How to Revise for A Level Further Maths

A Level Further Maths has a reputation for being one of the toughest A Level subjects you can choose. The jump from GCSE seems massive. Topics like complex numbers and matrices can seem completely alien at first.

And here's the thing: it's not just the new concepts. There's also more of them. You're juggling abstract algebra, mind-bending mechanics, and brand new areas like decision maths all at once. Many students feel overwhelmed before they've even started revising properly.

But here's the good news: with the right revision approach, you absolutely can master Further Maths. This guide will show you exactly how to tackle each module, which strategies actually work, and how to build the problem-solving confidence you need for exam success.

We've helped thousands of students succeed in Further Maths through our tailored revision resources and expert-written content. Let's get you exam-ready.

Key takeaways

• Break your revision into modules (Pure, Mechanics, Statistics, Decision) and focus on one area at a time

• Use active recall and spaced repetition to lock in complex concepts

• Start past papers early and learn from mark schemes and examiner reports

• Keep a problem log to track mistakes and revisit tricky questions

• Revise A Level Maths content alongside Further Maths to strengthen your foundations

• Aim for consistent practice rather than marathon study sessions

• Use worked solutions to understand the thinking process

Key topics in A Level Further Maths

A Level Further Maths is split into several modules. Each one complements your A Level Maths knowledge and often takes things much further.

Understanding exactly what's in each module helps you plan your revision time effectively.

We have a full list of topics for Edexcel A Level Further Maths. The article also contains information about how the other exam boards differ from Edexcel, with links to each board’s specification.

Pure Mathematics

Pure maths makes up the core of Further Maths. Some of the concepts will link directly to what you’ve learned in A Level Maths, while others will seem more distinct and new.

Some of the key concepts include:

• Complex numbers – learning to work with numbers involving √-1, plotting them on Argand diagrams, and using polar form

• Matrices – operations, determinants, inverses, and using them to solve equations or represent transformations

• Further algebra – proof by induction, series summations, De Moivre's theorem

• Further calculus – implicit differentiation, volumes of revolution, first-order differential equations

These topics are more abstract than some of the other areas of Further Maths. You're working with concepts you can't always "see" in the real world and their real-life applications may not be as obvious.

Some exam boards allow you to study Further or Additional Pure Mathematics modules. Whilst the content in these modules is obviously closely linked to the “core” pure content, for the purposes of revision it can be useful to think of them separately. This can help you structure your time more effectively and make the content seem less overwhelming. Make sure you know exactly which parts of the specification are assessed in each exam paper to help plan your revision.

Mechanics

Some topics in Mechanics build directly on what you learned in A Level Maths and stretch it further. For example you will need to use what you learned about resolving forces on slopes to solve many energy problems. Other topics use concepts you won’t have encountered in A Level Maths such as momentum.

You'll explore topics like:

• Momentum & Impulse and Collisions

• Work, Energy & Power

• Elastic Strings & Springs

The content in each exam board’s curriculum will vary but there will be some overlap. Depending on which options have been selected you may study mechanics in more or less depth. For example in Edexcel A Level Further Maths, you could study both Further Mechanics 1 and Further Mechanics 2 as your options. Make sure you know exactly what content is assessed in each exam paper.

Link with Physics

If you're also studying A Level Physics, you'll notice considerable overlap. The maths in Further Maths Mechanics is often the same as Physics problems, just with more rigorous mathematical treatment and more emphasis on algebra. Sometimes approaches may seem different in the two subjects but just remember that the underlying concepts are exactly the same. If you can master the underlying maths and physics in the problem, this will make your revision for both subjects much smoother.

Statistics and Decision Maths

Not all exam boards require Statistics and Decision, but they're common options.

Statistics extends your A Level knowledge into areas like:

• Chi-squared tests

• Probability distributions (Poisson, geometric)

• Further hypothesis testing

Decision Maths is entirely new territory. It covers:

• Algorithms (like Dijkstra's and Prim's)

• Graph theory and networks

• Linear programming

• Critical path analysis

Decision Maths can feel strange at first because it's so different from other maths you've studied. But it's also highly practical and often considered one of the more accessible parts of Further Maths. If you study A Level Computer Science you will also find that some topics overlap.

As with the other optional units, different exam boards will contain different content for their Statistics and Decision modules. Make sure you check exactly what content is covered in each exam paper. 

