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