Sign In
Unsure about Integration by Substitution?

Unsure about Integration by Substitution?

Let the fantastic wealth of resources below teach you all about Integration by Substitution.

Get the Study Pack - just £9.99

Teachers click here >

Covers the whole of the AH Maths course

Created by an experienced maths teacher

Resources used with students in Scottish Secondary Schools

Integration by Substitution

Welcome to advancedhighermaths.co.uk

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

2. Links and Exam Formulae

3. Integration Resources

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

10. Recommended AH Book

11. Exam Focused Online Study Pack – For students looking for a ‘good’ Pass

.

Advanced Higher Maths Resources

.

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.

Number
______		Topic
____________________________________________		Answers
_________
1Binomial TheoremAnswers
2Complex NumbersAnswers
3DifferentiationAnswers
4Differentiation (Further)Answers
5Differential Equations - Variables SeparableAnswers
6Differential Equations (Further)Answers
7Functions & GraphsAnswers
8IntegrationAnswers
9Integration (Further)Answers
10MatricesAnswers
11Number Theory - Methods of ProofAnswers
12Number Theory (Further) - Euclidean & Number BasesAnswers
13Partial FractionsAnswers
14Sequences & SeriesAnswers
15 Sequences & Series - Maclaurin Answers
16Systems of EquationsAnswers
17VectorsAnswers

2. Links and Exam Formulae

AH Maths - Home Page LinkHERE
AH Maths - Whole Course LinkHERE
AH Maths - Exam Formula ListHERE
Higher Maths - Exam Formulae ListHERE
AH Maths - Complete Formula ListHERE
SQA Full Course Content and OutlineHERE

.

3. Integration Resources

Thanks to the author(s) for making these available.

Integration Theory Guide HERE
Integration HSN Summary NotesHERE

.


4. Further Integration Resources

Thanks to the author(s) for making these available.

Further Integration Theory Guide 1HERE
Further Integration Theory Guide 2HERE
Further Integration HSN Summary NotesHERE

.

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 100Exercise 7.1Q1a-i,2a-i,3a-l,4a-f
Integration by SubstitutionPage 103Exercise 7.2Q1a,c,e,g,i,k,m,o,q,s,u,w
Integration by Substitution - Extra Revision!Page 103Exercise 7.2Q1b,d,f,h,j,l,n,p,r,t,v,x
Further Integration by SubstitutionPage 105Exercise 7.3Q2a,b,c,d,4a,b,c,d
Further Integration by SubstitutionPage 105Exercise 7.3Q6a,b,c,d
Further Int'n by Sub'n - sin^m(x), cos^n(x)Page 105Exercise 7.3Q7a,b,c,d,e,f
Further Integration by Substitution - logsPage 105Exercise 7.3Q11a,b,c,d
Substitution & Definite IntegralsPage 107Exercise 7.4Q1a,c,e,g,i,k
Area between curve & x-axisPage 120Exercise 7.10Q1,3
Area between curve & y-axisPage 120Exercise 7.10Q6,7
Volume - revolved around x-axis SQA Question2014 Q10 (SQA)
Volume - revolved around y-axis SQA Question2017 Q16 (SQA)
Volume - revolved around x-axisPage 120Exercise 7.10Q11,12
Applications of Integral CalculusPage 187Exercise 11.1Q4,14

.

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 FunctionsPage 111Exercise 7.6Q1,2,3,4a,b
Integration using Partial FractionsPage 113Exercise 7.7Q1a,b,2a,b,3a,b,4a,b,5a,b,6a,b
Integration by Parts - 1Page 116Exercise 7.8Q1a-l
Integration by Parts - 2Page 116Exercise 7.8Q2a,c,d,e,f,g,h
Integration by Parts - 3Page 116Exercise 7.8Q5a,b,Q6a,b
Integration by Parts - Special Cases - 1Page 118Exercise 7.9 Q1a,b,c,d
Integration by Parts - Special Cases - 2Page 118Exercise 7.9Q2a,b,c,d,e
First Order Diff Eqns - General SolnPage 128Exercise 8.1Q1a-j
First Order Diff Eqns - Particular SolnPage 128Exercise 8.1Q2a-g
Differential Equations in ContextPage 131Exercise 8.2Q2,4,5,6

.

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

  • is useful when the derivative of one part of the integrand is related to another part of the integrand
  • involves rewriting the entire integral (including the ” dx ” and any limits) in terms of another variable before integrating

Note that the answer for an indefinite integral must always be expressed in terms of the original variable.

Example

.

Exam Question

Source: SQA AH Maths Paper 2017 Question 6

.


