A-Level Further Maths (Edexcel)1,536 questions analysed · 5,263 total marks

Further Calculus6.5%

Advanced Applications2.9%

Integration Techniques2.3%

Reduction Formulae1.2%

Differential Equations6.2%

Second Order3.0%

First Order1.9%

Applications & SHM0.9%

Numerical Methods0.4%

Elastic Collisions5.5%

Oblique Impact3.7%

Collisions1.8%

Discrete Probability Distributions4.0%

Distributions3.0%

Expected Value & Variance1.0%

Further Algebra & Functions4.0%

Series3.0%

Roots of Polynomials1.0%

Complex Numbers3.7%

Argand Diagrams1.5%

Exponential Form & De Moivre1.2%

Complex Numbers Applications0.8%

Foundations & Operations0.2%

Linear Programming3.0%

Optimization3.0%

Further Sequences & Series2.9%

Recurrence Relations2.3%

Proof by Induction of Closed Forms0.6%

Further Vectors2.8%

3D Vector Geometry1.9%

Vector Product0.9%

Motion in a Circle2.8%

Vertical Circular Motion1.7%

Horizontal Circular Motion1.1%

Further Centres of Mass2.7%

Centre of Mass by Integration2.4%

Equilibrium of Rigid Bodies0.3%

Matrices2.4%

Determinants & Inverses1.2%

Transformations0.9%

Matrix Algebra0.2%

Further Dynamics2.3%

SHM & Elastic Oscillations1.6%

Variable Force in 1D0.7%

Number Theory2.1%

Congruences1.4%

Combinatorics0.5%

Division & Euclidean Algorithm0.2%

Continuous Probability Distributions2.0%

Mean, Variance & Shape1.0%

Continuous Uniform Distribution0.6%

PDF & CDF0.4%

Estimation & Confidence Intervals2.0%

Estimators1.1%

Normal Confidence Intervals & Tests1.0%

Algorithms on Graphs II2.0%

Route Inspection1.4%

Travelling Salesman Problem0.7%

Coordinate Systems2.0%

Conic Sections2.0%

Game Theory1.9%

Mixed Strategies1.9%

Critical Path Analysis1.9%

Project Management1.9%

Hypothesis Testing1.8%

Chi-Squared Tests1.5%

Testing a Poisson or Geometric Parameter0.2%

Work, Energy & Power1.8%

Energy & Power1.8%

Probability Generating Functions1.8%

PGF Methods1.8%

Algorithms & Graph Theory1.7%

Algorithms1.4%

Graph Theory0.2%

Dynamic Programming1.7%

Bellman's Principle1.7%

Further Hypothesis Tests1.6%

Tests on Variance1.6%

Polar Coordinates1.6%

Calculus1.6%

Quality of Tests1.6%

Type I & Type II Errors1.6%

Further Complex Numbers1.5%

Further Loci & Regions1.1%

Transformations of the Complex Plane0.5%

Elastic Strings & Springs1.5%

Hooke's Law & Applications1.5%

Transportation Problems1.5%

Transportation Algorithms1.5%

Centres of Mass of Plane Figures1.5%

Centre of Mass of Plane Figures1.1%

Moments & Discrete Mass Distributions0.4%

Algorithms on Graphs1.4%

Network Algorithms1.4%

Further Matrix Algebra1.4%

Eigenvalues & Eigenvectors0.7%

Diagonalization0.7%

Flows in Networks1.4%

Cuts & Maximum Flow1.4%

Combinations of Random Variables1.3%

Linear Combinations of Normal Variables1.3%

t-Distribution Methods1.3%

t-Tests & Confidence Intervals1.3%

Momentum & Impulse1.2%

Linear Momentum1.2%

Hyperbolic Functions1.2%

Definitions & Identities0.6%

Inverse Hyperbolic Functions0.6%

Groups1.1%

Group Axioms & Examples0.9%

Isomorphism0.2%

Linear Regression1.1%

Residual Analysis0.8%

Least Squares Regression0.3%

Allocation (Assignment) Problems1.0%

Hungarian Algorithm1.0%

Decision Analysis1.0%

Decision Trees & EMV1.0%

Central Limit Theorem0.9%

Sampling Distributions0.9%

Inequalities0.8%

Inequalities Methods0.8%

Proof0.7%

Methods of Proof0.7%

Correlation0.6%

Testing Correlation0.3%

Correlation Coefficients0.3%

Further Kinematics0.5%

Variable Acceleration0.5%

Further Numerical Methods0.5%

Advanced Methods0.5%

Further Trigonometry0.5%

Advanced Techniques0.5%

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A-Level Maths (AQA)861 questions analysed · 2,198 total marks

