Higher November 2021 Paper 1 Q18
18
(a) Here is a triangle.
Not drawn accurately
Give a reason why the length of side \(AB\) cannot be 35 m [1 mark]
(b) Here is a different triangle.
Not drawn accurately
Leah tries to use the sine rule to work out the size of angle \(x\).
Here are the first two lines of her working.
\(\dfrac{x}{\sin 31} = \dfrac{54}{\sin 72}\)
\(x = \dfrac{54 \sin 31}{\sin 72}\)
What error has she made in this working? [1 mark]
| Answer | Mark | Comments |
|---|---|---|
| Correct explanation | B1 | eg 35 is more than \(17 + 13\) |
Additional guidance
| It is more than 30 | B1 |
| \(AB\) cannot be more than \(AC + BC\) | B1 |
| \(AC + BC\) only add up to 30 | B1 |
| The triangle inequality | B1 |
| \(17 + 13\) is only 30 | B1 |
| \(17 + 13\) is 30 | B0 |
| It would be too long | B0 |
| Answer | Mark | Comments |
|---|---|---|
| Correct explanation | B1 | eg (it should be) \(\dfrac{31}{\sin x}\) |
Additional guidance
| \(x\) and 31 should be swapped | B1 |
| She has used 31 as an angle | B1 |
| She has used \(x\) as a length | B1 |
| It should be \(\dfrac{\sin x}{31} \left(= \dfrac{\sin 72}{54}\right)\) | B1 |