| Exam Board | OCR |
|---|---|
| Module | Further Pure Core 1 (Further Pure Core 1) |
| Year | 2021 |
| Session | June |
| Marks | 6 |
| Topic | Hyperbolic functions |
| Type | Express hyperbolic in exponential form |
| Difficulty | Standard +0.8 This is a Further Maths question requiring students to manipulate hyperbolic functions into exponential form and then integrate using substitution. Part (a) is straightforward algebraic manipulation, but part (b) requires recognizing a non-obvious substitution (likely u = e^x) and completing the integration of a rational function, which goes beyond routine application. The multi-step nature and the need for insight into the substitution place it moderately above average difficulty. |
| Spec | 4.07a Hyperbolic definitions: sinh, cosh, tanh as exponentials4.07d Differentiate/integrate: hyperbolic functions |
5 The function $\operatorname { sech } x$ is defined by $\operatorname { sech } x = \frac { 1 } { \cosh x }$.
\begin{enumerate}[label=(\alph*)]
\item Show that $\operatorname { sech } x = \frac { 2 \mathrm { e } ^ { x } } { \mathrm { e } ^ { 2 x } + 1 }$.
\item Using a suitable substitution, find $\int \operatorname { sech } x \mathrm {~d} x$.
\end{enumerate}
\hfill \mbox{\textit{OCR Further Pure Core 1 2021 Q5 [6]}}