Let the fantastic wealth of resources below teach you all about the Euclidean Algorithm.
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.
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 you may wish to consider subscribing to the fantastic additional exam focused resources available in the Online Study Pack.
To access a wealth of additional free resources by topic please either use the above Search Bar or click HERE selecting on the topic you wish to study.
We hope you find this website useful and wish you the very best of success with your AH Maths course in 2025. Please find below:
1. About the Euclidean Algorithm
2. Further Number Theory – Exam Worksheet & Theory Guides
3. Further Number Theory – Recommended Text Book Questions
4. AH Maths Past Exam Worksheets by Topic
5. AH Maths Past Paper Questions by Topic
6. AH Maths Past & Practice Exam Papers
7. AH Maths 2020 Specimen Exam Paper
8. AH Maths Prelim & Final Exam Practice Papers
10. AH Maths Course Outline, Formulae Sheets & Check List
11. Text Book Recommended Timings & Questions – Unit One
12. Text Book Recommended Timings & Questions – Unit Two
13. Text Book Recommended Timings & Questions – Unit Three
14. AH Maths Practice Unit Assessments – Solutions Included
16. AH Maths Recommended Text Book
17. Exam Focused Study Pack – Students looking for a ‘good’ Pass
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1. About the Euclidean Algorithm
To learn about the Euclidean Algorithm please click on any of the Theory Guide links in Section 2 below. For students working from the Maths In Action text book the recommended questions on this topic are given in Section 3. Worksheets including actual SQA Exam Questions are highly recommended.
If you would like more help understanding the Euclidean Algorithm there are full, easy to follow, step-by-step worked solutions to dozens of AH Maths Past & Practice exam questions on all topics in the AH Maths Online Study Pack. Also included in the Study Pack are full worked solutions to the recommended MIA text book questions. Please give yourself every opportunity for success, speak with your parents, and subscribe to the exam focused Online Study Pack today.
The Euclidean Algorithm
A common Further Number Theory style AH Maths exam question is;
Source: SQA AH Maths Paper 2015 Question 7
Worked Solution
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
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2. Further Number Theory – Exam Worksheet & Theory Guides
Thanks to the SQA and authors for making the excellent AH Maths Worksheet & Theory Guides freely available for all to use. These will prove a fantastic resource in helping consolidate your understanding of AH Maths. Clear, easy to follow, step-by-step worked solutions to all SQA AH Maths Questions in the worksheet below are available in the Online Study Pack.
| Worksheet/Theory Guides __________________________ | Resource Link _______________________________________________ | Answers ____________ |
| AH Maths Exam Questions | Number Theory (Further) - Euclidean & Number Bases | Answers |
| AH Maths Formulae List | AH Maths Fomulae List | |
| Theory Guide | Further Number Theory Guide |
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3. Further Number Theory – Recommended Text Book Questions
Recommended questions from the Maths In Action (2nd Edition) by Edward Mullan text book are shown below. Clear, easy to follow, step-by-step worked solutions to all questions below are available in the Online Study Pack.
| Subtopic _______________________________________ | Page Number _____________ | Exercise _________ | Recommended Questions _________________________ | Handwritten Worked Solutions __________________________ |
| Finding the Greatest Common Divisor (GCD) | Page 318 | Ex 16.3 | Q1a,c,e,g,i | In Online Study Pack |
| Expressing GCD in the form xa + yb = d | Page 320 | Ex 16.4 | Q1,2,3,4 | In Online Study Pack |
| Number Bases | Page 322 | Ex 16.5 | Q1a-d,2a-f | In Online Study Pack |
| Further Number Theory - SQA Questions | SQA Questions & Answers | In Online Study Pack |
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4. AH Maths Past Paper Exam Worksheets by Topic
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 AH Maths Questions below are available in the Online Study Pack.
| Number ______ | Topic ____________________________________________ | Answers _________ | Handwritten Worked Solutions _____________________________ | Courtesy __________________ |
| 1 | Binomial Theorem | Answers | Solutions in the Online Study Pack | Courtesy of the SQA |
| 2 | Complex Numbers | Answers | Solutions in the Online Study Pack | Courtesy of the SQA |
| 3 | Differentiation | Answers | Solutions in the Online Study Pack | Courtesy of the SQA |
| 4 | Differentiation (Further) | Answers | Solutions in the Online Study Pack | Courtesy of the SQA |
| 5 | Differential Equations - Variables Separable | Answers | Solutions in the Online Study Pack | Courtesy of the SQA |
| 6 | Differential Equations (Further) | Answers | Solutions in the Online Study Pack | Courtesy of the SQA |
| 7 | Functions & Graphs | Answers | Solutions in the Online Study Pack | Courtesy of the SQA |
| 8 | Integration | Answers | Solutions in the Online Study Pack | Courtesy of the SQA |
| 9 | Integration (Further) | Answers | Solutions in the Online Study Pack | Courtesy of the SQA |
| 10 | Matrices | Answers | Solutions in the Online Study Pack | Courtesy of the SQA |
| 11 | Number Theory - Methods of Proof | Answers | Solutions in the Online Study Pack | Courtesy of the SQA |
| 12 | Number Theory (Further) - Euclidean & Number Bases | Answers | Solutions in the Online Study Pack | Courtesy of the SQA |
| 13 | Partial Fractions | Answers | Solutions in the Online Study Pack | Courtesy of the SQA |
| 14 | Sequences & Series | Answers | Solutions in the Online Study Pack | Courtesy of the SQA |
| 15 | Sequences & Series - Maclaurin | Answers | Solutions in the Online Study Pack | Courtesy of the SQA |
| 16 | Systems of Equations | Answers | Solutions in the Online Study Pack | Courtesy of the SQA |
| 17 | Vectors | Answers | Solutions in the Online Study Pack | Courtesy of the SQA |
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5. 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 your ease of reference. Clear, easy to follow, step-by-step worked solutions to all SQA AH Maths questions below are available in the Online Study Pack.
