Roadmap
Pure Mathematics
Proof and mathematical language
Mp1, Ma1 - Proof, logic and mathematical arguments
Mp2 - Conjectures and counterexamples
Mp3 - Proof by contradiction
Algebra, equations and inequalities
Ma12, Ma13 - Rational indices and index laws
Ma10, Ma11 - Surds and rationalising denominators
Ma3, MC3 - Quadratic graphs and the discriminant
Ma2 - Solving quadratic equations and disguised quadratics
Ma4, Ma5 - Simultaneous equations and intersections
Ma7–Ma9 - Inequalities, sets and graphical regions
Mf1, Mf2 - Polynomials, division and the factor theorem
Ma16 - Rational expressions and algebraic division
Ma15 - Partial fractions with linear factors
Functions and graphs
Mf6, Mf7 - Modulus graphs, equations and inequalities
MC1, MC2, MC4, Ma6 - Polynomial graphs, roots and intercepts
MC6, Mg8 - Reciprocal graphs, asymptotes and intersections
Ma14 - Proportional relationships and models
Mf3 - Functions, mappings, domain and range
Mf4, Mf5 - Composite and inverse functions
MC7, MC8 - Transforming and combining graphs
Mf8 - Building, comparing and refining function models
Coordinate geometry
Mg1–Mg6 - Straight lines, distances and gradients
Mg7 - Straight line models and rates of change
Mg10 - Circle equations, centres and radii
Mg9, Mg11 - Circle intersections, chords and tangents
Mg12–Mg14 - Parametric curves and cartesian equations
Mg16 - Parametric models and restricted parameters
Sequences and series
Ms1, Ms2 - Integer binomial expansion and combinations
Ms3–Ms5 - Rational binomial expansions and approximation
Ms6–Ms11 - Sequences, recurrence and sigma notation
Locked
Ms12, Ms13 - Arithmetic sequences and sums
Locked
Ms14–Ms16 - Geometric series and sums to infinity
Locked
Ms17 - Modelling growth, decay and finance with sequences
Locked
Trigonometry
Mt1, Mt2, Mt8 - The unit circle, exact values and trigonometric graphs
Locked
Mt3, Mt4 - Triangle area, sine rule and cosine rule
Locked
Mt10, Mt11 - Radians, arc length and sector area
Locked
Mt12 - Small angle approximations
Locked
Mt9, Mt13–Mt15 - Reciprocal and inverse trigonometric functions
Locked
Mt5, Mt6 - Fundamental trigonometric identities
Locked
Mt16, Mt17 - Compound and double angle formulae
Locked
Mt18 - Combining sine and cosine into harmonic form
Locked
Mt7, Mt19 - Trigonometric equations on given intervals
Locked
Mt20 - Proving trigonometric identities
Locked
Mt21 - Trigonometric models in context
Locked
Exponentials and logarithms
ME1, ME8, ME9 - Exponential functions and the number e
Locked
ME2–ME5, ME10 - Logarithms, natural logs and their laws
Locked
ME6 - Solving exponential and logarithmic equations
Locked
ME7 - Linearising power and exponential models
Locked
ME11 - Exponential growth and decay models
Locked
Differentiation
Mc1–Mc4 - Derivatives as gradients and rates of change
Locked
Mc5 - First principles and the power rule
Locked
Mc9 - Tangents and normals to curves
Locked
Mc6–Mc8, MC5 - Second derivatives, stationary points and monotonicity
Locked
Mc17, Mc18, MC9 - Concavity and points of inflection
Locked
Mc10 - Differentiating exponential and logarithmic functions
Locked
Mc11 - Differentiating trigonometric functions
Locked
Mc12, Mc13 - Product and quotient rules
Locked
Mc14, Mc15 - The chain rule, inverse derivatives and connected rates
Locked
Mc16, Mg15 - Implicit and parametric differentiation
Locked
Differential equations
Mc31 - Forming differential equation models
Locked
Mc32, Mc33 - Separable differential equations and their solutions
