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Question 1 of 50
1. Question
Let Q, N, Z, C and Qc denote the set of Rational, Natural, Integer, Complex and Irrational numbers respectively. Which of the following set contains the whole set of real number?
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Question 2 of 50
2. Question
Determine the solution set of the inequality: 2x2-3x 2<0
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Question 3 of 50
3. Question
Evaluate the conjugate of the complex number: z = 1/-1+i
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Question 4 of 50
4. Question
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Question 5 of 50
5. Question
Find tan 750 in surd form
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Question 6 of 50
6. Question
Given that log102 = 0.3010, log103 = 0.4771 and log107= 0.8451, compute log1472.
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Question 7 of 50
7. Question
If U1 = 3, U2 = 4 and Un = a + bn, computer U6.
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Question 8 of 50
8. Question
Let α and β be the roots of the equation: x2 + 5x + 6 = 0 = 0. Deduce the equation whose roots are α2 and β2.
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Question 9 of 50
9. Question
Which form of partial fraction is equivalent to the algebraic fraction:
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Question 10 of 50
10. Question
Determine the center and the radius of the circle x2 + y2 – 2ax + 2yb + a2 = 0 in term of a and b.
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Question 11 of 50
11. Question
Express 1 + i in the conjugate of its polar
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Question 12 of 50
12. Question
A binary equation, ‘*’ is defined on the set of real numbers, R by : x*y = 1/5 (5x+ 5y-4) for any two real numbers x, y є R. Calculate the identity element.
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Question 13 of 50
13. Question
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Question 14 of 50
14. Question
Calculate the sum to infinity of 1 + tan300 + tan2300 + tan3300 + …
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Question 15 of 50
15. Question
Estimate the value of the product log23 log34 log45 log56 log67 log78
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Question 16 of 50
16. Question
Let the expression ax2 + bx + c = 8 at x = 1, if the derivative is 4x+2, determine the values of a, b and c respectively
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Question 17 of 50
17. Question
The distance, S in metres moved by a particle in time, t in seconds is given by S(t) = 3.5t3 – 2t. Evaluate its speed after 2 seconds.
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Question 18 of 50
18. Question
Calculate the gradient of the curve y = x3 – 3x2 + 7x + 23 at the point (2, 1)
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Question 19 of 50
19. Question
Find the derivative of the line joining the points A(3,5), to b(6,-8)
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Question 20 of 50
20. Question
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Question 21 of 50
21. Question
Give that x = Sin (t) and y = cos(t), then the letter t simply called that _______
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Question 22 of 50
22. Question
Given that y = Cos 2θ, x = Sin θ. Express in dy/dx term of θ.
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Question 23 of 50
23. Question
Let the given curve of a parabola be y2 = x. Estimate the area of the curve in terms of x.
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Question 24 of 50
24. Question
Find the derivative of the function y = loge tan 2x.
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Question 25 of 50
25. Question
The radius of a sphere in increasing at the rate of 0.1cm/s. Determine the rate at which the surface area is increasing when the radius is 5cm.
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Question 26 of 50
26. Question
Evaluate y in terms of x if dy/dx = 3x2 – 6x + 2, given that y = 7 when x = 0
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Question 27 of 50
27. Question
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Question 28 of 50
28. Question
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Question 29 of 50
29. Question
The expression or e-x is given as __________
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Question 30 of 50
30. Question
Describe the unit vector in the direction of 2i + j – 2k
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Question 31 of 50
31. Question
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Question 32 of 50
32. Question
An object of mass 2.5kg moving at a constant velocity or 12ms-1 comes in contact with a resistance of 10N. How long does it take the body to come to rest?
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Question 33 of 50
33. Question
With what velocity should a stone be thrown vertically upwards to reach the top of a hill 50m high?
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Question 34 of 50
34. Question
A truck travelling on level ground is subject to a resisting force (from the brakes and air resistance) of 250KN for a distance of 5km. How much kinetic energy does the train lose?
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Question 35 of 50
35. Question
A body starts from rest and moves with a uniform acceleration of 100ms-1. Calculate the distance it covers in the 4th second.
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Question 36 of 50
36. Question
A stone is dropped from the top of a building and reaches the ground after 2 seconds. Determine the height of the building (Take g = 9.8ms-2)
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Question 37 of 50
37. Question
A load of mass 70kg is placed in a lift. Calculate the reaction between the floor of the lift and the load when the lift moves upwards with an acceleration of 2ms-2.
(Take g = 9.8ms-2)
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Question 38 of 50
38. Question
A block of mass 3kg rests on a rough horizontal table. If the coefficient of friction between the block and the table is 0.43, determine the minimum horizontal forces that will make the (Take g = 9.8ms-2)
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Question 39 of 50
39. Question
Three-point A, B and C have spatial coordinates (-5, -2, 3), (-2, 5, 3) and (4, 5, 2) respectively. Find the scalar product of displacement vectors and AB and BC
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Question 40 of 50
40. Question
The mean score of 100 students in a class that took a statistics test is 72. IF the mean of score of the 70 boys in the class is 75, calculate the mean score of the girls in the class.
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Question 41 of 50
41. Question
In how many ways can be first, second and third position be won by six athletes in a race of 100 metres?
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Question 42 of 50
42. Question
A bag contains 5 white, 2 black and 3 green balls. IF three (3) balls are drawn at random without replacement, what is the probability that two (2) balls are white and one (1) ball is black?
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Question 43 of 50
43. Question
When a distribution is moderately skewed wit one mode, which of the following relation is correct?
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Question 44 of 50
44. Question
Which of the measures of central tendency is often affected by extreme values?
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Question 45 of 50
45. Question
The heights, xcm of a sample of 80 female students are summarized by the equation Ʃ(x-160) = 24.0. Compute the mean height of a female student.
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Question 46 of 50
46. Question
A fair coin is tossed 5 times, Find the probability of obtaining at least 4 heads.
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Question 47 of 50
47. Question
Deduce the mode of 6, 8, 2, 1, 1, 2, 4, 2, 3.
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Question 48 of 50
48. Question
A population with variance 16 has an unknown mean µ. Let X be the mean of a random sample of size 100 from this population. If X is used to estimate µ, determine the standard error of X.
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Question 49 of 50
49. Question
What is the mean value of a binominal variate whose number of repeated trials (n) equal to 8 and probability of success (p) equals 0.4?
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Question 50 of 50
50. Question
The probability that a patient will die while undergoing a delicate heart operation is 0.175. What is the probability of the patient surviving from the operation?
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