Femi's till at the corner shop keeps a running rounding adjustment, shown as a marked point on the number line below. During one afternoon the adjustment ch...
Question 1 Report
Femi's till at the corner shop keeps a running rounding adjustment, shown as a marked point on the number line below. During one afternoon the adjustment changes twice, as shown by the two labelled arrows.
- Write down the adjustment shown by the starting point. (1)
- Work out the adjustment after both arrows have been applied. (1)
- Find the total distance moved along the number line by both arrows, ignoring direction. (1)
Answer Details
Curved arrows on a number line represent a jump of a given size and direction: an arrow labelled with a positive value moves right (increases the value), and one labelled with a negative value moves left (decreases it).
(a) The marked starting point on the number line is \(-3\). [1 mark]
(b) Applying both arrows in turn: \(-3 + 5 - 6 = -4\), so the adjustment after both changes is \(-4\). [1 mark]
(c) "Total distance moved, ignoring direction" means adding the sizes of the two jumps rather than their signed values: the first arrow has length 5 and the second has length 6, so the total distance is \(5 + 6 = 11\). [1 mark]
Part (c) highlights an important distinction: the net change in part (b) (a movement of only 1, from \(-3\) to \(-4\)) is much smaller than the total distance actually travelled (11), because the two arrows move in opposite directions and partly cancel out.
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