Chapters
GCSE Further Mathematics is a challenging course. A quick trip to The Student Room confirms as much. But if you're still not convinced, you only need to look at AQA's Advance Information page. It lists all of the topics this exam covers:
- numbers
- algebra
- geometry and coordinate geometry
- calculus
- matrix transformations
These six mathematical topics form the springboard into more advanced sciences such as physics, engineering and, obviously, university-level further maths studies. This GCSE would make an impressive addition to your list of selected subjects. Even if you don't consider yourself particularly good at maths.
That's because there are plenty of resources online to help you to understand the concepts you'll learn about in class. You will also find lots of practice questions online, which can be particularly useful when you are studying maths. Applying what you have learned to these quizzes and question sets is often the best way of ensuring that you will remember everything during exams.
But before we get started on our list of best resources, we want to talk a bit about this qualification. What's the curriculum like? Which of those topics' components are included in the exam? Once we answer those vital questions, we'll direct you to those needed study resources.
Further Maths Curriculum Particulars
According to students who've taken this course, the curriculum is more like AS-level maths than anything you'll see at the GCSE level. Still, they maintain that it's no more challenging than, say, GCSE Chemistry or any other science GCSE. Particularly if you've got a good handle on maths concepts.
The Algebra component is, by far, the most extensive. You'll spend a lot of time working on functions and learning about factorisation and formulae. Specifically, changing the subject of formulae. The curriculum also touches on binomial expressions, inverse functions and simultaneous equations.
The Geometry section is the second most expansive. You'll cover theorems - circle and Pythagoras', the Sine rule and elements of geometric proof. And you'll cover lots of trigonometry. This topic's related discipline, coordinate geometry, explores lines, shapes and equations to calculate various geometric shapes. Numbers, calculus and matrix transformations round out your syllabus.
Beyond those major topics, you'll visit calculus, numbers and matrix transformations. You'll contend with all six topics across both of your exam papers. That format is different from some GCSEs whose topics divide neatly among the exam papers. And, unlike GCSE Maths, you won't have any word problems to solve. And you won't have to explain your reasoning.
Differences Between GCSE Maths and Further Maths
The amazing thing about maths is that, once you know it, you know it. Unlike Information and Communications Technology, there are no new technologies to master in maths. As long as you know how to build and resolve equations, that knowledge will serve you for the rest of your computational days. That's because, at this level, maths is more of a mindset than a skill.
GCSE Further Maths makes this distinction clear. Much of the coursework and subsequent exam revolve around algebraic manipulation. Contrast that with the standard GCSE Maths, which focuses more on problem-solving. That exam is designed to test your memory and thinking skills. GCSE Further Maths means to challenge you on an entirely different skill set. You'll use logic, reasoning and your ability to spot patterns to ace this qualification.
You'll notice that your Further Maths curriculum won't help much as you revise for your compulsory GCSE Maths exam. They both feature many of the same elements - algebra, geometry and so on, but in completely different applications. They're both labelled 'Maths' but, as noted above, they test you on different skills.
If you excel in algebra, you should be able to breeze right through this course. If you have a strong aptitude for maths, in general, but struggle in algebra, you will likely need some extra help to pass your GCSE exam. Fortunately, we've found lots of resources to help you hone your algebra (and other maths) skills ahead of your exams.
Further Maths Learning Resources
GCSE Further Maths doesn't receive quite the treatment that other GCSE subjects do. For instance, there is no BBC Bitesize study guide for GCSE Statistics. However, external revision resources abound for Statistics. That's not the case with Further Maths. For the most part, students have to pick through advanced-level maths resources to find needed information.
The BBC’s GCSE Bitesize website doesn’t have a section for GCSE Further Mathematics, either. However, some of your curriculum's topics are covered in their section for Scottish Higher Maths revision. If you are looking for explanations of key ideas or some extra problem sets, this could be a good place to find some.
And so it will be for the rest of the review materials below, unless otherwise indicated. The best place to start your revision is past papers. Successful Further Maths candidates all aver that these tools are the best possible resource. Getting familiar with how the questions are written is perhaps the greatest advantage you can give yourself, come time to sit your exam. Thanks to that tip, we start our list of learning tools with them.
Past Papers and Marking Schemes
Most students sit Edexcel GCSE Maths and then switch to AQA for their Further exam. Edexcel offers a Further Maths qualification but it seems that this exam board shift is the default process. Whatever the reasons for it, double the number of past papers is twice the benefit for you.
Students who've sat the Further Maths qualifications say it takes at least three mock exams to fully prepare for your ordeal. However, AQA only makes two years' worth of past papers available. So downloading a couple of Edexcel sets would probably serve you well. The exams aren't so different that you'll be thrown off course, regardless of which exam you'll sit. And besides, Further Maths is less about problem-solving than about algebraic manipulation, remember?
Unlike past paper sets you might download for your more mainstream GCSE courses, Further Maths doesn't provide any examiner's reports. Normally, you would read through that report before you begin your revision to find recommendations on how to improve on past students' performances. Not having access to this resource puts you in a bit of a Squid Game glass bridge situation. You don't know where other students went wrong so you're more likely to misstep, too.
