This website is built as a free resource to help everyone understand school level maths, especially those in resource poor settings. It was started by Jonas Thornhill as part of his Duke of Edinburgh Award and developed with the assistance of Google Gemini AI and Claude on GitHub using Jekyll and the Just the Docs theme.
Explore GCSE Maths
Every topic, with full notes, worked examples and practice questions with answers. Pick a topic:
…or jump straight to any of the 113 subtopics
Overview of NumbersAlgebra OverviewQuadratics OverviewGraphs OverviewRatio OverviewGeometry OverviewProbability OverviewStatistics OverviewBIDMAS / BODMASMultiplying BracketsFactorising QuestionsStraight Line GraphsUnits and Compound UnitsConventions and NotationTables and Frequency TreesSampling and PopulationsBIDMAS MisconceptionsChanging the SubjectFactorising AnswersGraphical InequalitiesScale Drawings and MapsConstructions and LociExpected OutcomesCharts and DiagramsPowers and RootsEquationsThe Quadratic FormulaGraphs of FunctionsOne Quantity as a FractionAngle Rules and PolygonsThe Probability ScaleHistograms and Cumulative FrequencyPrime NumbersAlgebraic FractionsFormula Cheat SheetRoots and Turning PointsRatio NotationTriangles and QuadrilateralsMutually Exclusive EventsAverages, Spread and Box PlotsFractions and DecimalsInequalitiesFormula QuestionsTranslations and ReflectionsSharing in a RatioCongruent TrianglesExperimental ProbabilityDescribing a PopulationRecurring DecimalsAlgebraic ManipulationFormula AnswersReal World GraphsMultiplicative RelationshipsGeometric ProofListing and Venn DiagramsScatter Graphs and CorrelationPercentagesIdentities and ProofsFormula ChecklistGraphs of CirclesProportion as Equal RatiosTransformationsSample Space DiagramsFactors and MultiplesSimultaneous EquationsCompleting the SquareRatios and Linear FunctionsCombined TransformationsTree DiagramsPrime FactorsSimultaneous QuadraticsCompleting the Square QuestionsPercentage ChangeParts of a CircleConditional ProbabilitySystematic ListingFunctionsCompleting the Square AnswersDirect and Inverse ProportionCircle TheoremsSurdsMore FunctionsAdvanced QuestionsCompound MeasuresCoordinate GeometryStandard FormIterative MethodsAdvanced AnswersSimilar Shapes3D ShapesStandard UnitsMore Iterative MethodsEquations of ProportionPlans and ElevationsRounding and AccuracySequencesGradient as a Rate of ChangeUnits of MeasureLimits of AccuracyMore SequencesInstantaneous Rates of ChangeMeasuring and BearingsGrowth and DecayArea and Volume FormulaeSurface Area and VolumeArcs and SectorsCongruence and SimilarityPythagoras and TrigonometryExact Trig ValuesSine and Cosine RulesVectors and TranslationsVector ArithmeticVector Proof
Explore FSMQ Additional Maths
The full OCR Level 3 FSMQ: Additional Maths (6993) course, with notes, worked examples and practice questions with answers:
AlgebraEnumerationCoordinate GeometryPythagoras and TrigonometryCalculusNumerical MethodsExponentials and Logarithms
…or jump straight to any of the 47 FSMQ pages
Algebra OverviewEnumeration OverviewCoordinate Geometry OverviewTrigonometry OverviewCalculus OverviewNumerical Methods OverviewExponentials and Logarithms OverviewAlgebraic ManipulationThe Binomial ExpansionStraight LinesRatios of Any AngleDifferentiationChange of SignExponential FunctionsPolynomials and the Factor TheoremThe Product Rule for CountingThe Geometry of CirclesThe Sine and Cosine RulesTangents and Normals by CalculusIterative MethodsLogarithms and Their LawsCompleting the SquarePermutationsSketching CurvesTrigonometric IdentitiesStationary PointsGradients from ChordsSolving Exponential EquationsSetting Up and Solving EquationsCombinationsTangents and NormalsTrigonometric EquationsMaximum and Minimum ProblemsEstimating AreasReduction to Linear FormLinear and Quadratic InequalitiesRepresenting OutcomesLinear Programming2-D and 3-D ProblemsIntegrationNumerical Methods in ContextGrowth and DecayInequalities in Two VariablesCounting in ProbabilityAreas Under and Between CurvesRecurrence RelationshipsApplication to Kinematics
