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 equations, functions, inequalities, and systems of equations, preparing students for further study in mathematics and related fields.

• Course Title: College Algebra (MATH 1314)

• Credit Hours: 3

• Lecture Hours: 3 per week

• Delivery Mode: Online/Hybrid (D2L, MyMathLab)

• Prerequisites: MATH 0310 or placement by testing

Instructor and Administrative Information

Contact Details

• Instructor: Oscar Rivera Borotto

• Email: [e-mail]

• Office Location: TECH 100G

• Office Hours: Monday to Thursday, 3:00 PM – 4:00 PM or by request

• Administrative Staff: Contact information for department staff is provided for additional support.

Course Objectives and Student Learning Outcomes

Core Objectives

The course is designed to foster critical thinking, effective communication, and quantitative skills. Students will:

• Recognize, solve, and apply systems of linear equations using matrices.

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

• Solve absolute value, polynomial, and rational inequalities.

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

• Apply graphing techniques.

• Evaluate all solutions of higher-degree polynomial and rational functions.

Required Materials and Technology

Textbook and Online Resources

• Textbook: Lial, M., Hornsby, J., Schneider, D., Daniels, C. (2018). Beginning and Intermediate Algebra and College Algebra: A Concise Solution (5th edition). Pearson Education.

• MyMathLab (MML): Online homework and assessment platform. Students must enroll in the designated course using the provided course code.

• Calculator: Graphing calculators may be required for some assignments and assessments at the instructor's discretion.

• Required Technology: Reliable computer with internet access, ability to use D2L, MyMathLab, and other online resources.

Assessment and Grading

Types of Assessments

• In-Class Activities: Collaborative work, discussion boards, research projects, and presentations.

• Section Assignments: Weekly assignments in MyMathLab and Homework Assignment Entry (HAE).

• Review Quizzes: Short quizzes in MyMathLab to reinforce learning objectives.

• Unit Tests: Comprehensive exams at the end of each unit, including proctored assessments using LockDown Browser and Monitor.

• Final Exam: Cumulative exam covering all course material.

Major Topics Covered

Equations and Inequalities

Students will learn to solve various types of equations and inequalities, including linear, quadratic, polynomial, rational, radical, exponential, and logarithmic forms.

• Linear Equations: Equations of the form $ax + b = c$

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

• Polynomial Equations: Equations involving terms with powers greater than one.

• Rational Equations: Equations involving ratios of polynomials.

• Radical Equations: Equations involving roots, such as $\sqrt{x}$.

• Exponential and Logarithmic Equations: Equations involving $a^x$ and $\log_a(x)$.

Example: Solve $2x^2 - 5x + 3 = 0$ using the quadratic formula:

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

For $a=2$, $b=-5$, $c=3$:

$x = \frac{5 \pm \sqrt{(-5)^2 - 4 \cdot 2 \cdot 3}}{2 \cdot 2} = \frac{5 \pm \sqrt{25 - 24}}{4} = \frac{5 \pm 1}{4}$

So $x = 1.5$ or $x = 1$.

Functions and Their Properties

Functions are central to algebra, describing relationships between variables. Students will study domain, range, operations, inverses, and graphing techniques.

• Definition: A function $f$ assigns each input $x$ exactly one output $f(x)$.

• Domain: The set of all possible input values.

• Range: The set of all possible output values.

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

• Inverse Functions: If $f(x)$ maps $x$ to $y$, then $f^{-1}(y)$ maps $y$ back to $x$.

Example: If $f(x) = 2x + 3$, then $f^{-1}(x) = \frac{x - 3}{2}$.

Systems of Equations and Matrices

Students will solve systems of linear equations using substitution, elimination, and matrix methods.

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

• Matrix Representation: Systems can be represented as matrices for efficient solution.

• Solving Methods: Substitution, elimination, and matrix operations (e.g., row reduction).

Example: Solve the system:

$\begin{cases} 2x + 3y = 7 \\ x - y = 1 \end{cases}$

Using elimination or substitution yields $x = 2$, $y = 1$.

Polynomials and Rational Functions

Students will analyze polynomial and rational functions, including factoring, graphing, and solving related equations and inequalities.

• Factoring: Expressing polynomials as products of simpler polynomials.

• Graphing: Understanding the shape and behavior of polynomial and rational functions.

• Solving Inequalities: Finding intervals where the function satisfies certain conditions.

Example: Factor $x^2 - 5x + 6 = (x - 2)(x - 3)$.

Exponential and Logarithmic Functions

These functions model growth and decay, and are essential in many applications.

• Exponential Function: $f(x) = a^x$

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

• Properties: Laws of exponents and logarithms, solving related equations.

Example: Solve $2^x = 8$:

$x = \log_2(8) = 3$

Course Policies and Guidelines

Attendance and Participation

• Attendance is tracked via enrollment in MyMathLab and participation in online activities.

• Active participation in discussion boards and assignments is required.

• Non-participation may result in withdrawal from the course.

Mobile Device Policy

• Cell phones and PDAs are not permitted during tests.

• Devices may be used for note-taking during class, but not for communication or browsing.

Make-up Policy

• Make-up exams require a valid excuse and must be scheduled with the instructor.

• Documentation may be required for excused absences.

HTML Table: Course Information Summary

Course Title	Credit Hours	Lecture Hours	Delivery Mode	Prerequisites
College Algebra (MATH 1314)	3	3 per week	Online/Hybrid (D2L, MyMathLab)	MATH 0310 or placement by testing

Additional info:

• Some details about specific assignments, deadlines, and grading weights are not included in the images but are typically found in the full syllabus on the course website.

• Students are encouraged to use support resources such as tutoring centers and online help.