Maths Headstart

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Maths Headstart Courses prepare students for the increased abstraction and pace of National 5, Higher and Advanced Higher Mathematics. Each course focuses on core algebraic and calculus-based skills introduced early in the academic year. Headstart Courses aim to teach 30-40% of the upcoming curriculum.

This course builds the core algebraic and numerical foundations required for success at National 5.

  • National 4 core skills
  • Expanding brackets
  • Fractions
  • Compound interest
  • Reverse percentages
  • Pythagoras
  • Volume
  • Indices rules

20 hours | National 4/5

Book National 4/5 Maths Headstart

This course strengthens key algebraic and graphical skills introduced early in the National 5 course.

  • Equations and inequalities
  • Changing the subject of a formula
  • Expanding and factorising
  • Fractions, functions, indices and surds
  • The straight line and statistics

20 hours | National 5

Book National 5 Maths Headstart

This course introduces foundational Higher topics and builds fluency in algebraic manipulation and calculus.

  • Essential National 5 skills
  • The Straight Line
  • Polynomials and Quadratics
  • Functions
  • Differentiation
  • Integration

20 hours | Higher

Book Higher Maths Headstart

This course focuses on the advanced calculus and algebraic reasoning required at Advanced Higher level.

  • Essential Higher skills
  • Differentiation
  • Further Differentiation
  • Partial Dractions
  • Algebraic Long Division
  • Integration and Further Integration

20 hours | Advanced Higher

Book Advanced Higher Maths Headstart

Our Maths Tutors

Maths Headstart courses are delivered by tutors with strong academic backgrounds in Mathematics and related disciplines.
Maths
+1

Gellert Neiszer

Masters Degree
University of Glasgow

Gellert is a final Year Masters Theoretical Physics undergraduate at The University of Glasgow (1st).

Maths

Ben Mitchell

Perfect Exam Score
University of Edinburgh

Ben is a Mathematical Physics undergraduate at The University of Edinburgh (1st).

Maths

Amna Farid

Medicine undergraduate
University of Glasgow

Amna is a 2nd Year Medicine undergraduate at The University of Glasgow (High 1st average).

Maths

Finlay Scheib

1st Class Honours average
University of Strathclyde

Finlay is a final Year Maths undergraduate at The University of Strathclyde (1st).

Maths
+1

Daniel Keane

1st Class Honours average
University of Glasgow

Daniel is a 5th Year Physics with Astrophysics undergraduate at The University of Glasgow (1st).

Maths

Emery-Rose Beggs

Reliable
University of Glasgow

Emery is MA(Soc) with Honours in Economics undergraduate at The University of Glasgow.

Maths
+1

John Watson

Reliable
University of Edinburgh

John is an MA Economics and Mathematics undergraduate at The University of Edinburgh (High 1st average).

Applications of Maths
+1

Grainne Owens

Masters Degree
University of Glasgow

Gráinne is a BSc Marine & Freshwater Biology undergraduate at The University of Glasgow.

Maths

Maria O'Neill

Worked Examples
University of Glasgow

Maria is a final year Maths undergraduate at The University of Glasgow

Maths
+1

Danny Lavery

1st Class Honours average
University of Glasgow

Danny is a final Year Mathematics and Physics undergraduate at The Universty of Glasgow (1st).

Maths
+2

Daniel McKay

Mastery-Based
University of St Andrews

Daniel is an integrated masters MPhys (Hons) Maths and Theoretical Physics undergraduate at The University of St. Andrews (1st).

Maths

Zubair Ahmed

1st Class Honours average
University of Edinburgh

Zubair is a BSc (Hons) Mathematics undergraduate at The University of Edinburgh (1st).

Chemistry
+1

Grace Left

1st Class Honours average
University of Glasgow

Grace is a 2nd Year Materials Chemistry undergraduate at The University of Glasgow (1st).

Maths

Abdullah Ehsan

Masters Degree
Imperial College London

Abdullah is a Masters Maths graduate from Imperial College London. He cuurently works as a Design Engineer with Cirrus Logic in Edinburgh.

Maths

Ubaida Freikh

Perfect Exam Score
University of Edinburgh

Ubaida is a Mechanical Engineering undergraduate at The University of Edinburgh (1st).

