| Exam Board | Edexcel |
|---|---|
| Module | FP3 (Further Pure Mathematics 3) |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Topic | Hyperbolic functions |
| Type | Solve mixed sinh/cosh linear combinations |
| Difficulty | Standard +0.8 This is a Further Maths question requiring substitution of hyperbolic definitions (e^x and e^-x), algebraic manipulation to form a quadratic in e^x, and solving to express answers as natural logarithms. While the technique is standard for FP3, it requires multiple steps and careful algebra, placing it moderately above average difficulty. |
| Spec | 4.07a Hyperbolic definitions: sinh, cosh, tanh as exponentials |
Solve the equation
$$10 \cosh x + 2 \sinh x = 11.$$
Give each answer in the form $\ln a$ where $a$ is a rational number. [7]
\hfill \mbox{\textit{Edexcel FP3 Q3 [7]}}