Past Papers and Solutions
Official UKMT Pages
If you do well in the UKMT Intermediate Maths Challenge then you might qualify for one of the follow on rounds. Like with the Junior and Senior competitions, there are two types of follow-on rounds – the Kangaroo and Olympiad, but at the Intermediate level this is further subdivided based on your year group as follows:
| Year 9 (S2) or below | Grey Kangaroo | Cayley Olympiad |
| Year 10 (S3) | Pink Kangaroo | Hamilton Olympiad |
| Year 11 (S4) | Pink Kangaroo | Maclaurin Olympiad |
Students from schools and colleges based in the UK may be invited (based on their scores in the Intermediate Maths Challenge) to take the Kangaroo rounds. Schools may also make `discretionary entries’ for other students, although there is a fee for such entries.
The Olympiad rounds are open to students both in the UK and overseas. Entries are free for those students qualifying directly from the Intermediate Maths Challenge. Schools may also make `discretionary entries’ for other students, although there is a fee for such entries.
Below you can find a table below shows the scores required in past Intermediate Maths Challenges to qualify for the follow on rounds, as well as past papers for all the Kangaroo and Olympiad rounds.
There’s also a YouTube video summarising and discussing all of this information here:
You can also find a detailed introduction to all of the challenges, including the IMC and follow-on rounds in this video:
The exact scores needed to qualify for the follow-on rounds vary from year to year. The following table shows the scores that were needed in previous years:
Past Intermediate Maths Challenge boundaries with follow on rounds:
| Year | Bronze | Silver | Gold | Grey | Pink | Cayley | Hamilton | Maclaurin |
| 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 |
| 2019 | 43 | 55 | 71 | 65 | 73 | 91 | 99 | 106 |
| 2018 | 48 | 59 | 73 | 68 | 76 | 93 | 100 | 104 |
| 2017 | 47 | 61 | 78 | 72 | 81 | 97 | 106 | 112 |
| 2016 | 40 | 50 | 62 | 60 | 66 | 81 | 89 | 95 |
| 2015 | 37 | 49 | 64 | 61 | 68 | 81 | 88 | 95 |
| 2014 | 42 | 55 | 72 | 67 | 78 | 90 | 96 | 103 |
| 2013 | 47 | 59 | 74 | 73 | 84 | 88 | 96 | 103 |
| 2012 | 50 | 62 | 77 | 77 | 87 | 90 | 96 | 101 |
| 2011 | 47 | 59 | 78 | 77 | 88 | 92 | 99 | 104 |
| 2010 | 45 | 56 | 70 | 70 | 80 | 83 | 91 | 97 |
| 2009 | 39 | 51 | 66 | 66 | 77 | 83 | 90 | 99 |
| 2008 | 42 | 54 | 70 | 70 | 82 | 85 | 95 | 102 |
| 2007 | 50 | 63 | 78 | 78 | 86 | 90 | 97 | 103 |
| 2006 | 46 | 58 | 72 | 72 | 80 | 84 | 92 | 99 |
| 2005 | 40 | 50 | 65 | 64 | 72 | 76 | 85 | 90 |
| 2004 | 40 | 51 | 68 | 67 | 79 | 84 | 93 | 100 |
| 2003 | 46 | 58 | 74 | 75 | 86 | 88 | 98 | 101 |
Past Papers and Solutions- Grey Kangaroo (Year 9)
This table contains links to past papers for the Grey Kangaroo – 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 | Grey Kangaroo Questions | Grey Kangaroo 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 Papers and Solutions – Pink Kangaroo (Years 10 + 11)
This table contains links to past papers for the Pink Kangaroo – 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 | Pink Kangaroo Questions | Pink Kangaroo 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 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 |
| 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 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 |
| 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 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 |
| 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 Kangaroo
| Year | Grey Kangaroo Merit (top 25%) | Pink Kangaroo Merit (top 25%) |
| 2024 | 89 | 74 |
| 2023 | 84 | 84 |
| 2022 | 78 | 86 |
| 2021 | 82 | 82 |
| 2020 | 101 | 91 |
Past Boundaries – Intermediate Olympiad
Cayley (Year 9)
| Year | Gold Medal (top 20) | Silver Medal (next 30) | Bronze Medal (next 50) | Distinction (top 25%) | Merit (top 40%) |
| 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)
| Year | Gold Medal (top 20) | Silver Medal (next 30) | Bronze Medal (next 50) | Distinction (top 25%) | Merit (top 40%) |
| 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)
| Year | Gold Medal (top 20) | Silver Medal (next 30) | Bronze Medal (next 50) | (next 50) Distinction (top 25%) | Merit (top 40%) |
| 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 |