Trig Function Integration

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A sound understanding of how to Integrate Trig Functions is essential to ensure exam success.

Please find resources for all other Maths courses HERE.

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Please find below:

1. Links and Exam Formulae

2. Integration Resources

3. Further Integration Resources

4. MIA Text Book Questions – Integration

5. MIA Text Book Questions – Further Integration

6. About Integrating Trig Functions

7. AH Maths Past and Practice Papers

8. AH Maths Past Paper Questions by Topic

9. Recommended AH Book

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

Advanced Higher Maths Resources

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. Integration Resources

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

Integration Theory Guide	HERE
Integration HSN Summary Notes	HERE

3. 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

4. MIA Text Book Questions – Integration

Recommended questions from the new MIA Text Book are shown below.

Worked solutions to all questions below are available in the Online Study Pack.

Subtopic ______________________________________	Page No __________	Exercise ___________	Questions _____________________	Worked Solutions ______________________
Integration (Higher Revision)	Page 100	Exercise 7.1	Q1a-i,2a-i,3a-l,4a-f	HERE
Integration by Substitution	Page 103	Exercise 7.2	Q1a,c,e,g,i,k,m,o,q,s,u,w	HERE
Integration by Substitution - Extra Revision!	Page 103	Exercise 7.2	Q1b,d,f,h,j,l,n,p,r,t,v,x	HERE
Further Integration by Substitution	Page 105	Exercise 7.3	Q2a,b,c,d,4a,b,c,d	HERE
Further Integration by Substitution	Page 105	Exercise 7.3	Q6a,b,c,d	HERE
Further Int'n by Sub'n - sin^m(x), cos^n(x)	Page 105	Exercise 7.3	Q7a,b,c,d,e,f	HERE
Further Integration by Substitution - logs	Page 105	Exercise 7.3	Q11a,b,c,d	HERE
Substitution & Definite Integrals	Page 107	Exercise 7.4	Q1a,c,e,g,i,k	HERE
Area between curve & x-axis	Page 120	Exercise 7.10	Q1,3	HERE
Area between curve & y-axis	Page 120	Exercise 7.10	Q6,7	HERE
Volume - revolved around x-axis SQA Question			2014 Q10 (SQA)	In Online Study Pack
Volume - revolved around y-axis SQA Question			2017 Q16 (SQA)	In Online Study Pack
Volume - revolved around x-axis	Page 120	Exercise 7.10	Q11,12	HERE
Applications of Integral Calculus	Page 187	Exercise 11.1	Q4,14	HERE

5. MIA Text Book Questions – Further Integration

Recommended questions from the new MIA Text Book are shown below.

Worked solutions to all questions below are available in the Online Study Pack.

Subtopic ______________________________________	Page No __________	Exercise ___________	Questions _____________________	Worked Solutions _______________
Integration using Inverse Trig Functions	Page 111	Exercise 7.6	Q1,2,3,4a,b	HERE
Integration using Partial Fractions	Page 113	Exercise 7.7	Q1a,b,2a,b,3a,b,4a,b,5a,b,6a,b	HERE
Integration by Parts - 1	Page 116	Exercise 7.8	Q1a-l	HERE
Integration by Parts - 2	Page 116	Exercise 7.8	Q2a,c,d,e,f,g,h	HERE
Integration by Parts - 3	Page 116	Exercise 7.8	Q5a,b,Q6a,b	HERE
Integration by Parts - Special Cases - 1	Page 118	Exercise 7.9	Q1a,b,c,d	HERE
Integration by Parts - Special Cases - 2	Page 118	Exercise 7.9	Q2a,b,c,d,e	HERE
First Order Diff Eqns - General Soln	Page 128	Exercise 8.1	Q1a-j	HERE
First Order Diff Eqns - Particular Soln	Page 128	Exercise 8.1	Q2a-g	HERE
Differential Equations in Context	Page 131	Exercise 8.2	Q2,4,5,6	HERE

6. About Integrating Trig Functions

For a more detailed explanation, please first read the Theory Guides above.

You are required to know how to apply the following standard integrals although they are given on the exam formulae list.

The above standard integrals can be extended.

Example

7. 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 _________________
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
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

8. 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
_________________

Q4 ,6 ,8

Q1 ,4 ,6

Q4 ,9 ,10

.

9. 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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10. 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 Integrating Trig Functions 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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