2025 AISS PRELIMS P1 Q10

2025 AISS PRELIMS P1 Q10

Secondary 4
9 marks
2025 Ahmad Ibrahim Secondary School Prelims A Math Paper 1
  1. Express \(\dfrac{1-3x-3x^2}{x(x+1)^2}\) in partial fractions.[5]
  2. Hence find \(\displaystyle \int \dfrac{1-3x-3x^2}{2x(x+1)^2}\, dx\).[4]

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Answer:\(\text{(a)}\hspace{0.5em}\dfrac{1}{x}-\dfrac{4}{x+1}-\dfrac{1}{(x+1)^2}\) \(\text{(b)}\hspace{0.5em}\dfrac12\ln|x|-2\ln|x+1|+\dfrac{1}{2(x+1)}+C\)

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