Learning pack · IGCSE handout

Functions

What's in this pack: printable worksheet PDF, matching answers PDF (IGCSE / Secure–Stretch practice). Function notation $f(x)$ means ‘apply the rule’. Composite functions apply rules in order; inverses undo.

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: 48_functions_handout.pdf · 48_functions_handout_answers.pdf

Full topic summary

Function notation $f(x)$ means ‘apply the rule’. Composite functions apply rules in order; inverses undo.

Key learning points

$f(a)$ is the output when $x=a$ .
$(fg)(x)=f(g(x))$ — right-to-left application.
Inverse: swap $x$ and $y$ , then rearrange; reflect $y=f(x)$ in $y=x$ .

Worked example 1 — Evaluate

$f(x)=2x-1$ . Find $f(5)$ .

Working

9

Substitute.

Worked example 2 — Composite

$f(x)=x+1$ , $g(x)=2x$ . Find $f(g(3))$ .

Working

7

Apply $g$ then $f$ .

Worked example 3 — Inverse

$f(x)=3x+2$ . Find $f^{-1}(x)$ .

Working

f^{-1}(x)=\tfrac{x-2}{3}

Swap and rearrange.

🎬 Topic videos

Basic Linear Functions - Math Antics
Math Antics · 13 min
Lower Secondary classroom-friendly explainer. Scaffold→stretch friendly; use with mixed-ability groups.
Understanding Exponential Functions and their Gradients: Intuitive Approach
Eddie Woo · 8 min
Lower Secondary classroom-friendly explainer. Scaffold→stretch friendly; use with mixed-ability groups.
x- and y-intercepts 2 | Linear equations and functions | 8th grade | Khan Academy
Khan Academy · 3 min
Lower Secondary classroom-friendly explainer. Scaffold→stretch friendly; use with mixed-ability groups.
Recognizing linear functions | Linear equations and functions | 8th grade | Khan Academy
Khan Academy · 4 min
Lower Secondary classroom-friendly explainer. Scaffold→stretch friendly; use with mixed-ability groups.
Composite Functions - GCSE Higher Maths
1st Class Maths · 5 min
Useful across Lower Secondary and early IGCSE. Keep LS board tag; exam boards retained for dual-use.
Higher order derivatives | Chapter 10, Essence of calculus
3Blue1Brown · 6 min
Classroom-ready explain of rates of change, functions. Use when teaching this topic in Lower Secondary / IGCSE.

More Lower Secondary packs

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