1. Calculate the surface area of a solid cylinder with base radius 3.5 cm and height 14 cm. (Take π = [sup]22[/sup]/[sub]7[/sub] )
2. A number is chosen at random from the set {1, 2, 3,…., 19, 20 }. What is the probability that the number is a factor of 5 and even?
3. The table below shows the frequencies (f) of some children of age x years.
|X| 1| 2| 3| 5| 6| 7| 8|
|Y| 3| 4| 5| 7| 6| 5| 4|
Find the mean of their ages
4. Evaluate log[sub]3[/sub] 27 + log[sub]9[/sub]3 – log[sub]3[/sub]22.
5. Find the number of years at which N25,000.00 kept in a bank at 2% per annum simple interest will amount to N27,500.00.
6. The nth of the sequence -1, 5, -7, 17, ……. is given
7. Determine the length of the chord of a circle with radius 9 cm subtending an angle of 120o at the centre.
8. Calculate the product of the matrix
9. The angle of elevation of the top of a communication mast from a point A is 60º. If the mast is 120m high, how far is the point A from the foot of the mast, correct to one decimal place?
10. Find the 12th term of the G.P -3, 6, -12, ……….
11. A manufacturing company is owned by Dr. A and Engr. B and they agreed that their profit will be shared in the ratio 4:7. At the end of the year, Dr. A received N7,500.00 less than Engr. B. What is the net profit of the company for the year ended?
12. Describe the shaded portion in the Venn diagram below?
13. A sector which subtends an angle of 90o was cut from a circle of radius 8 cm and folded to give a come. Find the radius of the cone.
14. Two villages X and Y are on (15ºS, 107ºE) and (15ºS, 17ºE) respectively, what is their distance apart, along the line of latitude? (Leave your answer in terms of π and R, the radius of the earth)
15. If 8[sup]x + 1[/sup] = [sup]1[/sup]/[sub]4[/sub] , find x.
16. If 12x – 5 = 9x - [sup]7[/sup]/[sub]2[/sub] , find 10x.
17. The product of 3 and (x - 2) is greater than or equal to the sum of 15 and twice of x, find the range of value of x.
18. Interior angle of a regular polygon is 162º. How many sides have the polygon?
19. For what value of x is the expression [sup](x-5)[/sup]/[sub](x[sup]2[/sup]-7x+10 )[/sub] undefined?
20. If x = 3, y = 2 and z = 4, what is the value of 3x[sup]2[/sup] – 2y + z ?
21. Write
as a single fraction.22. A rope of length 28cm was given to a boy during the mathematics practical exercise in the mathematics laboratory. He used it to form an isosceles triangle with base of length 12cm. Determine the smallest angle of the triangle. Correct your answer to 1d.p.
23.if
find 2P - Q
24. In the diagram below, /SP/= /SR/ and <PRS = 50º Calculate < PQR.
25. If A = { x: -1 ≤ x < 7} and
B = { x: 5 < x < 9} Where x is an integer, then find n (AUB).
26. Evaluate (204.7)[sup]2[/sup] – (105.3)[sup]2[/sup]
27. Simplify 2161[sup]¹[/sup]/[sub]³[/sub] x 16[sup]-½[/sup] x (3[sup]-2[/sup])[sup]0[/sup]
28. Town A is on a bearing of 025º from town B 10 km away. If town C is on a bearing of 162º and 6 km form town B, Find the distance between A and C to the nearest kilometer.
29. Find x if Cos x = 0.4
30. Find the gradient of a straight line that passes through the points (2,3) and (-1,2)
31. A coin is tossed 3 times. Find the probability of having one tail and two heads.
32. Find the equation whose roots are [sup]- 2[/sup]/[sub]3[/sub] and 3.
33. ABC is a triangle, if /AB/ = 5 cm, /BC/ = 4 cm, /AC/ = 6 cm and D is a point on AC such that BD is a bisector of ABC. Find /AD/.
34.
In the above figure, D is such that BD: CD = 1:2. Find /BC/.
35.
In the diagram above, O is the centre of the circle, POQ is a diameter and <MNQ is 490. What is the value of <MQP?
