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Question 1 of 125
1. Question
Solve for p in this following equation given in base two.
11(p+110) = 1001p
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Question 2 of 125
2. Question
In a class, 37 students take at least one of chemistry, economics and government, 8 students take chemistry, 19 take economics and 25 take government. 12 students take economics and government but nobody takes chemistry and economics. How many students take both chemistry and government?
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Question 3 of 125
3. Question
A businessman invested a total of N200,000 in two companies which paid dividends of 5% and 7% respectively. If he received a total of N11,600 as dividends, how much did he invest at 5%?
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Question 4 of 125
4. Question
A cyclist rode for 30 minutes at x km/hr. if the total distance covered is less than 60km, what is the range of values of x?
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Question 5 of 125
5. Question
Z is a partly constant and partly varies inversely as the square of d. when d = 1, z = 11, and when d= 2, z = 11, Find the value of z when d = 4.
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Question 6 of 125
6. Question
Factorize 16(3x+2y)2 — 25(a+2b)2
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Question 7 of 125
7. Question
Find the number of ways of selecting 8 subjects from 12 subjects for an examination.
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Question 8 of 125
8. Question
Let log y + log 3 = 3. Then, y is
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Question 9 of 125
9. Question
Expand the expression (x2-2x-3)(x2+x+1)
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Question 10 of 125
10. Question
A girl walks 30m from a point P on a bearing of 040o to a point Q. She then walks 30m on a bearing of 140° to a point R. the bearing of B from P is
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Question 11 of 125
11. Question
A regular polygon has each of it angles as 160°. What is the number of sides of the polygon?
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Question 12 of 125
12. Question
The interior angles of a pentagon are: 180o, 118o, 80o, 78o and x. The value of x is:
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Question 13 of 125
13. Question
All the vertices of an isosceles triangle lie on a circle and each of the base angles of the triangle is 65°. The angle subtended at the center of the circle: by the base of the triangle is:
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Question 14 of 125
14. Question
A square tile measures 20cm by 20cm. How many of such files will cover a floor measuring 5m by 4m.
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Question 15 of 125
15. Question
The volume of a certain sphere is numerically equal to twice its surface area. The diameter of the sphere is:
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Question 16 of 125
16. Question
A bearing of 310o, expressed as a compass bearing is:
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Question 17 of 125
17. Question
The average of the three children in a family is 9 years. If the average age of their parents is 39 years, the average age of the whole family is:
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Question 18 of 125
18. Question
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Question 19 of 125
19. Question
Evaluate x in base 3 if 41x – 22x = 17x
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Question 20 of 125
20. Question
A woman buys 4 bags of rice for N56 per bag and 3 bags of beans for N26 per bag using the currency “NAIRA” (N) in base 7. What is the total cost of the items in another currency “ANTI” (A) in base 8?
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Question 21 of 125
21. Question
When the price of egg was raised by N2 an egg, the’ number of eggs which can be bought for N120 is reduced by N5. The present price of an egg is
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Question 22 of 125
22. Question
How long will it take a sum of money invested at 8% simple interest to double the original sum?
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Question 23 of 125
23. Question
The journey from Lagos to Ibadan usually takes a motorist 1 hour 30 minutes. By increasing his average speed by 20km/hr, the motorist saves 15 minutes. his usual speed, in km/hr is
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Question 24 of 125
24. Question
The smallest section of a rod which can be cut into exactly equal sections, each of either 30cm or 36cm in length is
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Question 25 of 125
25. Question
If x = 0.0012 + 0.00074 + 0.003 174, what is the difference between x and 2 decimal places and x to 1 significant figure?
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Question 26 of 125
26. Question
The angle of depression of two-point A and B on a plane field from the top of a mast erected between A and B are 30° and 45° respectively. If A is westward of B, find |AB| if the height of the mast is 15 m from the field.
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Question 27 of 125
27. Question
The radius of a circle is given as 10cm subject to an error of 0.2cm. The error is the arc of the circle is?
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Question 28 of 125
28. Question
In a survey of 100 students in an institution, 80 students speak Yoruba, 22 speak Igbo, while 6 speak neither Igbo nor Yoruba. How many students speak Yoruba and Igbo.
