If (x + 2) and (x - 1) are factors of \(f(x) = 6x^{4} + mx^{3} - 13x^{2} + nx + 14\), find the (a) values of m and n. (b) remainder when f(x) is divided be ...

Find the equation of the tangent to the curve \(y = \frac{x - 1}{2x + 1}, x \neq -\frac{1}{2}\) at the point (1, 0).

The table shows the distribution of the ages of a group of people in a village. Ages (in years) 15 - 18 19 - 22 23 - 26 27 - 30 31 - 34 35 - 38 Frequency 40 ...

A body of mass 5 kg resting on a smooth horizontal plane, is acted upon by force 6i + 2j, 5i + 4j and 4i - j. Calculate the: (a) velocity of the body (b) Mag...

If \(2^{2x - 3y} = 32\) and \(\log_{y} x = 2\), find the values of x and y.

The sum of the 2nd and 5th terms of an arithmetic progression (AP) is 42. If the difference between the 6th and 3rd term is 12, find the (i) Common differenc...

An object is projected vertically upwards with a velocity of 80 m/s. Find the : (a) Maximum height reached (b) Time taken to return to the point of projectio...

(a) There are 6 points in a plane. How many triangles can be formed with the points? (b) A family of 6 is to be seated in a row . In how many ways can this b...

(a) Simplify \(\frac{\sqrt{75} - 3}{\sqrt{3} + 1}\), leaving your answer in the form \(a + b\sqrt{c}\); where a, b and c are rational numbers. (b) The points...