MAP Growth Math cheat sheet

Slope of a line through (x1, y1) and (x2, y2) is (y2 − y1)/(x2 − x1); a horizontal line has slope 0 and a vertical line has undefined slope.

Slope-intercept form y = mx + b: m is the slope, b is the y-intercept; parallel lines share m, perpendicular lines have slopes whose product is −1.

Area formulas: rectangle A = lw, triangle A = ½bh, circle A = πr², trapezoid A = ½(b1 + b2)h; circumference C = 2πr.

Volume formulas: rectangular prism V = lwh, cylinder V = πr²h, cone V = ⅓πr²h, sphere V = (4/3)πr³.

Pythagorean theorem a² + b² = c² holds only for right triangles, with c the hypotenuse opposite the right angle.

Percent change = (new − old)/old × 100; a percent increase then an equal percent decrease does not return to the original value.

Probability of an event = favorable outcomes ÷ total equally likely outcomes; probabilities of all outcomes sum to 1, and P(not A) = 1 − P(A).

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

A negative exponent means reciprocal: x^(−n) = 1/x^n; any nonzero number to the zero power equals 1.

Main idea = topic + the author's central point about it; supporting details answer who, what, when, where, why, or how and must be subordinate to the main idea.

Theme is a message about life or human nature stated as a full sentence; a topic is a single word or phrase and is not a theme.

First-person point of view uses I or we and limits knowledge to the narrator; third-person limited stays with one character's thoughts; third-person omniscient knows all characters.

To infer, combine explicit text evidence with prior knowledge; an inference must be supported by the passage, not merely plausible.

Author's purpose is usually to inform, persuade, entertain, or explain; the purpose determines which details are emphasized.

Text structures: cause and effect, compare and contrast, chronological, problem and solution, and description; signal words such as because, however, and first reveal the structure.

Fact is verifiable; opinion expresses a judgment or feeling; words like best, should, and beautiful often signal opinion.

Context clues include definition, example, synonym, antonym, and inference clues; the surrounding sentence, not the word's sound, determines meaning.

A complete sentence needs a subject and a predicate; a fragment lacks one, and a run-on joins two independent clauses without correct punctuation or a conjunction.

Comma splice fix options: use a period, use a semicolon, or add a coordinating conjunction (for, and, nor, but, or, yet, so) after the comma.

A noun names a person, place, thing, or idea; a pronoun replaces a noun and must agree with its antecedent in number and gender.

Subject-verb agreement: a singular subject takes a singular verb; phrases between subject and verb do not change the verb's number.

Active voice: the subject performs the action; passive voice: the subject receives it and typically uses a form of be plus a past participle.

Verb tense must stay consistent within a passage unless a time shift is signaled by words such as earlier, now, or next year.

Apostrophes show possession (the dog's bone) or contraction (it's = it is); its without an apostrophe is possessive.

Parallel structure requires items in a list or comparison to share the same grammatical form, such as all gerunds or all infinitives.

Precise word choice replaces vague verbs and adjectives with specific ones; connotation is the emotional association a word carries beyond its literal meaning.

The water cycle: evaporation, condensation, precipitation, and collection; energy driving it comes from the Sun.

Photosynthesis: plants use carbon dioxide, water, and light energy to make glucose and release oxygen; respiration reverses the equation.

Food chains begin with producers, then primary consumers, then higher consumers; energy decreases at each level, so food pyramids narrow upward.

Newton's laws: an object at rest stays at rest unless a net force acts; F = ma; every action has an equal and opposite reaction.

Speed = distance ÷ time; velocity includes direction; acceleration is a change in velocity over time.

States of matter: solid has fixed shape and volume, liquid has fixed volume but not shape, gas has neither; adding heat increases particle motion.

Inherited traits come from genes passed by parents; learned behaviors are acquired through experience and are not encoded in DNA.

Earth's layers from outside in: crust, mantle, outer core (liquid), inner core (solid); plate movement causes earthquakes, volcanoes, and mountain building.

A controlled experiment changes one independent variable while holding all other conditions constant so results can be attributed to that variable.