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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 2021/22. Please find below:
1. Circles – Videos, Theory, Mind Maps & Worksheets
2. Differentiation – Videos, Theory, Mind Maps & Worksheets
3. Exponentials & Logs – Videos, Theory, Mind Maps & Worksheets
4. Functions & Graphs – Videos, Theory, Mind Maps & Worksheets
5. Integration – Videos, Theory, Mind Maps & Worksheets
6. Polynomials & Quad’s – Videos, Theory, Mind Maps & Worksheets
7. Sequences – Videos, Theory, Mind Maps & Worksheets
8. Straight Lines – Videos, Theory, Mind Maps & Worksheets
9. Trigonometry – Videos, Theory, Mind Maps & Worksheets
10. Vectors – Videos, Theory, Mind Maps & Worksheets
11. Online Study Pack – Students looking for a ‘good’ pass
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1. Circles – Videos, Theory Guides & Mind Maps
Thanks to the authors for sharing the excellent resources below.
| Larbert Maths Videos __________________________ | maths180.com Video ___________________ | HSN Theory Guide _________________ | Mind Maps _____________ |
| Equations of Circles | Circles | Circle Theory (HSN) | Circle (HSN) |
| Equations of Tangents | Circle 1 | ||
| General Equation of a Cicle | Circle 2 | ||
| Intersection of Circles | |||
| Lines Intersecting Circles | |||
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Circles – Worksheets
Thanks to Mr Graham Rennie and the SQA for sharing the excellent resources below. Clear, easy to follow, step-by-step worked solutions to all worksheets below are available in the Online Study Pack.
| Higher Maths Worksheets ____________________________________ | Worksheet - Without Answers _________________________________ | Worksheet - With Answers ___________________________________________________________ |
| Heinemann Book - Circles | Ex 12B, 12D, 12F, 12H, 12J, 12K, 12L | Answers on Links |
| Essential Skills Exam Practice 12 | Circles | Answers |
| Essential Skills 8 | Tangent to a Circle | Answers |
| Essential Skills 9 | Intersection of Lines & Circles | Answers |
| Grade Booster Paper 1 | Circles | Worked Solutions (Study Pack Sample) |
| Higher Exam Worksheet - Recommended | Circles 1 (2000 - 2019) | Answers Included on Worksheet |
| Higher Exam Questions | Circles 2 (2000 - 2013) | For answers refer to Marking Schemes on SQA Past Paper Link HERE |
| Higher Exam Questions | Circles 3 (Old Higher) | Answers Included on Worksheet |
| Higher Exam Questions | Circles 4 | Answers |
| Exam Check List 2 | Circles |
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2. Differentiation – Videos, Theory Guides & Mind Maps
Thanks to the authors for sharing the excellent resources below.
| Larbert Maths Videos __________________________________ | maths180.com Videos ______________________________________ | HSN Theory Guides ____________________________ | Mind Maps ____________________________ |
| 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) | ||
| Derived Graphs | |||
| Equations of Tangents | |||
| Fractions & Roots | |||
| Increasing & Decreasing Functions | |||
| Introduction to Differentiation | |||
| Leibniz Notation | |||
| Optimisation | |||
| Stationary Points | |||
| Sin x & Cos x |
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Differentiation – Worksheets
Thanks to Mr Graham Rennie and the SQA for sharing the excellent resources below. Clear, easy to follow, step-by-step worked solutions to all worksheets below are available in the Online Study Pack.
