Calculate the gradient of the curve \(x^{3} + y^{3} - 2xy = 11\) at (2, -1).

(a) If the coefficient of \(x^{2}\) and \(x^{3}\) in the expansion of \((p + qx)^{7}\) are equal, express q in terms of p. (b) A man makes a weekly contribut...

Three school prefects are to be chosen from four girls and five boys. What is the probability that : (a) only boys will be chosen ; (b) more girls than boys ...

(a) Differentiate \(\frac{x^{2} + 1}{(x + 1)^{2}}\) with respect to x. (b)(i) Evaluate \(\begin{vmatrix} 1 & 2 & -1 \\ 2 & 3 & -1 \\ -1 & 1 & 3 \end{vmatrix}...

The table shows the distribution of ages of 22 students in a school. Age (years) 12-14 15-17 18-20 21-23 24-26 Frequency 6 10 3 2 1 Using an assumed mean of ...

The initial velocity of a particle of mass 0.1kg is 40 m/s in the direction of the unit vector j. The velocity of the particle changed to 30 m/s in the direc...

A stone is dropped vertically downwards from the top of a tower of height 45m with a speed of 20 ms\(^{-1}\). Find the : (a) time it takes to reach the groun...

A side of a rectangle is three times the other. If the perimeter increases by 2%, find the percentage increase in the area of the rectangle.

The line \(2y = x + 3\) meets the circle \(x^{2} + y^{2} - 2x + 6y - 15 = 0\) at points M and N, where N is in the first quadrant. Find the coordinates of M ...