Pearson Edexcel · A Level (UK)9FM0 A Level Further Mathematics
10 components67 topics67 with lessons
Source: Pearson Edexcel 9FM0 specification · Confirm the syllabus year with your school.
Exam infoExam structure, syllabus and formula booklet1 official documents
First teaching 2017
| Paper | Time | Marks | Weighting |
|---|
| Paper 1 Core Pure Mathematics 1 | 1 h 30 min | 75 | 25% |
| Paper 2 Core Pure Mathematics 2 | 1 h 30 min | 75 | 25% |
| Paper 3 Option (3A–3D) | 1 h 30 min | 75 | 25% |
| Paper 4 Option (4A–4D) | 1 h 30 min | 75 | 25% |
- Options: any two Paper 3 options, or a matching Paper 3 and Paper 4 pair (for example, 3B and 4B).
Summarised from the official specification, checked 16 Oct 2026. The board's document is the final word.
PDFIssue 4 (June 2023)
A Level Further Mathematics 9FM0 — specification
Four 1 h 30 min, 75-mark papers: Core Pure 1 and 2 are compulsory, plus two options. You can take any two Paper 3 options, or a matching Paper 3 and Paper 4 pair (for example, Further Statistics 1 and 2).
All Edexcel documents: exam rules, key dates and grade thresholds →
Paper 1Core Pure Mathematics 19 topics
- Proof
Proof by induction1 lessons - Complex numbers
Arithmetic and conjugates · The Argand diagram, modulus and argument · Polynomial equations and square roots · Polar and exponential forms · Loci and regions in the Argand diagram5 lessons - Matrices
Matrix algebra and inverses · Transformations, invariant points and lines2 lessons - Further algebra and functions
Roots of polynomial equations · Summation of series2 lessons - Further calculus
Volumes, mean values and improper integrals · Inverse trig and hyperbolic functions in calculus · Maclaurin series3 lessons - Further vectors
Vector product and planes · Shortest distances and triple products2 lessons - Polar coordinates
Polar curves and areas1 lessons - Hyperbolic functions
Hyperbolic functions and their inverses1 lessons - Differential equations
First-order equations: integrating factors · Second-order equations: auxiliary equation2 lessons
Paper 2Core Pure Mathematics 29 topics
- Proof
Proof by induction1 lessons - Complex numbers
Arithmetic and conjugates · The Argand diagram, modulus and argument · Polynomial equations and square roots · Polar and exponential forms · Loci and regions in the Argand diagram5 lessons - Matrices
Matrix algebra and inverses · Transformations, invariant points and lines2 lessons - Further algebra and functions
Roots of polynomial equations · Summation of series2 lessons - Further calculus
Volumes, mean values and improper integrals · Inverse trig and hyperbolic functions in calculus · Maclaurin series3 lessons - Further vectors
Vector product and planes · Shortest distances and triple products2 lessons - Polar coordinates
Polar curves and areas1 lessons - Hyperbolic functions
Hyperbolic functions and their inverses1 lessons - Differential equations
First-order equations: integrating factors · Second-order equations: auxiliary equation2 lessons
OptionFurther Pure Mathematics 17 topics
- Vectors
Vector product and planes · Shortest distances and triple products2 lessons - Conic sections
Parabola and rectangular hyperbola · Ellipse and hyperbola2 lessons - Inequalities
Rational inequalities1 lessons - The t-formulae
The t-substitution1 lessons - Taylor series
Taylor series, L'Hôpital and Leibniz1 lessons - Methods in calculus
Taylor series, L'Hôpital and Leibniz1 lessons - Numerical methods
Newton–Raphson, bisection and interpolation1 lessons
OptionFurther Pure Mathematics 26 topics
- Groups
Groups and subgroups1 lessons - Further calculus
Reduction formulae, arc length and surface area1 lessons - Further matrix algebra
Eigenvalues and diagonalisation1 lessons - Complex numbers
Loci and transformations1 lessons - Number theory
Divisibility and modular arithmetic1 lessons - Further sequences and series
Summation of series1 lessons
OptionFurther Statistics 18 topics
- Discrete probability distributions
Probability distributions · Expectation and variance2 lessons - Poisson and binomial distributions
The binomial distribution · Poisson probabilities · Scaling rates and sums · Poisson and normal approximations4 lessons - Geometric and negative binomial distributions
The geometric distribution1 lessons - Hypothesis testing
Binomial and Poisson tests1 lessons - Central limit theorem
The sample mean and the Central Limit Theorem1 lessons - Chi-squared tests
Goodness of fit and contingency tables1 lessons - Probability generating functions
Probability generating functions1 lessons - Quality of tests
Type I and Type II errors1 lessons
OptionFurther Statistics 26 topics
- Linear regression
The least squares regression line1 lessons - Continuous probability distributions
The continuous uniform distribution · Probability density functions · Mean and variance · Median and percentiles4 lessons - Correlation
Summary statistics and the PMCC1 lessons - Combinations of random variables
E and Var of aX + b and aX + bY · Sums of observations and multiples · Combining normal and Poisson variables3 lessons - Estimation, confidence intervals and tests
Sampling and unbiased estimates · Confidence intervals · Tests for a population mean3 lessons - Confidence intervals using the t-distribution
t-tests and confidence intervals1 lessons
OptionFurther Mechanics 15 topics
- Momentum and impulse
Momentum and impulse · Momentum and its conservation · Coalescing and loss of kinetic energy · Directions, rebounds and several collisions4 lessons - Work, energy and power
Work done · Kinetic and potential energy · The work–energy principle · Power4 lessons - Elastic strings and springs
Hooke's law and elastic energy1 lessons - Elastic collisions in one dimension
Newton's law of restitution1 lessons - Elastic collisions in two dimensions
Oblique impacts1 lessons
OptionFurther Mechanics 25 topics
- Motion in a circle
Kinematics of circular motion · Centripetal acceleration and force2 lessons - Centres of mass of plane figures
Centres of mass of laminas1 lessons - Further centres of mass
Centres of mass by calculus1 lessons - Further dynamics
Variable forces and differential equations1 lessons - Further kinematics
Kinematics with calculus and vectors1 lessons
OptionDecision Mathematics 15 topics
- Algorithms and graph theory
Sorting, searching and bin packing · Graphs and their properties2 lessons - Algorithms on graphs
Kruskal's and Prim's algorithms1 lessons - Algorithms on graphs II
Dijkstra's and Floyd's algorithms · Route inspection and TSP2 lessons - Critical path analysis
Activity networks and critical paths1 lessons - Linear programming
Formulating and solving linear programmes1 lessons
OptionDecision Mathematics 27 topics
- Transportation problems
The stepping-stone method1 lessons - Allocation problems
The Hungarian algorithm1 lessons - Flows in networks
Maximum flow and minimum cut1 lessons - Dynamic programming
Stages, states and Bellman’s principle1 lessons - Game theory
Zero-sum games1 lessons - Recurrence relations
Solving recurrence relations1 lessons - Decision analysis
Decision trees and utility1 lessons