Computing Science
+1

Lachlan Horsfield

Dux Award
University of St Andrews

Lachlan is a MSc Computer Science and Mathematics undergraduate at The Universit of St Andrews (1st average).

Chemistry
+1

Eilish Harkins

Medicine undergraduate
University of Edinburgh

Eilish is a Medicine undergraduate at The University of Edinburgh.

Maths

Katie Parker

Weak-Area Diagnosis
University of Edinburgh

Katie is a 2nd Year Physics undergraduate at The University of Edinburgh (1st average).

Maths

Heidi O'Keeffe

1st Class Honours average
University of Glasgow

Heidi is an Economics undergraduate at The University of Glasgow (1st).

Engineering Science
+1

Mya Wickham

University of Glasgow

Mya is a 2nd Year MEng Aeronautical Engineering undergraduate at The University of Glasgow (1st). Grades and AchievementsMya achieved AAAAA…

Maths
+1

Karan Shah

1st Class Honours average
University of Edinburgh

Karan is a Mathematics undergraduate at The University of Edinburgh (1st average).

Maths

Neema Fanaie

1st Class Honours average
University of Edinburgh

3rd-year Electrical and Mechanical Engineering undergraduate at the University of Edinburgh (High 1st average).

Maths

Edie Wight

Step-by-Step
University of Glasgow

Edie is a Mechanical Engineering undergraduate at The University of Glasgow.

Maths

Tom Baker

Problem Breakdown
University of Oxford

Tom has completed an MMath at The University of Oxford (2.1) and has a PhD in Mathematics from Imperial College London.

Maths

Francesca Lang

Perfect Exam Score
University of Edinburgh

Priya is a 2nd Year Medicine undergraduate at The University of Edinburgh.

Maths

Logan Train

Medicine undergraduate
University of Glasgow

Logan is a Medicine undergraduate at The University of Glasgow.

Maths

Kate Helen Robinson

1st Class Honours average
University of Edinburgh

Kate is an MA Mathematics with German Undergraduate at The University of Edinburgh (High 1st average).

Maths

Grace Sharp

1st Class Honours average
University of Edinburgh

Grace is a Mathematics undergraduate at The University of Edinburgh (1st).

Maths

Matthew Cumming

Step-by-Step
University of Dundee

Rishab is a Medicine undergraduate at The University of Dundee.

Maths
+2

Alex Denholm

Medicine undergraduate
University of Cambridge

Alex is a Medicine graduate from The University of Cambridge.

Applications of Maths
+1

Leyla Pizzolato

Top 5% of Cohort
University of Edinburgh

Leyla is an MA Politics with Quantitative Methods Undergraduate at The University of Edinburgh.

Maths

Annabelle Johnstone

University Admissions Support
University of Edinburgh

Annabelle is a 3rd Year Electrical & Mechanical Engineering undergraduate at The University of Edinburgh (2.1).

Engineering Science
+1

Megan McLeod

Conceptual Understanding
University of Glasgow

Megan is an MEng Mechanical Engineering with Aeronautics undergraduate at The University of Glasgow.

Applications of Maths
+1

Ben Shenken

Clear Explanations
University of Glasgow

Ben is a 3rd-year Accountancy and Finance undergraduate at the University of Glasgow (2.1).

Maths

Gregor Miller

Conceptual Understanding
University of St Andrews

Gregor is an Economics undergraduate at The University of St Andrews.

Maths

Naomi Blue

Conceptual Understanding
University of Glasgow

Naomi is a final year Microbiology undergraduate at The University of Glasgow.

Maths
+1

Katie Heggie

Top 5% of Cohort
University of Edinburgh

Katie is an integrated Masters Physics undergraduate at The University of Edinburgh

Accounting
+1

Lennon Brisbane

Masters Degree
University of Glasgow

Lennon is a Physics with Astrophysics undergraduate at The University of Glasgow (1st Average).

Maths
+2

Ben Lennox

1st Class Honours average
University of Edinburgh

Ben is a Masters Theoretical Physics graduate from UofE (1st).

Maths
+1

Gabriel D'Hulst

Masters Degree
University of Edinburgh

Gabriel is a final Year Masters Maths undergraduate at The University of Edinburgh (1st).

Maths

Finlay Webb

1st Class Honours average
University of Edinburgh

Finlay is a 3rd Year Mathematics undergraduate at The University of Edinburgh (1st average).

