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
 Corequisites
 None
 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


Learning Goals:
Course Specific:
The student will be able to: apply and extend algebraic skills.
 analyze calculusrelated concepts, such as limits, tangent to a curve, and the difference quotient.
 apply the properties of functions, such as finding the domain and range and developing the skill to graph them.
 accurately use a graphing calculator to find transformations of graphs.
 perform operations of functions: addition, subtraction, multiplication, division, and composition.
 find the inverse function and its graph.
 construct mathematical models with functions, using realworld applications or formulas.
 determine zeros of a function, symmetries of a function; use limits to determine end behavior of a function.
 solve problems involving maximizing and minimizing a quadratic function, both algebraically and graphically.
 find vertical, horizontal, and slant asymptotes for rational functions and graph.
 graph exponential and logarithmic functions, and accurately use the properties of logarithms and the definition of e.
 solve exponential and logarithmic equations and application problems, using exponents and logarithms.
 define trigonometric functions, using the unit circle and right triangle definition.
 graph trigonometric functions, find the inverse trigonometric functions, and verify trigonometric identities and formulas.
 solve trigonometric equations and solve problems, using realworld applications.
Course Learning Goals:
Category I:
Math or Science: The students will be able to: develop the ability to analyze, interpret, and apply quantitative information.
Core Learning Objectives:
Category I:
Math or Science: The student will be able to: accurately translate descriptive problems into mathematical formulas and solve them. (1)
Category III:
CRITICAL THINKING/PROBLEM SOLVING
The students will be able to: Demonstrate an understanding of solving problems by:
 recognizing the problem
 reviewing information about the problem
 developing plausible solutions
 evaluating the results
These skills are developed in VII.B.2.i, VII.3.b, VII.3.c, and VII.B.5.h. 
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.
 Review Topics (10 lessons)
 exponents & scientific notation
 radicals & rational exponents
 polynomials
 factoring polynomials
 rational expressions
 linear equations
 quadratic equations
 linear inequalities
 Graphs, Functions, and Models (9 lessons)
 graphs& graphing utilities
 lines and slopes
 distance & midpoint formulas, circles
 basic functions
 graphs of functions
 transformations of functions
 combinations of functions, composite functions
 inverse functions
 modeling with functions
 Polynomial & Rational Functions (9 lessons)
 complex numbers
 quadratic functions & applications
 polynomials functions, application & graphs
 dividing polynomials; remainder and factor theorem
 zeros of polynomial functions
 rational functions and graphs polynomial & rational inequalities
 Exponential & Logarithmic Functions (5 lessons)
 exponential functions
 logarithmic functions
 properties of logarithms
 exponential & logarithmic equations
 optional; modeling with exponential and logarithmic functions
 Trigonometric Functions & Analytical Trigonometry (10 topics)
 angles and their measure
 trigonometric functions; the unit circle
 right triangle trigonometry
 trigonometric functions of any angle
 graphs of sine and cosine functions
 graphs of other trigonometric functions
 inverse trigonometric functions
 applications of trigonometric functions
 verifying trigonometric identities
 sum and difference formulas
 double angle and half angle identities
 Additional Topics in Trigonometry (5 topics)
 optional: product to sum and sum to product formulas
 trigonometric equations
 the law of sines
 the law of cosines

Assessment Methods for Core Learning Goals:
All Core Critical Thinking and Problem Solving, College Level Mathematics or Science, and DisciplineSpecific 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 openended questions reflecting theoretical and applied situations.

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