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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
Identifying Variable Parts and Coefficients of Terms
1.2: Replacing Variables with Their Values
How to Write Multiplication in Algebra
Practice Evaluating Expressions in One Variable
Practice Evaluating Expressions in Two Variables
1.3: Order of Operations Review
Order of Operations
Practice Using PEMDAS
1.4: Commutative Property of Addition and Multiplication
Commutative Laws of Addition and Multiplication
1.5: Associative Property of Addition and Multiplication
Associative Laws of Addition and Multiplication
1.6: Distributive Property of Multiplication over Addition/Subtraction
Distributive Property of Multiplication over Addition
1.7: Definition and Examples of Like Terms
Like Terms
1.8: Simplifying Expressions by Combining Like Terms
Combining Like Terms
Practice Combining Like Terms with Negative Coefficients
Practice Combining Like Terms with Negative Coefficients and Distribution
Unit 2: Linear Equations
2.1: Definition of an Equation and a Solution of an Equation
Solving Linear Equations with One Variable
2.2: Addition/Subtraction Property of Equations
The Subtraction and Addition Properties of Equality
2.3: Multiplication/Division Property of Equations
The Division and Multiplication Properties of Equality
2.4: Equations of the Form
x
+
a
=
b
and
x
−
a
=
b
Adding and Subtracting the Same Thing to Both Sides
Practice Solving One-Step Equations
2.5: Equations of the Form
ax
=
b
and
x
/
a
=
b
Algebraic Equations with Multiplication and Division
Practice One-Step Equations with Multiplication and Division
2.6: Equations of the Form
ax
+
b
=
c
Solving More Complicated Equations
Practice Solving Two-Step Equations
2.7: Equations of the Form
ax
+
b
=
cx
+
d
Equations with Variables on Both Sides
Practice Solving Equations with Variables on Both Sides
2.8: Equations with Parentheses
Solving Equations with the Distributive Property
Practice Solving Multistep Equations with Distribution
2.9: Solving Literal Equation for One of the Variables
Solving Linear Equations with One Variable
Solving for One Variable
Unit 3: Word Problems
3.1: Mathematical Symbols and Expressions for Common Words and Phrases
Translating Words into Mathematical Symbols
3.2: Translating Verbal Expression into Mathematical Equations
Writing Algebraic Equations
3.3: Number Problems
Solving Algebraic Expressions and Equations Part I
3.4: Consecutive Integer Problems
Adding Consecutive and Odd Integers
Solving Algebraic Expressions and Equations Part II
3.5: General Statement Problems
Solving Linear Word Problems with Substitution
Simple Word Problems Resulting In Linear Equations
3.6: Applying the Uniform Motion Equation
Solving a Formula for a Specific Variable
3.7: Value Mixture Problems
Mixture Problems
Solving Mixture Word Problems
Practice Solving Mixture Word Problems
Solving Percent Word Problems
Practice Solving Percent Word Problems
Unit 4: Inequalities
4.1: Definition and Notation of an Inequality
Using the Language of Algebra
4.2: Graphing Inequalities on a Number Line
Plotting Inequalities on a Number Line
Introduction to Linear Inequalities
4.3: Solving One-Step Inequalities
One-Step Inequalities
One-Step Inequalities Word Problems
Practice Solving One-Step Inequalities
4.4: Solving Multi-Step Inequalities
Multi-step Inequalities with Variables on Both Sides
Practice Solving Multipstep Inequalities
Unit 5: Graphs of Linear Equations and Inequalities
5.1: Graphing Points in the Rectangular Coordinate Plane
Points in the Coordinate Plane
5.2: Ordered Pairs as Solutions of an Equation in Two Variables
Ordered Pair Solutions to Equations
Practice Ordered Pair Solutions to Linear Equations
5.3: Graphing Equations in Two Variables of the Form
Ax
+
By
=
C
Graphing Linear Equations with Two Variables
5.4: Intercepts of a Straight Line
Graphs with Intercepts
5.5: Definition of Slope and Slope Formula
Understanding the Slope of a Line
5.6: Slopes of Parallel and Perpendicular Lines
Parallel and Perpendicular Lines
5.7: Graphing Equations in Two Variables of the Form
y = mx + b
Using the Slope-Intercept Form of an Equation of a Line
5.8: Point-Slope Form
Linear Equations in Point-Slope Form
5.9: Graphing Linear Inequality of Two Variables on the Coordinate Plane
