A-level Further Mathematics is an advanced course offered in the UK, designed for students who have a strong interest in mathematics and are considering studying the subject (or related subjects) at university. It's typically taken alongside A-level Mathematics and goes beyond the material covered in the standard A-level Mathematics course.
The AQA Further Mathematics A-level (7367) is structured into both compulsory and optional content. As of my knowledge cutoff in 2021, the structure was as follows:
Further Pure Mathematics: This component deepens understanding of pure mathematics. It covers topics like complex numbers, matrices, further algebra and functions, further calculus, further vectors, polar coordinates, hyperbolic functions, and differential equations.
Students usually choose two of the following options:
Further Pure Mathematics: Some students opt for a second further pure unit which covers additional topics not found in the compulsory content.
Further Statistics: This builds on the statistics content in A-level Mathematics, covering topics like regression, correlation, distributions, hypothesis testing, chi squared tests, and non-parametric tests.
Further Mechanics: This extends the mechanics content in A-level Mathematics, studying topics like momentum and impulse, work, energy and power, elastic strings and springs, and elastic collisions in two dimensions.
Discrete Mathematics: This introduces a new branch of mathematics not typically covered in A-level Mathematics. It includes topics like algorithms, graph theory, network flows, linear programming, game theory, and recurrence relations.
The course is assessed through examinations. Typically, students sit exams for each module or unit they study. These exams often involve problem-solving tasks that require deep understanding and application of mathematical concepts.
Studying Further Mathematics can be challenging due to the high level of abstract thinking required and the complexity of the material. However, it can also be incredibly rewarding and beneficial for those who wish to study mathematics or related subjects (like physics or engineering) at a higher level.