News

Tomorrow morning, I am planning to run a full recalibration of the question difficulties used by the mastery system, together with a full recalculation of everyone’s mastery scores based on these updated difficulties.

When the mastery system was first introduced, the difficulty of many questions necessarily had to begin with my own estimates. That was a reasonable starting point, but now that a much larger number of students have attempted the questions, we have enough real performance data to increasingly let the model estimate question difficulty from how students actually perform.

After all, you probably don't want your mastery score to depend purely on what I happen to think is difficult — however impeccable my judgement may occasionally appear to me. 😊

I expect to carry this out at around 6–7am UK time tomorrow morning. In theory, there should be no disruption to the site at all, but I am deliberately doing it at a quieter time just in case something unexpected happens.

Please expect your mastery score to change a little after the recalibration, although I do not expect the change to be substantial. Whether it moves up or down, just remember that the change should be taking it in the direction of a more accurate estimate! 😊

I also plan to publish model-implied grade boundaries for both the Tyler Tutoring mock papers and my own JZ Maths mock papers tomorrow, so you will be able to get a rough idea of how a raw score on each paper corresponds to the current TMUA score scale.

I had originally planned to add a couple of TMUA worked examples to the Transformations article. On reflection, however, I think that if you want to see these ideas applied to TMUA-style questions, you will get more from attempting the new practice test and topic test—especially the topic test. This also gives you the opportunity to try each question yourself before reading the worked solution.

A few students have written to me after accidentally ending a paper—usually, I assume, by mis-clicking End Exam and then also confirming it; sometimes, apparently, by ending the wrong paper entirely. They have therefore asked me to allow them to delete the attempt and remove its effect on their mastery score.

I was initially reluctant to add this feature, for two reasons:

1. It would give students a way to game the system by deleting poor attempts.

2. Because of the way the mastery system works, removing the effect of a single attempt requires a complete recalculation of that student’s mastery score. This is an expensive calculation, so if too many of you do this too often, you are going to bankrupt me. 🙂 (Perhaps a slight exaggeration!)

However, on balance, I have decided to add it:

1. You are all highly intelligent and motivated students who understand perfectly well that there is no point in gaming the system. Doing so would only make your own mastery score less meaningful, so I trust that you will use the feature only for genuine mistakes.

2. That said, there will be a limit of three deletions in any seven-day period—haha, that’s right: I trust you, but not quite that much!

There is now a Delete button next to each attempt. Once you confirm the deletion, the attempt will be removed and your mastery score recalculated.

I hope this helps! Now, back to writing those transformation questions...

I have added a new section to the Transformations article on transforming the equation of a curve from first principles, because while writing questions, it became clear this new section would be highly useful. Rather than changing the input or output of a function, this method tracks what happens to an arbitrary point $(p,q)$ and recovers the equation from its image. It handles cases the usual approach struggles with — in particular curves that are not written in the form $y=f(x)$ at all.

The article was already too long before this, and now it's definitely too long! So I decided to split it into two sections. Sorry the other topics will have to wait, as I need to do this right! 🙂

• Part A — Core transformations and equations of curves: the vertical and horizontal transformations, the order in which they combine, reflections in $y=b$ and $x=a$, and the new first-principles method.
• Part B — Modulus transformations, point mapping and rotations: the modulus transformations $|f(x)|$ and $f(|x|)$, a shortcut for finding corresponding points directly, and the bonus section on rotating a curve through $90^\circ$.

I might add to this news update later today when I have completed the practice and topic tests, which I am writing right now!

I have now published the process that will be used to select the prize winner from the correct Egg Hunt entries. If you have entered, please read the Egg Hunt page for full details.

There is nothing further you need to do at this stage — unless you have not yet entered, in which case do it while there is still time! 🙂

Thanks to another helpful suggestion from a student, I have now added the ability to bookmark questions directly from attempt history summaries.

As a minor additional improvement, attempts at correction and bookmarked questions will now also contribute towards the activity heat map. Note also that they do not affect your mastery score directly.

A student made the excellent suggestion of allowing users to bookmark questions with particularly good learning or revision value, so that they can easily revisit and re-practise them later.

This is similar in spirit to the existing “Flag for Correction” feature, but is a more useful and flexible version. I have therefore replaced “Flag for Correction” with “Bookmark for Revision”. Your bookmarked questions can be accessed from the menu under your user account avatar.

Attempts at bookmarked questions do not affect your mastery score; they are treated in the same way as practice-mode attempts.

I had originally intended to write only about the order of transformations. However, it felt more appropriate to cover transformations as a whole. As a result, the article became much longer than planned and cost me quite a bit of sleep 😂, but I think the more complete treatment was worthwhile. The initial version of the Transformations article is now live. I may return to it in a few days with a fresh pair of eyes to make further improvements, and may also add a couple of illuminating TMUA worked examples later. (Update: it has since been expanded and split into Part A and Part B.)

