AQA A-Level Further Mathematics (7367): complete guide to the compulsory and optional content and the exams

AQA A-Level Further Mathematics (specification 7367) is a two-year linear course taken in addition to A-Level Mathematics and assessed by written papers at the end of Year 13. It pairs a large compulsory Core pure component with optional applied content chosen by the centre. This page is the index: below is a map of the Core pure content, the three optional areas, the exam demand, and how to study each one.

The compulsory Core pure content

Every Further Mathematics student studies Core pure, the mathematical backbone of the qualification and roughly half the assessment.

Complex numbers

Arithmetic and conjugates, the Argand diagram, modulus-argument and exponential form, de Moivre's theorem, roots of unity, complex roots of polynomials and loci.

Matrices

Arithmetic, determinants, inverses of $2 \times 2$ and $3 \times 3$ matrices, matrices as linear transformations, invariant points and lines, and solving linear systems.

Further algebra and functions

Series, the relationships between roots and coefficients of polynomials, and the method of differences.

Further calculus

Improper integrals, volumes of revolution, the mean value of a function, arc length, surface area of revolution, integration by partial fractions and the Maclaurin series.

Further vectors

Lines and planes in three dimensions, the scalar and vector products, angles, intersections and shortest distances.

Polar coordinates

Polar curves, the link to Cartesian coordinates, and areas enclosed by polar curves.

Hyperbolic functions

Definitions from exponentials, identities, logarithmic inverse forms, and differentiation and integration.

Differential equations

First order linear equations by integrating factor and second order constant-coefficient equations, with applications to damped and forced systems.

Proof by induction

Rigorous proofs for summation formulae, divisibility, recurrence relations and powers of matrices.

The optional applied areas

A centre chooses which optional content to teach, each examined in a dedicated paper.

• Further mechanics - dimensional analysis, momentum and collisions, work energy and power, circular motion, and centre of mass.
• Further statistics - discrete random variables, the Poisson distribution, further hypothesis testing, chi-squared tests, and confidence intervals.
• Discrete mathematics - graphs and networks, network algorithms, critical path analysis, linear programming, and game theory.

Exam demand

Further Mathematics is the most demanding A-Level for mathematical fluency. It assumes the whole of A-Level Mathematics and layers new objects and techniques on top. A calculator is allowed throughout and AQA provides a formulae booklet. Method marks dominate, so clear, accurate, logical working is essential, and there is no coursework.

How to study Further Mathematics

Further Mathematics rewards fluent technique and clear presentation.

1. Master Core pure first. It supplies the tools every applied option needs, so build it topic by topic.
2. Drill each method to automaticity. Dividing complex numbers, inverting matrices, evaluating improper integrals, solving differential equations and laying out induction proofs should be second nature.
3. Show every step. Method marks dominate, so write working an examiner can follow, especially in proofs and algorithms.
4. Then revise your optional areas. Practise each model or algorithm fully, in context.
5. Sit mixed timed papers. Combine topics under exam conditions from the start of Year 13.

The areas, topic by topic

Each area has specification-level answer pages with worked exam questions and cross-links, plus an overview guide and quiz:

• Core pure overview
• Further mechanics overview
• Further statistics overview
• Discrete mathematics overview

Browse the full set at /a-level-aqa/further-mathematics/syllabus.

For the official specification

AQA publishes the full specification (7367), past papers and mark schemes at aqa.org.uk. Always revise from the current specification and AQA's own past papers, because question style and the optional structure are board-specific.