A-Level Further Mathematics Scheme of Work

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Years 12–13 · A-Level Further Mathematics · Two-year linear course · Core Pure + Further Statistics + Further Pure · Aligned to Edexcel, AQA, OCR & OCR MEI

This free A-Level Further Mathematics scheme of work is a complete two-year linear plan for Year 12 and Year 13. It is co-taught alongside A-Level Mathematics and adds the Core Pure 1 & 2 content, plus the optional Further Statistics 1 and Further Pure 1 strands, that complete the Further Mathematics qualification.

The scheme is aligned to the linear A-Level Further Mathematics specifications for Edexcel, AQA, OCR (A) and OCR MEI. Every topic links to a dedicated teaching page; members get the full teaching package — interactive lesson presentation, exam-style worksheet and detailed worked solutions — so Further Mathematics departments can resource the full qualification without rebuilding from scratch.

Help your A-Level Further Mathematics students develop fluency with matrices, vectors and complex calculations using our ⁠free Casio calculator emulator, featuring interactive teaching tools and practice questions.

A-Level Further Mathematics scheme at a glance

The scheme is organised by strand (Core Pure 1 & 2, Further Statistics 1, Further Pure 1) across two years. Read across a row for the within-strand progression from Year 12 to Year 13; read down a column for the parallel Further Maths content covered in that year. This sits alongside the standard A-Level Mathematics scheme of work, which Further candidates take in parallel.

Who is this scheme for?

The A-Level Further Mathematics scheme of work is built for UK sixth form mathematics departments and sixth form colleges that offer Further Mathematics alongside the standard A-Level Mathematics qualification across Years 12 and 13. It assumes students are also following the A-Level Mathematics scheme in parallel.

• Heads of Further Mathematics writing a two-year MTP for Further Maths candidates and wanting one consistent backbone across all Further teachers.
• Classroom teachers of Year 12 or Year 13 Further Mathematics who want ready-made lessons, worksheets and worked solutions for Core Pure, Further Statistics and Further Pure topics.
• Heads of Sixth Form / progression leads supporting students applying to read mathematics, engineering, computer science, physics or economics at university, especially those preparing for STEP, MAT or TMUA admissions tests.
• Sixth form colleges and grammar schools co-teaching Further Mathematics within an A-Level Mathematics timetable.
• Independent tutors and home educators preparing students for linear A-Level Further Mathematics with a structured route they can follow week by week.

What’s included

A complete medium-term plan for two years of A-Level Further Mathematics, covering Core Pure 1 & 2 plus the most commonly selected optional papers (Further Statistics 1 and Further Pure 1):

• Year-by-year strand breakdown for Core Pure 1 & 2, Further Statistics 1 and Further Pure 1.
• Core Pure 1 coverage — complex numbers, Argand diagrams, sums of series, roots of polynomials, volumes of revolution, matrices, linear transformations, proof by induction and vectors.
• Core Pure 2 coverage — more complex numbers, series, methods in calculus, volumes of revolution, polar coordinates, hyperbolic functions, methods in differential equations and modelling with differential equations.
• Further Statistics 1 coverage — discrete random variables, the Poisson distribution, chi-squared tests, geometric and negative binomial distributions, central limit theorem, probability generating functions and quality of tests.
• Further Pure 1 coverage — vectors, conic sections, fractional inequalities, the t-formulae, numerical methods, Taylor series, methods in calculus and reducible differential equations.
• Direct links to every topic page — teaching overview, prerequisites, key concepts and common misconceptions.
• Member access to interactive lesson presentations, exam-style worksheets and detailed worked solutions for every topic.

How to use this scheme

Most Further Mathematics groups are timetabled with an additional 4–5 hours of Further teaching per fortnight on top of the standard A-Level Mathematics allocation. This scheme is designed to fit that model: Core Pure 1 & 2 runs across Year 12 and Year 13 and uses most of the Further teaching time; Further Statistics 1 and Further Pure 1 are typically delivered as half-courses in parallel during Year 12 and Year 13.

Where possible, sequence Further topics so they follow the corresponding A-Level Mathematics prerequisite — for example, teach Pure differentiation before Further differential equations, and Pure trigonometric identities before the t-formulae. The Year 12 Core Pure backbone (complex numbers → series → matrices → vectors) can run from September; Further Statistics is best held until the standard A-Level statistical distributions have been introduced.

