I never really learned how to revise for a maths exam at school. I’m sure people tried to teach me, but I generally wound up reading passively through my notes, maybe copying them out, and possibly writing big question marks on them in highlighter.

It worked ok for me, at least until a disastrous second-year exam at uni where I suddenly discovered that I didn’t know all the things I’d read. If you really want to get on top of material, you need to engage with it – you learn more from a conversation than from a lecture.

Here are a few ways I recommend:

You know what a textbook is, don’t you? It’s where teachers find you questions for homework.

Well… partly. But there’s more to it than that. Your textbook is full of explanations and worked examples you can follow, study and use to improve your understanding. It’s generally a good idea to find a topic you need help with, read through the explanation (looking up anything you don’t understand), before following along with the examples – I advocate copying them out – and tackling the questions at the end of the section to see how well you’ve taken it on board.

Probably 80% of what I do with students in class is based on past papers. If you want to do well in a test, it’s just common sense to figure out what the test looks like, what kinds of things you may be asked, how the questions are worded… and, by tackling the questions, see how you’re doing and where you need to do some extra work.

When you get something wrong, it’s worth trying to figure out why – I know it’s frustrating, and mark schemes aren’t meant as educational tools, but by trying to see where you went wrong, you can avoid making the same mistake next time.

(Also, you can drop me a message if you’re baffled about why a particular past paper question was wrong – I’ll get back to you as soon as I can make time.)

One of my favourite explanations of why maths tutoring works so well is that you learn more from a conversation than you do from a lecture. The thing is, though, you can can get almost the same benefit by having a conversation with other students. (Obviously, you don’t get quite so many immediate explanations, and the quality of comedy probably suffers, but it’s a pretty effective substitute).

The reason it still works is that two (or more) heads are better than one – the chances of everyone in your group having precisely the same strengths is very small indeed, so there will be places they can explain to you, just as there will be places you can explain to them. Frequently, there will be questions where one of you can see how to start and someone else will see how to finish – between you, you figure the whole thing out.

You may not have conveniently located mathematical friends to set up a study group, but you can still get some of the benefits of explaining things. One of the most effective ways to learn a new skill is to write down the steps you have to take – either as a list or as a flowchart.

The key is to make everything as detailed as possible – imagine you’re explaining it to an idiot, such as a parent or a younger sibling. You use a different part of your brain when you’re explaining things than when you’re reading or listening.

Flash cards, for some reason, are much less popular in the UK than in America. It’s actually quite hard to get hold of reasonably-priced index cards over here (it’s galling to pay Β£2 for something that costs about 20p in the States), but you can make flash cards out of sheets of paper easily enough. Just fold the paper in half, in half again, and in half again, then cut along the creases – presto, eight cards. You can make more as and when you need them.

The way they work is, you write a question or a prompt on one side (for instance, “What is the derivative of $\cos(2x)$?”) and the answer on the other (“$-2 \sin(2x)$”). You make a big pile of cards with everything you want to learn on it, and leaf through them one at a time. If you get the answer right, put that card to one side; if you get it wrong, put it to the back of the pile.

A student of mine took this one step further and taped flash cards to every door in her house – if she wanted to go through a door, she had to answer the question first. She got two A*s in Further Maths. Just saying.

A cheat sheet is just a big bit of paper with everything you could possibly want to know about written on it. For instance, a GCSE maths cheat sheet might have instructions on how to solve triangles, all of the stupid vocab words you need to remember, a few of the common mistakes that everyone makes…

Make it as fun as possible – drawing pictures or sticking on photos helps you remember things later on (“Oh! quadratic equations! They’re next to the picture of Stewart Lee!”) – and spend the last few minutes before your exam poring over it, to get as much of it as possible into your short-term memory.

Google. “[My topic] revision games.” Any questions?

If you’ve tried doing questions and just can’t see why they’re not working out, ask someone – a teacher, a friend, or even me. I’m colin@flyingcoloursmaths.co.uk – or you can ask in the comments below.

I’m most likely to reply if you give me details of what you’ve tried and where you got to (and if you give me permission to write about it on this ‘ere blog).

Meanwhile… what are you revising right now? And what are your best tips for someone who wants to revise for a maths exam?

(Picture by scubasteveo used under a Creative Commons CC-BY licence).

* Comments closed 2016-10-03.

Thanks 4 da best tips.I will surely practise them

Thank you so much for this. These techniques make so much more sense!

well.. i have an important exam tomorrow. thanks for the tips. tho i don’t quite understand number 6.

The idea of a cheat sheet is to write down the things you want to remember, and read it through right before the exam – just to help you remember them in the test. Good luck!

heyy! i got my results back. my previous exam, i did really badly. and by doing your methods, i improved by 24 marks! i feel happy about it. i will totally do your methods again for my final exam. THANK YOU VERY MUCH. π

DUDE! Way to go π When you do the right work, you get good results – keep it up. (And thank you for making my day!)

well, the flash cards really helped me a lot . π and i’ll surely practice the others too.

