Foundation November 2024 Paper 2 Q19
19 The diagram shows triangle \(PQR\)
Diagram NOT accurately drawn
Work out the value of \(x\)
Give your answer correct to one decimal place.
(3)
| Scheme | Marks |
|---|---|
\(\cos 43 = \dfrac{x}{8.6}\) or \(\tan 43 = \dfrac{8.6\sin 43}{x}\) or \(\sin(90 - 43) = \dfrac{x}{8.6}\) or \(\dfrac{x}{\sin(90 - 43)} = \dfrac{8.6}{\sin 90}\) or \((x^2 =)\;8.6^2 - (8.6\sin 43)^2\) or \((x^2 =)\;8.6^2 - 5.8(65\ldots)^2\) | M1 |
\((x =)\;8.6\cos 43\) or \((x =)\;\dfrac{8.6\sin 43}{\tan 43}\left(= \dfrac{\text{“}5.8(65\ldots)\text{”}}{\tan 43}\right)\) or \((x =)\;8.6\sin(90 - 43)\) or \((x =)\;\dfrac{8.6\sin 47}{\sin 90}\) or \((x =)\sqrt{8.6^2 - \text{“}5.8(65\ldots)\text{”}^2}\) | M1 |
| Correct answer scores full marks (unless from obvious incorrect working) Answer: 6.3 | A1 |
| (3) | |
| (3 marks) |
Notes
M1: a correct trig statement for \(x\) or \(QR\) or a correct Pythagoras statement for \(x^2\)
M1: a fully correct calculation to find \(x\)
(some students go straight to this and gain M2)
A1: awrt 6.3 seen even if then rounded incorrectly