# Question 1:

## Part (i)
| Answer | Mark | Guidance |
|--------|------|----------|
| $\text{area} = \frac{1}{2} \times 8 \times 10 \times \sin 65°$ | M1 | Attempt area of triangle using $\frac{1}{2}ab\sin\theta$. Must be correct formula including $\frac{1}{2}$. Allow if evaluated in radian mode (gives 33.1). If using $\frac{1}{2} \times b \times h$, then must be valid use of trig to find $h$ |
| $= 36.3$ | A1 | Obtain 36.3 or better. If $> 3$sf, allow answer rounding to 36.25 with no errors seen |

## Part (ii)
| Answer | Mark | Guidance |
|--------|------|----------|
| $BD^2 = 8^2 + 10^2 - 2 \times 8 \times 10 \times \cos 65°$ | M1 | Attempt use of correct cosine rule. Allow M1 if not square rooted, as long as $BD^2$ seen. Allow if evaluated in radian mode (gives 15.9). Allow if correct formula seen but then evaluated incorrectly. Allow any equiv method with valid use of trig |
| $BD = 9.82$ | A1 | Obtain 9.82 or better. If $> 3$sf, allow answer rounding to 9.817 with no errors seen |

## Part (iii)
| Answer | Mark | Guidance |
|--------|------|----------|
| $\frac{BC}{\sin 65} = \frac{8}{\sin 30}$ | M1 | Attempt use of correct sine rule (or equiv). Must get as far as attempting $BC$, not just quoting correct sine rule. Allow any equiv method with valid use of trig including attempt at any angles used. If using their $BD$ from part (ii) it must have been a valid attempt |
| $BC = 14.5$ | A1 | Obtain 14.5 or better. If $> 3$sf, allow answer rounding to 14.5 with no errors in method seen. In multi-step solutions (e.g. using 9.82) interim values may be slightly inaccurate — allow A1 if answer rounds to 14.5 |

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