PSAT 10 cheat sheet

Evidence questions: the correct choice must be supported by the specific cited lines or data, not merely consistent with the passage's general topic; a true statement that the text never establishes is wrong.

Command of evidence (quantitative): read the table or graph axes and units before the choices; the right option restates a data pattern accurately, including direction (increase/decrease) and comparison group.

Words in context: substitute each choice into the sentence and test for the meaning the surrounding clauses require; the most common dictionary sense is often the trap.

Transitions: classify the relationship between the two sentences as contrast (however, nevertheless), cause/effect (therefore, consequently), addition (moreover, similarly), or example (for instance); then match logic, not just tone.

Boundaries: a comma cannot join two independent clauses; use a period, semicolon, colon, or coordinating conjunction (FANBOYS: for, and, nor, but, or, yet, so).

Nonessential elements: a phrase set off by a pair of commas, dashes, or parentheses must be removable without breaking the sentence; check that both marks are present and matched.

Subject-verb agreement: locate the true subject by crossing out prepositional phrases and appositives; inverted sentences ("Among the reasons ... are ...") agree with the subject after the verb.

Punctuation with supplements: a colon must follow an independent clause and introduce an explanation, list, or quotation; a dash may do similar work but must not be paired with a colon in the same spot.

Rhetorical synthesis: read the bulleted notes for the stated goal (e.g., emphasize a similarity, introduce a contrast); the correct choice satisfies that goal using accurate details from the notes.

Linear model: slope = (y2 - y1)/(x2 - x1) = change in y per unit change in x; in y = mx + b, m is the rate and b the starting value, so interpret both in context.

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

Quadratics: for y = ax^2 + bx + c, the vertex x-coordinate is -b/(2a); the discriminant b^2 - 4ac gives two, one, or zero real solutions when positive, zero, or negative.

Factored and vertex forms: y = a(x - r)(x - s) shows x-intercepts r and s; y = a(x - h)^2 + k shows vertex (h, k); the axis of symmetry is x = h.

Exponential growth/decay: y = a(b)^t, where a is the initial amount; growth when b > 1, decay when 0 < b < 1, and percent change per period is (b - 1) x 100%.

Percent and proportional reasoning: percent change = (new - old)/old x 100%; successive percent changes multiply rather than add; direct proportion means y = kx.

Geometry essentials: circle area A = pi r^2 and circumference C = 2 pi r; triangle area = (1/2)bh; Pythagorean theorem a^2 + b^2 = c^2; 30-60-90 sides are x, xsqrt(3), 2x; 45-45-90 sides are x, x, xsqrt(2).

Right-triangle trigonometry: sin = opposite/hypotenuse, cos = adjacent/hypotenuse, tan = opposite/adjacent; sin(x) = cos(90 - x) for acute angles in degrees.

Statistics: mean is sensitive to outliers while median is not; standard deviation measures spread about the mean; correlation describes association, not causation, and a line of best fit predicts rather than proves.