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3. Exponentials & Logs – Videos, Theory Guides & Mind Maps
Thanks to the authors for sharing the excellent resources below.
| Larbert Maths Videos _____________________________ | maths180.com Video __________________ | HSN Theory Guide _____________________ | Mind Maps ________________________ |
| Introduction - Logs & Exponentials | Logs & Exponentials | Logs & Exponentials (HSN) | Logs & Exponentials (HSN) |
| Exponential Function | Logs & Exponentials 1 | ||
| Laws of Logs | Logs & Exponentials 2 | ||
| Graph Transformations | |||
| Linearising Data | |||
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Exponentials & Logs – Worksheets
Thanks to Mr Graham Rennie and the SQA for sharing the excellent resources below. Clear, easy to follow, step-by-step worked solutions to all worksheets below are available in the Online Study Pack.
| Worksheets ___________________________________ | Topic _____________________________________ | Answers/Worked Solutions ___________________________________________________________ |
| Heinemann Book - Exponentials & Logs | Ex15C, 15D, 15E. 15F, 15G, 15H, 15I, 15J, 15K, 15L | Answers on Links |
| Essential Skills Exam Practice 13 | Logarithms | Answers |
| Essential Skills 18 | Logarithmic Equations | Answers |
| Essential Skills 31 | Natural Logarithms | Answers |
| Essential Skills 32 | Logs: Connecting 2 Variables | Answers |
| Grade Booster Paper 11 | Exponential Functions (Half-Life) | Study Pack Sample - Solutions |
| Grade Booster Paper 13 | Log Equations & Graphs | Study Pack Sample - Solutions |
| Higher Exam Questions - Recommended | Exponentials & Logs 1 (2000 - 2019) | Answers Included on Worksheet |
| Higher Exam Questions | Exponentials & Logs 1 (2000 - 2013) | For answers refer to Marking Schemes on SQA Past Paper Link HERE |
| Higher Exam Questions | Exponentials & Logs 2 (Old Higher) | Answers Included on Worksheet |
| Higher Exam Questions | Exponentials & Logs 3 | Answers |
| Exam Check List 4 | Exponentials & Logs |
4. Functions & Graphs – Videos, Theory Guides & Mind Maps
Thanks to the authors for sharing the excellent resources below.
| Larbert Maths Videos _______________________ | maths180.com Videos _________________________ | HSN Theory Guides ________________________________________ | Mind Maps _______________________ |
| Composite Functions | Composite & Inverse Functions | Exponentials & Logs Theory (HSN) | Functions & Graphs (HSN) |
| Domains & Ranges | Functions & Graphs | Functions & Graphs Theory (HSN) | Functions & Graphs |
| Exact Values | Graph Transformations - Movement & Reflection | ||
| Exponentials & Logs | Graphs Transformations Summary Sheet | ||
| Inverse Functions | |||
| Transformations of Graphs |
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Functions & Graphs – Worksheets
Thanks to Mr Graham Rennie and the SQA for sharing the excellent resources below. Clear, easy to follow, step-by-step worked solutions to all worksheets below are available in the Online Study Pack.
| Worksheets _______________________________________ | Topic _________________________________ | Answers/Worked Solutions ___________________________________________________________ |
| Heinemann Book - Sets & Functions | Ex 2A, 2B, 2C, 2D, 2F, 2G, 2H, 2I | Answers on Links |
| Heinemann Book - Graphs of Functions | Ex 3A, 3C, 3E, 3G, 3I, 3K, 3M, 3N, 3O, 3P | Answers on Links |
| Heinemann Book - Trig Graphs & Equations | Ex 4A, 4B, 4C, 4E, 4H, 4I, 4J | Answers on Links |
| Essential Skills Exam Practice 6 | Functions | Answers |
| Essential Skills 17 | Graphs of Derived Functions | Answers |
| Essential Skills 20 | Related Graphs | Answers |
| Essential Skills 27 | Composite Functions | Answers |
| Essential Skills 28 | Inverse Functions | Answers |
| Higher Exam Questions - Recommended | Functions & Sets (2000 - 2019) | Answers Included on Worksheet |
| Higher Exam Questions | Functions & Graphs (2000 - 2013) | For answers refer to Marking Schemes on SQA Past Paper Link HERE |
| Higher Exam Questions | Functions 1 (Old Higher) | Answers Included on Worksheet |
| Higher Exam Questions | Functions 2 | Answers |
| Higher Exam Question | Functions & Graphs 4 | Answers |
| Higher Exam Questions | Functions | Answers |
| Higher Exam Questions - Recommended | Graphs of Functions 1 (2000 - 2019) | Answers Included on Worksheet |
| Higher Exam Questions | Graphs of Functions 2 | Answers |
| Higher Exam Questions | Domain Restrictions | |
| Worksheet 1 | Graph Transformations Grid | Answers |
| Worksheets 2 & 3 | Blank Grid 1, Blank Grid 2 | |
| Worksheets 4 | Graph Transformations | Answers |
| Worksheets 5 | Graphs of Trig Functions | |
| Worksheets 6 | Trig Functions - Period & Amplitude | |
| Exam Check List 6 | Graphs of Functions | |
| Exam Check List 13 | Trig Graphs & Equations |
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5. Integration – Videos, Theory Guides & Mind Maps
Thanks to the authors for sharing the excellent resources below.
