Two buses start from the same station at 9.00am and travel in opposite directions along the same straight road. The first bus travel at a speed of 72 km/h and the second at 48 km/h. At what time will they be 240km apart?
- A. 1:00 pm
- B. 12:00 noon
- C. 11:00 am
- D. 10:00 am
Given that x is directly proportional to y and inversely proportional to Z, x = 15 when y = 10 and Z = 4, find the equation connecting x, y and z
- A. x = \(\frac{6y}{z}\)
- B. x = \(\frac{12y}{z}\)
- C. x = \(\frac{3y}{z}\)
- D. x = \(\frac{3y}{2z}\)
Find the quadratic equation whose roots are \(\frac{1}{2}\) and -\(\frac{1}{3}\)
- A. 3x\(^2\) + x + 1 = 0
- B. 6x\(^2\) + x - 1 = 0
- C. 3x\(^2\) + x - 1 = 0
- D. 6x\(^2\) - x - 1 = 0
Make m the subject of the relation k = \(\sqrt{\frac{m – y}{m + 1}}\)
- A. m = \(\frac{y + k^2}{k^2 + 1}\)
- B. m = \(\frac{y + k^2}{1 - k^2}\)
- C. m = \(\frac{y - k^2}{k^2 + 1}\)
- D. m = \(\frac{y - k^2}{1 - k^2}\)
Solve \(\frac{1}{3}\)(5 – 3x) < \(\frac{2}{5}\)(3 – 7x)
- A. x > \(\frac{7}{22}\)
- B. x < \(\frac{7}{22}\)
- C. x > \(\frac{-7}{27}\)
- D. x < \(\frac{-7}{27}\)
The first term of a geometric progression (G.P) is 3 and the 5th term is 48. Find the common ratio.
- A. 2
- B. 4
- C. 8
- D. 16
The implication x \(\to\) y is equivalent to?
- A. ~ y \(\to\) ~ x
- B. y \(\to\) ~ x
- C. ~ x \(\to\) ~ y
- D. y \(\to\) x
Solve 3x – 2y = 10 and x + 3y = 7 simultaneously
- A. x = -4 and y = 1
- B. x = -1 and y = -4
- C. x = 1 and y = 4
- D. x = 4 and y = 1
If x = 3 and y = -1, evaluate 2(x\(^2\) – y\(^3\))
- A. 24
- B. 22
- C. 20
- D. 16
Given that \(\frac{\sqrt{3} + \sqrt{5}}{\sqrt{5}}\)
= x + y\(\sqrt{15}\), find the value of (x + y)
- A. 1\(\frac{3}{5}\)
- B. 1\(\frac{2}{5}\)
- C. 1\(\frac{1}{5}\)
- D. \(\frac{1}{5}\)
An amount of N550,000.00 was realized when a principal, x was saved at 2% simple interest for 5 years. Find the value of x
- A. N470,000.00
- B. N480,000.00
- C. N490,000.00
- D. N500,000.00
If 101\(_{\text{two}}\) + 12\(_y\) = 23\(_{\text{five}}\). Find the value of y
- A. 8
- B. 7
- C. 6
- D. 5
Express 1 + 2 log10\(^3\) in the form log10\(^9\)
- A. log10\(^{90}\)
- B. log10\(^{19}\)
- C. log10\(^{9}\)
- D. log10\(^{6}\)
Simplify; [(\(\frac{16}{9}\))\(^{\frac{-3}{2}}\) x 16\(^{\frac{-3}{4}}\)]\(^{\frac{1}{3}}\)
- A. \(\frac{3}{4}\)
- B. \(\frac{9}{16}\)
- C. \(\frac{3}{8}\)
- D. \(\frac{1}{4}\)
If X = {x : x < 7} and Y = {y:y is a factor of 24} are subsets of \(\mu\) = {1, 2, 3…10} find X \(\cap\) Y.
- A. {2, 3, 4, 6}
- B. {1, 2, 3, 4, 6}
- C. {2, 3, 4, 6, 8}
- D. {1, 2, 3, 4, 6, 8}
Evaluate and correct to two decimal places, 75.0785 – 34.624 + 9.83
- A. 30.60
- B. 50.29
- C. 50.28
- D. 30.63
In the diagram, \(\overline{RT}\) and \(\overline{RT}\) are tangent to the circle with centre O. < TUS = 68 °, < SRT = x, and < UTO = y. Find the value of x.
(b) Two tanks A and B am filled to capacity with diesel. Tank A holds 600 litres of diesel more than tank B. If 100 litres of diesel was pumped out of each tank, tank A would then contain 3 times as much diesel as tank B. Find the capacity of each tank.
(a) Given that sin y = \(\frac{8}{17}\) find the value of \(\frac{tan y}{1 + 2 tan y}\)
(b) An amount of N300,000.00 was shared among Otobo, Ada and Adeola. Otobo received N60,000.00, Ada received \(\frac{5}{10}\) of the remainder, while the rest went to Adeola. In what ratio was the money shared?
(a) The third and sixth terms of a Geometric Progression (G.P) are and \(\frac{1}{4}\) and \(\frac{1}{32}\) respectively.
Find:
(i) the first term and the common ratio;
(ii) the seventh term.
(b) Given that 2 and -3 are the roots of the equation ax\(^2\) ± bx + c = 0, find the values of a, b and c.
A woman bought 130 kg of tomatoes for 52,000.00. She sold half of the tomatoes at a profit of 30%. The rest of the tomatoes began to go bad, she then reduced the selling price per kg by 12%. Calculate:
(a) the new selling price per kg;
(ii) the percentage profit on the entire sales if she threw away 5 kg of bad tomatoes.
(a) Copy and complete the table of values for y = 2 cos x + 3 sin x for 0\(^o\) \(\geq\) x \(\geq\) 360\(^o\)
| x | 0\(^o\) | 60\(^0\) | 120\(^o\) | 180\(^o\) | 240\(^o\) | 300\(^o\) | 360\(^o\) |
| y | 2.0 | – 3.6 |
(b) Using a scale of 2cm to 60\(^o\) on the x-axis and 2cm to 1 unit in the y-axis, draw the graph of y = 2 cos x + 3 sin x for 0\(^o\) \(\geq\) 360\(^o\)
(c) Using the graph,
(i) Solve 2 cos x + 3 sin x = -1
(ii) Find, correct to one decimal place, the value of y when x = 342\(^o\)