AFCT cheat sheet

Context clues: the sentence around an unknown word often contains a definition, contrast signal (but, unlike, however), or example that reveals meaning.

Prefixes: pre- (before), post- (after), sub- (under), super- (above), anti- (against), pro- (for), mis- (wrongly), re- (again), inter- (between).

Roots: -cred- (believe), -dict- (say), -duc- (lead), -ject- (throw), -port- (carry), -scrib- (write), -tract- (pull), -vert- (turn), -bene- (good), -mal- (bad).

Suffixes that mark nouns: -tion, -ment, -ness, -ity, -ance. Adjective suffixes: -ous, -ive, -able, -ful, -less. Verb suffixes: -ize, -ify, -ate.

Synonyms share core meaning; antonyms are opposites. On synonym items, eliminate choices that are only loosely related or wrong in connotation (positive vs. negative).

Connotation tiers: words can be positive (thrifty), neutral (economical), or negative (stingy) while sharing denotation; pick the choice matching the stem's tone.

Homophones to distinguish by spelling: their/there/they're, its/it's, principal/principle, stationary/stationery, complement/compliment.

If two answer choices are near-identical in meaning, neither is usually correct; the answer is the choice that differs in a meaningful way.

Main idea = the central point the whole passage supports; it is broader than any single detail and is often stated in the first or last sentence.

Supporting details answer who, what, when, where, why, how; a detail that appears only once is usually not the main idea.

Inference must be logically forced by the text, not merely plausible; reject choices requiring outside assumptions.

Tone and purpose questions hinge on word choice: emotional or evaluative adjectives signal opinion; neutral verbs and data signal exposition.

Sequence questions: track time markers (first, then, after, finally) and cause-effect markers (because, therefore, as a result, consequently).

Comparison-contrast structure uses signals like however, whereas, on the other hand, similarly, likewise; the author's point often lands after the contrast.

Author's purpose falls into three broad types: inform/explain, persuade/argue, entertain/narrate.

For 'EXCEPT' or 'NOT' questions, verify each choice against the passage and select the one the text contradicts or never supports.

Percent change = (new - old) / old x 100; a 20% decrease then 20% increase does not return to the original value (result is 96% of original).

Percent of a number: part = percent/100 x whole. To find the whole given a part: whole = part / (percent/100).

Distance = rate x time; rearrange as rate = distance/time and time = distance/rate. Keep units consistent (minutes vs. hours).

Average (mean) = sum of values / count. To find a missing value: sum needed = mean x count, then subtract known values.

Work-rate problems: combined rate = 1/a + 1/b per unit time; time together = 1 / (1/a + 1/b).

Profit = revenue - cost; markup and discount are percentages of cost or original price respectively, applied before tax.

Simple interest: I = P x r x t (r as a decimal, t in years). Total owed = principal + interest.

Ratio problems: set up a proportion a/b = c/d and cross-multiply; scale all parts by the same factor to keep the ratio fixed.

Unit conversion chains: multiply by fractions equal to 1 (e.g., 12 in/1 ft) so unwanted units cancel.

Quadratic formula: x = [-b +/- sqrt(b^2 - 4ac)] / (2a) for ax^2 + bx + c = 0; discriminant b^2 - 4ac tells the number of real roots.

FOIL and factoring: (x + a)(x + b) = x^2 + (a+b)x + ab; difference of squares a^2 - b^2 = (a - b)(a + b).

Exponent rules: x^m x^n = x^(m+n); x^m / x^n = x^(m-n); (x^m)^n = x^(mn); x^0 = 1 (x not 0); x^(-n) = 1/x^n.

Slope = (y2 - y1)/(x2 - x1); point-slope form y - y1 = m(x - x1); parallel lines have equal slopes, perpendicular slopes multiply to -1.

Area formulas: rectangle lw; triangle (1/2)bh; circle pi r^2; trapezoid (1/2)(b1 + b2)h. Circumference = 2 pi r.

Volume: rectangular solid lwh; cylinder pi r^2 h; sphere (4/3)pi r^3; cone (1/3)pi r^2 h.

