Unsure about Equations of Tangents?

Unsure about Equations of Tangents?

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Covers the whole of the Higher Maths course

Created by an experienced maths teacher

Resources used with students in Scottish Secondary Schools

Equations of Tangents

Welcome to highermathematics.co.uk

A sound understanding of Equations of Tangents is essential to ensure exam success.

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 2025. Please find below:

1. Straight Lines & Differentiation – Worksheets

2. About Equations of Tangents

3. Straight Lines & Differentiation – Videos, Theory Guides & Mind Maps

4. Higher Maths Essential Skills 

5. Higher Maths Exam Worksheets by Topic

6. Higher Maths Past & Practice Papers by Topic 

7. Higher Maths Videos, Theory Guides, Mind Maps & Worksheets 

8. Higher Maths Past & Practice Papers 

9. 40 Non-Calculator Higher Maths Questions & Answers

10. 200 Higher Maths Questions & Answers 

11. Practice Exam Papers A to H – Answers Included

12. 264 SQA Exam Multiple Choice Questions & Answers

13. Higher Maths Exam Check Lists 

14. Old Higher Maths Exam Questions by Topic

15. Higher Maths Text Book Solutions

16. Higher Maths Theory Guides 

17. Higher Maths Mind Maps 

18. Higher Maths Practice Unit Assessments – Solutions Included

19. Higher Maths Past Paper Video Solutions

20. Higher Maths Recommended Text Book

21. Exam Focused Online Study Pack – For students looking for a ‘good’ Pass

 

Higher Maths Resources

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1. Straight Lines & Differentiation – Worksheets

Thanks to the SQA and authors for making the excellent resources below freely available. Please use regularly for revision prior to assessments, tests and the final exam.

Straight Lines – Worksheets

Clear, easy to follow, step-by-step worked solutions to all worksheets below are available in the Online Study Pack.

Notes
__________________
Higher Worksheets
__________________________
Worksheet
_________________________________
Without Answers
________________
Notes/Comments
_____________________
Courtesy
______________________
Straight Line Theory (HSN)Straight Line Theory (HSN)RecommendedCourtesy of HSN
Text Book SolutionsHeinemann Book - Straight Line Ex 1A, 1B, 1D, 1E, 1F, 1G, 1I, 1K, 1M, 1N, 1OAnswers on Links
Essential Skills Exam Practice 1Straight LineWithout Answers Answers OnlyCourtesy of Mr G Rennie
Essential Skills 1Median of a TriangleWithout AnswersAnswers OnlyCourtesy of Mr G Rennie
Essential Skills 2Perpendicular BisectorsWithout AnswersAnswers OnlyCourtesy of Mr G Rennie
Essential Skills 3Altitude of a TriangleWithout AnswersAnswers OnlyCourtesy of Mr G Rennie
Essential Skills 4Equation of a Tangent to a CurveWithout AnswersAnswers OnlyCourtesy of Mr G Rennie
Essential Skills 9Intersection of Lines & CirclesWithout AnswersAnswers OnlyCourtesy of Mr G Rennie
Essential Skills 29Angle between Line & x-axisWithout AnswersAnswers OnlyCourtesy of Mr G Rennie
Grade Booster Paper 5Straight LinesWithout Answers
2023 Included!Exam Worksheet 1Straight Lines 1 (2000 - 2023)Without AnswersRecommendedCourtesy of the SQA
Exam Worksheet 2Straight Lines 2 (2000 - 2019)Without AnswersCourtesy of the SQA
Exam Worksheet 3Straight Lines 3 (2015 - 2019)Without AnswersCourtesy of the SQA
54 SQA QuestionsExam Worksheet 4Straight Lines 4 (Old Higher)Without AnswersMultiple Choice Included!
Exam Worksheet 5Straight Lines 5 (Old Higher)Without AnswersCourtesy of the SQA
Exam Worksheet 6Straight Lines 6 (2000 - 2013)SQA Marking SchemesCourtesy of the SQA
Exam Worksheet 7Straight Lines 7 (Multiple Choice)SQA Marking SchemesCourtesy of the SQA
Worksheets 1 & 2Gradients of Perpendicular Lines 1, 2
CodebreakerWorksheet 3Codebreaker - Distance FormulaWithout Answers
Worksheet 4Distance Formula
Exam Check List 11Straight Lines

Differentiation – Worksheets

Clear, easy to follow, step-by-step worked solutions to all worksheets below are available in the Online Study Pack.

