Further Maths Exam Questions By Topic | A Level Maths Revision

Further Maths exam questions by topic are one of the most effective ways to prepare for A Level Further Maths exams. Practising questions organised by topic helps you build confidence with individual techniques, identify weak areas, and develop the problem-solving skills needed for the most challenging examination questions.

This page brings together a growing collection of Further Maths questions arranged by topic, helping you revise Core Pure, Further Statistics, Further Mechanics and Further Decision in a structured way. Each topic includes carefully selected questions, mark schemes and worked solutions where available, allowing you to practise independently and check your understanding step-by-step.

For the best revision results, topic-based exam practice should be combined with learning the underlying theory and completing full past papers under timed conditions. Alongside these Further Maths questions by topic, you may also find the following pages useful:

Further Maths Past Papers — complete exam papers and mark schemes for realistic exam practice
Further Maths Revision Notes — concise summaries of key Further Maths methods and concepts
Further Maths Video Tutorials — worked exam question videos and topic walkthroughs

Many students use this page as part of a wider revision journey: first learning a topic, then practising individual skills through worksheets and revision notes, followed by targeted exam questions, before finally attempting full Further Maths past papers under exam conditions.

Pure Core (All Exam boards)


Year	Exam Board	Strand	Topic	Title	Sheet 1 (From OCR)	Sheet 2 (From Edexcel)
1	All	Pure Core	Complex Numbers	Complex Numbers – Basic Operations	Questions Mark Scheme Worked Solutions	Questions Mark Scheme Worked Solutions
1	All	Pure Core	Complex Numbers	Complex Numbers – Square Roots of Complex Numbers	Questions Mark Scheme Worked Solutions	Not available
1	All	Pure Core	Complex Numbers	Complex Numbers – The Argand Diagram and Loci	Questions Mark Scheme Worked Solutions	Questions Mark Scheme Worked Solutions
1	All	Pure Core	Matrices	Matrices – 2×2 Transformations	Questions Mark Scheme Worked Solutions	Questions Mark Scheme Worked Solutions
1	All	Pure Core	Matrices	Matrices – 3×3 Determinants and Inverses	Questions Mark Scheme Worked Solutions	Questions Mark Scheme Worked Solutions
1	All	Pure Core	Matrices	Matrices – 3×3 Transformations	Questions Mark Scheme Worked Solutions	Questions Mark Scheme Worked Solutions
1	All	Pure Core	Matrices	Matrices – Invariant Points and Lines	Questions Mark Scheme Worked Solutions	Questions Mark Scheme Worked Solutions
1	All	Pure Core	Matrices	Matrices – Operations, Determinants and Inverses	Questions Mark Scheme Worked Solutions	Questions Mark Scheme Worked Solutions
1	All	Pure Core	Matrices	Matrices – Solving Simultaneous Equations	Questions Mark Scheme Worked Solutions	Questions Mark Scheme Worked Solutions
1	All	Pure Core	Proof By Induction	Proof By Induction (Divisibility)	Questions Mark Scheme Worked Solutions	Questions Mark Scheme Worked Solutions
1	All	Pure Core	Proof By Induction	Proof By Induction (Inductive Sequences)	Questions Mark Scheme Worked Solutions	Not available
1	All	Pure Core	Proof By Induction	Proof By Induction (Inequalities)	Questions Mark Scheme Worked Solutions	Not available
1	All	Pure Core	Proof By Induction	Proof By Induction (Matrices)	Questions Mark Scheme Worked Solutions	Questions Mark Scheme Worked Solutions
