British Mathematical Olympiad past paper

The United Kingdom Mathematics Trust (UKMT) was founded in 1996 and stands as a registered charity, whose charitable aim is to advance the education of young people in mathematics by offering a wide range of national-level competitions and activities for students from 11 to 18 years old in the UK.UKMT is also responsible for selecting UK National Mathematical Olympiad team to participate in the IMO. UKMT has a comprehensive mathematics assessment system, which not only encourages wide participation, develops interest, and experiences JMC/IMC/SMC and also includes BMO for selecting a national team.
BMO has two rounds: BMO Round 1 and BMO Round 2. Only the top 10% in BMO Round 1 can participate in Round 2. UKMT will select the top UK students from Round 2 to take part in the UK National Mathematical Olympiad camp and select the national team. Different from the multiple choice questions of the SMC, BMO is mainly a proof question, which requires students to specify the steps and process of solving the problem, and to investigate students’ comprehensive mathematical academic strength in depth. In the UK, only students with excellent SMC results are eligible to participate in BMO Round 1.