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Course Library

Foundations
Grades 6–8
Intermediate
Grades 9–10
Advanced
Grades 11–12

Numbers and Arithmetic

The Integers

Commutative, Associative and Distributive LawsCOMING SOON
Order of OperationsCOMING SOON
The Number LineCOMING SOON
Arithmetic with Negative NumbersCOMING SOON
Properties of ZeroCOMING SOON
Absolute ValueCOMING SOON
Place ValueCOMING SOON

Divisibility and Primes

Factors and MultiplesDivisibility RulesPrime NumbersThe Distribution of PrimesLowest Common MultiplesGreatest Common Factors

Fractions

IntroductionCOMING SOON
Simplifying and Expanding FractionsCOMING SOON
Adding and Subtracting FractionsCOMING SOON
Multiplying and Dividing FractionsCOMING SOON
Mixed NumbersCOMING SOON

Decimals

IntroductionCOMING SOON
Adding and Subtracting DecimalsCOMING SOON
Ordering DecimalsCOMING SOON
Multiplying DecimalsCOMING SOON
Dividing DecimalsCOMING SOON
Converting Decimals and FractionsCOMING SOON
RoundingCOMING SOON

Rates, Percentages and Ratios

Ratios and MixturesCOMING SOON
PercentagesCOMING SOON
Percentage Increase and DecreaseCOMING SOON
InterestCOMING SOON
Ratios and RatesCOMING SOON

Roots and Exponents

Square and Cube RootsCOMING SOON
Rational and Irrational NumbersCOMING SOON
Powers and ExponentsCOMING SOON
Large and Small NumbersCOMING SOON
Scientific NotationCOMING SOON

Equations and Functions

Introduction to Algebra

IntroductionCOMING SOON
Constants and VariablesCOMING SOON
Manipulating ExpressionsCOMING SOON
ModellingCOMING SOON

Proportional Relationships

IntroductionCOMING SOON
Direct and Inverse ProportionCOMING SOON
Graphing Proportional RelationshipsCOMING SOON
Constant of ProportionalityCOMING SOON

Linear Equations

Reasoning with Tape DiagramsCOMING SOON
Weighing and BalancingCOMING SOON
Manipulating EquationsCOMING SOON
Solving Linear EquationsCOMING SOON
InequalitiesCOMING SOON

Linear Functions

Input and OutputCOMING SOON
Graphing FunctionsCOMING SOON
Slope and InterceptCOMING SOON
Parallel and Perpendicular LinesCOMING SOON
Linear FunctionsCOMING SOON
Piecewise Functions and Systems of EquationsCOMING SOON

Geometry

Area and Shapes

IntroductionCOMING SOON
Parallelograms and TrianglesCOMING SOON
PolygonsCOMING SOON
Circles and CircumferencesCOMING SOON
Area of CirclesCOMING SOON

Angles and Polygons

AnglesCOMING SOON
Angles in PolygonsCOMING SOON
Drawing Triangles
Pythagoras’ TheoremCOMING SOON
The Coordinate PlaneCOMING SOON
Transformations and CongruenceCOMING SOON

3D Solids

PolyhedraCOMING SOON
Nets and Surface AreaCOMING SOON
Volumes and CuboidsCOMING SOON
Prisms and PyramidsCOMING SOON
Cylinders and ConesCOMING SOON
SpheresCOMING SOON

Units and Measuring

MeasuringCOMING SOON
Units and ConversionCOMING SOON
Scale DrawingsCOMING SOON
Scaling and DimensionsCOMING SOON
EstimationCOMING SOON

Probability and Statistics

Basic Probability

IntroductionCOMING SOON
Coins, Cards and DiceCOMING SOON
Multi-Step ExperimentsCOMING SOON
Designing SimulationsCOMING SOON

Combinatorics

FactorialsDraftPermutationsDraftCombinationsDraftWinning the LotteryDraft

Data and Statistics

IntroductionCOMING SOON
Dot Plots and HistogramsCOMING SOON
Box PlotsCOMING SOON
Mean, Median and ModeCOMING SOON
SamplingCOMING SOON
Comparing PopulationsCOMING SOON
Scatter Plots and Linear ModelsCOMING SOON

Geometry

Euclidean Geometry

IntroductionEuclid’s AxiomsRuler and Compass Construction
Even More ConstructionsCOMING SOON
Angles and ProofsCOMING SOON
Origami and Paper Folding

Transformations and Symmetry

IntroductionRigid Transformations
CongruenceCOMING SOON
SymmetrySymmetry Groups and WallpapersSymmetry in PhysicsDilations
SimilarityCOMING SOON

