| Exam Board | Edexcel |
|---|---|
| Module | FP3 (Further Pure Mathematics 3) |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Hyperbolic functions |
| Type | Solve using sech/tanh identities |
| Difficulty | Standard +0.8 This is a Further Maths question requiring knowledge of the hyperbolic identity sech²x = 1 - tanh²x, followed by solving a quadratic in tanh²x and using inverse hyperbolic functions. While systematic, it requires multiple specialized techniques beyond standard A-level and involves logarithmic form answers, placing it moderately above average difficulty. |
| Spec | 4.07a Hyperbolic definitions: sinh, cosh, tanh as exponentials4.07c Hyperbolic identity: cosh^2(x) - sinh^2(x) = 1 |
\begin{enumerate}
\item Find the exact values of x for which
\end{enumerate}
$$4 \tanh ^ { 2 } x - 2 \operatorname { sech } ^ { 2 } x = 3 ,$$
giving your answers in the form $\pm \ln \mathrm { a }$, where a is real.\\
\hfill \mbox{\textit{Edexcel FP3 Q1 [6]}}