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

Angle facts: straight line = 180 degrees; triangle interior angles sum to 180; quadrilateral to 360; vertical angles are equal.

Probability of an event = favorable outcomes / total outcomes; independent events multiply probabilities.

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.

Photosynthesis: 6CO2 + 6H2O + light energy -> C6H12O6 + 6O2, occurring in chloroplasts using chlorophyll.

Cellular respiration is essentially the reverse: glucose + oxygen -> carbon dioxide + water + ATP energy, occurring in mitochondria.

Water cycle stages: evaporation, transpiration, condensation, precipitation, and runoff/collection.

Earth's layers from outside in: crust, mantle, outer core (liquid), inner core (solid); tectonic plate motion causes earthquakes and volcanoes.

pH scale 0-14: below 7 acidic, 7 neutral, above 7 basic; each whole step is a tenfold change in hydrogen ion concentration.

States of matter: adding heat increases particle motion, causing solid to liquid to gas transitions at melting and boiling points.

Food chain energy flow: producers (plants) to primary consumers (herbivores) to higher consumers; energy decreases at each level.

Ohm's law: V = I x R; rearrange as I = V/R and R = V/I. Voltage in volts, current in amperes, resistance in ohms.

Power formulas: P = V x I = I^2 R = V^2 / R, measured in watts.

Series circuits: resistances add (R_total = R1 + R2 + ...); current is the same through all components; voltages add.

Parallel circuits: 1/R_total = 1/R1 + 1/R2 + ...; voltage is the same across branches; branch currents add.

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

A diode allows current in one direction only; an LED emits light when forward-biased.

Capacitors store charge in an electric field (units farads) and block DC while passing AC; inductors store energy in a magnetic field (henries).

AC reverses direction periodically (household is typically 60 Hz in the US); DC flows one direction, as from a battery.

A transformer changes AC voltage levels through mutual induction and does not work on steady DC.

Four-stroke engine cycle: intake, compression, power (combustion), exhaust; the crankshaft converts piston motion into rotation.

Engine basics: spark plugs ignite the fuel-air mixture in gasoline engines; diesel engines ignite by compression heat instead.

Cooling system circulates coolant from the engine through the radiator, where airflow removes heat; the thermostat regulates flow.

Battery, starter, and alternator form the charging/starting circuit: battery cranks the starter; the alternator recharges the battery while running.

Brake hydraulics: pressing the pedal pushes fluid through lines to calipers or wheel cylinders, applying friction to rotors or drums.

Hand tools: a claw hammer drives and pulls nails; a chisel cuts wood with a beveled edge; a plane shaves thin layers; a file abrades metal.

Saw types: crosscut saw cuts across wood grain; ripsaw cuts along the grain; hacksaw cuts metal with fine teeth.

Fasteners: machine screws thread into metal, wood screws have coarse threads and a tapered point, and bolts fasten with a nut.

Safety rule: keep blades sharp (dull blades slip and require excess force), and never remove guards from power tools.

Mechanical advantage of a lever: MA = effort arm length / resistance arm length; a longer effort arm reduces required force.

Lever classes: first class has the fulcrum between load and effort; second class has the load between fulcrum and effort; third class has effort between fulcrum and load.

Pulley systems: a single fixed pulley changes direction only (MA = 1); movable pulleys sharing the load give MA equal to the number of supporting rope segments.

Inclined plane MA = length of incline / height; a longer, gentler ramp requires less force over a greater distance.

Wedge and screw are variations of the inclined plane; the screw's MA relates to thread spacing (finer threads give greater advantage).

Gear ratios: driven gear teeth / driving gear teeth sets the torque-speed tradeoff; larger driven gears increase torque and reduce speed.

Pressure = force / area; the same force spread over a larger area produces lower pressure (why wide tires or snowshoes work).

Work = force x distance in the direction of force; machines trade force for distance but do not reduce total work (ignoring friction).

Center of gravity: an object is stable when its center of gravity lies over its base of support; a lower center and wider base increase stability.