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
_______________________________________
2019AH SpecimenSpecimenMarking Scheme
2019Advanced HigherExam PaperMarking Scheme
2018Advanced HigherExam PaperMarking Scheme
2017Advanced HigherExam PaperMarking Scheme
2016Advanced HigherExam PaperMarking Scheme
2016AH SpecimenSpecimenMarking Scheme
2016AH ExemplarExemplarMarking Scheme
2015Advanced HigherExam PaperMarking Scheme
2014Advanced HigherExam PaperMarking Scheme
2013Advanced HigherExam PaperMarking Scheme
2012Advanced HigherExam PaperMarking Scheme
2011Advanced HigherExam PaperMarking Scheme
2010Advanced HigherExam PaperMarking Scheme
2009Advanced HigherExam PaperMarking Scheme
2008Advanced HigherExam PaperMarking Scheme
2007Advanced HigherExam PaperMarking Scheme
2006Advanced HigherExam PaperMarking Scheme
2005Advanced HigherExam PaperMarking Scheme
2004Advanced HigherExam PaperMarking Scheme
2003Advanced HigherExam PaperMarking Scheme
2002Advanced HigherExam PaperMarking Scheme
2001Advanced HigherExam 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.

.
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
_________________
Specimen P1MarkingQ2Q4Q6Q8Q3Q5Q1Q7
Specimen P2MarkingQ3Q1Q2,4,8,10Q7Q11Q5Q13Q9Q6Q12
2019MarkingQ9Q4Q1a,b,6Q1c,5,10Q16bQ16aQ3Q18Q7,17Q2Q15Q11,14Q12Q13Q8
2018MarkingQ3Q2Q1bQ1a,c,6,13Q8Q15aQ16aQ4,10Q14Q17Q7,11Q16Q9,12Q5Q15b
2017MarkingQ1Q2Q3Q11,18Q16Q6Q12Q5Q17Q4,10Q7Q15Q13Q8Q9Q14
2016MarkingQ3Q13Q1a,bQ1c,11Q13Q9Q12Q4Q8Q2Q6Q7Q14Q5,10Q16Q15
2015MarkingQ1,9Q2Q4,6,8Q17Q10Q14Q13Q3Q5,11Q15Q12Q7Q18Q16
2014MarkingQ214bQ1,13Q1,4,6Q10,12Q15Q11Q3Q16Q14Q9Q7Q5Q7Q8
2013MarkingQ1Q2Q11Q4,6Q8Q13Q7,10Q17Q3Q15Q9,12Q5Q16Q14
2012MarkingQ415aQ1Q12,13Q8Q11Q7Q14Q3,16bQ2Q6Q9Q516aQ10Q15
2011MarkingQ2Q13b,73aQ1,11aQ1,11,16Q6Q10Q8,13Q5Q4Q15Q12Q9Q14
2010MarkingQ5Q1Q13Q15Q3,7Q10Q16Q2Q9Q4,14Q6Q8,12Q11
2009MarkingQ8Q14Q1aQ1b,11Q5,7Q9Q1316aQ6Q12Q14Q2Q16Q4Q10Q3Q15
2008MarkingQ8Q4Q10,15Q2,5Q4,9,10Q7Q3Q16Q1Q12Q6Q14Q11Q13
2007MarkingQ1Q4Q2Q13Q4,10Q4Q16Q3,11Q9Q6Q5Q15Q12Q7Q14Q8
MixedMixedMixedMixedMixedMixedMixedMixedMixedMixedMixedMixedMixedMixedMixedMixedMixed

.

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.
.


. 

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.

Get the Study Pack - just £9.99

Teachers click here >

  • 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

  • Mr M, Whole School Subscriber

    “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

Not just Integration by Substitution, but 70 other maths concepts covered in detail

Topic Links

Free resources to dozens of AH Maths topics are available by clicking on any of the links to the right.

Buy today

For Students

To ensure your success in 2019/20 there is a wealth of fantastic additional AH Maths exam focused resources for less than the cost of a text book.

Just £9.99 for a year

Buy now >

Buy now with PayPal

For Schools

Schools can get the AH Maths Online Study Pack also. Unlimited use for all the teachers and students in your school.

Just £99.99 for a year

Buy now >

Buy now with PayPal

Join our mailing list

  • This field is for validation purposes and should be left unchanged.

Follow us

Copyright © 2020 National 5 Maths
All rights reserved
Privacy Policy & Cookies
Site terms & conditions

Site by Inigo

SQA material is copyright © Scottish Qualifications
Authority and reproduced with permission from SQA.