SAT Math Formula Cheat Sheet for Quick Reference

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SAT Math Formulas

The Digital SAT includes a reference sheet with some geometry formulas, but it does not include everything you'll need. Knowing the most common formulas before test day helps you solve problems more quickly and reduces the chance of making simple mistakes.

Exponent Rules

For any nonzero number a:

a⁰ = 1

a¹ = a

aᵐ × aⁿ = aᵐ⁺ⁿ

aᵐ ÷ aⁿ = aᵐ⁻ⁿ

(aᵐ)ⁿ = aᵐⁿ

(ab)ⁿ = aⁿbⁿ

(a/b)ⁿ = aⁿ/bⁿ

a⁻ⁿ = 1/aⁿ

Remember

  • Multiply → add exponents.

  • Divide → subtract exponents.

  • A negative exponent means take the reciprocal.

Radicals

√a × √b = √(ab)

√a ÷ √b = √(a/b)

Examples

√49 = 7

√81 = 9

∛125 = 5

Perfect squares worth memorizing:

1, 4, 9, 16, 25, 36, 49, 64, 81, 100

121, 144, 169, 196, 225, 256, 289, 324, 361, 400

Linear Equations

Slope

m = (y₂ − y₁)/(x₂ − x₁)

Slope-intercept form

y = mx + b

Point-slope form

y − y₁ = m(x − x₁)

Standard form

Ax + By = C

Parallel lines have the same slope.

Perpendicular lines have negative reciprocal slopes.

Coordinate Geometry

Distance Formula

d = √[(x₂ − x₁)² + (y₂ − y₁)²]

Midpoint Formula

((x₁ + x₂)/2, (y₁ + y₂)/2)

Quadratic Equations

Standard form

ax² + bx + c = 0

Quadratic Formula

x = (−b ± √(b² − 4ac))/2a

Discriminant

b² − 4ac

Positive → two real solutions

Zero → one real solution

Negative → no real solutions

Vertex

x = −b/(2a)

Factoring Identities

Difference of Squares

a² − b² = (a + b)(a − b)

Perfect Square Trinomials

a² + 2ab + b² = (a + b)²

a² − 2ab + b² = (a − b)²

Circle Formulas

Circumference

C = 2πr

Area

A = πr²

Arc Length

(θ/360) × 2πr

Sector Area

(θ/360) × πr²

Diameter = 2r

Rectangles and Squares

Rectangle

Area = length × width

Perimeter = 2(length + width)

Square

Area = side²

Perimeter = 4 × side

Diagonal = side√2

Triangles

Area

½ × base × height

Pythagorean Theorem

a² + b² = c²

The angles inside every triangle add up to 180°.

An exterior angle equals the sum of the two opposite interior angles.

Special Right Triangles

45°–45°–90°

1 : 1 : √2

30°–60°–90°

1 : √3 : 2

These ratios are tested regularly.

Trigonometry

SOH CAH TOA

sin θ = opposite/hypotenuse

cos θ = adjacent/hypotenuse

tan θ = opposite/adjacent

tan θ = sin θ/cos θ

Polygons

Interior Angle Sum

(n − 2) × 180°

Each Interior Angle of a Regular Polygon of n vertics

[(n − 2) × 180°]/n

Volume

Cube

s³

Rectangular Prism

lwh

Cylinder

πr²h

Cone

⅓πr²h

Sphere

⁴⁄₃πr³

Surface Area

Cube

6s²

Cylinder

2πr² + 2πrh

Sphere

4πr²

Mean

Mean

Sum of all values ÷ Number of values

Weighted Mean

Σ(value × weight) ÷ Σ(weights)

Probability

P(Event)

Number of Favorable Outcomes ÷ Total number of Outcomes

Complement Rule

P(complement event ) =1 − P(Event)

A probability is always between 0 and 1.

Percents

Increase

Original × (1 + rate)

Decrease

Original × (1 − rate)

Percent Change

(New − Original)/Original × 100%

Simple Interest

I = Prt

P = Principal

r = Interest Rate

t = Time

Exponential Growth and Decay

Growth

A = P(1 + r)ᵗ

Decay

A = P(1 − r)ᵗ

Functions

Example

f(x) = 2x + 3

f(5) = 13

Replace x with the given value.

Useful Constants

π ≈ 3.14

√2 ≈ 1.414

√3 ≈ 1.732


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