A-Level Further Mathematics (AQA 7367)

Course Overview 课程介绍

AQA 进阶数学，线性结构，数学、物理、CS 顶尖高校强烈推荐或必修。

A-Level Further Mathematics (AQA 7367) is a linear qualification extending well beyond A-Level Mathematics, examined by three terminal papers at the end of two years. Two papers cover compulsory Further Pure content (complex numbers, matrices, further algebra and series, proof, hyperbolic functions, polar coordinates, differential equations) and the third paper offers one optional strand in Mechanics, Statistics, Discrete mathematics or Further Pure. It is highly recommended, and often required, for mathematics, physics, engineering and computer science at top UK universities.

Key Facts 基本信息

Exam Board (考试局)	Assessment and Qualifications Alliance (AQA) · Oxford International AQA
Specification Code	AQA 7367 · OxfordAQA 9673
Structure	Linear structure, terminal exams at end of 2 years
Grading (评分)	A* - E (A* only for full A-Level)
Exam Papers	Paper 1 (Pure) + Paper 2 (Pure) + Paper 3 (one option)
Practical Endorsement	Not applicable (no practical endorsement for Further Mathematics)

AS / Year 1 Syllabus AS 阶段章节

AS1. Complex numbers

Complex numbers, Argand diagrams, modulus-argument form, de Moivre's theorem (introductory), loci in the complex plane
AS2. Matrices

Matrices, matrix algebra, determinants, inverses of 2x2 and 3x3 matrices, linear transformations, solving systems of linear equations
AS3. Further algebra and functions

Roots of polynomials, Vieta's formulae, summation of series using standard results, Maclaurin series (introductory)
AS4. Vectors and proof

Three-dimensional vectors, scalar and vector product, vector equations of lines and planes, proof by induction and contradiction
AS5. Series

Method of differences, higher-order recurrence relations, generating functions (introductory)

A2 / Year 2 Syllabus A2 阶段章节

A26. Advanced complex numbers and matrices

de Moivre's theorem (full), nth roots of unity, eigenvalues and eigenvectors, diagonalisation of matrices, Cayley-Hamilton theorem
A27. Further calculus

Improper integrals, mean values, integration using reduction formulae, Maclaurin and Taylor series, arc length and surface area
A28. Polar coordinates and hyperbolic functions

Polar coordinates and curves, area in polar form, hyperbolic functions and their inverses, Osborne's rule
A29. Differential equations

First-order differential equations (separable, integrating factor), second-order linear differential equations, coupled systems, modelling
A210. Option (one of Paper 3)

Option A: Further mechanics (momentum, collisions, circular motion, SHM, centres of mass, moments) · Option B: Further statistics (continuous random variables, chi-squared tests, confidence intervals, regression) · Option C: Discrete mathematics (graphs, algorithms, network flows, linear programming, game theory) · Option D: Further Pure (groups, number theory, further matrices and complex numbers)

Exam Structure (AQA 7367) 考试结构

Paper 1	Compulsory Pure Mathematics · 2h · 100 marks · 33.3% of A-Level
Paper 2	Compulsory Pure Mathematics · 2h · 100 marks · 33.3% of A-Level
Paper 3	One option from Further Mechanics / Further Statistics / Discrete Mathematics / Further Pure Mathematics · 2h · 100 marks · 33.3% of A-Level
Notes	Linear structure, terminal exams at end of 2 years; assumes full A-Level Mathematics 7357 content; calculators permitted; formulae booklet provided

Suitable Majors & Pathway 适用专业与衔接

数学、物理、工程、CS 顶尖高校的推荐或必修科目，竞争力提升明显。

A-Level Further Mathematics (AQA) is strongly preferred or required by leading UK universities for mathematics, theoretical physics, engineering, computer science, economics and actuarial science. The linear terminal exams reward deep abstract reasoning and rigorous proof, providing direct preparation for university real analysis, linear algebra, abstract algebra, differential equations and mathematical methods modules. Students targeting Cambridge, Oxford, Imperial, Warwick or UCL for maths-rich degrees are strongly advised to take it.