Course Overview

Course Description

This College Algebra course provides an in-depth study and application of 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.

• Credits: 3

• Contact Hours: 48

• Modality: Standard (Online)

• Course Length: 15 weeks

Learning Outcomes

Core Outcomes

• Apply graphing techniques to various types of functions.

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

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

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

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

Additional Outcomes

• Communication Skills: Develop, interpret, and express ideas through written, oral, and visual communication.

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

• Empirical and Quantitative Skills: Manipulate and analyze numerical data or observable facts to reach informed conclusions.

Major Competencies

• CC1.1: Demonstrate and apply properties of functions, including domain, range, and intervals of increase/decrease/constancy.

• CC2.1: Create, graph, and interpret linear equations in various forms.

• CC3.1: Associate properties of graphs and perform transformational graphing techniques.

• CC4.1: Combine functions arithmetically and compose functions.

• CC5.1: Perform operations with quadratic equations.

• CC6.1: Evaluate roots of polynomial and rational functions.

• CC7.1: Perform operations with polynomial and rational equations.

• CC8.1: Demonstrate and apply knowledge of inverse functions.

• CC9.1: Perform operations with exponential functions.

• CC10.1: Perform operations with logarithms, logarithmic equations, and exponential equations.

• CC11.1: Perform algebraic operations on matrices.

• CC12.1: Solve systems of linear equations using matrix methods.

Course Structure and Assessment

Assignments and Assessments

• Mastery Assessments: Twelve major assessments, each focusing on a core topic (e.g., Functions, Linear Equations, Quadratic Functions, Matrix Algebra).

• Practice and Apply: Assignments for each unit, count as 20% of the overall grade, can be taken multiple times.

• Check for Understanding: Non-graded review assignments to aid preparation for Mastery Assessments.

• Proctored Exams: Some assessments require Respondus LockDown Browser and webcam.

Grading Scale

Grading Weights

• Each Mastery Assessment: 6 2/3% (total 80%)

• Practice and Apply Assignments: 20%

Key Topics Covered

• Linear Equations, Inequalities, and Applications

• Linear Equations, Graphs, and Functions

• Systems of Linear Equations

• Exponents, Polynomials, and Polynomial Functions

• Factoring

• Rational Expressions and Functions

• Roots, Radicals, and Root Functions

• Quadratic Equations and Inequalities

• Additional Graphs of Functions and Relations

• Inverse, Exponential, and Logarithmic Functions

• Polynomial and Rational Functions

• Conic Sections and Nonlinear Systems

• Further Topics in Algebra

Required Resources

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

• Calculator: Scientific calculator required; graphing calculator (e.g., TI-84+) recommended

• Software: Pearson MyLab Math (access via Canvas after Syllabus Quiz completion)

• Computer: Reliable desktop or laptop (not smartphone, Chromebook, or tablet)

• Webcam: Required for proctored assessments

Policies and Procedures

Academic Integrity

• Students must submit original work; use of AI-generated answers or unauthorized calculators is prohibited.

• Violations result in disciplinary action as per the Student Handbook.

Participation and Communication

• Active participation in Canvas and online meetings is required.

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

• Instructor response time: within 24 hours during business days.

Late Work and Deadlines

• Assignments accepted up to one week late with a 20% penalty.

• All work must be submitted by 5:00 p.m. on Wednesday of week 15.

Proctoring and Technical Requirements

• Respondus LockDown Browser required for some assessments; Chromebooks, iPads, and mobile devices are not compatible.

• Stable internet and professional virtual environment required.

Support Services

• Disability Services: Accommodations available upon request.

• Advising: Program and course navigation support.

• Advocacy & Resource Center: Basic needs support.

• CARE Team: Mental health and wellness support.

• Library Services: Access to databases, ebooks, and consultations.

• Tutoring Services: Available for 100+ courses and skill areas.

Sample Mastery Assessment Topics

• M1: Functions (definition, notation, evaluation, intervals of increase/decrease)

• M2: Linear Equations (forms, slope, graphing, parallel/perpendicular lines)

• M3: Symmetry & Graph Transformations (even/odd functions, transformations)

• M4: Combining & Composing Functions (operations, composition)

• M5: Quadratic Functions (standard/vertex form, applications)

• M6: Finding Roots (synthetic division, factoring, constructing polynomials)

• M7: Polynomial and Rational Equations (graphing, Intermediate Value Theorem, rational functions)

• M8: Inverse Functions (one-to-one, finding and graphing inverses)

• M9: Exponential Functions (solving, graphing, applications)

• M10: Logarithms (conversions, solving equations, properties, applications)

• M11: Matrix Algebra (operations, solving systems)

• M12: Gaussian Matrix Methods & Inverse Matrices (Gauss-Jordan, matrix algebra for systems)

Important Formulas and Concepts

• Linear Equation (Slope-Intercept Form):

• Quadratic Equation (Standard Form):

• Quadratic Formula:

• Function Notation:

• Exponential Function:

• Logarithmic Function:

• Matrix Multiplication: (where and are matrices)

• Inverse Matrix: (where is a square matrix)

Example Applications

• Solving Linear Systems: Use matrix methods (e.g., Gauss-Jordan elimination) to solve systems of equations.

• Graphing Functions: Apply transformations to basic graphs to model real-world scenarios.

• Factoring Polynomials: Factor expressions to solve equations and simplify rational functions.

• Evaluating Roots: Use synthetic division and the quadratic formula to find roots of polynomials.

Additional info:

• This syllabus covers all major topics required for a college-level algebra course, matching the standard chapter titles for College Algebra.

• Students are expected to use MyLab Math for all graded assignments and assessments.

• Support services are available for academic, technical, and personal needs.