Lesson 9.3.1

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

20 questions

In partnership with Revision Ninja

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.

Host it live on the board and students join with a game code on their own devices, or revise alone with Free Play. The answers are revealed in the game.

Host this setFree Play

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

All Pearson Edexcel Maths quizzes