Free Videos & Worksheets

Welcome to highermathematics.co.uk

This website is primarily a free Maths resource for pupils, adult learners, parents and teachers.

To access a wealth of additional Higher Maths resources by topic please use the above Search Bar or click on any of the topic links at the bottom of the Home Page HERE.

For students looking for extra help with the Higher Maths course in 2020/21 you may wish to consider subscribing to the fantastic additional exam focused resources available in the Online Study Pack.

We hope the resources on this website prove useful and wish you the very best of success with your Higher Maths course in 2020/21.

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. Exam Focused Study Pack – Students looking for a ‘good’ pass

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Higher Maths Resources

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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.

Worksheets ____________________	Topic __________________________	Answers ________
Essential Skills 8	Tangent to a Circle	Answers
Essential Skills 9	Intersection Lines and Circles	Answers
Higher Exam Questions	Circles	Answers

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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)	Preparing to Differentiate
Closed Intervals	Rate of Change & Tangent to a Curve		Differentiation 1
Complex Differentiation	Trig Functions & Chain Rule		Differentiation 2
Curve Sketching			Further Differentiation
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.

Worksheets ____________________	Topic _____________________________	Answers ________
Essential Skills 4	Equation of a Tangent to a Curve	Answers
Essential Skills 5	Stationary Points	Answers
Essential Skills 17	Derived Graphs	Answers
Essential Skills 22	Further Differentiation (Chain Rule)	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

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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 ________
Essential Skills 18	Logarithmic Equations	Answers
Essential Skills 31	Natural Logarithms	Answers
Essential Skills 32	Logs: Connecting 2 Variables	Answers
Higher Exam Questions	Exponentials & Logs	Answers

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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
Exact Values		Graphs Transformations (Movement & Reflection)	Functions & Graphs
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 ________
Essential Skills 17	Derived Graphs	Answers
Essential Skills 20	Related Graphs	Answers
Essential Skills 27	Composite Functions	Answers
Essential Skills 28	Inverse Functions	Answers
Higher Exam Questions	Functions	Answers
Higher Exam Questions	Functions & Graphs	Answers
Higher Exam Questions	Graphs of Functions	Answers

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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			Preparing to Integrate
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 ________
Essential Skills 23	Further Integration	Answers
Essential Skills 25	Differential Equations	Answers
Essential Skills 26	Definite Integrals	Answers
Higher Exam Questions	Integration - 1	Answers
Higher Exam Questions	Integration - 2	Answers
Higher Exam Questions	Integration - Area under a Curve	Answers

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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
Factorising Polynomials	Inequations		Quadratics
Factorising Functions from Graphs	Intersection of Parabolas & Lines		Polynomials & Quadratics
Finding Unknown Coefficients	Using the Discriminant
Solving Equations

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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 ________	Courtesy _______________________________________________
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
Higher Exam Questions	Polynomials	Answers
Higher Exam Questions	Quadratics	Answers
Higher Exam Questions	Polynomials & Quadratics	Answers
Worksheet 1	Completing the Square	Answers	Maths4Everyone.com kindly shared through TES website
Worksheet 2	Completing the Square - Advanced	Answers	Maths4Everyone.com kindly shared through TES website

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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 ____________________
Finding the Recurrence Relation	Sequences	Sequences	Sequences (HSN)
Limit of a Sequence			Recurrence Relations 1
Recurrence Relations			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 ________
Essential Skills 15	Limit of a Recurrence Relation	Answers
Essential Skills 24	Recurrence: Consecutive Terms	Answers
Higher Exam Questions	Recurrence Relations - 1	Answers
Higher Exam Questions	Recurrence Relations - 2	Answers

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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.

Worksheets ____________________	Topic __________________________	Answers ________
Essential Skills 1	Median of a Triangle	Answers
Essential Skills 2	Perpendicular Bisectors	Answers
Essential Skills 3	Altitude of a Triangle	Answers
Essential Skills 4	Equation of a Tangent to a Curve	Answers
Essential Skills 9	Intersection Lines and Circles	Answers
Essential Skills 29	Gradients and Angles	Answers
Higher Exam Questions	Straight Lines - 1	Answers
Higher Exam Questions	Straight Lines - 2	Answers

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.

Worksheets _______________________	Topic _______________________________	Answers __________
Essential Skills 11	Trigonometric Formula	Answers
Essential Skills 12	Related Angles	Answers
Essential Skills 13	Trigonometric Equations	Answers
Essential Skills 16	The Wave Function	Answers
Essential Skills 19	Proving Trigonometric Identities	Answers
Essential Skills 25	Sine Rule (N5 Maths)	Answers
Essential Skills 26	Cosine Rule (N5 Maths)	Answers
Higher Exam Questions	Trig Formulae & Equations - 1	Answers
Higher Exam Questions	Trig Formulae & Equations - 2	Answers

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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 ________
Essential Skills 10	Section Formula	Answers
Essential Skills 21	Scalar Product	Answers
Essential Skills 30	Angle between Vectors	Answers
Higher Exam Questions	Vectors	Answers

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11. Exam Focused 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 in 2021 you may wish to consider subscribing to the fantastic additional exam focused resources available in the Online Study Pack. 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 Higher Maths course in 2020/21.