plumiCoordinate geometry in the (x, y) plane: AQA A‑Level Maths questions
Every AQA A-Level Maths exam question on C Coordinate geometry in the (x, y) plane, 2018–2025, with its mark scheme and examiner’s report.
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![June 2025 Paper 1, question 13: A curve C has parametric equations x = 4(4t + 1)2 y = e–4t for – 1 4 ≤ t ≤ 0 13 (a) Find dy dx in terms of t [3 marks] 13 (b) Find an equation of the tangent to](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/73571-jun25-13-qp.webp)
![June 2024 Paper 2, question 1: One of the equations below is the equation of a circle. Identify this equation. [1 mark] Tick (✓) one box. (x + 1)2 – (y + 2)2 = –36 (x + 1)2 – (y + 2)2 = 36 (x](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/73572-jun24-01-qp.webp)
![June 2023 Paper 1, question 9: The points P and Q have coordinates (−6, 15) and (12, 19) respectively. 9 (a) (i) Find the coordinates of the midpoint of PQ [1 mark] 9 (a) (ii) Find the equati](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/73571-jun23-09-qp.webp)
![June 2023 Paper 2, question 3: A circle has equation (x − 5)2 + (y − 13)2 = 16 Find the radius of the circle. Circle your answer. [1 mark] 4 12 16 256 for the next question](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/73572-jun23-03-qp.webp)
![June 2022 Paper 2, question 1: A circle has centre (4, −5) and radius 6 Find the equation of the circle. Tick (3) one box. [1 mark] (x − 4)2 + (y + 5)2 = 6 (x + 4)2 + (y − 5)2 = 6 (x − 4)2 +](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/73572-jun22-01-qp.webp)
![November 2021 Paper 2, question 7: A circle has equation x2 + y2 − 6x − 8y = p 7 (a) (i) State the coordinates of the centre of the circle. [1 mark] 7 (a) (ii) Find the radius of the circle in te](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/73572-nov21-07-qp.webp)
All 25 questions on Coordinate geometry in the (x, y) plane, as a list
- June 2025, Paper 1, Q13 (9 marks): A curve C has parametric equations x = 4(4t + 1)2 y = e–4t for – 1 4 ≤ t ≤ 0 13 (a) Find dy dx in terms of t [3 marks] 13 (b) Find an equation of the tangent to
- June 2025, Paper 2, Q9 (9 marks): A circle with centre C has equation (x – 12)2 + (y – 2)2 = 100 The graph with equation y = │3x – 36│ – 8 intersects the circle at the points A, B and D as shown
- June 2024, Paper 2, Q1 (1 mark): One of the equations below is the equation of a circle. Identify this equation. [1 mark] Tick (✓) one box. (x + 1)2 – (y + 2)2 = –36 (x + 1)2 – (y + 2)2 = 36 (x
- June 2024, Paper 3, Q9 (9 marks): Figure 1 below shows a circle. Figure 1 y x O P Q The centre of the circle is P and the circle intersects the y-axis at Q as shown in Figure 1. The equation of
- June 2023, Paper 1, Q9 (9 marks): The points P and Q have coordinates (−6, 15) and (12, 19) respectively. 9 (a) (i) Find the coordinates of the midpoint of PQ [1 mark] 9 (a) (ii) Find the equati
- June 2023, Paper 2, Q3 (1 mark): A circle has equation (x − 5)2 + (y − 13)2 = 16 Find the radius of the circle. Circle your answer. [1 mark] 4 12 16 256 for the next question
- June 2023, Paper 3, Q9 (12 marks): A water slide is the shape of a curve PQ as shown in Figure 1 below. Figure 1 O P Q The curve can be modelled by the parametric equations x = t − 1 t + 4:8 y =
- June 2022, Paper 1, Q1 (1 mark): A curve is defined by the parametric equations x = cos y and y = siny where 0 − y − 2p Which of the options shown below is a Cartesian equation for this curve?
