Higher November 2022 Paper 4 Q11
11 The diagram shows two right-angled triangles that are joined together.
All measurements are given accurate to 2 significant figures.
Not to scale
Work out the value of \(x\).
Give your answer correct to an appropriate degree of accuracy.
You must show your working. [6]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| 9.6 with correct working | 6 | M5 for \(\sqrt{8.3^2 + (5.4\tan 42)^2}\) OR M2 for 5.4 × tan 42 oe or M1 for tan 42 = \(\frac{opp}{5.4}\) oe A1 for 4.8[6…] or 4.9 and M2 for \(\sqrt{8.3^2 + (their\ 4.8[6\ldots])^2}\) or M1 for \(8.3^2 + (their\ 4.8[6\ldots])^2\) If 0, 1 or 2 scored, instead award SC3 for answer 9.6 with no or insufficient working If 0 or 1 scored, instead award SC2 for answer 9.619… or 9.62 with no or insufficient working If 0 scored, instead award SC1 for 4.8[6…] or 4.9 with no or insufficient working | “Correct working” requires evidence of at least M1 M1 or M2 and also accept 2sf numbers 4.8[6…] or 4.9 can imply M2 if M1 given Alternative method (sine rule): M2 for \(\frac{5.4 \times \sin 42}{\sin(their\ 48)}\) oe or M1 for \(\frac{x}{\sin 42} = \frac{5.4}{\sin(their\ 48)}\) oe 9.619… or 9.6[2] can imply M2 if M1 awarded Allow full and correct equivalent trig. methods to score M2 in both triangles e.g. using the other angle in the first triangle, i.e. their 48 |