Intermediate Algebra Workbook: Learn, Practice and Master in One Place

At a Glance 
Preface 
About This Workbook 
How to Use This Workbook
Author’s Perspective 

Part I Core Skills and Linear Modeling
Module 1 Real Numbers, Fractions, and Operations
Key Vocabulary
1.1 Sets of Numbers
Number Sets (From Smallest to Largest) 
1.2 The Real Number Line and Intervals
1.3 Order of Operations (PEMDAS) 
PEMDAS Reminder
1.4 Fractions and Equivalent Forms 
Reducing Fractions
Mixed Numbers and Improper Fractions
Terminating Decimals to Fractions
1.5 Operations with Rational Numbers 
Adding/Subtracting Fractions
Multiplying/Dividing Fractions
1.6 Evaluating Expressions
1.7 Evaluating Absolute Value 
Definition of Absolute Value
Absolute Value on the Number Line
Common Mistake
Practice Module 1
Classify the Number 
Intervals 
Order of Operations
Fractions 
Operations with Rational Numbers 
Fill in the Blank 
Evaluating Expressions
Absolute Value 
Applications
Answer Key (Note: Answers are Simplified) 
Classify the Number 
Intervals 
Order of Operations
Fractions 
Operations with Rational Numbers 
Fill in the Blank 
Evaluating Expressions
Absolute Value 
Applications

Module 2 Solving Linear Equations 
2.1 Linear Equations with Visual Models
Solutions
2.2 Solving One-Step Linear Equations 
2.3 Two-Step Equation
2.4 Distributive Property
2.5 Variables on Both Sides
2.6 No Solution and Infinite Solutions 
Practice Module 2
Solve 
Applications
Answer Key 
Practice Answers
Application Answers

Module 3 Solving Linear Inequalities
Key Vocabulary
3.1 Inequalities, Solution Sets, and Graphing
3.2 Solving One-Step and Two-Step Inequalities
3.3 Inequalities with the Distributive Property 
3.4 Variables on Both Sides
3.5 Compound Inequalities (AND/OR)
3.6 Visual Modeling with Inequalities
Practice Module 3
Word Problems 
Answer Key 

Module 4 Lines and Equations of Lines 
4.1 The x–y Coordinate Plane
4.2 Slope: Meaning and Calculation
Slope as “Change in y over Change in x” 
Four Common Slope Types 
4.3 Equations of a Line
Slope–Intercept Form 
Point–Slope Form 
Standard (General) Form 
Converting from Standard Form to Slope–Intercept Form
4.4 Graphing Lines 
Method A: Graph from y = mx + b 
Method B: Graph Using Two Points 
4.5 Parallel and Perpendicular Lines 
4.6 Applications of Linear Equations
Practice Module 4
Answer Key 

Module 5 Solving Linear Systems in Two Variables
5.1 What Is a Linear System? 
Three Possible Outcomes (Number of Solutions) 
5.2 Solving a System by Graphing 
Note on Accuracy
5.3 Solving a System by Substitution
Steps for Substitution
5.4 Solving a System by Elimination (Addition/Subtraction)
Steps for Elimination 
Special Cases in Elimination 
5.5 Applications (Word Problems) 
Practice Module 5
Answer Key 
Instructor Checkpoint Verification Form

Part II Geometry and Polynomial Expressions 
Module 6 Distance, Midpoint, and Circles
6.1 Review: The Coordinate Plane 
6.2 Distance on a Real Number Line
6.3 Distance Between Two Points (Distance Formula) 
Triangle Example (Perimeter)
6.4 Midpoint of a Segment (Midpoint Formula) 
6.5 Circles: Center, Radius, and Standard Form
Special Circle: The Unit Circle
Practice Module 6
Answer Key 

Module 7 Exponents and Scientific Notation 
7.1 What Does an Exponent Mean? 
7.2 Laws of Exponents
7.3 Zero and Negative Exponents
7.4 Simplifying More Exponential Expressions
7.5 Scientific Notation 
Practice Module 7
Answer Key 

Module 8 Polynomial Expressions 
8.1 Polynomial Expressions
8.2 Types of Polynomials
8.3 Degree of a Polynomial 
8.4 Combining Like Terms
Common Mistake
8.5 Distributive Property
Practice Module 8
Simplify Each Polynomial Expression 
Answer Key 

Module 9 Multiplying Polynomial Expressions 
9.1 Multiplying a Monomial by a Polynomial
9.2 Multiplying Binomials
9.3 Special Products
Perfect Square Trinomials
Difference of Squares 
9.4 Multiplying Polynomials with Higher Degree and Multivariable 
Practice Module 9
Multiply Each Expression
Answer Key 

Module 10 Factoring Polynomials 
Key Vocabulary
10.1 Factoring by Greatest Common Factor
Steps
10.2 Factoring Trinomials When the Coefficient of x2 is 1 
10.3 Factoring by Grouping
Common Mistake
10.4 Factoring Trinomials When the Coefficient of x2 is Not 1 
AC Method Steps
Try-and-Check Method
10.5 Special Factoring Formulas
A. Difference of Squares 
B. Perfect Square Trinomials
10.6 Factoring Higher-Degree Polynomials
Key Idea
Practice Module 10
Answer Key 

Module 11 Solving Quadratic Equations
Key Vocabulary
What Does It Mean to “Solve”? 
Visual Connection: Solutions and the Graph
11.1 Method 1: Solving by Factoring 
Step-by-Step Procedure 
11.2 Method 2: Completing the Square
Step-by-Step Procedure 
11.3 Method 3: Quadratic Formula
Quadratic Formula 
Step-by-Step Procedure 
Discriminant and Number of Real Solutions
Choosing a Method
11.4 Real-Life Applications
Practice Module 11
Answer Key 
Instructor Checkpoint Verification Form

