A-level Further Maths
AS in Year 12, and the full A-level over Years 12 and 13.
Topics
Topics marked A-level aren't in AS.
1 Proof 1 topic
- Proof by Mathematical Induction A-level
2 Complex Numbers 7 topics
- Complex Arithmetic
- Complex Conjugates and Polynomial Roots
- Argand Diagrams
- Modulus-Argument Form
- Complex Loci
- De Moivre's Theorem A-level
- Roots of Complex Numbers and Roots of Unity A-level
3 Matrices 7 topics
- Matrix Arithmetic
- Zero, Identity and Inverse Matrices
- Matrices as Transformations
- Invariant Points and Lines
- Determinants
- Solving Equations with Matrices A-level
- Geometric Interpretation of Matrix Solutions A-level
4 Further Algebra & Functions 5 topics
- Polynomial Equations and Roots
- Transforming Polynomial Roots
- Summing Series A-level
- Method of Differences A-level
- Maclaurin Series A-level
5 Further Calculus 6 topics
- Improper Integrals A-level
- Volumes of Revolution A-level
- Mean Value of a Function A-level
- Further Integration Techniques A-level
- Inverse Trigonometric Functions A-level
- Trigonometric Substitution A-level
6 Further Vectors 4 topics
- Lines and Planes in 3D A-level
- Scalar Product in 3D A-level
- Angles in 3D Geometry A-level
- Intersections and Distances in 3D A-level
7 Polar Coordinates 3 topics
- Polar Coordinates A-level
- Sketching Polar Curves A-level
- Area in Polar Coordinates A-level
8 Hyperbolic Functions 4 topics
- Hyperbolic Functions and Their Graphs A-level
- Differentiating and Integrating Hyperbolic Functions A-level
- Inverse Hyperbolic Functions A-level
- Hyperbolic Substitution A-level
9 Differential Equations 6 topics
- First-Order Differential Equations A-level
- Second-Order Differential Equations A-level
- Auxiliary Equations and Types of Solution A-level
- Simple Harmonic Motion and Damped Oscillations A-level
- Coupled Differential Equations A-level
- Differential Equation Modelling A-level
Exam papers
- Two exam-style papers for every topic
- Two topic exams for most chapters in each tier, 1 hour 15 minutes each
- AS mock papers: Core Pure Mathematics, and Further Pure options, 1 hour 40 minutes each. A-level mock papers: Core Pure 1, Core Pure 2, Further Pure Mathematics 1 and Further Pure Mathematics 2, 1 hour 30 minutes each.
- Topic exams and mock papers show the grade you're working at
- In all, over 700 exam-style questions in 114 papers
Free and paid
Practice
- Over 450 practice questions, with worked solutions
- Recap cards for every topic
- A formula book
- One topic exam to try in each tier: Complex Numbers Topic Exam 1
Exam papers
- Every exam paper on this page
- AS and the full A-level
- Pay once, no subscription
Exam boards
Core Pure is shared by every exam board. The option papers here are Further Pure, so check which options your school takes.
Mock papers are set out like a typical exam paper. Your board's papers may be arranged differently, but the maths is the same.
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