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!

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KS Teng

KS has been teaching H2/H1 Mathematics and IB mathematics for the more than 10 years. Having taught students from all various Junior Colleges, KS adapts to students' abilities and help them better understand the topics. As someone who loves to teach mathematics and sees it as a truly useful tool in life, KS seeks to enable students to appreciate math. Therefore, his tuition mission is to motivate and cultivate students to be independent and confident thinkers.

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

KS Comments:

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