2026 NASS P2 Q11

2026 NASS P2 Q11

Secondary 4
10 marks

The curve \(C\) has equation \(y=x^3-5x^2+6x-1\). Line \(l\) has equation \(y=2x-1\). The curve \(C\) and the line \(l\) intersect at the points \(K\), \(L\) and \(M\), as shown in the diagram. The shaded region consists of the two regions \(R_1\) and \(R_2\).

  1. Find the coordinates of \(K\), \(L\) and \(M\).[4]
  2. Find the total shaded area.[6]

Solution:

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Answer:(a) \(K=(0,-1),L=(1,1),M=(4,7)\). (b) \(\dfrac{71}6\) square units.

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