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Coordinate geometry: WJEC A‑Level Maths questions

Every WJEC A-Level Maths exam question on P.3 Coordinate geometry, 2018–2025, with its mark scheme and examiner’s report.

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314 questions

  1. Q13

    Summer 2025 · Unit 3

    11 marksP.7 DifferentiationP.3 Coordinate geometry
    The whole paper ↗
    Summer 2025 Unit 3, question 13: 13. A curve is defined parametrically by 2 3 1 y 3 t 2 x  t  ,  . Show that the gradient of the curve at the point with parameter p is 1 (a) p . [4] t  . 1

  2. Q2

    Summer 2025 · AS Unit 1

    11 marksP.3 Coordinate geometry
    The whole paper ↗
    Summer 2025 AS Unit 1, question 2: 2. The line L1 passes through the points A(–2, 0) and B(3, 5). (a) Find the equation of L1. [3] The line L2 is perpendicular to L1, passes through B and interse

  3. Q8

    Summer 2025 · AS Unit 1

    10 marksP.3 Coordinate geometryP.7 Differentiation
    The whole paper ↗
    Summer 2025 AS Unit 1, question 8: 2 2 4 4 x  y  x  y  . 8. A circle C has centre A and equation (a) Find the coordinates of A and the radius of C. [3] y  2 x  , intersects the circle C at

  4. Q11

    Summer 2024 · Unit 3

    10 marksP.7 DifferentiationP.3 Coordinate geometry
    The whole paper ↗
    Summer 2024 Unit 3, question 11: 11. A curve is defined parametrically by x  2 sin2 y  1 cos2   , . Show that the gradient of the curve at the point with parameter  is tan  . (a) [6]

  5. Q7

    Summer 2024 · AS Unit 1

    11 marksP.3 Coordinate geometry
    The whole paper ↗
    Summer 2024 AS Unit 1, question 7: 7. (a) The line L1 passes through the points A(–3, 0) and B(1, 4). Determine the equation of L1. [3] y  3 x  . 3 (b) The line L2 has equation (i) Given that L

  6. Q18

    Summer 2024 · AS Unit 1

    12 marksP.3 Coordinate geometry
    The whole paper ↗
    Summer 2024 AS Unit 1, question 18: A circle C has centre (–3, –1) and radius 5. Show that the equation of C can be written 18. (a) 2 2 6 2 5 0 x  y  x  y   as . [2] (b) (i) Find the equation

  7. Q13

    Summer 2023 · Unit 3

    7 marksP.3 Coordinate geometry
    The whole paper ↗
    Summer 2023 Unit 3, question 13: The curve C1 has parametric equations x = 3p + 1, y = 9p2. 1 3 The curve C2 has parametric equations x = 4q, y = 2q. Find the Cartesian coordinates of the point

  8. Q3

    Summer 2023 · AS Unit 1

    15 marksP.3 Coordinate geometry
    The whole paper ↗
    Summer 2023 AS Unit 1, question 3: 3 The point A has coordinates (–2, 5) and the point B has coordinates (3, 8). The point C lies on the x-axis such that AC is perpendicular to AB. a) Find the eq

  9. Q7

    Summer 2023 · AS Unit 1

    13 marksP.3 Coordinate geometryP.2 Algebra and functions
    The whole paper ↗
    Summer 2023 AS Unit 1, question 7: y  2 x  5 x  12 y mx 14 The curve C has equation and the line L has equation   , 0 7 where m is a real constant. a) Given that L is a tangent to C, i) show

  10. Q16

    Summer 2022 · Unit 3

    8 marksP.3 Coordinate geometryP.7 Differentiation
    The whole paper ↗
    Summer 2022 Unit 3, question 16: 6 The parametric equations of the curve C are x = 3 – 4t + t2, y = (4 – t)2. a) Find the coordinates of the points where C meets the y-axis. [3] b) Show that th

