Lesson C3-C4

C3-C4 Parametric equations and modelling Quiz: AQA Maths, Unit 3

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

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Lesson C3-C4, Parametric equations and modelling: 20 multiple choice questions for the AQA Maths (7357), Unit 3: Coordinate geometry, written with Revision Ninja.

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The 20 questions

  1. What is a parametric equation?

    • An equation with x and y in one expression
    • An equation involving only x
    • Equations giving x and y each in terms of a third variable, the parameter
    • An equation with no variables

  2. Convert x = t + 1, y = t^2 to a Cartesian equation.

    • y = (x + 1)^2
    • y = x^2 + 1
    • y = x^2 - 1
    • y = (x - 1)^2

  3. Eliminate t from x = 2t and y = 3t - 1.

    • y = 3x/2 - 1
    • y = 6x - 1
    • y = 3x/2 + 1
    • y = 2x/3 - 1

  4. What is the point on x = t^2, y = 2t + 1 when t = 2?

    • (2, 4)
    • (2, 5)
    • (4, 4)
    • (4, 5)

  5. Which Cartesian equation is given by x = 3 cos t, y = 3 sin t?

    • x + y = 3
    • x^2 + y^2 = 3
    • x^2 + y^2 = 9
    • x^2 - y^2 = 9

  6. For x = t^2 and y = t^3, what is dy/dx in terms of t?

    • 2t/3
    • t/2
    • 3t/2
    • 3t^2

  7. For x = t^2 and y = t^3, what is the gradient at t = 1?

    • 3
    • 3/2
    • 2/3
    • 1

  8. What is the formula for dy/dx with parametric equations?

    • (dy/dt)/(dx/dt)
    • d^2y/dt^2
    • (dy/dt) x (dx/dt)
    • (dx/dt)/(dy/dt)

  9. Which is a parametric form of y = x^2?

    • x = 2t, y = t^2
    • x = t^2, y = t
    • x = t, y = t^2
    • x = t, y = t

  10. A projectile has x = 20t and y = 15t - 5t^2 (metres, seconds). How far does it travel horizontally before landing?

    • 20 m
    • 120 m
    • 45 m
    • 60 m

  11. For the projectile with y = 15t - 5t^2, what is the maximum height and when does it occur?

    • 11.25 m at t = 3 s
    • 22.5 m at t = 1.5 s
    • 11.25 m at t = 1.5 s
    • 15 m at t = 1 s

  12. A line is given by x = 1 + 2t, y = 3 - t. Which Cartesian equation does it satisfy?

    • x + 2y = 7
    • x - 2y = 1
    • x + 2y = 5
    • 2x - y = 1

  13. Where does the curve x = t + 1, y = t^2 - 4 cross the x-axis?

    • (0, -4) and (2, 0)
    • (3, 0) only
    • (1, 0) and (-3, 0)
    • (3, 0) and (-1, 0)

  14. What Cartesian equation is given by x = sec t, y = tan t?

    • x - y = 1
    • x^2 - y^2 = 1
    • y^2 - x^2 = 1
    • x^2 + y^2 = 1

  15. For x = cos t, y = sin t, what is dy/dx at t = pi/4?

    • -sqrt(2)
    • 1
    • 0
    • -1

  16. For x = t^2, y = 2t, what is the equation of the tangent at t = 2?

    • x - 2y + 4 = 0
    • x + 2y - 12 = 0
    • x - 2y - 4 = 0
    • 2x - y - 4 = 0

  17. A particle has x = 3t and y = t^2 - 2t. When is it at (6, 0)?

    • t = 2
    • t = 3
    • t = 6
    • t = 1

  18. Which describes the curve x = 2 + 3 cos t, y = 1 + 3 sin t?

    • Centre (2, 1), radius 9
    • Centre (2, 1), radius 3
    • Centre (3, 3), radius 2
    • Centre (-2, -1), radius 3

  19. A stone has horizontal displacement x = 8t and height y = 6t - 4.9t^2 metres. Roughly how long until it lands?

    • About 1.22 s
    • About 0.61 s
    • About 6 s
    • About 2.45 s

  20. For x = t and y = 1/t with t > 0, what Cartesian equation is satisfied?

    • y = x
    • xy = 1
    • x^2 + y^2 = 1
    • x + y = 1

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