Notes
_________________
Higher Worksheets
__________________________
Worksheets
__________________________________
Without Answers
________________
Notes/Comments
_________________________
Courtesy
______________________
Differentiation Theory (HSN)Differentiation Theory (HSN)RecommendedCourtesy of HSN
Further Calculus Theory (HSN)Further Calculus Theory (HSN)RecommendedCourtesy of HSN
Text Book SolutionsHeinemann - DifferentiationEx 6C, 6D, 6E, 6F, 6G, 6H, 6I, 6J, 6L, 6M
, 6N
, 6O, 6P, 6Q, 6R, 6S
Answers on Links
Text Book SolutionsHeinemann - Further CalculusEx 14B, 14C, 14E, 14G, 14H, 14I, 14J, 14KAnswers on Links
Essential Skills Exam Practice 3DifferentiationWithout AnswersAnswers OnlyCourtesy of Mr G Rennie
Essential Skills Exam Practice 9Further CalculusWithout AnswersAnswers OnlyCourtesy of Mr G Rennie
Essential Skills 4Equation of a Tangent to a CurveWithout AnswersAnswers OnlyCourtesy of Mr G Rennie
Essential Skills 5Stationary PointsWithout AnswersAnswers OnlyCourtesy of Mr G Rennie
Essential Skills 17Graphs of Derived FunctionsWithout AnswersAnswers OnlyCourtesy of Mr G Rennie
Essential Skills 22Further DifferentiationWithout AnswersAnswers OnlyCourtesy of Mr G Rennie
Essential Skills 23Further IntegrationWithout AnswersAnswers OnlyCourtesy of Mr G Rennie
Grade Booster Paper 4Stationary PointsWithout Answers
Grade Booster Paper 6Tangents to CurvesWithout Answers
Grade Booster Paper 14OptimisationWithout Answers
2023 Included!Exam Worksheet 1Differentiation 1 (2000 - 2023)Without AnswersRecommendedCourtesy of the SQA
Exam Worksheet 2Differentiation 2 (2014 - 2019)Without AnswersCourtesy of the SQA
Exam Worksheet 3Differentiation 3 (2000 - 2019)Without AnswersCourtesy of the SQA
Exam Worksheet 4Differentiation 4 (Optimisation)Without AnswersCourtesy of the SQA
123 SQA QuestionsExam Worksheet 5Differentiation 5 (Old Higher)Without AnswersMultiple Choice Included!Courtesy of the SQA
Exam Worksheet 6Differentiation 6 (Old Higher)Without AnswersCourtesy of the SQA
Exam Worksheet 7Differentiation 7 (2000 - 2013)SQA Marking SchemesCourtesy of the SQA
2023 Included!Exam Worksheet 8Further Calculus 1 (2000 - 2023)Without AnswersRecommendedCourtesy of the SQA
Exam Worksheet 9Further Calculus 2Without AnswersCourtesy of the SQA
Exam Worksheet 10Further Calculus 3 (Old Higher)Without AnswersMultiple Choice Included!Courtesy of the SQA
Worksheet 1Differentiation Introduction - 1
Worksheet 2Differentiation Introduction - 2Without AnswersAnswers Only
Worksheet 3Differentiation MatchingWithout AnswersAnswers Only
Exam Check List 3Differentiation
Exam Check List 5Further Calculus


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2. About Equations of Tangents 

To learn about Equations of Tangents please click on the Straight Line Theory (HSN) link and read from page 7 as well as the Differentiation Theory (HSN) link and read from page 8. Please also find in Sections 2 & 3 below videos (Differentiation – Equation of Tangents), mind maps  (see Perpendicular Lines (under Straight Lines) & Equations of Tangents (under Differentiation)) and worksheets on this topic to help your understanding. The Essential Skills worksheets, along with worksheets including actual SQA Exam Questions, are highly recommended.

If you would like more help understanding Equations of Tangents there are full, easy to follow, step-by-step worked solutions to dozens of Higher Maths Past & Practice exam questions on all topics in the Online Study Pack. Please give yourself every opportunity for success, speak with your parents, and subscribe to the exam focused Online Study Pack today.

Equations of Tangents

In the Higher Maths exam you may be asked to determine the equation of the tangent. The diagram below shows a line tangent to a circle – would you know how to find the equation of the tangent?

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  • A tangent is a straight line perpendicular to another line – at right angles
  • For perpendicular gradients m1m2 = -1
  • We use the equations y – b = m(x – a) or y = mx + c  to find the equation of a straight line
  • Differentiation is the rate of change of a function with respect to one of its variables
  • If we differentiate and substitute for x then this is the gradient of the tangent at that point
  • ‘Equations of tangents’ are in both the ‘Straight Lines‘ and ‘Differentiation‘ sections of the Higher Maths course

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3. Straight Lines & Differentiation – Videos, Theory Guides & Mind Maps

Thanks to the authors for making the excellent resources below freely available. Please use regularly for revision prior to assessments, tests and the final exam.

Straight Lines – Videos, Theory Guides & Mind Maps

Larbert Maths Videos
_____________________
maths180.com Video
___________________
HSN Theory Guide
_______________________
Mind Maps
__________________
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

Differentiation – Videos, Theory Guides & Mind Maps

Larbert Maths Videos
__________________________________
maths180.com Videos
______________________________________
HSN Theory Guides
____________________________
Mind Maps
____________________________
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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4. Higher Maths Essential Skills 

Thanks to Mr G Rennie for making the excellent resources below freely available. The Essential Skills Worksheets can be used for general revision, homework, consolidation of a topic or preparation for assessments, tests and exams. Clear, easy to follow, step-by-step worked solutions to all 33 Essential Skills worksheets below are available in the Online Study Pack

