College Algebra Syllabus and Study Guide

Course Overview

Introduction to College Algebra

This course provides a comprehensive foundation in algebraic concepts, focusing on exponents, radicals, polynomials, rational expressions, inequalities, relations and graphs, linear equations, quadratic equations, systems of equations, and applications. The course is designed to prepare students for further study in mathematics and related fields.

• Credit Hours: 3

• Offered: Fall and spring semesters, summer by demand

• Format: Online

Course Objectives

Learning Outcomes

Upon successful completion of this course, students will be able to:

• Simplify algebraic expressions using the properties of real numbers and established rules for exponents, radicals, and polynomials.

• Solve quadratic equations and equations in quadratic form using various methods, such as factoring.

• Solve systems of equations algebraically and graphically.

• Perform basic set operations and apply basic geometric formulas and theorems.

• Perform tasks in coordinate geometry, such as finding the slope and equation of a line or the equation of a circle.

• Solve various types of linear and quadratic application problems.

Main Topics and Weekly Schedule

Course Content Structure

The course is organized into weekly modules, each focusing on specific algebraic topics. Below is a summary of the main topics covered each week, along with the corresponding textbook chapters and assignments.

Week	Topics	Key Concepts
1	Real Numbers, Algebra Essentials, Geometry Essentials	Properties of real numbers, order of operations, basic algebraic manipulations, geometric formulas
2	Polynomials, Factoring, Synthetic Division	Polynomial operations, factoring techniques, division of polynomials
3	Rational Expressions, Equations and Inequalities	Simplifying rational expressions, solving linear equations and inequalities
4-5	Equations and Inequalities (continued), Radical Equations	Solving inequalities, equations with absolute value, radical equations
6-7	Graphs, Distance and Midpoint Formulas, Circles, Systems of Equations	Graphing equations, finding distance and midpoint, equations of circles, solving systems of linear equations
8	Comprehensive Review and Final Exam	Review of all topics and cumulative assessment

Key Algebraic Concepts

Real Numbers and Algebraic Expressions

• Real Numbers: The set of numbers including rational and irrational numbers.

• Properties: Commutative, associative, distributive, identity, and inverse properties.

• Example: Simplify $3(x + 2) - 4x$.

• Solution: $3x + 6 - 4x = -x + 6$

Polynomials and Factoring

• Polynomial: An expression consisting of variables and coefficients, involving only addition, subtraction, multiplication, and non-negative integer exponents.

• Factoring: Writing a polynomial as a product of its factors.

• Example: Factor $x^2 - 5x + 6$.

• Solution: $(x - 2)(x - 3)$

Rational Expressions and Equations

• Rational Expression: A fraction in which the numerator and/or denominator are polynomials.

• Key Operation: Simplifying, multiplying, dividing, adding, and subtracting rational expressions.

• Example: Simplify $\frac{x^2 - 9}{x + 3}$.

• Solution: $\frac{(x - 3)(x + 3)}{x + 3} = x - 3$ (for $x \neq -3$)

Equations and Inequalities

• Linear Equation: An equation of the form $ax + b = 0$.

• Quadratic Equation: An equation of the form $ax^2 + bx + c = 0$.

• Factoring Method: Set the equation to zero and factor.

• Quadratic Formula: $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

• Inequality: A mathematical sentence that shows the relationship between quantities that are not equal.

• Example: Solve $2x - 5 > 3$.

• Solution: $2x > 8 \implies x > 4$

Radicals and Radical Equations

• Radical: An expression that uses a root, such as a square root or cube root.

• Example: Simplify $\sqrt{50}$.

• Solution: $\sqrt{25 \times 2} = 5\sqrt{2}$

Graphs and Coordinate Geometry

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

• Midpoint Formula: $M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)$

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

• Example: Find the distance between (1,2) and (4,6).

• Solution: $d = \sqrt{(4-1)^2 + (6-2)^2} = \sqrt{9 + 16} = 5$

Systems of Equations

• System of Equations: A set of two or more equations with the same variables.

• Methods: Substitution, elimination, and graphical methods.

• Example: Solve $x + y = 5$ and $x - y = 1$.

• Solution: Adding equations: $2x = 6 \implies x = 3$, then $y = 2$.

Course Policies and Grading

Grading Scale

Grade	Percentage
A	90.0% or above
B	80.0% - 89.9%
C	70.0% - 79.9%
D	60.0% - 69.9%
F	Below 60.0%

Assessment Breakdown

• Homework: 25%

• Discussions: 5%

• Quizzes: 20%

• Tests and Final Exam: 50%

Academic Integrity and Student Responsibilities

Academic Honesty

• Cheating, plagiarism, and other forms of academic dishonesty are strictly prohibited.

• All work must be original and properly cited.

• Multiple submissions of the same work are not allowed without instructor approval.

Student Responsibilities

• Check email and course announcements regularly.

• Participate in online discussions and activities.

• Complete assignments on time and keep track of deadlines.

• Engage with peers and faculty in a professional manner.

Course Resources

Required Textbook

• Title: College Algebra (with MyLab Math & Digital Text) by Michael Sullivan

• ISBN: 9780135188949

• Publication Date: 2019-02-22

Support Links

• UC Academic Catalog

• UC Student Handbook

• Academic & Writing Center

• Library

Additional info:

• This syllabus provides a structured overview of the College Algebra course, including weekly topics, grading, and academic expectations. For detailed content, students should refer to the assigned textbook chapters and online resources.