JZMaths Videos

Lessons on TMUA maths and problem-solving. We work through problems together, exploring the thinking behind each solution.

17:28 (watch on YouTube, opens in a new tab)
Multivariate Factorisation: A More General Version of the Factor Theorem | TMUA (watch on YouTube, opens in a new tab)
11 October 2026Duration 17:28
The factor theorem works with more than one variable, and it can make some awkward-looking algebra much simpler. The idea behind multivariate polynomial factorisation and a few basic examples, then three problems: factorising a trigonometric equation (Multivariate Factorisation Topic Test, Q6), solving an inequality (JZ Exam Set B Paper 2, Q15) and finding the range of an angle (TMUA 2017 Paper 1, Q20). The focus is on spotting factors and understanding the structure of an expression, so you can recognise familiar ideas in unfamiliar questions.
- Multivariate factorisation
- Factor theorem
- Trigonometric equations
- Inequalities
Watch on YouTube →: Multivariate Factorisation: A More General Version of the Factor Theorem | TMUA (opens in a new tab)
6:00 (watch on YouTube, opens in a new tab)
Combinatorics: Do You Really Know How to COUNT!? | Bonus | TMUA (watch on YouTube, opens in a new tab)
10 October 2026Duration 6:00
One more counting problem to finish the series: a question from Hercules Set 2, Paper 1, Q18 — given that three non-negative integers add up to a fixed total, what is the probability that one takes a particular value? We solve this in two ways: flexible variables, and then a full proof.
- Combinatorics
- Stars and bars
- Probability
Watch on YouTube →: Combinatorics: Do You Really Know How to COUNT!? | Bonus | TMUA (opens in a new tab)
13:16 (watch on YouTube, opens in a new tab)
Combinatorics: Do You Really Know How to COUNT!? | Part 2 | TMUA (watch on YouTube, opens in a new tab)
10 October 2026Duration 13:16
You know the counting principles, but can you spot how to use them? Four TMUA-style questions — race results (TMUA Specimen Paper 2, Q13), coefficients in an expansion (TMUA 2016 Paper 1, Q19), dice probabilities given a total (JZ Exam Set B Paper 2, Q10) and counting functions where f(f(x)) = x (JZ Mock Set D Paper 2, Q10) — splitting problems into cases, accounting for repeated outcomes, and making sure everything is counted exactly once.
- Combinatorics
- Probability
- Binomial expansion
- Past papers
Watch on YouTube →: Combinatorics: Do You Really Know How to COUNT!? | Part 2 | TMUA (opens in a new tab)
15:02 (watch on YouTube, opens in a new tab)
Combinatorics: Do You Really Know How to COUNT!? | Part 1 | TMUA (watch on YouTube, opens in a new tab)
10 October 2026Duration 15:02
Counting sounds simple, until you need to be certain you've counted everything exactly once. The core ideas behind combinatorics — the multiplication principle, permutations, combinations, and arrangements with repeated objects — and why the formulas work, when to use them, and when dividing out duplicates can go wrong. Two questions guide us throughout: have we counted every possibility, and have we counted anything more than once?
- Combinatorics
- Permutations
- Combinations
Watch on YouTube →: Combinatorics: Do You Really Know How to COUNT!? | Part 1 | TMUA (opens in a new tab)
16:18 (watch on YouTube, opens in a new tab)
Flexible Variables: Bend Them to Your Will! | TMUA (watch on YouTube, opens in a new tab)
9 October 2026Duration 16:18
Sometimes the quickest way through a question is to give the letters convenient values. Five increasingly challenging TMUA past-paper questions — triangle areas, cubic roots, graph intersections, the distance between roots and quadratic inequalities — showing how well-chosen values can dramatically simplify the work. It is a legitimate method rooted in logic: the correct general answer must work for every permitted choice of values, so an option that fails for your chosen values can be eliminated. When it works, and how to choose useful values.
- Substitution
- Elimination
- Exam strategy
- Past papers
Watch on YouTube →: Flexible Variables: Bend Them to Your Will! | TMUA (opens in a new tab)
14:39 (watch on YouTube, opens in a new tab)
SSA Ambiguous Triangles: The Topic That Refuses to Go Away! (watch on YouTube, opens in a new tab)
8 October 2026Duration 14:39
The SSA ambiguous case is a relatively well-covered topic in trigonometry, yet many students still struggle with it, especially with variations on the standard problems. I hope this video gives some additional clarity on how to approach such problems.
- Ambiguous case
- Sine rule
- Trigonometry
- Area of a triangle
Watch on YouTube →: SSA Ambiguous Triangles: The Topic That Refuses to Go Away! (opens in a new tab)
13:37 (watch on YouTube, opens in a new tab)
TMUA: Sign Analysis — Inequalities Without Graph Sketching (watch on YouTube, opens in a new tab)
7 October 2026Duration 13:37
How can you solve an inequality without sketching the whole graph? A follow-up to "Making the Most of the Final Few Days": sign analysis through three worked questions, from algebraic fractions to a trigonometric inequality — where an expression can change sign, why some factors become zero without changing sign, how repeated factors affect the analysis, keeping track of excluded values and endpoints, and finding the total length of the intervals that satisfy an inequality. The aim is to understand what controls the sign of an expression, giving you a method you can apply across different questions.
