If you are applying to a competitive mathematics or engineering programme at a UK university, you have almost certainly come across the TMUA. Whether you are a home student in the middle of your A-levels, or an international applicant navigating the UK admissions system for the first time, the Test of Mathematics for University Admission works the same way for everyone. There are no percentage marks, no pass or fail. Just a number between 1.0 and 9.0, and a question in the back of your mind: is this good enough?
This guide breaks down TMUA grade boundaries across 2022, 2023, and 2024, explains how UK admissions teams use those scores, and gives you a realistic picture of where you need to land to strengthen your application, regardless of where in the world you are applying from.
What Are TMUA Grade Boundaries?
Before diving into specific years, it helps to understand what grade boundaries mean in the TMUA context, because the term works differently here than it does in standard exam marking.
The TMUA does not have a fixed pass mark. Raw scores from each paper are converted into a standardised score on the 1.0 to 9.0 scale using scaled scoring. This conversion accounts for year-to-year variation in difficulty, so a student who sat a harder paper is not penalised compared to someone who sat an easier one in a different year.
Each paper is scored separately and then combined into a single overall result. Paper 1 covers Mathematical Knowledge, and Paper 2 covers Mathematical Reasoning. The boundaries published by Cambridge Assessment Admissions Testing reflect the raw marks needed to achieve each point on that scale in a given sitting.
So when people talk about TMUA grade boundaries, they are really asking two things. First, how hard was this particular year's paper? Second, how does my raw mark translate to a standardised score that universities will actually see on my application?
For international students, it is worth noting that the TMUA is administered globally at approved test centres, and your score is reported to universities exactly as it would be for a UK-based applicant. There is no separate scoring system, and no adjustment is made based on where you took the test.
TMUA 2022 Grade Boundaries
The October 2022 sitting was taken by thousands of applicants targeting entry in September 2023. Candidates consistently described Paper 2 that year as the more demanding of the two, with the mathematical reasoning questions requiring multi-step logical deductions rather than straightforward calculation.
The 2022 grade boundaries reflected that difficulty. Paper 2 required fewer correct answers for an equivalent standardised score, because the raw-mark-to-scale conversion adjusted for the harder questions. Paper 1 boundaries stayed relatively high because the knowledge-based questions were more accessible.
Approximate 2022 Grade Boundary Estimates
| Scaled Score | Paper 1 (out of 20) | Paper 2 (out of 20) | What It Means for Your Application |
| 4.0 | 8 to 9 correct | 6 to 7 correct | Weak for selective courses |
| 5.0 | 10 to 12 correct | 9 to 10 correct | Acceptable at less selective programmes |
| 6.0 | 14 to 15 correct | 12 to 13 correct | Competitive at most TMUA universities |
| 6.5 | 16 to 17 correct | 13 to 14 correct | Strong baseline for top universities |
| 7.0 | 17 to 18 correct | 15 to 16 correct | Competitive for Cambridge and Imperial |
| 7.5+ | 19 to 20 correct | 17 to 18 correct | Exceptional, top decile performance |
A combined score of 6.5 is generally considered the lower threshold for competitive applicants at most universities requiring the TMUA. Students scoring above 7.0 in 2022 were in a strong position across almost all participating institutions.
TMUA 2023 Grade Boundaries
The 2023 sitting took place in October, with results released ahead of the January UCAS deadline. For international applicants, this timing matters: most UK universities expect you to submit your UCAS application by January, and TMUA results are typically available before that deadline.
Feedback from the 2023 cohort suggested a more balanced paper compared to 2022, with Paper 1 and Paper 2 sitting at a similar difficulty level. Because the 2023 paper was considered slightly more accessible overall, the raw mark boundaries shifted upward. Students needed to answer more questions correctly to reach the same standardised score. This catches many candidates off guard if they compare raw marks across years without accounting for the scaling adjustment.
