TMUA Circles and Circle Equations
TMUA loves circles and equations of circles - it is important to be very familiar indeed with this topic. Direct questions on circles tend to test understanding of the equation of a circle and its various characteristics, whereas indirect questions can test anything from intersections of circles with lines to tangents, areas or perimeters of sectors.
For those so interested, we offer both one to one TMUA coaching on circles and circle equations, as well as online group coaching via Zoom - 'TMUA Geometry and Shapes' is Session #12 of 20. Check our TMUA Group Coaching Schedule page for dates when this session is available - details of what we cover in each group session can be found on our TMUA Coaching Sessions Overview page. For more general information on our online sessions check out our 'Online Coaching FAQ'.
Feel free to contact us if you require more information regarding any of the above.
Free Revision Resources
The below list of questions links to short videos (teasers) on our YouTube channel which directly or indirectly test elements of what is required to succeed in answering TMUA questions on circles and circle equations - they also provide a detailed solution to the question posed, together with tips and tricks and are arranged roughly in increasing order of difficulty. All the videos are taken from the Gresty Academy YouTube podcast 'A Crash Course in TMUA Must Know Maths' which contains hundreds of TMUA style questions and is great for revision.
- Teaser #43 - tests knowledge of ellipse and circle characteristics - Standard
- Teaser #3 - tests how to find furthest distance of a circle from the origin - Standard
- Teaser #22 - tests ability to find coordinates of intersection of a parabola and circle - Standard
- Teaser #498 - tests how to establish when both axes are tangent to a circle - Medium
- Teaser #451 - tests which circle provides a counterexample to a statement - Medium
- Teaser #24 - tests finding the equation of a circle given its gradient y=mx+c - Medium
- Teaser #172 - tests how to find the area of a square inside multiple circles using symmetry - Medium
- Teaser #203 - tests how to find the radius of a circle inscribed in an equilateral triangle - Medium
- Teaser #491 - tests understanding of all steps required to correctly solve a log = log equation - Tough
[Note: We also have a 'Circles and Circle Theorems' playlist on our YouTube channel however the videos in this playlist are not all relevant to TMUA (some are too easy, some are too hard, and many cover topics not tested in TMUA).]
TMUA Past Questions on Circles and Circle Equations: SP p2 q1; 2016 p1 q9; 2016 p1 q12; 2017 p1 q6; 2017 p1 q9; 2018 p1 q3; 2019 p1 q6; 2020 p1 q16; 2021 p1 q1; 2021 p1 q17; 2021 p1 q20; 2021 p2 q7; 2021 p2 q15; 2022 p1 q2; 2022 p1 q4; 2022 p1 q14; 2022 p1 q19; 2022 p2 q4; 2022 p2 q19; 2023 p1 q13; 2023 p1 q17
Practice makes perfect - good luck in your studies!