How to prepare for and do well in STEP
Some of the many questions I often hear from the students I tutor are “How do I revise STEP effectively?”, “How do I prepare for STEP?” and “How do I do well in STEP?”. And as a current Cambridge Mathematics Student, having been through the STEP exams myself and having performed highly (1 in STEP 2 and 1 in STEP 3) I decided to write the following article in hopes of shedding some light on this area and potentially helping other students who are planning on sitting STEP. I aim to provide some valuable tips and advice on how to revise for STEP and several effective approaches which will help you to do well in STEP. I will also outline some of the most invaluable resources I came across, throughout and at the end of the article, including ones I am in the process of making to complement STEP preparation.
Preparing for STEP can feel like a daunting task, and from personal experience, I know the feeling well. But there are several things you can do to give yourself the best chance of success in the exam.
The most important piece of advice I would give is to start early. The more time you give yourself to work on STEP, the more time you have to problem solve, develop mathematical intuition, and improve. Practice is key.
Note: If you are starting STEP prep in Year 13, skip the first section.
1. Ease Yourself In
A valuable resource to make use of at the beginning of your preparation is the Step Support Programme. The foundation modules are ideal to work through when in Year 12; they get you applying concepts from AS Maths in STEP questions, as well as occasionally introducing new notation and new mathematical ideas which you may not have seen. They are an excellent way to get used to the longer and more demanding types of question. If instead you start with STEP 2 or STEP 3 questions outright, then you are likely to feel demoralised since you will not have covered much of the mathematics needed for the questions.
Another option that will give you a significant head start is to attend a specialist and intense STEP summer course. I created my own course called “Summer of STEP” which is tailored to each individual and designed to introduce students to the basic techniques required to start the process of “getting into” STEP. You will learn how to read STEP questions effectively, develop confidence with applying techniques and content from A Level Maths to more complex scenarios and improve your problem solving skills. You can read more about it on my STEP Tuition page.
2. Questions by Topic
Working through STEP questions based on topic is one of the best ways I found to prepare for and revise for STEP, as opposed to working through papers year by year. You can choose the topics for which you have already covered the content for at A-level, preventing you from wasting time tackling questions that you don’t have the background mathematics for. In addition, it allows you to really master each topic; you will have seen the variety of ways that the topic is presented in STEP questions and so will be well prepared for any type of question relating to that topic in the exam. Be adventurous and try out STEP Questions from all categories, even if you aren’t a fan of some, because it will allow you to develop different skills and further your mathematical intuition, benefiting you greatly in the exams.
Because I so strongly believe answering questions by topic is so effective, I have created several user-friendly tables sorting every single STEP 2 and STEP 3 question from 1998-2020 into the topics outlined in the 2021 STEP Specification.
In each row, there is a pdf of the question, the official mark scheme(where available) , the examiner’s comment (where available), plus a detailed worked solution written by myself. It also classifies which new spec paper the question could be asked on, thus allowing the old spec STEP questions to be incredibly valuable in preparation. You can find it here (it is currently a work in progress, but questions are added weekly).
3. Positive Attitude
There will be times (more often than not) when a STEP question seems impossible, or incredibly frustrating. This is not because you are not good enough but instead is because of how STEP questions are designed – they are intended to be challenging. It is easier said than done to ‘have a positive attitude’ but if you are in this situation and cannot seem to make progress, instead consider it a learning experience. First, find a worked solution; you can find those in my step questions and worked solutions database, here. Then peek at the first few lines of the part you are stuck on and see if this is enough to get you past the issue. If so, continue with the rest of the question. If this is not enough and you are still ultimately stuck and confused by the question, then work through the solution line by line, writing out each bit of mathematics. At each stage, ask yourself: why did they do a particular step, how might they have thought to do that, why didn’t your approach work and so on… This reflection whilst you work through the solution will consolidate what you’ve learned and allow you to answer similar questions more successfully in the future.
4. Mark Answers Immediately After
In my opinion, it’s always best to mark your answer as soon as you finish the question. Your working is still fresh in your mind, you can remember why you took a particular approach and so it’s much easier to follow the solution and compare. It also means that if your working is incorrect, then you are more likely to understand why it was wrong and thus your consolidation will be more effective.
5. Focus on Strengths near to the Exam
As the date of the exams get closer, worry and stress are likely to become more prominent and so it is important to try and maintain confidence and self-belief around this time. A good approach I found when revising for STEP in the final few weeks before the exam, is to focus on your strengths; go back and practise questions from your favourite topics. Perhaps redo questions which you struggled on and had to resort to using the solution for and see if you can now work through the question with no help. This will help highlight to yourself how much you have improved over the time you’ve been preparing and will hopefully allow you to keep a positive attitude in regard to the exam.
6. Timed Practice
Timed practice should be introduced into your preparation for STEP nearer to the time of exams, since it is only useful once you have acquired the problem-solving techniques and mathematical intuition from doing a significant number of questions. It allows you to translate your skills into a time pressured situation which you will experience in the exam.
There are two effective options for timed practice:
Timed Full Papers
Individually Timed Questions
Timed papers have the advantage of allowing you see what the full 3-hours feels like and you can put into practice some of the exam tips which are in the final section below.
Timing individual step questions is an alternative way to add time pressure without having to do a full 3-hour mock. Setting yourself an upper limit of around 40 minutes per question is a good way to ensure you are completing the question in a time similar to what you would ideally want to in the exam. In my own preparation, I used this technique most frequently.
7. General Tips for the STEP Exam
Have a quick flick through of the paper at the very beginning and identify the questions you think you will attempt. Look for those that correspond to your strengths. Don’t attempt more than 6 questions – only your best 6 attempts are marked, so you are better off spending more time on gaining more thorough answers to those 6 questions.
Start with the question you think you will have the most success at completing since it is a good way to ease yourself into the exam and will help with keeping a positive mindset.
Show all your working out and present it clearly. This is the best way to avoid making silly mistakes and to prevent yourself from losing marks for not having enough detail in your answer.
Try to aim to spend 40 minutes max per question, with exceptions of course when you are very close to finishing the whole question.
If you get stuck and have spent 5-10 minutes trying to figure it out and it still isn’t working, consider moving on to another question. Leave a couple of blank pages as this will allow you to come back to it later in the exam if you have any spare time.
And finally, always try to attempt 6 questions if you have time to. Even if some attempts are only the first few parts of a question or just a few lines of working. You want to maximise your marks and since up to 6 questions are marked, you should aim to submit 6 attempts, whether they are full or only partial/fragmented solutions.
Best of luck with your STEP preparation!
A few other useful resources I used in my preparation are listed below:
- Advanced Problems in Mathematics is a book written by Dr Stephen Siklos, filled with worked solutions to 75 STEP questions, along with insightful comments, hints and tips for each.
- STEP Questions by Topic
If you are struggling with STEP or if you would like to enhance your mathematical intuition and problem-solving techniques in order to achieve the top grades, S and 1, I offer one-to-one STEP Tuition. See here for more information.