Differentiation13.0%

Differentiation Applications9.2%

Differentiation Techniques3.3%

From First Principles0.4%

Sequences & Series9.7%

Series5.0%

Binomial Expansion3.4%

Sequences1.4%

Trigonometry9.5%

Identities & Equations6.5%

Trig Functions1.6%

Radian Measure1.4%

Algebra & Functions9.1%

Functions4.9%

Algebraic Manipulation3.0%

Quadratics & Inequalities1.2%

Integration8.7%

Core4.0%

Integration Techniques2.8%

Differential Equations1.9%

Kinematics7.2%

Motion in a Straight Line6.6%

Calculus in Kinematics0.5%

Coordinate Geometry7.1%

Circles3.1%

Parametric Equations2.6%

Straight Lines1.4%

Statistical Distributions6.9%

Models6.9%

Exponentials & Logarithms5.6%

Logarithms4.3%

Exponential Functions1.3%

Forces & Newton’s Laws5.2%

Laws & Applications5.2%

Hypothesis Testing4.2%

Hypothesis Testing Methods4.2%

Numerical Methods3.9%

Roots3.7%

Numerical Integration0.2%

Proof2.6%

Proof Methods2.6%

Probability2.3%

Foundations2.3%

Data Presentation & Interpretation1.5%

Summary Statistics0.9%

Graphical Methods0.6%

Vectors1.4%

Vectors Applications1.0%

Operations0.3%

Basics0.1%

Moments1.1%

Equilibrium of Rigid Bodies1.1%

Sampling1.1%

Concepts & Methods1.1%

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A-Level Maths (Edexcel)753 questions analysed · 2,097 total marks

Integration13.4%

Differential Equations4.9%

Basics & Areas4.7%

Integration Techniques3.9%

Differentiation9.8%

Differentiation Applications6.3%

Rules & Techniques2.0%

Foundations & First Principles1.5%

Kinematics9.5%

Projectiles (under constant g)4.0%

Calculus in Kinematics3.5%

Motion in a Straight Line2.0%

Algebra & Functions9.2%

Functions & Graphs5.7%

Quadratics & Inequalities1.8%

Polynomials & Rational Expressions1.5%

Indices & Surds0.1%

Trigonometry8.2%

Identities & Equations5.7%

Radians & Triangle Geometry1.6%

Trig Functions & Graphs0.7%

Proofs & Applications0.2%

Sequences & Series7.4%

Series3.9%

Binomial Expansion2.1%

Sequences1.3%

Statistical Distributions6.8%

Continuous Models5.1%

Discrete Models1.7%

Exponentials & Logarithms5.8%

Logarithms3.6%

Exponential Functions1.4%

Growth & Decay Modelling0.8%

Coordinate Geometry4.4%

Circles2.3%

Parametric Curves1.5%

Straight Lines0.6%

Numerical Methods4.2%

Roots of Equations3.2%

Numerical Integration1.0%

Data Presentation & Interpretation3.9%

Univariate Data2.7%

Bivariate Data1.2%

Forces & Newton’s Laws3.5%

Resolving & Dynamics in a Plane2.8%

Friction0.8%

Moments3.5%

Moments & Equilibrium of Rigid Bodies3.5%

Probability3.4%

Foundations & Conditionality3.3%

Modelling with Probability0.1%

Statistical Hypothesis Testing2.7%

Binomial Proportion Test1.0%

Correlation Testing0.9%

Normal Mean Test (σ known/assumed)0.8%

Vectors2.3%

Fundamentals2.3%

Proof2.0%

Methods of Proof2.0%

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A-Level Physics (AQA)702 questions analysed · 1,168 total marks

