AFQT cheat sheet

Percent change = (new value − original value) ÷ original value × 100; use the original value as the denominator.

Average = sum ÷ count; total = average × count; count = total ÷ average.

Combined work rate = rate A + rate B when both work on the same job; time together = 1 ÷ combined rate for a one-job task.

Distance = rate × time; rate = distance ÷ time; time = distance ÷ rate.

Simple interest: I = P × r × t, where r is the annual decimal rate and t is time in years.

Sale price after a discount = original price × (1 − discount rate).

In a part-to-part ratio, total parts = sum of ratio terms; each share = total quantity ÷ total parts × that term.

Profit = revenue − cost; loss occurs when cost exceeds revenue.

Order of operations: parentheses, exponents, multiplication and division left to right, addition and subtraction left to right.

Slope = (y₂ − y₁) ÷ (x₂ − x₁); horizontal slope = 0; vertical slope is undefined.

Slope-intercept form: y = mx + b, where m is slope and b is y-intercept.

Rectangle area = length × width; triangle area = ½ × base × height; circle area = πr²; circumference = 2πr.

Rectangular prism volume = length × width × height; cylinder volume = πr²h.

Pythagorean theorem: a² + b² = c² for a right triangle, with c the hypotenuse.

Exponent rules: a^m × a^n = a^(m+n); (a^m)^n = a^(mn); a^0 = 1 for a ≠ 0; a^(−n) = 1 ÷ a^n.

Linear equation rule: apply the same operation to both sides; undo addition/subtraction before multiplication/division.

Percent to decimal: divide by 100; decimal to percent: multiply by 100.

Context restatement clue: a definition may follow words like or, that is, or in other words; the unknown word matches the restated idea.

Context contrast clue: but, however, although, unlike signal an opposite meaning nearby.

Context example clue: for example, including, such as introduce examples that narrow an unfamiliar word's meaning.

Prefixes: un- = not; re- = again; pre- = before; dis- = not/opposite; mis- = wrongly; anti- = against; sub- = under; inter- = between.

Roots: aud = hear; bene = good; chron = time; dict = say; graph = write; ject = throw; port = carry; spect = look; vis/vid = see.

Suffixes: -less = without; -ful = full of; -able/-ible = capable of; -tion/-ment = state or action; -ous = full of.

Homophone decision rule: affect is usually a verb (influence); effect is usually a noun (result); principal = main or school head; principle = rule.

Connotation check: replace the word with a neutral synonym; if the sentence's feeling changes, the original carries a positive or negative connotation.

Adjective modifies a noun or pronoun; adverb modifies a verb, adjective, or another adverb.

Main idea = topic + author's central point; it is broader than any single supporting detail.

Supporting details answer who, what, when, where, why, or how and must relate to the main idea.

Valid inference rule: the conclusion must be supported by passage evidence, even if it is not directly stated.

Author's purpose categories: inform, persuade, entertain, explain; the overall message and tone indicate the purpose.

Tone is revealed by word choice, imagery, and examples; tone describes the author's attitude, not the reader's.

Sequence clues: first, next, then, after, finally signal order; follow these words to track steps or events.

Comparison/contrast clues: both, similarly, like signal similarity; unlike, however, whereas signal difference.

Fact statement can be verified; opinion statement expresses belief, judgment, or feeling and often uses evaluative words.

Vocabulary-in-context rule: use nearby sentences and the word's function in the sentence before choosing a meaning.