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

Covers the whole of the Higher Maths course

Created by an experienced maths teacher

Resources used with students in Scottish Secondary Schools

Welcome to highermathematics.co.uk

A sound understanding of Composite Functions is essential to ensure exam success.

Please find resources for all other Maths courses HERE.

For students looking for a ‘good’ pass at Higher Maths in 2019 you may wish to consider subscribing to the fantastic additional * exam focused* resources available in the Online Study Pack.

To return to the Home Page please click HERE.

We hope you find this website useful and wish you the very best with your studies.

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

7. Old Higher Maths Exam Questions by Topic

8. Higher Maths Text Book Solutions

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*

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**1. Higher Maths Course Description**

A description of the Higher Maths course is shown HERE.

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**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 Exam Formulae List | HERE | |

Check List 1 - Higher Maths Formulae List Not Given in Exam | HERE | |

Check List 2 - Higher Maths Exam Whole Course | HERE | |

Check List 3 - Higher Maths Exam Trig Revision Sheet | HERE | |

Check List 4 - One Page Summary Guide Unit 1 (HSN) | HERE | Courtesy of HSN |

Check List 5 - One Page Summary Guide Unit 2 (HSN) | HERE | Courtesy of HSN |

Check List 6 - One Page Summary Guide Unit 3 (HSN) | HERE | Courtesy 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 P1 | Marking P1 | Q4 | Q6,11 | Q2,11,15 | Q3,14 | Q10 | Q7 | Q1,8 | Q13 | Q5,9,12 | |||

2018 P2 | Marking P2 | Q5c,12 | Q3,9 | Q11 | Q6 | Q1 | Q4,7a,10 | 7b,c | Q5a,b | Q2 | Q8 | ||

2017 P1 | Marking P1 | Q2 | Q8,15c | Q12 | Q1,6,15a | Q3,13 | Q10,15b | Q4 | Q9 | Q7,11 | Q5 | Q14 | |

2017 P2 | Marking P2 | Q3,10 | Q4,7 | Q9 | Q2 | Q8 | Q1 | Q6,11 | Q5 | ||||

2016 P1 | Marking P1 | Q4,8 | Q2,9 | Q14 | Q6,10,12 | Q5 | Q15 | Q3 | Q1 | Q13 | Q7,11 | ||

2016 P2 | Marking P2 | Q4 | Q7 | Q6 | Q10,11b | 3b,9 | Q2,3a | Q1 | Q8b,11a | Q5 | Q8a | ||

2015 P1 | Marking P1 | Q11,14 | Q2,7 | Q6 | Q4,5,13 | Q12,15 | Q3,8 | Q9 | Q10 | Q1 | |||

2015 P2 | Marking P2 | Q5 | Q8 | Q2 | Q7a | Q4 | Q3 | Q1 | Q7b | Q6 | Q9 | ||

Specimen P1 | Marking P1 | Q11 | Q8 | Q10 | Q1 | Q4,7 | Q2,5,9 | Q6,12 | Q3 | ||||

Specimen P2 | Marking P2 | Q5 | Q3b,8 | Q4,7 | Q9 | Q3a | Q2 | Q1,6 | Q10 | ||||

Exemplar P1 | Marking P1 | Q1 | Q8,11 | Q10 | Q3 | Q2,5 | Q6 | Q4,7 | Q9 | ||||

Exemplar P2 | Marking P2 | Q2 | Q9,10 | Q7 | Q8 | Q4 | Q3 | Q1 | Q5,6 |

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**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 _________________ |

2018 | Higher (CfE) | Exam Paper | Marking Scheme |

2017 | Higher (CfE) | Exam Paper | Marking Scheme |

2016 | Higher (CfE) | Exam Paper | Marking Scheme |

2015 | Higher (CfE) | Exam Paper | Marking Scheme |

2015 | Specimen (CfE) | Specimen Paper | Marking Scheme |

2015 | Exemplar (CfE) | Exemplar Paper | Marking Scheme |

2015 | Higher (Old) | Exam Paper | Marking Scheme |

2014 | Higher | Exam Paper | Marking Scheme |

2013 | Higher | Exam Paper | Marking Scheme |

2012 | Higher | Exam Paper | Marking Scheme |

2011 | Higher | Exam Paper | Marking Scheme |

2010 | Higher | Exam Paper | Marking Scheme |

2009 | Higher | Exam Paper | Marking Scheme |

2008 | Higher | Exam Paper | Marking Scheme |

2007 | Higher | Exam Paper | Marking Scheme |

2006 | Higher | Exam Paper | Marking Scheme |

2005 | Higher | Exam Paper | Marking Scheme |

2004 | Higher | Exam Paper | Marking Scheme |

2003 | Higher | Exam Paper | Marking Scheme |

2002 | Higher | Exam Paper | Marking Scheme |

2002 | Higher (Winter Diet) | Exam Paper | |

2001 | Higher | Exam Paper | Solutions |

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**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.

