Polynomials
We have below bronze, silver and gold tutorials for our Higher Maths Polynomials 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; E+F 1.2a, E+F 1.2b, REL 1.1c, REL 1.3b
- Multiplying out brackets
- Factorising expressions
- Solving equations
- Solving quadratic equations
Contents:-
7.1 - Factorising polynomials
7.2 - Finding unknown values in polynomials
7.3 - Points of intersection 2
7.1 - Factorising polynomials
Go no further unless you have learned how to factorise quadratic expressions (i.e. National 5), including gold level!!! If you have mastered these skills, this module will show you how to factorise polynomials with powers greater than 2. At bronze level, we learn how to factorise cubic functions when given a factor. In silver, we discover how to factorise cubic expressions with no given factor and missing terms. In the gold section of this module we learn how to factorise polynomials of degree 4. Well worth a watch and well worth practicing the questions!
Video 66: Outcome 1 - Factorising cubic polynomials when given the factor. Grab a pen and your Rigour jotter. Make sure you try all the questions!
Video 67: Outcome 2 - Factorising cubic polynomials when not given the factor and missing terms. Remember to copy down the worked examples and take notes. These will help you revise and remember!
Video 68: Outcome 3 - Factorising polynomials of degree 4. 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.
7.2 - Finding missing terms in polynomials
Ensure you have completed the module above before attempting these questions. In this module we learn how to find missing terms in polynomials. At bronze level we practice this skill for some more straight forward algebraic expressions followed by the silver section when some of the expressions are a bit more complex.
At gold level we need to find the values of "a and b". Sound familiar? See if you can work out how to do it before you even watch the video!
Video 69: Outcome 1 - Finding 'k' in simple expressions. Grab a pen and your Rigour jotter. Make sure you try all the questions!
Video 70: Outcome 2 - Finding 'c' in trickier expressions. Remember to copy down the worked examples and take notes. These will help you revise and remember!
Video 71: Outcome 3 - Finding the values of 'a' and 'b'. 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.
7.3 - Points of intersection 2
In this module we are looking at points of intersection again. At bronze level, we learn how to find the points of intersection between a cubic curve and the x-axis. At silver level, we discover how to find the points of intersection between a cubic curve and a straight line.
At gold level we look at how to find the points of intersection between a cubic curve and a quadratic graph. Well worth a watch and a practise!
Video 72: Outcome 1 - Points of intersection between a cubic curve and the x axis. Grab a pen and your Rigour jotter. Make sure you try all the questions!
Video 73: Outcome 2 - Points of intersection between a cubic curve and a straight line. Remember to copy down the worked examples and take notes. These will help you revise and remember!
Video 74: Outcome 3 - Points of intersection between a cubic and a quadratic curve. 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.
SQA Exam Questions
You will find below a collection of Polynomials 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.
7.1 - Factorising polynomials
- 2023 Paper 1 Question 10
- 2022 Paper 1 Question 13
- 2019 Paper 2 Question 10
- 2018 Paper 2 Question 7
- 2017 Paper 2 Question 2
- 2016 Paper 2 Question 3(a)
- 2015 Paper 1 Question 3
- Specimen Paper 1 Question 7
- 2006 Paper 1 Question 9
- 2003 Paper 2 Question 1
- 2004 Paper 1 Question 2
7.2 - Finding unknown values in polynomials
7.3 - Points of intersection 2
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!
Calling all Parents & Students!
Click here for more information regarding access to our online learning portals to aid home revision.
Print 