genmath (pdf)

• Functions


  Mathematical models that represent real-life situations
• Representing real-life situations using functions

  1. Piece-wise functions

  2. Evaluating a function

  3. Performing operations on functions (addition, subtraction, multiplication, division, composition)
• Rational functions


  Mathematical models that represent real-life situations involving rational functions
• Representing real-life situations using rational functions

  1. Distinguishing rational function, rational equation, and rational inequality

  2. Solving rational equations and inequalities

  3. Representing a rational function through table of values, graph, and equation

  4. Finding domain and range of a rational function

  5. Determining intercepts, zeroes, and asymptotes of rational functions

  6. Graphing rational functions

  7. Solving problems involving rational functions, equations, and inequalities
• Inverse functions


  One-to-one functions where the input and output are reversed
• Representing real-life situations using one-to-one functions


  1. Determining the inverse of a one-to-one function

  2. Representing an inverse function through table of values and graph

  3. Finding domain and range of an inverse function

  4. Graphing inverse functions

  5. Solving problems involving inverse functions
• Exponential functions


  Mathematical models that represent real-life situations involving exponential growth or decay
• Representing real-life situations using exponential functions


  1. Distinguishing exponential function, exponential equation, and exponential inequality

  2. Solving exponential equations and inequalities

  3. Representing an exponential function through table of values, graph, and equation

  4. Finding domain and range of an exponential function

  5. Determining intercepts, zeroes, and asymptotes of an exponential function

  6. Graphing exponential functions

  7. Solving problems involving exponential functions, equations, and inequalities
• Logarithmic functions


  Mathematical models that represent real-life situations involving logarithmic growth or decay
• Representing real-life situations using logarithmic functions

  1. Distinguishing logarithmic function, logarithmic equation, and logarithmic inequality

  2. Solving logarithmic equations and inequalities

  3. Representing a logarithmic function through table of values, graph, and equation

  4. Finding domain and range of a logarithmic function

  5. Determining intercepts, zeroes, and asymptotes of a logarithmic function

  6. Graphing logarithmic functions

  7. Solving problems involving logarithmic functions, equations, and inequalities
• Inverse function


  A function that undoes the operation of another function
• Representing an inverse function

  1. Through its table of values

  2. Through its graph
• Inverse function


  • Finding the domain and range
• Exponential function


  A function that grows or decays exponentially
• Exponential equation


  An equation involving an exponential function
• Exponential inequality


  An inequality involving an exponential function
• Representing an exponential function

  1. Through its table of values

  2. Through its graph

  3. Through its equation
• Exponential function


  • Finding the domain and range
  • Determining the intercepts, zeroes, and asymptotes
• Logarithmic function


  The inverse of an exponential function
• Logarithmic equation


  An equation involving a logarithmic function
• Logarithmic inequality


  An inequality involving a logarithmic function
• Representing a logarithmic function


  1. Through its table of values

  2. Through its graph

  3. Through its equation
• Logarithmic function


  • Finding the domain and range
  • Determining the intercepts, zeroes, and asymptotes
• Simple interest


  Interest calculated on the principal amount only
• Compound interest


  Interest calculated on the principal amount and the accumulated interest
• Simple annuity


  A series of equal payments made at regular intervals
• General annuity


  A series of payments made at irregular intervals
• Stocks

  Shares of ownership in a company
• Bonds


  Debt instruments issued by governments or corporations
• Efficient markets theory


  The idea that stock prices fully reflect all available information
• Business loan


  A loan taken out by a business
• Consumer loan


  A loan taken out by an individual for personal use
• Proposition


  A statement that can be either true or false
• Simple proposition


  A proposition that cannot be broken down into smaller propositions
• Compound proposition


  A proposition that is made up of two or more simple propositions
• Conditional proposition


  A proposition that has the form "if p, then q"
• Tautology


  A proposition that is always true
• Fallacy


  An argument that appears to be valid but is not
• Direct proof


  A method of proving a statement by starting with the given information and logically deducing the conclusion
• Indirect proof


  A method of proving a statement by assuming the opposite and deriving a contradiction