Function Machines and Inverse Operations - Worksheets, Questions and Revision

31 original exam-style questions - 7 pages of questions with a full mark scheme - free printable PDF.

Download PDF Jump to mark scheme (page 8)Function Machines and Inverse Operations revision guide

This topic is chapter 4 of KS3 Maths: Algebra Practice Book 1.

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2.7 Function Machines and Inverse Operations

AQA KS3.M-A7 · Calculators not allowed · about 95 minutes

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

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)

Find the input when a machine does: multiply by 4 then add 6, and the output is 26.

(2)

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)

The machine does: subtract 2 then divide by 3. What input gives output 4?

(2)

Write a one-step machine instruction that is the inverse of: multiply by 7.

(3)

A machine does: add 12 then multiply by 1. Find the input that gives output 25. Explain the inverse step you use.

(2)

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)

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)

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)

The function machine: multiply by 2 then add 1. Find the output when the input is 4.

(2)

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)

Reverse the function: the machine does add 7. Work out the input when the output is 12.

(2)

A two-step machine does: multiply by 3, then subtract 4. Work out the output for input 6 and show the two steps.

(3)

The machine does: add 10, then divide by 2. For each input, find the output.

(a)Input 6(1)

(b)Input 0(1)

Work backwards: a machine does add 4 then multiply by 2. The final output is 18. What was the original input?

(2)

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)

A function machine does: add 5. Work out the output when the input is 3.

(1)

Work backwards: a machine does add 6, then multiply by 3. The final output is 30. What was the original input?

(2)

A machine does: square the number, then add 4. Work out the output for input 5.

(2)

Find the input when a machine does: multiply by 5, then add 3, and the output is 38.

(2)

A machine does: subtract 4, then divide by 3. What input gives output 5?

(2)

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)

A machine does: subtract 5, then multiply by 2. Write down, in the correct order, the two steps of the inverse machine.

(3)

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, to give the total cost in pounds.
(a) A customer with a loyalty card pays £41. 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)

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)

A function machine does: multiply by 4. Work out the output when the input is 6.

(1)

A function machine does: multiply by 3, then add 2. Work out the output when the input is 5.

(1)

A function machine does: subtract 7. Work out the input if the output is 10.

(1)

Write down the inverse operation of: subtract 5.

(1)

Write down the inverse operation of: multiply by 8.

(1)

A two-step machine does: multiply by 4, then subtract 3. Work out the output for input 5, showing both steps.

(2)

Mark scheme · 2.7 Function Machines and Inverse Operations

Question 1

(a) B1 3 cao
(a) Answer: 3
(b) B1 24 cao
(b) Answer: 24
(c) B1 8 cao
(c) Answer: 8

Question 2

M1 inverse steps attempted: 26 - 6 = 20 then 20 / 4 = 5
A1 5 cao
Answer: 5

Question 3

M1 correct first inverse: 16 + 5 = 21
M1 correct second inverse: 21 / 3 = 7
A1 5 cao
Answer: 5

Question 4

M1 inverse attempt: 4 x 3 = 12 then +2
A1 14 cao
Answer: 14

Question 5

M1 recognition that inverse is divide by 7
M1 correct phrasing, e.g. divide by 7
A1 divide by 7 cao
Answer: divide by 7

Question 6

M1 use inverse: input = output - 12 or recognise multiply by 1 does not change number
A1 13 cao
Answer: 13

Question 7

M1 first inverse step: 44 / 4 = 11
M1 second inverse step: 11 - 3 = 8
M1 third inverse step: 8 / 2 = 4
A1 4 cao
Answer: 4

Question 8

(a) M1 substitute 2: 5 x 2 + k = 17 or 10 + k = 17
(a) A1 7 cao
(a) Answer: 7
(b) B1 subtract 7 then divide by 5 oe
(b) Answer: subtract 7 then divide by 5

Question 9

(a) B1 15 cao
(a) Answer: 15
(b) B1 35 cao
(b) Answer: 35
(c) B1 -10 cao
(c) Answer: -10

Question 10

M1 correct method: 4 x 2 = 8 then +1
A1 9 cao
Answer: 9

Question 11

(a) B1 8 cao
(a) Answer: 8
(b) B1 3 cao
(b) Answer: 3

Question 12

M1 recognition of inverse: input = output - 7
A1 5 cao
Answer: 5

Question 13

M1 correct first step 6 x 3 = 18
M1 correct second step 18 - 4 = 14
A1 14 cao
Answer: 14

Question 14

(a) B1 8 cao
(a) Answer: 8
(b) B1 5 cao
(b) Answer: 5

Question 15

M1 inverse steps attempted: 18 / 2 = 9 or 9 - 4
A1 5 cao
Answer: 5

Question 16

(a) B1 subtract 9 oe
(a) Answer: subtract 9
(b) B1 multiply by 4 oe
(b) Answer: multiply by 4
(c) B1 divide by -2 oe
(c) Answer: divide by -2

Question 17

B1 8 cao
Answer: 8

Question 18

M1 correctly reverses the last step first, e.g. 30 / 3 = 10
A1 4 cao
Answer: 4

Question 19

M1 correctly squares the input, e.g. 5² = 25
A1 29 cao
Answer: 29

Question 20

M1 correctly reverses the last step first, e.g. 38 - 3 = 35
A1 7 cao
Answer: 7

Question 21

M1 correctly reverses the last step first, e.g. 5 x 3 = 15
A1 19 cao
Answer: 19

Question 22

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 23

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 24

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 cao (3 x 9, no discount)
Answer: 5 tickets; 3 tickets without the discount costs £27

Question 25

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

Question 26

B1 24 cao
Answer: 24

Question 27

B1 17 cao
Answer: 17

Question 28

B1 17 cao
Answer: 17

Question 29

B1 add 5 cao
Answer: add 5

Question 30

B1 divide by 8 cao
Answer: divide by 8

Question 31

M1 correctly applies the first step, e.g. 4 x 5 = 20
A1 17 cao
Answer: 17

Function Machines and Inverse Operations - Worksheets, Questions and Revision

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2.7 Function Machines and Inverse Operations

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