WJEC Unit 3 2023 June — Question 2 13 marks

Exam BoardWJEC
ModuleUnit 3 (Unit 3)
Year2023
SessionJune
Marks13
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicChain Rule
TypeImplicit differentiation
DifficultyModerate -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.
Spec1.07q Product and quotient rules: differentiation1.07r Chain rule: dy/dx = dy/du * du/dx and connected rates1.07s Parametric and implicit differentiation

  1. Differentiate each of the following with respect to \(x\).
    1. \(\left(\sin x + x^2\right)^5\) [2]
    2. \(x^3 \cos x\) [2]
    3. \(\frac{e^{3x}}{\sin 2x}\) [3]
  2. Find the equation of the tangent to the curve $$4y^2 - 7xy + x^2 = 12$$ at the point \((2, 4)\). [6]

\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]}}