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Foundations

Grades 6–8

Intermediate

Grades 9–10

Advanced

Grades 11–12

Numbers and Arithmetic

The Integers

Arithmetic

The Number Line

Negative Numbers

Absolute Value

Properties of Zero

Place Value

Divisibility and Primes

Factors and Multiples Divisibility Rules Prime Numbers The Distribution of Primes Lowest Common Multiples Greatest Common Factors

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

Triangles

Polygons

Circles and Circumferences

Area of Circles

Angles and Polygons

Angles

Angles in Polygons

Drawing Triangles

Pythagoras’ Theorem

The Coordinate Plane

Transformations and Congruence

3D Solids

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

Combinatorics

Factorials Permutations Combinations

Data and Statistics

Introduction

Center and Spread

Visualising Data

Sampling

Scatter Plots and Linear Models

Geometry

Euclidean Geometry

Introduction Euclid’s Axioms Ruler and Compass Construction

Even More Constructions

Angles and Proofs

Origami and Paper Folding

Transformations and Symmetry

Introduction Rigid Transformations

Congruence

Symmetry Symmetry Groups and Wallpapers Symmetry in Physics Dilations

Similarity

Triangles and Trigonometry

Introduction Properties of Triangles

Midsegments and Similarity

Triangle Congruence Pythagoras’ Theorem

Isosceles and Equilateral Triangles

Trigonometry Sine and Cosine Rules

Polygons and Polyhedra

Polygons Quadrilaterals Tessellations Polyhedra

Nets and Cross Sections

Scaling Shapes and Solids

Platonic Solids

Circles and Pi

Introduction Degrees and Radians Tangents, Chords and Arcs

The Circle Theorems

Cyclic Polygons

Spheres, Cones and Cylinders Conic Sections

Non-Euclidean Geometry

Spherical Geometry Map Projections Hyperbolic Geometry Metric Spaces Topology

Higher Dimensions

Algebra

Functions

Relations and Functions

Graphing and Interpreting Functions

Piecewise Functions

Absolute Value Functions

Inverse Functions

Rates of Change

Sequences and Patterns

Introduction Arithmetic and Geometric Sequences Figurate Numbers

Sequences as Functions

Fibonacci Numbers Special Sequences Pascal’s Triangle

Limits and Convergence

Quadratic Equations

Introduction

Binomial Expressions

Solving Quadratic Equations

The Quadratic Formula

Graphing Quadratics

Projectile Motion

More Applications

Inequalities and Systems of Equations

Systems of Linear Equations

Row Operations and Elimination

Linear Inequalities

Systems of Inequalities

Quadratic Inequalities

Exponential Functions

Carbon Dating

Exponential Growth and Decay

Comparing Models

Compound Interest

Population Dynamics

Probability and Discrete Mathematics

Probability

Introduction

Probability Trees and Venn Diagrams

Conditional Probability

The Monty Hall Problem

The Birthday Problem

True Randomness

Statistics and Data

Casino Mathematics

Data Visualisation

Center and Spread of Data

Sampling and Estimation

The Wisdom of Crowds

Spreadsheets and Frequency Tables

Linear Models

Graphs and Networks

Introduction The Bridges of Königsberg Handshakes and Dating Planar Graphs Map Colouring The Travelling Salesman Problem

Scheduling Problems

Graphs in Everyday Life

Codes and Ciphers

Introduction

Binary Numbers

Error Detection

Secret Codes

The Enigma

Public Key Cryptography

Game Theory

The Prisoners’ Dilemma

Cards, Coins and Dice

The Winning Move

Random Walks

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

Logic, Sets and Proof

Logic and Paradoxes

Axioms and Proof

Proof by Induction

Infinity and Hilbert’s Hotel

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

Fractals

Introduction The Sierpinski Triangle The Mandelbrot Set

Space Filling Curves

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

Introduction

Mathematical 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

Change Language

Sign in to Mathigon

Course LibraryExplore the Textbook of the Future

Numbers and Arithmetic

The Integers

Divisibility and Primes

Fractions

Decimals

Rates, Percentages and Ratios

Equations and Functions

Introduction to Algebra

Linear Equations

Linear Functions

Roots and Exponents

Geometry

Area and Shapes

Angles and Polygons

3D Solids

Units and Measuring

Probability and Statistics

Introduction to Probability

Combinatorics

Data and Statistics

Geometry

Euclidean Geometry

Transformations and Symmetry

Triangles and Trigonometry

Polygons and Polyhedra

Circles and Pi

Non-Euclidean Geometry

Algebra

Functions

Sequences and Patterns

Quadratic Equations

Inequalities and Systems of Equations

Exponential Functions

Probability and Discrete Mathematics

Probability

Statistics and Data

Graphs and Networks

Codes and Ciphers

Game Theory

Algebra and Analysis

Polynomials

Function Transformations

Rationals and Radicals

Exponentials and Logarithms

Sequences and Series

Logic, Sets and Proof

Geometry and Linear Algebra

Coordinate Geometry

Trigonometry

Conic Sections and Polar Coordinates

Vectors

Matrices

Complex Numbers

Fractals

Calculus

Differentiation

Integration

Numerical Methods

Differential Equations

Chaos Theory

Probability and Statistics

Random Variables

Statistics and Hypothesis Tests

Algorithms

Machine Learning

Course Library
Explore the Textbook of the Future