| Exam Board | Edexcel |
|---|---|
| Module | FP3 (Further Pure Mathematics 3) |
| Year | 2014 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Hyperbolic functions |
| Type | Solve mixed sinh/cosh linear combinations |
| Difficulty | Standard +0.3 Part (a) is a standard identity proof requiring direct substitution of exponential definitions and algebraic manipulation—routine for FP3 students. Part (b) involves substituting exponential forms, solving a quadratic in e^x, then taking logarithms—a textbook exercise with clear methodology. Both parts test recall and standard technique rather than problem-solving insight, making this easier than average even for Further Maths. |
| Spec | 4.07a Hyperbolic definitions: sinh, cosh, tanh as exponentials4.07c Hyperbolic identity: cosh^2(x) - sinh^2(x) = 1 |
Using the definitions of hyperbolic functions in terms of exponentials,
\begin{enumerate}[label=(\alph*)]
\item show that
$$\operatorname{sech}^2 x = 1 - \tanh^2 x$$
[3]
\item solve the equation
$$4 \sinh x - 3 \cosh x = 3$$
[4]
\end{enumerate}
\hfill \mbox{\textit{Edexcel FP3 2014 Q4 [7]}}