Essential Skills
__________________
Topic - Answers Included
______________________________
Without Answers
________________
Answers Only
______________
Worked Solutions
______________________
Essential Skills 1Median of a TriangleWithout AnswersAnswers OnlyIn Online Study Pack
Essential Skills 2Perpendicular BisectorsWithout AnswersAnswers OnlyIn Online Study Pack
Essential Skills 3Altitude of a TriangleWithout AnswersAnswers OnlyIn Online Study Pack
Essential Skills 4Equation of a Tangent to a CurveWithout AnswersAnswers OnlyIn Online Study Pack
Essential Skills 5Stationary PointsWithout AnswersAnswers OnlyIn Online Study Pack
Essential Skills 6Quadratic InequalitiesWithout AnswersAnswers OnlyIn Online Study Pack
Essential Skills 7Completing the SquareWithout AnswersAnswers OnlyIn Online Study Pack
Essential Skills 8Tangent to a CircleWithout AnswersAnswers OnlyIn Online Study Pack
Essential Skills 9Intersection of Lines & CirclesWithout AnswersAnswers OnlyIn Online Study Pack
Essential Skills 10Section FormulaWithout AnswersAnswers OnlyIn Online Study Pack
Essential Skills 11Trig FormulaWithout AnswersAnswers OnlyIn Online Study Pack
Essential Skills 12Related AnglesWithout AnswersAnswers OnlyIn Online Study Pack
Essential Skills 13Trig Equations (Double Angle Formula)Without AnswersAnswers OnlyIn Online Study Pack
Essential Skills 14Synthetic DivisionWithout AnswersAnswers OnlyIn Online Study Pack
Essential Skills 15Limit of a Recurrence RelationWithout AnswersAnswers OnlyIn Online Study Pack
Essential Skills 16The Wave FunctionWithout AnswersAnswers OnlyIn Online Study Pack
Essential Skills 17Graphs of Derived FunctionsWithout AnswersAnswers OnlyIn Online Study Pack
Essential Skills 18Logarithmic EquationsWithout AnswersAnswers OnlyIn Online Study Pack
Essential Skills 19Proving Trig IdentitiesWithout AnswersAnswers OnlyIn Online Study Pack
Essential Skills 20Related GraphsWithout AnswersAnswers OnlyIn Online Study Pack
Essential Skills 21Scalar ProductWithout AnswersAnswers OnlyIn Online Study Pack
Essential Skills 22Further DifferentiationWithout AnswersAnswers OnlyIn Online Study Pack
Essential Skills 23Further IntegrationWithout AnswersAnswers OnlyIn Online Study Pack
Essential Skills 24Recurrence: Consecutive TermsWithout AnswersAnswers OnlyIn Online Study Pack
Essential Skills 25Differential EquationsWithout AnswersAnswers OnlyIn Online Study Pack
Essential Skills 26Definite IntegralsWithout AnswersAnswers OnlyIn Online Study Pack
Essential Skills 27Composite FunctionsWithout AnswersAnswers OnlyIn Online Study Pack
Essential Skills 28Inverse FunctionsWithout AnswersAnswers OnlyIn Online Study Pack
Essential Skills 29Angle between Line & x-axisWithout AnswersAnswers OnlyIn Online Study Pack
Essential Skills 30Angle between VectorsWithout AnswersAnswers OnlyIn Online Study Pack
Essential Skills 31Natural LogarithmsWithout AnswersAnswers OnlyIn Online Study Pack
Essential Skills 32Logs: Connecting 2 VariablesWithout AnswersAnswers OnlyIn Online Study Pack
Essential Skills 33Using the DiscriminantWithout AnswersAnswers OnlyIn Online Study Pack

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5. Higher Maths Exam Worksheets by Topic

Thanks to the SQA and authors for making the excellent resources below freely available. The worksheets by topic are a fantastic study resource since they are actual past paper exam questions. Clear, easy to follow, step-by-step worked solutions to all new CfE Higher Maths Questions below are available in the Online Study Pack.

