# British Mathematical Olympiad

The **British Mathematical Olympiad** (**BMO**) forms part of the selection process for the UK International Mathematical Olympiad team and for other international maths competitions, including the European Girls' Mathematical Olympiad, the Romanian Master of Mathematics and Sciences, and the Balkan Mathematical Olympiad. 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.^{[1]}

## BMO Round 1[edit]

The first round of the BMO is held in late November or early December each year, and from 2006 is an open entry competition. The qualification to BMO Round 1 is through the Senior Mathematical Challenge for those eligible to represent the UK at the IMO, the eligibility criteria being that either they are British citizens, or will have completed at least 3 full years of full-time secondary education in the UK by the time they leave school.^{[2]} Students who are not eligible to represent the UK and/or who do not make the qualification through the Senior Mathematical Challenge may be entered at the discretion of their school for a fee of £22.^{[3]}

The paper lasts 3½ hours, and consists of six questions (from 2005), each worth 10 marks.^{[4]} The exam in the 2020-2021 cycle, however, is adjusted so that it consists of two sections, first section with 4 questions each worth 5 marks (only answers required), and second section with 3 question each worth 10 marks (full solutions required). The duration of the exam had been reduced to 2½ hours, due to considering the difficulties of upholding a 3½ hours exam under COVID-19.^{[5]}

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.^{[6]} So if an answer is judged incomplete or unfinished, it is awarded few marks for progress and relevant observations but usually capped at 3 or 4, whereas if it is presented as complete and correct, marks may be deducted for minor errors or poor reasoning but a candidate is likely to get a score of 7 or more. As a result, it is uncommon for an answer to score a middling mark between 4 to 6.

While around 1000 gain automatic qualification to sit the BMO1 paper each year,^{[4]} the additional discretionary and international students means that since 2016, on average, around 1600 candidates have been entered for BMO1 each year. Although these candidates represent the very best mathematicians in their age group, the difficulty level of the BMO papers mean that many of these attain a very low score.

The scores were particularly low until 2004, for example, when the median score was approximately 5-6 (out of 50). In 2005, UKMT changed the system and added an extra easier question meaning the median is now raised. In 2008, 23 students scored more than 40/60 ^{[7]} and around 50 got over 30/60.

In addition to the British students, until 2018, there was a history of about 20 students from New Zealand being invited to take part.^{[8]} In recent years, entries to BMO have been made from schools in Ireland, Kazakhstan, India, China, South Korea, Hong Kong, Singapore, and Thailand.

BMO1 paper for the cycle 2020-21 was held on 26 November 2020 and attracted 1706 entries. Only 11 candidates, or fewer than 1%, scored above 90%, with only three perfect scorers - Thomas Frith, Thien Udomsrirungruang, and Tommy Walker Mackay.^{[9]} A score of 18/50 was enough to earn a Distinction, awarded to top 25% of the candidates.

From the results of the BMO1, around 100 top scoring students who are eligible to represent the UK at the International Mathematical Olympiad are invited to sit the BMO2. For the 2020-21 cycle, the score needed for to automatically qualify for BMO2 was 27 for a year 13 pupil, 26 for a year 12 pupil, and 24 for a pupil in year 11 and below.^{[4]} Students who did not take the BMO1, or who did not qualify for an invitation, may be entered into the next round at the discretion of their school through payment of a fee of £29.^{[10]}

Typically, around top 20 scoring students in BMO1 feature on what is known as the BMO Leaderboard.

## BMO Round 2[edit]

BMO2 (known as the *Further International Selection Test, FIST* from 1972 to 1991) is normally held in late January or 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 merely to test knowledge of advanced mathematics but rather to test the candidate's ability to apply the mathematical knowledge to solve unusual problems and is an entry point to training and selection for the international competitions.

BMO2 paper for the cycle 2020-21 was held on 28 January 2021 and attracted around 250 entries. A score of 11/40 was enough to earn a Distinction, awarded to top 25% of the candidates.^{[11]} Only 16 candidates scored more than 20/40.

Twenty-four of the top scorers from BMO2 are subsequently invited to the training camp at Trinity College, Cambridge for the first stage of the IMO UK team selection.^{[1]}

The top 4 female scorers from BMO2 are selected to represent the UK at the European Girls' Mathematical Olympiad. The UK team for the EGMO 2021 was Aanya Goyal, Eleanor MacGillivray, Yuka Machino, and Jenni Voon.^{[12]}

## IMO Selection Papers[edit]

*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.^{[1]}

Since 2017, the tests are simply called Team Selection Tests (TSTs). Six TSTs were held in 2017 and 2018. Since 2019, the number of TSTs have been reduced to 4 or two rounds, the first round is held in late April and the second round in late May. The UK IMO squad of 10 is selected following the first round of tests with the final team of 6 to represent the UK at the International Mathematical Olympiad announced following the second round.^{[13]}

In 2021, the first round of TSTs was held on 16-17 April and the second round on 5-6 June. The UK squad for IMO 2021 was Mohit Hulse, Issac King, Samuel Liew, Yuka Machino, Daniel Naylor, and Jenni Voon, with Tommy Walker Mackay being the first reserve. This is only the second time over the last 54 years of the UK's participation at the International Mathematical Olympiad since 1967 that more than one female contestant has made the UK IMO team.^{[14]}

## See also[edit]

## References[edit]

- ^
^{a}^{b}^{c}http://www.bmoc.maths.org/home/bmo.shtml, BMO website, list of papers **^**"Policy on Eligibility". BMOS/BMOC.**^**"News: BMO entry fees". BMOS/BMOC. 29 September 2009.- ^
^{a}^{b}^{c}"The British Mathematical Olympiads". BMOS/BMOC. **^**https://bmos.ukmt.org.uk/home/bmo1-2021-report.pdf^{[bare URL PDF]}**^**"BMO Marking" (PDF). BMOS/BMOC.**^**"News: BMO Round 1 marked (12–14 December 2008)". BMOS/BMOC.**^**"BMO1 New Zealand results". Archived from the original on 8 February 2013.**^**"BMOS/BMOC: News: BMO Round 1 high scores (16 December 2020)".**^**"British Mathematical Olympiad Round 2 | UK Mathematics Trust". Archived from the original on 6 August 2019.**^**"British Mathematical Olympiad Round 2 | UK Mathematics Trust". Archived from the original on 6 August 2019.**^**"BMOS/BMOC: News: EGMO 2021 team (26 February 2021)".**^**"BMOS/BMOC: IMO Selection Tests".**^**"BMOS/BMOC: News: IMO team selected (6 June 2021)".