Further Mathematics Past Questions and Answers

(a) \(m \begin{pmatrix} 2 \\ 1 \end{pmatrix} + n \begin{pmatrix} -1 \\ 2 \end{pmatrix} = \begin{pmatrix} 5 \\ -4 \end{pmatrix}\) where m and n are scalars. Find the value of (m + n).
(b) A(-1, 3), B(2, -1) and C(5, 3) are the vertices of \(\Delta\) ABC.
(i) Express in column notation, the unit vectors parallel to AB and AC.
(ii) Use a dot product to calculate \(\stackrel \frown{BAC}\), correct to the nearest degree.

Which of the following sets is equivalent to \((P \cup Q) \cap (P \cup Q')\)?

Which of the following sets is equivalent to \((P \cup Q) \cap (P \cup Q')\)?

Simplify: \(\frac{\cos 2\theta - 1}{\sin 2\theta}\)

Solve the inequality \(x^{2} - 2x \geq 3\)