**6. About Composite Functions**

- Two functions can be “
**composed”**to form a new**composite function** - f [ g(x) ] ⇒ Is determined from two functions in Example One below
- f [ g(4) ] ⇒ Is determined from two functions in Example Two below

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**Example One**

**Example Two**

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Resources on Functions & Graphs can be found;

- Section 3 – New Higher Maths Exam Questions & Answers by Topic (6th Column)
- Section 7 – Old Higher Maths Exam Questions & Answers by Topic (Topics 4 & 6)
- Section 8 – Text Book Worked Solutions (Topics 2 & 3)
- Section 9 – Theory Guides (Theory Guides 2 & 11)
- Section 10 – Mind Maps (Mind Maps 9 & 10)
- Section 12 – Video Exam Solutions
- Online Study Pack –
*For students looking for a ‘good’ pass*

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**7. Old Higher Maths Exam Questions by Topic**

Thanks to the SQA for making these available.

Topic ________ | Topic Name ___________________________ | Link ________ | Notes ___________________ |

Topic 1 | Circles | HERE | Answers Included |

Topic 2 | Differentiation | HERE | Answers Included |

Topic 3 | Exponentials & Logarithms | HERE | Answers Included |

Topic 4 | Functions | HERE | Answers Included |

Topic 5 | Further Calculus | HERE | Answers Included |

Topic 6 | Graphs of Functions | HERE | Answers Included |

Topic 7 | Integration | HERE | Answers Included |

Topic 8 | Polynomials | HERE | Answers Included |

Topic 9 | Quadratics | HERE | Answers Included |

Topic 10 | Recurrence Relations | HERE | Answers Included |

Topic 11 | Straight Line | HERE | Answers Included |

Topic 12 | Trig Addition Formulae | HERE | Answers Included |

Topic 13 | Trig Graphs & Equations | HERE | Answers Included |

Topic 14 | Vectors | HERE | Answers Included |

Topic 15 | Wave Function | HERE | Answers Included |

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**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 1 | Straight Line | 1A | 1B | 1D | 1E | 1F | 1G | 1I | 1K | 1M | 1N | 1O | 1O | |||||

Topic 2 | Functions & Graphs 1 | 2A | 2B | 2C | 2D | 2F | 2G | 2I | ||||||||||

Topic 3 | Functions & Graphs 2 | 3A | 3C | 3K | 3N | 3O | 3P | |||||||||||

Topic 4 | Recurrence | 5A | 5B | 5B | 5C | 5D | 5F | 5H | 5I | |||||||||

Topic 5 | Differentiation | 6A | 6C | 6D | 6E | 6F | 6G | 6H | 6I | 6J | 6L | 6M | 6N | 6O | 6P | 6Q | 6R | 6S |

Topic 6 | Polynomials | 7B | 7C | 7D | 7E | 7F | 7G | 7H | 7I | 7J | ||||||||

Topic 7 | Quadratics | 8C | 8D | 8E | 8F | 8H | 8I | 8J | 8K | |||||||||

Topic 8 | Integration | 9G | 9H | 9I | 9L | 9N | 9P | 9Q | ||||||||||

Topic 9 | Trigonometry | 11B | 11C | 11D | 11E | 11F | 11G | 11H | ||||||||||

Topic 10 | Circles | 12B | 12D | 12F | 12H | 12J | 12K | 12L | ||||||||||

Topic 11 | Vectors | 13A | 13C | 13D | 13E | 13F | 13G | 13I | 13K | 13L | 13M | 13N | 13O | 13P | 13Q | 13R | 13S | 13U |

Topic 12 | Further Calculus | 14B | 14C | 14C | 14E | 14G | 14H | 14I | 14J | 14K | ||||||||

Topic 13 | Exp's & Logs | 15C | 15D | 15E | 15F | 15G | 15H | 15I | 15I | 15J | 15K | 15L | ||||||

Topic 14 | Wave Function | 16A | 16C | 16D | 16E | 16F | 16G | 16H |

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**9. Higher Maths Theory Guides **

Thanks to HSN for making these available.

