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Cambridge (CIE) · A Level

Mathematics — Further 9231

Extend pure mathematics, mechanics and statistics with more advanced methods and multi-step problems.

24 lessons and reviews0 practice setsSyllabus 2026–2027; 2028–2030
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At a glance

What you'll cover

  • Further Pure Mathematics 1
  • Further Pure Mathematics 2
  • Further Mechanics
  • Further Probability & Statistics
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Published syllabus exam years: 2023, 2024, 2025, 2026, 2027, 2028, 2029, 2030. Confirm exam-series and centre availability with your school and Cambridge.

Syllabus 2026–2027; 2028–2030

Cambridge International AS & A Level Further Mathematics 9231 syllabus map

2026–2027 Version 3; 2028–2030 Version 1

24 of 24 sections have teaching and practice

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Study options and assessment

All 24 syllabus sections across Further Pure Mathematics 1 and 2, Further Mechanics, and Further Probability & Statistics now link to original lessons with worked teaching, an explained check and guided, independent and transfer practice. Cambridge assumes prior 9709 knowledge. The syllabus map reflects topic teaching; it is not proof of exam readiness, an official Cambridge assessment or grade. Full timed mocks and human subject-specialist review remain pending.

The 2026–2027 update corrects a typographical error. Cambridge says the 2028–2030 syllabus has no significant changes affecting teaching. Check your exam year and entry route with your school.

Choose your paper route

  • AS Level onlyPaper 1 + Paper 3 or Paper 4

    Paper 1 Further Pure Mathematics 1 is compulsory. Choose Paper 3 Further Mechanics or Paper 4 Further Probability & Statistics for the second AS component; check availability with your centre.

  • A Level in stagesPaper 1 + one applied paper, then the other applied paper + Paper 2

    Cambridge permits the two AS components to be combined with the remaining applied component and Paper 2, subject to current carry-forward rules and time limits. Confirm the exact entry route with your school.

  • A Level in one seriesPapers 1, 2, 3 and 4

    All four papers are externally assessed written examinations. Paper 1 and Paper 2 are 2 hours each; Paper 3 and Paper 4 are 1 hour 30 minutes each.

Cambridge expects knowledge of the whole 9709 A Level Mathematics syllabus. Paper 1 draws on 9709 Pure Mathematics Papers 1 and 3. Paper 2 also assumes Further Pure Mathematics 1; Paper 3 assumes 9709 Mechanics; Paper 4 assumes 9709 Probability & Statistics Papers 5 and 6.

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The qualification has four components: Paper 1 Further Pure Mathematics 1 is compulsory; Paper 2 Further Pure Mathematics 2 is A Level only; candidates choose either Paper 3 Further Mechanics or Paper 4 Further Probability & Statistics for the second AS component. Full A Level candidates take all four papers, either in one series or through the staged route subject to Cambridge carry-forward rules. StudyForA maps all 24 syllabus sections. Its self-check practice does not simulate the full external examination.

Further Pure Mathematics 1

Further Pure Mathematics 2

Further Mechanics

Further Probability & Statistics

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  1. 01

    Roots of polynomial equations

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  2. 02

    Rational functions and their graphs

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  3. 03

    Summation of finite and infinite series

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  4. 04

    Matrices, inverses and geometric transformations

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  5. 05

    Polar coordinates and curve features

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  6. 06

    Vectors, lines and planes in three dimensions

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  7. 07

    Proof by mathematical induction

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  8. 08

    Hyperbolic functions and their inverses

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  9. 09

    Eigenvalues, eigenvectors and diagonalisation

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  10. 10

    Advanced differentiation and Maclaurin series

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  11. 11

    Advanced integration, reduction and curve measures

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  12. 12

    Complex numbers and de Moivre’s theorem

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  13. 13

    Linear differential equations and model solutions

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  14. 14

    Projectile motion

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  15. 15

    Equilibrium of a rigid body

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  16. 16

    Circular motion and radial forces

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  17. 17

    Hooke’s law, elastic strings and springs

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  18. 18

    Linear motion under a variable force

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  19. 19

    Momentum and coefficient of restitution

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  20. 20

    Continuous random variables and distribution functions

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  21. 21

    Inference with normal and t-distributions

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  22. 22

    χ² goodness-of-fit and independence tests

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  23. 23

    Sign and Wilcoxon non-parametric tests

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  24. 24

    Probability generating functions

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