A function machine does: add 3. For each input, write the output.
(a)Input 2(1)
(b)Input 10(1)
(c)Input 0(1)
(d)Input -4(1)
2
A function machine does: multiply by 5. For each input, write the output.
(a)Input 3(1)
(b)Input 7(1)
(c)Input -2(1)
3
The function machine: multiply by 2 then add 1. Find the output when the input is 4.
(2)
4
A function machine does: subtract 6. Work out the input if the output is given.
(a)Output 2. What was the input?(1)
(b)Output -3. What was the input?(1)
5
Reverse the function: the machine does add 7. Work out the input when the output is 12.
(2)
6
A two-step machine does: multiply by 3, then subtract 4. Work out the output for input 6 and show the two steps.
(3)
7
The machine does: add 10, then divide by 2. For each input, find the output.
(a)Input 6(1)
(b)Input 0(1)
8
Work backwards: a machine does add 4 then multiply by 2. The final output is 18. What was the original input?
(2)
9
Describe the inverse operation of each. Give the inverse as a one-step instruction.
(a)Original: add 9(1)
(b)Original: divide by 4(1)
(c)Original: multiply by -2(1)
10
A machine does: square the number, then subtract 1. For each input find the output.
(a)Input 2(1)
(b)Input 5(1)
(c)Input -3(1)
11
Find the input when a machine does: multiply by 4 then add 6, and the output is 26.
(2)
12
A machine does: add 2, multiply by 3, then subtract 5. The final output is 16. Work backwards to find the original input and show steps.
(3)
13
The machine does: subtract 2 then divide by 3. What input gives output 4?
(2)
14
Write a one-step machine instruction that is the inverse of: multiply by 7.
(3)
15
A machine does: add 12 then multiply by 1. Find the input that gives output 25. Explain the inverse step you use.
(2)
16
Challenge: A machine does: multiply by 2, add 3, multiply by 4. The final output is 44. Work backwards to find the original input. Show each inverse step clearly.
(4)
17
Stretch: A box contains a hidden input n. A function machine does: add n, then multiply by 3. The final output is 27. Find n.
(4)
18
Stretch: A two-step inverse puzzle. A machine does: multiply by 5 then add k. If an input of 2 gives output 17, find k. Then state the inverse one-step instruction for this machine.
(a)Find k(2)
(b)Give the inverse one-step instruction(1)
Mark scheme · KS3.M-A7 Function Machines and Inverse Operations