St. Stephen’s Girls’ College Form 4 M1 Supplementary Final Exam 2019-20

試題答案:

1. a) \(8 – 60x + 300x^{2} + … \)
   b) 50760
2. a) \(1 – 12x + 72x^{2} + …\)
   b) n = 5 or n = 2
3. a) \(2\sqrt{3}\)
   b) 4
4. a) \(y\\’ = e^{-x^{2} + 1} (-2x^{3} + 2x)\)
        \(y\\’\\’ = e^{-x^{2} + 1} (4x^{4} -10x^{2} + 2)\)
   b) \((2-2x)e^{-x^{2} + 1}\)
5. a) \(\dfrac{x – 11}{2(x – 3}^{3/2}\)
   b) -1/4
6. a) \(\mathrm{ln}\left(\dfrac{4400}{P} – 5\right) = \mathrm{ln} a + bt\)
   b i) a = 4, b = -0.01
     ii) \(\dfrac{dP}{dt} = 180e^{-0.01t}(4e^{-0.01t} + 5)^{-2}\)
          \(\dfrac{d^{2}P}{dt^{2}} = -1.8e^{-0.01t}(4e^{-0.01t} + 5)^{-2} + 14.4e^{-0.02t}(4e^{-0.01t} + 5)^{-3}\)     

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