SAT Math Formula Sheet

Algebra

Slope of a Line

m = (y₂ − y₁) / (x₂ − x₁)

Slope between two points (x₁, y₁) and (x₂, y₂)

Slope-Intercept Form

y = mx + b

m = slope, b = y‑intercept

Point-Slope Form

y − y₁ = m(x − x₁)

Line through (x₁, y₁) with slope m

Standard Form

Ax + By = C

Linear equation in standard form

Linear Equation (One Variable)

ax + b = c

Solve for x: x = (c − b) / a

System of Equations

a₁x + b₁y = c₁
a₂x + b₂y = c₂

Solve by substitution or elimination

Inequalities

ax + b > c or ax + b < c

Flip inequality sign when multiplying/dividing by negative

Average (Mean)

Average = sum / number of terms

Also called arithmetic mean

Advanced Math

Quadratic Formula

x = [−b ± √(b² − 4ac)] / 2a

For ax² + bx + c = 0

Discriminant

Δ = b² − 4ac

Δ > 0: two real roots; Δ = 0: one root; Δ < 0: no real roots

Vertex Form (Parabola)

y = a(x − h)² + k

Vertex at (h, k)

Vertex (Standard Form)

h = −b / 2a, k = f(h)

Vertex of y = ax² + bx + c

Laws of Exponents

xᵐ · xⁿ = xᵐ⁺ⁿ
xᵐ / xⁿ = xᵐ⁻ⁿ
(xᵐ)ⁿ = xᵐⁿ

Exponent rules for multiplication, division, and powers

Negative / Zero Exponents

x⁻ⁿ = 1 / xⁿ
x⁰ = 1 (x ≠ 0)

Definition of negative and zero exponents

Rational Exponents

x^(m/n) = ⁿ√(xᵐ)

Fractional exponents and radicals

Polynomial Operations

(a + b)(c + d) = ac + ad + bc + bd

FOIL method for binomials

Difference of Squares

a² − b² = (a + b)(a − b)

Factoring difference of squares

Perfect Square Trinomial

a² + 2ab + b² = (a + b)²
a² − 2ab + b² = (a − b)²

Factoring perfect squares

Geometry

Area of a Rectangle

A = l × w

Length × width

Area of a Triangle

A = ½ × b × h

Base × height ÷ 2

Area of a Circle

A = πr²

r = radius

Circumference

C = 2πr

Distance around a circle

Volume of a Rectangular Prism

V = l × w × h

Length × width × height

Volume of a Cylinder

V = πr²h

Area of base × height

Volume of a Sphere

V = (4/3)πr³

Four-thirds π r cubed

Volume of a Cone

V = (1/3)πr²h

One-third π r² h

Pythagorean Theorem

a² + b² = c²

In a right triangle: c = hypotenuse

Special Right Triangles

30‑60‑90: x, x√3, 2x
45‑45‑90: x, x, x√2

Side ratios for special triangles

Arc Length

s = rθ

θ in radians; s = arc length

Sector Area

A = ½r²θ

θ in radians

Statistics & Probability

Mean

x̄ = (∑xᵢ) / n

Sum of values divided by number of values

Median

Middle value (sorted)

If n is odd: middle; if even: average of two middle

Mode

Most frequent value

A data set can have one, more than one, or no mode

Range

Range = max − min

Difference between largest and smallest values

Probability

P(A) = favorable / total

Number of favorable outcomes ÷ total outcomes

Combinations

C(n, r) = n! / [r!(n−r)!]

Number of ways to choose r from n (order doesn't matter)

Permutations

P(n, r) = n! / (n−r)!

Number of ways to arrange r from n (order matters)

Standard Deviation (Concept)

σ = √[∑(xᵢ − x̄)² / n]

Measure of data spread around the mean

Coordinate Geometry

Distance Formula

d = √[(x₂ − x₁)² + (y₂ − y₁)²]

Distance between two points

Midpoint Formula

M = ((x₁+x₂)/2, (y₁+y₂)/2)

Midpoint between two points

Parallel Lines

m₁ = m₂

Parallel lines have equal slopes

Perpendicular Lines

m₁ · m₂ = −1

Product of slopes of perpendicular lines = −1