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6. AH Maths Past & Practice Exam Papers
Thanks to the SQA for making these available. Clear, easy to follow, step-by-step worked solutions to all SQA AH Maths questions below are available in the Online Study Pack.
| Year ___________ | Paper Type _________________ | Exam Paper ______________ | Marking Scheme _________________ | Handwritten Worked Solutions _________________________________ | Courtesy ________________________ |
| 2024 | Advanced Higher | Exam Paper | Marking Scheme | 2024 Solutions in the Online Study Pack | Courtesy of the SQA |
| 2023 | Advanced Higher | Exam Paper | Marking Scheme | 2023 Solutions in the Online Study Pack | Courtesy of the SQA |
| 2022 | Advanced Higher | Exam Paper | Marking Scheme | 2022 Solutions in the Online Study Pack | Courtesy of the SQA |
| 2021 | Advanced Higher | Exam Paper | Marking Scheme | 2021 Solutions in the Online Study Pack | Courtesy of the SQA |
| 2019 | AH Specimen | Specimen | Marking Scheme | 2019 Solutions in the Online Study Pack | Courtesy of the SQA |
| 2019 | Advanced Higher | Exam Paper | Marking Scheme | 2019 Solutions in the Online Study Pack | Courtesy of the SQA |
| 2018 | Advanced Higher | Exam Paper | Marking Scheme | 2018 Solutions in the Online Study Pack | Courtesy of the SQA |
| 2017 | Advanced Higher | Exam Paper | Marking Scheme | 2017 Solutions in the Online Study Pack | Courtesy of the SQA |
| 2016 | Advanced Higher | Exam Paper | Marking Scheme | 2016 Solutions in the Online Study Pack | Courtesy of the SQA |
| 2016 | AH Specimen | Specimen | Marking Scheme | 2016 Solutions in the Online Study Pack | Courtesy of the SQA |
| 2016 | AH Exemplar | Exemplar | Marking Scheme | 2016 Solutions in the Online Study Pack | Courtesy of the SQA |
| 2015 | Advanced Higher | Exam Paper | Marking Scheme | 2015 Solutions in the Online Study Pack | Courtesy of the SQA |
| 2014 | Advanced Higher | Exam Paper | Marking Scheme | 2014 Solutions in the Online Study Pack | Courtesy of the SQA |
| 2013 | Advanced Higher | Exam Paper | Marking Scheme | 2013 Solutions in the Online Study Pack | Courtesy of the SQA |
| 2012 | Advanced Higher | Exam Paper | Marking Scheme | 2012 Solutions in the Online Study Pack | Courtesy of the SQA |
| 2011 | Advanced Higher | Exam Paper | Marking Scheme | 2011 Solutions in the Online Study Pack | Courtesy of the SQA |
| 2010 | Advanced Higher | Exam Paper | Marking Scheme | 2010 Solutions in the Online Study Pack | Courtesy of the SQA |
| 2009 | Advanced Higher | Exam Paper | Marking Scheme | 2011 Solutions in the Online Study Pack | Courtesy of the SQA |
| 2008 | Advanced Higher | Exam Paper | Marking Scheme | 2008 Solutions in the Online Study Pack | Courtesy of the SQA |
| 2007 | Advanced Higher | Exam Paper | Marking Scheme | 2007 Solutions in the Online Study Pack | Courtesy of the SQA |
| 2006 | Advanced Higher | Exam Paper | Marking Scheme | Courtesy of the SQA | |
| 2005 | Advanced Higher | Exam Paper | Marking Scheme | Courtesy of the SQA | |
| 2004 | Advanced Higher | Exam Paper | Marking Scheme | Courtesy of the SQA | |
| 2003 | Advanced Higher | Exam Paper | Marking Scheme | Courtesy of the SQA | |
| 2002 | Advanced Higher | Exam Paper | Marking Scheme | Courtesy of the SQA | |
| 2001 | Advanced Higher | Exam Paper | Marking Scheme | Courtesy of the SQA | |
| 2024 Practice | Advanced Higher | Exam Paper | Without Answers | Answers | Courtesy of Madras College |
| X-Mas Special | Advanced Higher | Exam Paper | Without Solutions | Worked Solutions |
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7. AH Maths 2020 Specimen Exam Paper
Please find below two Specimen Papers courtesy of the SQA. Clear, easy to follow, step-by-step worked solutions to the SQA AH Maths Specimen Paper available in the Online Study Pack.
