--- title: "Further Maths Tuition Online · 1:1 A-Level Further Mathematics — Modern Age Coders" description: "Live 1:1 online Further Maths tuition for A-Level (Edexcel, AQA, OCR). Complex numbers, matrices, proof by induction, polar coordinates and further mechanics, stats and decision — taught from the ideas up. Same tutor, UK time. USD 100/month, 8 lessons. Free trial." canonical: https://learn.modernagecoders.com/further-maths-tuition-online keywords: ["further maths tuition online", "A-level further maths tutor", "further mathematics tutor", "complex numbers tutor", "matrices A-level", "proof by induction", "polar coordinates A-level", "further mechanics tutor", "further statistics", "decision maths tutor", "STEP MAT tutor", "further maths revision"] source: src/pages/further-maths-tuition-online.html --- > Live 1:1 online Further Maths tuition for A-Level (Edexcel, AQA, OCR). Complex numbers, matrices, proof by induction, polar coordinates and further mechanics, stats and decision — taught from the ideas up. Same tutor, UK time. USD 100/month, 8 lessons. Free trial. Why Further Maths trips up able students ## It's rarely the whole subject. It's usually one abstract idea that never became intuitive. Further Maths is taken by strong, motivated students — and they still hit walls, which surprises everyone. The reason is that the subject is fast and deeply abstract: complex numbers, matrices and proof by induction arrive quickly and are often taught as procedures to apply, not ideas to picture. So a capable student can manipulate complex numbers algebraically yet have no mental image of what they *are* — and the moment a question needs that intuition, they stall. Because Further Maths is sat alongside A-Level Maths, any wobble gets amplified by the sheer volume and pace. Past-paper grinding can paper over it, but the gap resurfaces on the unfamiliar questions. We fix the root. We make each abstract idea genuinely intuitive — what a complex number does geometrically, what a matrix transformation looks like — so the algebra finally has meaning behind it, and the harder problems become approachable. How we teach ## Make the abstract picturable, then build fluency on top. Worked to your board and your chosen options. ### Find the idea that didn't land Usually one or two — complex numbers, matrices, induction. We rebuild those from a picture, not a procedure. ### Give every concept a meaning A complex number as a rotation and scaling, a matrix as a transformation, induction as a chain of dominoes — intuition that the algebra then expresses. ### Build fluency for the volume Further Maths has long working and many topics; we drill until the routine steps are automatic, freeing thought for the hard part. ### Train problem-solving & proof The top-mark and STEP-style questions reward genuine reasoning, which we coach directly. See it for yourself ## Complex numbers — why multiplying by i is a 90° rotation. Worked example · core pure **What gets memorised:** "i is the square root of −1, and i² = −1." Students compute with it correctly but have no picture of what a complex number is — so Argand diagrams, modulus-argument form and De Moivre's theorem feel like disconnected rules. **How we do it.** Plot numbers on a plane: real part across, imaginary part up. Now watch what multiplying by i does to the number 1, which sits at the point (1, 0): 1 → ×i → i (the point (0, 1) — a quarter-turn anticlockwise)i → ×i → i² = −1 (the point (−1, 0) — another quarter-turn)−1 → ×i → −i (then back to 1)so multiplying by i = rotating 90° about the origin Suddenly i² = −1 isn't a strange rule — two 90° turns make a 180° turn, which flips 1 to −1. From this single picture, the modulus is a length, the argument is an angle, multiplication adds angles, and De Moivre's theorem becomes obvious. The entire complex-numbers module unlocks from one idea: these are points you can rotate. That intuition is exactly what carries students through the hardest Further Maths questions and into university. Why a coding school teaches Further Maths ## Further Maths is the maths that powers modern computing. ### Matrices everywhere The matrix transformations in Further Maths are exactly what drives computer graphics, robotics and machine learning. We teach them as the real, visual things they are. ### Proof by induction Induction is the mathematical twin of a loop and of recursive reasoning in code — the same "it works for the next case" logic. ### Abstraction as a tool Complex numbers and abstract structures show that the right abstraction makes hard problems easy — the core lesson of good software design too. We're Modern Age Coders, and Further Maths is where school maths meets the foundations of computing — graphics, cryptography, signal processing, AI. The visual, structural thinking we teach for programming is exactly what makes this content click, and our students carry it straight into competitive STEM degrees. What we cover ## Core pure plus your optional modules. Taught to your board and your exact combination of options. ### Complex numbers Argand diagrams, modulus-argument form, De Moivre's theorem, roots of unity and loci — taught from the geometry up. ### Matrices & transformations Matrix algebra, determinants and inverses, transformations of the plane, and solving systems — with the visual meaning. ### Proof & series Proof by induction, summation of series, the method of differences, and Maclaurin series. ### Further calculus & coordinate systems Hyperbolic functions, further integration, polar coordinates, and volumes of revolution. ### Optional applied modules Further mechanics, further statistics and decision maths — whichever your school offers. ### STEP & admissions STEP and MAT-style problem solving for students applying to the most competitive maths and STEM courses. Who this is for ## The right fit — and an honest word on what to expect. **This fits** the Further Maths student stuck on one or two abstract topics, the strong student aiming for an A* in both maths A-Levels, and the applicant targeting a top maths, engineering, physics or computer science degree. AS Further Maths students are welcome too. **What's realistic.