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
+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
+1

Karan Shah

1st Class Honours average
University of Edinburgh

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

Maths

Emery-Rose Beggs

Reliable
University of Glasgow

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

Maths

Ben Mitchell

Perfect Exam Score
University of Edinburgh

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

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).

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).

Maths

Amna Farid

Medicine undergraduate
University of Glasgow

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

Maths

Maria O'Neill

Worked Examples
University of Glasgow

Maria is a final year Maths 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).

Maths

Heidi O'Keeffe

1st Class Honours average
University of Glasgow

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

Maths

Katie Parker

Weak-Area Diagnosis
University of Edinburgh

Katie is a 2nd Year Physics undergraduate at The University of Edinburgh (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

Finlay Scheib

1st Class Honours average
University of Strathclyde

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

Chemistry
+1

Eilish Harkins

Medicine undergraduate
University of Edinburgh

Eilish is a Medicine undergraduate at The University of Edinburgh.

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).

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

Zubair Ahmed

1st Class Honours average
University of Edinburgh

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

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

Ubaida Freikh

Perfect Exam Score
University of Edinburgh

Ubaida is a Mechanical Engineering undergraduate at The University of Edinburgh (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

Logan Train

Medicine undergraduate
University of Glasgow

Logan is a Medicine undergraduate at The University of Glasgow.

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

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

Borys Staruzyk

Top 5% of Cohort
University of Edinburgh

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

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
+1

Kayleigh Innes

Friendly
University of Edinburgh

Kayleigh is a 4th Year MPhys Astrophysics Undergdauate 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).

Maths

Eirini Lymperi

Medicine undergraduate
University of Edinburgh

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

Maths

Bethany Cornthwaite

Problem Solving
University of Edinburgh

Bethany is a Maths undergraduate at The University of Edinburgh.

Maths

Alice Stevenson

Step-by-Step
University of Edinburgh

Alice is a Physics undergraduate at The University of Edinburgh

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

Naomi Blue

Conceptual Understanding
University of Glasgow

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

Maths

Rohan Janaki

1st Class Honours average
University of Edinburgh

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

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

Ben Meiklejohn

Exam Technique
University of Edinburgh

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

Engineering Science
+1

Megan McLeod

Conceptual Understanding
University of Glasgow

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

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.

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
+2

Ben Lennox

1st Class Honours average
University of Edinburgh

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

Maths

Parsa Sharifi

Very Organised
University of Edinburgh

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

Maths

Gemma Taylor

Clear Explanations
University of Glasgow

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

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
+1

Katie Heggie

Top 5% of Cohort
University of Edinburgh

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

Maths

Edie Wight

Step-by-Step
University of Glasgow

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

Maths

Beatriz Zahanaicu

Perfect Exam Score
University of Glasgow

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

Maths

Kiera Hill

Problem Solving
University of Glasgow

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

Engineering Science
+1

Elise Warde

Problem Solving
University of Glasgow

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

Maths

Grace Sharp

1st Class Honours average
University of Edinburgh

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

Maths

Phoebe Burke

1st Class Honours average
University of Edinburgh

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

Maths

Gregor Miller

Conceptual Understanding
University of St Andrews

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

Maths
+1

Cameron Hainey

Masters Degree
University of Edinburgh

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

Maths

Francesca Lang

Perfect Exam Score
University of Edinburgh

Priya is a 2nd Year Medicine 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

Andrew King

Masters Degree
University of Glasgow

Andrew is a Medicine undergraudate at The University of Glasgow.

Maths

Shaumya Kularajan

Masters Degree
University of Glasgow

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

Maths

Lena Lewis

1st Class Honours average
University of Edinburgh

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

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.

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).

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

Gianluca Iannetta

Problem Solving
University of Dundee

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

Maths

Finlay Webb

1st Class Honours average
University of Edinburgh

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

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

Leo Reid

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

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

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).

Maths
+2

Alex Denholm

Medicine undergraduate
University of Cambridge

Alex is a Medicine graduate from The University of Cambridge.

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

Isabel Aitman-Bevan

Perfect Exam Score
University of Edinburgh

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

Maths

Rowan Gilchrist

Past-Paper Focused
University of Edinburgh

Rowan is a Mathematics Science 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

Rob Lawless

Medicine undergraduate
University of Glasgow

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

Maths

Matthew Cumming

Step-by-Step
University of Dundee

Rishab is a Medicine undergraduate at The University of Dundee.

Maths
+1

Abdus Saboor

1st Class Honours average
University of Edinburgh

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

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

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).

