PROBLEM SOLVING

Function Machines

Learn the reliable method for function machines, then apply it to 11+ exam-style questions.

1 · WHAT YOU NEED TO KNOW

The idea

A function machine applies the same ordered operations to every input.

Picture itFollow what happens to the unknown
2 · THE METHOD

Follow these steps

  1. Read each operation in order.
  2. Apply the operations to the input.
  3. To work backwards, reverse both the order and each operation.
3 · WORKED EXAMPLES

See the method in action

Example 1

A function machine multiplies by 3. Its input is 6. What is its output?

  1. Apply the operation: 6 × 3 = 18.
Answer: 18
Example 2

A machine multiplies its input by 4 and then adds 9. Its output is 29. What was the input?

  1. Reverse the operations: 29 − 9 = 20, then 20 ÷ 4 = 5.
Answer: 5
4 · ELEVENSPRINT TIP

A useful shortcut

To work backwards, reverse both the order and each operation.

5 · COMMON MISTAKES

Watch out for these

6 · TRY IT YOURSELF

Three fresh questions

Ready to check the method? You will get three fresh, validated questions.