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A-Level Further Mathematics Tutor & Online Tuition

Short answer

The A-Level Further Mathematics course is one-to-one tutoring, taught live online: every lesson is 90 minutes.

A private group is for 3 or more friends who sign up together (the group programme is 30 hours per subject); there are no published start dates, and we agree the start date and lesson times with you.

In one-to-one tutoring, packages are from €85 a lesson.

A-Level Further Mathematics tutoring for Edexcel 9FM0 and other boards: Core Pure Mathematics plus Further Pure, Statistics, Mechanics or Decision options.

One-to-one and small groups · Live online · Pearson Edexcel, AQA, OCR and Cambridge International specifications

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From a TestPrep A-Level Further Mathematics private lesson — polar coordinates: converting to Cartesian form and the area enclosed by a polar curve

100% live online lessons

About the subject

A-Level Further Mathematics: what it covers and who it suits

A-Level Further Mathematics tutoring at TestPrep Europe covers the compulsory core (Core Pure Mathematics on Pearson Edexcel 9FM0) plus the board's options: Further Pure Mathematics, Further Statistics, Further Mechanics and Decision Mathematics. Pearson Edexcel, Cambridge International, AQA, OCR and OCR MEI each define the options differently, and we work to whichever specification the student is enrolled in.

Your lessons are taught by Jordan Carter, Kevin Nguyen, Marcus Johnson and Tuğçe Şahin, who teach A-Level Further Mathematics.

  • Core Pure as the spine: complex numbers, matrices, polar coordinates, hyperbolic functions, differential equations
  • Options chosen with the student to match degree intent (engineering vs CS vs economics)
  • Past papers from the student's actual board
Read more

A-Level Further Mathematics is required or strongly recommended for many selective mathematics, computer science and engineering degrees, including courses at Cambridge, Oxford, Imperial and Warwick. It covers complex numbers, matrices, further calculus and differential equations: content that leads straight into first-year university mathematics.

A-Level Further Mathematics extends and deepens A-Level Maths. On Pearson Edexcel 9FM0, two compulsory Core Pure Mathematics papers cover complex numbers (algebraically and geometrically), matrices and linear transformations, proof by induction and differential equations; the two optional papers come from Further Pure Mathematics, Further Statistics, Further Mechanics and Decision Mathematics. The course is the bridge to university mathematics, and selective universities read it as a strong sign of mathematical maturity. Our Further Mathematics lessons offer board-specific tutoring, help with choosing the optional papers and structured past-paper work aimed at A*.

One-to-one A-Level Further Mathematics tutoring

Our one-to-one A-Level tutoring is built around your current grade, your target grade and the exam board you are sitting. Each lesson works on your weak topics, drills Edexcel, AQA, OCR, CIE past-paper questions and walks through mark schemes, so you know exactly how marks are awarded.

A private group for A-Level Further Mathematics

There is no open group timetable for this subject. If 3 or more of you sign up together, we open a private group course for you. The price per student depends on how many subjects you take, with 30 hours of live lessons in each: 1 subject (30 hours) €1,031, 2 subjects (60 hours) €1,927, 3 subjects (90 hours) €2,689 and 4 subjects (120 hours) €3,496. Each student buys their own place online, and we let you know as soon as your group is ready.

Exam

A-Level Further Mathematics exam format

Exam boards: Edexcel, AQA, OCR, CIE

  • Paper 1: Core Pure Mathematics 1 (Edexcel 9FM0)

    25%

    1 hour 30 minutes, 75 marks. Questions may come from any Core Pure topic: Proof, Complex numbers, Matrices, Further algebra and functions, Further calculus, Further vectors, Polar coordinates, Hyperbolic functions, Differential equations.

  • Paper 2: Core Pure Mathematics 2 (Edexcel 9FM0)

    25%

    1 hour 30 minutes, 75 marks. The same Core Pure content as Paper 1; either paper may test any Core Pure topic.

