| Exam Board | AQA |
|---|---|
| Module | FP2 (Further Pure Mathematics 2) |
| Year | 2011 |
| Session | January |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Topic | Hyperbolic functions |
| Type | Find stationary points of hyperbolic curves |
| Difficulty | Standard +0.8 This is a Further Maths question requiring differentiation of hyperbolic functions, solving a transcendental equation (likely requiring logarithms), and algebraic manipulation to verify a relationship. While the techniques are standard for FP2, the multi-step nature and need to handle the transcendental equation elevate it above routine exercises. |
| Spec | 4.07a Hyperbolic definitions: sinh, cosh, tanh as exponentials4.07d Differentiate/integrate: hyperbolic functions |
4
\begin{enumerate}[label=(\alph*)]
\item Prove that the curve
$$y = 12 \cosh x - 8 \sinh x - x$$
has exactly one stationary point.
\item Given that the coordinates of this stationary point are $( a , b )$, show that $a + b = 9$.
\end{enumerate}
\hfill \mbox{\textit{AQA FP2 2011 Q4 [11]}}