College Algebra (MATH-1314) Syllabus and Course Structure Study Guide

Course Overview

Course Description

This course provides an in-depth study of fundamental algebraic concepts, focusing on polynomial, rational, radical, exponential, and logarithmic functions, as well as systems of equations using matrices. Additional topics may include sequences, series, probability, and conic sections. The course is designed to develop critical thinking, quantitative reasoning, and problem-solving skills essential for further study in mathematics and related fields.

• Course Code: MATH-1314 (College Algebra)

• Credits: 3

• Prerequisites: Satisfactory completion of TSI Algebraic Math requirements

Learning Outcomes

State-Defined Learning Outcomes

• Properties of Functions: Demonstrate and apply knowledge of domain, range, operations, compositions, and inverses.

• Function Types: Recognize and apply polynomial, rational, radical, exponential, and logarithmic functions; solve related equations.

• Graphing Techniques: Apply graphing methods to various functions.

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

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

Texas Core Objectives

• Critical Thinking Skills: Creative thinking, innovation, inquiry, analysis, evaluation, and synthesis of information.

• Communication Skills: Effective development, interpretation, and expression of ideas through written, oral, and visual communication.

• Empirical and Quantitative Skills: Manipulation and analysis of numerical data or observable facts resulting in informed conclusions.

• Teamwork: Ability to consider different points of view and work effectively with others.

• Personal Responsibility: Connecting choices, actions, and consequences to ethical decision-making.

• Social Responsibility: Intercultural competence, civic responsibility, and engagement in communities.

Course Structure and Grading

Graded Work Criteria

Type	Weight	Notes
MyLabMath Homework	16%	38 assignments; lowest 4 scores dropped; repeatable problems; late work allowed with penalty
In-Class Work	4%	Group work/quizzes; no make-ups for missed work
Exams	60%	4 unit exams (15% each); no retakes; strict exam policies
Final Exam	20%	Comprehensive; timed (110 minutes); may replace lowest unit exam score if higher

Grade Breakdown

Grade	Range	Notes
A	90-100%	Excellent
B	80-89%	Good
C	70-79%	Fair
D	60-69%	Poor
F	0-59%	Fail

Course Schedule

Weekly Topics

The course follows a structured weekly schedule, covering the following main topics:

• Ch. R - Review: Fundamental algebraic concepts and skills

• Ch. 1 - Equations and Inequalities: Linear equations, inequalities, and applications

• Ch. 2 - Graphs: Graphing techniques and interpretation

• Ch. 3 - Functions and Their Graphs: Function notation, domain, range, and transformations

• Ch. 4 - Linear and Quadratic Functions: Properties, graphs, and applications

• Ch. 5 - Polynomial and Rational Functions: Operations, roots, and graphing

• Ch. 6 - Exponential and Logarithmic Functions: Definitions, properties, and solving equations

• Ch. 8 - Systems of Equations and Inequalities: Solving systems using matrices

• Additional info: Sequences, series, probability, and conics may be included as time permits.

Key Course Policies

Attendance and Participation

• Regular attendance and punctuality are required for success.

• Attendance is recorded each class period.

Late Work and Missed Exam Policy

• Homework may be submitted late with a 15% penalty until the exam deadline for that material.

• Missed exams or quizzes may be allowed late submission only at instructor discretion with documentation.

Academic Integrity

• Academic dishonesty (e.g., unauthorized collaboration, use of unauthorized materials) is strictly prohibited.

• Penalties include exam score reduction and possible disciplinary action.

• Penalized exam scores cannot be replaced by the Final Exam score.

Support Resources

• Instructor Contact: Email, office hours, and Microsoft Teams for questions and support.

• Tutoring: Free in-person and online tutoring available to all students.

• Technical Support: Assistance with MyLab Math and college technology.

• Student Resources: Counseling, child care, housing, emergency aid, food pantries, and more.

Summary of Main College Algebra Topics

Equations and Inequalities

Solving linear, quadratic, and higher-degree equations and inequalities is fundamental in algebra. Techniques include factoring, using the quadratic formula, and applying properties of equality and inequality.

• Quadratic Formula:

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

• Example: Solve $x^2 - 5x + 6 = 0$ by factoring: $(x-2)(x-3) = 0 \Rightarrow x = 2, 3$

Functions and Their Graphs

Understanding functions, their domains and ranges, and how to graph them is essential. Functions can be combined, composed, and inverted.

• Function Notation: $f(x)$

• Domain and Range: Set of input and output values

• Example: $f(x) = x^2$ has domain $(-\infty, \infty)$ and range $[0, \infty)$

Polynomial and Rational Functions

Polynomials are expressions of the form $a_nx^n + \ldots + a_1x + a_0$. Rational functions are ratios of polynomials. Key skills include finding roots, factoring, and graphing.

• Example: $f(x) = \frac{x^2 - 1}{x - 1}$ simplifies to $f(x) = x + 1$ for $x \neq 1$

Exponential and Logarithmic Functions

Exponential functions have the form $f(x) = a^x$, and logarithmic functions are their inverses. Applications include growth and decay models.

• Logarithm Properties: $\log_a(xy) = \log_a x + \log_a y$

• Example: Solve $2^x = 8 \Rightarrow x = 3$

Systems of Equations

Systems can be solved using substitution, elimination, or matrix methods. Matrix methods are especially useful for larger systems.

• Matrix Equation: $AX = B$

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

Additional info:

• Topics such as sequences, series, probability, and conic sections may be included as time permits.