Online A Level Further Maths Tutor for Edexcel Core Pure
Harry Williams provides specialist one-to-one online A Level Further Maths tuition, focusing on Core Pure Mathematics 1 and 2. With more than ten years' teaching experience, including UK A Level Maths and Further Maths at Abingdon School and Bradfield College, Harry helps students develop the advanced mathematical understanding, reasoning, and problem-solving skills needed for success in Further Mathematics.
Harry is a fully qualified Maths teacher, former Head of Mathematics at Harrow School Online and Highgrove Education, and current Pearson Edexcel International A Level Maths and Further Maths examiner.
He specialises in the two compulsory Core Pure papers within Pearson Edexcel UK A Level Further Mathematics (9FM0), which together contribute 50% of the qualification. Tuition can cover the complete Core Pure syllabus or focus on challenging topics, examination questions, and areas where students are losing marks. The two optional papers are studied separately.
Every 55-minute tutorial is taught personally by Harry. Homework is set after every lesson, and submitted work is personally marked to identify weaknesses and guide further teaching.
@getmethatgrade This is question 5 from the Pearson Edexcel IAL Further Pure Mathematics F2 paper in January 2025 on the topic of polar calculus: differentiation to find tangents parallel to an initial tangent and integration to find an area swept out by a polar curve. So many students overcomplicated this in their exams in January 2025. #math #maths #calculus #integration #alevels ♬ original sound - Harry @ getmethatgrade.com
Who is Harry's A Level Further Maths tuition most suitable for?
Students beginning Core Pure Mathematics
Further Maths introduces more abstract mathematical ideas, including complex numbers, matrices, mathematical proof, and advanced calculus.
Harry helps students develop secure mathematical foundations and understand how new techniques build on their existing A Level Maths knowledge. Tuition can reinforce school teaching or provide a structured introduction to Core Pure topics.
Students struggling with demanding Further Maths topics
Understanding an individual technique is not always enough to solve more challenging Core Pure questions.
Harry helps students recognise connections between mathematical ideas, select appropriate methods, and work confidently through unfamiliar problems. Particular attention is given to mathematical reasoning, proof, and developing a deeper understanding of difficult topics.
Strong students working towards A or A*
Students already achieving high marks may need additional support with the most demanding examination questions, where a single problem can combine several areas of mathematics.
Tuition focuses on challenging, multi-stage problems, efficient solution methods, rigorous mathematical arguments, and the accuracy required to perform consistently at the highest level.
Students preparing for their Core Pure examinations
For students approaching their examinations, Harry can provide targeted revision of Core Pure 1 and Core Pure 2, using past papers to identify weaknesses, improve examination technique, and prioritise areas requiring attention.
Students studying Core Pure independently
Harry also supports home-educated students, private candidates, and students whose schools provide teaching for the optional Further Maths papers but who would benefit from additional Core Pure support.
Lessons can be planned around the student's current knowledge, examination timetable, and target grade, with regular homework and personal marking providing structure between tutorials.
How Harry's online A Level Further Maths tutorials work
Tutorials are live, one-to-one, and tailored to the student's Core Pure needs. Each lesson lasts 55 minutes and uses Google Meet and a shared Miro whiteboard.
1. Identify the underlying difficulty
Harry begins by reviewing the student's current understanding, recent schoolwork, assessments, and examination plans.
Examination-style questions help determine whether difficulties arise from gaps in earlier mathematics, unfamiliar Further Maths concepts, mathematical reasoning, inefficient methods, or avoidable errors.
2. Develop advanced mathematical understanding
Lessons combine clear explanations, worked examples, guided practice, and independent problem-solving.
Harry encourages students to understand why mathematical methods work, how different topics connect, and how to apply their knowledge to unfamiliar problems. Particular emphasis is placed on constructing sound mathematical arguments and developing confidence with abstract ideas.
3. Set and personally mark homework
Homework is set after every tutorial, with questions chosen to reinforce current learning and develop the student's Core Pure problem-solving skills.
Harry personally marks submitted work, identifying mistakes in reasoning, mathematical methods, accuracy, and presentation. This feedback helps determine what should be addressed in subsequent lessons.
Model solutions may also support independent revision, but do not replace personal marking.