But don't let that stop you from making full use of the papers at your disposal. First, read through them to get an idea of how the exam is structured. And then, Answer a few questions, selected randomly, just to gauge your comfort level. Finally, with exams a few weeks away, do three or four mocks. You'll be amazed at how much more confidently you'll navigate your exam.
Quizlet
Besides past papers and marking schemes, Quizlet GCSE Further Maths study sets are one of only two resources we found specifically meant for your GCSE Further Maths course. They comprise several flashcard decks, each one addressing a curriculum topic. Unfortunately, they're not neatly collated like other Quizlet GCSE study packs are. But, at least, they exist.
After going through your past papers and marking schemes, Quizlet should be your next stop. First, avail yourself of the 'Learn' function to get a list of everything that set teaches. Once you've got a handle on all the information, click on the 'Flashcards' button. You may choose whether to see the keyword, equation or graph first, or what they represent.
You might consider downloading the Quizlet app so you can go over the flashcards while you're out and about. You may have time to get through a whole set while on the bus, heading to school. And don't forget to activate Quizlet's test function. Once you feel you've mastered all of a Quizlet set's information, test your knowledge to see how well you do.
The Maths Society
This is the second learning initiative page intended for GCSE Higher Maths. This page has good resources if you want to practice some of your mathematical skills. You can find them by clicking on any of the video links embedded in the page. Don't forget to download the playlist so you can check off what you've already revised.
Feel free to poke around a bit. This site has some question sets and activities that to test your knowledge. And you'll also find recordings that explain some of the topics you'll come across in your course. You can find videos for the AQA, Edexcel, OCR and WJEC courses.
Integral Maths
This platform has some free maths study resources, including plenty of question sets dealing with your curriculum's topics. You will need to master them for your Further Mathematics exams so, even though they're not targeted at GCSE candidates, you should see what they have. You can access more help if you pay for a subscription, but guests can still find some useful resources without having to pay. (We did say GCSE Further Maths resources are hard to find, didn't we?)
The Math Centre
This site is full of resources that can help you understand key mathematical ideas and practise the techniques you have covered in class. These materials are not specifically for GCSE students. In fact, they're meant to support university students! Still, you can find lots of information. You only need to click on the 'Find resources by Course' button to access their stores of Maths guidance.
You can read quick reference leaflets summarising important information. You might watch video tutorials, or find question sets and online tests to practice your skills. They offer diagnostic tests, which are handy as they will give you some feedback on which areas of a topic you might need to work on. One of this site's best features is its different types of learning materials. It doesn’t matter if you prefer written materials, videos, or learning about practical applications. Surely, you'll find something here that can aid your studies.
Spark Notes
This page has some resources to help with many of the topics covered in the GCSE course. It can be a handy site if you are looking for an explanation of a particular concept, even if you have to dig around to find it. There are problem sets at the end of each section; one of its most helpful features. They give you a chance to test yourself on what you have learned. Overall, this site is more suitable for revising topics or understanding ideas you’ve found difficult than for testing your knowledge.
Mr Barton Maths
This website has links to past AQA Further Mathematics papers. You likely won't need those because you'll get yours straight from the AQA site. Mr Barton's page lists resources for other exam boards, too, should you decide to download Edexcel's Further Maths pages. Beyond those, this site has video guides to many of the topics you will see in your Further Maths syllabus. The videos are made by Raw Maths and Riley Maths, which you can also access through YouTube.
IXL website
You're likely already familiar with this page. It is packed with question sets designed to help you practice all of the mathematical skills that you need to master for your exams. This is a great revision tool as you can pick out the topics that you want to practice. And then, find out how quickly and correctly you get through the timed questions.
Kangaroo Maths
Here is another good site if you want to practice the maths techniques you are studying. You may need to look in the A-Level section to find some of the topics covered in your Further Mathematics syllabus. But this site is still a good source of practice questions. And their “five a day” approach is a good strategy for keeping your skills up to scratch.
NRICH
This site approaches maths reinforcement from a different perspective. You'll find loads of games and intriguing problems to make you think about maths in a new way. You may avail yourself of their curriculum-based resources to aid you in understanding your course. And you'll find some handy study tips to come up with a good strategy for your maths revision.
Note that this site isn’t closely linked to the Further Mathematics syllabus. It's not intended specifically for GCSE Further Maths revision. It might be more suitable if you want to learn more about a topic that you are studying in class. Or if you are interested in maths and thinking about studying it after your GCSEs.
Plus Magazine
Like NRich, Plush gives you a new take on maths. You can find puzzles and articles here that will help you to think about the concepts that you encounter in class in a new way. And if you have time for anything beyond your maths studies, this page features articles about current events as well as points of interest.
As mentioned early in this article, GCSE Further Maths study tools are not very plentiful. That's not uncommon, really. GCSE Construction candidates also labour with a dearth of materials. However, higher maths learning resources abound. So, if you can sort through these myriad pages without sacrificing too much time away from your studies, you might find more information than you were looking for. Good luck!
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Hi Brentyn, quite a few of those links don’t work – but the ones that do, are worth exploring. Thanks for collecting all this together.
Hey Rosalind! You’re right, a few of the links weren’t working. I’ve taken care of it and now every link in the article is fully functional. Hope you enjoyed the article!