| Exam Board | Edexcel |
|---|---|
| Module | FP3 (Further Pure Mathematics 3) |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Hyperbolic functions |
| Type | Surface area of revolution with hyperbolics |
| Difficulty | Challenging +1.8 This is a surface area of revolution problem requiring knowledge of hyperbolic identities, the formula S = 2π∫y√(1+(dy/dx)²)dx, and manipulation of exponentials. While it involves multiple steps (differentiation, simplification using cosh²-sinh²=1, integration of hyperbolic functions, and evaluation at logarithmic limits), the techniques are standard for FP3. The main challenge is algebraic manipulation rather than novel insight, placing it above average but not at the highest difficulty level for Further Maths. |
| Spec | 4.07a Hyperbolic definitions: sinh, cosh, tanh as exponentials4.08d Volumes of revolution: about x and y axes |
2.
\begin{figure}[h]
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\caption{Figure 1}
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Figure 1 shows part of the curve with equation $y = 2 \cosh \left( \frac { 1 } { 2 } x \right)$. The points $A$ and $B$ lie on the curve and have $x$-coordinates $- \ln 2$ and $\ln 2$ respectively. The arc of the curve joining $A$ and $B$ is rotated through $2 \pi$ radians about the $x$-axis.
Find the exact area of the curved surface area formed.\\
(Total 7 marks)\\
\hfill \mbox{\textit{Edexcel FP3 Q2 [7]}}