Log Out
Unsure about Optimisation?

Unsure about Optimisation?

Let the fantastic wealth of resources below teach you all about Optimisation.

Get the Study Pack - just £9.99

Teachers click here >

Covers the whole of the Higher Maths course

Created by an experienced maths teacher

Resources used with students in Scottish Secondary Schools

Optimisation

Welcome to highermathematics.co.uk

A sound understanding of Optimisation 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 in 2019/20 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 2019/20.

Please find below:

1. Higher Maths Course Description

2. Higher Maths Exam Check Lists

3. New Higher Maths Past & Practice Papers by Topic 

4. Higher Maths Past & Practice Papers 

5. 200 Higher Maths Questions & Answers 

6. About Optimisation 

7. Old Higher Maths Exam Questions by Topic

8. Higher Maths Text Book Solutions

9. Higher Maths Theory Guides 

10. Higher Maths Mind Maps 

11. Higher Maths Practice Unit Assessments (Solutions Included)

12. Higher Maths Past Paper Video Solutions

13. Higher Maths Recommended Text Book

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

.

Higher Maths Resources

.

1. Higher Maths Course Description

A description of the Higher Maths course is shown HERE.

 

2. Higher Maths Exam Check Lists 

Excellent check lists below to assess your Higher Maths knowledge. Please try to use these regularly for revision prior to tests, prelims and the final exam.

Description
___________________________________________________		Link
________		Acknowledgements
______________________
Higher Maths Course DescriptionHERE
SQA Higher Maths Exam Formulae ListHERECourtesy of SQA
Check List 1 - Higher Maths Formulae List Not Given in ExamHERE
Check List 2 - Higher Maths Exam Whole CourseHERE
Check List 3 - Higher Maths Exam Trig Revision SheetHERE
Check List 4 - One Page Summary Guide Unit 1 (HSN)HERECourtesy of HSN
Check List 5 - One Page Summary Guide Unit 2 (HSN)HERECourtesy of HSN
Check List 6 - One Page Summary Guide Unit 3 (HSN)HERECourtesy of HSN

.

3.  New Higher Maths Past & Practice Papers by Topic

Thanks to the SQA for making these available.

Questions and answers have been split up by topic for ease of reference.

Worked solutions to all questions below available in the Online Study Pack.

.
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
_________
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

.

4. Higher Maths Past & Practice Papers

Thanks to the SQA for making these available.

Worked solutions to all CfE Higher Papers below available in the Online Study Pack.

Year
_____		Paper Type
_________________		Exam Paper
______________		Marking Scheme
__________________
2019Higher (CfE)Paper 1, Paper 2Not Available Yet
2018Higher (CfE)Exam PaperMarking Scheme
2018 Specimen (CfE)Paper 1, Paper 2Marking Scheme
2017Higher (CfE)Exam PaperMarking Scheme
2016Higher (CfE)Exam PaperMarking Scheme
2015Higher (CfE)Exam PaperMarking Scheme
2015Specimen (CfE)Specimen PaperMarking Scheme
2015Exemplar (CfE)Exemplar PaperMarking Scheme
2015Higher (Old)Exam PaperMarking Scheme
2014HigherExam PaperMarking Scheme
2013HigherExam PaperMarking Scheme
2012HigherExam PaperMarking Scheme
2011HigherExam PaperMarking Scheme
2010HigherExam PaperMarking Scheme
2009HigherExam PaperMarking Scheme
2008HigherExam PaperMarking Scheme
2007HigherExam PaperMarking Scheme
2006HigherExam PaperMarking Scheme
2005HigherExam PaperMarking Scheme
2004HigherExam PaperMarking Scheme
2003HigherExam Paper Marking Scheme
2002HigherExam PaperMarking Scheme
2002Higher (Winter Diet)Exam Paper
2001HigherExam PaperSolutions

.

5. 200 Higher Maths Questions & Answers

Thanks to the SQA and author(s) for collating the questions below.

Worked solutions to all 200 questions are available in the Online Study Pack.

Exam Questions
_____________________		Answers
___________
Whole Booklet for PrintingAnswers
Exam Questions 1 - 20Answers
Exam Questions 21 - 40Answers
Exam Questions 41 - 60Answers
Exam Questions 61 - 80Answers
Exam Questions 81 - 100Answers
Exam Questions 101 - 120Answers
Exam Questions 121 - 140Answers
Exam Questions 141 - 160Answers
Exam Questions 161 - 180Answers
Exam Questions 181 - 200Answers

 

6. About Optimisation

  • We need to learn to work confidently with Optimisation type questions
  • The best practice is to do as many SQA past paper questions as possible
  • Usually involves finding max/min areas and volumes
  • First part of question is often a proof
  • Second part of question requires finding one or more stationary point(s)
  • To find the SP’s, set f ‘(x)= 0 and solve for x
  • The nature of the SP(s) is determined using a Nature Table
  • Exam questions are invariably in context and this is where past paper practice helps
  • A Higher Maths question on Optimisation is shown below ⇒  solution in Online Study Pack

.

Higher Maths Exam Question on Optimisation

Source: SQA 2008 Higher Exam Q6 P2

.

