UKMT Maths Challenge Practice Questions
The UKMT (United Kingdom Mathematics Trust) is a leading organization in the UK that promotes and supports mathematical education. It organizes various mathematical competitions, including the Junior Mathematical Challenge (JMC), the Intermediate Mathematical Olympiad (IMO), and the British Mathematical Olympiad (BMO).
At IITian Academy you will have practice Questions and ukmt past questions by topics.
UKMT Maths Challenge Practice Questions
Junior Competitions (Year 8 or Below)
Intermediate Competitions(Year 11 or Below)
- UKMT Intermediate Maths Challenge
Senior Competitions (Year 13 or Below)
- UMKT Senior Maths Challenge
UKMT Mathematical Challenges
The United Kingdom Mathematics Trust (UKMT) was founded in 1996 and stands as a registered charity, whose charitable aim is to advance the education of young people in mathematics by offering a wide range of national-level competitions and activities for students from 11 to 18 years old in the UK.
UKMT encourages mathematical reasoning, precision of thought, and fuency in using basic mathematical techniques to solve interesting problems.
Among many mathematical challenges organized by UKMT, their biggest competitions are the Junior, Intermediate and Senior Mathematical Challenge(JMC/IMC/SMC), which have over 700,000 entries from 6,000 schools each year, and are the UK’s most popular school Mathematical Challenges.
To recognize the highest performers in the Challenge, UKMT Mathematical Challenges award the top-scoring 50%-66% (JMC/IMC with 50%, SMC with 66%) of participants Bronze, Silver and Gold certifcates in the ratio 3:2:1.
- The UK’s most popular school Mathematical Challenges
- Over 700,000 participants all over the world annually
- Three levels suitable for different age groups
- Up to 50%-66% award ratio
UKMT Mathematical Challenges- JMC (junior Mathematical Challenge)
First-round Challenges
First round Challenges consist of the Junior, Intermediate and Senior Mathematical Challenges.
Junior Mathematical Challenge
- Time limit
- 60 minutes
- Age group
- England, Wales and Overseas: Year 8 and below
- Scotland: S2 or below
- Northern Ireland: Year 9 or below
- Competition Date
- Thursday 1st May 2025
Scoring
Scoring rules for the Junior Mathematical Challenge are as follows:
- 5 marks are awarded for each correct answer to questions 1 – 15
- 6 marks are awarded for each correct answer to questions 16 – 25
- In the Junior Mathematical Challenge you will NOT lose marks for getting questions wrong Answers left blank will be marked as 0
Follow-on Round –Junior Kangaroo
The Junior Kangaroo is an invitation-only competition open exclusively to UK schools. Students qualify based on their performance in the Junior Maths Challenge (JMC), with several thousand students making the cut annually
Time limit
- 60 minutes
Age group
- England and Wales: Year 8 and below
- Scotland: S2 or below
- Northern Ireland: Year 9 or below
Scoring
Scoring rules for the Junior Kangaroo are as follows:
- 5 marks are awarded for each correct answer to questions 1 – 15
- 6 marks are awarded for each correct answer to questions 16 – 25
- In the Junior Kangaroo you will NOT lose marks for getting questions wrong Answers left blank will be marked as 0
Awards and Thresholds
The top-scoring 25% of participants each receive a Certificate of Merit. Each participant below this thresholds receives a Certificate of Qualification or Participation depending on their entry route.
Year | Junior Kangaroo Certification Thresholds’ |
2024 | 103 |
2023 | 90 |
2022 | 97 |
2021 | 97 |
2020 | N/A |
Follow-on Round-Junior Mathematical Olympiad
Entry to the Junior Olympiad is by invitation based on a qualifying JMC score, or by discretionary entry. Around 1,200 students qualify from the JMC each year.
- Time limit
- 2 hours
- Age group
- England, Wales and Overseas: Year 8 and below
- Scotland: S2 or below
- Northern Ireland: Year 9 or below
- Competition Date
- Tuesday 10th June 2025
Scoring
Scoring rules for the Junior Mathematical Olympiad are as follows:
- Each question in Section A is worth 1 point
- Each question in Section B is worth up to 10 points
- Answers in Section B can be awarded partial marks depending on on the clarity of the participants Mathematical presentation.
