Find the distance between two towns P(45°N, 30°W) and Q(15°S, 30°W) if the radius of the earth is 7000km. [\(\pi = \frac{22}{7}\)]
- A. \(\frac{1100}{3}\)km
- B. \(\frac{2200}{3}\)km
- C. \(\frac{22000}{3}\)km
- D. \(\frac{1100}{3}\)km
In a triangle XYZ, < YXZ = 44° and < XYZ = 112°. Calculate the acute angle between the internal bisectors of < XYZ and < XZY.
- A. 12o
- B. 56o
- C. 68o
- D. 78o
If x = \(\begin{pmatrix} 1 & 2 \\ 0 & 3 \end{pmatrix}\) and y = \(\begin{pmatrix} 2 & 1 \\ 4 & 3 \end{pmatrix}\). Find xy.
- A. \(\begin{pmatrix} 10 & 7 \\ 12 & 9 \end{pmatrix}\)
- B. \(\begin{pmatrix} 2 & 7 \\ 4 & 17 \end{pmatrix}\)
- C. \(\begin{pmatrix} 10 & 4 \\ 4 & 6 \end{pmatrix}\)
- D. \(\begin{pmatrix} 4 & 3 \\ 10 & 9 \end{pmatrix}\)
\(\begin{vmatrix} -2 & 1 & 1 \\ 2 & 1 & k \\1 & 3 & -1 \end{vmatrix}\) = 23
- A. 1
- B. 2
- C. 3
- D. 4
Find the sum to infinity of the following sequence \(1, \frac{9}{10}, (\frac{9}{10})^{2}, (\frac{9}{10})^{3}\)
- A. \(\frac{1}{10}\)
- B. \(\frac{9}{10}\)
- C. \(\frac{10}{9}\)
- D. 10
If a \(\ast\) b = + \(\sqrt{ab}\), evaluate 2 \(\ast\)(12 \(\ast\) 27)
- A. 12
- B. 9
- C. 6
- D. 2
Which of the following binary operations is cumulative on the set of integers?
- A. a \(\ast\) b = a + 2b
- B. a \(\ast\) b = a + b - ab
- C. a \(\ast\) b = a2 + b
- D. a \(\ast\) b = \(\frac{a(b + 1)}{2}\)
Express \(\frac{5x – 12}{(x – 2)(x – 3)}\) in partial fractions
- A. \(\frac{2}{x + 2} - \frac{3}{x - 3}\)
- B. \(\frac{2}{x - 2} + \frac{3}{x - 3}\)
- C. \(\frac{2}{x - 3} - \frac{3}{x - 2}\)
- D. \(\frac{5}{x - 3} - \frac{4}{x - 2}\)
Simplify \(\frac{x^2 – 1}{x^3 + 2x^2 – x – 2}\)
- A. \(\frac{1}{x + 2}\)
- B. \(\frac{x - 1}{x + 1}\)
- C. \(\frac{x - 1}{x + 2}\)
- D. \(\frac{1}{x - 2}\)
The 4th term of an A.P. is 13 while the 10th term is 31. Find the 21st term.
- A. 175
- B. 85
- C. 64
- D. 45
Solve the inequality (x – 3)(x – 4) \(\leq\) 0
- A. 3 \(\leq\) x \(\leq\) 4
- B. 3 < x < 4
- C. 3 \(\leq\) x < 4
- D. 3 < x \(\leq\) 4
Factorize completely the expression \(abx^2 + 6y – 3ax – 2byx\)
- A. (ax - 2y)(bx - 3)
- B. (bx + 3)(2y - ax)
- C. (bx + 3)(ax - 2y)
- D. (ax - 2y)(ax - b)
The graph of f(x) = x2 – 5x + 6 crosses the x-axis at the points
- A. (-6, 0), (-1, 0)
- B. (-3, 0), (-2,0)
- C. (-6, 0),(1, 0)
- D. (2, 0), (3, 0)
Find T in terms of K, Q, and S if S = 2r\(\sqrt{\pi(QT + K)}\)
- A. \(\frac{S^2}{2 \pi r^2Q} - \frac{k}{Q}\)
- B. \(\frac{S^2}{2 \pi r^2Q}\) - k
- C. \(\frac{S^2}{4 \pi r^2Q} - \frac{k}{Q}\)
- D. \(\frac{s^2}{4 \pi r^2Q}\)
Finds a positive value of p if the expression 2x2 – px + p leaves a remainder 6 when divided by x – p and q
- A. 1
- B. 2
- C. 3
- D. 4
If x – 1 and x + 1 are both factors of the equation x\(^3\) + px\(^2\) + qx + 6 = 0, evaluate p and q
- A. -6, -1
- B. 6, 1
- C. 1, -1
- D. 6, -6
If S = (x : x\(^2\) = 9, x > 4), then S is equal to
- A. 4
- B. {0}
- C. \(\emptyset\)
- D. {\(\emptyset\)}
Four members of a school first eleven cricket team are also members of the first fourteen rugby team. How many boys play for at least one of the two teams?
- A. 25
- B. 21
- C. 16
- D. 3
Simplify \(\frac{\sqrt{12} – \sqrt{3}}{\sqrt{12} + \sqrt{3}}\)
- A. \(\frac{1}{3}\)
- B. 9
- C. 16cm
- D. 3
Evaluate \(\frac{(81)^{\frac{3}{4}} – (27)^{\frac{1}{3}}}{3 \times 2^3}\)
- A. 27
- B. 1
- C. \(\frac{1}{3}\)
- D. \(\frac{1}{8}\)
Express the product of 0.0014 and 0.011 in standard form
- A. 1.54 x 10-2
- B. 1.54 x 10-3
- C. 1.54 x 10-4
- D. 1.54 x 10-5