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

Abigail Mir

1st Class Honours average
University of Dundee

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

Applications of Maths
+1

Rishab Anthuvan

Medicine undergraduate
University of Edinburgh

Rishab is a Medicine undergraduate at The University of Edinburgh.

Maths

Maahir Patel

Masters Degree
University of Glasgow

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

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
Read all reviews
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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

Jas M 18th May 2026

TrustPilot
Karan provided fantastic tutoring to help prepare our son for his Advanced Higher Maths exam. Our son really enjoyed spending time with Karan and benefitted so much from Karan's encouragement and assistance.

Peter Henry 18th May 2026

Google
I have been very satisfied with the service we have received from Caledonia tutors. Both Katie and Seth are exceptionally knowledgeable in their respective fields and have a very engaging manner. My daughter enjoys her sessions and benefits massively from them. Thanks guys!

Nicola Hall 18th May 2026

Google
We’ve been delighted with the quality of the tuition Danny Lavery has provided for our son this year. Danny initially provided Higher maths tuition but was able to split his lessons so that he could provide physics support too. We really appreciated this and were impressed by the way in which Danny was able to explain to our son how to apply the maths theory to some of the problems he was grappling with in physics, in a way which was really engaging. We felt our son was relaxed and well-prepared for both exams, and are hoping this bodes well for his results.

Linda 17th May 2026

TrustPilot
I contacted Caledonian Tutors on the recommendation of a colleague. My daughter needs certain grades in her Advanced Highers for a conditional offer at university. We had Monique for biology & Bob for chemistry. I cannot recommend them highly enough. They were both supportive, encouraging & excellent at explaining the elements that my daughter was struggling with. This did wonders for her confidence & she is fairly certain that she has the grades in her post exam reflections. I will not hesitate to use Caledonian Tutors again in the future for our younger son.

Claire 17th May 2026

TrustPilot
I would happy recommend Caledonia Tutors. Aidan is very responsive and works with a wide range of excellant tutors. The tutors my daughter had most recently, Juliet and Ellie were both very knowledgeable, great communicators and great and guiding her through some tricky topics .

M.Y. 17th May 2026

TrustPilot
Caledonian Tutors is an exceptional experience from start to finish. Prompt and professional replies, suitable questions to clearly understand child's tutoring needs and lines them up with the most suitable tutor. This year we’ve had Ubaida as a maths tutor for both my daughter at Advanced Higher maths level and my son sitting his Nat 5’s. Ubaida has truly been exceptional for both needs. He’s equally professional and friendly and tracks exactly what each student needs to fully understand and work on. He gives updates and feedback and was always available for communication. His explanations of the work has, according to my kids, been very easy to understand and entirely stress free! Both my kids truly enjoyed their sessions with Ubaida on every level. He’s organised and his lessons well planned and coordinated. He’s a fabulous asset to Caledonian Tutors and you’d be lucky to have your child placed with him!

PL 17th May 2026

TrustPilot
Grace was an amazing tutor, really supported my daughter to not only increase her Nat 5 Maths grade but develop confidence in the subject. She was so relaxed before the exam!Grace was excellent at being flexible on the odd occasion we couldn't make the agreed time. Caledonian Tutors are easy to deal with, clear concise information and reply quickly to any emails.

Hamid Abdrabbo 16th May 2026

TrustPilot
We have had a great experience with Caledonia Tutors this year, especially with Katie Heggie for Physics and Harriet Graham for Chemistry. They really helped Lara enjoy the subjects and grow in confidence. Thanks to their support and hard work, Lara achieved 100% in Physics and 85% in Chemistry. We are very grateful and would definitely recommend them.

Jane Ruuskanen 16th May 2026

TrustPilot
My daughter got biology tutoring from Ananya. The whole process was effortless and efficient. Ananya was a fantastic tutor and my daughter certainly benefited hugely from her support. She also gave me regular updates on her progress. I would highly recommend Caledonia Tutors and would not hesitate to use them again.

Vaida Voitechovic 16th May 2026

TrustPilot
My son has been receiving support from Ubaida for around a year now. He moved schools with very little interest in Maths, Physics, or studying in general. Caledonian Tuition helped a lot with his motivation and confidence. He did well with his prelims, and it looks like he felt comfortable and prepared for his Maths exam. Ubaida was excellent throughout — he regularly shared updates on my son’s progress and explained what he needed to work on more by himself. Eventually, they were both able to agree on study dates independently, and my son started taking more responsibility for his own learning. I am very happy with Caledonian Tuition and truly appreciate all the support.
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