MATH125 Precalculus Mathematics

Department of Science, Technology, Engineering & Mathematics: Mathematics

I. Course Number and Title
MATH125 Precalculus Mathematics
II. Number of Credits
4 credits
III. Minimum Number of Instructional Minutes Per Semester
3000 minutes
IV. Prerequisites
MATH Placement Test score of 9, or MATH122 (C or better), or MATH120 (C or better) and High School Trigonometry
V. Other Pertinent Information
A comprehensive departmental final examination is included in this course.
VI. Catalog Course Description
This course introduces the foundations of analysis designed to precede the calculus sequence with emphasis on functions and graphs. Topics include properties of absolute value, polynomial, rational, exponential, logarithmic and trigonometric functions; techniques for solving equations and inequalities, and an introduction to the concept of limits and the difference quotient.
VII. Required Course Content and Direction
  1. Learning Goals:

    Course Specific:
    The student will be able to:
    1. apply and extend algebraic skills.
    2. analyze calculus-related concepts, such as limits, tangent to a curve, and the difference quotient.
    3. apply the properties of functions, such as finding the domain and range and developing the skill to graph them.
    4. accurately use a graphing calculator to find transformations of graphs.
    5. perform operations of functions: addition, subtraction, multiplication, division, and composition.
    6. find the inverse function and its graph.
    7. construct mathematical models with functions, using real-world applications or formulas.
    8. determine zeros of a function, symmetries of a function; use limits to determine end behavior of a function.
    9. solve problems involving maximizing and minimizing a quadratic function, both algebraically and graphically.
    10. find vertical, horizontal, and slant asymptotes for rational functions and graph.
    11. graph exponential and logarithmic functions, and accurately use the properties of logarithms and the definition of e.
    12. solve exponential and logarithmic equations and application problems, using exponents and logarithms.
    13. define trigonometric functions, using the unit circle and right triangle definition.
    14. graph trigonometric functions, find the inverse trigonometric functions, and verify trigonometric identities and formulas.
    15. solve trigonometric equations and solve problems, using real-world applications.

    Course Learning Goals:
    Category I:
    Math or Science:
    The students will be able to:
    1. develop the ability to analyze, interpret, and apply quantitative information.

    Core Learning Objectives:
    Category I:
    Math or Science:
    The student will be able to:
    1. accurately translate descriptive problems into mathematical formulas and solve them. (1)

    Category III:

    The students will be able to:
    1. Demonstrate an understanding of solving problems by:
      1. recognizing the problem
      2. reviewing information about the problem
      3. developing plausible solutions
      4. evaluating the results

      These skills are developed in VII.B.2.i, VII.3.b, VII.3.c, and VII.B.5.h.
  2. Planned Sequence of Topics and/or Learning Activities:

    The following is a list of the minimum amount of course material to be covered by the instructor. Accompanying each topic is an approximate number of lessons required to study the topic.

    1. Review Topics (10 lessons)
      1. exponents & scientific notation
      2. radicals & rational exponents
      3. polynomials
      4. factoring polynomials
      5. rational expressions
      6. linear equations
      7. quadratic equations
      8. linear inequalities

    2. Graphs, Functions, and Models (9 lessons)
      1. graphs& graphing utilities
      2. lines and slopes
      3. distance & midpoint formulas, circles
      4. basic functions
      5. graphs of functions
      6. transformations of functions
      7. combinations of functions, composite functions
      8. inverse functions
      9. modeling with functions

    3. Polynomial & Rational Functions (9 lessons)
      1. complex numbers
      2. quadratic functions & applications
      3. polynomials functions, application & graphs
      4. dividing polynomials; remainder and factor theorem
      5. zeros of polynomial functions
      6. rational functions and graphs polynomial & rational inequalities

    4. Exponential & Logarithmic Functions (5 lessons)
      1. exponential functions
      2. logarithmic functions
      3. properties of logarithms
      4. exponential & logarithmic equations
      5. optional; modeling with exponential and logarithmic functions

    5. Trigonometric Functions & Analytical Trigonometry (10 topics)
      1. angles and their measure
      2. trigonometric functions; the unit circle
      3. right triangle trigonometry
      4. trigonometric functions of any angle
      5. graphs of sine and cosine functions
      6. graphs of other trigonometric functions
      7. inverse trigonometric functions
      8. applications of trigonometric functions
      9. verifying trigonometric identities
      10. sum and difference formulas
      11. double angle and half angle identities

    6. Additional Topics in Trigonometry (5 topics)
      1. optional: product to sum and sum to product formulas
      2. trigonometric equations
      3. the law of sines
      4. the law of cosines
  3. Assessment Methods for Core Learning Goals:

    All Core Critical Thinking and Problem Solving, College Level Mathematics or Science, and Discipline-Specific Course Objectives will be assessed as follows:

    The student will apply mathematical concepts and principles to identify and solve problems presented through informal assessment, such as oral communication among students and between teacher and students and, for the core, formal assessment using open-ended questions reflecting theoretical and applied situations.

  4. Reference, Resource, or Learning Materials to be used by Students:

    Departmentally selected textbook and graphing calculator is required. Details provided by the instructor or each course section. See Course Format.
VIII. Teaching Methods Employed
Primary teaching methods are lecture, recitation, problem solving, and class discussion as appropriate.

Review/Approval Date - 3/06; Core Goals/Objectives added 10/04