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GCSE Maths: Function Machines

Use function machines to work forwards and backwards through a rule. Practise it with adaptive questions for AQA, Edexcel, OCR and Eduqas.

AlgebraFoundation & HigherAQA · Edexcel · OCR · Eduqas

What you need to know

The concepts examiners test on function machines, and what each one is really asking.

Find the output of a function machine from a given input
Find the input from a given output by working backwards
Write the rule of a function machine as an expression
Use inverse operations in the correct order

Where marks get lost

The exam technique that separates a correct method from a correct answer.

  • Undoing the operations in the wrong order — you must reverse the order as well as the operations
  • Using the same operation instead of its inverse, e.g. subtracting when you should divide
  • Forgetting the bracket when writing the rule, so 5(n - 2) becomes 5n - 2
  • Reading the machine left to right when the question gives you the output

Function Machines questions students ask

Is Function Machines on the Foundation paper?

Yes. Function Machines appears at both Foundation and Higher tier, though Higher papers take it further.

What should I know before starting Function Machines?

It builds on Order of operations (BIDMAS) and Inverse operations and Negative numbers. If those feel shaky, practise them first — Function Machines questions assume them.

What is the most common mistake in Function Machines?

Undoing the operations in the wrong order — you must reverse the order as well as the operations.

Which exam boards cover Function Machines?

All four we support — AQA, Edexcel, OCR and Eduqas. GCSE Maths subject content is set by the DfE, so the topic is common to every board; what changes is the paper structure and the grade boundaries.