Functions
We have below bronze, silver and gold tutorials for our Higher Maths Functions topic. Typically as you work through the modules, the difficulty of the skills increase by one step ensuring smooth progression. Simply click on the video to play it and pause it at the relevant points for you to attempt the questions. Each tutorial has a corresponding worksheet for you to download if additional practice is required. Make sure you have a pen and paper handy! Be sure to mark your work for every exercise attempted and record your score and time taken in your recording grid.
Essential prior knowledge:-
National 5 Maths; REL 1.1b, REL 1.1e, E+F 1.2a
- Use of functional notation
- Changing the subject of the formula
- Multiplying out brackets
- Factorising expressions
Contents:-
3.1 - Domain and Range
3.2 - Composite Functions
3.3 - Inverse Functions
3.1 - Domain and Range
In this module we learn about restrictions in the domain when functions involve fractions and square roots. We also learn how to write suitable ranges.
Video 32: Outcome 1 - Restrictions on the domain (fractions). Grab a pen and your Rigour jotter. Make sure you try all the questions!
Video 33: Outcome 2 - Restrictions on the domain (square roots). Remember to copy down the worked examples and take notes. These will help you revise and remember!
Video 34: Outcome 3 - Domain and range. This is the final video in this module. After completing the questions why don't you try the past paper questions on this section at the bottom of the page?
If you feel you have mastered these skills why not try this short quiz under exam conditions? You will be provided with instant feedback so be sure to view it. Remember to re-do any video lessons for any questions you answered incorrectly. Once you have completed the quiz record the score in your profile. After this, check to see if there are any past paper questions for this module at the bottom of this page to try.
3.2 - Composite Functions
In this module we progress our National 5 Function skills by learning how to substitute numbers into functions. We then learn how to substitute algebraic expressions into functions and finish off with solving equations using functional notation...
Video 35: Outcome 1 - Composite functions ('f(g(number)))'. Grab a pen and your Rigour jotter. Make sure you try all the questions!
Video 36: Outcome 2 - Composite functions ('f(g(x))'). Remember to copy down the worked examples and take notes. These will help you revise and remember!
Video 37: Outcome 3 - Composite functions (working backwards). This is the final video in this module. After completing the questions why don't you try the past paper questions on this section at the bottom of the page?
If you feel you have mastered these skills why not try this short quiz under exam conditions? You will be provided with instant feedback so be sure to view it. Remember to re-do any video lessons for any questions you answered incorrectly. Once you have completed the quiz record the score in your profile. After this, check to see if there are any past paper questions for this module at the bottom of this page to try.
3.3 - Inverse Functions
What do we mean by the inverse function? Do you know how to calculate the inverse function? Check out the tutorial below for the answers to these questions.
Video 38: Outcome 1 - Calculating inverse functions. This is the final video in this module. After completing the questions why don't you try the past paper questions on this section at the bottom of the page?
If you feel you have mastered these skills why not try this short quiz under exam conditions? You will be provided with instant feedback so be sure to view it. Remember to re-do any video lessons for any questions you answered incorrectly. Once you have completed the quiz record the score in your profile. After this, check to see if there are any past paper questions for this module at the bottom of this page to try.
Past Paper Questions
Multiple Choice Questions
We have below a selection of Multiple Choice Exam questions. Although the exam is not in this format any more these questions provide an excellent opportunity to quickly test you on your knowledge of the topic before you try the longer questions in the section after this. To try the questions, just click on the links below.
3.1 - Domain and Range
3.2 - Composite Functions
SQA Exam Questions
You will find below a collection of Functions SQA past paper questions. You should click on a question, pause the video when instructed and give the question your best shot. Then un-pause the video and watch the worked solution. If the question is from paper 1 you should NOT use a calculator. You should make this section a regular place to come back to when revising. Even if you get the correct answer, it is recommended that you try all these questions more than once at various stages throughout the year.
3.1 - Domain and Range
3.2 - Composite Functions
- 2023 Paper 1 Question 13
- 2019 Paper 1 Question 12
- 2017 Paper 1 Question 1
- 2016 Paper 1 Question 12
- Specimen Paper 1 Question 8
- 2014 Paper 2 Question 3
- 2012 Paper 2 Question 1
- 2009 Paper 2 Question 2
- 2007 Paper 1 Question 3
- 2006 Paper 1 Question 3
3.3 - Inverse Functions
Congratulations!
You have completed this module - well done! Remember to go back and redo any areas of weakness, that's how we improve. If you are happy with all areas, go back to the main menu and pick another topic to practice!
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