Covers the whole of the Higher Maths course
Created by an experienced maths teacher
Resources used with students in Scottish Secondary Schools
Welcome to highermathematics.co.uk
A sound understanding of Graphs of Derived Functions is essential to ensure exam success.
Passing the fast paced Higher Maths course significantly increases your career opportunities by helping you gain a place on a college/university course, apprenticeship or even landing a job. A ‘good’ pass at Higher Maths will set you up well for the AH Maths Course next year should you be interested. Please do your very best to keep on top of your studies.
For students looking for extra help with the Higher Maths course you may wish to consider subscribing to the fantastic additional exam focused resources available in the Online Study Pack.
To access a wealth of additional free resources by topic please either use the above Search Bar or click HERE selecting on the topic you wish to study.
We hope you find this website useful and wish you the very best of success with your Higher Maths course in 2021. Please find below:
To learn about Graphs of Derived Functions please click on the Differentiation Theory (HSN) link and read from page 25. Please also find in Sections 2 & 3 below videos, mind maps (see under Differentiation) and worksheets on this topic to help your understanding. The Essential Skills Worksheet 17, along with worksheets including actual SQA Exam Questions, are highly recommended.
If you would like more help understanding Graphs of Derived Functions there are full, easy to follow, step-by-step worked solutions to dozens of Higher Maths Past & Practice exam questions on all topics in the Online Study Pack. Please give yourself every opportunity for success, speak with your parents, and subscribe to the exam focused Online Study Pack today.
Graphs of Derived Functions
In the diagram below, the bottom graph is the derived graph of the top.
As shown above;
2. Differentiation – Worksheets
Thanks to the SQA and authors for making the excellent resources below freely available. Please use regularly for revision prior to assessments, tests and the final exam.
Clear, easy to follow, step-by-step worked solutions to all worksheets below are available in the Online Study Pack.
|Essential Skills 4||Equation of a Tangent to a Curve||Answers|
|Essential Skills 5||Stationary Points||Answers|
|Essential Skills 17||Graphs of Derived Functions||Answers|
|Essential Skills 22||Further Differentiation||Answers|
|Essential Skills 23||Further Integration||Answers|
|Higher Exam Questions||Derived Graphs||Answers|
|Higher Exam Questions||Differentiation - 1||Answers|
|Higher Exam Questions||Differentiation - 2||Answers|
|Higher Exam Questions||Differentiation (Optimisation)||Answers|
|Higher Exam Questions||Further Calculus||Answers|
3. Differentiation – Videos, Theory Guides & Mind Maps
Thanks to the authors for making the excellent resources below freely available. Please use regularly for revision prior to assessments, tests and the final exam.
|Larbert Maths Videos|
|HSN Theory Guides|
|Applications of Derivatives||Chain Rule - Increasing/Decreasing||Differentiation Theory (HSN)||Differentiation (HSN)|
|Chain Rule||Optimisation - More Challenging Examples||Further Calculus Theory (HSN)||Differentiation (Preparing For)|
|Closed Intervals||Rate of Change & Tangent to a Curve||Differentiation 1|
|Complex Differentiation||Trig Functions & Chain Rule||Differentiation 2|
|Curve Sketching||Differentiation (Further)|
|Equations of Tangents|
|Fractions & Roots|
|Increasing & Decreasing Functions|
|Introduction to Differentiation|
|Sin x & Cos x|
4. Higher Maths Essential Skills
Thanks to Mr G Rennie for making the excellent resources below freely available. The Essential Skills Worksheets can be used for general revision, homework, consolidation of a topic or preparation for assessments, tests and exams.