4. Prepare for demanding examinations
As students develop their understanding, tuition increasingly focuses on Core Pure examination questions and past papers.
Harry helps students recognise the mathematical structure of unfamiliar questions, select efficient approaches, write clear proofs, maintain accuracy through longer solutions, and manage their examination time effectively.
Parents can receive progress updates according to their agreed preferences.
Why choose Harry Williams as an A Level Further Maths tutor?
Experienced UK A Level Maths and Further Maths teacher
Harry has taught UK A Level Mathematics and Further Mathematics at Abingdon School and Bradfield College, supporting sixth-form students with challenging mathematical content and advanced examination preparation.
He holds Qualified Teacher Status (QTS) and a PGCE in Mathematics from the University of Reading. His career also includes serving as Head of Mathematics at Harrow School Online and Highgrove Education.
This combination of classroom teaching, departmental leadership, and individual online tuition gives Harry extensive experience helping students develop mathematical understanding, independence, and problem-solving skills.
Original Core Pure examination solutions for Save My Exams
Harry wrote original model solutions for the 2020 Pearson Edexcel UK A Level Further Mathematics Core Pure 1 and Core Pure 2 examination papers for Save My Exams.
These resources demonstrate Harry's familiarity with the exact papers covered by his UK Further Maths tuition, including the mathematical reasoning, methods, and presentation required to solve demanding Core Pure questions.
The full examination-paper solutions are available to Save My Exams members.
Harry has also written articles examining the hardest A Level Further Maths topics and questions, exploring how students can approach particularly challenging mathematical problems.
Current Pearson Edexcel examiner
Harry is a current Pearson Edexcel examiner for International A Level Mathematics and Further Mathematics. His official live-paper examining work to date has been in International A Level Pure Mathematics 1 (P1).
These examiner appointments relate to the international qualifications, rather than UK A Level Further Mathematics (9FM0). His examining experience complements his separate UK A Level teaching and Core Pure resource-writing experience.
A record of strong Further Mathematics results
Among the students Harry personally taught at Harrow School Online, his Pearson Edexcel International A Level Further Mathematics results included:
2024: 43% A*, 86% A*-A, and 100% A*-B.
2023: 80% A*, and 100% A*-A.
In 2024, his highest-performing Further Maths student achieved 598/600 UMS, the highest Further Mathematics score on their continent.
These results relate specifically to International A Level Further Mathematics, rather than the UK 9FM0 qualification, but demonstrate Harry's wider experience teaching advanced Mathematics.
Direct, individual teaching
Every tutorial is delivered personally by Harry, rather than students being allocated to different tutors.
Lessons are tailored to each student's Core Pure progress, mathematical strengths, examination timetable, and areas for improvement, with personally marked homework providing continuity between tutorials.
Pearson Edexcel A Level Further Maths (9FM0): Core Pure Mathematics 1 and 2
Harry provides specialist tuition for the two compulsory Core Pure Mathematics papers within Pearson Edexcel UK A Level Further Mathematics (9FM0).
The qualification is linear and consists of four externally examined papers, all taken in the same May/June examination series.
Paper 1 – Core Pure Mathematics 1 (9FM0/01)
Paper 2 – Core Pure Mathematics 2 (9FM0/02)
Together, the two Core Pure papers account for 50% of the complete A Level Further Mathematics qualification.
Across Core Pure 1 and 2, students study topics including:
Proof
Complex numbers
Matrices
Further algebra and functions
Further calculus
Further vectors
Polar coordinates
Hyperbolic functions
Differential equations
Both papers can assess content from across the Core Pure specification, so students need a secure understanding of the complete compulsory syllabus.
Each paper lasts 1 hour 30 minutes, is worth 75 marks, and contributes 25% of the final qualification.
Tuition can cover the complete Core Pure syllabus or concentrate on specific topics, challenging examination questions, or areas where students are losing marks.
Papers 3 and 4 – Further Mathematics options
Students also take two optional papers selected from the permitted combinations of:
Further Pure Mathematics
Further Statistics
Further Mechanics
Decision Mathematics
Each optional paper lasts 1 hour 30 minutes, is worth 75 marks, and contributes 25% of the final qualification.
