NS RWM8 cheat sheet
NS RWM8 · Keep the key ideas within reach.
Unverified content domain 1 (pending official confirmation) - reading, language, and written expression fundamentals
Main-idea test: a statement that is true of only one paragraph is a supporting detail; the main idea must be broad enough to cover every paragraph in the passage.
Inference rule: an inference must be defensible from text evidence plus ordinary reasoning; if support requires outside knowledge the passage never supplies, the answer is wrong.
Comma splice repair options: a period, a semicolon, or a comma plus a coordinating conjunction (for, and, nor, but, or, yet, so). Two independent clauses cannot be joined by a comma alone.
Subject-verb agreement: cross out prepositional phrases between the subject and verb; 'the box of tools is' stays singular because the subject is 'box', not 'tools'.
Pronoun-antecedent agreement: singular indefinite antecedents (each, either, neither, everyone, anybody) take singular pronouns in formal standard written English.
Transition mapping: contrast = however, although, nevertheless, in contrast; cause-effect = therefore, because, as a result, consequently; addition = moreover, furthermore, also.
Parallel structure: items joined by 'and' or 'or', or compared in a list, must share grammatical form - 'hiking, swimming, and biking' works; 'hiking, swimming, and to bike' does not.
Active vs. passive voice: in active voice the subject performs the action ('The committee approved the plan'); use passive voice when the actor is unknown or genuinely unimportant.
Modifier placement: a descriptive phrase must sit next to the noun it modifies; a modifier stranded at the start of a sentence describes whatever noun immediately follows the comma.
Unverified content domain 2 (pending official confirmation) - mathematics and quantitative reasoning fundamentals
Slope: m = (y₂ − y₁) / (x₂ − x₁). A horizontal line has slope 0; a vertical line has undefined slope because the run is zero.
Line equations: slope-intercept y = mx + b (b is the y-intercept at point (0, b)); point-slope y − y₁ = m(x − x₁).
Pythagorean theorem: for a right triangle, a² + b² = c², where c is the hypotenuse opposite the right angle. The converse (if a² + b² = c², the triangle is right) identifies right triangles.
Circles: area A = πr²; circumference C = 2πr = πd. Given a diameter, halve it before using any radius formula.
Percent change = (new value − old value) ÷ old value × 100. A positive result is an increase, a negative result a decrease; the divisor is always the original amount.
Order of operations: parentheses, then exponents, then multiplication and division left to right, then addition and subtraction left to right. Multiplication does not automatically precede division.
Exponent rules: aᵐ × aⁿ = aᵐ⁺ⁿ; aᵐ ÷ aⁿ = aᵐ⁻ⁿ; (aᵐ)ⁿ = aᵐⁿ; a⁰ = 1 for a ≠ 0. The product and quotient rules require identical bases.
Central tendency: the mean (sum ÷ count) shifts with outliers; the median (middle ordered value, or the average of the two middle values) resists them; the mode is the most frequent value.
Volume formulas: rectangular prism V = l × w × h; cylinder V = πr²h (base area times height). Report volume in cubic units matching the linear units given.