Which of these values would make \(\frac{3p – 1}{p^{2} – p}\) undefined?
- A. 1
- B. \(\frac{1}{3}\)
- C. -\(\frac{1}{3}\)
- D. -1
Simplify: \(\frac{x^2 – 5x – 14}{x^2 – 9x + 14}\)
- A. \(\frac{x - 7}{x + 7}\)
- B. \(\frac{x + 7}{x - 7}\)
- C. \(\frac{x - 2}{x + 4}\)
- D. \(\frac{x + 2}{x - 2}\)
There are 8 boys and 4 girls in a lift. What is the probability that the first person who steps out of the lift will be a boy?
- A. \(\frac{1}{6}\)
- B. \(\frac{1}{4}\)
- C. \(\frac{2}{3}\)
- D. \(\frac{1}{2}\)
If (0.25)\(^y\) = 32, find the value of y.
- A. y = - \(\frac{5}{2}\)
- B. y = -\(\frac{3}{2}\)
- C. y = \(\frac{3}{2}\)
- D. y = \(\frac{5}{2}\)
If 3p = 4q and 9p = 8q – 12, find the value of pq.
- A. 12
- B. 7
- C. -7
- D. -12
Bala sold an article for #6,900.00 and made a profit of 15%. Calculate his percentage profit if he had sold it for N6,600.00.
- A. 5%
- B. 10%
- C. 12%
- D. 13%
Simplify: \(\log_{10}\) 6 – 3 log\(_{10}\) 3 + \(\frac{2}{3} \log_{10} 27\)
- A. 3 \(\log_{10}^2\)
- B. \(\log_{10}^2\)
- C. \(\log_{10}^3\)
- D. 2 \(\log_{10}^3\)
Solve \(4x^{2}\) – 16x + 15 = 0.
- A. x = 1\(\frac{1}{2}\) or x = -2\(\frac{1}{2}\)
- B. x = 1\(\frac{1}{2}\) or x = 2\(\frac{1}{2}\)
- C. x = 1\(\frac{1}{2}\) or x = -1\(\frac{1}{2}\)
- D. x = -1\(\frac{1}{2}\) or x -2\(\frac{1}{2}\)
H varies directly as p and inversely as the square of y. If H = 1, p = 8 and y = 2, find H in terms of p and y.
- A. H = \(\frac{p}{4y^2}\)
- B. H = \(\frac{2p}{y^2}\)
- C. H = \(\frac{p}{2y^2}\)
- D. H = \(\frac{p}{y^2}\)
If m : n = 2 : 1, evaluate \(\frac{3m^2 – 2n^2}{m^2 + mn}\)
- A. \(\frac{4}{3}\)
- B. \(\frac{5}{3}\)
- C. \(\frac{3}{4}\)
- D. \(\frac{3}{5}\)
Evaluate: 2\(\sqrt{28} – 3\sqrt{50} + \sqrt{72}\)
- A. 4\(\sqrt{7} - 21 \sqrt{2}\)
- B. 4\(\sqrt{7} - 11 \sqrt{2}\)
- C. 4\(\sqrt{7} - 9 \sqrt{2}\)
- D. 4\(\sqrt{7} + \sqrt{2}\)
If 6, P, and 14 are consecutive terms in an Arithmetic Progression (AP), find the value of P.
- A. 9
- B. 10
- C. 6
- D. 8
If 23\(_y\) = 1111\(_{\text{two}}\), find the value of y
- A. 4
- B. 5
- C. 6
- D. 7
Evaluate; \(\frac{\log_3 9 – \log_2 8}{\log_3 9}\)
- A. -\(\frac{1}{3}\)
- B. \(\frac{1}{2}\)
- C. \(\frac{1}{3}\)
- D. -\(\frac{1}{2}\)
If T = {prime numbers} and M = {odd numbers} are subsets of \(\mu\) = {x : 0 < x ≤ 10} and x is an integer, find (T\(^{\prime}\) n M\(^{\prime}\)).
- A. {4, 6, 8, 10}
- B. {1. 4, 6, 8, 10}
- C. {1, 2, 4, 6, 8, 10}
- D. {1, 2, 3, 5, 7, 8, 9}
If 7 + y = 4 (mod 8), find the least value of y, 10 \(\leq y \leq 30\)
- A. 11
- B. 13
- C. 19
- D. 21
Simplify, correct to three significant figures, (27.63)\(^2\) – (12.37)\(^2\)
- A. 614
- B. 612
- C. 611
- D. 610
Solve: \(\frac{y + 1}{2} – \frac{2y – 1}{3}\) = 4
- A. y = 19
- B. y = -19
- C. y = -29
- D. y = 29
Evaluate: (0.064) – \(\frac{1}{3}\)
- A. \(\frac{5}{2}\)
- B. \(\frac{2}{5}\)
- C. -\(\frac{2}{5}\)
- D. -\(\frac{5}{2}\)
Express, correct to three significant figures, 0.003597.
- A. 0.359
- B. 0.004
- C. 0.00360
- D. 0.00359
(a)
In the diagram. \(\over{Rs}\) and \(\over{RT}\) are tangent to the circle with centre O, < TUS = 68\(^o\), < SRT = x and < UTO = y. Find the value of x.
(b) Two tanks A and B are filled to capacity with diesel. Tank A holds 600 litres diesel more than tank B. If 100 litres of diesel was pumped cut of each tank, tank A would then contain 3 times as much as tank B. Find the capacity of each tank.