IGCSE Mathematics Core Study Guide & Review

Prepare for Cambridge IGCSE Mathematics 0580 Core by selecting accurate methods, solving with and without a calculator, communicating complete working and repairing errors across the nine official Core Topic groups.

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  1. 01Learn concepts
  2. 02Practise questions
  3. 03Review mistakes

How to study Cambridge IGCSE Mathematics 0580 Core

Cambridge IGCSE Mathematics 0580 Core assesses method selection and communication across both papers, not a fixed split of easy and hard Topics. Build number sense and estimation through Core Number before connecting algebra and graphs to coordinate geometry and using the same modelling habits in statistics. Work from the 53 Core routes only; Extended outcomes are not part of this page.

Rebuild the representation and method in Concept and retrieve formulas, conditions, operations and notation in Mastery without prompts. Apply them through the Question Bank under the correct calculator condition. Estimate before solving, show the necessary stages and classify the first failure as representation, method, manipulation, calculator input, accuracy, unit or communication. Repair that exact Core Topic and retry a matched question before mixing Topics.

Practise 0580 Core by mathematical behaviour

Use distinct routines for non-calculator structure, calculator accuracy, representation and reasoning, and mixed-Topic error repair across the nine Core groups.

Build non-calculator fluency

Fractions, percentages, indices, algebraic manipulation, linear equations, exact values and estimation

Work line by line without calculator shortcuts, simplify before substituting and verify through inverse operations or estimation. Preserve exact values where required and identify which written transformation earns the method, rather than treating a correct final number as sufficient evidence.

Practise Estimation

Control calculator accuracy

Rates, percentages, mensuration, right-triangle trigonometry, statistics, units and limits of accuracy

Model the situation and estimate first, enter the calculation second and retain unrounded values for later parts. Check mode, sign, scale and units, then round only at the final stated or syllabus-default precision instead of correcting the display mechanically.

Practise Limits of Accuracy

Translate and justify representations

Practical graphs, coordinate geometry, angles, transformations, probability models and statistical diagrams

Turn the words into a labelled diagram, table, graph or equation, then select the property or relationship that controls the solution. Communicate geometrical reasons and notation explicitly, and check that the representation answers the stated Core question rather than an assumed one.

Practise Linear Graphs

Repair mixed-Topic problems

Ratio with geometry, money and rates, probability tables, graphs in context and compound measures

Attempt an unfamiliar mixed task and mark the first failure as representation, method, manipulation, input, accuracy, unit or communication. Repair one responsible Core skill, solve a parallel question and only then return to a timed mixed set.

Build a Core test

Where to start

Start from a known Core Topic or diagnose whether the repeated weakness is representation, method, manipulation, calculator use, accuracy, units or communication.

Choose your starting point

  1. I know the weak Topic

    Open its exact Core route, identify the failed representation or method and avoid any Extended-only revision material sharing the broad Topic name.

    Browse 53 Core Topics

  2. I do not know what is weak

    Use mixed Core questions to separate missing technique from representation, calculator dependence, accuracy, unit and working errors.

    Start a Core diagnostic

Choose the right 0580 Core starting point

  1. Explain and represent

    Choose the variables, diagram, table, graph or equation, state why the method applies and predict the form or size of the answer.

    Review a Concept

  2. Retrieve and check

    Reproduce the required technique, formula and conditions without notes, then estimate the likely magnitude before calculating or constructing.

    Check Mastery

  3. Apply, classify and repair

    Answer a fresh Core question, compare the working with marking evidence and repair the first invalid step before retrying.

    Practise Core questions

Explore the 2028–2030 Cambridge 0580 Core syllabus

The Core route contains 53 syllabus Topics across nine groups: Number through Statistics. Open one exact Core row, rebuild the method and connect it to related representations; this map excludes Extended-only outcomes even when both tiers share the same broad group title.

