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Further Mathematics - KS5
Studying A Level Further Maths provides a deeper understanding of mathematical methods and techniques, giving students a strong advantage in highly competitive university courses requiring advanced problem-solving and quantitative skills.
- Exam Board: Edexcel
- Qualification: Further Mathematics A Level 9FM0
The Edexcel A Level Further Mathematics specification is a qualification that extends the content of A Level Mathematics, covering more complex mathematical concepts and building on students' skills in proof, modelling, and reasoning. It is designed for students considering further study in mathematically intensive fields such as engineering, physics, and computer science.
In the Core Pure elements of the course, key topics include:
- Proof: Including proof by induction.
- Complex numbers: Covers complex number arithmetic, the Argand diagram, complex conjugates, roots of polynomials, and De Moivre's theorem.
- Matrices: Matrix algebra, determinants, and their use in linear transformations.
- Series: Summing series using the method of differences and other techniques.
- Further algebra and functions: Includes roots of polynomials and rational functions.
- Further calculus: Advanced differentiation and integration techniques, including improper integrals.
- Vectors: Vectors in three dimensions, including the vector product.
- Polar coordinates: Conversions between Cartesian and polar coordinates, and calculating areas.
- Hyperbolic functions: Identities and calculus.
- Differential equations: First and second-order differential equations.
By studying A Level Further Maths, students extend their knowledge of core topics such as algebra, calculus, and matrices, while also exploring advanced areas like complex numbers, differential equations, and decision mathematics. They gain the ability to tackle highly abstract problems, develop sophisticated methods of reasoning, and make connections across different branches of mathematics. These skills not only stretch their mathematical thinking but also prepare them for the demands of university-level study in maths, science, and engineering.
Students must achieve a grade 8 in GCSE maths in order to study A Level Further Maths.
They need to have exceptional algebra skills, and be highly motivated and hard-working. Since Further Maths A Level can only be studied alongside Maths A Level, two-thirds of lessons will be maths-based, so students need to have a genuine passion for the subject!
The most successful students will learn new concepts quickly but will always challenge themselves to deepen their understanding. They will know the connections between different maths topics, and will be fluent and accurate in their skills. They will be proactive in seeking help when needed, and will reflect on errors in order to improve.
The A Level Further Mathematics qualification is assessed through four equally-weighted, externally examined papers, each contributing 25% to the final grade.
Paper 1: Core Pure Mathematics 1 (9FM0/01)
Paper 2: Core Pure Mathematics 2 (9FM0/02)
Paper 3: Further Mathematics Option 1: Further Mechanics (9FM0/3C)
Paper 4: Further Mathematics Option 2: Decision (9FM0/3D)
Each paper is 1 hour and 30 minutes long and is worth 75 marks. The two optional papers (Papers 3 and 4) are chosen by the school from a list of available applied units.