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Sixth Term Examination Papers in Mathematics, often referred to as STEP (or as STEP papers through RAS syndrome), are examinations set in the United Kingdom by the University of Cambridge to assess applicants for undergraduate mathematics courses. Other universities may require STEP, including the University of Warwick. Students used to be entered for STEP through the OCR exam board, but as of 2008 are administered by its parent group, Cambridge Assessment.
Results from STEP papers are used to supplement candidates' existing exam results, which are often claimed to be insufficient to distinguish between the very brightest applicants. Each year, over 1,500 students take at least one STEP paper. The overall candidature is made up of: those applying for mathematics at the University of Cambridge or the University of Warwick; the University of Bristol, the University of Oxford, Imperial College London and the University of Bath may also encourage mathematics applicants to take STEP papers. In fact anyone, with or without the aim of seeking admission to an institution, may take STEP, making them public examinations.
All of the Cambridge colleges require candidates to achieve good STEP grades before accepting them onto the maths course. Mathematics applicants for some Cambridge colleges who compete in the International Mathematical Olympiad are often excused from taking STEP.
Before 2003, STEP papers were available for a wide range of subjects, including, for example, chemistry and biology, but the mathematics STEP paper is the only one now in use. Three STEP Maths papers are set each year. The university the candidate is applying to may specify which of the papers need to be taken: for example, for applicants to the University of Cambridge, it is usually STEP I (necessary for single maths candidates) and/or II (depends on which college, some do and some don't) if they are taking Mathematics A Level, and STEP II and III if they are also taking Further Mathematics. STEP Maths grades are also occasionally required for other courses at the University of Cambridge, such as computer science and engineering. These offers are usually STEP II (instead of STEP I or STEP III).
The syllabus for STEP I and STEP II is based on Mathematics A level content whilst the syllabus for STEP III is based on Further Mathematics A level. The questions on STEP II and III are intended to be of about the same difficulty, and both are harder than STEP I. Candidates are only expected to have knowledge of topics within the A level syllabus. Candidates who are not studying Further Mathematics will not be expected to sit STEP III.
Lined answer sheets and a formula booklet are provided for each paper. From June 2009 graph paper is no longer to be used by candidates in the STEP examinations as all the graphs required are sketches, it is neither necessary nor appropriate for candidates to produce detailed graphs on graph paper. Instead all graphs should be sketched inside the answer booklets alongside their answer to the question.
Calculators may not be used during STEP.
There are five possible grades awarded on STEP. From best to worst, these are 'S' (Outstanding), '1', '2', '3', and 'U' (Unclassified). The 'rule of thumb' is that four good answers (to a reasonable level of completion) will gain a grade 1; more may gain an S, and fewer will gain a correspondingly lower grade. However, the grade boundaries can shift dramatically from year to year, and the boundaries for Mathematics III are generally a small but appreciable margin lower. 
All STEP questions are marked out of 20. The mark scheme for each question is designed to reward candidates who make good progress towards a solution. A candidate reaching the correct answer will receive full marks, regardless of the method used to answer the question.
All the questions that are attempted by a student will be marked. However, only the 6 best answers will be used in the calculation of the final grade for the paper.
Numbers taking the exams (across all subjects before 2003):
Typically (based on all subjects; i.e. before 2003),
The following table lists the cumulative percentages of the grades achieved by candidates taking STEP in 2011:
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