Edexcel International AS Further Maths specification (XFM01)
Understanding the exam specification is key to doing well in your Edexcel International AS Further Maths exam. It lays out exactly what you need to learn, how you'll be assessed, and what skills the examiners seek. Whether you're working through the course for the first time or revising for your final exams, the specification helps you stay focused and confident in your preparation.
We've included helpful revision tools to support you in putting the specification into practice. Wherever you're starting from, you'll find everything you need to feel prepared, from the official specification to high-quality resources designed to help you succeed.
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In the next section, you'll find a simplified summary of the official Edexcel International AS Further Maths specification, along with a breakdown of key topics, assessment structure, and useful study resources. We've also included links to topic-level guides and revision tools to help you put the specification into practice.
Contents
Disclaimer
This page includes a summary of the official Edexcel International AS Further Maths (XFM01) specification, provided to support your revision. While we've made every effort to ensure accuracy, Save My Exams is not affiliated with the awarding body.
For the most complete and up-to-date information, we strongly recommend consulting the official Edexcel specification PDF.
Specification overview
Pearson Edexcel International Advanced Subsidiary in Further Mathematics is designed to deepen students’ understanding of mathematics beyond the core concepts of A Level. The course encourages learners to develop advanced problem-solving skills, mathematical reasoning, and logical thinking. It builds on knowledge gained in AS Mathematics, introducing complex numbers, matrix algebra, advanced algebraic methods, and proof techniques. The specification is structured flexibly with optional units, allowing a broad exploration of pure mathematics, mechanics, statistics, and decision mathematics. It supports progression to mathematics, engineering, physics, and other STEM-related degrees by fostering mathematical rigour, abstraction skills, and practical application of advanced concepts.
Subject content breakdown
FP1: Further Pure Mathematics 1
- Complex numbers: definitions, arithmetic, geometric representation, quadratic roots
- Roots of quadratic equations: sums, products, manipulation, formation with new roots
- Numerical solutions: interval bisection, linear interpolation, Newton-Raphson method
- Coordinate systems: parabolas, hyperbolas, parametric equations, focus-directrix property, tangents, normals
- Matrix algebra: addition, scalar multiplication, matrix products, 2×2 determinants, inverses
- Transformations using matrices: linear transformations, geometry, combinations, inverse transformations
- Series: summation of finite series
- Proof by induction: series summation, divisibility, recurrence relations, matrix products
FP2: Further Pure Mathematics 2
- Inequalities: algebraic and modulus inequalities
- Series: method of differences
- Complex numbers: Euler's relation, De Moivre’s theorem, trigonometric identities, Argand diagrams, transformations
- First order differential equations: separable, linear forms, substitutions
- Second order differential equations: linear with constant coefficients, reducible by substitution
- Maclaurin and Taylor series: derivation, use, differential equation solutions
- Polar coordinates: equations, sketches, area calculation, tangents
FP3: Further Pure Mathematics 3
- Hyperbolic functions: definitions, identities, inverses
- Coordinate systems: ellipses, hyperbolas, focus-directrix, tangents, normals
- Differentiation: hyperbolic functions, inverse functions
- Integration: hyperbolic, inverse functions, substitutions, reduction formulae, arc length, surface area
- Vectors: vector and scalar triple products, lines, planes, intersections
- Further matrix algebra: transformations in 3D, combinations, transpose, 3×3 determinants and inverses, eigenvalues, diagonalisation
Assessment structure
Unit FP1: Further Pure Mathematics 1
- 1 hour 30 minutes, 75 marks
- Externally assessed written exam
- Compulsory for IAS Further Mathematics
- Topics: complex numbers, roots of quadratics, numerical methods, coordinate systems, matrices, series, transformations, proof
Unit FP2: Further Pure Mathematics 2
- 1 hour 30 minutes, 75 marks
- Externally assessed written exam
- Optional unit for IAS Further Mathematics
- Topics: inequalities, series, advanced complex numbers, differential equations, Taylor and Maclaurin series, polar coordinates
Unit FP3: Further Pure Mathematics 3
- 1 hour 30 minutes, 75 marks
- Externally assessed written exam
- Optional unit for IAS Further Mathematics
- Topics: hyperbolic functions, coordinate geometry, differentiation, integration, vectors, matrix algebra
Assessment Approach
- Each unit equally weighted
- Assessments available in January and June
- Combination of compulsory and optional units for certification
- Calculators permitted in all examinations
- Modular assessment structure allows staged progression
Key tips for success
Doing well in your Edexcel International AS Further Maths isn't just about how much you study, but how you study. Here are a few proven tips to help you stay on track
- Start with a clear plan: Break the subject into topics and create a revision schedule that allows enough time for each. Start early to avoid last-minute stress.
- Focus on understanding, not memorising: Use our revision notes to build a strong foundation in each topic, making sure you actually understand the material.
- Practise regularly: Attempt past papers to familiarise yourself with the exam format and timing. Mark your answers to see how close you are to full marks.
- Be strategic with your revision: Use exam questions by topic to focus on weaker areas, and flashcards to reinforce important facts and terminology.
- Learn from mistakes: Whether it's from mock exams or practice questions, spend time reviewing what went wrong and why. This helps prevent repeat mistakes in the real exam.
- Stay balanced: Don't forget to take regular breaks, eat well, and get enough sleep, a healthy routine makes revision much more effective.
With the right approach and consistent practice, you'll build confidence and improve your chances of exam success.
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