| . Date __________ | . Paper ___________ | . Marking ______ | Binomial Theorem ________ | Partial Fractions ________ | . Differentiation ___________ | Further Differentiation ___________ | . Integration ___________ | Further Integration ____________ | Functions & Graphs ___________ | Systems of Equations ____________ | Complex Numbers __________ | Seq & Series _________ | Further Seq & Series ____________ | . Matrices _________ | . Vectors __________ | Methods of Proof __________ | Further No Theory ___________ | Differential Equations ____________ | Further Differential Eqns _________________ |
| June 2019 | Specimen P1 | Marking | Q2 | Q4 | Q6 | Q8 | Q3 | Q5 | Q1 | Q7 | |||||||||
| June 2019 | Specimen P2 | Marking | Q3 | Q1 | Q2,4,8,10 | Q7 | Q11 | Q5 | Q13 | Q9 | Q6 | Q12 |
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8. AH Maths Prelim & Final Exam Practice Papers
Thanks to the SQA and authors for making these freely available. Please use regularly for revision prior to assessments, tests and the final exam. Clear, easy to follow, step-by-step worked solutions to the first five Practice Papers below are available in the Online Study Pack.
| AH Practice Exam Paper _____________________ | Marking ________ | Handwritten Worked Solutions _____________________________ | Courtesy ________________________________ |
| Practice Exam Paper 1 | HERE | Solutions in the Online Study Pack | Courtesy to the author(s) and the SQA |
| Practice Exam Paper 2 | HERE | Solutions in the Online Study Pack | Courtesy to the author(s) and the SQA |
| Practice Exam Paper 3 | HERE | Solutions in the Online Study Pack | Courtesy to the author(s) and the SQA |
| Practice Exam Paper 4 | HERE | Solutions in the Online Study Pack | Courtesy to the author(s) and the SQA |
| Practice Exam Paper 5 | HERE | Solutions in the Online Study Pack | Courtesy to the author(s) and the SQA |
| Practice Exam Paper 6 | HERE | Courtesy to the author(s) and the SQA | |
| Practice Exam Paper 7 | HERE | Courtesy to the author(s) and the SQA | |
| Practice Exam Paper 8 | HERE | Courtesy to the author(s) and the SQA |
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9. AH Maths Theory Guides
Thanks to the authors for making the excellent AH Maths Theory Guides freely available for all to use. These will prove a fantastic resource in helping consolidate your understanding of AH Maths.
Unit One
| Topic 1 ______________________ | Topic 2 ___________________ | Topic 3 _____________________ | Topic 4 ___________________ | Topic 5 ___________________ | Topic 6 ___________________ |
| Partial Fractions 1 | Binomial 1 | Gaussian 1 | Functions 1 | Differentiation 1 | Integration 1 |
| Partial Fractions 2 | Binomial 2 | Gaussian 2 | Functions (HSN) | Differentiation 2 | Integration (HSN) |
| Partial Fractions (HSN) | Binomial (HSN) | Gaussian (HSN) | Differentiation (HSN) |
Unit Two
| Topic 1 ______________________ | Topic 2 ________________________ | Topic 3 ___________________ | Topic 4 ____________________ | Topic 5 _________________________ |
| Further Differentiation 1 | Further Integration 1 | Complex Numbers 1 | Sequences & Series 1 | Methods of Proof |
| Further Differentiation 2 | Further Integration 2 | Complex Numbers 2 | Sequences & Series 2 | Proof by Induction |
| Differentiation (HSN) | Integration (HSN) | Complex Nos (HSN) | Seq & Series (HSN) | Methods of Proof (HSN) |
Unit Three
| Topic 1 ________________________ | Topic 2 _________________ | Topic 3 _____________________ | Topic 4 _____________________ | Topic 5 ______________________________ |
| Vectors 1 | Matrices 1 | Maclaurin Series 1 | Differential Eqns 1 | Further Number Theory |
| Vectors 2 | Matrices 2 | MacLaurin Series 2 | Differential Eqns 2 | |
| Vectors 3 | Matrices 3 | Maclaurin Series (HSN) | Differential Eqns (HSN) | |
| Vectors (HSN) | Matrices (HSN) |
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10. AH Maths Course Outline, Formulae Sheets & Check List
Thanks to the SQA and authors for making the excellent resources below freely available. These are fantastic check lists to assess your AH Maths knowledge. Please try to use these regularly for revision prior to tests, prelims and the final exam.
| Title ____________________________________ | Link _______ | Courtesy ___________________ |
| AH Maths Course Outline & Timings | HERE | |
| SQA AH Maths Exam Formulae List | HERE | Courtesy of the SQA |
| SQA Higher Maths Exam Formulae List | HERE | Courtesy of the SQA |
| SQA AH Maths Support Notes | HERE | Courtesy of the SQA |
| AH Maths Complete Check List | HERE |
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11. Text Book Recommended Timings & Questions – Unit One
Course timings, along with specific text book exercises/questions for Unit One, courtesy of Teejay Publishers can be found HERE.
