Higher June 2022 Paper 2 Q18
18 \(PQR\) and \(QRS\) are triangles.
Calculate the length of \(QS\).
Give your answer correct to 3 significant figures.
You must show all your working. (4)
| Answer | Mark | Mark scheme |
|---|---|---|
| 7.63 | M1 | for process to use the cosine rule to find \(QR\), eg \((QR^2 =)\ 11^2 + 9.4^2 - 2 \times 11 \times 9.4 \cos(27)\) |
| M1 | for correct order of operations, eg \(QR = \sqrt{209.36 - 206.8 \times \cos 27}\ \ (= 5(.009\ldots))\) or \(QR = \sqrt{25(.09...)}\) or \(\sqrt{25.1}\) | |
| M1 | (dep on M1) for process to use the sine rule, eg \(\dfrac{QS}{\sin 88} = \dfrac{[QR]}{\sin 41}\) oe or \(QS = \dfrac{[QR] \times \sin 88}{\sin 41}\ (= 7.631...)\) oe | |
| A1 | for answer in range 7.61 to 7.632 |
Additional guidance
[\(QR\)] could be written as “5.009…” or could be a different figure, as long as this is clearly associated with the side \(QR\)
If an answer is given in the range in working and then rounded incorrectly award full marks.
Award 0 marks for a correct answer with no (or incorrect) supportive working