Free Videos & Worksheets

Welcome to highermathematics.co.uk

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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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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Comment
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Heinemann Book - CirclesEx 12B, 12D, 12F, 12H, 12J, 12K, 12LAnswers on LinksWhole text book solutions available in the Online Study Pack
Essential Skills Exam Practice 12CirclesAnswers
Essential Skills 8Tangent to a CircleAnswers
Essential Skills 9Intersection of Lines & CirclesAnswers
Grade Booster Paper 1CirclesAnswers
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)Differentiation (Preparing For)
Closed IntervalsRate of Change & Tangent to a CurveDifferentiation 1
Complex DifferentiationTrig Functions & Chain RuleDifferentiation 2
Curve SketchingDifferentiation (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.

Worksheets
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Topic
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Answers
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Comment
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Heinemann Book - DifferentiationEx 6C, 6D, 6E, 6F, 6G, 6H, 6I, 6J, 6L, 6M, 6N, 6O, 6P, 6Q, 6R, 6SAnswers on LinksWhole text book solutions available in the Online Study Pack
Heinemann Book - Further CalculusEx 14B, 14C, 14E, 14G, 14H, 14I, 14J, 14KAnswers on LinksWhole text book solutions available in the Online Study Pack
Essential Skills Exam Practice 3DifferentiationAnswers
Essential Skills Exam Practice 9Further CalculusAnswers
Essential Skills 4Equation of a Tangent to a CurveAnswers
Essential Skills 5Stationary PointsAnswers
Essential Skills 17Graphs of Derived FunctionsAnswers
Essential Skills 22Further DifferentiationAnswers
Essential Skills 23Further IntegrationAnswers
Grade Booster Paper 4Stationary PointsAnswers
Grade Booster Paper 6Tangents to CurvesAnswers
Grade Booster Paper 14OptimisationAnswers
Higher Exam QuestionsDerived GraphsAnswers
Higher Exam QuestionsDifferentiation - 1Answers
Higher Exam QuestionsDifferentiation - 2Answers
Higher Exam QuestionsDifferentiation (Optimisation)Answers
Higher Exam QuestionsFurther CalculusAnswers
Worksheet 1Differentiation Introduction - 1
Worksheet 2Differentiation Introduction (Ques Only), Ques & AnswersAnswers
Worksheet 3Differentiation Matching (Ques Only), Ques & AnswersAnswers

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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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Comment
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Heinemann Book - Exponentials & LogsEx15C, 15D, 15E. 15F, 15G, 15H, 15I, 15J, 15K, 15LAnswers on LinksWhole text book solutions available in the Online Study Pack
Essential Skills Exam Practice 13Logarithms Answers
Essential Skills 18Logarithmic EquationsAnswers
Essential Skills 31Natural LogarithmsAnswers
Essential Skills 32Logs: Connecting 2 VariablesAnswers
Grade Booster Paper 11Exponential Functions (Half-Life)Answers
Grade Booster Paper 13Log Equations & GraphsAnswers
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 & Graphs
Exact ValuesGraph Transformations - Movement & Reflection
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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Comment
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Heinemann Book - Sets & FunctionsEx 2A, 2B, 2C, 2D, 2F, 2G, 2H, 2IAnswers on LinksWhole text book solutions available in the Online Study Pack
Heinemann Book - Graphs of FunctionsEx 3A, 3C, 3E, 3G, 3I, 3K, 3M, 3N, 3O, 3PAnswers on LinksWhole text book solutions available in the Online Study Pack
Heinemann Book - Trig Graphs & EquationsEx 4A, 4B, 4C, 4E, 4H, 4I, 4JAnswers on LinksWhole text book solutions available in the Online Study Pack
Essential Skills Exam Practice 6FunctionsAnswers
Essential Skills 17Graphs of Derived FunctionsAnswers
Essential Skills 20Related GraphsAnswers
Essential Skills 27Composite FunctionsAnswers
Essential Skills 28Inverse FunctionsAnswers
Worksheet 1Graph Transformations GridAnswers
Worksheets 2 & 3Blank Grid 1, Blank Grid 2
Worksheets 4Graph TransformationsAnswers
Worksheets 5Graphs of Trig Functions
Worksheets 6Trig Functions - Period & Amplitude
Higher Exam QuestionsFunctionsAnswers
Higher Exam QuestionsFunctions & GraphsAnswers
Higher Exam QuestionsGraphs of FunctionsAnswers
Higher Exam QuestionsDomain Restrictions