Approximate 2023 Grade Boundary Estimates
| Scaled Score | Paper 1 (out of 20) | Paper 2 (out of 20) | What It Means for Your Application |
| 4.0 | 9 to 10 correct | 9 to 10 correct | Weak for selective courses |
| 5.0 | 11 to 12 correct | 11 to 12 correct | Acceptable at less selective programmes |
| 6.0 | 14 to 15 correct | 13 to 14 correct | Competitive at most TMUA universities |
| 6.5 | 15 to 17 correct | 14 to 16 correct | Strong baseline for top universities |
| 7.0 | 17 to 18 correct | 16 to 17 correct | Competitive for Cambridge and Imperial |
| 7.5+ | 19 to 20 correct | 18 to 19 correct | Exceptional, top decile performance |
The 2023 cohort also saw a higher number of applicants than previous years, partly because more universities had added the TMUA to their admissions requirements. This increased volume did not change individual scoring, but it does mean university thresholds remained competitive because the pool of high scorers was larger.
One development worth flagging from 2023: several universities that previously listed the TMUA as "recommended" moved it to "required" for shortlisting decisions.
TMUA 2024 Grade Boundaries
The 2024 sitting followed the same October schedule. Early reports from that cohort described Paper 1 as more straightforward than in previous years, while Paper 2 returned to the more challenging reasoning format seen in 2022.
This split difficulty pattern meant the 2024 grade boundaries were asymmetric. Paper 1 boundaries moved up, meaning more correct answers were needed for a given scaled score. Paper 2 boundaries moved down relative to 2023. Students who had focused heavily on mathematical knowledge content found Paper 1 relatively smooth but may have found the gap between their two paper scores wider than expected.
Approximate 2024 Grade Boundary Estimates
The 2024 sitting followed the same October schedule. Early reports from that cohort described Paper 1 as more straightforward than in previous years, while Paper 2 returned to the more challenging reasoning format seen in 2022.
This split difficulty pattern meant the 2024 grade boundaries were asymmetric. Paper 1 boundaries moved up, meaning more correct answers were needed for a given scaled score. Paper 2 boundaries moved down relative to 2023. Students who had focused heavily on mathematical knowledge content found Paper 1 relatively smooth but may have found the gap between their two paper scores wider than expected.
How UK Universities Use TMUA Scores
Knowing the boundaries is useful. Understanding how admissions teams actually read your score is more useful.
Most universities that require the TMUA do not use a single hard cutoff. They consider your TMUA score alongside your predicted grades, your personal statement, and in some cases an interview. For international applicants, predicted grades would be based on whatever qualification you are completing, whether that is the IB Diploma, A-levels taken at an international school, Indian Class XII boards, the US AP exams, or another recognised qualification.
The table below summarises how the main UK universities tend to approach TMUA scores:
| University | Courses Using TMUA | Typical Competitive Score Range | Notes for International Students |
| University of Cambridge | Mathematics, Economics, Engineering | 6.5 to 7.5 (many offers above 7.0) | Same expectations for home and overseas applicants |
| Imperial College London | Mathematics, joint honours courses | 6.5 as competitive baseline | Applies equally to international applicants |
| University of Leeds | Mathematics, Computer Science | 5.5 to 6.5 depending on course | Treated as one factor alongside qualification predictions |
| Cardiff University | Mathematics, Physics | 5.0 to 6.0 | Contextual use; particularly useful for borderline shortlisting |
| Lancaster University | Mathematics and Statistics | 5.5 to 6.5 | More weight given to TMUA when predicted grades are borderline |
| Durham University | Mathematics, Natural Sciences | 6.0 to 7.0 | Increasingly used in initial shortlisting rounds |
| University of Southampton | Mathematics, Actuarial Sciences | 5.5 to 6.5 | Growing use in recent admissions cycles |
Cambridge does not distinguish between home and international applicants when reviewing TMUA scores. The score you need is the same whether you are from Birmingham or Bangalore. What differs is that international applicants may also need to demonstrate English language proficiency separately through IELTS or equivalent tests, but that is a separate requirement handled entirely apart from the TMUA process.
What Is a Good TMUA Score?
This is the question everyone asks, and the honest answer is that it depends on where you are applying. The table below gives a general framework that applies to both home and international applicants:
| Scaled Score | Interpretation | Likely Outcome |
| Below 4.5 | Below competitive range | May weaken applications to selective programmes; consider whether to submit if optional |
| 4.5 to 5.5 | Acceptable | Suitable for mid-range selective courses; unlikely to strengthen Cambridge or Imperial applications |
| 5.5 to 6.5 | Competitive | Solid result that supports a well-rounded application at most TMUA universities |
| 6.5 to 7.5 | Strong | Will actively help your application at most institutions; demonstrates real mathematical ability |
| Above 7.5 | Exceptional | Top percentile; noticed at even the most selective programmes |
TMUA Score Percentiles: Where Do You Stand?
