A-Level Maths / Further Maths

A-Level Maths and Further Maths tutoring, taught by maths specialists

Live online tutoring for AQA, Edexcel and OCR students, run as a monthly subscription rather than ad-hoc hourly lessons. Every maths tutor on our team is a subject specialist who has taught A-Level for at least five years, so sessions are built around the actual mark schemes your child will be sitting, not general maths help.

We start with a free 20-minute diagnostic call to work out where the marks are being lost, then match the student with a tutor and a weekly pace that fits the exam timetable. Parents get regular progress reports so you can see what has changed between one report and the next.

The topics that cost students the most marks

Most students who come to us are not weak at maths. They are losing marks in a small number of predictable places, usually where a topic asks them to choose a method rather than follow one. These are the ones that come up again and again in diagnostic calls.

  1. 01

    Integration

    Differentiation is drilled to death in Year 12 and integration never quite catches up. Substitution, by parts, partial fractions and knowing which one a question is actually asking for is where the six-mark questions get abandoned halfway.

  2. 02

    Mechanics

    Connected particles, inclined planes, friction and projectiles. The maths is rarely the problem. Drawing a correct force diagram and resolving in the right direction is, and that is a teachable habit.

  3. 03

    Proof

    Proof by contradiction, proof by induction in Further Maths, and disproof by counter-example. Students often know the answer is true but cannot write the argument in a way that scores the structure marks.

  4. 04

    Statistics and hypothesis testing

    Stating hypotheses properly, choosing between binomial and normal models, interpreting the critical region and writing a conclusion in context. The last sentence is worth a mark and gets skipped constantly.

  5. 05

    Complex numbers

    Argand diagrams, modulus-argument form, loci and De Moivre's theorem. The moment questions move from algebra to geometry, confidence drops, so we teach the two views side by side.

  6. 06

    Matrices and transformations

    Invariant lines and points, determinants, and solving systems of three equations. Marks go missing on interpretation rather than arithmetic, so we work through what each answer means geometrically.

If your child recognises three or more of these, the diagnostic call will tell us which ones are worth the first month of sessions and which will sort themselves out.

Full spec coverage for AQA, Edexcel and OCR

A-Level Maths content is largely common across the boards, but the paper structure, the formula booklet and the way questions are worded are not. Tutors work from the specification your child is actually entered for, and revision material is filed by board so nothing you download is for the wrong paper.

How the content maps to each board
Content areaAQAEdexcelOCR (A and MEI)
PurePapers 1 and 2, pure mixed with appliedPapers 1 and 2, pure onlyPure across Papers 1 and 3 (OCR A)
MechanicsShared with statistics in Papers 2 and 3Paper 3, Section BPaper 2 (OCR A), problem-solving flavour in MEI
StatisticsPapers 2 and 3, large data setPaper 3, Section A, large data setPaper 3 (OCR A), pre-release data
Further PureCompulsory coreCore Pure 1 and 2Core Pure, plus MEI structure
Further optionsMechanics, statistics, discreteFurther Pure, Further Mechanics, Further Statistics, DecisionAdditional pure, mechanics, statistics, modelling with algorithms

Pure maths

  • Algebra, functions and partial fractions
  • Sequences, series and binomial expansion
  • Trigonometry, identities and small-angle approximations
  • Differentiation, including implicit and parametric
  • Integration and differential equations
  • Numerical methods, vectors and proof

Mechanics

  • Kinematics and constant acceleration
  • Variable acceleration with calculus
  • Forces, friction and Newton's laws
  • Connected particles and pulleys
  • Projectiles
  • Moments and rigid bodies

Statistics

  • Sampling and the large data set
  • Data presentation and interpretation
  • Probability and conditional probability
  • Binomial and normal distributions
  • Hypothesis testing and critical regions
  • Correlation and regression

Further Maths

  • Complex numbers and De Moivre's theorem
  • Matrices, determinants and invariance
  • Proof by induction
  • Polar coordinates and hyperbolic functions
  • Further calculus and volumes of revolution
  • Option modules by board and school choice

Teaching physics or chemistry alongside maths? See science tutoring, or combine subjects on one subscription.

