College Algebra Syllabus and Study Guide

Course Overview

Introduction to College Algebra

College Algebra is a foundational mathematics course designed to develop students' understanding of algebraic concepts, problem-solving skills, and mathematical reasoning. The course covers a range of topics including polynomial, rational, radical, exponential, logarithmic, and absolute value functions, as well as systems of equations and matrices.

• Course Title: College Algebra (MATH 1314)

• Credit Hours: 3

• Lecture Hours: 3 per week

• Delivery: Online and in-person options

• Prerequisites: MATH 0308 or placement by testing

Student Learning Outcomes

Key Competencies

Upon successful completion of College Algebra, students will be able to:

• Recognize, graph, and apply polynomial, rational, radical, exponential, logarithmic, and absolute value functions, and solve related equations.

• Formulate and solve systems of linear equations using matrices.

• Demonstrate and apply knowledge of properties of functions, including domain and range, operations, compositions, inverses, and piecewise-defined functions.

• Apply graphing techniques to polynomial and rational functions.

• Evaluate all roots of higher degree polynomial and rational functions.

• Core Skills: Solve absolute value, polynomial, and rational equations.

Major Topics Covered

Functions and Their Properties

Functions are central to algebra and are used to model relationships between quantities. Understanding their properties is essential for solving equations and analyzing mathematical models.

• Definition: A function is a relation in which each input (domain) has exactly one output (range).

• Types of Functions: Polynomial, rational, radical, exponential, logarithmic, and absolute value.

• Domain and Range: The set of possible input values (domain) and output values (range).

• Operations: Addition, subtraction, multiplication, division, and composition of functions.

• Inverse Functions: Functions that reverse the effect of the original function.

• Piecewise-Defined Functions: Functions defined by different expressions over different intervals.

• Example: The quadratic function $f(x) = x^2$ has domain $(- , )$ and range $[0, )$.

Polynomial and Rational Functions

Polynomial and rational functions are used to model a variety of real-world phenomena. Their graphs and roots are important for understanding their behavior.

• Polynomial Function: $f(x) = a_nx^n + a_{n-1}x^{n-1} + ... + a_1x + a_0$

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

• Roots: Solutions to $f(x) = 0$

• Graphing: Identify intercepts, asymptotes, and end behavior.

• Example: $f(x) = \frac{x^2 - 1}{x - 1}$ is undefined at $x = 1$.

Exponential and Logarithmic Functions

Exponential and logarithmic functions are used in growth and decay models, finance, and many scientific applications.

• 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

• Properties: Laws of exponents and logarithms

• Example: $\log_2(8) = 3$ because $2^3 = 8$

Systems of Equations and Matrices

Systems of equations are solved using various algebraic methods, including matrices, which provide a compact way to represent and solve linear systems.

• System of Linear Equations: A set of equations with multiple variables

• Matrix Representation: $\begin{bmatrix} a_{11} & a_{12} \\ a_{21} & a_{22} \end{bmatrix}$

• Solution Methods: Substitution, elimination, and matrix operations

• Example: Solve $\begin{cases} x + y = 3 \\ 2x - y = 0 \end{cases}$

Required Technology and Resources

MyMathLab and D2L

Students are required to use MyMathLab for assignments and D2L for course management. These platforms provide access to homework, quizzes, and course materials.

• MyMathLab: Online homework and assessment system

• D2L: Course management and communication platform

• Calculator: Scientific or graphing calculator may be required

Assessment Activities

Types of Assessments

Student progress is evaluated through a variety of activities and assignments:

• In-Class Activities: Worksheets, discussions, and collaborative projects

• Section Assignments: Homework and media assignments in MyMathLab

• Unit Tests: Comprehensive exams covering major topics

• Review Quizzes: Short assessments to reinforce learning

• Final Exam: Cumulative assessment of all course material

Core Curriculum Statement

General Education Objectives

This course supports the development of critical thinking, communication, empirical and quantitative skills, and social responsibility.

• Critical Thinking: Analyze, evaluate, and synthesize information

• Communication: Effectively interpret and express mathematical ideas

• Empirical & Quantitative Skills: Manipulate and analyze numerical data

Attendance and Participation

Guidelines

Regular attendance and active participation are required. Students must complete assignments in MyMathLab and participate in discussions and activities as outlined in the syllabus.

• Attendance: Tracked via online platforms and assignment completion

• Penalty for Non-Enrollment: Students not enrolled in MyMathLab by the deadline may be dropped from the course

• Mobile Device Policy: Cell phones and PDAs are not permitted during tests

Grading and Evaluation

Grading Components

Grades are based on performance in assignments, quizzes, tests, and participation. The following table summarizes the main grading components:

Component	Description	Weight
Homework & Assignments	Completed in MyMathLab and D2L	Varies by instructor
Quizzes	Short assessments to reinforce learning	Varies by instructor
Unit Tests	Comprehensive exams on major topics	Varies by instructor
Final Exam	Cumulative assessment	Varies by instructor
Participation	Attendance, discussion, and engagement	Varies by instructor

Required Textbook

Textbook Information

The required textbook for this course is:

• Title: Beginning and Intermediate Algebra and College Algebra: A Concise Solution (5th edition)

• Authors: Lial, M., Hornsby, J., Schneider, D., Daniels, C. (2018)

• Publisher: Pearson Education

• ISBN: 9780134986371

Additional Information

• Make-up Policy: Make-up exams require valid excuses and must be scheduled promptly.

• Preferred/Used Name: Students may update their preferred name in the college system.

• Support: Academic support is available through campus resources and online platforms.

Additional info: This syllabus provides a comprehensive overview of the College Algebra course, including learning outcomes, major topics, assessment methods, and required resources. For detailed policies and schedules, refer to the official course documents and online platforms.