Grade boundaries tell you what score you need. Percentile data tells you how you compare to everyone else who sat the test. Both matter when you are interpreting your result.
Cambridge Assessment does not publish full percentile breakdowns, but data collected from multiple cohorts gives a reasonable picture:
| Approximate Scaled Score | Estimated Percentile Rank | Context |
| 4.5 | Around 50th percentile | Median performance across all sitters |
| 5.5 | Around 65th to 70th percentile | Above average within a strong cohort |
| 6.0 | Around 75th percentile | Upper quarter of all candidates |
| 6.5 | Around 80th to 85th percentile | Strong position for most applications |
| 7.0 | Around 88th to 90th percentile | Top 10 to 12 percent of all sitters |
| 7.5 | Around 95th percentile | Top 5 percent |
| 8.0+ | Top 2 to 3 percent | Genuinely exceptional |
These are approximations based on cohort feedback and released data rather than official figures, but they align with what universities report seeing in their applicant pools. The important thing to remember is that the TMUA pool already skews toward strong mathematics students, particularly among international applicants who have sought the test out specifically. Landing at 5.0 here is still a meaningful result, but it is not where you want to be for a top-tier application.
Understanding your likely percentile position also helps you decide where to invest preparation time. Moving from 5.5 to 6.5 is achievable with focused work on Paper 2 reasoning skills. Moving from 6.5 to 7.5 requires more sustained effort and often comes down to eliminating careless errors rather than learning new material.
Why Grade Boundaries Change Each Year
Students from every background find it confusing that grade boundaries shift year to year when the format of the test stays the same. The explanation is straightforward: the TMUA adjusts to maintain consistency in what each score represents, not consistency in how hard the test is to sit.
If Paper 2 is harder in a given year, the raw-mark boundary for a score of 6.0 will be lower that year. The underlying mathematical ability that 6.0 represents stays constant across all sittings. This is why comparing raw marks across years is not very meaningful, but comparing scaled scores is.
It also means that using past papers is valuable not just for practice but for honest calibration. If you complete a 2022 paper under timed conditions and score 16 out of 20 on Paper 1, check the boundary estimates for that year to understand what scaled score that likely corresponds to, rather than assuming 80% is a fixed standard.
If you want structured support working through past papers alongside your other qualifications, whether that is A-levels, the IB, or another curriculum, the Acolyte Living TMUA preparation resources are a practical starting point alongside the official Cambridge Assessment materials.
Final Thoughts
The TMUA is one of the more transparent parts of a UK university application. Your score is a number, and admissions teams use it with more consistency than they apply to personal statements or predicted grades. That holds whether you are a home student sitting the test in Manchester or an international student taking it at a centre in Mumbai, Singapore, or Lagos.
Understanding the grade boundaries from 2022, 2023, and 2024 gives you a realistic picture of where strong performance sits. A score above 6.5 is your first target. Above 7.0 is where applications start to look genuinely competitive at the most selective institutions.
The TMUA rewards preparation more than raw talent. The patterns in the questions are learnable, and the scaling system means a harder paper will not unfairly penalise you if you have prepared properly.
If you are building your UK application strategy and want guidance on balancing TMUA preparation with your other qualifications, personal statement, and admissions timeline, explore the Acolyte Living student resources section for practical advice written with both home and international applicants in mind.
FAQs
What is the TMUA and which universities require it?
Covers the basics of the test, its purpose, and the list of participating universities. High search intent from applicants who are just starting their research.
What is a good TMUA score?
The single most asked question after results are released. Targets both first-time sitters planning their prep and students who have received their scores and want to know where they stand.
How is the TMUA scored and what do the grade boundaries mean?
Addresses the confusion around raw marks vs scaled scores and why the same raw mark can mean different things in different years.
Can international students sit the TMUA, and does it affect their application differently?
High demand from non-UK applicants who are unsure whether the test applies to them and whether they are judged on the same scale as home students.
How should I prepare for the TMUA, and how long does preparation take? Practical prep question with strong evergreen search volume. Students typically ask this 3 to 6 months before their sitting date.
What happens if I get a low TMUA score? Should I still submit it?
Asked most heavily in November and December after results are released. Targets students deciding whether to include a weak score in their UCAS application before the January deadline.