plumiCircles: OCR MEI A‑Level Maths questions
OCR MEI A-Level Maths past-paper questions on 3.2 Circles, 2018–2025, with mark schemes and examiner’s reports where available. Add MadAsMaths questions to your practice, or browse them separately by topic and difficulty.
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All 16 questions on Circles, as a list
- June 2025, Paper 2, Q1 (2 marks): 2 1 The equation of a circle is ( x 4 ) ( y 5 ) 64 0 . - + + - = (a) State the coordinates of the centre of the circle. [1] (b) State the radius of the circle.
- June 2025, AS Paper 2, Q11 (6 marks): A circle has centre (4, ‒1) and radius 13. (a) Write down the equation of the circle. [2] (b) Determine the equation of the tangent to the circle at the point (
- June 2024, Paper 1, Q15 (9 marks): 2 15 The circle x y 2 x 14 y 25 0 has its centre at the point C. The line y 7 x 25 intersects + + - + = = + the circle at points A and B. Prove that triangle AB
- June 2024, AS Paper 1, Q8 (10 marks): 2 8 A circle with centre C has equation x y 6 x 16 y 48 0 . + - - + = (a) Find the coordinates of C. [2] A line has equation y x - and intersects the circle at
- June 2023, Paper 2, Q2 (3 marks): The equation of a circle is 2 2 x 12 x y 8 y 3 0 . - + + + = (a) Find the radius of the circle. [2] (b) State the coordinates of the centre of the circle. [1]
- June 2023, Paper 2, Q6 (4 marks): The parametric equations of a circle are x 2 cos 3 and y 2 sin + . 1 = i - = i 2 2 Determine the cartesian equation of the circle in the form ( x a ) ( y b ) k
- June 2023, AS Paper 1, Q8 (9 marks): In this question you must show detailed reasoning. 2 2 (a) Find the centre and radius of the circle with equation x y 2 x 4 y 20 0 . [4] + - + - = (b) Find the
- June 2022, Paper 2, Q10 (7 marks): The parametric equations of a curve are x 2 5 cos and y 1 5 sin , where 0 2 . i i = + = + i r G G (a) Determine the cartesian equation of the curve. [3] (b) Hen
- November 2021, Paper 1, Q7 (10 marks): In this question you must show detailed reasoning. The points A (-1, 4) and B (7, -2) are at opposite ends of a diameter of a circle. (a) Find the equation of t
- November 2021, Paper 2, Q7 (4 marks): The parametric equations of a circle are x 7 5 cos , y 5 sin - , for 0 3 2 r. = + i = i G i G (a) Find a cartesian equation of the circle. [3] (b) State the coo
- November 2021, AS Paper 2, Q10 (6 marks): In this question you must show detailed reasoning. The points P, Q and R have coordinates (‒ 3, 7), (11, 5) and (9, ‒ 9) respectively. (a) Show that PQ is perpe
- November 2020, AS Paper 2, Q7 (8 marks): In this question you must show detailed reasoning. A circle has centre (2, - 1) and radius 5. A straight line passes through the points (1, 1) and (9, 5). Find
- June 2019, Paper 3, Q6 (7 marks): A circle has centre C (10, 4). The x-axis is a tangent to the circle, as shown in Fig. 6. y C (10, 4) x O Fig. 6 (a) Find the equation of the circle. [2] (b) Sh
- June 2019, AS Paper 2, Q4 (3 marks): 2 4 The equation of a circle is x y x y 8 6 39 0 . + + - - = (a) Find the coordinates of the centre of the circle. [2] (b) Find the radius of the circle. [1]
- June 2018, Paper 1, Q12 (14 marks): 2 12 Fig. 12 shows the circle ( x 1 ) ( y 1 ) 25 , the line y 4 3 x 32 and the tangent to the circle at the - + + = = - point A (5, 2). D is the point of inters
- June 2018, AS Paper 2, Q8 (7 marks): In this question you must show detailed reasoning. The centre of a circle C is at the point (−1, 3) and C passes through the point (1, −1). The straight line L
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