Lesson OT3.1-OT3.5

OT3.1-OT3.5 Mathematical modelling Quiz: AQA Further Maths, Unit 1

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

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Lesson OT3.1-OT3.5, Mathematical modelling: 20 multiple choice questions for the AQA Further Maths (7367), Unit 1: Overarching themes, written with Revision Ninja.

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The 20 questions

  1. What is a modelling assumption?

    • A simplifying statement about a situation that makes the mathematics manageable
    • A measurement taken directly from real data, used without any simplifying step at all
    • A proven fact about the real situation that needs no testing or checking against data
    • A value that is always exact and never needs to be estimated or rounded in the model

  2. Which of these is a reason to refine a mathematical model?

    • It has fewer equations than the original model
    • Its predictions differ noticeably from observed data
    • It was written by a well-known mathematician
    • It uses decimals rather than fractions

  3. In the model P = P0 e^(kt), what does P0 represent?

    • The initial value of P when t = 0
    • The growth rate per unit time
    • The value P approaches as t tends to infinity
    • The time at which P doubles

  4. Which statement about the modelling cycle is correct?

    • A model is correct if its mathematics is elegant and its notation is consistent throughout
    • A model should never be changed once it has been written, even if its outputs disagree with data
    • Outputs of a model need no interpretation in context because the numbers speak for themselves
    • A model can be refined by comparing its outputs with observed situations

  5. Which statement is a modelling assumption for a particle projected from the ground?

    • The particle is projected vertically upwards from the ground with no sideways motion
    • The launch speed is fixed at 9.8 m/s for every projectile in the experiment
    • Air resistance is negligible and the particle is treated as a point
    • The particle has a fixed mass of 2 kg, which is measured before the launch takes place

  6. A population is modelled by P = 200 x 1.1^t. After how many whole years does the model first predict more than 400?

    • 10 years, since 1.1^10 = 2, so the population doubles every ten years
    • 7 years, since P(7) is exactly 400 and the model then reaches its limit
    • 5 years, since 1.1^5 = 2, so the population has doubled by year five
    • 8 years, since P(7) is about 390 and P(8) is about 429

  7. In the cost model C = 500 + 12n for n items made, what does 500 represent?

    • The number of items made, which is the variable n in the cost model
    • The total revenue from sales, which the model shows as a separate term
    • Fixed costs that do not depend on the number of items made
    • The cost of each individual item made, which is the coefficient of n in the model

  8. A particle's velocity is modelled by v = 20 - 4t for 0 <= t <= 5. What is its velocity at t = 5 according to the model?

    • -4
    • 20
    • 5
    • 0

  9. A linear model predicts temperature T = 2t + 15. At t = 10 the observed temperature is 33. Which is correct?

    • The model predicts 35, an underestimate of 2 degrees
    • The model predicts 33, an exact match
    • The model predicts 35, an overestimate of 2 degrees
    • The model predicts 25, an underestimate of 8 degrees

  10. A cooling model is T = 20 + 60e^(-0.1t). What is the long-run temperature as t tends to infinity?

    • 20 degrees
    • 60 degrees
    • 0 degrees
    • 80 degrees

  11. Which assumption underlies a model with a constant growth rate for a population?

    • The population decreases over time
    • The population is always a whole number
    • The growth rate stays the same over the whole period
    • The growth rate changes randomly each year

  12. A car moves at a constant speed of 25 m/s according to the model distance = speed x time. How far does it travel in 12 seconds?

    • 37 m
    • 250 m
    • 300 m
    • 312 m

  13. A model predicts 42 for a quantity, while a refined model that includes air resistance predicts 37. Why is the refined model preferable?

    • It contains more terms, so it must be more accurate than the simpler model
    • It removes an unrealistic assumption and so fits the situation more closely
    • It is easier to solve by hand, which matters more than accuracy in any model
    • It gives a larger value, which is always safer to use in a practical decision

  14. A model N = 1000 e^(0.4t) describes bacteria. Using ln 10 = 2.303, roughly when does N reach 10000?

    • About 2.3 time units
    • About 5.8 time units
    • About 25 time units
    • About 10 time units

  15. Which statement best evaluates a population model that gives negative numbers of people for some values of t?

    • Negative outputs are always the result of a calculation error
    • Negative outputs show that the population is growing
    • The model is inappropriate for those values, so it needs refinement
    • The model is perfect because the mathematics is correct

  16. A model assumes a die is fair, but the die is loaded. Which statement is correct?

    • The model's probabilities may be wrong, so its predictions should be checked against data
    • The model is correct because dice are generally fair and the assumption is standard
    • The model must be discarded because probability cannot be used in any real situation
    • A loaded die makes no difference to any prediction that the model makes at all

  17. A tank's depth is modelled by h(t) = 2 + 0.5t for 0 <= t <= 8. What is the largest depth the model can validly predict?

    • 10
    • 8
    • 2
    • 6

  18. A logistic model N(t) = 500 / (1 + 4e^(-0.5t)) describes growth. What is the limiting value of N?

    • 2000
    • 4
    • 500
    • 125

  19. A sample decays to half its mass in 10 years under the model M = M0 e^(-kt). What is k?

    • k = 0.5
    • k = 10 / ln 2, about 14.4
    • k = 0.1
    • k = ln 2 / 10, about 0.0693

  20. A model P = 50 + 3t^2 for population, t >= 0, is claimed to show growth forever. What is the main weakness?

    • It is correct because it has the right degree and matches the observed growth shape
    • It is wrong because t^2 cannot be used for values of t that are non-negative
    • It ignores limits such as resources, so long-term predictions may be unrealistic
    • It fails because the constant 50 is a fixed term that stops it growing at all

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