GCSE · Formulae & rearranging

Number machines and function machinesExam-style questions

A number machine is a list of instructions carried out in order. How to run one forwards, how to run it backwards by undoing the last box first, why the order of the boxes matters, how to write a machine as an expression with the brackets in the right place, how to find the number a machine leaves unchanged or a box that is missing, and how to join two machines, undo one in algebra and solve with them.

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11 questions · GCSE (Higher) level · mark scheme and worked solution on each · no sign-up to try

DifficultyAllLevel 2Level 3Level 4
  1. 1
    Here is a number machine.

    Input→×  …→+  …→Output\text{Input} \to \boxed{\times\;\ldots} \to \boxed{+\;\ldots} \to \text{Output}

    When the input is 33, the output is 1717

    When the input is 77, the output is 3333

    Complete the number machine.

    (2 marks)
    Level 3 · 2 marksTry it
  2. 2
    Here is a number machine.

    input→+ 4→×6→output\text{input} \to \boxed{+\,4} \to \boxed{\times 6} \to \text{output}

    The output is 5454

    Ben works out the input. Here is his working.

    54−4=5050÷6=8.3…54 - 4 = 50 \qquad\qquad 50 \div 6 = 8.3\ldots
    (a) What mistake has Ben made?

    (1 mark)
    (b) Work out the input.

    (2 marks)
    Level 3 · 3 marksTry it
  3. 3
    Function A and function B are shown below.

    Function A:

    Input→×2→+ 9→Output\text{Input} \to \boxed{\times 2} \to \boxed{+\,9} \to \text{Output}

    Function B:

    Input→+ 3→×3→Output\text{Input} \to \boxed{+\,3} \to \boxed{\times 3} \to \text{Output}

    Ella puts the same number into both functions.

    Ella says, "The two outputs can never be equal."

    Is Ella correct?

    Show how you decide.

    (3 marks)
    Level 3 · 3 marksTry it
  4. 4
    Here are two number machines.

    Machine A:

    input→− 6→×3→output\text{input} \to \boxed{-\,6} \to \boxed{\times 3} \to \text{output}

    Machine B:

    input→÷2→+ 10→output\text{input} \to \boxed{\div 2} \to \boxed{+\,10} \to \text{output}

    The output of machine A is the input of machine B.
    (a) The input to machine A is 1010

    Work out the output of machine B.

    (2 marks)
    (b) The output of machine B is 44

    Work out the input to machine A.

    (2 marks)
    Level 3 · 4 marksTry it