Lesson 1.05q

1.05q Trigonometry in modelling Quiz: OCR Maths, Unit 5

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

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Lesson 1.05q, Trigonometry in modelling: 20 multiple choice questions for the OCR Maths (H240), Unit 5: Trigonometry, written with Revision Ninja.

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The 20 questions

  1. A tide model is d = 5 + 2 cos(pi t / 6), with d in metres and t in hours. What is the maximum depth?

    • 7 m
    • 2 m
    • 9 m
    • 5 m

  2. For the tide model d = 5 + 2 cos(pi t / 6), what is the period?

    • pi/6 hours
    • 6 pi hours
    • 12 hours
    • 6 hours

  3. A particle has displacement s = t^3 - 6t^2 + 9t metres. At which times is its velocity zero?

    • t = 0 and t = 3
    • t = 2 only
    • t = 1 and t = 2
    • t = 1 and t = 3

  4. A force of 10 N acts at 30 degrees above the horizontal. What is its horizontal component?

    • 10 N
    • 5 N
    • 5 sqrt(3) N
    • 10 sqrt(3) N

  5. A sound pressure model is p = A sin(440 pi t). What is its frequency in hertz?

    • 440 Hz
    • 220 Hz
    • 880 Hz
    • 110 Hz

  6. Using d = 5 + 2 cos(pi t / 6) (t in hours), at what first time after t = 0 is the depth 6 m?

    • 3 hours
    • 1 hour
    • 4 hours
    • 2 hours

  7. Forces of 6 N east and 8 N north act on a particle. What is the magnitude of the resultant?

    • 2 N
    • 10 N
    • 14 N
    • sqrt(14) N

  8. The depth model d = 5 + 2 cos(pi t/6) has which minimum depth?

    • 1 m
    • 3 m
    • 5 m
    • 2 m

  9. A particle has displacement s = t^3 - 6t^2 + 9t metres. What is its acceleration at t = 2 seconds?

    • -6 m/s^2
    • -3 m/s^2
    • 6 m/s^2
    • 0 m/s^2

  10. A pendulum-like displacement is x = 4 sin(2t). What is the amplitude?

    • 4
    • 2
    • pi
    • 8

  11. In the model x = 4 sin(2t), what is the period?

    • pi seconds
    • 2 seconds
    • 4 seconds
    • 2 pi seconds

  12. A horizontal tide height model is h = 2 + 1.5 sin(t) metres. What is the minimum height?

    • 2 m
    • -1.5 m
    • 0.5 m
    • 3.5 m

  13. A block on a slope of angle 20 degrees has weight 50 N. What is the component of weight along the slope?

    • 50 sin 70 N
    • 50 tan 20 N
    • 50 cos 20 N
    • 50 sin 20 N

  14. Velocity components are v = (2 cos t, 2 sin t). What is the speed at any time?

    • 2
    • 4
    • 2 sqrt(2)
    • 2 cos t

  15. A force of 8 N acts at 30 degrees above the horizontal. What is its vertical component?

    • 8 N
    • 4 sqrt(3) N
    • 2 N
    • 4 N

  16. For d = 5 + 2 cos(pi t / 6), what is the average depth over one period?

    • 5 m
    • 7 m
    • 2 m
    • 3 m

  17. A particle moves with s = 2t^2 - 8t. When is it momentarily at rest?

    • t = 1
    • t = 0 and t = 4
    • t = 2
    • t = 4

  18. The displacement of a wave is y = 3 cos(2 pi t / 5) with t in seconds. What is the period in seconds?

    • 2 pi/5 seconds
    • 10 pi seconds
    • 5 seconds
    • 2.5 seconds

  19. A particle has velocity v = 6 - 2t m/s. What is its displacement change from t = 0 to t = 3 seconds?

    • 9 m
    • 3 m
    • 18 m
    • 12 m

  20. A pressure wave has amplitude 0.5 and period 0.004 seconds. What is its frequency?

    • 0.004 Hz
    • 250 Hz
    • 4 Hz
    • 2.5 Hz

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