Let the fantastic wealth of resources below teach you all about Integration by Substitution.
Covers the whole of the AH Maths course
Created by an experienced maths teacher
Resources used with students in Scottish Secondary Schools
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A sound understanding of Integration by Substitution 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 2019/20 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 2019/20.
Please find below:
1. AH Maths Past Exam Worksheets by Topic
4. Further Integration Resources
5. MIA Text Book Questions – Integration
6. MIA Text Book Questions – Further Integration
7. About Integration by Substitution
8. AH Maths Past and Practice Papers
9. AH Maths Past Paper Questions by Topic
11. Exam Focused Online Study Pack – For students looking for a ‘good’ Pass
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1. 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 Higher Maths Questions below are available in the Online Study Pack.
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. Integration Resources
Thanks to the author(s) for making these available.
Integration Theory Guide | HERE |
Integration HSN Summary Notes | HERE |
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4. Further Integration Resources
Thanks to the author(s) for making these available.
Further Integration Theory Guide 1 | HERE |
Further Integration Theory Guide 2 | HERE |
Further Integration HSN Summary Notes | HERE |
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5. MIA Text Book Questions – Integration
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.
Subtopic ______________________________________ | Page No __________ | Exercise ___________ | Recommended Questions _____________________ |
Integration (Higher Revision) | Page 100 | Exercise 7.1 | Q1a-i,2a-i,3a-l,4a-f |
Integration by Substitution | Page 103 | Exercise 7.2 | Q1a,c,e,g,i,k,m,o,q,s,u,w |
Integration by Substitution - Extra Revision! | Page 103 | Exercise 7.2 | Q1b,d,f,h,j,l,n,p,r,t,v,x |
Further Integration by Substitution | Page 105 | Exercise 7.3 | Q2a,b,c,d,4a,b,c,d |
Further Integration by Substitution | Page 105 | Exercise 7.3 | Q6a,b,c,d |
Further Int'n by Sub'n - sin^m(x), cos^n(x) | Page 105 | Exercise 7.3 | Q7a,b,c,d,e,f |
Further Integration by Substitution - logs | Page 105 | Exercise 7.3 | Q11a,b,c,d |
Substitution & Definite Integrals | Page 107 | Exercise 7.4 | Q1a,c,e,g,i,k |
Area between curve & x-axis | Page 120 | Exercise 7.10 | Q1,3 |
Area between curve & y-axis | Page 120 | Exercise 7.10 | Q6,7 |
Volume - revolved around x-axis SQA Question | 2014 Q10 (SQA) | ||
Volume - revolved around y-axis SQA Question | 2017 Q16 (SQA) | ||
Volume - revolved around x-axis | Page 120 | Exercise 7.10 | Q11,12 |
Applications of Integral Calculus | Page 187 | Exercise 11.1 | Q4,14 |
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6. MIA Text Book Questions – Further Integration
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.
Subtopic ______________________________________ | Page No __________ | Exercise _________________ | Recommended Questions __________________________ |
Integration using Inverse Trig Functions | Page 111 | Exercise 7.6 | Q1,2,3,4a,b |
Integration using Partial Fractions | Page 113 | Exercise 7.7 | Q1a,b,2a,b,3a,b,4a,b,5a,b,6a,b |
Integration by Parts - 1 | Page 116 | Exercise 7.8 | Q1a-l |
Integration by Parts - 2 | Page 116 | Exercise 7.8 | Q2a,c,d,e,f,g,h |
Integration by Parts - 3 | Page 116 | Exercise 7.8 | Q5a,b,Q6a,b |
Integration by Parts - Special Cases - 1 | Page 118 | Exercise 7.9 | Q1a,b,c,d |
Integration by Parts - Special Cases - 2 | Page 118 | Exercise 7.9 | Q2a,b,c,d,e |
First Order Diff Eqns - General Soln | Page 128 | Exercise 8.1 | Q1a-j |
First Order Diff Eqns - Particular Soln | Page 128 | Exercise 8.1 | Q2a-g |
Differential Equations in Context | Page 131 | Exercise 8.2 | Q2,4,5,6 |
7. About Integration by Substitution
Recommended questions from the Maths In Action (2nd Edition) by Edward Mullan text book are shown below.
Integration by substitution
Note that the answer for an indefinite integral must always be expressed in terms of the original variable.
Example
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Exam Question
Source: SQA AH Maths Paper 2017 Question 6
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8. 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.
Year ____ | Paper Type _________________ | Exam Paper ______________ | Marking Scheme _______________________________________ |
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 |
9. 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.
10. 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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11. 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 Integration by Substitution 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 2019/20.
Topic Links
Free resources to dozens of AH Maths topics are available by clicking on any of the links to the right.