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    BMO Round 1 2025 Past Paper & Solutions

    British Mathematical Olympiad Round 1 2025 — 6 problems requiring full written proofs, 3 hours 30 minutes. Scoring: 10 marks per problem, awarded all-or-nothing in spirit — partial credit is rare.

    Papers in this sitting

    • BMO Round 1 2025 — 6 problems requiring full written proofs, official answer key included
    Open the official archive

    How to work through this paper

    1. Sit the full paper timed at 3 hours 30 minutes, no calculator or notes.
    2. Mark it against the official key before you look at any solution.
    3. Rewrite complete solutions for every question you missed or guessed — writing it out is what moves the technique into recall.
    4. Tag each loss by topic (Olympiad geometry, Number theory, Combinatorics, Algebra & inequalities, Proof writing).
    5. Re-sit the same paper one week later and compare the time to your first attempt.

    Topics tested in BMO Round 1 2025

    Olympiad geometryNumber theoryCombinatoricsAlgebra & inequalitiesProof writing

    Stuck on a BMO Round 1 2025 question?

    Send us the question number. A mentor who has sat and medalled in BMO Round 1 will reply with a step-by-step walkthrough and the faster competition method.

    Free to ask. No spam, ever — we only reply about your question.

    View the BMO Round 1 course

    FAQs

    Where can I find the BMO Round 1 2025 paper and answers?
    The official BMO Round 1 2025 paper and answer key are published by UKMT — use the official archive link on this page. We do not re-host copyrighted papers, but our mentors walk through every question with you step by step.
    How hard was the BMO Round 1 2025 paper?
    Like every year, the first section is speed-and-accuracy work and the final third carries the discrimination. Sit it timed (3 hours 30 minutes), mark it against the official key, then rewrite full solutions for anything you missed or guessed.
    Can I get worked solutions for BMO Round 1 2025?
    Yes. Book a free trial session and bring the questions you are stuck on — a mentor will work through the full solution and the faster competition method, then set targeted practice on the same archetype.