Free TMUA guide
TMUA multiple-choice elimination strategy
TMUA is multiple choice, with one mark for a correct answer and no penalty for an incorrect answer. Use elimination to create a defensible final choice, then answer every item rather than leaving a blank.
Start with the stem, not the options
- Underline the requested quantity and its domain.
- Rewrite a condition as an equation, inequality, implication or finite list.
- Estimate the sign, scale, parity or range before calculating.
- Use the options to choose the cheapest check that distinguishes the survivors.
Five reliable ways to remove an option
| Method | Use it when... | Record |
|---|---|---|
| Sign or range | The expression cannot be negative, exceed a bound or leave an interval | The inequality or bound that excludes it |
| Special value | The claim is universal or the options are formulas | One allowed substitution |
| Reverse check | The options propose values for an equation | The option that fails substitution |
| Dimension or unit | The stem combines lengths, areas, rates or probabilities | The unit or scale mismatch |
| Equivalent form | A factor, common base or symmetry is hidden | The rewrite that makes the comparison direct |
Worked example A range can do most of the work
Suppose and the options for include , , , and . Since , the expression is greater than .
The useful conclusion is not a decimal approximation. It is the order forced by the domain. If the question asks for a comparison, the interval has already eliminated several options.
Why this works: The domain supplies strict inequalities, so the options can be tested without choosing a particular value of .
Why the tempting route fails: Testing one convenient decimal can support a pattern, but it cannot establish a claim for every allowed .
Treat the option set as evidence, not a shortcut
Count the options shown on the screen. Published TMUA practice papers use different option counts and shapes, particularly when several statements must be classified. Do not assume that every item has five choices or that a familiar option pattern tells you the answer.
- For a statement list, test each statement independently before mapping the combination to an option.
- For numerical options, use bounds and parity before exact arithmetic.
- For graph options, compare intercepts, turning points, asymptotes and monotonicity in that order.
- For an 'except' stem, mark the requested exception at the top of the page before eliminating anything.
Worked example Answer the negative stem deliberately
A question asks which statement is not always true for a positive integer . You test each statement and find that three survive every allowed case, while one fails at .
The failed statement is the answer only because the stem asks for the exception. Circle the word 'not' before you return to the options.
Why this works: The domain and stem polarity decide what counts as a successful test. The option is selected for the requested exception, not for being the first statement you can verify.
Why the tempting route fails: Proving a statement true and selecting it on a negative stem reverses the question even when all the algebra is correct.
Finish with a recorded decision
When you move on, leave a short note: 'B and D remain; compare the sign at the endpoint' or 'C fails the domain'. A flag without a return task invites a full reread and spends the same time twice.
Sources
TMUA Content Specification. No penalty for incorrect answers, equal question weight and the current multiple-choice format. Read the specificationhttps://uat-wp.s3.eu-west-2.amazonaws.com/wp-content/uploads/2024/05/03165619/TMUA_Content_Specification.pdf
UAT-UK TMUA preparation materials. The official archive where option shapes and worked answers can be inspected directly. Open the archivehttps://esat-tmua.ac.uk/tmua-preparation-materials/
The worked items are new study examples. Elimination narrows a decision; it does not replace proving the surviving option.