ACT cheat sheet

Punctuation rule: use a comma before a coordinating conjunction (FANBOYS: for, and, nor, but, or, yet, so) only when it joins two independent clauses.

A semicolon joins two independent clauses with no conjunction; a colon must follow a complete clause and introduce an explanation, list, or example.

Nonessential (nonrestrictive) information is set off by a matched pair of commas, dashes, or parentheses; essential information takes no punctuation.

Subject-verb agreement: the verb matches the true subject, ignoring prepositional phrases; indefinite pronouns like each, everyone, nobody, and either are singular.

Pronoun case: use who/whom, I/me, and they/them according to grammatical role - subject pronouns for subjects, object pronouns after prepositions and verbs.

Modifier placement: an introductory descriptive phrase must modify the noun that immediately follows the comma; otherwise the sentence is misplaced or dangling.

Redundancy and wordiness are the most common wrong-answer traps; the shortest choice that preserves meaning and grammar is usually correct.

Transitions: choose by logical relationship - contrast (however, nevertheless), cause-effect (therefore, consequently), addition (moreover, furthermore), example (for instance).

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

Quadratic formula: x = [−b ± √(b² − 4ac)]/(2a); the discriminant b² − 4ac gives 2, 1, or 0 real solutions when positive, zero, or negative.

Circle: area = πr², circumference = 2πr; equation (x − h)² + (y − k)² = r² has center (h, k) and radius r.

Right-triangle ratios: sin = opposite/hypotenuse, cos = adjacent/hypotenuse, tan = opposite/adjacent; Pythagorean theorem a² + b² = c².

Distance = rate × time; average speed = total distance ÷ total time (not the average of the speeds).

Exponential growth/decay: y = a(1 ± r)^t, where r is the rate per period and t the number of periods; compound interest uses (1 + r/n)^(nt).

Log rules: log(ab) = log a + log b; log(a/b) = log a − log b; log(a^n) = n·log a; log_b x = y means b^y = x.

Sequences: arithmetic term a_n = a_1 + (n − 1)d; geometric term a_n = a_1·r^(n−1); sum of arithmetic series = n(a_1 + a_n)/2.

Main idea = topic + author's point about the topic; it must cover the whole passage, not one supporting detail.

Detail questions are answered by a single sentence or paraphrase in the passage; eliminate choices that add information not stated.

Inference answers must be logically forced by the text; a plausible real-world idea that the passage does not support is wrong.

Vocabulary-in-context: substitute each answer choice into the original sentence and test which meaning fits the surrounding logic.

Tone and attitude are signaled by connotation words (e.g., 'insisted,' 'admitted,' 'merely') rather than by topic alone.

Paired passage questions: identify the relationship first (agree, disagree, or qualify) before evaluating evidence choices.

Function questions ask why a sentence or paragraph exists (to illustrate, contrast, define, or transition), not what it says.

Eliminate extreme choices containing always, never, all, or none unless the passage states that absoluteness explicitly.

A hypothesis is a testable prediction; a theory is a well-supported explanation; a law describes a consistent relationship.

Independent variable is manipulated by the researcher; dependent variable is measured; controlled variables are held constant.

Validity concerns whether the experiment measures what it claims; reliability concerns whether repeated trials give consistent results.

In a data table or graph, the slope of a line equals the rate of change of the y-variable per unit x-variable.

Two variables are correlated when they change together; causation requires a controlled experiment isolating the variable.

Density = mass ÷ volume; concentration = amount of solute ÷ volume of solution; percent change = (new − old)/old × 100.

Viewpoint-conflict questions: identify each scientist's claim and the specific evidence cited, then locate where the claims diverge.

Read graph axes and units before interpreting trends; a curve's steepness indicates the magnitude of change, and plateaus indicate no change.

The ACT essay is optional and scored on a 2–12 scale across four domains: Ideas and Analysis, Development and Support, Organization, and Language Use and Conventions.

The prompt presents an issue with three given perspectives; a top-scoring essay analyzes all three and develops a nuanced position that engages them.

Ideas and Analysis rewards a precise thesis and evaluation of the relationships, assumptions, and implications among the perspectives.

Development and Support rewards specific, relevant examples and reasoning rather than generalized assertions.

Organization rewards a clear introduction, logically sequenced body paragraphs, and a conclusion that follows from the argument.

Language Use and Conventions rewards varied, precise sentence structure with few grammar, usage, and punctuation errors.

A strong body paragraph states a claim, supplies concrete evidence, and explains how the evidence supports the thesis.