Lagos State University of Science and Technology, Ikorodu

College of Basic Sciences

Department of Mathematical Sciences
First Semester Examination 2022/2023 Session.

COURSE TITLE: Elementary Mathematics I

COURSE CODE: MTH 101
CLASS: 100L CBS, COA, COE, CET
TIME ALLOWED: 2 hrs
INSTRUCTION: Answer ALL Questions. TYPE A

√
1. Find the value of x if 2 5x−1 =8 10. 4, 16, 256, x. Find x
A. 5 B. 3 C. 2 D. 4 A. 65536 B. 1536 C. 2304 D. 60416

2. Given the expansion (1 + kx)n = 1 + 12x + 60n2 Sum of 3 consecutive terms of an A.P. is 6 and
Find the values of k and n their product is -90. Use the given information to
A. 3,4 B. 2,6 C. 3,5 D. 4,5 answer questions 11 − 12.

If Z1 and Z2 are complex numbers represented by 11. Find the first term.
x1 + iy1 and x2 + iy2 respectively. Use the given A. 2 B. -2 C. -7 D. 7
information to answer question 3 − 8
12. Find the common difference
3. Evaluate |Z1 + Z2 |2 A. ±2 B. ±3 C. ±8 D. ±7
A. x21 + x1 x2 + x22 + y12 + y1 y2 + y22 ( √ √ )
13. The conjugate of 1 − 2 7 + 3 is
B. x21 + 2x1 x2 + x22 + y12 + 2y1 y2 + y22 √ √ √ √
C. x21 + 3x1 x2 + x22 + y12 + 3y1 y2 + y22 A. 1 − 2√ 7 + √ 3 B. 1 + 2√ 7 +√ 3
D. x21 + 4x1 x2 + x22 + y12 + 4y1 y2 + y22 C. 1 + 2 7 + 3 D. 1 − 7 − 3

14. Find the coefficient of x3 in the expansion of

4. Evaluate |Z1 − Z2 |2
(a + 4xy)6
A. x21 − x1 x2 + x22 + y12 − y1 y2 + y22
A. 280a3 y 3 B. 820a3 y 3 C. 1280a3 y 3 D. 1820a3 y 3
B. x21 − 3x1 x2 + x22 + y12 − 3y1 y2 + y22
C. x21 − 2x1 x2 + x22 + y12 − 2y1 y2 + y22
If A = {3, 5, 9, g, h}, B = {1, 2, 3, h, d, f }. Use
D. x21 − 4x1 x2 + x22 + y12 − 4y1 y2 + y22
the information to answer question 15 − 16.
5. Evaluate |Z1 + Z2 |2 + |Z1 − Z2 |2 above
15. Find (A − B) ∩ (B − A)
A. (x21 + x22 + y12 y2 + y22 )
A. {h} B. {1, 2, g} C. {2, 5, d, h} D. {5, d, h}
B. 2(x21 + x22 + y12 y2 + y22 )
C. 3(x21 + x22 + y12 y2 + y22 ) 16. Find A ∆ B
D. 4(x21 + x22 + y12 y2 + y22 ) A. {1, 2, 3, h, g} B. {1, 2, 3, 9, g, h}
C. {1, 2, 5, 9, d, g, f } D. {2, 5, g, h, f }
6. Find the value of |Z1 |2
A. x21 + y12 B. x21 − x22 C. x2 + y 2 D. x2 − y 2 17. Given that log 2 = c and log 3 = d, find log 24.
A. c + d B. 3c + d C. 3d + c D. c − d
7. Find the value of |Z2 |2
A. x21 + x22 B. x22 + y22 C. x2 + y 2 D. x2 − y 2 18. The sum of a series is 4n − 1 for all value of n. Find
the 1st three terms of the series.
8. Find the value of 2(|Z1 |2 + |Z2 |2 ) A. 2, 8, 32 B. 3, 12, 48 C. 3, 6, 32
A. 2(x21 + y12 + x22 + y22 ) D. 3, 12, 32
B. 2(x21 + y12 − x22 + y22 )
C. 2(x21 − y12 + x22 + y22 ) 2+i
If Z = −1+i use the given information to answer
D. 2(x21 − y12 + x22 − y22 ) question 19 − 21
√ √ √ √
9. ( 2√ + 5)( 2 − 5) is √ 19. Evaluate the value of Z
A. 3 3 B. −3 C. 3 D. 3 A. −1+i
2+i B.
−1−2i
2 C. −1−3i
2 D. 1+3i
2

1
20. Find the value if Z1 35. Find the value of ϕ
A. −1+i −1−3i
3+i B. 2+i C. −1−3i
2 D. 1+3i
2 A. 125◦ B. 135◦ C. 145◦ D. 155◦

