Higher June 2017 Paper 5 Q20
20 The diagram shows some land in the shape of a quadrilateral, ABCD.
Not to scale
AB = 3 km, AD = 5 km, CD = 12 km and angle BAC = 30°.
The land is sold for £10 million per square kilometre.
Calculate the total cost of the land. [7]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| 397.5 [million] | 7 | B6 for [area of field = ] 39.75 oe OR | For 7 marks, condone 397 500 000 For B6, accept \(\frac{159}{4}\) or better for 39.75 |
| B2 for [AC =] 13 or \(\sqrt{169}\) Or M1 for \(5^2 + 12^2\) oe | Check diagram for B marks and M marks | ||
| M2 for \(\frac{1}{2} \times 5 \times 12 + \frac{1}{2} \times 3 \times\) their \(13 \times \sin 30\) oe | their 13 must be their AC written or indicated and is not 3, 5 or 12 M2 can be given for adding costs if correct total area method is implied | ||
| Or M1 for \(\frac{1}{2} \times 5 \times 12\) oe or \(\frac{1}{2} \times 3 \times\) their \(13 \times \sin 30\) oe | [30] or [ 9.75 oe] 9.75 implies M1B1 | ||
| B1indep for sin 30 = 0.5 oe soi | |||