  • Papers 3 and 4: optional papers (Edexcel 9FM0)

    25% + 25%

    1 hour 30 minutes and 75 marks each. Students take either any two Option 1 papers (3A Further Pure Mathematics 1, 3B Further Statistics 1, 3C Further Mechanics 1, 3D Decision Mathematics 1) or a matching Option 1 and Option 2 pair (for example 3B with 4B Further Statistics 2): ten permitted combinations in all.

One-to-one A-Level tutoring

A-Level Further Mathematics Private Tutoring

Private A-Level lessons planned around your exam board's specification, your current grade and the grade you are aiming for. Every lesson is live and online, with a tutor who teaches this subject.

  • A lesson plan built around your exam board and target grade
  • Past-paper questions worked through with the board's mark schemes
  • Exam technique for each paper, from command words to timing
  • Lesson times that fit around your school week

How it works

  1. 1

    Tell us your goal

    We start from your school syllabus, your exam date and the result you are aiming for.

  2. 2

    Your own plan

    We map out the lessons you need, unit by unit.

  3. 3

    Live one-to-one lessons

    Meet your tutor online at times that suit your week.

  4. 4

    Regular progress checks

    Homework and a short check after each lesson show how you are getting on.

Start one-to-one A-Level Further Mathematics

Per lesson in a package

From €85

Single lesson €90

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Right for you if you want a plan built around your exam board, flexible lesson times and a tutor's full attention.

Book one-to-one lessons

Before choosing a package, you can book one paid lesson.

Our A-Level tutors began teaching in 2018 or earlier.

  • 100% First-Lesson Money-Back Guarantee

    Not satisfied? Full refund, no questions asked.

    We do not offer free trial lessons. Payment is required before your first lesson.

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  • Flexible Billing

    Local cards welcome, instalments available.

Lessons cancelled less than 3 hours before the start count as taken. Full terms

Included in lessons

Practice built into your A-Level Further Mathematics lessons

Every topic you cover in A-Level Further Mathematics is reinforced with question sets your tutor puts together for you. This programme has no separately sold question bank or practice test.

Mock exams included in the programme
  • Targeted questions on every topic
  • Practice sets built around your weak areas
  • Exam-style practice with past papers and mark schemes
  • Worked solutions and feedback on every question

Syllabus

A-Level Further Mathematics topics

Topic names are those of the Pearson Edexcel 9FM0 specification; other exam boards order and name them a little differently.

1

Paper 1 and Paper 2: Core Pure Mathematics

  • Proof
  • Complex numbers
  • Matrices
  • Further algebra and functions
  • Further calculus
  • Further vectors
  • Polar coordinates
  • Hyperbolic functions
  • Differential equations
2

Paper 3 and Paper 4: Further Mathematics Options

  • 3A: Further Pure Mathematics 1
  • 3B: Further Statistics 1
  • 3C: Further Mechanics 1
  • 3D: Decision Mathematics 1
  • 4A: Further Pure Mathematics 2
  • 4B: Further Statistics 2
  • 4C: Further Mechanics 2
  • 4D: Decision Mathematics 2

Approach

How we teach A-Level Further Mathematics

Study plan

  1. 1

    Year 12 — Core Pure foundations

    Spine of the course

    • Complex numbers
    • Matrices and linear transformations
    • Series and proof by induction
  2. 2

    Year 12 — First optional paper

    First option

    • Further Mechanics 1, Further Statistics 1, Further Pure Mathematics 1 or Decision Mathematics 1
  3. 3

    Year 13 — Core Pure depth

    Deeper Core Pure

    • Polar coordinates
    • Hyperbolic functions
    • Differential equations
  4. 4

    Year 13 — Second optional paper + mocks

    Second option + revision

    • Second optional paper
    • Past-paper mocks under timed conditions

How lessons work

  • Option choice as a strategy decision

    We help the student pick options that match the target university's preferences and the student's degree intent — Decision Maths leans toward CS, Further Mechanics toward engineering / physics, Further Statistics toward economics / biostatistics.

  • Pure-protection rule

    Core Pure is the spine. Every week protects Pure time so applied marks don't collapse from algebra mistakes.

