# Question 5(i):

| Answer | Marks | Guidance |
|--------|-------|----------|
| sector area $= \frac{1}{2} \times 16^2 \times 0.8 = 102.4$ | M1* | Attempt area of sector using $\frac{1}{2}r^2\theta$, or equiv. Condone omission of $\frac{1}{2}$, but no other errors. Must have $r=16$, not 7. M0 if $0.8\pi$ used not 0.8 |
| triangle area $= \frac{1}{2} \times 16 \times 7 \times \sin 0.8 = 40.2$ | M1* | Attempt area of triangle using $\frac{1}{2}ab\sin C$ or equiv. Condone omission of $\frac{1}{2}$. Must have sides of 16 and 7 |
| | M1d* | Attempt area of sector $-$ area of triangle. Using $\frac{1}{2} \times 16^2 \times (0.8 - \sin 0.8)$ will get M1 M0 M0 |
| area $BDC = 62.2\ \text{cm}^2$ | A1 | Obtain 62.2, or better. Allow answers in range $[62.20, 62.25]$ if $> 3$sf |

---

# Question 5(ii):

| Answer | Marks | Guidance |
|--------|-------|----------|
| $BD^2 = 16^2 + 7^2 - 2\times16\times7\times\cos 0.8$, $BD = 12.2$ | M1 | Attempt length of $BD$ using correct cosine rule. Must be correct cosine rule. M0 if $0.8\pi$ used not 0.8. Allow if evaluated in degree mode (gives 9.00) |
| | A1 | Obtain 12.2, or better. Allow any answer rounding to 12.2, with no errors seen |
| arc $BC = 16 \times 0.8 = 12.8$ | B1 | State or imply that arc $BC$ is 12.8. Allow if $16 \times 0.8$ seen, even if incorrectly evaluated |
| per $= 12.2 + 12.8 + 9 = 34.0\ \text{cm}$ | A1 | Obtain 34, or better. Accept 34 or 34.0, or any answer rounding to 34.0 if $>3$sf |