes direction of force. More pulleys = less effort needed.
Inclined Plane
Reduces effort by increasing distance traveled.
Wheel & Axle
Larger wheel = more mechanical advantage.
Screw
Inclined plane wrapped around cylinder.
Wedge
Two inclined planes, used to split or lift.
Gears & Mechanical Advantage
Gear Ratios
- • Driver gear turns driven gear in opposite direction
- • More teeth on driven gear = slower speed, more torque
- • Gear ratio = driven teeth / driver teeth
- • Idler gears change direction without changing ratio
Mechanical Advantage
- • MA = Output force / Input force
- • MA > 1 means force is multiplied
- • Trade-off: more force = more distance moved
- • Efficiency = (Work out / Work in) × 100%
Sample Practice Questions
Test your knowledge with these sample questions from various ASVAB subtests.
A car travels 240 miles in 4 hours. What is its average speed?
A) 40 mph
B) 50 mph
C) 60 mph
D) 70 mph
Show Answer
C) 60 mph — Speed = Distance / Time = 240 miles / 4 hours = 60 mph
"Candid" most nearly means:
A) Secretive
B) Honest
C) Fearful
D) Hostile
Show Answer
B) Honest — Candid means being open, frank, and straightforward in speech.
Which organelle is responsible for producing energy in a cell?
A) Nucleus
B) Ribosome
C) Mitochondria
D) Cell membrane
Show Answer
C) Mitochondria — The mitochondria are called the "powerhouse of the cell" because they produce ATP, the cell's main energy source.
If a circuit has 12 volts and 4 ohms of resistance, what is the current?
A) 2 amps
B) 3 amps
C) 8 amps
D) 48 amps
Show Answer
B) 3 amps — Using Ohm's Law: I = V/R = 12V / 4Ω = 3 amps
A gear with 20 teeth drives a gear with 40 teeth. If the driving gear spins at 100 RPM, how fast does the driven gear spin?
A) 25 RPM
B) 50 RPM
C) 100 RPM
D) 200 RPM
Show Answer
B) 50 RPM — The gear ratio is 20:40 or 1:2. The driven gear has twice as many teeth, so it spins half as fast: 100 / 2 = 50 RPM.
Study Tips for Success
Before You Study
- Take a diagnostic test to identify weak areas
- Create a study schedule (4-8 weeks ideal)
- Prioritize AFQT subjects first
- Gather all study materials in one place
While You Study
- Study in 25-50 minute focused blocks
- Use active recall, not passive reading
- Review vocabulary for 15 min daily
- Practice math without a calculator
Start Your Military Career Journey
Use this study guide alongside our practice tests to maximize your ASVAB score and qualify for the military job you want.
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