2014 A-level H2 Mathematics (9740) Paper 2 Question 1 Suggested Solutions

All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions.



\frac{dy}{dx}={\frac{dy}{dt}}\times {\frac{dt}{dx}}



At P, t=p, \frac{dy}{dx}=\frac{1}{p}
Equation of tangent: y-6p=\frac{1}{p}(x-3p^{2})
At D, x=0,  y=-3p+6p=3p
Therefore, D(0,3p).
Midpoint of PD = (\frac{0+3p^{2}}{2}, \frac{6p+3p}{2})=(\frac{3p^{2}}{2}, \frac{9p}{2})

As p varies, x=\frac{3}{2} p^{2}, y= \frac{9}{2}p
We have that p=\frac{2y}{9}
Then, x=\frac{3}{2}(\frac{2y}{9})^{2}
Thus, 27x=2y^{2}

Personal Comments:
This questions test students on their understanding of parametric equations and finding gradient. Find the cartesian equation can be slightly tricky if a student hasn’t been exposed to such questions before.

    pingbacks / trackbacks

    Leave a Comment

    Contact Us

    CONTACT US We would love to hear from you. Contact us, or simply hit our personal page for more contact information

    Not readable? Change text. captcha txt

    Start typing and press Enter to search