Don’t Lose Marks Unnecessarily in Your Maths Exams

There is statistical evidence that 1 in 7 of you will lose marks which you shouldn’t lose: in other words, there could be marks which you could easily gain, even if you can’t answer a question, but what you put on paper didn’t match the examiner’s mark scheme.

It’s unlikely you’re going to get 100%. Some questions you just can’t see what to do; some you think you can do, but you get the wrong answer; or you run out of time and don’t answer all the questions. OK, I’m not talking about the lost marks there. But remember this: there is generally only one mark for each answer, all the rest being for working. So here’s my first tip – and I would be very surprised if your maths teachers haven’t said this to you many times over the years:

You must show your working.

If it’s a ‘show that’ question then all the marks are for clear working. If it’s not, are you sure you have the right answer? Really? If you haven’t, but you just made an arithmetic or algebraic slip then it’s crucial that you gain as many working marks as you can.

• Clear handwriting
• Work from top to bottom
• Don’t leave things out (‘The examiner will know what I mean’)
• Make sure your answers are clear – underline them
• Even if you can’t get to the answer, write down anything you think might be relevant – there could be a mark or two there

Next tip: examinees often lose marks because, in their haste to get through the paper, they leave out bits of questions, or don’t answer exactly what was asked. For example, there might be a Q4, part (a), subpart (ii) that you just skipped by mistake, going straight on to part (b). Or the question asks for the turning point on the graph, but you only gave the x coordinate. Or it asked for the total interest paid on a sum invested for 5 years, but you worked out the total value.

Don’t miss anything; and answer exactly what the question asked for.

The best way not to lose marks from either of those causes is to check your work. It’s quite hard to go back and check when you want to move on to the next question but, believe me, there are marks to be gained here. When you first write your answers down you are working on a blank piece of paper, and it’s coming straight out of your brain. But when you go back and look through it, it’s the equivalent of marking someone else’s work! You’re far more likely to (a) spot mistakes you’ve made, (b) see that you’ve missed out a bit of a question, and (c) notice that what you’ve written doesn’t match what you were asked.

Now, some types of questions require working to be written out in a specific way. Proof by induction (HL) comes to mind, as do questions involving the various forms of statistical tests (chi squared, hypothesis testing …). Graph sketching is another important area: you will gain marks for giving an indication of scale, labelling the axes, sketching a graph of approximately the correct shape, possibly indicating key points (such as intercepts) if required. It’s just incredibly silly not to pick up these marks, but how do you know what is expected? Ask your teacher if you can see examples of a couple of mark schemes – these don’t just contain the answers, but give clear instructions to examiners on how to allocate each mark. So, get to know what is expected, and do it!

Know what the examiner is expecting to see, and make sure he sees it.

Domains and accuracy. These are a couple of specifics which are very easy to skip over in a question, but you need to take note of them to ensure that, even if you get the right answers, you present them in accordance with the question. A question may give you a function with a domain  -180° < x < 180°. Later in the question you solve an equation and find x = 30° or 330° but, although correct, one of them is out of the domain. Or you are given that a is a positive integer, and later you find a is 0.5 or 3. You missed the positive integer bit, so give both answers. In terms of accuracy, answers are normally given to 3SF. But a question may say to 3DP, or to the nearest 100, or something like that – don’t miss it. Also, look for clues in questions: ‘find the values of x‘, ‘find the turning points’. In both of these you will be looking for more than one answer.

Check domains; check required accuracy; check for clues.

So, my list above shows some of the ways you can easily ‘lose’ (ie: not gain) marks unnecessarily. But waiting until the actual exam before applying these methods is too late. I suggest very strongly that every time you practise a past paper question, you try and answer it as if you are in the exam. When sportsmen prepare for a championship event they not only try to get to the top of the game as far as their sporting skills are concerned; they also prepare for the event itself to ensure that they gain as many points as possible from the judges. In other words, however good a mathematician you are, you can still lose silly marks in exams by not giving the examiners what they want.

(You may also like to read this post I wrote a little while ago about how to avoid common errors when answering questions).