Fields and Their Consequences (A-level only)26.5%

Electric Fields & Capacitance11.6%

Gravitational Fields7.4%

Magnetic Fields & Electromagnetic Induction7.4%

Mechanics12.8%

Motion & Forces7.1%

Energy, Work & Momentum3.9%

Equilibrium & Moments1.9%

Nuclear Physics (A-level only)12.5%

Radioactivity & Nuclear Change6.3%

Nuclear Structure, Energy & Applications6.2%

Particles and Radiation11.6%

Quantum Phenomena5.1%

Particle Physics Foundations4.8%

Quarks, Leptons & Interactions1.8%

Waves10.6%

Refraction & Optics4.4%

Interference & Diffraction3.6%

Wave Behaviour & Superposition2.6%

Electricity9.4%

Circuit Laws & Analysis3.9%

EMF, Internal Resistance & Power2.6%

Components & I–V Characteristics1.8%

Charge, Current & Potential Difference0.8%

Resistance & Resistivity0.3%

Thermal Physics (A-level only)9.2%

Kinetic Theory & Ideal Gases6.4%

Thermal Properties & Phase2.8%

Further Mechanics (A-level only)5.4%

Circular Motion3.1%

Simple Harmonic Motion2.3%

Materials1.6%

Deformation & Elasticity1.4%

Mechanical Properties0.3%

Measurements and Their Errors0.3%

Units & Measurement0.3%

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IB Physics (Higher Level)631 questions analysed · 1,088 total marks

A — Space, Time and Motion26.0%

A.5 Galilean and Special Relativity (HL only)7.8%

A.2 Forces and Momentum7.6%

A.4 Rigid Body Mechanics (HL only)4.0%

A.1 Kinematics3.7%

A.3 Work, Energy and Power2.9%

C — Wave Behaviour22.1%

C.3 Wave Phenomena14.2%

C.4 Standing Waves and Resonance3.5%

C.5 Doppler Effect2.3%

C.1 Simple Harmonic Motion1.0%

C.2 Wave Model1.0%

E — Nuclear and Quantum Physics21.9%

E.5 Fusion and Stars9.1%

E.3 Radioactive Decay7.5%

E.1 Structure of the Atom3.0%

E.2 Quantum Physics (HL only)2.0%

E.4 Fission0.2%

B — The Particulate Nature of Matter16.1%

B.5 Current and Circuits6.7%

B.4 Thermodynamics (HL only)3.4%

B.3 Gas Laws3.0%

B.1 Thermal Energy Transfers2.2%

B.2 Greenhouse Effect0.7%

D — Fields14.0%

D.1 Gravitational Fields6.5%

D.2 Electric and Magnetic Fields4.0%

D.4 Induction (HL only)2.5%

D.3 Motion in Electromagnetic Fields0.9%

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IB Physics (Standard Level)641 questions analysed · 998 total marks

A — Space, Time and Motion31.2%

A.2 Forces and Momentum14.1%

A.1 Kinematics12.6%

A.3 Work, Energy and Power4.4%

B — The Particulate Nature of Matter24.6%

B.3 Gas Laws10.0%

B.5 Current and Circuits9.6%

B.1 Thermal Energy Transfers4.2%

B.2 Greenhouse Effect0.7%

C — Wave Behaviour21.0%

C.3 Wave Phenomena12.3%

C.4 Standing Waves and Resonance3.5%

C.5 Doppler Effect2.1%

C.1 Simple Harmonic Motion1.9%

C.2 Wave Model1.2%

E — Nuclear and Quantum Physics15.8%

E.3 Radioactive Decay7.2%

E.5 Fusion and Stars6.4%

E.1 Structure of the Atom1.9%

E.4 Fission0.3%

D — Fields7.4%

D.2 Electric and Magnetic Fields3.7%

D.3 Motion in Electromagnetic Fields2.9%

D.1 Gravitational Fields0.8%

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GCSE Maths (AQA)691 questions analysed · 1,614 total marks

Algebra29.5%

Equations & Inequalities9.0%

Graphs & Coordinate Geometry7.6%

Notation & Manipulation5.1%

Formulae & Substitution4.9%

Sequences2.9%

Geometry & Measures25.4%

Perimeter, Area & Volume8.4%

Pythagoras & Trigonometry6.4%

Transformations & Vectors3.7%

Circles & Theorems3.0%

Properties, Angles & Constructions2.5%

Congruence & Similarity1.4%

Number17.8%

Fractions, Decimals & Percentages6.6%

Number Structure & Calculation5.6%

Powers, Roots & Standard Form3.8%

Accuracy & Bounds1.7%

Ratio, Proportion & Rates of Change12.1%

Compound Measures & Gradients5.0%

Ratio & Scale5.0%

Percentages & Proportion2.0%

Probability8.3%

Combined & Conditional Events3.4%

Foundations & Representation2.9%

Experimental Probability2.1%

Statistics6.9%

Representation & Summary6.3%

Data Collection & Sampling0.3%

Bivariate Data0.2%

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GCSE Maths (Edexcel)647 questions analysed · 1,678 total marks

