SAT Math formula sheet: algebra, data, geometry and trigonometry

How to use this sheet

The SAT Math section has four content areas: Algebra, Advanced Math, Problem-Solving and Data Analysis, and Geometry and Trigonometry. Learn these formulas until you can use them without looking. Check the College Board for what the test itself gives you on the screen.

Algebra

• Slope of a line through two points: m = (y₂ − y₁) ÷ (x₂ − x₁).
• Slope-intercept form: y = mx + b, where b is the y-intercept.
• Parallel lines have the same slope. Perpendicular lines have slopes whose product is −1.
• Distance between two points: √((x₂ − x₁)² + (y₂ − y₁)²). Midpoint: the mean of the x values and the mean of the y values.
• To solve a system of two equations, use substitution or add the equations after you scale them.

Advanced Math

• Quadratic formula for ax² + bx + c = 0: x = (−b ± √(b² − 4ac)) ÷ 2a.
• Discriminant b² − 4ac: positive means two real roots, zero means one repeated root, negative means no real roots.
• Sum of the roots = −b ÷ a. Product of the roots = c ÷ a.
• Vertex form: y = a(x − h)² + k, with the vertex at (h, k).
• Exponential growth or decay: y = a(1 + r)ᵗ, where r is the rate for each period, and r is negative for decay.
• Laws of exponents: xᵃ × xᵇ = xᵃ⁺ᵇ, xᵃ ÷ xᵇ = xᵃ⁻ᵇ and (xᵃ)ᵇ = xᵃᵇ.

Problem-Solving and Data Analysis

• Percent change = (new − old) ÷ old × 100.
• Mean = sum of the values ÷ number of values. Median = the middle value of the ordered list. Mode = the most common value.
• Adding the same number to every value adds that number to the mean and the median. Multiplying every value by a number multiplies the mean and the median by that number.
• Probability = favourable outcomes ÷ total outcomes.
• Rate problems: distance = rate × time.

Geometry and Trigonometry

• Area of a triangle: ½ × base × height. Area of a rectangle: length × width.
• Circle: circumference = 2πr and area = πr². Equation of a circle with centre (h, k): (x − h)² + (y − k)² = r².
• Arc length = (θ ÷ 360) × 2πr and sector area = (θ ÷ 360) × πr², with θ in degrees.
• Pythagorean theorem: a² + b² = c². Common triples: 3, 4, 5 and 5, 12, 13.
• Special right triangles: a 45°, 45°, 90° triangle has sides in the ratio 1 : 1 : √2, and a 30°, 60°, 90° triangle has sides in the ratio 1 : √3 : 2.
• Volumes: rectangular box = lwh, cylinder = πr²h, sphere = (4/3)πr³, cone = (1/3)πr²h.
• Right triangle trigonometry: sin = opposite ÷ hypotenuse, cos = adjacent ÷ hypotenuse and tan = opposite ÷ adjacent.
• 180° = π radians. For complementary angles, sin x = cos (90° − x).

Practise on this site

Where this comes from

• College Board, SAT Suite: the Math section and its content areas (Algebra, Advanced Math, Problem-Solving and Data Analysis, Geometry and Trigonometry).
• These are standard school mathematics formulas, collected for this guide.