| Exam Board | AQA |
|---|---|
| Module | FP2 (Further Pure Mathematics 2) |
| Year | 2012 |
| Session | January |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Topic | Hyperbolic functions |
| Type | Intersection points of hyperbolic curves |
| Difficulty | Standard +0.8 This question requires understanding hyperbolic function graphs, solving a transcendental equation by converting to exponential form, and manipulating the resulting quadratic to extract a logarithmic answer. While the sketch is straightforward, part (b) involves multiple non-routine algebraic steps (substituting definitions, forming a quadratic in e^x, solving, and converting back to logarithmic form) that go beyond standard textbook exercises, though it remains within typical FP2 scope. |
| Spec | 4.07a Hyperbolic definitions: sinh, cosh, tanh as exponentials4.07b Hyperbolic graphs: sketch and properties |
1
\begin{enumerate}[label=(\alph*)]
\item Show, by means of a sketch, that the curves with equations
$$y = \sinh x$$
and
$$y = \operatorname { sech } x$$
have exactly one point of intersection.
\item Find the $x$-coordinate of this point of intersection, giving your answer in the form $a \ln b$.
\end{enumerate}
\hfill \mbox{\textit{AQA FP2 2012 Q1 [8]}}