## Topic 1 & 2: Exponential & Logarithmic Functions

Exponential Functions Basic shape and Translations

Exponential Functions Dilations

Exponential functions 2 Sketching

Exponential functions sketching part 2

Exponential functions 3 Finding equation from a sketch

Exponential Model and Applications

Logs 1 Intro to Logarithms

Solving Indicial equations

Harder Indicial Equations

Indicial equations super hard quadratic action

Indicial equations The hardest one

## Topic 3: Trigonometric Functions

Introduction to Radians

Converting Radians to Degrees and Degrees to Radians

Radians quick angles

Standard triangles

The Unit Circle

The Unit Circle The Tan Ratio

The Unit Circle and Symmetry

The unit circle CAST and why CAST works

Finding exact trig ratios involving negative angles

Finding exact values of trig ratios around the unit circle

The Unit Circle Finding exact values of negative trig ratios

The unit circle Boundary angles

The unit circle solving unknown angles

Solving Simple Trig Equations Worksheet (worksheet in Description)

The unit circle solving unknowns in trig equations

Pythagorean identity

Pythagorean identity rearrangement

Using Pythagorean Identities Part 1

Solving trig identity equations using quadratics

Solving trig identity equations using quadratics part 2

Sketching SinX and CosX

Sketching y = AsinX and AcosX

Sketching y = AsinX +D and AcosX + D

Sketching y = AsinBx + D or y = AcosBx +D

Sketching y = AsinB(x+C)+D

Finding the equation of a periodic function from a graph or sketch

Revision of radians and the unit circle

Solving and simplifying using trig identities

Solving Trig equations The Tricky 3 Quantum of Quadratics

Solving Trig equations The Tricky 3 Square or Die

Solving Trig equations The Tricky 3 Domain Domination

Sketching f(x) = tan(x) and why it looks like that.

## Topic 4: Introduction to Differential Calculus

Variable and constant rates of change

Average rates of change

Intro to instantaneous rates of change

The Gradient function

Differentiation from first principles

Differentiating polynomials by rule

Finding Stationary points

Nature of Stationary points

Optimisation when the function is unknown

Introduction to Kinematics

Finding the equation of a tangent

Finding the equation of a normal

## Topic 5: Further Differentiation and Applications 1

Derivatives of polynomials, negative and fractional powers by rule

Composite functions and the chain rule

The chain rule the fast way

The product rule

The quotient rule

## Topic 6: Discrete Random Variables 1

Discrete Random Variables: Introduction and Examples

Discrete Random Variables Uniform Distribution

Discrete Random Variable Worked Example

The Geometric Probability Distribution

Expected Value of discrete random distributions

Discrete random distributions Expected value challenging but important

Variance and Standard Deviation: Discrete Random Variables

Properties of Expected Value: aE(X)+b = E(aX + b)

The alternative Variance formula Proof

Alternative Variance Formula Worked Example