College Algebra Syllabus and Course Overview

Course Overview

This document provides the syllabus and course structure for a College Algebra course. It outlines the course objectives, learning outcomes, grading policies, weekly schedule, and important administrative information.

Course Description

• Topics Covered: Basic concepts of algebra, equations, and inequalities; functions and graphs; polynomial and rational functions; exponential and logarithmic functions; systems; matrices and determinants; linear programming; conic sections; sequences; series; and combinatorics.

Student Learning Outcomes

• General Outcome: Accurately explain thinking and mathematical processes. Ability to justify mathematical solutions effectively and accurately.

• Specific Outcome: Demonstrate proficiency in concepts to solve, graph, model, and apply various college-level algebraic functions.

Course Objectives

Upon completion of the course, students should be able to:

1. Solve polynomial and rational equations and inequalities.

2. Identify the domain, range, and inverses (and graph with the translations) of linear, polynomial, rational, exponential, and logarithmic functions.

3. Solve polynomial equations and solve polynomial equations using the Rational Zero Theorem, Synthetic Division, Remainder Theorem, and Factor Theorem.

4. Solve problems involving interest and other applications.

5. Solve systems of equations and inequalities, and solve radical equations.

6. Graph and analyze conic sections, sequences, series, and properties of radicals and complex fractions.

7. Manipulate polynomials, rational expressions, and rational equations using the Remainder Theorem and Factor Theorem.

8. Demonstrate knowledge of solving by mathematical modeling, and analyze the reasonableness of the results. Use appropriate technology such as calculators to generate arguments and aid in communicating mathematical solutions.

Key Topics and Concepts

Equations and Inequalities

• Equations: Mathematical statements asserting the equality of two expressions. Example: $2x + 3 = 7$

• Inequalities: Statements about the relative size or order of two objects. Example: $x^2 - 4 > 0$

• Solving Techniques: Factoring, quadratic formula, completing the square, and graphing.

Functions and Graphs

• Function: A relation in which each input has exactly one output. Notation: $f(x)$

• Domain and Range: The set of possible input values (domain) and output values (range).

• Graphing: Plotting points $(x, f(x))$ on the coordinate plane.

• Transformations: Shifts, reflections, stretches, and compressions of graphs.

• Inverse Functions: If $f(x)$ is a function, its inverse $f^{-1}(x)$ satisfies $f(f^{-1}(x)) = x$.

Polynomial and Rational Functions

• Polynomial Function: $f(x) = a_nx^n + a_{n-1}x^{n-1} + ... + a_1x + a_0$

• Rational Function: A function of the form $f(x) = \frac{P(x)}{Q(x)}$, where $Q(x) \neq 0$.

• Zeros of Polynomials: Solutions to $f(x) = 0$.

• Rational Zero Theorem: Provides a list of possible rational zeros for a polynomial equation.

• Synthetic Division: A shortcut method for dividing polynomials.

• Remainder Theorem: The remainder of $f(x)$ divided by $(x - c)$ is $f(c)$.

• Factor Theorem: $(x - c)$ is a factor of $f(x)$ if and only if $f(c) = 0$.

Exponential and Logarithmic Functions

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

• Logarithmic Function: $f(x) = \log_a(x)$, the inverse of the exponential function.

• Properties: $\log_a(xy) = \log_a(x) + \log_a(y)$, $\log_a\left(\frac{x}{y}\right) = \log_a(x) - \log_a(y)$, $\log_a(x^r) = r\log_a(x)$

• Applications: Compound interest, population growth, radioactive decay.

Systems of Equations and Inequalities

• System of Equations: A set of two or more equations with the same variables.

• Solving Methods: Substitution, elimination, and matrix methods.

• Matrix Representation: Systems can be written as $AX = B$ where $A$ is a matrix of coefficients.

• Determinants: Used to solve systems using Cramer's Rule.

Conic Sections

• Conic Sections: Curves obtained by intersecting a plane with a double-napped cone: circles, ellipses, parabolas, and hyperbolas.

• Standard Equations:

  • Circle: $(x - h)^2 + (y - k)^2 = r^2$

  • Ellipse: $\frac{(x - h)^2}{a^2} + \frac{(y - k)^2}{b^2} = 1$

  • Parabola: $y = a(x - h)^2 + k$

  • Hyperbola: $\frac{(x - h)^2}{a^2} - \frac{(y - k)^2}{b^2} = 1$

Sequences, Series, and Combinatorics

• Sequence: An ordered list of numbers, often defined by a formula.

• Series: The sum of the terms of a sequence.

• Arithmetic Sequence: $a_n = a_1 + (n-1)d$

• Geometric Sequence: $a_n = a_1 r^{n-1}$

• Summation Notation: $\sum_{i=1}^n a_i$

• Combinatorics: The study of counting, arrangements, and combinations.

• Permutations: $P(n, r) = \frac{n!}{(n - r)!}$

• Combinations: $C(n, r) = \frac{n!}{r!(n - r)!}$

Course Materials and Technology

• Textbook: College Algebra: Concepts Through Functions, A Corequisite Solution by Michael Sullivan

• Calculator: Graphing Calculator (TI 83/84)

• Online Homework: MyMathLab

Grading Policy

Component	Weight
Homework / Lecture Videos	10%
Online Quizzes	15%
Discussion Forums	10%
Exam 1	25%
Exam 2	15%
Final Exam	25%

• Grading Scale:

  • A: 90% - 100%

  • B: 80% - 89%

  • C: 70% - 79%

  • D: 60% - 69%

  • F: Below 60%

Course Schedule Overview

• Weeks 1-2: Orientation, syllabus review, initial assignments, and start of Chapter 1.

• Weeks 3-4: Chapter 2 (Equations and Inequalities), homework and discussion assignments.

• Week 5: Exam 1 (Chapters 1 & 2).

• Weeks 6-7: Chapter 3 (Functions and Graphs), homework and discussion assignments.

• Weeks 8-9: Chapter 4 (Polynomial and Rational Functions).

• Weeks 10-11: Exam 2 (Chapters 3, 4, 5), quizzes, and assignments.

• Weeks 12-13: Chapter 6 (Exponential and Logarithmic Functions).

• Weeks 14-15: Chapters 7 & 8 (Systems, Matrices, Sequences, Series, and Combinatorics).

• Week 16: Final Exam (Comprehensive).

Policies and Additional Information

• Attendance: Participation in weekly discussions and assignments is required. Inactivity may result in being dropped from the course.

• Makeup Exams: Only for documented emergencies; must contact instructor in advance.

• Academic Honesty: Cheating and plagiarism are not tolerated. Only one 8.5" x 11" sheet of handwritten notes is allowed during exams; no worked-out problems or examples.

• Accommodations: Students with disabilities should contact Special Programs and Services for support.

• Tutoring: Available through NetTutor and the Student Success Center.

Important Dates

• Last date to add class: September 7, 2025

• Last date to drop with a refund: September 6, 2025

Additional info: The syllabus includes detailed weekly assignments, exam dates, and policies for online learning, participation, and communication with the instructor. Students are expected to use MyMathLab for homework and Canvas for course management.