| Exam Board | WJEC |
|---|---|
| Module | Unit 3 (Unit 3) |
| Year | 2018 |
| Session | June |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Differentiating Transcendental Functions |
| Type | Find normal line equation |
| Difficulty | Moderate -0.3 This is a straightforward differentiation question testing standard techniques: chain rule for exponential/trig composition, quotient rule, and implicit differentiation with finding a normal line. All are routine A-level procedures with no novel problem-solving required, though the implicit differentiation part adds slight complexity beyond pure recall. |
| Spec | 1.07q Product and quotient rules: differentiation1.07r Chain rule: dy/dx = dy/du * du/dx and connected rates1.07s Parametric and implicit differentiation |
\begin{enumerate}[label=(\alph*)]
\item Differentiate the following functions with respect to $x$, simplifying your answer wherever possible.
\begin{enumerate}[label=(\roman*)]
\item $e^{3\tan x}$,
\item $\frac{\sin 2x}{x^2}$. [5]
\end{enumerate}
\item A function is defined implicitly by
$$3x^2y + y^2 - 5x = 5.$$
Find the equation of the normal at the point $(1, 2)$. [6]
\end{enumerate}
\hfill \mbox{\textit{WJEC Unit 3 2018 Q16 [11]}}