Lesson 9.3.1

9.3.1 Newton-Raphson method Quiz: Pearson Edexcel Maths, Unit 9

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

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Lesson 9.3.1, Newton-Raphson method: 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 is the standard iterative formula for the Newton-Raphson method?

    • xn + f(xn)/f'(xn)
    • xn - f'(xn)/f(xn)
    • xn+1 + f(xn)
    • xn - f(xn)/f'(xn)

  2. What causes the Newton-Raphson method to fail near certain points?

    • Large gradient
    • Small gradient
    • Undefined integral
    • Negative root

  3. Geometrically, what does the Newton-Raphson method use at each iteration?

    • Tangents
    • Trapezia
    • Asymptotes
    • Chords

  4. What is the general notation for the recurrence relation in iterative methods?

    • xn+1 = g(xn)
    • xn+1 = f'(xn)
    • xn = n + g(x)
    • xn = g(xn+1)

  5. When using the trapezium rule, what shape replaces the curve?

    • Trapezia
    • Triangles
    • Rectangles
    • Tangents

  6. For a convex curve, does the trapezium rule give an over-estimate or under-estimate?

    • Zero
    • Exact value
    • Under-estimate
    • Over-estimate

  7. What type of diagram helps demonstrate convergence or divergence of recurrence relations?

    • Argand diagram
    • Cobweb diagram
    • Box plot
    • Venn diagram

  8. Why might numerical methods be used to solve an equation?

    • Gives exact roots
    • Analytically insoluble
    • Always faster
    • Avoids decimals

  9. In two dimensions, what unit vectors are commonly used alongside column vectors?

    • p and q
    • r and s
    • i and j
    • x and y

  10. How are three-dimensional vectors commonly expressed using standard unit vectors?

    • x, y and z
    • a, b and c
    • i, j and k
    • i, j and l

  11. What mathematical notation represents the magnitude of a vector a?

    • det(a)
    • grad(a)
    • mod(a)
    • div(a)

  12. How do you find a unit vector in the direction of vector a?

    • a divided by |a|
    • |a| divided by a
    • a plus |a|
    • a multiplied by |a|

  13. If f(x) = x^3 - x - 1, what is f'(x) used in the Newton-Raphson formula?

    • 3x^2 - 1
    • x^2 - 1
    • 3x^2 - x
    • 3x^3 - 1

  14. What does the height of each strip represent in the trapezium rule?

    • Function value
    • Second derivative
    • Gradient
    • Area total

  15. If a curve is concave downwards, does the trapezium rule give an over or under-estimate?

    • Exact value
    • Undefined
    • Under-estimate
    • Over-estimate

  16. What must be calculated first to apply the Newton-Raphson method to f(x) = 0?

    • Inverse function
    • Second derivative
    • First derivative
    • Integral

  17. What term describes a vector with a magnitude of exactly one?

    • Unit vector
    • Zero vector
    • Base vector
    • Position vector

  18. When using numerical integration, what improves the accuracy of the trapezium rule estimate?

    • Higher derivative
    • Curved strips
    • Larger interval
    • More strips

  19. What graphical feature causes the Newton-Raphson iteration method to fail due to division by zero?

    • Point of inflection
    • Asymptote
    • Maximum point
    • Zero gradient

  20. What type of diagram uses cobwebs and staircases to illustrate the convergence of recurrence relations?

    • Geometrical diagram
    • Venn diagram
    • Argand diagram
    • Scatter diagram

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