ASVAB · Units 1–10 · Quick reference
ASVAB Review(CAT-ASVAB · Paper · PiCAT)
Grades 10–12+8 pages
All nine subtests in test order, the AFQT and line scores from public information, mechanical diagrams, test-day strategy and 32 original practice items. Not affiliated with or endorsed by the Department of Defense. No official test items are used.
1The test2Scores3AR: word problems4AR: rates & ratios5MK: numbers6MK: algebra7MK: geometry8Word Knowledge9Paragraphs10GS: life11GS: chemistry12GS: physics13GS: earth & space14Electronics15Auto16Shop17MC: machines18MC: fluids19Assembling Objects20Test day21Practice
1The ASVAB at a Glancenine tests, two formats
| Subtest (code) | What it covers | Paper: items / min | CAT: items / min | Paper pace | See |
|---|---|---|---|---|---|
| General Science (GS) | life, physical, earth and space science | 25 / 11 | 15 / 12 | 26 s | §10–§13 |
| Arithmetic Reasoning (AR)* | word problems, no calculator | 30 / 36 | 15 / 55 | 72 s | §3–§4 |
| Word Knowledge (WK)* | word meanings and synonyms | 35 / 11 | 15 / 9 | 19 s | §8 |
| Paragraph Comprehension (PC)* | short reading passages | 15 / 13 | 10 / 27 | 52 s | §9 |
| Mathematics Knowledge (MK)* | high-school math | 25 / 24 | 15 / 31 | 58 s | §5–§7 |
| Electronics Information (EI) | circuits, parts, safety | 20 / 9 | 15 / 10 | 27 s | §14 |
| Auto & Shop Information (AS) | cars, tools, shop practice | 25 / 11 | AI 10 / 7 + SI 10 / 6 | 26 s | §15–§16 |
| Mechanical Comprehension (MC) | forces, machines, fluids | 25 / 19 | 15 / 22 | 46 s | §17–§18 |
| Assembling Objects (AO) | how parts fit together | 25 / 15 | 15 / 18 | 36 s | §19 |
| Total, paper | 225 / 149 |
* AFQT subtests. CAT limits are without tryout questions. Source: officialasvab.com, What to Expect (Oct 2026).
CAT or paper?
- CAT-ASVAB (at MEPS or a MET site): adaptive, one item at a time; no skipping, no going back.
- Paper: one booklet for all; skip and review within a subtest only.
- PiCAT: a one-time CAT at home, confirmed by a supervised Verification Test.
- Student ASVAB (at school): career exploration; no AO.
Guessing
- Paper: wrong answers cost nothing; fill every bubble.
- CAT: rushed guesses at the end cost points; keep a steady pace.
Read this first
- Not affiliated with or endorsed by the Department of Defense. All practice is original; check rules at officialasvab.com.
Nine words, test order
Good Answers Win; Practice Makes Every Applicant More Able: GS, AR, WK, PC, MK, EI, AS, MC, AO.
2Scores: the AFQT and Line Scoreseligibility, then job fit
The AFQT box
- Not a separate test: a score built from AR, MK, WK and PC.
- WK + PC form VE (Verbal Expression); DoD gives AFQT = 2VE + AR + MK.
- A percentile, 1–99, against a 1997 sample of 18- to 23-year-olds: a 62 ties or beats 62 % of them; it is not 62 % correct.
- The AFQT decides who may enlist; each branch sets its own minimum.
| Army line score | Subtests |
|---|---|
| Clerical (CL) | VE + AR + MK |
| Combat (CO) | VE + AS + MC |
| Electronics (EL) | GS + AR + MK + EI |
| Field Artillery (FA) | AR + MK + MC |
| General Maintenance (GM) | GS + AS + MK + EI |
| General Technical (GT) | VE + AR |
| Mechanical Maintenance (MM) | AS + MC + EI |
| Skilled Technical (ST) | GS + VE + MC + MK |
| Air Force area | Subtests |
|---|---|
| Mechanical (M) | AR + AS + MC + VE |
| Administrative (A) | MK + VE |
| General (G) | AR + VE |
| Electronics (E) | AR + EI + GS + MK |
Other branches use their own combinations.
No honest AFQT from a practice test
- Practice tests lack official scaling. Track raw scores by subtest (21/30).
3Arithmetic Reasoning: Word Problemsplan, estimate, then compute
Three moves
- Read the last line first: what number, in what unit?
