(a) Two items are selected at random from four items labelled (p, q, r, s). (i) List the sample space if sampling is done (1) with replacement ; (2) without...

Express \(3x^{2} - 6x + 10\) in the form \(a(x - b)^{2} + c\), where a, b and c are integers. Hence state the minimum value of \(3x^{2} - 6x + 10\) and the v...

The gradient function of \(y = ax^{2} + bx + c\) is \(8x + 4\). If the function has a minimum value of 1, find the values of a, b and c.

Simplify \(^{n + 1}C_{4} - ^{n - 1}C_{4}\) = \(\frac{(n + 1)!}{4! (n - 3)!} - \frac{(n - 1)!}{4! (n - 5)!}\) = \(\frac{(n + 1)(n)(n - 1)(n - 2)(n - 3)!}{4! (...

Write down the first three terms of the binomial expansion \((1 + ax)^{n}\) in ascending powers of x. If the coefficients of x and x\(^{2}\) are 2 and \(\fra...

The twenty-first term of an Arithmetic Progression is \(5\frac{1}{2}\) and the sum of the first twenty-one terms is \(94\frac{1}{2}\). Find the : (a) first t...

Three forces \(-63j , 32.14i + 38.3j\) and \(14i - 24.25j\) act on a body of mass 5kg. Find, correct to one decimal place, the : (a) magnitude of the resulta...

The marks scored by 35 students in a test are given in the table below. Marks 1-5 6-10 11-15 16-20 21-25 26-30 Frequency 2 7 12 8 5 1 Draw a histogram for th...

Two functions g and h are defined on the set R of real numbers by \(g : x \to x^{2} - 2\) and \(h : x \to \frac{1}{x + 2}\). Find : (a) \(h^{-1}\), the inver...