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RWM102: Algebra

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COURSE INTRODUCTION

Course Syllabus

Unit 1: Variables and Variable Expressions

1.1: Variables, Constants, and Coefficients

1.2: Replacing Variables with Their Values

1.3: Order of Operations Review

1.4: Commutative Property of Addition and Multiplication

1.5: Associative Property of Addition and Multiplication

1.6: Distributive Property of Multiplication over Addition/Subtraction

1.7: Definition and Examples of Like Terms

1.8: Simplifying Expressions by Combining Like Terms

Unit 2: Linear Equations

2.1: Definition of an Equation and a Solution of an Equation

2.2: Addition/Subtraction Property of Equations

2.3: Multiplication/Division Property of Equations

2.4: Equations of the Form x + a = b and x − a = b

2.5: Equations of the Form ax = b and x/a = b

2.6: Equations of the Form ax + b = c

2.7: Equations of the Form ax + b = cx + d

2.8: Equations with Parentheses

2.9: Solving Literal Equation for One of the Variables

Unit 3: Word Problems

3.1: Mathematical Symbols and Expressions for Common Words and Phrases

3.2: Translating Verbal Expression into Mathematical Equations

3.3: Number Problems

3.4: Consecutive Integer Problems

3.5: General Statement Problems

3.6: Applying the Uniform Motion Equation

3.7: Value Mixture Problems

Unit 4: Inequalities

4.1: Definition and Notation of an Inequality

4.2: Graphing Inequalities on a Number Line

4.3: Solving One-Step Inequalities

4.4: Solving Multi-Step Inequalities

Unit 5: Graphs of Linear Equations and Inequalities

5.1: Graphing Points in the Rectangular Coordinate Plane

5.2: Ordered Pairs as Solutions of an Equation in Two Variables

5.3: Graphing Equations in Two Variables of the Form Ax + By = C

5.4: Intercepts of a Straight Line

5.5: Definition of Slope and Slope Formula

5.6: Slopes of Parallel and Perpendicular Lines

5.7: Graphing Equations in Two Variables of the Form y = mx + b

5.8: Point-Slope Form

5.9: Graphing Linear Inequality of Two Variables on the Coordinate Plane

Unit 6: Systems of Linear Equations and Inequalities

6.1: Solution of a System of Linear Equations

6.2: Solving Systems of Linear Equations by Graphing

6.3: Solving Systems of Linear Equations Using the Substitution Method

6.4: Solving Systems of Linear Equations Using the Elimination Method

6.5: Choosing a Strategy for Solving Systems of Linear Equations

6.6: Solving Word Problems by Using Systems of Equations

6.7: Graphing Systems of Linear Inequalities

6.8: Applications of Systems of Linear Inequalities

Unit 7: Operations with Monomials

7.1: Algebraic Exponential Expressions

7.2: Manipulating Exponents

7.3: Quotient of Exponents and Power of a Quotient

7.4: Negative Exponents

7.5: Multiplying Monomials

7.6: Dividing Monomials

Unit 8: Operations with Polynomials

8.1: Classifying Polynomials

8.2: Adding and Subtracting Polynomials

8.3: Multiplying a Polynomial by a Monomial

8.4: Multiplying Binomials (FOIL)

8.5: Complete the Square and Difference of Two Squares

8.6: Multiplying Polynomials with Any Number of Terms

8.7: Dividing a Polynomial by a Monomial

8.8: Dividing a Polynomial by a Binomial

Unit 9: Factoring Polynomials

9.1: Identifying Greatest Common Factor

9.2: Factoring Polynomials by Grouping

9.3: Revisiting FOIL by Working Backwards

9.4: Factoring Trinomials of the Form x² + bx + c when c is Positive

9.5: Factoring Trinomials of the Form x² + bx + c when c is Negative

9.6: Factoring by Grouping

9.7: Factoring Trinomials of the Form x² + bxy + cy² and ax² + bxy + cy²

9.8: Identifying and Factoring Complete Square Trinomials

9.9: Identifying and Factoring the Difference of Two Squares

9.10: Identifying and Factoring the Sum and Difference of Two Cubes

9.11: Factoring General Polynomials

9.12: The Principle of Zero Product and Identifying Solutions

9.13: Using Factoring to Solve Quadratic Equations

9.14: Applications for Solving Problems

Study Guide

Course Feedback Survey

Certificate Final Exam

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RWM102: Algebra

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Saylor Academy © 2010-2025 except as otherwise noted. Excluding course final exams, content authored by Saylor Academy is available under a Creative Commons Attribution 3.0 Unported license. Third-party materials are the copyright of their respective owners and shared under various licenses. See detailed licensing information. Saylor Academy®, Saylor.org®, and Harnessing Technology to Make Education Free® are trade names of the Constitution Foundation, a 501(c)(3) organization through which our educational activities are conducted.