Just wanted to say thanks for providing the great higher maths material. I am pleased to say I got an A in my higher maths course.
Your material really helped me focus my study efforts for the exam.
Let the fantastic wealth of resources below teach you all about the Discriminant.
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 the Discriminant 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 2025. Please find below:
1. Polynomials & Quadratics – Worksheets
3. Polynomials & Quadratics – Videos, Theory Guides & Mind Maps
4. Higher Maths Essential Skills
5. Higher Maths Exam Worksheets by Topic
6. Higher Maths Past & Practice Papers by Topic
7. Higher Maths Videos, Theory Guides, Mind Maps & Worksheets
8. Higher Maths Past & Practice Papers
9. 40 Non-Calculator Higher Maths Questions & Answers
10. 200 Higher Maths Questions & Answers
11. Practice Exam Papers A to H – Answers Included
12. 264 SQA Exam Multiple Choice Questions & Answers
13. Higher Maths Exam Check Lists
14. Old Higher Maths Exam Questions by Topic
15. Higher Maths Text Book Solutions
16. Higher Maths Theory Guides
18. Higher Maths Practice Unit Assessments – Solutions Included
19. Higher Maths Past Paper Video Solutions
20. Higher Maths Recommended Text Book
21. Exam Focused Online Study Pack – For students looking for a ‘good’ Pass
1. Polynomials & Quadratics – 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.
| Notes __________________ | Higher Worksheets ___________________________ | Worksheets __________________________________ | Without Answers ________________ | Notes/Comments _______________________ | Courtesy ______________________ |
| Polynomials & Quadratics Theory | Polynomials & Quadratics Theory (HSN) | Recommended | Courtesy of HSN | ||
| Text Book Solutions | Heinemann Book - Polynomials | Ex 7B, 7C, 7D, 7E, 7F, 7G, 7H, 7I, 7K | Answers on Links | ||
| Text Book Solutions | Heinemann Book - Quadratics | Ex 8C, 8D, 8E, 8F, 8I, 8J, 8K | Answers on Links | ||
| Essential Skills Exam Practice 2 | Quadratic Theory | Without Answers | Answers Only | Courtesy of Mr G Rennie | |
| Essential Skills Exam Practice 4 | Polynomials | Without Answers | Answers Only | Courtesy of Mr G Rennie | |
| Essential Skills 6 | Quadratic Inequalities | Without Answers | Answers Only | Courtesy of Mr G Rennie | |
| Essential Skills 7 | Completing the Square | Without Answers | Answers Only | Courtesy of Mr G Rennie | |
| Essential Skills 13 (N5 Maths) | Quadratic Formula (N5 Maths) | Without Answers | Answers Only | Courtesy of Mr G Rennie | |
| Essential Skills 14 | Synthetic Division | Without Answers | Answers Only | Courtesy of Mr G Rennie | |
| Essential Skills 33 | Using the Discriminant | Without Answers | Answers Only | Courtesy of Mr G Rennie | |
| Grade Booster Paper 3 | Polynomials | Without Answers | |||
| Grade Booster Paper 9 | Discriminant | Without Answers | |||
| 2024 Included! | Exam Worksheet 1 | Polynomials (2000 - 2024) | Without Answers | Recommended | Courtesy of the SQA |
| Exam Worksheet 2 | Polynomials (2000 - 2019) | Without Answers | Courtesy of the SQA | ||
| Exam Worksheet 3 | Polynomials (Old Higher) | Without Answers | Courtesy of the SQA | ||
| Exam Worksheet 4 | Polynomials & Quadratics (2015 - 2019) | Without Answers | Courtesy of the SQA | ||
| 109 SQA Questions | Exam Worksheet 5 | Polynomials & Quadratics (Old Higher) | Without Answers | Multiple Choice Included! | Courtesy of the SQA |
| Exam Worksheet 6 | Polynomials & Quadratics (2000 - 2013) | SQA Marking Schemes | Courtesy of the SQA | ||
| 2024 Included! | Exam Worksheet 7 | Quadratics (2000 - 2024) | Without Answers | Recommended | Courtesy of the SQA |
| Exam Worksheet 8 | Quadratics (2000 - 2018) | Without Answers | Courtesy of the SQA | ||
| Exam Worksheet 9 | Quadratics (Old Higher) | Without Answers | Multiple Choice Included! | Courtesy of the SQA | |
| Worksheet 1 | Factorising Trinomials | Without Answers | |||
| Worksheet 2 | Solving Quadratics by Factorising First | Answers | |||
| Worksheet 3 | Completing the Square | Answers | Courtesy of maths4everone | ||
| Worksheet 4 | Completing the Square - Advanced | Answers | Courtesy of maths4everone | ||
| Exam Check List 8 | Polynomials | ||||
| Exam Check List 9 | Quadratics |
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2. About the Discriminant
To learn about the Discriminant please click on the Polynomials & Quadratics Theory (HSN) link and read from page 3. Please also find in Sections 2 & 3 below videos, mind maps (see under Polynomials & Quadratics) and worksheets on this topic to help your understanding. The Essential Skills 33 worksheets, along with worksheets including actual SQA Exam Questions, are highly recommended.
