Worksheets · Foundation and Higher

Operation order, inverses and reciprocals

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

Question 1Non-calculator · 1 mark
(a) Work out 18 $-$ 2 $\times$ 5. (1)
1. 80
2. 8
3. 28
4. $-8$
Question 2Non-calculator · 4 marks
Number machine A adds 2, then multiplies by 3. Number machine B multiplies by 3, then adds 2.
(a) Find the difference between the outputs when both inputs are 7. (3)
(b) Find the reciprocal of $3$ . (1)
Question 3Non-calculator · 4 marks
Kian thinks of a number. He multiplies it by $3$ , subtracts $7$ , divides the result by $4$ and then squares it. His final answer is $16$ .
(a) Find all the possible numbers Kian could have started with. (4)

Answers and marks

(a) 8

(a) $4$

(b) $\frac{1}{3}$

(a) $-3$ or $\frac{23}{3}$

P1 Undoing the square to get both $4$ and $-4$ .
P1 Undoing the division and the subtraction in reverse order, reaching $23$ or $-9$ .
P1 Dividing by 3 at the end, for either value.
A1 Both $-3$ and $\frac{23}{3}$ (or $7\frac{2}{3}$ ).

Operation order, inverses and reciprocals

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