** When the abstract idea finally becomes intuitive, progress is often fast — but the volume of Further Maths means consistent work matters. We'll set an honest target around your options and timeline, and never promise a guaranteed grade. ### What we won't do - Teach complex numbers or matrices as rules with no picture. - Promise an A* on a timeline. - Drill papers without fixing the conceptual gap. - Cover options your board doesn't set. How lessons work ## Built for a fast, demanding subject. ### 1:1, live One student, one tutor, real-time video and a shared whiteboard for long working and diagrams. ### 8 lessons a month Two each week, around an hour, worked from your specification and options. ### UK time Evening and weekend slots in GMT/BST that fit around college. ### Exam ramp Targeted revision before mocks and the summer exams. Pricing ## One simple price. No contract. ### 1:1 Private Tuition $100 / month - 8 live one-to-one lessons a month (2 per week) - An expert tutor who knows your options - Concepts made intuitive, then fluency built - STEP/MAT coaching available · cancel any time ### Small-Group Cohort $40 / month - 8 live small-group lessons a month (2 per week) - A few students on the same options - Same teaching approach, lower price - Good for classmates · cancel any time [See the full course](/courses/college-mathematics-complete-masterclass) Need the main A-Level alongside? See our [**A-Level Maths Tuition →**](/a-level-maths-tuition-online) page. Who teaches you ## Tutors who genuinely love this material. Further Maths needs a tutor with real mathematical depth — someone who can show you what a matrix transformation *does*, not just how to multiply one. Ours have that, plus precise knowledge of how each board's harder papers are marked, and the patience to rebuild an abstract idea from scratch. You keep the same tutor through the year, so they know your options, your weak topics and your target, and aim every lesson there. "Complex numbers had completely lost her. One lesson on the Argand diagram and rotation, and the whole module suddenly made sense. She got an A* and an offer from her first-choice university." — Parent of a Year 13 student, Cambridge An honest comparison ## How we differ from the alternatives. | What matters | Modern Age Coders | Revision videos | A typical tutor | | --- | --- | --- | --- | | Makes abstract ideas intuitive | Yes, the core of it | Rarely | Varies | | Knows Further Maths deeply | Yes | Sometimes | Not all tutors | | Covers your exact options | Yes | Generic | Varies | | STEP/MAT coaching | Yes | Rarely | Rarely | | Monthly price | $100 (1:1) / $40 (group) | Free–£20 | £40–70/hr | Many general tutors don't teach Further Maths confidently. Ours specialise in it — and in making its hardest ideas feel obvious. Common questions ## Everything you might be wondering. What does A-Level Further Maths cover? Core pure — complex numbers, matrices, proof by induction, polar coordinates, hyperbolic functions, further calculus — plus optional further mechanics, statistics and decision maths. Is Further Maths much harder than A-Level Maths? More abstract and faster, and sat alongside A-Level Maths. Most who struggle are stuck on one topic — often complex numbers or matrices — which we make intuitive. Which exam boards do you cover? Edexcel, AQA and OCR (including OCR MEI), to your specification and chosen options. Do you also help with the main A-Level Maths alongside it? Yes — the two reinforce each other. See our [A-Level Maths](/a-level-maths-tuition-online) page if that's your main need. How much does it cost? USD 100 per month for private 1:1 — eight live lessons, two each week. Small-group option USD 40 per month. No contract; cancel any time. Is there a free trial? Yes — the first lesson is free, no card needed. Will I keep the same tutor? Yes — one tutor who knows your options and target. Can you prepare me for STEP, MAT or top university maths? Yes — STEP and MAT-style problem solving alongside the A-Level content. Are lessons live? Yes — live, one-to-one, with a shared whiteboard, which matters where the working is long. I'm doing AS Further Maths only. Can you help? Yes — AS and full A-Level, built around your modules and timeline. When should I start? Early in Year 12 is ideal because content builds quickly, but we help at any stage. Do lessons fit around college and exam season? Yes — evening and weekend slots in UK time, ramping up around exams. ## Book a free Further Maths trial lesson. Tell us your board, your options and the topic that's lost you. We'll show you how we'd make it intuitive — and you decide from there. No card needed. [See the full course](/courses/college-mathematics-complete-masterclass)Keep exploring ## More maths tuition from Modern Age Coders. [UK · examA-Level Maths Tuition](/a-level-maths-tuition-online)[UK · 16–19College & Sixth Form Maths](/online-maths-tuition-for-college-students-in-uk)[UK · competitionUKMT Maths Challenge](/ukmt-maths-challenge-tutoring)[USA · competitionMath Olympiad & AMC](/math-olympiad-amc-tutoring)[USA · APAP Calculus AB & BC](/ap-calculus-tutoring-online)[CourseCollege Mathematics Masterclass](/courses/college-mathematics-complete-masterclass) --- *Canonical: https://learn.modernagecoders.com/further-maths-tuition-online*