Specialist Oxbridge mathematics tuition

Develop the skill and judgement to excel in STEP and at interview.

Rigorous, highly personalised preparation for TMUA, STEP and Oxford or Cambridge mathematics interviews.

1,000+hours of one-to-one teaching
9+ yearsteaching mathematics
£200per 60-minute session

Most recent students

Most recent STEP studentachieved S grades in both papers
Two most recent interviewsboth candidates received Cambridge offers
1,000+ hoursof individual teaching experience

Tuition

Preparation for the exams that demand deeper mathematical understanding.

Lessons are built around diagnosis, guided problem solving and careful feedback—not memorised tricks.

01

Oxford admissions

TMUA Oxford’s current admissions test

Oxford now uses the TMUA for Mathematics and related courses. Preparation develops fluency, precision and the ability to recognise structure under time pressure, with selected MAT problems still used where they sharpen deeper reasoning.

  • Diagnostic assessment and individual plan
  • Conceptual gaps exposed and repaired
  • Timed technique and full-paper review
03

Oxford & Cambridge

Interview practice

Mock interviews recreate the rhythm of an Oxbridge tutorial: thinking aloud, responding to prompts, testing conjectures and recovering constructively when the first approach fails.

  • Authentic unseen problems
  • Pressure-tested mathematical dialogue
  • Specific feedback and follow-up priorities

Most recent students

Exceptional results, built through individual preparation.

Admissions success depends on far more than just mathematical ability. Good communication, confidence and the ability to thrive under pressure are particularly important. I tailor preparation to each student’s needs, helping them communicate their reasoning clearly and perform with confidence under pressure.

STEP S grades in both papers

My most recent STEP student achieved the highest grade classification in both STEP 2 and STEP 3.

Interviews Offers for both recent candidates

My two most recent Cambridge interview candidates both went on to receive offers.

Meet your tutor

Get a sense of your tutor and the teaching style.

01 · Introduction

Who I am and how I teach

A short introduction to my academic background, approach and what students can expect from lessons.

02 · Sample lesson

A past-paper problem, taught properly

A worked admissions problem showing how I question, prompt and build a rigorous solution with a student.

About Kai

Serious mathematics, taught with clarity.

Kai Hall tutoring a student at a table in front of a chalkboard

I studied Physics with Theoretical Physics at Imperial College London, graduating with First Class Honours, before completing Part III of the Mathematical Tripos at Cambridge with Distinction.

I grew up by the sea in North Devon, on England’s southwest coast. Over the past six years I’ve lived in London and Cambridge, and I’ve spent time travelling through the Balkans, Australia, Southeast Asia, China and Japan.

My academic interests lie where geometry and theoretical physics meet: gauge theory, differential geometry, quantum field theory, string theory and twistor methods. I was subsequently offered a Cambridge PhD place in mathematical aspects of M-theory and quantum field theory.

I have taught mathematics and physics one-to-one since 2017. My teaching interests centre on proof, inventive problem solving and helping ambitious students make the transition from performing familiar techniques to thinking independently about unfamiliar mathematics.

CambridgeMASt MathematicsPart III · Distinction
ImperialMSci Theoretical PhysicsFirst Class

Olympiad tuition: I also have extensive experience teaching British Mathematical Olympiad and British Physics Olympiad problems, and welcome enquiries from students seeking focused Olympiad preparation.

Academic work

Research informs the way I teach.

Advanced mathematics cultivates patience, an eye for underlying structure and the confidence to think abstractly. Those habits shape my approach to admissions tuition.

Book online

Choose a time for your lesson.

Start with a free trial, or book full one-to-one tuition. The calendars show available times.

Start here

Free trial lesson

Free / 30 minutes

Meet Kai and work through some mathematics together before deciding whether to continue.

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Questions before booking?

Ask me anything.

If you’re unsure which preparation would suit you, send a question. Otherwise you can choose an available time and book directly above.

Book a free trial instead Prefer to speak?+44 7786 998806

Send your question here and I’ll reply by email.