| Exam Board | AQA |
|---|---|
| Module | FP2 (Further Pure Mathematics 2) |
| Year | 2012 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Topic | Hyperbolic functions |
| Type | Solve using substitution u = cosh x or u = sinh x |
| Difficulty | Standard +0.3 This is a straightforward Further Maths question requiring standard techniques: sketching a basic hyperbolic function and solving a quadratic equation in cosh x using substitution u = cosh x, then applying the inverse hyperbolic function formula. While it's Further Maths content (inherently harder), the execution is routine with no novel problem-solving required—just direct application of learned methods. |
| Spec | 1.02f Solve quadratic equations: including in a function of unknown4.07a Hyperbolic definitions: sinh, cosh, tanh as exponentials4.07b Hyperbolic graphs: sketch and properties |
1
\begin{enumerate}[label=(\alph*)]
\item Sketch the curve $y = \cosh x$.
\item Solve the equation
$$6 \cosh ^ { 2 } x - 7 \cosh x - 5 = 0$$
giving your answers in logarithmic form.
\end{enumerate}
\hfill \mbox{\textit{AQA FP2 2012 Q1 [7]}}