- Picture the story: equal groups → ×; sharing → ÷; “how many more” → −; combining → +.
- Estimate before you compute. Wrong choices are often off by 10 or are the halfway number.
Mental math (no calculator)
- 7 × 48 = 7 × 50 − 7 × 2 = 336
- × 5: × 10, then halve: 5 × 86 = 430
- × 25: × 100, then ÷ 4: 25 × 36 = 900
- 15 % = 10 % + half of that: 15 % of $46 = 4.60 + 2.30 = $6.90
| Fraction | Decimal | Percent |
|---|---|---|
| 12 | 0.5 | 50 % |
| 13 | 0.333… | 33⅓ % |
| 23 | 0.666… | 66⅔ % |
| 14 | 0.25 | 25 % |
| 34 | 0.75 | 75 % |
| 15 | 0.2 | 20 % |
| 18 | 0.125 | 12.5 % |
| 38 | 0.375 | 37.5 % |
Percent problems Worked
$64 jacket, 25 % off, then 5 % tax: 64 × 0.75 = 48; 48 × 1.05 = $50.40pay 75 %, then 105 %
Rent rises from $800 to $860: 60 ÷ 800 = 7.5 %change ÷ original
$2,400 at 4 % simple interest for 18 months: 2,400 × 0.04 × 1.5 = $144I = Prt; months ÷ 12
Traps
- Discounts in a row don’t add: 20 % off, then 10 % off, is 28 % off (0.8 × 0.9 = 0.72).
- 5 % is 0.05, not 0.5.
- Use only the numbers the question needs.
4Arithmetic Reasoning: Rates, Ratios & Averagesd = rt, parts, means
| Idea | Rule |
|---|---|
| Distance | d = rt; t = d ÷ r; r = d ÷ t |
| Toward each other | closing speed = sum of the speeds |
| Chasing | closing speed = difference |
| Average speed | total distance ÷ total time |
| Work | add the rates: 1a + 1b = 1t |
| Ratio a : b | the whole has a + b parts |
| Mean | total ÷ count; missing value = needed total − known |
| Overtime | 1.5 × rate on hours over 40 |
| Simple interest | I = principal × rate × time (years) |
Traps: change minutes to hours first (20 min = 13 h). In 3 : 5 the smaller share is 38 of the whole. Lengths × k make areas × k².
Rates and work Worked
Trucks 330 mi apart drive toward each other at 50 and 60 mph: 330 ÷ 110 = 3 hsum
A car leaves 1 h after a 45 mph bus and drives 60 mph: 45 ÷ 15 = 3 hdifference
120 mi out at 60 mph, back at 40 mph: 240 ÷ (2 + 3) = 48 mphnot 50
Pumps fill a tank in 6 h and 3 h: 16 + 13 = 12, so 2 hadd rates
Ratios, proportions, means Worked
Split $720 in the ratio 3 : 5: one part = 720 ÷ 8 = 90, so $270 and $4508 parts
5 cups serve 8; for 20: 5 × 208 = 12.5 cupsscale
Scores 84, 90, 78; for a mean of 85 on four tests: 340 − 252 = 88work back
46 h at $18, time and a half over 40: 720 + 6 × 27 = $882only 6 h at 1.5×
5Math Knowledge: Numbers & Exponentsfactors, powers, roots
Primes, GCF, LCM
- A prime has exactly two factors. Under 30: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29. 1 is not prime.
- Not prime: 51 = 3 × 17, 57 = 3 × 19, 91 = 7 × 13.
- GCF(24, 36) = 12; LCM(24, 36) = 72. The GCF is never bigger than the smaller number.
PEMDAS (Traditional)
Please Excuse My Dear Aunt Sally: parentheses, exponents, then × and ÷ left to right, then + and − left to right.
| Rule | Example |
|---|---|
| aᵐ · aⁿ = aᵐ⁺ⁿ | x⁵ · x³ = x⁸ |
| aᵐ ÷ aⁿ = aᵐ⁻ⁿ | x⁷ ÷ x² = x⁵ |
| (aᵐ)ⁿ = aᵐⁿ | (x³)⁴ = x¹² |
| (ab)ⁿ = aⁿbⁿ | (2x)³ = 8x³ |
| a⁰ = 1 | 7⁰ = 1 |
| a⁻ⁿ = 1aⁿ | 2⁻³ = 18 |
Squares to know: 11² = 121, 12² = 144, 13² = 169, 14² = 196, 15² = 225. Cubes: 2³ = 8, 3³ = 27, 4³ = 64, 5³ = 125.
