Working through past Mathematics papers is an essential part of revising for exams. But how can you make sure that such practice improves your ability to answer exam questions? It is, of course, helpful to have the answers, preferably worked answers, so that you can check your progress, but just looking at the answers will not in itself improve your skills very much.
When you first start working through papers, I suggest that you have lots of resources available to help you when you get stuck: these will include notes, textbooks, internet searches and so on. By doing your own research you will learn and remember much better. Does this include working through papers with a friend? No problem: sharing revision time makes it a more enjoyable activity. But do beware of simply relying on someone else to do all the work: if it isn’t your brain that’s processing the questions, then you’re wasting your time. Later on, use the resources less and start working to time.
Working through questions should also alert you to those parts of the syllabus which require further revision – make notes of what you need to go back to so you don’t forget.
But what should you do if you still hit an impenetrable barrier, or if you just can’t see your way to the right answer? Make a note of the question, and make sure that when your teacher – or really bright mathematician friend! – is available, you ask them what the solution is. And take notes of what to do. Then, when you face a similar question, you should be able to find your way through the blockage.
So, apart from “blockages” what else can go wrong when you’re answering exam questions?
a) You didn’t read the question properly. This can lead to not answering exactly what was asked; missing parts of questions; putting the wrong information into formulae; doing more than necessary. The solution is simple. Read every word in the question, highlighting words or phrases that are important. Read right through the question if it’s a longer one – later parts may give clues to earlier parts. And, essentially, always check through your answers to ensure they match the question.
In longer questions, you will find that quite often you use the answer from an earlier part in a later one – be alert for this, because if you don’t spot it, you find you can’t go any further.
b) You think you’ve done everything right, but you’ve got the wrong answer. Maths is about detail: a misplaced minus sign, an incorrect expansion of a bracket, the wrong order of operations solving an equation, substituting incorrectly into a formula – one slip, and everything goes wrong. Check, check, check again. And, as with all your Maths revision, write down everything you learn so you can read through the list later and change the way your brain is operating!
I’ve written a book as part of the OSC Revision Guides series called Section B: Analysis and Practice of Long Answer Questions. The examples are all taken from the SL syllabus, but the techniques are equally applicable to HL and SL. I hope you might find it helpful.
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Ian is a Maths teacher with nearly 40 years’ experience. He has been involved with IB teaching from its earliest days. He is a regular teacher at OSC Spring Revision Courses and Summer Schools.