What a typical maths session looks like

Sessions run for an hour on a shared online whiteboard, so the tutor and student write together rather than one person talking at a screen. The shape below is the default. It flexes in the weeks before a mock or a real paper, when almost the whole hour goes to timed questions and marking.

  • Length 60 minutes, live
  • Group size 1-on-1, or small groups of up to four
  • Recorded Yes, replay available afterwards
  • Reports Sent to parents on a regular cycle
  1. Diagnostic questions

    First 10 minutes

    Two or three short questions on last week's topic and one on something from earlier in the course. It tells the tutor immediately whether the previous session stuck or needs revisiting, and it keeps older content warm instead of letting it decay until study leave.

  2. Worked method teaching

    Around 20 minutes

    The tutor works through the new method with the student, not at them. The student writes each step, explains the choice of method out loud, and the tutor stops at the exact points examiners take marks off. This is where method selection is trained rather than just method execution.

  3. Past-paper practice

    Around 20 minutes

    Real questions from the student's own exam board, done under something close to exam pace. They are then marked against the actual mark scheme so the student can see the difference between a right answer and a full-mark answer, which is usually one line of working.

  4. Follow-up work and notes

    Last 10 minutes

    Set work for the week, sized to fit around school homework rather than doubling it. The tutor logs what was covered, what to review, and any recorded lessons or walkthroughs worth watching before the next session.

Further Maths

Further Maths needs a different kind of tutor

Plenty of tutors can teach A-Level Maths well and still be a poor fit for Further Maths. It is not just harder content, it is content that many maths graduates have not touched since their own second year, taught at roughly double the pace, often in fewer timetabled lessons at school than the students need.

So we match Further Maths students only with tutors who have actually taught the qualification to exam classes, including the option modules. That matters because the option modules differ so much by school. A student doing Decision needs someone fluent in algorithms and network problems. A student doing Further Mechanics needs momentum, impulse and elastic collisions taught properly, not improvised from a textbook the night before.

  • Pace that matches the school's

    Further Maths is frequently taught alongside the main A-Level in compressed time. Sessions are planned against the school's scheme of work so tutoring runs slightly ahead, not two topics behind.

  • Option modules taken seriously

    We ask which options the school has entered the student for at the diagnostic call, then match on that specifically rather than assuming the standard combination.

  • Proof and rigour

    Induction, complex number geometry and matrix invariance reward students who can write a clean argument. We mark written proofs the way an examiner would, line by line.

  • Support for the AS route

    If a student is sitting Further Maths AS only, or dropping it after Year 12, we plan around that decision honestly rather than pushing sessions that will not affect their grade.

Past-paper walkthroughs and recorded maths lessons

Every subscription includes unlimited access to the on-demand maths library, so the work does not stop when the live session ends. It is filed by exam board and by topic, which means revision the night before a mock takes two minutes to find rather than twenty.

Past-paper walkthroughs

Whole papers worked through question by question by a maths tutor, with the mark scheme on screen. The commentary is about decisions: why this substitution, why this diagram first, where the method marks sit and what a student can still salvage when they cannot finish a part.

  • Filed by board and by year
  • Pure, mechanics and statistics papers
  • Further Maths core and common options

Recorded topic lessons

Short, self-contained lessons on single topics. Useful when a student misses school, or when a live session flagged a gap that needs re-teaching rather than a nudge.

Mark-scheme breakdowns

Side-by-side comparisons of a typical student answer and a full-mark answer, with the missing lines highlighted. This is usually the fastest single source of extra marks.

Exam-board revision packs

AQA, Edexcel and OCR specific question sets and formula-booklet drills, so students practise with the same booklet they will be handed in the exam hall.

Structured revision timetables

A written plan across the weeks to the exam, weighted towards the topics the diagnostic and progress reports show are weakest, and adjusted after each round of mocks.

