Sixth Term Examination Papers (STEP)
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 online help available via: https://support.admissionstestingservice.org/anonymous_requests/new; and a telephone help desk: 01223 553366.
There are three STEP mathematics papers, numbered I, II, and III. Your offer will usually include grades in two of the papers, but possibly I and II if you are not taking the full Further Mathematics Alevel (or an equivalent qualification) or II and III if you are taking Further Mathematics Alevel (or an equivalent qualification).
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 (there is no Further Mathematics core 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.

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.
Useful Links and Resources
 STEP Specification
 This can be found on the Admissions Testing Service website and at the end of the Advanced Problems in Core Mathematics booklet.
 Advanced Problems in Core Mathematics
 A booklet by Stephen Siklos, containing general advice on problem solving accompanied by 70 or so problems with hints and full solutions, and the STEP syllabuses. This would be a good starting point for your preparation.
 NRICH web site
 STEP preparation from NRICH.
 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.
 Advanced Problems in Mathematics
 This booklet by Stephen Siklos consists of 43 STEPlike problems with discussion, hints and full solutions. But beware: it was written before the current syllabuses were in place.