College Algebra Syllabus and Course Structure: Study Guide

Course Overview

Introduction to College Algebra

This course provides an in-depth study of algebraic concepts, focusing on polynomial, rational, radical, exponential, and logarithmic functions, as well as systems of equations and matrices. Additional topics may include sequences, series, probability, and conic sections. The course is designed to develop both conceptual understanding and practical problem-solving skills in algebra, preparing students for further study in mathematics and related fields.

Major Topics and Learning Outcomes

Core Algebraic Concepts

• Functions: Understanding the definition, properties, and representations of functions, including domain, range, and function notation.

• Linear Equations and Graphs: Solving and graphing linear equations, interpreting slope and intercepts, and working with different forms of linear equations.

• Systems of Equations: Solving systems using various methods, including matrices and the Gauss-Jordan method.

• Polynomials and Factoring: Performing operations with polynomials, factoring techniques, and solving polynomial equations.

• Rational Expressions and Equations: Simplifying, operating with, and solving rational expressions and equations.

• Roots and Radicals: Working with radical expressions, rational exponents, and solving radical equations.

• Quadratic Equations: Solving quadratics by factoring, completing the square, and the quadratic formula; analyzing graphs of quadratic functions.

• Exponential and Logarithmic Functions: Understanding and applying properties, solving related equations, and graphing these functions.

• Matrices: Performing algebraic operations on matrices and using them to solve systems of equations.

• Additional Topics: May include sequences, series, probability, and conic sections.

Course Structure and Assessment

Module-Based Learning

The course is divided into twelve modules (M1–M12), each focusing on a specific set of algebraic concepts. Each module includes practice assignments, mastery assessments, and feedback surveys. Students are expected to complete all assignments by the specified due dates.

Sample Module Topics

• M1: Functions – Identifying, representing, and evaluating functions.

• M2: Linear Equations – Working with different forms, calculating slope, and graphing.

• M3: Symmetry & Graph Transformations – Identifying even/odd functions and applying transformations.

• M4: Combining & Composing Functions – Performing algebraic operations and composition of functions.

• M5: Quadratic Functions – Properties and applications of quadratic equations.

• M6: Finding Roots – Techniques such as synthetic division and factoring.

• M7: Polynomial and Rational Equations – Graphing and solving, including the Intermediate Value Theorem.

• M8: Inverse Functions – Identifying and finding inverses, graphing inverse functions.

• M9: Exponential Functions – Solving, graphing, and applying exponential functions.

• M10: Logarithms – Properties, solving equations, and graphing logarithmic functions.

• M11: Matrix Algebra – Operations and solving systems with matrices.

• M12: Gaussian Matrix Methods & Inverse Matrices – Advanced matrix techniques for solving systems.

Assessment and Grading

• Mastery Assessments: Twelve major assessments, each worth approximately 6 2/3% of the final grade, covering the main topics of the course.

• Checks for Understanding: Assignments for each module, counting as 20% of the overall grade, designed to reinforce learning and prepare for mastery assessments.

• Grading Scale:

Grade	Percent	Description	Grade Points
A	90-100	Excellent/Superior Performance Level	4
B	80-89	Above Required Performance Level	3
C	70-79	Minimum Required Performance Level	2
D	60-69	Below Required Performance Level	1
F	Below 60	Failure to meet Performance Requirements	0
W	--	Withdrawal	0
IP	--	In Progress	0

Key Competencies

• Properties of Functions: Domain, range, and intervals of increase/decrease.

• Graphing Techniques: Creating, interpreting, and transforming graphs.

• Operations with Functions: Arithmetic operations and composition.

• Quadratic and Polynomial Equations: Solving and analyzing roots.

• Inverse, Exponential, and Logarithmic Functions: Operations and applications.

• Matrix Algebra: Operations and solving systems.

Required Resources

• Textbook: College Algebra and Trigonometry by Lial, Hornsby, Schneider, Daniels (7th Digital Update Edition).

• Calculator: A general scientific calculator is required; a TI-84+ graphing calculator is recommended.

• Software: Pearson's MyLab Math (access provided via Canvas after syllabus quiz completion).

• Technology: Reliable desktop or laptop computer, high-speed internet, and a webcam (not a cell phone).

Course Policies and Support

Participation and Communication

• Active participation in online modules and assignments is required.

• Students must use their official TSTC MyMail account for all course communications.

• Instructor responses to emails/voicemails will occur within 24 hours during business days.

Academic Integrity

• All work must be original; use of unauthorized websites or apps for assessments is prohibited.

• Violations of academic integrity will result in disciplinary action.

Support Services

• Disability accommodations, advising, counseling, library, and tutoring services are available to all students.

• Technical support is provided by the TSTC HelpDesk.

Sample Algebraic Concepts and Formulas

Key Definitions and Examples

• Function: A relation in which each input has exactly one output. Example: $f(x) = 2x + 3$

• Linear Equation (Slope-Intercept Form): $y = mx + b$ Example: $y = 4x - 7$

• Quadratic Equation (Standard Form): $ax^2 + bx + c = 0$ Quadratic Formula: $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

• Exponential Function: $f(x) = a \cdot b^x$ Example: $f(x) = 3 \cdot 2^x$

• Logarithmic Function: $y = \log_b(x)$ Example: $y = \log_{10}(x)$

• Matrix Multiplication: If $A$ is $m \times n$ and $B$ is $n \times p$, then $C = AB$ is $m \times p$.

Grading Weights Table

Assessment	Weight (%)
M1–M12 Mastery Assessments (each)	6 2/3
Checks for Understanding (total)	20

Additional Info

• All assessments are proctored and require the use of Respondus Lockdown Browser.

• Students may use one 8.5 x 11-inch sheet of personal notes and a hand-held calculator during assessments.

• Late work is accepted up to one week late with a 20% penalty; further extensions are at instructor discretion.

• Final grades ending in .5 or higher are rounded up to the next letter grade.