课程库

数字和算术

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

方程和函数

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

几何

Area and Shapes

Introduction
Parallelograms and 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

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

概率与统计

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

几何

欧几里得几何

引言欧几里得公理直尺与圆规构建
更多的构造
角度与证明
折纸

三角形与三角学

引言三角形的性质
中位线与相似性
三角形全等毕达哥拉斯定理
等腰与等边三角形
三角函数正弦与余弦定理

多边形四边形镶嵌多面体
网格和横截面
棱镜和金字塔
缩放形状和实体
柏拉图多面体

代数

Functions

Relations and Functions
Graphing and Interpreting Functions
Linear Functions and Equations
Piecewise Functions
Absolute Value Functions
Inverse Functions
Rates of Change

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

概率论与离散数学

概率

引言
概率树与维恩图
条件概率
蒙提霍尔问题(三门问题)
生日问题
真正的随机性

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

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

代数与分析

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

几何与线性代数

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

微积分

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

概率与统计

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