Quick Reference

ASVAB Cheat Sheet

All the formulas, facts, and terms you need — in one place.

📐 Math Formulas (AR & MK)

Geometry

Area of Rectangle = length × width
Area of Triangle = ½ × base × height
Area of Circle = π × r²  (π ≈ 3.14)
Circumference = 2πr  or  πd
Perimeter of Rectangle = 2(l + w)
Volume of Rectangular Prism = l × w × h
Volume of Cylinder = π × r² × h
Volume of Sphere = (4/3) × π × r³
Surface Area of Rectangular Prism = 2(lw + lh + wh)
Pythagorean Theorem: a² + b² = c²  (right triangles only)
Sum of Interior Angles = (n − 2) × 180°  (n = number of sides)
Common Pythagorean Triples: 3-4-5, 5-12-13, 8-15-17, 7-24-25

Algebra

Slope = (y₂ − y₁) / (x₂ − x₁) = rise / run
Slope-Intercept Form: y = mx + b
Quadratic Formula: x = (−b ± √(b² − 4ac)) / 2a
Difference of Squares: a² − b² = (a + b)(a − b)
FOIL: (a + b)(c + d) = ac + ad + bc + bd
Percent = (Part / Whole) × 100
Distance = Rate × Time
Simple Interest: I = P × r × t
Average (Mean) = Sum of values / Number of values
Probability = Favorable outcomes / Total outcomes

Conversions

1 foot = 12 inches  |  1 yard = 3 feet  |  1 mile = 5,280 feet
1 pound = 16 ounces  |  1 ton = 2,000 pounds
1 gallon = 4 quarts  |  1 quart = 2 pints  |  1 pint = 2 cups
°F to °C: C = (F − 32) × 5/9  |  °C to °F: F = C × 9/5 + 32
1 meter = 100 cm = 1,000 mm  |  1 km = 1,000 m
1 kg = 1,000 g  |  1 liter = 1,000 mL

🔬 Science Facts (GS)

Biology

Cell TheoryAll living things made of cells; cells come from existing cells; cells are basic unit of life
Photosynthesis6CO₂ + 6H₂O + light → C₆H₁₂O₆ + 6O₂ (in chloroplasts)
Cellular RespirationC₆H₁₂O₆ + 6O₂ → 6CO₂ + 6H₂O + ATP (in mitochondria)
DNA StructureDouble helix; base pairs: A-T, C-G; carries genetic instructions
MitosisCell division → 2 identical diploid cells (growth & repair)
MeiosisCell division → 4 unique haploid cells (sex cells/gametes)
Blood TypesA, B, AB (universal recipient), O (universal donor); Rh+ or Rh−
Blood ComponentsRed cells (oxygen), White cells (immune), Platelets (clotting), Plasma (fluid)
Taxonomy OrderKingdom → Phylum → Class → Order → Family → Genus → Species
Organ SystemsCirculatory, Respiratory, Digestive, Nervous, Skeletal, Muscular, Endocrine, Immune, Excretory, Reproductive, Integumentary

Earth & Space Science

Earth's LayersCrust → Mantle → Outer Core (liquid iron) → Inner Core (solid iron)
Atmosphere LayersTroposphere → Stratosphere (ozone) → Mesosphere → Thermosphere → Exosphere
Rock TypesIgneous (cooled magma), Sedimentary (compressed layers), Metamorphic (heat/pressure)
Rock CycleIgneous ↔ Sedimentary ↔ Metamorphic (continuous transformation)
Plate TectonicsConvergent (collide), Divergent (pull apart), Transform (slide past)
Planet OrderMercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune
Water CycleEvaporation → Condensation → Precipitation → Collection → Repeat
Mohs Hardness Scale1 (Talc) to 10 (Diamond) — measures mineral hardness

