Lesson 9.2.1

9.2.1 Solving equations by simple iteration Quiz: Pearson Edexcel Maths, Unit 9

20 questions

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Lesson 9.2.1, Solving equations by simple iteration: 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 form is rearranged to create an iterative formula for solving f(x) = 0?

    • f(x) = g(x)
    • ax² + bx + c = 0
    • x = g(x)
    • y = mx + c

  2. Which type of numerical method uses a starting value x₀ to generate a sequence?

    • Simple iteration
    • Integration by parts
    • Proof by induction
    • Linear regression

  3. In the iterative formula x_{n+1} = g(x_n), what does x₀ represent?

    • Final root
    • Initial approximation
    • Gradient
    • Y-intercept

  4. What does a cobweb diagram visually represent during an iteration?

    • Exact integration
    • Differentiation steps
    • Convergence or divergence
    • Polynomial degree

  5. If an iterative sequence spirals inwards towards the root, what is the behaviour?

    • Convergent
    • Divergent
    • Oscillating
    • Stationary

  6. If successive terms in an iteration move further away from the root, it is what?

    • Constant
    • Periodic
    • Convergent
    • Divergent

  7. What is the condition for an iteration to converge near the root alpha?

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

  8. Which algebraic method is closely related to simple iteration?

    • Binomial expansion
    • Implicit differentiation
    • Partial fractions
    • Fixed-point iteration

  9. Given x_{n+1} = (5 - x_n^3)/4 and x₀ = 1, what is x₁?

    • 1.25
    • 1
    • 0
    • 2

  10. Find x₁ for the iteration formula x_{n+1} = 2 / x_n with starting value x₀ = 4.

    • 1.5
    • 0.5
    • 2
    • 8

  11. If x_{n+1} = 4 / (x_n - 1) and x₀ = 3, what is the value of x₁?

    • 4
    • 1
    • 2
    • 3

  12. What is x₁ if x_{n+1} = e^{-x_n} and x₀ = 0?

    • 2.72
    • 0
    • 0.37
    • 1

  13. Evaluate x₁ for x_{n+1} = ln(10 - x_n) using x₀ = 2.

    • 2.08
    • 8.00
    • 2.30
    • 1.79

  14. Find x₁ given x_{n+1} = sin(x_n) + 1 and x₀ = 0.

    • 0
    • 3.14
    • 0.5
    • 1

  15. What causes an iterative formula to fail by moving away from the root?

    • Zero derivative
    • Stationary point
    • Converging sequence
    • Diverging sequence

  16. How do you rearrange x³ + x - 3 = 0 into the form x = g(x)?

    • x = 3 - x³
    • x³ = x - 3
    • x = 3 / x²
    • x = x³ - 3

  17. What does a staircase diagram on an iteration graph indicate?

    • Alternating convergence
    • Divergent oscillation
    • Zero gradient
    • Exact integration

  18. Which rearrangement of x³ - 5x + 2 = 0 creates a valid iterative formula?

    • x = 5x - 2
    • x = (x³ + 2) / 5
    • x = ∛(5x)
    • x = (5 - 2)/x²

  19. What graphical term describes an iteration converging in a monotonic staircase fashion?

    • Asymptote curve
    • Tangent line
    • Staircase diagram
    • Cobweb diagram

  20. Calculate x₁ for the iteration formula x_{n+1} = √(x_n + 6) using x₀ = 3.

    • 9
    • 3
    • 2
    • √3

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