Are you taking your GCSE Maths exam this summer and looking for advice on how to achieve a top grade? In this article, Keystone Tutors have compiled some useful insights, tips and guidance on how best to prepare for the GCSE Maths exam, top tips for achieving a Grade 9 and some interesting findings from the examiners reports.

## What do I need to know for GCSE Maths?

What you need to know for your GCSE Maths will depend on which syllabus you are sitting, and whether you are sitting foundation or higher level. You will be able to find this out from your teacher at school. Although there are some topics that come up reliably in all GCSE Maths exams, there are some subtle differences between syllabuses in terms of what you need to know. To see exactly which topics you need to revise, you need the specification for your syllabus, paying attention to only the foundation section if sitting foundation level, or both sections if sitting higher level. The locations of these can be found below for some popular exams:

These specifications will tell you how many GCSE maths papers there are for your exam, whether they are calculator or non-calculator, their length, any additional coursework, and a specific breakdown of the topics you need to know.

## What is the difference between GCSE Maths and IGCSE Maths?

The ‘I’ in IGCSE simply stands for international, meaning that this qualification is available internationally as well as in the UK. In terms of what difference it makes to you, the most important thing you bear in mind is that the syllabus is slightly different to the standard GCSE. When revising make sure you are referring to the IGCSE syllabus if this is the exam that you are sitting.

## How to revise for GCSE Maths

In general, it is best to use the specification to help you revise each topic individually to make sure you are confident with it before attempting past papers. Here are some tips to get you started:

**In topics you are struggling with, start small and work your way up. **

If you find yourself struggling with a topic, return to the basic principles and work your way up. It may be helpful to watch YouTube tutorials of the basics before working on more complex questions. An example of how you might break down a topic such as probability:

1. What is probability?

2. How can we form the probability of a single event?

3. How can we show combinations for multiple events?

4. How can we calculate the probability for multiple events?

Before moving onto the next level, ensure understanding and confidence at each level so that you can gradually build your confidence. If you are unsure how to break down a topic, ask your teacher for help with this.

**Practise exam papers as well as doing topic revision **

Practising exam papers is very important in your revision. It gives you a chance to pull your knowledge from different areas quickly when working through questions and also accustoms you to the exam-style question types you might see. If possible, work through them in timed conditions when you have revised through most topics, so you are not caught out by the timed conditions when it comes to the actual exam.

**In your revision, try everything **

When trying questions you may not always feel confident enough to create a plan from the outset. A common source of this issue is that although you might feel like you have the knowledge required, you may be unsure of how to apply it when approaching a question. Often, this means you won’t attempt the question. Instead, draw upon your knowledge and try to find out whatever you can with it. For example, in a question about straight-line graphs where you receive two coordinates on a line, you know you can always work out the equation of the line by using y=mx+c. If you receive two points in a question and you are not sure where to start, why not start here? An excellent resource to help with this is Goal Free Problems, where you are tasked to find out whatever information you can with the information you have available in the question, rather than simply a specific answer.

## How do you get a 9 in GCSE Maths?

As well as doing the above and working really hard with your revision, here are some additional pointers which may help you score the top mark:

**Remember to include base topics in your revision **It is all too easy to forget about the topics covered in school during year 8 and year 9, as well as the easier topics at GCSE, but these topics serve the basis for a lot of 9 level questions that you will encounter at GCSE. For example, you will not be able to solve a level 9 question involving solving equations without knowing how to simplify added terms first. On top of this, neglecting topics that you think are easier in your revision may mean you are caught out in the exam, so although there is something to be said for prioritising time in revision, make sure not to neglect where you believe your strengths to be.

**Embrace failure **If you make a mistake while doing any practice for GCSE Maths, do not worry about it! This is what revision is for - making mistakes and then learning to correct them. Correcting mistakes means you are generally learning something new, so note down what the issue was and then try to apply it in your questions going forwards.

**In the actual exam, prioritise your time **In the actual exam, if you find a question you are unsure of, leave it and come back to it at the end. Once you have attempted all the questions you feel confident in, you can come back to the questions you are unsure of and use some of the techniques you learnt doing goal-free problems to see if you can apply your knowledge and find a solution!

## Findings from past examiners reports

Pre-Covid, examiners released reports talking about how well students got on in that year’s

exams and highlighting common mistakes that were made. Given these examiners are the

ones who make the exams, we should probably pay attention to what they have to say!

We trawled through these examiners’ reports, as well as past exams, to put together a list of

the top 10 areas that students often stumble on. Sorting these out is sure to give you a great

head start on revision and help you feel much more confident in your GCSE maths skills.

**Significant Figures**

You’d be hard pressed to find a GCSE maths paper that doesn’t ask you to round at least one answer, so brushing up on this topic is sure to help net you a few easy marks in an exam. Most students are able to round to a given number of significant figures but still manage to fall into a few traps.

The most common mistake is students not rounding to the number of significant figures that the question tells them to. This won’t be the first time you’ve heard this advice but

always read the question!

The other common mistake students make is rounding their workings before their end answer. You should only be rounding answers right at the end of your working and never in the middle. Until the end of the question, it’s better to work in fractions instead of decimals to avoid this.

**2. Using Your Calculator**

Given how much students seem to loathe being parted from their calculators it’s always a surprise to see how many students can’t use them!

Take some time to learn the secret workings of your calculator. Try and be familiar with where all the buttons you usually need are and find out what those other mysterious buttons that you’ve never pressed do – some of them might be really handy! Learning how to use the memory and the ANS button can save a lot of time and effort in a bunch of questions – and in particular initeration questions.