Roots, order, notation Worked
√72 = √36 · √2 = 6√2pull out a square
√12 + √27 = 2√3 + 3√3 = 5√3like roots add
18 − 4 × 3 + 6 ÷ 2 = 18 − 12 + 3 = 9× ÷ before + −
−3² = −9, but (−3)² = 9the square hits 3 only
0.00052 = 5.2 × 10⁻⁴; (4 × 10³)(3 × 10⁵) = 1.2 × 10⁹scientific notation
6Math Knowledge: Algebrasolve, factor, check
Equations and inequalities Worked
4x − 7 = 2x + 9 → 2x = 16 → x = 8collect x on one side
x3 + 2 = 7 → x3 = 5 → x = 15undo + first, then ÷
−2x + 5 > 13 → −2x > 8 → x < −4divide by a negative: flip
|x − 2| = 5 → x − 2 = 5 or −5 → x = 7 or −3two cases
| Pattern | Example |
|---|---|
| FOIL | (x + 3)(x − 5) = x² − 2x − 15 |
| Common factor | 6x² + 9x = 3x(2x + 3) |
| Difference of squares | x² − 49 = (x + 7)(x − 7) |
| Trinomial | x² + 7x + 12 = (x + 3)(x + 4) |
| Perfect square | (x − 4)² = x² − 8x + 16 |
Traps: −(x − 3) = −x + 3; x² = 25 gives x = 5 or −5.
Systems, substitution, words Worked
x + y = 10 and x − y = 4: add → 2x = 14 → x = 7, y = 3elimination
a = 3, b = −2: a² − 2ab = 9 + 12 = 21parentheses for negatives
“Five less than twice a number is 17”: 2n − 5 = 17 → n = 11“less than” reverses order
7Math Knowledge: Geometry & Graphsangles, area, slope
| Shape | Formula | Shape | Formula | Solid | Formula |
|---|---|---|---|---|---|
| Rectangle | A = lw; P = 2l + 2w | Trapezoid | A = ½(b₁ + b₂)h | Box | V = lwh |
| Triangle | A = ½bh | Circle | A = πr² | Cube | V = s³; surface 6s² |
| Parallelogram | A = bh | C = 2πr = πd | Cylinder; cone | V = πr²h; V = ⅓πr²h |
Angles and triangles
- Straight line 180°; right angle 90°; vertical angles are equal.
- A triangle’s angles add to 180°; any polygon: (n − 2) × 180°.
- a² + b² = c² for a right triangle; triples 3-4-5, 5-12-13, 8-15-17 (and multiples).
Geometry Worked
Legs 9 and 12: c = √(81 + 144) = 153-4-5 × 3
r = 5: A = 25π ≈ 78.5; C = 10π ≈ 31.4π ≈ 3.14
Box 4 × 3 × 2.5 ft: V = 30 ft³lwh
Hexagon: (6 − 2) × 180 = 720°; each angle 120°regular
| Tool | Formula |
|---|---|
| Slope | m = y₂ − y₁x₂ − x₁ |
| Line | y = mx + b (b = y-intercept) |
| Distance | √((x₂ − x₁)² + (y₂ − y₁)²) |
| Midpoint | (x₁ + x₂2, y₁ + y₂2) |
| Quadratic formula | x = −b ± √(b² − 4ac)2a |
(1, 2) to (4, 8): slope 2, distance 3√5, midpoint (2.5, 5). Perpendicular slopes: 2 and −½.
8Word Knowledgeword parts, clues, habits
| Part | Meaning | Example | Part | Meaning | Example |
|---|---|---|---|---|---|
| bene- | good | benefit | chron | time | chronological |
| mal- | bad | malfunction | dict | say | predict |
| circum- | around | circumference | spect | look | inspect |
| contra-, anti- | against | contradict | port | carry | portable |
| sub- | under | submerge | ject | throw | eject |
| trans- | across | transport | scrib, script | write | inscribe |
| pre- | before | preview | ver | true | verify |
| post- | after | postpone | -ous | full of | courageous |
| un-, in-, im- | not | impossible | -ify | to make | simplify |
Method
- Cover the choices. Say what the word means in your own words.
- A word alone: put it in a phrase you know (“a placid lake” → calm).
