Numeracy Higher June 2018 Unit 2 Q8
8. The Headteacher of Ysgol Castell Gwyn wants to display pictures, drawn by pupils, along one side of a corridor.
The pictures are to be in one row with no gaps between them, as shown in the diagram below.
Diagram not drawn to scale
The pictures are all square, with sides of length 15 cm, correct to the nearest 0·5 cm.
The length of the corridor wall is 2010 cm, correct to the nearest 10 cm.
Calculate the smallest number of pictures and the greatest number of pictures that can be fitted in the row. [5]
| Smallest number of pictures | Greatest number of pictures |
|---|---|
| …………………… | …………………… |
| Scheme | Marks | Comments |
|---|---|---|
| Sight of 14·75 (cm) and 15·25 (cm) OR sight of 2005 (cm) and 2015 (cm) | B1 | Accept use of \(15 \cdot 24\dot{9}\) and \(2014 \cdot \dot{9}\) throughout, but do not accept use of 15·249 and 2014·9 |
| (Smallest number of pictures =) \(\dfrac{2005}{15{\cdot}25}\) | M1 | FT ‘their 2005 cm’ provided 2000 ≤ l < 2010 cm, and ‘their 15·25 cm’ provided 15 < w ≤ 15·5 cm |
| = 131 | A1 | CAO Accept unsupported 131 provided 2005 (cm) and 15·25 (cm) seen |
| (Greatest number of pictures =) \(\dfrac{2015}{14{\cdot}75}\) | M1 | FT ‘their 2015 cm’ provided 2010 < l ≤ 2020 cm, and ‘their 14·75 cm’ provided 14·5 ≤ w < 15 cm |
| = 136 | A1 | CAO Accept unsupported 136 provided 2015 (cm) and 14·75 (cm) seen |