The Product Rule

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A sound understanding of the Product Rule is essential to ensure exam success.

Please find resources for all other Maths courses HERE.

For students looking for a ‘good’ pass at AH Maths in 2019 you may wish to consider subscribing to the fantastic additional exam focused resources available in the Online Study Pack.

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We hope you find this website useful and wish you the very best with your studies.

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

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. 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

3. 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

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 ___________	Questions ____________________________	Worked Solutions _______________
Derivative from First Principles	Page 45	Exercise 4.1	Q1,3,5,7	HERE
The Chain Rule	Page 48	Exercise 4.3	Q1a,d,2a,c,3b,4a,5a	HERE
The Product Rule	Page 51	Exercise 4.5	Q1a-h,Q2b,Q3a-l	HERE
The Quotient Rule	Page 52	Exercise 4.6	Q1,2,3,4	HERE
Differentiation - A Mixture!	Page 53	Exercise 4.7	Q1,2,3,4,5	HERE
Sec, Cosec & Cot	Page 55	Exercise 4.8	Q1a,b,2a,c,d,3a,c,e,g	HERE
Exponential Functions	Page 58	Exercise 4.9	Q1a,c,e,2a,3e,4a,b,5a,e	HERE
Logarithmic Functions	Page 58	Exercise 4.9	Q1k,m,o,q,s,2f,g,3a,b,c,4d,e,5d	HERE
Nature & Sketching Polynomials	Page 70	Exercise 5.5	Q1a,b,c,2a,b	HERE
Concavity	Page 73	Exercise 5.7	Q5a,b,c,Q1a,b	HERE
Applications	Page 187	Ex 11.1	Q1a,b,e,f,2a,c,3a,c	HERE

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 ___________	Questions ___________________	Worked Solutions _______________
Inverse Trig Functions & Chain Rule	Page 85	Exercise 6.2	Q1a,b,c,Q2b,c,dQ3a,d	HERE
Inverse Trig Fns & Product/Quotient Rules	Page 86	Exercise 6.3	Q2,Q3	HERE
Implicit & Explicit Functions - 1	Page 89	Exercise 6.4	Q1,Q2	HERE
Implicit & Explicit Functions - 2	Page 89	Exercise 6.4	Q5,Q9,Q4	HERE
Second Derivatives of Implicit Functions	Page 90	Exercise 6.5	Q1a,d,f,k(i),6	HERE
Logarithmic Differentiation	Page 92	Exercise 6.6	Q1,Q2	HERE
Parametric Equations	Page 95	Exercise 6.7	Q1a,b,c	HERE
Parametric Eqns - Differentiation	Page 96	Exercise 6.8	Q1,2,3	HERE
Parametric Eqns - Differentiation (Alternative)	Page 96	Exercise 6.8	Q1(i)	HERE
Parametric Eqns - Differentiation (Alternative)	Page 96	Exercise 6.8	Q1(ii),Q2,Q3	HERE
Applications of Further Differentiation	Page 193	Exercise 11.2	Q1,Q2,Q3	HERE

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

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

Worked solutions to SQA Exam Questions 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 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.

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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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