Learning pack · Foundation · CIE Core

Formulas

What's in this pack: printable worksheet PDF, matching answers PDF (Foundation · CIE Core depth). Formula work means substituting carefully and rearranging (changing the subject) with inverse operations.

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: foundation-15 Formulas handout.pdf · foundation-15 Formulas handout answers.pdf

Full topic summary

Formula work means substituting carefully and rearranging (changing the subject) with inverse operations.

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

A=15

Substitute then evaluate.

Worked example 2 — Change the subject

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

Working

r=\sqrt{\frac{A}{\pi}}

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

Worked example 3 — Rearrange linear

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

Working

x=\frac{y-7}{3}

Undo operations in reverse.

🎬 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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