An Overview of TMUA Question of the Day (Q.o.t.D)
Hello to anyone reading this, and welcome to TMUA Question of the Day. From August 1st, you will have a little over 10 weeks until you sit the TMUA, and every one of those days can and should be spent doing something productive towards that goal. This page aims to be a good starting point for any given day’s revision; by doing every question that is supplied, you give yourself the best possible chance to experience everything the TMUA might throw at you.
Each day, you will be given 4 questions, and are recommended to complete (or at least very seriously attempt) them all. These questions will be categorised according to topic, difficulty, and priority; all of these concepts will be explained in depth later in this document. Below this, we shall attach generic and semi-specific advice; the former will be applicable to almost every question which we provide, whereas the latter is primarily (but not exclusively) intended for questions of a specific topic. This advice is best considered as a checklist to go through if you get stuck on a problem, before checking the question-specific advice.
Categories
The TMUA specification separates itself into 9 distinct categories, according to what concept primarily makes up the questions. However, this isn’t massively useful when you’re doing a question, especially if you’re stuck. Our philosophy separates TMUA and TMUA-adjacent questions into 4 classes, depending on how the questions are best approached and solved. There will often be a little overlap between classes, but you can safely assume that every question fits into the class it is labelled as.
These 4 categories are:
- A-Level+ – A lot of questions on the TMUA will inherently feel very similar to questions you might have seen during your A-Level studies. These questions in particular are so similar that they should be treated as such. Even though they are often difficult, you should attempt to solve them as you would a hard A-Level question.
- Algebra + Functions – This topic encompasses a large variety of questions, but they all share (at least) one thing in common: they are best started by looking closely at the algebra. There are usually small tells in these questions which will let you know where and how to start.
- Geometry + Functions – These functions, similarly to above, are best started geometrically. These questions often revolve around good diagrams and/or graphs, as their effective implementation allows for large steps to be made before more traditional methods take over.
- Logic – In these questions, the maths itself is not what makes them difficult; they will often have minimal or even no maths. These questions are often slower to approach, and should be solved very deliberately – rushing in will very rarely be the best way to the correct answer.
Prioritised Questions
For each day, there will usually be one or two questions labelled with a priority tag (this will be easy to recognise regardless of what is used). Questions labelled with the tag are meant to be prioritised; by prioritised, we do not necessarily mean that it should be attempted first, though if you find that useful please do follow it. In this context, prioritising a question means that some aspect of the solution is shared by a very large number of other questions, and as such deeply understanding this question’s solution and mechanics will greatly help you in the near future.
Difficulty
The difficulty of the questions provided will likely vary greatly between days and categories; each question will be supplied with a difficulty number from 0 to 10. However, that on its own means very little; here we shall supplement the difficulty number with a statement which aims to describe how a question of that difficulty might feel. Keep in mind that this number may not be accurate for you; your strengths and weaknesses may make a question multiple points easier or harder than described. The difficulty rankings are provided below.
- 0 is practically trivial; the first method you use will get you the answer reliably.
- 1 is very easy, though mistakes can be made if you underestimate them and/or work too quickly.
- 2 is easy, though some methods are less effective than others.
- 3 is quite easy, but brute force often becomes a little less effective, as you will have to think before using it.
- 4 is reasonable; some of the easier questions of the TMUA/ESAT are of this difficulty.
- 5 requires considerable thought, and brute force is only rarely useful for questions of similar or greater difficulty.
- 6 starts to become technical, and very difficult to do in your head.
- 7 is quite difficult, and may take a long time or multiple attempts.
- 8 is difficult, and is on par with the hardest questions of a TMUA/ESAT.
- 9 is slightly harder than almost all TMUA/ESAT questions, but some very hard questions are still on par. These questions almost always require specific techniques/intuitions to solve confidently.
- 10 is entirely beyond the difficulty of the TMUA/ESAT, although I would still recommend attempting and understanding these questions.
Advice for attempting questions
General Advice
- Keep your working out organised; neat is ideal, but don’t throw workings around the page and expect them to come together easily.
- Make sure you tidy up; factorise, collect/cancel like terms, etc.
- Check for effortless mistakes; +/- signs, fractions, expansions/factorisations.
Semi-specific advice
- Don’t overcomplicate your first attempt. (A-Level+)
- See if the question looks like something you want to work with. (Algebra + Functions)
- Ensure the equations you extract make sense. (Algebra + Functions)
- Make sure your diagrams are reasonable; they don’t need to be perfect, but a point with x-co-rdinate 2 should be to the right of a point with x-co-ordinate 1. (Geometry + Functions)
- Draw some useful properties onto your diagrams (right angles, radii, etc.) (Geometry + Functions)
- Look for any explicit contradictions. (Logic)
- Test ridiculous hypotheticals, provided they fit the conditions you’re working under. (Logic)