| Exam Board | WJEC |
|---|---|
| Module | Unit 3 (Unit 3) |
| Year | 2023 |
| Session | June |
| Marks | 13 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Chain Rule |
| Type | Implicit differentiation |
| Difficulty | Moderate -0.3 This is a standard differentiation question testing chain rule, product rule, quotient rule, and implicit differentiation. Part (a) involves routine application of standard rules with no problem-solving required. Part (b) requires implicit differentiation and finding a tangent line equation—a multi-step process but entirely procedural for A-level students who have practiced these techniques. Slightly easier than average due to straightforward application of learned methods. |
| 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 each of the following with respect to $x$.
\begin{enumerate}[label=(\roman*)]
\item $\left(\sin x + x^2\right)^5$ [2]
\item $x^3 \cos x$ [2]
\item $\frac{e^{3x}}{\sin 2x}$ [3]
\end{enumerate}
\item Find the equation of the tangent to the curve
$$4y^2 - 7xy + x^2 = 12$$
at the point $(2, 4)$. [6]
\end{enumerate}
\hfill \mbox{\textit{WJEC Unit 3 2023 Q2 [13]}}