Numeracy Higher June 2018 Unit 1 Q5
5. Michelle owns a café.
She stacks coffee mugs as shown in the diagram below.
Michelle measures the height of each coffee mug as 12 cm, correct to the nearest centimetre.
Each stacked coffee mug creates 4 cm extra height, correct to the nearest centimetre.
Diagram not drawn to scale
Michelle knows that the vertical height between two shelves is exactly 39 cm, as shown below.
Diagram not drawn to scale
Can Michelle be certain that she will be able to place one stack of 7 coffee mugs between the two shelves?
Give a reason for your answer.
You must show all your working. [5]
| Scheme | Marks | Comments |
|---|---|---|
| (Maximum cup height )12.5 (cm) AND (Maximum gap) 4.5 (cm) OR For use of 12.43 to 12.499... AND 4.43 to 4.499... | B1 | For sight of 12.5 and 4.5 (ignoring any least measures given) |
| (Maximum height of 7 coffee mugs is) 12.5 + 6 × 4.5 | M2 | FT ‘their 12.5’ and ‘their 4.5’ provided in ranges >12 to 12.5 and >4 to 4.5 respectively Award M1 only (A0) for 12.5 + 7× 4.5 (A0) |
| (=) 39.5 (cm) | A1 | |
| Conclusion or reason, e.g. ‘(as 39.5 cm > 39 cm) Michelle cannot be certain the mugs will fit’ | E1 | Depends on at least 2 marks previously awarded FT ‘their 39.5’ irrespective if <39 or >39 An unsupported 39.5 is no marks as no working shown |