Question 1
Below is a function machine.
1(a):
What is the output if the input is 5?
ANSWER: Simple Text Answer
Answer: 12
Workings:
29+8=37
37-15=22Marks = 2
1(b):
What is the input if the output is 29?
ANSWER: Simple Text Answer
Answer: 22
Workings:
29+15=44
44-8=36
Marks = 2
Question 2
Considering the new function machine below.
2(a):
What is the output if the input is 9?
ANSWER: Simple Text Answer
Answer: 18
Workings:
9\times 8 = 72
72\div 4 = 18
Marks = 2
2(b):
What is the input if the output is 14?
ANSWER: Simple Text Answer
Answer: 7
Workings:
14\times 4 = 56
56\div 8 = 7
Marks = 2
Question 3
Below is a function machine.
3(a):
What is the output if the input is 56?
ANSWER: Simple Text Answer
Answer: 17
Workings:
56\div 7 =8
8+9=17
Marks = 2
3(b):
What is the input if the output is 10?
ANSWER: Simple Text Answer
Answer: 7
Workings:
14\times 4 = 56
56\div 8 = 7
Marks = 2
Question 4
Below are some empty function machines.
4(a):
The number 48 is input into the machine.
The output is 18.
Fill in the missing operation.
ANSWER: Multiple Choice (Type 1)
A: +5
B: +6
C: +7
D: +8
Answer: B
Workings:
48\div 4 = 12
We need to get from 12 to 18.
The simplest way of doing this is just to add 6.
12+6=18
Marks = 2
4(b):
The number 18 is input into the machine.
The output is 26.
Fill in the missing operation.
ANSWER: Multiple Choice (Type 1)
A: +5
B:-7
C:\times 6
D: \div 9
Answer: D
Workings:
26 \div 13 = 2
We need to get back from 2 to 18.
The easiest way to do this is to multiply by 9.
Because we are working backwards the operator will be \div 9.
18\div 9 =2
2\times 13 = 26
Marks = 2
4(c):
The number 3 is input into the machine.
The output is 80.
Fill in the missing operation.
ANSWER: Multiple Choice (Type 1)
A: \times 30
B: - 20
C: + 10
D: \div 40
Answer: A
Workings:
Working backwards
80+10=90
We need to get from 90 to 3.
The easiest way to do this is divide by 30, but because we’re working backwards the operator will be \times 30.
3\times 30 = 90
90-10=80
Marks = 2
Question 5
5(a):
Complete the number machine so that a=2b-6.
ANSWER: Multiple Choice (Type 1)
A: Box 1: \times 2 Box 2: +3
B: Box 1: \times 2 Box 2: -6
C: Box 1: \div 2 Box 2: +2
D: Box 1: \times 3 Box 2: -1
Answer: B
Workings:
To get to 2b we need to multiply by 2 so the Box 1 operator will be \times 2.
We then need to subtract 6, so the Box 2 operator will be -6.
This gives us a=2b-6
Marks = 2
5(b):
Complete the number machine so that a=\dfrac{2+b}{3}
ANSWER: Multiple Choice (Type 1)
A: Box 1: +3 Box 2: \div 5
B: Box 1: -1 Box 2: \times 4
C: Box 1: +2 Box 2: \div 3
D: Box 1: +1 Box 2: \times 2
Answer: C
Workings:
To get b+2 we need to add 2, so the Box 1 operator will be +2.
We then need to divide by 3, so the Box 2 operator will be \div 3.
This gives us a=\dfrac{b+2}{3}.
Marks = 2
5(c):
Look at the function machine shown below.
Write down the output a, in terms of b.
ANSWER: Multiple Choice (Type 1)
A: 7b-14
B: 4b+7
C: -2b+7
D: -7b+2
Answer: A
Workings:
We first subtract 2 to get b-2.
Multiplying this by 7 gives 7(b-2).
Expanding this gives 7b-14.
Marks = 2
6(a):
Below are some empty function machines.
Which of the four options would take an input of 5 and give an output of 12.
ANSWER: Multiple Choice (Type 1)
A: Box 1: \div 4 Box 2: +7
B: Box 1: +3 Box 2: \times 4
C: Box 1: \times 2 Box 2: +2
D: Box 1: -1 Box 2: \div 2
Answer: C
Workings:
Multiplying by 2 will give us 10.
We can then add 2 to get 12.
So Box 1 = \times 2 and Box 2 = +2.
Marks = 2
6(b):
Which of the four options would take an input of 27 and give an output of 13?
ANSWER: Multiple Choice (Type 1)
A: Box 1: \div 3 Box 2: +4
B: Box 1: +4 Box 2: \div 3
C: Box 1: -5 Box 2: \div 2
D: Box 1: \div 2 Box 2: +1
Answer: A
Workings:
Dividing 27 by 3 gives 9.
Adding 4 to this then gives us 13.
So Box 1 = \div 3 and Box 2 = +4.
Marks = 2
Question 7
Below is a function machine.
7(a):
The number x is put through the machine.
The result is 3x.
What is x?
ANSWER: Simple Text Answer
Answer: 5
Workings:
We can write this as an equation: 6x-15=3x.
Rearranging gives 3x=15.
x=5
Marks = 3
7(b):
The number x is put through the same machine.
The result is 5x.
What is x?
ANSWER: Simple Text Answer
Answer: 15
Workings:
We can write this as an equation: 6x-15=5x.
Rearranging gives us x=15.
Marks = 3