Integration
We have below bronze, silver and gold tutorials for our Higher Maths Integration 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 1.1b, REL 1.3a
- Indices
- Quadratic Equations
Contents:-
9.1 - Indefinite Integrals
9.2 - Definite Integrals
9.3 - Differential Equations
9.4 - Shaded Area
9.1 - Indefinite Integrals
In this module we learn how to integrate, initially with basic terms followed up by a silver section with fractions and those laws of indices again!
In the gold section we learn how to integrate "a/b" standard integrals. A great way to consolidate your integration skills. Don't forget the + c!!!
Video 90: Outcome 1 - Indefinite integrals for basic integration. Grab a pen and your Rigour jotter. Make sure you try all the questions!
Video 91: Outcome 2 - Indefinite integrals with fractions and indices. Remember to copy down the worked examples and take notes. These will help you revise and remember!
Video 92: Outcome 3 - Indefinite integrals for harder integration. 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.
9.2 - Definite Integrals
This module shows us how to evaluate definate integrals. At bronze level with basic integration followed up by "exam standard" questions at silver level.
In the gold section we learn how to work backwards and calculate limits when given the final value o the definite integral. Well worth a watch!
Video 93: Outcome 1 - Definite integrals for basic integration. Grab a pen and your Rigour jotter. Make sure you try all the questions!
Video 94: Outcome 2 - Indefinite integrals with standard integration. Remember to copy down the worked examples and take notes. These will help you revise and remember!
Video 95: Outcome 3 - Using a definite integral to calculate the value of a limit of integration (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.
9.3 - Differential Equations
In this module we learn how to solve differential equations. 4 marks for a 2 step process??? Sounds like excellent value to me!
Video 96: Outcome 1 - Solving differential equations. This is the only 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.
9.4 - Shaded Area
At bronze level in this module we learn how to calculate the area between a curve and the x-axis. We then move on to calculating the shaded area between a curve and the straight line at silver level.
At gold level we learn how to calculate the area between 2 curves. We also learn how to calculate the limits of integration. Well worth a watch!
Video 97: Outcome 1 - Calculating the area between a curve and the x axis. Grab a pen and your Rigour jotter. Make sure you try all the questions!
Video 98: Outcome 2 - Calculating the area between a curve and a line. Remember to copy down the worked examples and take notes. These will help you revise and remember!
Video 99: Outcome 3 - Calculating the area between 2 curves. 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.
9.1 - Indefinate Integrals
- 2015 Paper 1 Question 7
- 2013 Paper 1 Question 7
- 2011 Paper 1 Question 11
- 2011 Paper 1 Question 16
- Specimen 1 Paper 1 Question 3
9.3 - Differential Equations
9.4 - Shaded Area
SQA Exam Questions
You will find below a collection of Integration 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.
9.1 - Indefinite Integrals
- 2023 Paper 1 Question 6
- 2019 Paper 2 Question 2
- Specimen Paper 1 Question 1
- 2005 Paper 2 Question 1
- 2001 Paper 2 Question 6
- 1999 Paper 1 Question 20
9.2 - Definite Integrals
- Exemplar Paper 1 Question 3
- 1998 Paper 1 Question 12
- 1997 Paper 1 Question 10
- 1992 Paper 1 Question 8
- 1988 Paper 1 Question 14
9.3 - Differential Equations
- 2023 Paper 2 Question 12
- 2022 Paper 2 Question 6
- 2019 Paper 2 Question 13
- 2018 Paper 1 Question 10
- 2016 Paper 2 Question 9
- 2015 Paper 1 Question 15
9.4 - Shaded Area
- 2023 Paper 2 Question 8
- 2022 Paper 2 Question 4
- 2019 Paper 1 Question 8
- 2018 Paper 2 Question 1
- 2017 Paper 1 Question 10
- 2016 Paper 2 Question 3
- 2015 Paper 1 Question 12
- 2015 Paper 2 Question 4
- Exemplar Paper 2 Question 4
- 2013 Paper 2 Question 4
- 2012 Paper 1 Question 21
- 2011 Paper 2 Question 4
- Specimen 1 Paper 2 Question 5
- 2007 Paper 1 Question 8
- 2005 Paper 2 Question 5
- 2002 Paper 2 Question 5
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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