Year | Junior Mathematical Olympiad Qualification | ||||
Merit | Distinction | Bronze Medal | Silver Medal | Gold Medal | |
2024 | 20 | 38 | 38 | 43 | 50 |
2023 | 21 | 36 | 36 | 44 | 51 |
2022 | 16 | 29 | 34 | 41 | 48 |
2021 | 12 | 37 | 37 | 47 | 57 |
2020 | N/A | N/A | N/A | N/A | N/A |
UKMT Mathematical Challenges- Intermediate Competitions
First-round Challenges- IMC
UKMT Intermediate Challenges are aimed at students year 11 and below. Starting with the Intermediate Maths Challenge, with the Kangaroos and Olympiads as follow-on rounds, these are designed to challenge and engage your students
Intermediate Mathematical Challenge
- Time limit
- 60 minutes
- Age group
- England, Wales and Overseas: Year 11 and below
- Scotland: S4 or below
- Northern Ireland: Year 12 or below
- Competition Date
- Wednesday 29th January 2025
Scoring
Scoring rules for the Intermediate Mathematical Challenge are as follows:
- 5 marks are awarded for each correct answer to questions 1 – 15
- 6 marks are awarded for each correct answer to questions 16 – 25
- Each incorrect answer to questions 16 – 20 loses 1 mark
- Each incorrect answer to questions 21 – 25 loses 2 marks Answers left blank will be marked as 0
Awards and Thresholds
To recognize the highest performers in the Challenge, we award the top-scoring 50% 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. Students not amongst the high scorers will receive a Certificate of Participation.
Year | Certificates | |||||||
Bronze | Silver | Gold | Grey Kangaroo Qualification | Pink Kangaroo Qualification | Cayley Olympiad Qualification | Hamilton Olympiad Qualification | Maclaurin Olympiad Qualification | |
2024 | 47 | 61 | 77 | 72 | 84 | 101 | 106 | 110 |
2023 | 42 | 55 | 71 | 67 | 77 | 95 | 100 | 103 |
2022 | 50 | 65 | 81 | 65 | 81 | 101 | 111 | 117 |
2021 | 55 | 68 | 86 | 68 | 86 | 100 | 110 | 118 |
2020 | 60 | 72 | 89 | 80 | 89 | 110 | 117 | 120 |
Follow-on Rounds – Grey and Pink Kangaroos
Entry to the Grey and Pink Kangaroos is by invitation based on a qualifying IMC score, or by discretionary entry. Several thousand UK-based students qualify from the IMC each year. Open to UK schools only
Grey and Pink Kangaroos
- Time limit
- 60 minutes
- Age group
Grey Kangaroo:
England and Wales: Year 9 and below
Scotland: S2 or below
Northern Ireland: Year 10 or belowPink Kangaroo:
England and Wales: Year 10 and 11
Scotland: S3 and S4
Northern Ireland: Year 11 or 12
- Competition Date
- Thursday 20th March 2025
Scoring
Scoring rules for the Grey & Pink Kangaroos are as follows:
- 5 marks are awarded for each correct answer to questions 1 – 15
- 6 marks are awarded for each correct answer to questions 16 – 25 In the
- Grey Kangaroo / Pink Kangaroo: you will NOT lose marks for getting questions wrong. Answers left blank will be marked as 0
Awards and Thresholds
The top-scoring 25% of participants each receive a Certificate of Merit
Year | Grey Kangaroo Merit | Pink Kangaroo Merit |
2024 | 89 | 74 |
2023 | 84 | 84 |
2022 | 78 | 86 |
2021 | 82 | 74 |
2020 | 101 | 101 |
Follow-on Rounds – Cayley, Hamilton and Maclaurin Mathematical Olympiads
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.
Cayley, Hamilton and Maclaurin Mathematical Olympiads
- Time limit
- 2 hours
- Age group
Cayley Maths Olympiad:
England, Wales and Overseas: Year 9 and below
Scotland: S2 or below
Northern Ireland: Year 10 or belowHamilton Maths Olympiad:
England, Wales and Overseas: Year 10
Scotland: S3
Northern Ireland: Year 11Maclaurin Maths Olympiad:
England, Wales and Overseas: Year 11
Scotland: S4
Northern Ireland: Year 12
- Competition Date
- Thursday 20th March 2025
Scoring
Scoring rules for the Cayley, Hamilton & Maclaurin Maths Olympiads are as follows:
- Each question is worth 10 points
- Answers can be awarded partial marks depending on the clarity of the participants Mathematical presentation
Awards and Thresholds
Each qualifying student receives a Certificate of Qualification or Participation depending on their entry route. The highest-scoring participants each receive Certificates of Distinction and Merit.
