Course Library
Foundations
Grade 6–8
Intermediate
High School
Advanced
High School
Recreational
Activities and Fun
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 multiplesDivisibility rulesPrime numbers and prime factorisationnLowest common multiple and Greatest common divisor
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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
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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
Geometry
Euclidean Geometry
History and definitionsCongruenceEuclid’s postulatesStraight-edge and compass constructionsOrigamiApplications
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Transformations and Symmetry
Reflections, rotations and translationsReflectional and rotational symmetrySymmetry groupsWallpaper symmetriesSimilarity
Triangles and Trigonometry
Triangle propertiesMedians, midsegments, incircle and circumcircleTriangle inequalityTriangle congruencePythagoras’ theoremIsosceles and equilateral trianglesTrigonometrySine and cosine rules
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Polygons and Polyhedra
Angles in polygonsPolygons propertiesQuadrilateralsTessellationsPolyhedraEuler’s FormulaPlatonic and Archimedean solids
Circles and Pi
Circles and PiRadiansChords, arcs and tangentsCircle theoremsInscribed shapes and anglesSpheres, cones and cylindersConic sections
Non-Euclidean Geometry
Metric spacesSpherical geometryHyperbolic geometryProjectionsHigher dimensionsTopologyMöbius strip and Klein bottle
Algebra
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Sequences and Patterns
Triangle, square and cube numbersLinear and quadratic sequencesFibonacci numbersPerfect numbersArithmetic and geometric sequencesRecursive equationsPascal’s triangle
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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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PreviewPolynomials and Factorisation
Adding, subtracting and multiplying polynomialsBinomialsDifference of squaresFactoring simple polynomials
Quadratics
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
Probability and Discrete Mathematics
Probability
IntroductionCoins, dice and rouletteVenn diagrams and probability treesIndependent and mutually exclusive eventsConditional probabilityThe Monty Hall problemRandomness
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FeaturedStatistics
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
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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
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Sequences and series
Binomial expansion of (a + bx)^nRecurrence relationsArithmetic and geometric seriesSigma notationMaclaurin seriesConvergence and divergence
Geometry, Trigonometry and Matrices
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Coordinate Geometry
Equation of lines and circlesDistances and midpointsParallel and perpendicular linesQuadrilaterals and polygons
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Conic Sections
Equation of a circleEllipsesParabolae and hyperbolaeKepler’s laws and planetary orbits
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Trigonometry
Unit circle definitionsTrigonometric functions and their graphsAmplitude and frequencyPythagorean identitiesDouble angle and addition formulasSecant, cosecant and cotangentInverse trigonometric functionsSimple trigonometric equationsHyperbolic functions
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Vectors
IntroductionMagnitude and directionVector arithmeticPosition vectorsScalar productEquation of lines and planes
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Matrices
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
Fractals
Dimension of fractalsThe Sierpinski gasketMandelbrot setFractals in nature and technology
Calculus
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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
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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
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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
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Chaos Theory
Double PendulumsThree body problemLogistic MapStrange AttractorsButterfly effectChaotic scattering
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
Applications of Mathematics
Learn about the countless hidden applications which mathematics has in everyday life: from computers to weather prediction, video games, medicine, sports and music.
Mathematical Origami
Explore the beautiful world of Origami and mathematics. Be amazed by stunning photographs, try our folding instructions, or learn about the mathematical background.
Simon Singh’s Parallel
A weekly collection of fun and challenging exercises, designed to encourage young mathematicians to explore mathematics, written by bestselling author Simon Singh.
When Alice falls down the rabbit hole, she discovers curious and wonderful mathematics: Pascal’s triangle on a colour changing floor, sequences of rabbit generations, and beautiful, never-ending fractals
Exploding Dots
Exploding Dots is an astounding mathematical story developed for the 2018 Global Math Week. Join millions of students and teachers in learning about place value, infinity and p-adic numbers.
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.
Treasure Hunt
Here is the most exciting mathematics lesson yet! This treasure hunt consists of ten clues distributed all over the school site, each containing a challenging maths puzzle.
Problems and Puzzles
A selection of our favourite mathematical puzzles and problems. Most are simple to understand, but the solutions require clever and unconventional thinking.
Ocean’s Infinity
How do you get infinitely rich without anyone noticing? By robbing a hotel with infinitely many rooms. In this slideshow, Danny Ocean will share all his underworld secrets…
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