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 of Asymptotes 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 2020/21 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 2020/21.
Please find below:
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.
|5||Differential Equations - Variables Separable||Answers|
|6||Differential Equations (Further)||Answers|
|7||Functions & Graphs||Answers|
|11||Number Theory - Methods of Proof||Answers|
|12||Number Theory (Further) - Euclidean & Number Bases||Answers|
|14||Sequences & Series||Answers|
|15||Sequences & Series - Maclaurin||Answers|
|16||Systems of Equations||Answers|
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. Functions and Graphs Resources
Thanks to the author(s) for making these available.
|Functions & Graphs Theory Guide||HERE|
|Functions & Graphs HSN Summary Notes||HERE|
4. MIA Text Book Questions – Functions and Graphs
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.
|Sketching Modulus Function y = |x|||Page 66||Exercise 5.2||Q1-9|
|Inverse Functions||Page 67||Exercise 5.3||Q1a,c,e,g,i,2a,c,e,3|
|Odd & Even Functions||Page 74||Exercise 5.8||Q3a-l|
|Vertical Asymptotes & Behaviour||Page 75||Exercise 5.9||Q1a-f|
|Horizontal & Oblique Asymptotes||Page 76||Exercise 5.10||Q1a,b,f,g,k,l|
|Sketching Graphs||Page 77||Exercise 5.11||Q1a,c,e,i,k|
5. About Asymptotes
For a more detailed explanation, please first read the Theory Guides above.
Consider y = 1/x
Vertical asymptotes of y = 1/x
Look at the denominator
Since x cannot be zero then y is undefined
Therefore there is a vertical asymptote at x = 0
Behaviour either side of the V.A.
If y is +’ve (x > 0) there is positive infinity – approaches from right
If y is -‘ve (x < 0) there is negative infinity – approaches from left
or, use a table below and go either side of the asymptote:
y = 1/x
|x|| - 0.1 (left of asymptote)|
| 0 (asymptote)|
| + 0.1 (right of asymptote)
|y||-'ve value||+'ve value|
|Curve||Approaches asymptote from left||Approaches asymptote from right|
.Non-vertical asymptotes of y = 1/x
Ask, is synthetic division required? (no – since degree of numerator is not ≥ degree of denominator)
As x ⇒ +/- ∞, y ⇒ 0
Therefore y = 0 is a horizontal asymptotes
Behaviour either side of the horizontal asymptote
Use the table below to help us understand the behaviour.
y = 1/x
|x||+ infinity||- infinity|
|y||+'ve value||-'ve infinity|
|Curve||Approaches asymptote from above||Approaches asymptote from below|
Analysis of both the vertical and horizontal asymptotes above, the sketch below can be drawn:
Given y = (x + 3)/((x + 2)
Synthetic division required (since the degree of numerator ≥ degree of denominator)
Here we divide to get:
y = 1 + 1/(x + 2)
Horizontal asymptote y = 1
Vertical asymptote x = -2
Source: SQA AH Maths Paper 2001 Question A8
6. 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.
|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||Marking Scheme|
7. 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.
|Systems of |
8. 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.
9. 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 Asymptotes 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 2020/21.
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Free resources to dozens of AH Maths topics are available by clicking on any of the links to the right.