Clear, easy to follow, step-by-step worked solutions to all 33 Essential Skills worksheets below are available in the Online Study Pack.
|Essential Skills 1||Median of a Triangle||Answers||Essential Skills 18||Logarithmic Equations||Answers|
|Essential Skills 2||Perpendicular Bisectors||Answers||Essential Skills 19||Proving Trig Identities||Answers|
|Essential Skills 3||Altitude of a Triangle||Answers||Essential Skills 20||Related Graphs||Answers|
|Essential Skills 4||Equation of a Tangent to a Curve||Answers||Essential Skills 21||Scalar Product||Answers|
|Essential Skills 5||Stationary Points||Answers||Essential Skills 22||Further Differentiation||Answers|
|Essential Skills 6||Quadratic Inequalities||Answers||Essential Skills 23||Further Integration||Answers|
|Essential Skills 7||Completing the Square||Answers||Essential Skills 24||Recurrence: Consecutive Terms||Answers|
|Essential Skills 8||Tangent to a Circle||Answers||Essential Skills 25||Differential Equations||Answers|
|Essential Skills 9||Intersection of Lines & Circles||Answers||Essential Skills 26||Definite Integrals||Answers|
|Essential Skills 10||Section Formula||Answers||Essential Skills 27||Composite Functions||Answers|
|Essential Skills 11||Trig Formula||Answers||Essential Skills 28||Inverse Functions||Answers|
|Essential Skills 12||Related Angles||Answers||Essential Skills 29||Angle between Line & x-axis||Answers|
|Essential Skills 13||Trig Equations (Double Angle Formula)||Answers||Essential Skills 30||Angle between Vectors||Answers|
|Essential Skills 14||Synthetic Division||Answers||Essential Skills 31||Natural Logarithms||Answers|
|Essential Skills 15||Limit of a Recurrence Relation||Answers||Essential Skills 32||Logs: Connecting 2 Variables||Answers|
|Essential Skills 16||The Wave Function||Answers||Essential Skills 33||Using the Discriminant||Answers|
|Essential Skills 17||Graphs of Derived Functions||Answers|
Thanks to the SQA and authors for making the excellent resources below freely available. The worksheets by topic are a fantastic study resource since they are actual past paper exam questions.
Clear, easy to follow, step-by-step worked solutions to all new CfE Higher Maths Questions below are available in the Online Study Pack.
|2||Circles (Old Higher)||Ans Included||22||Polynomials (Old Higher)||Ans Included|
|3||Differentiation - 1||Answers||23||Quadratics||Answers|
|4||Differentiation - 2||Answers||24||Quadratics (Old Higher)||Ans Included|
|5||Differentiation (Optimisation)||Answers||25||Recurrence Relations - 1||Answers|
|6||Differentiation (Old Higher)||Ans Included||26||Recurrence Relations - 2||Answers|
|7||Exponentials & Logs||Answers||27||Recurrence Relations (Old Higher)||Ans Included|
|8||Exponentials & Logs (Old Higher)||Ans Included||28||Straight Lines - 1||Answers|
|9||Functions||Answers||29||Straight Lines - 2||Answers|
|10||Functions & Graphs||Answers||30||Straight Lines (Old Higher)||Ans Included|
|11||Functions (Old Higher)||Ans Included||31||Trig Formulae & Equations - 1||Answers|
|12||Further Calculus||Answers||32||Trig Formulae & Equations - 2||Answers|
|13||Further Calculus (Old Higher)||Ans Included||33||Trig Addition Formula (Old Higher)||Ans Included|
|14||Graphs of Functions||Answers||34||Trig Graphs & Eqns (Old Higher)||Ans Included|
|15||Graphs of Functions (Old Higher)||Ans Included||35||Vectors||Answers|
|16||Integration - 1||Answers||36||Vectors (Old Higher)||Ans Included|
|17||Integration - 2||Answers||37||Wave Function||Answers|
|18||Integration - Area under a Curve||Answers||38||Wave Function (Old Higher)||Ans Included|
|19||Integration (Old Higher)||Ans Included||39||Prelim Revision Special||Answers|
|20||Polynomials & Quadratics||Answers|
6. Higher Maths Past & Practice Papers by Topic
Thanks to the SQA for making the excellent resources below freely available. Questions and answers have been split up by topic for your ease of reference.
