O-LevelAdditional MathematicsDifferentiation and integration4037/22 · May/June 2019 · Q45 Marks
A circle has diameter x which is increasing at a constant rate of 0.01 cm s⁻¹. Find the exact rate of change of the area of the circle when x = 6 cm.
- A circle has diameter x which is increasing at a constant rate of 0.01 cm s⁻¹. Find the exact rate of change of the area of the circle when x = 6 cm.[5]
Mark scheme
Marking points from the official mark scheme (May/June 2019). The mark or mark type is shown in brackets.
- [B1] Either: A = (1/4)πx² oe, soi
- [B1] dA/dx = (1/2)πx oe, soi
- [B1] dx/dt = 0.01 soi
- [M1] (dA/dx) * (dx/dt) evaluated when x = 6 (their (1/2)πx) * 0.01
- [A1] 0.03π or exact equivalent mark final answer
- [B1] Or: A = πr² and r = x/2 soi
- [B1] dA/dr = 2πr oe soi
- [B1] dr/dt = 0.005 oe soi
- [M1] (dA/dr) * (dr/dt) evaluated when r = 3 (their 2πr) * 0.005
- [A1] 0.03π or exact equivalent
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