2023 YTSS P2 Q9

2023 YTSS P2 Q9

Secondary 4
10 marks

The diagram shows the curve \(y=10x-x^2\), the line \(y=2x\) and the line \(y=16\). The line \(y=16\) intersects the curve at the points \(A\) and \(B\). The line \(y=2x\) also intersects the curve at point \(B\).

  1. Find the coordinates of \(A\).[2]
  2. Find the area of the shaded region \(OAB\).[8]

Solution:

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Answer:(a) \(A=(2,16)\). (b) \(\dfrac{148}3\text{ units}^2\).

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