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 Loci in the Complex Plane 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:
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. Complex Numbers Resources
Thanks to the author(s) for making these available.
|Complex Numbers Theory Guide 1||HERE|
|Complex Numbers Theory Guide 2||HERE|
|Complex Numbers Theory Guide (HSN)||HERE|
4. MIA Text Book Questions – Complex Numbers
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.
|Arithmetic with Complex Numbers||Page 207||Exercise 12.1||Q1,2,3,6,7,8|
|Division & Square Roots of Complex Nos||Page 209||Exercise 12.2||Q1a,b,c,2c,e,3a,b,f,5a,b|
|Argand Diagrams||Page 211||Exercise 12.3||Q3a,b,d,e,f,i,6a,b,f,7a,b,c|
|Multiplying/Dividing in Polar Form||Page 215||Exercise 12.5||Q1a,b,f,g|
|De Moivre's Theorem||Page 218||Exercise 12.6||Q1,2,3a,4g,h,i,j|
|Polynomials & Complex Numbers||Page 224||Exercise 12.8||Q2a,d,3a,b,4,5,6a,b|
|Loci on the Complex Plane||Page 213||Exercise 12.4||Q1a,b,d,f,j,3a,b,4a,b,c|
|Expanding Trig Formula||Page 219||Exercise 12.6||Q5,6,7a|
|Roots of a Complex Number||Page 222||Exercise 12.7||Q2a,b,c,d,e,f,1a(i)|
5. About Loci in the Complex Plane
For a more detailed explanation, please first read the Theory Guides above.
If the modulus of a complex number is restricted then a locus of the point is created as it moves on the complex plane.
Example | z | = 3 or arg (z) = Π/3
The complex number moves in the complex plane subject to the condition |z| = 3
(i) Find the equation of the locus of z
(ii) Interpret the locus geometrically
The locus of z is the set of points on the circumference of a circle centre (0,0) and radius 3
Source: SQA AH Maths Paper 2011 Question 10
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|
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 Loci in the Complex Plane 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.
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Free resources to dozens of AH Maths topics are available by clicking on any of the links to the right.