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Cheat sheet

SAT Math cheat sheet

A condensed reference for the formulas, graph-reading rules, and must-know facts most worth reviewing before exam day.

Algebra you must know cold

  • Slope: m = (y2 − y1) / (x2 − x1). Slope-intercept form y = mx + b; b is the y-intercept.
  • Solve a system by substitution or elimination; a system has no solution when the lines are parallel (same slope, different intercept) and infinite solutions when identical.
  • Linear function from a table: constant rate of change = slope; find b by plugging in a point.
  • Absolute value: |A| = k means A = k or A = −k (k ≥ 0).
  • For 'no solution / infinitely many' problems, match coefficients after writing both sides in the same form.

Advanced Math

  • Quadratic formula: x = [−b ± √(b² − 4ac)] / 2a. Discriminant b² − 4ac: positive → 2 real roots, 0 → one, negative → none.
  • Vertex form y = a(x − h)² + k has vertex (h, k); the parabola's axis of symmetry is x = h.
  • Factoring: difference of squares a² − b² = (a − b)(a + b); the sum/product trick for x² + bx + c.
  • Exponent rules: aᵐ·aⁿ = aᵐ⁺ⁿ, aᵐ/aⁿ = aᵐ⁻ⁿ, (aᵐ)ⁿ = aᵐⁿ, a⁻ⁿ = 1/aⁿ, a^(m/n) = ⁿ√(aᵐ).
  • Exponential growth/decay: y = a·(1 ± r)ᵗ — a is the start, r the rate per period, t the number of periods.

Problem-Solving & Data Analysis

  • Percent change = (new − old) / old × 100. 'x% of y' = (x/100)·y.
  • Ratios/proportions: set up equal fractions and cross-multiply; keep units consistent.
  • Mean = sum ÷ count. Median = middle value (average the two middle values if the count is even). Outliers move the mean more than the median.
  • Read scatterplots for line of best fit and interpret slope/intercept in context (units matter).
  • Linear grows by equal amounts each step; exponential grows by an equal factor (percentage) each step.

Geometry & Trig (reference sheet gives the formulas)

  • Pythagorean theorem a² + b² = c²; know the 3-4-5 and 5-12-13 triples and the 30-60-90 / 45-45-90 side ratios.
  • Circle: area = πr², circumference = 2πr; arc length and sector area scale with the central angle over 360°.
  • Right-triangle trig: SOH-CAH-TOA — sin = opp/hyp, cos = adj/hyp, tan = opp/adj.
  • Coordinate distance = √[(x2 − x1)² + (y2 − y1)²]; midpoint = ((x1+x2)/2, (y1+y2)/2).
  • Radians: 180° = π radians; multiply degrees by π/180 to convert.

Practice this first: Algebra - The largest content area and the base layer for everything else — linear equations, systems, and inequalities show up throughout.

Now put it to work - practice SAT Math free

Reviewing the sheet is step one. Passers are usually hitting about 70-80% on realistic practice before test day, so the fastest way to know you are ready is to start answering real questions.