20804203Intermediate Algebra 2
Course Information
Description
This course is a continuation of Intermediate Algebra 1, 20-804-202. Students expand their understanding of the structure of the real numbers (their construction, operations and properties); perform algebraic operations on rational and radical expressions; solve rational and radical equations; solve inequalities; solve absolute value equalities and inequalities; solve systems of three equations in three variables using the methods of substitution, addition (elimination), matrices and determinants; study complex numbers (their construction, operations and properties); solve second degree equations and inequalities in one variable; graph quadratic equations; solve exponential and logarithmic equations; understand and use functional notation and the arithmetic of functions; and solve application problems relative to the above topics.
Total Credits
3
Course Competencies
  1. Evaluate rational expressions and solve corresponding rational equations
    Assessment Strategies
    by a satisfactory score on all tests, quizzes, or graded assignment incorporating this competency
    Criteria
    you identify and simplify rational expressions
    you identify the domain of a rational expression
    you add subtract, multiply and divide rational expressions
    you simplify complex fractions
    you solve equations with rational expressions
    you translate and solve applications dealing with variations
    you solve applications problems involving rational expressions

  2. Solve 3x3 systems of equations and inequalities
    Assessment Strategies
    by a satisfactory score on all tests, quizzes, or graded assignments incorporating this competency
    Criteria
    you solve a system of linear equations by graphing, elimination, substitution, determinants, and matrix methods
    you classify system as being either consistent, inconsistent, dependent, or independent
    you solve systems of three linear equations by either elimination or matrix methods
    you translate applications problems into appropriate systems of equations
    you solve applications problems by using appropriate methods
    you solve systems of linear inequalities

  3. Solve inequalities and problem solving
    Assessment Strategies
    by a satisfactory score on all tests, quizzes, or graded assignments incorporating this competency
    Criteria
    you solve simple and compound inequalities
    you use interval notation
    you perform set operations with compound inequalities
    you translate absolute value inequalities into their corresponding compound inequalities and then solves the resulting inequalities
    you solve systems of linear inequalities by graphing

  4. Evaluate radical expressions and solve corresponding radical expressions
    Assessment Strategies
    by a satisfactory score on all tests, quizzes, or graded assignments incorporating this competency
    Criteria
    you convert from radical notation to exponential notation and vice versa
    you apply all of the rules of integer exponents to rational exponents
    you simplify radicals
    you add, subtract, multiply and divide radicals
    you solve equations which involve radicals
    you solve application problems which involve radicals
    you define and identify complex numbers
    you simplify radicals that include complex numbers

  5. Graph quadratic functions and solve quadratic equations
    Assessment Strategies
    by a satisfactory score on all tests, quizzes, or graded assignments incorporating this competency
    Criteria
    you use the square root property, factoring, completing the square, and the quadratic formula to solve quadratic equations
    you distinguish which of the above four techniques should be used to most effectively solve a quadratic equation
    you solve application problems which involve quadratic equations
    you use the Pythagorean Theorem to solve problems involving right triangles
    you graph quadratic functions and identifies its x- and y- intercepts, domain, range, vertex, axis of symmetry, concavity, and the intervals of increase or decrease
    you solve quadratic and rational inequalities
    you use the distance formula to determine the basic equation of a circle
    you recognize and graph equations of a circle

  6. Demonstrate knowledge of functions and relations
    Assessment Strategies
    by a satisfactory score on all tests, quizzes, or graded assignments incorporating this competency
    Criteria
    you distinguish between relations and functions
    you generate graphs of linear functions
    you identify domains and ranges of functions and relations
    you interpret and use functions notation correctly

  7. Use the algebra of functions
    Assessment Strategies
    by a satisfactory score on all tests, quizzes, or graded assignments incorporating this competency
    Criteria
    you add, subtract, multiply and divide functions
    you determine the composite of a function
    you identify a function as being one-to-one
    you determine and graph inverse functions
    you sketch miscellaneous functions: square root, cubics, absolute value

  8. Illustrate knowledge of exponential and logarithmic functions
    Assessment Strategies
    by a satisfactory score on all tests, quizzes, or graded assignments incorporating this competency
    Criteria
    you identify exponential functions
    you graph exponential functions
    you infer graphs of logarithmic functions by using the inverse of the exponential
    you graph logarithmic functions
    you rewrite exponential equations as logarithmic equations and vice versa
    you apply the properties of logarithms
    you solve exponential and logarithmic equations
    you solve applied problems involving exponential and logarithmic equations