| Exam Board | WJEC |
|---|---|
| Module | Further Unit 4 (Further Unit 4) |
| Year | 2024 |
| Session | June |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Hyperbolic functions |
| Type | Find stationary points of hyperbolic curves |
| Difficulty | Challenging +1.2 Part (a) is a standard derivation of the inverse hyperbolic sine derivative using implicit differentiation and the identity cosh²y - sinh²y = 1, requiring algebraic manipulation but following a well-established method. Part (b) requires implicit differentiation of a product, finding where dy/dx = 0, and proving uniqueness of the stationary point, likely involving showing a function is monotonic. While this involves multiple techniques and some problem-solving, it's a typical Further Maths question on hyperbolic functions without requiring particularly novel insight—moderately above average difficulty. |
| Spec | 4.07d Differentiate/integrate: hyperbolic functions4.08g Derivatives: inverse trig and hyperbolic functions |
\begin{enumerate}[label=(\alph*)]
\item By writing $y = \sinh^{-1}(4x + 3)$ as $\sinh y = 4x + 3$, show that $\frac{\mathrm{d}y}{\mathrm{d}x} = \frac{4}{\sqrt{16x^2 + 24x + 10}}$. [5]
\item Show that the graph of $e^{-3x} \cdot y = \sinh 2x$ has only one stationary point. [6]
\end{enumerate}
\hfill \mbox{\textit{WJEC Further Unit 4 2024 Q8 [11]}}