If (x + 1) and (x - 2) are factors of the polynomial \(g(x) = x^{4} + ax^{3} + bx^{2} - 16x - 12\), find the values of a and b.

(a) If \(f(x) = \frac{4 - 5x}{2}\), and \(g(x) = x + 6, x \in R\), find \(f \circ g^{-1}\). (b) P(x, y) divides the line joining (7, -5) and (-2, 7) internal...

(a) Given that \(\log_{10} p = a, \log_{10} q = b\) and \(\log_{10} s = c\), express \(\log_{10} (\frac{p^{\frac{1}{3}}q^{4}}{s^{2}}\) in terms of a, b and c...

Bottles of the same sizes produced in a factory are packed in boxes. Each box contains 10 bottles. If 8% of the bottles are defective, find, correct to two d...

The table shows the heights in cm of some seedlings in a certain garden. Height (cm) 36-40 41-45 46-50 51-55 56-60 Frequency 3 9 21 12 5 (a) Draw the cumulat...

A parallelogram MNQR has vertices M(4, -6), N(10, 2), Q(8, 16) and R(x, y). Find the coordinates of R.

Forces \(F_{1} (18N, 330°), F_{2} (10N, 090°)\) and \(F_{3} (25N, 180°)\) act on a body at rest. Find, correct to one decimal place, the magnitude and direct...

(a) Simplify : \(\frac{1}{1 - \cos \theta} + \frac{1}{1 + \cos \theta}\) and leave your answer in terms of \(\sin \theta\). (b) Find the equation of the line...

Evaluate : \(\int_{1}^{3} (\frac{x - 1}{(x + 1)^{2}}) \mathrm {d} x\).