Further Maths Exam Questions By Topic

Pure Core (Same For All Exam boards)

Year	Questions
Y1	Complex Numbers – Basic Operations
Y1	Complex Numbers – Square Roots of Complex Numbers
Y1	Complex Numbers – The Argand Diagram and Loci
Y1	Matrices – Operations, Determinants and Inverses
Y1	Matrices – 3×3 Determinants and Inverses
Y1	Matrices – Solving Simultaneous Equations
Y1	Matrices – 2×2 Transformations
Y1	Matrices – 3×3 Transformations
Y1	Matrices – Invariant Points and Lines
Y1	Proof By Induction – Matrices
Y1	Proof By Induction – Divisibility
Y1	Proof By Induction – Inductive Sequences
Y1	Proof By Induction – Inequalities
Y1	Roots of Polynomials
Y1	Vectors
Y2	Differentiation of Inverse Trigonometric and Hyperbolic Functions
Y2	Integration Involving Trigonometric and Hyperbolic Functions
Y2	Volumes of Revolution
Y2	Improper Integrals
Y2	Partial Fractions and Integration
Y2	Complex Roots Of Equations and Using Exponential and Polar Form
Y2	DeMoivre’s Theorem and Applications To Trigonometry
Y2	Summations – Proof By Induction
Y2	Proof By Induction – Challenging
Y2	First Order Differential Equations
Y2	First Order Differential Equations Involving Substitutions
Y2	Second Order Differential Equations
Y2	Applied First Order Differential Equations
Y2	Simple, Forced and Damped Harmonic Motion
Y2	Coupled Simultaneous First Order Differential Equations
Y2	Hyperbolic Functions Identities and Equations
Y2	Summations – Proof By Induction
Y2	Summations – Method Of Differences
Y2	Summations – Standard Formulae
Y2	Maclaurin Expansion
Y2	Lines and Planes – Equations, Angles Between and Intersection
Y2	Polar Coordinates
Y2	Distance Between Planes and Lines
Y2	Matrices, Simultaneous Equations and Applications to Intersections of Planes

OCR Optional Units

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

Edexcel Optional Units

Unit	Topic	Question Link	MS Link
FS1	Discrete Random Variables	Discrete Random Variables	MS
FS1	Expectation and Variance of Linear Transformations of Discrete Random Variables	Expectation and Variance of Linear Transformations of Discrete Random Variables	MS
FS1	Binomial Distribution	Binomial Distribution	MS
FS1	Poisson Distribution	Poisson Distribution	MS
FS1	Poisson Approximations to a Binomial Distribution	Poisson Approximations to a Binomial Distribution	MS
FS1	Hypothesis Tests for Mean of a Poisson Distribution	Hypothesis Tests for Mean of a Poisson Distribution	MS
FS1	Geometric Distribution	Geometric Distribution	MS
FS1	Hypothesis Tests for p in a Geometric Distribution	Coming Soon
FS1	Negative Binomial Distribution	Coming Soon
FS1	Central Limit Theorem	Central Limit Theorem	MS
FS1	Chi Squared Tests for Goodness of Fit	Chi Squared Tests for Goodness of Fit	MS
FS1	Chi-Squared Tests on Contingency Tables	Chi-Squared Tests on Contingency Tables	MS
FS1	Probability Generating Functions	Probability Generating Functions	MS
FS1	Quality of Hypothesis Tests	Quality of Hypothesis Tests	MS
FS2	Least Squares Regression Line	Least Squares Regression Line	MS
FS2	Hypothesis Tests for Linear Correlation	Hypothesis Tests for Linear Correlation	MS
FS2	Continuous Random Variables (Mean, Variance and Median)	Continuous Random Variables (Mean, Variance and Median)	MS
FS2	Continuous Random Variables (Cumulative Distributions)	Continuous Random Variables (Cumulative Distributions)	MS
FS2	Combinations of Continuous Random Variables	Combinations of Continuous Random Variables	MS
FS2	Estimation	Coming Soon
FS2	Further Hypothesis Tests	Coming Soon
FS2	Confidence Intervals and the t-Distribution	Coming Soon
FM1	Conservation of Momentum	Conservation of Momentum	MS
FM1	Work, Energy and Power	Work, Energy and Power	MS
FM1	Hooke’s Law	Hooke’s Law	MS
FM1	Coefficient of Restitution	Coefficient of Restitution	MS
FM1	Oblique Collisions	Oblique Collisions	MS
FM2	Horizontal Circular Motion	Horizontal Circular Motion	MS
FM2	Vertical Circular Motion	Vertical Circular Motion	MS
FM2	Problem Solving With Circular Motion	Problem Solving With Circular Motion	MS
FM2	Centres Of Mass	Centres Of Mass	MS
FM2	Centres of Mass Involving Integration	Centres of Mass Involving Integration	MS
FM2	Centres of Mass with Variable Density Involving Integration	Coming Soon
FM2	Linear Motion With Variable Acceleration	Linear Motion With Variable Acceleration	MS
FM2	Dynamics	Coming Soon

