Additional Mathematics 0606: DIFFERENTIATION Topical Past Paper Questions

(a) Differentiate $ x \sin(2x-3) $ with respect to x. [2] (b) Hence find $ \int_{0}^{\frac{1}{2}} x \cos(2x-3) \, dx $. [4]

In this question the units are metres and seconds. A particle moves along a straight line through a point A. Its displacement, s, from A at time t is given by $ s=\frac{10t+100}{\sqrt{2t^{2}+100}} $. The diagram shows the displacement–time graph for the first 30 seconds of the mo…

A cylinder, open at both ends, has base radius $ r \, \text{cm} $ and height $ 4r \, \text{cm} $. Its curved surface area is $ S \, \text{cm}^2 $. Given that $ r $ varies with time $ t $, find $ S $ at the instant when $ \frac{\mathrm{d}S}{\mathrm{d}t} = 6\frac{\mathrm{d}r}{\math…