Foundations

Grade 6–8

Intermediate

High School

Advanced

High School

Recreational

Activities and Fun

Coming soon### The Integers

UpdatedWhole number arithmeticNegative numbersThe number lineAbsolute valueInverse operationsOrder of operationsAssociative, commutative and distributive lawDivision by zero

Factors and multiplesPrime numbers and prime factorisationnLCM and HCFDivisibility rules

Coming soon### Fractions

Comparing fractionsSimplifying fractionsAddition and subtractionMultiplication and divisionMixed numbers and improper fractions

Coming soon### Decimals

Decimal notationDecimals on the number lineAddition and subtractionMultiplication and divisionConverting between fractions and decimals

Coming soon### Percentages and Ratios

PercentagesPercentage changeRatio notationCalculating ratios

Coming soon### Exponents and Roots

ExponentsExponent lawsRoots, negative and fractional exponentsRationalising the denominatorRational and irrational numbersApproximating irrational numbers using rationals

Coming soon### Place Value and Rounding

Place valueBig and small numbersOrderingRounding integers and decimalsScientific notationDifferent bases

Coming soon### Proportional Relationships

Direct and inverse proportionsGraphs of proportional relationshipsScale factorsRate of change

Coming soon### Introduction to Algebra

Introduction and historyVariablesWriting, manipulating and evaluating algebraic expressionsModelling using algebra

Coming soon### Linear Equations

Equations and identitiesManipulating and rearranging equationsLinear equations in one variableSolve simultaneous linear equationsLinear inequalities

Coming soon### Linear Functions

Introduction to functionsGraphs of linear equationsIntercepts and slopeParallel and perpendicular lines

Coming soon### Lines and Angles

Points, lines, segments and raysParallel and perpendicular linesAngles and classification (acute, right, obtuse)Adjacent, opposite, alternate and corresponding anglesThe coordinate plane

Coming soon### 2D Shapes

Area and perimeter of triangles and quadrilateralsArea and circumference of circlesSum of angles in polygonsRuler and compass constructionPythagoras’ theoremCongruence and similarity

Coming soon### 3D Solids

Cuboids, prisms and pyramidsCones, cylinders and spheresCavalieri’s principleDensity and weightsNets of 3D solidsCross-sections of 3D objectsModelling the real world

Coming soon### Units and Measuring

Space, time and weight unitsUnit conversionMeasuring angles distances in geometric figuresScale drawings

Coming soon### Basic Probability

IntroductionSimple probability experimentsUnions, intersections and Venn diagramsIndependent and mutually exclusive eventsCalculating probabilitiesTree diagrams

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

History and definitionsCongruenceEuclid’s postulatesStraight-edge and compass constructionsOrigamiApplications

UpdatedReflections, rotations and translationsReflectional and rotational symmetrySymmetry groupsWallpaper symmetriesSimilarity

UpdatedTriangle propertiesMedians, midsegments, incircle and circumcircleTriangle inequalityTriangle congruencePythagoras’ theoremIsosceles and equilateral trianglesTrigonometrySine and cosine rules

UpdatedAngles in polygonsPolygons propertiesQuadrilateralsTessellationsPolyhedraEuler’s FormulaPlatonic and Archimedean solids

Circles and PiTangentsCircle theoremsRadiansSectors and arcsInscribed shapes and anglesSpheres, cones and cylinders

Metric spacesSpherical geometryHyperbolic geometryProjectionsHigher dimensionsTopologyMöbius strip and Klein bottle

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

Coming soon### Polynomials and Factorisation

Adding, subtracting and multiplying polynomialsBinomialsDifference of squaresFactoring simple polynomials

Coming soon### 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

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

Coming soon### Statistics

UpdatedSampling and estimationTables, graphs and histogramsCentral tendency and spreadScatter plots and regressionCorrelation vs causationComparing models and data sets

IntroductionComplete and bipartite graphsKönigsberg bridgesPlanar graphsMap colouringTravelling salesman problemSocial networks and other applications

Coming soon### Codes and Ciphers

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

Coming soon### Algorithms and Computing

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

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

Coming soon### Coordinate Geometry

Equation of lines and circlesDistances and midpointsParallel and perpendicular linesQuadrilaterals and polygons

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

Dimension of fractalsThe Sierpinski gasketMandelbrot setFractals in nature and technology

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

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

These websites, apps and magazines showcase the incredible breadth and beauty 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…

Explore the beautiful world of Origami and Mathematics. Be amazed by stunning photographs, and discover folding instructions and mathematical explanations.

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, 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.

A selection of our favourite mathematical puzzles and problems. Most are very simple to explain, but the solutions require clever and unconventional thinking.

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