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Math 135: Pre-Calculus

This course is a dual credit course where students earn both high school and college credit.

Concurrent Enrollment Course Outline
High School Name:  Newfield Senior High School, Newfield, NY
Date Proposal Submitted/Prepared:   Wednesday, June 13, 2012
                                                            Revised: Saturday, August 6, 2016
Instructor:    Kristopher Williamson
TC3 Course #:    Math 135
TC3 Course Title:    Pre-Calculus
Credit Hours:    3 hours
Student Audience – Grade Level(s):    11th and 12th Grade students
Semester(s) Offered:  Fall 2016 Semester
Instructor e-mail and/or phone #:   Mr. Williamson    (607) 564-9955 x3210 (school)
Course Description:  Math 135 is a college level course which students learn key concepts to prepare them for Calculus 1. Topics that are covered include Introductions to Functions (definition, domain, range, graphs), Linear Functions, Quadratic Functions, Polynomial Functions, Rational Functions, Exponential Functions, Logarithmic Functions, Absolute Value Functions, Trigonometric Functions, Conic Sections, an Introduction to Calculus using Polynomial Functions (informal limits, definition of derivative, applying the derivative to graph functions, approximating the area under a curve, exact area using summation formula, integration and derivative shortcut methods), and additional topics, if time permits (polar coordinates, vectors).
Course Prerequisites: High School Algebra 2/Trigonometry
Minimal Basic Skills Needed to Complete Course Successfully:  Students must know how to factor polynomials and know the basics of functions. They also need to have strong organizational skills.
Course Objectives:  Learn mathematics topics at the college level that will prepare students to take Calculus 1. Develop an organized approach to problem solving.
Required Texts and Materials/Optional Materials as Appropriate:  Precalculus Functions and graphs: A Graphing Approach. By Larson, Hostetler, and Edwards
Class Modalities/Alternative Learning Strategies:  Lecture, discussions, individual practice, use of computer technology.
Required Readings, Presentations, Written Assignments, etc.:  Homework, quizzes, tests. Some selected readings from textbook.

Course Content Presented in Units or Segments:  Class meets 5 days a week for 43 minute periods. See the Course Outline for a list of topics in the order that they are planned to be taught.
Evaluation/Grading System:  Homework assignments will not be collected or graded; however, students are expected to complete their homework assignments and seek assistance where necessary. Grades will consist only of quizzes and tests, which will be averaged within each of the three marking periods. The final exam will count as a fourth grade. The overall course grade will be calculated by averaging the three marking periods with the final exam. Final grades will be issued as numbers for high school credit and as letters for college credit.
Statement of Academic Integrity:  In addition to TC3's Statement of Academic Integrity below, late work will only be accepted on occasion and by specific deadlines. If a student misses a quiz or test, they are responsible to take the quiz or test within 2 days of their return to school; afterward the student will earn a zero for their score.

Tompkins Cortland Community College's Statement of Academic Integrity
Every student at Tompkins Cortland Community College is expected to act in an academically honest fashion in all aspects of his or her academic work: in writing papers and reports, in taking examinations, in performing laboratory experiments and reporting the results, in clinical and cooperative learning experiences, and in attending to paperwork such as registration forms.
Any written work submitted by a student must be his or her own. If the student uses the words or ideas of someone else, he or she must cite the source by such means as a footnote. Our guiding principle is that any honest evaluation of a student's performance must be based on that student's work. Any action taken by a student that would result in misrepresentation of someone else's work or actions as the student's own — such as cheating on a test, submitting for credit a paper written by another person, or forging an advisor's signature — is intellectually dishonest and deserving of censure.
Make-Up Policy/Late Work:  Late work will only be accepted on occasion and by specific deadlines, usually within 2 days of the due date.  Students are responsible to approach the teacher for any notes and work missed when absent from school. Please visit the course website.
Attendance Policy:  Missing multiple days of class will result in a lower average. Students who miss an excessive amount of school and who do not make the effort to seek missed work could be removed from the class.
Student Responsibilities:  Students are responsible for maintaining a neat and organized binder that contains all notes taken in class as well as homework assignments, quizzes, and tests. If students have difficulty with certain topics, they are responsible for seeking extra help outside of class where necessary. Students are responsible for turning in all assignments by the specified due-dates. 

Course Outline – Math 135: Pre-Calculus
The following course outline matches closely with your textbook. It is suggested that you at least skim over the section in the textbook for the next day's lesson before you come to class. Some lessons are not in the textbook.
There will be a test at the end of each chapter. Longer chapters could have a quiz half-way through the chapter.
Chapter P: Prerequisites
P.1       Polynomials and Special Products
P.2       Factoring
P.3       Fractional Expressions
P.4       The Cartesian Plane
Chapter 1: Introduction to Functions
1.1        Lines in the Plane and Angle Between Lines
1.2        Distance from a Point to a Line
1.3        Functions
1.4        Graphs of Functions
1.5        Shifting, Reflecting, and Stretching Graphs
1.6        Combinations of Functions
1.7        Inverse Functions
Chapter 2: Solving Equations
2.1        Solving Equations Graphically
2.2        Complex Numbers
2.3        Solving Equations Algebraically (2 days)
2.4        Solving Inequalities Algebraically and Graphically
Chapter 3: Polynomial Functions
3.1        Quadratic Functions
3.2        Polynomial Functions of Higher Degree
3.3        Real Zeros of Polynomial Functions
3.4        Complex Zeros and the Fundamental Theorem of Algebra
Chapter 4: Rational Functions
4.1        Rational Functions and Asymptotes
4.2        Graphs of Rational Functions
4.3        Partial Fractions
4.4        Mixed Rational Functions Problems
4.5        Solving Rational Inequalities Algebraically
Chapter 5: Exponential and Logarithmic Functions
5.1        Exponential and Logarithmic Functions
5.2        Properties of Logarithms
5.3        Solving Exponential and Logarithmic Equations
5.4        Applications of Exponential and Logarithmic Functions
5.5        Mixed of Exponential and Logarithmic Problems
Chapter 6: Trigonometric Functions
6.1        Trigonometric Identities
6.2        Evaluating Trigonometric Expressions
6.3        Solving Trigonometric Equations
6.4        Trigonometric Formulas
6.5        Mixed Trigonometry Problems
6.6        Graphs of Sine and Cosine Functions
6.7        Graphs of Other Trigonometric Functions
6.8        More Practice Graphing Trigonometric Functions
Chapter 7: Derivatives
7.1        Introduction to Limits
7.2        Definition of Derivative
7.3        More Practice with Definition of Derivative
7.4        More Limits and Review
7.5        Derivative Shortcut Method and Applications of Derivatives
7.6        Derivative Rules
7.7        More Applications of Derivatives and Review
Chapter 8: Integration
8.1        Midpoint Rule and Trapezoid Rule
8.2        Summation Formula for Finding Exact Area
8.3        Mixed Area Problems
8.4        Introduction to Integration
8.5        Practice with Integration
8.6        Integration Using Partial Fractions
8.7        Mixed Integration Problems
Chapter 9: Conic Sections
9.1        Circles and Ellipses
9.2        Hyperbola
Review for Final Exam