Higher November 2024 Paper 1 Q16
16 \(OAPB\) is a sector of a circle, centre \(O\)
Diagram NOT accurately drawn
Angle \(AOB = 50^\circ\)
Area of triangle \(OAB = 120\) cm2
Work out the area of the sector \(OAPB\)
Give your answer correct to 3 significant figures.
(4)
| Scheme | Marks |
|---|---|
\(120 = \dfrac{1}{2} \times a \times b \times \sin 50\) oe or \(\dfrac{120 \times 2}{\sin 50}\) oe or \(120 = \dfrac{1}{2} \times 2x\sin 25 \times x\cos 25\) oe or \(\dfrac{120 \times 2}{2 \times \sin 25 \times \cos 25}\) oe or 313(.2977494) | M1 |
\((\textit{radius} =)\sqrt{\dfrac{120 \times 2}{\sin 50}}\) (= 17.7(0021891)) oe or \((\textit{radius} =)\sqrt{\dfrac{120 \times 2}{2 \times \sin 25 \times \cos 25}}\) (= 17.7(0021891)) oe or \((\textit{radius} =)\sqrt{313(.2977494)}\) (= 17.7(0021891)) | M1 |
| (area of \(OAPB\) =) \(\pi \times \text{“}17.7\text{”}^2 \times \dfrac{50}{360}\) oe | M1 |
| Correct answer scores full marks (unless from obvious incorrect working) Answer: 137 | A1 |
| (4) | |
| (4 marks) |
Notes
M1: for a correct equation for \(a \times b\) or \(r^2\) (allow any letters for \(a\) or \(b\))
or
for a correct expression for \(a \times b\) or \(r^2\)
or
for 313(.2977494)
M1: for a correct rearrangement to find the radius
or
for square rooting 313(.2977494)
or
for 17.7(0021891))
A1: awrt 137