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International GCSE

Cambridge IGCSE Mathematics 0580

Extended programme

A new two-year cohort beginning in 2026 should use its examination-year syllabus. Core/Extended are distinct from GCSE Foundation/Higher. Differentiation is included for Extended. For exams in 2027, consult the 2025–2027 syllabus.

Official source: 2028–2030 syllabus, version 2

Two-year teaching plan · 72 teaching weeks

Plan around four mathematics periods per week. Each module has three suggested sessions: explanation and worked examples; practice with correction; written application and feedback. Spread 70 modules over weeks 1–60, allowing extra time for difficult concepts. Use the remaining periods for diagnostics, retrieval, investigations and reteaching. Weeks 61–72 consolidate mixed problems and board-specific examination preparation.

Begin each term with retrieval and finish with a cumulative checkpoint. These original assessments support learning; they are not calibrated official mock exams and do not generate qualification grades. Use your board’s authorised specimen materials for final exam-format preparation.

Use the dedicated Foundation or Core route for lower-tier learners. Its lesson editions, practice and assessment papers are selected together; higher-tier extensions remain in the separate Higher and Extended routes. Review written reasoning alongside saved checks.

Course map and syllabus evidence

References are editorial links to syllabus topics, not certification that every possible examination problem is represented. Open a module in your workspace for teaching, examples, practice and its protected markscheme.