- Inequalities
- Sign analysis
- Algebraic fractions
- Trigonometry
Watch on YouTube →: TMUA: Sign Analysis — Inequalities Without Graph Sketching (opens in a new tab)
14:36 (watch on YouTube, opens in a new tab)
TMUA: Making the Most of the Final Few Days (watch on YouTube, opens in a new tab)
7 October 2026Duration 14:36
With the TMUA approaching, practical ideas for deciding what deserves your time in the final few days and what to leave alone: reviewing questions you got right but took too long on or guessed, choosing which questions to tackle first and when to move on, balancing checking against attempting more, finding small weaknesses you can realistically improve, and keeping sharp through active practice while making time for rest. Flexible examples, not targets — and a reminder that the TMUA does not define you or limit what you can achieve. Best of luck!
- Exam strategy
- Final preparation
- Revision
Watch on YouTube →: TMUA: Making the Most of the Final Few Days (opens in a new tab)
21:44 (watch on YouTube, opens in a new tab)
The NOTORIOUS Questions on JZMaths – Part 3 | TMUA Preparation (watch on YouTube, opens in a new tab)
6 October 2026Duration 21:44
Four innocent-looking questions with a few less innocent details: 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.
- Logarithms
- Exponentials
- Graphs
- Logic
Watch on YouTube →: The NOTORIOUS Questions on JZMaths – Part 3 | TMUA Preparation (opens in a new tab)
12:08 (watch on YouTube, opens in a new tab)
Odd and Even Functions: A Little Symmetry Goes a Long Way! — Part 2 (watch on YouTube, opens in a new tab)
5 October 2026Duration 12:08
Part 2 puts the ideas from Part 1 into practice with three challenging TMUA-style questions from JZMaths: spotting hidden symmetry in a polynomial to simplify a definite integral; using the Fundamental Theorem of Calculus and graph symmetry to count solutions without finding them; and completing a cube to reveal cancelling pairs in a sum of 101 terms.
- Odd and even functions
- Symmetry
- Integration
- Sequences and series
Watch on YouTube →: Odd and Even Functions: A Little Symmetry Goes a Long Way! — Part 2 (opens in a new tab)
12:54 (watch on YouTube, opens in a new tab)
Odd and Even Functions: A Little Symmetry Goes a Long Way! — Part 1 (watch on YouTube, opens in a new tab)
5 October 2026Duration 12:54
A little symmetry can save a lot of algebra. What makes a function odd or even and how that shows in its graph; sums, products and compositions of odd and even functions; the connections with differentiation and integration; and spotting symmetry when a graph has been shifted. Groundwork for Part 2's harder problems.
- Odd and even functions
- Symmetry
- Graphs
- Integration
Watch on YouTube →: Odd and Even Functions: A Little Symmetry Goes a Long Way! — Part 1 (opens in a new tab)
25:05 (watch on YouTube, opens in a new tab)
The Most NOTORIOUS Questions on JZMaths – Part 2 | TMUA Preparation (watch on YouTube, opens in a new tab)
4 October 2026Duration 25:05
Three challenging questions on polygons, triangles and circles, followed by an extra question on finding tangent equations. I explain the thinking behind each solution: how to test a geometric claim, recognise useful right angles, and connect circle geometry with algebra.
- Polygons
- Triangles
- Circle geometry
- Tangents
Watch on YouTube →: The Most NOTORIOUS Questions on JZMaths – Part 2 | TMUA Preparation (opens in a new tab)
15:41 (watch on YouTube, opens in a new tab)
Don't Underestimate Similar Triangles! (watch on YouTube, opens in a new tab)
3 October 2026Duration 15:41
Similar triangles are easy to underestimate, but spotting them can make a tricky geometry question much simpler. Four problems involving circles, common tangents, parallel lines and area ratios: how to spot the useful pair of triangles, match the corresponding sides and use their ratios to find a way through.
- Similar triangles
- Circle geometry
- Tangents
- Area ratios
Watch on YouTube →: Don't Underestimate Similar Triangles! (opens in a new tab)
25:38 (watch on YouTube, opens in a new tab)
The Most Notorious Questions on JZMaths — Part 1 (watch on YouTube, opens in a new tab)
2 October 2026Duration 25:38
Four questions that caught out a surprisingly large number of you, across hundreds and sometimes thousands of attempts: dividing by fractional powers in an inequality, the graph of sin(y/x) = 1/2, what a transformation does to a cubic's roots, and what really guarantees a rhombus.
- Inequalities
- Trigonometric graphs
- Transformations
- Logic
Watch on YouTube →: The Most Notorious Questions on JZMaths — Part 1 (opens in a new tab)
17:49 (watch on YouTube, opens in a new tab)
Number of Solutions — A New Way of Thinking (watch on YouTube, opens in a new tab)
1 October 2026Duration 17:49
How can you count the solutions to an equation without solving it? In this lesson, we work through three examples, including TMUA 2022 Paper 1, Question 20, and explore how rearranging an equation can make the graphs easier to sketch and their intersections easier to count.
- Graph sketching
- Number of solutions
- Modulus functions
Watch on YouTube →: Number of Solutions — A New Way of Thinking (opens in a new tab)