Further Mathematics Past Questions and Answers

Given that \(P = \begin{pmatrix} 2 & 1 \\ 5 & -3 \end{pmatrix}\) and \(Q = \begin{pmatrix} 4 & -8 \\ 1 & -2 \end{pmatrix}\), Find (2P - Q).

A binary operation, \(\Delta\), is defined on the set of real numbers by \(a \Delta b = a + b + 4\). Find the identity element.

The marks obtained by 10 students in a test are as follows: 3, 7, 6, 2, 8, 5, 9, 1, 4 and 10. Find the mean mark.

The marks obtained by 10 students in a test are as follows: 3, 7, 6, 2, 8, 5, 9, 1, 4 and 10. Find the variance.

If r denotes the correlation coefficient between two variables, which of the following is always true?