Harry's UK Further Maths tuition covers Core Pure 1 and 2; the optional papers are taught separately through the student's school or another provider.
This distinction applies specifically to the UK 9FM0 qualification. Harry's separate International A Level Further Maths tuition includes all three IAL Further Pure units, FP1, FP2, and FP3.
Working towards an A* in A Level Further Maths
Achieving an A* in Further Mathematics requires more than familiarity with advanced techniques. Students must combine mathematical ideas, solve unfamiliar problems, construct rigorous arguments, and maintain accuracy across demanding examination papers.
Harry supports high-attaining students who want to strengthen their Core Pure performance and improve their consistency in challenging examination questions.
Tuition focuses particularly on:
Mathematical reasoning and proof – developing clear, rigorous arguments.
Unfamiliar, multi-stage problems – recognising connections between different areas of mathematics.
Efficient solution methods – identifying approaches that reduce unnecessary working and save examination time.
Accuracy and presentation – avoiding errors in longer algebraic, calculus-based, and other advanced solutions.
Examination preparation – using past papers and personally marked work to identify where marks are being lost.
Harry can also identify gaps in earlier A Level Maths knowledge that may be affecting performance in Further Mathematics.
The two Core Pure papers account for half of the final qualification. Harry's tuition aims to maximise performance in these compulsory papers, while students prepare separately for their two optional papers.
Studying International A Level Further Maths instead?
Pearson Edexcel International A Level Further Mathematics (YFM01) is a separate, modular qualification from UK A Level Further Mathematics (9FM0).
Harry teaches both qualifications, but his coverage differs. For International A Level Further Maths, he teaches all three Further Pure units: FP1, FP2, and FP3, alongside the applied units he offers.
Students following the international qualification should visit Harry's dedicated International A Level Further Maths tuition page for the relevant syllabus, examination units, and booking information.
Also studying UK A Level Maths?
Harry teaches the complete Pearson Edexcel UK A Level Mathematics (9MA0) qualification, including Pure Mathematics, Statistics, and Mechanics.
Students taking both Maths and Further Maths can work with Harry on their A Level Maths course alongside Core Pure 1 and 2.
For full details, visit Harry's A Level Maths tuition page.
University Admissions Tests
Preparing for the next step
For students planning to study Mathematics, Engineering, Computer Science, Economics, or other mathematically demanding subjects at university, Harry also offers specialist preparation for TMUA, ESAT Mathematics 1 and 2, and STEP 2 and 3, where required for their chosen course.
Admissions-test preparation is offered separately from qualification tuition, focusing on the mathematical reasoning, problem-solving skills, and examination techniques needed for these assessments.
Testimonials and Google Reviews
“I wanted to improve the way I approached ESAT problems. Harry gave incredibly clear explanations and really helpful advice for dealing with the challenging time pressure of the test. Working with him changed the way I approach difficult problems and helped me spot the most time-efficient way of solving them. Harry’s help is 100% worth it. Even after my first session, I could already see ESAT questions differently and felt much more confident.”
“I wanted to develop deep mathematical knowledge and ensure the achievement of the highest grades. I found his explanations, guidance, and way of teaching things very useful; I have never grasped mathematical concepts so fast. Harry deepened my love with maths and took me from just a beginner to getting full UMS in P1 before the mid term break! I would particularly recommend his tuition to students who want the best grades and need to improve their understanding of Mathematics quickly.”
These are a selection of our most recent Google reviews. Read them all on our Google profile.
Frequently Asked Questions
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Harry specialises in the two compulsory Core Pure Mathematics papers within Pearson Edexcel UK A Level Further Mathematics (9FM0):
Core Pure Mathematics 1 – 9FM0/01
Core Pure Mathematics 2 – 9FM0/02
Together, these papers contribute 50% of the full A Level Further Mathematics qualification.
Tuition can cover the complete Core Pure content or focus on specific topics, challenging examination questions, proof, mathematical reasoning, or preparation for an individual paper.
Harry does not currently offer tuition for the optional UK Further Pure, Further Statistics, Further Mechanics, or Decision Mathematics papers.
