Function Machines - Worksheets, Questions and Revision

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2.8 Function Machines

EDEXCEL 1MA1 · Calculator allowed · about 75 minutes

Total Marks

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

The function machine below multiplies every input by 4.
input --> [ x 4 ] --> output

(a)Work out the output when the input is 3.(1)

(b)Work out the output when the input is 7.(1)

(c)Work out the output when the input is -2.(1)

(Total for Question 1 is 3 marks)

The function machine below has two steps.
input --> [ +5 ] --> [ x 2 ] --> output

(a)Work out the output when the input is 1.(1)

(b)Work out the output when the input is 4.(1)

(c)Work out the output when the input is -3.(2)

(Total for Question 2 is 4 marks)

The function machine below subtracts 6 from every input.
input --> [ -6 ] --> output
Work out the input for each output given.

(a)The output is 10. Find the input.(1)

(b)The output is -2. Find the input.(1)

(c)The output is 0. Find the input.(1)

(Total for Question 3 is 3 marks)

Which function machine represents 'multiply the input by 3, then subtract 5'?

A) input --> [ x3 ] --> [ -5 ] --> output
B) input --> [ -5 ] --> [ x3 ] --> output
C) input --> [ x5 ] --> [ -3 ] --> output
D) input --> [ /3 ] --> [ -5 ] --> output

(Total for Question 4 is 1 mark)

The function machine below has two steps.
input --> [ x 3 ] --> [ -4 ] --> output
Complete the table of outputs.

(a)input = 0(1)

(b)input = 2(1)

(c)input = 5(1)

(d)input = -1(1)

(Total for Question 5 is 4 marks)

The function machine below has two steps.
input --> [ +7 ] --> [ /2 ] --> output
Work out the input for each output given.

(a)The output is 5. Find the input.(2)

(b)The output is 1. Find the input.(2)

(Total for Question 6 is 4 marks)

Each part below shows a different function machine with input n. Select the expression that represents the output.

(a)input n --> [ x 2 ] --> [ +5 ] --> output. Which expression represents the output?(1)

A) 2n+5
B) 2(n+5)
C) n/2+5
D) 2n-5

(b)input n --> [ +3 ] --> [ x 4 ] --> output. Which expression represents the output?(1)

A) 4n+3
B) 4(n+3)
C) n/4+3
D) 4n-3

(c)input n --> [ x 5 ] --> [ -2 ] --> output. Which expression represents the output?(1)

A) 5n-2
B) 5(n-2)
C) 5n+2
D) (n-2)/5

(Total for Question 7 is 3 marks)

Two function machines are described below. Find the missing operation in each.

(a)A function machine has the rule: input --> [ ? ] --> output. When the input is 3 the output is 15, and when the input is 6 the output is 30. Find the missing operation.(1)

(b)A function machine has two steps: input --> [ x 2 ] --> [ ? ] --> output. When the input is 4 the output is 5, and when the input is 10 the output is 17. Find the missing second operation.(2)

(Total for Question 8 is 3 marks)

A function machine has the rule: input n --> [ x 4 ] --> [ +1 ] --> output. Write down an expression, in terms of n, for the output.

(Total for Question 9 is 2 marks)

A function machine has two steps: input --> [ x 5 ] --> [ +2 ] --> output.

(a)Write down the inverse function machine (reverse the order and use the inverse operations).(2)

(b)Use your inverse function machine to find the input when the output is 27.(2)

(Total for Question 10 is 4 marks)

A coach company uses the function machine below to work out the total cost, C (in pounds), for a group booking with p passengers:
p --> [ x 2.50 ] --> [ +1.20 ] --> C

(a)Work out the total cost for a group of 6 passengers.(2)

(b)Another group paid a total cost of GBP 26.20. Work out how many passengers were in the group.(3)

(Total for Question 11 is 5 marks)

A sequence is generated using the function machine: term --> [ x 2 ] --> [ -3 ] --> next term. The first term is 5.

(a)Work out the second term.(1)

(b)Work out the third term.(2)

(Total for Question 12 is 3 marks)

A function machine has three steps: input --> [ +1 ] --> [ x 5 ] --> [ -2 ] --> output.

(a)Work out the output when the input is 3.(1)

(b)Work out the output when the input is -2.(2)

(c)The output is 13. Find the input.(3)

(Total for Question 13 is 6 marks)

The equation 3x+7=25 can be shown as a function machine: x --> [ x 3 ] --> [ +7 ] --> 25. Use the function machine, working backwards, to find the value of x.

(Total for Question 14 is 2 marks)

Machine A: input --> [ x 2 ] --> [ +3 ] --> output.
Machine B: input --> [ +3 ] --> [ x 2 ] --> output.
For an input of 4, work out the output of Machine A and the output of Machine B, and state whether the two machines give the same output.

(Total for Question 15 is 3 marks)

A function machine has two steps: input --> [ x 1.5 ] --> [ -2.5 ] --> output.

(a)Work out the output when the input is 10.(2)

(b)The output is 5. Find the input.(3)

(Total for Question 16 is 5 marks)

A function machine has the rule: input --> [ x k ] --> [ +4 ] --> output, where k is a number. When the input is 3, the output is 19. Find the value of k.