Dear Professor,

I’d like to ask that there is some confusing questions in my math textbooks. There is one question asking to estimate the answers to the following maths problems but it doesn’t said whether we need to round the numbers to decimal places, significant figures. Therefore I’d like to ask for these type of questions, we use our common sense to solve it or is there any tips behind the questions?

Kind regard!

Good question! I’ll write something up and drop you an email.

i want to study maths

Good! Do :o)

Dear Colin,

I’ve never been good at maths and when it came to exams I never bothered to revise. But I have a serious exam coming up and I’d like to come out with a B, but it seems like every time I try and revise maths I feel seriously overwhelmed, have a mini panic attack and I am put of doing revision for other subjects.

Any advice?

Hiya, great question – and probably better suited to a blog post response than a comment. (I’ll do that, although it’ll be too late to be much use to you).

Meanwhile, way to go for deciding to take it seriously this time! Here’s what I suggest:

* break down what you want to learn, and put limits on it – “I’m going to take 20 minutes and see how far I get through this exercise – then I’ll do something else.”

* be nice to yourself. Don’t say “I’m no good at maths,” say “I haven’t got this yet, but I’m on it.”

* breathe. If you’re panicking, sit up straight, breathe deeply, take a little walk if you need to. It’s tough to revise if you’re panicking, so learn to spot the signs and step away.

Hope that helps – and good luck!

Thank you! Will try today.

Thank you for your tips! They are very much appreciated and they are slowly starting to work

Awesome! Keep up the good work π

Thanks for the great tips! π

Although, I am struggling to find a website that has questions on the higher tier paper for applications of mathematics (edexcel). I tried edexcel as it is the exam board but you need a login for it and i haven’t got one. Please help. :/

That’s a great question, Sami – I found a bundle here: https://glynmathsgcse.wikispaces.com/Applications+in+Mathematics (I googled “applications of mathematics” edexcel calculator tracing, reasoning that papers always say something about tracing paper.)

this is absoloutley wonderful. this has helped both me and my friends for revsion. im usually really really bad at maths and this has helped to gain more confidence over it. it has been around 3 weeks and im already seeing some improvements in myself. I really like how the methods re teenager friendly and are not hard to do. thank you very very much

*high five* π

Thanks for letting me know how you’re getting on – really happy it’s helping. Keep up the good work!

I am weak in maths..But i will use this method to inprove myself……Thanks..

Just for you, I’ll add a tip number 8: try to avoid saying “I’m weak in maths” – say “I’m getting better” or “I’m working hard.” The more positively you can frame things, the more likely you are to improve. That’s why you never hear athletes saying “We’re totally going to lose this important game” – it’s because they know that saying that would make it harder to win!

Keep working hard – you can do it!

Hi can you help meee this is my year for GCSE’S and I am really crap at maths any tips for me

First tip: stop saying you’re really crap at maths. That’s a self-fulfilling prophesy. Other than that, make a plan and study hard. Good luck!

i have a math test coming up soon. Those tips are really helpful. Wish me good luck π

Glad you found them handy — best of luck π

I got 13/25

Pls help me

I am in igcse

You might want to have a look here: http://www.flyingcoloursmaths.co.uk/ask-help/ and try again.

I have a very important exam coming I don’t know what to and I fail 3 times in maths plz help me

Hello,

I have two main suggestions: first, read this article about how to ask effectively for help; secondly, read through this article and the comments above yours for my best advice.

Good luck!

thanx alot

Hi I am gone to find some these useful as I already practise math papers in class and at home and I will find these useful as my exam is coming up now and starting panic a little.

Stay calm, you’re doing the right things π Good luck!

Hello Colin, do you have any tips on how can i do my revision? I’m left 3 days before my maths exam. Please help me.

I suggest that reading the eight tips in the article would be a good start! Good luck π

alright professor! thanks π

Is it more beneficial to ‘do’ Mathematics rather than ‘remember’ Mathematics? As in doing practice questions, tackling past papers rather than remembering the concepts/formulas etc.

Thanks much.

That’s a really good question! I don’t think it’s an either-or thing: if you’re learning a musical instrument, you do a mixture of theory, scales and pieces. If you’re learning maths, it’s much the same thing — to be good, you need to understand the theory, practise the techniques, and see how they work in application. Doing any one to the exclusion of the others will limit your mathematical development.

Alright, thanks for the reply. π

I will keep that in mind.

These tips are amazing!! Okay, soim predicted an A for my maths gcse but barely know the D C or B topics. It takes me a while to grasp concepts and ive already got the maths revision guide, maths watch cd for c-g topics, plus the higher one (c-A*). Maths is a progressive subject so im under alot of pressure to learn all this content so i can start learning b and A topicss. HOW SHALL I GO ABOUT IT? And do you thinks its possible to refresh so many topics in such a space of time? TYSM

Hello,

It’s quite possible to get the D-C-B material revised quite quickly if you put your mind to it. I’d start by looking through the first halves of past papers and keeping track of what you find tricky.

I’d also recommend getting a notebook to write down the tricks you miss — when someone tells you about an easier way to do something, make a note of it. Look in the notebook when you’re stuck.

Good luck!

