UK · Subject guide
Further Mathematics
A-Level Further Mathematics (AQA 7367), against the DfE/Ofqual subject content.
01 · Overview
Further Mathematics
A-Level Further Mathematics (AQA 7367), against the DfE/Ofqual subject content.
- Subject guide
- A-Levels
- Topics mapped
- 13
02 · Complete topic map
Complete topic map
Every topic recorded for this subject in the curriculum is reproduced below in its full hierarchy. The descriptions reflect the mapped scope without implying additional exam rules.
- 01
Proof
Constructing rigorous proofs, with an emphasis on proof by mathematical induction applied to series sums, divisibility results and powers of matrices.
- 02
Complex numbers
Arithmetic and geometry of complex numbers, including Argand diagrams, modulus-argument form, de Moivre's theorem, roots of unity and loci in the complex plane.
- 03
Matrices
Matrix algebra up to order 3x3, determinants and inverses, linear transformations in two and three dimensions, and solving systems of linear equations.
- 04
Further algebra and functions
Roots of polynomials and their relationships with coefficients, the method of differences, summation of series, and Maclaurin series expansions.
- 05
Further calculus
Improper integrals, volumes of revolution, mean values, partial fractions in integration, and arc length and surface area of revolution.
- 06
Further vectors
Vector and Cartesian equations of lines and planes, scalar and vector products, and finding intersections, angles and distances in three dimensions.
- 07
Polar coordinates
Working with polar coordinates, converting between polar and Cartesian forms, sketching polar curves and finding areas enclosed by them.
- 08
Hyperbolic functions
Definitions and properties of hyperbolic and inverse hyperbolic functions, their logarithmic forms, and their differentiation and integration.
- 09
Differential equations
Solving first-order equations via integrating factors and second-order linear equations, including modelling damped and forced oscillations.
- 10
Numerical methods
Numerical techniques for evaluating integrals and solving equations, such as the mid-ordinate rule, Simpson's rule and Euler's step-by-step methods.
- 11
Optional application: Mechanics
Optional applied route covering dimensional analysis, momentum and collisions, work-energy-power, circular motion, and centres of mass and moments.
- 12
Optional application: Statistics
Optional applied route covering discrete and continuous random variables, the Poisson and exponential distributions, hypothesis-test errors, chi-squared tests, t-distribution inference and confidence intervals.
- 13
Optional application: Discrete mathematics
Optional applied route covering graphs and networks, network flows, linear programming, critical path analysis, game theory and binary operations.
03 · Where this subject applies
Where this subject applies
These pathways and regions are explicitly connected to the subject in the curriculum.
Pathways and specifications
AS-Level
Advanced Subsidiary — the first year of A-Level study (standalone or first half of the full A-Level).
A-Level (A2)
The full Advanced Level — AS content plus the second-year A2 content.
Nations and regions
All registered regions
04 · Official sources
Official sources
The public sources below are referenced directly by this subject or by one of its topics.
This editorial selection points to the relevant official bodies. Always confirm current requirements, dates and amendments with your school or college and the appropriate awarding organisation.
2
Public references
UK · EuraStudy Guides
Place this subject inside the complete curriculum.
Open the curriculum guide to see every subject and topic, or continue to EuraStudy Summa to begin working with the material.