- June 2022, Paper 1, Q8 (11 marks): The lines L1 and L2 are parallel. L1 has equation 5x + 3y = 15 and L2 has equation 5x + 3y = 83 L1 intersects the y-axis at the point P. The point Q is the poin
- June 2022, Paper 1, Q13 (9 marks): Figure 2 shows the approximate shape of the vertical cross section of the entrance to a cave. The cave has a horizontal floor. The entrance to the cave joins th
- June 2022, Paper 2, Q1 (1 mark): A circle has centre (4, −5) and radius 6 Find the equation of the circle. Tick (3) one box. [1 mark] (x − 4)2 + (y + 5)2 = 6 (x + 4)2 + (y − 5)2 = 6 (x − 4)2 +
- June 2022, Paper 3, Q6 (9 marks): A design for a surfboard is shown in Figure 1. Figure 1 length width The curve of the top half of the surfboard can be modelled by the parametric equations x =
- November 2021, Paper 1, Q5 (6 marks): The line L has equation 3y − 4x = 21 The point P has coordinates (15, 2) 5 (a) Find the equation of the line perpendicular to L which passes through P. [2 marks
- November 2021, Paper 1, Q14 (10 marks): The curve C is defined for t × 0 by the parametric equations x = t2 + t and y = 4t2 − t3 C is shown in the diagram below. x y O 14 (a) Find the gradient of C at
- November 2021, Paper 2, Q7 (8 marks): A circle has equation x2 + y2 − 6x − 8y = p 7 (a) (i) State the coordinates of the centre of the circle. [1 mark] 7 (a) (ii) Find the radius of the circle in te
- November 2020, Paper 2, Q6 (8 marks): The line L has equation 5y + 12x = 298 A circle, C, has centre (7, 9) L is a tangent to C. 6 (a) Find the coordinates of the point of intersection of L and C. F
- November 2020, Paper 2, Q8 (10 marks): The curve defined by the parametric equations x = t2 and y = 2t − 2 p × t × 2 p is shown in Figure 1 below. Figure 1 x y O 8 (a) Find a Cartesian equation of th
- June 2019, Paper 1, Q4 (4 marks): The point A has coordinates (−1, a) and the point B has coordinates (3, b) The line AB has equation 5x + 4y = 17 Find the equation of the perpendicular bisector
- June 2019, Paper 1, Q15 (10 marks): (a) At time t hours after a high tide, the height, h metres, of the tide and the velocity, v knots, of the tidal flow can be modelled using the parametric equat
- June 2019, Paper 3, Q5 (5 marks): A circle has equation x2 + y2 − 6x − 8y = 264 AB is a chord of the circle. The angle at the centre of the circle, subtended by AB, is 0.9 radians, as shown in t
- June 2018, Paper 1, Q5 (6 marks): A curve is defined by the parametric equations x = 4 × 2−t + 3 y = 3 × 2t − 5 5 (a) Show that dy dx = −3 4 × 22t [3 marks] 5 (b) Find the Cartesian equation of
- June 2018, Paper 1, Q7 (8 marks): Three points A, B and C have coordinates A (8, 17), B (15, 10) and C (−2, −7) 7 (a) Show that angle ABC is a right angle. [3 marks] 7 (b) A, B and C lie on a ci
- June 2018, Paper 1, Q13 (10 marks): A company is designing a logo. The logo is a circle of radius 4 inches with an inscribed rectangle. The rectangle must be as large as possible. The company mode
- June 2018, Paper 3, Q1 (1 mark): A circle has equation (x − 4)2 + (y + 4)2 = 9 What is the area of the circle? Circle your answer. [1 mark] 3p 9p 16p 81p
- June 2018, Paper 3, Q3 (1 mark): The line L has equation 2x + 3y = 7 Which one of the following is perpendicular to L? Tick one box. [1 mark] 2x − 3y = 7 3x + 2y = −7 2x + 3y = −1 7 3x − 2y = 7
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