Function Machines Questions, Worksheets and Revision

Function Machines Questions, Worksheets and Revision

GCSE 4 - 5AQAEdexcelOCRWJECFoundationAQA 2022Edexcel 2022OCR 2022WJEC 2022

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.

Level 4-5 GCSE AQA Edexcel OCR WJEC

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?

Function Machines Input Output Multiply SubtractLevel 4-5GCSEAQAEdexcelOCRWJEC

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?

Function Machines Input Output Subtract Multiply

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

Level 4-5GCSEAQAEdexcelOCRWJEC
Level 4-5 GCSE AQA Edexcel OCR WJEC

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.

Function Machines Input Output Subtract DivideLevel 4-5GCSEAQAEdexcelOCRWJEC

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]

Function Machines Input Output Add Divide Missing Function

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

5+3=8

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

 

Level 4-5GCSEAQAEdexcelOCRWJEC

Example Questions

a) Inputting 35, we first multiply by 3:

 

35 \times 3 = 105

 

Then, add 15 to get

 

105+15=120

 

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

 

48-15=33

 

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, we first multiply by -2:

 

-5\times-2=10

 

Then, adding 7 we get,

 

10+7=17

 

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

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

 

3x\times\dfrac{1}{2}=\dfrac{3}{2}x

 

Then, dividing by 3 we get,

 

\dfrac{3}{2}x\div3=\dfrac{1}{2}x

 

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

 

Function Machines Input Output Multiply Subtract Minus Missing Operations Example

 

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

 

12x-25

 

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

 

12x-25=2x

 

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

 

10x-25=0

 

Adding 25 to both sides, we get

 

10x=25

 

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

 

x=25\div 10=2.5

Related Topics

MME

Types of Numbers Worksheets, Questions and Revision

Level 1-3GCSEKS3
MME

BIDMAS or BODMAS Questions, Revision and Worksheets

Level 1-3GCSEKS3

Worksheet and Example Questions

Site Logo

(NEW) Function Machines Exam Style Questions - MME

Level 4-5 GCSENewOfficial MME

You May Also Like...

GCSE Maths Revision Cards

Revise for your GCSE maths exam using the most comprehensive maths revision cards available. These GCSE Maths revision cards are relevant for all major exam boards including AQA, OCR, Edexcel and WJEC.

£8.99
View Product

GCSE Maths Revision Guide

The MME GCSE maths revision guide covers the entire GCSE maths course with easy to understand examples, explanations and plenty of exam style questions. We also provide a separate answer book to make checking your answers easier!

From: £14.99
View Product