Lesson 1.09g

1.09g Numerical methods in modelling Quiz: OCR Maths, Unit 9

20 questions

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Lesson 1.09g, Numerical methods in modelling: 20 multiple choice questions for the OCR Maths (H240), Unit 9: Numerical Methods, written with Revision Ninja.

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The 20 questions

  1. Numerical methods are primarily used when an equation cannot be solved using which approach?

    • Iterative methods
    • Graphical methods
    • Analytical methods
    • Trial and error

  2. Which of these is a numerical method for finding roots of an equation?

    • Implicit differentiation
    • Binomial expansion
    • Integration by parts
    • Newton-Raphson method

  3. Why must a calculated numerical root always be checked within a real-world context?

    • Domain expansion
    • Mathematical error
    • Exact convergence
    • Physical validity

  4. What precision is indicated when a numerical answer is quoted to 3 d.p.?

    • Three whole numbers
    • Three decimal places
    • Three decimal bounds
    • Three significant figures

  5. If a mathematical model produces a negative time value, what should be done?

    • Reject the root
    • Make it positive
    • Accept the root
    • Square the value

  6. What is the main purpose of sketching a graph before using a numerical method?

    • Eliminate all errors
    • Prove convergence speed
    • Calculate exact roots
    • Locate starting values

  7. Why is a numerical solution in modelling always given to a specified degree of accuracy?

    • Ensures exactness
    • Prevents rounding errors
    • Indicates precision level
    • Proves root uniqueness

  8. The function f(t) = t^3 - 6t + 2 has f(0) = 2 and f(1) = -3. Which interval contains a root by sign change?

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

  9. Newton-Raphson for 10t - 4.9t^2 - 1 = 0 starts at t0 = 1.5. Approximately what is t1?

    • 2.50
    • 2.13
    • 1.00
    • 3.00

  10. For 0.5x^3 - 2x - 1 = 0, which interval shows a sign change?

    • [3, 4]
    • [2, 3]
    • [0, 1]
    • [1, 2]

  11. Newton-Raphson for 0.5x^3 - 2x - 1 = 0 starts at x0 = 2. What is x1?

    • 1.75
    • 2.5
    • 2.25
    • 1.5

  12. A rainfall rate is 0, 2, 3 and 1 mm per hour at hours 0, 1, 2 and 3. What is the trapezium estimate of total rainfall?

    • 4.5 mm
    • 5.5 mm
    • 6 mm
    • 11 mm

  13. The iteration x(n+1) = cos(x(n)) starts at x0 = 1. It converges to a root near which value to 3 decimal places?

    • 0.739
    • 0.841
    • 1.000
    • 0.540

  14. For an iteration x_(n+1) = g(x) to converge to a root, what condition must |g'(x)| satisfy?

    • Equal to 0
    • Greater than 1
    • Equal to 1
    • Less than 1

  15. A model root lies in the interval 2.371 < x < 2.374. Quoted to 2 decimal places, what should be stated?

    • 2.4
    • 2.38
    • 2.37
    • 2.371

  16. For f(x) = 2^x - x - 3, which interval shows a sign change?

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

  17. For f(x) = 2^x - x - 3, Newton-Raphson starts at x0 = 2. Approximately what is x1?

    • 3.00
    • 2.56
    • 2.00
    • 2.50

  18. Why can the sign-change method not be used for the equation x^2 + 1 = 0?

    • Gradient is zero
    • Too many roots
    • No real roots
    • Interval is infinite

  19. For a continuous f, f(2.3415) < 0 and f(2.3425) > 0. To 2 decimal places, what is the root?

    • 2.35
    • 2.33
    • 2.36
    • 2.34

  20. For x_(n+1) = g(x) with fixed point a, what condition guarantees local convergence?

    • |g'(a)| < 1
    • |g'(a)| = 0
    • |g'(a)| > 1
    • |g'(a)| = 1

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