Formulas summary

Key learning points

• Substitute with brackets to protect negatives and fractions.
• Change subject: undo operations in reverse order.
• Units: convert before substituting when needed.

Worked example 1 — Substitute

$A=\tfrac{1}{2}bh$ with $b=6$, $h=5$. Find $A$.

Working

Substitute then evaluate.

Worked example 2 — Change the subject

Make $r$ the subject of $A=\pi r^2$.

Working

Divide by $\pi$, then square-root.

Worked example 3 — Rearrange linear

Make $x$ the subject of $y=3x+7$.

Working

Undo operations in reverse.

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.