IGCSE Math RevisionCambridge IGCSE Maths (0580) · Revision notes
Cambridge IGCSE Maths (0580) revision notes
Free revision notes for Cambridge IGCSE Mathematics (0580), the syllabus for exams in 2025, 2026 and 2027. The notes follow the syllabus topic by topic: every sub-topic says what you need to know, marked Core or Extended, with a short explanation and a worked example. Pick a topic below, then time yourself on the 0580 past papers.
- 9 topics
- 72 sub-topics
- 53 Core and Extended
- 19 Extended only
- 2025 to 2027 syllabus
The 0580 topics
1. Number
1.1 Types of number · 1.2 Sets · 1.3 Powers and roots · 1.4 Fractions, decimals and percentages · 1.5 Ordering · 1.6 The four operations · 1.7 Indices I · 1.8 Standard form · 1.9 Estimation · 1.10 Limits of accuracy · 1.11 Ratio and proportion · 1.12 Rates · 1.13 Percentages · 1.14 Using a calculator · 1.15 Time · 1.16 Money · 1.17 Exponential growth and decay (Extended) · 1.18 Surds (Extended)
2. Algebra and graphs
2.1 Introduction to algebra · 2.2 Algebraic manipulation · 2.3 Algebraic fractions (Extended) · 2.4 Indices II · 2.5 Equations · 2.6 Inequalities · 2.7 Sequences · 2.8 Proportion (Extended) · 2.9 Graphs in practical situations · 2.10 Graphs of functions · 2.11 Sketching curves · 2.12 Differentiation (Extended) · 2.13 Functions (Extended)
3. Coordinate geometry
3.1 Coordinates · 3.2 Drawing linear graphs · 3.3 Gradient of linear graphs · 3.4 Length and midpoint (Extended) · 3.5 Equations of linear graphs · 3.6 Parallel lines · 3.7 Perpendicular lines (Extended)
4. Geometry
4.1 Geometrical terms · 4.2 Geometrical constructions · 4.3 Scale drawings · 4.4 Similarity · 4.5 Symmetry · 4.6 Angles · 4.7 Circle theorems I · 4.8 Circle theorems II (Extended)
5. Mensuration
5.1 Units of measure · 5.2 Area and perimeter · 5.3 Circles, arcs and sectors · 5.4 Surface area and volume · 5.5 Compound shapes and parts of shapes
6. Trigonometry
6.1 Pythagoras' theorem · 6.2 Right-angled triangles · 6.3 Exact trigonometric values (Extended) · 6.4 Trigonometric functions (Extended) · 6.5 Non-right-angled triangles (Extended) · 6.6 Pythagoras' theorem and trigonometry in 3D (Extended)
7. Transformations and vectors
7.1 Transformations · 7.2 Vectors in two dimensions (Extended) · 7.3 Magnitude of a vector (Extended) · 7.4 Vector geometry (Extended)
8. Probability
8.1 Introduction to probability · 8.2 Relative and expected frequencies · 8.3 Probability of combined events · 8.4 Conditional probability (Extended)
9. Statistics
9.1 Classifying statistical data · 9.2 Interpreting statistical data · 9.3 Averages and measures of spread · 9.4 Statistical charts and diagrams · 9.5 Scatter diagrams · 9.6 Cumulative frequency diagrams (Extended) · 9.7 Histograms (Extended)
The 0580 papers (from 2025)
| Paper | Tier | Calculator | Time | Marks |
|---|---|---|---|---|
| Paper 1 | Core | No | 1 h 30 min | 80 |
| Paper 2 | Extended | No | 2 h | 100 |
| Paper 3 | Core | Yes | 1 h 30 min | 80 |
| Paper 4 | Extended | Yes | 2 h | 100 |
Core: Papers 1 and 3 (grades C to G). Extended: Papers 2 and 4 (grades A* to E). Half of the marks are on a non-calculator paper, so practise arithmetic, fractions, surds and exact values by hand. See the 0580 past papers and specimen papers.
How this site covers 0580
This site began with Edexcel International GCSE (4MA1), Higher tier, which shares most of its content with 0580 Extended. By our map of the two syllabuses:
- 55 sub-topics are the same mathematics: each links to our Edexcel 4MA1 notes, and the 0580 practice pages have our 4MA1 Higher questions for them (Extended level), plus questions written for 0580 Core wherever the sub-topic has Core content.
- 13 sub-topics are partly in 4MA1: the notes cover the missing part, with worked examples, and each has practice questions written for 0580.
- 4 sub-topics are not in 4MA1 (time, exact trigonometric values, classifying statistical data, scatter diagrams): new notes and worked examples, and practice questions written for 0580.
0580 practice: 456 questions written for 0580 (381 Core, 75 Extended, 279 non-calculator for Papers 1 and 2), each re-solved independently before publishing, plus the 4MA1 questions above. Practise by topic: Number · Algebra and graphs · Coordinate geometry · Geometry · Mensuration · Trigonometry · Transformations and vectors · Probability · Statistics. Practice is part of the IGCSE plan, with a free preview.
Core students: use the Core filter on a practice page to see only the questions written for 0580 Core; every sub-topic with Core content has them. Revising for Edexcel instead? Use the Edexcel 4MA1 revision notes.
Revise and practise
- Cambridge IGCSE Maths 0580 past papers and mark schemes, linked to Cambridge's own copies
- 0580 practice by topic, starting with Number: questions tagged Core or Extended and non-calculator or calculator
- Student hub: practise the shared topics, each question marked
- IGCSE Maths questions by topic, with worked answers
Questions about the 0580 notes
Which Cambridge IGCSE Maths syllabus do these notes follow?
Cambridge IGCSE Mathematics (0580), the syllabus for exams in 2025, 2026 and 2027: all 9 topic areas and all 72 sub-topics, Core and Extended. The statements are summarised in our own words, so check the official syllabus for the exact wording.
What is the difference between Core and Extended?
Core candidates sit Paper 1 (non-calculator) and Paper 3 (calculator), 1 hour 30 minutes and 80 marks each, for grades C to G. Extended candidates sit Paper 2 (non-calculator) and Paper 4 (calculator), 2 hours and 100 marks each, for grades A* to E. Extended includes all of the Core content.
Can I practise 0580 questions on this site?
Yes, with the IGCSE plan (free preview). 456 practice questions are written for 0580 (381 Core, 75 Extended, 279 non-calculator), with Cambridge-style mark schemes: every one of the 17 sub-topics that Edexcel 4MA1 does not teach or covers only in part, and Core questions on every sub-topic with Core content. For the 55 sub-topics that are the same mathematics in 4MA1, the 0580 practice pages add our 4MA1 Higher questions, which are Extended level. The 16 Extended-only sub-topics shared with 4MA1 are practised with those 4MA1 questions only.
Are the 0580 notes free?
Yes. Every note and worked example on these pages is free to read, with no sign-in.
Is this site affiliated with Cambridge?
No. IGCSE Math Revision is an independent revision site; the board name is used only to describe the syllabus covered.