Course Description: This course is designed to be the first, college-level math course that a student will take. It is intended to be a foundation course for further math education. The course focuses on skill-building in algebra and providing an introduction to mathematical abstractness, yet allowing for real-life application and investigation. A variety of instructional styles will be incorporated: lecture, group work, activity-based labs, and computer aided instruction.

Course Prepared by: John Gann
State/Campus: Pohnpei/National

Purpose of Course

Degree Requirement: ___X___
Degree Elective: ______
Certificate: ______
Remedial: ______
Other: ______

Prerequisite Course:"C" grade in MS 098 or by placement.

Date approved by Committee: 01 February 2000
Date approved by President: 01 February 2000

1. General Objectives: Students will acquire the basic mathematical tools that will enable them to develop long-range intellectual abilities involving:
   1. engaging in substantial mathematical problem solving
   2. learning mathematics through modeling real-world situations
   3. expanding their mathematical reasoning skills
   4. developing the view that mathematics is a growing discipline, interrelated with human culture, and understand its connections to other disciplines
   5. acquiring the ability to read, write, listen to, and speak mathematics
   6. using appropriate technology to enhance their mathematical thinking and understanding and to solve mathematical problems and judge the reasonableness of their results- and
   7. developing mathematical power by engaging in rich experiences that encourage independent, nontrivial exploration in mathematics, develop and reinforce tenacity and confidence in their abilities to use mathematics, and inspire them to pursue the study of mathematics and related disciplines as related to their personal life-time goals.
2. Specific Objectives: Students will demonstrate acquisition of basic mathematical tools listed in the Course Content category below. The students will demonstrate by successful (70% accuracy of better) performance in:
   1. Classroom discussion and practice of the mathematical tools
   2. Homework used to reinforce classroom discussion
   3. Projects (including computerized projects) used to expand on and synthesize the tools discussed
   4. Multiple tests or quizzes (as a minimum, one per chapter) covering the course content
   5. A Mid-Term and Final that will be comprehensive assessments of students' understanding of the course content.
3. Course Content:
   1. Work With Equations and Inequalities
      1. Solve linear equations and their applications
      2. Solve quadratic equations and their applications
         1. Using factoring
         2. Using complete the square
         3. Using quadratic formula
      3. Introduce complex numbers
         1. Meaning of equality
         2. Addition/subtraction
         3. Multiplication/division
      4. Solve other types of equations and their applications:
         1. containing absolute values
         2. containing radicals
         3. containing rational expressions
      5. Solve linear inequalities and their applications
      6. Solve quadratic inequalities and their applications
      7. Solve other types of inequalities and their applications
         1. containing absolute values
         2. containing rational expressions
      8. Graph solutions of equations and inequalities on a real numbered line
      9. As technology becomes available, explore the graphs of the above equations and inequalities
   2. Work with Functions and their Graphs
      1. Know how to graph lines in a plane and calculate slope
         1. Using the slope-intercept form: y = m x + b
         2. Using the point-slope form: y - y₁ = m (x - x₁)
         3. Using the standard form: A x + B y + C = 0
      2. Define the meaning of a function as interpreted in the following ways:
         1. As a black box with input, process, and unique output
         2. As a formula containing algebraic rules
         3. As a graph with independent and dependent variables
         4. As piecewise defined portions of other functions
      3. Know the meaning of, and be able to find, the implied domain and range of a function
      4. Analyze graphs of a function to include:
         1. Increasing, decreasing, and constant functions, or portions of a function
         2. Using the vertical line test for a function
         3. Testing for even and odd functions
      Demonstrate the shifting (translation), reflecting, and stretching of functions as shown by their graphs
      5. Know how to perform operations on functions:
      1. Addition/subtraction
      2. Multiplication/division
      3. Composition
      6. Find the inverse of a function, if possible
      7. Explore applications of functions
   3. Explore Polynomial Functions in More Depth
      1. Define a general polynomial function and derive the linear and quadratic functions from that definition
      2. Know how to use Synthetic Division
      3. Know the Standard Form of a quadratic function and how to use it to graph the function
      4. Be able to convert from the polynomial form to the standard form of a quadratic function
      5. Know the meaning of and how to find zeros (roots) of a polynomial function
      6. Know and be able to use the Fundamental Theorem of Algebra
         1. to find real (non-imaginary) solutions
         2. to find complex solutions
         3. to find a mixture of real (non-imaginary) and complex solutions
      7. Explore higher order polynomial functions and their graphs
      8. Explore applications of polynomial functions especially the meanings of direct and inverse variations
   4. Work with Rational Functions
      1. Recognize their form
      2. Find vertical and horizontal asymptotes
      3. Graph rational functions
      4. Perform partial fraction expansion
      5. Introduce the Conic Sections
   5. Introduce Exponential and Logarithmic Functions
4. Required Textbook: See: http://www.comfsm.fm/~dleeling/department/textbooks.html#ms100
5. Required Course Materials: The following is a minimum. Additional materials may also be used
   1. Calculator with four basic arithmetic operations and square root
   2. Computer tutorial that accompanies the text (if computers are available)
6. Reference Materials: Crossroads in Mathematics: Standards for Introductory College Mathematics Before Calculus, American Mathematical Association of Two-Year Colleges (AMATYC), 1995
7. Instructional Cost: Costs will be associated with printing hand outs for student use, buying and/or creating overhead transparencies, instructor-annotated textbooks/answer keys/test generation tools, printed tests/quizzes for assessments, computers and computer-assisted instructional tools if there are none currently available, and instructor-generated teaching aids/models. The actual costs to the different campuses of COM-FSM will vary depending on what is currently on hand.
8. Methods of Instruction: The instructor, in addition to lecture, will:
   1. incorporate appropriate levels of technology (computer, calculator, etc.).
   2. foster interactive learning through student writing, reading, speaking, and collaborative activities so that students can learn to work effectively in groups and communicate both orally and in writing.
   3. actively involve students in meaningful mathematics problems that build upon their experiences and build connections with other disciplines that are relevant to the students.
   4. model the use of multiple approaches: numerical, graphical symbolic, and verbal, to help students learn a variety of techniques for solving problems.
   5. provide learning activities, including projects, that promote independent thinking and develop student confidence in their ability to access and use mathematics and other technical information independently.
9. Evaluation: To advance to the next level of mathematics, the student must demonstrate proficiency to at least the "C" level. The student will be evaluated in a variety of ways including: homework, classwork, work in small groups, projects, quizzes, a midterm test and a comprehensive final test. Grades will be assigned according to the scale outlined in the COM-FSM catalog.
10. Credit by Examination: None.
11. Attendance Policy: As presented in the COM-FSM catalog.