General Mathematics I — 2025C Past Questions

University of Ilorin MTH101: 100 questions.

Topics: Binomial Theorem, Complex Number, Sequence and Series, Circular Measure, Set Theory and Venn Diagram, Quadratic Equation, Number System, Mathematical Induction

  1. Find the 4th term of a G.P whose first term is 6 and common ratio is 3.
    1. 162
    2. 486
    3. 54
    4. 18
  2. Find the 5th term of the G.P; 1/32, 1/8, 1/2
    1. 2
    2. 4
    3. 8
    4. 16
  3. Find the 6th term of the sequence 25, 5, 1, ...
    1. 1/25
    2. 1/125
    3. 1/625
    4. 1/3125
  4. Given n(μ) = 20, n(P) = 12, n(Q) = 15, find n(P ∩ Q).
    1. 7
    2. 8
    3. 9
    4. 10
  5. If n(P ∪ Q) = 50, n(P) = 40 and n(Q) = 18. Find n(P ∩ Q)
    1. 8
    2. 9
    3. 10
    4. 11
  6. What is the cardinality of the power set {x: x ∈ E, x < 11}
    1. 32
    2. 64
    3. 128
    4. 256
  7. Insert an arithmetic mean between x/y and (x²+2y)/xy
    1. (x+y)/y
    2. (x²+y)/xy
    3. (x+2y)/y
    4. (x²+2y)/2y
  8. In the principle of mathematical induction, the propositional statement Pn is true for?
    1. n = 1 only
    2. n = k only
    3. n = k+1 only
    4. n = 1 and if true for n = k, then true for n = k+1
  9. Suppose 3, w, x, y, z, -96 are G.P, find w
    1. -6
    2. 6
    3. -12
    4. 12
  10. Determine the 4th term of the expansion of (3x-y)⁵
    1. -270x²y³
    2. 270x²y³
    3. -90x³y²
    4. 90x³y²
  11. Determine the 7th term of the expansion of (x+y)⁹
    1. 84x³y⁶
    2. 84x⁶y³
    3. 126x³y⁶
    4. 126x⁶y³
  12. What is the coefficient of x³y² in the expansion of (x+y)⁵
    1. 5
    2. 10
    3. 15
    4. 20
  13. Determine the coefficient of x² in the expansion of (1-4x)⁵
    1. 40
    2. 80
    3. 160
    4. 320
  14. Express ⁴√(1.005)
    1. 1 + 0.00125
    2. 1 + 0.0025
    3. 1 + 0.005
    4. 1 + 0.01
  15. Z₁ = 7 + 3i, Z₂ = 6 - 7i and Z₃ = -2 - 3i. Evaluate Z₁ - Z₂ + 2Z₃
    1. -3 + 8i
    2. -3 - 8i
    3. 3 + 8i
    4. 3 - 8i
  16. Given that Z₁ = 3 + ⅓i, Z₂ = 3 - ⅓i and Z₃ = -3 - ⅓i, find Z₁ - 3Z₂ + Z₃
    1. -9 - i
    2. -9 + i
    3. 9 - i
    4. 9 + i
  17. (x+y) + (x-y)i = (3+2i) - (2+i) find x and y
    1. x = 1, y = 1
    2. x = 1, y = -1
    3. x = -1, y = 1
    4. x = -1, y = -1
  18. Simplify (4+i³)/(2-i)
    1. 1 + i
    2. 1 - i
    3. -1 + i
    4. -1 - i
  19. Simplify (1/(2-½i)) + (1/(2+½i))
    1. 8/17
    2. 16/17
    3. 32/17
    4. 64/17
  20. If Z = 1 + i, find Z²
    1. 2i
    2. -2i
    3. 2
    4. -2
  21. If Z = 2 + 3i, find the modulus of z²
    1. 13
    2. 26
    3. 169
    4. √13
  22. If tan (x+y) = 4/3 and tan x = ½, obtain tan y
    1. 1/2
    2. 1
    3. 2/3
    4. 5/6
  23. Express 3/2 + 3√3i/2 in polar form
    1. 3(cos π/6 + i sin π/6)
    2. 3(cos π/3 + i sin π/3)
    3. 3(cos π/4 + i sin π/4)
