El Camino College - Division of Mathematical Sciences

Math 41B
Elementary Algebra, Part II
3 units; 3 hours lecture

Catalog Description Course Objectives and Methods of Evaluation
Outline of Subject Matter Planned Instructional Activities

Grading Method: Letter

Associate Degree Credit --- Does not Transfers to CSU and
                                           Does not Transfers to UC

Prerequisite: Mathematics 23 or Mathematics 25 with a minimum grade of C in prerequisite, or qualification by testing (El Camino College Mathematics Placement Test) and assessment.

Catalog Description:
  This course continues the study of introductory algebraic concepts and includes the solutions and applications of systems of linear equations, factoring techniques, simplification of rational and radical expressions, and the solution of quadratic equations.
Note: Students enrolled in this course are required to participate in group activities.
Note: Mathematics 41A and 41B together are equivalent to Mathematics 40.

 
 Course Objectives and Methods of Evaluation:

  1. Course objectives (list the major objectives stated as student outcomes in behaviorally measurable terms.)
    1. Use the specialized vocabulary describing the real number system and its properties as well as the specialized vocabulary of rational, radical, and quadratic expressions.
    2. Manipulate (evaluate, simplify, or factor) algebraic expressions, including expressions with fractions and radicals.
    3. Solve quadratic equations and systems of linear equations.
    4. Solve various application problems using linear and quadratic modeling techniques.
    5. Graph systems of linear equations on a coordinate plane, isolating features such as points of intersection, intercepts, and slope.
  1. Methods of Evaluation - Associate Degree Credit Course
    1. Substantial writing assignments are inappropriate for this degree applicable course because:
      1. The course is primarily computational in nature
      2. The course primarily involves skill demonstrations or problem solving.
    2. Computational or non-computational problem-solving demonstrations, including:
      1. Exam
      2. Quizzes
      3. Homework problems
      4. Group Activities

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Outline of Subject Matter
 

Approximate Time

Major Topic

2 hours

I. The Specialized Vocabulary of Algebra
Basic concepts from Elementary Algebra::

  1. absolute value
  2. variables and coefficients
  3. radicals and exponents

14 hours

II. Operations and Manipulations with Algebraic Expressions

  1. Factorization of polynomials by recognizing common monomial factors, the difference of squares, patterns or grouping in simple and general trinomials, perfect square trinomials
  2. Algebraic fractions, operations with rational expressions including polynomial division
  3. Radical expressions, combining radicals; products and quotients of expressions involving radicals

14 hours

III. Equations and Inequalities

  1. Systems of equations in two variables: substitution and linear combination (elimination or addition)
  2. Literal equations
  3. Quadratic equations, factoring, the square root property, completing the square, and the quadratic formula

8 hours

IV.  Applications

  1. Development of algebraic techniques in the solution of problems involving geometric formulas (Perimeter, Area, Volume, and the Pythagorean Theorem)
  2. Translation of situations described in word problems to linear and quadratic expressions, equations and inequalities and solving problems
  3. Algebraic strategies for word problems such as "work," "distance," and "mixture" problems

8 hours

V. Graphing

  1. Graphing techniques
  2. Interpretation of graphs
  3. Solving of systems of linear equations in two variables using graphing

 8 hours

Examinations

Total:

54 Hours

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Planned Instructional Activities:

Lecture, class discussion, projects, group activities, calculator instruction, and individual assistance
Entrance Skills and Knowledge:

List the required skills and/or knowledge without which a student would be highly unlikely to receive a grade of A, B, C, or Credit (or for Health and Safety, would endanger self or others) in the Target Course.

  1. Manipulate algebraic expressions
  2. Solve linear equations and apply their solution to standard applications
  3. Graph linear equations in two variables using intercepts and slope
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Source of information: Course Outline of Record dated November, 2001



 Last Updated On: 4/20/06