GCSE · Iteration

Rearranging an equation into iterative formExam-style questions

How "show that the equation can be written as x = g(x)" works — isolate a lone x by honest rearranging — and why that form is exactly what an iteration machine needs.

Start practising Read the lesson

11 questions · GCSE (Higher) level · mark scheme and worked solution on each · no sign-up to try

DifficultyAllLevel 3Level 4Level 5
  1. 1
    An iteration for the equation x3−7x−8=0x^3 - 7x - 8 = 0 gives x4=3.094x_4 = 3.094

    Ella says, "x4x_4 is the exact solution of the equation."

    Explain why Ella is wrong, and state how a more accurate estimate could be found.
    Level 4 · 2 marksTry it
  2. 2
    Show that the equation x3+2x−30=0x^3 + 2x - 30 = 0 can be rearranged to give x=30−2x3x = \sqrt[3]{30 - 2x}
    Level 4 · 2 marksTry it
  3. 3
    Show that the equation x3−8x+3=0x^3 - 8x + 3 = 0 can be rearranged to give x=x3+38x = \dfrac{x^3 + 3}{8}
    Level 4 · 2 marksTry it