Methodology

This list is based on analysis of Cambridge IGCSE Mathematics 0580 past papers (2019–2025), examiner reports, mark schemes and syllabus topic structure. Topics are ranked by frequency of appearance and mark allocation.

Top 10 most frequently tested topics

1. Algebra (manipulation, equations)

Evidence: Algebra appears in almost every question. Examiner reports note manipulation and equation-solving errors.

Covers: expanding brackets; factorising; solving linear and quadratic equations; simultaneous equations.

2. Number (percentages, ratios, standard form)

Evidence: Proportion, percentage change and number operations appear regularly. Examiner reports note conversion and rounding errors.

Covers: percentages; ratio; proportion; standard form; significant figures.

3. Graphs (linear, quadratic, interpretation)

Evidence: Plotting, interpreting and using graphs. Examiner reports note gradient and intercept errors.

Covers: straight-line graphs; quadratic graphs; interpreting graphs; y = mx + c.

4. Geometry (angles, properties, circles)

Evidence: Angle properties, symmetry, circle theorems. Examiner reports note rotational symmetry and perimeter/area confusion.

Covers: angles in polygons; parallel lines; circle theorems; symmetry.

5. Trigonometry

Evidence: Right-angled trigonometry; sine and cosine rules. Examiner reports highlight trigonometry as a weaker area.

Covers: sine, cosine, tangent; Pythagoras; bearings; sine and cosine rules.

6. Probability and statistics

Evidence: Probability, averages, frequency tables.

Covers: probability (fractions, decimals); mean, median, mode; cumulative frequency; histograms.

7. Mensuration (area, volume, perimeter)

Evidence: Compound shapes, surface area, volume. Examiner reports note perimeter vs area confusion.

Covers: area of compound shapes; volume of prisms; surface area; circles.

8. Vectors and transformations

Evidence: Vectors, reflections, rotations, enlargements. Examiner reports note transformation errors.

Covers: vector addition; translation; reflection; rotation; enlargement.

9. Sequences and functions

Evidence: nth term, linear sequences. Examiner reports note sequence formula errors.

Covers: linear sequences; nth term; simple functions.

10. Indices and surds

Evidence: Laws of indices, simplification. Examiner reports note index law errors.

Covers: index laws; negative and fractional indices; surds (extended).

Revision priority

Algebra and number underpin most questions. Trigonometry and graphs carry significant marks and are often weaker areas. See common mistakes.

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Sources: Cambridge past papers 2019–2025, examiner reports, syllabus.

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