Higher November 2022 Paper 2 Q23
23 A race is measured to have a distance of 10.6 km, correct to the nearest 0.1 km.
Sam runs the race in a time of 31 minutes 48 seconds, correct to the nearest second.
Sam’s average speed in this race is \(V\) km/hour.
By considering bounds, calculate the value of \(V\) to a suitable degree of accuracy.
You must show all your working and give a reason for your answer. (5)
| Answer | Mark | Mark scheme |
|---|---|---|
| 20 | B1 | stating bound, eg 10.65 or 10.55 or 31 min 48.5sec or 31 min 47.5sec or 1908.5sec or 1907.5sec |
| P1 | (dep on B1) for a correct bound for time in hours, eg 0.5301(38…) or 0.5298(61…) Or a correct process to find one bound for speed in km per minute, eg [UB of S] = [UB of D]÷[LB of T] or [LB of S] = [LB of D]÷[UB of T] or a correct process to find one bound for speed in km per second, eg [UB of S] = [UB of D]÷[LB of T] or [LB of S] = [LB of D]÷[UB of T] | |
| P1 | (dep on P1) for correct process to find one bound for speed in km per hour, eg [UB of S] = [UB of D]÷ 0.5298(61…) or [LB of S] = [LB of D]÷ 0.5301(38…) OR Correct process to convert a bound for speed in km per minute to km per hour eg [UB of S] = [UB of D]÷[LB of T] × 60 or [LB of S] = [LB of D]÷[UB of T] × 60 OR Correct process to convert a bound for speed in km per second to km per hour eg [UB of S] = [UB of D]÷[LB of T] × 60 × 60 or [LB of S] = [LB of D]÷[UB of T] × 60 × 60 | |
| A1 | for both correct bounds from correct working, 20.099… and 19.900… | |
| C1 | for 20 correct to 2 significant figures as both bounds agree |
Additional guidance
Bound rounded or truncated to 4 dp
Where \(10.6 \lt \) [UB of D] \(\leqslant 10.65\) and 31 min 47.5 sec \(\leqslant\) [LB of T] \(\lt \) 31 min 48 sec
Or \(10.55 \leqslant\) [LB of D] \(\lt 10.6\) and 31 min 48 sec \(\lt \) [UB of T] \(\leqslant\) 31 min 48.5 sec
Where \(10.6 \lt \) [UB of D] \(\leqslant 10.65\) and 1907.5 sec \(\leqslant\) [LB of T] \(\lt \) 1908 sec
Or \(10.55 \leqslant\) [LB of D] \(\lt 10.6\) and 1908 sec \(\lt \) [UB of T] \(\leqslant\) 1908.5 sec
Time used in hours
Where \(10.6 \lt \) [UB of D] \(\leqslant 10.65\) and 31 min 47.5 sec \(\leqslant\) [LB of T] \(\lt \) 31 min 48 sec
Or \(10.55 \leqslant\) [LB of D] \(\lt 10.6\) and 31 min 48 sec \(\lt \) [UB of T] \(\leqslant\) 31 min 48.5 sec
Where \(10.6 \lt \) [UB of D] \(\leqslant 10.65\) and 1907.5 sec \(\leqslant\) [LB of T] \(\lt \) 1908 sec
Or \(10.55 \leqslant\) [LB of D] \(\lt 10.6\) and 1908 sec \(\lt \) [UB of T] \(\leqslant\) 1908.5 sec
Figures rounded or truncated to 3 sf or better