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Cambridge (CIE) · IGCSE

Mathematics 0580

Build understanding through Number and Algebra and graphs. Explain your reasoning, practise with less help, then apply the same ideas to an unfamiliar problem. Choose the pathway that matches your next learning goal.

49 teaching lessons2 practice setsSyllabus 2025–2027
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Syllabus expansion · 2025–2027

Your route through Mathematics

Number has 19 sequenced lessons addressing 18 of 18 section entries. Algebra and graphs adds 21 lessons addressing 13 of 13 entries, with Core and Extended requirements labelled. Choose a pathway, attempt the readiness check, then move through explanations and practice. The other seven syllabus areas still need full teaching sequences. Published lessons do not establish mastery or teacher verification.

Start the Number pathwayStart Algebra and graphs
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The nine syllabus areas

  1. 1 · Number19 sequenced lessons; 18 of 18 section entries have teaching and practice. Teacher review and broader assessment remain pending.
  2. 2 · Algebra and graphs21 sequenced lessons; 13 of 13 section entries have teaching and practice. Teacher review and broader assessment remain pending.
  3. 3 · Coordinate geometryExisting overview; full teaching sequence pending.
  4. 4 · GeometryExisting overview; full teaching sequence pending.
  5. 5 · MensurationExisting overview; full teaching sequence pending.
  6. 6 · TrigonometryExisting right-triangle overview; full teaching sequence pending.
  7. 7 · Transformations and vectorsExisting overview; full teaching sequence pending.
  8. 8 · ProbabilityExisting combined overview; full teaching sequence pending.
  9. 9 · StatisticsExisting combined overview; full teaching sequence pending.

A lesson link means teaching and practice are published for the section. It is not a claim of exhaustive exam-question coverage, teacher approval or your mastery.

Number: section-by-section teaching status

Algebra and graphs: section-by-section teaching status

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Teaching notes & worked examples

Number contains 19 sequenced lessons; Algebra and graphs contains 21. Nine earlier overviews support selected topics across the syllabus. The other seven syllabus areas, cumulative assessment and human teacher review are not yet complete. Written lesson practice is self-checked, not automatically graded.

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All subject practice

Open a lesson, practise its questions, then revisit it from memory. Progress below records your own study checks.

  1. 01

    Number families and reciprocals

    Readiness → guided practice → independent work → transfer

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  2. 02

    Factors, multiples and prime building blocks

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  3. 03

    Sets and Venn diagrams

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  4. 04

    Powers and roots: reversing a process

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  5. 05

    Fractions, decimals and percentages as one quantity

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  6. 06

    Ordering numbers and interpreting inequalities

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  7. 07

    Arithmetic operations and the order of calculation

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  8. 08

    Index laws from repeated factors

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  9. 09

    Standard form and calculations at different scales

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  10. 10

    Rounding, estimation and sensible accuracy

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  11. 11

    Measurement bounds and the limits of accuracy

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  12. 12

    Ratios and proportional reasoning in context

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  13. 13

    Rates, average speed and compound measures

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  14. 14

    Percentages, interest and recovering the original

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  15. 15

    Calculator techniques and interpreting the display

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  16. 16

    Time calculations, timetables and time differences

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  17. 17

    Money calculations and currency conversions

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  18. 18

    Exponential growth and decay models

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  19. 19

    Surds and rationalising a denominator

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  20. 20

    Algebraic language and substitution

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  21. 21

    Collecting terms and expanding brackets

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  22. 22

    Factorising quadratics and grouped expressions

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  23. 23

    Completing the square and locating a turning point

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  24. 24

    Algebraic fractions and excluded values

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  25. 25

    Algebraic indices and equal-base equations

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  26. 26

    Constructing and solving linear equations

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  27. 27

    Linear simultaneous equations and modelling

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  28. 28

    Quadratic equations with three solving methods

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  29. 29

    Rearranging formulas and repeated subjects

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  30. 30

    Fractional equations and checking forbidden roots

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  31. 31

    Simultaneous linear and non-linear equations

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  32. 32

    Inequalities and intervals on a number line

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  33. 33

    Inequality regions and boundary lines

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  34. 34

    Sequences from differences, powers and ratios

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  35. 35

    Direct and inverse proportion as equations

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  36. 36

    Travel graphs, rates and area under speed

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  37. 37

    Tables, function graphs and graphical solutions

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  38. 38

    Sketching curves from roots, symmetry and asymptotes

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  39. 39

    Differentiation, tangents and stationary points

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  40. 40

    Functions, domains, inverses and composition

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  41. 41

    Number, fractions and standard form

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  42. 42

    Bounds, ratios and rates

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  43. 43

    Algebra, equations and sequences

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  44. 44

    Coordinate geometry and stationary points

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  45. 45

    Geometry, circle theorems and similarity

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  46. 46

    Mensuration and exact answers

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  47. 47

    Right-triangle trigonometry

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  48. 48

    Transformations and vectors

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  49. 49

    Probability and statistics

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Opened and self-reported recall are study activity, not a mastery score. Only published topics are shown; syllabus coverage remains partial.

Original StudyForA lessons. AI-assisted editorial checks; human subject-teacher review remains pending.

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Practise this subject

IGCSE Mathematics 0580 · Extended Practice Paper 1

25 questions · 120 minute timed paper

Learn with feedback Open timed paper

IGCSE Mathematics 0580 · Mixed Skills Mini

6 questions · 40 minute timed paper

Learn with feedback Open timed paper
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Official papers

Historical and specimen papers may follow a different syllabus. Check the year and component before practising.