Higher June 2023 Paper 3 Q14
14 \(OAB\) is a triangle.
\(OBC\) is a sector of a circle, centre \(O\).
Calculate the area of \(OBC\).
Give your answer correct to 3 significant figures. (4)
| Answer | Mark | Mark scheme |
|---|---|---|
| 19.9 | P1 | for substituting into the cosine rule to find \(OB\), eg \((OB^2) = 9^2 + 6^2 - 2 \times 9 \times 6 \times \cos 35\) |
| P1 | for using correct order of operations eg \(81 + 36 - 88.46\ldots\ (= 28.5\ldots)\) | |
| P1 | for process to find the area of the sector, eg \(\dfrac{80}{360} \times \pi \times {\text{``}5.34\ldots\text{''}}^2\) | |
| A1 | for answer in the range 19.8 to 20 |
Additional guidance
May be implied by \(OB = 5.34\ldots\)
Values may be rounded or truncated.
If a correct answer within the range is shown in working but incorrectly rounded award full marks.