OCR MEI C4 2014 June — Question 5 7 marks

Exam BoardOCR MEI
ModuleC4 (Core Mathematics 4)
Year2014
SessionJune
Marks7
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicParametric curves and Cartesian conversion
DifficultyStandard +0.3 This is a standard C4 parametric differentiation question requiring the chain rule (dy/dx = (dy/dt)/(dx/dt)) and elimination of the parameter. Both parts follow routine procedures taught in the module with no novel insight required, making it slightly easier than average.
Spec1.03g Parametric equations: of curves and conversion to cartesian1.07s Parametric and implicit differentiation

A curve has parametric equations \(x = e^{2t}, y = te^{2t}\).
  1. Find \(\frac{dy}{dx}\) in terms of \(t\). Hence find the exact gradient of the curve at the point with parameter \(t = 1\). [4]
  2. Find the cartesian equation of the curve in the form \(y = ax^b \ln x\), where \(a\) and \(b\) are constants to be determined. [3]

A curve has parametric equations $x = e^{2t}, y = te^{2t}$.
\begin{enumerate}[label=(\roman*)]
\item Find $\frac{dy}{dx}$ in terms of $t$. Hence find the exact gradient of the curve at the point with parameter $t = 1$. [4]
\item Find the cartesian equation of the curve in the form $y = ax^b \ln x$, where $a$ and $b$ are constants to be determined. [3]
\end{enumerate}

\hfill \mbox{\textit{OCR MEI C4 2014 Q5 [7]}}