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    Cayley Mathematical Olympiad

    by UK Maths Trust

    A rigorous UKMT follow-on maths challenge built around full written solutions to Olympiad-style problems.

    Last verified: 18 Aug 2026Reviewed by:SSSean Stevens
    Cayley Mathematical Olympiad

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    Cayley Mathematical Olympiad at a glance: cost, dates and eligibility

    Current status

    Open now

    Eligibility

    IMC qualification or discretionary entry

    Age range / Year group

    Up to 14

    Location / Region

    Participating UKMT-registered schools in the UK and overseas

    Cost

    Free via qualification; £25 discretionary

    Prize highlight

    Medals, book prizes and certificates

    Entry format

    In-school written paper

    Deadline

    19 March 2027

    Save deadline

    Cayley Mathematical Olympiad summary

    The Cayley competition is UKMT’s younger Intermediate Olympiad, designed as a follow-on challenge for strong mathematical problem-solvers.

    Students tackle six Olympiad-style questions and must show complete reasoning, not simply provide final answers.

    It suits students who enjoy unfamiliar problems, proof-style thinking and communicating mathematics precisely.

    What is Cayley Mathematical Olympiad?

    The Cayley Mathematical Olympiad is one of UKMT’s Intermediate Olympiads and follows the Intermediate Maths Challenge. It is organised by UKMT as a demanding test of mathematical reasoning and written problem solving.

    Students work through six Olympiad-style problems under exam conditions. Each solution must explain the method and mathematical reasoning clearly, allowing markers to award partial credit for sound progress and presentation.

    Why Succeed highlights Cayley Mathematical Olympiad

    • The six-question paper rewards depth of reasoning rather than rapid multiple-choice technique.

    • Partial marks recognise meaningful mathematical progress and clear presentation.

    • Free Cayley past papers provide a strong, directly relevant preparation resource.

    • The published medal and certificate structure gives students several levels of recognition.

    • Markers’ comments are made available to Olympiad students through their individual portals.

    Who is Cayley Mathematical Olympiad for?

    Best for

    Confident young mathematicians who enjoy unfamiliar problems, proof-style reasoning and explaining every step.

    Not ideal if

    You prefer calculator-based work, short answers or a competition that can be completed independently at home.

    Is Cayley Mathematical Olympiad worth it?

    Yes, for a student ready to move beyond routine school exercises. The paper develops mathematical resilience, proof writing and the ability to communicate a logical argument, while past papers make preparation focused and accessible.

    The main limitation is access: entry is managed by a registered school, and discretionary participation depends on the school purchasing an entry. Recognition is meaningful, but the strongest value comes from engaging seriously with the problems and learning from the marked work.

    How much preparation does Cayley Mathematical Olympiad need?

    Effort level

    High.

    Best started

    Begin regular past-paper practice several weeks before the March sitting.

    Main challenge

    Turning promising ideas into complete, rigorous mathematical explanations.

    Typical preparation

    • Complete a Cayley past paper under timed conditions to establish a baseline.

    • Review official solutions and rewrite incomplete arguments in a clearer sequence.

    • Practise working without a calculator and keep final answers exact and fully simplified.

    Useful if

    You already enjoy non-routine problems and can persist when a method is not obvious.

    What do students do on Cayley Mathematical Olympiad?

    Students complete a school-invigilated paper containing six Olympiad-style problems. The school then scans and uploads the completed answer sheets for marking.

    Step-by-step process

    1. 1

      Qualify through the Intermediate Maths Challenge or receive a discretionary school entry.

    2. 2

      Prepare with Cayley past papers, solutions and related investigations.

    3. 3

      Sit the printed paper under strict exam conditions at school.

    4. 4

      Write full solutions that justify each method mathematically.

    5. 5

      Leave answers exact and fully simplified rather than using decimal approximations.

    6. 6

      Have the school scan and upload the completed answer sheets.

    7. 7

      Access results, certificates and marker feedback through UKMT’s competition system.

    Cayley Mathematical Olympiad dates and deadlines

    Accessible paper order

    18 February 2027

    Braille or large-print paper orders

    Upcoming

    Competition date

    18 March 2027

    Two-hour school sitting

    Upcoming

    Answer upload

    19 March 2027

    Paper answer sheets due by 11:59pm

    Upcoming
    Save deadline

    Eligibility and requirements

    • Qualifying Intermediate Maths Challenge score or discretionary entry

    • England, Wales and overseas: Year 9 or below

    • Scotland: S2 or below

    • Northern Ireland: Year 10 or below

    • Entry through a registered UKMT centre

    • One follow-on round per student

    How much does Cayley Mathematical Olympiad cost?

