Most A Level Further Maths students put in serious hours. They drill past papers, work through textbooks, and tackle the harder problems most of their peers avoid. Then results day arrives, and they discover the gap between an A* and an A is narrower than expected. The decision often comes down to small margins. Achieving an A* in A Level Further Maths takes more than effort. It takes algebraic precision under pressure, fluent method choice, and complete mastery of the most demanding topics.
This guide explains what separates an A* in A Level Further Maths from a solid A. We cover what your child should be doing in their revision. The guide also flags where most students lose marks they could easily keep. Whether your child is sitting Edexcel, AQA, MEI, or OCR A, the principles below apply.
What changes between an A and an A* in A Level Further Maths
The leap is rarely about content. It comes from algebraic precision, fluent method choice, and mastery of the harder topics. Most students at the A/A* threshold know the content; they need polish.
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What separates an A* from an A in A Level Further Maths?
The gap between A and A* in A Level Further Maths is rarely about knowing the methods. In fact, most students who score an A can list every technique on the specification. The issue is execution. Specifically, examiners look for clean working, the right method first time, and accuracy on the harder topics.
An A* response does something different. First, the algebra is precise and consistent throughout, even on the long Paper 3 questions. Second, the student picks the most efficient method rather than the first method that comes to mind. Third, they show every step of working, including the parts examiners require for full marks. By the end of the paper, the student has lost fewer marks to slips than to genuine misunderstanding.
How does your child master the demanding topics in A Level Further Maths?
A Level Further Maths covers content most A Level Maths students never see. The list includes complex numbers, matrices, polar coordinates, hyperbolic functions, and second-order differential equations. These topics often appear in higher-value questions on Paper 3. Mastering them is what lifts a student from an A to an A*.
Build algebraic fluency
Algebra is the substrate of every Further Maths technique. A student who is fluent saves time on every question and makes fewer slips under pressure. Your child should drill algebra until manipulations are automatic. The basics include completing the square, partial fractions, the factor theorem, and surd manipulation. What worked at A Level Maths needs upgrading for Further Maths demands.
Master complex numbers
Complex numbers are the gateway topic of Further Maths. They appear in every paper, often in questions involving roots of unity, polar form, or De Moivre’s theorem. Your child should switch fluidly between Cartesian form, polar form, and exponential form. They should also be confident applying complex numbers to geometry questions on the Argand diagram. Examiners reward students who handle complex numbers as one connected system, applying the same understanding across different question types.
Get confident with matrices
Matrices appear in both pure and the optional Mechanics or Decision modules. Your child needs to be confident with multiplication, inverses, transformations, and eigenvalues and eigenvectors. The exam often tests application of matrices to coordinate geometry or systems of equations. Memorising formulae is the start. Knowing when and how to apply them is what separates an A from an A*.
Tackle differential equations
Differential equations are a major topic in Further Maths Paper 3. Your child needs to recognise first- and second-order equations, choose the right solution method, and apply boundary conditions cleanly. Common methods include separation of variables, integrating factors, and the auxiliary equation approach for second-order. Strong students also know how to model real-world systems with differential equations. This often appears in higher-mark questions.
Which revision approach gets your child an A* in A Level Further Maths?
Effective A Level Further Maths revision is targeted. Your child should drill the harder topics deliberately. They should work past papers under timed conditions and learn to spot the right method quickly. The most successful students treat revision as a series of small, deliberate exercises focused on weaknesses.
Work through past papers strategically
Past papers are the single most useful resource for A Level Further Maths. Your child should work through every available paper from their exam board. Equivalent papers from other boards add extra practice. After each paper, they should mark against the scheme. The next step is identifying exactly which topics or method choices cost marks. For more on past paper technique, see our guide on A Level Maths past papers.
Drill method-choice questions
Many A Level Further Maths questions can be solved with multiple methods. The most efficient method earns the same marks faster and reduces the chance of slips. Your child should practise short bursts of questions where the same problem can be approached three different ways. They should then identify which method is fastest and most reliable for each problem type.
Time yourself ruthlessly
Further Maths papers are long, and time pressure costs students more marks than they realise. Your child should always work under exam conditions, with a strict time budget per question. A useful rule: roughly 1.5 minutes per mark. Anything significantly slower than that means the method choice is wrong or the algebra needs more practice.
Read examiner reports closely
Every exam board publishes examiner reports free after each sitting. The reports explain what the best answers did and where average answers fell short. They also flag the common mistakes that cost marks. Most A Level Further Maths students never read them. Those who do gain a clear advantage. For a wider view of A Level revision, our A Level revision strategies guide covers techniques across subjects.
Is your child stuck between A and A*?
A tutor can mark their papers question by question and tell them exactly what the examiner wants to see for the top grade.
