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 $x^3 - 5x + 1 = 0$ can be rearranged to give $x = \dfrac{x^3 + 1}{5}$

(b) Using $x_{n+1} = \dfrac{x_n^3 + 1}{5}$ with $x_1 = 0.2$ , work out the value of $x_2$
Level 5 · 3 marksTry it
2
(a) Show that the equation $x^3 - 4x - 9 = 0$ can be rearranged to give $x = \dfrac{x^3 - 9}{4}$

(b) Using the iteration $x_{n+1} = \sqrt[3]{4x_n + 9}$ with $x_1 = 2$ , work out $x_2$ . Give your answer correct to 4 decimal places.
Level 5 · 4 marksTry it