Triangles and Trigonometry

IntroductionProperties of Triangles
Midsegments and SimilarityCOMING SOON
Triangle CongruencePythagoras’ Theorem
Isosceles and Equilateral TrianglesCOMING SOON
TrigonometrySine and Cosine Rules

Polygons and Polyhedra

PolygonsQuadrilateralsTessellationsPolyhedra
Nets and Cross SectionsCOMING SOON
Prisms and PyramidsCOMING SOON
Scaling Shapes and SolidsCOMING SOON
Platonic Solids

Circles and Pi

IntroductionDegrees and RadiansTangents, Chords and Arcs
The Circle TheoremsCOMING SOON
Cyclic PolygonsCOMING SOON
Spheres, Cones and CylindersConic Sections

Non-Euclidean Geometry

IntroductionDraftMetric SpacesDraftSpherical GeometryDraftMap ProjectionsDraftHyperbolic GeometryDraft
Higher DimensionsCOMING SOON
TopologyDraft

Algebra

Functions

Relations and FunctionsCOMING SOON
Graphing FunctionsCOMING SOON
Solving Equations GraphicallyCOMING SOON
Domain and RageCOMING SOON
Absolute Value FunctionsCOMING SOON
Inverse FunctionsCOMING SOON
Rates of ChangeCOMING SOON

Sequences and Patterns

IntroductionArithmetic and Geometric SequencesFigurate Numbers
Sequences as FunctionsCOMING SOON
Fibonacci NumbersSpecial SequencesPascal’s Triangle
Limits and ConvergenceCOMING SOON

Linear Equations and Inequalities

Solving Linear EquationsCOMING SOON
Graphing Linear FunctionsCOMING SOON
Systems of Linear EquationsCOMING SOON
Row Operations and EliminationCOMING SOON
Linear InequalitiesCOMING SOON
Inequalities in Two VariablesCOMING SOON
Systems of InequalitiesCOMING SOON

Quadratic Equations

Introduction
Binomial ExpressionsCOMING SOON
Solving Quadratic EquationsCOMING SOON
The Quadratic FormulaCOMING SOON
Graphing QuadraticsCOMING SOON
Projectile MotionCOMING SOON
More ApplicationsCOMING SOON

Exponential Functions

Carbon DatingCOMING SOON
Exponential Growth and DecayCOMING SOON
Comparing ModelsCOMING SOON
Compound InterestCOMING SOON
Population DynamicsCOMING SOON

Probability and Discrete Mathematics

Probability

Introduction
Probability TreesCOMING SOON
Venn DiagramsCOMING SOON
Conditional ProbabilityCOMING SOON
The Monty Hall Problem
The Birthday ProblemCOMING SOON
True Randomness

Statistics and Data

Casino Mathematics
Data VisualisationCOMING SOON
Center and Spread of DataCOMING SOON
Sampling and EstimationCOMING SOON
Spreadsheets and Frequency TablesCOMING SOON
Linear ModelsCOMING SOON
Causation vs CorrelationCOMING SOON

Graphs and Networks

IntroductionThe Bridges of KönigsbergHandshakes and PartiesPlanar GraphsMap ColouringThe Travelling Salesman Problem
Scheduling ProblemsCOMING SOON
Graphs in Everyday Life

Codes and Ciphers

Simple CodesCOMING SOON
Error Detection and Error CorrectionCOMING SOON
Secret CodesCOMING SOON
The EnigmaCOMING SOON
RSA CryptographyCOMING SOON

Game Theory

The Winning MoveDraft
Cards, Coins and DiceCOMING SOON
The Prisoners’ DilemmaDraft
Gamblers’ RuinCOMING SOON

Algebra and Analysis

Polynomials

IntroductionCOMING SOON
Zeros of PolynomialsCOMING SOON
Sketching Polynomial FunctionsCOMING SOON
The Factor and Remainder TheoremsCOMING SOON
Systems of EquationsCOMING SOON

Function Transformations

Combining and Composing FunctionsCOMING SOON
Translating FunctionsCOMING SOON
Reflecting FunctionsCOMING SOON
Scaling FunctionsCOMING SOON
Inverse functionsCOMING SOON

Rationals and Radicals

Rational and Irrational NumbersCOMING SOON
Rational FunctionsCOMING SOON
Manipulating Rational ExpressionsCOMING SOON
Solving Rational EquationsCOMING SOON
Exponent LawsCOMING SOON
Radical FunctionsCOMING SOON
Solving Radical EquationsCOMING SOON

Exponentials and Logarithms

Exponential Growth and DecayCOMING SOON
Exponential FunctionsCOMING SOON
Introduction to LogarithmsCOMING SOON
Laws of LogarithmsCOMING SOON
The Number eCOMING SOON
Logarithmic FunctionsCOMING SOON