Geometry and Measures26.4%

Further trigonometry and vectors (Higher)5.3%

Volume, surface area and units4.5%

Properties of 2D shapes and angle facts3.6%

Perimeter, area and circles3.5%

Pythagoras and basic trigonometry3.5%

Congruence, similarity and scale drawings2.8%

Transformations and coordinates2.6%

Constructions and loci0.7%

Algebra25.9%

Graphs of linear and quadratic functions5.0%

Simultaneous equations and algebraic fractions (Higher)4.7%

Equations, formulae and inequalities4.0%

Quadratics and algebraic techniques (Higher emphasis)3.8%

Further graphs and functions (Higher)3.6%

Sequences3.0%

Algebraic expressions and manipulation1.8%

Number16.5%

Fractions, decimals and percentages5.1%

Standard form and surds (Higher)3.2%

Powers, roots and indices3.0%

Approximation and estimation2.9%

Factors, multiples and primes1.7%

Number operations and structure0.5%

Ratio, Proportion and Rates of Change14.8%

Rates of change and compound measures5.5%

Ratio and scaling5.0%

Direct and inverse proportion (Higher depth)2.6%

Proportion and percentages in context1.8%

Probability8.9%

Tree diagrams and independence3.7%

Single events and basic probability2.0%

Venn diagrams and set notation1.9%

Combined events and sample spaces1.3%

Statistics7.6%

Summary statistics and comparison4.7%

Representing data2.1%

Scatter graphs and bivariate data0.6%

Statistical enquiries and data collection0.2%

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IGCSE Maths (Cambridge Core)535 questions analysed · 960 total marks

Number29.8%

Types of Number7.7%

Fractions, Decimals and Percentages3.9%

Percentages3.6%

Estimation and Accuracy3.4%

Ratio and Proportion3.4%

Rates3.0%

Sets2.1%

Indices1.0%

Standard Form0.9%

Powers and Roots0.6%

Algebra and Graphs24.3%

Equations7.1%

Graphs of Functions6.9%

Substitution and Formulae3.9%

Sequences2.8%

Algebraic Manipulation2.2%

Graphs in Practical Situations1.1%

Inequalities0.3%

Geometry11.9%

Angles4.3%

Scale Drawings and Bearings2.2%

Circle Theorems2.0%

Geometrical Constructions0.9%

Symmetry0.9%

Geometrical Terms and Properties0.8%

Similarity and Congruence0.7%

Statistics9.8%

Statistical Charts and Diagrams4.8%

Averages and Measures of Spread2.7%

Scatter Diagrams2.3%

Mensuration9.2%

Surface Area and Volume4.5%

Area and Perimeter2.4%

Circles, Arcs and Sectors1.9%

Units of Measure0.4%

Transformations and Vectors8.9%

Transformations8.5%

Vectors0.3%

Probability2.3%

Introduction to Probability1.7%

Combined Events0.4%

Relative and Expected Frequencies0.2%

Coordinate Geometry2.0%

Equations of Lines2.0%

Trigonometry2.0%

Right-Angled Triangles2.0%

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IGCSE Maths (Cambridge Extended)494 questions analysed · 1,197 total marks

Algebra and Graphs30.7%

Equations8.3%

Differentiation5.7%

Functions3.4%

Algebraic Manipulation2.3%

Inequalities2.3%

Sequences2.3%

Algebraic Fractions2.0%

Proportion1.8%

Graphs of Functions1.4%

Graphs in Practical Situations0.8%

Substitution and Formulae0.3%

Number18.6%

Percentages4.3%

Indices3.2%

Estimation and Accuracy2.3%

Types of Number2.1%

Fractions, Decimals and Percentages2.0%

Ratio and Proportion1.4%

Sets1.2%

Rates0.9%

Standard Form0.6%

Surds0.4%

Powers and Roots0.2%

Trigonometry11.3%

Non-Right-Angled Triangles5.8%

3D Trigonometry2.7%

Trigonometric Functions1.8%

Right-Angled Triangles1.2%

Geometry8.6%

Circle Theorems2.6%

Similarity and Congruence2.5%

Angles2.1%

Scale Drawings and Bearings0.8%

Symmetry0.3%

Geometrical Constructions0.2%

Mensuration8.4%

Surface Area and Volume6.5%

Circles, Arcs and Sectors1.2%

Area and Perimeter0.7%

Statistics8.2%

Cumulative Frequency3.5%

Histograms2.3%

Averages and Measures of Spread1.3%

Statistical Charts and Diagrams0.9%

Scatter Diagrams0.2%

Transformations and Vectors7.3%

Vectors4.2%

Transformations3.1%

Coordinate Geometry3.8%

Equations of Lines3.8%

Probability3.0%

Combined Events1.5%

Conditional Probability0.7%

Relative and Expected Frequencies0.5%

Introduction to Probability0.3%

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GCSE Physics (AQA Triple Science)638 questions analysed · 1,477 total marks

