College Algebra Syllabus and Study Guide

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 $ax + b = c$.

• Example: Solve $2x - 5 > 7$ 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: $f(x)$ represents the output of function $f$ for input $x$.

• Intercepts: Points where the graph crosses the axes.

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

• Example: For $f(x) = x^2 - 4$, domain is all real numbers, range is $[ -4, ext{infinity} )$.

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: $ax^2 + bx + c = 0$

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

• Simplifying Roots: $\sqrt{ 16 } = 4$

• Example: Solve $x^2 - 5x + 6 = 0$ by factoring: $(x-2)(x-3)=0$ so $x=2$ or $x=3$.

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 $a_nx^n + ... + a_1x + a_0$

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

• Zero-Product Rule: If $ab=0$, then $a=0$ or $b=0$.

• Example: Factor $x^2 - 9 = (x-3)(x+3)$.

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: $a + bi$, where $i = \sqrt{ -1 }$

• Completing the Square: Transform $ax^2 + bx + c$ into $(x + d)^2 = e$

• Discriminant: $b^2 - 4ac$ determines the nature of roots.

• Example: Solve $x^2 + 4x + 5 = 0$ 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: $|x|$ is the distance of $x$ from zero.

• Compound Inequality: $a < x < b$ ("and"), $x < a$ or $x > b$ ("or")

• Example: Solve $|x - 3| < 5$.

Week 8: Division and Rational Functions

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

• Rational Function: $f(x) = \frac{p(x)}{q(x)}$

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

• Domain: All $x$ except where $q(x) = 0$.

• Example: For $f(x) = \frac{1}{x-2}$, domain is $x \neq 2$.

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 $\frac{x^2 - 4}{x^2 - 2x}$.

Week 10: Roots and Exponents

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

• Rational Exponent: $x^{1/n} = \sqrt[n]{x}$

• Radical Expression: An expression containing a root symbol.

• Example: $8^{1/3} = 2$

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: $(f \circ g)(x) = f(g(x))$

• Exponential Equation: $a^x = b$

• Logarithmic Form: $x = \log_a b$

• Example: If $f(x) = x+2$, $g(x) = 3x$, then $(f \circ g)(x) = f(g(x)) = 3x + 2$.

Course Grading Structure

Assignment Breakdown

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

Assignment	Percentage of Final Grade
Weekly Online Quiz	5%
Classwork / Attendance	15%
Online Homework	25%
Midterm Exam (online part and written part)	25%
Final Exam (online part and written part)	30%

Grading Standards

GRADES	Percentage
P	70-100%
F	0-69%

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.