Higher November 2020 Paper 2 Q8
8 The diagram shows an isosceles triangle.
Diagram NOT accurately drawn
Work out the area of the triangle.
(4)
| Scheme | Marks |
|---|---|
| \(8.5^2 - (8 \div 2)^2\) (= 56.25) or \(\cos x = \dfrac{4}{8.5}\) oe | M1 |
| \(\sqrt{\text{“}56.25\text{”}}\) (= 7.5) or \(x = \cos^{-1}\left(\dfrac{4}{8.5}\right)\) (= 61.927...) oe | M1 |
| 8 × “7.5” ÷ 2 oe or 0.5 × 8 × 8.5 × sin “61.927...” | M1 |
| Correct answer scores full marks (unless from obvious incorrect working) Answer: 30 | A1 |
| (4) | |
| (4 marks) |
Notes
M1: or eg \(\cos A = \dfrac{8^2 + 8.5^2 - 8.5^2}{2 \times 8 \times 8.5}\)
M1: or eg \((A =)\cos^{-1}\left(\dfrac{8^2 + 8.5^2 - 8.5^2}{2 \times 8 \times 8.5}\right)\) (61.927...)
(other angle = 56.144...)
M1: or eg 0.5 × 8.5 × 8 × sin “61.927...” oe