36. Evaluate [sup](a + b)[/sup]/[sub](a-b) [/sub] for a = -7, b = 3.
37. Two places on the same meridian have latitudes 10ºS and 53ºN. What is their distance apart measured along the meridian? (Take π= [sup]22[/sup]/[sub]7[/sub] , radius of the earth R = 6400 km)
38. A trapezium of area 175 cm[sup]2[/sup] and altitude 10 cm has the length of one of its parallel sides as 15 cm. What will be the length of the other?
39. Find the product of the median and the mode in the table below;
Score |0 |1 |2 |3 |4 |5
Frequency |2 |4 |4 |9 |6 |8
The pie chart above shows how a company spends its income. Use the information given to answer questions 40 and 41
40. What percentage of the company’s income was spent on Taxes?
41. If the company’s income is N240, 000.00, how much was on dividends?
A boy used a rope of x cm long to form two semi-circles of diameters 28 cm and 14 cm respectively, Use this information to answer questions 42 and 43. (Take π=22/7 )
42. Determine the value of x
43. What is the area of the enclosed region it formed?
44. In the diagram below, O is the centre of the circle. If <DOE =1200 and <DAE = 6x, find the value of 3x.
45. Factorize n[sup]2[/sup] + 24n – 81
46. Simplify
47. Evaluate log[sub]3√5[/sub]125
48. If [sup]1[/sup]/[sub]f [/sub]= [sup]1[/sup]/[sub]u[/sub] + [sup]1[/sup]/[sub]v[/sub] , make v the subject of the formula.
49. How far does the tip of a minute hand 10 cm long of a wall clock travels in 45 minutes? (Take∏ =3 [sup]1[/sup]/[sub]7[/sub] )
50. Which of the following is a root of the equation 3x[sup]2[/sup] – 2x - 3 = 0
51. The number 192039 was corrected to 192000 by a student. Which of the following can be the correct approximation of figure taken?
- To the nearest hundred.
- To the nearest thousand.
- To 3 significant figures.
- To 4 significant figures.
52. Find the coordinates of point P.
53. The shaded portion shows the outer boundary of the half plane defined by linear inequality
54. The angle of depression of a fowl on the ground from the top of a pole is 30º. If the distance from the fowl to the foot of the pole is 63 m, calculate the height of the pole and leave your answer in surd form.
Use the frequency table below to answer question 55 to 57.
|Score| 1| 2| 3| 6| 8| 9|
|Frequency| 4| 3| 5| 7| 2| 1|
55. Find the mean score.
56. Find the median score.
57. What is modal score?
58. Solve the inequality [sup](y-1)[/sup]/[sub]2[/sub] ≤ [sup]6[/sup]/[sub]y[/sub]
59. Which of the following is illustrated in the diagram above, if x varies over the set of real number?
60. If 2x + 3y = 19 and 8x = 11 + y, by how much is 7x greater than 2y?
61. Evaluate (1111[sub]two[/sub])[sup]2[/sup] and leave your answer in base 2.
62. Find the LCM of 2[sup]3[/sup] x 3[sup]2[/sup] x 5[sup]2[/sup], 2 x 3[sup]2[/sup] x 5 and 2[sup]2[/sup] x 3[sup]3[/sup] x 5
63. Simply (0.5 x 10[sup]5[/sup]) + (0.4 x 10[sup]7[/sup]), leaving your answer in the standard form
64. If p ∝ [sup]1[/sup]/[sub]q[/sub] , which of the following is true?
65. Simplify 3 √45 – 12 √5 + 16 √20 , leaving your answer in surd form.
66. Describe the set P = {-3.2 ≤ x < 5} where x is an integer?
67. Simplify: [sup]3x[sup]3[/sup][/sup]/[sub]3x[sup]3[/sup][/sub]
68. N140,000 is shared between Abu, Kayode and Uche. Abu has twice as much as Kayode and Kayode has twice as much as Uche. What is Kayode’s share?
69. Differentiate with respect to x; y = [sup]5[/sup]/[sub]x[sup]2[/sup][/sub] - [sup]1[/sup]/[sub]√x[/sub] + 8x[sup]3[/sup]
70. For what value of x is the expression [sup](2x-1)[/sup]/[sub](x+3)[/sub] not defined?
71. If x = 3, y = 1 and z = 5, what is the value of [sup]3x[sup]2[/sup]-2y[/sup]/[sub]z[/sub]
72. Solve the simultaneous equations: x + y = 2 and 3x - 2y = 1
73. If 3[sup]x + 1[/sup] = 9[sup]2x-1[/sup], find x.
74. The area of a square field is 110.25 m[sup]2[/sup]. Find the cost of fencing it round at N 75. 00 per meter.
75. A chord of length 6 cm is drawn in a circle of radius 5 cm. Find the distance of the chord from the centre of the circle.