(Total for Question 17 is 3 marks)

A plumber uses the function machine below to work out the total charge, C (in pounds), for a job lasting h hours:
h --> [ x 30 ] --> [ +45 ] --> C

(a)Work out the total charge for a job that takes 3 hours.(2)

(b)A job cost a total of GBP 165. Work out how many hours the job took.(3)

(Total for Question 18 is 5 marks)

Two function machines are connected. Machine 1: n --> [ x 2 ] --> [ +1 ] --> result. The result from Machine 1 becomes the input for Machine 2. Machine 2: result --> [ x 3 ] --> [ -4 ] --> final output.

(a)Work out the final output when n = 2.(1)

(b)Find the value of n that gives a final output of 29.(3)

(Total for Question 19 is 4 marks)

Mark scheme · 2.8 Function Machines

Question 1

(a) B1 12 cao
(a) Answer: 12
(b) B1 28 cao
(b) Answer: 28
(c) B1 -8 cao
(c) Answer: -8

Question 2

(a) B1 12 cao
(a) Answer: 12
(b) B1 18 cao
(b) Answer: 18
(c) M1 2 seen (correct value after the first step, -3+5)
(c) A1 4 cao
(c) Answer: 4

Question 3

(a) B1 16 cao
(a) Answer: 16
(b) B1 4 cao
(b) Answer: 4
(c) B1 6 cao
(c) Answer: 6

Question 4

B1 A cao
Answer: A

Question 5

(a) B1 -4 cao
(a) Answer: -4
(b) B1 2 cao
(b) Answer: 2
(c) B1 11 cao
(c) Answer: 11
(d) B1 -7 cao
(d) Answer: -7

Question 6

(a) M1 10 seen (reverse the division: 5 x 2)
(a) A1 3 cao
(a) Answer: 3
(b) M1 2 seen (reverse the division: 1 x 2)
(b) A1 -5 cao
(b) Answer: -5

Question 7

(a) B1 A cao
(a) Answer: A
(b) B1 B cao
(b) Answer: B
(c) B1 A cao
(c) Answer: A

Question 8

(a) B1 multiply by 5 oe (x5)
(a) Answer: x5 (multiply by 5)
(b) M1 8 or 20 seen (correct value after the x2 step for either pair)
(b) A1 subtract 3 oe (-3), ft
(b) Answer: -3 (subtract 3)

Question 9

M1 4n seen
A1 4n+1 oe cao
Answer: 4n+1

Question 10

(a) M1 correct inverse operations identified: -2 and /5
(a) A1 correct order stated: output --> [ -2 ] --> [ /5 ] --> input oe
(a) Answer: output --> [ -2 ] --> [ /5 ] --> input
(b) M1 25 seen (27-2)
(b) A1 5 cao
(b) Answer: 5

Question 11

(a) M1 15.00 seen (6 x 2.50)
(a) A1 16.20 cao (accept 16.2)
(a) Answer: GBP 16.20
(b) M1 25.00 seen (26.20-1.20)
(b) M1 complete method: 25.00 / 2.50
(b) A1 10 cao
(b) Answer: 10 passengers

Question 12

(a) B1 7 cao
(a) Answer: 7
(b) M1 correct method using the second term (ft): 7x2, then -3
(b) A1 11 cao
(b) Answer: 11

Question 13

(a) B1 18 cao
(a) Answer: 18
(b) M1 -5 seen (correct value after the first two steps)
(b) A1 -7 cao
(b) Answer: -7
(c) M1 15 seen (reverse the last step: 13+2)
(c) M1 3 seen (reverse the second step: 15/5)
(c) A1 2 cao (reverse the first step: 3-1)
(c) Answer: 2

Question 14

M1 18 seen (25-7)
A1 6 cao
Answer: 6

Question 15

M1 11 seen (Machine A: 4x2=8, 8+3=11)
M1 14 seen (Machine B: 4+3=7, 7x2=14)
A1 correct conclusion: not the same (11 is not equal to 14), oe with both values shown
Answer: Machine A = 11, Machine B = 14; not the same

Question 16

(a) M1 15 seen (10 x 1.5)
(a) A1 12.5 cao
(a) Answer: 12.5
(b) M1 7.5 seen (5+2.5)
(b) M1 complete method: 7.5 / 1.5
(b) A1 5 cao
(b) Answer: 5

Question 17

M1 3k+4=19 or equivalent equation formed
M1 3k=15 (correct rearrangement)
A1 k=5 cao
Answer: k=5

Question 18

(a) M1 90 seen (3 x 30)
(a) A1 135 cao (accept GBP 135)
(a) Answer: GBP 135
(b) M1 120 seen (165-45)
(b) M1 complete method: 120 / 30
(b) A1 4 cao
(b) Answer: 4 hours

Question 19

(a) B1 11 cao
(a) Answer: 11
(b) M1 11 seen (reverse Machine 2: (29+4)/3)
(b) M1 5 seen (reverse Machine 1: (11-1)/2)
(b) A1 n=5 cao
(b) Answer: 5

Question 19

4 marks

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Function Machines - Worksheets, Questions and Revision

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Question 9

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Question 12

Question 13

Question 14

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Question 16

Question 17

Question 18

Question 19

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Question 2

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Question 4

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Question 12

Question 13

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Question 15

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Question 17

Question 18

Question 19