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.

It is easy to take part:

  1. You enter the competition online and pay the entry fee, provided you are from a registered UKMT centre.
  2. We post the papers and instructions on how to administer the Challenge to your institution to arrive at least one week before the Challenge date.
  3. On the Challenge date, your students sit the Challenge under exam conditions.
  4. You post the completed answer sheets back to us.
  5. We mark the papers 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 and around 6000 to take part in the Senior Kangaroo.

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 (pack of 10)
Thu 5 Nov 2020
17:00 on Fri 15 Oct 2021
17:00 on Thu 15 Oct 2020
Open to
Year 13 or below S6 or below Year 14 or below
£13.00 per 10 papers
Entries to this competition are either not open yet or have already closed.

Please log in to enter this competition.