コースライブラリ

数字と算術

The Integers

Commutative, Associative and Distributive Laws近日公開
Order of Operations近日公開
The Number Line近日公開
Arithmetic with Negative Numbers近日公開
Properties of Zero近日公開
Absolute Value近日公開
Place Value近日公開

Fractions

Introduction近日公開
Fraction Arithmetic近日公開
Mixed Numbers近日公開
Dividing Fractions近日公開

Decimals

Introduction近日公開
Adding and Subtracting Decimals近日公開
Ordering Decimals近日公開
Multiplying and Dividing Decimals近日公開
Converting Decimals and Fractions近日公開
Rounding近日公開

Rates, Percentages and Ratios

Ratios and Mixtures近日公開
Percentages近日公開
Percentage Increase and Decrease近日公開
Interest近日公開
Ratios and Rates近日公開

Roots and Exponents

Square and Cube Roots近日公開
Rational and Irrational Numbers近日公開
Powers and Exponents近日公開
Large and Small Numbers近日公開
Scientific Notation近日公開

方程式と関数

Introduction to Algebra

Introduction近日公開
Constants and Variables近日公開
Manipulating Expressions近日公開
Modelling近日公開

Proportional Relationships

Introduction近日公開
Direct and Inverse Proportion近日公開
Graphing Proportional Relationships近日公開
Constant of Proportionality近日公開

Linear Equations

Reasoning with Tape Diagrams近日公開
Weighing and Balancing近日公開
Manipulating Equations近日公開
Solving Linear Equations近日公開
Inequalities近日公開

Linear Functions

Input and Output近日公開
Graphing Functions近日公開
Slope and Intercept近日公開
Parallel and Perpendicular Lines近日公開
Linear Functions近日公開
Piecewise Functions and Systems of Equations近日公開

ジオメトリ

Area and Shapes

Introduction近日公開
Parallelograms and Triangles近日公開
Polygons近日公開
Circles and Circumferences近日公開
Area of Circles近日公開

Angles and Polygons

Angles近日公開
Angles in Polygons近日公開
Drawing Triangles
Pythagoras’ Theorem近日公開
The Coordinate Plane近日公開
Transformations and Congruence近日公開

3D Solids

Introduction近日公開
Nets and Surface Area近日公開
Prisms and Pyramids近日公開
Cylinders and Cones近日公開
Spheres近日公開

Units and Measuring

Measuring近日公開
Units and Conversion近日公開
Scale Drawings近日公開
Scaling and Dimensions近日公開
Estimation近日公開

確率と統計

Introduction to Probability

Introduction近日公開
Computing Probabilities近日公開
Probability Trees近日公開
Venn Diagrams近日公開

Data and Statistics

Introduction近日公開
Center and Spread近日公開
Visualising Data近日公開
Sampling近日公開
Scatter Plots and Linear Models近日公開

ジオメトリ

Euclidean Geometry

IntroductionEuclid’s AxiomsRuler and Compass Construction
Even More Constructions近日公開
Angles and Proofs近日公開
Origami and Paper Folding

Triangles and Trigonometry

IntroductionProperties of Triangles
Midsegments and Similarity近日公開
Triangle CongruencePythagoras’ Theorem
Isosceles and Equilateral Triangles近日公開
TrigonometrySine and Cosine Rules

ポリゴン四辺形テッセレーション多面体
ネットと断面近日公開
プリズムとピラミッド近日公開
シェイプとソリッドのスケーリング近日公開
プラトンの固体

円と円周率

前書き度とラジアン接線、和音、円弧
サークル定理近日公開
循環ポリゴン近日公開
球、円錐、円柱円錐断面

Non-Euclidean Geometry

Spherical GeometryMap ProjectionsHyperbolic GeometryMetric SpacesTopology
Higher Dimensions近日公開

代数

Functions

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

Sequences and Patterns

IntroductionArithmetic and Geometric SequencesFigurate Numbers
Sequences as Functions近日公開
Fibonacci NumbersSpecial SequencesPascal’s Triangle
Limits and Convergence近日公開

Quadratic Equations

Introduction
Binomial Expressions近日公開
Solving Quadratic Equations近日公開
The Quadratic Formula近日公開
Graphing Quadratics近日公開
Projectile Motion近日公開
More Applications近日公開

Inequalities and Systems of Equations

Systems of Linear Equations近日公開
Row Operations and Elimination近日公開
Linear Inequalities近日公開
Systems of Inequalities近日公開
Quadratic Inequalities近日公開

Exponential Functions

Carbon Dating
Exponential Growth and Decay近日公開
Comparing Models近日公開
Compound Interest近日公開
Population Dynamics近日公開

確率と離散数学

Probability

Introduction
Probability Trees and Venn Diagrams近日公開
Conditional Probability近日公開
The Monty Hall Problem
The Birthday Problem近日公開
True Randomness

