Course

20804201 Intermediate Algebra
Course Information
Description
This course covers algebraic concepts with applications, an introduction to functions, and complex numbers. Students create and use equations involving one and two variables to solve problems. Topics include graphing and finding algebraic solutions for linear equations and inequalities, quadratic, exponential, polynomial, radical, and rational equations, as well as solving systems of equations. Students are introduced to linear, quadratic, square root, absolute value, exponential and logarithmic functions. The basic definitions of functions, relations, one-to-one functions and inverses are discussed along with the algebra and composition of functions. 
Total Credits
4
Course Competencies
  1. Solve linear equations
    Assessment Strategies
    Oral, Written, Graphic and/or Skill Assessment
    Criteria
    Solve equations in one variable
    Solve formulas for a specific variable
    Generate equations from given information
    Solve applications using formulas and linear equations

  2. Solve linear inequalities
    Assessment Strategies
    Oral, Written, Graphic and/or Skill Assessment
    Criteria
    Solve simple linear inequalities
    Solve compound linear inequalities
    Solve translated compound inequalities
    Solve applications using single inequalities
    Solve applications using compound inequalities
    Solve absolute value equations
    Solve absolute value inequalities

  3. Demonstrate graphing skills on the Cartesian coordinate plane
    Assessment Strategies
    Oral, Written, Graphic and/or Skill Assessment
    Criteria
    Identify x- and y- intercepts
    Find the distance between two points
    Find the midpoint of two points
    Calculate the slope between two points
    Identify the slope of a line on the x-y plane
    Use slope to determine if two lines are parallel, perpendicular, or neither
    Graph a line from given information
    Write the equation of a line in standard or point-slope form

  4. Analyze linear equations and inequalities in two variables
    Assessment Strategies
    Oral, Written, Graphic and/or Skill Assessment
    Criteria
    Generate the equation of a line given varying conditions
    Solve application problems involving rates of change
    Graph linear inequalities
    Solve application problems using linear inequalities

  5. Solve systems of equations
    Assessment Strategies
    Oral, Written, Graphic and/or Skill Assessment
    Criteria
    Solve systems of two linear equations by graphing methods
    Solve systems of two linear equations by elimination methods
    Solve systems of two linear equations by substitution methods
    Classify systems as consistent, inconsistent, or dependent
    Solve systems of three linear equations using elimination methods
    Translate application problems into appropriate system of equations
    Solve application problems with systems of equations
    Graph the feasible region for 2x2 systems of linear inequalities

  6. Solve polynomial equations
    Assessment Strategies
    Oral, Written, Graphic and/or Skill Assessment
    Criteria
    Factor using the greatest common factor
    Factor binomials
    Factor by grouping
    Factor trinomials
    Perform arithmetic operations with polynomials
    Factor the difference of two squares
    Factor the sum or difference of two cubes
    Use the zero product property of real numbers to solve polynomial equations
    Evaluate a polynomial function for a specified value

  7. Use rational equations to solve applied problems
    Assessment Strategies
    Oral, Written, Graphic and/or Skill Assessment
    Criteria
    Simplify rational expressions
    Find the domain of rational functions
    Perform arithmetic operations with rational expressions
    Simplify complex fractions
    Use a rational equation to solve an applied problem
    Interpret the solution of a rational equation in context
    Identify extraneous solutions
    Solve rational equations

  8. Solve radical equations
    Assessment Strategies
    Oral, Written, Graphic and/or Skill Assessment
    Criteria
    Convert between radical and exponential notation
    Apply rules of exponents with positive and negative rational exponents
    Perform arithmetic operations with radical expressions
    Evaluate a radical function for a specified value
    Find the domain of a radical function
    Solve equations containing radical expressions or rational exponents

  9. Operate within the complex number system
    Assessment Strategies
    Oral, Written, Graphic and/or Skill Assessment
    Criteria
    Simplify radicals that include complex numbers
    Perform arithmetic operations with complex numbers
    Solve equations with complex solutions
    Determine a complex conjugate

  10. Use quadratic equations to solve applied problems
    Assessment Strategies
    Oral, Written, Graphic and/or Skill Assessment
    Criteria
    Apply the square root principle
    Apply the quadratic formula
    Graph a quadratic function written in standard form or vertex form
    Perform transformations on a quadratic function
    Identify the domain and range of a quadratic function
    Interpret the solution of a quadratic equation in context
    Use the Pythagorean Theorem to solve an applied problem
    Use a quadratic equation to solve an applied problem

  11. Apply properties of functions
    Assessment Strategies
    Oral, Written, Graphic and/or Skill Assessment
    Criteria
    Distinguish the differences between relations and functions
    Find the domain and range of a relation
    Use function notation
    Solve applications involving functions
    Perform arithmetic operations with functions
    Identify the domain of a function algebraically
    Write a composite function
    Evaluate a composite function for a specified value
    Determine the inverse of a function algebraically

  12. Use exponential equations to solve applied problems
    Assessment Strategies
    Oral, Written, Graphic and/or Skill Assessment
    Criteria
    Identify an exponential function or relation
    Graph an exponential function
    Evaluate an exponential function for specified values
    Create an exponential function to model a given scenario
    Interpret the solution of an exponential equation in context
    Apply the definition of a logarithm to transform exponential equations
    Use properties of logarithms

  13. Use sociohistorical understanding of inequalities and underrepresentation within the STEM fields (science, technology, engineering, and math)
    Assessment Strategies
    Oral, Written, Graphic and/or Skill Assessment
    Criteria
    Analyze contemporary and historical systems that structure and reproduce societal inequalities
    Display awareness of other cultural dimensions (e.g. age, social class, race, religion, etc.)