Physical Science & Chemistry

States of MatterSolid → Liquid → Gas → Plasma (increasing energy)
Phase ChangesMelting, Freezing, Evaporation, Condensation, Sublimation, Deposition
pH Scale0–6 Acidic | 7 Neutral | 8–14 Basic/Alkaline
Chemical BondsIonic (transfer e⁻), Covalent (share e⁻), Metallic (electron sea)
Newton's Laws1st: Inertia | 2nd: F=ma | 3rd: Action = Reaction
EM SpectrumRadio → Microwave → IR → Visible → UV → X-ray → Gamma (↑ frequency, ↓ wavelength)
Speed of Light~3 × 10⁸ m/s or ~186,000 mi/s
Speed of Sound~343 m/s in air (varies with temp & medium)
Water PropertiesFreezes at 32°F/0°C, Boils at 212°F/100°C, Density: 1 g/mL
Periodic TableMetals (left), Nonmetals (right), Metalloids (staircase), Noble Gases (Group 18)

⚡ Electronics (EI)

Ohm's Law: V = I × R  (Voltage = Current × Resistance)
Power: P = V × I  (Watts = Volts × Amps)
Also: P = I²R  and  P = V²/R
Series Resistance: R_total = R₁ + R₂ + R₃ + ...
Parallel Resistance: 1/R_total = 1/R₁ + 1/R₂ + ...  (or R₁R₂/(R₁+R₂) for two)
Energy: E = P × t  (kilowatt-hours = kilowatts × hours)
Transformer: V₁/V₂ = N₁/N₂  (voltage ratio = turns ratio)
Capacitor Time Constant: τ = R × C
Series CircuitsOne path for current. Same current through all components. Voltages add up.
Parallel CircuitsMultiple paths. Same voltage across branches. Currents add up.
AC vs DCAC: alternating direction (household). DC: one direction (batteries).
US Household120V / 60Hz (standard outlets), 240V for large appliances
Wire Colors (US)Black = Hot, White = Neutral, Green/Bare = Ground, Red = 2nd Hot
ComponentsResistor (opposes current), Capacitor (stores charge), Inductor (stores in magnetic field), Diode (one-way), Transistor (switch/amplify)
UnitsVolts (V), Amps (A), Ohms (Ω), Watts (W), Farads (F), Henrys (H)
Fuse/BreakerProtects circuit from overcurrent by breaking the circuit

⚙️ Mechanical Comprehension (MC)

Work = Force × Distance  (W = Fd)
Power = Work / Time
Force = Mass × Acceleration  (F = ma)
Kinetic Energy = ½mv²
Potential Energy = mgh  (mass × gravity × height)
Pressure = Force / Area  (P = F/A)
Efficiency = (Output Work / Input Work) × 100%
MA (Lever) = Effort Arm / Load Arm
MA (Inclined Plane) = Length / Height
MA (Pulley) = Number of supporting ropes
MA (Wheel & Axle) = Wheel Radius / Axle Radius
Gear Ratio = Driven Gear Teeth / Driver Gear Teeth
Pascal's Law: F₁/A₁ = F₂/A₂  (hydraulics)
Boyle's Law: P₁V₁ = P₂V₂  (at constant temperature)
6 Simple MachinesLever, Inclined Plane, Wedge, Screw, Wheel & Axle, Pulley
Lever Classes1st: Fulcrum in middle (seesaw). 2nd: Load in middle (wheelbarrow). 3rd: Effort in middle (fishing rod).
GearsMeshing gears turn opposite directions. Larger gear = slower speed, more torque.
FrictionStatic > Kinetic. Opposes motion. Depends on surfaces & normal force.
Bernoulli's PrincipleFaster fluid → lower pressure. Explains lift on airplane wings.
BuoyancyArchimedes: upward force = weight of displaced fluid
Center of GravityLower center of gravity = more stability
Thermal ExpansionMaterials expand when heated, contract when cooled

🔧 Auto & Shop Information (AI/SI)

