Learning pack · IGCSE handout

Basic Algebra

What's in this pack: printable worksheet PDF, matching answers PDF (IGCSE / Secure–Stretch practice). Basic algebra is about collecting like terms, expanding brackets carefully, and simplifying expressions before solving.

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: 5_basic_algebra_handout.pdf · 5_basic_algebra_handout_answers.pdf

Full topic summary

Basic algebra is about collecting like terms, expanding brackets carefully, and simplifying expressions before solving.

Key learning points

Like terms share the same letter powers: $3x+5x=8x$ , but $3x+5x^2$ cannot combine.
Expand: $a(b+c)=ab+ac$ ; watch double negatives.
Substitute values only after simplifying when the question allows.

Worked example 1 — Collect like terms

Simplify $3a+5a-2a$ .

Working

6a

Add/subtract coefficients.

Worked example 2 — Expand and simplify

Expand $3(x-2)+4$ .

Working

3x-2

Distribute, then collect.

Worked example 3 — Factorise

Factorise $6x+9$ .

Working

3(2x+3)

Take out the HCF.

🎬 Topic videos

When a complicated proof simplifies everything
Stand-up Maths · 6 min
Enrichment / curiosity clip for Lower Secondary (Numberphile-style). Use for hooks, clubs, or stretch — not core exam content.
Factorising Algebraic Expressions (1 of 2: All Positives)
Eddie Woo · 8 min
Lower Secondary classroom-friendly explainer. Scaffold→stretch friendly; use with mixed-ability groups.
Algebra Basics: Simplifying Polynomials - Math Antics
Math Antics · 11 min
Lower Secondary classroom-friendly explainer. Scaffold→stretch friendly; use with mixed-ability groups.
Algebra Basics: Slope And Distance - Math Antics
Math Antics · 12 min
Lower Secondary classroom-friendly explainer. Scaffold→stretch friendly; use with mixed-ability groups.
Algebra Basics: Inequalities In Algebra - Math Antics
Math Antics · 14 min
Lower Secondary classroom-friendly explainer. Scaffold→stretch friendly; use with mixed-ability groups.
Substituting into an Algebraic Expression (Harder Example)
Eddie Woo · 10 min
Lower Secondary classroom-friendly explainer. Scaffold→stretch friendly; use with mixed-ability groups.

More Lower Secondary packs

Browse the hub Learning Packs & Summary, or open the compact Basic Algebra summary.