Introduction: The information and materials presented here are intended to provide a description of the course goals for current and prospective students as well as others who are interested in our courses. It is not intended to replace the instructional policies and course materials presented in class.Every effort is made to update this information on a routine basis. However, if you have questions about enrollment, purchasing materials, and prerequisite skills, please check with your advisor or instructor.
Additional Course Description: Math 115 - Precalculus, is designed to prepare students for Math 221, Calculus. Math 115 is an in-depth study of the concept of functions.Several function classes including linear, quadratic, polynomial, rational, exponential, logarithmic, and trigonometric functions are studied. Within each function class characteristics of the function are emphasized including the basic form and graph, equations and inequalities associated with the function, and applications. Both algebraic and graphical techniques will be used throughout the course. Appropriate prerequisite skills and understandings for this course are required for success in this course. Details are discussed in the course prerequisites below. Students who need to review algebra should register for M010.
Students who are planning on taking Math 241 Analytic Geometry and Calculus A should enroll in Math 117 - Precalculus for Scientists and Engineers, not Math 115. Math 115 will not sufficiently prepare students for Math 241. In addition, students unsure of their mathematics requirements for his/her major may wish to consult their advisor – Math 114, Math 113 might be more appropriate.
Although most students have studied precalculus in high school and many may have studied calculus, there are several important distinctions between high school and university mathematics courses that you should note: The pace of the course is considerably faster than most high school courses. You are expected to spend significant time outside of class reading the text, doing homework problems, and preparing yourself to participate in class. The amount of time needed for this course may come as a surprise to many students.
To succeed in this course, students need "extensive" algebra skills. Yet, many students coming from high school (even students who had calculus) do not have appropriate algebra skills. (See more details below under prerequisites.) There is very little time devoted to review of algebra topics. Students must have the appropriate background to succeed in this course. Usually several sections of this course are offered during the fall and spring semesters.
Course Content: The following list illustrates the topics intended for coverage in a typical semester. Your instructor may cover these topics in a different order or may add topics if necessary.
- Linear, Rational, Literal, and Quadratic Equations
- Linear Inequalities
- Graphs and Graphing Utilities
- Basics of Functions and Their Graphs
- Linear Functions and Slope
- More on Slope
- Transformation of Functions
- Combinations of Functions
- Inverse Functions
- Modeling with Functions
- Quadratic Functions
- Polynomial Functions and their Graphs
- Rational Functions and their Graphs
- Polynomial and Rational Inequalities
- Exponential Functions
- Logarithmic Functions
- Properties of Logarithms
- Exponential and Logarithmic Equations
- Exponential Growth and Decay Models
- Angles and Radian Measure
- Trigonometric Functions: The Unit Circle
- Right Triangle Trigonometry
- Applications of Trigonometric Functions
- Trigonometric Functions of Any Angle
- Graphs of Sine and Cosine Functions
- Verifying Trigonometric Identities
- Sum and Difference Formulas
- Double Angle Formulas
- Trigonometric Equations
Required Math Placement Test Level: P, S, B, C
Additional Prerequisite Discussion: It is expected that M115 students have a thorough understanding of algebra topics. Experience has shown those students who enroll without these important algebra skills and understandings will not succeed.
Fall/Spring semester: In most cases, during the fall and spring semesters, course meets three hours per week in either a MWF or Tues/Thur course format. Course enrollments are usually at most 70 students per class with some smaller classes during the spring semester.
Assessment activities generally include tests or quizzes or other course activities as determined by the instructor.
Winter/Summer semester: This course may be offered during the winter and summer sessions. Depending on the session, it may require daily course meetings. During these sessions, instructors may use a variety of assessment course activities and course policies.
Tutorial Resources: There are several campus resources that provide additional assistance.
Math Tutorial Site: This site provides free drop-in tutorial assistance for students enrolled in this course. It is staffed by qualified math and math education majors. Students are encouraged to use this resource to get assistance on mathematical questions. More information about the Math Tutorial Site can be found at the webpage: Tutorial Lab
Academic Enrichment Center: Located at 148-150 South College Avenue, this site provides a number of different course resources for students. Please visit their web site for more information: http://ae.udel.edu/
Satellite Campus Information: Students enrolled at other campuses should contact the math faculty for the specific campus for additional information about this course.