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. A population model P = kP with k > 0 predicts unlimited growth. What is a limitation of this model?

    • It ignores limited resources, so it predicts unrealistic growth for large t
    • It predicts that the population always declines
    • It predicts no change over time
    • It predicts a population of zero at all times

  2. For dv/dt = 9.8 - 0.2v, what does the terminal velocity represent?

    • The constant velocity reached when the acceleration is zero
    • The maximum acceleration of the object
    • The initial velocity of the object
    • The velocity at time t = 0

  3. For dP/dt = kP with k > 0, what does the model predict as t tends to infinity?

    • P grows without bound
    • P oscillates between two values
    • P tends to a fixed limit
    • P tends to zero

  4. What does a particular solution of a differential equation describe?

    • A family of curves with no constraints
    • The limit of the solution as x tends to infinity
    • A single curve that satisfies the given starting condition
    • The rate of change only

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

    • The particle is at rest
    • The particle has negative mass
    • The particle moves in the negative direction
    • The particle has zero displacement

  6. What is a limitation of a mathematical model in general?

    • A value that can never be calculated
    • An error in the mathematical working
    • A result that always matches the data
    • An assumption that may not hold in the real situation

  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. The model dv/dt = 9.8 - 0.2v assumes a constant resistance coefficient. Which is a limitation?

    • It predicts the object speeds up forever
    • It predicts a negative terminal velocity
    • The coefficient 0.2 may not hold at high speeds or in changing air density
    • It ignores gravity entirely

  9. A demand model Q = 200e^(-0.4p) is used for prices p. Which is a sensible interpretation and limitation?

    • Demand is always positive and never exactly zero, which may be unrealistic at very high prices
    • Demand is negative for every positive price
    • Demand stays at 200 for all prices
    • Demand is zero at price zero

  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. A particle is projected with velocity 60 m/s under dv/dt = 9.8 - 0.2v. What happens to its velocity?

    • It decreases to zero
    • It decreases towards 49 m/s
    • It increases without bound
    • It stays at 60 m/s

  16. Which change makes the population model dP/dt = kP more realistic for large populations?

    • Add a term that slows growth as P approaches a limit such as a carrying capacity
    • Set k to zero
    • Use dP/dt = kt instead
    • Replace k with a negative constant

  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. A velocity model v = 49(1 - e^(-0.2t)) m/s is used for large t. What value does the velocity approach?

    • 49 m/s
    • 0 m/s
    • 9.8 m/s
    • There is no limiting value

  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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