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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

I wasn’t planning to record a video this Sunday, but I thought, “Let’s do a quick one”—so here it is! There will be more parts to come.

Watch Part 2 on YouTube

All the videos are collected on the Videos page. If there’s a topic or question you’d like me to cover next, leave a comment on YouTube or email me at jzmaths@hotmail.com.

The grade boundaries for yesterday’s Tyler Exam Set B live mock are now available. Jackie and I hope to share the report with you tomorrow.

Have a good day of preparation—and remember to take a break too!

For the first time, over 900 students were active on JZMaths in a single day, answering more than 20,000 questions between them! It’s wonderful to see so many of you working hard. I’ll do what I can to help you make that effort count.

Well done to everyone who took part in today’s live mock, too. Whether you joined in or have been preparing in your own way, remember to give yourself time to learn from mistakes as well as tackle fresh questions. Grade boundaries should be available later tonight or tomorrow, and Jackie and I are aiming to share a report with you on Monday.

My third YouTube video is now up: Don’t underestimate similar triangles! This is a topic well worth getting fluent with—recognising the right pair of triangles can turn a tricky-looking question into a few simple steps.

I’m aiming to post a video on most days in the run-up to the exams to give you some extra help. If there’s a topic or question you’d like me to cover, email me. I can’t promise to get to everything, but I’d love to hear your suggestions.

Keep going, and I hope you find the videos useful!

PS: There will be another database restart around midnight tonight (UK time), so please expect a few minutes of downtime. Sorry for the interruption!

Quick announcement: There will be a short database restart around midnight tonight. Site will be up, but database functions may be interrupted for a few minutes.

Recording these is still incredibly uncomfortable for me, but my second video is up!

This time, I’ve picked out some of the questions that have caught out a surprisingly high proportion of you, with hundreds—and sometimes thousands—of attempts on each. In this video, I work through four of the worst offenders and explain what makes them tricky, and how to overcome them:

• Inequalities and fractional powers: when is it actually safe to divide by an expression? (JZ Exam Set A, Paper 2, Question 19)
• Trigonometric graphs: making sense of the graph of $\sin(y/x) = \tfrac12$. (Tyler Mock C, Paper 1, Question 20)
• Cubic graphs and transformations: what happens to the number of distinct real roots? (JZ Mock D, Paper 1, Question 11)
• Geometry and logic: what conditions really guarantee a rhombus? (JZ Mock C, Paper 2, Question 20)

The aim is to help you understand these four questions and take away ideas you can use when the next unfamiliar question turns up.

Watch Part 1 on YouTube

All the videos are also collected on the Videos page. I’m planning to record Part 2 tomorrow.

Please do let me know if an explanation is unclear, or if you struggle to make out what I’m saying! If you have any negative feedback, feel free to email me privately, haha—I really do want to know. Thank you!