Course Library
Foundations
Grade 6–8
Intermediate
High School
Advanced
High School
Recreational
Activities and Fun
Numbers and Arithmetic
Coming soon
UpdatedThe Integers
Whole number arithmeticNegative numbersThe number lineAbsolute valueInverse operationsOrder of operationsAssociative, commutative and distributive lawDivision by zero
Divisibility and Primes
Factors and multiplesPrime numbers and prime factorisationnLCM and HCFDivisibility rules
Coming soon
Fractions
Comparing fractionsSimplifying fractionsAddition and subtractionMultiplication and divisionMixed numbers and improper fractions
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Decimals
Decimal notationDecimals on the number lineAddition and subtractionMultiplication and divisionConverting between fractions and decimals
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Percentages and Ratios
PercentagesPercentage changeRatio notationCalculating ratios
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Exponents and Roots
ExponentsExponent lawsRoots, negative and fractional exponentsRationalising the denominatorRational and irrational numbersApproximating irrational numbers using rationals
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Place Value and Rounding
Place valueBig and small numbersOrderingRounding integers and decimalsScientific notationDifferent bases
Equations and Functions
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Proportional Relationships
Direct and inverse proportionsGraphs of proportional relationshipsScale factorsRate of change
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Introduction to Algebra
Introduction and historyVariablesWriting, manipulating and evaluating algebraic expressionsModelling using algebra
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Linear Equations
Equations and identitiesManipulating and rearranging equationsLinear equations in one variableSolve simultaneous linear equationsLinear inequalities
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Linear Functions
Introduction to functionsGraphs of linear equationsIntercepts and slopeParallel and perpendicular lines
Geometry
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Lines and Angles
Points, lines, segments and raysParallel and perpendicular linesAngles and classification (acute, right, obtuse)Adjacent, opposite, alternate and corresponding anglesThe coordinate plane
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2D Shapes
Area and perimeter of triangles and quadrilateralsArea and circumference of circlesSum of angles in polygonsRuler and compass constructionPythagoras’ theoremCongruence and similarity
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3D Solids
Cuboids, prisms and pyramidsCones, cylinders and spheresCavalieri’s principleDensity and weightsNets of 3D solidsCross-sections of 3D objectsModelling the real world
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Units and Measuring
Space, time and weight unitsUnit conversionMeasuring angles distances in geometric figuresScale drawings
Probability and Statistics
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Basic Probability
IntroductionSimple probability experimentsUnions, intersections and Venn diagramsIndependent and mutually exclusive eventsCalculating probabilitiesTree diagrams
Combinatorics
FactorialsPermutations and combinationsProbabilityRandom Walks
Coming soon
Data and Statistics
Mean, meadian and modeRange, quartiles, standard deviation and outliersSampling and estimationBar charts, pie charts, scatter plots and frequency tablesStem-and-leaf plots, box plots and histogramsMisleading statistics
Geometry
Updated
Euclidean Geometry
History and definitionsCongruenceEuclid’s postulatesStraight-edge and compass constructionsOrigamiApplications
Updated
Transformations and Symmetry
Reflections, rotations and translationsReflectional and rotational symmetrySymmetry groupsWallpaper symmetriesSimilarity
Updated
Triangles and Trigonometry
Triangle propertiesMedians, midsegments, incircle and circumcircleTriangle inequalityTriangle congruencePythagoras’ theoremIsosceles and equilateral trianglesTrigonometrySine and cosine rules
Updated
Polygons and Polyhedra
Angles in polygonsPolygons propertiesQuadrilateralsTessellationsPolyhedraEuler’s FormulaPlatonic and Archimedean solids
Circles and Pi
Circles and PiTangentsCircle theoremsRadiansSectors and arcsInscribed shapes and anglesSpheres, cones and cylinders
