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

Perimeter = d

4x + 2y + \pi x = d

Area, A = xy + \frac{1}{2} \pi x^2

A = x(\frac{d-4x-\pi x}{2}) + \frac{1}{2} \pi x^2

A = \frac{d}{2}x - 2x^2

\frac{dA}{dx} = \frac{d}{2} - 4x

Let \frac{dA}{dx} = 0 \Rightarrow, x =\frac{d}{8}

Since \frac{d^2A}{dx^2} = -4 \textless 0, A is maximum when x = \frac{d}{8}

A = 0.03125d^2

\therefore, k = 0.03125 = \frac{1}{32}

Back to 2015 A-level H2 Mathematics (9740) Paper 1 Suggested Solutions

KS Comments:

One important point here is that student must leave the exact answers as it is, and should not wrong off. It clearly stated in instructions to only wrong off non-exact answers, but this is very exact.

One Comment

Leave a Reply