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
 3000
 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.
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


Course Learning Goals
The student will be able to:
 analyze calculusrelated concepts, such as limits, tangent to a curve, and the difference quotient; L
 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;
 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 realworld applications or formulas;
 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;
 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 realworld applications;
 develop the ability to analyze, interpret, and apply quantitative information [Quantitative Literacy].

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 and scientific notation
 radicals and rational exponents
 polynomials
 factoring polynomials
 rational expressions
 linear equations
 quadratic equations
 linear inequalities
 Graphs, Functions, and Models (9 lessons)
 graphs and graphing utilities
 lines and slopes
 distance and midpoint formulas, circles
 basic functions
 graphs of functions
 transformations of functions
 combinations of functions, composite functions
 inverse functions
 modeling with functions
 Polynomial and Rational Functions (9 lessons)
 complex numbers
 quadratic functions and applications
 polynomials functions, application, and graphs
 dividing polynomials; remainder and factor theorem
 zeros of polynomial functions
 rational functions and graphs polynomial and rational inequalities
 Exponential and Logarithmic Functions (5 lessons)
 exponential functions
 logarithmic functions
 properties of logarithms
 exponential and logarithmic equations
 optional: modeling with exponential and logarithmic functions
 Trigonometric Functions and 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 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 openended questions reflecting theoretical and applied situations. 
Reference, Resource, or Learning Materials to be used by Student:
Departmentallyselected 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