Understanding Paper Difficulty and Recommended Times

Key points to take away

Why do the Mock Sets allow 120 minutes?

My older JZ Mock Sets contain many questions that are deliberately hard, long, or both. Some require substantial algebraic manipulation or calculation, even once you have found a good approach.

For example, a “How many of the following statements are true?” question might contain five statements rather than the more usual three. Each statement may require its own argument or counterexample. This adds work without necessarily making each individual argument more technically difficult.

The 120-minute recommendation mainly accommodates this extra length. These papers were written to provide challenging problem-solving practice, rather than to reproduce the experience of a 75-minute TMUA paper precisely.

However, 120 minutes was a time allowance I chose, not one established through a formal calibration process. It may be overly generous for some papers. That uncertainty matters when interpreting students’ results and the difficulty ratings derived from them.

Who decides the displayed difficulty ratings?

The displayed implied difficulty ratings are estimated from student performance, rather than simply being labels chosen by me.

Students’ results across both the Mock Sets and the Exam Sets inform these estimates. So far, the two groups appear to have broadly similar average implied difficulty, despite their different styles and recommended times.

This does not necessarily mean that they are equally difficult technically. Performance-based ratings cannot completely separate technical difficulty from question length and time pressure. They reflect how students perform under the conditions in which they attempt the papers.

Why might the average ratings be similar?

When writing the older Mock Sets, I concentrated heavily on questions I considered hard or very hard, often involving several stages of reasoning or calculation. I did not deliberately balance these with a substantial selection of easier questions.

For the newer Exam Sets, I have intentionally included a range of difficulties: accessible questions, moderately challenging problems and harder questions. This is closer to the experience of the real TMUA, where part of the challenge is recognising which questions to complete quickly and which to leave until later.

Those descriptions reflect my intentions as the author. The implied ratings reflect students’ performance — and the two do not always line up!

Based on those ratings, the older Mock Sets may not have been as difficult on average as I thought, while the newer Exam Sets have proved harder than I anticipated.

Timing may also help explain the similarity. If 120 minutes is more generous than the Mock Sets actually require, students may score higher because they have more time to think, calculate and check their answers. This could make the mocks appear less difficult in the performance data than they would under a tighter time limit.

It is hard to disentangle these effects. The similar averages could reflect my initial judgements, the different time allowances, or a combination of both. I would therefore avoid interpreting them as proof that the papers have exactly the same underlying technical difficulty.

What counts as a question of suitable TMUA length?

My working criterion for the newer Exam Sets is:

A question should be reasonably completable in around three and a half minutes when approached with a good method.

This does not mean everyone should finish every question within that time. Finding the right approach is part of the challenge. You may spend longer on some questions and make up that time on others.

The point is that an effective approach should lead to a manageable amount of reasoning and calculation.

Some older Mock Set questions do not meet this criterion. Even with a good method, there may still be substantial work to do. Every question in the newer Exam Sets is designed with this length target in mind.

How do the Exam Sets compare with the current TMUA?

The newer Exam Sets are designed to resemble the current, post-2024 TMUA much more closely in:

I currently judge them to be slightly more challenging technically, without being deliberately longer. My estimate of roughly 10–20% additional difficulty is an informal judgement as an author, not a statistically established figure or a rule for converting scores.

My reading of the available data is that the gap between these sets and the 2025 TMUA is not especially large. I discuss the evidence and its limitations in more detail in the JZ Exam Set B report.

For future sets, I intend to bring the technical difficulty closer still to the 2025 level, while recognising that this is itself difficult to pin down precisely. I will continue refining the balance as more results and feedback become available.

Which papers should I use?

Use the Mock Sets for extended practice with challenging problems, allowing for their longer questions.

Use the Exam Sets for a closer rehearsal of the current TMUA, working within the 75-minute time limit.

Both offer useful practice, but for judging your pacing and preparing for the experience of the real exam, the newer Exam Sets are the better match.

Make learning the priority

Across both the Mock Sets and the Exam Sets, one of my main goals is to expose you to a broad range of questions and less familiar applications of ideas, while staying within the mathematical scope of the TMUA.

I want the papers to help you build a wider repertoire of relevant ideas and methods, so that unfamiliar questions in the real exam are less likely to catch you off guard. Their value should extend well beyond the score you receive at the end.

Whichever sets you attempt, my recommendation is to approach each paper with the intention of learning something and becoming a little more capable than you were before. Review the questions that challenged you, understand the methods, and take those ideas into your next attempt.

A single paper is only one piece of evidence about your preparation. Try to give more attention to what it can teach you than to what its score might say about your eventual TMUA result.

I hope the papers help you learn — and that you have some fun along the way!