TMUA past papers
Every TMUA paper from 2016 to 2023, both papers each year, with the worked answers beside them. Sat by applicants to maths and economics at Cambridge, Imperial, Warwick, LSE and others.
Each paper below opens UAT UK's own PDF. Worked answers come with every paper, so you can mark your own.
Every series, newest first
Open a series to see its papers.
9 series, 18 papers.
2023 2 papers
Each paper below opens UAT UK's own PDF. Answer key for both papers. The TMUA preparation materials page has every year on it. 2023 is the last paper UAT UK will publish.
- Paper 1 Applications of mathematical knowledge Question paper Worked answers
- Paper 2 Mathematical reasoning Question paper Worked answers
| Raw score | Paper 1 | Paper 2 |
|---|---|---|
| 20 | 9.0 | 9.0 |
| 19 | 9.0 | 9.0 |
| 18 | 8.3 | 8.4 |
| 17 | 7.9 | 8.0 |
| 16 | 7.6 | 7.7 |
| 15 | 7.3 | 7.4 |
| 14 | 7.1 | 7.2 |
| 13 | 6.9 | 7.0 |
| 12 | 6.6 | 6.7 |
| 11 | 6.3 | 6.5 |
| 10 | 5.8 | 6.1 |
| 9 | 5.2 | 5.6 |
| 8 | 4.6 | 5.0 |
| 7 | 4.0 | 4.4 |
| 6 | 3.4 | 3.7 |
| 5 | 2.7 | 3.0 |
| 4 | 1.9 | 2.2 |
| 3 | 1.0 | 1.2 |
| 2 | 1.0 | 1.0 |
| 1 | 1.0 | 1.0 |
| 0 | 1.0 | 1.0 |
2022 2 papers
Each paper below opens UAT UK's own PDF. Answer key for both papers. The TMUA preparation materials page has every year on it. 2023 is the last paper UAT UK will publish.
- Paper 1 Applications of mathematical knowledge Question paper Worked answers
- Paper 2 Mathematical reasoning Question paper Worked answers
| Raw score | Paper 1 | Paper 2 |
|---|---|---|
| 20 | 9.0 | 9.0 |
| 19 | 9.0 | 8.9 |
| 18 | 8.5 | 8.2 |
| 17 | 8.1 | 7.8 |
| 16 | 7.8 | 7.4 |
| 15 | 7.5 | 7.2 |
| 14 | 7.3 | 6.9 |
| 13 | 7.1 | 6.7 |
| 12 | 6.9 | 6.4 |
| 11 | 6.7 | 5.8 |
| 10 | 6.5 | 5.2 |
| 9 | 6.1 | 4.6 |
| 8 | 5.6 | 4.0 |
| 7 | 5.0 | 3.4 |
| 6 | 4.4 | 2.8 |
| 5 | 3.8 | 2.1 |
| 4 | 3.0 | 1.3 |
| 3 | 2.1 | 1.0 |
| 2 | 1.0 | 1.0 |
| 1 | 1.0 | 1.0 |
| 0 | 1.0 | 1.0 |
2021 2 papers
Each paper below opens UAT UK's own PDF. Answer key for both papers. The TMUA preparation materials page has every year on it. 2023 is the last paper UAT UK will publish.
- Paper 1 Applications of mathematical knowledge Question paper Worked answers
- Paper 2 Mathematical reasoning Question paper Worked answers
| Raw score | Paper 1 | Paper 2 |
|---|---|---|
| 20 | 9.0 | 9.0 |
| 19 | 9.0 | 9.0 |
| 18 | 8.3 | 8.3 |
| 17 | 7.9 | 7.8 |
| 16 | 7.6 | 7.5 |
| 15 | 7.3 | 7.2 |
| 14 | 7.0 | 6.9 |
| 13 | 6.8 | 6.7 |
| 12 | 6.6 | 6.3 |
| 11 | 6.1 | 5.7 |
| 10 | 5.6 | 5.1 |
| 9 | 5.0 | 4.5 |
| 8 | 4.5 | 3.9 |
| 7 | 3.9 | 3.3 |
| 6 | 3.3 | 2.7 |
| 5 | 2.6 | 1.9 |
| 4 | 1.9 | 1.1 |
| 3 | 1.0 | 1.0 |
| 2 | 1.0 | 1.0 |
| 1 | 1.0 | 1.0 |
| 0 | 1.0 | 1.0 |
2020 2 papers
Each paper below opens UAT UK's own PDF. Answer key for both papers. The TMUA preparation materials page has every year on it. 2023 is the last paper UAT UK will publish.
- Paper 1 Applications of mathematical knowledge Question paper Worked answers
- Paper 2 Mathematical reasoning Question paper Worked answers
| Raw score | Paper 1 | Paper 2 |
|---|---|---|
| 20 | 9.0 | 9.0 |
| 19 | 8.9 | 9.0 |
| 18 | 8.2 | 8.4 |
| 17 | 7.8 | 7.9 |
| 16 | 7.4 | 7.6 |
| 15 | 7.1 | 7.3 |
| 14 | 6.9 | 7.0 |
| 13 | 6.7 | 6.8 |
| 12 | 6.4 | 6.5 |
| 11 | 5.8 | 6.0 |
| 10 | 5.3 | 5.4 |
| 9 | 4.7 | 4.8 |
| 8 | 4.2 | 4.2 |
| 7 | 3.6 | 3.6 |
| 6 | 3.0 | 2.9 |
| 5 | 2.3 | 2.2 |
| 4 | 1.6 | 1.3 |
| 3 | 1.0 | 1.0 |
| 2 | 1.0 | 1.0 |
| 1 | 1.0 | 1.0 |
| 0 | 1.0 | 1.0 |
2019 2 papers
Each paper below opens UAT UK's own PDF. Answer key for both papers. The TMUA preparation materials page has every year on it. 2023 is the last paper UAT UK will publish.
