| Exam Board | OCR |
|---|---|
| Module | H240/01 (Pure Mathematics) |
| Year | 2017 |
| Session | Specimen |
| Marks | 8 |
| Topic | Chain Rule |
| Type | Inverse function differentiation |
| Difficulty | Standard +0.3 This is a straightforward differentiation question using the product rule and chain rule, followed by finding where x=0 and computing dy/dx. The implicit differentiation aspect and solving ln(2y-7)=0 add minor complexity beyond routine exercises, but it remains a standard multi-part calculus question requiring well-practiced techniques without novel insight. |
| Spec | 1.07l Derivative of ln(x): and related functions1.07s Parametric and implicit differentiation |
A curve has equation $x = (y + 5)\ln(2y - 7)$.
\begin{enumerate}[label=(\alph*)]
\item Find $\frac{dx}{dy}$ in terms of y. [3]
\item Find the gradient of the curve where it crosses the y-axis. [5]
\end{enumerate}
\hfill \mbox{\textit{OCR H240/01 2017 Q10 [8]}}