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