2013 A-level H1 Mathematics (8864) Question 3 Suggested Solutions

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

(i)
Perimeter $= 3x + 4x + 2y + 5x = 20$

$\Rightarrow y = 10 -6x$

Area, $S = 4xy + \frac{1}{2}(3x)(4x) = 40 x - 18x^{2}$

(ii)
$\frac{dS}{dx} = 40 - 36x = 0$

$\Rightarrow x = \frac{10}{9}$

Since $\frac{d^{2}S}{dx^{2}} = -36 < 0$ , S is maximum when $x = \frac{10}{9}$

Required Area $= 40(\frac{10}{9}) - 18(\frac{10}{9})^{2} = \frac{200}{9}$

KS Comments

Students should bare in mind to check the second order to substantiate that its a maximum area.

About

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.

Comments

pingbacks / trackbacks

2013 A-level H1 Mathematics (8864) Suggested Solutions | The Culture
[…] Question 3 […]
August 13th, 2015 11:15 PM

Cart

2013 A-level H1 Mathematics (8864) Question 3 Suggested Solutions

KS Comments

Leave a Reply to 2013 A-level H1 Mathematics (8864) Suggested Solutions | The Culture Cancel reply