2024 TMJC H1 Q3
2024 TMJC H1 Q3
9 marks
A curve \(C\) has equation \(y = \frac{3}{2x+1}\).
- Sketch the graph of the curve \(C\). Give the equations of the asymptotes and the coordinates of the point(s) where the curve crosses the axes.[3]
A line has equation \(y = 2x - 1\). The curve and the line intersect at the points \(P\) and \(Q\).
- Find the \(x\)-coordinates of \(P\) and \(Q\).[2]
- Hence find the exact area of the region bounded by the curve \(C\), the line and the \(y\)-axis.[4]
Solution:
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Answer:(i) Asymptotes \(x=-\frac12\), \(y=0\); intercept \((0,3)\). (ii) \(x=-1,1\). (iii) \(\frac32\ln3\) square units.
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