Non-Euclidean Geometry
Metric spacesSpherical geometryHyperbolic geometryProjectionsHigher dimensionsTopologyMöbius strip and Klein bottle
Algebra
Updated
Sequences and Patterns
Triangle, square and cube numbersLinear and quadratic sequencesFibonacci numbersPerfect numbersArithmetic and geometric sequencesRecursive equationsPascal’s triangle
Coming soon
Functions
Function notationDomain and rangeAbsolute value and piecewise functionsIncreasing, decreasing, maxima and minimaRecognising and interpreting functionsApproximate solutions to equationsGraphing two-variable equationsAverage rate of changeArea under a curve
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Polynomials and Factorisation
Adding, subtracting and multiplying polynomialsBinomialsDifference of squaresFactoring simple polynomials
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Quadratics
Solving quadratic equationsCompleting the squareThe quadratic formulaParabolaeStandard and vertex formTransforming parabolae
Coming soon
Inequalities and Systems of Equations
Linear inequalitiesQuadratic inequalitiesGraphing two-variable inequalitiesSystems of equations with two unknownsElimination and substitution methods
Coming soon
Exponential and Rational Functions
Exponents, radicals and rational expressionsSquare and cube root equationsRadical functionsExponential growth and decayLinear vs exponential models
Probability and Discrete Mathematics
Updated
Probability
IntroductionCoins, dice and rouletteVenn diagrams and probability treesIndependent and mutually exclusive eventsConditional probabilityThe Monty Hall problemRandomness
Coming soon
UpdatedStatistics
Sampling and estimationTables, graphs and histogramsCentral tendency and spreadScatter plots and regressionCorrelation vs causationComparing models and data sets
Graphs and Networks
IntroductionComplete and bipartite graphsKönigsberg bridgesPlanar graphsMap colouringTravelling salesman problemSocial networks and other applications
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Codes and Ciphers
Simple codes and MorseError detection and correctionOne time padsThe Caesar and Vigenère cipherThe EnigmaRSA cryptography
Game Theory
Combinatorial games and NimTree diagramsPrisoners’ paradoxGames based on chanceThe lottery
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Algorithms and Computing
Introduction to computingComputational complexity and the O() notationSorting algorithmsLinear programming and the simplex algorithmData structuresGraphs, trees and networks
The Language of Mathematics
Logic, Sets and Proof
Set theoryLogic and proofProof by contradictionProof by induction
Imaginary and Complex Numbers
IntroductionComplex algebraThe complex planeModulus and argument formComplex conjugatesQuadratic, cubic and quartic equationsDe Moivre’s theoremEuler’s identityComplex roots of unity
Infinity
Hilbert’s hotelCountabilityCantor’s diagonalThe continuum hypothesis
Algebra and Analysis
Coming soon
Advanced Algebra
Manipulating rational expressionsSystems of quadratic equationsLinear and quadratic inequalitiesPartial fraction expansionPolynomialsPolynomial divisionFactor and remainder theoremBinomial theoremFundamental theorem of algebraSolve polynomial equations up to quartics
Coming soon
Advanced Functions
Combining and composing functionsInverse functionsFunction transformations (shifting and stretching)Polynomial functionsRational functions and discontinuitiesLimit behaviour of polynomial and rational functionsGraph sketching
Coming soon
Exponentials and Logarithms
Exponential equationsExponential growth and decayIntroduction to LogarithmsThe natural logarithm and eLogarithmic equationsGraphs of exponential and logarithmic functionsLogarithmic scale
Coming soon
Numerical Methods
Change of sign methodsInterval bisectionNewton-Raphson method
Coming soon
Sequences and series
Binomial expansion of (a + bx)^nRecurrence relationsArithmetic and geometric seriesSigma notationMaclaurin seriesConvergence and divergence
Geometry, Trigonometry and Matrices
Coming soon
Coordinate Geometry
Equation of lines and circlesDistances and midpointsParallel and perpendicular linesQuadrilaterals and polygons
Conic Sections
Equation of a circleEllipsesParabolae and hyperbolaeKepler’s laws and planetary orbits
Coming soon
Trigonometry
