Lesson I4

I4 Numerical methods in context Quiz: AQA Maths, Unit 9

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

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Lesson I4, Numerical methods in context: 20 multiple choice questions for the AQA Maths (7357), Unit 9: Numerical methods, written with Revision Ninja.

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The 20 questions

  1. When a numerical answer is obtained in a context problem, what should be checked?

    • Only whether it is a fraction
    • Only whether it is an integer
    • Nothing, if the method was followed
    • Its units and whether its size is sensible for the situation

  2. What should follow solving a context model numerically?

    • Substitute the answer back into the model and interpret it in context
    • Report the raw decimal without units
    • Use only the first iteration
    • Ignore all values except the largest

  3. A cost model x^3 - 4x - 10 = 0 uses x in hundreds of units. Find its positive root to 2 decimal places.

    • 2.70
    • 2.80
    • 2.85
    • 2.76

  4. Which interval, by change of sign, locates the positive root of x^3 - 4x - 10 = 0?

    • (0, 1)
    • (2, 3)
    • (3, 4)
    • (-3, -2)

  5. A tank's inflow rate in litres per minute is 3, 5, 4 and 2 at t = 0, 2, 4 and 6 minutes. Using the trapezium rule, what is the total inflow?

    • 16 litres
    • 26 litres
    • 23 litres
    • 14 litres

  6. Using Newton-Raphson on f(x) = x^2 - 5 starting at x0 = 2, what is x1?

    • 2.236
    • 2.25
    • 2.0
    • 2.5

  7. A river cross-section has depths 1.2, 2.0, 2.4 and 1.6 m at 0, 5, 10 and 15 m across. Using the trapezium rule, what is the cross-sectional area?

    • 14.5 m^2
    • 30 m^2
    • 29 m^2
    • 27.5 m^2

  8. Newton-Raphson is applied to x^3 - 4x - 10 = 0 starting at x0 = 3. What is x1 to 4 decimal places?

    • 2.7000
    • 2.7826
    • 2.8000
    • 3.2174

  9. Car speeds are 0, 4, 9 and 12 m/s at t = 0, 1, 2 and 3 s. Using the trapezium rule, what is the distance travelled?

    • 19 m
    • 17 m
    • 25 m
    • 21 m

  10. For x(n+1) = sqrt(10 - x(n)) with x0 = 2, what is x2 to 3 decimal places?

    • 2.828
    • 2.500
    • 2.702
    • 2.678

  11. A model needs a positive length, but a numerical solution gives x = -0.5. What is the best response?

    • Reject it as not meaningful in context, and check the model or the other roots
    • Square it to make it positive
    • Accept it as the length
    • Round it to 0.5

  12. Which interval, by change of sign, must contain a root of x^2 - 3x + 1 = 0?

    • (-2, -1)
    • (1, 2)
    • (0, 1)
    • (-1, 0)

  13. A trapezium estimate with n = 2 for x^2 over [0, 2] is 3. How large is the error compared with the exact value 8/3?

    • About 12.5% overestimate
    • About 50% overestimate
    • The estimate is exact
    • About 12.5% underestimate

  14. For x^3 - 4x - 10, f(2.76) is about -0.015. What does this suggest?

    • The root is about -0.015
    • The value 2.76 is very close to a root, since f is close to zero
    • The root is exactly 10
    • The root is about 5

  15. For an iteration x(n+1) = g(x(n)) near a root, |g'| is greater than 1. What happens?

    • The iteration converges to zero
    • The iteration converges quickly
    • The iteration settles at the starting value
    • The iteration moves away from the root

  16. Why is a trapezium estimate of distance from velocity data an approximation?

    • The velocity is negative
    • Distance cannot be calculated from velocity
    • The velocity is known only at discrete times, so the curve is replaced by straight segments
    • The trapezium rule only works for whole numbers

  17. A bisection-style search for a root in a model gives a sign change between 2.76 and 2.77. What is the next step?

    • Halve the interval and check the sign at the midpoint
    • Accept 2.76 as the exact root
    • Use the trapezium rule
    • Widen the interval to (2, 3)

  18. Why is a numerical method preferred to an exact solution for some context models?

    • The equation may have no algebraic solution, so an approximate root is found to the required accuracy
    • Numerical methods remove the need for a model
    • Numerical methods are always more accurate
    • Exact solutions cannot be checked

  19. A model gives 12.7 rabbits, but counts must be whole numbers. What is the best interpretation?

    • Discard the model entirely
    • Keep 12.7 as the count
    • About 13 rabbits, noting that the model is an approximation
    • Round down to 12 always

  20. Which is a sensible sign that an iterative method has converged in a context problem?

    • The iterates keep changing widely
    • The function value is exactly 1
    • The first value is always correct
    • Successive iterates agree to the required number of decimal places

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