O-LevelAdditional MathematicsDifferentiation and integration4037/11 · May/June 2010 · Q98 Marks
Variables x and y are related by the equation y = 5x + 2 – 4e⁻ˣ. Find dy/dx
- (a)(i)Variables x and y are related by the equation y = 5x + 2 – 4e⁻ˣ. Find dy/dx[2]
- (a)(ii)Hence find the approximate change in y when x increases from 0 to p, where p is small.[2]
- (b)A square of area A cm² has a side of length x cm. Given that the area is increasing at a constant rate of 0.5 cm2s⁻¹, find the rate of increase of x when A = 9.[4]
Mark scheme
Marking points from the official mark scheme (May/June 2010). The mark or mark type is shown in brackets.
- [2] (a)(i) M1 for attempt to differentiate; A1 for dy/dx = 5 + 4e^-x
- [2] (a)(ii) M1 for attempt to use small changes (dy ≈ dy/dx * dx); A1 for dy ≈ 9p
- [4] (b) B1 for dA/dt = 0.5; M1 for dA/dx = 2x and finding x=3; DM1 for correct use of rates of change (dx/dt = dA/dt * dx/dA); A1 for 1/12
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