Context clues: the sentence around an unknown word often contains a definition, contrast signal (but, unlike, however), or example that reveals meaning.

Prefixes: pre- (before), post- (after), sub- (under), super- (above), anti- (against), pro- (for), mis- (wrongly), re- (again), inter- (between).

Roots: -cred- (believe), -dict- (say), -duc- (lead), -ject- (throw), -port- (carry), -scrib- (write), -tract- (pull), -vert- (turn), -bene- (good), -mal- (bad).

Suffixes that mark nouns: -tion, -ment, -ness, -ity, -ance. Adjective suffixes: -ous, -ive, -able, -ful, -less. Verb suffixes: -ize, -ify, -ate.

Synonyms share core meaning; antonyms are opposites. On synonym items, eliminate choices that are only loosely related or wrong in connotation (positive vs. negative).

Connotation tiers: words can be positive (thrifty), neutral (economical), or negative (stingy) while sharing denotation; pick the choice matching the stem's tone.

Homophones to distinguish by spelling: their/there/they're, its/it's, principal/principle, stationary/stationery, complement/compliment.

If two answer choices are near-identical in meaning, neither is usually correct; the answer is the choice that differs in a meaningful way.

Main idea = the central point the whole passage supports; it is broader than any single detail and is often stated in the first or last sentence.

Supporting details answer who, what, when, where, why, how; a detail that appears only once is usually not the main idea.

Inference must be logically forced by the text, not merely plausible; reject choices requiring outside assumptions.

Tone and purpose questions hinge on word choice: emotional or evaluative adjectives signal opinion; neutral verbs and data signal exposition.

Sequence questions: track time markers (first, then, after, finally) and cause-effect markers (because, therefore, as a result, consequently).

Comparison-contrast structure uses signals like however, whereas, on the other hand, similarly, likewise; the author's point often lands after the contrast.

Author's purpose falls into three broad types: inform/explain, persuade/argue, entertain/narrate.

For 'EXCEPT' or 'NOT' questions, verify each choice against the passage and select the one the text contradicts or never supports.

Percent change = (new - old) / old x 100; a 20% decrease then 20% increase does not return to the original value (result is 96% of original).

Percent of a number: part = percent/100 x whole. To find the whole given a part: whole = part / (percent/100).

Distance = rate x time; rearrange as rate = distance/time and time = distance/rate. Keep units consistent (minutes vs. hours).

Average (mean) = sum of values / count. To find a missing value: sum needed = mean x count, then subtract known values.

Work-rate problems: combined rate = 1/a + 1/b per unit time; time together = 1 / (1/a + 1/b).

Profit = revenue - cost; markup and discount are percentages of cost or original price respectively, applied before tax.

Simple interest: I = P x r x t (r as a decimal, t in years). Total owed = principal + interest.

Ratio problems: set up a proportion a/b = c/d and cross-multiply; scale all parts by the same factor to keep the ratio fixed.

Unit conversion chains: multiply by fractions equal to 1 (e.g., 12 in/1 ft) so unwanted units cancel.

Quadratic formula: x = [-b +/- sqrt(b^2 - 4ac)] / (2a) for ax^2 + bx + c = 0; discriminant b^2 - 4ac tells the number of real roots.

FOIL and factoring: (x + a)(x + b) = x^2 + (a+b)x + ab; difference of squares a^2 - b^2 = (a - b)(a + b).

Exponent rules: x^m x^n = x^(m+n); x^m / x^n = x^(m-n); (x^m)^n = x^(mn); x^0 = 1 (x not 0); x^(-n) = 1/x^n.

Slope = (y2 - y1)/(x2 - x1); point-slope form y - y1 = m(x - x1); parallel lines have equal slopes, perpendicular slopes multiply to -1.

Area formulas: rectangle lw; triangle (1/2)bh; circle pi r^2; trapezoid (1/2)(b1 + b2)h. Circumference = 2 pi r.

Volume: rectangular solid lwh; cylinder pi r^2 h; sphere (4/3)pi r^3; cone (1/3)pi r^2 h.

