Course Overview

Introduction to College Algebra

This course provides foundational skills in algebra necessary for success in college-level mathematics. It covers essential topics such as inequalities, functions, polynomials, rational expressions, and quadratic equations, with a focus on problem-solving and real-world applications.

• Course Format: Traditional in-person class with weekly meetings and online assignments.

• Grading: Pass/Fail based on quizzes, attendance, homework, midterm, and final exam.

• Learning Goals: Develop discipline-specific content knowledge, critical thinking, and awareness of social justice in mathematics.

Course Topics and Weekly Breakdown

Week 1: Inequalities and Linear Equations

Students begin by learning to represent and solve inequalities using interval notation and algebraic methods. The week also introduces function values and solving linear equations.

• Inequality Representation: Use interval notation to express solution sets.

• Function Values: Evaluate functions for given inputs.

• Linear Equations: Solve equations of the form .

• Example: Solve and express the solution in interval notation.

Week 2: Functions and Graphs

This week focuses on writing equations using function notation, finding intercepts, and determining symmetry and domain/range from graphs.

• Function Notation: represents the output of function for input .

• Intercepts: Points where the graph crosses the axes.

• Domain and Range: The set of possible input and output values.

• Example: For , domain is all real numbers, range is .

Week 3: Quadratic Equations and Roots

Students learn to simplify square roots and solve quadratic equations using various methods, including factoring and the quadratic formula.

• Quadratic Equation:

• Quadratic Formula:

• Simplifying Roots:

• Example: Solve by factoring: so or .

Week 4: Polynomials and Factoring

This week covers polynomial operations, factoring using different methods, and solving polynomial equations using the zero-product rule.

• Polynomial: An expression of the form

• Factoring Methods: Grouping, difference of squares, trinomials.

• Zero-Product Rule: If , then or .

• Example: Factor .

Week 5: Complex Numbers and Quadratic Applications

Students identify and perform operations with complex numbers, solve quadratic equations by completing the square, and model applications using quadratic equations.

• Complex Number: , where

• Completing the Square: Transform into

• Discriminant: determines the nature of roots.

• Example: Solve by completing the square.

Week 6: Midterm Review

Review of all topics covered so far, including inequalities, functions, polynomials, and quadratic equations. Practice problems and sample test questions are provided.

• Review Strategies: Practice quizzes, group discussions, and concept summaries.

Week 7: Absolute Value and Compound Inequalities

Students compute the absolute value of real numbers and solve compound inequalities using "and" and "or" logic.

• Absolute Value: is the distance of from zero.

• Compound Inequality: ("and"), or ("or")

• Example: Solve .

Week 8: Division and Rational Functions

This week introduces division of polynomials, asymptotes of rational functions, and domain determination.

• Rational Function:

• Asymptotes: Vertical and horizontal lines the graph approaches but never touches.

• Domain: All except where .

• Example: For , domain is .

Week 9: Rational Expressions and Equations

Students simplify complex rational expressions and solve equations containing rational expressions.

• Rational Expression: A fraction with polynomials in numerator and denominator.

• Simplification: Factor and reduce common terms.

• Example: Simplify .

Week 10: Roots and Exponents

This week covers roots versus rational exponents and evaluates expressions involving radicals and rational exponents.

• Rational Exponent:

• Radical Expression: An expression containing a root symbol.

• Example:

Week 11: Function Composition and Exponential Functions

Students learn to compose functions and solve exponential equations, including writing expressions in logarithmic and exponential form.

• Function Composition:

• Exponential Equation:

• Logarithmic Form:

• Example: If , , then .

Course Grading Structure

Assignment Breakdown

The following table summarizes the grading components and their respective weight in the final grade.

Grading Standards

Course Policies and Expectations

Attendance and Participation

• Regular attendance and active participation are required.

• Absences must be communicated to the instructor via email.

• Make-up work is allowed with proper documentation.

Communication

• Check university email and Blackboard regularly for updates.

• Office hours are available for questions and support.

Materials

• Textbook: College Algebra Concepts Through Functions (Sullivan, Pearson).

• Online homework via MyLab Math.

Additional Info

• Course supports Roosevelt University's learning goals for undergraduate students.

• Some activities may include Desmos and interactive online games.

• Withdrawal deadlines and policies are outlined in the syllabus.