TMUA
The Test of Mathematics
for University Admission
A mathematics admissions test led by UAT-UK and delivered globally by Pearson VUE, recognised by Cambridge, Imperial, Warwick, LSE and other institutions, primarily assessing mathematical thinking and reasoning.
TMUA (The Test of Mathematics for University Admission) is primarily designed for mathematics, computer science, economics and related programmes, based on GCSE/AS level mathematics. The test comprises two papers, each 75 minutes with 20 multiple-choice questions, focusing on mathematical thinking and reasoning. Calculators and dictionaries are not permitted; there is no pass/fail threshold, with results reported as a single overall score on a 1.0–9.0 scale.
Schedule
Register NowOverview
Two-paper structure · Scoring scale · Exam regulations
Paper 1 (Applications of Mathematical Knowledge)：20 questions / 75 minutes, testing the ability to apply mathematical knowledge in new contexts (algebra, functions, sequences, geometry, coordinate geometry, etc.).
Paper 2 (Mathematical Reasoning)：20 questions / 75 minutes, testing mathematical reasoning and elementary logic (argumentation, proof) skills.
Scored by correct answers, no penalty for wrong answers; it is recommended to complete all questions.
Single score: 1.0–9.0 (to 0.1).
No pass/fail threshold, universities evaluate comprehensively with application materials.
Results are usually published through accounts about six weeks after the exam and sent to selected institutions.
Follow official specifications and sample questions, familiarize yourself with question types and answering rhythm; Paper 2 requires deliberate practice in logic and argumentation.
Timed 75-minute full papers, practice checking and guessing strategies.
Both papers are multiple choice, calculators and dictionaries are not allowed; bring valid ID and arrive on time.
Changes/cancellations and financial aid, accommodation measures, etc. must be applied for before booking.
Recognised Universities
Mandatory · Recommended · Supplementary · International
| Requirement Level | University | Applicable Major | Notes |
|---|---|---|---|
| Mandatory | Cambridge | Computer Science, Economics | Only accepts October session; ≥7.0 significantly competitive |
| Mandatory | Imperial College | Department of Computer Science, Business School (Economics/Finance/Data Science) | Replaced by TMUA from 2025; STEP can be used as substitute if not submitted |
| Mandatory | LSE | Economics, Econometrics/Mathematical Economics | Other business subjects (e.g., Financial Mathematics and Statistics) recommended for submission |
| Mandatory | Warwick | Computer Science, Economics (including Management/Political Economy), Discrete Mathematics | Mandatory for 16 majors; Mathematics department can use STEP 2 as substitute |
- G5: A score ≥7.0 is highly competitive (Cambridge CS recent average ≈7.2+).
- Durham/Warwick: A score ≥6.5 typically qualifies for reduced offers (Warwick accepts STEP 2 as an alternative).
- Imperial College and Warwick will fully replace the MAT with the TMUA starting in 2025.
- Recommend checking universities' websites for the latest admissions test requirements (e.g., UCL Economics' 2026 policy update).
Analysis
Score distribution · Exam characteristics · Annual trends · Module switching
- Scoring scale 1.0–9.0.
- Two papers, 75 minutes each with 20 questions; Paper 1 focuses on mathematical thinking (algebra/functions/geometry/trigonometry/calculus), Paper 2 on mathematical reasoning (proofs, logic).
- Overall difficulty remains similar to previous years; time management and procedural factors significantly impact performance.
- Common cross-dimensional combination questions with moderate to high computational load; recommend timed practice with recent past papers, focusing on Paper 1 stability and Paper 2 formal argumentation accuracy and completeness.
Preparation
Mathematics notes · Logic and proof · Action recommendations
Covers algebra & transformations, functions & graphs (exponential, logarithmic, piecewise, inverse, monotonicity, extrema), sequences, inequalities, estimation, trigonometric identities, analytic geometry, and introductory calculus.
Emphasizes calculator-free derivation and estimation, modeling word problems algebraically, and using graphical intuition (monotonicity, concavity) for rapid assessment.
Avoid mechanical application and neglecting boundaries/units. Instead, use a checklist for critical elements (dimensions, extrema, signs, special values).
Focuses on propositions & connectives, necessary & sufficient conditions, contrapositives, quantifiers, truth tables, equivalent transformations, sets, counterexamples, and proof construction.
Includes key proof methods (direct, contrapositive, contradiction, induction). Stress structured argumentation with clear "definition → reasoning → conclusion" flow.
First formalize & strategize, then select methods. Rigorous self-checking for counterexamples/boundaries ensures gap-free argumentation.
FAQ
Common questions · Policies and procedures · Exam day and results
Completed continuously in one sitting: TMUA total duration 150 minutes, including two papers:
Paper 1 (Mathematical Reasoning)：75 minutes, all 20 questions are multiple-choice.
Paper 2 (Mathematical Logic and Proof)：75 minutes, all 20 questions are multiple-choice.
After submitting Paper 1, you can choose whether to start Paper 2 immediately (you can take a break); the two papers are conducted consecutively.
Calculator：Calculator: Strictly prohibited (all questions require manual calculation, e.g., simplifying √50 / 2).
Dictionary：Dictionary: Strictly prohibited (mathematical terms are standard expressions).
Computer-based system functions：Computer-based system functions: Supports question flagging and question navigator (shows answer status and flags); no built-in calculator.
Draft tools：Draft tools: Official provides A4 single-sided whiteboards, markers, erasers, cloths; if whiteboard is not erased, raise hand to request replacement. Some test centers provide erasable plastic boards/sealed draft paper; candidates are prohibited from bringing their own materials (water, tissues, paper, pens, etc.).
Hint：Whiteboard space is limited, it is recommended to use it in sections (e.g., left half for scratch work for paper 1, right half for proofs for paper 2).
Approach: Build foundational knowledge first, then use past papers for speed training; combine with computer-based simulation. Target: 70% of common question types should be quickly recognizable.
① Paper 1：MAT A (multiple choice) | AMC 12 (first 15 questions) | PAT Mathematics | ENGAA Mathematics
② Paper 2：STEP basic modules (introductory questions) | Notes on Logic & Proof | Jacqueline Taylor
③ Extension / Consolidation：ECAA Advanced Mathematics | Hodder Three-in-One (STEP/TMUA/MAT) | UKMT Senior/Kangaroo (optional)
④ Past Papers Finale：75-minute full papers (establish timing rhythm) | Deep review (master optimal solutions) | Convert wrong questions to Anki cards (cyclical reinforcement)
- Score Release：Results released 6–8 weeks after exam; e.g., October 2025 session results expected late November, January 2026 session results expected late February.
- Score Validity：Valid only for current application cycle (2025 scores valid for 2026 admissions only).
- Score Submission Policy：Scores automatically sent to registered institutions (Cambridge requires "TMUA" selection in UCAS application).
- Interface Proficiency：Familiarize with computer-based exam interface to avoid exam day confusion.
- Real-time Countdown：Provides countdown functionality to prevent accidental time overruns.
- Whiteboard Simulation：Adapt to marker writing technique (avoid illegible handwriting during exam).
- Full Pressure Testing：Simulate extended high-intensity continuous answering (reduce exam anxiety).
Strict adherence to no-calculator rules and effective use of simulation systems maximizes exam performance.