| Exam Board | OCR |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Sine and Cosine Rules |
| Type | Triangle with circular sector |
| Difficulty | Standard +0.3 This is a straightforward two-part question applying sine rule to find an angle, then using the arc length formula. Part (i) is standard sine rule application, and part (ii) requires recognizing that BD is an arc with radius BC=8cm and calculating perimeter as AB + AD + arc BD. The question is slightly easier than average as it's methodical application of standard formulas with clear setup and no conceptual traps. |
| Spec | 1.05b Sine and cosine rules: including ambiguous case1.05d Radians: arc length s=r*theta and sector area A=1/2 r^2 theta |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Notes |
| \(\frac{\sin A}{8} = \frac{\sin 1.7}{14}\) | M1 | |
| \(\sin A = \frac{4}{7} \sin 1.7\) | ||
| \(\angle BAC = 0.5666\) | A1 | |
| \(\angle ACB = \pi - (1.7 + 0.5666) = 0.875\) (3sf) | M1 A1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Notes |
| \(AB^2 = 8^2 + 14^2 - (2 \times 8 \times 14 \times \cos 0.875)\) | M1 | |
| \(AB = 10.79...\) | A1 | |
| \(P = 10.79 + (14 - 8) + (8 \times 0.875) = 23.8\) cm (3sf) | M1 A1 | (8) |
# Question 6:
## Part (i):
| Answer/Working | Marks | Notes |
|---|---|---|
| $\frac{\sin A}{8} = \frac{\sin 1.7}{14}$ | M1 | |
| $\sin A = \frac{4}{7} \sin 1.7$ | | |
| $\angle BAC = 0.5666$ | A1 | |
| $\angle ACB = \pi - (1.7 + 0.5666) = 0.875$ (3sf) | M1 A1 | |
## Part (ii):
| Answer/Working | Marks | Notes |
|---|---|---|
| $AB^2 = 8^2 + 14^2 - (2 \times 8 \times 14 \times \cos 0.875)$ | M1 | |
| $AB = 10.79...$ | A1 | |
| $P = 10.79 + (14 - 8) + (8 \times 0.875) = 23.8$ cm (3sf) | M1 A1 | **(8)** |
---6.\\
\includegraphics[max width=\textwidth, alt={}, center]{30d4e6e5-8235-44b0-ad8e-c4c0b313677f-2_577_970_799_360}
The diagram shows triangle $A B C$ in which $A C = 14 \mathrm {~cm} , B C = 8 \mathrm {~cm}$ and $\angle A B C = 1.7$ radians.\\
(i) Find the size of $\angle A C B$ in radians.
The point $D$ lies on $A C$ such that $B D$ is an arc of a circle, centre $C$.\\
(ii) Find the perimeter of the shaded region bounded by the arc $B D$ and the straight lines $A B$ and $A D$.\\
\hfill \mbox{\textit{OCR C2 Q6 [8]}}