All about A level Mathematics – course information

A level Maths and A level Further Maths (two separate qualifications) build on topics that students learn at GCSE, such as algebra, geometry, trigonometry and probability. Three (sometimes four) broad areas are covered for both qualifications: Pure Maths, Mechanics and Statistics, or additionally Decision Maths if offered by the college.

Pure Maths, which deals with abstract problems and is the foundation for all other areas of maths, introduces students to mathematical proofs – the basis of the logic and philosophy behind whether a mathematical statement is true or false. A level Maths students expand their knowledge of algebra, inequalities, functions and their graphs, and trigonometry – and, of course, learn calculus, with differentiation and integration, and the geometric joy of vectors. Students will also work on arithmetic and geometric series and discover that the sky is not the limit.

Applied Maths consists of Mechanics and Statistics and involves mathematical modelling for practical real-world outcomes. For Mechanics, which is a branch of physics, students apply the knowledge of vectors, calculus and trigonometry, for example, to model how the motion of objects and the forces that act upon them work in the physical world. Statistics may involve examining data samples, looking at their distribution and making predictions based on probability.

Essentially, modelling is the process of describing a real-world problem in mathematical terms, considering what laws or mathematical principles may apply, solving the problem mathematically then drawing conclusions on how this can be used practically. Examples include forecasting the weather, working out the trajectory of a rocket, developing a new drug or predicting the collapse of the stock market. Importantly, models can be refined and limitations identified.

Decision Maths is closely aligned with computer science and is often applied in computing as well as industry, business and military operations. It involves optimising and modelling with algorithms, working out critical pathways, logistics, network flows and game theory, and uses only discrete rather continuous data; both of which are used in statistics.

A level Further Maths builds upon all areas covered in A level Maths. It explores how these topics are interconnected and delves deeper into the philosophy behind them. Students go on to

learn about the theory of complex numbers, matrices, polar coordinates, vectors, transformations and hyperbolic functions.

Students should have a strong foundation in GCSE Maths (or equivalent) having achieved at least a grade 6 or 7. A level Further Maths is far more challenging and involves learning complex topics and being prepared to drill down to first principles. Ideally, students considering it should have achieved GCSE grade 9 (or equivalent).

A problem-solving mindset, good imagination, hard work and determination to find solutions are key requirements for studying maths. It is also crucial to be able to show how you have arrived at solutions. Regular and consistent past paper question practice and timekeeping will be essential to develop understanding and to get a good A level result.

Yes, it is possible to take A level Maths in one year but students must be able, confident and committed as the course will be very intensive and fast-paced. Most students take it over two years.

For very capable students, it may be an advantage to complete A level Maths in year 12, then A level Further Maths in year 13. This allows students to take up a further subject in year 13, if desired, or commit more time to their Further Maths studies. Not all colleges follow this format and may only offer A level Maths and A level Further Maths concurrently over two years.

For students who find problem solving hard but rewarding, and are fascinated by why and how maths works, then A level Further Maths is a great choice.

Students applying for maths and/or engineering-related courses at top UK universities, including the London School of Economics, will typically be required to take A level Further Maths.

Both A level Maths and Further Maths qualifications are assessed by written examinations only; there is no coursework. Although exam board specifications may differ slightly, students can typically expect to sit two pure maths papers and one for mechanics and statistics, and/or decision maths. There may also be options for A level Further Maths students to sit only pure maths papers, without doing the applied.