Edexcel C2 — Question 9 12 marks

Exam BoardEdexcel
ModuleC2 (Core Mathematics 2)
Marks12
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicSine and Cosine Rules
TypeShaded region with arc
DifficultyStandard +0.3 This is a straightforward multi-part question testing standard C2 topics: cosine rule to find an angle, sector area formula, and combining areas/arc lengths. All parts follow routine procedures with no novel problem-solving required, making it slightly easier than average for A-level.
Spec1.05b Sine and cosine rules: including ambiguous case1.05d Radians: arc length s=r*theta and sector area A=1/2 r^2 theta

\includegraphics{figure_3} Fig. 3 Triangle ABC has AB = 9 cm, BC = 10 cm and CA = 5 cm. A circle, centre A and radius 3 cm, intersects AB and AC at P and Q respectively, as shown in Fig. 3.
  1. Show that, to 3 decimal places, ∠BAC = 1.504 radians. [3]
Calculate,
  1. the area, in cm², of the sector APQ, [2]
  2. the area, in cm², of the shaded region BPQC, [3]
  3. the perimeter, in cm, of the shaded region BPQC. [4]
END

\includegraphics{figure_3}

Fig. 3

Triangle ABC has AB = 9 cm, BC = 10 cm and CA = 5 cm.

A circle, centre A and radius 3 cm, intersects AB and AC at P and Q respectively, as shown in Fig. 3.

\begin{enumerate}[label=(\alph*)]
\item Show that, to 3 decimal places, ∠BAC = 1.504 radians. [3]
\end{enumerate}

Calculate,

\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item the area, in cm², of the sector APQ, [2]
\item the area, in cm², of the shaded region BPQC, [3]
\item the perimeter, in cm, of the shaded region BPQC. [4]
\end{enumerate}

END

\hfill \mbox{\textit{Edexcel C2  Q9 [12]}}