General Mathematics I — 2026-exam Past Questions

University of Ilorin MTH101: 167 questions.

Topics: Real Sequences and Series, Trigonometric Functions of Angles of Any Magnitude, Theory of Quadratic Equations, Addition and Factor Formulae, Binomial Theorem, Circular Measure, The Argand Diagram, Nth Roots of Unity, Algebra of Complex Numbers, De-Moivre's Theorem, Mathematical Induction, Union, Subsets, Intersection, Elementary Set Theory, Complements, Venn Diagrams

  1. Find the quadratic equation whose roots are 3 + i and 3 − i.
    1. x² − 6x + 10 = 0
    2. x² + 6x + 10 = 0
    3. x² − 3x + 10 = 0
    4. x² − 6x − 10 = 0
  2. Which term is the middle term in the expansion of (3a − b)⁸?
    1. 5th term
    2. 4th and 5th term
    3. 6th term
    4. 7th term
  3. What is (cosθ + i sinθ)⁻ⁿ?
    1. cos(nθ) + i sin(nθ)
    2. cos(nθ) − i sin(nθ)
    3. cos(−nθ) − i sin(−nθ)
    4. −cos(nθ) + i sin(nθ)
  4. sin(−740°) is the same as
    1. sin 20°
    2. −sin 20°
    3. cos 20°
    4. −cos 20°
  5. Express sin 405° in surd form.
    1. √2/2
    2. −√2/2
    3. √3/2
    4. 1/2
  6. Given U = natural numbers from 11 to 20, A = odd numbers from 11 to 20 and B = even numbers from 11 to 20, find A ∪ B.
    1. {11, 13, 15, 17, 19}
    2. {12, 14, 16, 18, 20}
    3. {11, 12, 13, 14, 15, 16, 17, 18, 19, 20}
    4. {13, 15, 17, 19}
  7. The second step in mathematical induction is
    1. Proving n = k
    2. Assuming n = k
    3. Proving n = k + 1
    4. Proving n = 1
  8. The equation kx² + (k + 1)x + k = 0 has equal roots. Find k.
    1. −1, 1/3
    2. 1, −1/3
    3. 1, 1/3
    4. −1, −1/3
  9. The equation 2x² + 3x − 2 = 0 has roots α and β. Find the equation whose roots are α/β and β/α.
    1. 4x² + 17x + 4 = 0
    2. 4x² − 17x + 4 = 0
    3. 2x² + 17x + 2 = 0
    4. 4x² + 7x + 4 = 0
  10. Simplify cos 190° without using tables.
    1. −cos 80°
    2. cos 180°
    3. −cos 10°
    4. cos 80°
  11. In the principle of mathematical induction, the propositional statement Pₙ is true for
    1. Natural numbers
    2. Whole numbers
    3. Integers
    4. Rational numbers
  12. In ax² + bx + c = 0, what is the nature of the roots if b² − 4ac = 0?
    1. Real and unequal
    2. Imaginary and unequal
    3. Real and equal
    4. Unreal and unequal
  13. cos(θ + 2πk), where k is an integer, is the same as
    1. cos(2θk)
    2. −sin(2k)
    3. cosθ
    4. sinθ
  14. Find the sixth roots of unity (the roots of z⁶ − 1 = 0).
    1. 1, −1, i, −i, (√3/2 + i/2), (−√3/2 + i/2)
    2. 1, −1, i, −i, (1/2 + (√3/2)i), (1/2 − (√3/2)i)
    3. 1, −1, (1/2 + (√3/2)i), (1/2 − (√3/2)i), (−1/2 + (√3/2)i), (−1/2 − (√3/2)i)
    4. 1, −1, 2, −2, i, −i
  15. Find the cube roots of unity (the roots of z³ − 1 = 0).
    1. 1, −1, i
    2. 1, (−1/2 + (√3/2)i), (−1/2 − (√3/2)i)
    3. 1, (1/2 + (√3/2)i), (1/2 − (√3/2)i)
    4. 1, −1/2, √3/2
  16. Express −1 + √3i in polar form.
    1. 2(cos 120° + i sin 120°)
    2. 2(cos 60° + i sin 60°)
    3. √2(cos 45° + i sin 45°)
    4. 2(cos 240° + i sin 240°)
  17. Find the fourth term in the fifth roots of unity (solutions to z⁵ − 1 = 0).
    1. cos(6π/5) + i sin(6π/5)
    2. cos(4π/5) + i sin(4π/5)
    3. cos(8π/5) + i sin(8π/5)
    4. cos(2π/5) + i sin(2π/5)
  18. If all the terms of a GP are doubled, what is the sum to infinity if the first term is 1?
    1. 2/(1 − r)
    2. 1/(1 − 2r)
