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.

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 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
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maths180.com Video
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HSN Theory Guide
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Mind Maps
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Equations of CirclesCirclesCircle Theory (HSN)Circle (HSN)
Equations of TangentsCircle 1
General Equation of a CicleCircle 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
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Topic
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Answers
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Essential Skills 8Tangent to a CircleAnswers
Essential Skills 9Intersection Lines and CirclesAnswers
Higher Exam QuestionsCircles 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
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maths180.com Videos
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HSN Theory Guides
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Mind Maps
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Applications of DerivativesChain Rule - Increasing/DecreasingDifferentiation Theory (HSN)Differentiation (HSN)
Chain RuleOptimisation - More Challenging ExamplesFurther Calculus Theory (HSN)Preparing to Differentiate
Closed IntervalsRate of Change & Tangent to a CurveDifferentiation 1
Complex DifferentiationTrig Functions & Chain RuleDifferentiation 2
Curve SketchingFurther 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
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Topic
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Answers
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Essential Skills 4Equation of a Tangent to a CurveAnswers
Essential Skills 5Stationary PointsAnswers
Essential Skills 17Derived GraphsAnswers
Essential Skills 22Further Differentiation (Chain Rule)Answers
Higher Exam QuestionsDerived GraphsAnswers
Higher Exam QuestionsDifferentiationAnswers
Higher Exam QuestionsDifferentiation (Optimisation)Answers
Higher Exam QuestionsFurther CalculusAnswers

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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
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maths180.com Video
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HSN Theory Guide
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Mind Maps
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Introduction - Logs & ExponentialsLogs & ExponentialsLogs & Exponentials (HSN)Logs & Exponentials (HSN)
Exponential FunctionLogs & Exponentials 1
Laws of LogsLogs & 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
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Topic
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Answers
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Essential Skills 18Logarithmic EquationsAnswers
Essential Skills 31Natural LogarithmsAnswers
Essential Skills 32Logs: Connecting 2 VariablesAnswers
Higher Exam QuestionsExponentials & LogsAnswers

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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
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maths180.com Videos
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HSN Theory Guides
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Mind Maps
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Composite FunctionsComposite & Inverse FunctionsExponentials & Logs Theory (HSN)Functions & Graphs (HSN)
Domains & RangesFunctions & GraphsFunctions & Graphs Theory (HSN)Functions
Exact ValuesGraphs Transformations (Movement & Reflection)Functions & Graphs
Exponentials & LogsGraphs 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
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Topic
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Answers
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Essential Skills 17Derived GraphsAnswers
Essential Skills 20Related GraphsAnswers
Essential Skills 27Composite FunctionsAnswers
Essential Skills 28Inverse FunctionsAnswers
Higher Exam QuestionsFunctions & GraphsAnswers

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5. Integration – Videos, Theory Guides & Mind Maps

Thanks to the authors for sharing the excellent resources below.

Larbert Maths Videos
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maths180.com Videos
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HSN Theory Guides
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Mind Maps
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Integration - IntroductionIndefinite & Definite IntegralsIntegration Theory (HSN)Integration (HSN)
Area Under a CurveArea Under and Between CurvesFurther Calculus Theory (HSN)Further Calculus (HSN)
Area Between CurvesPreparing to Integrate
Differential EquationsIntegration 1
Definite IntegralsIntegration 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
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Topic
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Answers
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Essential Skills 23Further IntegrationAnswers
Essential Skills 25Differential EquationsAnswers
Essential Skills 26Definite IntegralsAnswers
Higher Exam QuestionsIntegrationAnswers
Higher Exam QuestionsIntegration - Area under a CurveAnswers

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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
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maths180.com Videos
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HSN Theory Guide
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Mind Maps
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Introduction - PolynomialsCompleting the SquarePolynomials & Quadratics Theory (HSN)Polynomials & Quadratics (HSN)
Dividing PolynimialsDiscriminantPolynomials
Factorising PolynomialsInequationsQuadratics
Factorising Functions from GraphsIntersection of Parabolas & LinesPolynomials & Quadratics
Finding Unknown CoefficientsUsing 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
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Topic
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Answers
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Courtesy
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Essential Skills 6Quadratic InequalitiesAnswers
Essential Skills 7Completing the SquareAnswers
Essential Skills 13 Quadratic Formula (N5 Maths)Answers
Essential Skills 14Synthetic DivisionAnswers
Essential Skills 33Using the DiscriminantAnswers
Higher Exam QuestionsPolynomials & QuadraticsAnswers
Worksheet 1Completing the SquareAnswersMaths4Everyone.com kindly shared through TES website
Worksheet 2Completing the Square - AdvancedAnswersMaths4Everyone.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
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maths180.com Videos
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HSN Theory Guide
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Mind Maps
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Finding the Recurrence RelationSequencesSequencesSequences (HSN)
Limit of a SequenceRecurrence Relations 1
Recurrence RelationsRecurrence 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
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Topic
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Answers
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Essential Skills 15Limit of a Recurrence RelationAnswers
Essential Skills 24Recurrence: Consecutive TermsAnswers
Higher Exam QuestionsRecurrence RelationsAnswers

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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
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maths180.com Video
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HSN Theory Guide
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Mind Maps
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AltitudesStraight LinesStraight Line Theory (HSN)Straight Lines (HSN)
CollinearityStraight Lines 1
Distance between PointsStraight 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
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Topic
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Answers
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Essential Skills 1Median of a TriangleAnswers
Essential Skills 2Perpendicular BisectorsAnswers
Essential Skills 3Altitude of a TriangleAnswers
Essential Skills 4Equation of a Tangent to a CurveAnswers
Essential Skills 9Intersection Lines and CirclesAnswers
Essential Skills 29Gradients and AnglesAnswers
Higher Exam QuestionsStraight LinesAnswers

9. Trigonometry – Videos, Theory Guides & Mind Maps

Thanks to the authors for sharing the excellent resources below.

Larbert Maths Videos
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maths180.com Videos
______________________
HSN Theory Guide
_______________________
Mind Maps
_________________________
Addition FormulaSolving Trig EquationsTrigonometry Theory (HSN)Trigonometry (HSN)
Double Angle FormulaTrig GraphsWave Function (HSN)
Exact ValuesCompound Angle Formula
Radian MeasureTrigonometry 1
Trig Equations 1Trigonometry 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
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Topic
_______________________________
Answers
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Essential Skills 11Trigonometric FormulaAnswers
Essential Skills 12Related AnglesAnswers
Essential Skills 13Trigonometric EquationsAnswers
Essential Skills 16The Wave FunctionAnswers
Essential Skills 19Proving Trigonometric IdentitiesAnswers
Essential Skills 25Sine Rule (N5 Maths)Answers
Essential Skills 26Cosine Rule (N5 Maths)Answers
Higher Exam QuestionsTrig Formulae & EquationsAnswers

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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 CollinearityVectorsVectors Theory (HSN)Vectors (HSN)
Angle Between VectorsVectors 1
Basis VectorsVectors 2
Dividing a Line in a Given RatioVectors 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
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Topic
__________________________
Answers
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Essential Skills 10Section FormulaAnswers
Essential Skills 21Scalar ProductAnswers
Essential Skills 30Angle between VectorsAnswers
Higher Exam QuestionsVectorsAnswers

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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.

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.

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.

Covers the whole of the Higher Maths course

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Resources used with students in Scottish Secondary Schools

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