Forces21.3%

Forces and Motion13.4%

Forces and Elasticity2.8%

Moments, Levers and Gears2.4%

Pressure and Pressure Differences in Fluids1.3%

Forces and Their Interactions0.7%

Momentum0.5%

Electricity19.7%

Energy Transfers8.2%

Current, Potential Difference and Resistance7.6%

Static Electricity2.4%

Domestic Uses and Safety1.5%

Waves16.8%

Waves in Air, Fluids and Solids10.5%

Electromagnetic Waves6.4%

Energy12.3%

Energy Changes in a System11.0%

National and Global Energy Resources1.3%

Magnetism and Electromagnetism8.2%

The Motor Effect4.1%

Induced Potential, Transformers and the National Grid4.1%

Atomic Structure7.9%

Atoms and Nuclear Radiation4.9%

Hazards and Uses of Radioactivity1.2%

Nuclear Fission and Fusion1.1%

Atoms and Isotopes0.7%

Particle Model of Matter7.8%

Particle Model and Pressure3.0%

Internal Energy and Energy Transfers2.6%

Changes of State and the Particle Model2.2%

Space Physics6.0%

Solar System, Orbital Stability and Satellites4.5%

Red-Shift and the Big Bang1.4%

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GCSE Physics (AQA Combined Science)399 questions analysed · 980 total marks

Forces28.9%

Forces and Motion21.2%

Forces and Elasticity5.6%

Forces and Their Interactions2.0%

Electricity16.2%

Current, Potential Difference and Resistance7.5%

Energy Transfers5.8%

Series and Parallel Circuits1.9%

Domestic Uses and Safety0.9%

Energy13.5%

Energy Changes in a System11.5%

Conservation and Dissipation of Energy1.1%

National and Global Energy Resources0.8%

Waves12.2%

Electromagnetic Waves6.3%

Waves in Air, Fluids and Solids5.8%

Atomic Structure10.9%

Atoms and Nuclear Radiation9.0%

Atoms and Isotopes1.9%

Particle Model of Matter10.5%

Internal Energy and Energy Transfers4.3%

Changes of State and the Particle Model4.0%

Particle Model and Pressure2.2%

Magnetism and Electromagnetism7.9%

The Motor Effect6.0%

Permanent and Induced Magnetism, Magnetic Forces and Fields1.8%

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TMUA (Test of Mathematics for University Admission)320 questions analysed · 320 total marks

Algebra & Functions14.4%

Quadratics5.9%

Equations & Inequalities4.1%

Manipulating Expressions2.2%

Functions1.2%

Indices & Surds0.9%

Sequences & Series12.5%

Series6.2%

Binomial Expansion3.4%

Sequences2.8%

Logic of Arguments (Paper 2)10.9%

Reasoning Terms8.8%

Logical Connectives2.2%

Trigonometry10.6%

Trig Equations5.0%

Right-Angled & Triangle Trig2.5%

Trig Functions & Identities2.5%

Radians & Exact Values0.6%

Integration10.6%

Integration Applications7.8%

Integrating2.8%

Differentiation8.1%

Differentiation Applications5.6%

Derivatives2.5%

Coordinate Geometry6.2%

Circles3.8%

Straight Lines2.5%

Mathematical Proof (Paper 2)5.9%

Proof Methods4.4%

Constructing Arguments1.6%

Errors in Proofs (Paper 2)5.0%

Spotting Flawed Reasoning5.0%

Graphs & Transformations5.0%

Sketching Graphs2.8%

Transformations2.2%

Exponentials & Logarithms5.0%

Logarithms4.1%

Exponentials0.9%

Geometry & Measures3.1%

Angles & Polygons1.2%

Congruence & Similarity0.6%

Geometry Circles0.3%

Mensuration & 3D Shapes0.3%

Pythagoras & Coordinates0.3%

Transformations & Vectors0.3%

Probability0.9%

Combined Events0.9%

Statistics0.6%

Summary Statistics0.6%

Number0.6%

Powers, Roots & Standard Form0.3%

Surds & Exact Calculation0.3%

Ratio & Proportion0.3%

Ratio0.3%

For the TMUA specifically we go further: every question in the published papers from 2016 to 2023, split by paper — including why Paper 2 is 43.8% pure reasoning. But nothing beats seeing where you personally stand. Take the free TMUA readiness check →

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