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 Further Number Theory is essential to ensure exam success.
Study at Advanced Higher Maths level will provide excellent preparation for your studies when at university. Some universities may require you to gain a pass at AH Maths to be accepted onto the course of your choice. The AH Maths course is fast paced so please do your very best to keep on top of your studies.
For students looking for extra help with the AH Maths course in 2020/21 you may wish to consider subscribing to the fantastic additional exam focused resources available in the Online Study Pack.
We hope you find this website useful and wish you the very best with your studies in 2020/21.
Please find below:
Thanks to the SQA for making these available. The worksheets by topic below are an excellent study resource since they are actual SQA past paper exam questions.
Clear, easy to follow, step-by-step worked solutions to all SQA Higher Maths Questions below are available in the Online Study Pack.
|5||Differential Equations - Variables Separable||Answers|
|6||Differential Equations (Further)||Answers|
|7||Functions & Graphs||Answers|
|11||Number Theory - Methods of Proof||Answers|
|12||Number Theory (Further) - Euclidean & Number Bases||Answers|
|14||Sequences & Series||Answers|
|15||Sequences & Series - Maclaurin||Answers|
|16||Systems of Equations||Answers|
2. 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|
3. Further Number Theory Resources
Thanks to the author(s) for making these available.
|Further Number Theory Guide||HERE|
4. MIA Text Book Questions – Further Number Theory
Recommended questions from the Maths In Action (2nd Edition) by Edward Mullan 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||Q1a,c,e,g,i|
|Expressing GCD in the form xa + yb = d||Page 320||Ex 16.4||Q1,2,3,4|
|Number Bases||Page 322||Ex 16.5||Q1a-d,2a-f|
|Further Number Theory - SQA Questions||SQA Questions & Answers|
5. About Further Number Theory
For a more detailed explanation, please first read the Theory Guides above.
At AH Maths, the following is covered in the topic ‘Further Number Theory’:
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
6. 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.
|2019||AH Specimen||Specimen||Marking Scheme|
|2019||Advanced Higher||Exam Paper||Marking Scheme|
|2018||Advanced Higher||Exam Paper||Marking Scheme|
|2017||Advanced Higher||Exam Paper||Marking Scheme|
|2016||Advanced Higher||Exam Paper||Marking Scheme|
|2016||AH Specimen||Specimen||Marking Scheme|
|2016||AH Exemplar||Exemplar||Marking Scheme|
|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||Marking Scheme|
7. 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 |
8. 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.
9. 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 Further Number Theory 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.
Please speak with your mum/dad and show them our fantastic website.
We hope the resources on this website prove useful and wish you the very best of success with your AH Maths course in 2020/21.
I am e-mailing to let you know that your website has been a fantastic help!!! I used it regularly throughout the year and, after the 2019 AH Paper, I now hope to have achieved an ‘A’ pass. There is no way I would have done this without the help of your brilliant website.
Rebecca – May 2019
Just want to thank you for the amazing study guide pack, it’s helping me immensely in revising for the exam!
F. Roberts – 22nd April 2018
Hi I would like to thank you for the resource packs that you have here. Great for studying and without them I doubt I would pass AH. I can always count on this when I’m stuck on a question in a past paper or homework. Now I’m going to purchase the full AH Online Study Pack to prepare for the exam .. Thanks
Luke – 15th March 2018
I’ve been using this AH Maths website regularly for hand written solutions to the MIA Text Book. The solutions for the Intersection of 3 Planes was really helpful since the questions can be quite tricky when the matrix is inconsistent. It’s also been a great for exam questions by topic. I’ve informed my class about this fantastic resource – Thank you.
Mr D (AH Maths Teacher) – 11th March 2018
Great website, it has really helped me progress and advance within my work. This is for sure the best site I’ve come across. You’ve really helped me and I would strongly recommend this site.
John – 22nd Feb 2018
I really love this website, I was thinking about dropping my AH maths until I found this website. This is a very cheap price for what you get
James – 19th Feb 2018
This site is absolutely brilliant! I’ve been struggling with Advanced Higher ever since the year started. I just found this site a week ago and the resources are plentiful and easy to follow. I’ll smash my exam for sure with the help of this website!
Luke – 18th Dec 2017
I don’t know how much harder AH Maths is but with the assistance of your websites and my sons hard work over the past few years he has gained an ‘A’ in both his National 5 and Higher. So fingers crossed for the next level.
Mrs Donnelly – 3rd January 2018
Just came across this amazing website and couldn’t believe my luck! With my AH Prelim coming up I asked my mum to pay £9.99 for the Online Study Pack. It’s brilliant! There are easy to understand worked solutions to literally hundreds of past paper questions. Text book worked solutions, theory guides – it’s all there! Even my tutor bought the Online Study Pack and says it’s by far the best AH Maths resource out there. I am feeling so much more confident having found this superb website!
Oliver, AH Maths Student
“I really like how the Online Study Pack breaks the course down into 18 sections so my son can address his weaknesses – each section has dedicated topic theory guides, text book solutions, past paper questions, marking schemes and worked solutions. Mark is a lot more confident now having accessed the guides several times – with most tutors charging £30 an hour the website is excellent value for money – only a one off £9.99!”
Mrs Dunlop, Parent
“I am delighted to have been accepted for University to study a degree in Maths starting September 2018. I really want to achieve an ‘A’ Pass in AH Maths this year to give me confidence when I start. This website is absolutely brilliant as everything is here to help me achieve my goal”
Sarah, AH Maths Student
“The text book work solutions are great for helping me start some of the harder questions – if it wasn’t for these I would be really struggling with the course.”
Mark, AH Maths Student
“This fantastic website has made delivering the AH Maths course an absolute pleasure.
After teaching the theory, my students and I access the mobile friendly AH Maths 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!
I’m fully expecting all my students to pass AH Maths with flying colours in 2019!”
Mr M, Whole School Subscriber
Free resources to dozens of AH Maths topics are available by clicking on any of the links to the right.