Mathematics Past Questions and Answers

If y = 2x - sin2x, find dy/dx when x = π/4

A bowl is designed by revolving completely the area enclosed by y = x² - 1, y = 3 and x ≥ 0 around the axis. What is the volume of this bowl?

If the volume of a hemisphere is increasing at a steady rate of 18π m\(^{3}\) s\(^{-1}\), at what rate is its radius changing when its is 6m?

X and Y are two events. The probability of X or Y is 0.7 and that of X is 0.4. If X and Y are independent, find the probability of Y.

If the mean of the numbers 0, (x+2), (3x+6), and (4x+8) is 4, find their mean deviation.