- Swap test: put your choice in the sentence. Same meaning? Keep it.
- Traps: a same-topic word (arid means dry, not desert); look-alikes (eminent, famous, vs imminent, about to happen).
| Clue | Signal | Example (meaning) |
|---|---|---|
| Definition | is, means, or | an arid, or very dry, valley (dry) |
| Contrast | but, unlike, although | Unlike his gregarious sister, Paul sat alone (sociable) |
| Example | such as, like | Fragile items such as eggs and glass (easily broken) |
Build a word bank
- Ten new words a day beat a night of cramming.
- Card: word in front; meaning, sentence and synonym on the back. Recall before you flip.
9Paragraph Comprehensionread the question first
| Question type | What to do |
|---|---|
| Main idea or best title | umbrella test: it must cover every sentence |
| Stated detail | find the key word; read its whole sentence |
| Sequence | follow time words (first, before, after) |
| Inference | one small step you can point to in the text |
| Word in context | swap each choice into the sentence |
| Author’s purpose | inform, explain, persuade or entertain? |
Wrong-answer patterns
- Too narrow: one true detail. Too broad: bigger than the passage.
- True but not stated: real-world fact the passage never says.
- Twisted: the passage’s words, rearranged. Too far: a bold leap.
Pace
- Paper: about 52 s per question; the CAT allows 27 min for 10.
- Read the question stem, then the passage once, then the choices.
- Answer from the passage, not from what you already know.
Try it (original passage)
“Before a painter rolls a single coat, most of the job is done. Walls are washed, holes are filled and sanded, and edges are taped. Paint over dust or grease peels within months; paint on a clean, smooth wall can last ten years.”
Main idea: preparation decides how long paint lasts. Edges are taped is too narrow. Inference: skipping the washing means earlier peeling.
10General Science: Life Sciencecells, body, heredity, ecology
| Cell part | Job |
|---|---|
| nucleus | holds DNA; directs the cell |
| mitochondria | release energy from food |
| ribosomes | build proteins |
| cell membrane | controls what enters and leaves |
| chloroplasts (plants) | photosynthesis |
| cell wall (plants) | rigid support |
| vacuole | stores water and food |
Photosynthesis: CO₂ + water + light → sugar + O₂. Respiration: sugar + O₂ → CO₂ + water + energy.
| System | Main parts and job |
|---|---|
| circulatory | heart, blood, vessels: carry O₂ and food |
| respiratory | lungs, alveoli: swap O₂ and CO₂ |
| digestive | stomach, small intestine (absorbs most nutrients) |
| nervous | brain, spinal cord, nerves: signals |
| skeletal, muscular | support and movement |
| immune | white blood cells fight germs |
| endocrine | glands make hormones |
Arteries carry blood away from the heart; veins return it. Red cells carry O₂; platelets clot.
Heredity
- Each parent gives one allele. Tt × Tt → TT, Tt, Tt, tt: 3 of 4 show the dominant trait.
- Human body cells: 23 pairs, 46 chromosomes. Mendel worked it out with pea plants.
- DNA bases pair A–T and C–G.
Ecology
- Producers (plants) → herbivores → carnivores. Food-web arrows point to the eater.
- Only about 10 % of the energy passes up each level.
- Decomposers (fungi, bacteria) return nutrients to the soil.
- Kingdom, phylum, class, order, family, genus, species: “King Philip Came Over For Good Soup” (Traditional).
11General Science: Matter & Chemistryatoms, elements, reactions
The atom
- Protons (+) and neutrons (0) in the nucleus; electrons (−) around it.
- Atomic number = protons (it names the element). Neutrons = mass number − atomic number.
- Isotopes: same element, different neutrons. Ions: atoms that gained or lost electrons.
Chemistry Worked
Carbon-14: 6 protons; 14 − 6 = 8 neutrons
pH 3 vs pH 5: 10² = 100 times more acidic
60 g in 20 cm³: D = 3 g/cm³; it sinks
| Symbol | Element | Symbol | Element |
|---|---|---|---|
| Na | sodium | H | hydrogen |
| K | potassium | He | helium |
| Fe | iron | C | carbon |
| Cu | copper | N | nitrogen |
| Ag | silver | O | oxygen |
| Au | gold | Cl | chlorine |
| Pb | lead | Ca | calcium |
| Hg | mercury | Ne | neon |
Rows are periods; columns are groups that act alike. Noble gases (last column) hardly react.
