Course Description
The course will prepare students for the different style of questions that will appear on the TMUA, with a focus on developing the students’ problem-solving skills and refining their thought-processes when dealing with difficult and unfamiliar mathematical problems. Since the TMUA syllabus includes a section on Mathematical Logic, which is not on the A Level syllabus, we will also cover this in the course.
The course should not be considered to be all the preparation that the students will need. (No short course could legitimately claim to do this, since Mathematics is a subject which requires independent practice - it must be learned by doing rather than watching.) Instead, the course aims to equip the students with the tools that they need to prepare themselves during their own revision.
As such, we will discuss how the students can make the best use of their time when studying, including how to learn from problems that they weren’t able to do, so that when they see a similar problem in the future, they will be able to make progress.
We will spend most of our time in the course working through questions from the main categories of questions that will likely appear in the exam. These questions will consist of some past paper questions, as well as questions which are of the TMUA-style but not from official papers. These questions will either be written specifically for the course, or will be taken from similar papers like MAT and STEP. The students will have weekly homework based on this. The students will then be able to vote for which questions they would like to see worked answers to in the next session.
The TMUA is for students applying to study various Mathematics, Economics and Computer Science courses at Cambridge, Oxford, LSE, Imperial, Durham and Warwick.
Day 1: Introduction to the TMUA
- Structure of the TMUA
- Examples of types of questions on the TMUA
- Problem-solving techniques
- How to learn from hard problems.
Homework set: past paper 1.
Day 2, 3, 4 and 5: Split into two parts
First half:
- Discussion of past TMUA problems, with a focus on problem-solving and the ideal thought-process, including going through selected homework problems, depending on the students’ votes.
- Occasional deep-dives into theory, methods, and tricks for specific types of questions.
Homework set: more past papers, alternating between paper 1 and paper 2.
Second half:
Gradually working through the Mathematical Logic content:
- Negation and Counterexamples
- If and Only If
- Contrapositives and Converses
- Necessary and Sufficient Conditions
- Negating Implication using De Morgan's Laws for And/Or
- Quantifiers
- Negations of Statements with Quantifiers
- Applications of Negating Quantifiers.
Detailed feedback: An end of course report is sent on completion detailing the student’s achievements and areas for further work.
Interested in one-to-one tutoring in the meantime?
View our TMUA Tutors and enquire here.
Greg is a professional tutor with a stellar academic record - he achieved a first class Masters degree at Imperial College London. He has tutored with us full-time since leaving University, amassing over 10,200 hours of lessons and helping over 230 families.
- Maximum Class Size: We teach in groups of no more than 10 with the average number in our classes being 5
- Platform: Lessons will take place on Zoom, which is free and straightforward for students to use. A link will be sent out ahead of the course start date. Take a look at this video to see our online teaching in action.
- Age group: Year 13 in September 2026
- Course Dates: Summer Holidays (please sign up to our newsletter to be kept updated about our course dates)
- FAQs: Please click here.