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 evaluating a numerical solution to a real-world problem, what must always be checked?

    • Matrix determinant
    • Algebraic proofs
    • Exact integration
    • Units and context

  2. What step should always follow solving a contextual model numerically?

    • Interpret in context
    • Solve algebraically
    • Double the iterates
    • Differentiate the model

  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 numerical solution gives a length of -0.5 metres. What should you do?

    • Reject the root
    • Multiply by -10
    • Square the value
    • Accept the value

  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 rule estimate is 3 and the exact value is 8/3. What is the percentage error?

    • 12.5% overestimate
    • 25% overestimate
    • 25% underestimate
    • 12.5% underestimate

  14. If f(2.76) = -0.015 for a continuous function, what does this indicate?

    • Turning point
    • Close to root
    • Local maximum
    • Discontinuity

  15. In the iteration x_(n+1) = g(x_n), what happens if |g'(x)| > 1 near a root?

    • Oscillation stops
    • Iteration converges
    • Root doubles
    • Iteration diverges

  16. Why is applying the trapezium rule to velocity-time data an approximation?

    • Negative velocities
    • Constant acceleration
    • Discrete data points
    • Continuous tracking

  17. A sign change occurs between 2.76 and 2.77. What is the next bisection step?

    • Test x = 2.765
    • Test x = 2.78
    • Test x = 2.75
    • Stop the search

  18. Why are numerical methods often used to solve contextual equations?

    • No exact method
    • Prevents convergence
    • Always 100% exact
    • Eliminates rounding

  19. A population model predicts 12.7 rabbits. How should this result be interpreted?

    • Model is invalid
    • Exactly 12.7 rabbits
    • About 13 rabbits
    • Exactly 12 rabbits

  20. How is the required accuracy usually confirmed in an iterative method?

    • Constant gradient
    • Integer convergence
    • Zero remainder
    • Matching decimal places

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