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7 marksDifferentiation I

CAPE Pure Mathematics Unit 1 · May/June 2023 · Paper 2 · Question 6(c)

On the surface of the moon, the acceleration due to gravity is -1.625 m/s². A rocket is launched away from the moon with an initial height of 1 200 metres and an initial velocity of 30 m/s.

Determine the velocity and height of the rocket 5 seconds after launch.

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  1. 6(a)Calculate the volume of the solid generated by revolving the region bounded by the line y = 3x - 6 and the parabola y = x^2 + 3x - 2, on the interval [0, 1]…[7 marks]
  2. 6(b)The diagram below shows the curves y = \cos x and y = \sin x. Determine the area bounded by the curves between x = \pi/4 and x = 3\pi/2.[7 marks]
  3. 6(d)Determine \int \cos^3 2x \sin 2x \, dx.[4 marks]

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