| Exam Board | Pre-U |
|---|---|
| Module | Pre-U 9795 (Pre-U Further Mathematics) |
| Session | Specimen |
| Topic | Hyperbolic functions |
| Type | Solve mixed sinh/cosh linear combinations |
| Difficulty | Standard +0.3 This is a straightforward application of the definitions cosh x = (e^x + e^{-x})/2 and sinh x = (e^x - e^{-x})/2, leading to a simple quadratic in e^x. While it requires knowing hyperbolic function definitions and solving a quadratic, it's a standard textbook exercise with no conceptual difficulty beyond routine algebraic manipulation. |
| Spec | 4.07a Hyperbolic definitions: sinh, cosh, tanh as exponentials4.07b Hyperbolic graphs: sketch and properties4.07c Hyperbolic identity: cosh^2(x) - sinh^2(x) = 1 |
3 Solve the equation
$$5 \cosh x - \sinh x = 7$$
giving your answers in an exact logarithmic form.
\hfill \mbox{\textit{Pre-U Pre-U 9795 Q3}}