Learning pack · IGCSE handout

Circles

What's in this pack: printable worksheet PDF, matching answers PDF (IGCSE / Secure–Stretch practice). Circle measures use $\pi$ : circumference $2\pi r$ or $\pi d$ , area $\pi r^2$ . Leave answers in terms of $\pi$ when asked.

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: 4_circles_handout.pdf · 4_circles_handout_answers.pdf

Full topic summary

Circle measures use $\pi$ : circumference $2\pi r$ or $\pi d$ , area $\pi r^2$ . Leave answers in terms of $\pi$ when asked.

Key learning points

Radius vs diameter: $d=2r$ .
Arc length and sector area are fractions of the full circle: $\frac{\theta}{360}$ .
Exact answers often keep $\pi$ ; decimal answers need the degree of accuracy stated.

Worked example 1 — Circumference

Radius $7$ . Circumference in terms of $\pi$ ?

Working

C=2\pi r=14\pi

$C=2\pi r$ .

Worked example 2 — Area

Radius $7$ . Area in terms of $\pi$ ?

Working

A=\pi r^2=49\pi

Square the radius first.

Worked example 3 — Arc length

Radius $6$ , angle $60^\circ$ . Arc length in terms of $\pi$ ?

Working

\ell=\tfrac{60}{360}\times2\pi\times6=2\pi

Fraction of the circumference.

🎬 Topic videos

Pi - Numberphile
Numberphile · 10 min
Enrichment / curiosity clip for Lower Secondary (Numberphile-style). Use for hooks, clubs, or stretch — not core exam content.
Funny Fractions and Ford Circles - Numberphile
Numberphile · 14 min
Enrichment / curiosity clip for Lower Secondary (Numberphile-style). Use for hooks, clubs, or stretch — not core exam content.
New Recipe for Pi - Numberphile
Numberphile · 14 min
Enrichment / curiosity clip for Lower Secondary (Numberphile-style). Use for hooks, clubs, or stretch — not core exam content.
Squaring the Circle - Numberphile
Numberphile · 8 min
Enrichment / curiosity clip for Lower Secondary (Numberphile-style). Use for hooks, clubs, or stretch — not core exam content.
How many ways can circles overlap? - Numberphile
Numberphile · 10 min
Enrichment / curiosity clip for Lower Secondary (Numberphile-style). Use for hooks, clubs, or stretch — not core exam content.
Tau vs Pi Smackdown - Numberphile
Numberphile · 11 min
Enrichment / curiosity clip for Lower Secondary (Numberphile-style). Use for hooks, clubs, or stretch — not core exam content.

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