CAIE P2 2013 June — Question 5

Exam BoardCAIE
ModuleP2 (Pure Mathematics 2)
Year2013
SessionJune
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicParametric equations
5 The parametric equations of a curve are $$x = \mathrm { e } ^ { 2 t } , \quad y = 4 t \mathrm { e } ^ { t }$$
  1. Show that \(\frac { \mathrm { d } y } { \mathrm {~d} x } = \frac { 2 ( t + 1 ) } { \mathrm { e } ^ { t } }\).
  2. Find the equation of the normal to the curve at the point where \(t = 0\).
5 The parametric equations of a curve are

$$x = \mathrm { e } ^ { 2 t } , \quad y = 4 t \mathrm { e } ^ { t }$$

(i) Show that $\frac { \mathrm { d } y } { \mathrm {~d} x } = \frac { 2 ( t + 1 ) } { \mathrm { e } ^ { t } }$.\\
(ii) Find the equation of the normal to the curve at the point where $t = 0$.

\hfill \mbox{\textit{CAIE P2 2013 Q5}}
This paper (7 questions)
View full paper
Q1 Q2 Q3 Q4 Q5 Q6 Q7