21. Find the value if Z+ Z1 36. The√value of Z is given as

A. −7+i
3 B. −7+9i
10 C. −7−9i
3 D. −7−21i
10
A. √ 2(cos 125◦ + i sin 125◦ )
B. 2(cos 135◦ + i sin 135◦ )
22. If sin x = 0 then x = C. 2(cos 125◦ + i sin 125◦ )
A. nπ B. (2n+1)π
2 C. (n + 1)π D. nπ
2 D. 2(cos 135◦ + i sin 135◦ )
23. Which of the following is equal to log x? 37. 1 − cos2 x =
log x ln x ln 10 ln x
A. log 10 B. ln 10 C. ln x D. ln x A. sin x B. cos x C. sin 2x D. sin2 x

Use the given information to answer question Use the information to answer question 38&39.
24&25. Given that 9n − 1 is divisible by 8. As- Given that n3 − n is a multiple of 6. Assume that it
sume that it is true for n = 1, n = 2 and it is also is true for n = 1, n = 2 and it is also true for n = k.
true for n = k

24. Find the expression for n = k 38. Find the expression for when n = k
A. 9k − 1 = 8y + 1 B. 9k − 1 = 16y − 1 A. k 3 − k = 6y + 1 B. k 3 − k = 6y − 1
C. 9k − 1 = 8y D. 9k − 1 = 8y + 4 C. k 3 − k = 6y D. k 3 − k = 6y + 2
25. Find the expression for n = k + 1
A. 9k+1 = 8 (9y + 1) B. 9k+1 = 8 (9y − 1) ( 2 n = k + )1
39. Find the expression for when
3
A. (k + 1) − k − 1 = 6 k2 + k2 + y
C. 9k − 1 = 8y + 1 D. 9k − 1 = 8y + 4 ( 2 )
B. (k + 1)3 − k + 1 = 6 k3 + k + y
26. Find y if the equation (5y + 1) x2 − 8yx + 3y = 0 ( 2 )
has equal roots. C. (k + 1)3 − k + 1 = 6 k4 + k4 + y
( 2 )
A. y = 0 or y = 3 B. y = 0 or y = −3 D. (k + 1)3 − k + 1 = 6 k2 − k2 − y
C. y = −1 or y = 3 D. y = −1 or y = −3

27. Form an equation for which the sum of the roots is

40. If α, β are roots of the equation x2 −7x+2 = 0, find
5 and the sum of the square of the roots is 53.
without solving the equation, the value of α2 + β 2
A. x2 + 5x − 14 = 0 B. x2 − 5x − 14 = 0
A. -45 B. 43 C. 45 D. 44
C. x2 − 5x + 14 = 0 D. x2 + 5x + 14 = 0
41. log2 1 + log2 2 =
28. If cos x = 0 then x = 1
A. 1 B. 2 C. 3 D.
A. nπ B. (2n+1)π
2 C. (n + 1)π D. nπ
2
2

m+2x 3m−8x 42. sin(−45◦ ) =

29. Simplify y y5m−6x
y
A. 1 B. –1 C. √1 D. −1
√
2 2
A. y m B. y −x C. y −m D. y x
43. The equation 2(2x+3) + 1 = 9(2x ) is an example of
30. Simplify log2 3 log3 4 log4 5 log5 6 log6 7 log7 8
A. Linear equation
A. 2 B. 4 C. 8 D. 10
B. Quadratic equation
31. 1 − sin 245◦ = √
C. Exponential equation
A. 12 B. 1 C. 0 D. 3 D. Simultaneous equation.
2

44. cos(−60 ◦) =
32. Find the ranges of values of k which the equation √ √
x2 + (k − 3)x + k = 0 has real distinct roots A. 2−3 B. 12 C. 2
3
D. −1
2
A. k > 1, k > 9 B. k < 1, k > 9
C. k > −1, k > 9 D. k > 1, k > −9 45. 1◦ is
A. π B. 0.046 C. 0.1746 D. 0.01746
33. Given that 2(x/2) = 32, find x
A. 2 B. 3 C. 8 D. 7 Given that |Z − 1 + 2i| = 2 the locus of a circle.
Use the information to answer question 46 − 48
If Z = −1 + i = x + iy, where Z = r(cos ϕ +
i sin ϕ). Using this information answer questions 46. Find the equation of the circle
34 − 36. A. x2 − y 2 − 2x + 4y + 1 = 0
B. x2 + y 2 − 2x − 4y + 1 = 0
value of r
34. Find the √ C. x2 + y 2 − 2x + 4y − 1 = 0
A. 2 B. 2 C. 4 D. 5 D. x2 + y 2 − 2x + 4y + 1 = 0

2
47. Find the radius of the above circle 63. Find the missing number: 2, 5, 9, 14, −, 27.
A. 3 B. 1 C. 2 D. 4 A. 19 B. 20 C. 21 D. 22

