| Exam Board | Edexcel |
|---|---|
| Module | FP3 (Further Pure Mathematics 3) |
| Year | 2009 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Hyperbolic functions |
| Type | Solve using sech/tanh identities |
| Difficulty | Standard +0.8 This requires knowing the sech²x + tanh²x = 1 identity, substituting to get a quadratic in one hyperbolic function, then using definitions to solve for x. It's a multi-step Further Maths problem requiring both identity manipulation and logarithmic form, making it moderately harder than average A-level questions but standard for FP3. |
| Spec | 4.07a Hyperbolic definitions: sinh, cosh, tanh as exponentials |
\begin{enumerate}
\item Solve the equation
\end{enumerate}
$$7 \operatorname { sech } x - \tanh x = 5$$
Give your answers in the form $\ln a$ where $a$ is a rational number.\\
\hfill \mbox{\textit{Edexcel FP3 2009 Q1 [5]}}