Many maths students find that even if they are able to solve the problems set to them at school or in the textbook when they turn to exam questions they often get stumped. This is often because exams require students to solve problems not simply show they can do certain techniques (like differentiate, or factorise). And problem-solving is often not taught at schools at all! Obviously a lot depends on the exact problem you have, but if you are stuck on a particular maths problem, there are a few quick things you can try which might help get you ‘unstuck’.
1. Have you used all the information given in the question?
Because it must be possible to solve maths questions and the examiners are not deliberately trying to confuse you, maths questions always give you exactly enough information to answer them. But if you don’t use all that information then it’s unsurprising if you get stuck! So check that you have used all the information given and if there’s something you have missed that could be the clue you are looking for. Go back over the question carefully and check you have incorporated everything, no matter how small, included in the question. Also check that you have written everything down correctly – you’d be surprise how many times students make an error here!
2. Have you paid attention to the key words in the question?
Similar to the above, maths has its own language which is very precise but often ignored by students in their rush to get to the answer. Some particularly important terms to look out for:
– Hence: means you need to use the result from the previous question.
– Hence or otherwise: means that although there are other ways of doing it the easiest is to use what you just found!
– Exact value: means no rounded decimal answers are allowed. So answers must be either whole numbers, fractions or use constants such as e or ln3.
– Show / Prove: this means you have to take the information given and using maths and logic get to the answer they have provided. So you must not thing they are asking you to prove!
3. If it’s the later part of a question, have you tried using the earlier answers?
Maths questions in exams (particularly at A Level) are in the form of problems which have interconnected parts. Usually the easier, earlier questions are used to provide the basis for answering the later, harder parts. But too often students behave as if every part of the question is separate, when they are not.
Ask yourself what have I just found? What does that mean? What could I use that to find? Very often this will help solve your problem.
4. If you can, have you tried drawing a diagram or graph?
They say a picture paints a thousand words. Well in maths you might say a diagram paints a thousand equations! Graphs or diagrams are a brilliant way of combining the information given in a single picture. Very often this quickly provides the clue you are looking for, so it is almost always worth trying if possible. Just be careful that your diagram is neat, clear and not misleading (doesn’t suggest things that aren’t true). By looking at the diagram, sometimes from different angles or perspectives, the insight you need will often suddenly appear.
5. Could you solve a simpler version of the problem? If so, can you adapt that approach for this harder one?
Exams will only test you on topics you have (hopefully) already covered in class. But very often the questions in exams ‘look different’ or appear harder than the ones you have solved before. But often that appearance is largely illusory. If you can spot the type of question you are being asked and focus on how to solve problems of that type then very often this helps overcome this obstacle. Once you have noticed that a problem is still, say, factorising a quadratic, or still determining the maximum point on a curve, then you see you can still use the approach you have already learned.
I hope these methods help you solve more of your maths problems!