Composite Functions Worksheet GCSE Higher

Practise composite functions with one rule to hold on to: the letter next to the bracket goes first. 16 questions on one A4 page, full answers included.

Worksheet (questions 1 to 8): fg(4) starts with a pair of function machines showing g first and then f, with g(4) worked out. The prompts fade through fg and gf with numbers, including squared functions, then move on to finding fg(x) as an expression.

Further practice (questions 9 to 16): graded by difficulty. gf(x) in its simplest form, ff(x) for a savings account, solving fg(x) = 49, finding a from fg(2) = 25, comparing a sale discount and a voucher applied in either order, combining kelvin to Celsius to Fahrenheit into one function, solving fg(x) = gf(x), and testing a claim that fg(x) and gf(x) are always different.

Answers to all 16 questions are included as a separate file.

Suitable for GCSE Higher (AQA A7).

AI was used to help create this resource, working from my own lesson design.