CSEC Additional Mathematics Paper 3 May/June 2021 - Free CXC Past Paper with Answers

The area of the floor space of the rectangular room shown below can be expressed as the quadratic equation $A(x) = -x^2 - 4x + 45$.

Figure 1

Express the given equation in a suitable format and determine the maximum value of $A(x)$.

Determine the values of $a$ and $b$ that will provide corresponding solutions to the given equation $A(x) = 0$. Hence, write down the factors of $A(x)$.

Calculate the dimensions of the room using the maximum area found in (a) (i).

Given the dimensions of the room with maximum area, state ONE suitable conclusion about the shape of the room.

Using the grid provided below, sketch the graph of $A(x)$. Hence, determine the values of $x$ for which the area $A(x)$ is valid.

A sector of a circle has area $\frac{15\pi}{2}$ cm$^2$ and arc length $\frac{5\pi}{2}$ cm.

Determine the angle subtended by the sector, giving your answer in terms of $\pi$.

Determine an expression for the radius of a sphere at the point at which its volume is increasing at twice the rate of its radius. Give your answer in the simplest surd form. Use $V = \frac{4}{3}\pi r^3$ for volume of sphere.