Higher November 2021 Paper 6 Q9
9 The width, \(w\), of a kitchen cupboard is 60 cm, correct to the nearest centimetre.
(a) Complete the error interval for the width, \(w\).\[\ldots\ldots \leqslant w < \ldots\ldots\]
[2]
(b) Six of these kitchen cupboards are to be placed side by side along a kitchen wall.
The wall is 363 cm long, correct to the nearest centimetre.
The wall is 363 cm long, correct to the nearest centimetre.
(i) Show that the six cupboards may not fit along the wall. [3]
(ii) Find the upper bound of the space remaining if six cupboards do fit along the wall. [3]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| 59.5 60.5 | 2 | B1 for either one correct or both correct but reversed | |
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| Accept any correctly matched wall and 6 × cupboard where values quoted satisfy: wall < 6 × cupboard where 362.5 ⩽ wall < 363 and 362.5 < 6 × cupboard ⩽ 363 OR wall ÷ 6 < cupboard where 362.5 ⩽ wall < 363 and \(60.41\dot{6}\) to 60.42 < cupboard ⩽ 60.5 OR wall ÷ cupboard < 6 where 362.5 ⩽ wall < 363 and \(60.41\dot{6}\) to 60.42 < cupboard ⩽ 60.5 | 3 | B1 for 362.5 ⩽ wall value < 363 B1 for 362.5 < 6 × cupboard value ⩽ 363 or 60.416 to 60.42 < cupboard value ⩽ 60.5 | Example: [lower bound of] wall is 362.5 [upper bound of] cupboard is 60.5 362.5 ÷ 60.5 = 5.9[9…] < 6 |
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| 6.5 | 3 | M2 for 363.5 – 6 × their lower bound of cupboard or 363.5 – 357 or M1 for [upper bound of wall =] 363.5 or for 6 × their lower bound of cupboard or [6 cupboards =] 357 | |