Cambridge IGCSE Mathematics (0580), for examination from 2025, is offered at two levels: Core, with grades C to G, and Extended, with grades A* to E. This guide describes what the course contains, how the papers are organised, how to approach each one, and a revision routine that fits around school. Check with your teacher which level you are entered for, because it decides which papers you sit.
What the course covers
- Number: types of number, fractions, decimals, percentages, ratio, proportion, indices, standard form, and at Extended level surds and limits of accuracy.
- Algebra and graphs: expressions, equations, inequalities, sequences, straight-line and curved graphs, and at Extended level functions and differentiation.
- Coordinate geometry: gradients, equations of straight lines, midpoints and lengths.
- Geometry: angle facts, symmetry, circle properties, similarity, constructions, and mensuration of shapes and solids.
- Trigonometry: right-angled triangle work, bearings, and at Extended level the sine and cosine rules and three-dimensional problems.
- Transformations and vectors: reflection, rotation, translation, enlargement, and vector arithmetic.
- Statistics and probability: averages, charts, scatter diagrams, probability of single and combined events, and at Extended level cumulative frequency and histograms.
How you are assessed
| Level | Paper | Duration | Marks | Weighting | Calculator |
|---|---|---|---|---|---|
| Core (grades C to G) | Paper 1 | 1 h 30 min | 80 | 50% | Not allowed |
| Core (grades C to G) | Paper 3 | 1 h 30 min | 80 | 50% | Allowed |
| Extended (grades A* to E) | Paper 2 | 2 h | 100 | 50% | Not allowed |
| Extended (grades A* to E) | Paper 4 | 2 h | 100 | 50% | Allowed |
A list of formulas is provided in each paper. Learn what it contains so that you know which facts you must remember for yourself.
What each paper asks of you
Core Paper 1 and Extended Paper 2 (no calculator). These test your written methods and number sense. Expect questions on fractions, percentages, ratio, algebraic manipulation, and exact trigonometric or geometric reasoning. Practise long division and multiplication, working with fractions and mixed numbers, and estimating. Always show your steps, since an arithmetic slip is less costly when the method is visible.
Core Paper 3 and Extended Paper 4 (calculator). These contain more applied and multi-step questions, such as percentage and interest problems, trigonometry in triangles, statistics, and problems set in real contexts. Use the calculator for accuracy, but write down the calculation you are doing. Keep full values on the display until the final line, then round to the accuracy requested; if nothing is stated, three significant figures is usual, or one decimal place for angles in degrees.
Timing. A paper gives you a little over a minute per mark at both levels, so there is some time to check. Leave a question after a reasonable attempt and return to it, rather than losing ten minutes on four marks.
Core students aiming higher. If you are working towards the top Core grades, concentrate on being accurate in the early topics, because accurate work on the earlier topics secures the marks within your reach, and on attempting every part of the longer problem-solving questions.
Command words and how to answer them
- Calculate: work out a numerical answer, showing the method.
- Write down: give the answer without needing to show detailed working.
- Show that: the answer is given, so each step to reach it must be shown clearly.
- Find or work out: determine a value or expression using a suitable method.
- Solve: find the values that satisfy an equation or inequality.
- Explain: give a reason in words, referring to the values or shapes in the question.
- Sketch: draw a rough diagram or graph with the main features labelled.
- Draw: produce an accurate diagram or graph, using a ruler and careful plotting.
- Factorise and expand: write an expression as a product, or multiply out brackets.
- Give your answer correct to: round to the stated number of significant figures or decimal places.
Calculators
A scientific calculator is permitted in the calculator papers and is not permitted in the other two. Learn the fraction key, power and root keys, brackets, and trigonometric and statistics functions, and check that your calculator is set to degrees. In the papers without a calculator, bring a ruler, protractor and compasses as usual, as they are needed for constructions and measuring angles.
Because the list of formulas supplied in the paper is limited, make your own checklist of facts you must recall, such as angle rules, circle theorems, index laws, exact trigonometric values and the rules for probability. Test yourself on it every few days. Facts that are only half-remembered cost time in the exam and lead to avoidable slips, so be strict about which ones you truly know.
How to revise this course
- Monday: read one revision note and write out the key methods from memory.
- Tuesday: work through the flashcards for the topic and repeat any that you find slow or uncertain.
- Wednesday: complete 10 to 15 question-bank questions on the topic, writing full working. Check each answer and record any errors.
- Thursday: redo the incorrect questions from memory, then add a short mixed set from an earlier topic.
- Friday: sit a timed test of 20 to 30 minutes, using a calculator only when the paper style allows it.
- Weekend: review your mistakes list, and every few weeks complete a full paper in the correct time, alternating calculator and non-calculator versions.
Common errors
- Using a calculator rounding for an intermediate value, so that the final answer is slightly out.
- Mixing up area and perimeter, or using the radius when the diameter is given.
- Forgetting that the order of operations needs brackets when entering a fraction into a calculator.
- Reading values from a graph carelessly, rather than checking the scale on each axis.
- Giving only one answer for a quadratic equation or a square root, when there are two.
Exam tip: when a question says "show that", work forwards from the information given and finish on the stated result. Do not start from the answer and work backwards, as that does not show that the result follows.