| Exam Board | OCR |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Volumes of Revolution |
| Type | Rotation about x-axis: rational or reciprocal function |
| Difficulty | Moderate -0.8 Part (a) is a straightforward application of the reverse chain rule for integration, requiring only substitution or recognition of a standard form. Part (b) involves the volume of revolution formula with a simple function (1/2√x), requiring integration of x^(-1) which is routine. Both parts are standard textbook exercises with no problem-solving insight needed, making this easier than average for C3. |
| Spec | 1.08h Integration by substitution4.08d Volumes of revolution: about x and y axes |
\begin{enumerate}[label=(\alph*)]
\item Find $\int (3x + 7)^9 \, dx$. [3]
\item \includegraphics{figure_5b}
The diagram shows the curve $y = \frac{1}{2\sqrt{x}}$. The shaded region is bounded by the curve and the lines $x = 3$, $x = 6$ and $y = 0$. The shaded region is rotated completely about the $x$-axis. Find the exact volume of the solid produced, simplifying your answer. [5]
\end{enumerate}
\hfill \mbox{\textit{OCR C3 Q5 [8]}}