WJEC Unit 3 2018 June — Question 16 11 marks

Exam BoardWJEC
ModuleUnit 3 (Unit 3)
Year2018
SessionJune
Marks11
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicDifferentiating Transcendental Functions
TypeFind normal line equation
DifficultyModerate -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.
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 the following functions with respect to \(x\), simplifying your answer wherever possible.
    1. \(e^{3\tan x}\),
    2. \(\frac{\sin 2x}{x^2}\). [5]
  2. A function is defined implicitly by $$3x^2y + y^2 - 5x = 5.$$ Find the equation of the normal at the point \((1, 2)\). [6]

\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]}}