Pearson Edexcel Further Mathematics
9FM0 · A level · Issue 4, June 2023
Both compulsory papers can assess any core pure content. Book 1 and Book 2 are not exclusive paper scopes.
Current official specification · Checked 2026-10-07
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Topics in the specification
The topics currently listed on the site are shown below. Use the official specification to check the full course. Questions cover selected parts of each topic.
| Topic | Strand and clause | Practice |
|---|---|---|
| Composite functions | core · Assumed A-level Mathematics knowledge | Practice questions |
| Factor theorem | core · Assumed A-level Mathematics knowledge | Practice questions |
| Linear and quadratic equations | core · Assumed A-level Mathematics knowledge | Practice questions |
| Linear sequence nth terms | core · Assumed A-level Mathematics knowledge | Practice questions |
| Differentiating integer powers | core · Assumed A-level Mathematics knowledge | Practice questions |
| Matrix multiplication | core · Matrices | Practice questions |
| Complex number arithmetic | core · 2 Complex numbers | Practice questions |
| Modulus and argument | core · 2 Complex numbers | No questions yet |
| De Moivre and roots | core · 2 Complex numbers | Practice questions |
| Complex loci | core · 2 Complex numbers | Practice questions |
| Determinants | core · 3 Matrices | Practice questions |
| Inverse matrices | core · 3 Matrices | Practice questions |
| Proof by induction | core · 1 Proof | Practice questions |
| Sums of powers | core · 4 Further algebra and functions | No questions yet |
| Integration methods | core · 5 Further calculus | Practice questions |
| Areas in polar coordinates | core · 7 Polar coordinates | Practice questions |
| Hyperbolic functions | core · 8 Hyperbolic functions | Practice questions |
| First order differential equations | core · 9 Differential equations | Practice questions |
| Scalar products and vector geometry | core · 6 Further vectors | Practice questions |
| Arithmetic series sums | core · Assumed A-level Mathematics knowledge | Practice questions |
| Geometric series sums | core · Assumed A-level Mathematics knowledge | Practice questions |
| Binomial probabilities | FS1 · Discrete random variables | Practice questions |
| Shortest paths | D1 · Decision 1: algorithms on graphs | Practice questions |
| Momentum and impulse | FM1 · Momentum and impulse | Practice questions |
| Solving linear equations | core · Assumed A-level Mathematics knowledge | Practice questions |
| Two simultaneous linear equations | core · Assumed A-level Mathematics knowledge | Practice questions |
| Binomial coefficients for integer powers | core · Assumed A-level Mathematics knowledge | Practice questions |
| Inverting a linear function | core · Assumed A-level Mathematics knowledge | Practice questions |
| Inverting a restricted quadratic | core · Assumed A-level Mathematics knowledge | Practice questions |
| Equation of a tangent | core · Assumed A-level Mathematics knowledge | Practice questions |
| Equation of a normal | core · Assumed A-level Mathematics knowledge | Practice questions |
| A polynomial stationary point | core · Assumed A-level Mathematics knowledge | Practice questions |
| Exact polynomial definite integrals | core · 5 Further calculus | Practice questions |
| Dividing complex numbers | core · 2 Complex numbers | Practice questions |
| Conjugate roots of a real quadratic | core · 2 Complex numbers | Practice questions |
| Vector scalar product | core · 6 Further vectors | Practice questions |
| A point on a vector line | core · 6 Further vectors | Practice questions |
| Hyperbolic functions at logarithmic arguments | core · 8 Hyperbolic functions | Practice questions |
| An exponential growth differential equation | core · 9 Differential equations | Practice questions |
| Area swept by constant polar radius | core · 7 Polar coordinates | Practice questions |
| The algebra in an induction step | core · 1 Proof | Practice questions |
| Expected value of a discrete variable | FS1 · Discrete random variables | Practice questions |
| Constant acceleration | FM1 · Assumed A-level Mathematics mechanics knowledge | Practice questions |
| Partial fractions | core · Further calculus prerequisites | Practice questions |
| Linear recurrence calculation | FP2 · 6.1 Further sequences and series: recurrence relations D2 · 6.1 Recurrence relations | Practice questions |
| Polynomial division | core · Further algebra | Practice questions |
| A linear and nonlinear simultaneous pair | core · Assumed A-level Mathematics knowledge | Practice questions |
| Trigonometric solutions in an interval | core · Assumed A-level Mathematics knowledge | Practice questions |
| Second order differential equations | core · 9 Differential equations | Practice questions |
| Maclaurin expansions | core · 5 Further calculus | Practice questions |
| Eigenvalues of a 2 × 2 matrix | FP2 · 3.1 Further matrix algebra | Practice questions |
| An eigenvector of a 2 × 2 matrix | FP2 · 3.1 Further matrix algebra | Practice questions |
| An area swept by a limaçon | core · 7 Polar coordinates | Practice questions |
| A one-sided binomial critical region | FS1 · Hypothesis tests | Practice questions |
| Conditional probability | FS1 · Probability | Practice questions |
| Critical path in an activity network | D1 · Critical path analysis | Practice questions |
| Modular inverses | FP2 · Number theory | Practice questions |
| Gradient from a negative integer power | core · Assumed A-level Mathematics knowledge | Practice questions |
| A cubic with a rational root and complete equivalent product | core · Assumed A-level Mathematics knowledge | Practice questions |
| Powers of a complex number | core · 2 Complex numbers | Practice questions |
| All arguments of complex roots | core · 2 Complex numbers | Practice questions |
| An Argand perpendicular bisector | core · 2 Complex numbers | Practice questions |
| Intersecting an Argand circle and line | core · 2 Complex numbers | Practice questions |
| Eigenvalues of a non-triangular matrix | FP2 · 3.1 Further matrix algebra | Practice questions |
| An eigenvector of a non-triangular matrix | FP2 · 3.1 Further matrix algebra | Practice questions |
| A matrix power acting on a vector | FP2 · 3.1 Further matrix algebra | Practice questions |
| A parameter that makes a matrix singular | core · 3 Matrices | Practice questions |
| The algebra in a telescoping induction step | core · 1 Proof | Practice questions |
| A logarithm Maclaurin expansion | core · 5 Further calculus | Practice questions |
| A negative-power binomial expansion | core · 5 Further calculus | Practice questions |
| A differential equation with a repeated root | core · 9 Differential equations | Practice questions |
| A polynomial particular integral | core · 9 Differential equations | Practice questions |
| A first-order equation with a forcing term | core · 9 Differential equations | Practice questions |
| Recovering e^x from a hyperbolic value | core · 8 Hyperbolic functions | Practice questions |
| Hyperbolic double angles | core · 8 Hyperbolic functions | Practice questions |
| Area of one polar rose petal | core · 7 Polar coordinates | Practice questions |
| Area swept by a polar spiral | core · 7 Polar coordinates | Practice questions |
| An exact integral of an even sine power | core · 5 Further calculus | Practice questions |
| Intersecting a line and a plane | core · 6 Further vectors | Practice questions |
| The closest point on a line | core · 6 Further vectors | Practice questions |
| A one-dimensional collision with restitution | FM1 · Momentum and impulse | Practice questions |
| A geometric waiting-time probability | FS2 · 3.1 Geometric distributions | Practice questions |
| A minimum spanning tree | D1 · Decision 1: algorithms on graphs | Practice questions |