Unit circle definitionsTrigonometric functions and their graphsAmplitude and frequencyPythagorean identitiesDouble angle and addition formulasSecant, cosecant and cotangentInverse trigonometric functionsSimple trigonometric equationsHyperbolic functions
Coming soon
Vectors
IntroductionMagnitude and directionVector arithmeticPosition vectorsScalar productEquation of lines and planes
Coming soon
Matrices
IntroductionMatrix arithmeticMatrix multiplictionMatrices as transformationsDeterminantsMatrix inversesLinear systems of equationsGaussian elimination
Coming soon
Parametric and Polar Coordinates
Parametric curvesConversion between polar and cartesianSketching polar curvesArea enclosed by a polar curve
Fractals
Dimension of fractalsThe Sierpinski gasketMandelbrot setFractals in nature and technology
Calculus
Coming soon
Differentiation
Differentiation as gradient of tangentsLimits and rate of changeSimple derivativesProduct rule, quotient rule and chain ruleImplicit differentiationIncreasing, decreasing, convex and concave functionsEquations of tangents and normalsStationary points and optimisation problemsDerivatives of inverse functionsMean value theoremL’Hôpital’s rule
Coming soon
Integration
Integrals as anti-derivativesIntegrals as areas under a curveFundamental theorem of calculusTrapezium ruleIntegration by parts or substitutionIntegration using partial fraction expansionsIntegration using trigonometric identitiesImproper integralsArc lengthVolumes of revolution
Coming soon
Differential Equations
First order differential equationsSeparable equationsLogistic mapSecond order differential equationsHomogenous equations and particular integralCoupled differential equationsSimple harmonic motion and dampened oscillators
Probability and Statistics
Coming soon
Advanced Probability
Populations and sample spacesRandom variables and distributionsBinomial distributionPoisson distributionNormal distributionExpectation and varianceLaw of large numbersModelling
Coming soon
Hypothesis Tests
Designing statistical experimentsHypothesis testsEstimating population mean
Coming soon
Data Representation
Histograms and frequency tablesScatter plots and regressionMean and standard deviationData collectionData visualisation
Recreational Mathematics
These websites, apps and magazines showcase the incredible breadth and beauty of mathematics.
Applications of Mathematics
Learn about the countless hidden uses and applications which mathematics has in everyday life: From computers to traffic control, from weather prediction to video games, construction, medicine, sports, music or gambling…
Mathematical Origami
Explore the beautiful world of Origami and Mathematics. Be amazed by stunning photographs, and discover folding instructions and mathematical explanations.
Simon Singh’s Parallel
A weekly collection of fun and challenging exercises, designed to encourage young mathematicians to explore the world of mathematics, written by bestselling author Simon Singh.
Eureka Magazine
Eureka, published by the mathematical society of Cambridge University, is one of the oldest recreational mathematics magazines in the world. Authors include Stephen Hawking, Martin Gardner, Paul Dirac and Ian Stewart.
Problems and Puzzles
A selection of our favourite mathematical puzzles and problems. Most are very simple to explain, but the solutions require clever and unconventional thinking.
Fractal Fiction
The key to successful teaching is captivating storytelling – through real life applications, curious examples, historic background, or even fictional characters. These interactive slideshows combine an engaging narrative with beautiful graphics – explaining mathematical ideas in the context of popular stories and movies. They can be watched individually or be presented in classrooms.
When Alice falls down the rabbit hole, she discovers curious and wonderful mathematics she could have never imagined: Pascal’s triangle on a colour changing floor, sequences of rabbit generations, and beautiful, never-ending fractals and golden spirals…
How do you rob an infinite hotel, getting infinitely rich without anyone noticing? Only Danny Ocean knows. Did you know that there are things bigger than infinity? And that some things in mathematics can never be proven?
Coming Soon
One day at Hogwarts School of Mathematics: planetary orbits and conic sections in Astronomy, crystal polyhedra in Divination, Möbius transformations in Transfiguration, and hyperbolic geometry in the Room of Requirements.
Coming Soon