Function Machines worksheet

10 GCSE practice questions with answers, free to print. Every sheet is generated, so you can make a fresh one whenever you need it.

1. 2 marks

   Here is a function machine.

   Input	\(\times 5\)	\(- 8\)	Output
   \(3\)	→	→	?

   Work out the output when the input is \(3\).

2. 3 marks

   Here is a function machine.

   Input	\(+ 2\)	\(\times 6\)	\(- 2\)	Output
   \(3\)	→	→	→	?

   The input is \(3\).

   Work out the output.

3. 3 marks

   Here is a function machine.

   Input	\(\times 4\)	\(- 7\)	Output
   ?	→	→	\(9\)

   The machine gives an output of \(9\).

   Find the input.

4. 4 marks

   Here is a function machine.

   Input	\(- 10\)	\(\times 5\)	Output
   ?	→	→	?

   (a)

   Calculate the output when the input is \(11\).

   (b)

   Calculate the input when the output is \(25\).

5. 2 marks

   Here is a function machine. The first operation is missing.

   Input	\(\times \, ?\)	\(- 7\)	Output
   \(10\)	→	→	\(43\)

   Work out the missing number.

6. 4 marks

   Here is a function machine.

   Input	\(\times 5\)	\(+ 2\)	Output
   \(n\)	→	→	?

   (a)

   Find an expression, in terms of \(n\), for the output.

   (b)

   The output is \(37\). Work out the value of \(n\).

7. 2 marks

   Here is a function machine.

   Input	\(\times 7\)	\(- 7\)	Output
   \(3\)	→	→	?

   The input is \(3\).

   Work out the output.

8. 3 marks

   Here is a function machine.

   Input	\(+ 8\)	\(\times 4\)	\(- 2\)	Output
   \(3\)	→	→	→	?

   The input is \(3\).

   Work out the output.

9. 3 marks

   Here is a function machine.

   Input	\(\times 9\)	\(- 14\)	Output
   ?	→	→	\(85\)

   The machine gives an output of \(85\).

   Find the input.

10. 4 marks

    Here is a function machine.

    Input	\(- 1\)	\(\times 7\)	Output
    ?	→	→	?

    (a)

    Work out the output when the input is \(13\).

    (b)

    Work out the input when the output is \(70\).

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