Before going any further, I need to explain what I mean by "Unusual" in the title to this article. In some sense, all STEP questions are unusual, because they are written in such a way to challenge you to apply your mathematical knowledge and understanding in non-standard ways, and to get you thinking. So all STEP questions are unusual, but some are even more unusual than usual!

This article and the STEP Prep Module that accompanies it is intended to draw your attention to STEP questions that introduce a new piece of mathematics, or take you through a new way of thinking about a familiar mathematical object or idea.

Sometimes, when reading through a STEP paper and trying to decide which questions to tackle, you might come across something that looks totally unfamiliar. This doesn't necessarily mean it's asking about an area of mathematics you ought to know but don't, so it's worth taking the time to read the question and see whether it is introducing something new. A question which starts with several definitions might require very little prior knowledge to solve, and the challenge comes from being imaginitive enough to notice what is going on and make sense of some new mathematics. Remember, there are no trick questions on STEP - the examiner is not trying to catch you out!

There isn't really an obvious way to prepare for unusual STEP questions - after all, once a question has appeared, it's unlikely to appear again. That doesn't mean it's not worth having a go at these questions when you see them on past papers though. As with all mathematical problem solving, one of the best ways to get better is to practise. And of course, if you tackle some of the more weird and wonderful questions that past papers have to offer, you will be building your confidence and are likely to feel better about trying something more unfamiliar if it comes up on your own STEP papers.