Numerical Methods summary

Key learning points

• A sign change on a continuous function suggests a root in the interval.
• Refine brackets to the required decimal accuracy.
• Fixed-point iteration needs a converging rearrangement.
• State the conclusion clearly (e.g. root $=1.23$ to 2 d.p.).

Worked example 1 — Change of sign

For $f(x)=x^3-x-1$, show a root in $[1,2]$.

Working

Continuous ⇒ a root exists in between by the IVT.

Worked example 2 — A sign change on a continuous function suggests a root

Use this method from the Numerical Methods sheet: A sign change on a continuous function suggests a root in the interval.

Working

Each key learning point matches a question type on the printable worksheet.

Worked example 3 — Refine brackets to the required decimal accuracy

Use this method from the Numerical Methods sheet: Refine brackets to the required decimal accuracy.

Working

Each key learning point matches a question type on the printable worksheet.

Worked example 4 — Fixed-point iteration needs a converging rearrangement

Use this method from the Numerical Methods sheet: Fixed-point iteration needs a converging rearrangement.

Working

Each key learning point matches a question type on the printable worksheet.

Worked example 5 — State the conclusion clearly (e.g. root to 2 d.p.)

Use this method from the Numerical Methods sheet: State the conclusion clearly (e.g. root $=1.23$ to 2 d.p.).

Working

Each key learning point matches a question type on the printable worksheet.

Scaffolded Learning Sheet and answers (PDFs)

This page is a short, searchable overview for revision and search engines. Use the Scaffolded Learning Sheet first, then the Answers PDF for a full written solution. The printable PDFs remain the main classroom resource.