Exam infoExam structure, syllabus and formula booklet3 official documents
Syllabus for exams in 2026–2027
| Paper | Time | Marks | Weighting |
|---|
| Paper 1 Further Pure Mathematics 1 | 2 h | 75 | 60% AS · 30% A Level |
| Paper 2 Further Pure Mathematics 2 | 2 h | 75 | 30% A Level |
| Paper 3 Further Mechanics | 1 h 30 min | 50 | 40% AS · 20% A Level |
| Paper 4 Further Probability & Statistics | 1 h 30 min | 50 | 40% AS · 20% A Level |
- AS Level: Paper 1 with either Paper 3 or Paper 4.
- A Level: all four papers, either in one series or staged over two years.
- Exams are in June and November.
Summarised from the official specification, checked 16 Oct 2026. The board's document is the final word.
PDFExams 2026–2027Version 3
AS & A Level Further Mathematics 9231 syllabus — exams in 2026 and 2027
The current Further Mathematics syllabus: Further Pure 1 and 2, Further Mechanics, and Further Probability & Statistics, with the allowed AS and A Level routes.
PDFFrom 2028Version 1 (September 2025)
AS & A Level Further Mathematics 9231 syllabus — exams in 2028, 2029 and 2030
The next Further Mathematics syllabus. Cambridge states there are no significant changes that affect teaching.
PDFMF19, for use from 2020
List of formulae and statistical tables (MF19)
The same booklet as for 9709; the Further Pure, Further Mechanics and Further Probability & Statistics sections are the ones you will use most.
All Cambridge documents: exam rules, key dates and grade thresholds →
Paper 1Further Pure Mathematics 17 topics
- Roots of polynomial equations
Roots of polynomial equations1 lessons - Rational functions and graphs
Rational functions and asymptotes1 lessons - Summation of series
Summation of series1 lessons - Matrices
Matrix algebra and inverses · Transformations, invariant points and lines2 lessons - Polar coordinates
Polar curves and areas1 lessons - Vectors
Vector product and planes · Shortest distances and triple products2 lessons - Proof by induction
Proof by induction1 lessons
Paper 2Further Pure Mathematics 26 topics
- Hyperbolic functions
Hyperbolic functions and their inverses1 lessons - Matrices
Eigenvalues and diagonalisation1 lessons - Differentiation
Inverse trig and hyperbolic functions in calculus · Maclaurin series2 lessons - Integration
Inverse trig and hyperbolic functions in calculus · Reduction formulae, arc length and surface area2 lessons - Complex numbers
De Moivre's theorem and roots of unity1 lessons - Differential equations
First-order equations: integrating factors · Second-order equations: auxiliary equation2 lessons
Paper 3Further Mechanics6 topics
- Motion of a projectile
Projectile motion1 lessons - Equilibrium of a rigid body
Rigid bodies in equilibrium1 lessons - Circular motion
Kinematics of circular motion · Centripetal acceleration and force2 lessons - Hooke's law
Hooke's law and elastic energy1 lessons - Linear motion under a variable force
Variable forces and differential equations1 lessons - Momentum
Momentum and its conservation · Directions, rebounds and several collisions2 lessons
Paper 4Further Probability & Statistics5 topics
- Continuous random variables
Probability density functions · Mean and variance · Median and percentiles3 lessons - Inference using normal and t-distributions
t-tests and confidence intervals1 lessons - χ²-tests
Goodness of fit and contingency tables1 lessons - Non-parametric tests
Sign and Wilcoxon tests1 lessons - Probability generating functions
Probability generating functions1 lessons