9
syllabus groups
53
mapped topics

1. Number

Open unit questions
C1.1 Types of numberC1.2 SetsC1.3 Powers and rootsC1.4 Fractions, decimals and percentagesC1.5 OrderingC1.6 The four operationsC1.7 Indices IC1.8 Standard formC1.9 EstimationC1.10 Limits of accuracyC1.11 Ratio and proportionC1.12 RatesC1.13 PercentagesC1.14 Using a calculatorC1.15 TimeC1.16 Money

2. Algebra and graphs

Open unit questions
C2.1 Introduction to algebraC2.2 Algebraic manipulationC2.4 Indices IIC2.5 EquationsC2.6 InequalitiesC2.7 SequencesC2.9 Graphs in practical situationsC2.10 Graphs of functionsC2.11 Sketching curves

3. Coordinate geometry

Open unit questions
C3.1 CoordinatesC3.2 Drawing linear graphsC3.3 Gradient of linear graphsC3.5 Equations of linear graphsC3.6 Parallel lines

4. Geometry

Open unit questions
C4.1 Geometrical termsC4.2 Geometrical constructionsC4.3 Scale drawingsC4.4 SimilarityC4.5 SymmetryC4.6 AnglesC4.7 Circle theorems

5. Mensuration

Open unit questions
C5.1 Units of measureC5.2 Area and perimeterC5.3 Circles, arcs and sectorsC5.4 Surface area and volumeC5.5 Compound shapes and parts of shapes

6. Trigonometry

Open unit questions
C6.1 Pythagoras’ theoremC6.2 Right-angled triangles

7. Transformations and vectors

Open unit questions
C7.1 Transformations

8. Probability

Open unit questions
C8.1 Introduction to probabilityC8.2 Relative and expected frequenciesC8.3 Probability of combined events

9. Statistics

Open unit questions
C9.1 Classifying statistical dataC9.2 Interpreting statistical dataC9.3 Averages and rangeC9.4 Statistical charts and diagramsC9.5 Scatter diagrams

Cambridge IGCSE Mathematics 0580 Core assessment

Core candidates take two compulsory 90-minute papers worth 80 marks and 50% each. Both assess AO1 techniques and AO2 problem solving across Core content; the calculator condition changes the working habit, not a fixed Topic allocation.

Paper / componentQuestionsTime% of grade
Paper 1: Non-calculator (Core)Structured and unstructured compulsory questions; all Core content except C1.1480 marksCalculators are prohibited. Candidates write on the question paper, use the supplied formula list on page 2 and show all necessary working; the formula list does not contain every required relationship.How to prepare: Build exact arithmetic, estimation, algebraic manipulation, diagram and graph fluency without calculator dependence. Select efficient written methods, keep exact forms where required and verify through inverse operations or magnitude checks. Practise current-format timing because older Core papers used different calculator and assessment arrangements.1 hour 30 minutes50%
Paper 3: Calculator (Core)Structured and unstructured compulsory questions across all Core content80 marksA permitted scientific calculator is required; algebraic and graphical calculators are not allowed. Candidates also receive the formula list, must show necessary working and follow the stated accuracy conventions.How to prepare: Translate the context into mathematics before entering values, estimate the likely result and retain unrounded values for later parts. Record the model and intermediate reasoning, check calculator mode, scale and units, then apply the requested or syllabus-default final accuracy instead of treating the display as proof.1 hour 30 minutes50%

SourceCambridge International Education · Cambridge IGCSE Mathematics 0580 syllabus for exams in 2028, 2029 and 20300580 Core · 2028–2030 · Version 1 · September 2025

Cambridge IGCSE Mathematics 0580 Core questions

The Core route offers grades C–G. A learner aiming for a possible grade above C needs the Extended route, which has different content and Papers 2 and 4; discuss tier entry with your school or centre. Cambridge does not define one permanent raw percentage for grade C, because thresholds vary by series and paper variant.

Yes. A formula list appears on page 2 of both Core papers, but Cambridge states that it does not include every formula you may need. Learn which relationships are supplied and retrieve the rest from memory. The list does not remove the need to select the method, show working, use units or justify geometrical reasoning.

Use pre-2025 questions selectively for Topic practice, but not as exact current-format timed mocks. The assessment changed to a non-calculator Paper 1 and calculator Paper 3 with current marks, durations and weighting. Prioritise current-format specimen and live papers, then reconcile any older question with the 2028–2030 Core syllabus before using it.

No. Calculators are prohibited on Paper 1. Paper 3 requires a permitted scientific calculator, with algebraic and graphical calculators disallowed. Both papers still require all necessary working, and both provide the formula list. Practise the same Core ideas under different tool conditions rather than assigning complete Topics permanently to one paper.

No. Both tiers use the same nine broad Topic headings, but Core follows the official C-coded statements and this page exposes 53 Core Topic rows. Extended includes different and additional E-coded outcomes, different papers and a different grade range. Do not import Extended subtopics from a combined revision directory into Core preparation.