Highgrove Education

TMUA Preparation

This course follows on the Autumn and Spring term Sixth Form Maths Enrichment electives, and continues to prepare students to prepare students for topics relevant to those students looking to prepare for the TMUA university entrance exam. This course starts in the second half of the summer term of year 12, finishing at the end of the first half of the summer term. Students should note that these lessons will involve significant preparation outside of the live lessons, with students expected to work on problems to be discussed in the next session to make the most of the following session; in this way, the sessions are similar to the Oxbridge tutorial system.

Private Tuition

Key Information



Access Course Enrolment:
  • Enrolment in our pre-GCSE or pre-A level access course.
  • Access to our self-study materials and platform, live class lessons, and individual teacher support in Office Hours.
  • Weekly teacher-marked homework.
  • Half termly reports.
  • Support from our SENDCo for pupils with special educational needs or disabilities, including assessment for access arrangement entitlement.
  • Support with English for pupils whose first language is not English.
  • A Highgrove Education Office365 account, including Teams, SharePoint and a school email
TeacherMr Harry Williams, Head of Mathematics
Course Length10 weeks 
Live LessonsOne 45-minute lesson per week
HomeworkApproximately two hours a week
Entry RequirementsPupils must be taking Mathematics at AS, anticipating that they will continue to study the full A-level in Maths, and have attended the previous Sixth Form Maths Enrichment sessions in both Autumn and Spring terms. Studying Further Maths is advantageous but not essential for the TMUA. Students must be anticipating that they will be sitting the TMUA exams in mid-October of their year 13 year.

Course Syllabus

Lesson 1Mathematical statements, truth tables; Necessary and sufficient; if, then statements
Lesson 2Further mathematical logic: converse, contrapositive, there exists, for all
Lesson 3Proof techniques: direct proof, by contradiction, by the contrapositive, counterexamples
Lesson 4Common errors in proofs; more on the negation; summer preparation planning
Lesson 5TMUA past paper practice
Lesson 6TMUA past paper practice
Lesson 7TMUA past paper practice
Lesson 8TMUA past paper practice
Lesson 9Timed TMUA past paper practice
Lesson 10Timed TMUA past paper practice

Teacher Profile

Mr Williams has taught Maths and Further Maths for over ten years prior to joining Highgrove Education, most recently at Harrow School Online, where in 2023 his pupils achieved 90% A*-A in Maths and 100% A*-A in Further Maths. Before this he taught at Abingdon School where he was responsible for their UKMT challenges and Sixth Form Maths Enrichment. Mr Williams graduated with a First class Masters degree in Mathematics from the University of Sussex in 2013, then went on to complete his PGCE with the University of Reading. He is a keen advocate for the power of technology to enhance and indeed transform pupils’ enjoyment and understanding of Mathematics.