Partial Fractions
Recommended questions from the Maths In Action (2nd Edition) by Edward Mullan Text Book are shown below. Clear, easy to follow, step-by-step worked solutions to all questions below are available in the Online Study Pack.
| Subtopic _______________________________ | Page Number _____________ | Exercise _____________ | Recommended Questions _______________________ | Handwritten Worked Solutions _________________________________ |
| Type One - Partial Fractions | Page 23 | Exercise 2.2 | Q1, 5, 12, 18, 19, 22, 25 | Solutions in the Online Study Pack |
| Type Two - Partial Fractions | Page 24 | Exercise 2.3 | Q1, 3, 5, 10, 14, 18 | Solutions in the Online Study Pack |
| Type Three - Partial Fractions | Page 25 | Exercise 2.4 | Q1, 5, 7, 9, 11 | Solutions in the Online Study Pack |
| Algebraic Long Division Worksheet | Worksheet | Solutions on Page 8 | ||
| Partial Fraction - Long Division | Page 26 | Exercise 2.5 | Q1 a, b, e, j, l | Solutions in the Online Study Pack |
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Binomial Theorem
Recommended questions from the Maths In Action (2nd Edition) by Edward Mullan Text Book are shown below. Clear, easy to follow, step-by-step worked solutions to all questions below are available in the Online Study Pack.
| Subtopic ____________________________________ | Page Number _____________ | Exercise ___________ | Recommended Questions ____________________________ | Handwritten Worked Solutions __________________________________________________________________________________ |
| Combinations nCr | Page 33 | Exercise 3.3 | Q1a,b,c,2a,b,c,4a-d,5a,b,6a,7a,b,d | Solutions in the Online Study Pack |
| Expanding - Lesson 1 | Page 36 | Exercise 3.4 | Q1a,b,c,2a,i,ii,iii,iv | Solutions in the Online Study Pack |
| Expanding - Lesson 2 | Page 36 | Exercise 3.4 | Q3a-d,4a-f | THEORY - Questions 3 & 4 |
| Finding Coefficients | Page 38 | Exercise 3.5 | Q1a,b,c,4a,5a,6 | Solutions in the Online Study Pack |
| Approximation eg 1.05^5 = ? | Page 40 | Exercise 3.6 | Q1a,b,c,d | Solutions in the Online Study Pack |
| Simplifying General Term (SQA Questions) | SQA Questions & Answers | Common SQA Binomial Questions not in AH Text Book |
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Systems of Equations
Recommended questions from the Maths In Action (2nd Edition) by Edward Mullan Text Book are shown below. Clear, easy to follow, step-by-step worked solutions to all questions below are available in the Online Study Pack.
| Subtopic ______________________________ | Page Number _____________ | Exercise _______________ | Recommended Questions ______________________ | Handwritten Worked Solutions ________________________________ |
| Gaussian Elimination | Page 265 | Exercise 14.4 | Q1a,b,c,d,2a,b,c | Solutions in the Online Study Pack |
| Redundancy & Inconsistency | Page 268 | Exercise 14.6 | Q1a,b,c,2 | Solutions in the Online Study Pack |
| Redundancy SQA Question | 2016 Q4 (SQA) | Solutions in the Online Study Pack | ||
| Inconsistency SQA Question | 2017 Q5 (SQA) | Solutions in the Online Study Pack | ||
| ILL Conditioning | Page 274 | Exercise 14.9 | Q2a,b,c,d | Solutions in the Online Study Pack |
| ILL Conditioning SQA Question | 2012 Q14c (SQA) | Solutions in the Online Study Pack |
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Functions & Graphs
Recommended questions from the Maths In Action (2nd Edition) by Edward Mullan Text Book are shown below. Clear, easy to follow, step-by-step worked solutions to all questions below are available in the Online Study Pack.
| Subtopic ______________________________ | Page Number _____________ | Exercise ___________ | Recommended Questions _______________________ | Handwritten Worked Solutions ________________________________ |
| Sketching Modulus Function y = |x| | Page 66 | Exercise 5.2 | Q1-9 | Solutions in the Online Study Pack |
| Inverse Functions | Page 67 | Exercise 5.3 | Q1a,c,e,g,i,2a,c,e,3 | Solutions in the Online Study Pack |
| Odd & Even Functions | Page 74 | Exercise 5.8 | Q3a-l | Solutions in the Online Study Pack |
| Vertical Asymptotes & Behaviour | Page 75 | Exercise 5.9 | Q1a-f | Solutions in the Online Study Pack |
| Horizontal & Oblique Asymptotes | Page 76 | Exercise 5.10 | Q1a,b,f,g,k,l | Solutions in the Online Study Pack |
| Sketching Graphs | Page 77 | Exercise 5.11 | Q1a,c,e,i,k | Solutions in the Online Study Pack |
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Differential Calculus
Recommended questions from the Maths In Action (2nd Edition) by Edward Mullan Text Book are shown below. Clear, easy to follow, step-by-step worked solutions to all questions below are available in the Online Study Pack.
