Math (CETS)

• Real Numbers (R)


  contains all the values we know
• Counting / Natural Numbers (N)


  1, 2, 3, 4, 5, …
• Whole Numbers (W)


  when 0 is included in the set of natural numbers
• Composite Factor


  has other factors other than 1 and itself
• Integers (Z)


  set of whole numbers and their opposites (or negative numbers).
• Trichotomy Property


  exactly one of these statements is true: a>b, a=b, a<b
• Rational Numbers (Q)


  The entire set of numbers consisting of positive and negative integers, zero, and positive and negative fractions, or alternately, the set of all terminating or non-terminating repeating decimals
• Rational Numbers include any number in the form of m/n where m and n are integers and n =/ 0.
• Irrational Numbers


  numbers that cannot be expressed as a ratio of two integers

  • numbers whose decimal expansion does not terminate nor repeat.
• Percent of Increase or Decrease

  The percent of increase or decrease is found by putting the amount of increase or decrease over the original amount and changing this fraction to percent.

  New Value - Initial Value / Initial Value x 100%
• Density Property


  Between any two rational numbers, there is always another rational number, and between any two irrational numbers, there is always another irrational number. Likewise, between any two rational numbers, there is always an irrational numbers.
• Properties of Equality


  Reflexive Property: a=a

  Symmetric Property: a=b, then b=a

  Transitive Property: a=b and b=c, then a=c

  Substitution Property: a=b, then a may be replaced by b
• Two successive discounts of p% and q% allowed on an item are equivalent to a single discount of:

  (p + q - pq/100)%
• Principal (P)


  the amount of money (or sum) borrowed or given on loan and denoted by P.
• Rate of Interest (r%)


  is the amount of money paid for the use of money borrowed and is denoted by r%. It may be payable monthly, quarterly, semi-annually, or anually.
• Simple Interest


  interest is paid on the principal as it falls due

  Formula: SI = Prt / 100
• Simple Interest Amount Formula

  A = P + Prt / 100 OR A = P(1+rT/100)
• Ratio


  a comparison of two quantities

  • a/b or a:b
• Proportion

  statement of equality between two ratios

  • a/b = c/d OR a:b=c:d
• Difference of Two Squares

  a^2 - b^2 = (a + b)(a - b)
• Square of a Binomial

  (x + y)^2 = (x^2 + 2xy + y^2)

  (x - y)^2 = (x^2 - 2xy + y^2)
• Square of a Trinomial

  (x + y + z)^2 = x^2 + y^2 + z ^2 + 2xy + 2yz + 2xz
• Cube of a Trinomial

  (a + b)^3 = a^3 + 3a^2 + 3ab^2 + b^3

  (a - b)^3 = a^3 - 3a^2 + 2ab^2 - b^3
• Product of Binomial and Trinomial = Sum/Difference of Two Cubes

  (x + y)(x^2 - xy + y^2) = x^3 + y^3

  (x - y)(x^2 + xy + y^2) = x^3 - y^3
• Linear Equation

  ax + b = 0
• Quadratic Equation


  ax^2 + bx + c = 0
• Quadratic Formula

  Formula:

  A) -b +-

  B) b^2 - 4ac

  C) 2a

  
• Relation


  any set of ordered pairs

  (domain, range)
• Function

  a relation such that no two ordered pairs have the same first coordinate
• Logarithm to Exponential


  logb y = x

  Y = B^X
• logbxy = logbx + logby
• logbx/y = logbx - logby
• logb(x)^y = ylogbx
• Arithmetic Sequence

  an = a1 + (n-1)d
• Arithmetic Series

  Sn = n/2 (a1 + an)
• Geometric Sequence

  an = (a1)(r^n-1)
• Geometric Series


  Sn = a1 - an^r / 1 - r = a1 (1 - r^n) / 1 - r
• No. of Permutations of n things taken r at a time


  nPr = n! / (n-r)!
• Combination

  nCr = n! / r! (n-r)!
• Mean


  average number