IGCSE Further Maths Topics By Exam Board: Full List

If you’re studying IGCSE Further Maths, knowing exactly which topics you need to revise is one of the most effective ways to improve your results.

The IGCSE Further Maths syllabus varies slightly depending on your exam board. The two main options are Pearson Edexcel (Further Pure Mathematics, 4PM1) and Cambridge International (Additional Mathematics, 0606), and each includes a different mix of topics.

This guide gives you a complete breakdown of IGCSE Further Maths topics for each board, along with a comparison to help you focus your revision.

Key Takeaways

• The IGCSE Further Maths syllabus varies by exam board, with Edexcel IGCSE Further Pure Maths and Cambridge IGCSE Additional Maths covering different topic areas

• Edexcel focuses on pure mathematics, with topics including calculus, vectors, and logarithms

• Cambridge includes a broader range of topics, such as permutations, combinations, and circle geometry

• Both courses share core topics, including algebra, trigonometry, calculus, and vectors

• Understanding your exam board’s specific topics helps you focus your IGCSE Further Maths revision more effectively and avoid wasting time

Edexcel IGCSE Further Pure Maths Topics

The Edexcel IGCSE Further Pure Maths syllabus is split into several core content areas. 

Here's everything you'll cover.

Logarithmic Functions and Indices

• Exponential functions and graphs

• The number e

• Introduction to logarithms and logarithmic graphs

• Laws of indices

• Laws of logarithms, including change of base

• Solving exponential equations

The Quadratic Function

• Factorising quadratics and completing the square

• Solving quadratic equations

• Using the discriminant

• Sum and product of roots

Identities & Inequalities

• Algebraic division

• Factor theorem and remainder theorem

• Solving cubic equations

• Solving linear and quadratic inequalities

• Interpreting and sketching regions using inequalities

Graphs

• Midpoints, distances, and gradients

• Equations of straight lines, including parallel and perpendicular lines

• Graphing functions and identifying key features

• Quadratic, cubic, and rational function graphs

• Solving equations graphically

Series

• Sigma notation

• Arithmetic sequences and series

• Geometric sequences and series, including sum to infinity

• Binomial expansion (including general form)

Trigonometry

• Radian measure, arc length, and area of a sector

• Trigonometric ratios and exact values

• Graphs of trigonometric functions

• Sine and cosine rules and area of a triangle

• Trigonometric identities and addition formulae

• Solving trigonometric equations

Vectors

• Vector notation, addition, and subtraction

• Position and displacement vectors

• Magnitude of a vector and unit vectors

• Vector paths, parallel vectors, collinearity, and geometric proof

Calculus

• Differentiating powers of x

• Differentiating trigonometric functions and exponential functions

• Product rule, quotient rule, and chain rule

• Gradients, stationary points, tangents, and normals

• Interpreting gradients as rates of change

• Integration of powers, trigonometric functions, and exponentials

• Definite integrals and areas under curves

• Areas between curves

• Applications such as kinematics

Cambridge IGCSE Additional Maths Topics

The Cambridge IGCSE Additional Maths (0606) syllabus is organised as individual topics in the official specification.

The sections below group these topics into clear areas to make revision easier. For a full specification checklist, see our complete IGCSE Additional Maths topic list.

Algebra & Functions

• Functions: domain, range, modulus, inverse functions, and composite functions

• Solving quadratic equations (including equations reducible to quadratic form)

• Discriminants and their applications

• Quadratic graphs and sketching

• Quadratic inequalities

• Polynomial division

• Factor theorem and remainder theorem

• Solving cubic equations

• Modulus functions: graphs and equations

• Graphs of cubic polynomials and solving inequalities graphically

• Linear and quadratic simultaneous equations

• Exponential and logarithmic functions

• Laws of logarithms and change of base

• Solving exponential equations

• Transforming relationships to linear form

Coordinate Geometry

• Equations of straight lines, midpoints, and distances

• Parallel and perpendicular lines

• Coordinate geometry of the circle

• Equation of a circle, including centre and radius

• Tangents to circles

• Intersection of lines and circles

• Intersection of two circles and common chords

Trigonometry

• Radian measure, arc length, and area of a sector

• Trigonometric functions and graphs

• The unit circle

• Trigonometric identities

• Solving trigonometric equations

• Using identities to prove results

Sequences & Series

• Permutations, combinations, and factorials

• Binomial expansion

• Series notation (including sigma notation)