Why did you swear this is not appropite to kids

Dear Holly,

Why did I swear? Because it was the most appropriate word for me to use in that place, for my audience. You are welcome to disagree, but here’s the thing: this is

themost popular article on the whole website. If it wasn’t right for my audience, that wouldn’t be the case.So, thank you for your concern, but I’ll be the judge of what’s appropriate for the people I’m writing to, and they’ll be the judge of whether they read it.

Meanwhile, why did you misspell ‘appropriate’, and why didn’t you punctuate your comment? That’s not polite in any context.

i dont really know what to do but ill try thanks for the encouragement btw im a gcse student will try hard .)

Sir thanx for the suggestion its really work for me

Hi Colin !

You dont know how much this post encouraged me to try even harder!

I have failed maths in my both tries but of course im not going to give up but i was having a hard time telling my self i will be able to score an A or B in the upcoming IGCSE maths exam in may/june session so to convince my self i needed something like these tips!

They are extremely helpful, although i did not start applying them yet but it gives me the spark of encouragement that makes me sure that it will lead me to success !

Thank you so much for spending your time in writing these articles to help us students to succeed π

My best regards!

Thanks for letting me know, Lina! Good luck with the exams.

Thank you so much for this!! Every other ‘how to study for a maths test’ website was just like “attend every class, ask the teacher for help, read the text book” which is bloody useless! You actually gave useful, tangible things that actually told us ‘how’ to study for a maths exam, thank you again, this was so so so helpful!

I’m glad it was helpful — good luck!

Any Advice for a 45 year old Dummy that struggles with maths I am taking the big step of trying to gain this GCSE in maths later in life I did struggle with it a school and was always in the bottom groups at school are there any websites that can help me with my problem I do suspect I have dyslexia that was never diagnosed as did struggle with some elements at school..

The purpose is I would like to have a career change that will involve me going to University I cannot even get in the door without GCSE Maths .

Hi, James! First up, way to go for getting back into the maths saddle!

The GCSE Bitesize site would be my first port of call — it has explanations of all of the topics and examples for you to work through.

Best of luck with your exam — and with your career change!

Thanks alot for your help but what should I do because few months from now am gona sit for my UNEB final exams

Please help me

I think the advice above and in the comments here apply to pretty much any maths exam! Good luck :o)

Thank you very much MR Colin, I have learned good things from you to improve my maths. I am very good at class I get my work done it easy. when it come to exam I revise but not probably. I am going to give a go and see how it goes.

Good luck, Ahmed!

I have a maths test tommorow and im supposed to get a b grade. Im in year 8 and im really struggling to get there and its kinda stressing me out, any advice ?

I suggest following the advice in the post above and in the other comments. Good luck!

I have a question. Suppose that I have studied all chapters of my maths book. Just before 1 or 2 days of exam, it is impossible to practise each and every question. So, what should be my strategy to cover every question just before 1 day of exam?

Hi, Anup,

If you’ve covered everything in the book, I’d recommend finding a past paper via Google and working through that. That’ll help you practise a range of questions on different topics, with different difficulties. Good luck!

Hi Colin, I kind of need help with a maths question, how do you multiply fractions with mixed numbers?

Hello! Two possible ways I’d recommend to work out something like $3 \frac{1}{7} \times 2 \frac{2}{3}$:

First option, turn them both into improper (top-heavy) fractions: $3\frac{1}{7} = \frac{22}{7}$ and $2 \frac{2}{3} = \frac{8}{3}$. You can then multiply as normal to get $\frac{22 \times 8}{7 \times 3} = \frac{176}{21}$. You could turn that back into a mixed number (it’s $8 \frac{8}{21}$).

Second option, which I don’t recommend so strongly, is to treat the mixed number like a bracket: $3\frac{1}{7} \times 2 \frac{2}{3}$ is the same thing as $\left(3 + \frac{1}{7}\right)\left(2 + \frac{2}{3}\right)$. You can expand this like you would with algebraic factors to get $6 + \frac{2}{7} + 2 + \frac{2}{21} = 8 + \frac[8}{21}$, but I don’t think that saves any work.

I wana learn maths too

Er… good! Do.

Hi, how do you stop making silly mistakes? Please write it on your ‘ere blog! I keep making them and it’s really annoying.

I am already confident of getting an A* in my GCSEs but I want to be top of my class and year and I want to do my A level and my Uni degree early. I know my stuff but I can’t apply my knowledge to the problem, especially the weirdly worded ones. Could you please give me some tips for those?

I go to the best grammar school in the UK by the way, and I’m top set everything, so I’m not totally dumb.

* This comment was edited (ironically) for spelling and grammar.

Hi, Kim,

I’ve got a blog post about silly mistakes already here: http://www.flyingcoloursmaths.co.uk/can-avoid-mistakes/ — you might also find my book on Exam Technique ( http://bit.ly/examtechnique ) useful.

As for ‘weirdly worded questions’, I don’t know what you mean. I know that a lot of my students use it as a code for ‘I can’t be bothered to read and think’, which is why I listed it as an excuse that needs to die here: http://www.flyingcoloursmaths.co.uk/attack-of-the-mathematical-zombies-five-excuses-that-need-a-bullet-to-the-head/

Good luck with your studies!