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
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