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

Riverside Community College District
Integrated Course Outline of Record

Mathematics 35A


COURSE DESCRIPTION
35A Intermediate Algebra Units: 3.00
 
Prerequisite(s):
MAT-52, 52B or qualifying placement level
The first course in a two-course sequence (along with math 35B) for intermediate algebra. Math 35A is equivalent to the first half of math 35. Beginning algebra concepts are presented in greater depth. Topics include the real number system, linear equations and inequalities in one or two variables, systems of equations, exponents, factoring polynomials, polynomial and rational functions, and polynomial and rational equations. 54 hours lecture.
 
SHORT DESCRIPTION FOR CLASS SCHEDULE
The first in a two-course sequence of 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.
    • MAT 52 - 1.  Perform arithmetic operations on real numbers and polynomial, rational, and radical expressions.
    • MAT 52B - 1.  Perform operations with rational and radical expressions.

  2. Evaluate algebraic expressions.
    • MAT 52 - 2.  Evaluate algebraic expressions.
    • MAT 52B - 1.  Perform operations with rational and radical expressions.

  3. Solve equations involving linear, quadratic, rational, and radical expressions.
    • MAT 52 - 3.  Solve equations involving linear, quadratic, rational, and radical expressions.
    • MAT 52B - 2.  Solve rational, radical and quadratic equations.

  4. Graph linear equations in two variables. Find the equation of a line given its graph. Solve and graph single variable inequalities.
    • MAT 52 - 4.  Graph linear equations and inequalities given the equation and find the equation given the graph.
    • MAT 52B - 3.  Graph linear equations in two variables. Find the equation of a line given its graph.

  5. Factor single variable polynomials.
    • MAT 52 - 5.  Factor polynomials.

  6. Apply algebraic principles and techniques to the solution of applications.
    • MAT 52 - 6.  Apply algebraic principles and techniques to the solution of applications.
    • MAT 52B - 5. Apply algebraic principles and techniques to the solution of applications.

  7. Use the symbols and vocabulary of algebra to communicate mathematical concepts.
    • MAT 52 - 7.  Use the symbols and vocabulary of algebra to communicate mathematical concepts.    
    • MAT 52B - 5. Apply algebraic principles and techniques to the solution of applications.
STUDENT LEARNING OUTCOMES
 Upon successful completion of the course, students should be able to:
General Education SLO
Critical Thinking
  Analyze and solve complex problems across a range of academic and everyday contexts
  Integrate knowledge across a range of contexts
Communication Skills
  Read college-level materials with understanding and insight
Breadth of Knowledge
  Use the symbols and vocabulary of mathematics to solve problems and communicate the results

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

  1. Critical Thinking - Generalize appropriately from specific contexts
  2. Critical Thinking - Integrate knowledge across a range of contexts
  3. Communication Skills - Read college-level materials with understanding and insight
  4. Breadth of Knowledge - Use the symbols and vocabulary of mathematics to solve problems and communicate the results

2.  Solve linear, rational and 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. Communication Skills - Read college-level materials with understanding and insight
  4. Breadth of Knowledge - Use the symbols and vocabulary of mathematics to solve problems and communicate the results

3.  Solve linear inequalities in one and two variables. Solve absolute vale inequalities.

  1. Critical Thinking - Analyze and solve complex problems across a range of academic and everyday contexts
  2. Critical Thinking - Integrate knowledge across a range of contexts
  3. Communication Skills - Read college-level materials with understanding and insight
  4. Breadth of Knowledge - Use the symbols and vocabulary of mathematics to solve problems and communicate the results

4.  Graph equations of lines and linear inequalities, basic polynomial functions, absolute value functions, and reciprocal functions.

  1. Critical Thinking - Analyze and solve complex problems across a range of academic and everyday contexts
  2. Critical Thinking - Integrate knowledge across a range of contexts
  3. Communication Skills - Read college-level materials with understanding and insight
  4. Breadth of Knowledge - Use the symbols and vocabulary of mathematics to solve problems and communicate the results

5.  Recognize and determine the distinctions between functions and relations, and apply basic operations on functions.

  1. Critical Thinking - Recognize and assess evidence from a variety of sources
  2. Information Skills - Locate, evaluate and use information effectively
  3. Communication Skills - Read college-level materials with understanding and insight
  4. Breadth of Knowledge - Use the symbols and vocabulary of mathematics to solve problems and communicate the results
  5. Critical Thinking - Analyze and solve complex problems across a range of academic and everyday contexts
 
COURSE CONTENT
  TOPICS
 

1.    Real Numbers.

    a.    Set notation; subsets of the reals; order of operations; absolute values.

2.    Linear equations and inequalities.

    a.    Literal and absolute value equations and inequalities in one and two variables.

3.    Linear relations and functions.

    a.    Cartesian coordinate system; function notation and combinations of functions; linear functions; equations of lines; distance and midpoint formulas.

4.    Systems of equations.

    a.    Linear systems in two and three variables; Gaussian Elimination and Cramer’s Rule.

5.    Polynomials.

    a.    Basic operations on polynomials; factoring; solve quadratic equations by factoring.

6.    Rational expressions.

    a.    Integer exponents; basic operations on rational expressions; solving rational equations; complex fractions; division of polynomials; synthetic division.

 

Students are also assigned reading, writing and other outside assignments equivalent to two hours per one hour lecture.
 
METHODS OF INSTRUCTION
 Methods of instruction used to achieve student learning outcomes may include, but are not limited to:

1.    Class lectures, discussions, and demonstrations of the four basic operations as applied to real numbers, polynomial and rational expressions and functions; solving linear equations, inequalities or systems; graphing linear inequalities and basic functions; and recognizing and determining the distinctions between functions and relations. 


2.    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.


3.    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.


4.    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:

1.    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. 


2.    Quizzes and midterm/final examinations for conceptual understanding as well as correct technique and application of the four basic operations as applied to real numbers, polynomial, and rational expressions and functions; solving linear equations, inequalities or systems; graphing linear inequalities and basic functions; and recognizing and determining the distinctions between functions and relations.


3.    Assessment of classroom discovery activities for content knowledge and conceptual understanding.
ASSIGNMENTS

Required Reading Assignments

Read pages from the required text corresponding to sections covered in class, especially the definitions, theorems and examples. Read reference articles related to specific or broad algebra topics.


Required Writing Assignments

Write solutions for problems from the required text ( for example, section 3.2, Solving Quadratic Equations, pg. 237, # 1-31 odd). Write short paragraph responses to applications and mathematical procedures.


Other Outside-of-Class Assignments

Research (online, library, mathlab) alternative solving techniques. Complete printed or online practice exercises.
 
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 Publishing Company, 2006.
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