Online Further Maths tutoring for Years 12 and 13, from £14 a class: the compulsory Core Pure content plus whichever options your school has chosen. The same teacher every week, 55 minutes a class, and the first class is free.
Core Pure mathematicsCompulsoryAt least halfComplex numbers, matrices, proof by induction
Applied optionsChosen by the schoolMechanicsorStatisticsor Decision / Discrete, or Further Pure
One part fixed. One part your school picks.
Core Pure is shared by every board — the options are where schools differ
What is ClassArc?
ClassArc is live one-to-one online maths tutoring for school-age children.
One teacher and one child, for 55 minutes. The same teacher every week.
Classes run inside our own classroom software, not a video call: a shared
worksheet you both write on, a shared whiteboard, and answers that sync live.
Further Mathematics is a second A-Level, sat alongside A-Level Maths. It goes deeper into pure mathematics and adds applied options, and it is usually chosen by students heading for maths, physics, engineering, computer science or economics.
Every specification shares one spine: a compulsory Core Pure component making up at least half the qualification, then options chosen by the school. AQA sets three papers with the options in the third, while Edexcel sets four with the options in Papers 3 and 4. OCR arranges it differently again, so we read your board's specification rather than assume.
Because it leans on the A-Level Maths content, most schools teach the two subjects side by side. Some finish A-Level Maths in Year 12 and give Year 13 over to Further Maths.
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A-Levels, one teacher. The same person can cover A-Level Maths and Further Maths, planning each week around whichever needs the time.
Where it gets hard
Strong at maths, and still hitting a wall
Students taking this subject are rarely weak at maths. They stall on something new in kind: writing a proof that holds, treating a complex number as a point that rotates, or an option topic the class raced through.
The fix is usually understanding rather than more repetition. Once a student sees why multiplying by i turns a point a quarter-turn on the Argand diagram, De Moivre's theorem stops being a formula to memorise.
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A proof is marked on the argument. A correct last line after a gap in the reasoning is not a proof.
Why we watch every line
What decides the grade
Three things that decide a Further Maths grade.
i
A-Level Maths that holds.
The course assumes quick, accurate calculus, trigonometric identities and algebraic manipulation. The free class tests these first, because a weakness there leaks into every other topic.
ii
Proof written in full.
Induction questions reward complete reasoning, base case and inductive step both. On the shared worksheet the teacher sees each line as it is written and asks for the step that was skipped.
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The right options.
Further Mechanics and Decision Maths call for very different preparation. We confirm your school's choices before the first lesson, not three weeks in.
Inside a class
How a Further Maths class is spent
Fifty-five minutes, planned around the unit your school has reached this week.
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Homework first
The class opens with last time's homework, already reviewed by the teacher, and goes straight to the question that went wrong.
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The idea behind it
New content is taught for meaning rather than as a template: why a matrix moves a shape the way it does, why induction needs its base case.
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Your child writes
A question worked on the shared worksheet, with the teacher reading each line and stepping in only where the reasoning slips.
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Board-specific practice
Later in the course, timed questions from your own board's past papers, then a walk through the mark scheme to see where the marks sit.
Coverage
Core Pure and the options we teach
The full compulsory content, plus the main option routes across the boards.
Core Pure
Proof by induction: divisibility, series and matrix results
Complex numbers: Argand diagrams, modulus-argument form, loci, De Moivre's theorem, roots of unity
Roots of polynomials, summation of series, the method of differences
Further calculus: improper integrals, volumes of revolution, mean values, Maclaurin series
Polar coordinates, hyperbolic functions, and vector equations of lines and planes
Differential equations: integrating factors, second order with constant coefficients, simple harmonic motion
Further Mechanics
Momentum and impulse
Work, energy and power
Elastic strings and springs
Circular motion and centres of mass
Further Statistics
Discrete and continuous random variables
Poisson and geometric distributions
Chi-squared tests
Decision and Discrete
Graph algorithms and networks
Linear programming
Critical path analysis
Further Pure and Additional Pure
The content here differs most by board, from further vectors to number theory or conic sections. Tell us which paper your child sits and the teacher works from that specification.
Option content varies by board, so we always teach from your board's current specification rather than a generic list.
