How to Prepare for STEP


Rowan Wright

STEP is the most advanced of the university admissions tests currently in use, requiring students to combine ingenious methods and ideas with challenging and time-consuming algebra and calculations. Students can reliably improve their score by implementing a robust preparation plan, and it is best to practice ‘little and often’ rather than in rare, short bursts. A good time to begin preparation is at the start of the second term of Y13 (after the Christmas holidays), although some students might prefer to start their preparation sooner – perhaps as soon as Oxbridge interviews (if applicable) are out the way. Many students do start much later – perhaps due to receiving an unexpected STEP offer later in the year - and still achieve acceptable results. If you are serious about the exam, we advise finding at least ~5 hours per week per paper (i.e. 10 hours if you are taking STEP 2 and STEP 3) to dedicate to STEP preparation. You should decide exactly how much time you intend to spend studying each week and make a plan, detailing which resources and past papers you will be using.

Things to Memorise

Since 2019, there have been no formula booklet for STEP, and it is essential that you commit standard formulae to memory. The STEP specification [hyperlink here] published by Cambridge Assessment is thorough, and you shouldn’t be intimidated by its length: in places it states very elementary constant which you have likely known like the back of your hand since you were around 15! Some common pitfalls which catch people out are:

  • Formulae for the n’th term, or sum of first n terms of, an arithmetic or geometric sequence (including sum to infinity for geometric!)
  • Sine and cosine rules
  • Standard graph transformations
  • Standard results for integrals and derivatives, including complicated trigonometric functions
  • The binomial theorem, including in the case where the exponent is not a positive integer
  • Standard Maclaurin series (especially for STEP 3)
  • Trigonometric identities, including compound angle formulae
  • Standard transformation matrices e.g. rotation matrices

The now defunct pre-2019 STEP formula booklet provides a helpful guide as to the sorts of results which will frequently be useful and which you should therefore now commit to memory. You must also memorise the standard trig values. Even if you can deduce them using a triangle, there will be no time in the exam!

1. Taught Material

Although the STEP syllabus does not go beyond A level content, there is a ‘shadow syllabus’ of exam-specific ideas that prominently feature, year after year. You can gain a rough working understanding of these ideas through past paper practice, and many STEP students prefer to dive straight in with this, since there are so many papers to learn from. However, some students also like to encounter new ideas in an abstract context first. If you would like some taught material which is useful for STEP, we recommend the following resources:

  • The STEP Support Programme run by the Millennium Mathematics Project provides helpful, taught modules covering important topics for STEP. There are Foundation modules which build up the basics, as well as more advanced modules specific to STEP 2 and STEP 3. The topic notes are reasonably thorough and are a helpful way to plug any gaps in knowledge, although students might prefer to just read through the sections relevant to their weaknesses rather than covering the entirety of the content from start to finish. We would recommend skipping the ‘assignments’ which are based on past papers; it is much more effective to complete past paper questions by paper rather than by topic, as a large part of the difficulty in STEP is figuring out the topic a question is really about, and this layer of difficulty is artificially removed if the question is completed as part of a topic-based worksheet!
  • Skills for success in University Admissions Tests for Mathematicspublished by Hodder Education. Of the many books on the market, this is the one we would recommend. It provides a useful overview of some key ideas, but it isn’t     exam-specific (it is joint across STEP, MAT and TMUA) and it isn’t long     enough to go into a huge amount of detail.

2. Past Paper Practice

STEP past papers are available from 1987-2022; the style of the exam has been very consistent since 2007, although there were some small changes to the syllabus in 2019 (in particular, some applied topics were removed from the syllabus and ideas from first year A-Level Further Mathematics were added to STEP 2). We would generally not advise worrying about the pre-2007 papers unless you are starting your preparation very early, as these older papers often prioritised fiddly numerical work which is less relevant for the modern exam.

Past papers are by far the best resource available for acquainting yourself with the style of questioning used in STEP, and past paper practice should comprise the vast majority of your preparation time. You should aim to complete as many papers as possible in strict timed conditions, starting with the earliest you have time to complete, working towards the 2022 paper.

For students taking both STEP 2 and STEP 3, it is best to try and alternate between the two rather than doing e.g. all of STEP 2 first. Depending on the order in which your school or course covers content, it might sometimes be necessary to focus on STEP 2 at first until all of the requisite content for STEP 3 has been learned. STEP 1 was discontinued in 2020, and although these questions can provide a source of fun and interesting problems (helpful, for instance, for Oxbridge interview candidates), there are so many STEP 2 and STEP 3 papers available (which are more relevant) that it is not generally worth attempting STEP 1 problems. The only exception to this is if a student is starting extremely early; this would be worth discussing in a free consultation.

It is very important to work through the papers year by year, rather than finding the questions arranged by topic. This is because a significant part of the challenge is working out which ‘topic’ the question is on! Since students only attempt six out of the twelve/thirteen questions in the real exam, students will generally need to spend much longer than three hours to extract the full benefit from a question; anything from5-10 hours per paper is quite typical. The precise process we recommend is as follows:

  • Timed mock exam. You should complete as many past papers as possible in strict timed conditions. Regular timed practice will allow you o evolve the timing and exam technique strategy that works best for you. It will also help you to build stamina and track progress. Since it can be difficult to find a solid block of 3 hours in which to complete a mock, students should not be discouraged from e.g. splitting the time across two timed sessions, which is still better than nothing!
  • Second attempt. Set your timed work aside and, on separate paper or with a different colour pen, spend as long as you need trying to answer the questions you didn’t finish – including those which you didn’t choose to attempt in the real exam. Early on in the preparation process, we recommend that students make an attempt at every question. This is because - with practice - students often find that they have unexpected strengths in topic they wouldn't immediately choose. Seeing all of the questions for several years can also be very instructive in terms of cultivating a good ability to select which questions to attempt. Once you have accumulated more experience, you might choose to skip questions on topics you are confident you would definitely not attempt in the real exam.
  • Resist the temptation to move on from from your second attempt too quickly: every minute spent struggling on a difficult question is sharpening your mathematical problem-solving instinct, even if you don’t ultimately manage to solve the question. Make sure you don’t look at the mark scheme or solutions yet!
  • Mark work. When you have done all you can, mark your work, keeping a separate score for the questions completed under timed conditions. Cambridge provide solutions for 2004 onwards, although these do not provide a breakdown by marks and would have to be used to roughly estimate the marks gained. More formal mark schemes with breakdown by marks become available from 2013 onwards. Both the solutions and mark schemes are downloadable from the STEP resources page on our website. In our experience, students generally lose around 3 marks per question solely due to poor quality of presentation and explanation. There is much to be gained by having your work marked by a real examiner, which is a service we offer at Vantage.
  • Review. You should then carefully review your second attempt to ensure a complete understanding of every question. You can use the Cambridge solutions for this, and ask a teacher, friend, or online forum for help if you’re stuck. Vantage STEP preparation courses provide complete solution videos and booklets for all STEP 2 and 3 past papers from 2007-2023. They teach you how to ‘come up with’ ideas, thinking as trained mathematicians.

3. Individual Tuition

Many students opt to have individual tuition as part of their admissions test preparation. It provides an opportunity to smooth out any issues that were unresolvable with the available resources and ask questions. Tuition can be extremely beneficial, but students who do not receive tuition can still achieve high marks through diligent preparation.