Higher June 2018 Paper 2 Q21
21 Jackson is trying to find the density, in g/cm3, of a block of wood.
The block of wood is in the shape of a cuboid.
He measures
the length as 13.2 cm, correct to the nearest mm
the width as 16.0 cm, correct to the nearest mm
the height as 21.7 cm, correct to the nearest mm
He measures the mass as 1970 g, correct to the nearest 5 g.
By considering bounds, work out the density of the wood.
Give your answer to a suitable degree of accuracy.
You must show all your working and give a reason for your final answer. (5)
| Answer | Mark | Mark scheme |
|---|---|---|
| 0.43 | B1 | for one correct bound for mass or length eg 1967.5 or 1972.5 or 13.15 or 15.95 or 21.65 or 13.25 or 16.05 or 21.75 |
| P1 | for a correct process to find a bound for the volume, eg \(13.15 \times 15.95 \times 21.65\) (=454(0.925125)) or \(13.25 \times 16.05 \times 21.75\) (=462(5.409375)) | |
| P1 | for a correct process to find a bound for density, eg [mass LB] \(\div\ \text{``}462(5.409375)\text{''}\) (=0.425(367755)) where \(1965 \leqslant\) mass LB \(\lt 1970\) or [mass UB] \(\div\ \text{``}454(0.925125)\text{''}\) (=0.434(3828506)) where \(1970 \lt\) mass UB \(\leqslant 1975\) | |
| A1 | for both correct bounds, 0.425(367755) and 0.434(3828506) | |
| C1 | (dep on A1) for a correct statement on degree of accuracy e.g. UB and LB both round to 0.43 to 2 decimal places or 2 significant figures |
Additional guidance
B1: Can work in any units
P1 (volume): Accept volumes truncated or rounded to at least 3 sig fig
P1 (density): Accept densities truncated or rounded to at least 3 sig fig
A1: Accept bounds truncated or rounded to at least 3 sig fig
At this point correct units must be used
C1: Must be 0.43 not 0.4