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. Number of Instructional 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.

This course meets the General Education requirement for Quantitative Literacy.

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. Course Learning Goals

    The student will be able to:

    1. analyze calculus-related concepts, such as limits, tangent to a curve, and the difference quotient;
    2. L
    3. apply the properties of functions, such as finding the domain and range, determine zeros of functions, symmetries of a function, vertical, horizontal, and oblique asymptotes, use limits to determine end behavior of a function, develop the skills to graph functions, and accurately use a graphing calculator to find transformations of graphs;
    4. perform operations of functions - addition, subtraction, multiplication, division, composition, find and graph inverse functions, solve problems involving maximizing and minimizing a quadratic function, and construct mathematical models with functions using real-world applications or formulas;
    5. graph exponential and logarithmic functions, accurately use the properties of logarithms and the definition of e, solve exponential and logarithmic equations, and application problems using exponents and logarithms;
    6. define trigonometric functions, using the unit circle and right triangle definition, graph trigonometric functions, find the inverse trigonometric functions, verify trigonometric identities and formulas, solve trigonometric equations and solve problems, using real-world applications;
    7. develop the ability to analyze, interpret, and apply quantitative information [Quantitative Literacy].
  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 and scientific notation
      2. radicals and 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 and graphing utilities
      2. lines and slopes
      3. distance and 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 and Rational Functions (9 lessons)
      1. complex numbers
      2. quadratic functions and applications
      3. polynomials functions, application, and graphs
      4. dividing polynomials; remainder and factor theorem
      5. zeros of polynomial functions
      6. rational functions and graphs polynomial and rational inequalities
    4. Exponential and Logarithmic Functions (5 lessons)
      1. exponential functions
      2. logarithmic functions
      3. properties of logarithms
      4. exponential and logarithmic equations
      5. optional: modeling with exponential and logarithmic functions
    5. Trigonometric Functions and 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 Course Learning Goals

    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 formal assessment using open-ended questions reflecting theoretical and applied situations.
  4. Reference, Resource, or Learning Materials to be used by Student:

    Departmentally-selected textbook and graphing calculator is required. Details provided by the instructor or each course section. See course syllabus.

Review/Approval Date - 3/06; Core Goals/Objectives added 10/04; New Core 8/2015