El Camino College - Division of Mathematical Sciences

Math 70
Intermediate Algebra
5 units; 5 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 40 or Mathematics 41B with a minimum grade of C in prerequisite or qualification by testing (El Camino College Mathematics Placement Test) and assessment

Catalog Description:
  This course consists of the study of the real number system; complex numbers; functions and their graphs' operations on polynomial, algebraic, exponential and logarithmic functions; linear and quadratic equations and inequalities; algebraic, exponential and logarithmic equations; systems of equations; and applications.

Course Objectives and Methods of Evaluation:

  1. Course objectives (list the major objectives stated as student outcomes in behaviorally measurable terms.)
    1.  Carry out numerical operations and manipulate expressions, including expressions with rational and negative exponents, complex numbers and logarithms.
    2. Recognize functional relationships in the form of graphs, data or symbolic equations and solve a variety of problems involving functions.
    3. Graph a variety of functions and relations and connect the solutions of problems to their graphs
    4. Solve a variety of equations and inequalities, systems of equations and inequalities using algebraic and graphical methods, including radical, exponential and logarithmic equations.
    5. Model application problems using numerical, symbolic and graphical methods and interpret results; each type of function will have related applied problems.
  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. Homework problems
      3. Quizzes

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Outline of Subject Matter
 

Approximate Time

Major Topic

11 hours

I. Basic Numerical Operations and Manipulations

  1. Polynomials: review of operations and factoring, and binomial expansion
  2. Rational Expressions: review of operations
  3. Radical Expressions: review of operations and rewriting as expressions with rational exponents
  4. Expressions with Negative or Rational exponents: operations and rewriting as expressions with radicals; review of scientific notation
  5. Complex Numbers: operations
  6. Sets: union ("or"), intersection ("and")
  7. Logarithms: properties and conversion between logarithmic and exponential statements

16 hours

II. Functions as rules, as sets of ordered pairs, as solution sets of equations in two variables and as graphs

  1. Definition
  2. Notation
  3. Operations: addition, subtraction, multiplication, division, composition
  4. One-to-one Functions
  5. Inverse Functions
  6. Determining the equation for linear function given the graph of sufficient data

17 hours

III. Graphing

  1. Reading and interpretation
  2. Graphical solutions to equations and inequalities
  3. Quadratic: completing the square to identify vertex and extremum of a parabola or to identify the radius of a circle or to sketch other conic sections.
  4. Basic graphs: f(x) = x, x2, x3, x1/2, |x|, 1/x, ax, logax and relations x2 + y2 = 1
  5. Transformations: translations, reflections

19 hours

IV.  Equations/Inequalities: algebraic and graphical methods of solving; interval notation if appropriate

  1. Quadratic equations over the complex numbers and inequalities over the reals
  2. Other polynomial equations and inequalities
  3. Radical Equations including those with rational exponents, and their domains
  4. Rational equations and inequalities, and their domains
  5. Exponential and logarithmic equations and their domains
  6. Systems of 3x3 linear equations
  7. Equations and inequalities involving the absolute value of linear expressions

17 hours

V. Applications to be included throughout the semester

  1. Modeling of problems verbally, numerically, symbolically and graphically
  2. Pattern recognition strategies
  3. Perimeter and area of rectangles, triangles and circles; review of Pythagorean Theorem; rate (distance = rate x time,
    cost = unit price x quantity, etc.); and exponential growth/decay
  4. Applied problems related to the types of equation/inequality, functions or graphs of this course
  5. Problems involving 2x2 linear equations

10 hours

Final Examination

Total:

90 Hours

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Planned Instructional Activities:

Lecture, discussion, group work, computer aided instruction
 

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 including expressions with fractions and radicals
  2.  Solve quadratic equations and systems of linear equations
  3.  Graph systems of linear equations
  4.  Solve application problems using linear and quadratic equations
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Source of information: Course Outline of Record dated November, 2001


 Last Updated On: 4/20/06