Roadmap
Pure Mathematics
Proof and mathematical language
1.01a, 1.01b - Proof, logic and mathematical arguments
1.01c - Conjectures and counterexamples
1.01d - Proof by contradiction
Algebra, equations and inequalities
1.02a - Rational indices and index laws
1.02b - Surds and rationalising denominators
1.02d, 1.02e - Quadratic graphs and the discriminant
1.02f - Solving quadratic equations and disguised quadratics
1.02c - Simultaneous equations and intersections
1.02g–1.02i - Inequalities, sets and graphical regions
1.02j - Polynomials, division and the factor theorem
1.02k - Rational expressions and algebraic division
1.02y - Partial fractions with linear factors
Functions and graphs
1.02l, 1.02s, 1.02t - Modulus graphs, equations and inequalities
1.02m, 1.02n, 1.02p - Polynomial graphs, roots and intercepts
1.02o, 1.02q - Reciprocal graphs, asymptotes and intersections
1.02r - Proportional relationships and models
1.02u - Functions, mappings, domain and range
1.02v - Composite and inverse functions
1.02w, 1.02x - Transforming and combining graphs
1.02z - Building, comparing and refining function models
Coordinate geometry
1.03a, 1.03b - Straight lines, distances and gradients
1.03c - Straight line models and rates of change
1.03d, 1.03e - Circle equations, centres and radii
1.03f - Circle intersections, chords and tangents
1.03g - Parametric curves and cartesian equations
1.03h - Parametric models and restricted parameters
Sequences and series
1.04a, 1.04b - Integer binomial expansion and combinations
1.04c, 1.04d - Rational binomial expansions and approximation
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1.04e–1.04g - Sequences, recurrence and sigma notation
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1.04h - Arithmetic sequences and sums
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1.04i, 1.04j - Geometric series and sums to infinity
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1.04k - Modelling growth, decay and finance with sequences
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Trigonometry
1.05a, 1.05f, 1.05g - The unit circle, exact values and trigonometric graphs
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1.05b, 1.05c - Triangle area, sine rule and cosine rule
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1.05d - Radians, arc length and sector area
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1.05e - Small angle approximations
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1.05h, 1.05i, 1.05k - Reciprocal and inverse trigonometric functions
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1.05j - Fundamental trigonometric identities
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1.05l, 1.05m - Compound and double angle formulae
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1.05n - Combining sine and cosine into harmonic form
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1.05o - Trigonometric equations on given intervals
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1.05p - Proving trigonometric identities
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1.05q - Trigonometric models in context
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Exponentials and logarithms
1.06a, 1.06b - Exponential functions and the number e
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1.06c–1.06f - Logarithms, natural logs and their laws
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1.06g - Solving exponential and logarithmic equations
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1.06h - Linearising power and exponential models
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1.06i - Exponential growth and decay models
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Differentiation
1.07a–1.07c - Derivatives as gradients and rates of change
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1.07g, 1.07i - First principles and the power rule
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1.07m - Tangents and normals to curves
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1.07d, 1.07e, 1.07n, 1.07o - Second derivatives, stationary points and monotonicity
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1.07f, 1.07p - Concavity and points of inflection
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1.07j, 1.07l - Differentiating exponential and logarithmic functions
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1.07h, 1.07k - Differentiating trigonometric functions
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1.07q - Product and quotient rules
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1.07r - The chain rule, inverse derivatives and connected rates
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1.07s - Implicit and parametric differentiation
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Integration
1.08a, 1.08b - Integration, antiderivatives and constants
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1.08d, 1.08e, 1.08g - Definite integrals, signed area and limits of sums
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1.08c - Integrating exponential, logarithmic and trigonometric forms
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1.08f - Areas between curves and parametric areas
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1.08h - Integration by substitution
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1.08i - Integration by parts
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1.08j - Integrating rational functions with partial fractions
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Differential equations
1.07t - Forming differential equation models
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1.08k, 1.08l - Separable differential equations and their solutions
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Numerical methods
1.09a, 1.09b - Root intervals, accuracy and failed sign tests
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1.09c - Fixed point iteration and cobweb diagrams
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1.09d, 1.09e - Newton–Raphson and convergence failures
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1.09f - Trapezium rule and area bounds
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1.09g - Numerical solutions in context
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Vectors
1.10a, 1.10c, 1.10d - Vectors, components, magnitude and direction
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1.10e–1.10g - Position vectors, distances and vector problems
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1.10b - Vectors in three dimensions
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Statistics
Sampling and statistical enquiry
2.01a–2.01d - Samples, random sampling and bias
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Data presentation and interpretation
2.02a, 2.02b - Univariate diagrams, histograms and distributions
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2.02c–2.02e - Scatter diagrams, regression and correlation
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2.02f - Averages, percentiles and spread
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2.02g - Variance, standard deviation and grouped estimates
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2.02h–2.02j - Outliers, missing values and data cleaning
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Prescribed large data and technology
2b, 2c - Exploring the 2027 large data set
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Probability
2.03a, 2.03b - Events, independence and probability diagrams
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2.03c, 2.03d - Conditional probability and two-way data
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2.03e - Probability modelling and assumptions
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Statistical distributions
2.04a - Finite discrete probability distributions
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2.04b, 2.04c - Binomial models and probabilities
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2.04e–2.04g - Normal models, standardisation and inverse probabilities
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2.04d, 2.04h - Choosing distributions and the normal approximation
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Statistical hypothesis testing
2.05a, 2.05c - Hypotheses, significance and statistical decisions
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2.05b - Testing a binomial proportion
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2.05d, 2.05e - The sample mean and normal mean tests
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2.05f, 2.05g - Correlation coefficients and significance tests
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Mechanics
Models, quantities and units
3.01a–3.01c - Mechanical quantities, SI units and dimensions
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3.03a, 3.03f, 3.03g, 3.03i, 3.03j - Particles, forces and mechanical assumptions
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Kinematics
3.02a–3.02c - Motion language and kinematics graphs
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3.02d - Constant acceleration formulae
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3.02f - Variable acceleration and calculus in motion
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3.02e, 3.02g, 1.10h - Motion in two dimensions with vectors
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3.02h, 3.02i - Projectile motion and trajectories
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Forces and Newton's laws
3.03b–3.03d, 3.03h - Newton's laws and equations of motion
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3.03e, 3.03l, 3.03p - Resolving forces and dynamics in a plane
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3.03m, 3.03n - Particle equilibrium and polygons of forces
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3.03k, 3.03o - Connected particles, strings and pulleys
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3.03q - Variable forces and vector dynamics
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3.03r–3.03t - Contact forces, friction and limiting equilibrium
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3.03u - Static and limiting equilibrium on rough surfaces
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3.03v - Motion on rough surfaces
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Moments and rigid bodies
3.04a, 3.04b - Moments and rigid-body equilibrium
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3.04c - Beams, ladders and centres of mass
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