Subject articles and exam technique posts are on the blog. Plan details are on pricing and how it works.

Meet the maths tutors

Individual maths tutor profiles are being written up and photographed now, so rather than put up placeholder names, here is what is true of every tutor who takes a maths or Further Maths student with us.

See the full tutor team
  • Qualified subject specialists in maths
  • At least five years teaching A-Level
  • Matched by board: AQA, Edexcel or OCR
  • Further Maths only taught by those who have taught it

Pure and mechanics specialist

Name and profile: to be added

Teaches the pure core plus mechanics across all three boards, and works with students who are strong on method but lose marks on setting problems up.

Further Maths specialist

Name and profile: to be added

Covers Core Pure plus option modules, including Further Mechanics and Decision, and supports students sitting Further Maths alongside a full A-Level timetable.

Statistics and applied specialist

Name and profile: to be added

Focuses on the large data set, hypothesis testing and writing conclusions in context, which is where applied marks are most often dropped.

On the free diagnostic call we tell you which tutor we would match your child with and why, before you pay anything.

A-Level Maths tutoring questions

The questions parents and students ask us most often on the diagnostic call. If yours is not here, send it over and we will answer it honestly, including if the answer is that tutoring is not what your child needs right now.

How many sessions does it usually take to move up a grade?

It depends on where the marks are being lost, but a realistic pattern is a full term of consistent weekly sessions to move a grade, assuming the student does the follow-up work. Students losing marks on exam technique and presentation often see movement in mocks faster than that, because the underlying understanding is already there. Students with genuine content gaps from Year 12 take longer, and we will say so on the diagnostic call rather than promise a term.

Do you support students retaking A-Level Maths?

Yes. Retake students are one of the groups we work with most, whether they are resitting at school, at a college, or as a private candidate. We start by going through the actual paper breakdown where available, since a retake plan should be built on which papers and which question types went wrong rather than starting the whole course again from chapter one.

Is it better to start in Year 12 or Year 13?

Year 12 is easier and usually cheaper overall, because you are preventing gaps rather than repairing them, and the jump from GCSE to A-Level catches out a lot of strong GCSE students in the first term. Year 13 starts are completely normal though, and most of our maths students begin then. If you are starting in Year 13, earlier in the autumn term is far better than after the January mocks.

Can you prepare students for STEP and MAT?

Yes, where we have a tutor with relevant experience free, which is why we ask about it on the diagnostic call rather than after signup. STEP and MAT preparation is a different discipline from A-Level work: fewer, longer problems, no method handed to you, and a real emphasis on writing up an argument. We would usually run it alongside normal A-Level sessions, not instead of them.

Which plan suits a maths student best?

Essentials at £129 a month, with two sessions a week, works for a student keeping on top of one subject. Accelerate at £219 a month, with four sessions a week, suits students taking both Maths and Further Maths, or maths plus a science. Exam Sprint at £349 a month gives unlimited sessions for the final eight weeks before exams. Full details are on the pricing page.

Are sessions 1-on-1 or in a group?

Both are available. One-to-one is the default where a student has specific gaps, since the whole hour is spent on their own work. Small groups of up to four suit students who are broadly on track and want structured weekly practice, and they work best when everyone is on the same exam board and roughly the same point in the course. We recommend one or the other after the diagnostic call.

Get matched with a maths tutor

Start with the free 20-minute diagnostic call. We talk to the student, ask a few questions about where the marks are going, check the exam board and the school's pace, and then tell you which tutor and which plan we would recommend. No payment is taken on the call, and if we do not think we can help we will say that instead.

  • 1. Send the form with the subject, year group and exam board
  • 2. We book a 20-minute call at a time that suits
  • 3. You get a tutor match and a proposed weekly plan
  • 4. Start whenever you are ready, subscription monthly

Request the free diagnostic call

Prefer to talk first? Call 020 7946 0958 or email hello@apexalevels.co.uk.