Overview
The British Mathematical Olympiad (BMO) is the UK's main proof-based maths competition for school students, run by the United Kingdom Mathematics Trust (UKMT). It has two rounds, BMO1 and BMO2, and leads to selection for the UK team at the International Mathematical Olympiad.
Who can enter
Both rounds are open to students in:
England, Wales and overseas: Year 13 and below
Scotland: S6 or below
Northern Ireland: Year 14 or below
Entry to BMO1 is mainly by invitation from the Senior Mathematical Challenge (about 1,000 students), though schools may enter other eligible students. BMO2 is by invitation from BMO1 (about 100 students), with the same option for schools.
Levels or stages
BMO1
A 3.5 hour paper of six problems needing full written solutions. Calculators and protractors are not allowed; rulers, set squares and compasses are. One complete solution earns far more credit than partial attempts at all six. For 2026 it is held on Wednesday 18 November 2026, with answer sheets uploaded by 19 November 2026.
BMO2
A 3.5 hour paper of four problems, also with full written solutions. For 2027 it is held on Wednesday 20 January 2027, with uploads due by 21 January 2027.
Fees
Invited students enter free. Discretionary entries cost 40 pounds for BMO1 and 50 pounds for BMO2.
After the competition
Around 24 high-scoring students who are eligible to represent the UK at the International Mathematical Olympiad are invited to a training session in Cambridge around the Easter holidays.
Preparation tips
Practise writing complete, clear proofs, since marks depend on the quality of written arguments. Past BMO papers are the best guide to the style of problem.
Do I have to take the SMC first?
Qualification is normally through the Senior Mathematical Challenge or the Mathematical Olympiad for Girls, but schools may enter other students for a fee.
Are calculators allowed?
No. Calculators and protractors are banned; rulers, set squares and compasses are allowed.