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Further Mathematics
A-Level Further Mathematics is the most advanced school mathematics qualification in England, taken alongside A-Level Mathematics and set against the Department for Education subject content for Further Mathematics, here anchored on the AQA 7367 specification. A large compulsory core of pure mathematics — proof by induction, complex numbers, matrices, further algebra and calculus, further vectors, polar coordinates, hyperbolic functions and differential equations — is combined with a choice of optional applied strands in Mechanics, Statistics and Discrete (Decision) mathematics. The notes assume the whole of A-Level Mathematics as a prerequisite and build rigorously on it.
0/60 Texts13 Chapters~166 min total
AQA 7367 §3.1DfE Further Mathematics — ProofAQA 7367 §3.2DfE Further Mathematics — Complex numbersAQA 7367 §3.3DfE Further Mathematics — Matrices+14 moreStandardAdvanced
Table of contents · 13 ChaptersT·13
- Paper 1 — Compulsory pure content (AQA 7367/1)
- 2 hours, 100 marks, one third of the A-Level. Assesses only the compulsory core: proof (including proof by induction), complex numbers, matrices, further algebra and functions, further calculus, further vectors, polar coordinates, hyperbolic functions and differential equations. A mix of short 'show that' items and extended multi-step problems; a scientific or graphical calculator is permitted on every paper.
- Paper 2 — Compulsory pure content (AQA 7367/2)
- 2 hours, 100 marks, one third of the A-Level. Draws on the same compulsory core as Paper 1, so every core topic can appear on either paper; there is no separate 'Core Pure 1 / Core Pure 2' content split. Questions tend to be longer and to combine ideas across topics — for example a complex-number result proved by induction, or a reduction formula applied to a volume of revolution.
- Paper 3 — Optional application content (AQA 7367/3)
- 2 hours, 100 marks, one third of the A-Level. The student (through their centre) chooses their optional route: they are assessed on TWO of the three application areas — Discrete, Mechanics and Statistics — each worth 50 marks, or on a single application in greater depth, depending on the option combination entered. Only the options a student has studied are sat, so this dossier presents all three honestly as alternatives.
- Assessment objectives and grading
- Across the three papers the assessment objectives are weighted approximately AO1 (use and apply standard techniques) around 50%, AO2 (reason, interpret and communicate mathematically, including rigorous proof) around 30%, and AO3 (solve problems within mathematics and in context, including modelling) around 20% — proof and reasoning carry noticeably more weight than in A-Level Mathematics. The full A-Level is linear, graded A–E with U below; the A is awarded on high aggregate performance across the papers. AS Further Mathematics (7366) is a separate, smaller qualification graded A–E.