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TMUA PRACTICE QUESTIONS

Free TMUA practice questions with worked routes.

Use these questions as a diagnostic sample of the CF Maths style: compact, non-calculator problems where the route matters more than repetitive computation. Each topic page contains further free examples.

How to practise productively

Give each question a genuine attempt before opening the route. If you cannot identify a first move after two or three minutes, write down what the question is asking structurally: solve, count roots, compare conditions, find an area, locate a tangent, or disprove a claim.

When you read the solution, record the recognition step rather than copying every algebraic line. The most transferable note is usually something like ‘substitute the repeated exponential’, ‘compare turning heights’, or ‘one counterexample is enough’.

Move from topic practice to mixed practice

Topic pages are useful while a skill is being built because they let you see several variants of the same underlying idea. Once the idea is stable, mixed diagnostics and mocks are more valuable because they remove the topic label and force you to choose the method independently.

That progression mirrors the structure of the \(CF\) Maths Mastery notes: explanation, worked examples, independent topic practice, then mixed admissions-test questions.

FREE PRACTICE

Try these TMUA-style questions

These questions now draw from the current reviewed CF Maths banks, including image and diagram items where appropriate. Open the solution only after you have committed to a route.

QUESTION 1 · Algebraic modelling & equations
TMUA Algebraic modelling & equations question
Show answer & route
Answer: C
Correct answer: \(C\). This item is marked from the validated final 200-question answer key. Revision method: Algebraic modelling & equations. Rework the displayed question carefully and compare your algebra with the keyed option.
QUESTION 2 · Geometric sequences & series
TMUA Geometric sequences & series question
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Answer: C
Correct answer: \(C\). This item is marked from the validated final 200-question answer key. Revision method: Geometric sequences & series. Rework the displayed question carefully and compare your algebra with the keyed option.
QUESTION 3 · Circles, chords & tangents
TMUA Circles, chords & tangents question
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Answer: A
Correct answer: A. This item is marked from the validated final 200-question answer key. Revision method: Circles, chords & tangents. Rework the displayed question carefully and compare your algebra with the keyed option.
QUESTION 4 · Trigonometric geometry
TMUA Trigonometric geometry question
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Answer: C
Correct answer: \(C\). This item is marked from the validated final 200-question answer key. Revision method: Trigonometric geometry. Rework the displayed question carefully and compare your algebra with the keyed option.
QUESTION 5 · Logarithmic equations & constraints
TMUA Logarithmic equations & constraints question
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Answer: B
Correct answer: \(B\). This item is marked from the validated final 200-question answer key. Revision method: Logarithmic equations & constraints. Rework the displayed question carefully and compare your algebra with the keyed option.
QUESTION 6 · Gradients, tangents & normals
TMUA Gradients, tangents & normals question
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Answer: D
Correct option: \(D\) - \(\frac{48}{65}\). Use exact values, quadrant/sign information and the permitted identities; count solutions only after fixing the interval and period.
QUESTION 7 · Definite integrals & parameters
TMUA Definite integrals & parameters question
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Answer: D
Correct answer: \(D\). This item is marked from the validated final 200-question answer key. Revision method: Definite integrals & parameters. Rework the displayed question carefully and compare your algebra with the keyed option.
QUESTION 8 · Counterexamples - number
TMUA Counterexamples - number question
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Answer: H
Worked solution for Counterexamples - number
QUESTION 9 · Radical inequalities
TMUA Radical inequalities question
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Answer: E
Worked solution for Radical inequalities
QUESTION 10 · Statements about definite integrals
TMUA Statements about definite integrals question
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Answer: F
Worked solution for Statements about definite integrals

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