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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 CurvesIntegration (Preparing For)
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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Comment
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Heinemann Book - IntegrationEx 9G, 9H, 9I, 9L, 9N, 9P, 9Q, 9RAnswers on LinksWhole text book solutions available in the Online Study Pack
Heinemann Book - Further CalculusEx 14B, 14C, 14E, 14G, 14H, 14I, 14J, 14KAnswers on LinksWhole text book solutions available in the Online Study Pack
Essential Skills Exam Practice 8IntegrationAnswers
Essential Skills Exam Practice 9Further CalculusAnswers
Essential Skills 23Further IntegrationAnswers
Essential Skills 25Differential EquationsAnswers
Essential Skills 26Definite IntegralsAnswers
Grade Booster Paper 12IntegrationAnswers
Higher Exam QuestionsIntegration - 1Answers
Higher Exam QuestionsIntegration - 2Answers
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 & Quadratics
Factorising PolynomialsInequationsPolynomials
Factorising Functions from GraphsIntersection of Parabolas & LinesQuadratics
Finding Unknown CoefficientsUsing 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
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Topic
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Answers
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Courtesy/comments
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Heinemann Book - PolynomialsEx 7B, 7C, 7D, 7E, 7F, 7G, 7H, 7I, 7KAnswers on LinksWhole text book solutions available in the Online Study Pack
Heinemann Book - QuadraticsEx 8C, 8D, 8E, 8F, 8I, 8J, 8KAnswers on LinksWhole text book solutions available in the Online Study Pack
Essential Skills Exam Practice 2Quadratic TheoryAnswers
Essential Skills Exam Practice 4PolynomialsAnswers
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
Grade Booster Paper 3PolynomialsAnswers
Grade Booster Paper 9DiscriminantAnswers
Higher Exam QuestionsPolynomialsAnswers
Higher Exam QuestionsQuadraticsAnswers
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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Introduction to Recurrence RelationsSequencesSequencesSequences (HSN)
Limit of a SequenceRecurrence Relations 1
Recurrence Relation from a SequenceRecurrence 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 Exam Practice 10Recurrence RelationsAnswers
Essential Skills 15Limit of a Recurrence RelationAnswers
Essential Skills 24Recurrence: Consecutive TermsAnswers
Grade Booster Paper 2Recurrence RelationsAnswers
Higher Exam QuestionsRecurrence Relations - 1Answers
Higher Exam QuestionsRecurrence Relations - 2Answers

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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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Comment
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Heinemann Book - Straight Line Ex 1A, 1B, 1D, 1E, 1F, 1G, 1I, 1K, 1M, 1N, 1OAnswers on LinksWhole text book solutions available in the Online Study Pack
Essential Skills Exam Practice 1Straight LineAnswers
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 of Lines & CirclesAnswers
Essential Skills 19Simultaneous Equations (N5 Maths)Answers
Essential Skills 29Angle between Line & x-axisAnswers
Grade Booster Paper 5Straight LinesAnswers
Higher Exam QuestionsStraight Line - 1 (Multiple Choice)
Higher Exam QuestionsStraight Lines - 2Answers
Higher Exam QuestionsStraight Lines - 3Answers
Higher Exam QuestionsStraight Lines (Old Higher)Answers Included
Higher Exam QuestionsPolynomials & QuadraticsAnswersIncludes the Intersection of a Line & Curve
Worksheets 1 & 2Gradients of Perpendicular Lines 1, 2
Worksheet 3Distance Formula

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
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HSN Theory Guide
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Mind Maps
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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
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Answers
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Comment
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Heinemann Book - Trig Graphs & EquationsEx 4A, 4B, 4C, 4E, 4H, 4I, 4JAnswers on LinksWhole text book solutions available in the Online Study Pack
Heinemann Book - Addition FormulaeEx 11B, 11C, 11D, 11E, 11F, 11G, 11H, 11JAnswers on LinksWhole text book solutions available in the Online Study Pack
Heinemann Book - Further CalculusEx 14B, 14C, 14E, 14G, 14H, 14I, 14J, 14KAnswers on LinksWhole text book solutions available in the Online Study Pack
Heinemann Book - Wave FunctionEx 16A, 16C, 16D, 16E, 16F, 16G, 16HAnswers on LinksWhole text book solutions available in the Online Study Pack
Essential Skills Exam Practice 5Trigonometry Answers
Essential Skills Exam Practice 7Wave FunctionAnswers
Essential Skills 11Trig FormulaAnswers
Essential Skills 12Related AnglesAnswers
Essential Skills 13Trig Equations (Double Angle Formula)Answers
Essential Skills 16The Wave FunctionAnswers
Essential Skills 19Proving Trig IdentitiesAnswers
Essential Skills 25Sine Rule (N5 Maths)Answers
Essential Skills 26Cosine Rule (N5 Maths)Answers
Grade Booster Paper 8Wave FunctionAnswers
Grade Booster Paper 10Trig Equations with Double AnglesAnswers
Worksheets 1Graphs of Trig Functions
Worksheets 2Trig Functions - Period & Amplitude
Higher Exam QuestionsTrig Formulae & Equations - 1Answers
Higher Exam QuestionsTrig Formulae & Equations - 2Answers

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10. Vectors – 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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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
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Answers
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Essential Skills Exam Practice 11VectorsAnswers
Essential Skills 10Section FormulaAnswers
Essential Skills 21Scalar ProductAnswers
Essential Skills 30Angle between VectorsAnswers
Grade Booster Paper 7VectorsAnswers
Higher Exam QuestionsVectorsAnswers

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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.

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Resources used with students in Scottish Secondary Schools

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