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.

Comments
    pingbacks / trackbacks

    Leave a Comment

    four − 2 =

    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