In the meantime, I would like to thank R2Drew2 for his video walkthrough of my Mock E Paper 2, thereby completing his walkthroughs of all ten papers — a truly herculean effort. I have thoroughly enjoyed watching his videos too, and I highly recommend both his walkthroughs of my mocks and his other TMUA-related content.

I have finished the topic test for the Cauchy-Schwarz and AM-GM Inequalities section, again 10 questions, 40 minutes.

The questions mainly focus on direct applications of the two inequalities, with a couple of other topics mixed in.

The next topic is going to be on order of transformations.

A big thank you to everyone who has emailed me over the last few weeks to point out typos, small errors, or anything that did not look quite right. I really appreciate you taking the time to report them. Quite a few corrections have been made as a result, and every report helps me improve the resources for everyone.

I also want to flag one issue with the most recent update to the paper PDF downloads. Unfortunately, that update caused some of the questions in the downloaded PDFs to appear in the wrong order. This has now been fixed.

If you downloaded any of the papers recently, I recommend downloading them again, particularly if you want the question order to match the order used in R2Drew2's video solutions.

Apologies for the inconvenience, and thank you again to everyone who has helped me spot these things!

OK, by popular request, I have now written a new Cauchy-Schwarz and AM-GM Inequalities article, which has been added to the Additional Topics section.

HOWEVER, I should caution at this stage that this article has one of the lowest TMUA relevance scores. If I had followed my own priority list, it would probably have been the last article to be written.

To be clear, what I mean is that these inequalities are among the least likely topics to be directly relevant to the TMUA. The exam is highly unlikely to contain a question for which knowledge of either inequality is necessary, and my own mocks do not rely on them. They only made my list because there are occasional questions where they provide a very nice shortcut to the solution, and they have also appeared in mock papers written by several others recently, so I thought it was worth adding the article for the benefit of students.

I have also decided to add a TMUA Relevance Score to every article in the Additional Topics section, to help you decide which topics to prioritise. This relevance score is completely independent of the difficulty of the topic.

In any case, the article is now here. I hope you enjoy it!

PDF downloads are now available for both the Multivariate Factorisation Practice and the Multivariate Factorisation Topic Test. So, if you prefer working on paper, you can now download and print the questions rather than completing them online. My solutions are also available as separate PDF downloads.

I have also updated the paper download page to include links to R2Drew2's excellent YouTube walkthroughs of my mock papers. Thank you again to Rob for taking the time to do these walkthroughs — and for repeatedly managing to find clever unintended shortcuts to some of my questions. Unfortunately for you (students), I have since closed several of these escape routes. 😂

I am currently still travelling, so updates to Additional Topics will be a little sporadic until I return to the UK in the last week of August. After that, I hope to do a massive sprint and get them all finished by the end of August! Let's see how hardworking I manage to be. 🙂 No promises...

I have finished the topic test for the multivariate factorisation section: 10 questions, 40 minutes.

There are some nice questions in there. I would say the test leans towards the hard and very hard side of the TMUA difficulty scale; AND I made an honest effort to avoid anything unreasonably hard...

Enjoy! 🙂

A new Multivariate Factorisation Practice set has now been added to the end of the multivariate factorisation article.

The set contains 15 questions, starting with relatively straightforward homogeneous expressions before moving on to less familiar non-homogeneous and three-variable examples. Although this practice set is multiple choice, the questions are not intended to be TMUA-style questions. Their purpose is simply to help you become familiar and comfortable with the techniques involved in multivariate factorisation.

I am currently writing a topic test containing TMUA-style questions in which multivariate factorisation plays a critical role in reaching the solution. The topic test therefore will count towards your mastery.

I have now finished the first article for Additional Topics, covering multivariate factorisation — one of the topics students were most keen to see. I will be adding practice questions and a topic assessment for this section next.

I have finally decided to start work on the Additional Useful Topics section that I have had planned for some time, especially after a number of you emailed to request it!

These are methods and ideas that I think are particularly useful for TMUA preparation. Technically, it is possible to solve TMUA questions without explicitly knowing some (or maybe all) of them, and an examiner could reasonably argue that a competent student might arrive at some or all of these conclusions naturally through their mathematical studies.

In my experience, however, this is often not the case. For many students, these ideas remain unfamiliar, overlooked, poorly understood, or understood only superficially. This is not really the fault of students or their teachers! As many of these ideas simply receive relatively little attention in the mainstream mathematics curriculum. So my aim of this section is to address as many of these gaps as possible in detail, to help students further prepare for the TMUA.

Here is the current planned list — which I made into a poll so that you can indicate whichever you would most like me to write first.

The list is subject to change, expansion or omission as I work through it, and is intended to give you an idea of what I currently have in mind.

You are also very welcome to suggest further topics that you think would be useful!

