IGCSE Math: 10 Topics That Come Up Every Year 2026
Whether you're sitting Cambridge (0580) or Edexcel (4MA1), IGCSE Mathematics has a predictable structure. Certain topics appear in almost every paper, every year — and practising these strategically can have a bigger impact on your grade than trying to cover everything.
This guide identifies the 10 most consistent high-frequency topics across both boards, with what to practise for each.
The 10 Topics — Frequency and Mark Value
| Rank | Topic | Typical Marks per Paper | Board Focus |
|---|---|---|---|
| 1 | Algebra — Quadratics and Equations | 15-20 marks | Cambridge + Edexcel |
| 2 | Geometry — Angles and Circle Theorems | 10-15 marks | Cambridge + Edexcel |
| 3 | Trigonometry — Sine and Cosine Rules | 10-15 marks | Cambridge + Edexcel |
| 4 | Statistics — Cumulative Frequency | 8-12 marks | Cambridge + Edexcel |
| 5 | Probability — Combined Events | 8-12 marks | Cambridge + Edexcel |
| 6 | Transformations | 6-10 marks | Cambridge + Edexcel |
| 7 | Vectors | 6-10 marks | Cambridge (more) + Edexcel |
| 8 | Sequences — nth Term | 5-8 marks | Cambridge + Edexcel |
| 9 | Mensuration — Area and Volume | 8-12 marks | Cambridge + Edexcel |
| 10 | Functions and Graphs | 8-12 marks | Cambridge + Edexcel |
1. Algebra — Quadratics and Simultaneous Equations
Why it's always there: Algebra is the backbone of Extended/Higher IGCSE Math. Quadratic equations, simultaneous equations, and algebraic manipulation appear on every single paper.
What to practise:
- Factorising quadratics (including when a ≠ 1)
- Quadratic formula — memorise it and apply it accurately
- Simultaneous equations — both substitution and elimination methods
- Changing the subject of complex formulas
- Algebraic fractions — adding and simplifying
Common mistake: Sign errors in substitution. Always substitute back to check.
2. Geometry — Angles and Circle Theorems
Why it's always there: Geometry questions give examiners scope to test both recall (angle rules) and reasoning (justify your answer).
What to practise:
- All 8 circle theorems — know them well enough to state which one you're using
- Angle rules: parallel lines, polygons, exterior angles
- Congruence and similarity — including scale factors for area and volume
- Construction and loci
Common mistake: Not giving a reason for each angle. Marks are split between the answer AND the justification.
3. Trigonometry — SOH CAH TOA and Sine/Cosine Rules
Why it's always there: Trig is high-mark and tests multiple skills — calculation, setting up equations, and interpreting diagrams.
What to practise:
- Basic right-angle trig — SOH CAH TOA fluently
- Sine rule — for non-right triangles (sides and angles)
- Cosine rule — when you have two sides and included angle
- Area of triangle = ½ab sin C
- Bearings combined with trigonometry
- 3D trigonometry problems (Extended/Higher)
4. Statistics — Cumulative Frequency and Averages
What to practise:
- Cumulative frequency curves — drawing and reading off (median, quartiles, IQR)
- Box plots — drawing from a five-number summary
- Histograms — frequency density (often misunderstood)
- Mean from grouped frequency tables
- Comparing distributions using median and IQR
Common mistake: Histograms — plotting frequency instead of frequency density. This is one of the most common errors.
5. Probability — Tree Diagrams and Combined Events
What to practise:
- Tree diagrams — with and without replacement (completely different calculations)
- P(A and B) = P(A) × P(B) for independent events
- P(A or B) = P(A) + P(B) − P(A and B) for non-mutually exclusive
- Conditional probability using two-way tables
- Venn diagrams — set notation
6. Transformations
What to practise:
- Reflection — describe the mirror line precisely
- Rotation — describe centre, angle, and direction
- Translation — use column vectors
- Enlargement — describe scale factor AND centre
- Combined transformations
Common mistake: Not fully describing transformations. A rotation needs centre, angle, AND direction. Missing one costs marks.
7. Vectors
What to practise:
- Vector arithmetic — addition, subtraction, scalar multiplication
- Position vectors and routes between points
- Proving collinearity using vectors
- Midpoints using vectors
8. Sequences — nth Term
What to practise:
- Linear sequences — nth term formula
- Quadratic sequences — second difference method
- Geometric sequences — recognising and finding the ratio
- Fibonacci-type sequences
9. Mensuration — Area and Volume
What to practise:
- Area: circle, triangle, trapezium, sector
- Volume: prism, cylinder, cone, sphere, pyramid
- Surface area: cylinder, cone, sphere
- Arc length and sector area
- Compound shapes
Common mistake: Using diameter instead of radius for circles. Always double-check before substituting.
10. Functions and Graphs
What to practise:
- Function notation: f(x), fg(x), f⁻¹(x)
- Composite and inverse functions
- Sketching and interpreting graphs: quadratic, cubic, reciprocal, exponential
- Gradient and equation of a straight line
- Gradient at a point using a tangent
Your 2-Week Revision Plan
| Week | Days 1-3 | Days 4-5 | Days 6-7 |
|---|---|---|---|
| Week 1 | Algebra + Geometry | Trigonometry | Past paper — mark and review |
| Week 2 | Statistics + Probability + Transformations | Vectors + Sequences + Mensuration + Functions | Full past paper — timed |
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