plumiCoordinate geometry: OCR A‑Level Maths questions
Every OCR 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 AS Paper 1, question 3: - 2 3 (a) Express x 6 x in the form ( x p ) + , where p and q are constants. q [2] + (b) Hence or otherwise determine the centre and radius of the circle with e](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/h23001-jun25-03-qp.webp?v=3)
![June 2024 Paper 1, question 7: The point A has coordinates (1, 7), and the point B has coordinates (h, 10). (a) You are given that the gradient of the line AB is 2. Find the value of h. [2] (](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/h24001-jun24-07-qp.webp?v=3)
![June 2023 Paper 3, question 4: 2 4 A circle C has equation x y 6 x 10 y k 0 . + - + + = (a) Find the set of possible values of k. [2] (b) It is given that k 46 . =- 1 . [5] Determine the coor](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/h24003-jun23-04-qp.webp?v=3)
![June 2023 AS Paper 2, question 6: The vertices of triangle ABC are A ( 3 1 , ) , B 5 0 and ( , ) ( , ) C 9 7 . - (a) Show that AB BC . [2] = (b) Show that angle ABC is not a right angle. [2] (c)](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/h23002-jun23-06-qp.webp?v=3)
![June 2022 AS Paper 2, question 4: 2 4 The circle x y 6 x 4 y k 0 has radius 5. + - + + = Determine the value of k. [3]](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/h23002-jun22-04-qp.webp?v=3)
All 39 questions on Coordinate geometry, as a list
- June 2025, Paper 1, Q7 (9 marks): In this question you must show detailed reasoning. 3 2 2 A curve has parametric equations x t t , y t t2 for all real values of t. = + = + The curve passes thro
- June 2025, Paper 2, Q5 (8 marks): In this question you must show detailed reasoning. A circle has diameter PQ where P is ( 5 1 , ) and Q is (5, 1). The line x 2 y 12 meets the circle - + = at A
- June 2025, AS Paper 1, Q3 (5 marks): - 2 3 (a) Express x 6 x in the form ( x p ) + , where p and q are constants. q [2] + (b) Hence or otherwise determine the centre and radius of the circle with e
- June 2025, AS Paper 1, Q8 (8 marks): 2 8 A curve with equation y x 3 x 9 x 12 has stationary points A and B. = + - - Determine the coordinates of the point where the line through A and B meets the
- June 2025, AS Paper 2, Q1 (3 marks): Determine the equation of the line that passes through the point (1, 3) and is perpendicular to the line with equation x 3 6 y 5 0 . Give your answer in the for
- June 2024, Paper 1, Q7 (10 marks): The point A has coordinates (1, 7), and the point B has coordinates (h, 10). (a) You are given that the gradient of the line AB is 2. Find the value of h. [2] (
- June 2024, Paper 1, Q12 (11 marks): In this question you must show detailed reasoning. y 2 x O 2 2 The diagram shows the curve with parametric equations x , y 2 t 3 t for t 0 . = = + H 4 t2 ( 1 )
- June 2024, Paper 3, Q6 (6 marks): The curve C is defined, for 0 t 1 2 r, by the parametric equations G x 4 k k sin t , y 2 4 cos t , = + = + where k is a constant. (a) Find a cartesian equation
- June 2024, AS Paper 1, Q8 (5 marks): 2 8 A circle, C, has equation x 6 x y 16 . - + = A second circle, D, has the following properties: • The line through the centres of circle C and circle D has g
- June 2024, AS Paper 2, Q8 (7 marks): The points A and B have coordinates (4, 8) and (6, p) respectively, where p is a positive constant and p 8 . ! (a) Find, in terms of p, the coordinates of the m
- June 2023, Paper 2, Q4 (9 marks): x2 4 The diagram shows part of the graph of y . The normal to the curve at the point A(1, 1) meets = the curve again at B. Angle AOB is denoted by a. y B 2 A 1
- June 2023, Paper 2, Q6 (10 marks): A circle has centre C which lies on the x-axis, as shown in the diagram. The line y = meets the x circle at A and B. The midpoint of AB is M. y y =x B M A C x 2
- June 2023, Paper 3, Q4 (7 marks): 2 4 A circle C has equation x y 6 x 10 y k 0 . + - + + = (a) Find the set of possible values of k. [2] (b) It is given that k 46 . =- 1 . [5] Determine the coor
- June 2023, Paper 3, Q5 (9 marks): A mathematics department is designing a new emblem to place on the walls outside its classrooms. The design for the emblem is shown in the diagram below. y x O
- June 2023, AS Paper 1, Q8 (7 marks): In this question you must show detailed reasoning. 2 2 A circle has equation x y 6 x 4 y 12 0 . Two tangents to this circle pass through the + - - + = point (0,
- June 2023, AS Paper 2, Q6 (10 marks): The vertices of triangle ABC are A ( 3 1 , ) , B 5 0 and ( , ) ( , ) C 9 7 . - (a) Show that AB BC . [2] = (b) Show that angle ABC is not a right angle. [2] (c)
