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.

Higher Maths Worksheets
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Worksheet - Without Answers
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Worksheet - With Answers
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Heinemann Book - CirclesEx 12B, 12D, 12F, 12H, 12J, 12K, 12LAnswers on Links
Essential Skills Exam Practice 12CirclesAnswers
Essential Skills 8Tangent to a CircleAnswers
Essential Skills 9Intersection of Lines & CirclesAnswers
Grade Booster Paper 1CirclesWorked Solutions (Study Pack Sample)
Higher Exam Worksheet - RecommendedCircles 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 4Answers
Exam Check List 2Circles

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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.

Higher Maths Worksheets
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Worksheet - Without Answers
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Worksheet - With Answers
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Heinemann Book - DifferentiationEx 6C, 6D, 6E, 6F, 6G, 6H, 6I, 6J, 6L, 6M, 6N, 6O, 6P, 6Q, 6R, 6SAnswers on Links
Heinemann Book - Further CalculusEx 14B, 14C, 14E, 14G, 14H, 14I, 14J, 14KAnswers on Links
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 14OptimisationStudy Pack Exemplar
Higher Exam Worksheet - RecommendedDifferentiation 1 (2000 - 2019)Answers Included on Worksheet
Higher Exam Questions Differentiation 2 (2000 - 2013)For answers refer to Marking Schemes on SQA Past Paper Link HERE
Higher Exam Questions Differentiation 3 (Old Higher)Answers Included on Worksheet
Higher Exam Questions Differentiation 4Answers
Higher Exam Questions Differentiation 5Answers
Higher Exam Questions Differentiation 6 (Optimisation)Answers
Higher Exam QuestionsDerived GraphsAnswers
Higher Exam Questions - RecommendedFurther Calculus 1 (2000 - 2019)Answers Included on Worksheet
Higher Exam QuestionsFurther Calculus 2Answers
Worksheet 1Differentiation Introduction - 1
Worksheet 2Differentiation Introduction (Ques Only), Ques & AnswersAnswers
Worksheet 3Differentiation Matching (Ques Only), Ques & AnswersAnswers
Exam Check List 3Differentiation
Exam Check List 5Further Calculus

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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/Worked Solutions
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Heinemann Book - Exponentials & LogsEx15C, 15D, 15E. 15F, 15G, 15H, 15I, 15J, 15K, 15LAnswers on Links
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)Study Pack Sample - Solutions
Grade Booster Paper 13Log Equations & GraphsStudy Pack Sample - Solutions
Higher Exam Questions - RecommendedExponentials & Logs 1 (2000 - 2019)Answers Included on Worksheet
Higher Exam QuestionsExponentials & Logs 1 (2000 - 2013)For answers refer to Marking Schemes on SQA Past Paper Link HERE
Higher Exam QuestionsExponentials & Logs 2 (Old Higher)Answers Included on Worksheet
Higher Exam QuestionsExponentials & Logs 3Answers
Exam Check List 4Exponentials & Logs

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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/Worked Solutions
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Heinemann Book - Sets & FunctionsEx 2A, 2B, 2C, 2D, 2F, 2G, 2H, 2IAnswers on Links
Heinemann Book - Graphs of FunctionsEx 3A, 3C, 3E, 3G, 3I, 3K, 3M, 3N, 3O, 3PAnswers on Links
Heinemann Book - Trig Graphs & EquationsEx 4A, 4B, 4C, 4E, 4H, 4I, 4JAnswers on Links
Essential Skills Exam Practice 6FunctionsAnswers
Essential Skills 17Graphs of Derived FunctionsAnswers
Essential Skills 20Related GraphsAnswers
Essential Skills 27Composite FunctionsAnswers
Essential Skills 28Inverse FunctionsAnswers
Higher Exam Questions - RecommendedFunctions & Sets (2000 - 2019)Answers Included on Worksheet
Higher Exam QuestionsFunctions & Graphs (2000 - 2013)For answers refer to Marking Schemes on SQA Past Paper Link HERE
Higher Exam QuestionsFunctions 1 (Old Higher)Answers Included on Worksheet
Higher Exam QuestionsFunctions 2Answers
Higher Exam QuestionFunctions & Graphs 4Answers
Higher Exam QuestionsFunctionsAnswers
Higher Exam Questions - RecommendedGraphs of Functions 1 (2000 - 2019)Answers Included on Worksheet
Higher Exam QuestionsGraphs of Functions 2Answers
Higher Exam QuestionsDomain Restrictions
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
Exam Check List 6Graphs of Functions
Exam Check List 13Trig 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
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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/Worked Solutions
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Heinemann Book - IntegrationEx 9G, 9H, 9I, 9L, 9N, 9P, 9Q, 9RAnswers on Links
Heinemann Book - Further CalculusEx 14B, 14C, 14E, 14G, 14H, 14I, 14J, 14KAnswers on Links
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 Questions - RecommendedFurther Calculus 1 (2000 - 2019)Answers Included on Worksheet
Higher Exam QuestionsFurther Calculus 2Answers
Higher Exam Questions - RecommendedIntegration 1 (2000 - 2019)Answers Included on Worksheet
Higher Exam QuestionsIntegration 2 (2000 - 2013)For answers refer to Marking Schemes on SQA Past Paper Link HERE
Higher Exam QuestionsIntegration 3 (Old Higher)Answes Included on Worksheet
Higher Exam QuestionsIntegration 4Answers
Higher Exam QuestionsIntegration 5Answers
Higher Exam QuestionsIntegration 6 - Area under a CurveAnswers
Exam Check List 5Further Calculus
Exam Check List 7Integration