Sequences and Series

SequencesCOMING SOON
Series and Sigma NotationCOMING SOON
Arithmetic and Geometric SeriesCOMING SOON
The Binomial TheoremCOMING SOON

Logic, Sets and Proof

Logic and ParadoxesDraftSets, Axioms and ProofDraftProof by ContradictionDraftProof by InductionDraftInfinity and Hilbert’s HotelDraft

Geometry and Linear Algebra

Coordinate Geometry

Equations of LinesCOMING SOON
Parallel and Perpendicular LinesCOMING SOON
Equations of CirclesCOMING SOON
Properties of PolygonsCOMING SOON
TransformationsCOMING SOON

Trigonometry

The Unit Circle DefinitionCOMING SOON
Graphs of Trigonometric FunctionsCOMING SOON
Amplitude, Frequency and TransformationsCOMING SOON
Pythagorean IdentitiesCOMING SOON
More Trigonometric IdentitiesCOMING SOON
Inverse Trigonometric FunctionsCOMING SOON
Circular MotionCOMING SOON

Conic Sections and Polar Coordinates

Parametric CurvesCOMING SOON
Circles and EllipsesCOMING SOON
ParabolaeCOMING SOON
HyperbolaeCOMING SOON
Polar CoordinatesCOMING SOON

Vectors

IntroductionCOMING SOON
Vector ArithmeticCOMING SOON
Scalar Products and Equations of PlanesCOMING SOON
Cross Products and Equations of LinesCOMING SOON
Geometry ProblemsCOMING SOON

Matrices

Matrices as TransformationsCOMING SOON
Matrix ArithmeticCOMING SOON
DeterminantsCOMING SOON
Matrix InversesCOMING SOON
Cramer’s Rule and Gaussian EliminationCOMING SOON
Eigenvalues and EigenvectorsCOMING SOON

Complex Numbers

IntroductionDraft
The Complex PlaneCOMING SOON
Modulus and ArgumentCOMING SOON
Quadratic, Cubic and Quartic EquationsCOMING SOON
Euler’s Identity and De Moivre’s TheoremCOMING SOON
Complex Roots of UnityCOMING SOON

Fractals

IntroductionDraftThe Sierpinski GasketDraftThe Mandelbrot SetDraft

Calculus

Differentiation

IntroductionCOMING SOON
Limits and GradientsCOMING SOON
Differentiation Rules ICOMING SOON
Differentiation Rules IICOMING SOON
Optimisation problemsCOMING SOON

Integration

IntroductionCOMING SOON
Integration Rules ICOMING SOON
Integration Rules IICOMING SOON
Definite Integrals and Areas under a CurveCOMING SOON
Numerical IntegrationCOMING SOON
Improper IntegralsCOMING SOON
Solids of RevolutionCOMING SOON

Numerical Methods

Solving Equations NumericallyCOMING SOON
The Newton­-Raphson MethodCOMING SOON
Maclaurin and Taylor seriesCOMING SOON

Differential Equations

Simple Differential EquationsCOMING SOON
First Order Separable EquationsCOMING SOON
Second Order Differential EquationsCOMING SOON
Homogenous Equations and Particular IntegralsCOMING SOON
Simple Harmonic MotionCOMING SOON
Coupled Differential EquationsCOMING SOON

Chaos Theory

Introduction
Mathematical BilliardCOMING SOON
The Three Body ProblemCOMING SOON
Phase Space and Strange AttractorsCOMING SOON
The Logistic MapCOMING SOON

Probability and Statistics

Advanced Probability

IntroductionCOMING SOON
Discrete Random VariablesCOMING SOON
The Normal DistributionCOMING SOON
Binomial and Poisson DistributionCOMING SOON
Continuous Random VariablesCOMING SOON
Random WalksCOMING SOON

Statistics and Hypothesis Tests

Data RepresentationCOMING SOON
Experiments and SamplingCOMING SOON
Hypothesis TestsCOMING SOON
Estimation and Confidence IntervalsCOMING SOON
The Law of Large Numbers and Central Limit TheoremCOMING SOON
Chi Squared Tests and Correlation CoefficientsCOMING SOON
Bayesian StatisticsCOMING SOON

Algorithms

Introduction to ComputingCOMING SOON
Complexity and O NotationCOMING SOON
Sorting AlgorithmsCOMING SOON
Linear Programming and the Simplex AlgorithmCOMING SOON
Graphs, Trees and NetworksCOMING SOON

Machine Learning

IntroductionCOMING SOON
Linear RegressionCOMING SOON
Neural NetworksCOMING SOON
Support Vector MachinesCOMING SOON
Unsupervised LearningCOMING SOON
Tensor FlowCOMING SOON