1	All	Pure Core	Roots of Polynomials	Roots of Polynomials	Questions Mark Scheme Worked Solutions	Questions Mark Scheme Worked Solutions
1	All	Pure Core	Vectors	Vectors	Questions Mark Scheme Worked Solutions	Questions Mark Scheme Worked Solutions
2	All	Pure Core	Calculus	Differentiation of Inverse Trigonometric and Hyperbolic Functions	Questions Mark Scheme Worked Solutions	Questions Mark Scheme Worked Solutions
2	All	Pure Core	Calculus	Improper Integrals	Questions Mark Scheme Worked Solutions	Questions Mark Scheme Worked Solutions
2	All	Pure Core	Calculus	Integration Involving Trigonometric and Hyperbolic Functions	Questions Mark Scheme Worked Solutions	Questions Mark Scheme Worked Solutions
2	All	Pure Core	Calculus	Partial Fractions and Integration	Questions Mark Scheme Worked Solutions	Not available
2	All	Pure Core	Calculus	Volumes of Revolution	Questions Mark Scheme Worked Solutions	Questions Mark Scheme Worked Solutions
2	All	Pure Core	Complex Numbers	Complex Roots Of Equations and Using Exponential and Polar Form	Questions Mark Scheme Worked Solutions	Questions Mark Scheme Worked Solutions
2	All	Pure Core	Complex Numbers	DeMoivre’s Theorem and Applications To Trigonometry	Questions Mark Scheme Worked Solutions	Questions Mark Scheme Worked Solutions
2	All	Pure Core	Differential Equations	Applied First Order Differential Equations	Questions Mark Scheme Worked Solutions	Not available
2	All	Pure Core	Differential Equations	Coupled Simultaneous First Order Differential Equations	Questions Mark Scheme Worked Solutions	Questions Mark Scheme Worked Solutions
2	All	Pure Core	Differential Equations	First Order Differential Equations	Questions Mark Scheme Worked Solutions	Questions Mark Scheme Worked Solutions
2	All	Pure Core	Differential Equations	First Order Differential Equations Involving Substitutions	Questions Mark Scheme Worked Solutions	Not available
2	All	Pure Core	Differential Equations	Second Order Differential Equations	Questions Mark Scheme Worked Solutions	Questions Mark Scheme Worked Solutions
2	All	Pure Core	Differential Equations	Simple, Forced and Damped Harmonic Motion	Questions Mark Scheme Worked Solutions	Not available
2	All	Pure Core	Hyperbolics	Hyperbolic Functions – Identities and Equations	Questions Mark Scheme Worked Solutions	Questions Mark Scheme Worked Solutions
2	All	Pure Core	Polar Coordinates	Polar Coordinates	Questions Mark Scheme Worked Solutions	Questions Mark Scheme Worked Solutions
2	All	Pure Core	Proof By Induction	Proof By Induction (Challenging)	Questions Mark Scheme Worked Solutions	Not available
2	All	Pure Core	Proof By Induction	Summations (Proof By Induction)	Questions Mark Scheme Worked Solutions	Not available
2	All	Pure Core	Series	Maclaurin Expansion	Questions Mark Scheme Worked Solutions	Questions Mark Scheme Worked Solutions
2	All	Pure Core	Series	Summations (Method Of Differences)	Questions Mark Scheme Worked Solutions	Questions Mark Scheme Worked Solutions
2	All	Pure Core	Series	Summations (Standard Formulae)	Questions Mark Scheme Worked Solutions	Not available
2	All	Pure Core	Vectors	Distance Between Planes and Lines	Questions Mark Scheme Worked Solutions	Not available
2	All	Pure Core	Vectors	Lines and Planes (Equations, Angles Between and Intersection)	Questions Mark Scheme Worked Solutions	Not available
2	All	Pure Core	Vectors and Matrices	Matrices, Simultaneous Equations and Applications to Intersections of Planes	Questions Mark Scheme Worked Solutions	Not available

