Junior, Intermediate & Senior Challenges — BMO & Olympiads — free papers & solutions
The UK's most popular maths competition for Years 7–8 (ages 11–13). 25 multiple-choice questions in 60 minutes, testing logical reasoning and problem-solving. Over 300,000 students participate annually. Top scorers are invited to the Junior Kangaroo or Junior Mathematical Olympiad.
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For students in Years 9–11 (ages 13–16). 25 multiple-choice questions in 60 minutes covering algebra, geometry, number theory, and combinatorics. Top performers qualify for the Grey/Pink Kangaroo or the Intermediate Mathematical Olympiad (Cayley, Hamilton, or Maclaurin).
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The premier maths challenge for Years 12–13 (ages 16–19). 25 multiple-choice questions in 90 minutes. Covers topics up to and including A-Level. Top scorers qualify for the Senior Kangaroo or British Mathematical Olympiad Round 1. Over 100,000 students participate annually.
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An invitation-only competition for top JMC performers in Years 7–8. Two sections: Section A (10 short answer problems) and Section B (6 longer problems requiring full solutions). Tests deeper mathematical reasoning and proof-writing skills at the junior level.
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Three parallel olympiad papers for top IMC performers. Cayley (Year 9), Hamilton (Year 10), Maclaurin (Year 11). Each consists of 6 problems requiring full written solutions in 2 hours. Named after famous mathematicians, these bridge the gap between the IMC and senior-level olympiads.
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Round 1: For top ~1,000 SMC scorers. 6 problems in 3.5 hours requiring full proofs. Round 2: For top ~100 BMO1 scorers. 4 harder problems in 3.5 hours. The top BMO2 performers are selected for further training towards the UK IMO team.
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Students enter through the Challenges (JMC/IMC/SMC) based on year group. Top scorers progress to Kangaroos or Olympiads. The Senior pathway goes SMC → BMO1 → BMO2 → UK IMO Team selection. Over 700,000 students participate in UKMT competitions annually.
Each Challenge has 25 multiple-choice questions. Correct answers in the first 15 earn 5 marks each, the next 5 earn 6 marks each, and the last 5 earn no marks for wrong answers but penalise 1 mark to discourage guessing. Maximum score is 135.
JMC is comparable to AMC 8, IMC to AMC 10, SMC to AMC 12. BMO1 is similar to AIME difficulty, while BMO2 approaches USAMO level. The key structural difference is that UKMT uses a single competition per age group (no A/B versions).
UKMT competitions are primarily for schools in the UK. However, some international schools registered with UKMT can enter students. Contact UKMT directly for international participation details.