Course Library

Grade 6–8
High School
High School

Numbers and Arithmetic

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The 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

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Comparing fractionsSimplifying fractionsAddition and subtractionMultiplication and divisionMixed numbers and improper fractions

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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


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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


FactorialsPermutations and combinationsProbabilityRandom Walks

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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


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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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Solving quadratic equationsCompleting the squareThe quadratic formulaParabolaeStandard and vertex formTransforming parabolae

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Inequalities and Systems of Equations

Linear inequalitiesQuadratic inequalitiesGraphing two-variable inequalitiesSystems of equations with two unknownsElimination and substitution methods

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Exponential and Rational Functions

Exponents, radicals and rational expressionsSquare and cube root equationsRadical functionsExponential growth and decayLinear vs exponential models

Sequences and Patterns

Triangle, square and cube numbersLinear and quadratic sequencesFibonacci numbersPerfect numbersArithmetic and geometric sequencesRecursive equationsPascal’s triangle


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Euclidean Geometry

History and axiomsRuler and compass constructionGeometry softwareOrigami and paper foldingBearings and simple vectors

Transformations and Symmetry

Reflection, rotation, translation and scalingCongruence and similarityRequirements for triangle congruenceCombinations and invariance of transformationsSymmetry and groups

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Triangles and Trigonometry

Constructing trianglesCircumcircles and incirclesPythagoras’ TteoremTrigonometric functionsSine and cosine rules


Polygons and Polyhedra

Classification and properties of quadrilateralsConstructing regular polygonsPolyhedraEuler’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

Probability and Discrete Mathematics



IntroductionCoins, dice and rouletteVenn diagrams and probability treesIndependent and mutually exclusive eventsConditional probabilityThe Monty Hall problemRandomness

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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

Algebra and Analysis

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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

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Advanced Functions

Combining and composing functionsInverse functionsFunction transformations (shifting and stretching)Polynomial functionsRational functions and discontinuitiesLimit behaviour of polynomial and rational functionsGraph sketching

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Exponentials and Logarithms

Exponential equationsExponential growth and decayIntroduction to LogarithmsThe natural logarithm and eLogarithmic equationsGraphs of exponential and logarithmic functionsLogarithmic scale

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Numerical Methods

Change of sign methodsInterval bisectionNewton­-Raphson method

Sequences and series

Binomial expansion of (a + bx)^nRecurrence relationsArithmetic and geometric seriesSigma notationMaclaurin seriesConvergence and divergence

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


Hilbert’s hotelCountabilityCantor’s diagonalThe continuum hypothesis

Geometry, Trigonometry and Matrices

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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

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Unit circle definitionsTrigonometric functions and their graphsAmplitude and frequencyPythagorean identitiesDouble angle and addition formulaeSecant, cosecant and cotangentInverse trigonometric functionsSimple trigonometric equationsHyperbolic functions

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IntroductionMagnitude and directionVector arithmeticPosition vectorsScalar productEquation of lines and planes

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IntroductionMatrix arithmeticMatrix multiplictionMatrices as transformationsDeterminantsMatrix inversesLinear systems of equationsGaussian elimination

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Parametric and Polar Coordinates

Parametric curvesConversion between polar and cartesianSketching polar curvesArea enclosed by a polar curve


Dimension of fractalsThe Sierpinski gasketMandelbrot setFractals in nature and technology


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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

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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

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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

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Advanced Probability

Populations and sample spacesRandom variables and distributionsBinomial distributionPoisson distributionNormal distributionExpectation and varianceLaw of large numbersModelling

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Hypothesis Tests

Designing statistical experimentsHypothesis testsEstimating population mean

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Data Representation

Histograms and frequency tablesScatter plots and regressionMean and standard deviationData collectionData visualisation

Featured Courses

Recreational 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.

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.

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.

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.

Treasure Hunt

Welcome to the most exciting mathematics lesson yet! The treasure hunt consists of ten clues distributed all over the school site, each containing a challenging maths problem.

Fractal Fiction

Alice in Fractalland

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…

Ocean’s Infinity

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?

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Harry Potter and the Mysteries of Space

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.

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