AP Calculus AB Formulas

Quadratic Formula

ax² + bx + c = 0, given by x = (-b ± √(b² - 4ac)) / (2a).

Distance Formula

d = √(x₂ - x₁)² + (y₂ - y₁)²

Equation of a Circle

x² + y² = r² center at (0,0) and radius = r

Equation of an Ellipse

(x-h)²/a² + (y-k)²/b² = 1 for center (h, k).

Area of a Trapezoid

½ [base₁ + base₂](height)

Area of a Parallelogram

(base)(height)

Area of an Equilateral Triangle

(s² √3)/4

Area of a Circle

πr² (circumference = 2πr)

Volume of a Sphere

(4/3)πr³

Surface Area of a Sphere

4πr²

Volume of a Right Circular Cylinder

πr²h

Surface Area of a Right Circular Cylinder

Lateral S.A.: 2πrh

Total S.A.: 2πrh + 2πr²

Volume of a Right Circular Cone

1/3πr²h

Sin(0)

0

Sin(π/6)

½

Sin(π/4)

√2/2

Sin(π/3)

√3/2

Sin(π/2)

1

Sin(π)

0

Sin(3π/2)

-1

Sin(2π)

0

Cos(0)

1

Cos(π/6)

√3/2

Cos(π/4)

√2/2

Cos(π/3)

½

Cos(π/2)

0

Cos(π)

-1

Cos(3π/2)

0

Cos(2π)

1

Tan(0)

0

Tan(π/6)

√3/3

Tan(π/4)

1

Tan(π/3)

√3

Tan(π/2)

Undefined

Tan(π)

0

Tan(3π/2)

Undefined

Tan(2π)

0

sin(2θ)

2sin(θ)cos(θ)

cos(2θ)

cos² (θ) - sin² (θ)

1 - 2sin² (θ)

2cos² (θ) - 1²

cos² (θ)

(1 + cos(2θ))/2

sin² (θ)

(1 - cos(2θ))/2

sin² (θ) + cos² (θ)

1

1 + tan² (θ)

sec² (θ)

1 + cot² (θ)

csc² (θ)

limx→∞ 1/x

0

limx→0 (sin(x))/x

1

limh→0 (e^h - 1)/h

1

limx→0 (cos(x)-1)/x

0

limh→∞(1 + 1/h)^h

e

limx→0 (1+x)^(1/x)

e

Definition of the Derivative of a Function

f’(x) = limh→0 (f (x+h) - f(x))/h