OCR MEI Optional Units

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

Unit	Level	Topic	Question Link	MS Link
Mech	Major	Horizontal Circular Motion	Horizontal Circular Motion	MS
Mech	Major	Vertical Circular Motion	Vertical Circular Motion	MS
Mech	Minor	Conservation of Momentum	Conservation of Momentum	MS
Mech	Major	Coefficient of Restitution	Coefficient of Restitution	MS
Mech	Minor	Dimensional Analysis	Dimensional Analysis	MS
Mech	Minor	Forces	Coming Soon
Mech	Minor	Work, Energy and Power	Work, Energy and Power	MS
Mech	Minor	Centres of Mass of Systems of Particles and Shapes	Coming Soon
Mech	Major	Centres Of Mass	Centres Of Mass	MS
Mech	Major	Centres of Mass Involving Integration	Centres of Mass Involving Integration	MS
Mech	Major	Problem Solving With Circular Motion	Problem Solving With Circular Motion	MS
Mech	Major	Oblique Collisions	Oblique Collisions	MS
Mech	Major	Linear Motion With Variable Acceleration	Linear Motion With Variable Acceleration	MS
Mech	Major	Hooke’s Law	Hooke’s Law	MS
Stats	Minor	Discrete Random Variables	Discrete Random Variables	MS
Stats	Minor	Expectation and Variance of Linear Transformations of Discrete Random Variables	Expectation and Variance of Linear Transformations of Discrete Random Variables	MS
Stats	Minor	Binomial Distribution	Binomial Distribution	MS
Stats	Minor	Geometric Distribution	Geometric Distribution	MS
Stats	Minor	Discrete Uniform Distribution	Discrete Uniform Distribution	MS
Stats	Minor	Poisson Distribution	Poisson Distribution	MS
Stats	Minor	Chi Squared Tests (Contingency Tables)	Chi Squared Tests (Contingency Tables)	MS
Stats	Minor	Chi Squared Tests (Goodness of Fit)	Chi Squared Tests (Goodness of Fit)	MS
Stats	Minor	Hypothesis Tests for Linear Correlation	Hypothesis Tests for Linear Correlation	MS
Stats	Minor	Least Squares Regression Line	Least Squares Regression Line	MS
Stats	Minor	Confidence Intervals for the Sampling Mean of a Normal Distribution	Confidence Intervals for the Sampling Mean of a Normal Distribution	MS
Stats	Major	Continuous Random Variables (Mean, Variance and Median)	Continuous Random Variables (Mean, Variance and Median)	MS
Stats	Major	Continuous Random Variables (Cumulative Distributions)	Continuous Random Variables (Cumulative Distributions)	MS
Stats	Major	Continuous Uniform Distribution	Continuous Uniform Distribution	MS
Stats	Major	Exponential Distribution	Exponential Distribution	MS
Stats	Major	Combinations of Continuous Random Variables	Combinations of Continuous Random Variables	MS
Stats	Major	Using Central Limit Theorem	Using Central Limit Theorem	MS
Stats	Major	Hypothesis Tests Requiring Unbiased Estimators and Central Limit Theorem	Hypothesis Tests Requiring Unbiased Estimators and Central Limit Theorem	MS
Stats	Major	T-Distribution	Coming Soon

AQA Optional Units (Coming Soon)

Work in progress…

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