Following suggestions from a couple of students — one of whom even sent me a very good mock-up, thank you! — I have now added extra-time options for candidates who are eligible for access arrangements.

For everyone else, you should continue to complete exam-mode attempts under the standard time limit.

The new progression and mastery system is now live. You can read more about it in How mastery works.

Your historical exam-mode attempts are automatically used to estimate your current mastery score in the new dashboard. The model draws on the same family of Rasch methods used by UAT-UK to score and standardise the TMUA.

I hope you find it useful—I spent far longer building it than I had originally planned... :)

I’m making good progress on the new progression system. It is mostly complete, but as this is a substantial piece of work, I want to check everything thoroughly before releasing it.

In the meantime, you will shortly notice the difficulty ratings for questions change. These new ratings have been carefully calibrated using the official TMUA grade boundaries for past papers, together with anonymised performance data from students using the site. This should provide a much more consistent and reliable indication of how difficult each question really is, across both past papers and mock papers. The old ratings were only my very rough estimates!

These changes are being made in preparation for the new progression system, which I hope to release tomorrow, or by Friday at the latest.

Quick note to say I'm very much around, just deep in the workshop while on holiday!

As mentioned previously, I've been heads-down on a major revamp of the progress and dashboard system — a proper way to track how your mastery is developing over time as you work through the papers, rather than just a score at the end. The system is based on a version of the ELO scoring system, which involves some interesting maths! As a result, I got somewhat sidetracked researching it in possibly more detail than was needed. Oh well... not long now — I'm aiming to release it within the next 7 days.

And this is very much your fault, for using the exam simulator so much that I felt the need to replace the current, very basic placeholder progress tracking with something much more credible and useful.

OK, joking aside — I'm glad it's been useful to people. Keep at the papers!

I've been quietly planning this one for some time, and it's finally here: the Logic Course Easter Egg Hunt.

Hidden within the Logic Course is a puzzle. Each worksheet contains an Easter egg question — usually the slightly less serious one — and the correct answers reveal clues that combine to form a hidden treasure word. Find the word and submit it to enter the prize draw.

It's meant to be fun more than anything — an excuse to spend some time with logic, dressed up as a treasure hunt! Entries close on 31st August. Go and have a look. 🍀

Firstly, many thanks to Rob (R2Drew2), who has now posted walkthroughs of the first four of my mock papers on YouTube. If you have not seen them yet, do take a look - they are excellent.

I have finally finished reviewing the last set of my mock papers, Set E. I will probably take a short break from writing now to recharge a little!

I have also noticed that many of you are using the exam simulator for practice, and it is great to know that the tool is being used! As a result, I have been working on improving the analytics, as the current version is really only a placeholder.

The plan is to introduce an Elo-style progression system that should give a more meaningful measure of overall progress. This is what I am currently working on.

I will be away next week, so I am not sure exactly when it will be ready, but hopefully it will not be too long.

I have now finished full reviews of the first eight of my mock papers, covering Sets A through D. I sometimes tweak and swap questions in earlier papers too, so please make sure you download the latest version of any mock paper before attempting it. Alternatively, you can use the exam simulator, which is always up to date. Lastly, I have also finished transcribing Jackie Tyler's papers into the exam simulator up to and including Set C.

There are also a couple of Easter-egg-style questions in Paper 2 of my latest sets: unserious, but entirely rigorous. I just cannot seem to help myself. Enjoy!

Firstly, many thanks to Rob (R2Drew2) for making a full video walkthrough of my Set A Paper 1 on YouTube. I watched the walkthrough too: very slick as usual, with clear explanations. Thank you very much!

Secondly, Jackie Tyler has very kindly and meticulously gone through my Set A papers, made many helpful corrections, and spotted a couple of careless mistakes from me. Thank you very much as well.

All of these efforts will hopefully help students prepare for the next edition of the TMUA in October.

Lastly, Tyler Mock Set B is now live on the exam simulator.

Jackie Tyler's TMUA Mock Set A is now available in the JZ Maths exam simulator.

I have used Jackie Tyler's mock papers with many of my own students over the years, and I highly recommend them as excellent TMUA preparation materials.

A big thank you again to Jackie Tyler of tylertutoring.com for kindly giving me permission to include her papers on JZ Maths.

I aim to have the rest added this weekend.

A few updates to share:

1. Jackie Tyler of tylertutoring.com has very kindly agreed to allow me to include her papers in the exam simulator. I will look to transcribe her papers into the simulator over the next few days.

2. I have finally finished all the worksheets for the Logic Course, and installed the last of the Easter egg questions!

3. JZ Mock Set C Paper 2 has also been fully reviewed.

My immediate to-do list now is to complete the review of the remaining mocks. After that, I will move on to creating the section on Additional Useful Topics.

