British Mathematical Olympiad, Round 1 (BMO 1)
This is a 3½-hour paper with 6 problems (the first being intended to be more accessible than the rest), taken by students in their own schools. Selection is based on performance in the UK Senior Mathematical Challenge (UKSMC). Students achieving a certain score in UKSMC (this score varying from year to year depending on overall performance) and eligible to represent the UK at the IMO are entered automatically for BMO 1. Teachers are invited to use their judgement in entering other students. See BMO entry information for more details. Typically 1300 students sit BMO 1. A team of around 25 markers gathers in December to mark all the scripts over a 3-day period. The top 100 students receive prizes. See also notes on BMO marking (PDF) and guidance for BMO preparation.
A Mathematical Olympiad Primer, with hints and solutions for BMO1 problems from 1996–1997 to 2010–2011, may be purchased from UKMT; A Mathematical Olympiad Primer II, covering the period from 2011–2012 to 2022–2023, is also available; video solutions for BMO1 are also available from 2005–2006 onwards. Other UKMT publications of use for BMO preparation include Plane Euclidean Geometry: Theory and Problems, especially chapters 3–7, and Crossing the Bridge for further geometry preparation. Serious geometers may also be interested in New Problems in Euclidean Geometry.
British Mathematical Olympiad, Round 2 (BMO 2)
This is a 3½-hour paper with 4 problems, taken by students in their own schools. Based on performances in BMO 1, up to 100 students (who are eligible to represent the UK at the IMO) are invited to sit BMO 2, with selection taking account of age and other factors; others who entered BMO 1 may enter on payment of the entry fee. Marking is carried out by around ten people, under the direction of the current IMO Team Leader.
BMO2 solutions are included in A Mathematical Olympiad Companion, available from the UKMT.