Further Maths Exam Questions By Topic

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Year  QuestionsMark Schemes
Y1 FurtherComplex NumbersComplex Numbers – Basic OperationsComplex Numbers – Basic Operations MS
Y1 FurtherComplex NumbersComplex Numbers – Square Roots of Complex NumbersComplex Numbers – Square Roots of Complex Numbers MS
Y1 FurtherComplex NumbersComplex Numbers – The Argand Diagram and LociComplex Numbers – The Argand Diagram and Loci MS
Y1 FurtherMatricesMatrices – Operations, Determinants and InversesMatrices – Operations, Determinants and Inverses MS
Y1 FurtherMatricesMatrices – 3×3 Determinants and InversesMatrices – 3×3 Determinants and Inverses MS
Y1 FurtherMatricesMatrices – Solving Simultaneous EquationsMatrices – Solving Simultaneous Equations MS
Y1 FurtherMatricesMatrices – 2×2 TransformationsMatrices – 2×2 Transformations MS
Y1 FurtherMatricesMatrices – 3×3 TransformationsMatrices – 3×3 Transformations MS
Y1 FurtherMatricesMatrices – Invariant Points and LinesMatrices – Invariant Points and Lines MS
Y1 FurtherProof By InductionProof By Induction (Matrices)Proof By Induction (Matrices) MS
Y1 FurtherProof By InductionProof By Induction (Divisibility)Proof By Induction (Divisibility) MS
Y1 FurtherProof By InductionProof By Induction (Inductive Sequences)Proof By Induction (Inductive Sequences) MS
Y1 FurtherProof By InductionProof By Induction (Inequalities)Proof By Induction (Inequalities) MS
Y1 FurtherRoots of PolynomialsRoots of PolynomialsRoots of Polynomials MS
Y1 FurtherVectorsVectorsVectors MS
Y2 FurtherCalculusDifferentiation of Inverse Trigonometric and Hyperbolic FunctionsDifferentiation of Inverse Trigonometric and Hyperbolic Functions MS
Y2 FurtherCalculusIntegration Involving Trigonometric and Hyperbolic FunctionsIntegration Involving Trigonometric and Hyperbolic Functions MS
Y2 FurtherCalculusVolumes of RevolutionVolumes of Revolution MS
Y2 FurtherCalculusImproper IntegralsImproper Integrals MS
Y2 FurtherCalculusPartial Fractions and IntegrationPartial Fractions and Integration MS
Y2 FurtherComplex NumbersComplex Roots Of Equations and Using Exponential and Polar FormComplex Roots Of Equations and Using Exponential and Polar Form MS
Y2 FurtherComplex NumbersDeMoivre’s Theorem and Applications To TrigonometryDeMoivre’s Theorem and Applications To Trigonometry MS
Y2 FurtherProof By InductionSummations (Proof By Induction)Summations (Proof By Induction) MS
Y2 FurtherProof By InductionProof By Induction (Challenging)Proof By Induction (Challenging) MS
Y2 FurtherDifferential EquationsFirst Order Differential EquationsFirst Order Differential Equations MS
Y2 FurtherDifferential EquationsFirst Order Differential Equations Involving SubstitutionsFirst Order Differential Equations Involving Substitutions MS
Y2 FurtherDifferential EquationsSecond Order Differential EquationsSecond Order Differential Equations MS
Y2 FurtherDifferential EquationsApplied First Order Differential EquationsApplied First Order Differential Equations MS
Y2 FurtherDifferential EquationsSimple, Forced and Damped Harmonic MotionSimple, Forced and Damped Harmonic Motion MS
Y2 FurtherDifferential EquationsCoupled Simultaneous First Order Differential EquationsCoupled Simultaneous First Order Differential Equations MS
Y2 FurtherHyperbolicsHyperbolic Identities and EquationsHyperbolic Identities and Equations MS
Y2 FurtherSeriesSummations (Proof By Induction)Summations (Proof By Induction) MS
Y2 FurtherSeriesSummations (Method Of Differences)Summations (Method Of Differences) MS
Y2 FurtherSeriesSummations (Standard Formulae)Summations (Standard Formulae) MS
Y2 FurtherSeriesMaclaurin ExpansionMaclaurin Expansion MS
Y2 FurtherVectorsLines and Planes (Equations, Angles Between and Intersection)Lines and Planes (Equations, Angles Between and Intersection) MS
Y2 FurtherVectorsPolar CoordinatesPolar Coordinates MS
Y2 FurtherVectorsDistance Between Planes and LinesDistance Between Planes and Lines MS
Y2 FurtherVectors and MatricesMatrices, Simultaneous Equations and Applications to Intersections of PlanesMatrices, Simultaneous Equations and Applications to Intersections of Planes MS