    4. 3(cos π/2 + i sin π/2)
  24. If Z = -1/√2 - i/√2, express in polar form
    1. cos(3π/4) + i sin(3π/4)
    2. cos(5π/4) + i sin(5π/4)
    3. cos(7π/4) + i sin(7π/4)
    4. cos(π/4) + i sin(π/4)
  25. Determine the coefficient of the 3rd term in (1+x)¼
    1. -1/32
    2. 1/32
    3. -3/128
    4. 3/128
  26. What is the linear approximation of (0.998)⁶
    1. 0.988
    2. 0.992
    3. 0.996
    4. 0.999
  27. Find the linear approximation of (1.002)¹²
    1. 1.012
    2. 1.024
    3. 1.036
    4. 1.048
  28. What is the 5th term in (y+2x)⁷
    1. 280x⁴y³
    2. 560x⁴y³
    3. 280x³y⁴
    4. 560x³y⁴
  29. If a = 10, b = 20 & c = 30, what is the Arithmetic mean between a and b
    1. 10
    2. 15
    3. 20
    4. 25
  30. The sum of the first 12 terms of an AP is 456, the last term is 66, find the first term
    1. 2
    2. 4
    3. 6
    4. 8
  31. The 5th term of an AP is 17 and the 10th term is 32, find the sum of the first 15 terms
    1. 345
    2. 360
    3. 375
    4. 390
  32. What is the 5th term in the expansion of (2x-1/x)⁵
    1. -80x
    2. -40x
    3. 40x
    4. 80x
  33. What is the nature of roots of x²+11x+30=0
    1. Real and equal
    2. Real and distinct
    3. Imaginary
    4. Cannot be determined
  34. What is the nature of roots of x²+x-20=0
    1. Real and equal
    2. Real and distinct
    3. Imaginary
    4. Cannot be determined
  35. If the roots of the equation x²-4x+4 are a and b, what is the value of b
    1. 1
    2. 2
    3. 3
    4. 4
  36. Find (Cos 10° + i sin 30°)²
    1. cos 20° + i sin 60°
    2. cos 20° + i sin 30°
    3. cos 10° + i sin 60°
    4. cos 10° + i sin 30°
  37. (1+x)¼......find the sum of the first and second term
    1. 1 + x/4
    2. 1 + x/2
    3. 1 + x
    4. 1 + 2x
  38. 1/(1+x)². Find the first three terms
    1. 1 - 2x + 3x²
    2. 1 - 2x + 4x²
    3. 1 - x + x²
    4. 1 - x + 2x²
  39. (1+x)⅕. Find the fourth term
    1. -2/25x³
    2. 2/25x³
    3. -3/125x³
    4. 3/125x³
  40. What is the least possible value of k if 7n²+16n+k is to be divisible by 64
    1. 8
    2. 16
    3. 24
    4. 32
  41. If 16 students offer geography, 18 students offer chemistry, 5 offer both and 3 offer neither, how many students are in the class?
    1. 32
    2. 33
    3. 34
    4. 35
  42. Insert 2 geometric mean between 32 and 0.5
    1. 8, 2
    2. 8, 1
    3. 4, 2
    4. 4, 1
  43. What is 1/(1+i)³
    1. (1-i)/4
    2. (1+i)/4
    3. (-1-i)/4
    4. (-1+i)/4
  44. Given the mean of the first six terms of an A.P is 15. If d=2, what is the first term?
    1. 5
    2. 10
    3. 15
    4. 20
  45. If Sn = 3n²+2. What is the value of the first term?
    1. 2
    2. 5
    3. 8
    4. 11
  46. Given x, -x², x³, ......Find the sum to Infinity
    1. x/(1+x)
    2. x/(1-x)
    3. 1/(1+x)
    4. 1/(1-x)
