Cognivia Tutoring offers 1:1 A-Level Further Maths lessons with Archie Dyer, a second-year Theoretical Physics student at UCL. Lessons are one hour, online on Google Meet or in person around Marylebone, London, and follow your own exam board and chosen options. They cost £45 an hour online or £55 in person, and the 30-minute trial is free.
By Archie Dyer, founder and tutor · Last updated 11 October 2026
Compulsory pure, plus optionsEvery board sets a pure core, then options such as mechanics, statistics and discrete or decision maths.
Taught by Archie DyerSecond-year Theoretical Physics at UCL, after a First in his first year.
Follows your board and optionsLessons use the student’s own specification, papers and chosen options.
£45 online, £55 in personOne hour, 1:1. No group classes.
Free 30-minute online trialNo card needed.
Enhanced DBS checkedArchie is the founder and the only tutor.
How A-Level Further Maths is assessed
A-Level Further Maths is a separate A-Level with its own written papers. Every specification below has the same shape: compulsory pure mathematics that all students sit, and optional papers or sections that depend on what the school teaches. The number of papers and the list of options differ from board to board.
A-Level Further Mathematics paper structure by exam board and specification
Specification
Papers and options
AQA (7367)
Three 2-hour papers of 100 marks, each 33⅓% of the A-Level. Papers 1 and 2 may each assess any of the compulsory content: proof, complex numbers, matrices, further algebra and functions, further calculus, further vectors, polar coordinates, hyperbolic functions, differential equations and numerical methods. Paper 3 covers two options chosen from mechanics, statistics and discrete mathematics, with a separate question paper answer booklet for each.
Pearson Edexcel (9FM0)
Four papers of 1 hour 30 minutes and 75 marks, each 25% of the qualification. Papers 1 and 2 are the mandatory Core Pure Mathematics 1 and 2, and either may contain questions on any pure topic. The other two are options from eight papers: Further Pure Mathematics 1 and 2, Further Statistics 1 and 2, Further Mechanics 1 and 2, and Decision Mathematics 1 and 2. Students take either any two of the “1” papers or “a matching pair of Option 1 and Option 2 papers”, which makes ten possible pairs.
OCR A (H245)
Four 90-minute papers of 75 marks, each 25% of the A-Level. Pure Core 1 and Pure Core 2 are mandatory, and both assess content from the whole of the Pure Core. The other two papers are any two of Statistics, Mechanics, Discrete Mathematics and Additional Pure Mathematics.
OCR B (MEI) (H645)
One mandatory Core Pure paper of 2 hours 40 minutes, worth 50% of the A-Level, plus options. A major option is a 2 hour 15 minute paper worth 33⅓%; a minor option is a 1 hour 15 minute paper worth 16⅔% (1 hour 45 minutes for Further Pure with Technology). There are three routes: Core Pure with Mechanics Major and one minor other than Mechanics Minor; Core Pure with Statistics Major and one minor other than Statistics Minor; or Core Pure with three minors. The minor options are Mechanics Minor, Statistics Minor, Modelling with Algorithms, Numerical Methods, Extra Pure and Further Pure with Technology.
When
All papers at the end of the course. AQA: “This qualification is linear. Linear means that students will sit all their exams at the end of the course.” Pearson: “Students must complete all assessments in May/June in any single year.” OCR describes both of its specifications as “a linear qualification in which all papers must be taken in the same examination series”.
Calculator
AQA: “A calculator is required for use in all assessments in this specification.” AQA adds that it should, as a minimum, have an iterative function, handle matrices up to order 3 × 3, and compute summary statistics and probabilities from standard distributions. Pearson: “Students may use a calculator in all A Level Further Mathematics examinations.” OCR A and OCR B (MEI): “Learners are permitted to use a scientific or graphical calculator for all papers.”
With A-Level Maths
Further Maths assumes A-Level Maths content. AQA says it “builds on the skills, knowledge and understanding set out in the whole GCSE (9–1) subject content for mathematics and the subject content for AS and A-level mathematics”. OCR A: “Learners are assumed to know the content of GCSE (9–1) Mathematics and A Level Mathematics.” In practice it is studied alongside, or after, A-Level Maths, and not in place of it.
