El Camino College - Division of Mathematical Sciences

Math 180
Precalculus
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 --- Transfers to CSU and Transfers to UC

Prerequisite: Mathematics 170 with a minimum grade of C.

Catalog Description:
  This course includes a study of algebraic, exponential, logarithmic and trigonometric functions; an introduction to the algebra of matrices; sequence and series; an introduction to analytic geometry; and applications.

 Course Objectives and Methods of Evaluation:

  1. Course objectives (list the major objectives stated as student outcomes in behaviorally measurable terms.)
    1.  Manipulate and simplify complex numbers and algebraic expressions at the Precalculus level.
    2. Factor polynomials and find the zeroes of polynomial functions using polynomial division and the Factor Theorem.
    3. Solve algebraic, exponential, logarithmic and trigonometric equations, and equations with absolute value.
    4. Solve quadratic and rational inequalities and inequalities with absolute value.
    5. Graph algebraic, exponential, logarithmic and trigonometric functions.
    6. Solve systems of equations and inequalities.
    7. Solve problems using matrices and determinants.
    8. Evaluate trigonometric functions and their inverses.
    9. Solve problems and verify trigonometric identities using the sum, difference, double-angle and half-angle formulas.
    10. Sketch functions in polar and parametric form.
    11. Solve problems involving arithmetic and geometric sequences and series.
    12. Solve application problems at the Precalculus level.
    13. Use Mathematical Induction to write proofs.
    14. Use technology (graphing or scientific calculators and/or computer software) to solve 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. Quizzes
      3. Homework Problems

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Outline of Subject Matter
 

Approximate Time

Major Topic

5 hours

I. Algebraic Expressions

  1. Polynomials
  2. Radicals and exponents
  3. Rational expressions

5 hours

II. Linear and Quadratic Equations and Inequalities

  1. Linear and quadratic equations
  2. Inequalities
  3. Application problems involving linear and quadratic equations

5 hours

III. Functions and Graphs

  1. Graphs of Functions
  2. Transformations of Functions
  3. Composition and inverse of functions

10 hours

IV.  Conic Sections, Polar and Parametric Equations

  1. Conic Sections
  2. Polar Equations
  3. Parametric Equations

10 hours

V. Polynomial and Rational Functions

  1. Polynomial Functions and their Graphs
  2. Polynomial Division and the Factor Theorem
  3. Complex Numbers, Nonreal Solutions of Polynomial Equations and the Fundamental Theorem of Algebra
  4. Rational Functions and their Graphs
10 hours

VI. Exponential and Logarithmic Functions

  1. Graphing and Properties
  2. Equations and Applications
15 hours

VII. Trigonometric Functions

  1. The Unit Circle
  2. Trigonometric Functions
  3. Graphs and Inverses of Sine, Cosine and Tangent
  4. Identities
  5. Addition, Double-Angle and Half-Angle Formulas for Sine and Cosine
  6. Equations
10 hours

VIII. Matrices and Systems of Equations

  1. Systems of equations
  2. Algebra of Matrices
  3. Matrix Equations
  4. Determinant
  5. Systems of Inequalities
  6. Partial Fraction Decomposition
15 hours

IX. Sequences, Series and Mathematical Induction

  1. Sequences and Series
  2. Arithmetic and Geometric Sequences and Series
  3. Mathematical Induction
  4. Binomial Theorem

 5 hours

Examinations

Total:

90 Hours

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Planned Instructional Activities:

Lecture, discussion, individual assistance, calculator activities, 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. Solve problems involving right triangle trigonometry.
  2. Solve trigonometric equations and problems requiring the Laws of Sines and Cosines.
  3. Solve basic application problems using trigonometry.
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Source of information: Course Outline of Record dated November, 2001


 Last Updated On: 4/20/06