Changes and properties
- Physical: melting, freezing, boiling, dissolving, sublimation (dry ice). Chemical: new color, gas, solid or heat and light.
- Balanced: 2H₂ + O₂ → 2H₂O (4 H and 2 O on each side). Mass is conserved.
- Density D = m ÷ V; denser than water (1 g/cm³) sinks.
- pH 7 neutral; below is acid, above is base. Each step is × 10.
12General Science: Physicsmotion, energy, heat, waves
Newton’s laws
- 1st (inertia): objects keep doing what they are doing unless a net force acts.
- 2nd: F = ma. Weight W = mg; on the Moon mass stays, weight drops.
- 3rd: every action has an equal and opposite reaction (a rocket pushes gas down; gas pushes it up).
Physics Worked
10 → 30 m/s in 5 s: a = 20 ÷ 5 = 4 m/s²
1,200 kg × 3 m/s² = 3,600 NF = ma
Double the speed → 4 × the KEv is squared
440 Hz × 0.78 m ≈ 343 m/ssound in air
| Quantity | Formula |
|---|---|
| Speed | d ÷ t |
| Acceleration | (final v − starting v) ÷ t |
| Force | F = ma |
| Kinetic energy | KE = ½mv² |
| Potential energy | PE = mgh |
| Work; power | W = Fd; P = W ÷ t |
| Waves | v = fλ |
Free fall: g ≈ 9.8 m/s² (often rounded to 10).
Heat and waves
- Heat flows hot → cold by conduction (contact), convection (moving fluid) and radiation (waves, even through space).
- Sound needs matter (about 340 m/s in air, faster in water and steel); light crosses a vacuum at about 186,000 mi/s.
- Higher frequency = higher pitch; bigger amplitude = louder.
- Spectrum, long to short waves: radio, microwave, infrared, visible, ultraviolet, X-ray, gamma.
13General Science: Earth & Spacerocks, weather, the sky
| Rock | How it forms | Examples |
|---|---|---|
| Igneous | molten rock cools | granite (slow), basalt, obsidian (fast) |
| Sedimentary | layers pressed and cemented | sandstone, shale, limestone; most fossils |
| Metamorphic | changed by heat and pressure | marble (from limestone), slate (from shale) |
Mohs hardness: talc 1, gypsum 2, calcite 3, fluorite 4, apatite 5, feldspar 6, quartz 7, topaz 8, corundum 9, diamond 10.
Inside Earth and weather
- Crust, mantle, liquid outer core, solid inner core.
- Air: about 78 % nitrogen, 21 % oxygen. Weather happens in the troposphere; ozone sits in the stratosphere.
- Low pressure brings clouds and storms; high pressure, fair skies. Cold fronts are fast and stormy.
- Tools: barometer (pressure), anemometer (wind speed), hygrometer (humidity).
Sun, Earth, Moon
- Planets from the Sun: Mercury, Venus, Earth, Mars, Jupiter (largest), Saturn, Uranus, Neptune.
- Seasons come from the 23.5° tilt of Earth’s axis, not its distance from the Sun.
- Solar eclipse: the Moon blocks the Sun. Lunar eclipse: Earth’s shadow falls on the Moon.
“While the earth remaineth, seedtime and harvest, and cold and heat, and summer and winter, and day and night shall not cease” (Genesis 8:22, KJV).
14Electronics InformationOhm’s law to safety
Color code in order
Better Be Ready Or Your Great Big Venture Goes Wrong: black, brown, red, orange, yellow, green, blue, violet, gray, white.
| Rule | Formula |
|---|---|
| Ohm’s law | V = IR; I = V ÷ R; R = V ÷ I |
| Power | P = VI = I²R = V² ÷ R |
| Series | R = R₁ + R₂ + …; same current |
| Parallel | 1R = 1R₁ + 1R₂ + …; same voltage |
| Two in parallel | R = R₁R₂R₁ + R₂ |
| Transformer | V outV in = turns outturns in |
Parallel total is less than the smallest branch. 1 mA = 0.001 A; 1 kΩ = 1,000 Ω.