Theory Guides _________________ | Topic ____________________________________________ | Link _______ |

Theory Guide 1 | All Topics Unit 1 Theory (HSN) | HERE |

Theory Guide 2 | All Topics Unit 1 - One Page Summary Guide (HSN) | HERE |

Theory Guide 3 | All Topics Unit 2 Theory (HSN) | HERE |

Theory Guide 4 | All Topics Unit 2 - One Page Summary Guide (HSN) | HERE |

Theory Guide 5 | All Topics Unit 3 Theory (HSN) | HERE |

Theory Guide 6 | All Topics Unit 3 - One Page Summary Guide (HSN) | HERE |

Theory Guide 7 | All Topics Units 1,2 & 3 Theory (HSN) | HERE |

Theory Guide 8 | Circles Theory (HSN) | HERE |

Theory Guide 9 | Differentiation Theory (HSN) | HERE |

Theory Guide 10 | Exponentials & Logarithms Theory (HSN) | HERE |

Theory Guide 11 | Functions & Graphs Theory (HSN) | HERE |

Theory Guide 12 | Further Calculus Theory (HSN) | HERE |

Theory Guide 13 | Graphs Transformations Theory (Movement & Reflection) | HERE |

Theory Guide 14 | Graphs Transformations Summary Sheet | HERE |

Theory Guide 15 | Integration Theory (HSN) | HERE |

Theory Guide 16 | Polynomials & Quadratics Theory (HSN) | HERE |

Theory Guide 17 | Sequences Theory (HSN) | HERE |

Theory Guide 18 | Straight Line Theory (HSN) | HERE |

Theory Guide 19 | Trigonometry Theory (HSN) | HERE |

Theory Guide 19 | Vectors Theory (HSN) | HERE |

Theory Guide 20 | Wave 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 1 | Circle 1 | Mind Map 16 | Polynomials & Quadratics |

Mind Map 2 | Circle 2 | Mind Map 17 | Polynomials |

Mind Map 3 | Composite Functions | Mind Map 18 | Quadratics |

Mind Map 4 | Compound Angle Formula | Mind Map 19 | Recurrence Relations 1 |

Mind Map 5 | Differentiation (Preparation) | Mind Map 20 | Recurrence Relations 2 |

Mind Map 6 | Differentiation 1 | Mind Map 21 | Straight Lines 1 |

Mind Map 7 | Differentiation 2 | Mind Map 22 | Straight Lines 2 |

Mind Map 8 | Differentiation (Further) | Mind Map 23 | Trigonometry 1 |

Mind Map 9 | Functions & Graphs | Mind Map 24 | Trigonometry 2 |

Mind Map 10 | Functions | Mind Map 25 | Vectors 1 |

Mind Map 11 | Integration (Preparation) | Mind Map 26 | Vectors 2 |

Mind Map 12 | Integration 1 | Mind Map 27 | Vectors 3 |

Mind Map 13 | Integration 2 | Mind Map 28 | Wave Function 1 |

Mind Map 14 | Logs & Exponentials 1 | Mind Map 29 | Wave Function 2 |

Mind Map 15 | Logs & Exponentials 2 |

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**11. Higher Maths Practice Unit Assessments (Solutions Included)**

Block _________ | Outcome _____________________________________ | Revision A ____________ | Revision B _______________________ |

One | A1.1, A1.3, A1,4, EF1.3, RC1.3 | Revision A | Revision B |

One | A1.1, EF1.3, EF1.4, RC1.1, RC1.2 | Practice Test 1 | Practice Test 2 (No Solns) |

Two | A1,2, A1.4, EF1.2, RC1.1, RC1.2, RC1.4 | Revision A | Revision B |

Three | A1,2, A1.4, EF1.2, RC1.1, RC1.2, RC1.4 | Revision A | Revision B |

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**12. Higher Maths Past Paper Video Solutions**

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**13. Higher Maths Recommended Text Book**

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

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**14. Exam Focused Higher Maths Online Study Pack **

Through step-by-step worked solutions to exam questions available in the Online Study Pack we cover everything you need to know about Composite Functions to pass your final exam.

As well as students studying Higher Mathematics, the resources will benefit young adults studying A-Level Mathematics and undergraduates who need a little extra help. Particular benefit will be to students who are looking to go to College or University and are therefore required to pass in order to gain entry onto the course of their choice.

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 2018/19.

Topic Links

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