Ohio State Tests/EOC cheat sheet

Central idea is the main point of a whole text; theme is a universal message about life conveyed through characters and events, stated as a full sentence rather than one word.

Cite the strongest textual evidence by choosing a quotation that directly supports the claim, then explain the link between quotation and claim in your own words.

An argument's claim must be debatable; a statement of fact or a summary cannot serve as a claim because no reasonable person would dispute it.

Counterclaim: acknowledge an opposing position, then refute it with evidence; ignoring the other side weakens rather than strengthens an argument.

Rhetorical appeals: ethos builds credibility through the speaker, pathos targets emotion, logos uses logic and data; identify which appeal a passage leans on.

Author's purpose is usually stated as a verb plus object: to persuade readers to adopt a policy, to inform an audience about a process, or to entertain through narrative.

Word choice analysis: connotation is the emotional shading a word carries (cheap vs. affordable), denotation is its literal dictionary meaning.

Inference requires combining explicit textual details with background knowledge; an inference must be defensible from the text, not merely plausible.

Grammar rules tested most often: subject-verb agreement with interrupting phrases, pronoun-antecedent agreement, comma use with introductory clauses, and avoiding run-ons and fragments.

Slope between two points: m = (y2 - y1)/(x2 - x1); parallel lines share the same slope, perpendicular slopes are negative reciprocals (product = -1).

Linear form y = mx + b gives slope m and y-intercept b; point-slope form y - y1 = m(x - x1) is faster when a point and slope are known.

Quadratic formula: x = (-b ± √(b² - 4ac))/(2a); the discriminant b² - 4ac gives two, one, or zero real roots when positive, zero, or negative.

Exponential growth or decay: y = a(1 ± r)^t, where a is the initial amount and r is the rate per period; decay uses (1 - r).

Function notation: f(3) means substitute 3 for x, not multiply f by 3; the domain excludes values that make a denominator zero or a radicand negative.

Systems of two linear equations: substitution works when one variable is isolated; elimination works when coefficients can be matched and subtracted.

Transformations: f(x) + k shifts vertically by k, f(x + h) shifts horizontally opposite the sign, and a·f(x) stretches vertically by factor a.

Probability of independent events multiplies: P(A and B) = P(A)·P(B); conditional probability divides by the condition, P(A|B) = P(A and B)/P(B).

Mean is sensitive to outliers while median is not; standard deviation measures spread, so a larger value means data points sit farther from the mean.

Newton's second law: F = ma; net force and acceleration point in the same direction, and doubling mass halves acceleration for a fixed force.

Conservation of energy: energy changes form (kinetic, potential, thermal) but total energy in a closed system stays constant; friction converts mechanical energy to thermal.

Kinetic energy KE = ½mv², so doubling speed quadruples kinetic energy; gravitational potential energy PE = mgh.

Newton's third law: forces come in equal and opposite pairs acting on different objects, which is why they do not cancel.

In a chemical equation, coefficients balance atoms on each side; subscripts inside a formula cannot be changed to balance it.

Photosynthesis converts light energy, carbon dioxide, and water into glucose and oxygen; cellular respiration reverses this to release usable energy as ATP.

DNA base pairing: adenine pairs with thymine, guanine with cytosine; transcription makes mRNA from DNA, translation builds protein at the ribosome.

Natural selection requires heritable variation, differential reproductive success, and environmental pressure; individuals do not evolve, populations do.

Plate tectonics: divergent boundaries create new crust, convergent boundaries cause subduction or mountain building, and transform boundaries produce strike-slip faults.

Separation of powers divides legislative, executive, and judicial functions; checks and balances let each branch limit the others, as in veto and judicial review.

Federalism splits authority between national and state governments; the Supremacy Clause makes federal law prevail when the two conflict.

The Bill of Rights, the first ten amendments, protects individual liberties; the First Amendment covers speech, religion, press, assembly, and petition.

Constitutional amendments require a two-thirds vote in Congress and ratification by three-fourths of states, which explains why amendments are rare.

Primary-source analysis asks about author, date, audience, and purpose before interpreting meaning; sourcing changes how reliable a document is.

Causes of the Civil War include sectional conflict over slavery's expansion, economic differences, and political disputes over federal versus state power.

Push and pull factors drive migration: push factors expel people from a place, pull factors attract them to a destination.

Supply and demand: price rises when demand exceeds supply, falls when supply exceeds demand; equilibrium is where the curves intersect.

Economic systems differ by who owns production: market economies rely on private ownership and price signals, command economies on state direction.