| Subtopic ___________________________ | Page Number ____________ | Exercise ___________ | Recommended Questions _______________________ | Handwritten Worked Solutions ________________________________ |
| Derivative from First Principles | Page 45 | Exercise 4.1 | Q1,3,5,7 | Solutions in the Online Study Pack |
| The Chain Rule | Page 48 | Exercise 4.3 | Q1a,d,2a,c,3b,4a,5a | Solutions in the Online Study Pack |
| The Product Rule | Page 51 | Exercise 4.5 | Q1a-h,Q2b,Q3a-l | Solutions in the Online Study Pack |
| The Quotient Rule | Page 52 | Exercise 4.6 | Q1,2,3,4 | Solutions in the Online Study Pack |
| Differentiation - A Mixture! | Page 53 | Exercise 4.7 | Q1,2,3,4,5 | Solutions in the Online Study Pack |
| Sec, Cosec & Cot | Page 55 | Exercise 4.8 | Q1a,b,2a,c,d,3a,c,e,g | Solutions in the Online Study Pack |
| Exponential Functions | Page 58 | Exercise 4.9 | Q1a,c,e,2a,3e,4a,b,5a,e | Solutions in the Online Study Pack |
| Logarithmic Functions | Page 58 | Exercise 4.9 | Q1k,m,o,q,s,2f,g,3a,b,c,4d,e,5d | Solutions in the Online Study Pack |
| Nature & Sketching Polynomials | Page 70 | Exercise 5.5 | Q1a,b,c,2a,b | Solutions in the Online Study Pack |
| Concavity | Page 73 | Exercise 5.7 | Q5a,b,c,Q1a,b | Solutions in the Online Study Pack |
| Applications | Page 187 | Ex 11.1 | Q1a,b,e,f,2a,c,3a,c | Solutions in the Online Study Pack |
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Integral Calculus
Recommended questions from the Maths In Action (2nd Edition) by Edward Mullan Text Book are shown below. Clear, easy to follow, step-by-step worked solutions to all questions below are available in the Online Study Pack.
| Subtopic ______________________________________ | Page No ________________ | Exercise ___________ | Recommended Questions _____________________ | Handwritten Worked Solutions ________________________________ |
| Integration (Higher Revision) | Page 100 | Exercise 7.1 | Q1a-i,2a-i,3a-l,4a-f | Solutions in the Online Study Pack |
| Integration by Substitution | Page 103 | Exercise 7.2 | Q1a,c,e,g,i,k,m,o,q,s,u,w | Solutions in the Online Study Pack |
| Integration by Substitution - Extra Revision! | Page 103 | Exercise 7.2 | Q1b,d,f,h,j,l,n,p,r,t,v,x | Solutions in the Online Study Pack |
| Further Integration by Substitution | Page 105 | Exercise 7.3 | Q2a,b,c,d,4a,b,c,d | Solutions in the Online Study Pack |
| Further Integration by Substitution | Page 105 | Exercise 7.3 | Q6a,b,c,d | Solutions in the Online Study Pack |
| Further Int'n by Sub'n - sin^m(x), cos^n(x) | Page 105 | Exercise 7.3 | Q7a,b,c,d,e,f | Solutions in the Online Study Pack |
| Further Integration by Substitution - logs | Page 105 | Exercise 7.3 | Q11a,b,c,d | Solutions in the Online Study Pack |
| Substitution & Definite Integrals | Page 107 | Exercise 7.4 | Q1a,c,e,g,i,k | Solutions in the Online Study Pack |
| Area between curve & x-axis | Page 120 | Exercise 7.10 | Q1,3 | Solutions in the Online Study Pack |
| Area between curve & y-axis | Page 120 | Exercise 7.10 | Q6,7 | Solutions in the Online Study Pack |
| Volume - revolved around x-axis SQA Question | Theory & Worksheet | 2014 Q10 (SQA) | Solutions in the Online Study Pack | |
| Volume - revolved around y-axis SQA Question | 2017 Q16 (SQA) | Solutions in the Online Study Pack | ||
| Volume - revolved around x-axis | Page 120 | Exercise 7.10 | Q11,12 | Solutions in the Online Study Pack |
| Applications of Integral Calculus | Page 187 | Exercise 11.1 | Q4,14 | Solutions in the Online Study Pack |
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12. Text Book Recommended Timings & Questions – Unit Two
Course timings, along with specific text book exercises/questions for Unit Two, courtesy of Teejay Publishers can be found HERE.
Further Differentiation
Recommended questions from the Maths In Action (2nd Edition) by Edward Mullan Text Book are shown below. Clear, easy to follow, step-by-step worked solutions to all questions below are available in the Online Study Pack.
| Subtopic _____________________________________________ | Page Number _____________ | Exercise ______________ | Recommended Questions _____________________ | Handwritten Worked Solutions ________________________________ |
| Inverse Trig Functions & Chain Rule | Page 85 | Exercise 6.2 | Q1a,b,c,Q2b,c,dQ3a,d | Solutions in the Online Study Pack |
| Inverse Trig Fns & Product/Quotient Rules | Page 86 | Exercise 6.3 | Q2,Q3 | Solutions in the Online Study Pack |
| Implicit & Explicit Functions - 1 | Page 89 | Exercise 6.4 | Q1,Q2 | Solutions in the Online Study Pack |
| Implicit & Explicit Functions - 2 | Page 89 | Exercise 6.4 | Q5,Q9,Q4 | Solutions in the Online Study Pack |
| Second Derivatives of Implicit Functions | Page 90 | Exercise 6.5 | Q1a,d,f,k(i),6 | Solutions in the Online Study Pack |
| Logarithmic Differentiation | Page 92 | Exercise 6.6 | Q1,Q2 | Solutions in the Online Study Pack |
| Parametric Equations - Finding Constraint Equation | Page 95 | Exercise 6.7 | Q1a,b,c | Solutions in the Online Study Pack |
| Parametric Eqns - Differentiation | Page 96 | Exercise 6.8 | Q1,2,3 | Solutions in the Online Study Pack |
| Parametric Eqns - Differentiation (Alternative) | Page 96 | Exercise 6.8 | Q1(i) | Solutions in the Online Study Pack |
| Parametric Eqns - Differentiation (Alternative) | Page 96 | Exercise 6.8 | Q1(ii),Q2,Q3 | Solutions in the Online Study Pack |
| Applications of Further Differentiation | Page 193 | Exercise 11.2 | Q1,Q2,Q3 | Solutions in the Online Study Pack |
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Further Integration
Recommended questions from the Maths In Action (2nd Edition) by Edward Mullan Text Book shown below. Clear, easy to follow, step-by-step worked solutions to all questions below are available in the Online Study Pack.
