Year-Round STEM & Engineering Mentoring
Lucas Rey · Oxford DPhil · Cambridge MRes · Aerothermal Researcher
Bespoke Mathematics, Physics, and Engineering academic mentoring for ambitious international students aged 13 to 18. Combining rigorous first-principles problem solving, supercurricular technical projects, and structured preparation for Oxford, Cambridge, Imperial, and competitive UK university admissions.
Not sure where to start? 7 places to go
Start with your question
Why visitors arrive: You need an engineering, physics, or maths tutor - or help with Oxford admissions or ESAT/PAT/TMUA - and want to see real qualifications first.
Your question: What does Lucas Rey teach, and what on this site backs that up?
You may also be asking
- Do you tutor physics and mathematics as well as engineering?
- Can you help with Oxford or Cambridge engineering interviews?
- Are there free curriculum resources before booking?
- How do ESAT, PAT, and TMUA preparation work here?
- How do I enquire about sessions?
Where to go next
- Sit a sample module against the clock: four sample papers, five worked questions in every module, with a timed test at the top of each page
- Fluid mechanics curriculum: Open modules and problem sets
- Oxbridge lexicon: Admissions terminology reference
- Calculators: Quantitative tools used in teaching
- Technical notes: Derivations and methods for revision
- Engineering hub: Full learning platform and tools
- Teaching enquiry: Contact form with teaching intent
- Who: Lucas Rey, aerothermal engineer, Oxford DPhil candidate (Rolls-Royce sponsored), Cambridge MRes (Whittle Laboratory), ESAT tutor with Oxbridge Applications · ORCID · About Lucas
- Mentorship Model: Year-round structured programmes with live 1:1 sessions, weekly tailored problem sets, personal error logs, supercurricular project supervision, and monthly written parent reports.
- Admissions Specialisms: ESAT (Maths 1, Physics, Advanced Maths), TMUA, STEP, and Oxford/Cambridge engineering interview problem-solving, including the retired PAT archive as interview practice.
- Partner Pathways: Dedicated frameworks for Educational Consultants and International Schools.
- Open Resources: STEM Roadmap, ESAT Solutions Hub, Fluid Mechanics Curriculum, Engineering Calculators, and Oxbridge Lexicon.
For Parents & Students: How We Work Together
Curricula and age ranges, the weekly cadence, and parent reporting
Applying for Engineering, Physics, or Mathematics at Oxford, Cambridge, Imperial, or top global universities requires far more than passive exam cramming. My mentoring provides a structured, year-round framework:
Curricula & Age Ranges
Specialised for students aged 13 to 18 across International Baccalaureate (IB HL Math AA & Physics), A-Levels (Maths, Further Maths, Physics), AP Physics C, and university undergraduate STEM.
The Weekly Cadence
Weekly live 1:1 sessions $\rightarrow$ bespoke extension problem set $\rightarrow$ error-log submission $\rightarrow$ feedback loop. Students build rigorous independent working habits.
Parent Reporting
Parents receive monthly written progress summaries outlining topics covered, velocity metrics, error-log elimination, and next milestone focus areas.
Who We Are
Checked before it goes out, both universities deliberately, and one person accountable for it
The open resources on this site are written and checked by us: doctoral researchers and recent graduates in engineering, physics and mathematics at Oxford and Cambridge, who teach the subjects. I am Lucas Rey, an aerothermal engineer, Oxford DPhil candidate and Cambridge MRes, and I teach these tests. Nothing here is bought in or syndicated, and no question is published that has not been read.
Checked Before It Goes Out
Every paper passes a build gate that refuses it if a question is malformed, if two questions repeat a shape, if the credited answers bunch on one letter, or if the timing falls outside the published budget. What a machine cannot judge, whether a solution actually explains anything, is read. Questions that do not survive that pass do not go out.
