Course Introduction

This study guide summarizes the key information and foundational topics for Elementary Algebra I (MTH 005-90), a college-level course designed for students with little or no background in high school algebra. The course covers essential algebraic concepts, problem-solving skills, and applications, preparing students for further study in mathematics.

Course Structure and Requirements

• Format: Distance learning (no set class time); materials and assignments are accessed online.

• Instructor: Professor Kimberly Calvert

• Required Materials:

  • TI-84 Plus Graphing Calculator

  • MyLab Math with Pearson e-text: Elementary and Intermediate Algebra

  • 3-ring binder with tab dividers

• Technical Requirements: Google Chrome browser, desktop/laptop/Chromebook with webcam, microphone, and speakers.

Course Outcomes

Upon successful completion, students will be able to:

• Identify the structure, order, and properties of the real number system and simplify numerical expressions.

• Translate phrases and sentences into algebraic expressions, equations, and inequalities.

• Solve linear equations and inequalities.

• Analyze, graph, and write linear equations in standard, slope-intercept, and point-slope form.

• Apply the laws of exponents to simplify exponential expressions.

• Add, subtract, and multiply polynomials.

• Apply mathematical concepts and skills to solve real-world applications.

Course Outline

Unit 1: Introduction to Algebraic Expressions

• 1.1 Introduction to Algebra Definition: Algebra is a branch of mathematics dealing with symbols and the rules for manipulating those symbols to solve problems. Key Concepts:

  • Variables and constants

  • Algebraic expressions

  • Translating words into mathematical symbols

  Example: The phrase "five more than a number x" translates to .

• 1.2 The Commutative, Associative, and Distributive Laws Commutative Law: and Associative Law: and Distributive Law:

• 1.3 Fraction Notation Definition: A fraction represents a part of a whole and is written as , where .

• 1.4 Positive and Negative Real Numbers Real Numbers: All numbers on the number line, including positive, negative, and zero.

• 1.5 Addition of Real Numbers Rule: Adding numbers with the same sign, add their absolute values and keep the sign. With different signs, subtract the smaller absolute value from the larger and keep the sign of the larger.

• 1.6 Subtraction of Real Numbers Rule: Subtracting a number is the same as adding its opposite: .

• 1.7 Multiplication and Division of Real Numbers Rule: The product or quotient of two numbers with the same sign is positive; with different signs, negative.

• 1.8 Exponential Notation and Order of Operations Exponential Notation: means is multiplied by itself times. Order of Operations: Parentheses, Exponents, Multiplication/Division (left to right), Addition/Subtraction (left to right).

Unit 2: Equations, Inequalities, and Problem Solving

• 2.1 Solving Equations Equation: A statement that two expressions are equal. Example: ; solve for by isolating the variable: .

• 2.2 Applications, Problem Solving Application: Using equations to solve real-world problems, such as distance, rate, and time: .

• 2.3 Inequalities Inequality: A mathematical sentence that compares expressions using .

• 2.4 Solving Linear Inequalities Rule: When multiplying or dividing both sides of an inequality by a negative number, reverse the inequality sign.

Unit 3: Elementary Algebra: Graphs and Models

• 3.1 Reading Graphs, Plotting Points, and Scaling Graphs Coordinate Plane: A two-dimensional surface defined by an -axis (horizontal) and -axis (vertical).

• 3.2 Graphing Equations Graph: The set of all points that satisfy an equation.

• 3.3 Linear Equations and Intercepts Linear Equation: An equation of the form where is the slope and is the -intercept.

• 3.4 Rates Rate: A ratio comparing two quantities with different units, such as speed ().

• 3.5 Slope Slope Formula:

• 3.6 Slope-Intercept Form Equation:

• 3.7 Point-Slope Form Equation:

Unit 4: Polynomials

• 4.1 Exponents and Their Properties Product Rule: Quotient Rule: Power Rule:

• 4.2 Negative Exponents and Scientific Notation Negative Exponent: Scientific Notation: where and is an integer.

• 4.3 Polynomials Definition: An expression consisting of variables and coefficients, involving only addition, subtraction, and multiplication.

• 4.4 Addition and Subtraction of Polynomials Rule: Combine like terms (terms with the same variable and exponent).

• 4.5 Multiplication of Polynomials Distributive Property: Multiply each term in one polynomial by each term in the other.

• 4.6 Polynomials in Several Variables Example: is a polynomial in variables and .

Grading and Assessment

• Exams: 80% of the grade (each 4-unit exam = 5% of final grade; final exam = 50% or average of all exams, whichever is higher).

• Daily Grades: 20% of the grade (homework, quizzes, and completed notes).

• Homework: Completed in MyLab Math; must show all work and process for each question.

• Quizzes: Timed, proctored online; follow all instructions for academic integrity.

Sample Table: Course Outline by Unit and Topic

Academic Success Tips

• Attend all classes and participate actively.

• Keep an organized notebook divided into reference, notes, and homework sections.

• Complete all assignments on time and seek help when needed.

• Use the tutoring center and online resources for additional support.

Additional info:

• This guide is based on the course syllabus and outline for MTH 005-90: Elementary Algebra I, Fall 2025, Penn College.

• For detailed procedures on homework, testing, and academic policies, refer to the official course documents.