| Exam Board | CAIE |
|---|---|
| Module | P1 (Pure Mathematics 1) |
| Year | 2010 |
| Session | November |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Radians, Arc Length and Sector Area |
| Type | Compound shape area |
| Difficulty | Standard +0.3 This is a straightforward application of basic radian geometry formulas. Part (i) requires simple angle arithmetic (π - 2×2.3), and part (ii) involves calculating a sector area using the standard formula A = ½r²θ. Both parts are routine calculations with no problem-solving insight required, making it slightly easier than average. |
| Spec | 1.05d Radians: arc length s=r*theta and sector area A=1/2 r^2 theta |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(1.683(18\ldots)\) | B1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \((2) \times \frac{1}{2} \times 3^2\sin2.3\) | M1 | Condone omission of factor 2 |
| \(\frac{1}{2} \times 3^2 \times \text{their } 1.683\) | M1 | NB M0 if using angle of 2.3 |
| Triangle \(AOC + COB +\) sector | M1 | Two correct triangles + sector |
| \(14.3\) | A1 | co |
## Question 4:
**Part (i)**
| Answer/Working | Marks | Guidance |
|---|---|---|
| $1.683(18\ldots)$ | B1 | |
**Part (ii)**
| Answer/Working | Marks | Guidance |
|---|---|---|
| $(2) \times \frac{1}{2} \times 3^2\sin2.3$ | M1 | Condone omission of factor 2 |
| $\frac{1}{2} \times 3^2 \times \text{their } 1.683$ | M1 | NB M0 if using angle of 2.3 |
| Triangle $AOC + COB +$ sector | M1 | Two correct triangles + sector |
| $14.3$ | A1 | co |
---4\\
\includegraphics[max width=\textwidth, alt={}, center]{ae57d8f1-5a0d-426c-952d-e8b99c6aeaba-2_720_645_1183_751}
The diagram shows points $A , C , B , P$ on the circumference of a circle with centre $O$ and radius 3 cm . Angle $A O C =$ angle $B O C = 2.3$ radians.\\
(i) Find angle $A O B$ in radians, correct to 4 significant figures.\\
(ii) Find the area of the shaded region $A C B P$, correct to 3 significant figures.
\hfill \mbox{\textit{CAIE P1 2010 Q4 [5]}}