St. Stephen’s Girls’ College Form 4 M1 Mid-Year Exam 2021-22

試題答案:

1. a) \(x^{n} + 3nx^{n+1} + \dfrac{9n(n-1)}{2}x^{n+2}  + …\)
   b) n =5
   c) 62
2. a) \((1 + 3a + 3a^{2} + a^{3}) – (3ak + 6a^{2}k + 3a^{3}k)x +\dfrac{3ak^{2} + 12a^{2}k^{2}+9a^{3}k^{2}}{2}x^{2} + …\)
   b) a = 1
   c) 12
3. a) –
   b) k = 5 or k = -2
4. a) \(\alpha = \dfrac{1}{e^{5}}  \quad or \quad \beta = e\)
5. a) \(ln(\dfrac{45}{A} – 2) = (-k ln a) t + 2 ln a\)
   b i) a = 3
   ii) 45/11 thousand m²
   iii) Claim is correct.

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