Higher November 2020 Paper 3 Q29
29 A shape is made by joining triangle ABC to a semicircle with diameter AC.
Not drawn accurately
Work out the total area of the shape. [5 marks]
| Answer | Mark | Comments |
|---|---|---|
| \(0.5 \times 8 \times 10 \times \sin 114\) or [36.5, 36.542] | M1 | oe |
| \(8^2 + 10^2 - 2 \times 8 \times 10 \times \cos 114\) or [229, 229.1] | M1 | oe eg \(164 - 160 \times \cos 114\) |
| \(\sqrt{8^2 + 10^2 - 2 \times 8 \times 10 \times \cos 114}\) or [15.1, 15.14] or [7.55, 7.57] | M1dep | oe dep on 2nd M1 |
| \(0.5 \times \pi \times (0.5 \times \text{their } [15.1, 15.14])^2\) or \(0.5 \times \pi \times \text{their } [7.55, 7.57]^2\) or [89.49, 90.03] | M1dep | dep on 2nd and 3rd M1 |
| [125.99, 126.572] | A1 |
Additional guidance
Diameter must come from using the cosine rule
2nd mark is not dependent on the first