News

This is something many of you have clearly needed, and it is long overdue. The last few months have been hectic, but here it is finally!

Some of you have sat papers far too hard for your stage of preparation, especially the original JZ Mocks, and come away disheartened. So when you press Start on the exam simulator, you’ll now see how that paper is likely to suit you: Comfortable, Well matched, Challenging or A substantial stretch, with an expected score range based on your current mastery. Full exam mode does the same for each paper on the setup page.

It is advice, not a restriction. Every paper is still there for you to start - if you so wish! The suitability guidance is there to help you decide.

About the JZ Mocks: I originally wrote these for a couple of very able students, to stretch their thinking. I also let my question-writing imagination run wild, producing some interesting—but unrealistic—TMUA questions! These are advanced challenge papers for learning and stretching, not realistic TMUA mocks. However, they attracted more attention than I expected, and some students attempted them before they were ready. I’m sorry for the discouraging experience—I should have made their purpose clearer. I have also now put these mocks at the end of the list of paper sets.

They now carry an explanatory note and appear last rather than first in the simulator! 😃 You can still sit individual papers, but they are no longer offered as full two-paper exams. My recommendation: attempt them only if your mastery score is at least 7.0.

If anything in the guidance seems off for you, please let me know jzmaths@hotmail.com.

Joe

The October TMUA is over! To everyone who sat it, well done on getting through the preparation and the exam itself. Whatever your impression of how it went, I hope you can now enjoy a well-earned break.

Jackie Tyler and I send you our very best wishes for your results and the rest of the university admissions process. Thank you for making JZMaths part of your preparation, and for all the messages, suggestions and corrections along the way. Hearing that our work has helped means a great deal to both of us.

I’m also planning to post a video or two on my YouTube channel in the next couple of weeks to help those of you preparing for Oxford or Cambridge interviews.

A new home for your feedback

You can now find Feedback in your account menu, where you can send us private feedback or choose to publish a review for other students to read.

I wanted somewhere for you to tell us what worked, what didn’t, and what we could do better. Public reviews also help future students understand what to expect from JZMaths. Kind words and grievances are both welcome—though I cannot promise to apologise for every difficult question. 😄

You decide what to share, what name to display, and whether to include details such as papers completed or time spent. You can preview your review before publishing and edit or unpublish it whenever you wish. Free and PLUS users are equally welcome.

When your October result arrives, you can also return to this page to share your TMUA score. It can stay private, and it will help us improve our score calibrations. There is no need to wait for your result before leaving feedback.

You’re also welcome to leave an honest review on Trustpilot. Here, there, both, or simply private feedback—whichever suits you. There is no obligation, and I’m grateful for any time you choose to give us.

Looking ahead to January 2027

For those preparing for January, Jackie and I have been discussing what would make the biggest difference to your preparation.

One thing has become clear: having plenty of papers does not necessarily make it easy to know what to work on next. Doing paper after paper can be frustrating if the same difficulties keep appearing.

Over the coming weeks, we’ll be working towards two connected additions to PLUS: guided preparation and TMUA skill diagnosis and remedy.

The intended approach is:

One or two recommended papers → identify areas to work on → targeted teaching and practice → another suitable paper to check progress.

The guidance will help you choose papers appropriate to your current level. The diagnosis will use a new set of TMUA skills, separate from—and more detailed than—the broad topic categories currently on the site. For example, it might identify difficulty recognising when an SSA triangle has two possible solutions, or using the properties of even and odd functions, rather than simply telling you to “revise trigonometry” or “work on functions”.

For each skill you need to revisit, there will be at least one teaching video and a set of focused practice questions that gradually increase in difficulty, helping you level up that skill before we recommend moving on to another paper set.

This is my attempt to bring more of what I do with my own tutees into JZMaths: helping you understand what is holding you back and giving you a useful next step, so you can prepare more efficiently and get more out of the time you put in.

We’ll also make paper difficulty clearer to guide you choose papers suited to your stage of preparation. Several October students told us that the harder papers left them unnecessarily worried about the real exam. That feedback matters, and we want to help you use challenging material at the right stage and interpret your results more sensibly.

Free teaching videos, and a refreshed site

My aim over the next few months is to cover the full TMUA teaching content, with at least one teaching video for each TMUA skill. All these videos will be available on YouTube for free.

The planned PLUS features will connect that teaching to your own preparation: which skills to revisit, what to practise, and what to attempt afterwards. These additions are intended to be included for existing bundle holders.

There will also be a substantial redesign of the site interface to make room for the new features and make everything easier to find. The navigation has rather outgrown my original plans!

These improvements will arrive gradually. I’ll share updates as they become ready.

Two more live mocks

We’re also planning two live mocks for the January cohort, using new papers: one set written by me and one by Jackie. Dates and details will follow. These are included for bundle holders.

For now, October students: enjoy your break, and do keep us posted on how you get on. January students: I hope what we’re building will make your preparation more focused, more manageable, and perhaps a little more enjoyable too.

Joe

I’ve started a new series on transformations, and three videos are up already. I prioritised what I think will help the most over the next few days, so they’ve been made in a weird order!

In Part 3: Various modulus transformations, we look at what changes when the modulus goes inside a function, outside it, or around $y$: $y = |f(x)|$, $y = f(|x|)$ and $|y| = f(x)$. We then treat $|x - a|$ as a distance, which makes sums of moduli and their minimum values much easier to see, and finish with two questions from the JZMaths mock papers.

