UKMT Intermediate Maths Olympiads (Cayley, Hamilton and Maclaurin)
Past Papers and Grade Boundaries
Below is a table with the grade boundaries for past papers for the UKMT Intermediate Grey and Pink Kangaroos, as well as a table with links to lots of past papers and solutions. You can also see more info about these papers, including FAQs, here:
If you’re preparing for the Grey or Pink Kangaroos, join thousands of other students who have used these online courses to prepare:
Past Papers and Solutions – Cayley Olympiad (Year 9)
This table contains links to past papers for the Cayley Olympiad – these papers are hosted at the UKMT website. The most recent papers are usually made available a couple of days after the challenge takes place and may briefly be available at the official website before this table is updated.
| Year | Cayley Olympiad Questions | Cayley Olympiad Solutions | Video Solutions |
| 2025 | 2025 Questions | 2025 Solutions | |
| 2024 | 2024 Questions | 2024 Solutions | |
| 2023 | 2023 Questions | 2023 Solutions | |
| 2022 | 2022 Questions | 2022 Solutions | Online course with hints YouTube: Q1 Q2 Q3 Q4 Q5 Q6 |
| 2021 | 2021 Questions | 2021 Solutions | |
| 2020 | 2020 Questions | 2020 Solutions | |
| 2019 | 2019 Questions | 2019 Solutions | |
| 2018 | 2018 Questions | 2018 Solutions | |
| 2017 | 2017 Questions | 2017 Solutions | |
| 2016 | 2016 Questions | 2016 Solutions | |
| 2015 | 2015 Questions | 2015 Solutions |
Past Papers and Solutions – Hamilton Olympiad (Year 10)
This table contains links to past papers for the Hamilton Olympiad – these papers are hosted at the UKMT website. The most recent papers are usually made available a couple of days after the challenge takes place and may briefly be available at the official website before this table is updated.
| Year | Hamilton Olympiad Questions | Hamilton Olympiad Solutions | Video Solutions |
| 2025 | 2025 Questions | 2025 Solutions | |
| 2024 | 2024 Questions | 2024 Solutions | Online course with hints YouTube: Q1 Q2 Q3 Q4 Q5 Q6 |
| 2023 | 2023 Questions | 2023 Solutions | |
| 2022 | 2022 Questions | 2022 Solutions | |
| 2021 | 2021 Questions | 2021 Solutions | |
| 2020 | 2020 Questions | 2020 Solutions | |
| 2019 | 2019 Questions | 2019 Solutions | |
| 2018 | 2018 Questions | 2018 Solutions | |
| 2017 | 2017 Questions | 2017 Solutions | |
| 2016 | 2016 Questions | 2016 Solutions | |
| 2015 | 2015 Questions | 2015 Solutions |
Past Papers and Solutions – Maclaurin Olympiad (Year 11)
This table contains links to past papers for the Maclaurin Olympiad – these papers are hosted at the UKMT website. The most recent papers are usually made available a couple of days after the challenge takes place and may briefly be available at the official website before this table is updated.
| Year | Maclaurin Olympiad Questions | Maclaurin Olympiad Solutions |
| 2025 | 2025 Questions | 2025 Solutions |
| 2024 | 2024 Questions | 2024 Solutions |
| 2023 | 2023 Questions | 2023 Solutions |
| 2022 | 2022 Questions | 2022 Solutions |
| 2021 | 2021 Questions | 2021 Solutions |
| 2020 | 2020 Questions | 2020 Solutions |
| 2019 | 2019 Questions | 2019 Solutions |
| 2018 | 2018 Questions | 2018 Solutions |
| 2017 | 2017 Questions | 2017 Solutions |
| 2016 | 2016 Questions | 2016 Solutions |
| 2015 | 2015 Questions | 2015 Solutions |
Past Boundaries – Intermediate Olympiad
Note: These are the certificate boundaries for the Olympiad papers themselves. The scores needed to qualify from the Intermediate Maths Challenge can be found on the page here.
Cayley (Year 9) Boundaries
| Year | Gold Medal (top 20) | Silver Medal (next 30) | Bronze Medal (next 50) | Distinction (top 25%) | Merit (top 40%) |
| 2025 | 45 | 39 | 34 | 30 | 17 |
| 2024 | 45 | 38 | 31 | 26 | 14 |
| 2023 | 50 | 42 | 35 | 31 | 12 |
| 2022 | 51 | 44 | 38 | 33 | 20 |
| 2021 | 37 (top 50 book prize) | 31 (top 100 all got same medal) | 28 | 10 | |
| 2020 | no medal | due to | pandemic | 44 | 10 |
Hamilton (Year 10) Boundaries
| Year | Gold Medal (top 20) | Silver Medal (next 30) | Bronze Medal (next 50) | Distinction (top 25%) | Merit (top 40%) |
| 2025 | 41 | 34 | 30 | 23 | 10 |
| 2024 | 50 | 40 | 33 | 29 | 14 |
| 2023 | 52 | 44 | 38 | 34 | 18 |
| 2022 | 44 | 36 | 31 | 28 | 13 |
| 2021 | n/a | 34 (top 50 book prize) | 27 (top 100 all got same medal) | 23 | 10 |
| 2020 | no medals | due to | pandemic | 32 | 10 |
Maclaurin (Year 11) Boundaries
| Year | Gold Medal (top 20) | Silver Medal (next 30) | Bronze Medal (next 50) | (next 50) Distinction (top 25%) | Merit (top 40%) |
| 2025 | 45 | 37 | 31 | 27 | 16 |
| 2024 | 46 | 39 | 33 | 27 | 14 |
| 2023 | 47 | 39 | 33 | 29 | 18 |
| 2022 | 44 | 36 | 29 | 24 | 10 |
| 2021 | n/a | 42 (top 50 book prize) | 32 (top 100 all got same medal) | 29 | 10 |
| 2020 | no medals | due to | pandemic | 29 | 10 |