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Pearson Edexcel A Level Further Mathematics (9FM0) is a linear qualification comprising four examination papers:
Paper 1: Core Pure Mathematics 1 (9FM0/01)
Paper 2: Core Pure Mathematics 2 (9FM0/02)
Paper 3: First optional Further Mathematics paper
Paper 4: Second optional Further Mathematics paper
Each paper lasts 1 hour 30 minutes, carries 75 marks, and contributes 25% of the final qualification. All four assessments are completed in the same May/June examination series.
Optional papers are available in Further Pure Mathematics, Further Statistics, Further Mechanics, and Decision Mathematics, with restrictions on permitted combinations.
Both compulsory Core Pure papers may assess content from across the Core Pure specification, rather than having completely separate topic lists.
The full structure and permitted options are detailed in Pearson Edexcel's official Further Mathematics specification.
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Harry provides specialist tuition for the compulsory Core Pure Mathematics 1 and 2 papers, which together account for half of the UK A Level Further Mathematics qualification (9FM0).
He does not currently teach the two optional papers as complete courses.
Students whose school or another tutor provides the optional-paper teaching can work with Harry specifically on Core Pure, allowing them to receive focused support with the compulsory half of the qualification.
Harry can tailor tuition to the student's Core Pure progress, examination timetable, mathematical strengths, and areas where marks are being lost.
For students studying Pearson Edexcel International A Level Further Mathematics (YFM01), Harry offers broader coverage, including all three Further Pure units (FP1, FP2, and FP3). See the dedicated IAL Further Maths page.
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A Level Further Maths is a significant step up from A Level Maths, introducing more advanced and abstract mathematical concepts alongside a substantial additional workload.
Core Pure Mathematics includes topics such as complex numbers, matrices, mathematical proof, polar coordinates, hyperbolic functions, and differential equations.
The challenge is not simply learning additional techniques. Students must combine mathematical ideas, construct rigorous arguments, and solve unfamiliar multi-stage problems with increasing independence.
Strong foundations in algebra, functions, trigonometry, calculus, and mathematical reasoning are essential.
Harry can identify whether difficulties arise from new Further Maths content or gaps in earlier A Level Mathematics knowledge, allowing tuition to address the underlying problem.
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Yes. Past-paper preparation is central to Harry's Core Pure tuition, helping students apply their mathematical knowledge accurately and efficiently under examination conditions.
Tuition focuses on:
Recognising the mathematical structure of unfamiliar or multi-stage questions.
Selecting efficient solution methods.
Constructing clear proofs and complete mathematical arguments.
Maintaining accuracy through longer algebraic and calculus-based solutions.
Managing examination time and avoiding errors that cost marks.
Harry personally marks submitted Core Pure examination-style work and identifies whether difficulties arise from knowledge gaps, mathematical reasoning, inefficient methods, or examination technique.
Subsequent tutorials target the areas where improvement could make the greatest difference.
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Yes. Harry supports high-attaining Further Maths students aiming to improve their performance from an A towards an A*, concentrating on the compulsory Core Pure Mathematics papers.
Together, Core Pure 1 and 2 contribute 50% of the final qualification, making strong performance in these papers an important part of achieving a top grade.
Harry focuses on challenging mathematical concepts, unfamiliar multi-stage questions, proof, efficient methods, and accuracy under examination conditions.
Through personally marked practice papers and targeted feedback, he identifies the specific weaknesses preventing students from reaching their potential.
The final UK A Level Further Mathematics grade is determined by marks across all four papers, including the two optional papers, and the grade boundaries for the relevant examination series.
Harry's tuition therefore aims to maximise the student's performance in Core Pure, while their optional-paper preparation is provided separately.
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Yes. Harry teaches the complete Pearson Edexcel UK A Level Mathematics (9MA0) qualification, including Pure Mathematics, Statistics, and Mechanics.
Students taking both A Level Mathematics and Further Mathematics can work with Harry on the complete 9MA0 specification alongside Core Pure Mathematics 1 and 2 from 9FM0.
This can be particularly useful where gaps in algebra, calculus, vectors, or other A Level Maths foundations are affecting a student's Further Maths progress.
For full details of standard A Level Mathematics tuition, visit our dedicated Pearson Edexcel A Level Maths page.
