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What is STEP?

STEP (Sixth Term Examination Paper) is a maths admissions test used primarily by the University of Cambridge and the University of Warwick. Other UK universities sometimes ask for STEP as part of their offer. STEP questions are designed to reflect the difficulty of undergraduate maths.

STEP is a long and daunting paper, so it is easy to be overwhelmed and waste time picking questions as opposed to actually doing the maths. Don’t worry, we’re here to help you make those three hours really count.

Choosing the right questions

STEP 1 is made up of 11 questions, and STEP 2 and 3 are both made up of 12. But you’ll only be marked on your six best answers, so you need to disregard about half the questions. This is a hard decision to make. How can you know which questions you’ll score best on?

The first thing to do when you open your STEP paper is to skim through it and immediately put aside any questions that cover content you aren’t sure of. For example, you may not be familiar with some of the mechanics and statistics content covered in STEP 2 and 3. If so, ignore those questions immediately.

Having done this, you may find you only have six questions left. You can be confident that you’ve made the right decisions.

If you have more than six remaining, the next thing to go off is familiarity. If you’ve prepared well for STEP, it is very likely that you will recognise the style and format of certain questions. These ones are a good place to start, as they will most likely boost the number of marks you have in the bank, and increase your confidence when it comes to tackling the harder questions. 

After this, go for questions that interest you. If you are interested in solving the problem, you will enjoy the paper more, and STEP is the sort of paper you should be enjoying!

It is important to look through the questions carefully, but you want to have as much time as possible to actually do the maths and pick up marks. To strike the right balance, give yourself ten minutes at the start of the paper to read through the questions and label them “definitely”, “maybe”, or “no”. 

You should mark any questions where you are not confident with the foundational material as “no”, and then avoid those questions for the rest of the paper. The “maybe” questions are the ones you are a little unsure about, but potentially find interesting and see that you could reach some part of a solution. The “definitely” questions are the ones you want to start with, where you think you can form and follow a clear route through the question, and you are confident with all of the material covered. 

You need to find an equilibrium between randomly picking questions and rushing through them, and thus not scoring as well as you could, and carefully deliberating for hours which questions you want to answer, thus wasting valuable time. If you give yourself no more than 10 minutes at the start, this leaves you 2 hours and 50 minutes to attempt your chosen six questions, which is 25 minutes per question, giving you 20 minutes to check questions or spend more time on some of the harder parts.

Answering your chosen questions

Once you’ve found your six questions, how can you spend the remaining time really showing off your mathematical abilities to the examiner? 

Everyone has different exam styles. Some people like to go through each question and answer all of the easier sections first, leaving all the remaining time to tackle the harder parts of the questions. Others like to methodically spend a full 25 minutes on each question before moving onto the next one. Everyone works differently, so practice different styles when you are preparing; this will help you work out what’s best for you. 

Personally, I would recommend working through a question within the allocated 25 minute time frame, until you cannot get any further with it. You may be able to answer the first three parts on some questions, or only the first part on others, but I think the best way to answer the questions is to keep going until you reach some kind of wall. When you realise you have been gnawing your pencil without writing anything down for the past three minutes, it’s definitely time to move on. 

But before you move on, read the latter part of the question. It will fizzle in the back of your brain while you attempt the harder questions, and then, when you have time to come back to it at the end, you will have been thinking about additional ways to tackle the problem. You will likely not spend the full 25 minutes on each question the first time through, and this method will ideally leave you about an hour at the end to solve the harder parts of the questions you initially left. 

What happens if I run out of time?

If you’re facing a time constraint or you don’t know exactly how to solve a specific question, my top tip is to write out what you would do to answer this question.

“Even if writing out what you would do only nets you an extra mark, that mark could be the difference between a grade boundary. It was for me.”

Nick T, Maths, Cambridge

Here’s a list of ways to try and gain at least one mark on a question without explicitly solving it. Although you’re aiming to try and solve the problems, sometimes this isn’t possible in the time-pressured exam environment. 

  • Write a list of potential methods you would use to answer this question. This is the best way to approach a question that you’re not actually sure how to solve. You may also realise which of the methods will work when you are writing the list. 
  • Write out your method, like a recipe in a cookbook, for how to solve the question. This is the best way to approach a question if you don’t have time to actually solve it, but think you would be able to with more time.
  • Write any relevant working you can, even if just for the later parts of the questions. You never know where you might gain a valuable extra mark!

In the exam, it’s also worth trying to work out where the majority of the marks for a question lie. Although you won’t be given a mark-by-mark breakdown of each question on the paper, you can gain a sense of what the tutors are looking for by doing enough practice. It’s important to focus on the mark-heavy sections rather than spending ages trying to solve a later part of a question that may only be worth one mark. 


Gaining a few extra marks can make all the difference in any exam, and STEP is no different. So use our top tips to make sure you perform your best on the big day. For more STEP info, read our STEP/MAT/AEA guidebook. Best of luck for your application!