I thought I would take this opportunity to pass on some advice for GCSE and A-Level Mathematics students and, to a certain extent, any mathematics students.

I suppose the big question that everyone wants to ask when they’re preparing for exams is something along the lines of, “How can I do well in my Maths exams?” So here’s some things that I think are important in order for you to do well in your Maths exams. These are written in no particular order but just as they come to me.

  1. Give yourself time to find a solution to a problem. Sometimes this might be 20 minutes, half an hour or even an hour. I know you don’t have this time to spare in an exam but you’re NOT in the exam now! You have to learn to solve problems and you have to start slowly like anything else. Sometimes problems take time to solve – the solutions don’t just leap out of the page at you. Be prepared to work hard for a solution.
  2. Don’t be overly reliant on a calculator. Yes I realise that you can use a calculator in your exam but, I’ve already said it once and I’ll say it again, you’re NOT in the exam now. If you jump on the calculator at each and every opportunity then you will not develop the understanding that you need in the same way that you can’t learn to play a musical instrument by getting someone else to play it for you.
  3. Don’t be overly reliant on mark-schemes and ‘the answers in the back of the book’. You need to learn to determine for yourself whether your solutions are correct. This will develop your understanding and build your confidence. If you can see for yourself that something is correct then you know you have the marks in the bag. Try solving the same problem in different ways to see if you arrive at the same answer – if so, then you probably have the right answer. If not, try to figure out what’s gone wrong yourself.
  4. Challenge yourself. You may be fantastic at using the cosine rule and you might be able to solve quadratic equation like nobody’s business but are you prepared to combine these, or indeed any combination of ‘topics’ in the same problem? If not then you may not be challenging yourself. It is better to spend an hour working hard to solve a single problem than to spend that hour factorising oodles of quadratics or doing some other repetitive ‘type of problem’.
  5. Be interested in the subject. Unfortunately this is something that you can’t really fake – either you are interested in maths or you’re not. If you’re not then you will have to either try to get interested or accept that things are just going to be more difficult for you. Sometimes you get interested in something by accident (like I did with mathematics) – just be open-minded. Enjoy the subject!
  6. Don’t be afraid to go beyond the specification. Sometimes people will happily scour a specification and spend a couple of hours coming up with a reason why they don’t need to learn something. And yet, it would only have taken them 15 minutes to learn it! The thing is, learning something beyond the specification might help you understand things more clearly – so even though it’s not expected knowledge, sometimes it still comes in very useful.
  7. Concentrate on solutions. Mathematics is NOT about just writing the correct number or expression somewhere on the page – an answer without a valid solution is absolutely worthless. You need to concentrate on your solutions and make sure you understand how the parts fit together. If you understand this then the correct answers will naturally follow. If you’re ONLY interested in the answers then I suggest that you simply copy out the answers from the mark scheme or textbook that you’re using.
  8. Don’t just learn to copy someone else’s solutions. Your teacher will give you worked examples. Your textbook will contain worked examples. DO NOT try to learn these solutions as simply a series of bullet-point steps. Learn to understand the solutions and why they work – you will find that your workload drops significantly!
  9. Take your mind off the exam. Yes you will have exams – but if everything you learn is motivated purely by the fact that you have an exam then your learning will end up being laborious and very inefficient. Be more concerned with just ‘problem solving’ – solving challenging problems on a regular basis. If you do this then you will automatically learn the skills that you need for your exam and you may just need a bit of fine-tuning nearer the exam period.
  10. Work hard. If you want to do well then YOU will have to work hard. How hard depends on all sorts of things but don’t try to dodge the hard work. Working hard doesn’t necessarily mean working looooong into the night (although it might) but using your time wisely. It is both quality AND quantity to a certain degree, but quality ALWAYS trumps quantity. There are no guarantees that you will ace your exams – but you can give yourself much more certainty by working hard!

So that’s it for now – I hope that you find something useful here. There are loads of other things that I could add to the list but I’ll leave thode for now; I think these are the main points that I want to make right now. I would love to hear from other people what their advice is on doing well. Good luck with your learning over the coming year!

Over the last couple of months I have been working hard to make and upload quite a number of videos to Youtube. Some of the videos that I have uploaded cover some GCSE Maths topics – the above link is to a playlist on my Youtube channel of all of my GCSE Maths tutorial videos.

These videos cover a range of topics including finding the $n^{th}$ term of quadratic sequences, solving inequalities, transformations of graphs and many other topics. These videos have often been made with the intention of clarifying often overlooked aspects of GCSE Mathematics and sometimes extend slightly beyond the GCSE Maths specification but that’s not to say that the content of the videos is not understandable to GCSE Maths students – I am careful to explain (in language that a GCSE maths student can understand) WHY things work the way they do rather than just HOW to do something. So for example – WHY is the number in front of $n^{2}$ in the $n^{th}$ term of a quadratic sequence equal to half of the second difference of the sequence? The answer to this question is provided in my video on quadratic sequences. WHY does the transformation $f(x-a)$ represent a translation of $f(x)$ in the $x$-direction? You can find out by watching my videos on transformations of graphs.

I am uploading new videos every week to my Youtube channel and I encourage you to watch some of my videos if you need help with your GCSE maths. If there are any topics that you need help with and you would like me to make a video on it then please let me know and, IF I feel that I have something original to contribute rather than just repeating something that is already out there and been done-to-death by dozens of others, then I will make a video on that topic.

This is a video that I made recently which brings together some of what I’ve learned through my time as a professional maths tutor in Leeds tutoring GCSE maths students. I’ve noticed that each year there are a similar set of problems that many GCSE maths students will have to deal with so hopefully this video will give you a bit of advice about how you could avoid some of the pitfalls that some students end up falling into and how you can become a much more successful GCSE maths student that can go on to ace your GCSE maths exams!

The video is more about your habits and attitudes to maths as a subject and isn’t just a list of topics to revise and shortcut methods or anything like that. I do mention a couple of important topics that I think every GCSE maths students needs to know but there are so many videos and resources out there that cover the individual topics that there wasn’t really anything new that I could add – everything is already out there. What I certainly did think that I could add were my unique personal experiences as a tutor!

I’ve tutored lots of GCSE maths students – particularly for GCSE higher level – over the last half a decade and I’ve got some real insight into the things that trip students up. Working one to one with people means that I can really find out how they work, their strengths, weaknesses and what really causes them problems when it comes to GCSE maths.

I hope that this video will be useful to you. I plan to do some more videos on A Level maths and QTS Numeracy over the coming weeks – so keep an eye out for those. If you have any questions for me about your GCSE maths studies then just get in touch – I will get back to you as soon as I can with any answers that I can give.