Electronics Worked
60 W lamp on 120 V: I = 60 ÷ 120 = 0.5 A; R = 240 ΩP = VI
250 mA through 40 Ω: V = 0.25 × 40 = 10 VmA → A
120 V, 200 turns to 20 turns: 12 Vstep-down
| Part | What it does |
|---|---|
| capacitor | stores charge; blocks DC once charged, passes AC |
| inductor (coil) | opposes changes in current |
| diode | current one way only; rectifies AC to DC |
| LED | diode that lights; needs a series resistor |
| transistor | small base current switches or amplifies a large one |
| fuse, breaker | opens when current is too high |
Color code, AC and safety
- Bands: black 0, brown 1, red 2, orange 3, yellow 4, green 5, blue 6, violet 7, gray 8, white 9. Two digits, then the zeros: yellow-violet-red = 4,700 Ω.
- US outlets: about 120 V AC, 60 Hz. Batteries give DC; cells in series add volts.
- Shut off the breaker and test before touching. Never put in a bigger fuse. The round prong is the ground.
15Auto Informationengine, systems, diagnosis
| System | Key parts and facts |
|---|---|
| Fuel | pump, filter, injectors (or carburetor); rich = too much fuel, lean = too little |
| Ignition | coil steps 12 V up to thousands of volts; spark plug |
| Cooling | water pump, radiator, thermostat (opens when warm), fan |
| Lubrication | oil pump, filter; 5W-30: the W number is the cold rating |
| Starting, charging | battery (12.6 V at rest), solenoid, starter; alternator recharges |
| Drivetrain | clutch or torque converter → transmission → driveshaft → differential → axles |
| Brakes | master cylinder pushes fluid to calipers (pads on rotors) or wheel cylinders (shoes in drums) |
| Steering, suspension | rack and pinion, tie rods; springs, shocks or struts |
Engine facts
- Piston → connecting rod → crankshaft → flywheel → transmission.
- Compression ratio = volume at bottom ÷ volume at top: 500 cc ÷ 50 cc = 10 : 1.
- Diesel: no spark plugs; squeezed air gets hot enough to light the fuel (glow plugs help cold starts).
- Two-stroke engines fire every turn; oil is mixed into the fuel.
Lights and codes
- Red = stop soon (oil pressure, temperature, charging, brakes). Amber = check soon.
- A flashing check-engine light means a misfire: ease off.
- OBD-II port on cars since the 1996 model year; codes start P, B, C or U.
| Symptom | Likely cause |
|---|---|
| click, no crank | weak battery or corroded cables |
| cranks, won’t start | no fuel, no spark or no compression |
| overheating | low coolant, stuck thermostat, bad pump or fan |
| blue smoke | burning oil |
| black smoke | too rich |
| sweet white smoke | burning coolant |
| squeal when braking | worn pads |
| keeps bouncing | worn shocks |
16Shop Informationtools, fasteners, measuring
| Job | Tools |
|---|---|
| Striking | claw hammer (nails), ball-peen (metal, punches), mallet (no marks) |
| Turning | box-end grips 6 corners; open-end; socket and ratchet; torque wrench for exact tightness |
| Gripping | slip-joint, needle-nose and locking pliers |
| Cutting wood | crosscut saw across the grain, rip saw along it, coping saw for curves, chisel |
| Cutting metal | hacksaw (teeth point forward; cuts on the push), tin snips, file |
| Shaping | plane smooths wood; rasp rough-shapes wood; file shapes metal |
| Checking | level, square, tape, caliper, micrometer (0.001 in) |
| Fastener | Use |
|---|---|
| wood screw | tapered, coarse threads |
| sheet-metal screw | sharp, threaded to the head |
| machine screw, bolt | fine threads into a nut or tapped hole |
| lag screw | big hex head for heavy wood |
| rivet | permanent; pop rivets from one side |
| finishing nail | small head, set below the surface |
| lock washer | keeps a nut from loosening |
Measuring and materials
- A tape is marked in sixteenths: 3 in and 11 marks = 3 1116 in.
- A “2 × 4” is about 1½ × 3½ in.
- Hardwoods (oak, maple) from broadleaf trees; softwoods (pine, fir) from conifers.
- Cast iron is hard but brittle; stainless steel resists rust; brass = copper + zinc; bronze = copper + tin.
- Welding: stick (coated rod), MIG (wire feed), TIG (tungsten), oxy-acetylene.
Shop safety
- Eye protection always. Unplug before changing a blade or bit.
- Clamp the work; use a push stick on a table saw.
- No loose sleeves or jewelry near spinning tools.
