| Exam Board | Pre-U |
|---|---|
| Module | Pre-U 9795 (Pre-U Further Mathematics) |
| Session | Specimen |
| Marks | 6 |
| Topic | Hyperbolic functions |
| Type | Solve mixed sinh/cosh linear combinations |
| Difficulty | Standard +0.3 This is a straightforward hyperbolic equation requiring substitution of standard definitions (cosh x = (e^x + e^-x)/2, sinh x = (e^x - e^-x)/2), simplification to a quadratic in e^x, and conversion to logarithmic form. While it involves hyperbolic functions (a Further Maths topic), the solution method is mechanical and requires no novel insight—just careful algebraic manipulation following a standard procedure. |
| Spec | 4.07a Hyperbolic definitions: sinh, cosh, tanh as exponentials4.07c Hyperbolic identity: cosh^2(x) - sinh^2(x) = 14.07f Inverse hyperbolic: logarithmic forms |
Solve exactly the equation
$$5 \cosh x - \sinh x = 7,$$
giving your answers in logarithmic form. [6]
\hfill \mbox{\textit{Pre-U Pre-U 9795 Q3 [6]}}