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.

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

DifficultyAll Level 3 Level 4 Level 5

1
(a) Show that the equation $x^3 - 3x - 5 = 0$ can be rearranged to give $x = \sqrt[3]{3x + 5}$ (1 mark)

(b) Starting with $x_0 = 2$ , use the iteration $x_{n+1} = \sqrt[3]{3x_n + 5}$ to find $x_1$ , $x_2$ and $x_3$ . Give your answers correct to 4 decimal places. (2 marks)

(c) Write down an estimate of the solution correct to 2 decimal places. (1 mark)
Level 3 · 4 marksTry it
2
Show that the equation $x^3 - 7x - 8 = 0$ can be rearranged to give $x = \sqrt[3]{7x + 8}$
Level 3 · 2 marksTry it
3
Show that the equation $x^3 + x - 20 = 0$ can be rearranged to give $x = \sqrt[3]{20 - x}$
Level 3 · 2 marksTry it
4
Show that the equation $x^2 - 3x - 7 = 0$ can be rearranged to give $x = \sqrt{3x + 7}$
Level 3 · 2 marksTry it
5
Show that the equation $x^3 - 4x - 9 = 0$ can be rearranged to give $x = \sqrt[3]{4x + 9}$
Level 3 · 2 marksTry it

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