Clear, easy to follow, step-by-step worked solutions to all questions below are available in the Online Study Pack.
|2019 P1||Marking P1||Q3,16||Q1||Q14||Q10,12||Q6,11,17b||Q8||Q2||Q4||Q5,7||Q13,15,17a||Q9|
|2019 P2||Marking P2||Q15||Q7b,11||Q9,12||Q5,8||Q2,13||Q7,10||Q4||Q1||Q6b||Q3,14||Q6a|
|2018 P1||Marking P1||Q4||Q6,11||Q2,11,15||Q3,14||Q10||Q7||Q1,8||Q13||Q5,9,12|
|2018 P2||Marking P2||Q5c,12||Q3,9||Q11||Q6||Q1||Q4,7a,10||7b,c||Q5a,b||Q2||Q8|
|2017 P1||Marking P1||Q2||Q8,15c||Q12||Q1,6,15a||Q3,13||Q10,15b||Q4||Q9||Q7,11||Q5||Q14|
|2017 P2||Marking P2||Q3,10||Q4,7||Q9||Q2||Q8||Q1||Q6,11||Q5|
|2016 P1||Marking P1||Q4,8||Q2,9||Q14||Q6,10,12||Q5||Q15||Q3||Q1||Q13||Q7,11|
|2016 P2||Marking P2||Q4||Q7||Q6||Q10,11b||3b,9||Q2,3a||Q1||Q8b,11a||Q5||Q8a|
|2015 P1||Marking P1||Q11,14||Q2,7||Q6||Q4,5,13||Q12,15||Q3,8||Q9||Q10||Q1|
|2015 P2||Marking P2||Q5||Q8||Q2||Q7a||Q4||Q3||Q1||Q7b||Q6||Q9|
|Specimen P1||Marking P1||Q11||Q8||Q10||Q1||Q4,7||Q2,5,9||Q6,12||Q3|
|Specimen P2||Marking P2||Q5||Q3b,8||Q4,7||Q9||Q3a||Q2||Q1,6||Q10|
|Exemplar P1||Marking P1||Q1||Q8,11||Q10||Q3||Q2,5||Q6||Q4,7||Q9|
|Exemplar P2||Marking P2||Q2||Q9,10||Q7||Q8||Q4||Q3||Q1||Q5,6|
Dozens of Higher Maths Videos provide quality lessons by topic. Also included are excellent Theory Guides, Mind Maps and Revision Worksheets with actual Higher Maths exam questions.
Please click on our new Higher Maths Videos & Worksheets by topic dedicated page.
8. Higher Maths Past & Practice Papers
Thanks to the SQA for making the excellent resources below freely available.
Clear, easy to follow, step-by-step worked solutions to all CfE Higher Papers below are available in the Online Study Pack.
|2019||Higher (CfE)||Exam Paper||Marking Scheme|
|2018||Higher (CfE)||Exam Paper||Marking Scheme|
|2018||Specimen (CfE)||Paper 1, Paper 2||Marking Scheme|
|2017||Higher (CfE)||Exam Paper||Marking Scheme|
|2016||Higher (CfE)||Exam Paper||Marking Scheme|
|2015||Higher (CfE)||Exam Paper||Marking Scheme|
|2015||Specimen (CfE)||Specimen Paper||Marking Scheme|
|2015||Exemplar (CfE)||Exemplar Paper||Marking Scheme|
|2015||Higher (Old)||Exam Paper||Marking Scheme|
|2014||Higher||Exam Paper||Marking Scheme|
|2013||Higher||Exam Paper||Marking Scheme|
|2012||Higher||Exam Paper||Marking Scheme|
|2011||Higher||Exam Paper||Marking Scheme|
|2010||Higher||Exam Paper||Marking Scheme|
|2009||Higher||Exam Paper||Marking Scheme|
|2008||Higher||Exam Paper||Marking Scheme|
|2007||Higher||Exam Paper||Marking Scheme|
|2006||Higher||Exam Paper||Marking Scheme|
|2005||Higher||Exam Paper||Marking Scheme|
|2004||Higher||Exam Paper||Marking Scheme|
|2003||Higher||Exam Paper||Marking Scheme|
|2002||Higher||Exam Paper||Marking Scheme|
|2002||Higher (Winter Diet)||Exam Paper|
Thanks to the SQA and authors for making the excellent resources below freely available. Start with these questions to help build your confidence. Once finished, you may like to move onto the 200 Higher Maths Exam Questions in the next section checking your answers as you go. If stuck, always ask your teacher for help as soon as possible.
