CAT-ASVAB cheat sheet

At standard pressure water boils at 100 °C (212 °F) and freezes at 0 °C (32 °F); boiling point drops as atmospheric pressure falls.

Photosynthesis: 6CO2 + 6H2O + light energy yields C6H12O6 + 6O2, occurring in the chloroplasts of plant cells.

Newton's laws: an object stays at rest or in uniform motion unless acted on by a net force; F = ma; every action has an equal and opposite reaction.

pH below 7 is acidic, 7 is neutral, above 7 is basic; each whole unit represents a tenfold change in hydrogen ion concentration.

Mitosis produces two identical diploid cells; meiosis produces four genetically distinct haploid gametes.

Rock classes: igneous (cooled magma or lava), sedimentary (compacted deposited particles), metamorphic (altered by heat and pressure).

Plate boundaries: divergent (plates separate), convergent (plates collide or one subducts), transform (plates slide past each other).

Speed of light in a vacuum is about 3.0 x 10^8 meters per second; light travels slower through any medium such as glass or water.

Percent problems: part = rate x whole. Percent change = (new - old) / old x 100%.

Average = sum of values / number of values, so sum = average x number of values.

Distance = rate x time; therefore rate = distance / time and time = distance / rate.

Combined work: if one worker takes a hours and another b hours, together they take t hours where 1/t = 1/a + 1/b.

Simple interest: I = P x r x t, with r as a decimal annual rate and t in years. Compound amount: A = P(1 + r/n)^(nt).

Discount: sale price = original price x (1 - discount rate). Markup: new price = cost x (1 + markup rate).

Ratios: for a ratio a:b the total is a + b parts, and value per part = total / (a + b).

Unit conversion: multiply by conversion factors arranged so unwanted units cancel, then compute.

Prefixes: ante- (before), anti- (against), circum- (around), hyper- (over), hypo- (under), bene- (good), mal- (bad).

Roots: cred (believe), dict (say), scrib/script (write), aud (hear), chron (time), graph (write), sens/sent (feel).

Suffixes: -ology (study of), -phobia (fear of), -cide (killing), -ism (doctrine or practice), -ous (full of).

Connotation separates near-synonyms: thrifty is positive, stingy negative; confident is positive, arrogant negative.

Easily confused pairs: affect (verb, to influence) vs. effect (noun, result); principal (main) vs. principle (rule); eminent vs. imminent.

Part of speech limits choices: a blank needing a verb cannot be filled by a noun or adjective answer choice.

Opposite-meaning distractors are common; confirm direction before choosing a synonym.

The main idea is the point the whole passage supports; it is broader than any single detail and often appears in a first or last sentence.

"According to the passage" questions require an answer explicitly stated in the text, not an inference.

An inference must follow necessarily from the evidence given; a merely plausible statement is not sufficient.

Tone and attitude are signaled by word choice, loaded adjectives, and qualifiers such as admittedly or unfortunately.

Common organizational patterns: chronological, cause-effect, compare-contrast, and problem-solution.

Answer choices that are too broad, too narrow, or contradictory to the passage can be eliminated.

Author's purpose is usually one of four: to inform, to persuade, to entertain, or to explain a process.

A correct answer must fall within the passage's scope, which is set by the topic and the concluding sentence.

Quadratic formula: x = (-b +/- sqrt(b^2 - 4ac)) / (2a) for ax^2 + bx + c = 0.

Areas: circle = pi r^2; triangle = 1/2 b h; trapezoid = 1/2 (b1 + b2) h; parallelogram = b h.

Volumes: cylinder = pi r^2 h; cone = 1/3 pi r^2 h; sphere = 4/3 pi r^3; rectangular solid = l w h.

Pythagorean theorem: a^2 + b^2 = c^2 in a right triangle; common triples are 3-4-5, 5-12-13, and 8-15-17.

Slope m = (y2 - y1)/(x2 - x1); parallel lines have equal slopes, perpendicular lines have slopes whose product is -1.

Exponent rules: x^a x^b = x^(a+b); (x^a)^b = x^(ab); x^0 = 1; x^(-a) = 1/x^a.

Factoring patterns: (a + b)^2 = a^2 + 2ab + b^2; (a + b)(a - b) = a^2 - b^2.

Angle sums: triangle = 180 degrees; quadrilateral = 360 degrees; n-gon = (n - 2) x 180 degrees.

Circumference = 2 pi r = pi d; an inscribed angle equals half the measure of its intercepted arc.

Ohm's law: V = I x R. Power: P = V x I = I^2 R = V^2 / R.

Series circuits: R total = R1 + R2 + ..., current is the same everywhere, and voltage divides across components.

Parallel circuits: 1/R total = 1/R1 + 1/R2 + ..., voltage is the same across branches, and current divides.

Resistor color values: black 0, brown 1, red 2, orange 3, yellow 4, green 5, blue 6, violet 7, gray 8, white 9; gold = 5% tolerance, silver = 10%.

Capacitors store charge in an electric field and are rated in farads; they block DC and pass AC. Inductors store energy in a magnetic field and are rated in henries.

A diode conducts in one direction only; an LED emits light when forward biased; a bridge rectifier converts AC to pulsating DC.

In an NPN transistor, base current controls the larger collector-to-emitter current, allowing amplification or switching.

US household power is AC at 60 Hz, supplied at roughly 120 V and 240 V; conductors include copper, silver, gold, and aluminum, while rubber and glass insulate.

Four-stroke cycle: intake, compression, power (spark ignition), exhaust; the crankshaft makes two revolutions per cycle.

Engine displacement = volume of one cylinder x number of cylinders; cylinder volume depends on bore and stroke.

Compression ratio = (swept volume + clearance volume) / clearance volume; a diesel engine ignites fuel by compression heat alone.

Manual transmissions use a clutch to engage the engine; automatic transmissions use a torque converter.

Cooling system parts: radiator, water pump, thermostat, coolant; the thermostat regulates coolant flow to hold operating temperature.

Hydraulic brakes transmit force through fluid; disc brakes use calipers and pads, drum brakes use wheel cylinders and shoes.

A 12-volt lead-acid battery starts the car; the alternator recharges it and powers electrical loads while the engine runs.

Saw teeth: a rip saw cuts with the grain, a crosscut saw cuts across the grain; a claw hammer drives and pulls nails.

Drilling: a pilot hole smaller than the screw shank prevents splitting; harder material requires slower speed and lighter feed.

Lever mechanical advantage = effort arm / resistance arm, both measured from the fulcrum; class 1, 2, and 3 levers differ in the order of fulcrum, load, and effort.

A single fixed pulley changes direction only (MA = 1); a single movable pulley has MA = 2 because two rope segments support the load.

Inclined plane mechanical advantage = length of the incline / vertical height; a gentler slope needs less force over a longer distance.

Gear ratio = driven gear teeth / driving gear teeth; a larger driven gear turns slower and delivers more torque.

Work = force x distance (in the direction of the force); power = work / time.

Torque = force x perpendicular lever arm distance from the pivot.

Pascal's principle: pressure applied to a confined fluid is transmitted undiminished, so F1/A1 = F2/A2 in a hydraulic system.

Efficiency = useful output work / total input work x 100%; friction converts part of the input work into heat.

An object is more stable when its center of gravity is low and lies above the center of its base of support.