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

Angle facts: straight line = 180 degrees; triangle interior angles sum to 180; quadrilateral to 360; vertical angles are equal.

Probability of an event = favorable outcomes / total outcomes; independent events multiply probabilities.

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.

Photosynthesis: 6CO2 + 6H2O + light energy -> C6H12O6 + 6O2, occurring in chloroplasts using chlorophyll.

Cellular respiration is essentially the reverse: glucose + oxygen -> carbon dioxide + water + ATP energy, occurring in mitochondria.

Water cycle stages: evaporation, transpiration, condensation, precipitation, and runoff/collection.

Earth's layers from outside in: crust, mantle, outer core (liquid), inner core (solid); tectonic plate motion causes earthquakes and volcanoes.

pH scale 0-14: below 7 acidic, 7 neutral, above 7 basic; each whole step is a tenfold change in hydrogen ion concentration.

States of matter: adding heat increases particle motion, causing solid to liquid to gas transitions at melting and boiling points.

Food chain energy flow: producers (plants) to primary consumers (herbivores) to higher consumers; energy decreases at each level.

Ohm's law: V = I x R; rearrange as I = V/R and R = V/I. Voltage in volts, current in amperes, resistance in ohms.

Power formulas: P = V x I = I^2 R = V^2 / R, measured in watts.

Series circuits: resistances add (R_total = R1 + R2 + ...); current is the same through all components; voltages add.

Parallel circuits: 1/R_total = 1/R1 + 1/R2 + ...; voltage is the same across branches; branch currents add.

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

A diode allows current in one direction only; an LED emits light when forward-biased.

Capacitors store charge in an electric field (units farads) and block DC while passing AC; inductors store energy in a magnetic field (henries).

AC reverses direction periodically (household is typically 60 Hz in the US); DC flows one direction, as from a battery.

A transformer changes AC voltage levels through mutual induction and does not work on steady DC.

Four-stroke engine cycle: intake, compression, power (combustion), exhaust; the crankshaft converts piston motion into rotation.

Engine basics: spark plugs ignite the fuel-air mixture in gasoline engines; diesel engines ignite by compression heat instead.

Cooling system circulates coolant from the engine through the radiator, where airflow removes heat; the thermostat regulates flow.

Battery, starter, and alternator form the charging/starting circuit: battery cranks the starter; the alternator recharges the battery while running.

Brake hydraulics: pressing the pedal pushes fluid through lines to calipers or wheel cylinders, applying friction to rotors or drums.

Hand tools: a claw hammer drives and pulls nails; a chisel cuts wood with a beveled edge; a plane shaves thin layers; a file abrades metal.

Saw types: crosscut saw cuts across wood grain; ripsaw cuts along the grain; hacksaw cuts metal with fine teeth.

Fasteners: machine screws thread into metal, wood screws have coarse threads and a tapered point, and bolts fasten with a nut.

Safety rule: keep blades sharp (dull blades slip and require excess force), and never remove guards from power tools.

Mechanical advantage of a lever: MA = effort arm length / resistance arm length; a longer effort arm reduces required force.

Lever classes: first class has the fulcrum between load and effort; second class has the load between fulcrum and effort; third class has effort between fulcrum and load.

Pulley systems: a single fixed pulley changes direction only (MA = 1); movable pulleys sharing the load give MA equal to the number of supporting rope segments.

Inclined plane MA = length of incline / height; a longer, gentler ramp requires less force over a greater distance.

Wedge and screw are variations of the inclined plane; the screw's MA relates to thread spacing (finer threads give greater advantage).

Gear ratios: driven gear teeth / driving gear teeth sets the torque-speed tradeoff; larger driven gears increase torque and reduce speed.

Pressure = force / area; the same force spread over a larger area produces lower pressure (why wide tires or snowshoes work).

Work = force x distance in the direction of force; machines trade force for distance but do not reduce total work (ignoring friction).

Center of gravity: an object is stable when its center of gravity lies over its base of support; a lower center and wider base increase stability.