Coming soon### The Integers

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

Factors and multiplesDivisibility rulesPrime numbers and prime factorisationnLowest common multiple and Greatest common divisor

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

PreviewIntroductionSimple 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

Reflections, rotations and translationsReflectional and rotational symmetrySymmetry groupsWallpaper symmetriesSimilarity

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

Angles in polygonsPolygons propertiesQuadrilateralsTessellationsPolyhedraEuler’s FormulaPlatonic and Archimedean solids

Circles and PiRadiansChords, arcs and tangentsCircle theoremsInscribed shapes and anglesSpheres, cones and cylindersConic sections

PreviewMetric 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

PreviewAdding, subtracting and multiplying polynomialsBinomialsDifference of squaresFactoring simple polynomials

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

Sampling 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

PreviewSimple 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

Coming soon### Imaginary and Complex Numbers

PreviewIntroductionComplex 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

Coming soon### 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

PreviewParametric 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

PreviewFirst 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

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