College Algebra Syllabus and Study Guide Overview

Course Overview

Course Description

This College Algebra course is designed to refine students' understanding of algebraic topics and prepare them for Pre-Calculus and college-level mathematics courses. The course covers fundamental algebraic concepts, including operations with polynomials, graphs of linear functions, algebraic fractions, systems of linear equations, quadratic functions, and their graphs.

• Credit Hours: 3 equivalent hours plus a required lab hour.

• Target Audience: Students with basic background knowledge of algebra.

• Topics: Polynomial operations, graphing, linear and quadratic equations, algebraic fractions, systems of equations.

Prerequisites

• MAT108 or high school equivalent

• Standardized placement test

Course Objectives

• Graphical and Algebraic Representation: Define and describe graphical and algebraic representations of concepts.

• Elementary Algebraic Computations: Use course concepts to perform elementary algebraic computations.

• Problem Solving: Apply course concepts to solve complex problems.

• Evaluation: Evaluate solutions to problems, including word problems and cases with erroneous solutions.

Course Topics

Linear Equations and Inequalities in One Variable

Linear equations and inequalities form the foundation of algebra. Students will learn to solve, graph, and interpret these equations and inequalities.

• Definition: A linear equation in one variable has the form $ax + b = 0$.

• Solving: Isolate the variable using inverse operations.

• Graphing: Represent solutions on a number line.

• Example: Solve $2x - 5 = 9$.

Linear Equations in Two Variables

Linear equations in two variables are represented as straight lines on the Cartesian plane.

• Standard Form: $ax + by = c$

• Slope-Intercept Form: $y = mx + b$

• Graphing: Plot using slope and y-intercept.

• Example: Graph $y = 2x + 3$.

Systems of Linear Equations

Systems of equations involve finding values that satisfy multiple equations simultaneously.

• Methods: Graphical, substitution, and elimination.

• Example: Solve the system:

  • $x + y = 5$

  • $x - y = 1$

Exponents and Polynomials

Polynomials are algebraic expressions involving sums of powers of variables. Exponents follow specific rules for operations.

• Exponent Rules:

  • $a^m \cdot a^n = a^{m+n}$

  • $(a^m)^n = a^{mn}$

  • $a^0 = 1$

• Polynomial Operations: Addition, subtraction, multiplication, and division.

• Example: Expand $(x + 2)^2$.

Factoring Polynomials

Factoring is the process of expressing a polynomial as a product of its factors.

• Common Methods: Factoring out the greatest common factor, factoring trinomials, difference of squares.

• Example: Factor $x^2 - 9$.

Rational Expressions

Rational expressions are quotients of polynomials. Simplification and operations are key skills.

• Definition: $\frac{P(x)}{Q(x)}$, where $Q(x) \neq 0$.

• Operations: Addition, subtraction, multiplication, division, and simplification.

• Example: Simplify $\frac{x^2 - 9}{x + 3}$.

Basics of Functions

Functions describe relationships between variables. Understanding domain, range, and function notation is essential.

• Definition: A function $f$ assigns each input $x$ exactly one output $f(x)$.

• Domain and Range: The set of possible inputs and outputs.

• Example: $f(x) = x^2$

Quadratic Equations and Functions

Quadratic equations have the form $ax^2 + bx + c = 0$. Their graphs are parabolas.

• Factoring: Express as a product of binomials.

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

• Graphing: Identify the vertex, axis of symmetry, and direction.

• Example: Solve $x^2 - 4x + 3 = 0$.

Exponential and Logarithmic Functions

Exponential functions involve variables in the exponent. Logarithms are their inverses.

• Exponential Form: $y = a^x$

• Logarithmic Form: $y = \log_a x$

• Properties: $\log_a(ab) = \log_a a + \log_a b$

• Example: Solve $2^x = 8$.

Radicals, Radical Functions, and Rational Exponents

Radicals and rational exponents extend the concept of powers and roots.

• Radical Form: $\sqrt[n]{x}$

• Rational Exponent Form: $x^{1/n}$

• Example: Simplify $\sqrt{16}$ and $16^{1/2}$.

Conic Sections and Systems of Nonlinear Equations

Conic sections include circles, ellipses, parabolas, and hyperbolas. Nonlinear systems involve equations that are not linear.

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

• Example: Graph $y = x^2$ and $y = 2x + 1$ and find intersection points.

Sequences, Series, and the Binomial Theorem

Sequences and series are ordered lists and sums of terms. The Binomial Theorem expands powers of binomials.

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

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

• Binomial Theorem: $(a + b)^n = \sum_{k=0}^n \binom{n}{k} a^{n-k} b^k$

• Example: Expand $(x + 1)^3$.

Course Requirements

• In-Class Exams

• Homework and Quizzes

• Attendance

• Departmental Final Exam

• Some assignments completed on MyMathLab.

Required Texts

• Textbook: Intermediate Algebra (6th Edition) by Bittinger, M. L. & Johnson, B. L.

Grading Policy

Grade	Numeric Value	Standard
A	90-100	Excellent
B+	85-89	Good
B	80-84	Good
C+	75-79	Average
C	70-74	Average
D	60-69	Min. Passing
F	Below 60	Failing

Minimum passing grade for mathematics classes is a 'C'.

Course Schedule (Topics by Week)

Week	Topic	Main Sections
Week Topic: Mainview, Diagnostic Exam	Sections 1.8, 4.1-4.4, 4.5-4.8
3	Operations with Polynomials, Factoring	Sections 5.1-5.2, 5.5
4	Factoring Algebraic Expressions, Solving Quadratic Equations	Sections 5.3-5.4, 5.7-5.8
5	Quadratic Equations, Word Problems	Sections 5.7-5.9
6	Algebraic Fractions, Operations with Algebraic Fractions	Sections 6.1, 6.2
7	Algebraic Fractions (continued), Common and Uncommon Denominators	Sections 6.4-6.6
8	Algebraic Fractions, Rational Equations, Solving Quadratic Equations with Rational Equations	Sections 6.7-6.8, 11.2-11.2
9	Review for Exam 2	Review Sheet
10	Exponents, Radicals, and Rational Exponents	Sections 10.2-10.6
11	NO CLASS (Holiday)
12	Writing Equations of Lines, Solving Systems of Linear Equations	Sections 7.5, 8.1-8.3
13	Word Problems with Systems of Linear Equations, Distance and Mixture Formulas	Sections 8.4, Objective G
14	Review for Exam 3	Review Sheet
15	Graphing Quadratic Functions, Parabolas, Discriminant, Function Types	Sections 11.4-11.6
16	Final Exam	Comprehensive

Academic Assistance

• Library: Access to print and electronic resources.

• Peer Tutoring: Available via Zoom; schedules posted online.

• Online Resources: MyMathLab, Zoom, Starfish, and various math help websites.

Policies and Procedures

• Academic Honesty: Cheating and plagiarism are strictly prohibited.

• Disability Support: Accommodations available for students with documented needs.

• Attendance: Regular attendance required; excessive absences may result in grade reduction.

• Discrimination and Harassment: Zero tolerance policy.

• Mental Health: Free and confidential counseling available.