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Question 29 of 125
29. Question
A bag contains 5 yellow balls, 6 green and 9 black balls. A ball is drawn from the bag. What is the inability that it is a black or yellow ball?
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Question 30 of 125
30. Question
The expression a3 + b3 is equal to
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Question 31 of 125
31. Question
A cylinder has height 4cm and base radius 5cm. its volume to 3 significant figure is
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Question 32 of 125
32. Question
Find the value of P if the line joining (P, 4) and (6, -2) is perpendicular to the line joining (2, P) and (-1, 3)
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Question 33 of 125
33. Question
Dividing 2x – x – 5x + 1 by x + 3 gives the remainder
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Question 34 of 125
34. Question
Let f(x) = 2x – 3x – 5x + 6. If x – 1 divides f(x) find the zeros of the function.
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Question 35 of 125
35. Question
The difference of two numbers is 10, while their product is 39. Find these numbers
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Question 36 of 125
36. Question
The average age of x pupils in a class is 14 years 2 months. A pupil of 15 years 2 months joins the class and the average age is increased by one month. Find x.
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Question 37 of 125
37. Question
If the distance covered by a body in time t seconds is s = t3 – 6t2 – 5t, what is its initial velocity?
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Question 38 of 125
38. Question
In a throw of a fair die the probability of obtaining an even number is
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Question 39 of 125
39. Question
Two fair coins are tossed simultaneously. What is the probability of obtaining at least 1 tail turns up?
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Question 40 of 125
40. Question
One angle of a polygon has each of its angles as 160°. What is the number of sides of the polygon?
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Question 41 of 125
41. Question
One angle of an octagon is 100o while the other sides are equal. Find each of these exterior angles.
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Question 42 of 125
42. Question
In a right-angled triangle, tan Ө = -3/4, what is the value of sin Ө + cosӨ?
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Question 43 of 125
43. Question
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Question 44 of 125
44. Question
The coordinates of the point dividing the line AB (-1, 2) and B(3, 4) extremely in the ratio 3:2 is
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Question 45 of 125
45. Question
The point P (p, 5) lies on the line joining A (1, 2) and B (-4, 7). The ratio AP: AB is
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Question 46 of 125
46. Question
The ends of a diameter of a circle are (-2, 3) and 4, 7). The equation of the circle is
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Question 47 of 125
47. Question
The centre and radius of the circle with the equation x2 + – 2x + 6y + 5 = 0 are respectively
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Question 48 of 125
48. Question
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Question 49 of 125
49. Question
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Question 50 of 125
50. Question
When the expression pm2 + qm + 1 is divided by (m – 1), it has a remainder of and when divided by (m + l) the remainder is 4. Find p and q respectively.
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Question 51 of 125
51. Question
If a and ß are the roots of the equation x2 – 5x – 7 = 0. a2ß + aß2 is
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Question 52 of 125
52. Question
For what values of m does the equation x2 + 9 (4m + 1)x have equal roots?
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Question 53 of 125
53. Question
If one root of the equation 27x2 + bx + 8 b is the square of the other. Find b
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Question 54 of 125
54. Question
For what values of m does the equation x2 + 9 (4m + 1)x have equal roots?
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Question 55 of 125
55. Question
If log102 = y, express log1012.5 in terms of y
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Question 56 of 125
56. Question
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Question 57 of 125
57. Question
Find the roots of x3 – 2x2 – 5x + 6 = 0
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Question 58 of 125
58. Question
Find the remainder when 3x3 + 5x2 – l1x +4 is divided by x + 3
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Question 59 of 125
59. Question
What factor is common to all the expressions x2 -x, 2x2 – 1 and x2 – 1?
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Question 60 of 125
60. Question
In class of 40 students, 32 offers Mathematics, 24 offer Physics and offer neither Mathematics nor Physics. How many offer both Mathematics and Physics?
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Question 61 of 125
61. Question
The probability of a student passing any exam is 2/3. If the student takes three exams, what is the probability that he will not pass any of them?
