CSEC Additional Mathematics Paper 3 May/June 2024 - Free CXC Past Paper with Answers

The diagram below shows that layout of the bean crops watered by the drone.

If the green beans are planted in the sector inscribed by the angle $\theta = \frac{11\pi}{12}$ radians and the kidney beans in the remaining portion of the circular area, find the area of land that contains kidney beans that will be watered by the drone. (Give your answer correct to 2 decimal places.)

If the farmer wishes to fence the area within the range of the drone that contains green beans in order to treat those crops only, what length of fencing should be used?

The harvested beans will be packed for shipping in cartons. The length of each carton is 3 times the width and each carton has a volume of $0.135 \text{ m}^3$. (i) Show that the surface area, $A$, of EACH carton is given by $A = 6x^2 + \frac{9}{25x}$, where $x$ represents the width of the carton.

Hence, determine the minimum surface area, $A$, of the carton and prove that this area is a minimum.