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Unsure about the Product Rule?

Unsure about the Product Rule?

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Covers the whole of the AH Maths course

Created by an experienced maths teacher

Resources used with students in Scottish Secondary Schools

The Product Rule

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. Links and Exam Formulae

2. Differentiation Resources

3. Further Differentiation Resources

4. MIA Text Book Questions – Differentiation

5. MIA Text Book Questions – Further Differentiation

6. About The Product Rule

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

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Advanced Higher Maths Resources

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1. 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

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2. Differentiation Resources

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

Differentiation Theory Guide 1HERE
Differentiation Theory Guide 2HERE
Differentiation HSN Summary NotesHERE

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3. Further Differentiation Resources

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

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

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4. MIA Text Book Questions – Differentiation

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 Number
____________		Exercise
___________		Recommended Questions
_______________________
Derivative from First PrinciplesPage 45Exercise 4.1Q1,3,5,7
The Chain RulePage 48Exercise 4.3Q1a,d,2a,c,3b,4a,5a
The Product RulePage 51Exercise 4.5Q1a-h,Q2b,Q3a-l
The Quotient RulePage 52Exercise 4.6Q1,2,3,4
Differentiation - A Mixture!Page 53Exercise 4.7Q1,2,3,4,5
Sec, Cosec & CotPage 55Exercise 4.8Q1a,b,2a,c,d,3a,c,e,g
Exponential FunctionsPage 58Exercise 4.9Q1a,c,e,2a,3e,4a,b,5a,e
Logarithmic FunctionsPage 58Exercise 4.9Q1k,m,o,q,s,2f,g,3a,b,c,4d,e,5d
Nature & Sketching PolynomialsPage 70Exercise 5.5Q1a,b,c,2a,b
ConcavityPage 73Exercise 5.7Q5a,b,c,Q1a,b
ApplicationsPage 187Ex 11.1Q1a,b,e,f,2a,c,3a,c

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5. MIA Text Book Questions – Further Differentiation 

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 Number
_____________		Exercise
______________		Recommended Questions
_____________________
Inverse Trig Functions & Chain RulePage 85Exercise 6.2Q1a,b,c,Q2b,c,dQ3a,d
Inverse Trig Fns & Product/Quotient RulesPage 86Exercise 6.3Q2,Q3
Implicit & Explicit Functions - 1Page 89Exercise 6.4Q1,Q2
Implicit & Explicit Functions - 2Page 89Exercise 6.4Q5,Q9,Q4
Second Derivatives of Implicit FunctionsPage 90Exercise 6.5Q1a,d,f,k(i),6
Logarithmic DifferentiationPage 92Exercise 6.6Q1,Q2
Parametric EquationsPage 95Exercise 6.7Q1a,b,c
Parametric Eqns - Differentiation Page 96Exercise 6.8Q1,2,3
Parametric Eqns - Differentiation (Alternative)Page 96Exercise 6.8Q1(i)
Parametric Eqns - Differentiation (Alternative)Page 96Exercise 6.8Q1(ii),Q2,Q3
Applications of Further DifferentiationPage 193Exercise 11.2Q1,Q2,Q3

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6. 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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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
_______________________________________
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

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8. AH Maths Past Paper Questions by Topic

Worked solutions to SQA Exam Questions available in the Online Study Pack.

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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

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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 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.

Get the Study Pack - just £9.99

Teachers click here >

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