A student emailed me with a feature request: to make attempt summaries permanently available for students to view. It was a good suggestion and relatively easy to implement, so it is now live. Thank you, Abdul, for the suggestion!

I have also fixed a few errors pointed out by several students. Thank you to everyone who notified me. These corrections are now live, and both the exam simulator and PDF downloads have been updated.

A reminder that the first five papers are considered fully polished. The remaining five are on my list for a full review.

Worksheets have been added to the sections on the contrapositive and proof by contradiction. I hope you find them useful.

I’ve added a series of Easter egg questions throughout the Logic course worksheets. Can you find them all?

Some worksheets have now been added to the first three sections of my course on logic.

I have also updated the front pages of my papers with guidance notes to remind students that my mock papers contain only hard, very hard, and occasionally unreasonably hard questions :). The routine and easier material has been deliberately left out, so students should not be discouraged if they find the papers difficult or need longer than the recommended time.

The main aim of these papers is improvement rather than measurement: meet difficult problems, struggle with them, learn from them, and get better each time!

Last a couple of days, I have obsessively worked to complete my course on logic, it has finally been completed. I will look to add some worksheets to each section in due course, and perhaps do a video version of this on YouTube.

I have now completed a full review of two more papers. At the same time, my logic course is taking shape, and I hope to release it in the next couple of days.

A couple of weeks ago I decided to do a full review of the mock papers I wrote thus far, to further improve them based on the experience of writing these 5 sets of papers. So far I have fully reviewed the first 3 papers, currently working on the 4th (Set B paper 2). So if you are new here and want to try my papers, start with the first three. I hope to complete the review in a couple of weeks.

In addition, I also have plans for the following sections

• logic course: a free medium style course on logic, in sections, each section will have some worksheets to help students practice the ideas.
• additional useful topics: where I will do some tutorial posts about various useful topics which are nice to know, or knowledge of which may speed up \ make easier certain questions. Some of the topics that will be included are: modulo arithmetic, reflections on lines $x=a$ and $y=b$, and others.

Time scale wise, I hope to have these ready soon as possible, it helps that exams are over and I am basically on holiday now!

The latest set E is now up. I also have a pipeline of questions for the next set.

I have been busy last a few weeks with the exams! Finally set D is completed and up.

Set C is now up, I have also adjusted a few questions in sets A and B after further reviews. My mock papers are generally more difficult, as I believe for practice purposes, you are better served with more demanding questions. However, my design philosophy is that difficulty comes not from increased calculations or brute force work, but in ways of thinking, traps, misdirections, all of which, are designed to train logical thinking! Overcoming these, should in principle, improve your logical thinking.

Another set of mocks done, enjoy, there are a couple of very very hard questions in them!

These took longer than I had expected to write! It is of course also exam season, therefore I didn't have much spare time either. In any case, here they are, available in both the exam simulator, and for standalone download. I should warn you that these questions are perhaps harder than past exam papers, as I kept scrapping questions that I deemed too easy, but now its definitely leaning on the more difficult side. Oh well, doing these hard questions can only make you stronger!

The solutions are temporary. I will look to update them when I have more time.

In the exam simulator you can now flag a question for correction, if you wish to attempt it again (regardless if it you got it right or wrong) in corrections. This can be useful for questions that you want to be reminded of again for revision.

Now you can do corrections of mistakes of exam paper simulation to help with revision. I made it so that the corrections do not add to mastery and only practice exam paper adds to mastery. The mastery diagram feature in the dashboard is a very early first version design, I expect it to evolve in the way it works over time.

I have been working on my own mock papers, will expect to be adding a few of them some point next week. In the meantime, I have now added untime practice mode to exam simulator. It means you can practice a paper spread out over a few session, without time limit, have progress saved, should make practicing easier.

Made first version of spider mastery diagram as a nice visual way to view overall mastery progress. I also added randomization (optional) to simulator, because that's what happens in the real exam. Later, I will look to make the choices also random.

All remaining past papers — 2022, 2023, and the official specimen papers — have been added to the exam simulator. A dedicated paper downloads page has also gone live, so you can grab the PDFs directly if you'd rather work through them on paper.

Three more years' worth of past papers are now available in the exam simulator. Just 2022 and 2023 to go.

Every question in the exam simulator now carries a topic tag (algebra, coordinate geometry, logic, and so on). The dashboard uses these to show you a per-topic strength/weakness breakdown, which is very useful for working out where to focus your next revision session.

You can now create an account with an email and password. Signing up is optional, but it lets the site remember your attempts and track your progress over time. Anonymous users can still sit papers — your progress just won't persist across devices or sessions.

Both 2017 and 2018 past papers (Paper 1 and Paper 2) are now available in the exam simulator.

The exam simulator is live. Paper 1 and Paper 2 from 2016 are both available to sit under timed Pearson VUE-style conditions. More papers to follow shortly.

Hello world!