Four-Stroke CycleIntake → Compression → Power → Exhaust ("Suck, Squeeze, Bang, Blow")
Cooling SystemRadiator, Thermostat, Water Pump, Coolant/Antifreeze, Hoses, Fan
Braking SystemMaster Cylinder → Brake Lines → Calipers (disc) or Drums → Brake Fluid (DOT 3/4/5)
Alternator vs StarterAlternator: charges battery while running. Starter: cranks engine to start.
Catalytic ConverterReduces CO, HC, and NOx emissions in exhaust
DifferentialAllows wheels to turn at different speeds (cornering)
Clutch vs Torque ConverterClutch: manual transmission. Torque converter: automatic transmission.
OBD-IIOn-Board Diagnostics standard for monitoring emissions and performance
Engine TypesInline (I4, I6), V-type (V6, V8), Flat/Boxer, Rotary (Wankel)
Tap vs DieTap: internal threads (holes). Die: external threads (bolts).
Sandpaper GritLower # = coarser. Higher # = finer. 60=rough, 220=medium, 400+=fine
Soldering FluxCleans surfaces, prevents oxidation for proper solder flow
Torque WrenchMeasures rotational force applied to fasteners (ft-lbs or N·m)
Center PunchMakes indentation to prevent drill bit from wandering
File TypesSingle-cut (one direction), Double-cut (crossing teeth), Rasp (rough wood)
Saw TypesBand saw (curves), Table saw (straight rip), Circular saw (portable), Jig saw (detail curves)

📖 Vocabulary Power Words (WK)

Abatereduce in intensity
Absolvefree from blame
Alleviatemake less severe
Ambiguousunclear, multiple meanings
Benevolentkind, well-meaning
Brevityshortness, conciseness
Candidtruthful, straightforward
Coerceforce or threaten
Complacentsmugly satisfied
Concedeadmit, yield
Consensusgeneral agreement
Corroborateconfirm, support
Debilitateweaken
Deferencerespect, submission
Diligentcareful, persistent
Discrepancyinconsistency, difference
Eloquentfluent, persuasive
Emulateimitate, match
Erraticunpredictable, irregular
Exemplaryoutstanding, model
Fortitudecourage in adversity
Frugaleconomical, thrifty
Hinderobstruct, delay
Imminentabout to happen
Impededelay, obstruct
Integrityhonesty, strong morals
Lethargicsluggish, lacking energy
Meticulousvery careful, precise
Mitigatemake less severe
Negligentfailing to take care
Notoriousfamous for bad
Obsoleteoutdated, no longer used
Perseverepersist despite difficulty
Pragmaticpractical, realistic
Precludeprevent, make impossible
Prolificproducing abundantly
Redundantunnecessary, superfluous
Replenishrefill, restore
Resilientrecovers quickly
Scrutinizeexamine closely
Sporadicirregular, occasional
Subordinatelower in rank
Substantiateprove, provide evidence
Tenaciouspersistent, firm
Ubiquitouseverywhere
Validateconfirm accuracy
Verbosewordy, too many words
Volatileunpredictable, unstable
Zealousenthusiastic, passionate

🎖️ ASVAB Test Facts

AFQT SubtestsAR + MK + WK + PC → determines enlistment eligibility
AFQT MinimumsArmy: 31 | Navy: 31 | Marines: 32 | Air Force: 36 | Coast Guard: 36 | Space Force: 36
CAT-ASVAB135 scored questions + ~10 try-out items, 10 subtests, ~2.5 hours
No Going BackOn the CAT-ASVAB, once you answer, you cannot go back
Adaptive TestingQuestions adjust in difficulty. Correct → harder, Wrong → easier
Score RangeStandard scores 1–99 per subtest. AFQT is a percentile (1–99).
Retest Policy1st retest: 1 month. 2nd: 1 month. After: 6-month waits
Line ScoresComposite scores from subtest combinations — determine MOS eligibility
GT ScoreAR + WK + PC — used for many Army MOS qualifications (110+ preferred)
CL ScoreAR + MK + WK + PC — Clerical composite
EL ScoreGS + AR + MK + EI — Electronics composite
MM ScoreAR + MC + AI + SI + EI — Mechanical Maintenance composite