| Larbert Maths Videos __________________________ | maths180.com Videos ___________________________ | HSN Theory Guides __________________________ | Mind Maps ________________________ |
| Integration - Introduction | Indefinite & Definite Integrals | Integration Theory (HSN) | Integration (HSN) |
| Area Under a Curve | Area Under and Between Curves | Further Calculus Theory (HSN) | Further Calculus (HSN) |
| Area Between Curves | Integration (Preparing For) | ||
| Differential Equations | Integration 1 | ||
| Definite Integrals | Integration 2 | ||
| Integrating Sin & Cos | |||
| Integrating With The Chain Rule | |||
| Integration - Further Examples | |||
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Integration – Worksheets
Thanks to Mr Graham Rennie and the SQA for sharing the excellent resources below. Clear, easy to follow, step-by-step worked solutions to all worksheets below are available in the Online Study Pack.
| Worksheets __________________________________ | Topic _______________________________ | Answers/Worked Solutions ___________________________________________________________ |
| Heinemann Book - Integration | Ex 9G, 9H, 9I, 9L, 9N, 9P, 9Q, 9R | Answers on Links |
| Heinemann Book - Further Calculus | Ex 14B, 14C, 14E, 14G, 14H, 14I, 14J, 14K | Answers on Links |
| Essential Skills Exam Practice 8 | Integration | Answers |
| Essential Skills Exam Practice 9 | Further Calculus | Answers |
| Essential Skills 23 | Further Integration | Answers |
| Essential Skills 25 | Differential Equations | Answers |
| Essential Skills 26 | Definite Integrals | Answers |
| Grade Booster Paper 12 | Integration | Answers |
| Higher Exam Questions - Recommended | Further Calculus 1 (2000 - 2019) | Answers Included on Worksheet |
| Higher Exam Questions | Further Calculus 2 | Answers |
| Higher Exam Questions - Recommended | Integration 1 (2000 - 2019) | Answers Included on Worksheet |
| Higher Exam Questions | Integration 2 (2000 - 2013) | For answers refer to Marking Schemes on SQA Past Paper Link HERE |
| Higher Exam Questions | Integration 3 (Old Higher) | Answes Included on Worksheet |
| Higher Exam Questions | Integration 4 | Answers |
| Higher Exam Questions | Integration 5 | Answers |
| Higher Exam Questions | Integration 6 - Area under a Curve | Answers |
| Exam Check List 5 | Further Calculus | |
| Exam Check List 7 | Integration |
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6. Polynomials & Quadratics – Videos, Theory Guides & Mind Maps
Thanks to the authors for sharing the excellent resources below.
| 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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Polynomials & Quadratics – Worksheets
Thanks to Mr Graham Rennie and the SQA for sharing the excellent resources below. Clear, easy to follow, step-by-step worked solutions to all worksheets below are available in the Online Study Pack.
