MAP Growth cheat sheet

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

Slope-intercept form y = mx + b: m is the rate of change per unit x, b is the y-value where the line crosses the y-axis (x = 0).

Pythagorean theorem a² + b² = c² applies only to right triangles, where c is the hypotenuse opposite the right angle.

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

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

Percent change = (new − old)/old × 100; a 20% increase multiplies by 1.20, a 20% decrease multiplies by 0.80.

Probability of an event = favorable outcomes / total equally likely outcomes; probabilities range from 0 to 1 and sum to 1 across all outcomes.

Mean = sum ÷ count; median = middle value of ordered data; mode = most frequent value; the mean is pulled toward outliers more than the median.

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

Main idea = what the passage is mostly about; supporting details answer who, what, when, where, why, and how about that idea.

Theme is a message or insight about life conveyed by a literary text; it is stated as a general statement, not a plot summary.

First-person point of view uses I/we; third-person limited stays inside one character's thoughts; third-person omniscient knows all characters' thoughts.

Inference = a conclusion drawn from textual evidence plus background knowledge; it is implied, not directly stated.

Text structures: cause–effect, compare–contrast, chronological, problem–solution, and description each use distinct signal words (because, however, first, therefore).

Author's purpose is usually to inform, persuade, entertain, or explain; the purpose shapes word choice and which details are included.

Context clues include definition, example, synonym, antonym, and general sense of the sentence; they help determine an unknown word's meaning.

Fact can be verified; opinion expresses a judgment or feeling and often uses evaluative words such as best, should, or beautiful.

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: replace the comma with a period, a semicolon, or a comma plus a coordinating conjunction (for, and, nor, but, or, yet, so).

Apostrophes mark possession (the dog's bone, the dogs' bowls) or contraction (it's = it is); possessive its has no apostrophe.

Subject–verb agreement: singular subjects take singular verbs; indefinite pronouns such as everyone, each, and nobody are singular.

Pronoun case: use I/he/she for subjects, me/him/her for objects, and who for subjects versus whom for objects of verbs or prepositions.

Verb tense must stay consistent within a passage unless a time shift is signaled; irregular past forms include went, wrote, and brought.

Modifiers should sit next to the word they describe; a dangling modifier at the start of a sentence must match the subject that follows.

Active voice (The chef cooked the meal) is more direct than passive voice (The meal was cooked by the chef); passive is useful when the doer is unknown.

Colons introduce a list or explanation after an independent clause; semicolons join two closely related independent clauses.

A cell is the basic unit of life; plant cells have cell walls and chloroplasts, while animal cells do not.

Photosynthesis converts carbon dioxide and water into glucose and oxygen using light energy in chloroplasts; cellular respiration reverses the energy flow.

In a food chain, energy flows from producers to consumers; only about 10% of energy passes to each higher trophic level.

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 per unit time.

States of matter change at melting, freezing, boiling, and condensation points; during a phase change, temperature stays constant while energy is absorbed or released.

In a series circuit there is one path for current; in a parallel circuit there are multiple paths, so removing one bulb does not break the others.

Earth's seasons result from the tilt of Earth's axis, not from distance to the Sun; the Moon's phases result from its orbital position relative to Earth and the Sun.

Inherited traits come from genes passed by parents; acquired traits result from environment or experience and are not passed on genetically.