College Algebra Syllabus and Course Structure Overview

Course Overview: College Algebra

Introduction

This syllabus outlines the structure, objectives, and policies for a College Algebra course. The course is designed for students who need to review basic algebra before advancing to higher-level mathematics. Topics include equations, inequalities, functions, graphs, polynomials, rational expressions, exponential and logarithmic functions, and analytic geometry.

Course Topics and Objectives

Learning Outcomes

• Algebraic Manipulation: Develop proficiency in manipulating algebraic expressions and solving equations and inequalities.

• Graphical Analysis: Understand and interpret graphs of equations, inequalities, and functions.

• Function Properties: Analyze and classify functions, including linear, quadratic, polynomial, rational, exponential, and logarithmic functions.

• Application: Apply algebraic and graphical methods to solve real-world problems.

• Analytic Geometry: Explore geometric properties of lines, circles, and conic sections.

Textbook and Resources

Required Textbook

• College Algebra: Graphs and Models (Authors: Bittinger, Beecher, Ellenbogen, Penna, 5th Edition)

Online Homework

• Assignments are completed in MyMathLab. Students must have a valid access code.

Tutoring Resources

• Math Resource Center located in 101 Cunningham Hall. Students are encouraged to seek help, form study groups, and attend office hours.

Course Schedule and Topics

Weekly Breakdown

• Weeks 1-2: Review of prerequisite algebraic concepts (Sections R.2, R.4, R.5, R.8)

• Weeks 3-4: Solving equations and inequalities, complex roots, applications

• Weeks 5-6: Graphs, symmetry, intercepts, lines, distance formula, circles

• Weeks 7-8: Functions, properties, library of functions, quadratic functions, applications

• Weeks 9-10: Polynomial functions, division, synthetic division, graphing, complex zeros

• Weeks 11-12: Rational functions, inequalities, one-to-one and inverse functions

• Weeks 13-15: Exponential and logarithmic functions, graphs, properties, equations, applications

Evaluation and Grading

Assessment Components

• Exams: Three midterm exams (15% each), Final Exam (32%)

• Homework: 12%

• Quizzes: 11%

Grading Table

Total Score (%)	Grade
90-100	A
80-89	B
70-79	C
60-69	D
Below 60	F

Class Policies

Attendance

• Attendance is expected and required. Excessive absences may result in penalties.

• Students must notify instructors and Student Affairs of absences due to illness or emergencies.

Equipment

• Cell phones and electronic devices are prohibited during exams and quizzes.

• No calculators allowed on exams unless specified.

Withdrawal and Emergencies

• Withdrawal is permitted with approval before the tenth week.

• Students must communicate with instructors in case of emergencies or absences.

Key Mathematical Concepts Covered

Equations and Inequalities

• Linear Equations: $ax + b = 0$

• Quadratic Equations: $ax^2 + bx + c = 0$

• Inequalities: $ax + b > 0$, $ax^2 + bx + c < 0$

Functions and Graphs

• Function Definition: A relation where each input has a unique output.

• Graphing: Plotting $y = f(x)$ on the coordinate plane.

• Properties: Domain, range, intercepts, symmetry.

Polynomials and Rational Functions

• Polynomial Functions: $f(x) = a_nx^n + a_{n-1}x^{n-1} + ext{...} + a_0$

• Rational Functions: $f(x) = \frac{P(x)}{Q(x)}$ where $Q(x) \neq 0$

Exponential and Logarithmic Functions

• Exponential Function: $f(x) = a^x$

• Logarithmic Function: $f(x) = \log_a(x)$

Analytic Geometry

• Distance Formula: $d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

• Equation of a Circle: $(x - h)^2 + (y - k)^2 = r^2$

Study Tips

• Attend all classes and participate actively.

• Complete all homework and practice problems.

• Utilize tutoring resources and office hours.

• Form study groups for collaborative learning.