GCSE · Iteration

Showing a root exists — change of signExam-style questions

Why a sign change in a continuous function traps a root between two values, how to present the argument for full marks, and how the same idea justifies a root to a given accuracy.

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

DifficultyAllLevel 3Level 4Level 5
  1. 1
    f(x)=x3+x−20f(x) = x^3 + x - 20

    The equation f(x)=0f(x) = 0 has a solution close to x=2.6x = 2.6

    Show that this solution is x=2.59x = 2.59, correct to 2 decimal places.
    Level 5 · 3 marksTry it
  2. 2
    f(x)=x3−4x−9f(x) = x^3 - 4x - 9

    The equation f(x)=0f(x) = 0 has a solution close to x=2.7x = 2.7

    Show that this solution is 2.72.7 correct to 1 decimal place.
    Level 5 · 3 marksTry it