Clear, easy to follow, step-by-step worked solutions to all 40 questions below are available in the Online Study Pack.
|Sheet A - 10 Questions||Answers|
|Sheet B - 10 Questions||Answers|
|Sheet C - 10 Questions||Answers|
|Sheet D - 10 Questions||Answers|
|Whole Booklet for Printing||Answers|
10. 200 Higher Maths Questions & Answers
Thanks to the SQA and authors for making the excellent resources below freely available. Please try to do as many questions as possible, checking your answers as you go. If stuck, always ask your teacher for help as soon as possible.
Clear, easy to follow, step-by-step worked solutions to all 200 questions below are available in the Online Study Pack.
|Exam Questions 1 - 20||Answers|
|Exam Questions 21 - 40||Answers|
|Exam Questions 41 - 60||Answers|
|Exam Questions 61 - 80||Answers|
|Exam Questions 81 - 100||Answers|
|Exam Questions 101 - 120||Answers|
|Exam Questions 121 - 140||Answers|
|Exam Questions 141 - 160||Answers|
|Exam Questions 161 - 180||Answers|
|Exam Questions 181 - 200||Answers|
|Whole Booklet for Printing||Answers|
Thanks to the SQA and Larkhall Academy for making the excellent resources below freely available. Please use regularly for revision prior to assessments, tests and the final exam.
Clear, easy to follow, step-by-step worked solutions to Practice Papers A to E are available in the Online Study Pack.
|Papers 1 & 2|
|Paper A||Paper 1||Paper 2||Papers 1 & 2||Answers|
|Paper B||Paper 1||Paper 2||Papers 1 & 2||Answers|
|Paper C||Paper 1||Paper 2||Papers 1 & 2||Answers|
|Paper D||Paper 1||Paper 2||Papers 1 & 2||Answers|
|Paper E||Paper 1||Paper 2||Papers 1 & 2||Answers|
|Paper F||Paper 1||Paper 2||Papers 1 & 2||Answers|
|Paper G||Paper 1||Paper 2||Papers 1 & 2||Answers|
|Paper H||Paper 1||Paper 2||Papers 1 & 2||Answers|
|Prelim Special||Questions||Questions & Answers||Answers|
|Prelim Special||X-Mas Theme||Questions & Answers||Answers|
Thanks to the SQA and authors for making the excellent resources below freely available. Multiple choice are primarily C level questions and a great place to start your revision. If stuck, always ask your teacher for help as soon as possible.
| Exam Multiple Choice |
| Exam Multiple Choice |
|Exam Multiple Choice
|1 - 20||2015||Questions Only||Questions & Answers||Answers Only|
|21 - 40||2014||Questions Only||Questions & Answers||Answers Only|
|41 - 60||2013||Questions Only||Questions & Answers||Answers Only|
|61 - 80||2012||Questions Only||Questions & Answers||Answers Only|
|81 - 100||2011||Questions Only||Questions & Answers||Answers Only|
|101 - 120||2010||Questions Only||Questions & Answers||Answers Only|
|121 - 264||Mixed||Questions Only||Questions & Answers||Answers Only|
Thanks to the SQA and authors for making the excellent resources below freely available. These are fantastic check lists to assess your Higher Maths knowledge. Please try to use these regularly for revision prior to tests, prelims and the final exam.
