Higher November 2023 Paper 2 Q4
4. Jan has a large piece of card.
The card has width 60 cm and length 96 cm.
She uses a machine to cut identical circles out of the card.
Each circle has a radius of 6 cm.
Diagram not drawn to scale
Jan has cut five circles as shown on the diagram above.
She continues in this way to cut as many circles as possible from the card.
(a) What is the maximum number of circles Jan can cut out of the card? [1]
(b) Jan cuts out the maximum number of circles from the card.
What area of card is left over? [4]
What area of card is left over? [4]
| Scheme | Marks | Comments |
|---|---|---|
| 40 (circles) | B1 |
| Scheme | Marks | Comments |
|---|---|---|
| \(60\times96 - 40\times\pi\times6^2\) | M3 | May be seen in stages. FT their 40 provided between 6 and 50 inclusive M2 for \(40\times\pi\times6^2\) M1 for \(60\times96 - k\pi\) sight of \(\pi\times6^2\) or 113(.09..) |
| Answer in the range 1235.5 to 1238.4(cm2) | A1 | CAO. If no marks, allow M1 for sight of \(\pi\times6^2\) or 113(.09..) seen in (a) or by the diagram |
| (5) |