| Exam Board | Pre-U |
|---|---|
| Module | Pre-U 9794/2 (Pre-U Mathematics Paper 2) |
| Year | 2012 |
| Session | Specimen |
| Marks | 5 |
| Topic | Volumes of Revolution |
| Type | Volume with exact answer required |
| Difficulty | Standard +0.3 This is a straightforward volumes of revolution question requiring integration of y² with respect to x. The integrand (1/(5x+3)) is simple after squaring, leading to a standard logarithm result. While it requires careful algebraic manipulation to reach the exact simplified form, the technique is routine and well-practiced at A-level, making it slightly easier than average. |
| Spec | 4.08d Volumes of revolution: about x and y axes |
- State or imply $\pi \int \frac{1}{5x+3}\,\mathrm{d}x$ or unsimplified version [B1]
- Obtain integral of form $k\ln(5x+3)$ (may or may not include $\pi$) [M1]
- Obtain $\frac{1}{5}\pi\ln(5x+3)$ or $\frac{1}{5}\ln(5x+3)$ [M1]
- Show correct use of $\ln a - \ln b$ property [M1]
- Obtain $\frac{1}{5}\pi\ln 6$ [A1]
**Total: 5 marks**7\\
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The diagram shows the region $R$ bounded by the curve $y = \frac { 1 } { \sqrt { 5 x + 3 } }$ and the lines $x = 0$, $x = 3$ and $y = 0$. Find the exact volume of the solid formed when the region $R$ is rotated completely about the $x$-axis, simplifying your answer.
\hfill \mbox{\textit{Pre-U Pre-U 9794/2 2012 Q7 [5]}}