A-LevelMathematicsDifferentiation9709/12 · May/June 2010 · Q88 Marks
A solid rectangular block has a square base of side x cm. The height of the block is h cm and the total surface area of the block is 96 cm². (i) Express h in terms of x and show that the volume, V cm³, of the block is given by V = 24x - ½x³. Given that x can vary, (ii) find the stationary value of V, (iii) determine whether this stationary value is a maximum or a minimum.
- (i)Express h in terms of x and show that the volume, V cm³, of the block is given by V = 24x - ½x³.[3]
- (ii)find the stationary value of V,[3]
- (iii)determine whether this stationary value is a maximum or a minimum.[2]
Mark scheme
Marking points from the official mark scheme (May/June 2010). The mark or mark type is shown in brackets.
- [M1] Needs to consider at least 5 areas.
- [A1] co
- [M1] for V = x²h with h as f(x)
- [B1] co
- [M1] Sets differential to 0 and solves.
- [A1] co
- [M1 A1√] Any valid method. co.
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