Sixth Term Examination Paper (STEP)

This admissions test is taken for some Cambridge courses.
Last updated: 11 months, 1 week ago


STEP are exams taken in addition to A Levels which make up part of the application to Mathematics tripos. This guide was put together with the help and advice of lots of current Cambridge students!

How to Prepare

Here are some general resources related to the Sixth Term Examination Paper (STEP). Use this page as a hub to branch off and use other resources!

The idea of STEP can be very overwhelming and confusing for applicants, but STEP should never be a deterrent from applying to Cambridge. Here is an explanation of the papers and their content, along with some tips on marking and timing and other useful resources. If you know absolutely nothing about STEP, this is the place to start.

After interview, successful candidates are given conditional offers based on both their A Level results and usually 2 STEP grades. For this reason, there is plenty of time between when you apply, and when the exams are due to take place! It is recommended that you start preparing for STEP during your pre-interview application and, then, if successful, to spend more time working towards the exams which are sat in June.

All Cambridge colleges incorporate STEP into their offers for Mathematics. Some colleges include STEP in their offers for other subjects (Economics, Engineering, combined Computer Science).

Offical STEP information 🔗 🌟 This webpage from Cambridge Assessment Admissions Testing explains everything you need to know about STEP - how to register, how to prepare, how results work, and FAQs.

The Papers

There are 2 STEP papers. Each paper is assessed on, at most, 6 questions (your six highest scores will count).

  • STEP 2 (12 questions) is based on both A-Level and AS Further Mathematics. It has 12 questions (8 pure, 2 mechanics, and 2 statistics/probability).
  • STEP 3 (12 questions) is meant to be as difficult as STEP 2 but based on the A-Level Further Mathematics syllabus. It has 12 questions (8 pure, 2 mechanics, and 2 statistics/probability).

An offer usually includes grades in STEP 2 and 3. The grades are, from highest to lowest, S, 1, 2, 3, and U.
Each paper costs around £55 to sit; ask your school whether this is/could be covered by them.

‘STEP exams explained’ webinar 🔗 🌟 This webinar was recorded by the Cambridge Department of Mathematics for the Virtual Open Day in 2020. This video should give you a good broad overview of what the university thinks about STEP, answers FAQs, and is a good resource if you are unable to attend an in-person Open Day. However, please note that STEP 1 was discontinued in 2020, and now only STEP 2 and STEP 3 exist.

Content and Preparation

As you can see in the paper breakdown, most of the STEP exam content should not be new to you by the time exams come around in June. What sets STEP apart is the type of question that you’ll be tackling! The University is asking that you apply Maths and Further maths content that you are familiar with into questions that rely on more critical and creative thinking than your A Levels do. The first step is to learn this content inside out; this will come in handy anyway to get a jump on your A Level revision.

The following resources will give you an idea of what STEP questions look like. It is wise, in your revision, to work through old papers and questions to build up the skill of answering questions like this. Practice makes perfect when learning how to answer new types of problems; the more you do, the more familiar you’ll become with this different type of critical thinking.

STEP Specification 2023 🔗 🌟 This could help you get a feel for the purpose and content of the exams.

STEP question database 🔗 🌟 This is a database of every step question ever made. While it may seem tempting or useful to try and complete as many as possible, or even all, of these as preparation, this would take an awfully long time. Keep in mind that each exam is only 3 hours long and you are marked on your solutions to only 6 questions. Try not to sacrifice revision for your other A Level(s) by becoming bogged down with the entirety of the database. Instead, you could work to cover a good amount of questions from the different subject areas (pure, mechanics, and statistics/probability), focusing on your weaknesses, and avoid questions that are similar to each other. Make sure to spend a long time thoroughly marking your solutions (examples of marking criteria are further down in this document) and reflecting on them.

Don’t be disheartened if you do not excel at solving the problems when you first start attempting them! They are different from what most students are used to and it does not make you a bad mathematician if it takes some time to get the hang of them.

Once you feel comfortable and used to the questions, it’s a very good idea to start sitting full papers. You can find these online, or you could make them yourself with the questions in the database (perhaps when you get closer to the exams, you could build yourself a mock that includes the topics/types of questions you struggle with most to test yourself further). It is really important to have these mock run-throughs in order to practice working under time pressure and figure out the best way to delegate time for you. Everyone works differently and so will spend more or less time on different elements of the paper (reading it over, thinking, planning, solving, and revising it).

Official Resources

The following links are provided directly by the University: try to make the most of the wisdom right from the source! These pages are written by academics directly involved with STEP and were made for applicants like you. They will help you identify what the examiners are looking for exactly and might provide more reliable advice and support than less formal anecdotal advice/sources. All three are worth looking at.

Cambridge Introduction to STEP 🔗 🌟 More information about STEP format and content can be found here, including links to many online free resources.

Step Support Programme offered by Cambridge 🔗 🌟 This webpage provides free online resources recommended by the University.

Cambridge Assessment Admissions Testing: Preparing for STEP 🔗 🌟 Containing more past papers.

Other Useful Resources

What Uni? 🔗 An unofficial guide to STEP.

The Oxbridge Formula: Top Tips for Preparing for STEP 🔗 Contains links to other resources.

Mathsaurus 🔗 🌟 YouTube channel ‘Mathsaurus’ hosts a series of videos that solve and discuss past STEP questions.

Advanced Problems in Mathematics workbook 🔗 Including worked solutions.

More tips for solving questions 🔗 Specifically related to the STEP.


It is a good idea to spend some time at the beginning of each exam reading through the paper. This matters in STEP just as much, if not more, as it does any other exam since you’ll have to decide which questions you think you’ll succeed in best. Go for low hanging fruit; it is better to fully solve a question you might find less engaging than half completing a more interesting question. If you aim to have completed 4 questions fully in each 3-hour exam, you’re in fairly good stead. That being said, keep in mind that your 6 highest scores will make up your final mark. Divide your time accordingly.

If you get stuck on a solution, while it is important to take the time to really think it through, do not spend more than 10 minutes or so without any written progress. It would be wise to also allocate some time to review your solutions before the end of the exam; sometimes a fresh eye can help you identify mistakes and save you marks.


Each question is marked independently out of 20. The mark scheme operates just like the A-Level one does. Marks will be awarded to candidates who work towards the solution, even if it is not completed. In some questions, the method is provided. You will be expected to follow the given method when it is. Otherwise, all correct and justified solutions will receive due marks regardless of which approach you take.

You will be marked on your 6 highest scoring questions, and it is recommended that you submit no more than 6 questions.

There is variation between years because of the size and quality of the applicant pool roughly what score will award you which grade. A ballpark for grading STEP 2, marked out of 120, is 80 for a 1 and 100 for an S. For STEP 3, since the paper is more conceptually difficult, out of 120, 70 for a 1 and 90 for an S.

A typical offer is a 1 on both STEP 2 and 3 papers. A typical gap year offer is an S and a 1.

Physics and Maths Tutor 🔗This website has some papers and mark schemes on it. It’s a good idea to familiarise yourself with the mark schemes to ensure that your solutions are complete or, if not, are scoring as high as possible.

Final Advice

You’ve made a great STEP if you’ve read through this document. The prospect of STEP can be challenging but, if you’re even considering it, have some faith in yourself! You should be proud of yourself and your achievement this far.

Best of luck!