Resources on Differentiation can be found

  • Section 3 –  New Higher Maths Exam Questions & Answers by Topic (4th & 7th Column)
  • Section 7  – Old Higher Maths Exam Questions & Answers by Topic (Topic 2 & 5)
  • Section 8 – Text Book Worked Solutions (Topics 5 & 12)
  • Section 9 –  Theory Guides (Theory Guides 2, 6 , 9  & 12)
  • Section 10 – Mind Maps (Mind Maps 5, 6, 7 & 8)
  • Section 12 – Video Exam Solutions
  • Online Study Pack  – For students looking for a ‘good’ pass

.

7. Old Higher Maths Exam Questions by Topic

Thanks to the SQA for making these available.

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

.

8. Higher Maths Text Book Solutions 

Heinemann Higher Maths text book solutions below are courtesy of AHS.

These may prove extremely useful allowing students to progress their knowledge.

Topic
______________		Topic Name
____________________
Topic 1Straight Line1A1B1D1E1F1G1I1K1M1N1O1O
Topic 2Functions & Graphs 12A2B2C2D2F2G2I
Topic 3Functions & Graphs 2 3A3C3K3N3O3P
Topic 4Recurrence5A5B5B5C5D5F5H5I
Topic 5Differentiation6A6C6D6E6F6G6H6I6J6L6M6N6O6P6Q6R6S
Topic 6Polynomials7B7C7D7E7F7G7H7I7J
Topic 7Quadratics8C8D8E8F8H8I8J8K
Topic 8Integration9G9H9I9L9N9P9Q
Topic 9Trigonometry11B11C11D11E11F11G11H
Topic 10Circles12B12D12F12H12J12K12L
Topic 11Vectors13A13C13D13E13F13G13I13K13L13M13N13O13P13Q13R13S13U
Topic 12Further Calculus14B14C14C14E14G14H14I14J14K
Topic 13Exp's & Logs15C15D15E15F15G15H15I15I15J15K15L
Topic 14Wave Function16A16C16D16E16F16G16H

.

9. Higher Maths Theory Guides 

Thanks to HSN for making these available.

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

.

10. Higher Maths Mind Maps

These will prove an excellent resource in helping you prepare for the final exam.

Mind Map
____________		Topic
____________________________		Mind Map
___________		Topic
____________________________
Mind Map 1Circle 1Mind 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 (Preparation)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 10FunctionsMind Map 25Vectors 1
Mind Map 11Integration (Preparation)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

.

11. Higher Maths Practice Unit Assessments (Solutions Included)

Block
_________		Outcome
_____________________________________		Revision A
____________		Revision B
_______________________
OneA1.1, A1.3, A1,4, EF1.3, RC1.3Revision ARevision B
OneA1.1, EF1.3, EF1.4, RC1.1, RC1.2Practice Test 1Practice Test 2 (No Solns)
TwoA1,2, A1.4, EF1.2, RC1.1, RC1.2, RC1.4Revision ARevision B
ThreeA1,2, A1.4, EF1.2, RC1.1, RC1.2, RC1.4Revision ARevision B

.

12. Higher Maths Past Paper Video Solutions

.

13. Higher Maths Recommended Text Book

Work solutions to the Heinemann Higher Maths text book below can be found HERE.

.

.

14. Exam Focused 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 Optimisation 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.

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 2019/20.

Get the Study Pack - just £9.99

Teachers click here >

  • My daughter says the Higher website was really helpful. She achieved an ‘A’ for Higher Maths this year and is now undertaking Advanced Higher Maths for which she would like me to subscribe to your AH website . I shall go and do that now –  Thanks again.

    Mrs Gove – November 2018

  • Just wanted to say thanks for providing the great higher maths material. I am pleased to say I got an A in my higher maths course.
    Your material really helped me focus my study efforts for the exam.

    Mike – August 2018

  • Just a HUGE thank you from me – I’ve been teaching Higher Maths for about 20 years and your site has made this so much easier. Having topic by topic past paper questions, HSN notes and SQA papers all on one site is wonderful. So easy just to direct students to your amazing site! – Thank you.

    Karen – March 2018

  • Thought I’d drop you a note to say that I think the website is absolutely fantastic. The N5 Maths site helped me enormously and I’m delighted that there is now a dedicated site for Higher Maths to help me pass my exam in May!

    Mark – March 2018

  • Firstly, I wanted to say the materials on the new website are great.

    I have just had my Prelim at Fife College for my Higher Maths evening class. It has highlighted the need to do loads of past papers before the exam. I found the worked solutions provided for the past papers in the Online Study Pack so much more helpful than the marking schemes.

    Mike – March 2018

  • The Higher Maths website is great – only £9.99 is such good value for what you get. I am feeling a lot more confident for the exam now!

    John – March 2018

Not just Optimisation, but 70 other maths concepts covered in detail

Topic Links

Free resources to dozens of Higher Maths topics are available by clicking on any of the links to the right.

Buy today

For Students

To ensure your success in 2019/20 there is a wealth of fantastic additional Higher Maths exam focused resources for less than the cost of a text book.

Just £9.99 for a year

Buy now >

Buy now with PayPal

For Schools

Schools can get the Online Study Pack also. Unlimited use for all the teachers and students in your school.

Just £99.99 for a year

Buy now >

Buy now with PayPal

Join our mailing list

  • This field is for validation purposes and should be left unchanged.

Follow us

Copyright © 2019 National 5 Maths
All rights reserved
Privacy Policy & Cookies
Site terms & conditions

Site by Inigo

SQA material is copyright © Scottish Qualifications
Authority and reproduced with permission from SQA.