Edexcel Optional Units


Year	Exam Board	Strand	Topic	Title	Resources
1	Edexcel	D1	D1	Critical Path Analysis	Questions Mark Scheme
1	Edexcel	D1	D1	General Algorithms and Flowcharts	Questions Mark Scheme
1	Edexcel	D1	D1	Graph Theory	Questions Mark Scheme
1	Edexcel	D1	D1	Linear Programming – Forming Problems	Questions Mark Scheme
1	Edexcel	D1	D1	Linear Programming – Graphical Method	Questions Mark Scheme
1	Edexcel	D1	D1	Minimum Spanning Trees	Questions Mark Scheme
1	Edexcel	D1	D1	Route Inspection	Questions Mark Scheme
1	Edexcel	D1	D1	Shortest Path	Questions Mark Scheme
1	Edexcel	D1	D1	Sorting And Bin Packing	Questions Mark Scheme
2	Edexcel	D1	D1	Critical Path Analysis – Resource Histograms And Scheduling	Questions Mark Scheme
2	Edexcel	D1	D1	Planarity Algorithm	Questions Mark Scheme
2	Edexcel	D1	D1	Simplex Method	Questions Mark Scheme
2	Edexcel	D1	D1	Simplex Method – Two Stage And Big-M	Questions Mark Scheme
2	Edexcel	D1	D1	Travelling Salesman Problem	Questions Mark Scheme
1	Edexcel	FM1	FM1	Coefficient of Restitution With Multiple Collisions	Questions Mark Scheme Worked Solutions
1	Edexcel	FM1	FM1	Coefficient of Restitution With Single Collision	Questions Mark Scheme Worked Solutions
1	Edexcel	FM1	FM1	Inelastic Collisions	Questions Mark Scheme Worked Solutions
1	Edexcel	FM1	FM1	Power	Questions Mark Scheme Worked Solutions
1	Edexcel	FM1	FM1	Work-Energy Principle	Questions Mark Scheme Worked Solutions
2	Edexcel	FM1	FM1	Hooke's Law	Questions Mark Scheme Worked Solutions
2	Edexcel	FM1	FM1	Momentum As A Vector	Questions Mark Scheme Worked Solutions
2	Edexcel	FM1	FM1	Oblique Collisions	Questions Mark Scheme Worked Solutions
2	Edexcel	FM1	FM1	Oblique Collisions With Vectors	Questions Mark Scheme Worked Solutions
1	Edexcel	FS1	FS1	Chi-Squared Contingency Tables	Questions Mark Scheme Worked Solutions
1	Edexcel	FS1	FS1	Chi-Squared Goodness Of Fit Tests	Questions Mark Scheme Worked Solutions
1	Edexcel	FS1	FS1	Discrete Random Variables	Questions Mark Scheme Worked Solutions
1	Edexcel	FS1	FS1	Poisson Hypothesis Tests	Questions Mark Scheme Worked Solutions
1	Edexcel	FS1	FS1	Poisson and Binomial Distribution	Questions Mark Scheme Worked Solutions
2	Edexcel	FS1	FS1	Central Limit Theorem	Questions Mark Scheme Worked Solutions
2	Edexcel	FS1	FS1	Geometric And Negative Binomial Distribution	Questions Mark Scheme Worked Solutions
2	Edexcel	FS1	FS1	Geometric Distribution Hypothesis Tests	Questions Mark Scheme Worked Solutions
2	Edexcel	FS1	FS1	Probability Generating Functions	Questions Mark Scheme Worked Solutions
2	Edexcel	FS1	FS1	Quality Of Hypothesis Tests	Questions Mark Scheme Worked Solutions

Edexcel Optional Units (Old Questions)