    Entry cost

    Free or £25 — Qualifiers enter free; discretionary entries cost £25

    How to enter Cayley Mathematical Olympiad

    1. 1

      Ask your school whether it is a registered UKMT centre.

    2. 2

      Complete the Intermediate Maths Challenge and check whether you qualified for Cayley.

    3. 3

      If you did not qualify automatically, discuss a discretionary entry with your school coordinator.

    4. 4

      The school coordinator purchases any required entry through the UKMT Competition Profile.

    5. 5

      The school downloads and prints the question paper and personalised answer sheets.

    6. 6

      After the sitting, the school scans and uploads the answer sheets through its profile.

    Save this competition in Succeed, keep the deadline visible, and track your progress before you submit.

    Start your entry checklist

    Submission requirements

    Solutions are marked for both mathematical correctness and the clarity of the written reasoning.

    • Full written solutions for each attempted problem

    • Mathematical reasons supporting every method

    • Fully simplified, exact final answers

    • No decimal approximations

    • No calculators or measuring instruments

    • No squared paper

    • Do not submit rough work

    • Scanned answer sheets under 14MB per upload

    Prizes and recognition

    Gold medal

    The top 20 scorers receive a gold medal and book prize.

    Silver medal

    The next 30 scorers receive a silver medal and book prize.

    Bronze medal

    The next 50 scorers receive a bronze medal and book prize.

    Distinction certificate

    Awarded to the top-scoring 25% of participants.

    Merit certificate

    Awarded to the next 40% of participants.

    Other certificates

    Qualification or Participation certificates depend on entry route.

    What this may help with

    Demonstrating advanced mathematical engagement and reflecting on proof-based problem solving.

    What it does not guarantee

    University admission, selection for another competition or a particular academic outcome.

    Judging criteria

    • 10 marks — Each of the six problems
    • Mathematical correctness of the solution
    • Complete reasoning supporting the method
    • Clarity of mathematical presentation
    • Partial marks for meaningful progress
    • Exact and fully simplified answers

    How to stand out

    1. Write a logical sequence that another mathematician can follow without filling in gaps.
    2. Explain why each important step works instead of relying on unexplained calculations.
    3. Attempt every promising problem, because partial progress can earn marks.
    4. Keep notation tidy and define any variables or constructions before using them.
    5. Check that final expressions are exact and fully simplified.
    6. Use past papers to identify recurring weaknesses in proof structure and presentation.

    Cayley Mathematical Olympiad FAQs

    It is a UKMT follow-on round to the Intermediate Maths Challenge. Students solve six Olympiad-style problems and present full written reasoning.

    Students may be invited after achieving a qualifying Intermediate Maths Challenge score. Schools can also purchase discretionary entries for eligible students.

    No. UKMT competitions are normally entered through institutions registered as UKMT centres, not by individual students, parents or private tutors.

    No. Calculators and measuring instruments are forbidden, while blank paper may be used for rough working.

    Yes. Full written solutions must include mathematical reasons explaining why the method is correct. A correct answer without sufficient reasoning earns very few marks.

    Yes. Markers can award partial credit for meaningful progress and clear mathematical presentation.

    UKMT recommends using its past papers, solutions and investigations. Timed practice should be followed by careful comparison with full solutions.

    Participants may receive Distinction, Merit, Qualification or Participation certificates, depending on performance and entry route.

    Alternatives to Cayley Mathematical Olympiad

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    Sean Stevens

    Content reviewed by

    Sean Stevens

    Co-founder, Succeed | Founder, Immerse Education (2012–2026)

    Sean works at the intersection of academic enrichment, programme quality and university preparation, with expertise in evaluating pre-university experiences for ambitious secondary school students.

    View author page

    Sources & verification

    Source types reviewed

    • Competition Handbook - Order T&Cs
    • Competition Handbook - FAQs
    • Competition Handbook - Quick-Step Guide
    • Competition Handbook - Orders & Payments
    • Competition Handbook - UKMT Competitions
    • Cayley, Hamilton and Maclaurin Mathematical Olympiads Awards - UKMT
    • Competition Calendar 2026-27 - UKMT
    • Cayley, Hamilton and Maclaurin Mathematical Olympiads - UKMT

    Succeed uses official provider information where available, but keeps this public page focused on comparison and planning inside Succeed.

    What we verified (on 18 Aug 2026)

    • Competition date checked

    • Eligibility rules reviewed

    • Entry cost verified

    • Candidate instructions checked

    • Awards structure reviewed

    • School process confirmed

    How Succeed uses this information

    We use source material to verify core facts, then show older cycle dates as reference when a current cycle is not available. Always check current submission instructions before entering.