2012 A-level H2 Mathematics (9740) Paper 2 Question 1 Suggested Solutions

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

\frac{dy}{dx} = 16x - 3x^2 + C

y = 8x^2 - \frac{3}{4} x^4 + Cx + D


\int \frac{1}{16 - 9u^2} du = \int 1 dt

\frac{1}{3} \times \frac{1}{8} \mathrm{ln} |\frac{4+3u}{4-3u}| = t + C

Let u = 1, t = 0,

C = \frac{1}{24} \mathrm{ln} 7

\Rightarrow \frac{1}{24} \mathrm{ln} |\frac{4+3u}{4-3u}| = t + \frac{1}{24} \mathrm{ln} 7

T = \frac{1}{24} \mathrm{ln} |\frac{4+3u}{7(4-3u)}|

KS Comments:

Students need to be reminded to put modulus due to the presence of ln. The integration formula in (ii) can be found in MF15 too.

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