College Algebra Syllabus and Study Guide Overview

Course Overview

Introduction to College Algebra

College Algebra is a foundational mathematics course designed to prepare students for further study in mathematics and related fields. The course covers essential algebraic concepts, including equations, inequalities, functions, polynomials, rational expressions, exponential and logarithmic functions, and systems of equations. Applications and problem-solving skills are emphasized throughout.

Course Topics and Learning Outcomes

Core Topics

• Equations & Inequalities: Study and solve linear, quadratic, polynomial, rational, radical, exponential, and logarithmic equations and inequalities.

• Graphs of Equations: Analyze and sketch graphs of various types of equations and functions.

• Functions: Understand the concept of functions, including domain, range, and function notation. Evaluate and analyze basic functions such as linear, quadratic, polynomial, absolute value, square root, and rational functions.

• Polynomial Functions: Factor polynomials completely and solve polynomial equations.

• Rational Functions: Simplify and perform operations on rational expressions and solve rational equations.

• Exponential & Logarithmic Functions: Solve exponential and logarithmic equations, convert between exponential and logarithmic forms, and analyze their graphs.

• Systems of Equations: Algebraically solve systems of linear equations in two variables.

• Radical Expressions: Simplify radical expressions and solve radical equations.

• Modeling: Construct mathematical models using direct, inverse, and joint variation.

Student Learning Outcomes (SLOs)

• Factor polynomials completely and solve polynomial equations.

• Solve quadratic equations by factoring and applying the quadratic formula.

• Simplify/perform operations on rational expressions and solve rational equations.

• Simplify radical expressions and solve radical equations.

• Determine if a given relation is a function.

• Evaluate a given function using function notation.

• Determine the domain and range of a given function.

• Graph and analyze basic functions, including but not limited to linear, quadratic, polynomial, absolute value, square root, and rational.

• Show that a function is one to one.

• Find the inverse of a one-to-one function.

• Convert a logarithmic equation to exponential form and vice-versa.

• Solve and evaluate logarithmic expressions.

• Solve exponential and logarithmic equations.

• Construct models using direct, inverse, and joint variation.

• Solve real-world applications that are integrated throughout the course content.

• Algebraically solve systems of linear equations in two variables.

Key Definitions and Formulas

Equations and Inequalities

• Linear Equation: An equation of the form $ax + b = 0$.

• Quadratic Equation: An equation of the form $ax^2 + bx + c = 0$.

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

• Inequality: A mathematical statement that compares two expressions using <, >, ≤, or ≥.

Functions

• Function: A relation in which each input has exactly one output.

• Domain: The set of all possible input values.

• Range: The set of all possible output values.

• Function Notation: $f(x)$ represents the value of function $f$ at input $x$.

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

Polynomials and Rational Expressions

• Polynomial: An expression of the form $a_nx^n + a_{n-1}x^{n-1} + \ldots + a_1x + a_0$.

• Factoring: Writing a polynomial as a product of its factors.

• Rational Expression: An expression of the form $\frac{P(x)}{Q(x)}$, where $Q(x) \neq 0$.

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.

• Change of Base Formula: $\log_a(x) = \frac{\log_b(x)}{\log_b(a)}$

Systems of Equations

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

• Solution: The values of variables that satisfy all equations in the system.

Course Structure and Assessment

Units and Assignments

• The course is divided into 4 units, each with homework, quizzes, and discussion board posts.

• Midterm and final exams cover cumulative material.

Grading Breakdown

Component	Percentage
Homework	15%
Discussion Board	10%
Unit Quizzes	25%
Midterm	25%
Final Exam	25%

Grading Scale

Percentage	Grade
90% to 100%	A
80% to 89%	B
70% to 79%	C
65% to 69%	D
Anything below 65%	F

Course Policies and Expectations

Attendance and Participation

• Active participation in online campus and completion of assignments is required.

• Discussion board posts are part of the grade.

Academic Honesty

• Cheating and fabrication are not tolerated.

• Plagiarism includes copying work or ideas without proper acknowledgment.

Technology Requirements

• Reliable internet connection and access to MyMathLab are required.

• Assignments and exams may require a calculator; cell phones and other websites are not permitted during proctored exams.

Textbook and Resources

Required and Optional Materials

• MyMathLab access is required and included with tuition.

• Optional Textbook: Algebra for College Students by Robert F. Blitzer (ISBN: 9780321878744).

Example Applications

• Solving Quadratic Equations: Use the quadratic formula to find the roots of $x^2 - 5x + 6 = 0$.

• Graphing Functions: Sketch the graph of $f(x) = x^2$ and identify its vertex and axis of symmetry.

• Modeling with Exponential Functions: Use $f(x) = 2^x$ to model population growth.

• Solving Systems: Solve the system $\begin{cases} 2x + y = 5 \\ x - y = 1 \end{cases}$ using substitution or elimination.

Additional info: These notes are based on the official syllabus for College Algebra at Columbia State Community College, summarizing course structure, topics, learning outcomes, and policies. For detailed study, refer to the course textbook and MyMathLab assignments.