  • Admissions-test signposting

    Students applying to the most selective maths and computing courses often need an admissions test such as STEP, MAT or TMUA alongside Further Maths. We signpost separate test preparation where it's needed and build the early skills into Further sessions.

Advice

A-Level Further Mathematics: common mistakes and study tips

  • MistakeTreating complex numbers as 'imaginary'.

    FixComplex numbers are a 2-D number system with the same algebraic and trigonometric structure as reals. Treat them as ordinary objects on an Argand diagram.

  • MistakeMis-multiplying matrices because of row-column confusion.

    Fix(AB)ᵢⱼ = sum over k of Aᵢₖ Bₖⱼ. Write the formula on the page once before computing.

  • MistakeConfusing polar and rectangular conversions.

    Fixx = r cos θ, y = r sin θ; r² = x² + y². Practise both directions until reflexive.

  • MistakeForgetting that a matrix doesn't always have an inverse.

    FixA matrix is invertible iff det ≠ 0. Always check the determinant before attempting an inverse.

  • MistakeChoosing options at the last minute.

    FixChoose options early and stick with them — switching mid-year wastes the prep already done.

Study tips

  • Develop strong geometric intuition for complex numbers and matrices using the Argand diagram and matrix transformations.
  • Choose your two optional papers early (from Further Pure Mathematics, Further Statistics, Further Mechanics and Decision Mathematics) and plan your practice around them.
  • On proof questions, especially proof by induction, write every logical step explicitly; a gap in the chain of reasoning is a frequent source of lost marks.
  • Make sure your standard A-Level Maths is rock-solid before pushing on Further Maths, which builds on it relentlessly.

Ready to raise your A-Level Further Mathematics grade?

You can start one-to-one A-Level Further Mathematics lessons with a single lesson. Every package and price is on one page.

  • Live one-to-one lessons online
  • No package needed — book a single lesson
  • Lesson times that fit your school week
Chat on WhatsAppSee all pricesCall us: +44 7862 610215

You can also write to us through our contact page.

Other subjects

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FAQ

A-Level Further Mathematics Prep — Frequently Asked Questions

The questions students ask most about A-Level Further Mathematics preparation.

Usually in Year 12 alongside standard A-Level Maths. Some schools deliver an intensive single-year programme in Year 13. All four Pearson Edexcel 9FM0 papers are sat in the same May/June series, so starting in Year 12 leaves the most time for past-paper practice.

As a rough guide: Further Mechanics for engineering, Further Statistics for data science and economics, Further Pure Mathematics for theoretical mathematics, and Decision Mathematics for algorithms and computer science. On Pearson Edexcel 9FM0 you take either two Option 1 papers or a matching Option 1 and Option 2 pair (ten valid pairs in all). Check which options your school offers and what your target courses prefer.

It is essentially required for the Mathematics course. For Engineering and Natural Sciences it is a very strong preference, but the formal requirement varies.

Many of the most selective maths degrees require Further Mathematics where the school offers it, or strongly recommend it; for engineering and physics it is usually a strong advantage rather than a formal requirement. Requirements differ by university and change over time, so always check the target course's current entry requirements.

Further is broader and faster, not necessarily 'harder' per topic. The challenge is breadth — students cover Core Pure plus two optional papers in the same time the standard A-Level uses for one syllabus.

Yes — many schools offer Further AS as an enrichment for students who don't need full Further. A full Further A-Level is the stronger signal for top maths / engineering applications.

Some of the most selective maths and computing courses set an admissions test: Cambridge uses STEP for mathematics, and other universities use tests such as the MAT or the TMUA. Tests and requirements change, so check each course's current admissions page. We coordinate Further Maths lessons with separate test preparation where it's needed.

The money-back guarantee covers live lessons. If you are not satisfied after your first private lesson, we refund your payment in full. We do not offer free trial lessons. Payment is required before your first lesson.

You can cancel a lesson package at any time. Lessons already given are charged at the single-lesson price and the rest is refunded. The first-lesson guarantee applies on top.

Lessons cancelled less than 3 hours before the start count as taken and are not refunded. A lesson that has not been paid for 3 hours before it starts is cancelled automatically.

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