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Question 62 of 125
62. Question
Find the mean of the data: 7, -3, 4, -2, 5, -9, 4,.8, -6, 12
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Question 63 of 125
63. Question
Find the value of a if the line 2y — ax + 4 = 0 i perpendicular to the line y + (x/4)7=0
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Question 64 of 125
64. Question
A hunter 1 .6m tall, views a bird on top of a tree at an angle of 45 degrees. If the distance between the hunter and the tree is 10.4m, find the height of the tree.
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Question 65 of 125
65. Question
The sum of the interior angles of a polygon is 20 right angles. How many sides does the polygon have?
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Question 66 of 125
66. Question
A bucket is 12 cm in diameter at the top, 8 cm in diameter at the bottom and 4 cm deep. Calculate its volume
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Question 67 of 125
67. Question
If tan θ= 4/3, calculate sin2 — cos2
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Question 68 of 125
68. Question
Given that R = (1, 3,5,7,9), S = (3, 4, 5) and R = (4,6,8,10), then U is
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Question 69 of 125
69. Question
The binary operation * is defined on the set of integers p and q by p * q pq + p + q. Find 2 * (3 * 4).
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Question 70 of 125
70. Question
The inverse function f(x) = 3x +4 is
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Question 71 of 125
71. Question
If the 9th term of an A.P. is five times the 5 the term, find the relationship between a and d.
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Question 72 of 125
72. Question
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Question 73 of 125
73. Question
Find the derivative of y sin2 (5x) with respect to x.
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Question 74 of 125
74. Question
The value of oC, is the same as the value of
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Question 75 of 125
75. Question
Find the derivative of y sin2 (5x) with respect to x
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Question 76 of 125
76. Question
A circle with radius 5cm has its radius increasing at the rate of 0.2 m/s. What will be the corresponding increase in the area?
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Question 77 of 125
77. Question
The slope of the tangent to the curve y = 3x2 – 2x + 5 at the point (1, 6) is
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Question 78 of 125
78. Question
If dy/dx = 2x — 3 and y = 3 when x = 0, find yin terms of x.
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Question 79 of 125
79. Question
Evaluate: (0.21 x 0.072 x 0.00054) ÷ (0.006 x 1.68 x 0.063), correct to 4 s.f.
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Question 80 of 125
80. Question
If log 10 to base 8 = X, evaluate log 5 to base 8 in terms of X
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Question 81 of 125
81. Question
If {(a2b3c)314)/a-1b4c5} = apbacr. What is the value of p + 2q?
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Question 82 of 125
82. Question
A trader bought 100 oranges at 5 for Nl.20, 20 oranges got spoilt and the remaining were sold at for N1.50. Find the percentage gain or loss.
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Question 83 of 125
83. Question
If 29 x (3Y)9 = 35 x (3Y)5, find the value of Y
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Question 84 of 125
84. Question
If m*n = (m/m —n/m) form, n belongs to R, evaluate 3*4
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Question 85 of 125
85. Question
Factorize completely X2 + 2XY +Y2 + 3X + 3Y — 18
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Question 86 of 125
86. Question
Tope bought X mangoes at N5 .00 each and some apples at N4.00 each. If she bought twice as many apples as mangoes and spent at least N65.00 and at most N130.00, find the range of values of X
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Question 87 of 125
87. Question
Express 1/(x3 — 1) in partial fraction.
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Question 88 of 125
88. Question
Divide 4x3—3x—l by 2x—1.
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Question 89 of 125
89. Question
In AMNO, MN = 6 units, MO =4 units and NO = 12 units. If the bisector of N and M meets NO at P, calculate NP
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Question 90 of 125
90. Question
From a point P, the bearings of two points Q and R are 67°W and N23°E respectively. If the bearing of R from Q is N68°E and PQ = 150m, calculate PR.
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Question 91 of 125
91. Question
A two -digit number, say AB was mistakenly written as BA by an overworked student. Due to this error, the student was working with a number bigger in value, and its difference with the actual number is one less than the actual number. If the sum of the two digits is half a score. What is the actual number?
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Question 92 of 125
92. Question
Evaluate ʃzo (sin x – cos x) dx. Where letter z π /4
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Question 93 of 125
93. Question
Let P={l,2,u,v,w,x};Q={2,3,u,v,w,5,6,y}and R={2,3,4,v,x,y}. Determine (P – Q) n R.
