Higher November 2017 Paper 2 Q20
20
\(OAC\) is a sector of a circle, centre \(O\), radius 10 m.
\(BA\) is the tangent to the circle at point \(A\).
\(BC\) is the tangent to the circle at point \(C\).
Angle \(AOC = 120^\circ\)
Calculate the area of the shaded region.
Give your answer correct to 3 significant figures. (5)
| Answer | Mark | Notes |
|---|---|---|
| 68.5 | B1 | for angle \(OAB = 90^\circ\) or angle \(OCB = 90^\circ\), may be seen on diagram |
| P1 | for a process to find the length of \(AB\) or the length of \(CB\) \((= 10\sqrt{3}\) oe\()\) eg \(10 \times \tan 60^\circ\ (= 17.3\ldots)\) or the length of \(OB\ (= 20)\), eg \(10 \div \cos 60^\circ\) | |
| P1 | for a process (dep previous P1) to find the area of the triangle \(OAB\) \((= 50\sqrt{3}\) oe\()\) or area of triangle \(OCB\) \((= 50\sqrt{3}\) oe\()\) or area of kite \(OABC\) \((= 100\sqrt{3}\) oe\()\) | |
| P1 | for a process to find the area of the sector \(OAC\) e.g. \(\dfrac{1}{3} \times \pi \times 10^2\ (= 104.7\ldots)\), accept rounded or truncated to 3 significant figures or more | |
| A1 | for 68.4 − 68.6 |