AFOQT cheat sheet

Analogies are written A : B :: C : D; build a precise sentence linking A to B, then apply that same sentence to C and select the choice for D.

Standard bridges: synonym, antonym, part-to-whole, whole-to-part, cause-to-effect, object-to-function, degree of intensity, worker-to-tool, category-to-member.

The grammatical class and word order of A:B must match C:D; if the bridge sentence requires a different part of speech for the answer pair, the choice is wrong.

Degree analogies keep direction: warm : hot :: cool : cold both move toward greater intensity; a choice that reverses direction is incorrect.

Prefixes: bene- good, mal- bad, ambi- both, circum- around, e-/ex- out, in-/im- not, pre- before, post- after, sub- under, super- above, anti- against.

Suffixes: -ous full of, -ity state of, -ify to make, -ism doctrine, -cide killing, -logy study of, -phobia fear, -able capable of.

High-frequency opposite pairs: garrulous/taciturn, frugal/profligate, ephemeral/perpetual, zealous/indifferent, abstruse/obvious, candid/evasive.

Word-knowledge distractors often share a root with the stem but differ in connotation; the correct choice matches the exact sense used in the sentence or stem.

When two choices both fit, prefer the one with the same relationship type, the same degree of intensity, and the same word order as the stem pair.

Percent change = (new value − old value) ÷ old value × 100; percent of a number = rate × base.

Distance = rate × time; average speed for a whole trip = total distance ÷ total time, never the average of the separate speeds.

Combined work time for individual times a and b is ab ÷ (a + b) hours, because the rates add as 1/a + 1/b.

Simple interest I = Prt, with t in years (6 months = 0.5); total amount A = P + I.

Area: rectangle lw, triangle ½bh, circle πr², trapezoid ½(b₁ + b₂)h, parallelogram bh.

Volume: box lwh, cylinder πr²h, cone ⅓πr²h, sphere (4/3)πr³.

Right triangles: a² + b² = c²; common triples 3-4-5, 5-12-13, 8-15-17; 45-45-90 sides are x, x, x√2; 30-60-90 sides are x, x√3, 2x.

Mean = sum ÷ count; median = middle value of an ordered list; mode = most frequent value; range = maximum − minimum.

Probability of independent events both occurring = product of their probabilities; of mutually exclusive events = sum.

Block counting: total blocks = sum of the heights of every visible column, because each column rests on the ground and contains no internal gaps.

Cube facts: 6 square faces, 12 edges, 8 vertices; each face touches four neighbors and is parallel to exactly one opposite face, so opposite faces are never adjacent.

Rotated blocks: a 90° turn moves a marked face to an adjacent position, a 180° turn moves it to the opposite face, and a 270° turn mirrors the 90° result in the other direction.

Hidden figures: the target shape appears at the same size and orientation as displayed; follow straight line segments through the clutter instead of judging the overall outline.

Table reading: identify the row label and column label first, then read the cell at their intersection; confirm the units given in the header before answering.

Altimeter: short hand = thousands of feet, long hand = hundreds of feet; one full sweep of the long hand equals 1,000 feet.

Airspeed indicator reads in knots (white arc = flap range, green arc = normal range, red line = maximum); the VSI reads feet per minute, needle above zero = climb, below zero = descent.

Bernoulli principle: faster-moving air exerts lower pressure, so lower pressure over the curved upper wing surface versus higher pressure below produces lift.

Physical science constants and formulas: F = ma, density = mass ÷ volume, V = IR, work = force × distance, speed of sound ≈ 343 m/s, speed of light ≈ 3 × 10⁸ m/s.