Lesson 1.07m

1.07m Tangents, normals and stationary points Quiz: OCR Maths, Unit 7

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

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Lesson 1.07m, Tangents, normals and stationary points: 20 multiple choice questions for the OCR Maths (H240), Unit 7: Differentiation, written with Revision Ninja.

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The 20 questions

  1. For a tangent of gradient m, what is the gradient of the normal?

    • 1/m
    • -m
    • m
    • -1/m

  2. What condition must be satisfied at a stationary point on a curve?

    • dy/dx > 0
    • dy/dx = 0
    • y = 0
    • d2y/dx2 = 0

  3. What condition must be met for a point to be a point of inflection?

    • f'(x) changes sign
    • f''(x) > 0
    • f'(x) = 0
    • f''(x) changes sign

  4. The function f is increasing where:

    • f''(x) > 0
    • f'(x) > 0
    • f'(x) < 0
    • f(x) > 0

  5. At a stationary point with f''(x) < 0, the point is a:

    • Maximum
    • Point of inflection
    • Cannot be classified
    • Minimum

  6. What is the tangent to y = x^2 - 4x + 1 at x = 3?

    • y = x - 5
    • y = -2x - 8
    • y = 2x - 8
    • y = 2x + 4

  7. What is the normal to y = x^2 at x = 1?

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

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

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

  9. Classify the stationary point at x = 1 on y = x^3 - 3x.

    • Point of inflection
    • Maximum
    • Not stationary
    • Minimum

  10. For which values of x is the function y = x^3 - 3x increasing?

    • |x| < 1
    • -1 < x < 1
    • |x| > 1
    • x > 0

  11. What type of stationary point occurs on y = x^4 - 4x^3 at x = 0?

    • Local maximum
    • Non-stationary inflection
    • Local minimum
    • Stationary inflection

  12. How is the stationary point (0, 0) on the curve y = x^3 classified?

    • Asymptote
    • Local minimum
    • Point of inflection
    • Local maximum

  13. What is the tangent to y = e^x at x = 0?

    • y = x - 1
    • y = 1
    • y = e x
    • y = x + 1

  14. At what x is the tangent to y = ln x of gradient 1/2?

    • x = 1/2
    • x = e
    • x = 2
    • x = 4

  15. Which points on y = x^3 - 6x^2 + 9x have a horizontal tangent?

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

  16. For y = x^3 - 3x^2, what is the nature of the stationary point at x = 2?

    • Not stationary
    • Minimum
    • Point of inflection
    • Maximum

  17. For y = x^2 + kx + 4 to have a horizontal tangent at x = 3, what is k?

    • -6
    • 6
    • -3
    • 3

  18. Which condition makes the tangent to y = f(x) horizontal at x = a?

    • f''(a) = 0
    • f'(a) = 0
    • f'(a) = 1
    • f(a) = 0

  19. What is the gradient of the normal to y = x^2 at x = 2?

    • -1/4
    • 4
    • 1/4
    • -4

  20. What is the tangent to y = 1/x at x = 1?

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

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