Book a LessonCommon mistakes that keep students at an A in A Level Further Maths
Even strong students lose marks they could keep. Some mistakes appear so consistently in examiner reports that they are worth flagging directly to your child. Fixing them is often the difference between an A and an A* in A Level Further Maths.
Algebraic slips under time pressure
This is the most common reason students stay at an A in A Level Further Maths. A single slip on Paper 3 can cost three or four marks, often enough to drop a grade. Your child should slow down on the algebra steps in early questions and check substitutions carefully. The marks gained from speed elsewhere are usually lost to corrections in the algebra steps.
Choosing the wrong method
Many questions can be solved several ways, but only one is efficient. Choosing the wrong method costs time and increases the chance of error. Your child should practise spotting key features of a question that suggest a specific method. For example, integration by parts is signalled by products of a polynomial and an exponential or trigonometric function.
Skipping working
Further Maths mark schemes reward working that examiners can follow. A correct final answer with no working will lose method marks in many questions. Your child should write every step, even when they think it is obvious. Method marks add up across a paper, and they often make the difference at the A* threshold.
Misreading the question
Further Maths questions often contain a critical phrase that defines the required answer. Phrases like ‘in exact form’, ‘state any restrictions’, and ‘verify that’ change what counts as a complete response. Your child should underline these phrases before starting any working. A correct calculation with the wrong form of answer typically loses the final accuracy marks.
Which tutors help your child secure an A* in A Level Further Maths?
The right A Level Further Maths tutor can lift a student’s grade band in a single term. They work on technique directly, mark papers question by question, and model the exact precision an A* requires. For students working towards an A* in A Level Further Maths, focused tutoring is often the missing ingredient. Below are three Greenhill tutors who specialise in A Level Further Maths.
Martin
Martin holds an MSc in Mathematical Sciences from Oxford. He is now reading for a PhD in Applied Maths and Theoretical Physics at Cambridge. He earned A*A*A*A at A Level, including A* in Further Maths. Martin has taught A Level Further Maths to four class groups at The British School of Córdoba. Every student in his groups achieved A* in both Maths and Further Maths. He focuses on building algebraic fluency, method choice, and precision under exam pressure. Martin is particularly effective with students aiming for top grades and Oxbridge STEM applications.
Ejaz
Ejaz is in the final year of an MSci in Mathematics at Imperial College London, expecting a First. He completed the International Baccalaureate at King Edward’s School with 44 out of 45 points. His Higher Level subjects scored 7s in Maths, Physics, and Economics. Over 100 hours of tutoring, Ejaz has worked with GCSE and A Level Maths students. His students include Further Maths candidates and applicants preparing for the MAT and TMUA admissions tests. He focuses on developing speed, accuracy, and confidence with the harder topics that separate an A from an A*.
Kevin
Kevin holds an MSc in Financial Economics from Oxford’s Saïd Business School. He graduated with Distinction and made the Dean’s List. He earned a BSc in Economics from Erasmus University Rotterdam, ranking in the top 1% of 2,500 students. Kevin tutors A Level Further Maths, Statistics, and Economics, with particular strength in helping strong students achieve exceptional results. His approach builds systematic problem-solving frameworks: pattern recognition, argument structure, and applying methods to unfamiliar questions. Kevin has helped over ten mentees gain admission to Oxford Saïd, LBS, LSE, and RSM CEMS.
When should your child start working with an A Level Further Maths tutor?
Timing matters with A Level Further Maths. The earlier your child builds the right habits, the easier the work becomes in Year 13. Most students benefit from at least one term of tutoring before mock exams. That gives the tutor time to diagnose technique weaknesses and set targeted exercises. Improvement becomes measurable before the real assessments begin.
Year 13 students can still lift an A to an A* with a focused block of weekly sessions. Six to ten weeks is often enough. The key is choosing a tutor who can mark papers quickly, give specific feedback, and rebuild technique under time pressure. For students aiming to convert an A into an A*, the final stretch is more about polish than new content. For a structured approach to the final A Level stretch, our final month A Level revision guide lays out a clear plan.
Expert A Level Further Maths tutoring with Greenhill Academics
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Our tutors identify the specific habits costing your child marks in A Level Further Maths and fix them before the exam. Matches made within 48 hours.
Book a LessonPart of our A Level grade guide series
This post is part of a series for parents on how to lift A Level grades from a B to an A (or from an A to an A*). The patterns differ subject to subject, but the technique fixes are universal.
Other quantitative guides in the series:
→ How to Get an A in A Level Maths
→ How to Get an A in A Level Physics
Plus the science grade guides:
→ How to Get an A in A Level Biology
→ How to Get an A in A Level Chemistry
And the humanities guides:
→ How to Get an A in A Level History
→ How to Get an A in A Level Geography
Frequently asked questions about A Level Further Maths
Below are the questions we hear most often from parents whose children are aiming for an A* in A Level Further Maths.
Common questions parents ask