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Yes. Harry also offers specialist preparation for university Mathematics admissions tests, including:
TMUA – Test of Mathematics for University Admission
ESAT – Mathematics 1 and Mathematics 2
STEP – STEP 2 and STEP 3
These assessments are relevant to applicants for certain competitive university courses in Mathematics, Computer Science, Economics, Engineering, and related subjects.
Admissions preparation focuses on advanced mathematical reasoning, unfamiliar problems, efficient solution strategies, and examination time management.
Admissions-test tuition is a separate service from standard A Level Further Maths tuition.
See our Maths university admissions tests page for full details.
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Yes. Harry is a fully qualified Mathematics teacher, holding a PGCE in Mathematics from the University of Reading and Qualified Teacher Status (QTS).
He has more than ten years' experience teaching Mathematics and Further Mathematics, including UK A Level teaching at Abingdon School and Bradfield College, and has previously served as Head of Mathematics at Harrow School Online and Highgrove Education.
Harry is also a current Pearson Edexcel examiner for International A Level Mathematics and Further Mathematics, registered to examine the IAL units he teaches.
His official live-paper marking to date has been in IAL Pure Mathematics 1 (P1), owing to the particularly high demand for examiners for that paper.
His current examining appointments relate to Pearson Edexcel's international qualifications, rather than the UK A Level Further Mathematics (9FM0) examinations.
Harry has also written original model solutions for the 2020 Pearson Edexcel UK A Level Further Mathematics Core Pure 1 and 2 examination papers for Save My Exams.
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Yes. Harry provides one-to-one UK A Level Further Maths tuition for students attending independent (private) schools, state schools, international schools, and online schools, as well as home-educated students and private candidates.
Tuition can complement school teaching or provide structured support for students studying Core Pure independently.
For home-educated students, Harry can provide a planned programme of Core Pure Mathematics teaching, including homework, personal marking, and examination preparation. The two optional UK Further Maths papers must be studied separately.
Students outside the UK are also welcome, provided they are following Pearson Edexcel UK A Level Further Mathematics (9FM0), rather than the separate International A Level qualification (YFM01).
Private candidates must arrange official examination entries through an appropriate examination centre.
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Yes. Harry sets homework after every tutorial and personally marks work submitted by students.
Homework is tailored to the student's Core Pure topics, mathematical understanding, and areas for improvement. This may include advanced algebra, complex numbers, calculus, proof, and challenging examination-style problems.
Harry's marking helps identify weaknesses in mathematical reasoning, methods, accuracy, and presentation, allowing subsequent tutorials to address the areas where support is most needed.
Model solutions may also be provided for additional self-review, but they are not a substitute for Harry's personal marking.
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Harry monitors students' understanding, progress through Core Pure topics, and performance on examination-style questions, identifying recurring errors and areas requiring further work.
Feedback to parents is tailored to the student's needs and the family's preferences. The frequency and format of updates can be agreed individually, rather than following a fixed reporting schedule for every student.
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Yes. Harry holds an Enhanced Disclosure and Barring Service (DBS) certificate and is registered with the DBS Update Service.
A copy of his DBS certificate is automatically included in his first communication with parents, before tuition begins. There is no need to request it.
The DBS Update Service also allows eligible checks of his certificate's status, with his consent and in accordance with DBS requirements.
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Harry generally offers one-to-one Maths tutorials seven days a week, between 9 am and 10 pm UK time, although specific availability varies according to existing bookings.
Students in the UK and internationally can check the live A Level Maths booking calendar for available appointments and choose times that suit their schedules.
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Individual 55-minute Core Pure 1 and 2 tutorials cost £100. A package of 10 tutorials costs £800, equivalent to £80 per tutorial, and is valid for 100 days from purchase.
New Maths clients can use FIRSTCLASS for 20% off their first individual tutorial, reducing the price to £80. The offer is limited to one use per client and excludes packages and Biology tuition.
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You can book your first 55-minute one-to-one A Level Further Maths tutorial directly through our A Level and International A Level Maths booking page.
Simply choose an available appointment and complete your booking.
Ready to begin?
All Maths tutorials last 55 minutes and are scheduled in one-hour slots.
All prices are per tutorial.
Book a 55-minute one-to-one A Level Further Maths lesson or purchase one of our 10 lesson packages through the online scheduling system.