CSEC Additional Mathematics Paper 3 May/June 2019 - Free CXC Past Paper with Answers

A programmer designs a game in which a a ship must travel in a circular motion, relative to a centre at origin, $O$ . The ship intersects a square as shown in Figure 1, in order to be awarded points.

Figure 1.

Determine the coordinates, relative to the origin, $O$ , of all intersections if the ship must maintain a distance of 5 cm from the origin at all times, the sides of the square are parallel to the coordinate axes and EACH side of the square is of length 8 cm.

The ship in the game has a rectangular-shaped stern, shown in Figure 2, that takes in water at a rate of $2500 \text{ m}^3 \text{ s}^{-1}$ whenever a wrong turn is made.

Show that when a wrong turn is made the stern is filled after 6 seconds, if the rate of change of volume of water to height of the stern is given by $\frac{dV}{dh} = 200 \text{ m}^2$ .

CSEC Additional Mathematics Paper 3 May/June 2019 Questions

Question 1 (20 marks)

Figure 1.