• Arithmetic sequences and series

• Geometric sequences and series

Vectors

• Vector notation, magnitude, and position vectors

• Vector addition and subtraction

• Vector geometry and problem solving

Calculus

• Differentiation of powers, trigonometric functions, and exponential functions

• Chain rule, product rule, and quotient rule

• Gradients, tangents, and normals

• Increasing and decreasing functions

• Stationary points and second-order derivatives

• Applications of differentiation, including optimisation

• Integration of powers, trigonometric functions, and exponential functions

• Definite integrals and areas under curves

Edexcel vs Cambridge: Topic Comparison

Both Edexcel IGCSE Further Pure Mathematics and Cambridge IGCSE Additional Mathematics cover a strong core of algebra, trigonometry, calculus, and vectors.

However, there are some important differences in content and focus.

Topics more emphasised in Edexcel:

• Volumes of revolution

• Geometric series, including sum to infinity

• Rational function graphs

• More detailed treatment of binomial expansion (including general form)

Topics unique or prominent in Cambridge:

• Permutations and combinations

• Modulus functions and graphs

• Coordinate geometry of the circle

• Transforming relationships to linear form

• Applications of differentiation, including optimisation

Shared core topics:

• Quadratic and cubic equations, including polynomial division

• Logarithmic and exponential functions

• Inequalities and simultaneous equations

• Coordinate geometry of straight lines

• Trigonometry (identities, equations, graphs, radians)

• Arithmetic and geometric series, including binomial expansion

• Differentiation and integration (including chain, product, and quotient rules)

• Vectors

Key difference in approach

Cambridge IGCSE Additional Mathematics tends to cover a broader range of topics, including areas like permutations and circle geometry, as well as applications of mathematics.

Edexcel IGCSE Further Pure Mathematics focuses more deeply on pure mathematical techniques, with greater emphasis on algebraic methods, calculus, and formal problem solving.

Tips for Studying IGCSE Further Maths

IGCSE Further Maths is a step up from standard IGCSE Maths, so a focused revision strategy is essential. Here are a few ways to make your revision more effective.

Start with foundational topics. Many areas build on each other. Calculus relies on algebra and functions, while trigonometric equations depend on identities.Build (opens in a new tab) confidence in quadratics, indices, and basic trigonometry first.

Use past papers by topic, not just by year. Practising topic-based questions helps you recognise patterns and is more effective than full papers when learning new content. Save My Exams has a range of IGCSE Further Maths exam questions to help you do this. 

Strengthen your algebra skills. Algebra underpins almost every topic, from calculus to trigonometry. Improving your algebra skills will be a huge advantage if you want to improve your IGCSE grades in IGCSE Further Maths.

Focus on exam board-specific topics. Cambridge students should practise permutations and circle geometry until they feel automatic. Edexcel students should focus on pure techniques such as volumes of revolution. Check the hardest IGCSE maths questions to see where students commonly lose marks.

If you want to explore how these topics link to future study, our guide to A Level Further Maths topics shows how the course develops.  And for a wider picture about what comes next, our guide to what's next after IGCSEs covers your options.

Save My Exams has revision notes, exam questions, and past papers for IGCSE Further Maths and a wide range of IGCSE subjects, all written by expert teachers and examiners to help you ace your exams.

Frequently Asked Questions

What topics are covered in IGCSE Further Maths?

IGCSE Further Maths covers advanced algebra, trigonometry, calculus, series, vectors, and coordinate geometry.

The exact topics depend on whether you're taking Edexcel or Cambridge.

Is IGCSE Further Maths hard?

It's more challenging than standard IGCSE Maths because it introduces topics you'd normally first meet at A Level, such as calculus, logarithms, and series. 

However, with consistent practice and a strong understanding of the basics, most students can manage the step up.

What's the difference between IGCSE Maths and IGCSE Further Maths?

Standard IGCSE Maths covers core topics such as number, algebra, geometry, and statistics.

IGCSE Further Maths builds on this with more advanced topics, including calculus, logarithms, series, and vectors.

Do I need IGCSE Further Maths for A Level?

You don't need it, but it gives you a significant head start. Topics like calculus, logarithms, and trigonometric identities appear in A Level Maths from day one. 

Students who have studied these topics in IGCSE Further Maths often find the transition to A Level Maths much smoother.

References:

• Cambridge IGCSE Mathematics - Additional (0606) (opens in a new tab)

• Edexcel International GCSE Further Pure Mathematics (2017) (opens in a new tab)