Higher June 2023 Paper 6 Q12
12 A box contains 200 matches, correct to the nearest ten matches.
(a) Complete the error interval for \(n\), the number of matches in the box.\[\ldots\ldots \leqslant n \leqslant \ldots\ldots\] [2]
(b) The box is a cuboid with
- length 7 cm, correct to the nearest cm
- width 5 cm, correct to the nearest cm
- volume 248 cm3, correct to the nearest cm3.
Show that the smallest possible height of the box is 6 cm. [3]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| 195 [\(\leqslant n \leqslant\)] 204 | 2 | B1 for 195 or 204 in correct position or for both 195 and 204 but in wrong position | Do not accept < 205 where \(\leqslant\) has been crossed out and replaced |
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| \(\frac{247.5}{7.5 \times 5.5} = 6\) | 3 | Max 2 marks if answer is incorrect B1 for 247.5 B1 for 7.5 and 5.5 M1 for \(\frac{their\ 247.5}{their\ 7.5 \times their\ 5.5}\) where \(247.5 \leqslant their\ 247.5 \leqslant 248.5\), \(6.5 \leqslant their\ 7.5 \leqslant 7.5\) and \(4.5 \leqslant their\ 5.5 \leqslant 5.5\) | May be done in stages. 6 must not come from a rounded answer or other wrong working. If choice, mark the bounds used in the calculation. If no calculation, then 0 each time upper and lower bounds are both given 7.5 × 5.5 × 6 = 247.5 scores just the second mark. If they then explicitly state that 247.5 is the lower bound of 248 they also get the first mark but not for “247.5 rounds to 248” |