The Circle
We have below bronze, silver and gold tutorials for our Higher Maths The Circle 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 1.1a
- Multiplying out brackets
- Factorising
- Equation of a straight line
Contents:-
11.1 - Equations of a Circle
11.2 - Equation of the Tangent to a Circle
11.3 - Points of Intersection 4
11.4 - Intersecting Circles
11.1 - Equations of a Circle
At bronze level in this module we learn how to write the the equation of a circle in the form (x - a)2 + (y - b)2 = r2. At silver level, we learn how to calculate the centre and the radius from the general equation x2 + y2 - 2gx - 2fy + c = 0. Don't worry, they're both given to you in the formula sheet!
At gold level, we learn how to calculate the equation of a circle when given two end points as a diameter.
Video 109: Outcome 1 - The equation of a circle in the form (x - a)2 + (y - b)2 = r2. Grab a pen and your Rigour jotter. Make sure you try all the questions!
Video 110: Outcome 2 - The general equation of a circle. Remember to copy down the worked examples and take notes. These will help you revise and remember!
Video 111: Outcome 3 - Finding the equation of a circle when given two end points as a diameter. 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?
11.2 - Equation of the Tangent to a Circle
At bronze level, we learn how to calculate the gradient of the tangent to a circle. At silver level, we progress onto calculating the equation of the tangent to a circle, when given the equation of the circle and the point of contact.
In our gold video we discover how to calculate the equation of the tangent to a circle when given the equation of a circle and the other end point on the diameter from the point of contact.
Video 112: Outcome 1 - The gradient of the tangent to a circle. Grab a pen and your Rigour jotter. Make sure you try all the questions!
Video 113: Outcome 2 - The equation of the tangent to a circle. Remember to copy down the worked examples and take notes. These will help you revise and remember!
Video 114: Outcome 3 - The equation of the tangent to a circle when given the other end point of the diameter. 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?
11.3 - Points of Intersection 4
At bronze level in this module we learn how to find two points of intersection. At silver level, we learn how to show a line is a tangent to a circle.
In the gold section we learn how to prove that a line does NOT intersect a circle.
Video 115: Outcome 1 - Two points of contact. Grab a pen and your Rigour jotter. Make sure you try all the questions!
Video 116: Outcome 2 - One point of contact. Remember to copy down the worked examples and take notes. These will help you revise and remember!
Video 117: Outcome 3 - No points of contact. 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?
11.4 - Intersecting Circles
In the bronze section of this module we learn how to prove that two circles overlap, i.e. intersect each other at two points. At silver level we learn how to show that two circles touch at one point.
In the gold section we learn how to prove that two circles do NOT intersect each other.
Video 118: Outcome 1 - Two points of contact. Grab a pen and your Rigour jotter. Make sure you try all the questions!
Video 119: Outcome 2 - One point of contact. Remember to copy down the worked examples and take notes. These will help you revise and remember!
Video 120: Outcome 3 - No points of contact. 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?
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.
11.1 - Equations of a Circle
- 2010 Paper 1 Question 8
- 2009 Paper 1 Question 2
- 2008 Paper 1 Question 2
- Specimen 1 Paper 1 Question 10
11.2 - Equation of the Tangent to a Circle
- 2014 Paper 1 Question 2
- 2011 Paper 1 Question 6
- 2008 Paper 1 Question 5
- Specimen 1 Paper 1 Question 15
11.3 - Points of Intersection 4
11.4 - Intersecting Circles
SQA Exam Questions
You will find below a collection of The Circle 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.
11.1 - Equations of a circle
- 2019 Paper 1 Question 3
- 2019 Paper 1 Question 16
- 2016 Paper 1 Question 4
- 2015 Paper 1 Question 14
- 2014 Paper 2 Question 8
- 2007 Paper 1 Question 5
11.2 - Equation of the tangent to a circle
- 2023 Paper 2 Question 15
- 2019 Paper 2 Question 15
- 2018 Paper 1 Question 4
- 2017 Paper 1 Question 2
- 2015 Paper 1 Question 11
- 2006 Paper 1 Question 2
- 2002 Paper 1 Question 1
- 1998 Paper 1 Question 4
- 1996 Paper 1 Question 4
- 1991 Paper 1 Question 8
- 1988 Paper 1 Question 2
11.3 - Points of Intersection 4
- 2022 Paper 2 Question 9
- 2017 Paper 2 Question 3
- 2016 Paper 1 Question 8
- 2013 Paper 1 Question 22
- 2012 Paper 2 Question 2
- 2010 Paper 2 Question 3
- 2004 Paper 2 Question 8
- 2003 Paper 2 Quesion 4
11.4 - Intersecting circles
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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