Paper structures, timings, weightings, options and calculator rules checked against each board’s own specification: AQA 7367 at a glance and specification PDF; the Pearson Edexcel 9FM0 specification (Issue 4); the OCR H245 specification; and the OCR H645 (MEI) specification. Checked on 11 October 2026. Cognivia Tutoring is independent and is not affiliated with or endorsed by any exam board; your school can confirm which specification and options you are entered for.
What is the difference between A-Level Maths and Further Maths?
A-Level Maths is one A-Level covering pure mathematics, statistics and mechanics. A-Level Further Maths is a second, separate A-Level that assumes that content and goes beyond it. Its compulsory pure content adds topics such as complex numbers, matrices, hyperbolic functions and polar coordinates, and students also choose options such as mechanics, statistics or discrete mathematics.
The structure differs as well. The four A-Level Maths specifications set out on the A-Level Maths page have no optional papers, so every student on a specification sits the same three. In Further Maths the options decide between a third and a half of the marks, depending on the board, so two Further Maths students at different schools can be preparing for quite different exams. The A-Level Maths page sets out that course board by board.
Compulsory content lists from the AQA 7367 and Pearson Edexcel 9FM0 specifications; A-Level Maths structure from the AQA 7357 specification and the others cited on the A-Level Maths page. Checked on 11 October 2026.
Where A-Level Further Maths is demanding
What follows is observation drawn from the specifications themselves. It is not a set of statistics about results, and it is not a claim about any particular student.
Complex numbers are a new number system, not a new technique. AQA’s content runs from solving any quadratic with real coefficients through Argand diagrams, modulus-argument form and loci to de Moivre’s theorem. One statement notes that “knowledge of radians and compound angle formulae is assumed”, which is A-Level Maths content.
Matrices are both arithmetic and geometry. Students multiply “conformable matrices” and also “use matrices to represent linear transformations in 2D”. Seeing a matrix as a transformation is a different skill from computing with one.
Proof by induction is examined. Proof is the first section of the compulsory content at AQA and Pearson Edexcel. AQA asks students to “construct proofs using mathematical induction; contexts include sums of series, divisibility, and powers of matrices”. A proof is marked on its structure and wording as well as its algebra.
The pace depends on A-Level Maths. The Further Maths content assumes the A-Level Maths content, and Pearson describes its specifications as designed so that schools can “deliver Maths and Further Maths in parallel”. OCR notes that its Further Maths content sometimes assumes knowledge from the second stage of A-Level Maths. A gap in the single A-Level shows up quickly in the second.
Options change the course. Pearson Edexcel has ten possible option pairs and OCR B (MEI) has three routes. A student taking mechanics and statistics is revising different material from one taking decision or discrete mathematics, so general Further Maths resources do not always fit.
Half the marks are not for routine technique. AQA’s overall weighting is approximately 50% for using and applying standard techniques, 25% for reasoning and communicating mathematically, and 25% for solving problems. On its options paper the problem-solving share rises to approximately 35%.
Content statements and assessment objective weightings from the AQA 7367 specification and scheme of assessment; option rules from the Pearson Edexcel 9FM0, OCR H245 and OCR H645 specifications. Checked on 11 October 2026.
Further Maths, the TMUA and the ESAT
Many Further Maths students are also applying for courses that ask for an admissions test. It is worth being plain about how the two relate: Further Maths is not preparation for these tests, and the tests do not examine Further Maths content.
UAT-UK says the TMUA “is based on content typically covered within Higher Level GCSE mathematics courses or AS level mathematics”. It is two 75-minute papers of 20 multiple-choice questions with no calculator, where every Further Maths paper allows one. Of the ESAT, UAT-UK says it “uses science and mathematics that you are likely to have already learned in your school studies”, in 40-minute modules of 27 multiple-choice questions.
Lessons are with Archie Dyer, the founder of Cognivia Tutoring and its only tutor. There is no panel of tutors behind the website and no one else you might be passed to.
Second-year Theoretical Physics student at UCL (University College London), after a First in his first year.
43 out of 45 in the IB, with 7s in HL Maths, Physics and Economics.
