How to get a 9 in GCSE Maths

I am often asked how to go about getting a 9 in GCSE Maths and in this article I will give you tips and tricks that will help you to achieve this demanding goal. After graduating from Oxford with a PhD in Mathematics, I went on to spend ten years teaching top sets at both GCSE and A Level, specialising in getting able students from a grade 7 to a grade 9. These high grade boundaries are my comfort zone and in this article I am going to share my advice for anyone looking to bridge this considerable gap.

Top ten tips and tricks for a grade 9 in GCSE maths

To get a grade 9 in GCSE maths you basically need to answer every question on the paper correctly (or at least that is what you should aim for, as we never really know where the grade boundaries will lie). Here are my top tips and tricks for achieving full marks.

1. Get good at graphs

I find that a lot of able mathematicians prefer doing algebra to sketching or plotting graphs, as graphs take more effort. Yet graphs will always come up as big questions with lots of marks available, and often with a hard part at the end. My advice is to concentrate on bringing your graph skills up to the same level as your algebra skills. I would expect a grade 9 student to be able to predict the shape of a curve from its equation before even sketching it, knowing details such as positive and negative shapes, x- and y-intercepts and any standard symmetries (especially for the Trigonometric Graphs). 

2. Develop a sense for disaster points

If I see a big question with multiple parts that add up to lots of marks, I think of my first few lines of working as potential disaster points – if they go wrong, the whole question comes tumbling down. For example, even the slightest misread of 'y is inversely proportional to the cube of x' could lead to a massive loss of marks (and don’t assume any errors will be carried forward). When I used to set tests in class, I could see the grade 9 students slowing down at these points, triple checking, rereading the question again and again, appreciating how crucial it is to get these bits right. A grade 7 student, however, might race through these bits (often saying they are the easy parts), without realising just how important they are!

3. Find more space and start again

When you get stuck in a calculation, it is natural to scan back up your working to look for the error. I see students trying to edit their old incorrect working by writing over it with new signs, new numbers and so on, hoping that this will lead to the right answer. However, a grade 9 student knows that the entire structure of a solution, including any choices made along the way, can all change completely if a small error is detected near the beginning. So, my advice is to leave the incorrect working to one side and find a completely new space on the page to redo the solution; that way you won’t get subconsciously swept back into making the same mistake as before. 

4. Don’t underestimate the last line of algebra

Some of the hardest questions in algebra are not due to beginnings or middles, but due to their ends. For example, if a question asks you to show that a formula rearranges into a particular form, a grade 8 student might reach a different but correct form, then think that they are wrong; they cannot see how to make theirs look like the one in the question. The hardest part is that last line of algebra and this is where grade 9 students should concentrate. Some of my favourite grade 9 skills here include simplifying Algebraic Fractions, simplifying expressions under square-root signs, rewriting negative fractional indices as roots and Completing the Square for harder quadratics. 

5. Test your answers

There are some areas of maths where there is no excuse to get it wrong! For example, it is very easy to test if your solutions to a pair of Simultaneous Equations are correct: just substitute them back into the original equations. Most students know this, of course, but in my experience grade 7 students often don’t put in that last bit of effort to do the check (they are just relieved to have reached a final answer, or are sometimes too scared to find out!). I find that grade 9 students will always check their answers, often by reversing operations; for example, in a question on Factorisation they would expand their answer to check. A trick I like to use for checking expressions or formulae is to substitute numbers into the original question then substitute those same numbers into my answer to see if they agree.

6. Don’t play it too safe

I would say that one of the biggest barriers stopping grade 8 students from becoming a 9 is that they have played it too safe for too long; they have learnt the syllabus back-to-front, done all the past papers and can perform all the required methods very well. And they will do well, as long as the questions in their exam are similar to ones they have seen before (anything else, they would say, is 'unfair'). But how do you prepare for unfamiliar questions? Being challenged under time pressure is stressful for anyone, so my advice is to train yourself to experience the frustration of being properly stuck. Find harder resources to challenge yourself, such as the free Intermediate Maths Challenge papers from the UK Maths Trust, or notes and questions from courses such as AQA GCSE Further Maths. I would always prefer a student to work through one really hard problem-solving question than do 20 questions they were comfortable with.

7. Tick through the official specification

I used to give my students copies of the official specification from the exam board (such as Edexcel GCSE Maths) so they could go through it and cross off each bullet point when they had mastered it. I advise anyone who is serious about getting a grade 9 to do this; you stumble upon parts of the syllabus that you did not know existed (perhaps a topic you were taught a few years ago, or perhaps an unfamiliar bullet point on the end of a familiar topic). Go to your teacher to have these explained! I used to offer free drop-in sessions at break times and often saw grade 9 students asking about specific bullet points; they wanted to know that they had covered everything. Knowing the official syllabus is also my way of teaching students how to Form Equations from contexts. First, you read through the question, then you decide which part of the specification it is from, then you ask yourself which formulae are in that part, then you use those to create an equation. You can also find the official formulae sheets online to see what you are given in the exam. (I have seen very able students lose marks because they didn’t learn the formula for density!)

8. Dont cheat, but do use model solutions

It is very easy to skip over questions you cannot do, or check the answers while doing a question, then say to yourself, 'yes, I could have done that'. This only moves you further away from a grade 9, not closer towards it. When you get stuck on a question, go and find a well-presented model solution from that topic (such as the worked examples in our Revision Notes) where you can see all the stages clearly, then cover up that model solution and completely redo it yourself to see if you get the same answer. Similarly, it is very easy to revise from a past paper with its mark scheme open in front of you, but try to move away from this as quickly as possible; it is making you believe that you know more of the course than you actually do. Instead, I recommend doing blocks of at least five questions in one go, and then double-checking that your solutions are exam-ready before looking up any answers. 

9. Don’t rush your explanations

Surprisingly, I see a lot of grade 9 students losing 1 or 2 marks from simple explanation questions in the middle of the paper, rather than the harder questions at the end of the paper. There will always be a few marks dedicated to some sort of explanation, for example commenting on a diagram, determining where a solution has gone wrong, describing trends in some data or commenting on a mathematical model. This is where I would ask potential grade 9 students to slow down and think about what the exam writers are trying to test. My advice is to give a thorough mathematical answer that includes numbers from the question, relevant mathematical vocabulary and a spoon-fed conclusion in full sentences (copying the exact phrases from the question).

10. Learn off by heart

If I were to recommend three topics to learn off by heart to get you closer to a grade 9, I would say all the Circle Theorems, all the Graph Transformations and all the Exact Trigonometric Values. These are actually relatively straightforward to learn, but are seen as hard topics because most students only learn them a few weeks before the exam!

Summary

So, how do you go about getting a 9 in GCSE maths? By incorporating all the advice above, as well as doing your regular Past Paper practice and schoolwork. The more you push yourself out of your comfort zone by doing harder questions (without skipping to the answer), the better you will become. Good luck with your journey to the highest grade boundary!