| Subtopic ______________________________________ | Page No __________ | Exercise _________________ | Recommended Questions __________________________ | Handwritten Worked Solutions ________________________________ |
| Integration using Inverse Trig Functions | Page 111 | Exercise 7.6 | Q1,2,3,4a,b | Solutions in the Online Study Pack |
| Integration using Partial Fractions | Page 113 | Exercise 7.7 | Q1a,b,2a,b,3a,b,4a,b,5a,b,6a,b | Solutions in the Online Study Pack |
| Integration by Parts - 1 | Page 116 | Exercise 7.8 | Q1a-l | Solutions in the Online Study Pack |
| Integration by Parts - 2 | Page 116 | Exercise 7.8 | Q2a,c,d,e,f,g,h | Solutions in the Online Study Pack |
| Integration by Parts - 3 | Page 116 | Exercise 7.8 | Q5a,b,Q6a,b | Solutions in the Online Study Pack |
| Integration by Parts - Special Cases - 1 | Page 118 | Exercise 7.9 | Q1a,b,c,d | Solutions in the Online Study Pack |
| Integration by Parts - Special Cases - 2 | Page 118 | Exercise 7.9 | Q2a,b,c,d,e | Solutions in the Online Study Pack |
| First Order Diff Eqns - General Soln | Page 128 | Exercise 8.1 | Q1a-j | Solutions in the Online Study Pack |
| First Order Diff Eqns - Particular Soln | Page 128 | Exercise 8.1 | Q2a-g | Solutions in the Online Study Pack |
| Differential Equations in Context | Page 131 | Exercise 8.2 | Q2,4,5,6 | Solutions in the Online Study Pack |
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Complex Numbers
Recommended questions from the Maths In Action (2nd Edition) by Edward Mullan Text Book are shown below. Clear, easy to follow, step-by-step worked solutions to all questions below are available in the Online Study Pack.
| Subtopic _________________________________ | Page Number _____________ | Exercise ______________ | Recommended Questions ______________________ | Handwritten Worked Solutions _____________________________ |
| Arithmetic with Complex Numbers | Page 207 | Exercise 12.1 | Q1,2,3,6,7,8 | Solutions in the Online Study Pack |
| Division & Square Roots of Complex Nos | Page 209 | Exercise 12.2 | Q1a,b,c,2c,e,3a,b,f,5a,b | Solutions in the Online Study Pack |
| Argand Diagrams | Page 211 | Exercise 12.3 | Q3a,b,d,e,f,i,6a,b,f,7a,b,c | Solutions in the Online Study Pack |
| Multiplying/Dividing in Polar Form | Page 215 | Exercise 12.5 | Q1a,b,f,g | Solutions in the Online Study Pack |
| De Moivre's Theorem | Page 218 | Exercise 12.6 | Q1,2,3a,4g,h,i,j | Solutions in the Online Study Pack |
| Polynomials & Complex Numbers | Page 224 | Exercise 12.8 | Q2a,d,3a,b,4,5,6a,b | Solutions in the Online Study Pack |
| Loci on the Complex Plane | Page 213 | Exercise 12.4 | Q1a,b,d,f,j,3a,b,4a,b,c | Solutions in the Online Study Pack |
| Expanding Trig Formula | Page 219 | Exercise 12.6 | Q5,6,7a | Solutions in the Online Study Pack |
| Roots of a Complex Number | Page 222 | Exercise 12.7 | Q2a,b,c,d,e,f,1a(i) | Solutions in the Online Study Pack |
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Sequences & Series, Sigma Notation
Recommended questions from the Maths In Action (2nd Edition) by Edward Mullan Text Book are shown below. Clear, easy to follow, step-by-step worked solutions to all questions below are available in the Online Study Pack.
