2026 HGV P2 Q10

2026 HGV P2 Q10

Secondary 4
12 marks

The diagram shows part of a curve \(y=x^3+x^2-2x\).

  1. Find the coordinates of \(Q\).[3]
  2. Given that the gradient of line \(PQ\) is 2, show that the coordinates of \(P\) are \((-1,2)\).[6]
  3. Find the area of the shaded region bounded by the curve, the line \(PQ\) and the \(x\)-axis.[3]

Solution:

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Answer:(a) \(Q(-2,0)\). (b) \(P(-1,2)\) (shown). (c) \(\dfrac{25}{12}\text{ units}^2\).

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