O-LevelAdditional MathematicsDifferentiation and integration4037/22 · May/June 2010 · Q67 Marks
The diagram shows part of the line y = 12 – 2x. The point Q(x, y) lies on this line and the points P and R lie on the coordinate axes such that OPQR is a rectangle. [Figure 6]
- (i)Write down an expression, in terms of x, for the area A of the rectangle OPQR.[2]
- (ii)Given that x can vary, find the value of x for which A has a stationary value.[3]
- (iii)Find this stationary value of A and determine its nature.[2]
This question uses a diagram from the original paper, which isn't shown here. Open the full paper from the past papers archive to see it.
Mark scheme
Marking points from the official mark scheme (May/June 2010). The mark or mark type is shown in brackets.
- M1 for A = xy
- A1 for A = 12x - 2x² oe
- B1√ for dA/dx = 12 - 4x
- M1 for equate to 0 and solve
- A1√ for x = 3
- A1 for A = 18
- B1√ for Completely correct method and maximum
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