4MA0 Higher June 2014 Paper 3 Q22
22 The diagram shows a metal plate.
Diagram NOT accurately drawn
The metal plate is made from a sector OAB of a circle, centre O, and a triangle OCB.
Angle \(AOB = 65^\circ\) Angle \(OCB = 35^\circ\)
\(OA = OB = 8\) cm.
AOC is a straight line.
(a) Calculate the length of BC.
Give your answer correct to 3 significant figures. (3)
Give your answer correct to 3 significant figures. (3)
(b) Calculate the total area of the metal plate.
Give your answer correct to 3 significant figures. (4)
Give your answer correct to 3 significant figures. (4)
| Scheme | Marks |
|---|---|
| \(\dfrac{8}{\sin 35} = \dfrac{BC}{\sin(180 - 65)}\) or \(\dfrac{\sin 35}{8} = \dfrac{\sin(180 - 65)}{BC}\) | M1 |
| \((\text{“}BC\text{”} =)\ \dfrac{8\sin\text{“}115\text{”}}{\sin 35}\) oe | M1 |
| 12.6 | A1 |
| (3) |
Notes
M1: for correct substitution into the sine rule
Condone use of 65 instead of 115
M1: dep
A1: awrt 12.6
| Scheme | Marks |
|---|---|
| 0.5 x 8 x “12.6” sin (180 – 115 – 35) oe (= 25.28..) | M1ft |
| 65/360 x \(\pi\) x \(8^2\) (=36.30) | M1 |
| “25.28” + “36.30” | M1 |
| 61.6 | A1 |
| (4) | |
| (7 marks) |
Notes
M1ft: 0.5 x 8 x “12.6” sin (180 – 115 – 35) oe or 25.2 – 25.3
“12.6” must be from clear final answer from (a) to allow ft
M1: Accept \(\frac{65}{360} \times 201\ldots\) or \(\frac{104\pi}{9}\) oe or 36.3... (correct to the first 3 SF)
M1: dep on M2
A1: 61.5 - 61.6