Elementary Algebra Syllabus and Study Guide: Foundations for College Algebra

Course Overview

Introduction to Elementary Algebra

This course provides a foundational study of algebra, focusing on the real number system, linear equations and inequalities, graphing, and systems of equations. It is designed to prepare students for further study in College Algebra and related mathematics courses.

• Course Title: Elementary Algebra (MTH-098)

• Credits: 4

• Delivery Method: In-person (Prattville Campus)

• Textbook: Introductory and Intermediate Algebra for College Students by Blitzer, Pearson, 6th Edition (Access via MyMathLab)

Course Objectives and Learning Outcomes

Key Skills Developed

By the end of the course, students will be able to:

• Solve mathematical problems involving real numbers.

• Solve problems involving linear equations and inequalities in one variable.

• Graph and write linear equations and inequalities in two variables.

• Solve systems of equations in two variables using various methods.

Course Outline of Topics

Major Topics and Subtopics

The following topics are covered, organized to build foundational algebra skills:

• Review of Algebra

  • Define terms associated with algebra.

  • Perform operations on signed real numbers.

  • Apply the properties of real numbers.

  • Evaluate and simplify algebraic expressions.

  • Translate word phrases into algebraic expressions.

  • Solve application problems involving operations with real numbers.

• Equations & Inequalities

  • Solve linear equations and inequalities (one-step and multi-step).

  • Solve literal equations for a specified variable.

  • Express solution sets of linear inequalities in interval notation.

  • Graph solutions of inequalities.

  • Solve compound inequalities.

  • Solve application problems involving linear equations and inequalities.

• Graphs of Equations

  • Graph ordered pairs on a rectangular coordinate system.

  • Identify solutions to linear equations in two variables.

  • Identify x and y intercepts and the slope of a line.

  • Calculate the slope of a line.

  • Identify the slope and equation of horizontal and vertical lines.

  • Determine if lines are parallel, perpendicular, or neither.

  • Graph linear equations in two variables using various methods.

  • Write the equation of a line given its slope and a point.

  • Graph linear inequalities in two variables.

• Systems of Equations & Inequalities

  • Solve systems of linear equations using graphing, substitution, and elimination methods.

  • Solve application problems involving systems of linear equations.

  • Solve systems of linear inequalities using the graphing method.

Key Concepts and Examples

Review of Algebra

Algebra is the branch of mathematics dealing with symbols and the rules for manipulating those symbols. It forms the basis for solving equations and understanding mathematical relationships.

• Real Numbers: The set of numbers including rational and irrational numbers.

• Properties of Real Numbers: Commutative, associative, distributive, identity, and inverse properties.

• Example: Simplify $2(x + 3) - 4x$. Solution: $2x + 6 - 4x = -2x + 6$

Equations & Inequalities

Solving equations and inequalities is fundamental to algebra. Equations are statements of equality, while inequalities express a range of possible values.

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

• Linear Inequality: An inequality such as $ax + b < 0$ or $ax + b > 0$.

• Interval Notation: Used to express solution sets, e.g., $(-\infty, 3]$.

• Example: Solve $3x - 5 = 10$. Solution: $3x = 15 \Rightarrow x = 5$

Graphs of Equations

Graphing is a visual method to represent equations and inequalities. The coordinate plane is used to plot points, lines, and regions.

• Ordered Pair: $(x, y)$ represents a point in the plane.

• Slope: $m = \frac{y_2 - y_1}{x_2 - x_1}$

• Equation of a Line: $y = mx + b$

• Example: Find the slope between $(2, 3)$ and $(5, 11)$. Solution: $m = \frac{11 - 3}{5 - 2} = \frac{8}{3}$

Systems of Equations & Inequalities

Systems involve solving for multiple variables simultaneously. Methods include graphing, substitution, and elimination.

• System of Equations: Two or more equations with the same variables.

• Substitution Method: Solve one equation for a variable and substitute into the other.

• Elimination Method: Add or subtract equations to eliminate a variable.

• Example: Solve: $x + y = 5$ $x - y = 1$ Solution: Add equations: $2x = 6 \Rightarrow x = 3$. Substitute: $3 + y = 5 \Rightarrow y = 2$.

Evaluation and Assessment

Grading Breakdown

Students are assessed through homework, quizzes, exams, and a final exam. The grading weights are as follows:

Assessment Type	Weight	Platform
Homework	10%	MyMathLab/Canvas
Quizzes	15%	MyMathLab/Canvas
Exams	45%	In Class
Written Assignments	5%	In Class
Final Exam	25%	In Class

Pacing Guide

Suggested Schedule

Students should follow the pacing guide to stay on track with assignments and exams. Key dates include orientation, chapter reviews, exams, and the final exam.

• Orientation and Chapter 1: August 18-27

• Exam 1: September 8

• Chapter 2 and Exam 2: September 10-29

• Chapter 9 and Exam 3: October 6-15

• Chapter 3 and Exam 4: October 20-November 5

• Chapter 4 and Exam 5: November 10-December 1

• Final Exam: December 7-11

Course Policies

Expectations and Academic Integrity

• Attend and participate in all classroom meetings.

• Complete all homework assignments with a 100% score.

• Take quizzes (two attempts allowed, 60-minute time limit).

• Complete exam reviews and exams at the end of each unit.

• Academic integrity is strictly enforced; unauthorized use of AI tools is prohibited.

Additional Information

Support and Accessibility

• Office hours available by appointment.

• Accommodations for disabilities provided upon request.

• Attendance is required; excessive absences may affect course completion.

• Emergency procedures and campus safety information are provided via Schoolcast and email.

Summary Table: Major Algebra Topics

Main Topic	Key Concepts	Example
Review of Algebra	Real numbers, properties, expressions	$2(x + 3) - 4x = -2x + 6$
Equations & Inequalities	Linear equations, inequalities, interval notation	$3x - 5 = 10 \Rightarrow x = 5$
Graphs of Equations	Coordinate plane, slope, intercepts	$m = \frac{8}{3}$ between $(2, 3)$ and $(5, 11)$
Systems of Equations	Graphing, substitution, elimination	$x + y = 5, x - y = 1 \Rightarrow x = 3, y = 2$

Additional info: This syllabus covers foundational algebra topics that are directly relevant to College Algebra, focusing on equations, inequalities, graphing, and systems. The course prepares students for more advanced algebraic concepts.