PSAT/NMSQT cheat sheet

Command of Evidence (textual): the correct choice must be a specific detail from the passage that, if true, makes the stated claim more or less likely; a choice that merely restates the claim or adds unrelated information is wrong.

Command of Evidence (quantitative): read the graph's axis labels and units before the choices; the right answer usually names a specific value, trend, or comparison that directly supports or weakens the claim in the passage.

Words in context: replace the underlined word with each choice and test the whole sentence; the correct answer fits the surrounding logic (contrast, cause, degree), not just the dictionary's first definition.

Text structure and purpose: distinguish the function of a sentence (e.g., introducing a counterclaim, providing an example, qualifying a previous statement) from its topic; purpose questions ask why the author included it, not what it says.

Cross-text connections: identify each author's central claim first, then classify the relationship as agreement, disagreement, or one author responding to a limitation in the other's argument.

Transitions: classify the logical relationship between the two sentences (addition, contrast, cause-effect, example, concession) before choosing; 'however' signals contrast, 'therefore' signals conclusion, 'for example' signals illustration.

Rhetorical synthesis: state the goal in the bullet prompt (e.g., emphasize a similarity, introduce a debate), then pick the choice that uses the notes to achieve that specific goal while remaining accurate to the notes.

Boundaries: a sentence containing two independent clauses needs a semicolon, a period, or a comma plus a coordinating conjunction (FANBOYS); a comma alone creates a comma splice.

Form, structure, and sense: match verbs to their subjects across intervening phrases, keep pronoun referents unambiguous, and ensure modifiers sit next to the word they describe.

Linear equations: slope m = (y2 - y1)/(x2 - x1); slope-intercept form y = mx + b; parallel lines share m, perpendicular lines have slopes whose product is -1.

Systems of two linear equations: no solution when slopes are equal and intercepts differ; infinitely many solutions when the equations are equivalent multiples.

Quadratics: vertex form y = a(x - h)^2 + k gives vertex (h, k); standard form vertex x = -b/(2a); discriminant b^2 - 4ac > 0 gives two real roots, = 0 gives one, < 0 gives none.

Exponential growth and decay: y = a(1 + r)^t for growth and y = a(1 - r)^t for decay, where r is the rate per period and t counts periods; doubling corresponds to a factor of 2 per period.

Percent and proportional reasoning: percent change = (new - old)/old x 100; successive percent changes multiply rather than add; unit rates require matching units before dividing.

Geometry and trigonometry: circle equation (x - h)^2 + (y - k)^2 = r^2; circumference 2(pi)r, area (pi)r^2; right-triangle ratios sin = opposite/hypotenuse, cos = adjacent/hypotenuse, tan = opposite/adjacent; special triangles 30-60-90 (1 : sqrt3 : 2) and 45-45-90 (1 : 1 : sqrt2).

Statistics: mean is sensitive to outliers while median is resistant; standard deviation measures spread, so a data set with values clustered near the mean has a smaller standard deviation; correlation does not establish causation.

Data and probability: probability = favorable outcomes / total outcomes; for independent events multiply probabilities; a two-way table supports conditional probability by restricting the denominator to the given row or column.

Word problems: define the variable, translate each phrase into an expression, and check the answer against the units and constraints (e.g., nonnegative lengths) before selecting a choice.