GCSE & iGCSE Functions worksheet

Functions worksheet for GCSE and iGCSE maths: function machines, evaluating f(x), composite and inverse functions, graph transformations.

A complete functions worksheet for Pearson Edexcel GCSE (1MA1) and International GCSE (4MA1), written so one resource works for both tiers. Every section is clearly labelled Foundation or Higher, and questions get harder as you go.

What’s covered — Foundation

Using function machines forwards and backwards
Evaluating f(x) and solving f(x) = k
Recognising linear, quadratic, cubic and reciprocal graphs

What’s covered — Higher (grades 6 to 9)

Composite functions fg(x)
Inverse functions f⁻¹(x)
Transformations of graphs

How it’s structured

A. Worked examples & Your turn — a model solution beside a matching question to try
B. Fluency — core skills
C. Reasoning — explain it
D. Problem solving — unfamiliar, multi-step questions
E. Exam practice — exam-style questions with mark allocations

123 marks across Sections B to E (61 Foundation, 62 Higher), with a progress tracker on the front page so students can record their score per section. Function machines are used to build the notation rather than as a separate topic, so f(x) arrives as shorthand for something students already do.

How to use it

Works as a full lesson, homework, a cover lesson or targeted intervention. Because each tier is labelled, you can set the Foundation sections to one group and the Higher sections to another from the same print.

What’s included

14-page worksheet (PDF, printable, with answer spaces)
6-page full worked solutions (PDF) — complete method for every question, not just final answers
No calculator

Specification

Pearson Edexcel GCSE Mathematics (1MA1) and International GCSE Mathematics (4MA1), Algebra. All questions are original.