Numeracy Higher November 2020 Unit 2 Q4
4. Ruth measures the lengths of 5 square pictures.
The measurements she records are as follows.
21 cm 22 cm 23 cm 24 cm 26 cm
Each of these measurements is correct to the nearest cm.
She plans to display all 5 pictures in a line, edge to edge, on a shelf of a bookcase.
The length of the shelf is 120 cm, correct to the nearest 5 cm.
Show that the shelf could be 1 cm too short to display all 5 of these pictures.
You must show all your working. [4]
| Scheme | Marks | Comments |
|---|---|---|
| Allow 0.4999(....) for 0.5 throughout, must clearly be a recurring 9 digit | ||
| (Greatest total length of pictures) 21.5 + 22.5 + 23.5 + 24.5 + 26.5 or 21 + 22 + 23 + 24 + 26 + 5 × 0.5 | M1 | Allow for sight of upper bounds of pictures: 21.5(cm), 22.5(cm), 23.5(cm), 24.5(cm), 26.5(cm) |
(=) 118.5 (cm) | A1 | |
| (Lower bound of shelf) 117.5(cm) | B1 | |
| Difference of 1 cm stated or sight of 118.5 – 117.5 = 1(cm) | B1 | CAO from use of appropriate correct upper bounds and lower bound Accept FT from clearly recurring 9s, as 0.9999999…. is considered as equivalent to 1 Accept 117.5 – 118.5 = -1(cm) Allow 117.5 – 118.5 = 1(cm difference) If no marks, award SC1 for correct sum of ‘their upper bounds’ provided they are all increased but less than 0.5cm greater than the measurements given in the question |