Lesson G3

G3 Tangents, normals, stationary points and increasing or decreasing Quiz: AQA Maths, Unit 7

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

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Lesson G3, Tangents, normals, stationary points and increasing or decreasing: 20 multiple choice questions for the AQA Maths (7357), Unit 7: Differentiation, written with Revision Ninja.

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The 20 questions

  1. What is the gradient of the normal to a curve at a point where the tangent has gradient m, with m not equal to 0?

    • m
    • -m
    • -1/m
    • 1/m

  2. What condition defines a stationary point on a curve y = f(x)?

    • y = 0
    • dy/dx is undefined
    • dy/dx = 0
    • d^2y/dx^2 = 0 always

  3. When is a function increasing on an interval?

    • d^2y/dx^2 > 0 throughout the interval
    • dy/dx > 0 throughout the interval
    • dy/dx < 0 throughout the interval
    • dy/dx = 0 throughout the interval

  4. How is a local maximum distinguished from a local minimum at a stationary point using the second derivative?

    • A minimum occurs when f'' < 0 and a maximum when f'' > 0
    • A maximum occurs when f'' > 0 and a minimum when f'' = 0
    • The second derivative cannot distinguish maxima from minima
    • A maximum occurs when f'' < 0 and a minimum when f'' > 0

  5. What is the equation of the tangent to y = f(x) at (a, b) with gradient m?

    • y + b = m(x + a)
    • y - a = m(x - b)
    • y - b = m(x - a)
    • y - b = -(x - a)/m

  6. If the tangent to a curve has gradient 2 at a point, what is the gradient of the normal there?

    • 1/2
    • 2
    • -2
    • -1/2

  7. Which statement about a stationary point where f''(a) = 0 is true?

    • It is always a minimum point of the curve
    • It is always a maximum point of the curve
    • The point may be a maximum, a minimum or a point of inflection, so further testing is needed
    • It cannot be a stationary point of the curve

  8. Find the stationary point of y = x^2 - 6x + 5.

    • (3, -4)
    • (6, 5)
    • (-3, 14)
    • (3, 4)

  9. What is the gradient of the tangent to y = x^3 at x = -1?

    • -3
    • 1
    • -1
    • 3

  10. Find the equation of the tangent to y = x^2 at the point (1, 1).

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

  11. Find the equation of the normal to y = x^2 at the point (1, 1).

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

  12. Find the x-coordinates of the stationary points of y = x^3 - 3x.

    • x = 0 only
    • x = 1 and x = -1
    • x = 1 only
    • x = 3 and x = -3

  13. For y = x^3 - 3x, what type of stationary point is at x = 1?

    • A local maximum, since f'' = 6x = 6 is positive
    • Not a stationary point, since the gradient is nonzero
    • A local minimum, since f'' = 6x = 6 is positive
    • A point of inflection with zero second derivative

  14. For which values of x is y = 2x^3 - 9x^2 increasing?

    • All real values of x
    • 0 < x < 3
    • x > 3 only
    • x < 0 or x > 3

  15. On which interval is y = x^2 decreasing?

    • All real values of x
    • x < 0
    • x > 0
    • No interval, since it is never decreasing

  16. Find the equation of the normal to y = 1/x at x = 2.

    • y = -x/4 + 1
    • y = -4x + 17/2
    • y = 4x - 15/2
    • y = 4x - 8

  17. How many stationary points does y = x^4 - 8x^2 + 1 have?

    • 3
    • 2
    • 4
    • 1

  18. Find k such that y = x^2 + kx + 4 has a stationary point at x = 3.

    • k = 6
    • k = -6
    • k = 3
    • k = -3

  19. For f'(x) = (x - 1)^2 (x - 3), which statement about x = 1 is correct?

    • It is a stationary point where the gradient does not change sign, so it is neither a maximum nor a minimum
    • It is a minimum since f' is non-negative around it
    • It is a maximum since the gradient is zero there
    • It is not stationary because f'' is zero there

  20. For which x is y = x^3 - 3x^2 + 3x decreasing?

    • For all x in the interval (0, 2)
    • For x > 1 only
    • For x < 1 only
    • Nowhere, since dy/dx = 3(x - 1)^2 is never negative

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