Lesson H8

H8 Interpreting solutions of differential equations Quiz: AQA Maths, Unit 8

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

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Lesson H8, Interpreting solutions of differential equations: 20 multiple choice questions for the AQA Maths (7357), Unit 8: Integration, written with Revision Ninja.

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The 20 questions

  1. What key real-world factor is ignored by the exponential population growth model dP/dt = kP?

    • Limited resources
    • Initial population
    • Time dependence
    • Constant birth rate

  2. What is the acceleration of an object moving at its terminal velocity?

    • 0 m/s²
    • -0.2 m/s²
    • 9.8 m/s²
    • 49 m/s²

  3. For dP/dt = kP with k > 0, what happens to P as t approaches infinity?

    • Tends to infinity
    • Remains constant
    • Approaches k
    • Tends to zero

  4. What determines a particular solution from a general solution of a differential equation?

    • Integrating factor
    • Differential order
    • Initial conditions
    • Arbitrary constants

  5. In a 1D kinematics model, what does a negative velocity indicate?

    • Decreasing speed
    • Constant displacement
    • Backward motion
    • Zero acceleration

  6. Why might a mathematical model produce inaccurate predictions in real life?

    • Universal constants
    • Exact calculations
    • Infinite precision
    • Simplified assumptions

  7. For s = 4t - t^2 metres, at what time does the particle momentarily stop?

    • t = 0 s
    • t = 2 s
    • t = 4 s
    • t = 1 s

  8. Why might a constant air resistance coefficient in dv/dt = g - kv be a limitation?

    • Gravity increases
    • Mass changes continuously
    • Air density varies
    • Speed remains constant

  9. For the demand model Q = 200e^(-0.4p), what happens to Q at extremely high prices?

    • Approaches zero
    • Reaches zero
    • Tends to infinity
    • Becomes negative

  10. For dP/dt = 0.05P, what is the doubling time of the population, to 1 decimal place?

    • 20 years
    • 13.9 years
    • 7 years
    • 0.05 years

  11. A particle satisfies v = 49(1 - e^(-0.2t)) m/s. What is its velocity at t = 10 s, to 1 decimal place?

    • 49 m/s
    • 21.6 m/s
    • 42.4 m/s
    • 9.8 m/s

  12. The population model P = 500e^(0.02t) gives P at t = 100. Which value is the model's prediction, to the nearest whole number?

    • 3695
    • 10000
    • 1000
    • 500

  13. A particle has displacement s = 2t^3 - 9t^2 + 12t. At which times does it change direction?

    • t = 1 s only
    • t = 0 s and t = 3 s
    • t = 2 s and t = 4 s
    • t = 1 s and t = 2 s

  14. A particle has velocity v = 10 - 2t. At what time does it come to rest?

    • 2 s
    • 10 s
    • 5 s
    • 2.5 s

  15. What is the terminal velocity for a particle governed by dv/dt = 9.8 - 0.2v?

    • 60 m/s
    • 49 m/s
    • 9.8 m/s
    • 0 m/s

  16. Which concept is added to simple population models to limit maximum growth?

    • Carrying capacity
    • Damping factor
    • Initial velocity
    • Exponential decay

  17. For dv/dt = 9.8 - 0.2v with v = 0 at t = 0, how long does it take to reach 90% of terminal velocity, to 1 decimal place?

    • 9.8 s
    • 11.5 s
    • 22.0 s
    • 4.5 s

  18. For s = 4t - t^2, what is the average velocity over 0 <= t <= 4?

    • -2 m/s
    • 2 m/s
    • 0 m/s
    • 4 m/s

  19. What value does v = 49(1 - e^(-0.2t)) approach as time t approaches infinity?

    • 49 m/s
    • 0 m/s
    • 9.8 m/s
    • Infinity

  20. For a particle with displacement s = 2t^2 - 8t metres, what is the displacement at t = 2 s?

    • 8 m
    • 0 m
    • -8 m
    • -16 m

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