Unit	URL
FS1	Discrete Random Variables
FS1	Expectation and Variance of Linear Transformations of Discrete Random Variables
FS1	Binomial Distribution
FS1	Poisson Distribution
FS1	Poisson Approximations to a Binomial Distribution
FS1	Hypothesis Tests for Mean of a Poisson Distribution
FS1	Geometric Distribution
FS1	Central Limit Theorem
FS1	Chi Squared Tests for Goodness of Fit
FS1	Chi-Squared Tests on Contingency Tables
FS1	Probability Generating Functions
FS1	Quality of Hypothesis Tests
FS2	Least Squares Regression Line
FS2	Hypothesis Tests for Linear Correlation
FS2	Continuous Random Variables (Mean, Variance and Median)
FS2	Continuous Random Variables (Cumulative Distributions)
FS2	Combinations of Continuous Random Variables
FM1	Conservation of Momentum
FM1	Work, Energy and Power
FM1	Hooke’s Law
FM1	Coefficient of Restitution
FM1	Oblique Collisions
FM2	Horizontal Circular Motion
FM2	Vertical Circular Motion
FM2	Problem Solving With Circular Motion
FM2	Centres Of Mass
FM2	Centres of Mass Involving Integration
FM2	Linear Motion With Variable Acceleration

OCR Optional Units


Year	Exam Board	Strand	Topic	Title	Resources
1	OCR A	Mechanics	Circular Motion	Horizontal Circular Motion	Questions Mark Scheme Worked Solutions
1	OCR A	Mechanics	Circular Motion	Vertical Circular Motion	Questions Mark Scheme Worked Solutions
1	OCR A	Mechanics	Collisions	Coefficient of Restitution	Questions Mark Scheme Worked Solutions
1	OCR A	Mechanics	Collisions	Conservation of Momentum	Questions Mark Scheme Worked Solutions
1	OCR A	Mechanics	Dimensional Analysis	Dimensional Analysis	Questions Mark Scheme Worked Solutions
1	OCR A	Mechanics	Work, Energy and Power	Work, Energy and Power	Questions Mark Scheme Worked Solutions
2	OCR A	Mechanics	Centres of Mass	Centres Of Mass	Questions Mark Scheme Worked Solutions
2	OCR A	Mechanics	Centres of Mass	Centres of Mass Involving Integration	Questions Mark Scheme Worked Solutions
2	OCR A	Mechanics	Circular Motion	Problem Solving With Circular Motion	Questions Mark Scheme Worked Solutions
2	OCR A	Mechanics	Collisions	Oblique Collisions	Questions Mark Scheme Worked Solutions
2	OCR A	Mechanics	Differential Equations	Linear Motion With Variable Acceleration	Questions Mark Scheme Worked Solutions
2	OCR A	Mechanics	Forces and Energy	Hooke's Law	Questions Mark Scheme Worked Solutions
1	OCR A	Statistics	Combinatorics	Permutations and Combinations	Questions Mark Scheme Worked Solutions
1	OCR A	Statistics	Distributions	Binomial Distribution	Questions Mark Scheme Worked Solutions
1	OCR A	Statistics	Distributions	Discrete Random Variables	Questions Mark Scheme Worked Solutions
1	OCR A	Statistics	Distributions	Discrete Uniform Distribution	Questions Mark Scheme Worked Solutions
1	OCR A	Statistics	Distributions	Expectation and Variance of Linear Transformations of Discrete Random Variables	Questions Mark Scheme Worked Solutions
1	OCR A	Statistics	Distributions	Geometric Distribution	Questions Mark Scheme Worked Solutions
1	OCR A	Statistics	Distributions	Poisson Distribution	Questions Mark Scheme Worked Solutions
1	OCR A	Statistics	Hypothesis Testing	Chi Squared Tests (Contingency Tables)	Questions Mark Scheme Worked Solutions
1	OCR A	Statistics	Hypothesis Testing	Chi Squared Tests (Goodness of Fit) (Year 1)	Questions Mark Scheme Worked Solutions
1	OCR A	Statistics	Hypothesis Testing and Linear Regression	Hypothesis Tests for Linear Correlation	Questions Mark Scheme Worked Solutions
1	OCR A	Statistics	Linear Regression	Least Squares Regression Line	Questions Mark Scheme Worked Solutions
2	OCR A	Statistics	Confidence Intervals	Confidence Intervals for the Mean of a Sampling Distribution	Questions Mark Scheme Worked Solutions
2	OCR A	Statistics	Distributions	Combinations of Continuous Random Variables	Questions Mark Scheme Worked Solutions
2	OCR A	Statistics	Distributions	Continuous Random Variables (Cumulative Distributions)	Questions Mark Scheme Worked Solutions
2	OCR A	Statistics	Distributions	Continuous Random Variables (Functions of CRVs)	Questions Mark Scheme Worked Solutions
2	OCR A	Statistics	Distributions	Continuous Random Variables (Mean, Variance and Median)	Questions Mark Scheme Worked Solutions
2	OCR A	Statistics	Distributions	Continuous Uniform Distribution	Questions Mark Scheme Worked Solutions
2	OCR A	Statistics	Distributions	Exponential Distribution	Questions Mark Scheme Worked Solutions
2	OCR A	Statistics	Distributions	Geometric Distribution Questions (with Year 2 Content)	Questions Mark Scheme Worked Solutions
2	OCR A	Statistics	Hypothesis Testing	Chi Squared Tests (Goodness of Fit) (Year 2)	Questions Mark Scheme Worked Solutions
2	OCR A	Statistics	Hypothesis Testing	Hypothesis Tests Requiring Unbiased Estimators and Central Limit Theorem	Questions Mark Scheme Worked Solutions
2	OCR A	Statistics	Hypothesis Testing	Single Sample and Paired Sample Sign Tests	Questions Mark Scheme Worked Solutions
2	OCR A	Statistics	Hypothesis Testing	Using Central Limit Theorem	Questions Mark Scheme Worked Solutions
2	OCR A	Statistics	Hypothesis Testing	Wilcoxon Rank Sum Tests	Questions Mark Scheme Worked Solutions
2	OCR A	Statistics	Hypothesis Testing	Wilcoxon Single Sample and Paired Sample Hypothesis Tests	Questions Mark Scheme Worked Solutions

