Let the fantastic wealth of resources below teach you all about Proof by Counterexample.
Covers the whole of the AH Maths course
Created by an experienced maths teacher
Resources used with students in Scottish Secondary Schools
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A sound understanding of Proof by Counterexample 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. AH Maths Past Exam Worksheets by Topic
4. Methods of Proof Worksheets and Solutions
5. About Proof by Counterexample
6. AH Maths Past & Practice Papers
7. AH Maths Past Paper Questions by Topic
8. AH Maths Recommended Text Book
9. Exam Focused Online Study Pack – For students looking for a ‘good’ Pass
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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.
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. Methods of Proof Resources
Thanks to the author(s) for making these available.
Methods of Proof Theory Guide 1 | HERE |
Methods of Proof Theory Guide 2 | HERE |
Methods of Proof HSN Summary Notes | HERE |
4. Methods of Proof Worksheets and Solutions
Thanks to the author(s) for making these available.
Topic _______________________________ | Lessons __________ | Questions _________ | Typed Solutions _______________ | Handwritten Solutions ______________________ | Exam Questions - Worked Solutions in Online Study Pack ______________________________________________________ |
Direct Proof | Lesson 1 | Ex 1 & 2 | Ex 1 & 2 Handwritten Solns | 2018-Q9,2015-Q12, 2010-Q8a | |
Proof by Counterexample | Lesson 2 | Ex 3 | Ex 3 Typed Solns | Ex 3 Handwritten Solns | 2016-Q10, 2013-Q12, 2008-Q11 |
Proof by Counterexample | Ex 4 | Ex 4 Typed Solns | Ex 4 Handwritten Solns | 2016-Q10, 2013-Q12, 2008-Q11 | |
Proof by Contradiction | Lesson 3 | Ex 5 | Ex 5 Typed Solns | Ex 5 Handwritten Solns | 2010-Q12 |
Proof by Contrapositive | Lesson 4 | Ex 6 | Ex 6 Typed Solns | Ex 6 Handwritten Solns | 2017-Q13 |
Proof by Induction | Lesson 5 | Ex 7 | Ex 7 Typed Solns | Ex 7 Handwritten Solns | 2014-Q7,2013-Q9,2012-Q16a,2011-Q12,2010-Q8b,2009-Q4,2007-Q12 |
Proof by Induction - Sigma Notation | Lesson 6 | Ex 8 | Ex 8 Typed Solns | Ex 8 Handwritten Solns | 2018-Q12,2016-Q5, 2013-Q9,2009-Q4 |
5. About Proof by Counterexample
For a more detailed explanation, please first read the Theory Guides above.
Here, if you can find one example to disprove the statement, then it must be false.
Example
For all values of x, where x ∈ W, 5x > 4x
Solution
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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.
Year ____ | Paper Type _________________ | Exam Paper ______________ | Marking Scheme _______________________________________ |
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 |
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7. AH Maths Past Paper Questions by Topic
Worked solutions to SQA Exam Questions available in the Online Study Pack.
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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.
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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 Proof by Counterexample 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 2019/20.
Topic Links
Free resources to dozens of AH Maths topics are available by clicking on any of the links to the right.