Further Maths Exam Questions By Topic | A Level Maths Revision

Pure Core (All Exam boards)

Year	Strand	Topic	Subtopic	Sheet 1 (From OCR Papers)	Sheet 2 (From Edexcel Papers)
Y1	Pure	Complex Numbers	Complex Numbers – Basic Operations	Sheet 1 (OCR)	Sheet 2 (Edexcel)
Y1	Pure	Complex Numbers	Complex Numbers – Complex Roots Of Polynomials	Use Sheet 2	Sheet 2 (Edexcel)
Y1	Pure	Complex Numbers	Complex Numbers – Square Roots of Complex Numbers	Sheet 1 (OCR)	Use Sheet 1
Y1	Pure	Complex Numbers	Complex Numbers – The Argand Diagram and Loci	Sheet 1 (OCR)	Sheet 2 (Edexcel)
Y1	Pure	Matrices	Matrices – Operations, Determinants and Inverses	Sheet 1 (OCR)	Sheet 2 (Edexcel)
Y1	Pure	Matrices	Matrices – 3×3 Determinants and Inverses	Sheet 1 (OCR)	Sheet 2 (Edexcel)
Y1	Pure	Matrices	Matrices – Solving Simultaneous Equations	Sheet 1 (OCR)	Sheet 2 (Edexcel)
Y1	Pure	Matrices	Matrices – 2×2 Transformations	Sheet 1 (OCR)	Sheet 2 (Edexcel)
Y1	Pure	Matrices	Matrices – 3×3 Transformations	Sheet 1 (OCR)	Sheet 2 (Edexcel)
Y1	Pure	Matrices	Matrices – Invariant Points and Lines	Sheet 1 (OCR)	Sheet 2 (Edexcel)
Y1	Pure	Proof By Induction	Proof By Induction – Matrices	Sheet 1 (OCR)	Sheet 2 (Edexcel)
Y1	Pure	Proof By Induction	Proof By Induction – Divisibility	Sheet 1 (OCR)	Sheet 2 (Edexcel)
Y1	Pure	Proof By Induction	Proof By Induction – Inductive Sequences	Sheet 1 (OCR)	Not On Edexcel Pure Core
Y1	Pure	Proof By Induction	Proof By Induction – Inequalities	Sheet 1 (OCR)	Not On Edexcel Pure Core
Y1	Pure	Proof By Induction	Proof By Induction – Series	Yr2 For OCR (See Below)	Sheet 2 (Edexcel)
Y1	Pure	Roots of Polynomials	Roots of Polynomials	Sheet 1 (OCR)	Sheet 2 (Edexcel)
Y1	Pure	Vectors	Vectors	Sheet 1 (OCR)	Sheet 2 (Edexcel)
Y1	Pure	Series	Sums Of Series	Yr 2 For OCR (See Below)	Sheet 2 (Edexcel)
Y2	Pure	Hyperbolics	Hyperbolic Functions Identities and Equations	Sheet 1 (OCR)	Sheet 2 (Edexcel)
Y1	Pure	Calculus	Volumes of Revolution	Yr 2 For OCR (See Below)	Sheet 2 (Edexcel)
Y2	Pure	Calculus	Differentiation of Inverse Trigonometric and Hyperbolic Functions	Sheet 1 (OCR)	Sheet 2 (Edexcel)
Y2	Pure	Calculus	Integration Involving Trigonometric and Hyperbolic Functions	Sheet 1 (OCR)	Sheet 2 (Edexcel)