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Question 94 of 125
94. Question
A man wishes to keep his money in a savings deposit at 25% compound interest so that after three years he can buy a car for Nl50,000. How much does he need to deposit?
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Question 95 of 125
95. Question
If 31410 —2567 = 340x, find x.
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Question 96 of 125
96. Question
The third term of an A.P. is 4x — 2y and the tenth term is 10x — 8y. Find the common difference.
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Question 97 of 125
97. Question
A trader realizes 10x — x2 naira profit from the sale of x bags of corn. How many bags will give him the desired profit?
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Question 98 of 125
98. Question
Solve the inequality 2 – x> x2
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Question 99 of 125
99. Question
If a and β are the roots of the equation 3x2 + 5x —2 = 0, find the value of 1/ a + 1/ β
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Question 100 of 125
100. Question
An equilateral triangle of side √3cm is inscribed n a circle. Find the radius of the circle.
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Question 101 of 125
101. Question
If y = 2x — sin 2x, find dy/dx when x = π/4.
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Question 102 of 125
102. Question
If the volume of a hemisphere is increasing at a steady rate of 18 m/s, at what rate is its radius changing when it is 6m?
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Question 103 of 125
103. Question
If the mean of the numbers 0, (x + 2), (3x +6) and (4x + 8) is 4, find their mean deviation.
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Question 104 of 125
104. Question
In how many ways can the word MATHEMATICS be arranged?
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Question 105 of 125
105. Question
The variance of x, 2x, 3x, 4x and 5x is
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Question 106 of 125
106. Question
Find the sum of the range and the mode of the set of numbers: 10, 9, 10, 9, 8, 7, 7, 10, 8, 10, 8, 4, 6, 9, 10, 9, 10, 9, 7, 10, 6, 5
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Question 107 of 125
107. Question
In how many ways can a delegation of 3 be chosen from among 5 men and 3 women, if at least one man and at least one woman must be included?
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Question 108 of 125
108. Question
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Question 109 of 125
109. Question
Find the range of these fractions: 1/6, 1/3, 3/2, 2/3, 8/9 and 4/3
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Question 110 of 125
110. Question
Find the number of ways of selecting 8 subjects from 12 subjects for an examination.
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Question 111 of 125
111. Question
Teams P and Q are involved in a game of football. What is the probability that the game ends in a draw?
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Question 112 of 125
112. Question
Find the rate of change of the volume V of a sphere with respect to its radius r, when r = 1
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Question 113 of 125
113. Question
Differentiate (2x + 5)2 (x -4) with respect to x.
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Question 114 of 125
114. Question
P (-6, 1) and Q (6, 6) are the two ends of the diameter of a given circle. Calculate the radius.
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Question 115 of 125
115. Question
Find the number of sides of a regular polygon whose interior angle is twice the exterior angle
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Question 116 of 125
116. Question
A sector of a circle of radius 7.2 cm which subtends an angle of 300 at the centre is used to form a cone. What is the radius of the base of the cone?
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Question 117 of 125
117. Question
Solve the equations: m2+n2= 29, m+ n 7
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Question 118 of 125
118. Question
Find the principal which amounts to N5,500 at a simple interest in 5 years at 2% per annum.
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Question 119 of 125
119. Question
If x = (y/2), evaluate {(x3/y3) + (1/2)} ÷ {(1/2) — (x2/y2)}
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Question 120 of 125
120. Question
Expression ax2 + bx + c equals 5 at x = 1. If its derivative is 2x + 1, what re the values of a, b, c respectively?
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Question 121 of 125
121. Question
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Question 122 of 125
122. Question
If the minimum value of y = 1 + hx – 3x2 is 13, find h.
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Question 123 of 125
123. Question
In a youth club with 94 members, 60 like modem music, and 50 like traditional music. The number of members who like both traditional and modem music is three times that of those who do not like any type of• music. How many members like only one type of muscle?
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Question 124 of 125
124. Question
Simplify 3(2 n+1) – 4(2 n-1) ÷2 n+1 – 2n
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Question 125 of 125
125. Question
If (x – 1), (x + 1) and (x – 2) are factors of the polynomial ax3 + bx2 + cx — 1, find a, b, c in that order
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