| Exam Board | OCR |
|---|---|
| Module | Further Pure Core 1 (Further Pure Core 1) |
| Year | 2021 |
| Session | June |
| Marks | 7 |
| Topic | Hyperbolic functions |
| Type | Solve mixed sinh/cosh linear combinations |
| Difficulty | Standard +0.3 This is a straightforward Further Maths question requiring standard techniques: part (a) uses definitions of sinh/cosh to convert to exponentials and solve a quadratic, while part (b) is direct integration of hyperbolic functions. Both parts are routine applications of learned methods with no novel insight required, making it slightly easier than average even for Further Maths. |
| Spec | 4.07a Hyperbolic definitions: sinh, cosh, tanh as exponentials4.07d Differentiate/integrate: hyperbolic functions |
3 The diagram shows part of the curve $y = 5 \cosh x + 3 \sinh x$.\\
\includegraphics[max width=\textwidth, alt={}, center]{ef967953-70b5-4dd1-a342-ad488b5fa79f-02_426_661_906_260}
\begin{enumerate}[label=(\alph*)]
\item Solve the equation $5 \cosh x + 3 \sinh x = 4$ giving your solution in exact form.
\item In this question you must show detailed reasoning.
Find $\int _ { - 1 } ^ { 1 } ( 5 \cosh x + 3 \sinh x ) \mathrm { d } x$ giving your answer in the form $a \mathrm { e } + \frac { b } { \mathrm { e } }$ where $a$ and $b$ are integers to be determined.
\end{enumerate}
\hfill \mbox{\textit{OCR Further Pure Core 1 2021 Q3 [7]}}