Worksheets · Foundation and Higher

Signed arithmetic and number lines

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

Question 1Non-calculator · 1 mark
(a) Write down the smallest of these numbers: $-1.4$ , $-7$ /5, $-1.45$ , $-1.04.$ (1)
Question 2Non-calculator · 5 marks
At 06:00 the temperature is $-9^\circ$ C. It rises by $5^\circ$ C, then falls by $4^\circ$ C.
(a) Work out the final temperature. (3)
(b) How many degrees must the temperature rise to reach $5^\circ$ C? (2)
Question 3Non-calculator · 6 marks
The mean of six temperatures is $-1.5\,^{\circ}\text{C}$ . Five of the temperatures, in $^{\circ}\text{C}$ , are $-6.5$ , $2$ , $-4$ , $3.5$ and $-1$ .
(a) Work out the sixth temperature. (3)
(b) A seventh temperature is added to the six. The mean of all seven temperatures is a whole number, and the range of all seven is the same as the range of the six. Find all the possible values of the seventh temperature. (3)

Answers and marks

(a) $-1.45$

(a) $-8$ °C

(b) $13$ °C

(a) $-3\,^{\circ}\text{C}$

(b) $-5$ and $2$

P1 Finding the range of the six, $10$ , and so the limits $-6.5 \le t \le 3.5$ .
P1 Writing the total of seven as $-9 + t$ and requiring it to be a multiple of 7.
A1 Both $-5$ and $2$ , and no other values.

Signed arithmetic and number lines

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