|Higher Maths Course Description||HERE|
|SQA Higher Maths Exam Formulae List||HERE||Courtesy of SQA|
|Check List 1 - Higher Maths Exam Whole Course||HERE||Courtesy of Zeta Maths|
|Check List 2 - Higher Maths Formulae List Not Given in Exam||HERE|
|Check List 3 - Higher Maths Exam Whole Course||HERE|
|Check List 4 - Higher Maths Exam Trig Revision Sheet||HERE|
|Check List 5 - One Page Summary Guide Unit 1 (HSN)||HERE||Courtesy of HSN|
|Check List 6 - One Page Summary Guide Unit 2 (HSN)||HERE||Courtesy of HSN|
|Check List 7 - One Page Summary Guide Unit 3 (HSN)||HERE||Courtesy of HSN|
14. Old Higher Maths Exam Questions by Topic
Thanks to the SQA for making the excellent resources below freely available. The worksheets by topic are a fantastic additional study resource.
|Topic 1||Circles||HERE||Answers Included|
|Topic 2||Differentiation||HERE||Answers Included|
|Topic 3||Exponentials & Logarithms||HERE||Answers Included|
|Topic 4||Functions||HERE||Answers Included|
|Topic 5||Further Calculus||HERE||Answers Included|
|Topic 6||Graphs of Functions||HERE||Answers Included|
|Topic 7||Integration||HERE||Answers Included|
|Topic 8||Polynomials||HERE||Answers Included|
|Topic 9||Quadratics||HERE||Answers Included|
|Topic 10||Recurrence Relations||HERE||Answers Included|
|Topic 11||Straight Line||HERE||Answers Included|
|Topic 12||Trig Addition Formulae||HERE||Answers Included|
|Topic 13||Trig Graphs & Equations||HERE||Answers Included|
|Topic 14||Vectors||HERE||Answers Included|
|Topic 15||Wave Function||HERE||Answers Included|
15. Higher Maths Text Book Solutions
Thanks to the AHS for providing the Heinemann Higher Maths text book solutions below. These will prove extremely useful in helping to progress your Higher Maths knowledge. Please note that there may be the odd arithmetic error.
|Topic 1||Straight Line||1A||1B||1D||1E||1F||1G||1I||1K||1M||1N||1O||1O|
|Topic 2||Functions & Graphs 1||2A||2B||2C||2D||2F||2G||2I|
|Topic 3||Functions & Graphs 2||3A||3C||3K||3N||3O||3P|
|Topic 12||Further Calculus||14B||14C||14C||14E||14G||14H||14I||14J||14K|
|Topic 13||Exp's & Logs||15C||15D||15E||15F||15G||15H||15I||15I||15J||15K||15L|
|Topic 14||Wave Function||16A||16C||16D||16E||16F||16G||16H|
16. Higher Maths Theory Guides
Thanks to HSN for making the excellent Higher Maths Theory Guides freely available for all to use. These will prove a fantastic resource in helping you consolidate your understanding of Higher Maths.
|Theory Guide 1||All Topics Unit 1 Theory (HSN)||HERE|
|Theory Guide 2||All Topics Unit 1 - One Page Summary Guide (HSN)||HERE|
|Theory Guide 3||All Topics Unit 2 Theory (HSN)||HERE|
|Theory Guide 4||All Topics Unit 2 - One Page Summary Guide (HSN)||HERE|
|Theory Guide 5||All Topics Unit 3 Theory (HSN)||HERE|
|Theory Guide 6||All Topics Unit 3 - One Page Summary Guide (HSN)||HERE|
|Theory Guide 7||All Topics Units 1,2 & 3 Theory (HSN)||HERE|
|Theory Guide 8||Circles Theory (HSN)||HERE|
|Theory Guide 9||Differentiation Theory (HSN)||HERE|
|Theory Guide 10||Exponentials & Logarithms Theory (HSN)||HERE|
|Theory Guide 11||Functions & Graphs Theory (HSN)||HERE|
|Theory Guide 12||Further Calculus Theory (HSN)||HERE|
|Theory Guide 13||Graphs Transformations Theory (Movement & Reflection)||HERE|
|Theory Guide 14||Graphs Transformations Summary Sheet||HERE|
|Theory Guide 15||Integration Theory (HSN)||HERE|
|Theory Guide 16||Polynomials & Quadratics Theory (HSN)||HERE|
|Theory Guide 17||Sequences Theory (HSN)||HERE|
|Theory Guide 18||Straight Line Theory (HSN)||HERE|
|Theory Guide 19||Trigonometry Theory (HSN)||HERE|
|Theory Guide 19||Vectors Theory (HSN)||HERE|
|Theory Guide 20||Wave Function Theory (HSN)||HERE|
17. Higher Maths Mind Maps
Thanks to the authors for providing the excellent resources below. These will prove a fantastic resource in helping you prepare for assessments, tests and the final exam.