  11. Q3

    Summer 2022 · AS Unit 1

    11 marksP.3 Coordinate geometry
    The whole paper ↗
    Summer 2022 AS Unit 1, question 3: The line L1 passes through the points A(0, 5) and B(3, –1). 0 3 a) Find the equation of the line L1. [3] The line L2 is perpendicular to L1 and passes through t

  12. Q5

    Summer 2022 · AS Unit 1

    9 marksP.3 Coordinate geometryP.2 Algebra and functions
    The whole paper ↗
    Summer 2022 AS Unit 1, question 5: 5 The curve C1 has equation y = –x2 + 2x + 3 and the curve C2 has equation y = x2 – x – 6. The two curves intersect at the points A and B. a) Determine the coor

  13. Q7

    Summer 2022 · AS Unit 1

    11 marksP.3 Coordinate geometry
    The whole paper ↗
    Summer 2022 AS Unit 1, question 7: 7 A circle C has centre A and equation x2 + y2 – 4x – 6y = 3. a) Find the coordinates of A and the radius of C. [3] The line L with equation y = x + 5 intersect

  14. Q6

    Summer 2019 · Unit 3

    11 marksP.7 DifferentiationP.3 Coordinate geometry
    The whole paper ↗
    Summer 2019 Unit 3, question 6: A curve C has parametric equations x = sinθ, y = cos2θ. 0 6 π The equation of the tangent to the curve C at the point P where θ= is a) 4 y = mx + c. Find the ex

  15. Q4

    Summer 2019 · AS Unit 1

    15 marksP.3 Coordinate geometry
    The whole paper ↗
    Summer 2019 AS Unit 1, question 4: 4 The line L1 passes through the points A(–1, 3) and B(2, 9). The line L2 has equation 2y + x = 25 and intersects L1 at the point C. L2 also intersects the x-ax

  16. Q9

    Summer 2019 · AS Unit 1

    12 marksP.3 Coordinate geometry
    The whole paper ↗
    Summer 2019 AS Unit 1, question 9: 9 The points A(–2, 4) and B(6, 10) are such that AB is the diameter of a circle. a) Show that the centre of the circle has coordinates (2, 7). [1] The equation

  17. Q10

    Summer 2018 · Unit 3

    14 marksP.3 Coordinate geometryP.7 Differentiation
    The whole paper ↗
    Summer 2018 Unit 3, question 10: 0 The equation of a curve C is given by the parametric equations x = cos2θ , y = cosθ. a) Find the Cartesian equation of C. [2] π Show that the line x – y + 1 =

  18. Q2

    Summer 2018 · AS Unit 1

    14 marksP.3 Coordinate geometry
    The whole paper ↗
    Summer 2018 AS Unit 1, question 2: The points A and B have coordinates (–1, 10) and (5, 1) respectively. The straight line L 0 2 has equation 2x – 3y + 6 = 0. a) The line L intersects the line AB

