## Numbers and Arithmetic

### The Integers

Arithmetic

The Number Line

Negative Numbers

Absolute Value

Properties of Zero

Place Value

### Fractions

Introduction

Fraction Arithmetic

Mixed Numbers

Dividing Fractions

### Decimals

Introduction

Adding and Subtracting Decimals

Ordering Decimals

Multiplying and Dividing Decimals

Converting Decimals and Fractions

Rounding

### Rates, Percentages and Ratios

Ratios and Mixtures

Percentages

Percentage Increase and Decrease

Interest

Ratios and Rates

## Equations and Functions

### Introduction to Algebra

Proportional Relationships

Graphs an Variables

Manipulating Expressions

Modelling

### Linear Equations

Weighing and Balancing

Tape Diagrams

Solving Linear Equations

Inequalities

### Linear Functions

Input, Output and Graphs

Slope and Intercept

Parallel and Perpendicular Lines

Systems of Equations

### Roots and Exponents

Square and Cube Roots

Rational and Irrational Numbers

Powers and Exponents

Scientific Notation

## Geometry

### Area and Shapes

Introduction

Parallelograms and Triangles

Polygons

Circles and Circumferences

Area of Circles

### Angles and Polygons

Angles

Angles in Polygons

Drawing TrianglesPythagoras’ Theorem

The Coordinate Plane

Transformations and Congruence

### Examples

Introduction

Nets and Surface Area

Prisms and Pyramids

Cylinders and Cones

Spheres

### Units and Measuring

Measuring

Units and Conversion

Scale Drawings

Scaling and Dimensions

Estimation

## Probability and Statistics

### Introduction to Probability

Introduction

Computing Probabilities

Probability Trees

Venn Diagrams

### Data and Statistics

Introduction

Center and Spread

Visualising Data

Sampling

Scatter Plots and Linear Models

## Algebra and Analysis

### Polynomials

Introduction

Zeros of Polynomials

Sketching Polynomial Functions

The Factor and Remainder Theorems

Systems of Equations

### Function Transformations

Combining and Composing Functions

Translating Functions

Reflecting Functions

Scaling Functions

Inverse functions

### Rationals and Radicals

Rational and Irrational Numbers

Rational Functions and Expressions

Solving Rational Equations

Exponent Laws

Radical Functions

Solving Radical Equations

### Exponentials and Logarithms

Exponential Growth and Decay

Exponential Functions

Introduction to Logarithms

Laws of Logarithms

The Number e

Logarithmic Functions

### Sequences and Series

Sequences

Series and Sigma Notation

Arithmetic and Geometric Series

The Binomial Theorem

## Geometry and Linear Algebra

### Coordinate Geometry

Equations of Lines

Parallel and Perpendicular Lines

Equations of Circles

Properties of Polygons

Transformations

### Trigonometry

The Unit Circle Definition

Graphs of Trigonometric Functions

Amplitude, Frequency and Transformations

Pythagorean Identities

More Trigonometric Identities

Inverse Trigonometric Functions

Circular Motion

### Conic Sections and Polar Coordinates

Parametric Curves

Circles and Ellipses

Parabolae

Hyperbolae

Polar Coordinates

### Vectors

Introduction

Vector Arithmetic

Scalar Products and Equations of Planes

Cross Products and Equations of Lines

Geometry Problems

### Matrices

Transformations

Matrix Arithmetic

Determinants

Matrix Inverses

Cramer’s Rule and Gaussian Elimination

Eigenvalues and Eigenvectors

### Complex Numbers

Introduction

Complex Arithmetic

Euler’s Formula

Solving Polynomials

De Moivre’s Theorem and Roots of Unity

## Calculus

### Differentiation

Introduction

Limits and Gradients

Differentiation Rules I

Differentiation Rules II

Optimisation problems

### Integration

Introduction

Integration Rules

Definite Integrals and Areas under a Curve

Improper Integrals

Solids of Revolution

### Numerical Methods

Solving Equations Numerically

The Newton-Raphson Method

Numerical Integration

Maclaurin and Taylor series

### Differential Equations

Simple Differential Equations

First Order Separable Equations

Second Order Differential Equations

Homogenous Equations and Particular Integrals

Simple Harmonic Motion

Coupled Differential Equations

### Chaos Theory

IntroductionMathematical Billiard

The Three Body Problem

Phase Space and Strange Attractors

The Logistic Map

## Probability and Statistics

### Random Variables

Introduction

Discrete Random Variables

Binomial and Poisson Distribution

Continuous Random Variables

The Normal Distribution

The Central Limit Theorem

### Statistics and Hypothesis Tests

Sampling and Estimation

Hypothesis Tests and Confidence Intervals

Linear Models and Correlation Coefficients

Contingency tables and Chi Squared Tests

Bayesian Statistics

### Algorithms

Introduction to Computing

Complexity and O Notation

Sorting Algorithms

Linear Programming and the Simplex Algorithm

Graphs, Trees and Networks

### Machine Learning

Introduction

Linear Regression

Support Vector Machines

Neural Networks

Unsupervised Learning