College Algebra Syllabus and Course Structure Study Guide

Course Overview

Introduction

This study guide summarizes the structure, objectives, and key policies of the College Algebra course (Math 1030) at the University of Missouri – St. Louis. The course covers foundational algebraic concepts and prepares students for further study in mathematics and related fields.

Course Content and Topics

Main Topics

• Fundamental Concepts of Algebra: Factoring, radicals, rational exponents, and simplifying rational functions.

• Equations and Inequalities: Linear, quadratic, rational, and absolute value equations and inequalities.

• Functions and Graphs: Properties, transformations, combinations, and inverse functions.

• Polynomial and Rational Functions: Zeros, graphs, division, remainder and factor theorems, and inequalities.

• Exponential and Logarithmic Functions: Definitions, properties, and solving related equations.

• Systems of Equations and Matrices: Linear and nonlinear systems, matrix operations, and solving systems using matrices.

Weekly Schedule Overview

• Weeks 1-4: Prerequisites, equations, factoring, radicals, complex numbers, quadratic equations, inequalities.

• Weeks 5-8: Functions, graphs, transformations, combinations, inverse functions, circles, distance and midpoint formulas.

• Weeks 9-11: Quadratic and polynomial functions, division, zeros, rational functions, inequalities.

• Weeks 12-13: Exponential and logarithmic functions, properties, equations.

• Weeks 14-15: Systems of equations, matrices, review, and final exam.

Course Objectives

Learning Outcomes

• Solving linear, rational, quadratic, and absolute value equations.

• Solving linear and absolute value inequalities.

• Describing functions algebraically and geometrically.

• Analyzing polynomial functions by their zeros and graphs.

• Solving polynomial and rational inequalities.

• Solving exponential and logarithmic equations.

• Solving systems of equations in two and three variables.

• Performing arithmetic operations with matrices.

• Solving systems of linear equations using matrix methods.

Assessment Structure

Assignments and Exams

• Homework: Weekly assignments (approx. 20 questions each), unlimited time and attempts, submitted online. Late submissions incur a 20% penalty per day.

• Quizzes: Weekly, timed (60 minutes), two attempts allowed, submitted online.

• Tests: Four module tests, proctored online, 80 minutes each, one attempt, no calculators or notes allowed.

• Final Exam: Comprehensive, proctored online, 120 minutes, one attempt, no calculators or notes allowed.

Weight Distribution

Assessment	Weight (%)
Homework	12.5
Quizzes	12.5
Tests (4)	50 (12.5 each)
Final Exam	25
Total	100

Grading Scale

Grade	GPA
A	4.0
A-	3.7
B+	3.3
B	3.0
B-	2.7
C+	2.3
C	2.0
C-	1.7
D+	1.3
D	1.0
D-	0.7
Ex (Excused)	-
DL (Delayed)	-
FN (Failure/non-participation)	-

Participation and Expectations

Student Responsibilities

• Engage consistently in all academic activities: assignments, quizzes, tests, discussion boards.

• Monitor course announcements and emails regularly.

• Seek help proactively from instructor, Active Learning Assistants, or Math Academic Center.

• Maintain respectful and professional communication in all online interactions.

Policies and Support

Academic Integrity

• Plagiarism and cheating are strictly prohibited and may result in disciplinary action.

• Refer to the University’s Student Conduct Code for details.

Disability and Communication Support

• Contact Disability Access Services for accommodations.

• Contact International Students and Scholar Services for language support.

Technical and Student Support

• Canvas technical support is available via phone, email, and website.

• Student Success Center offers tailored assistance.

Sample Key Concepts from Course Topics

Factoring Polynomials

• Definition: Factoring is the process of expressing a polynomial as a product of its factors.

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

Solving Linear Equations

• Definition: A linear equation is an equation of the form $ax + b = 0$.

• Solution: $x = -\frac{b}{a}$

• Example: $2x + 3 = 0 \Rightarrow x = -\frac{3}{2}$

Quadratic Equations

• Definition: A quadratic equation is an equation of the form $ax^2 + bx + c = 0$.

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

• Example: $x^2 - 4x + 3 = 0 \Rightarrow x = 1, 3$

Functions and Their Graphs

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

• Example: $f(x) = x^2$

• Graph: The graph of $f(x) = x^2$ is a parabola opening upwards.

Exponential and Logarithmic Functions

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

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

• Properties: $\log_a(a^x) = x$ and $a^{\log_a(x)} = x$

Systems of Equations and Matrices

• System of Linear Equations: Two or more linear equations considered together.

• Matrix Representation: $\begin{pmatrix} a & b \\ c & d \end{pmatrix}$

• Solving: Methods include substitution, elimination, and matrix methods (e.g., Gaussian elimination).

Time Management and Study Tips

• Allocate at least 4-5 hours per week for course activities.

• Complete assignments gradually, not at the last minute.

• Use available resources: MyMathLab, Active Learning Assistants, Math Academic Center.

• Review feedback and grades regularly to monitor progress.

Conclusion

Success in College Algebra requires consistent engagement, timely completion of assignments, and proactive use of support resources. Mastery of the outlined topics will provide a strong foundation for further mathematical study.