2024 IGCSE Additional Mathematics May/June 0606/13 Q3

2024 IGCSE Additional Mathematics May/June 0606/13 Q3

9 marks
  1. Find the coordinates of the stationary points on the curve \(y=(2x+1)^2(x-3)\).[4]
  2. On the axes, sketch the graph of \(y=(2x+1)^2(x-3)\), stating the intercepts with the axes.[3]
  3. Write down the values of \(k\) for which the equation \((2x+1)^2(x-3)=k\) has exactly one solution.[2]

Solution:

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Answer:(a) \(\left(-\dfrac12,0\right)\), \(\left(\dfrac{11}6,-\dfrac{686}{27}\right)\). (b) Sketch shown; intercepts \(\left(-\dfrac12,0\right),(3,0),(0,-3)\). (c) \(k>0\) or \(k<-\dfrac{686}{27}\).

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