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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/Worked Solutions
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Heinemann Book - PolynomialsEx 7B, 7C, 7D, 7E, 7F, 7G, 7H, 7I, 7KAnswers on Links
Heinemann Book - QuadraticsEx 8C, 8D, 8E, 8F, 8I, 8J, 8KAnswers on Links
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 3PolynomialsStudy Pack Sample - Solutions
Grade Booster Paper 9DiscriminantStudy Pack Sample - Solutions
Higher Exam Questions - RecommendedPolynomials (2000 - 2019)Answers Included on Worksheet
Higher Exam QuestionsPolynomials & Quadratics (2000 - 2013)For answers refer to Marking Schemes on SQA Past Paper Link HERE
Higher Exam QuestionsPolynomials (Old Higher)Answes Included on Worksheet
Higher Exam Questions - RecommendedQuadratics (2000 - 2019)Answers Included on Worksheet
Higher Exam QuestionsQuadratics (Old Higher)Answers Included on Worksheet
Higher Exam QuestionsPolynomials & Quadratics
Answers
Higher Exam QuestionsPolynomials Answers
Higher Exam QuestionsQuadratics Answers
Higher Exam QuestionsPolynomials & QuadraticsAnswers
Worksheet 1Completing the SquareAnswers
Worksheet 2Completing the Square - AdvancedAnswers
Exam Check List 8Polynomials
Exam Check List 9Quadratics

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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/Worked Solutions
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Heinemann Book - Recurrence RelationsEx 5A, 5B, 5C, 5D, 5H, 5IAnswers on Links
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 1 (2000 - 2013)For answers refer to Marking Schemes on SQA Past Paper Link HERE
Higher Exam QuestionsRecurrence Relations 2 (Old Higher)Answers Included on Worksheet
Higher Exam QuestionsRecurrence Relations 3Answers
Higher Exam QuestionsRecurrence Relations 4Answers
Exam Check List 10Recurrence 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
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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/Worked Solutions
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Heinemann Book - Straight Line Ex 1A, 1B, 1D, 1E, 1F, 1G, 1I, 1K, 1M, 1N, 1OAnswers on Links
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 LinesStudy Pack Sample - Solutions
Higher Exam Questions - RecommendedStraight Lines 1 (2000 - 2019)Answers Included on Worksheet
Higher Exam QuestionsStraight Lines 2 (2000 - 2013)For answers refer to Marking Schemes on SQA Past Paper Link HERE
Higher Exam QuestionsStraight Lines 3 (Old Higher)Answers Included on Worksheet
Higher Exam QuestionsStraight Lines 4Answers
Higher Exam QuestionsStraight Lines 5 Answers
Higher Exam QuestionsStraight Lines 6 (Multiple Choice)
Worksheets 1 & 2Gradients of Perpendicular Lines 1, 2
Worksheet 3Distance Formula
Exam Check List 11Straight Lines

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/Worked Solutions
___________________________________________________________
Heinemann Book - Trig Graphs & EquationsEx 4A, 4B, 4C, 4E, 4H, 4I, 4JAnswers on Links
Heinemann Book - Addition FormulaeEx 11B, 11C, 11D, 11E, 11F, 11G, 11H, 11JAnswers on Links
Heinemann Book - Further CalculusEx 14B, 14C, 14E, 14G, 14H, 14I, 14J, 14KAnswers on Links
Heinemann Book - Wave FunctionEx 16A, 16C, 16D, 16E, 16F, 16G, 16HAnswers on Links
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 Questions - RecommendedAddition Formulae (2000 - 2019)Answers Included on Worksheet
Higher Exam Questions - RecommendedFurther Calculus (2000 - 2019)Answers Included on Worksheet
Higher Exam Questions - RecommendedTrigonometry 1 (2000 - 2015)Answers Included on Worsksheet
Higher Exam QuestionsTrigonometry 2 (2000 - 2013)For answers refer to Marking Schemes on SQA Past Paper Link HERE
Higher Exam Question - RecommendedTrig Addition Formulae 1 (2000 - 2019)Answers Included on Worksheet
Higher Exam QuestionsTrig Addition Formula 2 (Old Higher)Answes Included on Worksheet
Higher Exam QuestionsTrig Graphs & Eqns 3 (Old Higher)Answers Included on Worksheet
Higher Exam QuestionsTrig Formulae & Equations 4Answers
Higher Exam QuestionsTrig Formulae & Equations 5Answers
Higher Exam Questions - RecommendedWave Function 1 (2000 - 2019)Answers Included on Worksheet
Higher Exam QuestionsWave Function 2 (2000 - 2013)For answers refer to Marking Schemes on SQA Past Paper Link HERE
Higher Exam QuestionsWave Function 3 (Old Higher)Answes Included on Worksheet
Higher Exam QuestionsWave Function 4Answers
Exam Check List 1Addition Formulae
Exam Check List 13Trig Graphs & Equations
Exam Check List 15Wave Function

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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
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Answers/Worked Solutions
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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 7VectorsStudy Pack Sample - Solutions
Higher Exam Questions - RecommendedVectors 1 (2000 - 2019)Answers Included on Worksheet
Higher Exam QuestionsVectors 2 (2000 - 2013)For answers refer to Marking Schemes on SQA Past Paper Link HERE
Higher Exam QuestionsVectors 3 (Old Higher)Answers Included on Worksheet
Higher Exam QuestionsVectors 4Answers
Exam Check List 14Vectors

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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.

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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