Edexcel C2 — Question 17 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 integrating the difference of two functions. 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 equations1.08e Area between curve and x-axis: using definite integrals1.08f Area between two curves: using integration

\includegraphics{figure_7} Figure 2 shows the line with equation \(y = x + 1\) and the curve with equation \(y = 6x - x^2 - 3\). The line and the curve intersect at the points \(A\) and \(B\), and \(O\) is the origin.
  1. Calculate the coordinates of \(A\) and the coordinates of \(B\). [5]
The shaded region \(R\) is bounded by the line and the curve.
  1. Calculate the area of \(R\). [7]

\includegraphics{figure_7}

Figure 2 shows the line with equation $y = x + 1$ and the curve with equation $y = 6x - x^2 - 3$.

The line and the curve intersect at the points $A$ and $B$, and $O$ is the origin.

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

The shaded region $R$ is bounded by the line and the curve.

\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item Calculate the area of $R$. [7]
\end{enumerate}

\hfill \mbox{\textit{Edexcel C2  Q17 [12]}}