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.
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 you have difficulty finding a test centre where to 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
There are three STEP mathematics papers, numbered I, II, and III. Your offer will usually include grades in two of the papers. If you are taking Further Mathematics Alevel (or an equivalent qualification) the offer is likely to include grades in papers II and III, but if you are not taking the full Further Mathematics Alevel (or an equivalent qualification) the offer will possibly include grades in papers I and II.
Each paper consists of 13 questions: 8 pure, 3 mechanics, and 2 statistics and 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 for Mathematics I and II is based on a typical single subject Alevel syllabus: the Pure Mathematics content is very slightly more than the Alevel common core. The syllabuses for the Mechanics and the Probability and Statistics sections are each equivalent to two or three Alevel modules but, since there is no common core for these areas, the material may not coincide with the modules of your particular Alevel. Paper I is intended specifically for candidates who are not taking Further Mathematics (or the equivalent) and the questions are intended to be easier than those in Paper II. The syllabus for Mathematics III is based on a typical Further Mathematics Alevel syllabus and the questions are intended to be of about the same level of difficulty as those of Paper II.
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 problemsolving 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 Alevel mathematics candidates. It is therefore important to adjust your sights when tackling a STEP paper. The questions are much longer and more demanding than Alevel questions (they are intended to take about 45 minutes, rather than the 10 or so minutes for an Alevel question). They therefore look daunting; but you should not be daunted. In recent years, you only had to give good (not perfect) answers to four questions for a grade 1.
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 problemsolving skills and prepare for sitting STEP Mathematics examinations. The STEP Support programme includes online modules for individual additional study, starting in the summer of Y12, and an online discussion forum. The programme is free and open to everyone: find all the resources at maths.org/STEP.
The STEP Support programme consists of three introductory modules for students to try in the summer holidays between Year 12 and 13, followed by 30 more modules released weekly from September. Each module assignment starts with some warmup exercises, followed by preparatory work leading to a STEP question. Supportive selfevaluation and development material will be published after each assignment, to help you assess your progress and identify areas that need more work.
The programme also includes an online discussion forum to support students preparing for STEP. You can ask for help and hints if you’re stuck, share what you have tried so far, offer advice to others and get guidance from Cambridge University students who’ve taken STEP themselves.
Other Useful Links and Resources
 STEP Specification
 This can be found on the Admissions Testing Service website.
 Advanced Problems in Mathematics: Preparing for University
 A book by Dr Stephen Siklos, containing general advice on problem solving accompanied by 70 or so problems with hints and full solutions, and the STEP syllabuses. This is available as a free pdf or as a paperback, and provides extremely useful help in preparing for any undergraduate mathematics course.
 NRICH Advanced ProblemSolving Modules
 Free online resources from NRICH, designed for selfstudy, to help you develop and consolidate your problemsolving skills.
 Underground Mathematics web site
 Selected STEP questions with fully worked solutions.
 Meikleriggs Mathematics
 Dr Peter Mitchell's web site contains lots of useful mathematics including complete solutions to STEP papers from past years.
 Stephen Siklos's website
 This contains some additional material, including a few video solutions of STEP questions.