Highgrove Education

Maths Enrichment & University Access Exams

This course will start you on your journey of mathematical enrichment and introduce you to the topics relevant for a range of mathematics university entrance exams required by some British universities for admission to maths and computer science degrees, such as STEP, MAT and TMUA. It will begin with preparation for the UKMT Senior Maths Challenge held in early October, then introduce you to topics tested in university access examinations. Pupils who complete this programme will have the option to take a dedicated university exam elective preparing for the specific maths examination/s required y their chosen universities. Please 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 following session; in this way, the programme stands as an introduction to the Oxbridge tutorial system.

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 Length20 weeks
Live LessonsOne 45-minute lesson per week
HomeworkApproximately half an hour a week
Entry RequirementsPupils must be taking Maths or Further Maths at AS or A level in year 12, or pass an entry test to check their ability level prior to joining this elective.

Course Syllabus

Autumn 1Preparation for UKMT Senior Maths Challenge;
Autumn 2Series, geometric proofs, trigonometry, probability, roots of equations
Spring 1The compound trigonometry formula; unusual functions; divisibility of expressions; graph sketching & concavity
Spring 2Factorisation, Fibonacci numbers; Sequences; Trigonometric inequalities; modular arithmetic; Curve sketching and fractals 

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 master’s degree in Maths 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 Maths.