2011 A-level H2 Mathematics (9740) Paper 2 Question 2 Suggested Solutions

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

(i)
$V = PQ \times QR \times \mathrm{height}$

$= (2n-2x)(n-2x)x$

$= 2n^2x-6nx^2+4x^3$

(ii)
$\frac{dV}{dx}=2n^2 - 12nx +12x^2$

Let $\frac{dV}{dx}=0$

$\Rightarrow 6x^2 -6nx + n^2 = 0$

$x = (\frac{3 \pm \sqrt{3}}{6})n$

Since $2x \textless n, ~ x \textless \frac{n}{2} \Rightarrow x = (\frac{3- \sqrt{3}}{6})n$

We reject $x=\frac{3+\sqrt{3}}{6}n$ since $\frac{3+\sqrt{3}}{6}n > \frac{n}{2}$

$\therefore$ Required stationary value of $x = \frac{3-\sqrt{3}}{6}n$

KS Comments:

Students do not need to carry out the second derivative test since question only ask for the stationary value, instead of maximum of minimum. Question wants students to explain why there is one answer only, so a clear precise explanation will be expected.

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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.

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2011 A-level H2 Mathematics (9740) Paper 2 Question 2 Suggested Solutions

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