plumiCoordinate geometry: OCR MEI A‑Level Maths questions
Every OCR MEI A-Level Maths exam question on P.3 Coordinate geometry, 2018–2025, with its mark scheme and examiner’s report.
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![June 2025 Paper 2, question 1: 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.](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/h64002-jun25-01-qp.webp?v=3)
![June 2025 Paper 3, question 14: (a) Draw and label a suitable triangle on the diagram in the Printed Answer Booklet to show y that tan , as given in line 30. [1] i = x 2 a ( 3 t ) 2 4 at - (b)](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/h64003-jun25-14-qp.webp?v=3)
![June 2025 AS Paper 2, question 11: 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 (](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/h63002-jun25-11-qp.webp?v=3)
![June 2024 Paper 2, question 1: Calculate the exact distance between the points (2, 1 - ) and (6, 1). Give your answer in the form a b, where a and b are prime numbers. [2]](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/h64002-jun24-01-qp.webp?v=3)
![June 2024 Paper 3, question 15: 15 (a) Show that, for the curve y ax bx + , the equation of the tangent at the point with c = + 2 x‑coordinate t is y ( 2 at b x ) at + . c [3] = + - 2 (b) Henc](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/h64003-jun24-15-qp.webp?v=3)
![June 2024 Paper 3, question 17: x 1 x2 t t2 is y 2 17 Show that, for the curve y , the equation of the normal at the point ( , ) t , = =- + + 2 t 2 as given in line 27. [3]](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/h64003-jun24-17-qp.webp?v=3)
![June 2024 AS Paper 1, question 8: 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](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/h63001-jun24-08-qp.webp?v=3)
![June 2023 Paper 1, question 7: Determine the exact distance between the two points at which the line through (4, 5) and (6, -1) 2 meets the curve y 2 x 7 x + . 1 [7] = -](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/h64001-jun23-07-qp.webp?v=3)
![June 2023 Paper 2, question 2: 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]](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/h64002-jun23-02-qp.webp?v=3)
All 43 questions on Coordinate geometry, 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, Paper 3, Q3 (10 marks): The straight line with equation x 2 y 6 crosses the x‑axis at A and the y‑axis at B. + = (a) Draw the line with equation x 2 y 6 on the grid in the Printed Answ
- June 2025, Paper 3, Q14 (5 marks): (a) Draw and label a suitable triangle on the diagram in the Printed Answer Booklet to show y that tan , as given in line 30. [1] i = x 2 a ( 3 t ) 2 4 at - (b)
- June 2025, AS Paper 1, Q3 (4 marks): In this question you must show detailed reasoning. The graph below shows the line y 3 x - and the line through P and Q where P is (–1, 3) and Q 4 = is (5, 0). y
- 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, Paper 2, Q1 (2 marks): Calculate the exact distance between the points (2, 1 - ) and (6, 1). Give your answer in the form a b, where a and b are prime numbers. [2]
- June 2024, Paper 3, Q12 (9 marks): The diagram shows the curve with parametric equations x sin 2 + , 2 y 2 cos cos 2 for 0 1 2 . , r = i = i + i G i y x O (a) In this question you must show detai
- June 2024, Paper 3, Q13 (1 mark): Substitute appropriate values of t1 and t2 to verify that t t 1 2 gives the correct value for the y‑coordinate of the point of intersection of the tangents at t
- June 2024, Paper 3, Q14 (1 mark): 2 2 14 Substitute appropriate values of t1 and t2 to verify that the expression t t t t gives the + + + 2 1 2 1 2 correct value for the y‑coordinate of the poin
- June 2024, Paper 3, Q15 (6 marks): 15 (a) Show that, for the curve y ax bx + , the equation of the tangent at the point with c = + 2 x‑coordinate t is y ( 2 at b x ) at + . c [3] = + - 2 (b) Henc
