Topic summary · IGCSE handout

Rearranging Formulas summary

Changing the subject is inverse-operation discipline — especially with fractions, roots and formulas with the new subject on both sides.

Open Learning Sheet — Rearranging Formulas Download Rearranging Formulas answers PDF

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Key learning points

Clear fractions by multiplying through by the denominator.
If the subject appears twice, collect terms and factorise.
Square roots: isolate the root, then square both sides (check extraneous results if the context requires).

Worked example 1 — Subject on both sides

Make $x$ the subject of $ax+b=cx+d$ .

Working

x=\frac{d-b}{a-c}

Collect $x$ terms.

Worked example 2 — With fractions

Make $v$ the subject of $\tfrac{1}{f}=\tfrac{1}{u}+\tfrac{1}{v}$ .

Working

v=\frac{fu}{u-f}

Combine, invert, rearrange.

Worked example 3 — Roots

Make $r$ the subject of $V=\tfrac{4}{3}\pi r^3$ .

Working

r=\sqrt[3]{\frac{3V}{4\pi}}

Clear coefficient, then cube-root.

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.

Open Learning Sheet Answers PDF

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