| Subtopic _______________________________ | Page Number _____________ | Exercise ____________ | Recommended Questions _______________________ | Handwritten Worked Solutions _____________________________ |
| Arithmetic Sequences | Page 151 | Exercise 9.1 | Q1a-f,2a-f,Q3,Q4,Q6 | Solutions in the Online Study Pack |
| Finding Sum - Arithmetic Sequence | Page 153 | Exercise 9.2 | Q1a,b,c,Q3a-d,Q4a,b,Q5a | Solutions in the Online Study Pack |
| Geometric Sequence | Page 156 | Exercise 9.3 | Q1a-e,Q2,Q3,Q5 | Solutions in the Online Study Pack |
| Finding Sum - Geometric Sequence | Page 159 | Exercise 9.4 | Q1a-f,Q2a-d,Q3a-d,Q4 | Solutions in the Online Study Pack |
| Finding Sum to Infinity | Page 162 | Exercise 9.5 | Q1,2,3,4,6 | Solutions in the Online Study Pack |
| Sigma Notation | Page 168 | Exercise 10.1 | Q1a-e,Q2a-e | Solutions in the Online Study Pack |
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Number Theory & Proof
| Topic _______________________________ | Lessons __________ | Questions _________ | Typed Solutions _______________ | Handwritten Solutions ______________________ | Exam Questions - Worked Solutions in Online Study Pack ______________________________________________________ |
| Direct Proof | Lesson 1 | Ex 1 & 2 | Ex 1 & 2 Handwritten Solns | 2018-Q9,2015-Q12, 2010-Q8a | |
| Proof by Counterexample | Lesson 2 | Ex 3 | Ex 3 Typed Solns | Ex 3 Handwritten Solns | 2016-Q10, 2013-Q12, 2008-Q11 |
| Proof by Counterexample | Ex 4 | Ex 4 Typed Solns | Ex 4 Handwritten Solns | 2016-Q10, 2013-Q12, 2008-Q11 | |
| Proof by Contradiction | Lesson 3 | Ex 5 | Ex 5 Typed Solns | Ex 5 Handwritten Solns | 2010-Q12 |
| Proof by Contrapositive | Lesson 4 | Ex 6 | Ex 6 Typed Solns | Ex 6 Handwritten Solns | 2017-Q13 |
| Proof by Induction | Lesson 5 | Ex 7 | Ex 7 Typed Solns | Ex 7 Handwritten Solns | 2014-Q7,2013-Q9,2012-Q16a,2011-Q12,2010-Q8b,2009-Q4,2007-Q12 |
| Proof by Induction - Sigma Notation | Lesson 6 | Ex 8 | Ex 8 Typed Solns | Ex 8 Handwritten Solns | 2018-Q12,2016-Q5, 2013-Q9,2009-Q4 |
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13. Text Book Recommended Timings & Questions – Unit Three
Course timings, along with specific text book exercises/questions for Unit Three, courtesy of Teejay Publishers can be found HERE.
Vectors
Recommended questions from the Maths In Action (2nd Edition) by Edward Mullan Text Book are shown below. Clear, easy to follow, step-by-step worked solutions to all questions below are available in the Online Study Pack.
| Subtopic __________________________________ | Page Number _____________ | Exercise ______________ | Recommended Questions ______________________ | Lesson/Notes _____________ | Handwritten Worked Solutions _____________________________ |
| Higher Revision On Vectors | Page 282 | Exercise 15.1 | Q6,7,8 | Solutions in the Online Study Pack | |
| The Vector Product - 1 | Page 286 | Exercise 15.3 | Q1,2a,b,5,7,8a,b,10 | Lesson 1 | Solutions in the Online Study Pack |
| The Vector Product - 2 | Page 286 | Exercise 15.3 | Q3,4,6,12 | Lesson 2 | Solutions in the Online Study Pack |
| The Equations of a Line | Page 298 | Exercise 15.8 | Q1a,b,2a,3a,c,e,5 | Lesson 3 | Solutions in the Online Study Pack |
| Vector Equation of a Straight Line | Page 298 | Exercise 15.9 | Q2 | Lesson 3 | Solutions in the Online Study Pack |
| The Equation of a Plane | Page 291 | Exercise 15.5 | Q1a,b,c,d,2a,b,3,4a,c,9,10 | Lesson 4 | Solutions in the Online Study Pack |
| Angle Between 2 Planes | Page 293 | Exercise 15.6 | Q1,2,3 | Lesson 5 | Solutions in the Online Study Pack |
| Intersection of Line & Plane | Page 300 | Exercise 15.10 | Q1a,b,c,2a,b,3,4a | Lesson 6 | Solutions in the Online Study Pack |
| Intersection of 2 Lines | Page 302 | Exercise 15.11 | Q1,2 | Lesson 7 | Solutions in the Online Study Pack |
| Intersection of 2 Planes using Gaussian | Page 303 | Exercise 15.12 | Q1,2 | Lesson 8 | Solutions in the Online Study Pack |
| Intersection of 2 Planes - Alternative | Page 303 | Exercise 15.12 | Q1,2 | Solutions in the Online Study Pack | |
| Intersection of 3 Planes | Page 307 | Exercise 15.3 | Q1a,c,2a,c | Lesson 9 | Solutions in the Online Study Pack |
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Matrices
Recommended questions from the Maths In Action (2nd Edition) by Edward Mullan Text Book are shown below. Clear, easy to follow, step-by-step worked solutions to all questions below are available in the Online Study Pack.
