Whole number arithmeticNegative numbersThe number lineAbsolute valueInverse operationsOrder of operationsAssociative, commutative and distributive lawDivision by zero
Prime numbers represent both the most basic properties and the most complex unsolved problems. Here you can learn about the building blocks of mathematics.
Comparing fractionsSimplifying fractionsAddition and subtractionMultiplication and divisionMixed numbers and improper fractions
Decimal notationDecimals on the number lineAddition and subtractionMultiplication and divisionConverting between fractions and decimals
PercentagesPercentage changeRatio notationCalculating ratios
ExponentsExponent lawsRoots, negative and fractional exponentsRationalising the denominatorRational and irrational numbersApproximating irrational numbers using rationals
Place valueBig and small numbersOrderingRounding integers and decimalsScientific notationDifferent bases
Direct and inverse proportionsGraphs of proportional relationshipsScale factorsRate of change
Introduction and historyVariablesWriting, manipulating and evaluating algebraic expressionsModelling using algebra
Equations and identitiesManipulating and rearranging equationsLinear equations in one variableSolve simultaneous linear equationsLinear inequalities
Introduction to functionsGraphs of linear equationsIntercepts and slopeParallel and perpendicular lines
Points, lines, segments and raysParallel and perpendicular linesAngles and classification (acute, right, obtuse)Adjacent, opposite, alternate and corresponding anglesThe coordinate plane
Area and perimeter of triangles and quadrilateralsArea and circumference of circlesSum of angles in polygonsRuler and compass constructionPythagoras’ theoremCongruence and similarity
Cuboids, prisms and pyramidsCones, cylinders and spheresCavalieri’s principleDensity and weightsNets of 3D solidsCross-sections of 3D objectsModelling the real world
Space, time and weight unitsUnit conversionMeasuring angles distances in geometric figuresScale drawings
IntroductionSimple probability experimentsUnions, intersections and Venn diagramsIndependent and mutually exclusive eventsCalculating probabilitiesTree diagrams
FactorialsPermutations and combinationsProbabilityRandom Walks
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 is one of the oldest parts of mathematics – and one of the most useful. Its logical, systematic approach has been copied in many other areas.
Symmetry can be seen everywhere in nature – but it also underlies completely invisible laws of nature. Mathematics can explain why that is the case.
Triangles are some of the most important shapes in geometry: they have countless interesting properties and appear everywhere in engineering and technology.
Geometric shapes are everywhere around us. In this course you will learn about angels, polygons, tessellations, polyhedra and nets.
Circles and PiRadiansChords, arcs and tangentsCircle theoremsInscribed shapes and anglesSpheres, cones and cylindersConic sectionsPreview
Metric spacesSpherical geometryHyperbolic geometryProjectionsHigher dimensionsTopologyMöbius strip and Klein bottle
Learn about some of the most fascinating patterns in mathematics, from triangle numbers to the Fibonacci sequence and Pascal’s triangle.
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
Adding, subtracting and multiplying polynomialsBinomialsDifference of squaresFactoring simple polynomials
Solving quadratic equationsCompleting the squareThe quadratic formulaParabolaeStandard and vertex formTransforming parabolae
Linear inequalitiesQuadratic inequalitiesGraphing two-variable inequalitiesSystems of equations with two unknownsElimination and substitution methods
Exponents, radicals and rational expressionsSquare and cube root equationsRadical functionsExponential growth and decayLinear vs exponential models
Cards, dice, roulette and game shows: probability is one of the most fun areas of mathematics, full of surprises and real life applications.
Sampling and estimationTables, graphs and histogramsCentral tendency and spreadScatter plots and regressionCorrelation vs causationComparing models and data sets
Discover the mathematical principles that connect our world: from shaking hands to travel and navigation, colouring maps and social networks.
Simple codes and MorseError detection and correctionOne time padsThe Caesar and Vigenère cipherThe EnigmaRSA cryptography
Combinatorial games and NimTree diagramsPrisoners’ paradoxGames based on chanceThe lottery
Introduction to computingComputational complexity and the O() notationSorting algorithmsLinear programming and the simplex algorithmData structuresGraphs, trees and networks
Set theoryLogic and proofProof by contradictionProof by induction
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
Manipulating rational expressionsSystems of quadratic equationsLinear and quadratic inequalitiesPartial fraction expansionPolynomialsPolynomial divisionFactor and remainder theoremBinomial theoremFundamental theorem of algebraSolve polynomial equations up to quartics
Combining and composing functionsInverse functionsFunction transformations (shifting and stretching)Polynomial functionsRational functions and discontinuitiesLimit behaviour of polynomial and rational functionsGraph sketching
Exponential equationsExponential growth and decayIntroduction to LogarithmsThe natural logarithm and eLogarithmic equationsGraphs of exponential and logarithmic functionsLogarithmic scale
Change of sign methodsInterval bisectionNewton-Raphson method
Binomial expansion of (a + bx)^nRecurrence relationsArithmetic and geometric seriesSigma notationMaclaurin seriesConvergence and divergence
Equation of lines and circlesDistances and midpointsParallel and perpendicular linesQuadrilaterals and polygons
Equation of a circleEllipsesParabolae and hyperbolaeKepler’s laws and planetary orbits
Unit circle definitionsTrigonometric functions and their graphsAmplitude and frequencyPythagorean identitiesDouble angle and addition formulasSecant, cosecant and cotangentInverse trigonometric functionsSimple trigonometric equationsHyperbolic functions
IntroductionMagnitude and directionVector arithmeticPosition vectorsScalar productEquation of lines and planes
IntroductionMatrix arithmeticMatrix multiplictionMatrices as transformationsDeterminantsMatrix inversesLinear systems of equationsGaussian elimination
Parametric curvesConversion between polar and cartesianSketching polar curvesArea enclosed by a polar curve
Dimension of fractalsThe Sierpinski gasketMandelbrot setFractals in nature and technology
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
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
First order differential equationsSeparable equationsLogistic mapSecond order differential equationsHomogenous equations and particular integralCoupled differential equationsSimple harmonic motion and dampened oscillators
Double PendulumsThree body problemLogistic MapStrange AttractorsButterfly effectChaotic scattering
Populations and sample spacesRandom variables and distributionsBinomial distributionPoisson distributionNormal distributionExpectation and varianceLaw of large numbersModelling
Designing statistical experimentsHypothesis testsEstimating population mean
Histograms and frequency tablesScatter plots and regressionMean and standard deviationData collectionData visualisation