ACCUPLACER cheat sheet

The main idea must be broad enough to cover every paragraph; a statement that is true of only one sentence is a supporting detail, not the main idea.

An inference is valid only if the passage forces it; a choice that requires outside knowledge or a guess is wrong.

For 'most nearly means' items, substitute each choice into the original sentence and keep the one that preserves the sentence's overall meaning.

Contrast signals (but, however, although, yet, despite) mark a turn; the claim after the signal usually carries the author's emphasis.

Cause-effect words (because, since, therefore, as a result, consequently) signal a causal link; sequence words (then, next, finally) only order events.

Author's-purpose answers are verb phrases: to inform, to persuade, to explain, to criticize, to entertain.

Tone is judged from the author's adjectives and verbs, not from the topic: a passage about war can still be neutral in tone.

Check pronoun reference by number and gender, and by re-reading the sentence that comes before the pronoun.

Structural patterns to look for: general to specific, problem to solution, claim to evidence, comparison and contrast; the correct answer names the pattern the passage actually uses.

A comma alone cannot join two independent clauses; use a period, a semicolon, or a comma plus a coordinating conjunction (for, and, nor, but, or, yet, so).

A semicolon must be followed by an independent clause and never precedes a coordinating conjunction.

A colon must follow a complete sentence and introduces a list, an explanation, or a quotation.

For subject-verb agreement, cross out prepositional phrases between the subject and the verb; the verb agrees with the subject.

Indefinite pronouns (each, either, neither, everyone, anybody, nobody) are singular and take singular verbs and pronouns.

An introductory modifying phrase must describe the subject of the main clause; otherwise it dangles.

Items in a series, and pairs after not only... but also, either... or, both... and, must share the same grammatical form.

'It's' = it is or it has, while 'its' is possessive; 'they're' = they are, 'their' is possessive, and 'there' shows place or acts as an expletive.

Use between for two items and among for three or more; use fewer with count nouns and less with noncount nouns.

Slope m = (y2 - y1)/(x2 - x1); parallel lines have equal slopes and perpendicular lines have slopes that are negative reciprocals (product = -1). Slope-intercept form is y = mx + b.

Quadratic formula: x = (-b +/- sqrt(b^2 - 4ac)) / (2a) for ax^2 + bx + c = 0.

Factoring shortcuts: a^2 - b^2 = (a - b)(a + b); a^2 + 2ab + b^2 = (a + b)^2.

Exponent rules: x^a * x^b = x^(a+b); (x^a)^b = x^(ab); x^0 = 1 for x not equal to 0; x^(-a) = 1/x^a.

Areas: rectangle A = lw; triangle A = (1/2)bh; circle A = pir^2 with circumference C = 2pi*r.

Right triangles: a^2 + b^2 = c^2; the common triples 3-4-5 and 5-12-13 and their multiples satisfy it.

Percent change = (new - old)/old * 100; percent of a number = (percent/100) * number.

Mean = sum / count; median = middle value of an ordered list (average the two middle values when the count is even); mode = most frequent value.

Distance = rate * time; order of operations is parentheses, exponents, multiplication and division left to right, then addition and subtraction left to right.

The topic sentence, usually first or last in a paragraph, states the paragraph's main idea; the remaining sentences support it.

Sequence signals (first, next, then, after, before, finally) show the order of events, not the cause of events.

Cause-and-effect signals (because, since, so, therefore, as a result) show why something happened.

Use context clues: a definition after a comma or dash, an example after 'such as', or an opposite after 'unlike' or 'but'.

Pronouns such as it, they, and this refer to the nearest earlier noun that matches in number and meaning.

Words that reverse meaning (not, never, except, hardly, unless) change which answer is correct, so read the question stem twice.

Comparison signals (like, both, similar, unlike, whereas, in contrast) tell whether two things are alike or different.

Choose an answer only if the passage states or clearly implies it; a statement that is true in general is wrong if the passage does not support it.

Simple present third-person singular adds -s or -es (he works, she watches); the base form is used with I, you, we, and they.

Present perfect = have/has + past participle, used with since and for for actions that continue to the present.

Regular past-tense verbs add -ed; irregular verbs (go/went, take/took, see/saw) must be memorized.

Articles: a or an for one unspecified item, the for a specific or previously mentioned item, and no article for general plurals (Books are expensive).

Much and little modify noncount nouns (water, information, advice); many and few modify count plurals.

Prepositions of time: in + month, year, or season; on + day or date; at + clock time.

Adjectives come before nouns and never take -s; adverbs modify verbs and adjectives and usually end in -ly.

Modals (can, must, should, will) are followed by the base verb without to: 'She must study,' not 'She must to study.'

Comparatives use -er or more ... than; superlatives use the -est or the most.

Stressed words in speech are content words (nouns, main verbs, adjectives, adverbs); articles, prepositions, and auxiliaries are reduced.

Contractions change meaning: I'll = I will, they're = they are, should've = should have, can't = cannot.

-teen numbers are stressed on the second syllable (thirTEEN); -ty numbers are stressed on the first (THIRty).

Yes/no questions usually rise at the end; wh-questions and statements usually fall.

Lecture signals ('first', 'next', 'on the other hand', 'to sum up') mark structure and often come just before the answer.

Homophones (there/their/they're, to/too/two, hear/here) are distinguished by grammar and context, not by sound.

Negative cues in speech (hardly, not really, unlikely, instead of) mean the correct answer is negative.

Polite requests carry indirect meaning: 'Could you speak up?' asks for volume, and 'I'm not following' means the speaker does not understand.

An essay has an introduction ending in a thesis, two or three body paragraphs, and a conclusion that restates the thesis without adding new evidence.

The thesis is one sentence stating the claim and the order of the body paragraphs; it is not a plain fact and not a question.

Each body paragraph opens with a topic sentence naming one controlling idea, then explains it, gives an example, and links back to the thesis.

Transitions by function: addition (furthermore, in addition), contrast (however, on the other hand), cause (therefore, as a result), example (for instance).

Every sentence needs a subject and a complete verb; a group of words punctuated as a sentence without both is a fragment.

Avoid run-ons by joining clauses with a period, a semicolon, or a coordinating conjunction rather than a comma alone.

Keep one tense unless the meaning requires a shift; describe events in a literary work in the present tense.

In a timed essay, plan an outline in about five minutes, write for about twenty, and leave five minutes to proofread agreement and punctuation.