    3. 2/(1 − 2r)
    4. 1/(1 − r)
  19. Given A = {0, 0, 1}, what is the measure (number of distinct elements) of the set A?
    1. 2
    2. 3
    3. 1
    4. 0
  20. If sin²θ = 4/13, find cosecθ.
    1. √13/2
    2. 2/√13
    3. √13/3
    4. 3/√13
  21. U = {x : 11 ≤ x ≤ 20}, A = odd numbers in U and B = even numbers in U. Find B′ (the complement of B in U).
    1. {12, 14, 16, 18, 20}
    2. {11, 13, 15, 17, 19}
    3. {11, 12, 13, 14}
    4. {15, 16, 17, 18}
  22. What is the product of (4 + 2i)(3 − 2i)?
    1. 16 − 2i
    2. 16 + 2i
    3. 12 − 2i
    4. 12 + 2i
  23. If sinθ = 2/3, what is cotθ?
    1. √5/2
    2. 2/√5
    3. √5/3
    4. 3/√5
  24. For the sequence 2, 2/5, 2/25, …, find the 6th term.
    1. 2/3125
    2. 2/625
    3. 2/1250
    4. 2/15625
  25. Given x² − 4x + 3 = 0 with roots α and β, find (α − β)².
    1. 4
    2. 0
    3. 2
    4. 1
  26. The equation x² − 7x + 3 = 0 has roots α and β. Find α − β (taking α > β).
    1. √37
    2. 7
    3. √13
    4. 3
  27. Evaluate sin(60° − 45°) in surd form.
    1. √2(√3 − 1)/4
    2. √2(√3 − 1)/2
    3. (√3 − 1)/2
    4. (√6 + √2)/4
  28. Find cos 210° in surd form.
    1. −√3/2
    2. −1/2
    3. √3/2
    4. 1/2
  29. An AP consists of 2m terms. The sum of the first m terms is x and the sum of the second m terms is y. Find (x − y)².
    1. m³d²
    2. m⁴d²
    3. m³d
    4. m²d²
  30. Find tan 120° in surd form.
    1. √3
    2. −√3
    3. 1/√3
    4. −1/√3
  31. Simplify (cos 10π + i sin 10π)^(1/5).
    1. cos 2π + i sin 2π
    2. cos π + i sin π
    3. cos 5π + i sin 5π
    4. cos 10π + i sin 10π
  32. If cosec²θ = 9/4, find cosθ.
    1. √5/3
    2. 2/3
    3. √5/2
    4. 3/√5
  33. Z₁ = cos 45° + i sin 45° and Z₂ = cos 60° + i sin 60°. Calculate Z₁/Z₂.
    1. cos(−15°) + i sin(−15°)
    2. cos 15° + i sin 15°
    3. cos 105° + i sin 105°
    4. cos(−105°) + i sin(−105°)
  34. A complex number has modulus √2 and argument −15°. The complex number is
    1. √2(cos 15° − i sin 15°)
    2. √2(−cos 15° + i sin 15°)
    3. √2(cos 15° + i sin 15°)
    4. √2(cos(−15°) − i sin(−15°))
  35. Find the sum of the coefficients in the expansion of (x + y)⁸.
    1. 128
    2. 256
    3. 512
    4. 1024
  36. If α and β are roots of a quadratic equation, expand α(α + 1)(β + 1).
    1. α²β + αβ + α² + α
    2. α²β + αβ + α
    3. αβ(α + β + 1)
    4. αβ + 1
  37. Evaluate sin(120° + 30°).
    1. 1
    2. 0
    3. −1
    4. 1/2
  38. Find sin(−500°).
    1. sin 140°
    2. −sin 140°
    3. sin 40°
    4. cos 140°
  39. Find sin 550°.
    1. sin 190°
    2. −sin 10°
    3. sin 10°
    4. None
  40. Evaluate cos(120° + 30°) in surd form.
    1. −√3/2
    2. −1/2
    3. √3/2
    4. 1/2
  41. Convert 9π/5 radians to degrees.
    1. 324°
    2. 180°
    3. 162°
    4. 270°
  42. Convert 240° to radians.
    1. 4π/3
    2. 3π/4
    3. 5π/6
    4. 2π/3
  43. Find the coefficient of the fourth term in the expansion of (x − 2y)¹⁰.
    1. −960
    2. 960
    3. −120
    4. 120
  44. Evaluate cos(120° + 45°).
    1. −√6/4 − √2/4
    2. √6/4 − √2/4
    3. √6/4 + √2/4
    4. −√6/4 + √2/4
  45. Evaluate tan 330°.
    1. √3
    2. −√3
    3. 1/√3
    4. −1/√3
  46. Evaluate (−1 + 3i)³.
    1. −28 + 18i
    2. −28 − 18i
    3. 26 + 18i
    4. 26 − 18i
  47. Find the middle term in the expansion of (x + b)⁸.
    1. 4th term
    2. 5th term
    3. 6th term
    4. 7th term
