St. Stephen’s Girls’ College Form 4 M1 Final Exam 2018-19

試題答案:

1. a) –
   b) 7/4
2. The claim is incorrect.
3. a) \(1 – 10x + 50x^{2} + …\)
   b) a = -1 and n = 4
4. a) \(\dfrac{3x-2}{\sqrt{2x+4}}\)
   b) tangent at A:  y = 4x – 24
        tangent at B: y = -x – 12
   c) The claim is incorrect.
5. a) \(\mathrm{ln}\left(\dfrac{4000}{N} – 5\right) = \mathrm{ln} a + kt\)
   b i) a = 45, k = -0.4
     ii) 80
    iii) 800
    iv) \(\dfrac{72000 e^{-0.4t}}{(5 + 45e^{-0.4t})^{2}}\)
     v) N is increasing during the first 10 days as \(\dfrac{dN}{dt} > 0\) for 0 ≤ t ≤ 10.

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