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.

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.

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