Sixth Term Examination Paper

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Sixth Term Examination Papers in Mathematics, often referred to as STEP (or as STEP papers through RAS syndrome), are university admissions tests for undergraduate Mathematics courses developed by the University of Cambridge.

STEP papers are typically taken post-interview, as part of a conditional offer of an undergraduate place. There are also a number of candidates who sit STEP papers as a challenge. The papers are designed to test ability to answer questions similar in style to undergraduate Mathematics.[1]

Candidates applying to study Mathematics at the University of Cambridge and the University of Warwick are required to take STEP papers as part of the terms of their conditional offer. In addition, a number of other UK universities encourage their applicants to take STEP papers.

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 who are taking Mathematics A Level, it is usually STEP 1 (necessary for single Mathematics candidates) and/or STEP 2 (depends on the College) or STEP 2 and STEP 3 if they are also taking Further Mathematics. STEP grades are also occasionally required for other courses at the University of Cambridge, such as Computer Science and Engineering.[2]


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 Mathematics papers are set each year.

The number of candidates taking STEP Mathematics papers by 2013 had more than doubled since 2005:

Year STEP 1 STEP 2 STEP 3 Total
2005 353 565 430 1,348
2006 389 614 451 1,454
2007 565 712 483 1,760
2008 697 851 552 2,100
2009 908 917 528 2,353
2010 1,098 980 554 2,632
2011 1,181 1,031 635 2,847
2012 1,166 1,004 653 2,823
2013 1,494 1,134 706 3,334


The test consists of up to three paper-based examinations: STEP 1, STEP 2 and STEP 3. In all three STEP papers, candidates have 3 hours to complete at most six questions from a choice of 13 (eight Pure Mathematics questions, three Mechanics questions, and two Probability and Statistics questions).

No restrictions are placed on the number of questions that may be attempted and all questions carry the same weight. A candidate’s grade will be based on the six questions best answered.[3]

The syllabus for STEP 1 and STEP 2 is based on Mathematics A Level content while the syllabus for STEP 3 is based on Further Mathematics A Level. The questions on STEP 2 and 3 are intended to be of about the same difficulty. Both STEP 2 and STEP 3 are harder than STEP 1.[4]

Lined answer sheets and a formula booklet are provided for each paper. Since June 2009, graph paper has not been allowed in STEP examinations as the test requires only sketches, not detailed graphs. Instead, all graphs should be sketched inside the answer booklets alongside the answer to the question.

Calculators may not be used during STEP. Rulers, protractors and compasses can be taken into the examination. Candidates who don’t have English as a first language are allowed to use bilingual dictionaries.


There are five possible grades awarded. 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 from year to year, and the boundaries for STEP 3 are generally a small but appreciable margin lower.[5]

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 six best answers will be used in the calculation of the final grade for the paper.

Timing and results[edit]

Candidates who have received offers for Mathematics courses at the University of Cambridge sit STEP as a post-interview test. STEP papers are normally sat at a candidate’s school or college. Alternatively, the test can be taken at one of Cambridge Assessment Admissions Testing’s authorised ‘open centres’ worldwide.

Entries for STEP papers are typically accepted from the start of March until the end of April and late entries (with late entry fees) accepted until mid-May. STEP papers are taken mid to late June, with online results available mid-August, issued on the same date as A Level results.


There is some variation in how institutions make use of the results – candidates can contact the relevant institution(s) for more information. However, STEP papers are taken post-interview and results typically used to supplement candidates’ exam results. University College London (UCL) does not require the candidate to take STEP paper but getting grade 1 or 2 in any of the STEP papers could make up for an A*. Imperial college usually ask candidate to take STEP papers who are pursuing for Mathematics or Computer Science degree if they are unable to take MAT or if they apply to Imperial College London after the MAT exam.

Candidates’ answers are made available to admissions officers. This enables officers to make judgements on the basis of candidates’ actual work, rather than on just their marks or grade.[6]


STEP papers do not require a lot of extra knowledge as they are designed to test skills and knowledge of topics within the A Level syllabus. Candidates who are not studying Further Mathematics will not be expected to sit STEP 3.

Practice materials, including past papers, example solutions and a STEP formula booklet, are available for free from the Cambridge Assessment Admissions Testing website.

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