- Paper 1 Applications of mathematical knowledge Question paper Worked answers
- Paper 2 Mathematical reasoning Question paper Worked answers
| Raw score | Paper 1 | Paper 2 |
|---|---|---|
| 20 | 9.0 | 9.0 |
| 19 | 9.0 | 8.8 |
| 18 | 8.5 | 8.1 |
| 17 | 8.0 | 7.6 |
| 16 | 7.7 | 7.3 |
| 15 | 7.4 | 7.0 |
| 14 | 7.2 | 6.8 |
| 13 | 6.9 | 6.5 |
| 12 | 6.7 | 5.9 |
| 11 | 6.5 | 5.4 |
| 10 | 5.9 | 4.8 |
| 9 | 5.3 | 4.3 |
| 8 | 4.8 | 3.7 |
| 7 | 4.2 | 3.1 |
| 6 | 3.5 | 2.5 |
| 5 | 2.8 | 1.8 |
| 4 | 2.0 | 1.0 |
| 3 | 1.1 | 1.0 |
| 2 | 1.0 | 1.0 |
| 1 | 1.0 | 1.0 |
| 0 | 1.0 | 1.0 |
2018 2 papers
Each paper below opens UAT UK's own PDF. Answer key for both papers. The TMUA preparation materials page has every year on it. 2023 is the last paper UAT UK will publish.
- Paper 1 Applications of mathematical knowledge Question paper Worked answers
- Paper 2 Mathematical reasoning Question paper Worked answers
| Raw score | Paper 1 | Paper 2 |
|---|---|---|
| 20 | 9.0 | 9.0 |
| 19 | 9.0 | 9.0 |
| 18 | 9.0 | 9.0 |
| 17 | 9.0 | 9.0 |
| 16 | 8.5 | 9.0 |
| 15 | 7.7 | 9.0 |
| 14 | 7.0 | 8.3 |
| 13 | 6.4 | 7.7 |
| 12 | 5.8 | 7.1 |
| 11 | 5.3 | 6.5 |
| 10 | 4.7 | 6.0 |
| 9 | 4.1 | 5.5 |
| 8 | 3.6 | 4.9 |
| 7 | 3.0 | 4.3 |
| 6 | 2.4 | 3.6 |
| 5 | 1.7 | 3.0 |
| 4 | 1.0 | 2.2 |
| 3 | 1.0 | 1.2 |
| 2 | 1.0 | 1.0 |
| 1 | 1.0 | 1.0 |
| 0 | 1.0 | 1.0 |
2017 2 papers
Each paper below opens UAT UK's own PDF. Answer key for both papers. The TMUA preparation materials page has every year on it. 2023 is the last paper UAT UK will publish.
- Paper 1 Applications of mathematical knowledge Question paper Worked answers
- Paper 2 Mathematical reasoning Question paper Worked answers
| Raw score | Paper 1 | Paper 2 |
|---|---|---|
| 20 | 9.0 | 9.0 |
| 19 | 9.0 | 9.0 |
| 18 | 9.0 | 9.0 |
| 17 | 9.0 | 9.0 |
| 16 | 8.4 | 8.6 |
| 15 | 7.8 | 8.0 |
| 14 | 7.1 | 7.4 |
| 13 | 6.6 | 6.9 |
| 12 | 6.0 | 6.4 |
| 11 | 5.5 | 5.9 |
| 10 | 5.0 | 5.4 |
| 9 | 4.5 | 5.0 |
| 8 | 4.0 | 4.5 |
| 7 | 3.5 | 4.0 |
| 6 | 2.9 | 3.4 |
| 5 | 2.3 | 2.8 |
| 4 | 1.6 | 2.1 |
| 3 | 1.0 | 1.4 |
| 2 | 1.0 | 1.0 |
| 1 | 1.0 | 1.0 |
| 0 | 1.0 | 1.0 |
2016 2 papers
Each paper below opens UAT UK's own PDF. Answer key for both papers. The TMUA preparation materials page has every year on it. 2023 is the last paper UAT UK will publish.
- Paper 1 Applications of mathematical knowledge Question paper Worked answers
- Paper 2 Mathematical reasoning Question paper Worked answers
| Raw score | Paper 1 | Paper 2 |
|---|---|---|
| 20 | 9.0 | 9.0 |
| 19 | 9.0 | 9.0 |
| 18 | 9.0 | 9.0 |
| 17 | 9.0 | 9.0 |
| 16 | 9.0 | 9.0 |
| 15 | 9.0 | 9.0 |
| 14 | 8.6 | 9.0 |
| 13 | 7.9 | 8.7 |
| 12 | 7.3 | 8.1 |
| 11 | 6.7 | 7.4 |
| 10 | 6.1 | 6.8 |
| 9 | 5.5 | 6.2 |
| 8 | 4.8 | 5.6 |
| 7 | 4.2 | 4.9 |
| 6 | 3.4 | 4.2 |
| 5 | 2.7 | 3.4 |
| 4 | 1.8 | 2.5 |
| 3 | 1.0 | 1.4 |
| 2 | 1.0 | 1.0 |
| 1 | 1.0 | 1.0 |
| 0 | 1.0 | 1.0 |
Early specimen 2 papers
Published before the first live sitting, so useful for extra practice but not a real paper.
Each paper below opens UAT UK's own PDF. Answer key for both papers. The TMUA preparation materials page has every year on it. 2023 is the last paper UAT UK will publish.
- Paper 1 Applications of mathematical knowledge Question paper Worked answers
- Paper 2 Mathematical reasoning Question paper Worked answers
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