| Exam Board | CAIE |
|---|---|
| Module | P1 (Pure Mathematics 1) |
| Year | 2011 |
| Session | November |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Radians, Arc Length and Sector Area |
| Type | Triangle and sector combined - area/perimeter with given values |
| Difficulty | Moderate -0.3 This is a straightforward multi-part question testing basic applications of radian measure, sector area, and arc length formulas. All parts require direct formula application with given values (angle 0.8 rad, sides 10 cm) and minimal problem-solving. The parallelogram area uses standard sine formula, and the sector calculations are routine. Slightly easier than average due to the step-by-step structure and lack of conceptual challenges. |
| Spec | 1.05c Area of triangle: using 1/2 ab sin(C)1.05d Radians: arc length s=r*theta and sector area A=1/2 r^2 theta |
| Answer | Marks | Guidance |
|---|---|---|
| (i) \(10^2 \sin 0.8 = 71.7\) | M1A1 [2] | Completely correct method for a triangle |
| Answer | Marks | Guidance |
|---|---|---|
| Total area \(= 80\) | M1, A1 [2] | Correct formula used for a sector |
| Answer | Marks | Guidance |
|---|---|---|
| \(16+20 = 36\) | M1, A1 [2] | Correct formula used for an arc |
**(i)** $10^2 \sin 0.8 = 71.7$ | M1A1 [2] | Completely correct method for a triangle
**(ii)** sector(s) $= (2) \times \frac{1}{2} \times 10^2 \times 0.8 = (2) \times 40$
Total area $= 80$ | M1, A1 [2] | Correct formula used for a sector
**(iii)** arc(s) $= (2) \times 10 \times 0.8$
$16+20 = 36$ | M1, A1 [2] | Correct formula used for an arc
---\includegraphics{figure_4}
In the diagram, $ABCD$ is a parallelogram with $AB = BD = DC = 10$ cm and angle $ABD = 0.8$ radians. $APD$ and $BQC$ are arcs of circles with centres $B$ and $D$ respectively.
\begin{enumerate}[label=(\roman*)]
\item Find the area of the parallelogram $ABCD$. [2]
\item Find the area of the complete figure $ABQCDP$. [2]
\item Find the perimeter of the complete figure $ABQCDP$. [2]
\end{enumerate}
\hfill \mbox{\textit{CAIE P1 2011 Q4 [6]}}