O-LevelAdditional MathematicsDifferentiation and integration4037/21 · Oct/Nov 2010 · Q76 Marks
A rectangular sheet of metal measures 60 cm by 45 cm. A scoop is made by cutting out squares, of side x cm, from two corners of the sheet and folding the remainder as shown. [Figure 7.1]
- (i)Show that the volume, V cm³, of the scoop is given by V = 2700x – 165x² + 2x³.[2]
- (ii)Given that x can vary, find the value of x for which V has a stationary value.[4]
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Mark scheme
Marking points from the official mark scheme (Oct/Nov 2010). The mark or mark type is shown in brackets.
- [M1] (i) V = (45 – 2x)(60 – x)x
- [A1] (i) Correctly reach V = 2700x – 165x² + 2x³
- [B2,1,0] (ii) dV/dx = 2700 – 330x + 6x²
- [M1] (ii) Solve 3 term quadratic expression for dV/dx = 0.
- [A1] (ii) 10 only
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