A Level Further Mathematics Tutoring, for Every Board
A Level Further Mathematics is where school mathematics stops being a set of methods and starts demanding proof, abstraction and long chains of reasoning — complex numbers, matrices, hyperbolic functions, differential equations. Boards also differ sharply in what a student actually sits, because the optional papers decide whether the course leans towards mechanics, statistics, discrete or further pure mathematics.
Short answer
A Level Further Mathematics is offered online, one-to-one.
A private lesson runs 90 minutes and starts at USD 95 per lesson; lessons are booked singly or in packages.
No group class runs for this exam.
From USD 95 per lesson
- Structure shown for AQA, OCR, Pearson Edexcel, Cambridge International
- Live online lessons of 90 minutes
- From USD 95 per lesson
How A Level Further Mathematics is assessed, board by board
4 awarding bodies examine this subject, and they do not examine it the same way: different papers, different weightings, different practical arrangements. Find your board — it is printed on your school's timetable and on past papers — and read that block. Nothing on this page describes one board's paper as though it applied to all of them.
AQA
AQA A-level Further Mathematics (7367)
| Component | Share of grade | Length | Marks | Format |
|---|---|---|---|---|
| Paper 1 — Compulsory core: proof, complex numbers, matrices, further algebra, further calculus, further vectors, polar coordinates, hyperbolic functions, differential equations, numerical methods | 33⅓% | 2 hours | 100 marks | structured questions and problem solving |
| Paper 2 — The same compulsory core as Paper 1 | 33⅓% | 2 hours | 100 marks | structured questions and problem solving |
| Paper 3 — Two optional booklets: Discrete and Statistics, or Statistics and Mechanics, or Mechanics and Discrete | 33⅓% | 2 hours | 100 marks | structured questions and problem solving |
Checked on 22 September 2026
OCR
OCR A Level Further Mathematics A (H245)
| Component | Share of grade | Length | Marks | Format |
|---|---|---|---|---|
| Pure Core 1 (Y540) — The whole of the mandatory Pure Core | 25% | 1 hour 30 min | 75 marks | structured questions |
| Pure Core 2 (Y541) — The whole of the mandatory Pure Core | 25% | 1 hour 30 min | 75 marks | structured questions |
| Two optional papers — Statistics (Y542), Mechanics (Y543), Discrete Mathematics (Y544) or Additional Pure Mathematics (Y545) — each 1 hour 30 minutes and worth 25% | 50% | 1 hour 30 min | 75 marks | structured questions |
- The same board also awards Further Mathematics B (MEI) (H645), which is examined differently. Check the specification code on your syllabus before assuming the structure above applies.
Checked on 22 September 2026
Pearson Edexcel
Pearson Edexcel International A Level Further Mathematics (YFM01)
| Component | Share of grade | Length | Marks | Format |
|---|---|---|---|---|
| Unit FP1: Further Pure Mathematics 1 — Compulsory | 16⅔% | 1 hour 30 min | 75 marks | structured questions |
| Unit FP2 or FP3 — At least one of the two is compulsory | 16⅔% | 1 hour 30 min | 75 marks | structured questions |
| Four further units — From FP2, FP3, M1–M3, S1–S3 and D1 — each 1 hour 30 minutes and worth 16⅔% | 66⅔% | 1 hour 30 min | 75 marks | structured questions |
- This is a modular qualification: units are sat in January, June and October, can be taken in stages, and can be re-sat, with the best result counting. That changes how a two-year plan is built — and it is the main reason a Pearson student and a Cambridge student in the same class need different revision schedules.
- A student certificating both Mathematics and Further Mathematics needs twelve distinct unit results: a unit cashed in for one qualification cannot be reused for the other. Getting that wrong is an administrative failure that costs a grade.
Checked on 22 September 2026
Cambridge International
Cambridge International AS & A Level Further Mathematics (9231)
| Component | Share of grade | Length | Marks | Format |
|---|---|---|---|---|
| Paper 1: Further Pure Mathematics 1 — Compulsory for AS Level and A Level | 30% | 2 hours | 75 marks | structured questions |
| Paper 2: Further Pure Mathematics 2 — Compulsory for A Level | 30% | 2 hours | 75 marks | structured questions |
| Paper 3: Further Mechanics | 20% | 1 hour 30 min | 50 marks | structured questions |
| Paper 4: Further Probability & Statistics | 20% | 1 hour 30 min | 50 marks | structured questions |
- Cambridge Further Mathematics assumes the content of Mathematics 9709 alongside it. It is not a standalone course and cannot sensibly be started without the pure content in place.
Checked on 22 September 2026
Specifications are revised periodically. Each block links to the specification it was read from and gives the date it was checked; if your school has moved to a newer specification, that document takes precedence.
What A Level Further Mathematics covers
The syllabus areas most boards share. Which ones appear, in what order and on which paper differs by board and by specification code — your own specification is the final word. Topic names are left in English, as they appear on the paper.
Core Pure
Complex numbers: Argand diagram, De Moivre's theorem, roots · Matrices: transformations, eigenvalues, eigenvectors · Proof methods: induction, contradiction · Polar coordinates and hyperbolic functions
Further Mechanics
Momentum and impulse, elastic and inelastic collisions · Circular motion and centripetal force · Energy methods and the work-energy relationship
Further Statistics / Further Pure
Probability distributions: Poisson, geometric · Chi-square and t-tests · Additional calculus topics and systems of differential equations
Where A Level Further Mathematics marks are usually lost
Writing a proof that only looks complete
Proof by induction is examined at every board, and it is marked line by line. Students lose marks by assuming what they are meant to show, by skipping the step that carries one case to the next, or by leaving out the concluding statement. A correct idea with a missing logical link earns far less than students expect, and examiners do not fill the gap for them.
Reading matrix answers off the calculator
Calculator rules differ: AQA requires a calculator that can handle matrices, OCR permits graphical calculators, and Cambridge allows only scientific calculators and gives no marks for unsupported calculator answers. Students used to reading a determinant or an inverse off the screen lose the method marks when a question says “show that” or “hence”, because an answer without working earns little or nothing.
Assuming the Mathematics course covered everything
The applied papers in Further Mathematics build on the Mathematics course. Cambridge’s Further Mechanics assumes the Mechanics paper of its Mathematics syllabus and Further Probability & Statistics assumes both statistics papers, but no Cambridge Mathematics route includes all three, so every Cambridge student has a gap to close. At Pearson Edexcel, a unit result used for Mathematics cannot be reused for Further Mathematics, which limits the choice of applied units.
How we teach A Level Further Mathematics
A tutor starts by establishing exactly which papers or units the student will sit, because the course differs with each combination. The core pure content — complex numbers and the Argand diagram, matrices and transformations, series and induction, polar coordinates, hyperbolic functions, further calculus and differential equations — is taught for understanding first: why de Moivre’s theorem works, what a matrix does to the plane, where a method breaks down. Each topic is then practised on past questions from the student’s own board, with written solutions checked for the logical steps examiners credit, not only the final line. The applied options are taught on top of the Mathematics content they rely on, and any gap there is closed first. Closer to the exams, full timed papers build stamina for long multi-part questions.
Your starting point is reviewed before the study plan is finalised. The exact method depends on the programme and is agreed on the intro call — for some students that means a timed section, for others it means reading a recent score report or a piece of marked work. We will tell you which applies to you before you book anything, rather than describing a process here that may not be the one you get.
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A Level prices
A Level tutoring from USD 95 per 90-minute lesson. Compare lesson packages and included materials.
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