Higher June 2024 Paper 1 Q19
19 Here is quadrilateral \(ABCD\)
Diagram NOT accurately drawn
Work out the value of \(x\)
Give your answer correct to 3 significant figures.
(5)
| Scheme | Marks |
|---|---|
| \(\dfrac{(BD)}{\sin 62} = \dfrac{12.8}{\sin 40}\) oe or | M1 |
| \((BD =)\dfrac{12.8}{\sin 40} \times \sin 62\) (= 17.5(82…)) | M1 |
| \(\text{``}{17.5(82...)}\text{''}^2 = 13.4^2 + 15.2^2 - 2 \times 13.4 \times 15.2 \times \cos x\) or 309(.139) = 179(.56) + 231(.04) – 407(.36)cos\(x\) oe | M1 |
\((\cos x =)\dfrac{13.4^2 + 15.2^2 - \text{``}{17.5(82...)}\text{''}^2}{2 \times 13.4 \times 15.2}\) oe or \((\cos x =)\dfrac{179(.56) + 231(.04) - 309(.139...)}{407(.36)}\) oe or \((\cos x =)\dfrac{410(.6) - 309(.139...)}{407(.36)}\) oe or \((\cos x =)\, 0.247 - 0.256\) oe | M1 |
| Working not required, so correct answer scores full marks (unless from obvious incorrect working) Answer: 75.6 | A1 |
| (5) | |
| (5 marks) |
Notes
M1: for correct use of sine rule for \(BD\)
M1: for finding \(BD\) (truncated or rounded)
M1: for correct use of cosine rule
M1: for a correct rearrangement of \(\cos x\)
A1: accept 75.1 – 75.7
M2 for (first two M1 marks)
\((CD =)\dfrac{12.8}{\sin 40} \times \sin 78\)
(= 19.4(781…)) and
\((BD =)\dfrac{\text{``}{19.4(781...)}\text{''}}{\sin 78} \times \sin 62\)
(= 17.5(82…))