  47. What is the value of i⁻⁵?
    1. i
    2. -i
    3. 1
    4. -1
  48. Find the linear approximation of (0.999)³
    1. 0.997
    2. 0.998
    3. 0.999
    4. 1.000
  49. Find first 3 terms in the binomial expansion of (1-x)⁻¹²
    1. 1 + 12x + 78x²
    2. 1 - 12x + 78x²
    3. 1 + 12x - 78x²
    4. 1 - 12x - 78x²
  50. If the root of the quadratic equation 3x²-7x-5 is a and b, find equation whose roots are (1/a) and (1/b)
    1. 5x²+7x-3=0
    2. 5x²-7x-3=0
    3. 3x²+7x-5=0
    4. 3x²-7x+5=0
  51. sin²120° + cos²120° = ________
    1. 0
    2. 1
    3. 2
    4. √3
  52. Solve (Cos75° + i sin50°)^⅗ (final answer in surd form)
    1. (√6-√2)/4 + i(√6+√2)/4
    2. (√6-√2)/4 - i(√6+√2)/4
    3. (√6+√2)/4 + i(√6-√2)/4
    4. (√6+√2)/4 - i(√6-√2)/4
  53. If the 5th term of an AP is 17 and the 10th term is 32, find sum of first 15 terms
    1. 345
    2. 360
    3. 375
    4. 390
  54. Solve cos75° in surd form
    1. (√6-√2)/4
    2. (√6+√2)/4
    3. (√3-1)/4
    4. (√3+1)/4
  55. Solve (1.001)³
    1. 1.003
    2. 1.003001
    3. 1.003003
    4. 1.003003001
  56. Insert 4 geometric mean between -1 and 243
    1. -3, 9, -27, 81
    2. 3, -9, 27, -81
    3. 3, 9, 27, 81
    4. -3, -9, -27, -81
  57. If Z₁=1+i and Z₂=3-i, find the modulus of Z₁·Z₂
    1. √10
    2. √20
    3. √30
    4. √40
  58. Find the coefficient of x⁸y² in the binomial expansion (x+y)¹⁰
    1. 35
    2. 45
    3. 55
    4. 65
  59. Find the first term if the sum of term of a progression is 5n²-n
    1. 4
    2. 5
    3. 6
    4. 7
  60. If Tan (a+b) = 4/3 and Tan a = 1/2. Find Tan b.
    1. 1/2
    2. 1
    3. 2/3
    4. 5/6
  61. Express [1/(1- 2sin60°)] in surd form
    1. 2+√3
    2. 2-√3
    3. 1+√3
    4. 1-√3
  62. If Sin A= 3/5, find sec A
    1. 3/4
    2. 4/3
    3. 5/3
    4. 5/4
  63. Find first 3 terms of the binomial expansion (1-2b)⁻⁴
    1. 1 + 8b + 40b²
    2. 1 - 8b + 40b²
    3. 1 + 8b - 40b²
    4. 1 - 8b - 40b²
  64. If Z₁= 3+(1/3)i, Z₂= 3-(1/3)i and Z₃= 3+(1/3)i, find Z₁ - 3Z₂ - Z₃
    1. -6 - (1/3)i
    2. -6 + (1/3)i
    3. 6 - (1/3)i
    4. 6 + (1/3)i
  65. Find the 4th term of a G.P whose first term is 6 and common ratio is 3
    1. 54
    2. 162
    3. 486
    4. 1458
  66. Find the 5th term of the G.P , 1/32, 1/8,1/2
    1. 2
    2. 4
    3. 8
    4. 16
  67. Find the 6th term of the sequence 25,5,1
    1. 1/25
    2. 1/125
    3. 1/625
    4. 1/3125
  68. Given n(μ) = 20, n(p)=12 ,n(Q)= 15, find n(P ∩ Q)
    1. 7
    2. 8
    3. 9
    4. 10
  69. n(P ∪ Q) = 50, n(p)=40,n(Q)=18, find n(p ∩ Q)
