Lesson 9.5.1

9.5.1 Numerical methods in context Quiz: Pearson Edexcel Maths, Unit 9

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

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Lesson 9.5.1, Numerical methods in context: 20 multiple choice questions for the Pearson Edexcel Maths (9MA0), Unit 9: Numerical methods, written with Revision Ninja.

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The 20 questions

  1. What real-world quantity does finding a root often represent in applied maths?

    • Maximum value
    • Equilibrium point
    • Rate of change
    • Total area

  2. If a profit function P(x) has a root at x = 15, what does this represent?

    • Break-even point
    • Zero sales
    • Maximum profit
    • Initial investment

  3. When modelling population growth, what does a root of the adjusted model equation signify?

    • Growth rate
    • Carrying capacity
    • Extinction rate
    • Initial population

  4. Which numerical method relies on repeatedly bisecting a closed interval containing a sign change?

    • Iteration method
    • Bisection method
    • Newton-Raphson
    • Trapezium rule

  5. What condition must a continuous function satisfy on [a, b] to apply the bisection method?

    • Opposite signs
    • Zero derivative
    • Always positive
    • Equal values

  6. What is the primary drawback of using the bisection method to solve contextual problems?

    • Requires calculus
    • Complex setup
    • Slow convergence
    • Diverges often

  7. Which iterative formula type is used for finding roots in the form x_(n+1) = f(x_n)?

    • Newton-Raphson
    • Trapezium rule
    • Fixed-point iteration
    • Linear interpolation

  8. What causes a fixed-point iteration scheme to fail and diverge from the actual root?

    • Zero gradient
    • Continuous domain
    • Negative root
    • Derivative too large

  9. Which numerical technique uses tangents to rapidly approximate roots in real-world problems?

    • Newton-Raphson method
    • Fixed-point iteration
    • Bisection method
    • Simpson's rule

  10. What is the standard iterative formula for the Newton-Raphson method?

    • x + f(x)/f'(x)
    • x - f(x)/f'(x)
    • f'(x) / f(x)
    • f(x) / x

  11. What potential issue occurs if the starting point in Newton-Raphson has a zero derivative?

    • Infinite domain
    • Slow convergence
    • Division by zero
    • Negative output

  12. Why might Newton-Raphson cycle endlessly without finding a root in certain contexts?

    • Small intervals
    • Linear graphs
    • Positive gradients
    • Stationary points

  13. In a physics context, what does a root of velocity against time graph represent?

    • Maximum speed
    • Total distance
    • Constant acceleration
    • Instantaneous rest

  14. When modelling cost minimisation, what feature of the cost function are we usually locating?

    • Stationary point
    • Asymptote
    • Root
    • Y-intercept

  15. If f(2) = -3 and f(3) = 4, what is the initial interval for root-finding?

    • [2.5, 3]
    • [-3, 4]
    • [0, 5]
    • [2, 3]

  16. What geometric feature does the bisection method ignore when locating roots?

    • Continuity
    • Function gradient
    • Domain bounds
    • Sign changes

  17. Which numerical method generally requires the fewest steps to achieve high precision?

    • Graphical tracing
    • Newton-Raphson
    • Bisection method
    • Fixed-point iteration

  18. What real-world scenario is best modelled by setting a cubic cost function to zero?

    • Average revenue
    • Marginal cost
    • Peak efficiency
    • Break-even volumes

  19. What must be true for a function to be suitable for the Newton-Raphson method?

    • Always positive
    • Quadratic only
    • Differentiable
    • Linear

  20. In financial modelling, what does a root of the net present value equation represent?

    • Initial investment
    • Total profit
    • Payback period
    • Internal rate of return

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