| Worksheets __________________________________ | Topic ___________________________________ | Answers/Worked Solutions ___________________________________________________________ |
| Heinemann Book - Polynomials | Ex 7B, 7C, 7D, 7E, 7F, 7G, 7H, 7I, 7K | Answers on Links |
| Heinemann Book - Quadratics | Ex 8C, 8D, 8E, 8F, 8I, 8J, 8K | Answers on Links |
| Essential Skills Exam Practice 2 | Quadratic Theory | Answers |
| Essential Skills Exam Practice 4 | Polynomials | Answers |
| Essential Skills 6 | Quadratic Inequalities | Answers |
| Essential Skills 7 | Completing the Square | Answers |
| Essential Skills 13 | Quadratic Formula (N5 Maths) | Answers |
| Essential Skills 14 | Synthetic Division | Answers |
| Essential Skills 33 | Using the Discriminant | Answers |
| Grade Booster Paper 3 | Polynomials | Study Pack Sample - Solutions |
| Grade Booster Paper 9 | Discriminant | Study Pack Sample - Solutions |
| Higher Exam Questions - Recommended | Polynomials (2000 - 2019) | Answers Included on Worksheet |
| Higher Exam Questions | Polynomials & Quadratics (2000 - 2013) | For answers refer to Marking Schemes on SQA Past Paper Link HERE |
| Higher Exam Questions | Polynomials (Old Higher) | Answes Included on Worksheet |
| Higher Exam Questions - Recommended | Quadratics (2000 - 2019) | Answers Included on Worksheet |
| Higher Exam Questions | Quadratics (Old Higher) | Answers Included on Worksheet |
| Higher Exam Questions | Polynomials & Quadratics | Answers |
| Higher Exam Questions | Polynomials | Answers |
| Higher Exam Questions | Quadratics | Answers |
| Higher Exam Questions | Polynomials & Quadratics | Answers |
| Worksheet 1 | Completing the Square | Answers |
| Worksheet 2 | Completing the Square - Advanced | Answers |
| Exam Check List 8 | Polynomials | |
| Exam Check List 9 | Quadratics |
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7. Sequences – Videos, Theory Guides & Mind Maps
Thanks to the authors for sharing the excellent resources below.
| Larbert Maths Videos __________________________________ | maths180.com Videos ____________________ | HSN Theory Guide __________________ | Mind Maps ____________________ |
| Introduction to Recurrence Relations | Sequences | Sequences | Sequences (HSN) |
| Limit of a Sequence | Recurrence Relations 1 | ||
| Recurrence Relation from a Sequence | Recurrence Relations 2 |
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Sequences – Worksheets
Thanks to Mr Graham Rennie and the SQA for sharing the excellent resources below. Clear, easy to follow, step-by-step worked solutions to all worksheets below are available in the Online Study Pack.
| Worksheets __________________________________ | Topic _______________________________ | Answers/Worked Solutions ___________________________________________________________ |
| Heinemann Book - Recurrence Relations | Ex 5A, 5B, 5C, 5D, 5H, 5I | Answers on Links |
| Essential Skills Exam Practice 10 | Recurrence Relations | Answers |
| Essential Skills 15 | Limit of a Recurrence Relation | Answers |
| Essential Skills 24 | Recurrence: Consecutive Terms | Answers |
| Grade Booster Paper 2 | Recurrence Relations | Answers |
| Higher Exam Questions | Recurrence Relations 1 (2000 - 2013) | For answers refer to Marking Schemes on SQA Past Paper Link HERE |
| Higher Exam Questions | Recurrence Relations 2 (Old Higher) | Answers Included on Worksheet |
| Higher Exam Questions | Recurrence Relations 3 | Answers |
| Higher Exam Questions | Recurrence Relations 4 | Answers |
| Exam Check List 10 | Recurrence Relations |
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8. Straight Lines – Videos, Theory Guides & Mind Maps
Thanks to the authors for sharing the excellent resources below.