Note
_____________
Worksheets
_________________
Worksheet Topic
__________________________________
Without Answers
___________________
Comments
_________________________
2023 Included!Exam Worksheet 1Addition Formulae & Trig (2000 - 2023)Without AnswersRecommended
2023 Included!Exam Worksheet 2 Circles 1 (2000 - 2023)Without AnswersRecommended
Exam Worksheet 3Circles 2 (2000 - 2013)Without Answers
Exam Worksheet 4Circles 3 (Old Higher)Without AnswersMultiple Choice Included!
Exam Worksheet 5Circles 4 (Old Higher)Without AnswersMultiple Choice Included!
Exam Worksheet 6Circles 5Without AnswersMultiple Choice Included!
2023 Included!Exam Worksheet 7Differentiation 1 (2000 - 2023)Without AnswersRecommended
Exam Worksheet 8Differentiation 2Without Answers
Exam Worksheet 9Differentiation 3Without Answers
Exam Worksheet 10Differentiation 4 (Optimisation)Without Answers
Exam Worksheet 11Differentiation 5 (Old Higher)Without AnswersMultiple Choice Included!
Exam Worksheet 12Differentiation 6 (Old Higher)Without Answers
Exam Worksheet 13Differentiation 7 (2000 - 2013)SQA Marking Schemes
2023 Included!Exam Worksheet 14Exponentials & Logs 1 (2000 - 2023)Without AnswersRecommended
Exam Worksheet 15Exponentials & Logs 2 (2010 - 2019)Without Answers
Exam Worksheet 16Exponentials & Logs 3 (Old Higher)Without AnswersMultiple Choice Included!
Exam Worksheet 17Exponentials & Logs 4 (Old Higher)Without AnswersMultiple Choice Included!
Exam Worksheet 18Exponentials & Logs 5 (2000 - 2013)SQA Marking Schemes
Exam Worksheet 19Functions 1 (Old Higher)Without AnswersMultiple Choice Included!
Exam Worksheet 20Functions 2Without Answers
2023 Included!Exam Worksheet 21Functions & Sets (2000 - 2023)Without AnswersRecommended
Exam Worksheet 22Functions & Graphs 1 (2015-2019)Without Answers
Exam Worksheet 23Functions & Graphs 2 (2000 - 2013)SQA Marking Schemes
Exam Worksheet 24Functions & Graphs 3 (Old Higher)Without AnswersMultiple Choice Included!
2023 Included!Exam Worksheet 25Further Calculus 1 (2000 - 2023)Without AnswersRecommended
Exam Worksheet 26Further Calculus 2Without Answers
Exam Worksheet 27Further Calculus 3 (Old Higher)Without AnswersMultiple Choice Included!
2023 Included!Exam Worksheet 28 Graphs of Functions 1 (2000 - 2023)Without AnswersRecommended
Exam Worksheet 29Graphs of Functions 2Without Answers
Exam Worksheet 30Graphs of Functions 3 (Old Higher)Without AnswersMultiple Choice Included!
2023 Included!Exam Worksheet 31Integration 1 (2000 - 2023)Without AnswersRecommended
Exam Worksheet 32Integration 2 (2014 - 2019)Without Answers
Exam Worksheet 33Integration 3 (2000 -2018)Without Answers
Exam Worksheet 34Integration 4 (Old Higher)Without AnswersMultiple Choice Included!
Exam Worksheet 35Integration 5 (Old Higher)Without AnswersMultiple Choice Included!
Exam Worksheet 36Integration 5 - Area under a CurveWithout Answers
Exam Worksheet 37Integration 6 (2000 - 2013)SQA Marking Schemes
2023 Included!Exam Worksheet 38Polynomials 1 (2000 - 2023)Without AnswersRecommended
Exam Worksheet 39Polynomials 2 (2000 - 2019)Without Answers
Exam Worksheet 40Polynomials 3 (Old Higher)Without Answers
Exam Worksheet 41Polynomials & Quadratics 1Without Answers
Exam Worksheet 42Polynomials & Quadratics 2 (2000 - 2013)SQA Marking Schemes
Exam Worksheet 43Polynomials & Quadratics 3 (Old Higher)Without AnswersMultiple Choice Included!
2023 Included!Exam Worksheet 44Quadratics 1 (2000 - 2023)Without AnswersRecommended
Exam Worksheet 45Quadratics 2 (2000 - 2018)Without Answers
Exam Worksheet 46Quadratics 3 (Old Higher)Without AnswersMultiple Choice Included!
Exam Worksheet 47Recurrence Relations 1 (2000 - 2019)Without AnswersRecommended
Exam Worksheet 48Recurrence Relations 2 (2000 - 2019)Without Answers
Exam Worksheet 49Recurrence Relations 3 (2015 - 2019) Without Answers
Exam Worksheet 50Recurrence Relations 4 (Old Higher)Without AnswersMultiple Choice Included!
Exam Worksheet 51Recurrence Relations 5 (Old Higher)Without AnswersMultiple Choice Included!
Exam Worksheet 52Recurrence Relations 6 (2000 - 2013)SQA Marking Schemes
2023 Included!Exam Worksheet 53Sets & Functions (2000 - 2023)Without AnswersRecommended
2023 Included!Exam Worksheet 54Straight Lines 1 (2000 - 2023)Without AnswersRecommended
Exam Worksheet 55Straight Lines 2 (2000-2019)Without Answers
Exam Worksheet 56Straight Lines 3 (2015 - 2019)Without Answers
Exam Worksheet 57Straight Lines 4 (Old Higher)Without AnswersMultiple Choice Included!
Exam Worksheet 58Straight Lines 5 (Old Higher)Without AnswersMultiple Choice Included!
Exam Worksheet 59Straight Lines 6 (2000 - 2013)SQA Marking Schemes
Exam Worksheet 60Straight Lines 7 (Multiple Choice)SQA Marking Schemes
2023 Included!Exam Worksheet 61Trigonometry 1 (2000 - 2023)Without AnswersRecommended
Exam Worksheet 62Trigonometry 2 (Old Higher)Without AnswersMultiple Choice Included!
Exam Worksheet 63Trigonometry 3 (2000 - 2013)SQA Marking Schemes
2023 Included!Exam Worksheet 64Trig Addition Formulae 1 (2000 - 2023)Without AnswersRecommended
Exam Worksheet 65Trig Addition Formulae 2 (Old Higher)Without AnswersMultiple Choice Included!
Exam Worksheet 66Trig Graphs & Equations (Old Higher)Without AnswersMultiple Choice Included!
Exam Worksheet 67Trig Formulae & Equations 1Without Answers
Exam Worksheet 68Trig Formulae & Equations 2Without Answers
Exam Worksheet 69Vectors 1 (2000 - 2019)Without AnswersRecommended
Exam Worksheet 70Vectors 2 (2015 - 2019)Without Answers
Exam Worksheet 71Vectors 3 (Old higher)Without AnswersMultiple Choice Included!
Exam Worksheet 72Vectors 4 (Old Higher)Without AnswersMultiple Choice Included!
Exam Worksheet 73Vectors 5 (2000 - 2013)SQA Marking Schemes
2023 Included!Exam Worksheet 74Wave Function 1 (2000 - 2023)Without AnswersRecommended
Exam Worksheet 75Wave Function 2Without Answers
Exam Worksheet 76Wave Function 3 (Old Higher)Without Answers
Exam Worksheet 77Wave Function 4 (2000 - 2013)SQA Marking Schemes
Prelim SpecialPrelim Revision Special, With AnswersAnswers OnlyRecommended
2022 SQA Adapted2022 Adapted SQA PaperSQA Marking SchemesRecommended
Ultimate Guide 1Ultimate Revision Guide 1Recommended
Ultimate Guide 2Ultimate Revision Guide 2 (Multiple Choice)Multiple Choice Included!

