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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 administered by the Admissions Testing Service (which is part of Cambridge Assessment, the parent company of the OCR examination board) and are taken in 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.

The Admissions Testing Service has a dedicated STEP website, which has all the details of the examination (method of entry, dates, syllabus, etc) as well as downloadable past papers. (There is also an Admissions Testing Service helpdesk which can be contacted online or by phone: 01223 553366.)

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, the STEP online help may be able to advise you, and you can also use their online search to find a test centre, in the UK or abroad.

STEP format

The papers

  • There are three STEP mathematics papers: STEP 1, STEP 2, and STEP 3.  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. The paper for STEP I has 11 questions (8 pure and 3 mechanics or statistics/probability, with at least one mechanics and one statistics/probability). Each paper is assessed on answers to at most 6 questions. There are five grades, which are (from highest to lowest) S, 1, 2, 3, and U. 

The syllabus

  • STEP 1 is based on A-level Mathematics only, and the questions are intended to be easier than those in STEP 2.
  • 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 Admissions Testing Service website. Note: even though the specification for STEP in 2019 onwards has changed from that in previous years, the style of the questions is unaltered and questions from previous papers can be used for preparation.


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. The meaning of A-level grades may differ significantly between the different boards, so STEP provides a fairer 'across the board' comparison.

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 has launched 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 (they are intended to take about 45 minutes, rather than the 10 or so minutes for an A-level question). 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 Problem-Solving resources from NRICH. This is an accessible and structured introduction to advanced problem solving, which will help build confidence, fluency and speed. An excellent starting point.
  • 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.
  • 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.
  • All past papers from 1998 are available to download from Cambridge Assessment and include:
    • answers to all questions from 2004,
    • solutions with explanation and mark scheme for the 2011 STEP I paper.
  • Meikleriggs Mathematics: Dr Peter Mitchell's web site contains lots of useful mathematics including complete solutions to STEP papers from past years.