Differentiate, with respect to x, \(x^{3} + 2x\) from the first principle.

The magnitude of a force \(xi + 15j\) is 17N. Find the : (a) possible values of x ; (b) directions of the forces, correct to the nearest degree.

A car travelling at a velocity of 50kmh\(^{-1}\), covers a distance of 20km. If it was accelerating at 6kmh\(^{-1}\), calculate, correct to one decimal place...

(a) The sum of the first n terms of a sequence is given by \(S_{n} = \frac{5n^{2}}{2} + \frac{5n}{2}\). Write down the first four terms of the sequence and a...

A function F is defined on the set R, of real numbers by \(f : x \to px^{2} + qx + 2\), where p and q are constants. If \(f(-2) = 0\) and \(f(1) = 3\), find ...

If \(\sin A = \frac{3}{5}\) and \(\cos B = \frac{15}{17}\), where A is an obtuse angle and B is acute, find the value of \(\cos (A + B)\).

In a hotel, the breakfast is a choice between yam (Y) or plantain (P) or both. The Venn diagram shows the choices made by 25 guests of the hotel. (a) Find th...

The table shows the distribution of marks obtained by some candidates in a test. Marks 10-14 15-24 25-29 30-39 40-44 45-49 No of candidates 14 30 22 18 12 4 ...

A straight line passes through the point P(-1, 3). Another line which passes through Q(-4, 4) intersects the first line at the point R(k, 5), where k is a co...