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LearnCambridge97092026–2027Paper 3 · Pure Mathematics 3Numerical solution of equations
Paper 3 · Module

Numerical solution of equations

3 subtopics≈ 115 min in total
Start the module: Locating roots: sketches and sign changesOpen graphing calculator

  1. Locating roots: sketches and sign changes

    Most equations have no exact solution. Before you can approximate a root you need to know how many there are and roughly where: sketch two graphs to count them, then trap each one with a change of sign.

    ≈ 35 min

  2. Fixed-point iteration

    Feed a number into a formula, feed the answer back in, and repeat. When the values settle down they settle on a root. This lesson is the engine of every P2 and P3 numerical question.

    ≈ 40 min

  3. Rearrangements, staircases and cobwebs

    One equation can be rearranged into x=F(x)x=F(x) in many ways, and they do not all work. See why some iterations close in on a root, some zigzag towards it, and some run away, and learn to find the equation a limit satisfies.

    ≈ 40 min