YearStrand  QuestionsMark Schemes
Y1 FurtherMechCircular MotionHorizontal Circular MotionHorizontal Circular Motion MS
Y1 FurtherMechCircular MotionVertical Circular MotionVertical Circular Motion MS
Y1 FurtherMechCollisionsConservation of MomentumConservation of Momentum MS
Y1 FurtherMechCollisionsCoefficient of RestitutionCoefficient of Restitution MS
Y1 FurtherMechDimensional AnalysisDimensional AnalysisDimensional Analysis MS
Y1 FurtherMechWork, Energy and PowerWork, Energy and PowerWork, Energy and Power MS
Y2 FurtherMechCentres of MassCentres Of MassCentres Of Mass MS
Y2 FurtherMechCentres of MassCentres of Mass Involving IntegrationCentres of Mass Involving Integration MS
Y2 FurtherMechCircular MotionProblem Solving With Circular MotionProblem Solving With Circular Motion MS
Y2 FurtherMechCollisionsOblique CollisionsOblique Collisions MS
Y2 FurtherMechDifferential EquationsLinear Motion With Variable AccelerationLinear Motion With Variable Acceleration MS
Y2 FurtherMechForces and EnergyHooke’s LawHooke’s Law MS
Y1 FurtherStatsCombinatoricsPermutations and CombinationsPermutations and Combinations MS
Y1 FurtherStatsDistributionsDiscrete Random VariablesDiscrete Random Variables MS
Y1 FurtherStatsDistributionsExpectation and Variance of Linear Transformations of Discrete Random VariablesExpectation and Variance of Linear Transformations of Discrete Random Variables MS
Y1 FurtherStatsDistributionsBinomial DistributionBinomial Distribution MS
Y1 FurtherStatsDistributionsGeometric DistributionGeometric Distribution MS
Y1 FurtherStatsDistributionsDiscrete Uniform DistributionDiscrete Uniform Distribution MS
Y1 FurtherStatsDistributionsPoisson DistributionPoisson Distribution MS
Y1 FurtherStatsHypothesis TestingChi Squared Tests (Contingency Tables)Chi Squared Tests (Contingency Tables) MS
Y1 FurtherStatsHypothesis TestingChi Squared Tests (Goodness of Fit) (Year 1)Chi Squared Tests (Goodness of Fit) (Year 1) MS
Y1 FurtherStatsHypothesis Testing and Linear RegressionHypothesis Tests for Linear CorrelationHypothesis Tests for Linear Correlation MS
Y1 FurtherStatsLinear RegressionLeast Squares Regression LineLeast Squares Regression Line MS
Y2 FurtherStatsConfidence IntervalsConfidence Intervals for the Mean of a Sampling DistributionConfidence Intervals for the Mean of a Sampling Distribution MS
Y2 FurtherStatsDistributionsGeometric Distribution Questions (with Year 2 Content)Geometric Distribution Questions (with Year 2 Content) MS
Y2 FurtherStatsDistributionsContinuous Random Variables (Mean, Variance and Median)Continuous Random Variables (Mean, Variance and Median) MS
Y2 FurtherStatsDistributionsContinuous Random Variables (Cumulative Distributions)Continuous Random Variables (Cumulative Distributions) MS
Y2 FurtherStatsDistributionsContinuous Uniform DistributionContinuous Uniform Distribution MS
Y2 FurtherStatsDistributionsContinuous Random Variables (Functions of CRVs)Continuous Random Variables (Functions of CRVs) MS
Y2 FurtherStatsDistributionsExponential DistributionExponential Distribution MS
Y2 FurtherStatsDistributionsCombinations of Continuous Random VariablesCombinations of Continuous Random Variables MS
Y2 FurtherStatsHypothesis TestingChi Squared Tests (Goodness of Fit) (Year 2)Chi Squared Tests (Goodness of Fit) (Year 2) MS
Y2 FurtherStatsHypothesis TestingSingle Sample and Paired Sample Sign TestsSingle Sample and Paired Sample Sign Tests MS
Y2 FurtherStatsHypothesis TestingWilcoxon Single Sample and Paired Sample Hypothesis TestsWilcoxon Single Sample and Paired Sample Hypothesis Tests MS
Y2 FurtherStatsHypothesis TestingWilcoxon Rank Sum TestsWilcoxon Rank Sum Tests MS
Y2 FurtherStatsHypothesis TestingUsing Central Limit TheoremUsing Central Limit Theorem MS
Y2 FurtherStatsHypothesis TestingHypothesis Tests Requiring Unbiased Estimators and Central Limit TheoremHypothesis Tests Requiring Unbiased Estimators and Central Limit Theorem MS

