Let the fantastic wealth of resources below teach you all about the Product Rule.
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 the Product Rule 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 Differentiation Resources
5. MIA Text Book Questions – Differentiation
6. MIA Text Book Questions – Further Differentiation
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. Differentiation Resources
Thanks to the author(s) for making these available.
Differentiation Theory Guide 1 | HERE |
Differentiation Theory Guide 2 | HERE |
Differentiation HSN Summary Notes | HERE |
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4. Further Differentiation Resources
Thanks to the author(s) for making these available.
Further Differentiation Theory Guide 1 | HERE |
Further Differentiation Theory Guide 2 | HERE |
Further Differentiation HSN Summary Notes | HERE |
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5. MIA Text Book Questions – Differentiation
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 Number ____________ | Exercise ___________ | Recommended Questions _______________________ |
Derivative from First Principles | Page 45 | Exercise 4.1 | Q1,3,5,7 |
The Chain Rule | Page 48 | Exercise 4.3 | Q1a,d,2a,c,3b,4a,5a |
The Product Rule | Page 51 | Exercise 4.5 | Q1a-h,Q2b,Q3a-l |
The Quotient Rule | Page 52 | Exercise 4.6 | Q1,2,3,4 |
Differentiation - A Mixture! | Page 53 | Exercise 4.7 | Q1,2,3,4,5 |
Sec, Cosec & Cot | Page 55 | Exercise 4.8 | Q1a,b,2a,c,d,3a,c,e,g |
Exponential Functions | Page 58 | Exercise 4.9 | Q1a,c,e,2a,3e,4a,b,5a,e |
Logarithmic Functions | Page 58 | Exercise 4.9 | Q1k,m,o,q,s,2f,g,3a,b,c,4d,e,5d |
Nature & Sketching Polynomials | Page 70 | Exercise 5.5 | Q1a,b,c,2a,b |
Concavity | Page 73 | Exercise 5.7 | Q5a,b,c,Q1a,b |
Applications | Page 187 | Ex 11.1 | Q1a,b,e,f,2a,c,3a,c |
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6. MIA Text Book Questions – Further Differentiation
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 Number _____________ | Exercise ______________ | Recommended Questions _____________________ |
Inverse Trig Functions & Chain Rule | Page 85 | Exercise 6.2 | Q1a,b,c,Q2b,c,dQ3a,d |
Inverse Trig Fns & Product/Quotient Rules | Page 86 | Exercise 6.3 | Q2,Q3 |
Implicit & Explicit Functions - 1 | Page 89 | Exercise 6.4 | Q1,Q2 |
Implicit & Explicit Functions - 2 | Page 89 | Exercise 6.4 | Q5,Q9,Q4 |
Second Derivatives of Implicit Functions | Page 90 | Exercise 6.5 | Q1a,d,f,k(i),6 |
Logarithmic Differentiation | Page 92 | Exercise 6.6 | Q1,Q2 |
Parametric Equations | Page 95 | Exercise 6.7 | Q1a,b,c |
Parametric Eqns - Differentiation | Page 96 | Exercise 6.8 | Q1,2,3 |
Parametric Eqns - Differentiation (Alternative) | Page 96 | Exercise 6.8 | Q1(i) |
Parametric Eqns - Differentiation (Alternative) | Page 96 | Exercise 6.8 | Q1(ii),Q2,Q3 |
Applications of Further Differentiation | Page 193 | Exercise 11.2 | Q1,Q2,Q3 |
7. About The Product Rule
For a more detailed explanation, please first read the Theory Guides above.
The Product Rule is used to find the derivatives of products of functions.
It can be expressed as:
or ((f (x)) g(x))’ = f ‘(x) g (x ) + f (x) g ‘(x)
When using the Product Rule, answers should always be simplified as far as possible.
Examples
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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
Worked solutions to SQA Exam Questions 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 the Product Rule 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.