OAR cheat sheet

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

To add or subtract fractions, rewrite over a common denominator; to multiply, multiply numerators and denominators; to divide, multiply by the reciprocal.

Percent change = (new − old) ÷ old × 100%; a part is percent × whole, and the whole is part ÷ percent.

Ratio a:b compares parts; a proportion a/b = c/d is solved by cross-multiplication ad = bc.

Average (mean) = sum of values ÷ number of values; median is the middle value when ordered.

Distance = rate × time; total work = rate × time; set up a table for combined-rate problems.

Area: rectangle lw, triangle ½bh, circle πr²; circumference 2πr; volume of a rectangular solid lwh.

1 foot = 12 inches, 1 yard = 3 feet, 1 mile = 5,280 feet; 1 gallon = 4 quarts; 1 hour = 60 minutes.

Exponent rules: x^a·x^b = x^(a+b), (x^a)^b = x^(ab), x^0 = 1 for x ≠ 0.

Main idea = central claim the passage supports; it is broader than any single detail but narrower than the topic.

Supporting details answer who, what, when, where, why, or how and must be traceable to the passage.

An inference is a conclusion logically required by the text plus common knowledge, not a guess.

Tone is the author’s attitude; identify it from word choice, connotations, and emphasis, not subject alone.

Author’s purpose is usually to inform, persuade, explain, or entertain; the verbs in the question signal which.

Vocabulary in context: substitute each answer choice into the sentence and test whether the passage’s logic remains intact.

Passage structure: compare/contrast, cause/effect, problem/solution, chronological, or description; structure predicts where key info sits.

For exception questions, three choices are supported and one is not; verify each choice against a line or paragraph.

Avoid extreme answer choices with words like always, never, or all unless the passage states them explicitly.

Work = force × distance moved in the direction of the force; unit is the joule (N·m).

Power = work ÷ time; unit is the watt (J/s); more power means the same work done faster.

Mechanical advantage (MA) = output force ÷ input force = effort arm ÷ resistance arm for a lever.

First-class lever: fulcrum between effort and load; second-class: load between fulcrum and effort; third-class: effort between fulcrum and load.

For a pulley system, MA equals the number of rope segments supporting the movable load, ignoring friction.

Gear ratio = number of teeth on driven gear ÷ number of teeth on driving gear; larger driven gear turns slower with more torque.

Pressure = force ÷ area; same force over smaller area produces greater pressure (sharp edges cut easily).

Density = mass ÷ volume; an object denser than the fluid sinks, less dense floats.

Friction opposes motion, acts along the contact surface, and increases with normal force or rougher surfaces; it converts motion to heat.