Edexcel C34 2018 June — Question 2 7 marks

Exam BoardEdexcel
ModuleC34 (Core Mathematics 3 & 4)
Year2018
SessionJune
Marks7
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicParametric curves and Cartesian conversion
TypeFind dy/dx at a point
DifficultyModerate -0.3 This is a straightforward parametric equations question requiring standard techniques: differentiation using the chain rule (dy/dx = (dy/dt)/(dx/dt)) and algebraic manipulation to eliminate the parameter. Part (a) is routine calculus, and part (b) involves rearranging to make t the subject from one equation and substituting into the other—a standard textbook exercise with no novel insight required. Slightly easier than average due to the simple algebraic forms involved.
Spec1.03g Parametric equations: of curves and conversion to cartesian1.07s Parametric and implicit differentiation

2. A curve \(C\) has parametric equations $$x = \frac { 3 } { 2 } t - 5 , \quad y = 4 - \frac { 6 } { t } \quad t \neq 0$$
  1. Find the value of \(\frac { \mathrm { d } y } { \mathrm {~d} x }\) at \(t = 3\), giving your answer as a fraction in its simplest form.
  2. Show that a cartesian equation of \(C\) can be expressed in the form $$y = \frac { a x + b } { x + 5 } \quad x \neq k$$ where \(a , b\) and \(k\) are integers to be found.

2. A curve $C$ has parametric equations

$$x = \frac { 3 } { 2 } t - 5 , \quad y = 4 - \frac { 6 } { t } \quad t \neq 0$$
\begin{enumerate}[label=(\alph*)]
\item Find the value of $\frac { \mathrm { d } y } { \mathrm {~d} x }$ at $t = 3$, giving your answer as a fraction in its simplest form.
\item Show that a cartesian equation of $C$ can be expressed in the form

$$y = \frac { a x + b } { x + 5 } \quad x \neq k$$

where $a , b$ and $k$ are integers to be found.
\end{enumerate}

\hfill \mbox{\textit{Edexcel C34 2018 Q2 [7]}}