2025 PHS PRELIMS P1 Q12

2025 PHS PRELIMS P1 Q12

Secondary 4
9 marks
2025 Presbyterian High School Prelims A Math Paper 1
  1. By using long division, divide \(4x^3+5x^2+x-1\) by \(x^2(x+1)\).[1]
  2. Hence, express \(\dfrac{4x^3+5x^2+x-1}{x^2(x+1)}\) in partial fractions.[5]
  3. Hence, find \(\displaystyle \int \dfrac{4x^3+5x^2+x-1}{x^2(x+1)}\,dx\).[3]

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Answer:(a) quotient \(4\), remainder \(x^2+x-1\) (b) \(4+\dfrac{2}{x}-\dfrac{1}{x^2}-\dfrac{1}{x+1}\) (c) \(4x+2\ln|x|+\dfrac{1}{x}-\ln|x+1|+C\)

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