| Exam Board | WJEC |
|---|---|
| Module | Unit 3 (Unit 3) |
| Year | 2023 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Numerical integration |
| Type | Trapezium rule with stated number of strips |
| Difficulty | Moderate -0.3 This is a straightforward applied integration question requiring recognition of an ellipse equation, setting up a volume integral (given formula to show), applying trapezium rule with clear instructions (6 ordinates), and identifying concavity. All techniques are standard A-level procedures with no novel problem-solving required, making it slightly easier than average. |
| Spec | 1.08e Area between curve and x-axis: using definite integrals1.09f Trapezium rule: numerical integration |
The aerial view of a patio under construction is shown below.
\includegraphics{figure_9}
The curved edge of the patio is described by the equation $9x^2 + 16y^2 = 144$, where $x$ and $y$ are measured in metres.
To construct the patio, the area enclosed by the curve and the coordinate axes is to be covered with a layer of concrete of depth 0.06 m.
\begin{enumerate}[label=(\alph*)]
\item Show that the volume of concrete required for the construction of the patio is
given by $0.015 \int_0^4 \sqrt{144 - 9x^2}\,dx$. [3]
\item Use the trapezium rule with six ordinates to estimate the volume of concrete required. [4]
\item State whether your answer in part (b) is an overestimate or an underestimate of the volume required. Give a reason for your answer. [1]
\end{enumerate}
\hfill \mbox{\textit{WJEC Unit 3 2023 Q9 [8]}}