Download past papers, solutions and investigations

Promoting a love of problem solving

The Senior Mathematical Challenge is a 90-minute, multiple-choice competition aimed at students across the UK.

It encourages mathematical reasoning, precision of thought, and fluency in using basic mathematical techniques to solve interesting problems.

The problems on the Senior Mathematical Challenge are designed to make students think. Most are accessible, yet still challenge those with more experience.

How do I take part?

The competition is aimed at students in schools and colleges based in the UK. Entries must be made by registered UKMT centres, not private tutors, individual students or their parents.

You can order physical papers for your students via this page, online logins here or a combination of both (paper option is not available for overseas schools). The online and paper Challenge will both run from the 2nd-5th November and the results of both combined. We hope this will make it easier for you to find available space and time and allow you to run the Challenge in smaller sessions to adhere to social distancing requirements, if relevant at the time.

Regardless of whether you order online, paper or a combination of entries you will be sent login details for the new online Challenge site, which is separate from the UKMT main website. This is because all results and your downloadable certificates will be made available on the online Challenge site.

What about the follow on rounds?

Kangaroo - These will be run over 2 days and you will automatically be given login details for your student(s) to sit this round online. However if you would prefer physical papers for your students you will have the option to request this when we email you regarding your entries.
Olympiads - These will be run on a specific day, on paper only. Question papers will be available to download.

What if my school closes due to Covid-19?

All online entries can be used at home using the same format as would have been used in school. If you order paper entries and your school closes due to Covid-19 we can convert your entries to online entries for an additional cost of £1 per student. To convert your entries please email enquiry@ukmt.org.uk or call 0113 365 1121.

Please note that no refunds will be issued for online orders and no refunds will be issued for paper orders once they have been posted. Entry to the Challenges guarantees first round entry only. Please see our terms and conditions on ordering for more details. 

How do I enter?

  1. You enter the competition online and pay the entry fee, provided you are from a registered UKMT centre.
  2. You will be sent online logins for your students, physical papers or a combination of both, depending on your order.
  3. During the Challenge date range your students sit the Challenge under exam conditions.
  4. Where relevant, you post the completed answer sheets back to us ASAP.
  5. We mark the papers and online entries and notify you of the results.

What happens after the Challenge?

To recognise the highest performers in the Challenge, we award the top-scoring 60% of participants Bronze, Silver and Gold certificates in the ratio 3:2:1.

In addition, we invite around 1000 of the very highest performers to take part in the British Mathematical Olympiad Round 1 (on paper) and around 6000 to take part in the Senior Kangaroo (on paper or online, depending on how they sat the first round).

How can I prepare for the Challenge?

We hope that taking part in the Senior Mathematical Challenge is a stimulating and rewarding experience for all students, whether or not they have prepared.

Teachers can use past Senior Mathematical Challenge papers as a source of high-quality problems to encourage their students to think mathematically and to prepare for the competition. We are delighted to be working with DrFrostMaths to help teachers use past problems in the classroom.

We also sell downloadable past papers and books which can help students to prepare for our competitions.

What is the entry fee used for?

As a charity, we do not make a profit from entry fees. We spend all the money we raise on advancing the education of young people in mathematics.

Can you help us?

If you or someone you know has benefited from our activities then please consider making a donation.

Find out more about volunteering with us.

Senior Mathematical Challenge 2020 Paper
Mon 2 Nov 2020
23:59 on Fri 16 Oct 2020
This competition is UK only.
Open to
Year 13 or below S6 or below Year 14 or below
£13.00 per 10 papers

Please log in to enter this competition.