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6. Higher Maths Past & Practice Papers by Topic

Thanks to the SQA for making the excellent resources below freely available. Questions and answers have been split up by topic for your ease of reference. Clear, easy to follow, step-by-step worked solutions to all questions below are available in the Online Study Pack.

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Paper
_____________
.
Marking
__________
.
Circles
______
Differentiation
& Optimisation
____________
Exp's
& Logs
________
Functions
& Graphs
_________
Further
Calculus
________
.
Integration
_________
Polynomials
& Quadratics
____________
Recurrence
Relations
__________
Straight
Lines
_________
Trig Formulae
& Equations
____________
.
Vectors
________
Wave
Function
_________
2019 P1Marking P1Q3,16Q1Q14Q10,12Q6,11,17bQ8Q2Q4Q5,7Q13,15,17aQ9
2019 P2Marking P2Q15Q7b,11Q9,12Q5,8Q2,13Q7,10Q4Q1Q6bQ3,14Q6a
2018 P1Marking P1Q4Q6,11Q2,11,15Q3,14Q10Q7Q1,8Q13Q5,9,12
2018 P2Marking P2Q5c,12Q3,9Q11Q6Q1Q4,7a,107b,cQ5a,bQ2Q8
2017 P1Marking P1Q2Q8,15cQ12Q1,6,15aQ3,13Q10,15bQ4Q9Q7,11Q5Q14
2017 P2Marking P2Q3,10Q4,7Q9Q2Q8Q1Q6,11Q5
2016 P1Marking P1Q4,8Q2,9Q14Q6,10,12Q5Q15Q3Q1Q13Q7,11
2016 P2Marking P2Q4Q7Q6Q10,11b3b,9Q2,3aQ1Q8b,11aQ5Q8a
2015 P1Marking P1Q11,14Q2,7Q6Q4,5,13Q12,15Q3,8Q9Q10Q1
2015 P2Marking P2Q5Q8Q2Q7aQ4Q3Q1Q7bQ6Q9
Specimen P1Marking P1Q11Q8Q10Q1Q4,7Q2,5,9Q6,12Q3
Specimen P2Marking P2Q5Q3b,8Q4,7Q9Q3aQ2Q1,6Q10
Exemplar P1Marking P1Q1Q8,11Q10Q3Q2,5Q6Q4,7Q9
Exemplar P2Marking P2Q2Q9,10Q7Q8Q4Q3Q1Q5,6

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7. Higher Maths Videos, Theory Guides, Mind Maps & Worksheets

Dozens of Higher Maths Videos provide quality lessons by topic. Also included are excellent Theory Guides, Mind Maps and Revision Worksheets with actual Higher Maths exam questions. Please click on our new Higher Maths Videos & Worksheets by topic dedicated page.

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8. Higher Maths Past & Practice Papers

Thanks to the SQA for making the excellent resources below freely available. Clear, easy to follow, step-by-step worked solutions to all CfE Higher Papers below are available in the Online Study Pack.

