Lesson G5

G5 Implicit and parametric differentiation Quiz: AQA Maths, Unit 7

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

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Lesson G5, Implicit and parametric differentiation: 20 multiple choice questions for the AQA Maths (7357), Unit 7: Differentiation, written with Revision Ninja.

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The 20 questions

  1. For the implicit curve x^2 + y^2 = 25, what is dy/dx?

    • -y/x
    • 2x
    • x/y
    • -x/y

  2. Differentiating y^3 with respect to x, what is the result?

    • 3y dy/dx
    • 3y^2
    • y^3 dx/dy
    • 3y^2 dy/dx

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

    • 3t/2
    • 3/2
    • 2t/3
    • 3/(2t^2)

  4. The formula dy/dx = (dy/dt)/(dx/dt) for parametric curves comes from which rule?

    • The chain rule
    • Integration by parts
    • The product rule
    • The quotient rule applied to x only

  5. Differentiate implicitly the relation xy = 4.

    • dy/dx = 4
    • y dy/dx = 4
    • x dy/dx = 4
    • y + x dy/dx = 0

  6. Why is implicit differentiation needed for a curve such as x^2 + y^2 = 1?

    • Because the curve is a straight line and needs no differentiation
    • Because the curve has no gradient at any point
    • Because y cannot easily be written as a single function of x, so the chain rule is applied to both sides
    • Because y is constant on the curve

  7. A curve is given by x = 2t and y = t^2. What is dy/dx?

    • 1/t
    • t
    • 2t
    • t^2

  8. Find dy/dx for x^2 + y^2 = 25 at the point (3, 4).

    • -3/4
    • -4/3
    • 3/4
    • 4/3

  9. Find the gradient of x^3 + y^3 = 9 at the point (2, 1).

    • -4
    • 4
    • -1/4
    • -2

  10. For x = 3 cos t and y = 3 sin t, what is dy/dx at t = pi/4?

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

  11. For x = t + 1 and y = t^2 - 4t, what is dy/dx at t = 2?

    • 0
    • -2
    • 2
    • 1

  12. Find dy/dx for x^2 y + y^2 = 6x.

    • (6 - 2xy)/(x^2 - 2y)
    • (3 - xy)/(x^2 + y)
    • (6 - 2xy)/(x^2 + 2y)
    • (6 + 2xy)/(x^2 + 2y)

  13. For the curve y^2 = 4x, what is dy/dx in terms of y?

    • y/2
    • 2/x
    • 4/y
    • 2/y

  14. For x = e^t and y = t, what is dy/dx?

    • t e^t
    • e^t
    • 1/t
    • e^(-t)

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

    • 1
    • 2/3
    • 3/2
    • 2

  16. For the curve x^3 + y^3 = 6xy, what is dy/dx at the point (3, 3)?

    • -1
    • -3
    • 3
    • 1

  17. A curve has x = t^2 + 1 and y = t^3 - t. What is the gradient at t = 1?

    • 1/2
    • 1
    • 2
    • -1

  18. For x = sin t and y = cos 2t, what is dy/dx at t = pi/6?

    • 2
    • -sqrt(3)/2
    • -1/2
    • -2

  19. Differentiate implicitly e^y = x + 1 to find dy/dx.

    • x + 1
    • 1/(x + 1)
    • y/(x + 1)
    • e^y

  20. For x^2 + xy + y^2 = 7, what is dy/dx at the point (1, 2)?

    • 4/5
    • -4/5
    • -5/4
    • -1/2

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