Edexcel C2 — Question 8 12 marks

Exam BoardEdexcel
ModuleC2 (Core Mathematics 2)
Marks12
PaperDownload PDF ↗
TopicAreas by integration
TypeArea between curve and line
DifficultyModerate -0.3 This is a standard C2 integration question requiring finding intersection points by solving a quadratic equation, then computing the area between a line and parabola using definite integration. While it involves multiple steps (12 marks total), each step follows routine procedures taught in C2 with no novel problem-solving required, making it slightly easier than average.
Spec1.02q Use intersection points: of graphs to solve equations1.08f Area between two curves: using integration

\includegraphics{figure_2} The line with equation \(y = 3x + 20\) cuts the curve with equation \(y = x^2 + 6x + 10\) at the points \(A\) and \(B\), as shown in Figure 2.
  1. Use algebra to find the coordinates of \(A\) and the coordinates of \(B\). [5]
The shaded region \(S\) is bounded by the line and the curve, as shown in Figure 2.
  1. Use calculus to find the exact area of \(S\). [7]

\includegraphics{figure_2}

The line with equation $y = 3x + 20$ cuts the curve with equation $y = x^2 + 6x + 10$ at the points $A$ and $B$, as shown in Figure 2.

\begin{enumerate}[label=(\alph*)]
\item Use algebra to find the coordinates of $A$ and the coordinates of $B$.
[5]
\end{enumerate}

The shaded region $S$ is bounded by the line and the curve, as shown in Figure 2.

\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item Use calculus to find the exact area of $S$.
[7]
\end{enumerate}

\hfill \mbox{\textit{Edexcel C2  Q8 [12]}}