Y2	Pure	Calculus	Volumes of Revolution	Sheet 1 (OCR)	Sheet 2 (Edexcel) – With Yr2 Integrals
Y2	Pure	Calculus	Improper Integrals	Sheet 1 (OCR)	Sheet 2 (Edexcel)
Y2	Pure	Calculus	Mean Value Of A Function	Use Sheet 2	Sheet 2 (Edexcel)
Y2	Pure	Calculus	Partial Fractions and Integration	Sheet 1 (OCR)	Use Sheet 1
Y2	Pure	Complex Numbers	Complex Roots Of Equations and Using Exponential and Polar Form	Sheet 1 (OCR)	Sheet 2 (Edexcel)
Y2	Pure	Complex Numbers	DeMoivre’s Theorem and Applications To Series	Use Sheet 2	Sheet 2 (Edexcel)
Y2	Pure	Complex Numbers	DeMoivre’s Theorem and Applications To Trigonometry	Sheet 1 (OCR)	Sheet 2 (Edexcel)
Y2	Pure	Proof By Induction	Summations – Proof By Induction	Sheet 1 (OCR)	Yr1 For Edexcel (See Above)
Y2	Pure	Proof By Induction	Proof By Induction – Challenging	Sheet 1 (OCR)	Use Sheet 1
Y2	Pure	Differential Equations	First Order Differential Equations	Sheet 1 (OCR)	Sheet 2 (Edexcel)
Y2	Pure	Differential Equations	First Order Differential Equations Involving Substitutions	Sheet 1 (OCR)	Not On Edexcel Pure Core
Y2	Pure	Differential Equations	Applied First Order Differential Equations	Sheet 1 (OCR)	Use Sheet 1
Y2	Pure	Differential Equations	Second Order Differential Equations	Sheet 1 (OCR)	Sheet 2 (Edexcel)
Y2	Pure	Differential Equations	Simple, Forced and Damped Harmonic Motion	Sheet 1 (OCR)	Use Sheet 1
Y2	Pure	Differential Equations	Coupled Simultaneous First Order Differential Equations	Sheet 1 (OCR)	Sheet 2 (Edexcel)
Y2	Pure	Series	Summations – Proof By Induction	Sheet 1 (OCR)	Yr 1 For Edexcel (See Above)
Y2	Pure	Series	Summations – Method Of Differences	Sheet 1 (OCR)	Sheet 2 (Edexcel)
Y2	Pure	Series	Summations – Standard Formulae	Sheet 1 (OCR)	Yr 1 For Edexcel (See Above)
Y2	Pure	Series	Maclaurin Expansion	Sheet 1 (OCR)	Sheet 2 (Edexcel)
Y2	Pure	Vectors	Lines and Planes – Equations, Angles Between and Intersection	Sheet 1 (OCR)	Yr 1 For Edexcel (See Vectors)
Y2	Pure	Polar Coordinates	Polar Coordinates	Sheet 1 (OCR)	Sheet 2 (Edexcel)
Y2	Pure	Vectors	Distance Between Planes and Lines	Sheet 1 (OCR)	Yr 1 For Edexcel (See Vectors)
Y2	Pure	Vectors and Matrices	Matrices, Simultaneous Equations and Applications to Intersections of Planes	Sheet 1 (OCR)	Yr 1 For Edexcel (See Vectors)

