| Exam Board | OCR |
|---|---|
| Module | PURE |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Topic | Differentiating Transcendental Functions |
| Type | Find gradient at a point - direct evaluation |
| Difficulty | Easy -1.2 This is a straightforward two-part question testing basic exponential functions and differentiation. Part (a) requires simple logarithm manipulation (ln(10)/3), and part (b) requires routine differentiation of e^(3x) using the chain rule. Both are standard textbook exercises with no problem-solving or insight required, making this easier than average. |
| Spec | 1.06a Exponential function: a^x and e^x graphs and properties1.06d Natural logarithm: ln(x) function and properties1.07j Differentiate exponentials: e^(kx) and a^(kx) |
A curve has equation $y = e^{3x}$.
\begin{enumerate}[label=(\alph*)]
\item Determine the value of $x$ when $y = 10$. [2]
\item Determine the gradient of the tangent to the curve at the point where $x = 2$. [2]
\end{enumerate}
\hfill \mbox{\textit{OCR PURE Q4 [4]}}