  48. Given sinA = √5/5 and cosB = 2/√5, find cos(A + B). (A and B are acute.)
    1. 1/5
    2. −1/5
    3. 3/5
    4. −3/5
  49. Find sin 115° in surd form.
    1. (√6 + √2)/4
    2. (√6 − √2)/4
    3. (√3 + 1)/2
    4. (√3 − 1)/2
  50. The third term of an AP is 10 and the seventh term is 34. Find the product of the first term and the common difference.
    1. 10
    2. −10
    3. 12
    4. −12
  51. What is the minimum number of terms a binomial expression can have?
    1. Two
    2. One
    3. Three
    4. Four
  52. Find the sum of the coefficients of (1 − 2x)⁷.
    1. −1
    2. 0
    3. 1
    4. −128
  53. The third term of a GP is 63 and the fifth term is 567. Find the product of the common ratio and the first term (take r > 0).
    1. 21
    2. 63
    3. 189
    4. 27
  54. The sequence π + 3, 2π + 5, 3π + 7, … is an AP. Find the sum of the first ten terms.
    1. 55π + 120
    2. 55π + 110
    3. 45π + 110
    4. 65π + 120
  55. Convert 360°48′ to decimal degrees.
    1. 360.48°
    2. 360.8°
    3. 360.08°
    4. 360.048°
  56. Find sec²θ when tan²θ = 2/3.
    1. 5/3
    2. 3/2
    3. 4/3
    4. 7/3
  57. Given Z₁ = (π/2, 30°) and Z₂ = (2π, 90°) in polar form (modulus, argument), find Z₁/Z₂ in Cartesian (surd) form.
    1. (1 − √3i)/8
    2. (1 + √3i)/8
    3. (√3 − i)/8
    4. (1 − √3i)/4
  58. If tan²x = 10/7, find cot²x.
    1. 7/10
    2. 10/7
    3. 3/7
    4. 7/3
  59. Find the measure (number of elements) of the set A = {0, 1, 2}.
    1. 0
    2. 1
    3. 2
    4. 3
  60. Express (1 + √3i)⁶ in polar form.
    1. 64(cos 2π/3 + i sin 2π/3)
    2. 64(cos π + i sin π)
    3. 64(cos 4π/3 + i sin 4π/3)
    4. 64(cos 0 + i sin 0)
  61. The second term of a GP is 24 and the fifth term is 81. Find the product of the first term and the common ratio.
    1. 12
    2. 24
    3. 36
    4. 18
  62. The sum to infinity of a GP is 6 and the first term is 4. Find the common ratio.
    1. 1/3
    2. 2/3
    3. 1/2
    4. 3/4
  63. Find tan 120° + tan 45°.
    1. 1 − √3
    2. 1 + √3
    3. √3 − 1
    4. √3 + 1
  64. Find the sum of the first 6 terms of 5, 10, 20, …
    1. 315
    2. 155
    3. 635
    4. 160
  65. Find the 6th term of 1, 3, 9, …
    1. 81
    2. 243
    3. 729
    4. 27
  66. Given (4k + 1)x² + (k + 1)x + (k + 1) = 0, find k if the sum of the roots = −2/5.
    1. 1
    2. −1
    3. 2
    4. −2
  67. If cosA = 1/2 and sinB = √3/2, find cos(A + B). (A and B are acute.)
    1. 1/2
    2. √3/2
    3. −1/2
    4. −√3/2
  68. A binomial expression is the sum of ____ dissimilar terms.
    1. One
    2. Two
    3. Multiple
    4. Zero
  69. Insert an arithmetic mean between 2x + 7y and 4x + 5y.
    1. x − y
    2. 3(x − 2y)
    3. x + y
    4. 3x + 6y
  70. Determine the sum to infinity (limiting sum) of 6 − 2 + 2/3 − 2/9 + …
    1. 9/2
    2. 8
    3. 18
    4. 6
  71. What is the coefficient of xⁿ in the expansion of (1 − x)⁻¹?
    1. −1
    2. 1
    3. n
    4. (−1)ⁿ
  72. Find the geometric mean of 5 and 5/4.
    1. 4/5
    2. 2/5
    3. 5/2
    4. 5/8
  73. If S∞ = 25 and a = 10, find the common ratio.
    1. 0.6
    2. 0.4
    3. 0.5
    4. 0.25
  74. Find the total number of distinct terms in the expansion of (1 + 2x + x²)¹⁰.
    1. 11
    2. 22
    3. 21
    4. 10
  75. If A = {0, 0, 1}, how many subsets does A have?
    1. 8
    2. 4
    3. 1
    4. 16
