Learning pack · IGCSE handout

Quadratic Equations

What's in this pack: printable worksheet PDF, matching answers PDF (IGCSE / Secure–Stretch practice). Quadratics solve by factorising, completing the square, or the quadratic formula. Sketching links roots to intercepts.

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: 42_quadratic_equations_handout.pdf · 42_quadratic_equations_handout_answers.pdf

Full topic summary

Quadratics solve by factorising, completing the square, or the quadratic formula. Sketching links roots to intercepts.

Key learning points

Factorise when integer roots are likely; formula always works.
$x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$ ; discriminant $b^2-4ac$ counts real roots.
Expand to check factorisation.

Worked example 1 — Factorise and solve

Solve $x^2-5x+6=0$ .

Working

(x-2)(x-3)=0\Rightarrow x=2\text{ or }3

Factor pairs.

Worked example 2 — Quadratic formula

Solve $x^2+2x-5=0$ in surd form.

Working

x=-1\pm\sqrt{6}

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$ .

Worked example 3 — Completing the square

Write $x^2+6x+5$ in completed-square form.

Working

(x+3)^2-4

Half of 6 is 3.

🎬 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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