Worksheets · Foundation and Higher

Input/output and inverse number machines

3 exam-style questions. Answers and the mark for each step are on the last page.

Question 1Calculator · 2 marks
(a) A function machine multiplies an input by 4, then subtracts 7. Its output is 21. What was the input? (2)
1. 3.5
2. 77
3. 7
4. 28
Question 2Non-calculator · 4 marks
A number machine multiplies by 3 then subtracts 7.
(a) Find the input when the output is 14. (2)
(b) Write the inverse machine as a sequence of operations. (2)
Question 3Non-calculator · 4 marks
A number machine: input $\rightarrow$ square $\rightarrow$ multiply by 2 $\rightarrow$ subtract 8 $\rightarrow$ output.
(a) The output is 64. Find all the possible inputs. (2)
(b) Explain why the output can never be $-10$ . (2)

Answers and marks

(a) 7

(a) $7$

(b) Add 7, then divide by 3.

(a) $6$ and $-6$

P1 Reaching 36 by undoing the subtraction and the multiplication in reverse order.
A1 Both $6$ and $-6$ .

(b) The square is never negative, so $2x^2 - 8 \ge -8$ .

B1 Writing the output as $2x^2 - 8$ or saying the smallest output is $-8$ .
C1 Explaining that a square cannot be negative, so the output cannot be less than $-8$ .

Input/output and inverse number machines

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