HiSET cheat sheet

Main idea = what a passage is mostly about; theme = a universal message about life or human nature the text conveys.

An inference is a conclusion supported by textual evidence but not stated directly; an unsupported guess is not an inference.

Tone is the author's attitude (revealed by diction and detail choice); mood is the feeling the reader experiences (created by setting and imagery).

Five common text structures: cause-effect, compare-contrast, chronological, problem-solution, and description; transition words signal which one is used.

Author's purpose questions resolve to inform, persuade, entertain, or explain - check whether the text relies on facts, emotional appeals, or narrative.

Context clue types: definition (set off by commas or 'is'), example ('such as'), contrast ('unlike'), and general sense inferred from surrounding sentences.

First person uses I/we; third-person limited follows one character's perspective; third-person omniscient reveals multiple characters' thoughts.

A statement is a fact if it can be verified; it is an opinion if it expresses judgment or value - words like 'should,' 'best,' and 'beautiful' signal opinion.

Loaded language, appeals to fear, and omission of opposing evidence are signals of bias in persuasive text.

A complete sentence needs a subject, a predicate, and an independent clause; a fragment is missing one of these.

Fix a comma splice with a period, a semicolon, or a comma plus a coordinating conjunction (for, and, nor, but, or, yet, so).

Match verbs to the true subject, not to nouns in intervening prepositional phrases; each, everyone, neither, and nobody are singular.

Pronouns must agree with their antecedents in number and gender; vague or missing antecedents must be replaced with a clear noun.

Place modifiers next to the word they describe; an introductory descriptive phrase must refer to the subject of the main clause.

Keep list items and comparisons parallel - all nouns, all gerunds, or all infinitives, not a mix.

Transition meanings: however = contrast; therefore = result; for example = illustration; moreover = addition; meanwhile = time.

Apostrophes mark possession (singular 's, plural s') or contraction; never use an apostrophe to form a plural noun.

Prefer active voice unless the doer is unknown or the receiver of the action deserves the emphasis.

Slope m = (y2 - y1) / (x2 - x1); slope-intercept form is y = mx + b, where b is the y-intercept.

Percent change = (new - original) / original x 100; percent of a number = rate x number.

Right triangles: a^2 + b^2 = c^2, where c is the hypotenuse opposite the right angle.

Area: rectangle = lw, triangle = (1/2)bh, circle = pi x r^2. Circumference = 2 x pi x r. Volume: prism = lwh, cylinder = pi x r^2 x h.

Mean = sum / count; median = middle value of ordered data; mode = most frequent value; range = maximum - minimum.

Probability of an event = favorable outcomes / total equally likely outcomes; every probability falls between 0 and 1.

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

Distance = rate x time; rearranged, rate = distance / time and time = distance / rate.

Exponent rules: (x^a)(x^b) = x^(a+b); (x^a)^b = x^(ab); x^0 = 1 for any nonzero x.

Photosynthesis: 6CO2 + 6H2O + light energy -> C6H12O6 + 6O2; it occurs in chloroplasts and stores energy in glucose.

Cellular respiration releases that energy in mitochondria: C6H12O6 + 6O2 -> 6CO2 + 6H2O + ATP.

Newton's laws: an object stays at rest or in uniform motion unless acted on by a net force; F = ma; every action has an equal and opposite reaction.

Speed = distance / time; acceleration = change in velocity / time; velocity is speed with a direction.

Density = mass / volume; an object less dense than the surrounding fluid floats, and a denser object sinks.

Atomic number = number of protons; mass number = protons + neutrons; a neutral atom has equal numbers of protons and electrons.

pH below 7 is acidic, 7 is neutral, above 7 is basic; each whole pH step is a tenfold change in hydrogen ion concentration.

Energy flows from producers to consumers to decomposers, with roughly 10 percent transferred to each higher trophic level.

Earth's rotation on its axis produces day and night; its revolution around the Sun produces the year and the seasons.

Legislative branch (Congress) makes laws; executive branch (president) enforces laws; judicial branch (courts) interprets laws.

Checks and balances include the veto, congressional override, Senate confirmation of appointees, judicial review, and impeachment.

The First Amendment protects speech, press, religion, assembly, and petition; the Fifth guarantees due process and protection against self-incrimination.

Federalism divides power: delegated powers belong to the national government, reserved powers to the states, concurrent powers to both.

Economic systems: traditional (custom), command (government decisions), market (supply and demand), and mixed (elements of both).

Demand curves slope downward and supply curves slope upward; equilibrium is the price where quantity demanded equals quantity supplied.

Push factors drive migration away from a place (famine, war, persecution); pull factors attract migrants (jobs, safety, freedom).

Primary sources are firsthand records such as letters, diaries, and artifacts; secondary sources interpret them, as textbooks and documentaries do.