How to Get Faster at the TMUA

“I can do the questions, but I cannot do them quickly enough.”

If this sounds familiar, the useful next question is: where is the time going?

You might take a long time to recognise an approach, choose a method that involves unnecessary work, or struggle with the calculation itself. You might also spend too long on a few questions at the expense of others.

These are different difficulties, and they need different responses. Simply telling yourself to go faster is unlikely to resolve them.

My view is that much of mathematical speed comes from recognising useful ideas sooner and choosing your work more intelligently. With thoughtful practice, those are things you can develop.

1. Practise recognising ideas, not just completing solutions

People give mathematical intuition various names: maths sense, instincts, or even “triggers and automatic responses”.

What matters is what this familiarity allows you to do. You see a feature of a question and a promising idea comes to mind. You recognise a structure that previously took several minutes to untangle. You have a better sense of which approaches are worth trying.

Practice can help build that familiarity, particularly when you pay attention to the reasoning behind your solutions.

After a question, ask:

• What feature suggested the useful approach?
• What did I notice late that I could have noticed earlier?
• Why was this method promising?
• What would need to change before this method stopped being useful?

For example, you may learn to consider a graph when asked about the number of solutions, or to inspect symmetry before beginning a long calculation. These are possibilities to investigate, not instructions that always work.

The aim is to develop informed judgement. A superficial resemblance to a familiar problem should not stop you checking the actual conditions.

2. Find out where you are slow

When reviewing a question that took too long, distinguish between stages.

You may find more than one issue in a single question.

Try to make your conclusion specific. “I need to be faster at algebra” is a broad ambition. “I expanded everything before noticing a common factor” gives you something concrete to learn.

3. Compare methods, especially on questions you got right

A correct answer does not establish that your method was efficient.

Sometimes an algebraic approach is best. Sometimes a graph, a diagram, a simple case or an observation about the answer options saves considerable work.

After solving a question, compare your method with the written solution. If the solution is shorter, identify why. Did it exploit a feature you missed, avoid an unnecessary calculation, or answer the precise question without solving a larger problem?

In my own solutions, I often spend considerable time choosing an efficient approach and explaining what makes it useful. Where I include alternatives, it is because I think the comparison has learning value.

You do not need to replace your method simply because mine is different. Another method can be just as effective. The useful question is what the comparison teaches you.

Be careful with collecting shortcuts. A method you understand and can recognise is valuable; a large collection of special-case tricks that you cannot reliably choose between may add confusion.

4. Build fluency without making your working less reliable

Some delays come from basic operations requiring more attention than they should.

If rearranging fractions, manipulating indices or solving a straightforward equation repeatedly slows you down, focused practice may help. Work on the particular operation, with enough attention to accuracy that you do not simply rehearse errors.

The main aim is not to write faster. It is to spend less time hesitating, taking unnecessary steps and recovering from mistakes.

Even when you select your final answer on screen, clear written working can help you think. Removing every intermediate step may make a solution look shorter while making it harder to carry out or check.

Aim for working that is concise enough to be efficient and clear enough to trust.

5. Use the answer options thoughtfully

Multiple-choice options are part of the information available to you.

Depending on the question, it may be useful to substitute a proposed value, eliminate an impossible sign, compare magnitudes, or check a boundary case before committing to a full calculation.

But always ask whether your reasoning actually distinguishes the options. Checking one example does not generally prove a statement that claims to hold for every value.

Similarly, narrowing the choices down and taking an educated guess can be a sensible decision under time pressure. It does not mean the underlying difficulty has been resolved. Revisit it afterwards.

Efficient reasoning and incomplete reasoning are not the same thing.

6. Learn when to move on

Getting more marks within the available time does not require becoming faster at every question.

Suppose you spend several extra minutes pursuing one difficult question and consequently never reach another that you could have solved readily. The problem is partly how you allocated your time.

Practise noticing when an approach has stopped producing progress. You might leave the question, attempt others, and return with more time or a fresh perspective.

I would avoid treating an identical time limit for every question as a universal rule. Questions differ, and so do your strengths. Instead, ask whether you have a credible route forward and how much more work it appears to require.

After a timed paper, look at the questions you did not reach. If some turn out to be accessible, improving your move-on decisions may be a useful priority.

7. Combine untimed learning with timed practice

Timed practice shows you what you can currently do under pressure. Untimed practice gives you room to develop what you cannot yet do efficiently.

If you do not understand an idea, repeatedly trying to apply it against the clock is unlikely to be the best starting point.

Learn it carefully, practise using it, then check whether you can recognise and apply it in mixed questions. As the reasoning becomes more dependable, add time pressure.

Harder untimed problems can also be useful. They give you opportunities to explore approaches and practise getting yourself unstuck. That experience may help you make better decisions later, although it does not mean every difficult problem is a good use of your preparation time.

Return to How to Prepare for the TMUA for the wider balance between learning, problem-solving and exam practice.

8. Review your timing with context

On JZMaths, you can compare your recorded time for a question with the median time taken by students who answered it correctly on their first attempt.

That provides a useful reference point. If your time is substantially longer, investigate the reason—even if you got the answer right.

It is not a requirement to match or beat the median on every question. Students differ in experience, and an interrupted or untimed attempt is not directly comparable with a focused exam attempt.

Use the comparison to identify opportunities: a better method, more fluent manipulation, earlier recognition, or less unnecessary checking.

For a full review process, see How to Review a TMUA Paper Properly.

9. Revisit ideas, then test them on unfamiliar questions

Returning to a question after a gap can help consolidate an approach. Try to reconstruct the reasoning rather than remember a sequence of steps.

Then look for opportunities to apply the idea elsewhere. Solving a familiar question quickly is useful practice, but it is not independent evidence that you can recognise the same structure in a fresh problem.

Variety matters alongside repetition. You want to understand which features are essential to the method and which were incidental to that particular example.

This is how practice can contribute to faster intuition: you gradually have more useful experiences to draw on, and a better sense of what is worth trying.

A practical focus for your next week

Choose a few questions that took longer than you would like. Work out where the time went, then select one recurring issue to address.

You might practise a particular manipulation, study a more efficient approach, work on recognising a skill, or make a deliberate effort to move on sooner during your next timed attempt.

Check the result on suitable fresh material. Look for improved accuracy and efficiency together, rather than celebrating a faster time that came with more mistakes.

If you are working consistently but cannot identify what is helping, see Why Your TMUA Score Isn’t Improving.

Speed is something you can work on. Much of that work happens while you are learning carefully: noticing structure, comparing methods, becoming fluent and understanding why an idea works. The aim is to arrive at useful reasoning sooner—and carry it through reliably.