Why families choose us
Six reasons this suits a Further Maths student
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Specialist teaching, from home
Specialist teaching for this subject can be hard to find locally, especially for the applied options. Online, the teacher is matched to the course rather than the postcode.
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One teacher for both A-Levels
The second A-Level builds straight on the first, so a teacher who sees both can spot where one is holding the other back.
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The reasoning is visible
Teacher and student write on the same live worksheet. For proof and multi-part questions, watching the argument form matters more than checking the answer.
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Your board, your options
AQA, Edexcel and OCR, including OCR B (MEI), taught to whichever options your school has chosen.
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Honest about time
If the exam is close and the gap is wide, we say what is realistic in the weeks left rather than promising an outcome.
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Priced for two years
From £14 a class, in blocks that never renew by themselves, with unused classes refunded if you stop.
Can one tutor help with both A-Level Maths and Further Maths?
Yes. The same ClassArc teacher can cover both, which helps because the Further Maths content builds directly on A-Level Maths. Classes are planned around whichever subject needs the time that week.
Which Further Maths options do you teach?
Further Pure, Further Mechanics, Further Statistics and Decision or Discrete, plus Additional Pure where a school uses OCR B (MEI). Tell us the board and the options when you book, so the teacher prepares the right papers.
My child's school does not offer Further Maths. Can they still take it?
We can teach the content, but your child would also need a school or exam centre willing to enter them as a private candidate, and centres usually charge a fee. Check that first, because the entry itself is outside what a tutor can arrange.
Is Further Maths much harder than A-Level Maths?
It is more abstract and moves faster, particularly in proof, complex numbers and matrices. Students who are comfortable with A-Level algebra and calculus usually manage well with steady, regular support.
How many Further Maths classes a week are typical?
Two a week suits most students, sometimes split between the two A-Levels with the same teacher. Three a week in the months before the summer exams is common.
Is the first Further Maths class free?
Yes, and no card is needed. It is a real 55-minute lesson, usually opening with the A-Level Maths skills the course depends on, and afterwards you get a straight account of what the teacher found.
free
First class
On us, always
55 minutes. The real classroom. No card. We confirm details on email and WhatsApp within a day.
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A full 55-minute class, exactly like a real lesson, not a sales pitch.
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Schedule details sent via email and WhatsApp within 24 hours.
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If it doesn't click, you owe nothing. No card, no commitment.
When you book a demo or sign up for classes, we collect your name, your child's name, email, WhatsApp number, time zone, and the grade you're inquiring about. That's it. We don't ask for or store any payment details on this website. We don't use trackers, cookies for advertising, or third-party analytics that profile you.
How we use it
Only to schedule and run your classes, send you class reminders, share homework and progress, and answer your questions. We'll reach out by email or WhatsApp, depending on what you tell us works better for you.
Who sees it
Your teacher, and the small team supporting them at ClassArc. We never sell, rent, or share your information with anyone outside ClassArc. We use Web3Forms to receive form submissions, and standard email and WhatsApp for messaging, nothing else.
Your child's information
We treat any information about your child with extra care. We only collect what we need to teach them well, such as their grade and what they're working on. We never use a child's photo, name, or work in any marketing without the parent's explicit written permission.
Your rights
You can ask us to show you what we have on file, correct anything inaccurate, or delete your data entirely, at any time. Just email hello@theclassarc.com and we'll handle it within a few days.
ClassArc is a one-on-one online tutoring service. We provide live, scheduled classes between a teacher and a student, along with homework, feedback, and study support.
Classes and scheduling
Each class is 55 minutes. You can reschedule or cancel a class up to 5 minutes before it starts. If you miss a class without notice, we usually credit it back to your balance and reschedule based on what works for the teacher and student.
Payment
The first demo class is free, no card required. After that, plans are billed in advance for the number of classes you choose (8, 24, or ~48). We'll send you a payment link directly once you've picked a plan.
Refunds
If you want to stop classes at any point, we refund whatever class balance is left on your plan. No questions asked, no friction. Refunds are processed within 7 business days.
Code of conduct
We expect students and parents to treat teachers with respect, and teachers to do the same. We reserve the right to end the relationship if classes become unsafe, abusive, or disruptive, with a full refund of any unused balance.
Changes to these terms
If we update these terms, we'll email you before the changes take effect, so you have time to review them.