Given that p = \(\begin{pmatrix} m + 1 & m – 1 \\ m + 4 & m – 8 \end{pmatrix}\) and |p| = – 34, find the value of m.
- A. 5
- B. 4
- C. 3
- D. 2
If p = \(\begin{pmatrix}2 \\ 4 \end{pmatrix}\) and q = \(\begin{pmatrix} 10 \\ -1 \end{pmatrix}\), find a vector, r such that 2p – 3r = q
- A. \(\begin{pmatrix} -2 \\ 3 \end{pmatrix}\)
- B. \(\begin{pmatrix} -26 \\ 11 \end{pmatrix}\)
- C. \(\begin{pmatrix} 2 \\ 3 \end{pmatrix}\)
- D. \(\begin{pmatrix} 6 \\ -9 \end{pmatrix}\)
Solve 2\(^{2x}\) – 5(2\(^x\)) + 4 = 0
- A. x = 0 and 2
- B. x = 1 and 2
- C. x = 0 and 1
- D. x = 2 and 4
If f(x) = \(\frac{2 – x}{x}\), x ≠ 0, find the inverse of f.
- A. \(\frac{2}{x - 1}\), x ≠ 1
- B. \(\frac{2}{x+1}\), x ≠ -1
- C. \(\frac{2}{1-x}\), x ≠ 1
- D. \(\frac{x}{2 + x}\), x ≠ -2
Evaluate: \(\frac{cos^2 300º – 4sin^2 120º}{tan^2 135º}\)
- A. -2\(\frac{3}{4}\)
- B. -3\(\frac{3}{4}\)
- C. -2\(\frac{1}{4}\)
- D. -3\(\frac{1}{4}\)
If log\(_2^x\) = 2, evaluate log\(_x^{128}\).
- A. 7
- B. 2
- C. \(\frac{7}{2}\)
- D. \(\frac{2}{7}\)
If 5x + 7 \(\equiv\) P(x + 3) + Q(x – 1), find the value of p
- A. 3
- B. 2
- C. 1
- D. 0
If h(x) = x\(^2\) + px + 2 is divided by (x + 3), the remainder is 5, find p
- A. 4
- B. 3
- C. 2
- D. 1
If the n\(^{th}\) term of a linear sequence (A.P) is (5n – 2), find the sum of the first 12 terms of the sequence.
- A. 120
- B. 183
- C. 366
- D. 732
A binary operation * is defined on the set of real numbers, R by x * y = \(\frac{y^2 – x^2}{2xy}\), x, y ≠ 0, where x and y are real numbers. Evaluate -3 * 2
- A. \(\frac{5}{12}\)
- B. \(\frac{13}{12}\)
- C. -\(\frac{5}{12}\)
- D. -\(\frac{13}{12}\)
\(\sqrt{x}\) – \(\frac{6}{\sqrt{x}}\) = 1, find the value of x
- A. 36
- B. 16
- C. 9
- D. 25
Given that f: x → \(\sqrt{x}\) and g : x → 25 – x\(^2\), find the value of f o g(3)
- A. 4
- B. 3
- C. 2
- D. 1
If \(\frac{5}{\sqrt{2}}\) – \(\frac{\sqrt{8}}{8}\) = m\(\sqrt{2}\), find the value of m
- A. \(\frac{12}{5}\)
- B. \(\frac{9}{4}\)
- C. \(\frac{7}{3}\)
- D. \(\frac{5}{2}\)