Top revision strategies for Further Maths

I have taught A Level Further Maths for several years. There are some revision strategies that work more or less well than others in this highly specialised subject. I have collated a list below of the revision strategies for Further Maths that I find students get the most out of.

Spaced repetition and active recall

Spaced repetition involves reviewing information at increasingly spaced intervals. This  enhances long-term memory retention (opens in a new tab) using the “spacing effect”.

Active recall boosts your memory by making you actively retrieve information: Instead of just rereading notes, you test yourself to strengthen your long-term recall and improve exam confidence.

To implement these together you might practice exam questions on a particular topic. You then come back to the same topic or concept more frequently at first, and then gradually increase the time between reviews.

Spaced repetition is particularly effective for retaining large amounts of information over extended periods. Find out more about spaced repetition in this guide, and you can read more about active recall in this article.

Use worked solutions effectively

When answering questions by topic or past papers, always try the question yourself first without looking at the solution. This is important retrieval practice for recalling definitions and methods; it is also active recall as you actually have to use the information too.

Then compare your working with the model solution. Even if you got to the correct final answer, it is valuable to look over the worked solutions carefully and ask yourself:

• What did they do that I didn't?

• Where did my method differ?

• Is their method easier or harder?

Often in Maths there may be a shorter (or longer!) method than you first considered. Understanding different perspectives on solving a problem will make you a better problem solver yourself.

Practise with your calculator and formula booklet

If you were training for a football match; you’d probably wear the boots you’re going to wear in the game. When answering practice questions for A Level Further Maths, make sure you use the calculator model you are going to use in the exam, and use a printed copy of your formula booklet. This will help your speed in the exam where you’ll know exactly which formulas are given to you, and where to find them quickly when you need them. 

Getting to know your calculator’s functions inside-out is really important too, as it can speed up a lot of your work and checking of your answers. Functions like matrix multiplication, complex number conversions, and plotting graphs to find minimum and maximum points are especially useful in Further Maths.

Keep a problem log

Create a document or notebook where you make a note of mistakes you make and misconceptions you find during practice.

Write down:

• The question you got wrong (so you can revisit it)

• Why you got it wrong

• What the correct method is

• Key take-away for next time

Revisit this log weekly. You'll start to spot patterns in your mistakes and this can help make your future revision more targeted and effective.

Studies on metacognitive reflection (opens in a new tab) show that students who analyse their errors improve problem-solving accuracy significantly.

You have to be really honest with yourself when using this method, it may be uncomfortable at first but when you notice that it is making you a better mathematician it will feel worth it!

Focus on the foundations

Further Maths assumes rock-solid A Level Maths knowledge. If you're shaky on core concepts (like trig identities, differentiation, or vectors), you'll struggle.

Dedicate time each week to revising A Level Maths content alongside your Further Maths work. Depending on how your school or college structures your studies for Maths and Further Maths, you may be studying for both sets of exams at the same time. It is also quite common for students to be studying Further Maths whilst resitting their A Level Maths to improve their grade. In my experience with these students they find that they both complement each other well, and studying Further Maths thoroughly improves their problem solving skills in A Level Maths.

Consistent practice rather than marathon sessions

Break your revision into focused sessions with clear goals: "master two exam questions on parametric equations" or "complete a timed mechanics paper."

Focused bursts of study with breaks are more effective than marathon sessions. For this reason many of the students I have worked with found success using the pomodoro technique. 

How to use past papers effectively

Most of the students I have taught consider past papers to be their most valuable revision tool. But timing and technique matter.

When to start using past papers

Don't wait until you've "finished" all your revision. Start using past papers earlier than you think.

• Early in your revision: Use them to identify weak topics and practice exam-level questions on the topics you’ve covered so far

• Mid-revision: Practice individual questions by topic to build confidence

• Close to exams: Complete full papers under timed conditions

How to analyse mark schemes

Mark schemes tell you exactly what examiners want to see. Don't just check if your answer is right.

Look at:

• Which steps earn marks (even if your final answer is wrong)

• Key words or phrases examiners expect

• Common methods for solving problems

Read examiner reports too

Examiner reports reveal what students typically get wrong and why. They're published by exam boards after each exam series.

These reports give you insider knowledge about common pitfalls to avoid.

