Higher June 2022 Paper 4 Q6

OCRHigherCurrent spec5 marksCompound Measures

6 A machine can dig, on average, 2 cm of tunnel each minute.
It operates 24 hours each day.

(a) Work out how many days it should take to dig a tunnel of length 3.5 km.
Give your answer to the nearest day. [4]

(b) The machine actually digs an average of 2.5 cm of tunnel each minute for most of the time and an average of 1.5 cm each minute for the rest of the time.
How would this affect your answer to part (a)? [1]

Mark scheme (a)

Answer	Marks	Part marks and guidance
122	4	B3 for 121.5[…] leading to an answer 121[.5…] or 1215.2[…] leading to an answer 1215 or 12.15[…] leading to an answer 12	ignore any units throughout
		OR
		M3 for \(\frac{3.5 \times 1000 \times 100}{2 \times 60 \times 24}\) oe	e.g. 3500 ÷ 28.8 M1 M1 may be implied by 0.0288
		OR
		M1 for correct time conversion to a day e.g. [2×] 60×24	M1 may be implied by e.g. 1440 or 14.4 or 0.0144 or 2880 or 28.8
		and M1 for one distance km to cm or one distance cm to km or two distances to metres	M1 may be implied by e.g. 0.02 and 28.8 or 3500 and (0.02 or 28.8) or 0.000 02 or 350 000
		and M1 for distance divided by rate e.g. \(\frac{3.5 \times 100 \times 100}{2 \times 60 \times 24}\) to a maximum of M2	M1 may be implied by e.g. \(\frac{\textit{figs}35}{\textit{figs}288}\) or \(\frac{3.5 \times 1000 \times 100}{2 \times 60 \times 60 \times 24}\) or figs 175

Mark scheme (b)

Answer	Marks	Part marks and guidance
It will take less time [than their 122 days]	1		accept any correct explanation (see appendix) and select best comment if more than one providing they do not conflict

Appendix: exemplar responses for Q6(b)

Response	Mark
it will take less time [than their 122 days]	1
my answer to part (a) will decrease	1
it will take longer on some parts and less time on other parts	0
it will increase	0
it will change the time	0
it will not affect my answer	0
it will take 4 days not 5 days (incorrect statement)	0
it make it faster to dig the tunnel	0