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IGCSE Maths (0580) Syllabus: Every Chapter & Topic (2026)

PapaMarks Team · July 17, 2026 · 9 min read
#IGCSE #Maths #0580 #Syllabus #Topics #Revision

The Cambridge IGCSE Mathematics (0580) syllabus spans nine big chapters — from Number all the way through to Algebra & Sequences — and it's easy to lose track of what you've covered and what you've skipped. Knowing the whole map is the fastest way to plan your revision and spot the gaps before the exam does. Every topic below links straight to real past-paper practice, so you can revise each part exactly where it lives.

⚡ The 60-second version
  • Nine chapters make up the whole syllabus: Number, Coordinate Geometry & Graphs, Geometry, Lengths/Areas/Volumes, Pythagoras & Trigonometry, Vectors & Transformations, Probability, Statistics, and Algebra & Sequences.
  • Number and Algebra are the biggest chapters — they underpin almost every other topic, so master them first.
  • Geometry, trigonometry and statistics carry a lot of method marks — the technique matters more than memory.
  • Sit the Extended tier if you're aiming for an A* — the top grades are only available on the Extended papers.
  • Use the map below to tick off every topic and drill the weak ones on past papers.

Chapter 1: Number

The foundation of the whole course — how numbers behave, from fractions and percentages to standard form, surds and bounds.

Number Toolkit

Set Notation & Venn Diagrams

Prime Factors, HCF & LCM

Powers, Roots & Standard Form

Fractions Toolkit

Percentages Toolkit

Simple & Compound Interest, Growth & Decay

Surds

Working with FDP

Working with Ratios

Compound Measures

Time, Currency & Conversions

Rounding, Estimation & Bounds

Using a Calculator

Chapter 2: Coordinate Geometry & Graphs

Everything on the coordinate grid — straight lines, curves, inequalities, real-life graphs and an introduction to differentiation.

Coordinate Geometry

Linear Graphs

Further Graphs & Tangents

Solving & Graphing Inequalities

Real-Life Graphs

Differentiation

Chapter 3: Geometry

The building blocks of shape and space — symmetry, 2D and 3D shapes, units, plus the angle, construction and circle-theorem work that runs throughout the paper.

Geometry Toolkit

This chapter also covers Angles in Polygons & Parallel Lines, Bearings, Constructions & Scale Drawings and Circle Theorems — big exam earners that show up woven through geometry and trigonometry questions rather than as standalone practice sets.

Chapter 4: Lengths, Areas & Volumes

Measuring flat shapes and solids — perimeter, area, circles, volume, surface area and the powerful similarity scale factors.

Area & Perimeter

Circles, Arcs & Sectors

Volume & Surface Area

Congruence & Similarity

Chapter 5: Pythagoras & Trigonometry

From right-angled triangles to the sine and cosine rules and trig graphs — one of the most method-heavy, high-mark chapters on the Extended paper.

Right-Angled Triangles

Sine, Cosine Rule & Area of Triangles

Trigonometric Graphs & Equations

Chapter 6: Vectors & Transformations

Describing movement and change of position — column vectors, vector paths and the four transformations.

Vectors

Transformations

Chapter 7: Probability

Measuring chance — from basic probability through tree diagrams to conditional probability.

Basic Probability

Probability Diagrams

Conditional Probability

Chapter 8: Statistics

Handling data — averages, statistical diagrams, histograms, cumulative frequency and correlation.

Averages & Range

Statistical Diagrams

Histograms

Cumulative Frequency

Scatter Graphs & Correlation

Chapter 9: Algebra & Sequences

The engine room of IGCSE Maths — notation, brackets, equations, quadratics, functions and sequences. Get fluent here and the rest of the paper falls into place.

Algebra Toolkit

Algebraic Roots & Indices

Expanding & Factorising Brackets

Linear Equations & Inequalities

Quadratic Equations

Rearranging Formulas

Simultaneous Equations

Algebraic Fractions

Forming & Solving Equations

Functions

Sequences

Proportion

✍️
Maths is a skill, not a set of facts. You don't revise Maths by re-reading notes — you revise it by doing questions until the method is automatic. Reading a worked solution feels productive, but the marks come from your own pen moving on paper. Pick any topic above and work through past-paper questions on it; that's where the improvement actually happens.

How to use this syllabus map

  1. Audit yourself chapter by chapter
    Scroll through all nine chapters and RAG-rate each topic: green (confident), amber (shaky), red (haven't covered). This turns a vague "I need to revise Maths" into a precise to-do list.
  2. Lead with Number and Algebra
    These two chapters underpin nearly everything else — solving equations, ratios and indices show up inside geometry, trig and stats questions. Shore them up first for the biggest ripple effect.
  3. Click through to practise each weak topic
    Every leaf topic above links to real past-paper questions. Work the amber and red topics until they turn green, then move on — don't waste time re-drilling what you already know.
  4. Finish with mixed past papers
    Once your gaps are closed, sit full papers under timed conditions. This trains you to switch between topics quickly and spot which method a question is really asking for.
📚
Ready to revise? Practise by topic with instant AI marking on our IGCSE Maths 0580 past papers, see where the marks concentrate in the most-tested topics, and follow the full strategy in how to get an A* in IGCSE Maths 0580. Still deciding your options? Our guide to choosing IGCSE subjects can help you build the right combination around Maths.

FAQ

How many topics are in IGCSE Maths 0580?
The Cambridge IGCSE Mathematics 0580 syllabus is organised into nine main chapters, which break down into well over a hundred individual topics — from Types of Numbers right through to Inverse Proportion. This map links every examinable leaf topic so you can revise each one where it lives.
What are the main chapters in IGCSE Maths?
The nine chapters are: Number; Coordinate Geometry & Graphs; Geometry; Lengths, Areas & Volumes; Pythagoras & Trigonometry; Vectors & Transformations; Probability; Statistics; and Algebra & Sequences. Number and Algebra are the largest and underpin most of the others.
What's the difference between Core and Extended?
Core covers the foundation content and is capped at grade C (or 4/5), while Extended includes all the Core material plus harder topics such as surds, the sine and cosine rules, and differentiation. Only the Extended papers can award the top grades, so if you're aiming for an A* you must sit Extended.
Which Maths topics are most important?
Number and Algebra carry the most weight and feed into almost every other question, so they're the highest-value places to be fluent. Beyond those, algebraic manipulation, trigonometry and handling data appear again and again. For a frequency-ranked breakdown, see our most-tested IGCSE Maths 0580 topics post.
How should I revise IGCSE Maths?
By doing questions, not re-reading notes. Use this map to find your weak topics, drill each one on past papers until the method is automatic, then sit full timed papers to practise switching between topics. Maths is a skill — consistent practice beats passive revision every time.

Treat this page as your revision command centre for IGCSE Maths 0580. Work methodically through the nine chapters, lead with Number and Algebra, close every red-rated gap on real past papers, and finish with timed mixed practice — and you'll walk into the exam knowing exactly what to expect and where every mark is hiding.

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