48. Find the center of the circle 64. Which of the following is equal to x24 for all posi-
A. (1,2) B. (1,-2) C. (-1,2) D. (-1,-2) tive values of x?
A. x12 + x12 B. (−x12 )−2 C. (x6 )6
49. The nth roots of complex number is given by
1 θ 1 θ+2πk D. (x72 )1/3
A. zk = r n ei( n ) B. zk = r n ei( −n )
1 θ+2πk 1 θ−2πk
C. zk = r n ei( n ) D. zk = r n ei( n ) 65. For what value of x is 82x−4 = 16x ?
A. 2 B. 3 C. 4 D. 6
50. Evaluate log32 ( 12 )
A. −1
5 B. 15 C. 23 D. 1
2 66. 50100 = k(10050 ), what is the value of k?
A. 250 B. 2550 C. 5050 D. ( 12 )50
51. If an angle of an 60◦ and the length of arc is 20cm.
Find the radius of the circle from which arc is inter- 67. The remainder when 599 is divided by 13 is
cepted. A. 6 B. 8 C. 9 D. 10
A. 18.08cm B. 17.07cm C. 19.09cm D. 18cm
( ) c
68. If (7a )(7b ) = 77d , what is d in terms of a, b and c?
52. If γ, δ are roots of the equation log 3x2 + 2bx − 5 c
A. ab B. c − a − b C. a + b − c D. a+b c
= 1.The sum and product of the roots are
A. −2b −2b
3 , 3 B. 3 , −5 C. 3 , −3 D. 3 , 3
2b 2b
69. Which of the following is equal to (78 × 79 )10
53. If (0.25)y = 32, find the value of y. A. 49820 B. 782 C. 7170 D. 49170
A. y = −52 B. y = −3 2 C. y = 32 D. y = 5
2
70. For every natural number n, n(n + 1) is always
54. If we start to rotate and after completing one revo- A. Even B. Odd C. Multiple of 3
lution again initial side overlap with terminal side, D. Multiple of 4
then the angle formed is
A. 0◦ B. 180◦ C. 90◦ D. 360◦ 71. Find the value of log2 8 + log5 125.
A. 3 B. 2 C. 5 D. 6
55. Simplify: log 6 − 3 log 3 + 23 log 27.
A. 3log 2 B. log 2 C. log 3 D. 2log3 72. If 32a+b = 16a+2b , then a =
A. b B. 2b C. 3b D. b + 2
Given that Z = 1 + 2i, the square root Z is de-
termine. Use the information to answer 56 − 57. 73. 41, 40, 38, 35, 31, a. Find a
A. 24 B. 26 C. 28 D. 30
56. The√first root of Z is √ √
−θ
74. Find the value of i64 − 2i−64
θ θ θ
A. 6ei( 2 ) B. 5ei( 2 ) C. 6ei( 2 ) D. 5ei( 2 )
A. 1 B. -2 C. -1 D. 0
57. The magnitude
√ of
√ this complex number is ( )5
A. 5 B. 6 C. 5 D. -6 75. Find the fourth term of the expansion 1 + x12
A. 10x6 B. 10x5 C. 10x−6 D. 10x−5
58. If length of arc is 40 cm and radius of circle of arc
is 10 cm then find the angle made by the arc [ ]− 2
76. Simplify 278
3
= A. 49 B. 94 C. 23 D. 32
A. 720◦ B. 240◦ 51′ 53′′ C. 229◦ 10′ 59′′
D. 233◦ 11′ 48′′ 77. Given that log x = a and log y = b, find log xy n in
−2 3 −4 terms of a and b.
59. Simplify a b6 c × a3 b−3 9
c4 A. ab B. a + nb C. nab D. na + b
A. 23 a−5 b6 c−8 B. 23 a−5 b6 c−8 C. 23 a5 b6 c−8
D. 23 a−5 b−6 c−8 78. Which of the following is equal to log3 5?
log3 3 log5 3
60. (23 − 1)(23 + 1)(26 + 1)(212 + 1) = A. log 5 log 3
log 3 B. log 5 C. log 5 D. log 5
5 3

A. (224 − 1) B. (224 + 1) C. (248 − 1) ◦

D. (296 + 1) 79. Evaluate e−i90
A. 2 B. 0 C. i D. -i
(0.5)11
61. =
(0.5)9
A.0.0125 B. 0.025 C. 0.1 D. 0.25
80. The sum of an nth term of an A.P. is 2n + 3n2 . Find
62. If α, β are the roots of the equation 3x2 −4x+6 = 0. the common difference and the 3rd term of the se-
Find α3 β + αβ 3 quence.
A. -12.67 B. 12.67 C. -12 D. 12 A. 4,15 B. 6,15 C. 6,17 D. 5,15

