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GCSE Further Maths Topics: Full List

Jamie Wood

Written by: Jamie Wood

Reviewed by: Roger B

Published

Student holding chalk and set square in front of maths symbols and a board with a triangle for GCSE Further Maths Topics on a purple background

Contents

  1. 1. AQA GCSE Further Maths Topics
  2. 2. GCSE Further Maths Topics for OCR and Edexcel
  3. 3. Improve Your Grades with Save My Exams

GCSE Further Maths is a qualification studied at GCSE level, usually alongside GCSE Maths by the highest attaining students. It aims to broaden the range of maths topics studied by GCSE maths students, as well as extend their existing knowledge.

AQA GCSE Further Maths (8365) is the most popular course of its type, and the topics for this course are detailed below. You will also find helpful links to our resources to aid you with your revision. Having a thorough GCSE Further Maths topic list can be a useful starting point for your revision, to help ensure you cover everything you need to know. 

There are two alternative GCSE Further Maths courses in addition to AQA, provided by OCR and Edexcel. These are detailed at the end of the article. 

AQA GCSE Further Maths Topics

AQA GCSE Further Maths (8365) can be broadly split into several topic areas. Some of these areas will be more broad than others, and what is contained in each area is detailed below.

  1. Number

  2. Algebra & Functions

  3. Coordinate Geometry

  4. Calculus

  5. Matrix Transformations

  6. Geometry

1. Number

The topic of number consolidates and extends some of the content from GCSE Maths. It includes the following areas:

  • Surds

  • Counting Principles

2. Algebra & Functions

The topic of algebra & functions also consolidates and extends some of the content from GCSE Maths. In addition, it contains some content which will be brand new to GCSE students. It includes the following areas:

  • Algebra Toolkit

  • Binomial Expansion

  • Algebraic Fractions

  • Rearranging Formulae

  • Indices

  • Algebraic Proof

  • Polynomials & Factor Theorem

  • Shapes of Graphs

  • Simultaneous Equations

  • Solving Inequalities

  • Functions

  • Sequences

3. Coordinate Geometry

The topic of coordinate geometry consolidates the content from GCSE Maths, and exam questions will be more involved than in GCSE Maths. It includes the following areas:

  • Coordinate Geometry & Straight Lines

  • Equation of a Circle

    • IncludingTangents to Circles

4. Calculus

Calculus is a topic which will be brand new to GCSE level students. Calculus concerns rates of change of functions and graphs. It includes the following areas:

  • Differentiation

  • Applications of Differentiation 

    • including Tangents, Normals, and Stationary Points

5. Matrix Transformations

Matrices will be brand new to GCSE level students. Matrix Transformations covers the basics of matrices and matrix multiplication, and links them to geometry. It includes the following areas:

  • Matrix Multiplication

  • Matrix Transformations

    • Including combining transformations

6. Geometry

The topic of geometry consolidates the content from GCSE Maths, and extends GCSE knowledge, in particular in relation to trigonometry. It includes the following areas:

  • Geometric Proof

  • Trigonometry in 2D and 3D

  • Trigonometric Graphs & Equations

    • Including solving Trigonometric Equations with identities

What is covered in each AQA GCSE Further Maths paper?

AQA’s Level 2 Certificate in Further Mathematics (8365) is assessed by two equally weighted exam papers, both of which can assess content drawn from any part of the specification. 

There is no specific split between “Paper 1 content” vs. “Paper 2 content”. All six topic areas (Number, Algebra, Coordinate Geometry, Calculus, Matrix Transformations, and Geometry) may appear in both exams. 

The main difference between the two papers is that Paper 1 is non-calculator and Paper 2 allows a calculator. Both papers are 1 hour and 45 minutes in length.

Revision Resources for AQA GCSE Further Maths

Although needing to have a sound knowledge of all content within the GCSE Further Maths course may sound daunting, we have you covered with our course-specific revision resources! 

We’ve carefully combed through the specification to make sure that our Revision Notes, Exam Questions, and Past Papers are all perfectly aligned with AQA’s specification and style. Check out the links below.

AQA GCSE Further Maths Revision Resources

GCSE Further Maths Topics for OCR and Edexcel

There are two other qualifications which are alternatives to AQA GCSE Further Maths. They are:

  • OCR Level 3 certificate in Additional Mathematics (6993)

  • Edexcel Level 2 Extended Maths certificate (7M20)

OCR Additional Mathematics Topics

OCR Additional Mathematics is assessed with a single 2-hour exam, rather than two papers. The topics covered vary slightly from AQA.

  • Calculus: Includes both differentiation and integration (AQA only has differentiation).

  • Exponentials and logarithms: Taught in some depth, which is not a core focus in AQA’s specification.

  • Numerical methods: Covers approximation methods, iteration, trapezium rule for areas, etc.

  • No matrix transformations: Unlike AQA, OCR does not include 2×2 matrix transformations.

You can find more details about OCR Additional Mathematics on the OCR website. We also have many past papers and mark schemes on our website. 

Edexcel Extended Maths Topics

Similar to AQA, the Edexcel qualification is assessed by two exam papers (non-calculator and calculator). These are weighted equally and are each 1 hour and 15 minutes in length.

The topics covered vary slightly from AQA.

  • A balance of algebra, coordinate geometry, and some calculus (differentiation only)

  • Matrix transformations (2×2) for enlargements, reflections, and rotations

  • The focus is more on extending previously-taught concepts from GCSE, rather than introducing a lot of brand new content and concepts

  • This includes further algebraic techniques, polynomial factorisation, proof, and some circle theorems

You can find more details about Edexcel Extended Maths on the Edexcel website.

Improve Your Grades with Save My Exams

Save My Exams is here to help you achieve the best grade possible in GCSE Further Maths by offering expert-written resources specifically made for your exam board. We’ve got everything you need:

  • Detailed, exam-aligned revision notes

  • Exam-style questions with student friendly worked solutions

  • Past papers with mark schemes

Whether you want to improve your understanding of key topics, test your knowledge, or sharpen your exam techniques, Save My Exams makes it easier and more effective for you to revise.

Explore Our GCSE Further Maths Resources

References

AQA GCSE Further Mathematics

OCR Additional Mathematics

Edexcel Extended Maths

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Author
Reviewer
Jamie Wood

Author: Jamie Wood

Expertise: Maths Content Creator

Jamie graduated in 2014 from the University of Bristol with a degree in Electronic and Communications Engineering. He has worked as a teacher for 8 years, in secondary schools and in further education; teaching GCSE and A Level. He is passionate about helping students fulfil their potential through easy-to-use resources and high-quality questions and solutions.

Roger B

Reviewer: Roger B

Expertise: Maths Content Creator

Roger's teaching experience stretches all the way back to 1992, and in that time he has taught students at all levels between Year 7 and university undergraduate. Having conducted and published postgraduate research into the mathematical theory behind quantum computing, he is more than confident in dealing with mathematics at any level the exam boards might throw at you.

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