SAT Math — Essential Formulas (Quick Reference)

Digital SAT Math one-pager — Algebra, Advanced Math, Problem-Solving & Data, Geometry & Trig. Pair it with Quick Drill for 15-minute reviews.

Algebra

• Slope-intercept: y = mx + b
• Point-slope: y − y₁ = m(x − x₁)
• Slope: m = (y₂ − y₁) / (x₂ − x₁)
• Parallel: same slope. Perpendicular: slopes multiply to −1
• Systems: substitution or elimination. Watch for "no solution" (parallel) and "infinite" (same line)

Advanced Math

• Quadratic formula: x = (−b ± √(b² − 4ac)) / (2a)
• Vertex form: y = a(x − h)² + k → vertex (h, k)
• Factor: if (x − p)(x − q) = 0, x = p or q
• Discriminant: b² − 4ac (counts real solutions)
• Exponent rules: x^a·x^b = x^a+b; (x^a)^b = x^ab; x^−a = 1/x^a
• Function composition: f(g(x)) — evaluate inside first

Problem-Solving & Data Analysis

• Percent change: (new − old) / old × 100%
• Average: sum / count
• Ratio/proportion: a/b = c/x → cross-multiply
• Probability: favorable / total (simplify the fraction)
• Mean vs median: outliers move the mean more than the median

Geometry & Trigonometry

• Pythagorean: a² + b² = c²
• Triples: 3-4-5, 5-12-13, 8-15-17, 7-24-25 (any scalar)
• 30-60-90: 1 : √3 : 2; 45-45-90: 1 : 1 : √2
• SOHCAHTOA: sin = opp/hyp; cos = adj/hyp; tan = opp/adj
• Circle: area πr², circumference 2πr, arc length = (θ/360)·2πr
• Triangle area: ½·base·height. Rectangle: bh. Trapezoid: ½(b₁+b₂)h
• Volume: cylinder πr²h; cone ⅓πr²h; sphere (4/3)πr³

Test-Day Pacing

• Digital SAT Math: 44 questions in 70 minutes ≈ 1.6 minutes per question
• Calculator allowed throughout, plus embedded Desmos
• If a question takes > 2 minutes, mark and move on. Come back at the end.

Common Mistakes

• Forgetting both roots of a quadratic
• Using mean when problem asks for median (or vice versa)
• Pythagorean on a non-right triangle
• Misreading diameter vs radius

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