17Mechanical Comprehension: Machinestrade force for distance
Trains, belts and cams
- In a gear train, neighbors turn opposite ways; gears 1, 3, 5 turn the same way. An idler changes direction, not speed.
- Open belt: same direction. Crossed belt: reversed. The smaller pulley spins faster.
- A cam turns rotation into back-and-forth motion; a crank’s stroke is 2 × its radius.
- Friction makes real MA smaller; efficiency = work out ÷ work in, always under 100 %.
| Machine | Ideal mechanical advantage |
|---|---|
| Any | MA = load ÷ effort = effort distance ÷ load distance |
| Lever | W × its distance = E × its distance (from the fulcrum) |
| Pulleys | strands holding the load |
| Gears | teeth × rpm match: T₁ × rpm₁ = T₂ × rpm₂ |
| Wheel and axle | wheel radius ÷ axle radius |
| Ramp | length ÷ height |
| Screw | advance = turns × pitch; pitch = 1 ÷ threads per inch |
Work = force × distance (ft·lb). Power = work ÷ time; 1 hp = 550 ft·lb per second. No machine gives out more work than you put in.
Machines Worked
120 lb, 2 ft from the fulcrum; effort 6 ft away: 120 × 2 ÷ 6 = 40 lblever
4 strands hold 200 lb: 50 lb; pull 4 ft of rope per foot of liftpulleys
24-tooth gear at 30 rpm drives a 12-tooth gear: 60 rpmgears
200 lb up a 12 ft ramp, 3 ft high: 50 lbramp
15 in crank, 3 in drum: MA 5wheel and axle
16 threads per inch: ½ in takes 8 turnsscrew
Crossed belt, 4 in pulley driving an 8 in pulley: half speed, reversedbelt
Lift 50 lb 4 ft: 200 ft·lb of workW = Fd
Wedges, screws, wheels
- A wedge is a moving ramp (axe, chisel, doorstop): longer and thinner gives more MA.
- A screw is a ramp wrapped around a post: finer threads give more MA but take more turns.
- A wheel and axle (doorknob, steering wheel, screwdriver handle) multiplies the force on the rim at the axle.
- Every machine trades: more force means more distance, and more speed means less force.
18Mechanical Comprehension: Fluids & Structurespressure, buoyancy, strength
Pressure
- P = F ÷ A. 180 lb on 60 in² of boot = 3 psi; on 360 in² of snowshoe = 0.5 psi.
- In a liquid, pressure grows with depth and pushes equally in all directions; tank width does not matter.
- Liquids barely compress; gases compress.
Structures and materials
- A loaded beam: top in compression, bottom in tension. The nearer support carries more.
- A board on edge is far stiffer: twice as deep is 8 × as stiff.
- Triangles hold their shape; concrete needs steel rebar for tension.
- A spring stretches in proportion: 10 lb → 2 in, so 25 lb → 5 in.
Hydraulics (Pascal) Worked
Pistons of 2 in² and 40 in²: 30 lb in gives 600 lb outF₁A₁ = F₂A₂
…but the small piston moves 20 in for each inch of liftpay in distance
Buoyancy Worked
A 3 lb block held under water displaces 5 lb of water: net push up 2 lbbuoyant force − weight
Beam Worked
12 ft beam, 300 lb load 4 ft from support A: A carries 300 × 812 = 200 lb, B carries 100 lbload × far distance ÷ span
Buoyancy and flow
- The upward push equals the weight of fluid displaced. A floating object displaces its own weight.
- A narrower pipe makes faster flow (A₁v₁ = A₂v₂); faster flow has lower pressure (a carburetor venturi).
Heat, balance and motion
- Metals expand when heated: hot water loosens a tight metal lid.
- A bimetal strip bends toward the metal that expands less (a thermostat).
- A low center of gravity and a wide base make an object stable.
- On a curve, a loose object keeps going straight until something pushes it.
- Hard is not tough: glass resists scratches but shatters.
19Assembling Objects & Spatial Skillsturns yes, flips no
Track a landmark
Follow one feature (a dot, a notch, a corner). “Top left” changes when a piece turns; a landmark does not.
What AO measures
- How parts look put together. Pieces turn but never flip, and sizes never change. Not in the AFQT.
Fit-the-pieces items
- Count the pieces first; the answer uses the same number.
- Compare the largest and smallest pieces; sizes never change.
- Cross out a choice the moment one piece fails.
