College Algebra Syllabus and Study Guide

Course Overview

Introduction to College Algebra

This course provides a comprehensive study of algebraic concepts, including functions, equations, inequalities, and graphing. It is designed for students who have completed introductory algebra and wish to deepen their understanding of mathematical reasoning and problem-solving.

• Prerequisite: Completion of introductory algebra or equivalent placement score.

• Textbook: College Algebra by Michael Sullivan, 12th Edition.

• Calculator Policy: Only scientific calculators are allowed. Graphing calculators and electronic devices are not permitted during exams.

Topics Covered

Chapter 1: Review of Real Numbers

This chapter revisits the properties and operations of real numbers, which form the foundation for algebraic manipulations.

• Key Concepts: Properties of real numbers, order of operations, absolute value.

• Example: Simplify $| -7 + 3 |$.

Chapter 2: Linear Equations and Inequalities

Linear equations and inequalities are essential tools for modeling and solving real-world problems.

• Definition: A linear equation is an equation of the form $ax + b = c$.

• Solving Linear Equations: Isolate the variable using inverse operations.

• Solving Linear Inequalities: Similar to equations, but remember to reverse the inequality sign when multiplying or dividing by a negative number.

• Example: Solve $2x - 5 = 9$.

Chapter 3: Functions and Graphs

This chapter introduces the concept of functions, their representations, and how to graph them.

• Definition: A function is a relation that assigns exactly one output to each input.

• Function Notation: $f(x)$ denotes the value of the function at $x$.

• Graphing: Plot points $(x, f(x))$ on the coordinate plane.

• Example: If $f(x) = 2x + 1$, find $f(3)$.

Chapter 4: Polynomial and Rational Functions

Polynomial and rational functions extend the concept of linear functions to higher degrees and ratios of polynomials.

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

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

• Example: Find the zeros of $f(x) = x^2 - 4$.

Chapter 5: Exponential and Logarithmic Functions

Exponential and logarithmic functions are used to model growth, decay, and other phenomena involving repeated multiplication.

• Exponential Function: $f(x) = a^x$, where $a > 0$ and $a \neq 1$

• Logarithmic Function: $f(x) = \log_a(x)$, the inverse of the exponential function.

• Example: Solve $2^x = 8$.

Chapter 6: Systems of Equations and Inequalities

Systems of equations involve finding values that satisfy multiple equations simultaneously.

• Solving by Substitution: Replace one variable with its equivalent from another equation.

• Solving by Elimination: Add or subtract equations to eliminate a variable.

• Example: Solve the system: $x + y = 5$, $x - y = 1$.

Grading Policy

Assessment Components

Grades are determined by a combination of homework, quizzes, tests, and a final exam.

Component	Percentage
Paper/Pencil Homework	14%
Online Homework	15%
Three Tests	51%
Final Exam	20%

Grading Scale

Grade	Percentage Range
A	93.5 – 100%
A-	89.5 – 93.4%
B+	87.5 – 89.4%
B	83.5 – 87.4%
B-	79.5 – 83.4%
C+	77.5 – 79.4%
C	73.5 – 77.4%
C-	69.5 – 73.4%
D+	67.5 – 69.4%
D	63.5 – 67.4%
D-	59.5 – 63.4%
F	0 – 59.4%

Course Policies

Attendance and Participation

Regular attendance and active participation are required. Students are expected to read assigned sections and complete homework on time.

• Homework: Assignments may be completed online or on paper. Late homework may not be accepted.

• Exams: Three tests and a cumulative final exam will be administered.

Academic Integrity

Cheating and plagiarism are serious offenses and will be treated according to university policy. Collaboration is encouraged for learning, but all submitted work must be your own.

Support Services

• Math Learning Center: Free tutoring and support for math courses.

• Disability Services: Accommodations are available for students with documented needs.

• Counseling and Health: Resources are available for student wellness and support.

Important Dates

• Last day to add a class without a W: September 12, 2025

• Mid-term grades due: October 22, 2025

• Deadline to change grade option to Pass/Fail: November 4, 2025

• Last day to withdraw with a W: November 17, 2025

Standard Learning Outcomes

Student Competencies

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

• Demonstrate understanding of algebraic concepts and problem-solving strategies.

• Communicate mathematical reasoning clearly in written form.

• Apply algebraic methods to real-world problems.