Both Universities, Deliberately
The ESAT is now the test at Cambridge, Imperial and Oxford alike: Oxford retired the PAT after the October 2025 sitting and uses the ESAT for Physics, Physics and Philosophy and Engineering Science. So a candidate applying to two of those universities is preparing one paper rather than two, and the PAT archive earns its place as interview practice instead.
One Named Person
Mentoring itself is delivered one to one by a named researcher who stays with the student throughout. I do not operate a pool of interchangeable tutors, and I do not subcontract.
Programmes are led by Lucas Rey, aerothermal engineer, Oxford DPhil candidate and Cambridge MRes. Schools and parents are welcome to ask who specifically would be working with a student before committing to anything.
What We Have Published, in Numbers
10 five-question practice sets, 4 full mock papers, the shortcut library, and what is missing
The open resources are free, and their size is the easiest thing to check about us before you get in touch. Every figure below is countable from the pages themselves:
10 five-question practice sets
50 Questions
Two sets in each of the five ESAT subjects, written to the depth of a question in a real paper. Every question carries a full worked solution, and each set hub names the specification sub-topic every one of its questions was written against.
4 full mock papers
100 Questions
Five sample questions from each of the twenty subject modules, every one worked in full, with a timed test set to the real pace. A full module runs to 27 questions and is written for one school.
Shortcut library
105 Methods
Each shortcut is the fastest correct route through one kind of ESAT question, named, explained and linked to the questions that drill it.
Every question published here is complete, and nothing carries a gap marker. Where a question in the wider library could not be reconstructed to the standard the rest is held to, it is left unpublished rather than filled in with a plausible-sounding guess. How every solution is checked before it is published is set out in our Quality Assurance standards.
The Mentoring Philosophy: First-Principles & Independence
First-principles rigour, personal error logging, and supercurricular context
Standard tutoring often relies on memorised templates and passive question drilling. My mentorship builds independent mathematical intuition, deep physical understanding, and genuine scientific curiosity:
First-Principles Rigour
Deriving equations and understanding why principles hold. Students learn dimensional analysis, scaling laws, and Fermi estimation, the core thinking tested in university interviews.
Personal Error Logging
Every student maintains a structured error journal classifying mistakes into conceptual gaps, speed bottlenecks, or calculation slips, transforming weaknesses into systematic strengths.
Supercurricular Context
Connecting textbook mathematics and physics to real-world engineering research (turbomachinery, aerodynamics, energy systems), turning students into passionate scholars.
Structured Programmes & Offerings
STEM Foundations, Engineering Scholar, and the Admissions & ESAT Accelerator
Tailored to the student's developmental stage and academic objectives:
Ages 13 to 15 · Middle / Early High School
STEM Foundations
Building exceptional mathematical agility, scientific curiosity, and independent study habits before senior exam pressures.
- 4 live 1:1 mentoring sessions monthly (60 min)
- Weekly bespoke problem sets & extension challenges
- Foundational mechanics and algebra mastery
- Monthly written progress summary for parents
Ages 15 to 18 · IB / A-Level / Pre-University
Engineering Scholar
Comprehensive year-round academic development, advanced thermofluids/mechanics, and supercurricular project supervision.
- 4 or 8 live 1:1 mentoring sessions monthly
- Independent technical project mentorship (CFD/CAD/Derivations)
- Advanced problem-solving & dimensional analysis
- Monthly comprehensive parent report & roadmap review
Application Year · Year 13 / IB2
Admissions & ESAT Accelerator
High-intensity preparation for ESAT, TMUA, personal statements, and Oxbridge/Imperial technical interviews.
- Initial 90-min comprehensive diagnostic & benchmark
- Timed exam-strategy, speed training, and error logs
- Full mock exams under realistic timed conditions
- Oxford & Cambridge interview problem-solving clinics
How Mentorship Works: The 4-Step Intake
The 20-min assessment call, the paid academic diagnostic, structured mentoring, and monthly progress reports
A structured, high-touch process designed to ensure a mutual fit and clear academic progression:
Step 1
20-Min Assessment Call
Free initial conversation with parents and student to evaluate curriculum, academic goals, target universities, and current challenges.
