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Undergraduate Admissions


Achievement in the Sixth Term Examination Papers (STEP) normally forms part of a conditional offer to read mathematics at Cambridge. The examinations are set and administered by the OCR examination board and are usually taken in mid to late June. There is extensive free online support offered by the Faculty and NRICH to help you prepare for STEP, and many other free online resources are also available.

OCR has a dedicated STEP website, which has all the details of the examination (method of entry, dates, specifications, etc) as well as downloadable past papers. (There is also a Customer Support Service which can be contacted by email or by phone: 01223 553998.)

If your school or college is not already registered as a centre, they can apply to become a test centre (UK or abroad). If you have difficulty finding a test centre where you can take STEP, you can use their online search to find a test centre, in the UK or abroad, otherwise the Customer Support Service may be able to advise you.

STEP format

The papers

  • There are two STEP mathematics papers: STEP 2, and STEP 3 (STEP 1 was discontinued in 2020). 
    Your offer will usually include grades in papers 2 and 3.
  • The papers for STEP 2 and STEP 3 each consist of 12 questions: 8 pure, 2 mechanics, and 2 statistics/probability. 
  • All answers that you submit in the examination are carefully assessed, but your final score is based on the six highest scoring questions only. Each question is marked out of  20, so the maximum mark you can achieve on either STEP paper is 120. There are five grades, which are (from highest to lowest) S, 1, 2, 3, and U. 

The specifications

  • STEP 2 is based on A level Mathematics and AS level Further Mathematics (or the equivalent).
  • STEP 3 is based on a typical Further Mathematics A-level syllabus and the questions are intended to be about the same level of difficulty as those of STEP 2.

The full STEP specification is available on the OCR webpages about 'Preparing for STEP'. Note: even though the specification for STEP in 2019 onwards has changed from that in previous years, the style of the questions is unaltered, so most questions from previous papers can be used for preparation. Candidates should be aware that a small number of past paper questions are no longer on the specification and require mathematics that is no longer examined. STEP 1 papers are available and, although STEP 1 is no longer set, the papers provide useful preparation material. The STEP 1 specification was roughly equivalent to that of A level mathematics.


Cambridge Colleges like to make offers involving STEP for the following main reasons:

  1. STEP is a far better predictor of success in the Mathematical Tripos than A-levels. One reason for this is that the questions are less standard and less structured, which helps to distinguish between ability (or potential) and good teaching.
  2. Preparation for STEP serves as useful preparation for our course.
  3. The STEP marks and the scripts themselves are available for inspection by college staff. This means that it is possible to make allowances for a near miss and to make judgements on the actual work rather than on just the marks or grades.
  4. Candidates apply to Cambridge with a wide range of different UK based and international qualifications. STEP provides a fairer 'across the board' comparison.
  5. Using STEP allows us to make offers to many more candidates who show mathematical potential at interview, but do not have quite enough mathematical knowledge and skills because of educational disadvantage, then provide sustained support to motivate them and help them prepare for the exam and for mathematics at University level. So STEP is also a powerful tool for widening participation.

Many other universities recommend that their mathematics applicants practise on past STEP papers as preparation for university-style mathematics, and some encourage applicants to take STEP papers and may take STEP results into account.

Important Advice

Do not worry if your school is not able to provide much help with STEP.

There is plenty of material with which you can help yourself. The best preparation for STEP is to work through past papers. Full solutions are available to guide you if you get stuck. NB: the Faculty of Mathematics provides a free online STEP Support programme to help you develop your advanced problem-solving skills, from the summer of Y12 onwards, and prepare for STEP - see below for more details.

Do not worry if the STEP questions seem very difficult.

STEP is supposed to be difficult: it is aimed at the top 5% or so of all A-level mathematics candidates. It is therefore important to adjust your sights when tackling a STEP paper. The questions are much longer and more demanding than A-level questions (in A levels you are expected to answer 11-14 questions in two hours whereas in STEP papers you are expected to answer no more than 6 questions in three hours). They therefore look daunting; but you should not be daunted. With enough practice you will get better at tackling STEP questions and you will be well prepared to achieve the grades you need.

STEP Support Programme

The Faculty of Mathematics, in collaboration with NRICH, has developed a free online STEP Support programme to help potential university applicants develop their advanced problem-solving skills and prepare for sitting STEP Mathematics examinations. This includes:

These resources are free and open to everyone. Find all the resources at

Other Free Online Resources 

There are a number of other free resources. There are also a number of commercial resources that the Faculty neither endorses nor recommends, since there are more than enough free resources.

  • Advanced Problems in Mathematics by Dr Stephen Siklos. We emphasise that Dr Siklos' book is free to download in PDF format (as well as being available as a paperback to purchase), and we recommend using this link (rather than links on some third-party sites). The book, which is a revised and extended version of two earlier books, analyses recent STEP questions selected to address the syllabus for Papers I and II. Each question is followed by a comment and a full solution. The solutions point students to the methodology required to address advanced mathematical problems critically and independently.
  • The STEP database is a searchable database of all STEP questions from the 1986 specimen papers until 2018 papers.
  • All past papers from 2014 are available to download from the OCR website and also include:
    • answers to all questions,
    • solutions with explanation and mark scheme for the 2011 STEP I paper.
  • The MEI website has full solutions to the papers for 1996 to 2019, to guide you if you get stuck.
  • Advanced Problem-Solving resources from NRICH. This is an accessible and structured introduction to advanced problem solving, which will help build confidence, fluency and speed. This is a useful resource if you feel uncertain about your mathematical preparation, and you'd like a gentler introduction or just something to 'dip into' at the start to explore some particular topics.
  • STEP questions with solutions at Underground Mathematics. The Underground Mathematics website, funded by the DfE and based at the University of Cambridge, offers free resources to support the teaching of A level mathematics, as well as selected past STEP questions with fully worked solutions and explanations.