Higher June 2023 Paper 2 Q16
16.
Diagram not drawn to scale
The diagram shows a sector, \(ABD\), of a circle with centre \(D\) and a triangle, \(BCD\).
\(A\hat{D}C\) is a right angle.
Show that the area of \(ABCD\) is 150 m2, correct to 3 significant figures. [5]
| Scheme | Marks | Comments |
|---|---|---|
| (area sector =) \(\dfrac{62}{360} \times \pi \times 15^2\) | M1 | |
| 121.7(3...) | A1 | CAO; accept \(\dfrac{155}{4}\pi\); allow 122 |
| (area triangle =) \(\dfrac{1}{2} \times 15 \times 8 \times \sin(90 - 62)\) | M1 | |
| 28.17 or 28.168(2....) | A1 | FT ‘their derived 28°’ but must use 15 and 8 m; allow 28 or 28.2 |
| A sum of correct areas that rounds to 150 e.g. 121.7(3...) + 28.16(8...) = 149.9... (=150) | B1 | CAO; sight of 149.9(0…) implies 5 marks providing M1 M1 awarded Allow e.g. 122 + 28.2 = 150.2 but not 122 + 28 = 150 |
| (5) |