| Subtopic __________________________________ | Page Number _____________ | Exercise ______________ | Recommended Questions _________________________ | Handwritten Worked Solutions _____________________________ |
| Basic Properties & Operations of Matrices | Page 231 | Exercise 13.1 | Q1,2,3a,4a,c,e,i,p,t,7a,f,9,10 | Solutions in the Online Study Pack |
| Matrix Multiplication | Page 235 | Exercise 13.3 | Q1a,c,2a,c,k,m,o,3a,4,5a,c | Solutions in the Online Study Pack |
| Properties of Matrix Multiplication | Page 236 | Exercise 13.4 | Q6a,b,7a,b,8a | Solutions in the Online Study Pack |
| Determinant of a 2 x 2 Matrix | Page 240 | Exercise 13.6 | Q1a,b,d,h | Solutions in the Online Study Pack |
| Determinant of a 3 x 3 Matrix | Page 247 | Exercise 13.9 | Q4a,b,c,d,5a,b | Solutions in the Online Study Pack |
| Inverse of a 2 x 2 Matrix | Page 243 | Exercise 13.7 | Q1,2,4,8,9a,b,c | Solutions in the Online Study Pack |
| Inverse of a 3 x 3 Matrix | Page 275 | Exercise 14.10 | Q1a,b,c,d | Solutions in the Online Study Pack |
| Transformation Matrices | Page 251 | Exercise 13.10 | Q1,2,5 | Solutions in the Online Study Pack |
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Further Sequences & Series (Maclaurin Series)
Recommended questions from the Maths In Action (2nd Edition) by Edward Mullan Text Book are shown below. Clear, easy to follow, step-by-step worked solutions to all questions below are available in the Online Study Pack.
| Subtopic ________________________________ | Page Number _____________ | Exercise ______________ | Recommended Questions _______________________ | Handwritten Worked Solutions _____________________________ |
| Maclaurin Series for f(x) | Page 179 | Exercise 10.5 | Q1a,b,c,d,3a,b | Solutions in the Online Study Pack |
| Maclaurin Series - Composite Functions | Page 182 | Exercise 10.7 | Q1a,f,2a,3a,6a,7a,8a,b | Solutions in the Online Study Pack |
| Maclaurin Series - SQA Questions | SQA Questions & Answers | Solutions in the Online Study Pack |
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Further Differential Equations
Recommended questions from the Maths In Action (2nd Edition) by Edward Mullan Text Book are shown below. Clear, easy to follow, step-by-step worked solutions to all questions below are available in the Online Study Pack.
| Subtopic __________________________________ | Page Number _____________ | Exercise ______________ | Recommended Questions _____________________ | Handwritten Worked Solutions ________________________________ |
| 1st Order Linear Differential Equations | Page 136 | Exercise 8.3 | Q1a,b,2a,3a,b | Solutions in the Online Study Pack |
| 2nd Order Differential Equations (Roots Real & Distinct) | Page 140 | Exercise 8.4 | Q1a,b,c,2a,b | Solutions in the Online Study Pack |
| 2nd Order Differential Equations (Roots Real & Coincident) | Page 141 | Exercise 8.5 | Q1a,b,c,2a,b | Solutions in the Online Study Pack |
| 2nd Order Differential Equations (Roots Not Real) | Page 142 | Exercise 8.6 | Q1a,b,c,2a,b | Solutions in the Online Study Pack |
| Non-Homogeneous Differential Equations (Finding General Solution) | Page 146 | Exercise 8.9 | Q1a,b,c | Solutions in the Online Study Pack |
| Non-Homogeneous Differential Equations (Finding Particular Solution) | Page 146 | Exercise 8.9 | Q2a,b,c | Solutions in the Online Study Pack |
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Further Number Theory & Proof
Recommended questions from the Maths In Action (2nd Edition) by Edward Mullan Text Book are shown below. Clear, easy to follow, step-by-step worked solutions to all questions below are available in the Online Study Pack.
| Subtopic _______________________________________ | Page Number _____________ | Exercise _________ | Recommended Questions _________________________ | Handwritten Worked Solutions __________________________ |
| Finding the Greatest Common Divisor (GCD) | Page 318 | Ex 16.3 | Q1a,c,e,g,i | In Online Study Pack |
| Expressing GCD in the form xa + yb = d | Page 320 | Ex 16.4 | Q1,2,3,4 | In Online Study Pack |
| Number Bases | Page 322 | Ex 16.5 | Q1a-d,2a-f | In Online Study Pack |
| Further Number Theory - SQA Questions | SQA Questions & Answers | In Online Study Pack |
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14. AH Maths Practice Unit Assessments – Solutions Included
Thanks to maths777 for making the excellent resources freely available for all to use. This will prove a fantastic resource in helping you prepare for assessments, tests and the final exam.
| Methods in Algebra & Calculus __________________________ | Applications of Algebra & Calculus ____________________________ | Geometry, Proof & Systems of Equations ____________________________________ |
| Practice 1 | Practice 1 | Practice 1 |
| Practice 2 | Practice 2 | Practice 2 |
| Practice 3 | Practice 3 | Practice 3 |
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15. AH Maths Video Links
Please click DLB Maths to view AH Maths Past Paper video solutions. There are also many videos showing worked examples by topic on the St Andrews StAnd Maths YouTube Channel link. Both video links are excellent resources in helping you prepare for assessments, tests and the final exam.
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16. 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.
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17. Advanced Higher Maths Online Study Pack
Through step-by-step worked solutions to exam questions and recommended MIA text book questions available in the Online Study Pack we cover everything you need to know about the Euclidean Algorithm to pass your final exam.
For students looking for a ‘good’ pass at AH Maths you may wish to consider subscribing to the fantastic additional exam focused resources available in the Online Study Pack. Subscribing could end up being one of your best ever investments.
Please give yourself every opportunity for success, speak with your parents, and subscribe to the exam focused Online Study Pack today.
We hope the resources on this website prove useful and wish you the very best of success with your AH Maths course in 2025.
Topic Links
Free resources to dozens of AH Maths topics are available by clicking on any of the links to the right.
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