2025 PHS P1 Q3

2025 PHS P1 Q3

Secondary 4
5 marks
  1. Find the derivative of \((3x^2-4)^5\).[2]
    1. Factorise \(x^3+1\).[1]
    2. Hence find \(\displaystyle\int\dfrac{x^3+1}{x+1}\,\mathrm{d}x\).[2]

Solution:

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Answer:(a) \(30x(3x^2-4)^4\). (b)(i) \((x+1)(x^2-x+1)\). (ii) \(\dfrac{x^3}3-\dfrac{x^2}2+x+C\), \(x\ne-1\).

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