|Mind Map 1||Circle 1||Mind Map 16||Polynomials & Quadratics|
|Mind Map 2||Circle 2||Mind Map 17||Polynomials|
|Mind Map 3||Composite Functions||Mind Map 18||Quadratics|
|Mind Map 4||Compound Angle Formula||Mind Map 19||Recurrence Relations 1|
|Mind Map 5||Differentiation (Preparing For)||Mind Map 20||Recurrence Relations 2|
|Mind Map 6||Differentiation 1||Mind Map 21||Straight Lines 1|
|Mind Map 7||Differentiation 2||Mind Map 22||Straight Lines 2|
|Mind Map 8||Differentiation (Further)||Mind Map 23||Trigonometry 1|
|Mind Map 9||Functions & Graphs||Mind Map 24||Trigonometry 2|
|Mind Map 10||Graph Transformations||Mind Map 25||Vectors 1|
|Mind Map 11||Integration (Preparing For)||Mind Map 26||Vectors 2|
|Mind Map 12||Integration 1||Mind Map 27||Vectors 3|
|Mind Map 13||Integration 2||Mind Map 28||Wave Function 1|
|Mind Map 14||Logs & Exponentials 1||Mind Map 29||Wave Function 2|
|Mind Map 15||Logs & Exponentials 2|
18. Higher Maths Practice Unit Assessments – Solutions Included
Thanks to the authors for making the excellent resources below freely available for all to use. Please use regularly for revision prior to assessments, tests and the final exam.
|Unit One||Practice A||Solutions|
|Unit One||Practice B||Solutions|
|Unit Two||Practice A||Solutions|
|Unit Two||Practice B||Solutions|
|Unit Three||Practice A||Solutions|
|Unit Three||Practice B||Solutions|
|Unit Four||Practice A||Solutions|
19. Higher Maths Past Paper Video Solutions
Please click DLB Maths to view Higher Maths Past Paper video solutions. This will prove an excellent resource in helping you prepare for assessments, tests and the final exam.
20. Higher Maths Recommended Text Book
Please find below our highly recommended text book which can be ordered by clicking on the book/link.
21. Higher Maths 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 Graphs of Derived Functions to pass your final exam.
For students looking for a ‘good’ pass at Higher Maths you may wish to consider subscribing to the fantastic additional exam focused resources available in the Online Study Pack. Subscribing could end up being one of your best ever investments.
Please give yourself every opportunity for success, speak with your parents, and subscribe to the exam focused Online Study Pack today.
We hope the resources on this website prove useful and wish you the very best of success with your Higher Maths course in 2021.
My daughter says the Higher website was really helpful. She achieved an ‘A’ for Higher Maths this year and is now undertaking Advanced Higher Maths for which she would like me to subscribe to your AH website . I shall go and do that now – Thanks again.
Mrs Gove – November 2018
Mike – August 2018
Just a HUGE thank you from me – I’ve been teaching Higher Maths for about 20 years and your site has made this so much easier. Having topic by topic past paper questions, HSN notes and SQA papers all on one site is wonderful. So easy just to direct students to your amazing site! – Thank you.
Karen – March 2018
Mike – March 2018
The Higher Maths website is great – only £9.99 is such good value for what you get. I am feeling a lot more confident for the exam now!
John – March 2018
Free resources to dozens of Higher Maths topics are available by clicking on any of the links to the right.