Quarter turns
- 90° clockwise: top → right → bottom → left → top.
- 180°: top and bottom swap, and left and right swap.
Joined-at-a-point items
- Name each marked point by a landmark: “middle of the short edge by the notch.”
- Find the same landmark in each choice.
- Flip check: walk the edge clockwise; a mirror image reverses the landmark order.
20Test Day & Study Planpace, review, plan
| Paper | CAT-ASVAB | |
|---|---|---|
| Skip and return | yes, within a subtest | no |
| Change an answer | yes, until time is up | no: answers are final |
| Blanks | never: guess on all | not allowed; answer each one |
| Last minute | fill every bubble | keep a steady pace; no rushed guesses |
Pace: seconds each = minutes × 60 ÷ questions. At half time, be about half done.
| Miss type | Fix |
|---|---|
| didn’t know it | relearn the fact or formula; add a card |
| set it up wrong | rework it slowly; write Asked and Given |
| careless slip | circle words like NOT; check the row |
| ran short of time | timed sets of 10 |
Two-week plan
- 30–40 minutes a day on the weakest AFQT subtest: review, 10 timed questions, log misses.
- Week 2: add the weakest line-score subtest.
- Take the course’s Practice Test A, review, then Practice Test B. One rest day a week.
- Test morning: normal sleep, breakfast, water; confirm ID, time and place with your recruiter.
“And whatsoever ye do, do it heartily, as to the Lord, and not unto men” (Colossians 3:23, KJV).
21Practice Setoriginal items, answers checked
| # | Question | Answer | # | Question | Answer |
|---|---|---|---|---|---|
| 1 | (GS) Which cell part releases energy from food? | mitochondria | 9 | (AR) Mean of 72, 88, 91 and 85? | 84 |
| 2 | (GS) Atomic no. 17, mass no. 35: neutrons? | 18 | 10 | (WK) Candid most nearly means | frank |
| 3 | (GS) What causes Earth’s seasons? | the tilt of its axis | 11 | (WK) Diligent most nearly means | hard-working |
| 4 | (GS) Does sound travel faster in air or in steel? | steel | 12 | (WK) Unlike her lethargic brother, Ana rose at dawn. | sluggish |
| 5 | (AR) 84 ft of fence in 3.5 h: feet per hour? | 24 | 13 | (WK) Benevolent (bene = good) | kind |
| 6 | (AR) A $45 drill is 20 % off. Sale price? | $36 | 14 | (PC) “Mulch keeps soil damp.” Infer: bare soil … | dries out faster |
| 7 | (AR) Flour : sugar = 5 : 2. Sugar in 21 cups? | 6 cups | 15 | (MK) Solve 3(x − 4) = 2x + 1 | x = 13 |
| 8 | (AR) Hoses fill a pool in 4 h and 12 h. Together? | 3 h | 16 | (MK) Simplify (2a³)² | 4a⁶ |
| # | Question | Answer | # | Question | Answer |
|---|---|---|---|---|---|
| 17 | (MK) Simplify √50 | 5√2 | 25 | (AS) Crankshaft at 3,000 rpm: camshaft rpm? | 1,500 |
| 18 | (MK) Triangle area, base 14, height 9 | 63 | 26 | (AS) Blue exhaust smoke usually means | burning oil |
| 19 | (MK) Slope through (−1, 4) and (3, −4) | −2 | 27 | (AS) Tape reads 5 in and 7 sixteenth marks | 5 716 in |
| 20 | (MK) Solve x² − 9x + 20 = 0 | 4 or 5 | 28 | (MC) 90 lb 2 ft from fulcrum; effort at 6 ft | 30 lb |
| 21 | (EI) 24 V across 8 Ω: current? | 3 A | 29 | (MC) 3 strands hold 240 lb: effort? | 80 lb |
| 22 | (EI) 6 Ω and 3 Ω in parallel | 2 Ω | 30 | (MC) 36 teeth at 20 rpm drive 12 teeth | 60 rpm, reversed |
| 23 | (EI) Which part passes current one way only? | diode | 31 | (MC) Pistons 1 in² and 25 in²; push 40 lb | 1,000 lb |
| 24 | (EI) Brown-black-red resistor | 1,000 Ω | 32 | (MC) 150 lb up a 10 ft ramp, 2 ft high | 30 lb |
AO is a picture test: practice with the course’s Lessons 10.1–10.2, Practice Tests A and B and the free official samples.