Pure Y2

Domain

Set of possible inputs

Range

Set of possible outputs

Function

A mapping such that every element of the domain is mapped to exactly on element of the range

Types of function

• Many-to-one, eg. x²

• One-to-one, eg. 2x + 1

Inverse function

• Does opposite of orig funct

• x & y axis swapped, reflected in y = x

• Domain and range swapped

• Orig funct must be one-to-one, inverse mapping would be one to many which is not a function

y = |f(x)|

• All negative values of y become positive

• Anything under x-axis flipped above it

y = f(|x|)

• All inputted x-values would be positive

• So would produce same graph as positive values

• So graph produced by positive values of x is flipped onto the negative values of x 

Ark lengthin radians

L = rθ

Area in radians

(1/2)θr²

Segment Area in radians

(1/2)r²(θ - sinθ)

Arithmetic n^th term

Arithmetic sum

Geometric n^th

Geometric sum

Geometric sum to infinity

• For convergent geometric series

• When |r| < 1

Sigma notation

Strictly increasing sequence

Terms are always increasing

Strictly decreasing sequence

Terms are always decreasing

Periodic sequence

• Sequence of terms is always repeating

• Order k of a sequence is how often it repeats

Binomial expansion formula 

How to tell if expansion is valid

|x| < 1

When would approximations be more vaild

When x is smaller

Double angle formulas

Harmonic Identity

Domain and range of cartesian

• Domain is the range of x equation

• Range is the range of the y equation

When & how to use Chain Rule

• Composite function

When & how to use Product Rule

• Product rule

When & how to use Quotient Rule

• Division of two functions

What is an implicit function

When the y is not in terms of x, e.g. x² + y² = 25

Implicit differentiation

When differentiating a function of y, but with respect to x, multiply by dy/dx

Concave

• f’’(x) <= 0

• Swerving right

Point of infleciton

• f’’(x) = 0

• Gradient doesn’t change

Convex

• f’’(x) >= 0

• Swerving left