Each of the top 20 scorers receive a gold medal, the next 30 a silver medal and the next 50 a bronze medal. All medalists will also be awarded a book prize; the title varies from year to year.
Previous Cayley Thresholds
Year | Merit | Distinction | Bronze | Silver | Gold |
2024 | 14 | 26 | 31 | 38 | 45 |
2023 | 12 | 31 | 35 | 42 | 50 |
2022 | 20 | 33 | 38 | 44 | 51 |
2021 | 10 | 28 | 31 | – | – |
2020 | N/A | N/A | N/A | N/A | N/A |
Previous Hamilton Thresholds
Year | Merit | Distinction | Bronze | Silver | Gold |
2024 | 14 | 29 | 33 | 40 | 50 |
2023 | 18 | 34 | 38 | 44 | 52 |
2022 | 13 | 28 | 31 | 36 | 44 |
2021 | 10 | 23 | – | 27 | – |
2020 | N/A | N/A | N/A | N/A | N/A |
Previous Maclaurin Thresholds
Year | Merit | Distinction | Bronze | Silver | Gold |
2024 | 14 | 27 | 33 | 39 | 46 |
2023 | 18 | 29 | 33 | 39 | 47 |
2022 | 10 | 24 | 29 | 36 | 44 |
2021 | 10 | 29 | – | – | 23 |
2020 | N/A | N/A | N/A | N/A | N/A |
UKMT Mathematical Challenges- Senior Competitions
First-round Challenges- Senior Mathematical Challenge
UKMT Senior Mathematical Challenge first round aimed at students year 13 or below. The problems on the Senior Maths Challenge are designed to make students think. Stimulating problems for both beginners and experienced problem-solvers
Intermediate Mathematical Challenge
- Time limit
- 60 minutes
- Age group
- England, Wales and Overseas: Year 13 and below
- Scotland: S6 or below
- Northern Ireland: Year 14 or below
- Competition Date
- TBD
Scoring
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 Thresholds
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. Students not amongst the high scorers will receive a Certificate of Participation.
Previous Thresholds
Year | Certificates | Senior Kangaroo Qualification | BMO1 Qualification | ||
Bronze | Silver | Gold | |||
2024 | 49 | 66 | 83 | 83 | 110 |
2023 | 49 | 64 | 80 | 80 | 106 |
2022 | 48 | 62 | 76 | 76 | 100 |
2021 | 49 | 66 | 85 | 85 | 108 |
2020 | 59 | 73 | 91 | 91 | 108 |
First-round Challenges- Andrew Jobbings Senior Kangaroo
Entry to the Andrew Jobbings Senior Kangaroo is by invitation based on a qualifying Senior Mathematical Challenge score, or by discretionary entry. Several thousand UK-based students qualify from the SMC each year. Open to UK schools only.
Intermediate Mathematical Challenge
- Time limit
- 60 minutes
- Age group
- England and Wales: Year 13 and below
- Scotland: S6 or below
- Northern Ireland: Year 14 or below
- Competition Date
- Wednesday 20th November 2024
Scoring
Scoring rules for the Andrew Jobbings Senior Kangaroo are as follows:
- 5 marks are awarded for each correct answer
- In the Senior Kangaroo you will NOT lose marks for getting questions wrong
Awards and Thresholds
Each participant receives a Certificate of Qualification or Participation, depending on their entry route, and the top-scoring 25% of participants each receive a Certificate of Merit.
Previous Thresholds
Year | Senior Kangaroo Qualification |
Merit | |
2024 | – |
2023 | 50 |
2022 | 40 |
2021 | 45 |
First-round Challenges- British Mathematical Olympiad Round 1
As a follow-on Round to the Senior Mathematical Challenge (SMC), the British Mathematical Olympiad Round 1 (BMO1) is a 3.5 hour Olympiad consisting of six problems requiring full written solutions.
As well as challenging high-scorers from the SMC, the British Mathematical Olympiad is an entry point to the training and selection programme for international competitions.
