AP Calculus AB - Summer Quiz

Double angle Formulas

Sin 2θ

2sinθ * cosθ

Cos2θ

cos²θ - sin²θ

Tan2θ

2tanθ/1-tan²θ

Power Reducing Formulas

Sin²θ

1-cos2θ/2

Cos²θ

1+cos2θ/2

Tan²θ

1-cos2θ / 1 +cos2θ

Sum and Difference Formulas

Sin (u±v)

sin u * cos v ± cos u * sin v

Cos (u±v)

cos u * cos v -/+ sin u * sin v

Tan (u ± v)

(tan u ± tan v) / (1 -/+ tan u * tan v)

Logarithms

Log Format

log₁₀100 = 2 because 10² = 100

logs ask 10 to what power = 100

Natural Log

log_ex = ln x

ln e^x = x

asks e to what power = e^x

Product Rule

ln (A*B) = ln A + ln B

Quotient Rule

ln (A / B) = ln A - ln B

Power Rule

ln Aⁿ = n * ln A

Converting from log to exponent form

Surface area of a right circular cylinder

A = 2πrh + 2πr²

split into circles and rectangle

Inverse Functions

Swap y and x

solve the new equation for y

Even, odd, neither

Even: if f(-x) = f(x)

Odd: if f(-x) = -f(x)

Neither: doesn’t match either pattern

Point Slope Form

y - y₁ = m(x - x₁)

Graphs

y = 1/x

y = e^x

y = ln x

y = tan x

Ellipses and Hyperbolas

x² - y² = 1

x² + 4y² = 4

Summations

3 = k value you start at

6 = k value you end at

add up all your answers

Inequalities

Interval Notation