plumiCircles: Edexcel A‑Level Maths questions
Edexcel A-Level Maths past-paper questions on 3.2 Circles, 2010–2025, 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 15 questions on Circles, as a list
- June 2025, Pure 1, Q2 (5 marks): The circle C has equation (x + 3) 2 + (y – 4) 2 = 24 (a) (i) State the coordinates of the centre of C. (ii) Find the radius of C writing your answer as a fully
- June 2025, AS Pure, Q4 (6 marks): The circle C has equation x 2 + y 2 + 10x – 4y + 1 = 0 (a) Find (i) the coordinates of the centre of C (ii) the exact radius of C (3) The line with equation y =
- June 2024, Pure 2, Q14 (8 marks): The circle C1 has equation x y x y 2 2 6 14 33 0 (a) Find (i) the coordinates of the centre of C1 (ii) the radius of C1 (3) A different circle C2 • has centre w
- June 2024, AS Pure, Q10 (8 marks): C P Q l O y x Figure 4 Figure 4 shows a sketch of the circle C • the point P (–1, k + 8) is the centre of C • the point Q (3, k 2 – 2k) lies on C • k is a posit
- June 2023, Pure 1, Q10 (9 marks): A circle C has equation x 2 + y 2 + 6kx – 2ky + 7 = 0 where k is a constant. (a) Find in terms of k, (i) the coordinates of the centre of C (ii) the radius of C
- June 2023, AS Pure, Q6 (5 marks): The circle C has equation where k is a constant. (a) Find the coordinates of the centre of C. (2) Given that C does not cut or touch the x-axis, (b) find the ra
- June 2022, Pure 1, Q3 (5 marks): A circle has equation x2 + y2 − 10x + 16y = 80 (a) Find (i) the coordinates of the centre of the circle, (ii) the radius of the circle. (3) Given that P is the
- June 2022, AS Pure, Q11 (8 marks): C O l y x Figure 3 Figure 3 shows the circle C with equation x2 + y2 – 10x – 8y + 32 = 0 and the line l with equation 2y + x + 6 = 0 (a) Find (i) the coordinate
- November 2021, Pure 1, Q7 (9 marks): The circle C has equation x2 + y2 − 10x + 4y + 11 = 0 (a) Find (i) the coordinates of the centre of C, (ii) the exact radius of C, giving your answer as a simpl
- November 2021, AS Pure, Q15 (9 marks): P l O x y N C Figure 4 Figure 4 shows a sketch of a circle C with centre N(7, 4) The line l with equation y = 1 3 x is a tangent to C at the point P. Find (a) t
- November 2020, Pure 1, Q11 (8 marks): y C2 B A O C1 x Figure 3 Circle C1 has equation x2 + y2 = 100 Circle C2 has equation (x − 15)2 + y2 = 40 The circles meet at points A and B as shown in Figure 3
- November 2020, Pure 2, Q14 (7 marks): A circle C with radius r ● lies only in the 1st quadrant ● touches the x-axis and touches the y-axis The line l has equation 2x + y = 12 (a) Show that the x coo
- November 2020, AS Pure, Q11 (9 marks): (i) A circle C1 has equation x2 + y2 + 18x – 2y + 30 = 0 The line l is the tangent to C1 at the point P(–5, 7). Find an equation of l in the form ax + by + c =
- June 2019, AS Pure, Q10 (5 marks): A circle C has equation x2 + y2 – 4x + 8y – 8 = 0 (a) Find (i) the coordinates of the centre of C, (ii) the exact radius of C. (3) The straight line with equati
- June 2018, Pure 1, Q6 (10 marks): Not to scale y C A P l O x Figure 3 The circle C has centre A with coordinates (7, 5). The line l, with equation y = 2x + 1, is the tangent to C at the point P,
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