Lesson B11

B11 Functions in modelling Quiz: AQA Maths, Unit 2

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

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Lesson B11, Functions in modelling: 20 multiple choice questions for the AQA Maths (7357), Unit 2: Algebra and functions, written with Revision Ninja.

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The 20 questions

  1. Which is a limitation of a linear model used over a long time period?

    • It has no parameters to estimate
    • It always gives exact predictions
    • It may not reflect behaviour beyond the range of the data
    • It can never be checked against data

  2. What is the validity range of a model?

    • The maximum possible value of the output
    • The range of values over which the model gives reasonable predictions
    • The range of the gradient of the model
    • The number of data points used to fit the model

  3. A model gives P = 200 + 15t. What is the predicted value when t = 10?

    • 300
    • 400
    • 350
    • 150

  4. Cost is modelled by C = 40 + 12n pounds for n items. What is the cost for 25 items?

    • 300
    • 340
    • 352
    • 312

  5. The height of a projectile is h = 30t - 5t^2 metres. After how long does it return to the ground, other than at t = 0?

    • 15 s
    • 3 s
    • 6 s
    • 5 s

  6. Which refinement would make the population model P = 100 + 20t more realistic over a long period?

    • Introduce a limit so the population cannot exceed a carrying capacity
    • Make t negative only
    • Remove the constant term
    • Fix the gradient at zero

  7. A taxi charges £3 plus £2 per mile for the first 5 miles, then £1.50 per mile after that. What is the fare for 8 miles?

    • £16.00
    • £19.00
    • £17.50
    • £18.50

  8. In the cost model C = 40 + 12n, what does the 12 represent?

    • The cost per item
    • The total cost for zero items
    • The number of items
    • The fixed cost

  9. Two models are y = 2x + 5 and y = x^2. Which grows faster for large positive x?

    • y = x^2
    • Neither grows
    • y = 2x + 5
    • Both grow at the same rate

  10. For the model y = 0.5x^2 - 3x + 4, what is the minimum value and where does it occur?

    • 0.5 at x = 3
    • 4 at x = 0
    • -0.5 at x = 3
    • -3 at x = 0.5

  11. Price is p = 100 - 2q, and revenue is R = pq. At what output is revenue maximised, and what is the maximum?

    • q = 25, R = 1250
    • q = 12.5, R = 625
    • q = 25, R = 2500
    • q = 50, R = 2500

  12. Profit is P = 12x - 300 for x items sold. What is the least whole number of items that gives a positive profit?

    • 26
    • 25
    • 300
    • 24

  13. What does it mean to refine a mathematical model?

    • To ignore the model's limitations
    • To make it more realistic by adjusting assumptions or adding factors
    • To make it simpler by removing all variables
    • To replace the data with random numbers

  14. A temperature model is T = 25 - 3t, where t is hours. When does the temperature reach 10 degrees?

    • 10 hours
    • 7.5 hours
    • 5 hours
    • 3 hours

  15. A rectangular garden has a 40 m perimeter with width x. Its area is A = x(20 - x). What is the maximum area?

    • 100 m^2 at x = 10 m
    • 100 m^2 at x = 20 m
    • 400 m^2 at x = 20 m
    • 200 m^2 at x = 10 m

  16. A linear model passes through (0, 3) and (4, 11). What is the predicted y-value at x = 10?

    • 13
    • 21
    • 23
    • 25

  17. A projectile model ignores air resistance. What is a limitation of this assumption?

    • It overestimates the range and maximum height
    • It makes the trajectory a straight line
    • It makes the model impossible to solve
    • It removes gravity from the equations

  18. A population model is N = 50 + 5t. When does N reach 120?

    • t = 14
    • t = 13
    • t = 15
    • t = 12

  19. A vehicle's distance is d = 60t - 2t^2 for 0 <= t <= 30. What is the maximum distance, and when?

    • 225 at t = 15
    • 450 at t = 15
    • 900 at t = 15
    • 450 at t = 30

  20. Which property makes a quadratic model unsuitable for long-run prediction of a population?

    • It is always a straight line
    • It eventually decreases, so it predicts falling values when the population is growing
    • It has no turning points
    • It never passes through the origin

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