Roadmap
Pure Mathematics 1
Algebraic foundations
P1 1.1 - Rational indices
P1 1.2 - Simplifying surds
P1 1.10 - Expanding and factorising
Quadratics and inequalities
P1 1.3, P1 1.5 - Quadratic graphs and completed squares
P1 1.5 - Solving quadratic equations
P1 1.4 - Counting real roots
P1 1.6 - Simultaneous equations
P1 1.7, P1 1.9 - Solving inequalities
P1 1.8 - Shading inequalities
Graphs and straight lines
P1 2.1, P1 2.2 - Straight-line equations
P1 1.11 - Cubic and reciprocal graphs
P1 1.12 - Moving and stretching graphs
Trigonometry
P1 3.1 - Solving triangles
P1 3.1 - The ambiguous sine rule
P1 3.2 - Radians and sectors
P1 3.3, P1 1.11, P1 1.12 - Trigonometric graphs
Differentiation
P1 4.1 - Gradients and rates of change
P1 4.2, P1 4.1 - Differentiating powers
P1 4.3 - Tangents and normals
Integration
P1 5.1, P1 5.2 - Integrating powers
P1 5.2 - Finding a curve from its gradient
Pure Mathematics 2
Proof and polynomial algebra
P2 1.1–P2 1.3 - Proof and counterexamples
P2 2.1 - Dividing polynomials
P2 2.1 - Factor and remainder theorems
Circles
P2 3.1 - Equations of circles
P2 3.1 - Tangents and chords
Exponentials and logarithms
P2 5.1 - Exponential functions
P2 5.2 - Logarithms and their laws
P2 5.3 - Solving exponential equations
Sequences and series
P2 4.1, P2 4.3 - Describing sequences
P2 4.2 - Arithmetic sequences and sums
P2 4.4 - Geometric sequences and finite sums
P2 4.4 - Infinite geometric sums
P2 4.5 - Binomial expansion
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Trigonometric equations
P2 6.1 - Using trigonometric identities
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P2 6.2 - Solving trigonometric equations
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Calculus applications
P2 7.1 - Stationary points and curve shape
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P2 7.1 - Optimisation in context
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P2 8.1, P2 8.2 - Definite integrals and area
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P2 8.3 - The trapezium rule
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Pure Mathematics 3
Functions and graphs
P3 1.1 - Simplifying rational expressions
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P3 1.2 - Functions domain and range
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P3 1.2 - Composite and inverse functions
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P3 1.3 - Modulus graphs and equations
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P3 1.4 - Combining graph transformations
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Trigonometric functions
P3 2.1 - Reciprocal trigonometric functions
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P3 2.1, P3 2.2 - Inverse functions and identities
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P3 2.3 - Compound and double angles
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P3 2.3 - Combining sine and cosine
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Exponentials and models
P3 3.1, P3 3.2 - The exponential and natural logarithm
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P3 3.3 - Straightening curves with logarithms
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Differentiation
P3 4.1 - Differentiating standard functions
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P3 4.2 - Product and chain rules
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P3 4.2, P3 4.3 - Quotient and inverse derivatives
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P3 4.4 - Modelling growth and decay
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Integration
P3 5.1 - Integrating standard functions
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P3 5.2 - Recognising reverse chain rules
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Numerical methods
P3 6.1 - Locating roots
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P3 6.2 - Iterative solutions
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Pure Mathematics 4
Proof and algebra
P4 1.1 - Proof by contradiction
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P4 2.1 - Partial fractions
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P4 4.1 - Binomial series with rational powers
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Parametric curves and rates
P4 3.1 - Parametric equations
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P4 5.1 - Implicit and parametric differentiation
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P4 5.2 - Connected rates and differential equations
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Integration methods
P4 6.2 - Integration by substitution
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P4 6.2 - Integration by parts
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P4 6.3 - Integrating rational functions
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P4 6.4 - Solving separable differential equations
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P4 6.5 - Areas from parametric equations
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P4 6.1 - Volumes of revolution
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Vectors
P4 7.1–P4 7.3 - Vectors in two and three dimensions
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P4 7.4–P4 7.6 - Position vectors and lines
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P4 7.7 - The scalar product
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Mechanics 1
Models and vectors
M1 1.1 - Modelling objects and forces
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M1 2.1, M1 2.2 - Vectors in motion
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Straight-line motion
M1 3.1 - Reading motion graphs
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M1 3.1 - Constant acceleration
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Forces and motion
M1 4.1, M1 5.1 - Newton's laws and force components
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M1 4.4, M1 4.2 - Motion with friction
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M1 4.2 - Connected particles
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M1 4.3 - Momentum and impulse
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Equilibrium and moments
M1 5.2, M1 5.3 - Particle equilibrium
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M1 6.1 - Moments and parallel forces
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Mechanics 2
Variable motion and projectiles
M2 1.3, M2 1.4 - Motion using calculus
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M2 1.1, M2 1.2 - Projectile motion
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Centres of mass
M2 2.1 - Centres of mass of particles
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M2 2.2 - Centres of mass of shapes
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M2 2.3 - Equilibrium of a lamina
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Energy and power
M2 3.1 - Work and mechanical energy
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M2 3.1 - Power and motion
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Impacts and rigid bodies
M2 4.1, M2 4.2 - Momentum and restitution
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M2 4.3 - Successive collisions
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M2 5.1, M2 5.2 - Rigid-body equilibrium
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Statistics 1
Data and modelling
S1 1.1 - Modelling with data
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S1 2.1 - Reading statistical diagrams
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S1 2.2, S1 2.3 - Location and spread
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S1 2.4 - Skewness and outliers
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Probability
S1 3.1, S1 3.2 - Events and sample spaces
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S1 3.2–S1 3.4 - Conditional probability and independence
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S1 3.4 - Tree diagrams and repeated sampling
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Correlation and regression
S1 4.1, S1 4.2 - Regression and prediction
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S1 4.3 - Measuring correlation
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Random variables
S1 5.1, S1 5.2 - Discrete probability distributions
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S1 5.3 - Expectation and variance
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S1 5.4 - The discrete uniform model
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Normal distribution
S1 5.1 - Normal probabilities
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S1 5.1 - Finding Normal parameters
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Statistics 2
Discrete distributions
S2 1.1, S2 1.2 - The binomial distribution
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S2 1.1–S2 1.3 - The Poisson distribution
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Continuous random variables
S2 2.1, S2 2.2 - Probability density functions
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S2 2.2, S2 2.3, S2 2.5 - Cumulative functions and quantiles
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S2 2.4 - Continuous expectation and variance
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Continuous distributions
S2 3.1 - The continuous uniform model
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S2 3.2 - Normal approximations
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Sampling and hypothesis tests
S2 4.1, S2 4.2 - Samples and sampling distributions
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S2 4.3–S2 4.5 - Hypotheses and critical regions
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S2 4.6 - Testing a binomial probability
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S2 4.6 - Testing a Poisson mean
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Decision Mathematics 1
Algorithms
D1 1.1 - Following an algorithm
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D1 1.2 - Sorting lists
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D1 1.2 - Searching and bin packing
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Networks and routes
D1 2.1 - Graphs and network matrices
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D1 2.1 - Minimum spanning trees
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D1 2.2 - Dijkstra's algorithm
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D1 3.1 - Route inspection
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D1 3.2–D1 3.4 - Travelling salesman bounds
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Project planning
D1 4.1, D1 4.2 - Activity networks
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D1 4.3 - Critical paths and event times
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D1 4.4 - Float and scheduling
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Linear programming
D1 5.1 - Formulating linear programs
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D1 5.2, D1 5.3 - Solving linear programs
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