Year
___________________
Paper Type
____________________
Exam Paper
______________________
Electronic FilesMarking Scheme
____________________
Worked Solutions
______________________
Comments
___________________
2024Higher (CfE)Exam PaperTo be added asapIn Online Study Pack
2023 Higher (CfE)Exam PaperMarking SchemeIn Online Study Pack
2022Higher (CfE)Exam Paper Marking SchemeIn Online Study Pack
2021Higher (CfE)Exam PaperMarking SchemeIn Online Study Pack
2019Higher (CfE)Exam PaperMarking SchemeIn Online Study Pack
2018Higher (CfE)Exam PaperMarking SchemeIn Online Study Pack
2018 Specimen (CfE)Specimen PaperMarking SchemeIn Online Study Pack
2017Higher (CfE)Exam PaperMarking SchemeIn Online Study Pack
2016Higher (CfE)Exam PaperMarking SchemeIn Online Study Pack
2015Higher (CfE)Exam PaperMarking SchemeIn Online Study Pack
2015Specimen (CfE)Specimen PaperMarking SchemeIn Online Study Pack
2015Exemplar (CfE)Exemplar PaperMarking SchemeIn Online Study Pack
2015Higher (Old)Exam PaperMarking Scheme
2014HigherExam PaperMarking SchemeWorked Solutions
2013HigherExam PaperMarking SchemeWorked Solutions
2012HigherExam PaperMarking SchemeWorked Solutions
2011HigherExam PaperMarking SchemeWorked Solutions
2010HigherExam PaperMarking SchemeWorked Solutions
2009HigherExam PaperMarking SchemeWorked Solutions
2008HigherExam PaperMarking SchemeWorked Solutions
2007HigherExam PaperMarking SchemeWorked Solutions
2006HigherExam PaperMarking SchemeWorked Solutions
2005HigherExam PaperMarking SchemeWorked Solutions
2004HigherExam PaperMarking SchemeWorked Solutions
2003HigherExam Paper Marking SchemeWorked Solutions
2002HigherExam PaperMarking SchemeWorked Solutions
2002Higher (Winter Diet)Exam Paper
2001HigherExam PaperWorked Solutions
2000HigherExam PaperWorked Solutions
Ultimate Guide 1RecommendedUltimate Revision Guide 1CfE Papers in Study Pack
Ultimate Guide 2RecommendedUltimate Revision Guide 2 Multiple Choice Included!CfE Papers in Study Pack
2024 - Essential SkillsHigher (CfE)Practice Papers 1 & 2Answers OnlyIn Online Study PackCourtesy of Mr G Rennie
2024 - Last MinuteHigher (CfE)Condensed Paper & SolnsAnswers IncludedCourtesy of Mr Smith
2023 - Essential SkillsHigher (CfE)Practice Papers 1 & 2Answers OnlyWorked SolutionsCourtesy of Mr G Rennie
2022 Adapted2022 Adapted PaperExam PaperMarking 2019, 18, Spec'nIn Online Study Pack

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9. 40 Non-Calculator Higher Maths Questions & Answers

Thanks to the SQA and authors for making the excellent resources below freely available. Start with these questions to help build your confidence. Once finished, you may like to move onto the 200 Higher Maths Exam Questions in the next section checking your answers as you go. If stuck, always ask your teacher for help as soon as possible. Clear, easy to follow, step-by-step worked solutions to all 40 questions below are available in the Online Study Pack.

Worksheet
______________
Exam Questions & Answers
________________________
Without Answers
_______________
Answers
__________
Worked Solutions
___________________
Worksheet 1Sheet A - 10 QuestionsWithout AnswersAnswersIn Online Study Pack
Worksheet 2Sheet B - 10 QuestionsWithout AnswersAnswersIn Online Study Pack
Worksheet 3Sheet C - 10 QuestionsWithout AnswersAnswersIn Online Study Pack
Worksheet 4Sheet D - 10 QuestionsWithout AnswersAnswersIn Online Study Pack
Whole BookletWhole Booklet for PrintingWithout AnswersAnswersIn Online Study Pack

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10. 200 Higher Maths Questions & Answers

Thanks to the SQA and authors for making the excellent resources below freely available. Please try to do as many questions as possible, checking your answers as you go. If stuck, always ask your teacher for help as soon as possible. Clear, easy to follow, step-by-step worked solutions to all 200 questions below are available in the Online Study Pack.

Worksheet
______________
Exam Questions & Answers
________________________
Without Answers
_______________
Answers Only
______________
Worked Solutions
___________________
Worksheet 1Exam Questions 1 - 20Without AnswersAnswers OnlyIn Online Study Pack
Worksheet 2Exam Questions 21 - 40Without AnswersAnswers OnlyIn Online Study Pack
Worksheet 3Exam Questions 41 - 60Without AnswersAnswers OnlyIn Online Study Pack
Worksheet 4Exam Questions 61 - 80Without AnswersAnswers OnlyIn Online Study Pack
Worksheet 5Exam Questions 81 - 100Without AnswersAnswers OnlyIn Online Study Pack
Worksheet 6Exam Questions 101 - 120Without AnswersAnswers OnlyIn Online Study Pack
Worksheet 7Exam Questions 121 - 140 Without AnswersAnswers OnlyIn Online Study Pack
Worksheet 8Exam Questions 141 - 160Without AnswersAnswers OnlyIn Online Study Pack
Worksheet 9Exam Questions 161 - 180Without AnswersAnswers OnlyIn Online Study Pack
Worksheet 10Exam Questions 181 - 200Without AnswersAnswers OnlyIn Online Study Pack
Whole BookletWhole Booklet for PrintingWithout AnswersAnswers OnlyIn Online Study Pack

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11. Practice Exam Papers A to H – Answers Included

Thanks to the SQA and Larkhall Academy for making the excellent resources below freely available. Please use regularly for revision prior to assessments, tests and the final exam. Clear, easy to follow, step-by-step worked solutions to Practice Papers A to E are available in the Online Study Pack.

Practice Paper
_____________
Paper 1
_____________
Paper 2
_____________
Papers 1 & 2
_____________________
Answers
_____________
Paper APaper 1Paper 2Papers 1 & 2Answers
Paper BPaper 1Paper 2Papers 1 & 2Answers
Paper CPaper 1Paper 2Papers 1 & 2Answers
Paper DPaper 1Paper 2Papers 1 & 2Answers
Paper EPaper 1Paper 2Papers 1 & 2Answers
Paper FPaper 1Paper 2Papers 1 & 2Answers
Paper GPaper 1Paper 2Papers 1 & 2Answers
Paper HPaper 1Paper 2Papers 1 & 2Answers
Exam Revision QuestionsQuestions & AnswersAnswers
Prelim SpecialQuestionsQuestions & AnswersAnswers
Prelim SpecialX-Mas ThemeQuestions & AnswersAnswers

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12. 264 SQA Exam Multiple Choice Questions & Answers 

Thanks to the SQA and authors for making the excellent resources below freely available. Multiple choice are primarily C level questions and a great place to start your revision. If stuck, always ask your teacher for help as soon as possible.