Step 2
Paid Academic Diagnostic
A 75 to 90 minute intensive diagnostic evaluating mathematical reasoning, physics fluency, and timed problem-solving velocity, followed by a written roadmap.
Step 3
Structured Mentoring
Weekly live 1:1 sessions, tailored homework, personal error-log tracking, technical project development, and admissions coaching.
Step 4
Monthly Progress Reports
Written reports for parents and educational consultants tracking concept mastery, mock scores, and upcoming milestones.
The International Student's Engineering Roadmap (Ages 13 to 18)
Ages 13 to 14, ages 15 to 16, ages 16 to 17, and the application year
What ambitious STEM applicants should focus on each year to build a world-class application profile:
Ages 13 to 14 (Years 8 to 9 / Grade 8): Mathematical Curiosity & Foundations
Focus on building deep algebraic fluency, geometry, and physical intuition. Participate in introductory mathematics competitions (UKMT Junior/Intermediate). Read popular science and foundational engineering books.
Ages 15 to 16 (Years 10 to 11 / GCSE / Pre-IB): Core Mechanics & Supercurricular Exploration
Master introductory calculus, Newtonian mechanics, and electricity. Begin an independent technical project (e.g. building a computational model, fluid simulation, or rocketry project). Read academic articles and explore the Fluid Mechanics Curriculum.
Ages 16 to 17 (Year 12 / IB1): Advanced Problem Solving & Test Preparation
Study non-syllabus problem-solving techniques, dimensional analysis, and senior Physics Olympiad problems. Deepen supercurricular engineering design. Begin structured admissions test preparation using the ESAT Solutions Hub, or the TMUA, MAT and STEP pages. The Oxford PAT was retired after October 2025, so its archive is interview practice rather than test preparation. Finalise university and college choices.
Application Year (Year 13 / IB2): Execution, Timed Mocks & Technical Interviews
Complete UCAS application with a rigorously academic personal statement. Sit the ESAT / admissions test in Autumn. Conduct intensive mock technical interviews practicing estimation, thinking aloud under pressure, and tackling unfamiliar engineering scenarios.
Read the Full Year-by-Year STEM Preparation Roadmap & Reading List →
Partnerships: Consultants & Schools
For educational consultants, and for international schools
Dedicated collaboration tracks for education professionals:
For Educational Consultants
Technical STEM & Engineering partnership. Subcontracted mentoring, white-label delivery, and transparent written progress reports for your client families.
For International Schools
Enrichment workshops, "Thinking Like an Engineer" masterclasses, parent webinars, and ESAT admissions test briefings for STEM departments. Separately, I write full ESAT mock paper packs for sixth forms: a free sample pack is published, and unseen packs are written for a single school and issued to nobody else. The free question sets on this site are for individual candidates rather than for class use, so a cohort takes a pack.
Frequently Asked Questions
Six questions: subjects and levels, programme structure, the diagnostic session, ESAT and TMUA preparation, time zones, and getting started
What subjects and levels does Lucas Rey tutor?
I specialise in Mathematics, Physics, Mechanics, and Engineering Admissions for international students aged 13 to 18 (IGCSE, A-Level, IB HL, AP), as well as undergraduate STEM modules (Fluid Mechanics, Thermofluids, Engineering Mathematics).
How are the monthly programmes structured?
Programmes are delivered as structured monthly retainers (e.g. STEM Foundations or Engineering Scholar). They include live 1:1 video sessions, personalised between-session problem sets, personal error logging, project supervision, and monthly written parent reports.
What happens in the Initial Diagnostic Session?
Following a free 20-minute qualification call, I conduct a 75 to 90 minute diagnostic evaluating the student's mathematical agility, physical intuition, question selection strategy, and problem-solving speed. Parents receive a detailed written report and customised study roadmap.
