Edexcel C2 — Question 7 11 marks

Exam BoardEdexcel
ModuleC2 (Core Mathematics 2)
Marks11
PaperDownload PDF ↗
TopicRadians, Arc Length and Sector Area
TypeTriangle and sector combined - area/perimeter with given values
DifficultyStandard +0.3 This is a straightforward multi-part question testing standard formulas for arc length and sector area with basic triangle calculations. Part (a) directly applies s=rθ, part (b) requires finding BC using cosine rule then adding lengths, and part (c) uses sector area minus triangle area. All techniques are routine C2 content with no novel problem-solving required, making it slightly easier than average.
Spec1.05c 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

\includegraphics{figure_1} Figure 1 shows the triangle \(ABC\), with \(AB = 8\) cm, \(AC = 11\) cm and \(\angle BAC = 0.7\) radians. The arc \(BD\), where \(D\) lies on \(AC\), is an arc of a circle with centre \(A\) and radius 8 cm. The region \(R\), shown shaded in Figure 1, is bounded by the straight lines \(BC\) and \(CD\) and the arc \(BD\). Find
  1. the length of the arc \(BD\), [2]
  2. the perimeter of \(R\), giving your answer to 3 significant figures, [4]
  3. the area of \(R\), giving your answer to 3 significant figures. [5]

\includegraphics{figure_1}

Figure 1 shows the triangle $ABC$, with $AB = 8$ cm, $AC = 11$ cm and $\angle BAC = 0.7$ radians. The arc $BD$, where $D$ lies on $AC$, is an arc of a circle with centre $A$ and radius 8 cm. The region $R$, shown shaded in Figure 1, is bounded by the straight lines $BC$ and $CD$ and the arc $BD$.

Find

\begin{enumerate}[label=(\alph*)]
\item the length of the arc $BD$,
[2]

\item the perimeter of $R$, giving your answer to 3 significant figures,
[4]

\item the area of $R$, giving your answer to 3 significant figures.
[5]
\end{enumerate}

\hfill \mbox{\textit{Edexcel C2  Q7 [11]}}