AP Calculus BC

Quadratic Formula

Inverse sin derivative

Inverse cos derivative

Inverse tan derivative

Inverse csc derivative

Inverse sec derivative

Inverse cot derivative

Linear Approximation

f(x) ≈ f(a) + f’(a) (x-a)

General Equation of Tangent Line

y = f(a) +f’(a) (x-a)

Newton’s Method

Exponential Growth

y = y₀e^kt

Exponential Decay

y = y₀e^-kt

Derivative of y = a^u

General equation of a Cardioid

a + a cosθ

a - a cosθ

a - a sinθ

a + a sinθ

Limacon without inner loop

Limacon with inner loop

Leminscate

Rose with three petals

Rose with four petals

Logarithm notation

∫a^u du

1/ln a a^u + C

45-45-90 special triangle

30-60-90 special triangle

Newton’s First Law

An object at rest will stay at rest, and an object in motion will stay in motion with the same velocity (speed and direction) unless acted upon by an unbalanced force

Newton’s Second Law

(F = ma) The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass

Newton’s Third Law

For every action, there is an equal and opposite reaction. 

When one object exerts a force on a second object, the second object exerts a force back on the first that is equal in magnitude and opposite in direction