Function Machines Questions | Worksheets and Revision | MME

Function Machines Questions, Worksheets and Revision

Level 4-5
GCSE Maths Revision Guide

Function Machines

A function machine takes an input, applies a series of mathematical operations to it, and then outputs a result. Function machines are quite a common question type, especially in foundation maths papers. There are 3 main types of questions you could be asked. 

Make sure you are happy with the following topics before continuing.

Type 1: Input to Output

Here, you will be given an input and a function machine and then asked to produce the output. 

Example: A function machine is shown below, what is the output if the input is 10?

If the input is 10 we need to follow the operations listed in the function machine in the order they are listed. 

Operation 1: 10 \times 6 = 60

Operation 2: 60 - 5 = 55

This gives the output as 55

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Type 2: Output back to Input

Here, you will be given an Output, a function machine, and then asked to find the Input which produced it. 

Example: A function machine is shown below. What was the input if the output is 48?

If the output is 48 we need to follow the operations of the function machine in reverse and do the opposite operation.

First we must reverse Operation 2 which is \times 3, this means we must \div \, 3.

48 \div 3 = 16

Next, Operation 1 which is -10, this means we must +10.

16+10 = 26

This shows the input was 26

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Type 3: Creating Function Machines 

You may be asked to create a function machine from an equation given. 

Example: Draw a function machine below so that b = \dfrac{a-3}{5}

Here we have an input of a and an output of b.

We must next look at the order of operations, for this we will use BIDMAS

As this is a fraction the first operation will be a-3

The Second would then be (a-3) \div 5

Using this we can create the function machine shown below. 

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Example: Function Machines problems

Inputting 5 into the function machine below would give an output of 4.

Find the value of x in the function machine below. 

[2 marks]

So, if we input 5 into the function machine then we must first add \textcolor{orange}3:


Now, the question tells us that the result of dividing 8 by some number gives us 4, so we divide by \textcolor{orange}2 to complete the function machine

x = 2


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Example Questions

a) Inputting 35, we first multiply by 3:


35 \times 3 = 105


Then, add 15 to get




b) We must work backwards and do the opposite operations. So, first subtracting 15 from the given output, we get




Then, dividing by 3 we get,


33\div 3=11


Meaning that 11 is the input required to give an output of 48.

Inputting -5[/latex], we first multiply by -2:




Then, adding 7 we get,




Meaning that -5 is the input required to give an output of 17.

Inputting 3x, we first multiply by \dfrac{1}{2}




Then, dividing by 3 we get,




Meaning that 3x is the input required to give an output of \dfrac{1}{2}x

Two operations are, 


Multiplying by 4, so 9 \times 4 = 36


Subtracting 9, so 36 - 9 = 27



Any combination of operations which produce an output of 27 would be a correct answer.

We have to see what we get if we input x into the function machine. First, multiplying x by 12


12\times x=12x


Then, subtracting 25 to get




This is the output of inputting x but we know the output is equal to 2x, so we are left with the equation




Now we can solve this equation for x. Subtracting 2x from both sides, we get




Adding 25 to both sides, we get




Finally, dividing both sides by 10 we find x to be


x=25\div 10=2.5

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