3
81. If A, B, C are subsets of the same universal set then, ( )
A. A − (B − C) = (A − B) ∪ (A − C) 1 + 2n −4n
Given that An = ,
B. B − (A − C) = (B − A) ∪ (B − C) n 1 − 2n
C. (A − B) − C = ϕ
D. (B − C) ∩ A = ϕ 92. find(A3k−1 ) ( )
1 + 3k −12k 6k − 1 4 − 12k
A. B.
If S(x) = 12 (ex − e−x ) and 3k 1 − 6k 3k − 1 1 − 6k
( ) ( )
C(x) = 12 (ex + e−x ). Use the given information 6k − 1 4 + 12k 6n + 1 4 + 12k
C. D.
to answer questions 82 − 84 3k − 1 2 − 3k 3n + 1 1 − 6k
( √ )
82. Find S ln(1 + 2)
√ √ 93. Rewrite
{ explicitly the element of }
A. 1 B. 2 C. 2 D. 3 Y = x : x3 + x2 − 4x − 4 = 0 for all values of
( √ ) x
83. Find C ln(1 + 2)
√ √ A. {x = 0, 4, −4} B. {x = −2, −1, 2}
A. 1 B. 2 C. 2 D. 3
C. {x = 0, 2, −4} D. {x = −1, 0, 2}
( √ ) ( √ )
84. Find S ln(1 + 2) + C ln(1 + 2)
√ √ √ If the universal set µ, such that µ =
A. 1 B.1 + 2 C. 2 + 2 D. 3 + 3
{1, 2, 3, 4, · · · 9} and subsets A = {1, 2, 3, 5},
If m is a positive even integer whose sum (2m + B = {2, 4, 7, 8, 9} and C = {3, 4, 7, 8, 9}.
1) + (2m + 3) + (2m + 5) + . . . + (4m − 1) is
divisible by 12. Assume that it is true n = 1, n = 2
94. What
[{ 1 is 1the ] of R if N (R)
} cardinality =
A ∪ B ∩ {B ∪ C}
and it is true it is also true for n = k. Use the given A. 4 B. 5 C. 6 D. 7
information to answer question 85&86.

85. Which of the following is the k th term of the series?

A. 3k 2 B. 6k 2 C. 4k D. 12k 2

86. Find the (k + 1)term of the above series.

A. 3(k + 1)2 B. 12(k + 1)2 C. 4(k + 1)
D. 12(k − 1)2

If m is a positive even integer whose sum (2m +

1) + (2m + 3) + (2m + 5) + . . . + (4m − 1) is
divisible by 3. Assume that it is true n = 1, n = 2
Use the above venn diagram to answer questions
and it is true it is also true for n = k. Use the given
95 − 100.
information to answer question 87&88.
95. What is the set notation for 1?
87. Which of the following is the k th term of the series?
A. P ∩ Qc ∩ Rc B. Q ∩ P c ∩ Rc
A. 3k 2 B. 3(k − 1)2 C. 3k D. 12k 2
C. R ∩ P c ∩ Qc D. P ∩ Q ∩ R
88. Find the (k + 1)term of the above series.
96. What is the set notation for 2?
A. 3(k + 1)2 B. 12(k + 1)2 C. 4(k + 1)
A. P ∩ Q ∩ Rc B. Q ∩ P c ∩ Rc
D. 12(k − 1)2
C. R ∩ P c ∩ Qc D. P ∩ Q ∩ R
In a given quadratic equation ex2 + f x + g = 0. 97. What is the set notation for 3?
Use the given information to answer 89 − 91. A. P ∩ Qc ∩ Rc B. Q ∩ P c ∩ Rc
C. R ∩ P c ∩ Qc D. P ∩ Q ∩ R
89. The roots of the given equation will be distinct if
A. b2 − 4ac > 0 B. b2 − 4ac < 0 98. What is the set notation for 4?
C. f 2 − 4eg > 0 D. f 2 − 4eg < 0 A. P ∩ Qc ∩ Rc B. Q ∩ R ∩ P c
C. R ∩ P c ∩ Qc D. P ∩ Q ∩ R
90. The roots of the given equation will be equal roots
if 99. What is the set notation for 5?
A. f 2 − 4eg = 0 B. b2 + 4ac = 0 A. P ∩ Qc ∩ Rc B. Q ∩ P c ∩ Rc
C. b2 − 4ac = 0 D. f 2 + 4eg < 0 C. R ∩ P c ∩ Qc D. P ∩ Q ∩ R

91. The given equation will have no roots if 100. What is the set notation for 6?
A. b2 − 4ac > 0 B. b2 − 4ac < 0 A. P ∩ Qc ∩ Rc B. Q ∩ P c ∩ Rc
C. f 2 − 4eg > 0 D. f 2 − 4eg < 0 C. P ∩ R ∩ Qc D. P ∩ Q ∩ R