76. A sector of a circle of radius 14 cm containing an angle 600 is folded to form a cone. Calculate the radius of the base of the cone.
77. Find the sum to infinity of the G.P 9, -3 , + 1, - . . .
78. Find the volume of a solid cylinder with base radius 10 cm and height 14 cm. (Take π = 22/7 )
79. In the diagram, /EF/ = 8 cm, /FG/ = x cm, /GH/ = (x +2) cm, <EFG = 90º. If the area of the shaded portion is 40cm[sup]2[/sup], find the area of EFG.
80. The subtraction below is in base seven. Find the missing number:
81. Simplify: [sup](3x-y)[/sup]/[sub]xy[/sub]-[sup](2x+3y)[/sup]/[sub]2xy[/sub]+[sup]1[/sup]/[sub]2[/sub]
82. Find the value of p if ¼p+3q=10 and 2p-[sup]1[/sup]/[sub]3[/sub]q = 7))
83. If [sup](√2+√3)[/sup]/[sub]√3[/sub] is simplified as m+n√6 , find the value of (m + n).
84. Given the function f: x ----------> 5x – 2, find f[sup]-1[/sup](-1).
85. If a : b = 5 : 3, evaluate [sup]6a+b[/sup]/[sub]a-[sup]1[/sup]/[sub]3[/sub]b[/sub]
86. Solve the equation
. 87. Calculate the mean deviation of 5, 3, 0, 7, 2, 1.
88. The probabilities that kebab, Esa and Saidi will hit a target are [sup]2[/sup]/[sub]3[/sub],[sup]3[/sup]/[sub]4[/sub] and [sup]4[/sup]/[sub]5[/sub] respectively.
Find the probability that only Kebab will hit the target.
89. The angle of elevation of an aircraft from a point k on the ground is 30º. If the aircraft is 800m above the ground, how far is it from K?
90. Simplify the surd;
91. Simplify
92. If
, find the value of x.93. Given that log[sub]x[/sub]64=3, evaluate x log[sub]2[/sub]8.
94. If m = 4,n = 9 and r = 16, evaluate
95. The gradient of the curve 3 + 2x - x[sup]2[/sup] at the point x = -2.5
96. Given that
.Find a+b-c .97. A fair die with faces numbered 1,2,3,4,5,6 is rolled. What is the probability of getting a prime number?
98. Evaluate:
99. The volume of a cone of height 3 cm is 38.5 cm[sup]3[/sup]. Find the radius of its base.
100. Simplify:
101. The operation * on the set Q of rational numbers is defined by:
103. Simplify
104. Simplify
104. Express the product of 0.09 and 0.06 in standard form.
105. Evaluate4610[sub]eight[/sub]-2675[sub]eight[/sub].
106. Simplify
107. Given that log 2 = 0.3010 and log 3 = 0.4771, find the value of log(1.5)[sup]2[/sup] .
108. The shorter hand of the clock points at 9. What number did it point to 30 hours ago?
109. Evaluate log[sub]10[/sub](6x[sup]2[/sup]+x-1)=0
110. The present ages of a mother and her daughter are in the ratio 11: 3 and the daughter’s age is 9. What will be the ratio of the mother to that of her daughter in 5 years’ time?
111. Give the nth term of a sequence as
. Find the first three terms.112. Given the matrix
113. The first term of an Arithmetic Progression is equal to twice the common difference d. find in terms of d, the fifth term of the A.P.
114. If U={x:12≤x<12,x is an integer}, list all the members of U.
115. The common ratio of a Geometric Progression is 2. If the 5th term is greater than the first term by 45, find the 5th term.
117. In a class of 80 students, every student has to offer Economics or Geography or both, if 65 students offered Economics and 50 offered Geography, how many students offered both subjects?
