Further Maths Exam Questions By Topic

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YearQuestions
Y1Complex Numbers – Basic Operations
Y1Complex Numbers – Square Roots of Complex Numbers
Y1Complex Numbers – The Argand Diagram and Loci
Y1Matrices – Operations, Determinants and Inverses
Y1Matrices – 3×3 Determinants and Inverses
Y1Matrices – Solving Simultaneous Equations
Y1Matrices – 2×2 Transformations
Y1Matrices – 3×3 Transformations
Y1Matrices – Invariant Points and Lines
Y1Proof By Induction – Matrices
Y1Proof By Induction – Divisibility
Y1Proof By Induction – Inductive Sequences
Y1Proof By Induction – Inequalities
Y1Roots of Polynomials
Y1Vectors
Y2Differentiation of Inverse Trigonometric and Hyperbolic Functions
Y2Integration Involving Trigonometric and Hyperbolic Functions
Y2Volumes of Revolution
Y2Improper Integrals
Y2Partial Fractions and Integration
Y2Complex Roots Of Equations and Using Exponential and Polar Form
Y2DeMoivre’s Theorem and Applications To Trigonometry
Y2Summations – Proof By Induction
Y2Proof By Induction – Challenging
Y2First Order Differential Equations
Y2First Order Differential Equations Involving Substitutions
Y2Second Order Differential Equations
Y2Applied First Order Differential Equations
Y2Simple, Forced and Damped Harmonic Motion
Y2Coupled Simultaneous First Order Differential Equations
Y2Hyperbolic Identities and Equations
Y2Summations – Proof By Induction
Y2Summations – Method Of Differences
Y2Summations – Standard Formulae
Y2Maclaurin Expansion
Y2Lines and Planes – Equations, Angles Between and Intersection
Y2Polar Coordinates
Y2Distance Between Planes and Lines
Y2Matrices, Simultaneous Equations and Applications to Intersections of Planes
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-DistributionComing Soon

Work in progress…