The diagram shows part of the curve $y=\dfrac{8}{2+3x}$. A line, $l$, passes through the curve a

Question

The diagram shows part of the curve $y=\dfrac{8}{2+3x}$. A line, $l$, passes through the curve at point $A(0,4)$ and is parallel to the tangent to the curve at $x=-2$. Show that the equation of line $l$ is $y=-\dfrac{3}{2}x+4$.[3] Find the area of the shaded region and leave your answer in the form $a+b\ln 2$.[6] The coefficients in the requested exact form are rational numbers.

Accepted Answer

(a) $y=-\dfrac{3}{2}x+4$ (b) $5-\dfrac{16}{3}\ln 2$ square units

2025 AHS PRELIMS P2 Q9

2025 AHS PRELIMS P2 Q9

Solution:

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