Many Further groups use end-of-topic problem sets for STEP, MAT and TMUA preparation alongside this scheme — the Year 13 Core Pure 2 topics (hyperbolic functions, polar coordinates, methods in differential equations) and Further Pure 1 (Taylor series, reducible differential equations) are particularly useful entry points.

Curriculum rationale

A-Level Further Mathematics is a linear qualification examined entirely at the end of Year 13. All boards require students to take Core Pure 1 & 2 and then choose two further options from a list including Further Statistics 1, Further Mechanics 1, Further Pure 1, Decision Mathematics 1 (and Edexcel additionally offers Year 2 papers in each). This scheme provides the most commonly chosen pairing — Further Statistics 1 + Further Pure 1 — and works well as a Pure-leaning route into university mathematics.

• Year 12 Core Pure 1 — secures complex numbers and Argand diagrams, sums of series, roots of polynomials, volumes of revolution, matrices, linear transformations, proof by induction and vectors.
• Year 12 Further Options — Further Statistics introduces discrete random variables, the Poisson distribution and chi-squared tests; Further Pure introduces vectors, conic sections, fractional inequalities, the t-formulae and numerical methods.
• Year 13 Core Pure 2 — extends complex numbers, series, methods in calculus, polar coordinates, hyperbolic functions and differential equation methods, ending with modelling.
• Year 13 Further Options — Further Statistics adds geometric/negative binomial distributions, the central limit theorem, probability generating functions and quality of tests; Further Pure adds Taylor series, methods in calculus and reducible differential equations.

Departments offering alternative option pairings (Further Mechanics + Further Pure, or Decision + Further Pure) should adapt this scheme — Core Pure 1 & 2 remains compulsory in all cases.

Related schemes of work

Frequently asked questions

Which Further Mathematics specification is this scheme aligned to?

The topic list, sequence and worked-solution style are aligned to the Edexcel A-Level Further Mathematics (9FM0) specification, which is the most widely used in the UK. The DfE-approved Further Mathematics core (Core Pure 1 & 2) is shared across all boards, so almost all Core Pure topics map directly to AQA (7367), OCR (A) (H245) and OCR MEI (H645). The choice of Further Statistics 1 and Further Pure 1 here matches Edexcel’s most commonly selected option pairing — departments using different optional papers (Further Mechanics 1, Decision 1) can substitute those strands in place of either option.

Why are these particular optional papers chosen?

The combination Further Statistics 1 + Further Pure 1 is one of the most common choices for Further Mathematics groups in the UK because it is Pure-leaning (supporting mathematics, physics, engineering and economics applications at university) while still developing strong statistical reasoning. Departments preparing students for mathematics and physics applications often switch Further Statistics for Further Mechanics; departments with a computing or operations research focus often substitute Decision Mathematics.

Should Further Mathematics be co-taught with A-Level Mathematics?

Yes — Further Mathematics is co-taught with A-Level Mathematics in almost all UK sixth forms. Further candidates take the same A-Level Mathematics course as the rest of the cohort, then receive 4–5 additional hours per fortnight (rising to more in Year 13 in some schools) for the Further-specific content. Sequence the Further content so its prerequisites — for example, Pure differentiation before differential equations, Pure trigonometric identities before the t-formulae — have been covered in the standard A-Level first.

How long does each topic take to teach?

Core Pure topics in this scheme typically run for 2–3 weeks of Further teaching time (8–12 lessons), with longer time on harder topics (matrices and linear transformations, polar coordinates, differential equation methods). Further Statistics 1 and Further Pure 1 topics typically run for 2 weeks each because they are timetabled less frequently. Plan time in the Year 13 spring term for synoptic past-paper practice and STEP/MAT preparation if relevant.

Is Further Mathematics good preparation for university maths admissions tests?

Yes. Further Mathematics is essentially a requirement for STEP-graded offers (e.g. Cambridge, Warwick, Imperial mathematics) and is strongly recommended for the MAT (Oxford) and TMUA (UCL, Durham and Lancaster). The Year 13 Core Pure 2 content (hyperbolic functions, polar coordinates, methods in differential equations) and Further Pure 1 (Taylor series, reducible differential equations) directly support STEP and MAT problem-solving.

What’s included for free, and what needs membership?

The scheme of work — every topic link, curriculum rationale and the Year 12/Year 13 strand structure — is free for all teachers to use. Each topic page is free to read for its teaching overview, prerequisites, key concepts and common misconceptions. Mr Mathematics membership unlocks the full classroom package per topic: interactive lesson presentations, exam-style worksheets and detailed worked solutions.