British Mathematical Olympiad Round 1
- Time limit
- 3.5 hours
- Age group
- England, Wales and Overseas: Year 13 and below
- Scotland: S6 or below
- Northern Ireland: Year 14 or below
- Competition Date
- Wednesday 20th November 2024
Scoring
Scoring rules for the British Mathematical Olympiad Round 1 (BMO1) are as follows:
- Each question carries 10 marks
- Partial marks are awarded depending on the clarity of the participants Mathematical presentation. We advise working in rough first, then writing up your best attempt.
- One complete solution will gain more credit than several unfinished attempts.
Awards and Thresholds
The top scoring students will receive a Certificate of Distinction or a Certificate of Merit depending on their score.
Each of the top 20 scorers receive a gold medal, the next 30 a silver medal and the next 50 a bronze medal. All medalists will also be awarded a book prize; the title varies from year to year. Each qualifying student receives a Certificate of Qualification or Participation depending on their entry route.
Previous Thresholds
Year | BMO Round 1 | |||||
Merit | Distinction | BMO2 invite | Bronze | Silver | Gold | |
2024 | – | – | – | – | – | – |
2023 | 13 | 30 | Y13: 43 Y12: 42 Y11: 39 Y10: 37 | 44 | 49 | 58 |
2022 | 12 | 25 | Y13: 38 Y12: 36 Y11: 34 Y10: 33 | 39 | 43 | 51 |
2021 | 11 | 21 | Y13: 33 Y12: 32 Y11: 31 Y10: 29 | 33 | 38 | 45 |
2020 | 10 | 18 | Y13: 27 Y12: 26 Y11: 24 Y10: NA | 29 | 34 | 40 |
First-round Challenges- British Mathematical Olympiad Round 2
As a follow-on Round to the BMO1 , as well as challenging high-scorers from the SMC, the British Mathematical Olympiad is an entry point to the training and selection programme for international competitions. UKMT invites around 100 qualifying students from BMO1, those who did not participate in BMO1 can be entered at the discretion of their schools
British Mathematical Olympiad Round 1
- Time limit
- 3.5 hours
- Age group
- England, Wales and Overseas: Year 13 and below
- Scotland: S6 or below
- Northern Ireland: Year 14 or below
- Competition Date
- Wednesday 22 January 2025
Scoring
Scoring rules for the British Maths Olympiad Round 2 are as follows:
- Each question, which require full written solutions, is worth 10 points
- Marks awarded depend on the clarity of the participants Mathematical presentation. We advise working in rough first, then writing up your best attempt
- One or two complete solutions will gain far more credit than partial attempts for all four questions
Awards and Thresholds
The top scoring students will receive a Certificate of Distinction or a Certificate of Merit depending on their score.
Each qualifying student receives a Certificate of Qualification or Participation depending on their entry route.
Previous Thresholds
Year | BMO Round 2 | |
Merit | Distinction | |
2024 | 6 | 15 |
2023 | 7 | 11 |
2022 | 10 | 17 |
2021 | 6 | 18 |
2020 | 7 | 15 |
UKMT Mathematical Challenges- Mathematical Olympiad for Girls
First-round Challenges- Mathematical Olympiad for Girls
The Mathematical Olympiad for Girls is aimed at girls and young women across the UK and consists of five challenging problems.
Entry to MOG is by discretionary entry
British Mathematical Olympiad Round 1
- Time limit
- 2.5 hours
- Age group
- England and Wales: Year 13 and below (younger students may be entered at the school’s discretion)
- Scotland: S6 and below
- Northern Ireland: Year 14 and below
- Competition Date
- Wednesday 25th September 2024
Scoring
Scoring rules for the Mathematical Olympiad for Girls as follows:
- Each question carries 10 marks
- Partial marks may be awarded for incomplete or partially correct answers
- One fully correct answer will gain you more credit than several guesses
- There are no negative marks for incorrect answers
Awards and Thresholds
The top scoring students will receive a Certificate of Distinction or a Certificate of Merit depending on their score. The top 30 scorers will also be awarded a book prize; the title varies from year to year. Each student receives a Certificate of Participation.
Previous Thresholds
Year | Merit | Distinction | Book Prize |
2024 | – | – | – |
2023 | 16 | 26 | 43 |
2022 | 20 | 36 | 50 |
2021 | 10 | 23 | 43 |
2020 | N/A | N/A | N/A |