USSS SAEE cheat sheet

Denotation is a word's dictionary meaning; connotation is its emotional association. 'Cheap' and 'inexpensive' share a denotation but differ sharply in connotation.

Context clue types: definition (set off by dashes or 'that is'), restatement/synonym, contrast/antonym (signaled by but, unlike, however), example (for instance), and cause-effect.

Prefixes: bene- good, mal- bad, circum- around, pre- before, post- after, anti- against, syn- together, tele- far off.

Roots: cred- believe, dict- speak, spec-/spect- look, tempor- time, aud- hear, path- feeling, phil- love, scrib-/script- write.

Suffixes: -able/-ible capable of, -ous full of, -ify/-fy to make, -ism doctrine or practice, -tion act or state, -less without.

Analogy strategy: build a precise sentence from the stem pair (for example, 'a fin is a part of a fish'), then apply the same sentence to every option; both relationship type and direction must match.

Commonly confused pairs: affect (verb, to influence) / effect (noun, result); principal (main, or school head) / principle (rule); complement (to complete) / compliment (to praise).

Register: formal prose avoids contractions, slang, and first person; a passage written in formal register usually signals an academic or official purpose.

Main idea equals topic plus the author's claim about that topic; it covers the whole passage, while a detail covers only a sentence or two.

Inference rule: an answer is correct only if it must be true given the text. If it merely could be true, eliminate it.

Choices containing absolutes (all, never, always, only, must) are usually wrong on inference and tone questions unless the passage states them.

Purpose verbs: inform, explain, persuade, argue, entertain, describe, criticize, compare. Match the verb to the overall text, not to a single paragraph.

Structure signals: chronological (then, later), cause-effect (because, therefore), compare-contrast (unlike, similarly), problem-solution (however, one remedy).

'EXCEPT' and 'NOT' questions ask for the one choice that is false or unsupported; verify three choices against the text before selecting the fourth.

Scope test: reject choices that are too broad, too narrow, or off-topic; the correct answer stays within the passage's exact subject and time frame.

Tone vocabulary to distinguish: objective, neutral, critical, laudatory, ironic, sardonic, nostalgic, cautious, resigned.

Subject-verb agreement: cross out prepositional phrases between subject and verb, then match the verb to the head noun; subjects joined by 'and' take a plural verb.

With either/or and neither/nor, the verb agrees with the nearer subject: 'Neither the manager nor the clerks were informed.'

A fragment lacks a subject, a verb, or a complete thought; a run-on joins two independent clauses with no punctuation or with only a comma.

Coordinating conjunctions (FANBOYS: for, and, nor, but, or, yet, so) may join two independent clauses when preceded by a comma.

Colon rule: a colon must follow an independent clause and introduces a list, an explanation, or a quotation.

Modifier placement: keep a modifier next to the word it describes; an introductory participial phrase modifies the subject of the main clause.

Pronoun agreement: singular antecedents (each, everyone, neither, anybody) take singular pronouns and singular verbs.

Apostrophes: 's marks singular possession, s' plural possession, and 's marks contractions; an apostrophe never forms a plain plural.

Comparisons: fewer with count nouns, less with mass nouns; between for two items, among for three or more.

Percent of a number: part = whole x rate (rate as a decimal); 15% of 80 = 0.15 x 80 = 12.

Percent change = (new - old) divided by old, then x 100; an increase is positive, a decrease is negative.

Average = sum divided by count, so sum = average x count; this rearrangement solves most missing-value and new-average problems.

d = rt, and also r = d/t and t = d/r. For round trips, total distance and total time are summed separately before computing average speed.

Simple interest: I = Prt, total = P + I. Compound amount: A = P(1 + r/n)^(nt).

Combined work: add the rates (1/a + 1/b), then invert the sum to get the time; pipes filling in 4 and 6 hours together take 2.4 hours.

Proportions: convert to the same units, then cross multiply, a/b = c/d gives ad = bc.

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

Conversions: 1 mile = 5,280 ft; 1 yard = 3 ft; 1 gallon = 4 quarts = 8 pints; 1 hour = 3,600 seconds; 1 kg = 2.2 lb.

Linear equation: ax + b = c gives x = (c - b)/a; when a variable appears on both sides, collect like terms before dividing.

Slope m = (y2 - y1)/(x2 - x1); parallel lines have equal slopes, and perpendicular slopes are negative reciprocals.

Quadratic formula: x = [-b +/- sqrt(b^2 - 4ac)]/(2a); the discriminant b^2 - 4ac is positive for two real roots, zero for one, negative for none.

Pythagorean theorem a^2 + b^2 = c^2 applies only to right triangles; 3-4-5, 5-12-13, and 8-15-17 are common triples.

Area: rectangle lw, triangle 0.5bh, circle pi r^2. Volume: rectangular solid lwh, cylinder pi r^2 h.

Angle sums: triangle 180 degrees, quadrilateral 360 degrees; an exterior angle of a triangle equals the sum of the two remote interior angles.

Probability = favorable outcomes divided by total outcomes; for independent events, multiply the separate probabilities.

Backsolving: substitute answer choices, starting with the middle value, and eliminate. Plugging in small numbers tests problems with variables in the choices.

Reasonableness check: a result larger than the whole, or a negative time, length, or count, signals a setup error.