**3. Percentages**

Speaking of calculators, examiners’ feedback year on year is that students aren’t comfortable with dealing with percentages on their calculators. Examiners always mention that many students will use non-calculator methods when dealing with percentages even on calculator papers. Not only will this waste your time in an exam, but it will mean there’s more opportunity for mistakes to creep into your work using a longer method relying more on your mental maths than on the calculator. So, make sure you’re up to scratch on calculating percentages using a decimal approach or a multiplier approach. Knowing that method inside-out will also help with dealing with those tricky inverse percentage questions that everyone hates!

**4. Bounds**

This seems to be one of those topics that students manage to trick their teachers into thinking that they understand, but actually are more than a little bit clueless! It can be easy to learn and apply the process of finding upper and lower bounds, but GCSE maths needs more from you than just repeating a process. GCSE maths needs you to actually understand what you’re doing and know what upper and lower bounds actually mean. Specifically, GCSE maths needs you to be able to decide which particular bound to use in some particular context. Sometimes, GCSE maths even needs you to even explain why you choose that particular bound in that particular context. To make sure you can cater to all of GCSE maths’ many needs, take some time to fully understand what upper and lower bounds are and try some practice questions to work out how to think through deciding which is correct.

**5. Trial and Error**

Ah, trial and error. It used to be so useful. Alas, as of 2015, trial and error has been struck from the GCSE maths course. Unfortunately, many students seem to have not got the message and still try and use it liberally throughout their GCSE maths exams. On the surface this isn’t a problem, but with a little bit of digging we can see that it’s definitely time for you ditch trial and error too. Since trial and error is a valid method, if you use it to correctly get an answer you will still get full marks. However, since it isn’t part of the GCSE maths course if you don’t get the correct answer you won’t be awarded any of those precious workings marks that your teachers are always banging on about. On top of that, trial and error is a notoriously slow method and in all honesty is quite difficult to use correctly. You might not be too sure how to answer some questions without trial and error, but the solution 99% of the time is a little bit of thinking and a little bit of algebra. Practice turning word questions into algebraic sentences and you’ll soon be wondering why you ever needed trial and error in the first place!

**6. Know your formulae**

GCSE maths is more about thinking and understanding, not just memorising a bunch of information. But you do need to learn a few things – mainly formulae. There aren’t too many but knowing them is crucial. How are you going to calculate the area of a circle if you can’t remember the formula to calculate the area of a circle? Find out which formulae you need to learn and which will be provided in an exam. Don’t forget to learn what all the various symbols and letters mean too!

**7. Dealing with 3D problems**

Trigonometry is hard enough when it’s just inside a triangle. Unfortunately for you, GCSE maths also tests trigonometry inside 3D shapes. Students often find these types of questions really confusing and the diagrams that GCSE maths provides to try and help students out just confuses them more. A really helpful approach is to practice lots of these types of questions with a model. Get a bit crafty and build some cuboids and triangular prisms out of pipe cleaners and use these to help work exactly what lengths and angles you’re trying to calculate. Of course, you can’t take pipe cleaner models into your GCSE maths exams, but practicing with them helps you build up the visualisation skills you need to be able to answer questions without them.

**8. Forgotten Topics**

Since GCSE maths manages to pack in so much maths, students will usually spend 2 or more years studying it in school before they face their final exams. This can mean that you haven’t even thought about a topic for two whole years when it suddenly crops up in your GCSE maths exam. Examiners often say in their reports that students fall short of top grades because they just don’t know enough topics! Topics that are often studied at the start of Year 10 (or sometimes even in Year 9!) include angles in polygons, converting recurring decimals into fractions, and dealing with fractions without your helpful calculator.

These topics usually aren’t the most difficult but you don’t want the first time you’ve seen them in two years to be during your GCSE maths exam. So, make sure that you brush up on those ancient topics that have been gathering dust in the back of your

mind to maximise your chances of getting the highest grades.

**9. Algebraic Fraction**

Algebraic fractions are one of the most complicated maths objects that you have to deal with in GCSE maths. They often mix together topics like factorising, simplifying, surds and solving equations all wrapped up in a fraction – nightmare! However, there is one particular part of dealing with algebraic fractions that GCSE examiners say students especially struggle with and that is cancelling. Students like things to look simpler (which is a great mathematical instinct!) but sometimes in their eagerness to simplify they cancel things which they actually can’t. In an algebraic fraction you can only cancel factors from the numerator and denominator if that factor is in every term. This means you definitely can’t cross out that x2 in the numerator and denominator because there isn’t an x2 factor for every term! Make sure you really understand how you cancel factors in algebraic fractions to make sure you don’t make the same mistake.

**10. Organised workings**

The last tip in the list is a bit cliché but examiners highlight it as something that separates the students that get top grades from those that don’t nearly every year. Making sure that your workings are clearly organised won’t just make it easier for

the examiner to mark (gaining you more of those precious workings marks) but will make it easier for you follow too. Sometimes students will get so lost in their own messy workings when trying to solve particularly tricky questions that they confuse themselves to the point that they can’t answer the question! Try and follow a few simple rules to make your workings that extra bit neater: always work down the page, only ever have one equals sign on a line, and label calculations in plain old English so you know what it is you are trying to calculate.

And there it is! 10 areas that the examiners themselves say you should look into to get a leg-up on the competition. If you find that you’re struggling in any of these areas then the internet is your friend. In a few clicks you can find videos on all these topics and more. But if you need a more personal approach then one-on-one tutoring is a fast and effective way to help you with any GCSE maths topics you might be struggling on.

Don’t hesitate to get in touch and learn about our excellent GCSE maths tutors and courses!

## GCSE and IGCSE Maths Tuition

With tutors based in London and available online to families around the world, Keystone is one of the UK’s leading private tutoring organisations. Find out more about our GCSE Maths Tutors and our IGCSE Maths Tutors.