In Part 5: Functions of Periodic Functions, we sketch graphs such as $\sin(\cos x)$ and $\cos(\sin(\cos x))$ by working from the inside out, and finish by counting the solutions of $\cos(\sin(\cos x)) = \sin(\cos(\sin x))$.

The Part 5 bonus takes the ideas further with a quadratic function of $\sin x$ and a rational function of $\cos x$. Treat it as enrichment rather than typical TMUA material.

Watch Part 3 · Watch Part 5 · Watch the Part 5 bonus · Browse all videos

Today’s video is Multivariate Factorisation: A More General Version of the Factor Theorem. Similar to what I covered in the additional topics, but with a couple of question examples. This is a little topic that sometimes can come very handy, and does not take long to learn.

I begin with the idea behind it and a few basic examples, then apply it to three problems: factorising a trigonometric equation, solving an inequality, and finding the range of an angle in a triangle (TMUA 2017 Paper 1, Q20).

If you’d like more, the Multivariate Factorisation article has more worked examples, a practice set and a topic test.

Watch Multivariate Factorisation · Browse all videos

Counting sounds simple—until you need to be certain you’ve counted everything exactly once. Today I’ve uploaded a three-part series, Combinatorics: Do You Really Know How to COUNT!?

In Part 1, I work through the core ideas: the multiplication principle, permutations, combinations, and arrangements with repeated objects—not just the formulas, but why they work and when dividing out duplicates can go wrong.

In Part 2, we put those principles to work on four TMUA-style questions: race results, coefficients in an expansion, dice probabilities and counting functions where $f(f(x)) = x$.

And in a short bonus video, we finish with one more problem, solved in two ways: using flexible variables, and then a proper proof.

Throughout, two questions guide us: have we counted every possibility, and have we counted anything more than once?

Watch Part 1 · Watch Part 2 · Watch the bonus · Browse all videos

Today’s video is one of the most useful I’ve made. In Flexible Variables: Bend Them to Your Will!, I work through five increasingly challenging TMUA past-paper questions where the quickest route is to give the letters some convenient values.

It’s a legitimate method rooted in logic: the correct general answer must work for every permitted choice of values, so any option that fails for your chosen values can be eliminated. I also look at when it works and how to choose useful values.

Watch Flexible Variables · Browse all videos

Today’s video is on a topic that refuses to go away: the SSA ambiguous case. In SSA Ambiguous Triangles: The Topic That Refuses to Go Away!, I work through the standard setup and some variations that can still catch you out. When a question gives you two sides and a non-included angle, how do you decide whether there are zero, one or two possible triangles?

Watch SSA Ambiguous Triangles · Browse all videos

JZMaths in numbers

I’ve also added a new page: JZMaths in numbers. It shows how much maths you’ve all been doing on the simulator since 1 July: questions answered, students who have practised, time spent on exam papers, and corrections completed. The figures refresh every ten seconds, so you might even see them change while you’re there.

It’s lovely to see how much work you’ve all been putting in. I hope the papers and explanations are helping you feel more confident with the maths, and that you’re finding some enjoyment in the challenge too. Thank you for being part of JZMaths.

For those sitting the TMUA over the coming days, good luck!

With the TMUA approaching, many of you have asked how best to use these final few days. In TMUA: Making the Most of the Final Few Days I share some practical ideas to help you decide how to make the best use of this time. I also made a follow-up, TMUA: Sign Analysis — Inequalities Without Graph Sketching, to show you what I mean by small but useful topics that can still be covered in these last few days.

Watch Making the Most of the Final Few Days · Watch Sign Analysis · Browse all videos

I wish you all the very best of luck!

We’re now on Trustpilot.

If you fancy a break from studying, JZMaths is now on Trustpilot—somewhere to formally air your grievances about my torturous questions. 😄

Joking aside, I’d really appreciate your honest feedback, positive or otherwise. It helps other students decide whether JZMaths is for them, and helps me understand what I could do better. Whether you use the free resources or PLUS, you’re equally welcome to leave a review.

Absolutely no rush—this can happily wait until after your exam!

Leave a review on Trustpilot

Part 3 is up! This time we tackle four questions on logarithms, functions, graphs and logic—some innocent-looking questions with a few less innocent details!

We look at how logarithmic restrictions affect a curve, why the base matters in an exponential function, how graphs help us count solutions, and why disproving a statement isn’t quite the same as writing down its negation.

Watch Part 3 on YouTube · Browse all videos

I hope you find the video useful!

I’ve just uploaded both parts of Odd and Even Functions: A Little Symmetry Goes a Long Way! A little symmetry can save a lot of algebra, and there’s more to this topic than you might first expect.

In Part 1, we look at what makes a function odd or even, how these properties behave under sums, products and compositions, and their connections with differentiation and integration. We also explore how to spot symmetry when a graph has been shifted. This lays the groundwork for Part 2.

In Part 2, we put those ideas into practice with three challenging TMUA-style questions: hidden symmetry in a definite integral, counting solutions using calculus and symmetry, and a sum of 101 terms that cancels in pairs.

Watch Part 1 on YouTube · Watch Part 2 on YouTube · Browse all videos

I’ve also put together the Tyler Exam Set B report, looking at Saturday’s live mock results, how difficult the set was, and how I think it compares with TMUA 2023 and 2025.

Thank you to everyone who took part—I hope the report help you put your score into perspective and decide what to work on next.

Read the Tyler Exam Set B report