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Cambridge IGCSE

Mathematics 0580

Number, algebra, geometry, trigonometry, probability and statistics, with separate non-calculator and calculator papers on Core and Extended routes.

Syllabus version: 2025–2027 syllabusChecked against the Cambridge syllabusExam year 2027 is covered by the 2025–2027 syllabus.
Subject review complete (20 Oct 2026). All 40 Mathematics questions were re-solved and checked against the syllabus and Cambridge mark-scheme conventions, and their auto-marking was tested with correct and incorrect answers: 30 approved as written, 10 corrected.
Paper 2 Non-calculator (Extended): 50%Paper 4 Calculator (Extended): 50%Weighting2 papers
  • Paper 2 Non-calculator (Extended)50%
  • Paper 4 Calculator (Extended)50%
Original questions40
Topics covered9/9
Papers2
Mock papers2

What is assessed

2 components on the Extended tier. Question formats: short answer, structured.

Paper 2 Non-calculator (Extended)Extended
2 h100 marksWeighting 50%

Structured and unstructured questions on the Extended content (except E1.14 Using a calculator), answered on the paper without a calculator.

What the paper looks like

About 20 questions worth 100 marks in 2 hours, without a calculator, on the full Extended content. Early short items (indices, surds, standard form, simple algebra) lead to longer unstructured problems needing exact answers: surds, fractions and multiples of π. Typical later items cover algebraic fractions, quadratics, functions, differentiation, vector geometry, circle theorems with reasons and conditional probability. Exact working must be shown; “Show that” items need every step.

Short answerStructuredGeometrical instruments (compasses, protractor, ruler); Extended list of formulas printed on page 2; tracing paper on request
Checked against the Cambridge syllabus
Paper 4 Calculator (Extended)Extended
2 h100 marksWeighting 50%

Structured and unstructured questions on the Extended content; non-exact answers to 3 significant figures (angles to 1 decimal place).

What the paper looks like

Around 16 longer structured questions worth 100 marks in 2 hours, with a scientific calculator. Many questions combine topics in a context and run to 6–12 marks over several parts, with some unstructured problem-solving and “Show that” parts. Expect sine/cosine rules and 3D trigonometry, compound growth and reverse percentages, graphs of functions with tables to complete, grouped statistics, histograms and cumulative frequency, and probability trees. Accuracy: 3 s.f., angles 1 d.p., intermediate values to at least 4 s.f.

Short answerStructuredScientific calculator required; geometrical instruments; Extended list of formulas (including quadratic formula, sine and cosine rules) printed on page 2; tracing paper on request
Checked against the Cambridge syllabus

Assessment overview

From the 2025–2027 syllabus. Checked against the Cambridge syllabus

Core
Paper 1Paper 3
Core content only; eligible for grades C to G.
Extended
Paper 2Paper 4
Extended content (includes all Core content); eligible for grades A* to E.
Assessment objectiveIGCSE weighting
AO1 Knowledge and understanding of mathematical techniquesCore 60–70% · Extended 40–50%
AO2 Analyse, interpret and communicate mathematicallyCore 30–40% · Extended 50–60%
Changes in this syllabus version
  • New structure from 2025: Papers 1 and 2 are non-calculator and Papers 3 and 4 are calculator papers (previously all four papers allowed a calculator).
  • New timings and marks: Paper 1 and Paper 3 are 1 hour 30 minutes, 80 marks each; Paper 2 and Paper 4 are 2 hours, 100 marks each; each paper is 50% of the qualification.
  • Learning outcomes reworded with extra notes and examples to clarify depth of teaching; content refreshed with some outcomes added and removed.
  • Removed from Core: adding/subtracting vectors, multiplying a vector by a scalar, and data collection (no longer examined). Added to Core: inequalities; recall of certain squares, cubes and roots.
  • Removed from Extended: proper subsets, linear programming, congruence criteria, data collection and box-and-whisker plots. Added: surds, domain and range, exact trigonometric values, ax^n graphs with n = ±1/2, recall of squares, cubes and roots.
  • Version 2 (Feb 2024): the term prism clarified (C5.4/E5.4), expectations for drawing reciprocal and exponential graphs clarified (E2.11), and random added to guidance in C8.2.2/E8.2.2. Version 3 (May 2024): layout alignment only.
Command words used in Mathematics papers (13)
Calculate
Work out a result from the facts, figures or information given
Construct
Make an accurate drawing using the instruments allowed
Determine
Find or establish something with certainty
Describe
State the main points or features, e.g. all the details of a transformation
Explain
Give reasons or make relationships clear, supported by evidence such as geometric facts
Give
Produce an answer from a given source or from memory
Plot
Mark one or more points accurately on a graph
Show (that)
Give structured working that leads step by step to the stated result
Sketch
Make a simple freehand drawing showing the key features, e.g. intercepts and turning points
State
Express clearly and briefly
Work out
Calculate from the information given, with or without a calculator
Write
Give an answer in a particular form, e.g. standard form or simplest fraction
Write down
Give the answer without needing significant working
Examiner guidance from recent reports (13)
Number. Never round in the middle of a calculation: keep at least 4 significant figures (or the calculator value) in working and round only the final answer to 3 significant figures. Exact answers such as 21.55 or 1250 should be left exact, not rounded.
Number. When rounding, keep place value: 4876 to the nearest hundred is 4900, not 49. For bounds, the upper bound of 23.6 (1 d.p.) is 23.65, not 23.69 or 23.649.
Number. In reverse-percentage questions divide by the multiplier (e.g. ÷ 1.12); finding 12% of the new price and subtracting is a classic error that scores nothing.
Algebra and graphs. Show every step when solving equations and simultaneous equations, especially when the question says “show all your working”: an answer with no method can score zero on non-calculator papers.
Algebra and graphs. For inverse functions, swap x and y and rearrange carefully, dividing every term; for composite functions remember fg(x) means apply g first.
Algebra and graphs. Plot points accurately to within half a small square, join non-linear graphs with a smooth curve (not ruled segments), and read roots where the curve crosses the required line.
Coordinate geometry. Give a line’s equation in full (y = mx + c), not just the gradient. For perpendicular lines use the negative reciprocal gradient and substitute a known point to find c.
Geometry. Give reasons using correct geometric language, such as “angle in a semicircle is 90°” or “alternate segment theorem”; vague phrases like “because of the circle” earn no credit. Draw north lines before working out bearings.
Mensuration. Convert units before calculating (e.g. 1.2 m to 120 cm) and remember 1 litre = 1000 cm³. Use the formula sheet, but substitute the radius, not the diameter.
Trigonometry. Check your calculator is in degrees, label sides opposite/adjacent/hypotenuse first, and keep full calculator values when one trigonometric result feeds the next.
Transformations and vectors. Describe a single transformation completely: rotation needs centre, angle and direction; enlargement needs centre and scale factor; translation needs a column vector (no fraction line between components). Never give two transformations.
Probability. Give probabilities as fractions, decimals or percentages, never as ratios or “1 in 4”. In without-replacement questions reduce both numerator and denominator on the second branch.
Statistics. For grouped data use midpoints to estimate the mean, and divide by the total frequency, not by the number of classes. Histogram bar heights are frequency densities (frequency ÷ class width).

Topic map

Practice types

Free sample questions

FAQs

Are these official 0580 past-paper questions?

No. They are original questions written to match the Mathematics syllabus topics. Official past papers are available to schools through Cambridge.

Why choose an exam year?

Cambridge updates syllabuses periodically. Your exam year selects the matching configuration so topics and components follow the right version.

Is a calculator allowed?

It depends on the paper. Each component card shows the calculator rule from this configuration.