A function machine does: add 5. Work out the output when the input is 3.
(1)
2
A function machine does: multiply by 4. Work out the output when the input is 6.
(1)
3
A function machine does: multiply by 3, then add 2. Work out the output when the input is 5.
(1)
4
A function machine does: subtract 7. Work out the input if the output is 10.
(1)
5
A function machine does: add 9. Work out the input when the output is 15.
(1)
6
Write down the inverse operation of: subtract 5.
(1)
7
Write down the inverse operation of: multiply by 8.
(1)
8
A two-step machine does: multiply by 4, then subtract 3. Work out the output for input 5, showing both steps.
(2)
9
A machine does: add 8, then divide by 2. Work out the output for input 6.
(2)
10
Work backwards: a machine does add 6, then multiply by 3. The final output is 30. What was the original input?
(2)
11
A machine does: square the number, then add 4. Work out the output for input 5.
(2)
12
Find the input when a machine does: multiply by 5, then add 3, and the output is 38.
(2)
13
A machine does: subtract 4, then divide by 3. What input gives output 5?
(2)
14
A machine does: add 3, multiply by 4, then subtract 6. The final output is 26. Work backwards to find the original input, showing each inverse step clearly.
(3)
15
A car park charges according to a two-step rule: it doubles the number of hours parked, then adds a fixed 2 pound booking fee, to give the total charge in pounds. A driver is charged 14 pounds. Form the calculation needed and find how many hours they parked for.
(3)
16
A machine does: subtract 5, then multiply by 2. Write down, in the correct order, the two steps of the inverse machine.
(3)
17
A three-step machine does: subtract 2, multiply by 5, then add 1. The final output is 26. Work backwards to find the original input, showing each inverse step clearly.
(4)
18
A theatre's ticket-pricing machine works as follows: it takes the number of tickets, multiplies by 9, then subtracts a loyalty-card discount of 4 pounds, to give the total cost in pounds. (a) A customer with a loyalty card pays 41 pounds. Form the calculation and work backwards to find how many tickets they bought. (b) Work out the cost for 3 tickets without the loyalty discount.
(4)
19
Stretch. A two-step machine multiplies the input by k, then adds 5, where k is unknown. When the input is 3, the output is 20. Find the value of k. Then state the inverse of the complete machine as two one-step instructions, in the correct order.
(4)
Mark scheme · KS3.M-A7D Function Machines and Inverse Operations: Fluency and Exam Drill
Question 1
B1 8 cao
Answer: 8
Question 2
B1 24 cao
Answer: 24
Question 3
B1 17 cao
Answer: 17
Question 4
B1 17 cao
Answer: 17
Question 5
B1 6 cao
Answer: 6
Question 6
B1 add 5 cao
Answer: add 5
Question 7
B1 divide by 8 cao
Answer: divide by 8
Question 8
M1 correctly applies the first step, e.g. 4 x 5 = 20
A1 17 cao
Answer: 17
Question 9
M1 correctly applies the first step, e.g. 6 + 8 = 14
A1 7 cao
Answer: 7
Question 10
M1 correctly reverses the last step first, e.g. 30 / 3 = 10
A1 4 cao
Answer: 4
Question 11
M1 correctly squares the input, e.g. 52 = 25
A1 29 cao
Answer: 29
Question 12
M1 correctly reverses the last step first, e.g. 38 - 3 = 35
A1 7 cao
Answer: 7
Question 13
M1 correctly reverses the last step first, e.g. 5 x 3 = 15
A1 19 cao
Answer: 19
Question 14
M1 reverses the last step correctly, e.g. 26 + 6 = 32
M1 reverses the second step correctly, e.g. 32 / 4 = 8
A1 5 cao (after reversing the first step, 8 - 3)
Answer: 5
Question 15
M1 reverses the booking fee correctly, e.g. 14 - 2 = 12
M1 reverses the doubling correctly, e.g. 12 / 2 = 6
A1 6 hours cao
Answer: 6 hours
Question 16
M1 recognises the order of the two steps must be reversed
M1 correctly finds the inverse of each operation (divide by 2; add 5)
A1 divide by 2, then add 5 cao
Answer: divide by 2, then add 5
Question 17
M1 reverses the last step correctly, e.g. 26 - 1 = 25
M1 reverses the second step correctly, e.g. 25 / 5 = 5
M1 reverses the first step correctly, e.g. 5 + 2 = 7
A1 7 cao
Answer: 7
Question 18
M1 reverses the discount correctly, e.g. 41 + 4 = 45
M1 reverses the multiplication correctly, e.g. 45 / 9 = 5
A1 5 tickets cao
A1 27 pounds cao (3 x 9, no discount)
Answer: 5 tickets; 3 tickets without the discount costs 27 pounds
Question 19
M1 correct equation formed, e.g. 3k + 5 = 20
M1 correct rearrangement, e.g. 3k = 15
A1 k = 5 cao
A1 subtract 5, then divide by 5 cao (correct inverse steps, correct order)
Answer: k = 5; inverse: subtract 5, then divide by 5