Cambridge IGCSE Mathematics (0580) — Complete Syllabus (Core & Extended)

A simple, student-friendly guide to every topic, the exam pattern, what to expect in Core vs Extended papers, and how to prepare effectively.

What this syllabus aims to do

• Build number fluency, algebraic skill, geometry, statistics and problem solving.
• Develop logical reasoning, clear mathematical communication and exam technique.
• Provide a pathway for higher study (A levels) or practical use of mathematics.

Assessment Overview — Papers & rules

All candidates take two written components. You choose Core (for grades C–G) or Extended (for A*–E).

Papers are weighted equally within a tier (50% each). Use of calculators follows the rules above. More details in the official syllabus documents.

How to use this page (quick study plan)

1. Decide Core or Extended (Extended = aim for A*/A/B/C). Use paper list above to choose.
2. Study topics in order: Number → Algebra → Geometry → Trig → Coordinate geometry → Mensuration → Transformations & Vectors → Probability → Statistics.
3. Practice with non-calculator questions weekly to build accuracy, then use calculator practice for Papers 3/4.
4. Use past papers + mark schemes and the formula list (given in exam papers) to learn required answers and presentation.

Full topics — What you must know (Core)

The Core content covers all essential topics students must master for grades C–G. Study each bullet carefully.

1. Number

• Types of number, HCF & LCM, primes, squares, cubes, reciprocals.
• Fractions, decimals, percentages, ratio & proportion, rates, standard form, estimation, limits of accuracy.
• Using a calculator efficiently (Core Paper 3 practice encourages this).

2. Algebra & Graphs

• Algebraic notation, simplification, expanding, factorising, indices (basic rules).
• Linear equations, simple simultaneous equations, inequalities, sequences, drawing and interpreting linear & simple quadratic graphs.

3. Coordinate Geometry

• Cartesian coordinates, equations of straight lines (y = mx + c), gradient, intercepts, parallel lines.

4. Geometry & Mensuration

• Basic geometry vocabulary, angles, properties of triangles and polygons, circle terms, area & perimeter formulas, surface area & volume of solids (prism, cylinder, cone, sphere). Formula list is provided in Core papers.

5. Trigonometry

• Sine, cosine, tangent in right triangles; simple applications (heights & distances) and using calculators where allowed.

6. Transformations & Vectors

• Translation, rotation, reflection, enlargement, and basic 2D vector notation and operations.

7. Probability & Statistics

• Probability scale, simple combined events (tree & sample space), relative frequency, basic statistics: mean, median, mode, range, charts and simple interpretation (bar, pie, histograms, box plots).

Extended — Additional topics & deeper skills

Extended candidates study everything in Core plus these additions (aim for A*/A/B/C).

• Advanced algebra: quadratics (factorisation, formula), indices, surds, exact values and more complex graph sketching (cubic, reciprocal, exponential).
• Advanced trigonometry: exact trig values, sine rule, cosine rule, area of a triangle using trig.
• More advanced statistics: grouped data, histograms, box-and-whisker plots, scatter & correlation, and simple interpretation of regression ideas.
• Additional geometry: similarity, symmetry, scale diagrams, and constructions with compasses/ruler.

Formula list & command words

Core papers include a short list of formulas (area, volume, circle formulas). Extended papers include the same list plus any extra formulas the paper gives. Make sure you know when formulas are provided and when you must recall them. Also learn common exam command words (e.g. ‘show’, ‘find’, ‘explain’), they define the expected depth of your answer.

Top exam tips (quick)

1. Start non-calculator practice early — accuracy matters.
2. Show working clearly: examiners give method marks if reasoning is visible.
3. Use the formula sheet on the paper — but practise deriving formulas so you understand them.
4. Practice past papers under timed conditions (same break-down as official papers above).
5. For Extended, review exact trig values, surds and solving quadratics thoroughly.

FAQs — Quick answers

Which paper should I choose — Core or Extended? Choose Extended if you aim for grade C or higher and are comfortable with algebra and proof-style problems; otherwise choose Core.

Are calculators allowed? Yes for Papers 3 and 4 only; Papers 1 and 2 are non-calculator.

Where to practice? Use specimen papers, past papers and mark schemes provided by Cambridge; they mirror exam style and command words.

 syllabus summary is based on the official Cambridge IGCSE Mathematics (0580) syllabuses (2025–2027 and 2028–2030).