Higher June 2024 Unit 2 Q20
20. In the diagram below, \(AB\) = 13 cm, \(AD\) = 17 cm, \(BC\) = 19 cm and \(DC\) = 11 cm.
Diagram not drawn to scale
Calculate the size of angle \(x\).
You must show all your working. [6]
From the formula list: In any triangle \(ABC\): Cosine rule \(a^2 = b^2 + c^2 - 2bc\cos A\)
| Scheme | Marks | Comments | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| Complete strategy to calculate \(x\), e.g. first an attempt to use the cosine rule to calculate BD and then an attempt to use the cosine rule by rearrangement to calculate \(x\) using BD. | S1 | Stating the formulae is insufficient. Both stages must be seen. If many attempts are offered for both stages and they are not clearly identified as being used to evaluate BD and then \(x\), then mark final attempt. | |||||||||
| (BD2 =) 132 + 172 – 2×13×17×cos43 | M1 | Allow an alternative complete correct method for M1. | |||||||||
| (BD2 =) 134·7(…) OR (BD =) 11·6(…cm) | A1 |
| |||||||||
| \(\cos x = \dfrac{11^2 + 19^2 - 11{\cdot}6(\ldots)^2}{2 \times 11 \times 19}\) | M2 | FT ‘their stated or derived BD’, provided 8 < ‘their BD’ < 30 M1 for 11·6(…)2 = 112 + 192 – 2×11×19×cos \(x\) Allow an alternative complete correct method for M2. | |||||||||
| (\(x\) =) 33·8(…°) | A1 | Accept an answer which rounds to 33·8(°) Allow an answer of 34(°) from correct working. An answer of 36(·039…) from BD=12 is: S1M1A0M2A1. Note: The first A1 is only withheld if 12 (rounded from 11.6) is used in the subsequent cosine rule to find the angle \(x\) AND only if the work is worthy of any further marks. |