When \(f(x) = 2x^{3} + mx^{2} + nx + 11\) is divided by \(x^{2} + 5x + 1\), the quotient is \(2x - 5\) and the remainder is \(30x + 16\). Find the values of...

Given that (5, 2), (-4, k) and (2, 1) lie on a straight line, find the value of k.

(a) If \(f(x + 2) = 6x^{2} + 5x - 8\), find \(f(5)\). (b) Express \(\frac{7\sqrt{2} + 3\sqrt{3}}{4\sqrt{2} - 2\sqrt{3}}\) in the form \(p + q\sqrt{r}\), wher...

Given that \(p = \begin{pmatrix} 5 \\ 3 \end{pmatrix}, q = \begin{pmatrix} -1 \\ 2 \end{pmatrix}\) and \(r = \begin{pmatrix} 17 \\ 5 \end{pmatrix}\) and \(r ...

(a) A body of mass 3kg moves with a velocity of 8ms\(^{-1}\). It collides with a second body moving in the same direction with a velocity of 5ms\(^{-1}\). Af...

The probabilities that Ago, Sulley and Musa will gain admission to a certain university are \(\frac{4}{5}, \frac{3}{4}\) and \(\frac{2}{3}\) respectively. Fi...

A binary operation \(*\) is defined on the set, R, of real numbers by \(m * n = m + n + 2\). Find the : (a) identity element under the operation ; (b) invers...

(a) Without using mathematical tables or calculator, evaluate \(\frac{\frac{3}{2}\log 27 - 3\log 5\sqrt{5}}{\log 0.6}\) (b) Two linear transformations A and ...

The mean of the numbers 1, 4, k, (k + 4) and 11 is (k + 1). Calculate the : (a) value of k ; (b) standard deviation.