Further Mathematics Questions and Answers

A binary operation * is defined on the set of real number, R, by x*y = x$^2$ - y$^2$ + xy, where x, $\in$  R. Evaluate ($\sqrt{3}$)*($\sqrt{2}$)

 

${\color{red}2x} \times 3$

Evaluate: $^{lim}_{x \to 1} \begin{pmatrix} \frac{1 - x}{x^2 - 3x + 2} \end {pmatrix}$

A uniform beam, PQ. is 100 m long and weighs 35 N. It is placed on a support at a point 40 cm from P. If weights of 54 N and FN are attached at P and Q respectively in order to keep it in a horizontal position, calculate, correct to the nearest whole number, the value of F.

Given that X and Y are independent events such that P(X) = 0.5, P(Y) = m and P(X U Y) = 0.75, find the value of m. 

The probabilities that John and Jane will pass an examination are 0.9 and 0.7 respectively. Find the probability that at least one of them will pass the examination.