- June 2024, Paper 3, Q17 (3 marks): x 1 x2 t t2 is y 2 17 Show that, for the curve y , the equation of the normal at the point ( , ) t , = =- + + 2 t 2 as given in line 27. [3]
- June 2024, Paper 3, Q18 (2 marks): 18 A student is investigating the intersection points of tangents to the curve y 6 x 7 x + . She 1 = - uses software to draw tangents at pairs of points with x‑
- 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 2024, AS Paper 2, Q6 (4 marks): Determine the equation of the line which passes through the point (4, ‒1) and is perpendicular to the line with equation x 2 3 y 6 . + = Give your answer in the
- June 2023, Paper 1, Q7 (7 marks): Determine the exact distance between the two points at which the line through (4, 5) and (6, -1) 2 meets the curve y 2 x 7 x + . 1 [7] = -
- 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, Paper 3, Q5 (8 marks): In this question you must show detailed reasoning. 3 2 This question is about the curve y x 5 x 6 x . = - + (a) Find the equation of the tangent, T, to the curv
- June 2023, Paper 3, Q6 (10 marks): (a) Quadrilateral KLMN has vertices K ( - , 1), L (5, 1 4 - ), M (6, 2) and N (2, 5), as shown in Fig. 6.1. Fig. 6.1 y N (2, 5) R S M (6, 2) K (−4, 1) Q x O P L
- 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 2023, AS Paper 2, Q5 (3 marks): Show that the distance between the points (5, 2) and (11, ‒1) is a b, where a and b are integers to be determined. [3]
- June 2022, Paper 1, Q8 (10 marks): t2 8 A particle moves in the x-y plane so that its position at time t s is given by x t t8 , y for = - = 3 5 . 1 t 1 3 5 . . The units of distance are metres. T
- 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
- June 2022, Paper 3, Q8 (16 marks): 3 8 The curves y h ( ) x and y h - ( ) x , where ( ) h x x - , are shown below. 8 = = = The curve y h ( ) x crosses the x-axis at B and the y-axis at A. = 1 The
- June 2022, AS Paper 1, Q10 (9 marks): A triangle has vertices A ( , ), 1 4 B ( , ) 7 0 and C - ( 4 , 1 ). - (a) Show that the equation of the line AC is y x 3 . [2] = + M is the midpoint of AB. The
- 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 1, Q1 (2 marks): Find the coordinates of the point of intersection of the lines y 3 x - and 2 x 2 y 10 . [2] = + =
- 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, Paper 1, Q10 (9 marks): In this question you must show detailed reasoning. 1 1 1 Fig. 10 shows the curve given parametrically by the equations x , y , for t 2 0 . = = - t 2 3 t t y x O
- November 2020, AS Paper 1, Q8 (7 marks): The point A has coordinates (-1, -2) and the point B has coordinates (7, 4). The perpendicular bisector of AB intersects the line y 2 x k at P. + = Determine th
- 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 1, Q2 (3 marks): Show that the line which passes through the points ( , 2 4 ) and ( 1 5 , ) does not intersect the line - - 3 x y 10 . [3] + =
- June 2019, Paper 1, Q12 (6 marks): t4 2 12 Fig. 12 shows a curve C with parametric equations x , y t4 . The point P, with parameter t, = = is a general point on the curve. Q is the point on the l
- 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, Paper 3, Q12 (2 marks): Show that the equation of the line in Fig. C2 is ry hx hr , as given in line 24. [2] + =
- 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 2019, AS Paper 2, Q10 (10 marks): In this question you must show detailed reasoning. 2 x 2 The equation of a curve is y + . A tangent and a normal to the curve are drawn at the 1 = + x 4 point w
- 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, Paper 3, Q7 (8 marks): In this question you must show detailed reasoning. 2 Fig. 7 shows the curve y 5 x x . = - y x O Fig. 7 2 The line y kx crosses the curve y x x on the x-axis and
- June 2018, Paper 3, Q8 (8 marks): t t 8 A curve has parametric equations x , y t , where 1 . ! - = = 3 3 1 t 1 t + + (i) In this question you must show detailed reasoning. Determine the gradient
- 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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