20 multiple-choice questions. 75 minutes. No calculator. One mark per correct answer and no penalty for a wrong answer.
Its official purpose is to assess how well you apply mathematical knowledge in new situations. Both the content and the decisions matter.Five options per question in the published papers.
An average of 3 minutes 45 seconds, not a per-question rule.
Methods must work cleanly by hand.
Answer every question before time expires.
What Paper 1 is really testing
Most of the underlying mathematics is familiar from higher-tier GCSE and AS-level study. The difficulty comes from deciding what the information means, choosing a short enough route and carrying it out without computational support.
A question can therefore be difficult without using an advanced topic. It may hide a simple invariant inside a diagram, make direct algebra deliberately unpleasant, or provide answer choices that reveal a faster way to test possibilities.
A quadratic, similar triangle, transformation or counting argument may be present without being named.
A full symbolic derivation may work but take too long. Substitution, elimination or a structural observation may be better.
Signs, domains, endpoint cases, reversals of inequalities and diagram assumptions frequently separate options.
The official content, organised by decision
The complete checklist belongs on the TMUA specification page. The map below groups the material by the kind of decision a question often demands. It is not a claim that every question fits only one group.
Algebra, equations, inequalities and sequences
Expect manipulation to be a means rather than the whole task. A question may reward factoring before expanding, comparing expressions without solving completely, or recognising the useful form of a sequence.
Functions, coordinate geometry and graphs
Translate between formula, transformation and picture. Check the domain before using an inverse, identify what a parameter changes and use intercepts or symmetry before trying to sketch every detail.
Coordinate, Euclidean and trigonometric geometry
Do not trust appearance. Mark equal lengths, parallel lines, angles and known constraints. Coordinates can turn a geometric claim into algebra; geometry can make an ugly coordinate calculation disappear.
Differentiation, integration and rates of change
Paper 1 often tests meaning as much as technique. A derivative may be used to compare behaviour or identify a tangent, while an integral may represent area rather than demand a long calculation.
Counting, probability and elementary statistics
Define the outcomes before calculating. Complementary probability, conditional information and double counting are more important than memorising a large formula collection.
Use the answer choices mathematically
Multiple choice does not mean guessing instead of solving. It means the options are additional information. A direct solution is still best when it is short. When it is not, the options can help you disprove claims, test cases or decide which quantity the question is sensitive to.
Determine sign, size or rough location before exact work.
Remove options that violate the domain, diagram or a necessary condition.
Use one clean value or special case when it is logically sufficient.
Check that the surviving option answers the original question.
Be careful with testing. One successful example cannot prove a statement claimed for every value. It can, however, disprove a universal statement or distinguish options when the question permits it.
A simple preparation loop
1. Cover the content
Use the official specification as a checklist. For each item, ask whether you can perform the standard method accurately without a calculator. Paper 1 is a poor place to discover that a routine identity or graph transformation is missing.
2. Solve real questions
Move from topic practice to mixed problems and then full papers. Keep the question wording intact. The ability to identify the topic is part of the test, so endless worksheets labelled “trigonometry” cannot provide the whole preparation.
3. Review properly
Redo every missed or guessed question before reading the full solution. Then write down the first useful observation, not a transcript of all the algebra. Finish by identifying what would let you recognise the same structure next time.
How Paper 1 differs from Paper 2
Both papers use mathematical knowledge and both require reasoning. Paper 2 places additional emphasis on mathematical reasoning and elementary logic, including the material in Section 2 of the specification. Do not treat Paper 2 as merely a harder version of Paper 1.
Prepare the shared mathematical content, then give Paper 2's logic language its own attention. The Paper 2 logic guide covers implication, necessary and sufficient conditions, quantifiers, proof and counterexamples.
Primary sources
Put the decisions inside a full paper.
Use unseen questions, the real clock and solutions that explain what unlocks each problem.
Explore TMUA mock papers