2010 A-level H2 Mathematics (9740) Paper 1 Question 4 Suggested Solutions

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

(i)
Differentiating the given equation by x,

\Rightarrow 2x - 2y \frac{dy}{dx} + 2x \frac{dy}{dx} + 2y = 0

(x-y)\frac{dy}{dx} = -y-x

\frac{dy}{dx} = \frac{x+y}{y-x}

(ii)
Tangent parallel to x-axis \Rightarrow \frac{dy}{dx} = 0

Then, y= -x

\Rightarrow x^2 - (-x)^2 + 2x (-x)+4=0

x^2 = 2

x = \pm \sqrt{2}

y = -\sqrt{2}, ~\sqrt{2}

Therefore, coordinates are (\sqrt{2}, -\sqrt{2}) and (-\sqrt{2}, \sqrt{2}).

KS Comments:

Quite straight forward with the implicit differentiations at (i). Students should understand what it means when tangents are parallel to x-axis. Lastly, since the question wants coordinates, students are expected to give in coordinates instead of merely the x and y values!

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