Applications of Maths
+1

Ashish Nath

1st Class Honours average
University of Edinburgh

Ashish is an MInf Informatics undergraduate at The University of Edinburgh (1st).

Maths

Lena Lewis

1st Class Honours average
University of Edinburgh

Lena is a Mathematics undergraduate at The University of Edinburgh (High 1st average).

Maths

Andrew King

Masters Degree
University of Glasgow

Andrew is a Medicine undergraudate at The University of Glasgow.

Maths

Alice Stevenson

Step-by-Step
University of Edinburgh

Alice is a Physics undergraduate at The University of Edinburgh

Maths

Rob Lawless

Medicine undergraduate
University of Glasgow

Rob is a 4th Year Medicine undergraduate at The University of Glasgow (1st average).

Maths

Eirini Lymperi

Medicine undergraduate
University of Edinburgh

Irene is a Medicine undergraduate at The University of Edinburgh (1st average).

Maths
+1

Kayleigh Innes

Friendly
University of Edinburgh

Kayleigh is a 4th Year MPhys Astrophysics Undergdauate at The University of Edinburgh

Applications of Maths
+1

Poppy Voce

Masters Degree
University of Glasgow

Poppy is a final year Zoology undergraduate at The University of Glasgow (1st average).

Maths
+1

Nadia Ditta

1st Class Honours average
University of Edinburgh

Nadia is a Mechanical Engineering graduate from The University of Edinburgh (1st). Nadia is a Maths and Physics tutor.

Maths

Rohan Janaki

1st Class Honours average
University of Edinburgh

Rohan is a Mathematics and Computer Science undergraduate at The University of Edinburgh.

Maths
+1

Anna Hendry

1st Class Honours average
University of Glasgow

Anna is a Physics undergraduate at The University of Glasgow (1st).

Maths

Gemma Taylor

Clear Explanations
University of Glasgow

Gemma is a final year Maths and Statistics undergraduate at The University of Glasgow (1st).

Maths

Parsa Sharifi

Very Organised
University of Edinburgh

Parsa is a Mechanical Engineering undergraduate at The University of Edinburgh.

Maths

Phoebe Burke

1st Class Honours average
University of Edinburgh

Phoebe is an MMath Mathematics undergraduate at The University of Edinburgh (1st average).

Applications of Maths
+1

Rishab Anthuvan

Medicine undergraduate
University of Edinburgh

Rishab is a Medicine undergraduate at The University of Edinburgh.

Maths

Gianluca Iannetta

Problem Solving
University of Dundee

Luca is a Maths and Physics undergraduate at The University of Dundee.

Maths

Shaumya Kularajan

Masters Degree
University of Glasgow

Shaumya is a 5th Year Medicine undergraduate at The University of Glasgow

Maths

Borys Staruzyk

Top 5% of Cohort
University of Edinburgh

Boris is an Applied Mathematics undergraduate at The University of Edinburgh (High 1st average).

Maths

Ben Meiklejohn

Exam Technique
University of Edinburgh

Ben is a Computer Science with Mathematics undergraduate at The University of Edinburgh.

Engineering Science
+1

Elise Warde

Problem Solving
University of Glasgow

Elise is a Mechanical Engineering Undergraduate at The University of Glasgow (1st).

Maths
+1

Cameron Hainey

Masters Degree
University of Edinburgh

Cameron is a 3rd Year MPhys Astrophysics undergraduate at The University of Edinburgh (1st).

Maths

Sophia Cauter

1st Class Honours average
University of Edinburgh

Sophia is a 2nd Year Mathematics undergraduate at The University of Edinburgh (High 1st average).

Maths

Hamish Hazlewood

Heriot-Watt University

Hamish is a 3rd year Maths undergraduate at Heriot-Watt University (1st average).

Maths

Maahir Patel

Masters Degree
University of Glasgow

Maahir is an M.Eng. Aeronautical Engineering undergraduate at The University of Glasgow.

Maths

Bethany Cornthwaite

Problem Solving
University of Edinburgh

Bethany is a Maths undergraduate at The University of Edinburgh.

Maths

Beatriz Zahanaicu

Perfect Exam Score
University of Glasgow

Beatriz is a Computing Science undergraduate at The University of Glasgow.

