ACT Aspire Grade 9 cheat sheet

A complete sentence needs a subject, a finite verb, and an independent clause; a fragment lacks one of these.

A comma splice joins two independent clauses with only a comma; fix it with a period, semicolon, or coordinating conjunction.

Coordinating conjunctions are for, and, nor, but, or, yet, so; they join grammatically equal elements.

A pronoun agrees with its antecedent in number and person; singular indefinite antecedents such as each and everyone take singular pronouns.

A modifier should sit next to the word or phrase it describes; a misplaced modifier creates unintended meaning.

In a list of three or more items, commas separate items; semicolons separate items that already contain commas.

Active voice names the doer before the action; passive voice makes the receiver the subject and often adds a by-phrase.

A colon follows an independent clause and introduces a list, explanation, or quotation.

Slope formula: m = (y2 - y1)/(x2 - x1); horizontal lines have slope 0, and vertical lines have undefined slope.

Slope-intercept form y = mx + b gives slope m and y-intercept b.

Linear systems can be solved by substitution, which isolates one variable, or by elimination, which adds or subtracts equations to cancel a variable.

Area formulas: triangle A = 1/2 bh; circle A = πr²; rectangle A = lw.

Volume of a right prism or cylinder is V = Bh, where B is base area and h is height.

Pythagorean theorem a² + b² = c² applies to right triangles, with c the hypotenuse.

Percent change = (new - old)/old × 100%; a positive result is an increase, and a negative result is a decrease.

Probability of an event = favorable outcomes / total equally likely outcomes; complementary probability is 1 - P(event).

Mean = sum / count; median is the middle ordered value; mode is the most frequent value.

Main idea is the central claim covering the whole passage; a supporting detail explains or illustrates only part.

An inference must follow from stated evidence; it is not a guess unsupported by the text.

Tone is the author's attitude, while mood is the feeling created in the reader.

In fiction, conflict is the central struggle; characterization reveals traits through speech, actions, thoughts, and others' reactions.

A summary includes the main idea and key supporting points but excludes minor details and personal opinion.

Sequence questions rely on time words such as before, after, while, and then; cause-effect questions rely on because, therefore, and as a result.

An analogy compares relationships; identify the relationship in the first pair before applying it to the second.

When two answers seem true, the correct one is supported by the most direct textual evidence.

Scientific method: question, hypothesis, controlled experiment, data analysis, conclusion; a hypothesis must be testable and falsifiable.

Independent variable is changed by the experimenter; dependent variable is measured; controlled variables are kept constant.

Mean = sum of values / number of values; range = maximum - minimum.

Density = mass / volume; units may be g/cm³ for solids or g/mL for liquids.

Speed = distance / time; acceleration = change in velocity / time.

In a food chain, arrows show energy flow from producer to consumer; only about 10% of energy transfers to the next trophic level.

Atoms contain protons and neutrons in the nucleus and electrons in orbitals; atomic number equals proton count.

Newton's second law: F = ma; weight = mg, where g is gravitational acceleration.

A thesis statement states the essay's main claim and often previews the organization.

A paragraph usually has a topic sentence, supporting evidence, and a concluding or linking sentence.

Transitions signal relationships: addition (also), contrast (however), cause (therefore), and example (for instance).

Evidence should be specific and relevant; commentary explains how evidence supports the claim.

An introduction identifies the topic and purpose; a conclusion restates the claim and explains significance without new evidence.

Revision changes content and organization; editing corrects grammar, usage, punctuation, and spelling.

In argument writing, a counterclaim is an opposing view; a rebuttal responds to it with evidence.

Sentence variety combines simple, compound, and complex sentences; a complex sentence has an independent and a dependent clause.