    1. 8
    2. 9
    3. 10
    4. 11
  70. What is the cardinality of the power set { x:x∈E, x<11}
    1. 32
    2. 64
    3. 128
    4. 256
  71. Insert an arithmetic mean between x/y and (x²+2y)/xy
    1. (x+y)/y
    2. (x²+y)/xy
    3. (x+2y)/y
    4. (x²+2y)/2y
  72. In The principle of mathematical induction, the propositional statement Pn is true for?
    1. n = 1 only
    2. n = k only
    3. n = k+1 only
    4. n = 1 and if true for n = k, then true for n = k+1
  73. Suppose 3,w,x,y,z,-96 are in a G.P ,find w
    1. -6
    2. 6
    3. -12
    4. 12
  74. Determine the 4th term of the expansion of (3x-y)⁵
    1. -270x²y³
    2. 270x²y³
    3. -90x³y²
    4. 90x³y²
  75. Determine the 7th term of the expansion of (x+y)⁹
    1. 84x³y⁶
    2. 84x⁶y³
    3. 126x³y⁶
    4. 126x⁶y³
  76. What is the coefficient of x³y² in the expansion of (x+y)⁵
    1. 5
    2. 10
    3. 15
    4. 20
  77. Determine the coefficient of x² in the expansion of (1-4x)⁵
    1. 40
    2. 80
    3. 160
    4. 320
  78. Express ⁴√(1.005)
    1. 1 + 0.00125
    2. 1 + 0.0025
    3. 1 + 0.005
    4. 1 + 0.01
  79. Z1 = 7 +3i, Z2= 6-7i,Z3 = -2-3i, evaluate Z1-Z2+2Z3
    1. -3 + 8i
    2. -3 - 8i
    3. 3 + 8i
    4. 3 - 8i
  80. Z1= 3 + ⅓i, Z2=3-⅓i,Z3= -3-⅓i, find Z1-3Z2+Z3
    1. -9 - i
    2. -9 + i
    3. 9 - i
    4. 9 + i
  81. (x+y) +(x-y)i=(3+2i)-(2+i) find x and y
    1. x = 1, y = 1
    2. x = 1, y = -1
    3. x = -1, y = 1
    4. x = -1, y = -1
  82. Simplify (4+i³)/(2-i)
    1. 1 + i
    2. 1 - i
    3. -1 + i
    4. -1 - i
  83. Simplify (1/(2-½i)) + (1/(2+½i))
    1. 8/17
    2. 16/17
    3. 32/17
    4. 64/17
  84. If Z = 1 + i, find Z²
    1. 2i
    2. -2i
    3. 2
    4. -2
  85. If Z = 2 +3i, find the modulus of z²
    1. 13
    2. 26
    3. 169
    4. √13
  86. If tan (x+y)= 4/3 & tan x = ½, obtain tan y
    1. 1/2
    2. 1
    3. 2/3
    4. 5/6
  87. Express ³/2 + 3√3i/2 in polar form
    1. 3(cos π/6 + i sin π/6)
    2. 3(cos π/3 + i sin π/3)
    3. 3(cos π/4 + i sin π/4)
    4. 3(cos π/2 + i sin π/2)
  88. If Z = -1/√2 - i/√2, express in polar form
    1. cos(3π/4) + i sin(3π/4)
    2. cos(5π/4) + i sin(5π/4)
    3. cos(7π/4) + i sin(7π/4)
    4. cos(π/4) + i sin(π/4)
  89. Determine the coefficient of the 3rd term in (1+x)¼
    1. -1/32
    2. 1/32
    3. -3/128
    4. 3/128
  90. What is the linear approximation of (0.998)⁶
    1. 0.988
    2. 0.992
    3. 0.996
    4. 0.999
  91. Find the linear approximation of (1.002)¹²
    1. 1.012
    2. 1.024
    3. 1.036
    4. 1.048
  92. What is the 5th term in (y+2x)⁷
    1. 280x⁴y³
    2. 560x⁴y³
    3. 280x³y⁴
    4. 560x³y⁴
  93. If a = 10, b= 20 & c =30, what is the Arithmetic mean between a and b
    1. 10
    2. 15
    3. 20
    4. 25
  94. The sum of the first 12 terms of an AP is 456, the last term is 66, find the first term
    1. 2
    2. 4
    3. 6
    4. 8
  95. The 5th term of an AP is 17 and the 10th term is 32, find the sum of the first 15 terms
    1. 345
    2. 360
    3. 375
    4. 390
  96. What is the 5th term in the expansion of (2x-1/x)⁵
    1. -80x
    2. -40x
    3. 40x
    4. 80x
  97. What is the nature of roots of x²+11x+30=0
    1. Real and equal
    2. Real and distinct
    3. Imaginary
    4. Cannot be determined
  98. What is the nature of roots of x²+x-20=0
    1. Real and equal
    2. Real and distinct
    3. Imaginary
    4. Cannot be determined
  99. If the roots of the equation x²-4x+4 are a and b, what is the value of b
    1. 1
    2. 2
    3. 3
    4. 4
  100. A rectangular water tank has dimensions 4 m × 3 m × 2 m. How many liters of water can it hold?
    1. 24000
    2. 25000
    3. 26000
    4. 27000

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