Maths
+1

Abdus Saboor

1st Class Honours average
University of Edinburgh

Abdus is a MSc Physics graduate from The University of Edinburgh (1st).

Maths

Abigail Mir

1st Class Honours average
University of Dundee

Abigail is a Mathematics and Astrophysics graduate at The University of Dundee (1st average).

Maths

Arun Hamilton

Step-by-Step
University of Glasgow

Arun is a Maths and History joint honours undergraduate at The University of Glasgow (2.1).

Maths
+1

Daire Byrne

Dux Award
University of Edinburgh

Dáire is a 5th Year Masters Maths graduate at The University of Edinburgh (1st). He is currently undertaking his PhD at The Universit of Dublin.

Maths

Isabel Aitman-Bevan

Perfect Exam Score
University of Edinburgh

Zoe is a 3rd Year Geography undergraduate at The University of Edinburgh (2.1).

Maths

Sarah Rose Jamieson

In teacher training / wants to be a teacher
University of Glasgow

Sarah is a Mathematics undergraduate at The University of Edinburgh

Maths

Rowan Gilchrist

Past-Paper Focused
University of Edinburgh

Rowan is a Mathematics Science undergraduate at The University of Edinburgh.

Maths

Katie Tweedie

1st Class Honours average
University of Glasgow

Katie is a final year MA Psychology undergraduate at The University of Glasgow (1st).

Applications of Maths
+1

Saioa Galvin

University of Edinburgh

Saioa is a 5th Year MMath Mathematics at the University of Edinburgh (1st), with Direct Entry into 2nd Year.

Maths

Kiera Hill

Problem Solving
University of Glasgow

Kiera is an Aeronautical Engineering undergraduate at The University of Glasgow.

Chemistry
+1

Lily Hinde

Masters Degree
University of Glasgow

Lily is a Chemistry and Maths MSci undergraduate at The University of Glasgow (1st average).

Maths

Rachael Foster

Top 5% of Cohort
University of Glasgow

Rachael is a final year Maths and Psychology undergraduate at The University of Glasgow (High 1st average).

Applications of Maths
+1

Leo Reid

In teacher training / wants to be a teacher
University of Edinburgh

Leo is a BSc Astrophysics undergraduate at The University of Edinburgh.

Applications of Maths
+1

Hugh Graham

1st Class Honours average
University of Edinburgh

Hugh is an Applied Mathematics undergraduate at The University of Edinburgh (1st).

Maths

Aishee Das

1st Class Honours average
University of Edinburgh

Aishee is a final Year Computer Science with Maths undergraduate at The University of Edinburgh (1st).

Accounting
+1

Lucy Wright

In teacher training / wants to be a teacher
University of Glasgow

Lucy is a Maths undergraduate from The University of Glasgow (2.1). She is currently undertaking her PGDE.

Build Confidence

Students begin the academic year familiar with key topics and expectations.

Reduce Early-Year Pressure

Strong foundations reduce stress during the first term and prevent early gaps forming.

Structured Content

Each course focuses on the most important transition topics between levels.

Personalised Delivery

All courses are delivered 1:1 and tailored to the individual student.

Details and Pricing

How the Course Works

  • 20 hours of 1:1 teaching
  • Two 2-hour lessons per week
  • Optional short break midway for holidays
  • Final assessment and feedback session
  • Typically delivered over 4-6 weeks
  • Delivered 1-1 online

Course Fees

  • National 4/5 Headstart: £580
  • Higher Headstart: £640
  • Advanced Higher Headstart: £680

£80 non-refundable deposit required to secure a place. Remaining balance due after first 2-hour lesson. Summer dates fill quickly, so early booking is recommended.

Find a Maths Tutor

Complete the short form below and we’ll confirm availability and send full course details.