  76. If A = {0, 0, 1} and B = {0, 1, 2}, find m(A ∩ B).
    1. 0
    2. 1
    3. 2
    4. 3
  77. Find the modulus and argument of the complex number (π/3)i.
    1. π/3, 90°
    2. π/3, 0°
    3. 3/π, 90°
    4. 1, π/3
  78. Find the first two roots of z⁶ − 1 = 0.
    1. 1, −1
    2. 1, cos 60° + i sin 60°
    3. cos 60° + i sin 60°, cos 120° + i sin 120°
    4. 1, i
  79. 2.5π radians is
    1. > 450°
    2. = 150°
    3. < 150°
    4. = 450°
  80. If Z = (2, 45°) in polar form, find Z in ordinary (Cartesian) form.
    1. √2 + √2i
    2. 1 + i
    3. 2 + 2i
    4. √2 + i
  81. If A = {0, 0, 1} and B = {0, 1, 1, 2}, find A ∪ B.
    1. {1, 2}
    2. {0, 1, 2}
    3. {0, 0, 1, 1, 2}
    4. {0, 2}
  82. Simplify (cos 3° + i sin 3°)¹⁰.
    1. cos 30° + i sin 30°
    2. cos 3° + i sin 3°
    3. cos 300° + i sin 300°
    4. cos 60° + i sin 60°
  83. Z₁ = (2, π/4) and Z₂ = (1, π/6) in polar form. Find Z₁/Z₂.
    1. (2, π/12)
    2. (2, π/4)
    3. (1, π/12)
    4. (2, π/6)
  84. If tan²θ = 3/4, find cosθ. (θ is acute.)
    1. 2/√7
    2. √3/2
    3. 2/√3
    4. √3/√7
  85. Given sinA = √5/5 and tanB = 1/3, find tan(A + B). (A and B are acute.)
    1. 1
    2. 2/3
    3. 1/3
    4. 3/2
  86. In a Venn diagram of sets A and B inside the universal set U, the whole region is shaded except the part of B that lies outside A. The shaded region represents
    1. A ∪ B′
    2. A − B
    3. A ∪ B
    4. B − A
  87. In a Venn diagram of sets A and B, only the part of A that lies outside B is shaded. The shaded region represents
    1. A′ ∩ B
    2. A ∪ B
    3. A ∩ B′
    4. B − A
  88. What is the first term of the series Σ (n = 1 to ∞) 12(1/3)ⁿ⁻¹?
    1. 1/3
    2. 12
    3. 4
    4. 1
  89. What is the common ratio of the series Σ (n = 1 to ∞) 12(1/3)ⁿ⁻¹?
    1. 12
    2. 3
    3. 1/3
    4. −1/3
  90. What is the sum to infinity of the series Σ (n = 1 to ∞) 12(1/3)ⁿ⁻¹?
    1. 12
    2. 16
    3. 18
    4. 24
  91. When all the terms of a geometric series are doubled and the first term is a = 1, what is the sum to infinity in terms of the common ratio r?
    1. 1/(1 − r)
    2. 1/(1 − r)²
    3. 1/(1 − 2r)
    4. 1/(1 − 2r)²
  92. On an Argand diagram, z₁ is plotted at the point (5, −4) and z₂ at the point (5, 4). Identify z₁ and z₂ and find their sum z₁ + z₂.
    1. 5 + 0i
    2. 10 + 0i
    3. 5 + 8i
    4. 10 + 8i
  93. Find the sum to infinity of the series Σ (k = 0 to ∞) 3(2/4)ᵏ.
    1. 3
    2. 4.5
    3. 6
    4. 9
  94. Find sin(−135°) in surd form.
    1. −√2/2
    2. √2/2
    3. −√3/2
    4. √3/2
  95. Find tan 135°.
    1. 1
    2. −1
    3. √3
    4. −√3
  96. Find tan 15°.
    1. 2 − √3
    2. 2 + √3
    3. √3 − 2
    4. √3 + 2
  97. Write (2, π/3) in Cartesian form.
    1. 1 + √3i
    2. √3 + i
    3. 2 + √3i
    4. 1 + 2i
  98. If all the terms of a GP are squared, find the new sum to infinity, given that the original sum is S = 1/(1 + r).
    1. 1/(1 + r²)
    2. 1/(1 − r²)
    3. 1/(1 + 2r)
    4. 1/(1 − 2r)
  99. Insert 5 arithmetic means between 3 and 12.
    1. 4½, 6, 7½, 9, 10½
    2. 4, 5, 6, 7, 9
    3. 5, 6, 7, 8, 9
    4. 3, 5, 6, 7, 8
  100. If sin²A = 2/9, find sec²A.
    1. 9/7
    2. 9/2
    3. 2/7
    4. 7/2

Register free to unlock all 167 questions with answers and explanations

SmartDriller logo

SmartDriller

Loading your past questions, mock exams, notes, and video tutorials...

Starting up…