Questions
__________
Year
______
Exam Multiple Choice
__________________
Exam Multiple Choice
__________________
Exam Multiple Choice
__________________
1 - 202015Questions OnlyQuestions & AnswersAnswers Only
21 - 402014Questions OnlyQuestions & AnswersAnswers Only
41 - 602013Questions OnlyQuestions & AnswersAnswers Only
61 - 802012Questions OnlyQuestions & AnswersAnswers Only
81 - 1002011Questions OnlyQuestions & AnswersAnswers Only
101 - 1202010Questions OnlyQuestions & AnswersAnswers Only
121 - 264MixedQuestions OnlyQuestions & AnswersAnswers Only

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13. Higher Maths Exam Check Lists

Thanks to the SQA and authors for making the excellent resources below freely available. These are fantastic check lists to assess your Higher Maths knowledge. Please try to use these regularly for revision prior to tests, prelims and the final exam.

Check List
______________
Topic
____________________________
Check List 1Whole Course - Leckie & Leckie
Check List 2Whole Course - Zeta Maths
Check List 3Whole Course - Free Higher Maths
Check List 4HSN Unit 1 - One Page Summary
Check List 5HSN Unit 2 - One Page Summary
Check List 6HSN Unit 3 - One Page Summary
Check List 7Addition Formulae
Check List 8Circles
Check List 9Differentiation
Check List 10Exponentials & Logs
Check List 11Further Calculus
Check List 12Graphs of Functions
Check List 13Integration
Check List 14Polynomials
Check List 15Quadratics
Check List 16Recurrence Relations
Check List 17Straight Lines
Check List 18Sets & Functions
Check List 19Trig Graphs & Equations
Check List 20Vectors
Check List 21Wave Function
Check List 22Formulas not given in Exam
Check List 23SQA Formula Sheet
Check List 24Course Description
Check List 25Trig Revision Sheet

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14. Old Higher Maths Exam Questions by Topic

Thanks to the SQA for making the excellent resources below freely available. The worksheets by topic are a fantastic additional study resource.

Topic
________
Topic Name
___________________________
Link
________
Notes
___________________
Topic 1CirclesHEREAnswers Included
Topic 2DifferentiationHEREAnswers Included
Topic 3Exponentials & LogarithmsHEREAnswers Included
Topic 4FunctionsHEREAnswers Included
Topic 5Further CalculusHEREAnswers Included
Topic 6Graphs of FunctionsHEREAnswers Included
Topic 7IntegrationHEREAnswers Included
Topic 8PolynomialsHEREAnswers Included
Topic 9QuadraticsHEREAnswers Included
Topic 10Recurrence RelationsHEREAnswers Included
Topic 11Straight LineHEREAnswers Included
Topic 12Trig Addition FormulaeHEREAnswers Included
Topic 13Trig Graphs & EquationsHEREAnswers Included
Topic 14VectorsHEREAnswers Included
Topic 15Wave FunctionHEREAnswers Included

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15. Higher Maths Text Book Solutions 

Thanks to the AHS for providing the Heinemann Higher Maths text book solutions below. These will prove extremely useful in helping to progress your Higher Maths knowledge. Please note that there may be the odd arithmetic error.

Topic
_______________________
Topic Name
___________________
Check List
__________
Topic 1 - Updated SolutionsStraight LinesCheck ListEx_1AEx_1BEx_1DEx_1EEx_1FEx_1GEx_1IEx_1KEx_1MEx_1NEx_1O
Topic 2 - Updated SolutionsSets & FunctionsCheck ListEx_2AEx_2BEx_2CEx_2DEx_2FEx_2GEx_2HEx_2I
Topic 3 - Updated SolutionsGraphs of FunctionsCheck ListEx_3AEx_3CEx_3EEx_3GEx_3IEx_3KEx_3MEx_3NEx_3OEx_3P
Topic 4 - Updated SolutionsTrig Graphs & EquationsCheck ListEx_4AEx_4BEx_4CEx_4EEx_4HEx_4IEx_4J
Topic 5 - Not in 2022/23Recurrence RelationCheck ListEx_5AEx_5BEx_5CEx_5DEx_5HEx_5I
Topic 6 - Updated SolutionsDifferentiationCheck ListEx_6CEx_6DEx_6EEx_6FEx_6GEx_6HEx_6IEx_6JEx_6LEx_6MEx_6NEx_6OEx_6PEx_6QEx_6REx_6S
Topic 7 - Updated SolutionsPolynomialsCheck ListEx_7BEx_7CEx_7DEx_7EEx_7FEx_7GEx_7HEx_7IEx_7K
Topic 8 - Updated SolutionsQuadraticsCheck ListEx_8CEx_8DEx_8EEx_8FEx_8IEx_8JEx_8K
Topic 9 - Updated SolutionsIntegrationCheck ListEx_9GEx_9HEx_9IEx_9LEx_9NEx_9PEx_9QEx_9R
Topic 10 - Updated SolutionsAddition FormulaeCheck ListEx_11BEx_11CEx_11DEx_11EEx_11FEx_11GEx_11HEx_11J
Topic 11 - Updated SolutionsCirclesCheck ListEx_12BEx_12DEx_12FEx_12HEx_12JEx_12KEx_12L
Topic 12 - Not in 2022/23VectorsCheck ListEx_13AEx_13BEx_13CEx_13DEx_13EEx_13FEx_13GEx_13IEx_13KEX13_LEx_13MEx_13NEx_13OEx_13PEX_13QEx_13REx_13SEx_13U
Topic 13 - Updated SolutionsFurther CalculusCheck ListEx_14BEx_14CEx_14EEx_14GEx_14HEx_14IEx_14JEx_14K
Topic 14 - Updated SolutionsExponentials & LogsCheck ListEx_15CEx_15DEx_15EEx_15FEx_15GEx_15HEx_15IEx_15JEx_15KEx_15L
Topic 15 - Updated SolutionsWave FunctionCheck ListEx_16AEx_16CEx_16DEx_16EEx_16FEx_16GEx_16H

