Introduction
STEP is part of the entry requirements for the Mathematics course in Cambridge, Imperial and Warwick. It consists of 3 papers (Papers I, II and III) but you will only have to do one or two papers.
Format
Each paper has 13 long questions, 8 of which are Pure and the remaining 5 shared between Mechanics and Statistics. Each question is worth 20 marks. The time limit for each paper is 3 hours, and they will mark a maximum of only 6 questions (so maximum total mark is 120).
For each paper you will be given a grade: (from lowest to highest) U, 3, 2, 1 or S. Very roughly, the grade boundaries in the past few years have been around 90 for an S, 70 for a grade 1 and 55 for a grade 2, but they change significantly every year.
More info here
Papers I and II are based on the A-levels Mathematics course, and paper III on the A-Levels Further Mathematics course. Although you won’t need to learn new material to tackle the course, you will very likely find the papers to be extremely difficult at the start. This is normal.
The questions are designed to really challenge how well you understand (not memorize!) your syllabus, and how fast you can adapt to new mathematical techniques. Very often, one actually learns a new piece of mathematical trick after coming out from the exam. The examiners are more interested in seeing how you think rather than catching you out with knowledge beyond your ken.
It’s hard to describe, but try a few Paper I questions.
Generally, if you are trying to enter Cambridge, they will ask for an A*AA in A-Levels (Maths and Further Maths required of course), and usually, grade 1 in both STEP Paper II and III (not Paper I).
Tips & advice
One complete answer is valued more than two half-answers.
For example, a rough guide would be that answering 1⁄2 the question would probably give only 1⁄3 of the 20 marks, while answering 3⁄4 of the question would get about 3⁄4 of the marks. STEP rewards deep understanding of mathematics rather than a broad but shallow one.
Looking at the marks, you only need to fully answer 4 questions from a choice of 13 questions to more or less secure a grade 1 in any paper, and you have 3 hours. This might sound easy, but it really isn’t. The only way to prepare for STEP is to practice lots of questions. The STEP website is very good for this: their booklets of questions “Advanced Problems in…”, and the past papers (all of which can be found in the previous link) are enough to prepare you for the exam.
For the keen beans among us, here is a good repository that stretches back till 1987.
Solutions for the older papers are available here.
Again, at the start, you will find a lot of questions to be nearly impossible. This is NORMAL. Do not be discouraged and remember that almost everyone doing STEP feels like this in the beginning. Even by the day before the exam, you will find that you struggle with many questions on the paper. But this is a good preparation and taster for university mathematics: unlike A-Levels, you will find that you can’t be good at everything. Remember this and do not despair. If you don’t like this feeling, then you may want to reconsider doing mathematics.
Start EARLY!
The STEP exam is held in June. I would say start doing some questions in January (if not earlier!) and see how you do. The best way to prepare for STEP is to do as many questions as possible, which means working through the booklets till you feel comfortable with the type of questions, and then the past papers. Give yourself two hours per question at the start (that is not a joke, you’ll get faster once you’re used to it).
Alternatively, you might want to start by doing some STEP I papers, and then only moving on to the other two. Also, based on the shared experience of many who have taken the exam, it is generally best to focus on the Pure questions as they tend to be more accessible in terms of required knowledge. The Mechanics, and especially the Statistics, questions tend to be harder and more advanced.
But of course, different people have different background knowledge and different strengths, so this advice should be carefully considered.
Closing remarks
STEP is frustrating and difficult, but hopefully, you will find a certain satisfaction every time you finish a question. You would probably learn more about mathematics practising the papers than you would in your Pre-U Maths course. And perhaps you’ll start to enjoy being stuck on difficult problems, and suddenly, after a few hours, seeing the solution in your head. That’s Mathematics.
Everything you need to know about STEP is at their official website.
Talk to your university exams officer (or teacher) to see if they canoffer STEP exam for you. Otherwise the British Council in KL, Penang, Sabah and Kuching offers STEP.