OCR MEI Optional Units

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

Unit	Level	Question Link	MS Link
Mech	Major	Horizontal Circular Motion	MS
Mech	Major	Vertical Circular Motion	MS
Mech	Minor	Conservation of Momentum	MS
Mech	Major	Coefficient of Restitution	MS
Mech	Minor	Dimensional Analysis	MS
Mech	Minor	Work, Energy and Power	MS
Mech	Major	Centres Of Mass	MS
Mech	Major	Centres of Mass Involving Integration	MS
Mech	Major	Problem Solving With Circular Motion	MS
Mech	Major	Oblique Collisions	MS
Mech	Major	Linear Motion With Variable Acceleration	MS
Mech	Major	Hooke’s Law	MS
Stats	Minor	Discrete Random Variables	MS
Stats	Minor	Expectation and Variance of Linear Transformations of Discrete Random Variables	MS
Stats	Minor	Binomial Distribution	MS
Stats	Minor	Geometric Distribution	MS
Stats	Minor	Discrete Uniform Distribution	MS
Stats	Minor	Poisson Distribution	MS
Stats	Minor	Chi Squared Tests (Contingency Tables)	MS
Stats	Minor	Chi Squared Tests (Goodness of Fit)	MS
Stats	Minor	Hypothesis Tests for Linear Correlation	MS
Stats	Minor	Least Squares Regression Line	MS
Stats	Minor	Confidence Intervals for the Sampling Mean of a Normal Distribution	MS
Stats	Major	Continuous Random Variables (Mean, Variance and Median)	MS
Stats	Major	Continuous Random Variables (Cumulative Distributions)	MS
Stats	Major	Continuous Uniform Distribution	MS
Stats	Major	Exponential Distribution	MS
Stats	Major	Combinations of Continuous Random Variables	MS
Stats	Major	Using Central Limit Theorem	MS
Stats	Major	Hypothesis Tests Requiring Unbiased Estimators and Central Limit Theorem	MS