| Exam Board | SPS |
|---|---|
| Module | SPS FM Pure (SPS FM Pure) |
| Year | 2022 |
| Session | February |
| Marks | 8 |
| Topic | Hyperbolic functions |
| Type | Solve mixed sinh/cosh linear combinations |
| Difficulty | Standard +0.3 Part (a) requires differentiating hyperbolic functions and showing the derivative is never zero—straightforward calculus with standard identities. Part (b) involves using the R cos(x + α) form (or exponential definitions) to solve a hyperbolic equation, which is a standard Further Maths technique but requires recognizing the approach. Overall slightly easier than average due to being a textbook application of hyperbolic function methods. |
| Spec | 4.07a Hyperbolic definitions: sinh, cosh, tanh as exponentials4.07d Differentiate/integrate: hyperbolic functions |
You are given that $f(x) = 4\sinh x + 3\cosh x$.
\begin{enumerate}[label=(\alph*)]
\item Show that the curve $y = f(x)$ has no turning points. [3]
\item Determine the exact solution of the equation $f(x) = 5$. [5]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS FM Pure 2022 Q10 [8]}}