Statistics and Data

Casino Mathematics
Data Visualisation近日公開
Center and Spread of Data近日公開
Sampling and Estimation近日公開
Spreadsheets and Frequency Tables近日公開
Linear Models近日公開

Codes and Ciphers

Introduction
Binary Numbers近日公開
Error Detection近日公開
Secret Codes近日公開
The Enigma近日公開
Public Key Cryptography近日公開

Game Theory

The Prisoners’ Dilemma
Cards, Coins and Dice近日公開
The Winning Move
Random Walks近日公開

代数と分析

Polynomials

Introduction近日公開
Zeros of Polynomials近日公開
Sketching Polynomial Functions近日公開
The Factor and Remainder Theorems近日公開
Systems of Equations近日公開

Function Transformations

Combining and Composing Functions近日公開
Translating Functions近日公開
Reflecting Functions近日公開
Scaling Functions近日公開
Inverse functions近日公開

Rationals and Radicals

Rational and Irrational Numbers近日公開
Rational Functions and Expressions近日公開
Solving Rational Equations近日公開
Exponent Laws近日公開
Radical Functions近日公開
Solving Radical Equations近日公開

Exponentials and Logarithms

Exponential Growth and Decay近日公開
Exponential Functions近日公開
Introduction to Logarithms近日公開
Laws of Logarithms近日公開
The Number e近日公開
Logarithmic Functions近日公開

Sequences and Series

Sequences近日公開
Series and Sigma Notation近日公開
Arithmetic and Geometric Series近日公開
The Binomial Theorem近日公開

幾何学と線形代数

Coordinate Geometry

Equations of Lines近日公開
Parallel and Perpendicular Lines近日公開
Equations of Circles近日公開
Properties of Polygons近日公開
Transformations近日公開

Trigonometry

The Unit Circle Definition近日公開
Graphs of Trigonometric Functions近日公開
Amplitude, Frequency and Transformations近日公開
Pythagorean Identities近日公開
More Trigonometric Identities近日公開
Inverse Trigonometric Functions近日公開
Circular Motion近日公開

Conic Sections and Polar Coordinates

Parametric Curves近日公開
Circles and Ellipses近日公開
Parabolae近日公開
Hyperbolae近日公開
Polar Coordinates近日公開

Vectors

Introduction近日公開
Vector Arithmetic近日公開
Scalar Products and Equations of Planes近日公開
Cross Products and Equations of Lines近日公開
Geometry Problems近日公開

Matrices

Matrices as Transformations近日公開
Matrix Arithmetic近日公開
Determinants近日公開
Matrix Inverses近日公開
Cramer’s Rule and Gaussian Elimination近日公開
Eigenvalues and Eigenvectors近日公開

Complex Numbers

Introduction近日公開
Complex Arithmetic近日公開
Quadratic, Cubic and Quartic Equations近日公開
Euler’s Identity近日公開
De Moivre’s Theorem and Roots of Unity近日公開

微積分

Differentiation

Introduction近日公開
Limits and Gradients近日公開
Differentiation Rules I近日公開
Differentiation Rules II近日公開
Optimisation problems近日公開

Integration

Introduction近日公開
Integration Rules近日公開
Definite Integrals and Areas under a Curve近日公開
Improper Integrals近日公開
Solids of Revolution近日公開

Numerical Methods

Solving Equations Numerically近日公開
The Newton­-Raphson Method近日公開
Numerical Integration近日公開
Maclaurin and Taylor series近日公開

Differential Equations

Simple Differential Equations近日公開
First Order Separable Equations近日公開
Second Order Differential Equations近日公開
Homogenous Equations and Particular Integrals近日公開
Simple Harmonic Motion近日公開
Coupled Differential Equations近日公開

Chaos Theory

Introduction
Mathematical Billiard近日公開
The Three Body Problem近日公開
Phase Space and Strange Attractors近日公開
The Logistic Map近日公開

確率と統計

Random Variables

Introduction近日公開
Discrete Random Variables近日公開
Binomial and Poisson Distribution近日公開
Continuous Random Variables近日公開
The Normal Distribution近日公開
The Central Limit Theorem近日公開

Statistics and Hypothesis Tests

Sampling and Estimation近日公開
Hypothesis Tests and Confidence Intervals近日公開
Linear Models and Correlation Coefficients近日公開
Contingency tables and Chi Squared Tests近日公開
Bayesian Statistics近日公開

Algorithms

Introduction to Computing近日公開
Complexity and O Notation近日公開
Sorting Algorithms近日公開
Linear Programming and the Simplex Algorithm近日公開
Graphs, Trees and Networks近日公開

Machine Learning

Introduction近日公開
Linear Regression近日公開
Support Vector Machines近日公開
Neural Networks近日公開
Unsupervised Learning近日公開