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Mathematics (Further)
The Further Mathematics course is a separate course which stands alongside the main A-Level course.
Further Mathematics allows you to explore a greater range of topics in the mathematical canon, with the standard of the topics at the same level as the main A-Level course. Further Mathematics is not just for those who wish to study mathematics at university. Anyone who wants to study a mathematics related degree should consider the advantage of having an A-Level in Further Mathematics.
You will study a wide variety of different areas of mathematics, including pure mathematics, decision mathematics and statistics.
Further Mathematics will enable you to improve your mathematical understanding and your standard in the A-Level Mathematics course. It will also considerably develop your problem-solving skills helping you to make a smooth transition on to any degree or training programme containing mathematical elements.
Entry Criteria
7 in GCSE Mathematics (preferably 8 and above).
Companion Subjects
Career Paths
- Medicine
- Accounting/Finance
- Software Development
- Engineering
- Actuary/Insurance
- Research
- Data Analysis
- Business Management
Subject Intent
Further Maths is for students who love a challenge. It deepens understanding of core mathematical ideas and introduces exciting new areas—like complex numbers, matrices, and differential equations. This course prepares students for competitive university courses in maths, physics, engineering, and economics, and develops confidence in abstract thinking, logical reasoning, and problem-solving.
Course Overview
Students take A-Level Maths alongside Further Maths. You’ll build on A-Level content and explore three areas:
Core Pure Mathematics
- Complex numbers
- Matrices
- Proof by induction
- Polar coordinates
- Further sequences and series
- Hyperbolic functions
- Further vectors
- Further integration
- Differential equations
- Numerical methods
Mechanics
- Centres of mass
- Forces and energy
- Momentum
- Circular motion
Discrete Mathematics
- Graph theory
- Networks
- Critical path analysis
- Linear programming
- Group theory
Assessment Overview
All papers are calculator-allowed. Questions include structured, multi-step problems requiring high-level mathematical thinking.
- Paper 1 - Pure Mathematics
- 2 hours
- 100 Marks
- 33⅓%
- Paper 2 - Pure Mathematics
- 2 hours
- 33⅓%
- Paper 3 - Mechanics and Discrete
- 2 hours
- 33⅓%
Homework & Independent Study
- Regular problem-solving tasks and past paper practice
- Review of example problems and teacher-led model solutions
- Exploration of extension topics and university-level questions
- Independent research for deeper mathematical insight
Enrichment Opportunities
- UKMT Senior Maths Challenge and Olympiad preparation
- Trips to university taster lectures or outreach events
- Extension classes for STEP, MAT or TMUA entrance exams
- Access to mathematical journals, puzzles, and careers workshops
Where Can Further Maths Take You?
Further Maths is highly regarded for courses in:
- Mathematics, Physics, Engineering, Economics, Computer Science
- It’s recommended (or required) for many top universities in STEM fields
- It also opens doors to careers in data science, software development, finance, research, teaching, and more.