Topics
The moves the TMUA actually tests.
A hub for each search-intent cluster on the test. Each one names the specific moves the cluster rewards and links to free preview problems from the in-app bank.
- Paper 18 problems
TMUA Polynomials
Factor theorem, remainder theorem, and the moves you make on a polynomial when one root is given for free.
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- Paper 18 problems
TMUA Quadratics
Discriminants, vertex form, parameter conditions — Paper 1's most-tested algebra family.
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- Paper 17 problems
TMUA Stationary Points
Differentiate, set to zero, classify with the second derivative. Then read the question.
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- Paper 17 problems
TMUA Trigonometric Equations
Multiple-angle substitution, the unit circle, and counting solutions in a fixed interval.
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- Paper 16 problems
TMUA Coordinate Geometry
Lines, circles, gradients, distances, and the algebra of where two shapes meet.
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- Paper 16 problems
TMUA Inequalities
Sign analysis, denominator traps, and the rules you can't apply to inequalities without checking the sign.
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- Paper 16 problems
TMUA Sequences and Series
Arithmetic, geometric, sum to infinity, and the binomial expansion for positive integer powers.
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- Paper 15 problems
TMUA Exponentials and Logarithms
Substitute, factor, solve — quadratic-in-disguise is the most common pattern on Paper 1.
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- Paper 15 problems
TMUA Graph Sketching and Transformations
Where curves go, how they shift, and how to read a transformed graph back into algebra.
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- Paper 15 problems
TMUA Integration with the Power Rule
Area between curves, definite integrals, recovering a function from its derivative — the calculus core of Paper 1.
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- Paper 25 problems
TMUA Mathematical Reasoning (Paper 2)
Necessary and sufficient, proof by contradiction, quantifier negation, and the moves Paper 2 is built around.
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- Paper 15 problems
TMUA Trigonometric Identities
Pythagorean, double-angle, compound-angle, and the small set of moves that collapses a long expression into one line.
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