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Math 117

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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.

Course Description

Additional Course Description:

This four credit mathematics course is designed to help you prepare for Math 241 Analytic Geometry and Calculus A. Placement in this course means you will have the opportunity to acquire both a conceptual and procedural understanding of algebra, precalculus, and trigonometry. This knowledge will serve you well because understanding Math 241 requires a thorough knowledge of these topics.

Our experience has shown that students without appropriate mathematical background do not succeed in this important first semester calculus course. Invariably, unprepared students fall behind because they cannot learn the material in calculus while filling in gaps from prerequisite material. (Prerequisite skills are discussed in more detail below.) The consequences can be severe. Unsuccessful students find themselves behind in their course sequence and higher level courses required for their major program, have lower course grades, and may not graduate in a timely manner. The Math Placement Exam will assist in determining if you have the appropriate background. Filling these gaps is crucial for your success in our mathematics courses and your degree program.

In addition to learning specific topics, another goal of this course is to provide a math course experience similar to the level of intensity of Math 241. Research has shown many freshmen do not have the mathematical reasoning skills, critical thinking skills, problem solving skills, and the ability to draw inferences to reach conclusions. Furthermore, college math courses have a greater emphasis on conceptual understanding than high school math courses and require a high standard of mathematical reasoning skills not necessarily addressed in high school. College mathematics courses are generally faster-paced requiring students to quickly and effectively learn and apply mathematical concepts and procedures. College mathematics instructors frequently require substantial "outside of the classroom" assignments. All these aspects of college math courses emphasize the importance of taking Math 117 prior to Math 241.

Course Content:

The following list illustrates the topics intended for coverage in a typical semester. Chapter references apply to the current textbook. Your instructor may cover these topics in a different order or may add topics if necessary.

    Chapter One

  •         The Real Numbers
  •         Operations with Real Numbers
  •         Polynomials and Rational Expressions
  •         Exponents and Radicals

    Chapter Two

  •         The Cartesian Coordinate System: Graphing Straight Lines and Equations of Circles
  •         Slope
  •         Equations of a Line
  •         Relations and Functions
  •         Function Notation
  •         Relating Functions to Their Graphs
  •         Introduction to Graph Sketching: Symmetry
  •         Basic Graphing Principles
  •         More Graphing Principles; Types of Functions
  •         Extracting Functions from "Real Life" Situations
  •         Quadratic Functions
  •         Operations on Functions
  •         Inverse Functions
  •         Polynomial Functions
  •         More Polynomial Functions and Mathematical Models
  •         Polynomial Division, Roots, Remainder and Factor Theorems
  •         Rational Functions
  •         Radical Functions
  •         Exponential Functions
  •         Logarithmic Functions
  •         Properties of Logarithms; Logarithmic Equations
  •         Common and Natural Logs; Change of Base; Exponential Equations
  •         Applications
  •         Systems of Equations and Inequalities
  •         Non-Linear Systems of Equations and Inequalities
  •         Angle Measurement and Two Special Triangles
  •         The Trigonometric Functions of a General Angle
  •         Right Triangle Trigonometry and Applications
  •         The Trigonometric Functions as Functions of Real Numbers
  •         The Sine and Cosine Functions and Their Graphs
  •         The Tangent, Secant, Cosecant, and Cotangent Functions and Their Graphs
  •         Basic Identities
  •         Trigonometric Equations
  •         The Inverse Trigonometric Functions
  •         The Addition Formulas
  •         The Double-Angle and Half-Angle Formulas
  •         The Law of Sines and the Law of Cosines

Current Syllabus: MATH 117 Fall 2011 Syllabus  

Links to sample exams:

Required Math Placement Test Level: S, B, C

Additional Prerequisite Discussion:

This course requires a strong ability to perform algebraic operations and understands algebraic procedures. This includes the ability to perform operations with rational expressions and numerical fractions (without the use of a calculator), working with radicals and rational exponents, factoring polynomials, solving quadratic equations using the quadratic formula, solving absolute value equations and inequalities, and the ability to use algebra to solve word problems and other applications. Many of these topics are covered in a typical Algebra II course or Intermediate Algebra (Math 010) course. A minimum of two years of high school algebra is recommended. A high school background including a high school precalculus course in addition to two algebra courses would be preferred.

Prerequisite Skills Example Document: MATH 117 Prerequisite Skills Examples  


The following are the textbooks typically used in this course. Students should wait until the first day of class to ensure the appropriate textbook and other course materials are purchased.

Precalculus: Mathematics for Calculus, 7th Edition, by Stewart, Loose-Leaf version. Also required is the EWA (Enhanced Web Assign) associated with this text.

Calculator Requirement: Currently, graphing calculators are not allowed. A scientific calculator is required for exams.

Course Format:

Fall/Spring semester:

In most cases, during the fall and spring semesters, course meets four hours per week in a MWF course lecture and a discussion on Thursdays. Course enrollments are usually at most 45 students per class. Assessment activities generally include tests or quizzes or other course activities as determined by the instructor. If many sections of the course are offered, the exams are common exams. Generally there are three common exams and a cumulative final exam. Other assessment activities such as quizzes, group work, and textbook assignments may also be required.

Winter/Summer semester:

This course is offered during the winter session but not the summer. During the winter session, it requires daily course meetings.

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 La​b

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:

Satellite Campus Information: Students enrolled at other campuses should contact the math faculty for the specific campus for additional information about this course.

​Updates coming in May

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Math 117
  • Department of Mathematical Sciences
  • University of Delaware
  • 501 Ewing Hall
  • Newark, DE 19716, USA
  • Phone: 302-831-2653