- June 2022, Paper 1, Q12 (12 marks): c m. 1 1 2 12 A curve has parametric equations x t y , 2 t . The point P is ,p p = = 2 (a) Show that the equation of the tangent at P can be written as y 2 p x
- June 2022, Paper 3, Q3 (4 marks): The points P and Q have coordinates (2, -5) and (3, 1) respectively. Determine the equation of the circle that has PQ as a diameter. Give your answer in the for
- June 2022, AS Paper 1, Q7 (8 marks): (a) In this question you must show detailed reasoning. Find the range of values of the constant m for which the simultaneous equations y mx and = 2 2 x y 6 x 2
- June 2022, AS Paper 2, Q4 (3 marks): 2 4 The circle x y 6 x 4 y k 0 has radius 5. + - + + = Determine the value of k. [3]
- November 2021, Paper 1, Q9 (10 marks): A particle moves in the x-y plane so that at time t seconds, where t 0 , its coordinates are given by H - . 2 t t 3 t x e 4 e 3 , y 2 e = - + = (a) Explain why
- November 2021, Paper 2, Q5 (8 marks): In this question you must show detailed reasoning. Points A, B and C have coordinates (0, 6), (7, 5) and (6, −2) respectively. (a) Find an equation of the perpe
- November 2021, AS Paper 1, Q9 (6 marks): In this question you must show detailed reasoning. Find the equation of the straight line with positive gradient that passes through (0, 2) and is a 2 tangent t
- November 2021, AS Paper 2, Q3 (5 marks): Sam invested in a shares scheme. The value, £V, of Sam’s shares was reported t months after investment. • Exactly 6 months after investment, the value of Sam’s
- November 2021, AS Paper 2, Q7 (9 marks): y A x O 55 4 C D –11 B 2 2 The diagram shows the circle with equation x y 6 x 9 y 19 0 and centre C. + - + + = (a) Find the following. • The coordinates of C. •
- November 2020, Paper 1, Q11 (10 marks): In this question you must show detailed reasoning. y A P x O 2 2 The diagram shows a circle with equation x y 10 x 14 y 64 0 . A tangent is drawn from + - - + =
- November 2020, Paper 2, Q7 (8 marks): A and B are fixed points in the x-y plane. The position vectors of A and B are a and b respectively. State, with reference to points A and B, the geometrical si
- November 2020, Paper 3, Q6 (11 marks): In this question you must show detailed reasoning. y P x O Q 2 2 The diagram shows the curve with equation 4 xy 2 ( x 4 y ) 9 x . = + - y x y d = 4 4 - . 9 - (a
- November 2020, AS Paper 2, Q6 (6 marks): In this question you must show detailed reasoning. y x O ^ h ,3 – 2 The diagram shows the line y 3 x 7 which is a tangent to a circle with centre ( , 3 2 ) . +
- June 2019, Paper 2, Q3 (9 marks): (a) A circle is defined by the parametric equations x 3 2 cos , y 4 2 sin . = + =- + i i (i) Find a cartesian equation of the circle. [2] (ii) Write down the ce
- June 2019, Paper 3, Q2 (8 marks): 2 2 A circle with centre C has equation x y 6 x 4 y 4 0 . + - + + = (a) Find (i) the coordinates of C, [2] (ii) the radius of the circle. [1] (b) Determine the
- June 2019, AS Paper 1, Q2 (4 marks): 2 2 The circle x y 4 x ky 12 0 has radius 1. + - + + = Find the two possible values of the constant k. [4]
- June 2019, AS Paper 2, Q2 (6 marks): ^ h 2 - 2 2 (a) Express x 5 20 x + in the form 3 p x q r , where p, q and r are integers. [3] + + 2 (b) State the coordinates of the minimum point of the curve
- June 2018, Paper 1, Q1 (4 marks): The points A and B have coordinates (1, 5) and (4, 17) respectively. Find the equation of the straight line which passes through the point (2, 8) and is perpend
- June 2018, Paper 1, Q5 (8 marks): 2 5 The equation of a circle is x y x y 6 2 10 0 . + + - - = (i) Find the centre and radius of the circle. [3] 2 2 (ii) Find the coordinates of any points where
- June 2018, Paper 1, Q10 (10 marks): 2 10 A curve has parametric equations x t and y t , for t 0 . ! = + = - t t d in terms of t, giving your answer in its simplest form. y (i) Find x [4] d (ii) Ex
- June 2018, Paper 3, Q1 (3 marks): 2 1 A circle with centre C has equation x y 8 x 2 y 7 0 . + + - - = Find (i) the coordinates of C, [2] (ii) the radius of the circle. [1]
- June 2018, AS Paper 1, Q8 (6 marks): In this question you must show detailed reasoning. 1 1 The lines y x and y x are tangents to a circle at (2, 1) and (-2, 1) respectively. Find the equation = =-
- June 2018, AS Paper 2, Q5 (5 marks): In this question you must show detailed reasoning. 2 - The line x 5 y k is a tangent to the curve x 4 y 10 . Find the value of the constant k. [5] + = =
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