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.

Start practising Read the lesson

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

DifficultyAll Level 2 Level 3 Level 4

1
This function machine changes a temperature in degrees Celsius ( $^\circ$ C) to degrees Fahrenheit ( $^\circ$ F).

${}^\circ\text{C} \to \boxed{\times 9} \to \boxed{\div 5} \to \boxed{+\,32} \to {}^\circ\text{F}$
(a) Change $35\,^\circ$ C to $^\circ$ F.

(1 mark)
(b) Change $59\,^\circ$ F to $^\circ$ C.

(2 marks)

There is one temperature that is the same number in $^\circ$ C and in $^\circ$ F.
(c) Find this temperature.

You must show your working.

(3 marks)
Level 4 · 6 marksTry it
2
Caleb uses the two function machines shown below.

Function P:

$\text{Input} \to \boxed{+\,2} \to \boxed{\times 4} \to \text{Output}$

Function Q:

$\text{Input} \to \boxed{\times 3} \to \boxed{-\,7} \to \text{Output}$
(a) Caleb puts the number $n$ into function P.

Write an expression, in terms of $n$ , for the output.

(1 mark)
(b) Caleb chooses a number and puts it into function Q.

He then uses the output from function Q as the input to function P.

The final output is $8$ times the number Caleb chose.

Find the number Caleb chose.

You must show your working.

(5 marks)
Level 4 · 6 marksTry it
3
Here are two function machines, S and T.

Function S:

$\text{Input} \to \boxed{\times 6} \to \boxed{+\,2} \to \text{Output}$

Function T:

$\text{Input} \to \boxed{-\,4} \to \boxed{\div 2} \to \text{Output}$
(a) The number $x$ comes out of function T.

Write an expression, in terms of $x$ , for the number that was put into function T.

(2 marks)

A number, $n$ , is put into function S. The output from S is then put into function T.
(b) Write an expression, in terms of $n$ , for the output from function T.

Give your answer in its simplest form.

(3 marks)
(c) One function machine with two operations does the same as function S followed by function T.

Complete this function machine.

$\text{Input} \to \boxed{\;\ldots\ldots\;} \to \boxed{\;\ldots\ldots\;} \to \text{Output}$

(1 mark)
Level 4 · 6 marksTry it
4
Two function machines, D and E, are shown below.

Function D:

$\text{Input} \to \boxed{\times 3} \to \boxed{+\, a} \to \text{Output}$

Function E:

$\text{Input} \to \boxed{-\,2} \to \boxed{\times\, b} \to \text{Output}$

When $3$ is put into function D, the output is the same as when $6$ is put into function E.

When $5$ is put into function E and the output is then put into function D, the final output is $43$ .

Find the value of $a$ and the value of $b$ .

You must show your working.

(5 marks)
Level 4 · 5 marksTry it
5
Here is a number machine.

$\text{Input} \to \boxed{+\, c} \to \boxed{\times 4} \to \text{Output}$

$c$ is a number.

When the input is $n$ , the output is $m$ .
(a) Write an expression for $m$ in terms of $n$ and $c$ .

(1 mark)
(b) The input is increased by $3$

Jo says,

"The output will also increase by $3$ "

Is Jo correct?

Show working to support your answer.

(2 marks)
Level 4 · 3 marksTry it

1 more question on number machines and function machines

Free with an account — just an email, no card. The whole bank, every mark scheme and worked solution.

Start free