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16. Higher Maths Theory Guides 

Thanks to HSN for making the excellent Higher Maths Theory Guides freely available for all to use. These will prove a fantastic resource in helping you consolidate your understanding of Higher Maths.

Theory Guides
_________________
Topic
____________________________________________
Link
_______
Theory Guide 1All Topics Unit 1 Theory (HSN)HERE
Theory Guide 2All Topics Unit 1 - One Page Summary Guide (HSN)HERE
Theory Guide 3All Topics Unit 2 Theory (HSN)HERE
Theory Guide 4All Topics Unit 2 - One Page Summary Guide (HSN)HERE
Theory Guide 5All Topics Unit 3 Theory (HSN)HERE
Theory Guide 6All Topics Unit 3 - One Page Summary Guide (HSN)HERE
Theory Guide 7All Topics Units 1,2 & 3 Theory (HSN)HERE
Theory Guide 8Circles Theory (HSN)HERE
Theory Guide 9Differentiation Theory (HSN)HERE
Theory Guide 10Exponentials & Logarithms Theory (HSN)HERE
Theory Guide 11Functions & Graphs Theory (HSN)HERE
Theory Guide 12Further Calculus Theory (HSN)HERE
Theory Guide 13Graphs Transformations Theory (Movement & Reflection)HERE
Theory Guide 14Graphs Transformations Summary SheetHERE
Theory Guide 15Integration Theory (HSN)HERE
Theory Guide 16Polynomials & Quadratics Theory (HSN)HERE
Theory Guide 17Sequences Theory (HSN)HERE
Theory Guide 18Straight Line Theory (HSN)HERE
Theory Guide 19Trigonometry Theory (HSN)HERE
Theory Guide 19Vectors Theory (HSN)HERE
Theory Guide 20Wave Function Theory (HSN)HERE

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17. Higher Maths Mind Maps

Thanks to the authors for providing the excellent resources below. These will prove a fantastic resource in helping you prepare for assessments, tests and the final exam.

Mind Map
____________
Topic
____________________________
Mind Map
___________
Topic
____________________________
Mind Map 1Circle 1 Mind Map 16Polynomials & Quadratics
Mind Map 2Circle 2Mind Map 17Polynomials
Mind Map 3Composite FunctionsMind Map 18Quadratics
Mind Map 4Compound Angle FormulaMind Map 19Recurrence Relations 1
Mind Map 5Differentiation (Preparing For)Mind Map 20Recurrence Relations 2
Mind Map 6Differentiation 1Mind Map 21Straight Lines 1
Mind Map 7Differentiation 2Mind Map 22Straight Lines 2
Mind Map 8Differentiation (Further)Mind Map 23Trigonometry 1
Mind Map 9Functions & GraphsMind Map 24Trigonometry 2
Mind Map 10Graph TransformationsMind Map 25Vectors 1
Mind Map 11Integration (Preparing For)Mind Map 26Vectors 2
Mind Map 12Integration 1Mind Map 27Vectors 3
Mind Map 13Integration 2Mind Map 28Wave Function 1
Mind Map 14Logs & Exponentials 1Mind Map 29Wave Function 2
Mind Map 15Logs & Exponentials 2

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18. Higher Maths Practice Unit Assessments – Solutions Included

Thanks to the authors for making the excellent resources below freely available for all to use. Please use regularly for revision prior to assessments, tests and the final exam.

Unit
_________
Paper
____________
Solutions
___________
Unit OnePractice ASolutions
Unit OnePractice BSolutions
Unit TwoPractice ASolutions
Unit TwoPractice BSolutions
Unit ThreePractice ASolutions
Unit ThreePractice BSolutions
Unit FourPractice ASolutions

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19. Higher Maths Past Paper Video Solutions

Please click DLB Maths to view Higher Maths Past Paper video solutions. This will prove an excellent resource in helping you prepare for assessments, tests and the final exam.

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20. Higher Maths Recommended Text Book

Please find below our highly recommended text book which can be ordered by clicking on the book/link.

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21. 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 Equations of Tangents 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 2025.

Get the Study Pack - just £20

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Not just Equations of Tangents, but 70 other maths concepts covered in detail

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