If you would like more help understanding the Discriminant 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.
The Discriminant
The correct language is essential to gain full marks in exams:
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3. Polynomials & Quadratics – 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 _____________________________ | maths180.com Videos ___________________________ | HSN Theory Guide ________________________________ | Mind Maps _________________________ |
| Introduction - Polynomials | Completing the Square | Polynomials & Quadratics Theory (HSN) | Polynomials & Quadratics (HSN) |
| Dividing Polynimials | Discriminant | Polynomials & Quadratics | |
| Factorising Polynomials | Inequations | Polynomials | |
| Factorising Functions from Graphs | Intersection of Parabolas & Lines | Quadratics | |
| Finding Unknown Coefficients | Using the Discriminant | ||
| Solving Equations | |||
| Sketching Quadratics |
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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.
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5. Higher Maths Exam Worksheets by Topic
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.
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.
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7. Higher Maths Videos, Theory Guides, Mind Maps & Worksheets
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.
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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.
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9. 40 Non-Calculator Higher Maths Questions & Answers
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.
| Worksheet ______________ | Exam Questions & Answers ________________________ | Without Answers _______________ | Answers __________ | Worked Solutions ___________________ |
| Worksheet 1 | Sheet A - 10 Questions | Without Answers | Answers | In Online Study Pack |
| Worksheet 2 | Sheet B - 10 Questions | Without Answers | Answers | In Online Study Pack |
| Worksheet 3 | Sheet C - 10 Questions | Without Answers | Answers | In Online Study Pack |
| Worksheet 4 | Sheet D - 10 Questions | Without Answers | Answers | In Online Study Pack |
| Whole Booklet | Whole Booklet for Printing | Without Answers | Answers | In Online Study Pack |
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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.
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11. Practice Exam Papers A to H – Answers Included
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.
| Practice Paper _____________ | Paper 1 _____________ | Paper 2 _____________ | Papers 1 & 2 _____________________ | Answers _____________ |
| 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 |
| Exam Revision | Questions | Questions & Answers | Answers | |
| Prelim Special | Questions | Questions & Answers | Answers | |
| Prelim Special | X-Mas Theme | Questions & Answers | Answers |
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12. 264 SQA Exam Multiple Choice Questions & 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.
| Questions __________ | Year ______ | 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 |
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13. Higher Maths Exam Check Lists
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.
| Check List ______________ | Topic ____________________________ |
| Check List 1 | Whole Course - Leckie & Leckie |
| Check List 2 | Whole Course - Zeta Maths |
| Check List 3 | Whole Course - Free Higher Maths |
| Check List 4 | HSN Unit 1 - One Page Summary |
| Check List 5 | HSN Unit 2 - One Page Summary |
| Check List 6 | HSN Unit 3 - One Page Summary |
| Check List 7 | Addition Formulae |
| Check List 8 | Circles |
| Check List 9 | Differentiation |
| Check List 10 | Exponentials & Logs |
| Check List 11 | Further Calculus |
| Check List 12 | Graphs of Functions |
| Check List 13 | Integration |
| Check List 14 | Polynomials |
| Check List 15 | Quadratics |
| Check List 16 | Recurrence Relations |
| Check List 17 | Straight Lines |
| Check List 18 | Sets & Functions |
| Check List 19 | Trig Graphs & Equations |
| Check List 20 | Vectors |
| Check List 21 | Wave Function |
| Check List 22 | Formulas not given in Exam |
| Check List 23 | SQA Formula Sheet |
| Check List 24 | Course Description |
| Check List 25 | Trig Revision Sheet |
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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 ________ | Topic Name ___________________________ | Link ________ | Notes ___________________ |
| 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 |
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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.
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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 Guides _________________ | Topic ____________________________________________ | Link _______ |
| 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 ____________ | Topic ____________________________ | Mind Map ___________ | Topic ____________________________ |
| 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 |
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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 _________ | Paper ____________ | Solutions ___________ |
| 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 |
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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.
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20. Higher Maths Recommended Text Book
Please find below our highly recommended text book which can be ordered by clicking on the book/link.
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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 the Discriminant 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 2025.
Topic Links
Free resources to dozens of Higher Maths topics are available by clicking on any of the links to the right.
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