How do you prepare students for the ESAT and the TMUA?
Preparation focuses on speed, first-principles reasoning and error analysis rather than superficial drills. Neither test deducts marks for a wrong answer, so the work is pacing, distractor traps and knowing when to guess and move on rather than risk management. All of it is supported by the free ESAT Solutions Hub, and by full mock papers sat under timed conditions. The MAT was retired after 2025 and Oxford now uses the TMUA for its mathematics courses, so preparation for it has moved accordingly.
Do you work with international students across different time zones?
Yes. I work with students across the UK, Europe, the Middle East, and Asia (e.g. UAE, Singapore, Hong Kong). Sessions are scheduled via a dedicated student portal to accommodate school timetables and international time zones.
How do I get started?
Submit a teaching enquiry on the contact page with details of the student's current year, curriculum, and target universities. We will schedule a 20-minute introductory assessment call.
Part of
This page sits within the broader knowledge structure on lucasrey.com:
- Teaching - Engineering-informed teaching, mentoring, and quantitative reasoning.
Connected work
Related content from the same research and engineering work:
- ESAT worked solutions
- For Educational Consultants
- For International Schools
- Fluid mechanics curriculum
- Teaching - Referenced from Engineering
- Teaching hub - Referenced from Problem-solving procedures
- Teaching hub - Referenced from Viscous flow - problems
Engineering knowledge platform
More tools, curriculum, notes, and research from the same body of work:
- Engineering - Central knowledge platform - tools, curriculum, notes, research, and applied engineering work.
- TMUA Preparation - 2 mock papers with worked solutions, split between applying mathematics and reasoning about it, plus a method library and a dated plan.
- MAT Preparation - Mock Section A with worked solutions, for a test that rewards insight over technique.
- PAT Archive (Retired Test) - 6 mock papers of physics and mathematics with worked solutions. Oxford retired the PAT after the October 2025 sitting and now uses the ESAT. Kept as interview practice and ESAT physics.
- STEP Preparation - Four full-length mock papers with written mark schemes, a method library, and a dated preparation plan. STEP 2 and STEP 3, which are the papers currently sat.
In my engineering work
Teaching is informed by the same technical work published and built here:
- Engineering calculators - Interactive tools for thermophysical and measurement problems.
- Publications - Research in aerothermal and fluid engineering.
- Projects - Applied engineering work and case studies.
- Fluid mechanics curriculum - Structured learning paths from first principles.
- Articles - Long-form reference writing (pilot collection).
- Oxbridge lexicon - Terminology reference for admissions contexts.
- ESAT worked solutions - Step-by-step worked solutions and exam preparation guide.
- Engineering hub - Central knowledge platform - tools, curriculum, notes, and research.
- Instrumentation & measurement - Probe calibration and uncertainty workflows from published research.
- Turbomachinery deterioration - Flagship HPT research programme at Oxford Thermofluids.
- Experimental aerothermal measurement - Methods article on traceability, similarity, and facility transfer - links instrumentation, curriculum, and tools.
- CFD-experiment validation - Methods article on closing the loop between RANS simulations and transient aerothermal measurements.
- Engineering notes - Reference material and methods documentation - instrumentation and turbomachinery clusters.
- about - Central knowledge platform - tools, curriculum, notes, and research assets.
- Collaborate - Central knowledge platform - tools, curriculum, notes, and research assets.
Where to go from here
Everything on this site is free to read. These are the things worth doing next.
- Find out where you actually stand - Fifteen questions, twenty minutes, scored instantly, with a worked solution for every one you miss
- Work a practice set at full paper depth - Ten sets of five questions, two in every module, each one worked in full
- See what can actually be checked about this tutor - What is published, counted from the pages themselves, and the credentials behind it
- Enquire about one-to-one preparation - For candidates who want the gap closed rather than mapped. Places are limited and taken by application
Everything linked above is free and stays free. One-to-one places are limited and taken by application, not by the hour.