| Larbert Maths Videos _____________________ | maths180.com Video ___________________ | HSN Theory Guide _______________________ | Mind Maps __________________ |
| Altitudes | Straight Lines | Straight Line Theory (HSN) | Straight Lines (HSN) |
| Collinearity | Straight Lines 1 | ||
| Distance between Points | Straight Lines 2 | ||
| Equation of a Line | |||
| Gradient Revision | |||
| Gradient from an Angle | |||
| Medians | |||
| Midpoints | |||
| Perpendicular Bisectors | |||
| Perpendicular Gradients | |||
| Points of Intersection |
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Straight Lines – Worksheets
Thanks to Mr Graham Rennie and the SQA for sharing the excellent resources below. Clear, easy to follow, step-by-step worked solutions to all worksheets below are available in the Online Study Pack.
9. Trigonometry – Videos, Theory Guides & Mind Maps
Thanks to the authors for sharing the excellent resources below.
| Larbert Maths Videos _______________________________ | maths180.com Videos ______________________ | HSN Theory Guide _______________________ | Mind Maps _________________________ |
| Addition Formula | Solving Trig Equations | Trigonometry Theory (HSN) | Trigonometry (HSN) |
| Double Angle Formula | Trig Graphs | Wave Function (HSN) | |
| Exact Values | Compound Angle Formula | ||
| Radian Measure | Trigonometry 1 | ||
| Trig Equations 1 | Trigonometry 2 | ||
| Trig Equations 2 | |||
| Trig Identities | |||
| Wave Function - Introduction | |||
| Wave Function - All Forms | |||
| Wave Function - Equations | |||
| Wave Functions - Graphs | |||
| Wave Function - Max & Min Values | |||
| Wave Function - Multiple Angles |
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Trigonometry – Worksheets
Thanks to Mr Graham Rennie and the SQA for sharing the excellent resources below. Clear, easy to follow, step-by-step worked solutions to all worksheets below are available in the Online Study Pack.
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10. Vectors – Videos, Theory Guides & Mind Maps
Thanks to the authors for sharing the excellent resources below.
| Larbert Maths Videos ______________________________ | maths180.com Video ___________________ | HSN Theory Guide _________________ | Mind Maps _________________ |
| 3-D Collinearity | Vectors | Vectors Theory (HSN) | Vectors (HSN) |
| Angle Between Vectors | Vectors 1 | ||
| Basis Vectors | Vectors 2 | ||
| Dividing a Line in a Given Ratio | Vectors 3 | ||
| Perpendicular Vectors | |||
| Position Vectors | |||
| Properties of Scalar Products | |||
| Scalar Products | |||
| Scalar Products from Components | |||
| Unit Vectors |
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Vectors – Worksheets
Thanks to Mr Graham Rennie and the SQA for sharing the excellent resources below. Clear, easy to follow, step-by-step worked solutions to all worksheets below are available in the Online Study Pack.
| Worksheets ________________________________ | Topic ____________________ | Answers/Worked Solutions ___________________________________________________________ |
| Essential Skills Exam Practice 11 | Vectors | Answers |
| Essential Skills 10 | Section Formula | Answers |
| Essential Skills 21 | Scalar Product | Answers |
| Essential Skills 30 | Angle between Vectors | Answers |
| Grade Booster Paper 7 | Vectors | Study Pack Sample - Solutions |
| Higher Exam Questions - Recommended | Vectors 1 (2000 - 2019) | Answers Included on Worksheet |
| Higher Exam Questions | Vectors 2 (2000 - 2013) | For answers refer to Marking Schemes on SQA Past Paper Link HERE |
| Higher Exam Questions | Vectors 3 (Old Higher) | Answers Included on Worksheet |
| Higher Exam Questions | Vectors 4 | Answers |
| Exam Check List 14 | Vectors |
11. 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 Higher Maths 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 2022.
Covers the whole of the Higher Maths course
Created by an experienced maths teacher
Resources used with students in Scottish Secondary Schools
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