For example, Edexcel publishes examiner reports (opens in a new tab) that highlight frequent student errors in Further Maths papers.

Time management tips

When practising full papers:

• Use a timer and stick to exam conditions

• Note which questions take you longest

• Practice moving on from questions you're stuck on (you can return later)

• Aim to finish with 10-15 minutes for checking

Don’t necessarily expect to complete every question within the allotted time at your first attempt, it takes practice. 

Resources to help you revise A Level Further Maths

You don't have to tackle your revision alone.

Save My Exams offers comprehensive resources designed specifically for A Level Further Maths students:

• Revision notes: Clear explanations of every concept, written by experienced teachers

• Past papers: Practice real exam papers exactly as they appeared

• Exam questions by topic: For effective and targeted practice of the topics you need to focus on

Our resources are organised by exam board, so you'll always be practising the relevant material. We have past papers for AQA, Edexcel, OCR, and OCR MEI. We have revision notes, past papers, and exam questions by topic for Edexcel. 

Frequently asked questions

Do I need to take A Level Maths to do Further Maths?

Yes, absolutely. A Level Further Maths is studied alongside or after A Level Maths, not instead of it.

Most students study both simultaneously. Some schools let you take A Level Maths in Year 12 and Further Maths in Year 13, but this is less common.

How much harder is Further Maths than A Level Maths?

Further Maths is generally considered to be harder than standard A Level Maths. But that doesn't mean you can't succeed.

The difficulty comes from:

• More abstract concepts (like complex numbers and matrices)

• Faster pace and heavier workload

• Questions that require multiple steps and creative problem-solving

On the other hand you should remember that half of the Further Maths qualification is designed to be taught in Year 12, so it doesn’t all rely on a full knowledge of A Level. There are also several areas which are more about broadening your maths knowledge, as opposed to just making it deeper or more difficult.

Students who enjoy maths and are willing to practise regularly tend to do very well. Universities and employers recognise Further Maths as one of the most challenging A Levels, which makes it an impressive addition to your CV.

AMSP (opens in a new tab) suggests that it is a highly desirable qualification that universities recognise the benefits of and often make differentiated offers for.

How many hours should I revise each week for Further Maths?

This depends on where you are in the course and how confident you feel.

During term time:

As a teacher I always recommended at least as much time as you spent in class. So if you had 6 hours per week of maths lessons, I would expect you to be completing at least 6 hours per week of study outside of lessons.

During exam revision period:

Increase this to at least 10-15 hours per week. This should include topic revision, past papers, and reviewing mistakes. As you approach your exam this may increase even more, especially as you start to complete exams in other subjects which may reduce the number of subjects you have left to revise for.

Remember: consistency matters more than marathon sessions. It's better to do one hour daily than seven hours in one sitting.

Adjust based on your other subjects and commitments. But make Further Maths a priority; it demands regular practice to stay sharp.

Final thoughts

A Level Further Maths is tough. There's no way around that.

But with the right approach, good grades are absolutely achievable. Focus on building strong foundations, practise consistently, and use your resources wisely.

Break your revision into manageable chunks. Work through each module systematically. Learn from your mistakes and don't be afraid to revisit topics multiple times.

Keep a problem-solving mindset. Further Maths rewards persistence and curiosity. The satisfaction of cracking a difficult problem is one of the best feelings in education.

With dedication and smart revision, you can master Further Maths and open doors to top universities and careers in STEM fields.

You've got this.

Improve your grades with Save My Exams

Save My Exams is here to help you achieve the best grade possible in A Level Further Maths by offering expert-written resources specifically made for your exam board. We’ve got everything you need:

• Detailed revision notes

• Exam-style questions with student friendly worked solutions

• Past papers with mark schemes

Whether you want to improve your understanding of key topics, test your knowledge, or sharpen your exam techniques, Save My Exams makes it easier and more effective for you to revise.

Explore Our A Level Further Maths Resources

References

Ebbinghaus H (opens in a new tab). Memory: A contribution to experimental psychology.

Schraw, Crippen, Hartley (opens in a new tab). Promoting Self-Regulation in Science Education: Metacognition as Part of a Broader Perspective on Learning

AMSP (opens in a new tab) (Advanced Mathematics Support Programme). What is A level Further Mathematics?