Exam Technique Tips for the TMUA

In this article, we share some advice to help you improve your timing and approach to answering TMUA questions. The best way to determine a good exam strategy is through frequent practice of timed mock exams, because it will depend on your individual strengths and weaknesses. The more you practice, the more familiar you will become with the questioning style and common tricks used by the examiners.

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1. Watch the clock

The TMUA is the most time-pressured of the mathematics admissions tests and being disciplined with timing is a key to success. Each paper is 75 minutes long and consists of 20 multiple choice questions. Therefore, you have an average of only 3 minutes and 45 seconds to spend on each question. A very common source of underperformance is sinking too much time into one problem: in the exam, even a period of 15 minutes can pass in the blink of an eye if you don’t keep your eye on the clock! There is enormous variation in the difficulty of the questions, but they are all worth the same number of marks. It can be catastrophic to spend so long on a difficult problem that you are unable to attempt another easier question.

It is worth noting that, while the first few questions are typically easier and the last few harder, there is no general trend of increasing difficulty through the paper. Therefore, there is no reason to attempt the questions in order; rather, you may choose to just pick the questions in the order you like the look of them. The examples below are from the same paper but it is immediately obvious that one is much easier, so it would be good strategy to attempt it first. It's crucial to remember that all TMUA questions are worth the same number of marks, so you won't gain any extra credit for prioritising harder questions!

If you do run out of time, remember that you don’t lose marks for incorrect answers, so it’s better to make a good guess than leave an answer blank.

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2. Eliminate

As on any multiple-choice exam, it is often easier to proceed by elimination of the wrong answers rather than directly identifying the correct answer. In fact, this is occasionally the only feasible way to find the correct answer, for example:

This approach is particularly useful in questions that require you to identify the correct graph.

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3. Wishful thinking

It is important to remember that TMUA questions are designed to be solvable by a good Y13 student in a reasonable timeframe. If a problem looks far too complicated to be solvable using methods on the specification unless something miraculous happens, you can bet on the fact it probably will! This means you should often attempt algebraic simplifications and other calculations, even if they seem unlikely to succeed.

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4. Remaster arithmetic

Your arithmetic skills will likely have atrophied since taking calculator-only courses, and you will have no calculator for the TMUA. It’s certainly worth reviewing:

• Times tables up to 20
• Methods for adding, subtracting, multiplying and dividing numbers with many digits
• Square numbers up to 20²
• Cube numbers up to 10³

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5. Think graphically

TMUA examiners have a strong bias towards setting problems which use graphical reasoning. In particular, you will often be asked to count the number of solutions to an equation which cannot be solved algebraically, so you must get into the habit of thinking graphically. In other cases, solving a problem algebraically would be extremely laborious (though possible), but the solution is almost immediate when using graphical methods.

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6. Avoid complacency

Students are likely to become complacent with algebra slips or other mistakes because the exam is multiple choice. The examiners are particularly devious: they put a great deal of work into anticipating the common errors students might make and ensure that the results of such errors are included among the given options. This is why it is important to work through algebra carefully and set your work out clearly so that it’s easy to check.

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7. Use counterexamples

Counter examples can be very useful for ruling out options, especially when questions involve necessary and sufficient conditions.

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8. Stick to the specification

The syllabus contains first year A level content only, but students are often tempted to attempt questions using second year methods. These off-syllabus methods, such as the compound angle formula or advanced integration methods, can sometimes be used to good effect in TMUA questions. Nevertheless, it is usually a bad idea to use them because the questions have been designed to be solved in a particular way (using first year methods), and there is a good chance you'll make the question harder than intended if you go 'off-piste'.

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