 

Head start programme was excellent for my son. We did two topics – Chemistry and Physics. Gave my son a flying start and he got A’s in his…

Graeme Hendry
National 5 Chemistry & Physics

I found Caledonia Tutors as my son required additional help with school. We started with the maths Headstart course last summer and it was excellent. …

A.C.S
Higher Maths

Logan provided a really great experience on the National 5 Chemistry Headstart course. My S3 had slipped back from getting As to Cs but is now back on…

Renee S
National 5 Chemistry

We have been using Caledonian Tutors for a few years now and they are always top quality. My daughter also did one of the headstart courses for Higher…

Donald MacAngus
Higher Biology

The Headstart Course has helped give me confidence with maths and Daire has been a really helpful tutor. He covers the material well, making it easy t…

Karen Skinner
Advanced Higher Maths

My daughter was lacking confidence in maths, so took the Headstart course with Hannah last summer. Covering problem areas in Nat 5 gave Megan a solid …

Jane D
Higher Maths

My son had Georgia over the summer as a tutor and he really enjoyed the sessions. We decided to get him some tutoring because he got 3/30 in one of …

Nicola Charles
National 5 English
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How Tutors Are Selected

Applications are reviewed carefully, and only a proportion of applicants are invited to interview.

How Tutors Are Selected

📄 Application

Applicants submit a CV, cover letter, academic history, and tutoring experience.

🎤 Interview

Shortlisted applicants attend an interview assessing subject knowledge and communication skills.

🎓 Qualification Checks

Applicants provide evidence of exam results and university transcripts.

🛡 Safeguarding Checks

All tutors hold PVG certification and complete safeguarding training and assessment.

📊 Ongoing Review

Feedback from families is reviewed and tutors must maintain professional standards.

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Reviews

Caledonia Tutors

Customer Reviews

Chetana B Misra 18th August 2026

TrustPilot
My son has been associated with them since S4. He has been coached by excellent qualified tutors and their efforts reflects in the scores he has achieved. Extremely thankful to Aidan and his team of tutors for supporting my son's learning journey.

Edward Creaney 16th August 2026

Google Reviews
Very good experience with Caledonian Tutors, Anna was a great support and guide for our son's Advanced Higher Maths this year, coming out with an A pass! The service including setting up and invoicing is very well managed.

Ashley Candy 16th August 2026

TrustPilot
My daughter was crashing Nat 5 chemistry and had sessions every week with Aminah. She was brilliant. Put her at ease with the first meeting and was very thorough and really made her feel confident going into the exam. She got an A and couldn’t have done it without her.

Shona Mathers 13th August 2026

TrustPilot
My son failed his English prelim so we decided to get him a tutor. He worked with Skye online on a weekly basis from Jan-April (before his diagnosis of Dyslexia). Delighted that my son got a B in his English Nat 5! Thanks to Skye for all her support. 🙏🏽 P.S. I would have scored 5/5 if F2F was available which was my son's preference.

LMR 11th August 2026

TrustPilot
My daughter had excellent tutoring for Advanced Higher Chemistry through Caledonia Tutors. Tutor Jessica was knowledgeable, well-organised, flexible and very friendly and encouraging. We couldn't have asked for anyone better. The results came out last week and my daughter got an A - she is delighted. Thank you Jessica!

Lucy 10th August 2026

TrustPilot
Very well organised. Good communication. Excellent tutoring. Would absolutely recommend!!!

Mila Pavelka 9th August 2026

Google Reviews
Juliet Bigley helped my daughter get an A in Higher Biology. Juliet was a delightful tutor from start to finish. Always happy to explain and get into details. We would highly recommend her.

Mira P 7th August 2026

Google Reviews
Absolutely recommend. Our son did prelims with C grade (English is his second language), we arranged lessons twice a week, with wonderful tutor Michael and three months later got B for the Nat5. Arranging lessons also was very fast, easy process, very welcoming team. Thanks a lot.

Laura Rodgers 6th August 2026

Google Reviews
Exceptional support for Higher Spanish! We are so pleased with the tutoring our daughter received from Elsie for her Higher Spanish exam. Elsie is not only incredibly knowledgeable, but she was also brilliant at adapting her teaching to suit my daughter’s specific learning style. She made every session engaging and enjoyable, which really helped build my daughter's confidence. Beyond the academics, Elsie was incredibly caring; she messaged after the exam to see how it went and checked in again on results day. She was always reliable, and nothing was ever too much trouble. We also had a fantastic experience with Caledonian Tutors as an agency. They are reliable, responsive, transparent, and a real pleasure to deal with. We are delighted with the grade our daughter achieved, and we will definitely be using them again. Highly recommended!

Chika Ugwuanyi 6th August 2026

Google Reviews
Excellent I would recommend. Cameron took my daughter from C in Maths (Prelim) to A in Maths final exams(Highers).
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