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Weekly Challenges

The NRICH Stage 5 weekly challenges are shorter problems aimed at Post-16 students or enthusiastic younger students. There are 52 of them.

Choosing Questions

Stage: 5
Article by Alison Kiddle

Published September 2014.

In many mathematics tests and examinations, you are expected to attempt every question, and so for a lot of STEP students, the STEP examination is the first where there is a decision to be made about which question to answer.

It may be that you haven't given a lot of thought to choosing which questions to tackle. After all, you've spent months preparing to answer questions, you're expecting to sit an exam that is likely to be one of the most challenging of your life so far, and deciding which question to do might seem like an insignificantly small part of the challenge. In this article, I will try to convince you that question choice is a really important part of STEP success, and offer you some advice on how to improve your question selection skills.

Imagine you are sitting in your STEP examination. The paper in front of you has thirteen questions. You have three hours. Although it's tempting to rush in and start straight away on answering any question that seems remotely tractable, think for a moment. STEP questions are more subtle than other maths exam questions. What seems difficult on first reading might actually turn out to be a problem ideally suited to your thining style! You will only be marked on your best six questions, so there is really little point attempting more than six, and you can still do well on STEP even if you only attempt four or five questions but do them very well. So it makes sense to devote a little bit of time at the start of the exam to reading through the paper and deciding which questions to attempt.

On your first reading, you might outright reject some questions. Perhaps they are asking about an area of mathematics you are unfamiliar with (such as a mechanics or statistics question on content you have not covered). In that case, it's ok to rule it out straight away. But do take a look at our material on Unusual STEP questions, as sometimes a question will introduce a new piece of mathematics that no-one is familiar with, and if you are the sort of mathematician who copes well with making sense of new ideas quickly, an unfamiliar-looking question might be right up your street!

While you are reading the paper through, if a question really sings out at you to be solved, then try it first. Trust your instincts. If you can already see the first few steps of the problem in your mind, it could be a good confidence boost to get started. But do read through the whole question before starting! If there isn't one question that leaps out, then make a shortlist of four or five questions and then just tackle them in question order. If there's time you can attempt a fifth or sixth question, but first of all aim to get four good solutions down on paper as a minimum.

Once you've selected your questions and are ready to get started, there's plenty of good advice on how to solve problems in our Guide to Problem Solving. In the exam, keep an eye on the time - three hours seems like a long time but can go by in a flash, so if you're spending too long on part of a problem move on and go back to it later.

That's just about all, but in order to give yourself practice in choosing questions, why not set yourself a couple of past papers to do as a timed test? Find somewhere quiet where you won't be disturbed, set aside a good long time (preferably the full three hours if you can manage it) and practise the whole process, reading through the questions, deciding which to try, planning your solution, getting started, getting stuck, getting unstuck, explaining your thinking, and completing a question before moving on to the next. By the time you're sitting in the examination doing it for real, all the practice will have paid off... Good luck!