Numerical methods in context

Numerical methods in context Quiz

Spec 9.5 · Edexcel A-Level Maths: Quiz

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5 questions, one answer each

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  1. 1. Which interval contains the root of x3−x−1=0x^3-x-1=0?

    • A. [1.2,1.3][1.2,1.3]
    • B. [1.3,1.4][1.3,1.4]
    • C. [1.4,1.5][1.4,1.5]
    • D. [1.5,1.6][1.5,1.6]

  2. 2. Using xn+1=xn+13x_{n+1}=\sqrt[3]{x_n+1} with x0=1x_0=1, find x1x_1 to 3 d.p.

    • A. 1.0001.000
    • B. 1.4141.414
    • C. 1.2601.260
    • D. 2.0002.000

  3. 3. Which function could have a sign change on [−1,1][-1,1] without a root there?

    • A. x3x^3
    • B. x2−0.5x^2-0.5
    • C. xx
    • D. 1x\frac{1}{x}

  4. 4. Using xn+1=e−xnx_{n+1}=e^{-x_n} with x0=0.5x_0=0.5, find x1x_1 to 3 d.p.

    • A. 0.6070.607
    • B. 0.5450.545
    • C. 0.3680.368
    • D. 1.6491.649

  5. 5. A convergent iteration xn+1=g(xn)x_{n+1}=g(x_n) tends to α\alpha. Which statement must be true?

    • A. g(α)=0g(\alpha)=0
    • B. g′(α)=0g'(\alpha)=0
    • C. g(α)=αg(\alpha)=\alpha
    • D. g(α)=x0g(\alpha)=x_0

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