UnitTopicQuestion LinkMS Link
FS1Discrete Random VariablesDiscrete Random VariablesMS
FS1Expectation and Variance of Linear Transformations of Discrete Random VariablesExpectation and Variance of Linear Transformations of Discrete Random VariablesMS
FS1Binomial DistributionBinomial DistributionMS
FS1Poisson DistributionPoisson DistributionMS
FS1Poisson Approximations to a Binomial DistributionPoisson Approximations to a Binomial DistributionMS
FS1Hypothesis Tests for Mean of a Poisson DistributionHypothesis Tests for Mean of a Poisson DistributionMS
FS1Geometric DistributionGeometric DistributionMS
FS1Hypothesis Tests for p in a Geometric DistributionComing Soon
FS1Negative Binomial DistributionComing Soon
FS1Central Limit TheoremCentral Limit TheoremMS
FS1Chi Squared Tests for Goodness of FitChi Squared Tests for Goodness of FitMS
FS1Chi-Squared Tests on Contingency TablesChi-Squared Tests on Contingency TablesMS
FS1Probability Generating FunctionsProbability Generating FunctionsMS
FS1Quality of Hypothesis TestsQuality of Hypothesis TestsMS
FS2Least Squares Regression LineLeast Squares Regression LineMS
FS2Hypothesis Tests for Linear CorrelationHypothesis Tests for Linear CorrelationMS
FS2Continuous Random Variables (Mean, Variance and Median)Continuous Random Variables (Mean, Variance and Median)MS
FS2Continuous Random Variables (Cumulative Distributions)Continuous Random Variables (Cumulative Distributions)MS
FS2Combinations of Continuous Random VariablesCombinations of Continuous Random VariablesMS
FS2EstimationComing Soon
FS2Further Hypothesis TestsComing Soon
FS2Confidence Intervals and the t-DistributionComing Soon
FM1Conservation of MomentumConservation of MomentumMS
FM1Work, Energy and PowerWork, Energy and PowerMS
FM1Hooke’s LawHooke’s LawMS
FM1Coefficient of RestitutionCoefficient of RestitutionMS
FM1Oblique CollisionsOblique CollisionsMS
FM2Horizontal Circular MotionHorizontal Circular MotionMS
FM2Vertical Circular MotionVertical Circular MotionMS
FM2Problem Solving With Circular MotionProblem Solving With Circular MotionMS
FM2Centres Of MassCentres Of MassMS
FM2Centres of Mass Involving IntegrationCentres of Mass Involving IntegrationMS
FM2Centres of Mass with Variable Density Involving IntegrationComing Soon
FM2Linear Motion With Variable AccelerationLinear Motion With Variable AccelerationMS
FM2DynamicsComing Soon

These questions are only partially complete. Over the coming academic year more relevant content will appear.

UnitLevelTopicQuestion LinkMS Link
MechMajorHorizontal Circular MotionHorizontal Circular MotionMS
MechMajorVertical Circular MotionVertical Circular MotionMS
MechMinorConservation of MomentumConservation of MomentumMS
MechMajorCoefficient of RestitutionCoefficient of RestitutionMS
MechMinorDimensional AnalysisDimensional AnalysisMS
MechMinorForcesComing Soon
MechMinorWork, Energy and PowerWork, Energy and PowerMS
MechMinorCentres of Mass of Systems of Particles and ShapesComing Soon
MechMajorCentres Of MassCentres Of MassMS
MechMajorCentres of Mass Involving IntegrationCentres of Mass Involving IntegrationMS
MechMajorProblem Solving With Circular MotionProblem Solving With Circular MotionMS
MechMajorOblique CollisionsOblique CollisionsMS
MechMajorLinear Motion With Variable AccelerationLinear Motion With Variable AccelerationMS
MechMajorHooke’s LawHooke’s LawMS
StatsMinorDiscrete Random VariablesDiscrete Random VariablesMS
StatsMinorExpectation and Variance of Linear Transformations of Discrete Random VariablesExpectation and Variance of Linear Transformations of Discrete Random VariablesMS
StatsMinorBinomial DistributionBinomial DistributionMS
StatsMinorGeometric DistributionGeometric DistributionMS
StatsMinorDiscrete Uniform DistributionDiscrete Uniform DistributionMS
StatsMinorPoisson DistributionPoisson DistributionMS
StatsMinorChi Squared Tests (Contingency Tables)Chi Squared Tests (Contingency Tables)MS
StatsMinorChi Squared Tests (Goodness of Fit)Chi Squared Tests (Goodness of Fit)MS
StatsMinorHypothesis Tests for Linear CorrelationHypothesis Tests for Linear CorrelationMS
StatsMinorLeast Squares Regression LineLeast Squares Regression LineMS
StatsMinorConfidence Intervals for the Sampling Mean of a Normal DistributionConfidence Intervals for the Sampling Mean of a Normal DistributionMS
StatsMajorContinuous Random Variables (Mean, Variance and Median)Continuous Random Variables (Mean, Variance and Median)MS
StatsMajorContinuous Random Variables (Cumulative Distributions)Continuous Random Variables (Cumulative Distributions)MS
StatsMajorContinuous Uniform DistributionContinuous Uniform DistributionMS
StatsMajorExponential DistributionExponential DistributionMS
StatsMajorCombinations of Continuous Random VariablesCombinations of Continuous Random VariablesMS
StatsMajorUsing Central Limit TheoremUsing Central Limit TheoremMS
StatsMajorHypothesis Tests Requiring Unbiased Estimators and Central Limit TheoremHypothesis Tests Requiring Unbiased Estimators and Central Limit TheoremMS
StatsMajorT-Distribution

Work in progress…