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 Mathematics 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).

Problems booklets including full worked solutions may be purchased from UKMT, as may A Mathematical Olympiad Primer, with hints and solutions for BMO1 problems from 1996–1997 to 2006–2007.

Past papers:

• For older past papers (BMO 1965–1991, BMO 1 1992–1996), with hints and outline solutions 1975–1996, see Tony Gardiner, The Mathematical Olympiad Handbook: An introduction to problem solving based on the first 32 British Mathematical Olympiads 1965–1996 (OUP, 1997).
• An extra more accessible question was added to the start of the paper in 2005; previous papers here consist of five questions without this more accessible question.
• 13 January 1993
• 19 January 1994
• 18 January 1995
• 17 January 1996
• 15 January 1997
• 14 January 1998
• 13 January 1999
• 12 January 2000
• 17 January 2001
• 5 December 2001
• 11 December 2002
• 3 December 2003
• 1 December 2004 (last five-question paper); histogram of distribution of marks
• 30 November 2005 (first six-question paper); list of prizewinners
• 1 December 2006
• 30 November 2007
• 4 December 2008

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.

Past papers:

• This paper was known as the Further International Selection Test (FIST) from 1972 to 1991.
• 11 February 1993
• 24 February 1994
• 16 February 1995
• 15 February 1996
• 27 February 1997
• 26 February 1998
• 25 February 1999
• 23 February 2000
• 27 February 2001
• 26 February 2002
• 25 February 2003
• 24 February 2004
• 1 February 2005
• 31 January 2006
• 30 January 2007
• 31 January 2008
• 29 January 2009