Discipline: Mathematics Degree Credit  [X]
Non Credit  [ ]
Nondegree Credit  [ ]
Comm Service  [ ]
 

Riverside Community College District
Integrated Course Outline of Record

Mathematics 35


COURSE DESCRIPTION
35 Intermediate Algebra Units: 5.00
 
Prerequisite(s): MAT 52: Elementary Algebra
The concepts introduced in beginning algebra are presented again, but in greater depth. In addition to the basic operations, logarithms, exponential equations, systems of linear and nonlinear equations, Cramer’s Rule, the Binomial Theorem, the complex number system, and sequences and series are included. 90 hours lecture.
 
SHORT DESCRIPTION FOR CLASS SCHEDULE
The algebra preparation for college level mathematics
 
ADVISORY ENTRY SKILLS
Before entering the course, students will be able to:
  1. Perform arithmetic operations on real numbers and polynomial, rational, and radical expressions.

  2. Evaluate algebraic expressions.

  3. Solve equations involving linear, quadratic, rational, and radical expressions.

  4. Graph linear equations and inequalities given the equation and find the equation given the graph.

  5. Factor polynomials.

  6. Apply algebraic principles and techniques to the solution of applications.

  7. Use the symbols and vocabulary of algebra to communicate mathematical concepts.
STUDENT LEARNING OUTCOMES
 Upon successful completion of the course, students should be able to:

Apply the basic operations of algebra on the set of real and complex numbers, polynomials, rational and radical expressions at an intermediate algebra level.

  1. Critical Thinking - Analyze and solve complex problems across a range of academic and everyday contexts
  2. Critical Thinking - Generalize appropriately from specific contexts
  3. Critical Thinking - Integrate knowledge across a range of contexts
  4. Breadth of Knowledge - Use the symbols and vocabulary of mathematics to solve problems and communicate the results
  5. Application of Knowledge - Maintain and transfer academic and technical skills to workplace

Solve linear, rational, quadratic, exponential, radical, logarithmic, absolute value equations, and systems of equations.

  1. Critical Thinking - Analyze and solve complex problems across a range of academic and everyday contexts
  2. Critical Thinking - Generalize appropriately from specific contexts
  3. Critical Thinking - Integrate knowledge across a range of contexts
  4. Breadth of Knowledge - Use the symbols and vocabulary of mathematics to solve problems and communicate the results
  5. Application of Knowledge - Maintain and transfer academic and technical skills to workplace

Solve inequalities in one or two variables.

  1. Critical Thinking - Analyze and solve complex problems across a range of academic and everyday contexts
  2. Breadth of Knowledge - Use the symbols and vocabulary of mathematics to solve problems and communicate the results
  3. Application of Knowledge - Maintain and transfer academic and technical skills to workplace

Graph equations of lines and linear inequalities; graph basic functions; identify conic sections.

  1. Critical Thinking - Analyze and solve complex problems across a range of academic and everyday contexts
  2. Critical Thinking - Generalize appropriately from specific contexts
  3. Critical Thinking - Integrate knowledge across a range of contexts
  4. Breadth of Knowledge - Use the symbols and vocabulary of mathematics to solve problems and communicate the results
  5. Application of Knowledge - Maintain and transfer academic and technical skills to workplace

Recognize and determine the distinctions between functions and relations; apply basic operations on functions and find inverse functions.

  1. Application of Knowledge - Maintain and transfer academic and technical skills to workplace
  2. Critical Thinking - Analyze and solve complex problems across a range of academic and everyday contexts
  3. Critical Thinking - Generalize appropriately from specific contexts
  4. Breadth of Knowledge - Use the symbols and vocabulary of mathematics to solve problems and communicate the results

Calculate terms of sequences. Calculate sums of series.

  1. Critical Thinking - Analyze and solve complex problems across a range of academic and everyday contexts
  2. Breadth of Knowledge - Use the symbols and vocabulary of mathematics to solve problems and communicate the results
  3. Application of Knowledge - Maintain and transfer academic and technical skills to workplace
 
COURSE CONTENT
  TOPICS
 

1.   Real Numbers
      a.   Set notation; subsets of the reals; order of operations; 
            absolute values
2.   Polynomials
      a.   Basic operations on polynomials; factoring; solve quadratic 
            equations by factoring.
3.   Rational expressions
      a.   Integer exponents; basic operations on rational expressions; 
            complex fractions; division of polynomials; synthetic division.
4.   Linear equations and inequalities
      a.   Literal and absolute value equations and inequalities.
5.   Exponential and radical expression
      a.   Rational exponents; radical equations; complex numbers.
6.   relations and functions
      a.   Cartesian system; function notation and combinations of
            functions; linear functions; equations of lines; distance and
            midpoint formulas.
7.   Quadratic equations / functions and their graphs
      a.   Complete the square; quadratic formula; polynomial and 
            rational inequalities
8.   Conic sections
      a.   Parabolas, circles, ellipses, hyperbolas
9.   Exponential and logarithmic functions
      a.   Inverse functions; properties of logarithms
10.  Systems of equations
      a.   Linear systems in two and three variables; Gaussian 
            Elimination and Cramer’s Rule.
11.  Sequences and series
 
METHODS OF INSTRUCTION
 Methods of instruction used to achieve student learning outcomes may include, but are not limited to:

  • Class lectures, discussions, and demonstrations of the four basic operations as applied to real and complex numbers, polynomial, rational, radical and logarithmic expressions and functions; solving linear and non-linear equations, inequalities or systems; graphing linear and non-linear inequalities and basic functions; identifying conic sections; recognizing and determining the distinctions between functions and relations; and calculating series and terms of sequences.
  • Drills and pattern practices utilizing hand-outs and/or computer-based tools in order to assist the students in mastering the techniques involved in applying the algebraic principles and techniques to the solution of applications utilizing the four basic mathematical operations in tandem with those topics mentioned in 1.
  • Provision and employment of a variety of learning resources such as videos, slides, audio tapes, computer-based tools, manipulatives, and worksheets in order to address multiple learning styles and to reinforce material.
  • Pair and small group activities, discussions, and exercises in order to promote mathematics discovery and enhance problem solving skills.

 
 
METHODS OF EVALUATION
 Students will be evaluated for progress in and/or mastery of learning outcomes by methods of evaluation which may include, but are not limited to:

  • Evaluation of written homework assignments and/or computerized homework assignments for correct application of algebraic principles as well as the correct use of symbols and vocabulary of algebra.
  • Quizzes and midterm/final examinations for conceptual understanding as well as correct technique and application of the four basic operations as applied to real and complex numbers, polynomial, rational, radical and logarithmic expressions and functions; solving linear and non-linear equations, inequalities or systems; graphing linear and non-linear inequalities and basic functions; identifying conic sections; recognizing and determining the distinctions between functions and relations; and calculating series and terms of sequences.
  • Assessment of classroom discovery activities for content knowledge and conceptual understanding.

 
ASSIGNMENTS

Required Reading Assignments


Required Writing Assignments


Other Outside-of-Class Assignments
 
COURSE MATERIALS
 All materials used in this course will be periodically reviewed to ensure that they are appropriate for college level instruction. Possible texts include:

  • Tussy, Gustafson. Intermediate Algebra. 3rd ed. Brooks/Cole, 2005.
  • Lial, Hornsby, McGinnis. Intermediate Algebra. 8th ed. Addison-Wesley, 2006.
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