(a) The functions \(f : x \to x^{2} + 1\) and \(g : x \to 5 - 3x\) are defined on the set of the real numbers, R. (i) State the domain of \(f^{-1}\), the in...

There are 8 boys and 6 girls in a class. If two students are selected at random from the class, find the probability that they are of (a) the same sex ; (b) ...

Forces of magnitude 3N, 4N and 2N act along the vectors \(j ; -i + j\) and \(i + j\) respectively. Calculate, correct to one decimal place, the magnitude of ...

Points (2, 1) and (6, 7) are opposite vertices of a square which is inscribed in a circle. Find the : (a) centre of the circle ; (b) equation of the circle.

Five finalists in a beauty pageant were ranked by two judges X and Y as shown in the table : Judges Anne Linda Susan Rose Erica X 1 4 3 5 2 Y 3 2 4 5 1 Calcu...

A car moving with an initial velocity, u, travels in a straight line with a constant acceleration of 3ms\(^{-2}\) until it attains a velocity of 33ms\(^{-1}\...

If \(f ' '(x) = 2\), \(f ' (1) = 0\) and \(f(0) = - 8\), find f(x).

A binary operation A is defined on the set of real numbers, R, by \(a \Delta b = a^{3} - b^{3}\). Without using calculator, find the value of \((\sqrt{3} + \...

Solve : \(\tan (2x - 15)° - 1 = 0\), for values of x such that \(0° \leq x \leq 360°\).