Promoting a love of problem solving

The Senior Mathematical Challenge is a 90-minute, multiple-choice Challenge.

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.

Date: 10-11 November 2021 Please note:  Schools on China Standard Time (UTC +08:00) need to sit the Challenge on Friday 12th November.

If your students sit the paper on the first day please ensure you collect the question papers back in from students and only release them back to the students at the end of the second day. You may wish to arrange the Challenge on the second day, if you are able, so that students’ enthusiasm to discuss the questions after the paper has been taken is not curbed.

Eligible year groups: England, Wales and Overseas - Year 13 or below, Scotland S6 or below, Northern Ireland - Year 14 or below

Time allowed: 90 minutes

Entry fee: £13 for a pack of 10 entries

Entries open now!

Entry deadline (paper): Midnight, Sunday 17th October 2021

Entry deadline (online): Midnight, Tuesday 9th November 2021

How to take part

  1. Entries must be made by registered UKMT centres on behalf of students.
  2. You can order a paper or online version or a combination of both (schools outside of the UK can only participate online)
  3. The Challenge must be sat under exam conditions.
  4. We mark both the paper and online entries electronically and notify you of the results.

Challenge entries

Purchasing entries

Entries into the Senior Mathematical Challenge can be purchased via your online Challenges Profile.

If you purchase online entries you will be provided with an online login for each student, which enables them to log in to the Challenges site and participate in an online format.

If you purchase paper entries we will send you question papers via post, however answer sheets will need to be downloaded and printed in school. Your student's answer sheets will then need to be uploaded to your Challenges Profile for us to mark electronically. Please note that we are no longer able to mark hard copy answer sheets, so please ensure these are not sent back to the UKMT via post.

Download the Challenge Handbook to help navigate you through hosting the Senior Mathematical Challenge.

Preparing 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.

You can utilise our previous past papers, solutions and investigations here. They are a great resource containing high-quality problems designed to encourage mathematical thinking and prepare students for the Challenge. We are also 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 with your preparation.


Scoring rules for the Senior Mathematical Challenge are as follows:

  • All participants start with 25 points
  • 4 marks are awarded for each correct answer
  • 1 mark is deducted for each incorrect answer
  • Answers left blank will be marked as 0

Awards and follow-on rounds

All students will receive a certificate of participation. To recognize the highest performers in the Challenge, we award the top-scoring 66% of participants Bronze, Silver and Gold certificates in the ratio 3:2:1. Students that are 'Best in Year' or 'Best in School' will also receive a badge to denote this on their certificates. Certificates have the student names pre-populated and can be downloaded and printed as soon as results are released.

In addition, we invite around 1,000 of the very highest performers to take part in the British Mathematical Olympiad Round 1 and around 6,000 to take part in the Senior Kangaroo.

The 2021 award thresholds were:

85+ Gold, 66+ Silver, 49+ Bronze. Thresholds for invitation to Senior Kangaroo 85+ and BMO1 108+ depending on eligibility.

Contributing to our work

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. If you would like to support us further then please consider making a donation.

Our volunteers are at the heart of everything UKMT does from creating the Challenges to running our Enrichment activities. If you would like to find out more about volunteering with us please do get in touch.