Further Mathematics Past Questions and Answers

Given that \(P = \begin{pmatrix} 4 & 9 \end{pmatrix}\) and \(Q = \begin{pmatrix} -1 & -2 \\ 3 & 2 \end{pmatrix}\). Which of the following operations is possible?

A \(QP\)
B \(P^{2}\)
C \(Q^{2}P\)
D \(PQ\)

Question 227:

Given that \(P = \begin{pmatrix} 4 & 9 \end{pmatrix}\) and \(Q = \begin{pmatrix} -1 & -2 \\ 3 & 2 \end{pmatrix}\). Evaluate \(|Q|P\).

A \(\begin{pmatrix} 16 & 36 \end{pmatrix}\)
B \(\begin{pmatrix} 8 & 18 \end{pmatrix}\)
C \(\begin{pmatrix} 8 & 0 \end{pmatrix}\)
D \(\begin{pmatrix} 1 & 2 \end{pmatrix}\)

Question 228:

The equation of a circle is given by \(x^{2} + y^{2} - 4x - 2y - 3\). Find the radius and the coordinates of its centre.

A \(3, (-1, 2)\)
B \(2\sqrt{2}, (2, -1)\)
C \(2\sqrt{2}, (2, 1)\)
D \(9, (2, 1)\)

Question 229:

Simplify \(\frac{^{n}P_{3}}{^{n}C_{2}} + ^{n}P_{0}\)

A N - 5
B N - 3
C 2n - 1
D 2n - 3

Question 230:

X and Y are two independent event. If \(P(X) = \frac{1}{5}\) and \(P(X \cap Y) = \frac{2}{15}\), find \(P(Y)\).

A \(\frac{2}{3}\)
B \(\frac{2}{5}\)
C \(\frac{1}{3}\)
D \(\frac{1}{5}\)