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:

NumberAlgebraQuadraticsGraphsRatio and ProportionGeometry and MeasuresProbabilityStatistics

…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

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