FAST cheat sheet

The central idea is the main point about the topic; supporting details explain, illustrate, or prove it.

A theme is a universal message about life, while a topic is simply what a text is about.

An objective summary states key ideas or events in order and excludes minor details and personal opinions.

Textual evidence can be a direct quotation, a paraphrase, or a specific detail; it must be explained, not just listed.

A character's motive is inferred from actions, dialogue, thoughts, and other characters' reactions.

Story plot follows exposition, rising action, climax, falling action, and resolution.

In informational text, distinguish cause (why something happened) from effect (what happened).

An inference combines explicit details with prior knowledge; it is not a guess unsupported by the text.

Tone is the author's or narrator's attitude toward the subject; mood is the feeling created in the reader.

Simile uses like or as; metaphor states a comparison directly; personification gives human traits to nonhuman things.

Common text structures are chronological, cause-effect, compare-contrast, problem-solution, and description.

An author's purpose is often to inform, explain, persuade, or entertain; evidence and audience reveal it.

First-person point of view uses I or we; third-person limited shows one character's thoughts; omniscient shows many.

A paragraph or section can introduce, develop, transition, emphasize, or conclude an idea.

Ethos appeals to credibility, logos to logic and evidence, and pathos to emotion.

Connotation is a word's emotional association; denotation is its dictionary meaning.

Short sentences tend to speed pace and create tension; long sentences often slow pace and add detail.

To compare texts, identify the shared topic first, then compare each author's claim, evidence, and viewpoint.

An argument contains a claim, reasons, evidence, and often a counterclaim with a rebuttal.

An unsupported claim lacks sufficient evidence; an opinion expresses judgment rather than verifiable fact.

Source reliability depends on author expertise, publication reputation, publication date, bias, and corroboration.

When integrating sources, note where they agree, where they conflict, and what each source leaves out.

For a graph or chart, read the title, axis labels, units, and legend before interpreting the data.

A fact can be verified; an opinion expresses a belief, feeling, or judgment.

Drawing a conclusion requires combining explicit text details with relevant background knowledge.

Context clues include definition, example, synonym, antonym, and general inference from surrounding sentences.

Prefixes: un- and non- mean not; re- means again; pre- means before; mis- means wrongly; sub- means under.

Suffixes: -tion and -ment often form nouns; -able and -ful form adjectives; -ly often forms adverbs.

Common roots include bio (life), graph (write), tele (far), aud (hear), spec (see), port (carry), and dict (say).

Homophones sound alike but differ in spelling and meaning, such as to, too, and two.

Homographs share spelling but may differ in meaning and pronunciation, such as lead (guide) and lead (metal).

A word's connotation can be positive, negative, or neutral even when denotation is the same.

Subject-verb agreement: a singular subject takes a singular verb; a phrase between them does not change the subject.

A pronoun must agree with its antecedent in number and gender.

A thesis or claim states a debatable position and is supported by reasons and evidence.

A text-based response answers the prompt, cites relevant evidence, and explains how the evidence supports the answer.

A strong body paragraph contains a topic sentence, evidence, explanation, and a link to the claim.

Quotations must be accurate, enclosed in quotation marks, and followed by explanation.

Transitions signal addition, contrast, cause-effect, sequence, or examples between ideas.

Revision improves clarity, organization, and word choice; editing corrects grammar, spelling, and punctuation.

Narrative writing establishes a situation, characters, conflict, point of view, and pacing.

Informative writing organizes facts with definitions, examples, and clear categories.

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

Each place value is ten times the place to its right; in 3.47 the 4 means four tenths.

Equivalent fractions are formed by multiplying or dividing numerator and denominator by the same nonzero number.

To add or subtract fractions, use a common denominator; to divide, multiply by the reciprocal.

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

Adding integers with the same sign keeps the sign; with different signs, subtract absolute values and keep the larger absolute value's sign.

Absolute value is distance from zero and is never negative.

A proportion states two ratios are equal and can be solved by cross-multiplying.

When rounding, look at the digit immediately to the right of the place being rounded.

A variable represents an unknown quantity; an expression has no equals sign, while an equation states two expressions are equal.

Solving an equation uses inverse operations to isolate the variable while keeping both sides balanced.

Distributive property: a(b + c) = ab + ac; combine like terms after distributing.

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

Slope = (y2 − y1)/(x2 − x1) for two points on a line.

Multiplying or dividing an inequality by a negative number reverses the inequality symbol.

A function assigns exactly one output to each input; the vertical line test checks a graph.

A proportional relationship has the form y = kx and its graph passes through the origin.

The sum of interior angles is 180° in a triangle and 360° in a quadrilateral.

Area formulas: rectangle lw, triangle ½bh, circle πr²; circumference = 2πr.

Volume formulas: rectangular prism lwh, cylinder πr²h.

Pythagorean theorem: a² + b² = c², where c is the hypotenuse of a right triangle.

Similar figures have equal corresponding angles and proportional corresponding side lengths.

Complementary angles sum to 90°; supplementary angles sum to 180°; vertical angles are equal.

Surface area is the sum of the areas of all faces or surfaces of a solid.

Transformations: translation slides, rotation turns, reflection flips, dilation scales size.

The coordinate plane has four quadrants; distance between points on a horizontal or vertical line is the absolute difference of coordinates.

Mean = sum of values ÷ number of values; median = middle value in ordered data; mode = most frequent value.

Range = maximum − minimum and measures spread, not center.

An outlier can strongly change the mean but affects the median less.

Probability = favorable outcomes ÷ total outcomes when outcomes are equally likely; it ranges from 0 to 1.

Complement rule: P(not A) = 1 − P(A).

For independent events, P(A and B) = P(A) × P(B).

Bar graphs compare categories; line graphs show change over time; histograms group numerical data into intervals.

A scatter plot shows the relationship between two variables; correlation does not prove causation.

A random sample is more likely to represent a population; biased samples distort conclusions.