| Exam Board | AQA |
|---|---|
| Module | FP2 (Further Pure Mathematics 2) |
| Year | 2013 |
| Session | January |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Topic | Hyperbolic functions |
| Type | Solve mixed sinh/cosh linear combinations |
| Difficulty | Moderate -0.3 Part (a) is direct substitution of hyperbolic function definitions requiring only algebraic simplification. Part (b) involves solving a quadratic in e^x after substitution, then taking logarithms—a standard FP2 technique with straightforward arithmetic. While this is Further Maths content, the question follows a routine template with no conceptual challenges or novel problem-solving required, making it slightly easier than an average A-level question overall. |
| Spec | 4.07a Hyperbolic definitions: sinh, cosh, tanh as exponentials4.07f Inverse hyperbolic: logarithmic forms |
\begin{enumerate}[label=(\alph*)]
\item Show that
$$12 \cosh x - 4 \sinh x = 4\text{e}^x + 8\text{e}^{-x}$$ [2 marks]
\item Solve the equation
$$12 \cosh x - 4 \sinh x = 33$$
giving your answers in the form $k \ln 2$. [5 marks]
\end{enumerate}
\hfill \mbox{\textit{AQA FP2 2013 Q1 [7]}}