Edexcel Optional Units

Year	Strand	Textbook Chapter	Edexcel Questions
Y1	D1	1	General Algorithms and Flowcharts
Y1	D1	1	Sorting And Bin Packing
Y1	D1	2	Graph Theory
Y1	D1	3	Minimum Spanning Trees
Y1	D1	3	Shortest Path
Y1	D1	4	Route Inspection
Y1	D1	6	Linear Programming – Forming Problems
Y1	D1	6	Linear Programming – Graphical Method
Y1	D1	8	Critical Path Analysis
Y2	D1	2	Planarity Algorithm
Y2	D1	5	Travelling Salesman Problem
Y2	D1	7	Simplex Method
Y2	D1	8	Simplex Method – Two Stage And Big-M
Y2	D1	8	Critical Path Analysis – Resource Histograms And Scheduling
Y1	FM1	1	Inelastic Collisions
Y1	FM1	2	Work-Energy Principle
Y1	FM1	2	Power
Y1	FM1	4	Coefficient of Restitution With Single Collision
Y1	FM1	4	Coefficient of Restitution With Multiple Collisions
Y2	FM1	1	Momentum As A Vector
Y2	FM1	3	Hooke’s Law
Y2	FM1	5	Oblique Collisions
Y2	FM1	5	Oblique Collisions With Vectors
Y1	FS1	1	Discrete Random Variables
Y1	FS1	2	Poisson and Binomial Distribution
Y1	FS1	4	Poisson Hypothesis Tests
Y1	FS1	6	Chi-Squared Goodness Of Fit Tests
Y1	FS1	6	Chi-Squared Contingency Tables
Y2	FS1	3	Geometric And Negative Binomial Distribution
Y2	FS1	4	Geometric Distribution Hypothesis Tests
Y2	FS1	5	Central Limit Theorem
Y2	FS1	7	Probability Generating Functions
Y2	FS1	8	Quality Of Hypothesis Tests

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	Strand	Topic	Questions
Y1	Mech	Circular Motion	Horizontal Circular Motion
Y1	Mech	Circular Motion	Vertical Circular Motion
Y1	Mech	Collisions	Conservation of Momentum
Y1	Mech	Collisions	Coefficient of Restitution
Y1	Mech	Dimensional Analysis	Dimensional Analysis
Y1	Mech	Work, Energy and Power	Work, Energy and Power
Y2	Mech	Centres of Mass	Centres Of Mass
Y2	Mech	Centres of Mass	Centres of Mass Involving Integration
Y2	Mech	Circular Motion	Problem Solving With Circular Motion
Y2	Mech	Collisions	Oblique Collisions
Y2	Mech	Differential Equations	Linear Motion With Variable Acceleration
Y2	Mech	Forces and Energy	Hooke’s Law
Y1	Stats	Combinatorics	Permutations and Combinations
Y1	Stats	Distributions	Discrete Random Variables
Y1	Stats	Distributions	Expectation and Variance of Linear Transformations of Discrete Random Variables
Y1	Stats	Distributions	Binomial Distribution
Y1	Stats	Distributions	Geometric Distribution
Y1	Stats	Distributions	Discrete Uniform Distribution
Y1	Stats	Distributions	Poisson Distribution
Y1	Stats	Hypothesis Testing	Chi Squared Tests (Contingency Tables)
Y1	Stats	Hypothesis Testing	Chi Squared Tests (Goodness of Fit) (Year 1)
Y1	Stats	Hypothesis Testing and Linear Regression	Hypothesis Tests for Linear Correlation
Y1	Stats	Linear Regression	Least Squares Regression Line
Y2	Stats	Confidence Intervals	Confidence Intervals for the Mean of a Sampling Distribution
Y2	Stats	Distributions	Geometric Distribution Questions (with Year 2 Content)
Y2	Stats	Distributions	Continuous Random Variables (Mean, Variance and Median)
Y2	Stats	Distributions	Continuous Random Variables (Cumulative Distributions)
Y2	Stats	Distributions	Continuous Uniform Distribution
Y2	Stats	Distributions	Continuous Random Variables (Functions of CRVs)
Y2	Stats	Distributions	Exponential Distribution
Y2	Stats	Distributions	Combinations of Continuous Random Variables
Y2	Stats	Hypothesis Testing	Chi Squared Tests (Goodness of Fit) (Year 2)
Y2	Stats	Hypothesis Testing	Single Sample and Paired Sample Sign Tests
Y2	Stats	Hypothesis Testing	Wilcoxon Single Sample and Paired Sample Hypothesis Tests
Y2	Stats	Hypothesis Testing	Wilcoxon Rank Sum Tests
Y2	Stats	Hypothesis Testing	Using Central Limit Theorem
Y2	Stats	Hypothesis Testing	Hypothesis Tests Requiring Unbiased Estimators and Central Limit Theorem

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