Explore A Level Maths Year 1
The first year of A Level Mathematics — pure, statistics and mechanics — with notes, worked examples and practice questions with answers:
ProofAlgebra and FunctionsCoordinate GeometryTrigonometryExponentials and LogarithmsDifferentiationIntegrationVectorsStatisticsProbability and DistributionsHypothesis TestingMechanics
…or jump straight to any of the 53 Year 1 pages
Proof OverviewAlgebra OverviewCoordinate Geometry OverviewTrigonometry OverviewExponentials and Logarithms OverviewDifferentiation OverviewIntegration OverviewVectors OverviewStatistics OverviewProbability OverviewHypothesis Testing OverviewMechanics OverviewProof by Deduction and ExhaustionIndices and SurdsStraight LinesSine and Cosine RulesExponential Functions and eDifferentiation from First PrinciplesIndefinite IntegrationVectors in Two DimensionsStatistical SamplingProbability and Venn DiagramsThe Language of Hypothesis TestingQuantities, Units and ModellingDisproof by Counter-exampleQuadratic FunctionsCirclesTrigonometric GraphsLogarithms and Their LawsDifferentiating Powers of xDefinite Integrals and AreasVector GeometryPresenting DataThe Binomial DistributionBinomial Hypothesis TestsMotion GraphsSimultaneous EquationsTrigonometric IdentitiesExponential and Log EquationsTangents and NormalsMeasures of Location and SpreadConstant Acceleration (suvat)Linear and Quadratic InequalitiesTrigonometric EquationsExponential ModellingStationary Points and OptimisationCorrelation and OutliersVariable AccelerationPolynomials and the Factor TheoremForces and Newton's LawsCurve Sketching and ProportionTransformations of GraphsThe Binomial Expansion
Explore A Level Maths Year 2
The second year of A Level Mathematics, completing the full course:
ProofAlgebra and FunctionsParametric EquationsSequences and SeriesTrigonometryDifferentiationIntegrationNumerical MethodsVectorsStatisticsHypothesis TestingMechanics
…or jump straight to any of the 56 Year 2 pages
Proof OverviewAlgebra OverviewParametric Equations OverviewSequences and Series OverviewTrigonometry OverviewDifferentiation OverviewIntegration OverviewNumerical Methods OverviewVectors OverviewStatistics OverviewHypothesis Testing OverviewMechanics OverviewProof by ContradictionAlgebraic and Partial FractionsParametric and Cartesian FormsSequences and Sigma NotationRadians, Arcs and SectorsExponentials, Logs and TrigStandard IntegralsLocating RootsVectors in Three DimensionsRegression and Exponential ModelsTesting for CorrelationMomentsThe Modulus FunctionParametric ModellingArithmetic Sequences and SeriesSmall Angle ApproximationsChain, Product and Quotient RulesIntegration by SubstitutionIterationConditional ProbabilityTesting a Normal MeanResolving Forces and Inclined PlanesComposite and Inverse FunctionsGeometric Sequences and SeriesReciprocal and Inverse FunctionsImplicit and Parametric DifferentiationIntegration by PartsThe Newton-Raphson MethodThe Normal DistributionFrictionCombined TransformationsThe General Binomial ExpansionCompound and Double AnglesConcavity and Points of InflectionIntegrating with Partial FractionsThe Trapezium RuleChoosing a DistributionProjectilesThe R cos(x + a) FormConnected Rates of ChangeAreas and Integration as a LimitKinematics with Calculus and VectorsTrigonometric Proof and ModellingDifferential Equations
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