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Cayley, Hamilton and Maclaurin Mathematical Olympiads

As follow-on Rounds to the Intermediate Maths Challenge, the Cayley, Hamilton and Maclaurin Maths Olympiads are 2 hour Challenges consisting of six Olympiad style problems.

Entry to the Intermediate Olympiads is by invitation based on a qualifying IMC score, or by discretionary entry. Around 1,800 students qualify from the IMC each year.

Time limit
2 hours

£25 per discretionary
entry, free entry via qualification.
Sold individually

Age group
Cayley Maths Olympiad:
England, Wales and Overseas: Year 9 and below
Scotland: S2 or below
Northern Ireland: Year 10 or below

Hamilton Maths Olympiad:
England, Wales and Overseas: Year 10
Scotland: S3
Northern Ireland: Year 11

Maclaurin Maths Olympiad:
England, Wales and Overseas: Year 11
Scotland: S4
Northern Ireland: Year 12

Deadline for Braille/Large Print paper order
Tuesday 25th February 2025

Competition Date
Thursday 20th March 2025

Deadline for paper answer sheets upload
Friday 21st March 2025 (by midnight)

How it works


Register your school


Purchase entries


Sit challenge


Receive results

For full information on how to host the Cayley, Hamilton and Maclaurin Mathematical Olympiads please visit the Challenge Handbook.

Preparing for the challenge

We are delighted to be working with Dr Frost Maths to help teachers use UKMT past papers and problems in the classroom.

You can utilise UKMT past papers, solutions and investigations as preparation materials for your students. They are a great resource containing high-quality problems from previous years designed to encourage mathematical thinking.


The use of blank paper for rough working is allowed; squared paper, calculators and measuring instruments are forbidden.

Do not hand in rough work

Your answers should be fully simplified, and exact. They may contain symbols such as π, fractions, or square roots, if appropriate, but not decimal approximations.

You should give full written solutions, including mathematical reasons as to why your method is correct. Just stating an answer, even a correct one, will earn you very few marks; also, incomplete or poorly presented solutions will not receive full marks.

To accommodate candidates in other time zones, please do not discuss any aspect of the paper on the internet until 8am GMT on Saturday 23 March. Candidates in time zones more than 5 hours ahead of GMT must sit the paper on Friday 22 March (as defined locally).

Ready to join the
Cayley, Hamilton and Maclaurin Mathematical Olympiads

Past Papers

Download UKMT’s free past papers to help students achieve better results.

Maths Books

Browse UKMT’s range of maths books and older past papers on Amazon to help you and your students prepare for maths challenges.

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