10 A*s at IGCSE.
Tutoring for over two years.
Enhanced DBS checked, and based in Marylebone, London.
Archie did not sit A-Levels, so he did not take Further Maths himself. He took the IB Diploma, scoring a 7 in Higher Level Maths, and now studies Theoretical Physics at UCL. He tutors the A-Level Further Maths specifications; he does not hold A-Level grades. Lessons follow the student’s own exam board and chosen options, so say which board and which options at the trial.
Nothing here is a promise about a grade. A-Levels are marked by the exam boards, and no tutor can guarantee the result.
How he teaches. In Archie’s words: “I find where the understanding actually breaks down, which is usually two or three topics further back than where the marks were lost, and we rebuild from there. I keep lessons relaxed. I would far rather a student asked me something they think is obvious than sat quietly and nodded.” The free 30-minute trial is the way to judge that for yourself: bring a topic you find difficult. There is more on the About Archie page.
Prices and practical details
A-Level Further Maths prices at Cognivia Tutoring
What
Online
In person
One 1-hour 1:1 lesson
£45
£55
5-pack — five 1-hour lessons, £15 off
£210
£260
30-minute trial lesson
Free
Online only
A-Level Further Maths costs the same as the other A-Level subjects, whichever exam board and options the student is on. A 5-pack is held in a My lessons account, so the five lessons can be booked one at a time.
1 hour, 1:1. Every lesson is with Archie, built around one student. There are no group classes.
Online on Google Meet, or in person around Marylebone, London (+£10). The Meet link is in your confirmation email; times are shown in your own time zone.
Free 30-minute online trial, no card needed. A relaxed session to meet and see if it clicks.
24 hours’ notice to cancel, by email or phone. See the refund policy.
Payment by Stripe at booking. Card, Apple Pay or Google Pay.
Full prices for every subject and level are on the pricing section of the home page. Parents receive a short note after each lesson on what was covered and what to practise next.
At Cognivia Tutoring, A-Level Further Maths lessons are £45 an hour online, or £55 an hour in person around Marylebone, London. A 5-pack of five 1-hour lessons saves £15: £210 online or £260 in person. The 30-minute online trial is free and needs no card.
It covers more mathematics, and more abstract mathematics. Further Maths assumes the A-Level Maths content and adds compulsory pure topics such as complex numbers, matrices, proof by induction, hyperbolic functions and polar coordinates, plus the options a student chooses. It is a second A-Level on top of the first. How hard that feels differs from student to student.
Lessons follow the student’s own exam board and chosen options. This page sets out the paper structure for AQA (7367), Pearson Edexcel (9FM0), OCR A (H245) and OCR B (MEI) (H645). Archie did not sit any of them himself, because he took the IB Diploma, so tell him the board and the options at the trial.
Yes. Online lessons run on Google Meet, with the link in the booking confirmation email. The booking calendar shows times in your own time zone, and students join from the UK and across Europe.
Yes. In-person lessons take place around Marylebone, London, and cost £10 more than online, at £55 an hour. See the Marylebone page for details.
Requirements vary by university and by course, so check the entry requirements on each course page. As one example, the University of Cambridge’s Mathematics course page, for entry in 2027, lists A-Level Further Mathematics among the subjects needed to apply, and asks applicants whose school does not offer it to contact their shortlisted Colleges for advice. Other courses differ. Checked on 11 October 2026.
No. Archie took the IB Diploma, not A-Levels, and scored a 7 in Higher Level Maths as part of 43 out of 45 overall. He is now a second-year Theoretical Physics student at UCL, after a First in his first year, and tutors the A-Level Further Maths specifications.
Book the free 30-minute online trial and bring a topic you find difficult. You will see how Archie explains it and whether his teaching suits you before paying anything, and no card is needed. After every paid lesson, parents receive a short note on what was covered and what to practise next, so progress stays visible.
Where to go next
A free 30-minute trial is the simplest way to find out whether this is the right fit. Nothing is charged and no card is needed.
Talk through the exam board, the options being taken, the topics that are proving difficult and when the exams are, before booking anything. Online, free, and no card needed.