Graphs of Linear Inequalities
Unit 6: Systems of Linear Equations and Inequalities
6.1: Solution of a System of Linear Equations
Checking Solutions for Systems of Linear Equations
6.2: Solving Systems of Linear Equations by Graphing
Using Graphs to Solve Linear Equations
6.3: Solving Systems of Linear Equations Using the Substitution Method
Using the Substitution Method
Practice Using the Substitution Method
6.4: Solving Systems of Linear Equations Using the Elimination Method
The Elimination Method
Practice Solving Linear Equations with Elimination
6.5: Choosing a Strategy for Solving Systems of Linear Equations
Comparing Methods for Solving Linear Systems
6.6: Solving Word Problems by Using Systems of Equations
Coin and Mixture Problems
Solving Word Problems with Linear Systems
Solving Word Problems with Linear Systems
6.7: Graphing Systems of Linear Inequalities
Graphing Systems of Linear Inequalities
6.8: Applications of Systems of Linear Inequalities
Solving Applications of Linear Inequalities
Linear Programming
Unit 7: Operations with Monomials
7.1: Algebraic Exponential Expressions
Exponential Expressions
7.2: Manipulating Exponents
Exponential Properties Involving Products
7.3: Quotient of Exponents and Power of a Quotient
Exponential Properties Involving Quotients
7.4: Negative Exponents
Negative Exponent Intuition
Practice Solving Problems with Negative Exponents
7.5: Multiplying Monomials
Multiplication Properties of Exponents
7.6: Dividing Monomials
Dividing Monomials
Unit 8: Operations with Polynomials
8.1: Classifying Polynomials
Introduction to Polynomials
8.2: Adding and Subtracting Polynomials
Adding and Subtracting Polynomials
More on Adding and Subtracting Polynomials
8.3: Multiplying a Polynomial by a Monomial
Multiplying Monomials by Polynomials
8.4: Multiplying Binomials (FOIL)
Using the FOIL Technique to Multiply Binomials
Multiplying Binomials by a Binomial
8.5: Complete the Square and Difference of Two Squares
Finding the Square of a Binomial with One Variable
Special Products of Polynomials
8.6: Multiplying Polynomials with Any Number of Terms
Multiplying a Polynomial by a Binomial
Multiplying Polynomials
8.7: Dividing a Polynomial by a Monomial
Dividing Polynomials with Monomials with Remainder
Dividing Polynomials
8.8: Dividing a Polynomial by a Binomial
Dividing Polynomials by Binomials
Dividing Polynomials by Binomials
Unit 9: Factoring Polynomials
9.1: Identifying Greatest Common Factor
The Language of Factoring
Using the Greatest Common Factor and Factoring by Grouping
9.2: Factoring Polynomials by Grouping
Factor by Grouping
Practice Factoring Polynomials
9.3: Revisiting FOIL by Working Backwards
Basic Concepts Involved in Factoring Trinomials
9.4: Factoring Trinomials of the Form
x
² +
bx
+
c
when
c
is Positive
Factoring Trinomials
Practice Factoring Polynomials
9.5: Factoring Trinomials of the Form
x
² +
bx
+
c
when
c
is Negative
Factoring Trinomials of the Form x² + bx + c when c is Negative
9.6: Factoring by Grouping
Factoring by Grouping
Practice Factoring by Grouping
9.7: Factoring Trinomials of the Form
x
² +
bxy
+
cy
² and
ax
² +
bxy
+
cy
²
Factoring Trinomials with Two Variables
Practice Factoring Trinomials with Two Variables
9.8: Identifying and Factoring Complete Square Trinomials
Factoring Using Perfect Square Trinomials
Factoring Perfect Square Trinomials
9.9: Identifying and Factoring the Difference of Two Squares
Factoring Using Difference of Squares
9.10: Identifying and Factoring the Sum and Difference of Two Cubes
Factoring Sum of Cubes
9.11: Factoring General Polynomials
Factoring Polynomials
More on Factoring Polynomials
Practice Factoring Polynomials
9.12: The Principle of Zero Product and Identifying Solutions
Using the Principle of Zero Product to Solve Quadratic Equations
9.13: Using Factoring to Solve Quadratic Equations
Using Factoring to Solve Quadratic Equations
Using Factoring to Solve Complicated Quadratic Equations
9.14: Applications for Solving Problems
Using Factoring to Solve Problems
Study Guide
RWM102 Study Guide
Course Feedback Survey
Course Feedback Survey
Certificate Final Exam
RWM102: Certificate Final Exam
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RWM102: Algebra
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