Covers the whole of the AH Maths course
Created by an experienced maths teacher
Resources used with students in Scottish Secondary Schools
Welcome to advancedhighermaths.co.uk
A sound understanding of the Euclidean Algorithm is essential to ensure exam success.
Please find resources for all other Maths courses HERE.
For students looking for a ‘good’ pass at AH Maths in 2019 you may wish to consider subscribing to the fantastic additional exam focused resources available in the Online Study Pack.
To return to the Home Page please click HERE.
We hope you find this website useful and wish you the very best with your studies.
Please find below:
1. Links and Exam Formulae
|AH Maths - Home Page Link||HERE|
|AH Maths - Whole Course Link||HERE|
|AH Maths - Exam Formula List||HERE|
|Higher Maths - Exam Formulae List||HERE|
|AH Maths - Complete Formula List||HERE|
|SQA Full Course Content and Outline||HERE|
2. Further Number Theory Resources
Thanks to the author(s) for making these available.
|Further Number Theory Guide||HERE|
3. MIA Text Book Questions – Further Number Theory
Recommended questions from the new MIA Text Book are shown below.
Worked solutions to all questions below are available in the Online Study Pack.
|Finding the Greatest Common Divisor (GCD)||Page 318||Ex 16.3||1a,c,e,g,i||HERE|
|Expressing GCD in the form xa + yb = d||Page 320||Ex 16.4||Q1,2,3,4||HERE|
|Number Bases||Page 322||Ex 16.5||Q1a-d,2a-f||HERE|
|Further Number Theory - SQA Questions||SQA Questions & Answers||Worked Solutions in Online Study Pack|
4. About the Euclidean Algorithm
For a more detailed explanation, please first read the Theory Guides above.
A common style AH Maths exam question on Further Number Theory is;
Source: SQA AH Maths Paper 2015 Question 7
Step 1 – Start by finding the Greatest Common Divisor (GCD)
3066p + 713q = 1 —– (1)
Euclidean Algorithm Process ….
⇒ 3066 = 4 × 713 + 214 —– (2)
⇒ 713 = 3 × 214 + 71 —– (3)
⇒ 214 = 3 × 71 + 1 —– (4)
⇒ 71 = 71 × 1 + 0 —– (5)
Hence the GCD (3066,713) = 1 … relatively prime!
Step 2 – Now work backwards using equations (4), (3) & (2) above
⇒ 214 = 3.71 + 1 —– (4)
⇒ 1 = 214 – 3.71 … re-arranging eqn (4)
⇒ 1 = 214 – 3.(713 – 3.214) … substituting 71 for eqn (3)
⇒ 1 = 214 – 3.713 + 9.214 … multiplying out the brackets
⇒ 1 = 10.214 – 3.713 … simplifying
⇒ 1 = 10.(3066 – 4.713) – 3.713 … substituting 214 for eqn (2)
⇒ 1 = 10.3066 – 40.713 – 3.713 … multiplying out the brackets
⇒ 1 = 10.3066 – 43.713 … simplifying
Step 3 – Compare with equation (1)
1 = 10.3066 – 43.713
1 = 3066p + 713q —– (1)
Hence p = 10, q = – 43
5. AH Maths Past & Practice Papers
Thanks to the SQA for making these available.
Worked solutions to SQA Exam Questions available in the Online Study Pack.
|2018||Advanced Higher||Exam Paper||Marking Scheme|
|2017||Advanced Higher||Exam Paper||Marking Scheme|
|2016||Advanced Higher||Exam Paper||Marking Scheme|
|2016||AH Exemplar||Exemplar||Exemplar Guidance|
|2015||Advanced Higher||Exam Paper||Marking Scheme|
|2014||Advanced Higher||Exam Paper||Marking Scheme|
|2013||Advanced Higher||Exam Paper||Marking Scheme|
|2012||Advanced Higher||Exam Paper||Marking Scheme|
|2011||Advanced Higher||Exam Paper||Marking Scheme|
|2010||Advanced Higher||Exam Paper||Marking Scheme|
|2009||Advanced Higher||Exam Paper||Marking Scheme|
|2008||Advanced Higher||Exam Paper||Marking Scheme|
|2007||Advanced Higher||Exam Paper||Marking Scheme|
|2006||Advanced Higher||Exam Paper||Marking Scheme|
|2005||Advanced Higher||Exam Paper||Marking Scheme|
|2004||Advanced Higher||Exam Paper||Marking Scheme|
|2003||Advanced Higher||Exam Paper||Marking Scheme|
|2002||Advanced Higher||Exam Paper||Marking Scheme|
|2001||Advanced Higher||Exam Paper|
6. AH Maths Past Paper Questions by Topic
Thanks to the SQA for making these available.
Questions and answers have been split up by topic for ease of reference.
Worked solutions to all SQA questions below available in the Online Study Pack.
|Systems of |
7. AH Maths Text Book – Maths In Action (2nd Edition) by Edward Mullan
A fully revised course for the new Curriculum for Excellence examination that is designed to fully support the course’s new structure and unit assessment. A part of the highly regarded Maths in Action series, it provides students with a familiar, clear and carefully structured learning experience that encourages them to build confidence and understanding.
8. Exam focused Online Study Pack
Through step-by-step worked solutions to exam questions available in the Online Study Pack we cover everything you need to know about the Euclidean Algorithm to pass your final exam.
As well as students studying Advanced Higher Mathematics, the resources will benefit young adults studying A-Level Mathematics and undergraduates who need a little extra help. Particular benefit will be to students who have gained a ‘Conditional’ University place and are therefore required to pass in order to gain entry onto the course of their choice.
Subscribing to the Online Study Pack may therefore be one of your best ever investments. Please click Online Study Pack to view screenshots, examples and instructions on how to subscribe.
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We hope the resources on this website prove useful and wish you the very best of success with your AH Maths course in 2018/19.
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After teaching the theory, my students and I access the Online Study Pack to compare our answers with the correct, easy to follow, laid out solutions. We do the same almost every period and nobody is ever stuck for long!
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Free resources to dozens of AH Maths topics are available by clicking on any of the links to the right