2026 NORTHBROOKS P2 Q10

2026 NORTHBROOKS P2 Q10

Secondary 4
11 marks
  1. Given that \(\displaystyle\int_2^k3(2x-3)^{1/2}\,\mathrm{d}x=26\), find the value of \(k\).[3]
  2. The gradient function of a curve is \(-3(x-2)^2\).
    1. Find the x-coordinate of the stationary point of the curve and find the nature of this stationary point.[4]
      It is given further that the normal to the curve at \(x=1\) cuts the \(x\)-axis at \((18,0)\).
    2. Find the equation of the normal.[4]

Solution:

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Answer:(a) \(k=6\). (b)(i) \(x=2\), stationary point of inflection. (ii) \(y=\dfrac13x-6\).

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