  19. Q18

    Summer 2018 · AS Unit 1

    8 marksP.3 Coordinate geometry
    The whole paper ↗
    Summer 2018 AS Unit 1, question 18: 8 The coordinates of three points A, B, C are (4, 6), (–3, 5) and (5, –1) respectively. $ a) Show that BAC is a right angle. [3] b) A circle passes through all
All 19 questions on Coordinate geometry, as a list
  1. Summer 2025, Unit 3, Q13 (11 marks): 13. A curve is defined parametrically by 2 3 1 y 3 t 2 x  t  ,  . Show that the gradient of the curve at the point with parameter p is 1 (a) p . [4] t  . 1
  2. Summer 2025, AS Unit 1, Q2 (11 marks): 2. The line L1 passes through the points A(–2, 0) and B(3, 5). (a) Find the equation of L1. [3] The line L2 is perpendicular to L1, passes through B and interse
  3. Summer 2025, AS Unit 1, Q8 (10 marks): 2 2 4 4 x  y  x  y  . 8. A circle C has centre A and equation (a) Find the coordinates of A and the radius of C. [3] y  2 x  , intersects the circle C at
  4. Summer 2024, Unit 3, Q11 (10 marks): 11. A curve is defined parametrically by x  2 sin2 y  1 cos2   , . Show that the gradient of the curve at the point with parameter  is tan  . (a) [6]
  5. Summer 2024, AS Unit 1, Q7 (11 marks): 7. (a) The line L1 passes through the points A(–3, 0) and B(1, 4). Determine the equation of L1. [3] y  3 x  . 3 (b) The line L2 has equation (i) Given that L
  6. Summer 2024, AS Unit 1, Q18 (12 marks): A circle C has centre (–3, –1) and radius 5. Show that the equation of C can be written 18. (a) 2 2 6 2 5 0 x  y  x  y   as . [2] (b) (i) Find the equation
  7. Summer 2023, Unit 3, Q13 (7 marks): The curve C1 has parametric equations x = 3p + 1, y = 9p2. 1 3 The curve C2 has parametric equations x = 4q, y = 2q. Find the Cartesian coordinates of the point
  8. Summer 2023, AS Unit 1, Q3 (15 marks): 3 The point A has coordinates (–2, 5) and the point B has coordinates (3, 8). The point C lies on the x-axis such that AC is perpendicular to AB. a) Find the eq
  9. Summer 2023, AS Unit 1, Q7 (13 marks): y  2 x  5 x  12 y mx 14 The curve C has equation and the line L has equation   , 0 7 where m is a real constant. a) Given that L is a tangent to C, i) show
  10. Summer 2022, Unit 3, Q16 (8 marks): 6 The parametric equations of the curve C are x = 3 – 4t + t2, y = (4 – t)2. a) Find the coordinates of the points where C meets the y-axis. [3] b) Show that th
  11. Summer 2022, AS Unit 1, Q3 (11 marks): The line L1 passes through the points A(0, 5) and B(3, –1). 0 3 a) Find the equation of the line L1. [3] The line L2 is perpendicular to L1 and passes through t
  12. Summer 2022, AS Unit 1, Q5 (9 marks): 5 The curve C1 has equation y = –x2 + 2x + 3 and the curve C2 has equation y = x2 – x – 6. The two curves intersect at the points A and B. a) Determine the coor
  13. Summer 2022, AS Unit 1, Q7 (11 marks): 7 A circle C has centre A and equation x2 + y2 – 4x – 6y = 3. a) Find the coordinates of A and the radius of C. [3] The line L with equation y = x + 5 intersect
  14. Summer 2019, Unit 3, Q6 (11 marks): A curve C has parametric equations x = sinθ, y = cos2θ. 0 6 π The equation of the tangent to the curve C at the point P where θ= is a) 4 y = mx + c. Find the ex
  15. Summer 2019, AS Unit 1, Q4 (15 marks): 4 The line L1 passes through the points A(–1, 3) and B(2, 9). The line L2 has equation 2y + x = 25 and intersects L1 at the point C. L2 also intersects the x-ax
  16. Summer 2019, AS Unit 1, Q9 (12 marks): 9 The points A(–2, 4) and B(6, 10) are such that AB is the diameter of a circle. a) Show that the centre of the circle has coordinates (2, 7). [1] The equation
  17. Summer 2018, Unit 3, Q10 (14 marks): 0 The equation of a curve C is given by the parametric equations x = cos2θ , y = cosθ. a) Find the Cartesian equation of C. [2] π Show that the line x – y + 1 =
  18. Summer 2018, AS Unit 1, Q2 (14 marks): The points A and B have coordinates (–1, 10) and (5, 1) respectively. The straight line L 0 2 has equation 2x – 3y + 6 = 0. a) The line L intersects the line AB
  19. Summer 2018, AS Unit 1, Q18 (8 marks): 8 The coordinates of three points A, B, C are (4, 6), (–3, 5) and (5, –1) respectively. $ a) Show that BAC is a right angle. [3] b) A circle passes through all

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