Number
  1. Signed numbers and operation order

    Introductory · 3 models · 12 checks · written application

    N1 · N2 · N3 · E1.5 · E1.6

  2. Primes, factors and multiples

    Introductory · 3 models · 12 checks · written application

    N4 · E1.1

  3. Fractions and mixed numbers

    Introductory · 3 models · 12 checks · written application

    N2 · N8 · N10 · R3 · E1.4 · E1.6

  4. Decimals, percentages and recurring notation

    Introductory · 3 models · 12 checks · written application

    N8 · N10 · N12 · E1.4

  5. Exact recurring decimals

    Advanced · 3 models · 12 checks · written application

    N10 · E1.4

  6. Powers, roots and index laws

    Introductory · 3 models · 12 checks · written application

    N6 · N7 · E1.3 · E1.7 · E1.1

  7. Negative and fractional indices

    Advanced · 3 models · 12 checks · written application

    N7 · E1.7 · E2.4

  8. Standard form and calculator displays

    Introductory · 3 models · 12 checks · written application

    N9 · E1.8 · E1.14

  9. Estimation, rounding and error intervals

    Introductory · 3 models · 12 checks · written application

    N14 · N15 · E1.9 · E1.10

  10. Bounds in calculations

    Advanced · 3 models · 12 checks · written application

    N16 · E1.10

  11. Surds and rationalising denominators

    Advanced · 3 models · 12 checks · written application

    N8 · A4 · E1.18

Ratio and rates
  1. Ratios, sharing and proportional reasoning

    Introductory · 3 models · 12 checks · written application

    N11 · R4 · R5 · R6 · R7 · R8 · E1.11

  2. Percentage change, reverse percentages and interest

    Introductory · 3 models · 12 checks · written application

    R9 · E1.13

  3. Compound growth, decay and iterative models

    Advanced · 3 models · 12 checks · written application

    R16 · E1.17

  4. Direct and inverse proportion

    Advanced · 3 models · 12 checks · written application

    R10 · R13 · R14 · E2.8

  5. Units, money, timetables and compound measures

    Introductory · 3 models · 12 checks · written application

    N13 · R1 · R11 · G14 · E1.12 · E1.15 · E1.16 · E5.1

  6. Scale drawings and best value

    Introductory · 3 models · 12 checks · written application

    R2 · E1.11 · E4.3

  7. Square, cube and root proportion models

    Advanced · 3 models · 12 checks · written application

    R10 · R13 · E2.8

Algebra
  1. Algebraic language and substitution

    Introductory · 3 models · 12 checks · written application

    A1 · A2 · A3 · E2.1

  2. Collecting terms and expanding brackets

    Introductory · 3 models · 12 checks · written application

    A4 · E2.2

  3. Factorising and equivalent expressions

    Advanced · 3 models · 12 checks · written application

    A4 · E2.2

  4. Linear equations and modelling

    Introductory · 3 models · 12 checks · written application

    A17 · A21 · E2.5

  5. Rearranging formulae

    Advanced · 3 models · 12 checks · written application

    A5 · E2.5

  6. Algebraic fractions and fractional equations

    Advanced · 3 models · 12 checks · written application

    A4 · A17 · E2.3 · E2.5

  7. Simultaneous linear equations

    Introductory · 3 models · 12 checks · written application

    A19 · A21 · E2.5

  8. Quadratic equations by factorisation

    Advanced · 3 models · 12 checks · written application

    A18 · E2.5

  9. Completing the square and the quadratic formula

    Advanced · 3 models · 12 checks · written application

    A11 · A18 · E2.2 · E2.5 · E2.11

  10. Linear–quadratic simultaneous equations

    Advanced · 3 models · 12 checks · written application

    A19 · E2.5

  11. Linear inequalities and feasible regions

    Introductory · 3 models · 12 checks · written application

    A22 · E2.6

  12. Linear, figurate and recursive sequences

    Introductory · 3 models · 12 checks · written application

    A23 · A24 · A25 · E2.7

  13. Quadratic, cubic and geometric patterns

    Advanced · 3 models · 12 checks · written application

    A24 · A25 · E2.7

  14. Functions, inverses and composition

    Advanced · 3 models · 12 checks · written application

    A7 · E2.13

Graphs
  1. Coordinates, length and midpoint

    Introductory · 3 models · 12 checks · written application

    A8 · G11 · E3.1 · E3.4

  2. Straight-line graphs and gradients

    Introductory · 3 models · 12 checks · written application

    A9 · A10 · R14 · E3.2 · E3.3 · E3.5 · E3.6

  3. Perpendicular lines and circle tangents

    Advanced · 3 models · 12 checks · written application

    A9 · A16 · E3.7

  4. Quadratic, cubic, reciprocal and exponential graphs

    Advanced · 3 models · 12 checks · written application

    A11 · A12 · A14 · E2.10 · E2.11

  5. Travel graphs, tangents and area under graphs

    Advanced · 3 models · 12 checks · written application

    A14 · A15 · R15 · E2.9

IGCSE extension
  1. IGCSE differentiation and stationary points

    Advanced · 3 models · 12 checks · written application

    E2.12 · Pearson 3.4

Geometry
  1. Angle facts, triangles and polygons

    Introductory · 3 models · 12 checks · written application

    G1 · G3 · G4 · E4.1 · E4.6

  2. Quadrilaterals, symmetry and solids

    Introductory · 3 models · 12 checks · written application

    G1 · G4 · G12 · E4.1 · E4.5

  3. Congruence, similarity and geometrical proof

    Introductory · 3 models · 12 checks · written application

    G5 · G6 · G19 · E4.4

  4. Ruler-and-compass constructions and loci

    Introductory · 3 models · 12 checks · written application

    G2 · E4.2 · Pearson 4.5

  5. Nets, plans and elevations

    Introductory · 3 models · 12 checks · written application

    G12 · G13 · E4.2

  6. Bearings and scale geometry

    Introductory · 3 models · 12 checks · written application

    G15 · E4.3

  7. Reflections, rotations and translations

    Introductory · 3 models · 12 checks · written application

    G7 · G8 · E7.1

  8. Enlargement and area/volume scale factors

    Advanced · 3 models · 12 checks · written application

    G7 · G19 · R12 · E4.4 · E7.1

  9. Circle theorems and proof

    Advanced · 3 models · 12 checks · written application

    G10 · E4.7 · E4.8

Mensuration
  1. Perimeter, area and compound shapes

    Introductory · 3 models · 12 checks · written application

    G16 · G17 · E5.2 · E5.5

  2. Circles, arcs, sectors and segments

    Advanced · 3 models · 12 checks · written application

    G9 · G17 · G18 · E5.3

  3. Prisms, cylinders and surface area

    Introductory · 3 models · 12 checks · written application

    G16 · G17 · E5.4

  4. Cones, pyramids, spheres and frustums

    Advanced · 3 models · 12 checks · written application

    G17 · E5.4 · E5.5

Trigonometry
  1. Pythagoras and its converse

    Introductory · 3 models · 12 checks · written application

    G6 · G20 · E6.1

  2. Right-triangle trigonometry

    Introductory · 3 models · 12 checks · written application

    G20 · E6.2

  3. Exact trig values and trigonometric graphs

    Advanced · 3 models · 12 checks · written application

    G21 · A12 · E6.3 · E6.4

  4. Sine rule, cosine rule and triangle area

    Advanced · 3 models · 12 checks · written application

    G22 · G23 · E6.5

  5. Three-dimensional Pythagoras and angles

    Advanced · 3 models · 12 checks · written application

    G20 · E6.6

Vectors
  1. Vector arithmetic and magnitude

    Advanced · 3 models · 12 checks · written application

    G24 · G25 · E7.2 · E7.3 · Pearson 5.1

  2. Vector ratios and collinearity proofs

    Advanced · 3 models · 12 checks · written application

    G25 · E7.4

Probability
  1. Sets, Venn diagrams and counting

    Advanced · 3 models · 12 checks · written application

    P6 · P9 · E1.2

  2. Probability scale and exhaustive outcomes

    Introductory · 3 models · 12 checks · written application

    P1 · P3 · P4 · E8.1

  3. Experiments, relative frequency and expected counts

    Introductory · 3 models · 12 checks · written application

    P1 · P2 · P5 · E8.2

  4. Sample spaces, tables and independent events

    Introductory · 3 models · 12 checks · written application

    P6 · P7 · P8 · E8.3

  5. Tree diagrams without replacement and conditional probability

    Advanced · 3 models · 12 checks · written application

    P8 · P9 · E8.3 · E8.4

Statistics
  1. Sampling, bias and statistical questions

    Introductory · 3 models · 12 checks · written application

    S1 · E9.1 · S5

  2. Mean, median, mode, range and comparisons

    Introductory · 3 models · 12 checks · written application

    S2 · S4 · E9.3

  3. Frequency tables and grouped estimates

    Introductory · 3 models · 12 checks · written application

    S2 · S4 · E9.1 · E9.3

  4. Bar charts, pie charts, stem-and-leaf and time series

    Introductory · 3 models · 12 checks · written application

    S2 · E9.2 · E9.4

  5. Histograms and frequency density

    Advanced · 3 models · 12 checks · written application

    S3 · E9.7

  6. Cumulative frequency, quartiles and box plots

    Advanced · 3 models · 12 checks · written application

    S3 · S4 · E9.6

  7. Scatter diagrams, lines of best fit and interpretation

    Introductory · 3 models · 12 checks · written application

    S6 · E9.5

Review edition · Mathematical keys and application criteria are checked before release. Independent human subject moderation and board-specific paper calibration remain pending.