Locked
Integration
Mc19–Mc21 - Integration, antiderivatives and constants
Locked
Mc22, Mc23, Mc25 - Definite integrals, signed area and limits of sums
Locked
Mc24 - Integrating exponential, logarithmic and trigonometric forms
Locked
Mc26 - Areas between curves and parametric areas
Locked
Mc27, Mc28 - Integration by substitution
Locked
Mc29 - Integration by parts
Locked
Mc30 - Integrating rational functions with partial fractions
Locked
Numerical methods
Me1, Me2 - Root intervals, accuracy and failed sign tests
Locked
Me3 - Fixed point iteration and cobweb diagrams
Locked
Me4, Me5 - Newton–Raphson and convergence failures
Locked
Mc34, Mc35 - Trapezium rule and area bounds
Locked
Me6 - Numerical solutions in context
Locked
Vectors
Mv1–Mv3 - Vectors, components, magnitude and direction
Locked
Mv4–Mv6 - Position vectors, distances and vector problems
Locked
Mv7 - Vectors in three dimensions
Locked
Mathematical comprehension
OT1.5, OT2.1, OT2.3 - Reading and checking an unfamiliar mathematical passage
Locked
OT2.2, OT2.5, OT3.2, OT3.3 - Applying and extending mathematics from an unfamiliar passage
Locked
Statistics
Sampling and statistical enquiry
Mp21–Mp25 - Samples, random sampling and bias
Locked
Data presentation and interpretation
MD1–MD5 - Univariate diagrams, histograms and distributions
Locked
MD6–MD8 - Scatter diagrams, regression and correlation
Locked
MD10, MD11 - Averages, percentiles and spread
Locked
MD12 - Variance, standard deviation and grouped estimates
Locked
MD9, MD13, MD14 - Outliers, missing values and data cleaning
Locked
Prescribed large data and technology
2b, 2c - Exploring the 2027 large data set
Locked
Probability
Mu1–Mu5 - Events, independence and probability diagrams
Locked
Mu6, Mu7 - Conditional probability and two-way data
Locked
MR13 - Probability modelling and assumptions
Locked
Statistical distributions
MR6, MR7 - Finite discrete probability distributions
Locked
MR1–MR5 - Binomial models and probabilities
Locked
MR9–MR12 - Normal models, standardisation and inverse probabilities
Locked
MR8 - Choosing distributions and the normal approximation
Locked
Statistical hypothesis testing
MH1–MH3 - Hypotheses, significance and statistical decisions
Locked
MH4–MH6 - Testing a binomial proportion
Locked
MH7–MH9 - The sample mean and normal mean tests
Locked
MH10, MH11 - Correlation coefficients and significance tests
Locked
Mechanics
Models, quantities and units
Mp33–Mp35 - Mechanical quantities, SI units and dimensions
Locked
Mp31, Mp32, MF1–MF3 - Particles, forces and mechanical assumptions
Locked
Kinematics
Mk1–Mk4 - Motion language and kinematics graphs
Locked
Mk7, Mk8 - Constant acceleration formulae
Locked
Mk5, Mk6 - Variable acceleration and calculus in motion
Locked
Mk9–Mk12 - Motion in two dimensions with vectors
Locked
My1–My5 - Projectile motion and trajectories
Locked
Forces and Newton's laws
Mn1–Mn3, Mn6 - Newton's laws and equations of motion
Locked
MF4, MF6, Mn7 - Resolving forces and dynamics in a plane
Locked
MF5, MF7–MF9 - Particle equilibrium and polygons of forces
Locked
Mn4, Mn5 - Connected particles, strings and pulleys
Locked
Mn7, Mk12 - Variable forces and vector dynamics
Locked
MF10, MF11 - Contact forces, friction and limiting equilibrium
Locked
MF12 - Static and limiting equilibrium on rough surfaces
Locked
MF12 - Motion on rough surfaces
Locked
Moments and rigid bodies
MF13–MF15 - Moments and rigid-body equilibrium
Locked
MF16 - Beams, laminas and centres of mass
Locked