Praxis Core cheat sheet

Main idea = the claim the whole passage supports; a detail supports only one paragraph and cannot serve as the main idea.

Inference must be forced by the text: if a conclusion needs outside knowledge or a guess, it is not supported.

Tone words carry the author's attitude (e.g., 'admittedly,' 'fortunately,' 'merely'); neutral reporting signals an objective stance.

Compare/contrast passages: identify what both authors accept as shared ground before locating where they diverge.

A pronoun or 'this' referring backward must agree in number and logic with its antecedent; mismatches signal a misread.

Cause vs. correlation: passages describing sequence or coexistence do not establish causation unless the text asserts it.

Vocabulary in context: substitute each answer choice into the sentence and keep only the one preserving the sentence's logic.

Author's purpose categories: to inform, to persuade, to explain a process, to evaluate; purpose differs from topic.

A sentence needs a subject and a finite verb; a dependent clause alone (e.g., 'Because the rain stopped.') is a fragment.

Comma splice = two independent clauses joined by only a comma; fix with a period, semicolon, or coordinating conjunction.

Nonessential (nonrestrictive) clauses take commas; essential clauses that identify the noun take none.

Subject-verb agreement: the verb agrees with the head noun, not with intervening prepositional phrases.

Pronoun case: subject pronouns for subjects, object pronouns after prepositions and as direct objects.

Modifiers must sit next to what they describe; a sentence-opening participial phrase modifies the subject that follows.

Parallel structure: items in a list or comparison must share grammatical form (all nouns, all infinitives, etc.).

Revision questions: choose the option that is grammatical, concise, and preserves the original meaning.

Percent change = (new − old) ÷ old × 100; a 20% increase then 20% decrease leaves a net 4% decrease.

Fractions: a/b ÷ c/d = a/b × d/c; multiply numerators and denominators before simplifying.

Slope = (y₂ − y₁)/(x₂ − x₁); parallel lines share slope, perpendicular slopes multiply to −1.

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

Mean = sum ÷ count; median = middle value of ordered data; the mean shifts with outliers, the median resists them.

Probability of independent events = product of individual probabilities; 'at least one' = 1 − P(none).

Ratio and proportion: set up a/b = c/d and cross-multiply; keep units consistent on both sides.

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