118. If X = {all perfect squares less than 25} and Y = {all odd numbers from 1 to 10}, Find X∩Y.
119. Find the product of a and b if a,[sup]3[/sup]/[sub]2[/sub],[sup]6[/sup]/[sub]7[/sub],b are in a geometric progression.
120. Solve for x if log[sub]x[/sub][sup]1[/sup]/[sub]6[/sub]=[sup]-1[/sup]/[sub]2[/sub].
121. Make k the subject of the formula
y=[sup](px-r)[/sup]/[sub](qx+k)[/sub].
122. Solve the equation7x[sup]2[/sup]=3x.
123. Solve for x if
124. Factorize 7y[sup]2[/sup]+4ay-3a[sup]2[/sup]
125. Solve the simultaneous equations:
3y-2x=1
4y-5x=13
126. Solve the equation 8x[sup]-2[/sup]=[sup]2[/sup]/[sub]25[/sub].
127. Find the equation of the line which passes through P(-5, 3) and Q(2, 3).
128. Given the expression
what value of x is the expression not defined?129. Given that a = 3, b = 9 and c = 1. Evaluate
.130. Simplify x(3x+7)+11x[sup]2[/sup].
131. Factorize 6a[sup]2[/sup]-14a-12.
132. P varies directly as q and inversely as r. if p = 12, r = 19 and q = 8, find q when p = 17 and r =27.
133. Given that ax[sup]2[/sup]+bx+c=0 and a ≠ 0. If b[sup]2[/sup]-4ac >0, then describe the roots.
134. The square root of a number is 4m. What is half of the number?
135. A rectangular tank can hold 15.7 litres of water. If the breadth of the tank is 16.3cm and the height is 45.1cm, calculate its length to 1 decimal place.
In the diagram below, find the value of a + b. correct your answer to one decimal place.
136. A pyramid has a volume of 216 cm3. If the length of the square base is 9 cm, calculate the height of the pyramid.
137. A cone has a base radius of 3cm and a slant height of 5cm. Calculate the volume of the cone in terms of π.
138. A cone is formed from a cylinder. If the radius and the vertical height remain the same, calculate the volume of the cone if that of the cylinder is 102 cm3
139. A point P moves such that it is equidistant from points Q and R. Find /QR/ when /PR/ = 8cm and < PRQ = 30º
140. In the figure below, CD//AE, reflex BCD = 2600 and BAE = 400. Find ABC.
141. PQR is a triangle, given that /PQ/ = 15cm, /QR/ = 17 cm and /RP/ = 18 cm. find the area of the triangle to the nearest whole number.
142. The bearing of Q from P is 0350 while the bearing of R from Q is 1900. If /PQ/ = 24m, and /QR/ = 30 m, find /PR/ to the nearest whole number.
143. Find the value of in the diagram below:
144. In the figure below, O is the centre of the circle , /BO/ is produced to X such that DOX = 37º, calculate DCB.
145. In PQR, p = 5cm , q = 7cm and PRQ = 60º. Find the value of r, correct to two decimal places.
146. If the shadow of a pole 7m high is ½ its length, what is the angle of elevation of the sun, correct to the nearest degree
147. The bearing of a point Q from a point R is 074º. . What is the bearing of R from Q?
148. The angle of the elevation of P from Q is 30º. If /PQ/ = 40m, how high is P above the level of Q
149. Given the set P defined as follows P = {x:-1<x≤7,x is an integer}. Find the probability that an integer chosen at random from P is less than 4.
150. Given the numbers 6, 9, 14, 20 and x. if the angle representing x on the pie chart is 66˚, find x.
151. Two students are chosen at random without replacement from a class consisting of seven boys and seven girls. What is the probability that the two students selected are both boys
152. In a team of 22 players, the heights of six players are measured to be 5.5m each, that of 9 players 6.5m each while the remaining players 7.5m each. Find the average height of the players, correct your answer to one decimal place.
153. Calculate the mean deviation of the following scores: 1, 5,7,8,9.
154. Calculate the variance of the following numbers: 4, 8, 9, 10, 11,12.
155. There are 9 red, 18 green and 27 white balls in a box. If a ball is picked at random, what is the probability that it is red or white ball?
