2025 TKSS PRELIMS P1 Q9

2025 TKSS PRELIMS P1 Q9

Secondary 4
7 marks
2025 Tanjong Katong Secondary School Prelims A Math Paper 1

A company manufactures open square-based cuboid casings for high-precision instruments, where \(x\) cm is the length of the side of the base. The material for the base of the casing cost twice as much as the material for the sides. The total material cost for one casing is \(\$600\), with the material for the side costing \(\$1/\mathrm{cm}^2\).

  1. Show that the volume of the casing, \(V\ \mathrm{cm}^3\), is given by \(V=\frac{300x-x^3}{2}\).[3]
  2. Given that \(x\) can vary, find the stationary value of \(V\) and determine its nature.[4]

Solution:

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Answer:(a) \(V=\frac{300x-x^3}{2}\text{ cm}^3\) (b) Maximum stationary value \(=1000\text{ cm}^3\), at \(x=10\text{ cm}\).

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