2025 SMBSS P2 Q10

2025 SMBSS P2 Q10

Secondary 4
10 marks

The diagram shows the line \(y=-x+7\) intersecting the curve \(y=x^2-6x+11\) at the point \(A\) and \(B\).

  1. Determine the coordinates of \(A\) and \(B\).[4]
  2. Hence calculate the area enclosed by the curve \(y=x^2-6x+11\) and the line \(y=-x+7\).[6]

Solution:

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Answer:(a) \(A=(1,6),B=(4,3)\). (b) \(4.5\text{ units}^2\).

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