156. The gradient function of a curve is 8x + 2 and it passes through (1, 3). Find the value of the gradient.
157. Find the mean of the distribution: 5, 8, 9, 10, 11,12.
158. Find the median mark: 4, 8, 9, 10, 10,13.
159. Differentiate 3x[sup]2[/sup]+4x-8 with respect to x.
160. The sixth term of an arithmetical progression is half of its twelfth term. Find the first term.
161. Factorize: 4x[sup]2[/sup] – 9y[sup]2[/sup] + 20x + 25
162. If the gradients of the curve y = 2kx[sup]2[/sup] + x + 1 at x = 1 is 9, find k.
163. Find the number of sides of a regular polygon whose interior angle is twice the exterior angle.
164. Evaluate:
, correct to 3 decimal places.165. .A cylindrical tank has a capacity of 3080m3. What is the depth of the tank if the diameter of its base is 14m?
166.
167.
In the figure above, PQR is a straight line segment, /PQ/ = /QT/. Triangle PQT is an isosceles triangle, <SRQ is 75º and <QPT is 25º. Calculate the value of <RST.
168. Simply 0.000215 X 0.000028 and express your answer in standard form.
169. If
make x the subject of the formula.170. Solve the following simultaneous equations; 2x + 3y = 7, x + 5y =0.
171. Evaluate (0. 13)3 correct to three significant figures.
172. Solve the following and illustrates the solution of (3x + 4) < x + 3 on a number line.
174. Arrange the following numbers in descending order of magnitude: 22[sub]three[/sub], 34[sub]five[/sub], 21[sub]six[/sub].
175. Express the square root of 0.00014 in standard form.
176. What must be added to x[sup]2[/sup] – 3x to make it a perfect square?
177. The diameter of a bicycle wheel is 42 cm. if the wheel makes 16 complete revolutions, what will be the total distance covered by the wheel? [Take π = 22/7]
178. In the diagram / TP/ = 12cm and it is 4 cm from O, the centre. Calculate <TOP.
179. In the diagram, O is the centre of the circle. Find the value of x.
180.
In the diagram, the two circles have a common centre O. If the area of the larger circle is 100π and that of the smaller circle is 49π, find x.
181. Make f the subject of the formula
182. Find the gradient of the line joining the points (2,5) and ( - 6, 3).
183. If the angle of a sector of a circle radius 2.5cm is 108º, find the area of the sector.
(Take π = 22/7)
184. Find the coordinate of the mid-point of the line joining the points (-1, -1) and (-3, 5).
185. A polygon has the following interior angles: yº, (y+30)º, 9y+40)º, (y+50)º, (y+60)º
186. Find the radius of the parallel of latitude 60º N correct to 3 significant figures.
(Take R = 6400 km).
187. What is the volume (cm[sup]3[/sup]) of air required to fill a football whose diameter is 8.4 cm? (Take π = 3.14)
188. A (lat. 480N, long. 60º W) and B (Lat. 360S, long. 60ºW) are two places on earth’s surface. Calculate the distance AB along a great circle, correct to three significant figures.(Take π = 22/7 and R= 6400 km)
189. Janet spends her salary as follows: Food 35%, loan repayment 25%, car expenses 12.5%, rents 7.5%, savings 10% and others 10%. What is the sectorial angle of her car expenses?
190. In a set of 100 numbers, ∑fd[sup]2[/sup] = 2500. Find standard deviation.
191. Two dice are thrown together once. What is the probability that the sum of the scores is 8 or 10?
192. The length of a rectangle is thrice as long as its width. If the perimeter is 88cm, find the dimension of the rectangle.
193. Simplify
194. The width of a classroom floor is 5m less than the length. If its area is 24m[sup]2[/sup], find the perimeter of the floor.
195. Solve the equation x(x-5) = 14
196. Evaluate √∪[sup]2[/sup] +2 as when U = 11, a = 4 and s = 13
197. The sum of 3rd and 11th terms of an A.P is 59 and 8th term is 34. Find its common difference.
198. Find the value of x if 27[sup](2x+1)[/sup] =81[sup](x+1)[/sup]
199. Solve the equation 2x -[sup]2[/sup]/[sub]3[/sub] = 8
200. If y = (21x[sup]2[/sup] + 7)[sup]4[/sup], find [sup]dy[/sup]/[sub]dx[/sub]
, leaving your answer in standard form. 
, find the possible values of x if β = 45º
, find scalars m and n such that mx + ny = z.