Unsure about Sketching the Modulus Function?

Unsure about Sketching the Modulus Function?

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Sketching the Modulus Function

Welcome to advancedhighermaths.co.uk

A sound understanding of how to Sketch the Modulus Function 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.

To return to the Home Page please click HERE.

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. Functions and Graphs Resources

3. MIA Text Book Questions – Functions and Graphs 

4. About Sketching the Modulus Function

5. AH Maths Past & Practice Papers

6. AH Maths Past Paper Questions by Topic

7. AH Maths Recommended Text Book

8. 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. Functions and Graphs Resources

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

Functions & Graphs Theory GuideHERE
Functions & Graphs HSN Summary Notes HERE

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3. MIA Text Book Questions – Functions and Graphs 

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
_______________
Sketching Modulus Function y = |x|Page 66Exercise 5.2Q1-9HERE
Inverse FunctionsPage 67Exercise 5.3Q1a,c,e,g,i,2a,c,e,3 HERE
Odd & Even FunctionsPage 74Exercise 5.8Q1a-lHERE
Vertical Asymptotes & BehaviourPage 75Exercise 5.9Q1a-fHERE
Horizontal & Oblique AsymptotesPage 76Exercise 5.10Q1a,b,f,g,k,lHERE
Sketching GraphsPage 77Exercise 5.11Q1a,c,e,i,kHERE

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4. About Sketching the Modulus Function

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

The modulus, or absolute value, of x is denoted by |x|.

|x| is always a positive numerical value of regardless of whether x itself is positive or negative.

Given a function of f(x), since |f(x)| is always positive, the graph of |f(x)| will lie entirely on or above the x-axis.

The graph of |f(x)| is obtained from f(x) by:

  1. Leaving the section of the graph of f(x) which lies on or above the x-axis unchanged
  2. Reflecting, in the x-axis, the section of the graph of f(x) which lies below the x-axis

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Example

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5. 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
_________________
2018Advanced HigherExam PaperMarking Scheme
2017Advanced HigherExam PaperMarking Scheme
2016Advanced HigherExam PaperMarking Scheme
2016AH SpecimenSpecimen
2016AH ExemplarExemplarExemplar Guidance
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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6. 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.

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Paper
______
.
Marking
______
Binomial
Theorem
________
Partial
Fractions
________
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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
_________________
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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7. 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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8. 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 Sketching the Modulus Function 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 2018/19.

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