British Mathematical Olympiad
The British Mathematical Olympiad (BMO) forms part of the selection process for the UK International Mathematical Olympiad team. It is organised by the British Mathematical Olympiad Subtrust, which is part of the United Kingdom Mathematics Trust. There are two rounds, the BMO1 and the BMO2.
BMO Round 1
The first round of the BMO is held in December, and from 2006 is an open entry competition, costing £17 to enter. However, this fee is waived for those who (1) achieve the qualifying mark in the Senior Mathematical Challenge and (2) are British citizens, or will have studied for 3 full years of full-time secondary education in the UK by the time they leave school. The paper lasts 3½ hours, and consists of six questions (from 2005), each worth 10 marks.
Candidates are encouraged to write full proofs to the questions they attempt, as a full answer to a question is worth many more marks than incomplete answers to several questions. This is because of the marking scheme: an answer is marked on either a "0+" or a "10-" mark scheme, depending on whether the answer looks generally complete or not. So if an answer is judged incomplete or unfinished, it is awarded a few marks for progress and relevant observations, whereas if it is presented as complete and correct, marks are deducted for faults, poor reasoning, or unproven assumptions. As a result, it is quite uncommon for an answer to score a middling mark (i.e. 4–6).
Roughly 1300 students sit the BMO1 paper each year, and many of these attain a very low score as a percentage of the total number of marks available—the median score in 2004 was approximately 5 or 6 (out of 50). However, the paper is meant to be a way of selecting the best young mathematicians in the country, and is therefore very difficult. In addition to the British students, there is a history of about 20 students from New Zealand being invited to take part. Generally only about 30–40 students will score more than 50% in BMO1, with perhaps only 1 or 2 scoring above 90%.
In 2005, UKMT changed the system and added an extra easier question meaning the median is now raised. In 2008, 23 got over 40 out of 60 and around 50 got over 30. 31 was the mark needed to get into the BMO2.
For the December 2010 paper, the mark needed for a year 13 pupil to automatically qualify for BMO2 was 28; it was 22 for a year 12 pupil and 17 for a year 11 pupil.
From the results of BMO1, 100 students are chosen to be invited to sit BMO2—generally from amongst the top scorers, although younger students scoring slightly less than their older counterparts are often chosen also. It is possible to pay £22 to sit BMO2, but the candidate must have sat BMO1.
BMO Round 2
BMO2 (known as the Further International Selection Test, FIST from 1972 to 1991) is normally held in early February, and is significantly more difficult than BMO1. BMO2 also lasts 3½ hours, but consists of only four questions, each worth 10 marks. Like the BMO1 paper, it is not designed to test knowledge of advanced mathematics, but rather the candidate's ability to apply basic ideas to unusual problems.
Half of the candidates score less than 10, and it is rare for someone to score more than 35.
IMO Selection Papers
For more information about IMO selection in other countries, see International Mathematical Olympiad selection process
Since 1985, further selection tests have been used after BMO2 to select the IMO team. (The team was selected following the single BMO paper from 1967 to 1971, then following the FIST paper for some years from 1972.) Initially these third-stage tests resulted in selection of both team and reserve; from 1993 a squad (team plus reserve) was selected following these tests with the team being separated from the reserve after further correspondence training, and after further selection tests from 2001 onwards. The third-stage tests have had names including FIST 2 (1985), Second International Selection Test (SIST), Reading Selection Test (1987), Final Selection Test (FST, 1992 to 2001) and First Selection Test (FST, from 2002); the fourth-stage tests have been Team Selection Test (TST, 2001) and Next Selection Test (NST, 2002 onwards). These tests have been held at training and selection camps in several locations, recently Trinity College, Cambridge and Oundle School.
- http://www.bmoc.maths.org/home/bmo.shtml, BMO website, list of papers
- "News: BMO entry fees". BMOS/BMOC. 29 September 2009.
- "Policy on Eligibility". BMOS/BMOC.
- "The British Mathematical Olympiads". BMOS/BMOC.
- "BMO Marking" (PDF). BMOS/BMOC.
- "BMO1 New Zealand results". Archived from the original on 8 February 2013.
- "News: BMO Round 1 marked (12–14 December 2008)". BMOS/BMOC.