A-Level Maths Topics: The Complete List for Edexcel, AQA, OCR A & MEI

The complete A-Level Maths syllabus

A-Level Maths content is nationally defined — every exam board (Edexcel, AQA, OCR A, OCR MEI) covers the same core content, though the order of teaching and specific question styles differ.

This is the complete topic list. Use it to check coverage and identify gaps.

Pure Mathematics (67% of A-Level)

Algebra and Functions

• Laws of indices and surds
• Quadratic functions, completing the square, discriminant
• Simultaneous equations (linear and quadratic)
• Inequalities (linear, quadratic, rational)
• Polynomials: factor theorem, remainder theorem
• Partial fractions (including repeated factors)
• Algebraic long division
• Functions: domain, range, composite, inverse
• Modulus function and equations/inequalities
• Transformations of graphs

Coordinate Geometry

• Straight line geometry: gradient, parallel, perpendicular
• Circle equation: (x−a)² + (y−b)² = r²
• Tangent and normal to a circle
• Intersection of lines and circles

Sequences and Series

• Arithmetic sequences: nth term, sum
• Geometric sequences: nth term, sum, sum to infinity
• Binomial expansion: (1+x)ⁿ for positive integer n
• Binomial expansion: (1+x)ⁿ for any rational n, range of validity

Trigonometry

• Exact values: 30°, 45°, 60° (sin, cos, tan)
• Radians: converting, arc length, sector area
• Trigonometric identities: Pythagorean identities
• Compound angle formulae
• Double angle formulae
• R sin(θ + α) or R cos(θ + α) form
• Inverse trig functions: arcsin, arccos, arctan
• Solving trigonometric equations in a given range
• Reciprocal trig functions: sec, cosec, cot

Exponentials and Logarithms

• Exponential function: y = eˣ and its graph
• Logarithms: natural log ln x, log₁₀
• Laws of logarithms
• Solving exponential equations
• Exponential growth and decay models

Calculus — Differentiation

• First principles (limit definition)
• Power rule, chain rule, product rule, quotient rule
• Differentiating: eˣ, ln x, sin x, cos x, tan x, sec x, cosec x, cot x
• Implicit differentiation
• Parametric differentiation
• Second derivative, concavity, points of inflection
• Stationary points and optimisation
• Connected rates of change

Calculus — Integration

• Reverse power rule
• Integration of standard functions
• Integration by substitution
• Integration by parts
• Integration using partial fractions
• Definite integrals and areas under/between curves
• Trapezium rule (numerical integration)
• Differential equations: separating variables
• Differential equations: integrating factor (some boards)

Proof

• Proof by deduction
• Proof by contradiction
• Proof by exhaustion
• Disproof by counterexample

Numerical Methods (Edexcel/OCR)

• Locating roots by sign change
• Newton-Raphson method
• Iteration: xₙ₊₁ = f(xₙ)
• Fixed point iteration convergence

Vectors

• 2D and 3D vectors: addition, scalar multiplication
• Magnitude and unit vectors
• Position vectors
• Dot product and angle between vectors
• Equation of a line in vector form
• Intersection of lines (or showing they don't intersect)

Statistics (17% of A-Level)

• Data presentation: histograms, cumulative frequency, box plots
• Measures of location and spread: mean, median, IQR, variance, standard deviation
• Outliers and cleaning data
• Correlation and linear regression
• Probability: AND/OR rules, tree diagrams
• Conditional probability and independence
• Discrete probability distributions
• Binomial distribution: conditions, mean, variance
• Normal distribution: standardisation, finding probabilities, inverse normal
• Hypothesis testing: binomial and normal
• Statistical hypothesis test: H₀, H₁, significance level, critical region, p-value
• Large data set interpretation (AQA, OCR — pre-release data)

Mechanics (17% of A-Level)

• Kinematics in 1D: SUVAT equations
• Kinematics in 2D: vectors, projectile motion
• Graphs: displacement-time, velocity-time, acceleration-time
• Forces and Newton's laws of motion
• Weight, normal reaction, friction (including F = μN)
• Resolving forces: inclined planes, equilibrium
• Momentum and impulse (some boards)
• Moments and static equilibrium (some boards)
• Connected particles: Atwood machine, particles on surfaces
• Variable acceleration: calculus (v = dx/dt, a = dv/dt)

OCR MEI Additional Content

OCR MEI includes additional components:

• Comprehension paper (unseen mathematical text)
• Further Statistics or Further Mechanics or Decision Mathematics
• Additional pure content: hyperbolic functions, polar coordinates (in Further Maths pathway)

How to use this list

Go through every topic. Mark each one:

• Green: I can answer any question on this
• Amber: I know the basics but would struggle with harder questions
• Red: I'd lose most marks on questions here

Every amber and red topic needs questions generated in Infinity Stars until it moves to green. This list is your audit tool, not your reading list.