Learning pack · IGCSE handout

Rearranging Formulas

What's in this pack: printable worksheet PDF, matching answers PDF (IGCSE / Secure–Stretch practice). Changing the subject is inverse-operation discipline — especially with fractions, roots and formulas with the new subject on both sides.

Resources at the top · full summary · videos with short notes below.

🎒 Resources in this pack

Jump straight to the printable files, or scroll to the summary and videos.

Scaffolded Learning Sheet — attempt the worksheet, then use the Answers for a full written solution.

📝 Open Learning Sheet ✅ Open answers 🎬 More topic videos (6)📖 Full summary

Files: 30_rearranging_formulas_handout.pdf · 30_rearranging_formulas_handout_answers.pdf

Full topic summary

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

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.

🎬 Topic videos

Beautiful Visual Explanation of Completing the Square
Eddie Woo · 4 min
Lower Secondary classroom-friendly explainer. Scaffold→stretch friendly; use with mixed-ability groups.
Introduction to Matrices (1 of 3: Systems of Linear Equations)
Eddie Woo · 5 min
Lower Secondary classroom-friendly explainer. Scaffold→stretch friendly; use with mixed-ability groups.
Math Antics - Basic Inequalities
Math Antics · 13 min
Lower Secondary classroom-friendly explainer. Scaffold→stretch friendly; use with mixed-ability groups.
Is there an equation for a triangle?
Stand-up Maths · 16 min
Enrichment / curiosity clip for Lower Secondary (Numberphile-style). Use for hooks, clubs, or stretch — not core exam content.
Why is there no equation for the perimeter of an ellipse‽
Stand-up Maths · 21 min
Enrichment / curiosity clip for Lower Secondary (Numberphile-style). Use for hooks, clubs, or stretch — not core exam content.
Behold all-new equations for triangles!
Stand-up Maths · 22 min
Enrichment / curiosity clip for Lower Secondary (Numberphile-style). Use for hooks, clubs, or stretch — not core exam content.

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