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    UKMT SMC 2023 Past Paper & Solutions

    Senior Mathematical Challenge 2023 — 25 multiple-choice questions, 90 minutes. Scoring: 5 marks for Q1–15, 6 marks for Q16–25, penalties in the back section.

    Download the UKMT SMC 2023 PDFs

    Official UKMT files — each link opens the PDF directly.

    Question paper (PDF)Solutions (PDF)Extended solutions (PDF)Solutions (PDF)

    Papers in this sitting

    • UKMT SMC 2023 — 25 multiple-choice questions, official answer key included
    Open the official archive

    How to work through this paper

    1. Sit the full paper timed at 90 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 (Algebra & functions, Trigonometry, Combinatorics, Geometry, Proof habits).
    5. Re-sit the same paper one week later and compare the time to your first attempt.

    Topics tested in UKMT SMC 2023

    Algebra & functionsTrigonometryCombinatoricsGeometryProof habits

    Stuck on a UKMT SMC 2023 question?

    Send us the question number. A mentor who has sat and medalled in UKMT SMC 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 UKMT SMC course

    FAQs

    Where can I find the UKMT SMC 2023 paper and answers?
    The official UKMT SMC 2023 question paper and solutions are published free by UKMT, and the download buttons on this page open those PDFs directly. We link the official files rather than re-hosting them, and our mentors walk through every question with you step by step.
    How hard was the UKMT SMC 2023 paper?
    Like every year, the first section is speed-and-accuracy work and the final third carries the discrimination. Sit it timed (90 minutes), mark it against the official key, then rewrite full solutions for anything you missed or guessed.
    Can I get worked solutions for UKMT SMC 2023?
    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.