math mcqs

• Number System


  • Complex numbers
  • Rational numbers
  • Irrational numbers
  • Terminating decimals
  • Recurring decimals
  • Real numbers
• Rational number


  A number that can be written in the form p/q, where p and q are integers and q ≠ 0
• Terminating decimal


  A decimal which has a finite number of digits in its decimal part
• Recurring decimal


  A decimal which has an infinite number of repeating digits
• 5.333... is a recurring decimal
• π is an irrational number
• 22/7 is a rational number
• Multiplicative inverse


  The reciprocal of a non-zero real number
• Properties of real numbers

  • Reflexive
  • Symmetric
  • Transitive
  • Trichotomy
• Golden rule of fractions

  For k ≠ 0, a/b = ka/kb
• The set {1, -1} possesses closure property with respect to multiplication
• If a < b

  1/a > 1/b
• Modulus of a complex number z = a + ib


  √(a^2 + b^2)
• i^13 = i
• Multiplicative inverse of (4, -7)

  (4/65, 7/65)
• (0,3)(0,5) = -15
• (-1)^(-1/2) = -i
• √3 is irrational
• √(-2) × √(-2) = 2
• z = -1 - i then z = (-1,1)
• Property 7.8 + (-7.8) = 0


  '+' inverse
• If x = 0 then the multiplicative inverse of x is not defined
• (-i)^15 = i
• A recurring decimal represents a rational number
• Every recurring decimal is a rational number
• Imaginary part of (-2 + 3i^3) is -3
• The product of two conjugate complex numbers is a real number
• (0,1)^3 = 1
• If n is an even integer, then (i)^n = 1
• Factors of 3(x^2 + y^2) are 3(x + iy)(x - iy)
• Real part of (2+i)/i is -2
• Sets, Functions and Groups


  • Union of sets
  • Subsets
  • Complement of a set
  • Disjoint sets
  • Propositions and their converses
  • Properties of groups
• If x ∈ L ∪ M then x ∈ L or x ∈ M
• The total number of subsets that can be formed from the set {x, y, z} is 8
• If x ∈ B' = U - B then x ∉ B and x ∈ U
• If L ∪ M = L ∩ M then L = M
• Set


  • Well defined and distinct objects
• The set of odd numbers between 1 and 9 is {3, 5, 7}
• Every recurring non-terminating decimal represents a rational number
• Diagram representing a set

  Venn diagram