Part III Functions and Rational and Radical Expressions 
Module 12 Rational Expressions and Rational Equations
12.1 Rational Expressions and Domain
To Find the Domain 
12.2 Simplifying Rational Expressions (Factoring and Reducing) 
12.3 Multiplying and Dividing Rational Expressions 
A. Multiplication
B. Division 
12.4 Adding and Subtracting Rational Expressions
Steps
12.5 Solving Rational Equations 
Steps
12.6 Applications (Real Life) 
Practice Module 12
Problems
Answer Key 

Module 13 Radicals 
Key Vocabulary
Square Root 
General nth Root
13.1 Definition of a Radical and Its Components
13.2 Simplifying Square Roots (Reducing Radicals)
13.3 Combining Like Radicals
13.4 Multiplying and Dividing Radicals
13.5 Rationalizing the Denominator (Basic: Square Root) 
13.6 Radicals with Variables
13.7 Writing Rational Exponents as Radicals (and Vice Versa)
13.8 Simplifying Higher Roots (Cube Roots and Fourth Roots)
13.9 Solving Radical Equations (Square Root and Cube Root)
Note
General Steps
A. Square-Root Equations 
B. Cube-Root Equations
13.10 Real-World Applications 
Practice Module 13
Applications
Answer Key 

Module 14 Relations and Functions
14.1 Relations
Key Idea
Common Representations
14.2 Domain and Range 
Domain and Range from Ordered Pairs
Domain and Range from a Graph
14.3 Functions and the Vertical Line Test
How to Use the Test
14.4 Function Notation 
How to Evaluate
14.5 Linear and Quadratic Functions
14.6 Operations on Functions
14.7 Graphing Linear Functions and Quadratic Functions
A. Linear Function
B. Quadratic Functions and Finding the Vertex
Finding the Vertex from Standard Form 
14.8 Practical Application of Functions and Evaluating Functions
Practice Module 14
Answer Key 

Module 15 Combining Functions and Inverse Functions
15.1 Composition (Doing One Function After Another)
15.2 Inverse Functions
Key Idea
How to Find an Inverse (When It Exists) 
15.3 One-to-One and the Horizontal Line Test
Practice Module 15
Answer Key 
Instructor Checkpoint Verification Form 3

Part IV Exponential and Logarithmic Expressions 
Module 16 Exponential and Logarithmic Expressions
16.1 Exponentials and Logarithms Are Inverses 
16.2 Converting Between Log and Exponential Form 
16.3 Special Bases: Base 10 and Base e 
16.4 Evaluating Logarithms Without a Calculator 
16.5 Exponential and Logarithmic Functions as Functions (Graphs and Connection)
16.6 Solving Exponential Equations
A. When Both Sides Share a Common Base 
B. When the Bases Are NOT the Same
16.7 Real-World Situations Using Logarithmic Expressions
Practice Module 16
Convert to Exponential Form
Convert to Logarithmic Form 
Evaluate 
Solve 
Answer Key 

Module 17 Logarithms: Domains, Properties, Equations, Change of Base, and Applications
17.1 Logarithms and Exponentials (Inverse Relationship)
17.2 Domain of Logarithmic Expressions
17.3 Properties of Logarithms 
17.4 Combining Logarithms into a Single Log 
17.5 Solving Basic Logarithmic Equations
17.6 Solving Log Equations by Combining Logs First 
17.7 How Log and Exponential Functions Cancel 
a. Big Idea 
b. Why Do ln and Exponential Cancel? 
c. General Strategy for ex = b 
17.8 Applications
Common Mistakes to Avoid
17.9 Change of Base 
17.10 More Applications (Real-World Logarithms)
Practice Module 17
Find the Domain of
Expand   Each:
Combine into One Log 
Solve: 
Change of Base:
Answer Key 

Module 18 Exponential Growth and Decay Models 
18.1 Discrete Exponential Growth and Decay Model 
18.2 Natural Exponential Model
Doubling Time 
Half-Life 
Practice Module 18
Answer Key 

Part V Real-World Applications and Data 
Module 19 Money, Interest, and Investment Models 
19.1 Simple Interest
Meaning of the Variables
19.2 Compound Interest
What Does n Mean?
19.3 Continuous Compounding
Who Benefits?
Key Idea
19.4 Visual Comparison of Growth Models
Graph Comparison
Table of Values
Practice Module 19
Answer Key 

Module 20 Basic Statistics for Intermediate Algebra: Introduction to data, graphs, measures of center, and measures of spread 
20.1 What Is Statistics?
20.2 Types of Data 
A. Qualitative Data (Categorical Data)
B. Quantitative Data (Numerical Data)
20.3 Organizing Data with Tables and Graphs
Frequency Table
Bar Graph
Histogram 
Dot Plot and Scatter Plot
Step 1: Frequency Table
Step 2: Bar Graph Representation 
Step 3: Interpretation 
20.4 Measures of Center: Mean, Median, and Mode 
20.5 Measures of Variation 
Interpreting Standard Deviation
Important Remark
Population Variance 
Sample Variance
Why Do We Divide by n − 1? 
20.6 Quartiles, Five-Number Summary, and Boxplots
Five-Number Summary 
Box Plot 
What the IQR Tells Us
20.7 Mini Project: Exploring Real-Life Data 
Possible Data Ideas
Personal Habits
School-Related Data 
Daily Life Measurements 
Final Thought
Practice Module 20
A. Mean
B. Median and Mode
C. Range, Variance, and Standard Deviation 
D. Frequency, Tables, and Graphs 
E. Quartiles, Five-Number Summary, and IQR
F. Applications 
Answer Key 
Instructor Checkpoint Verification Form 4

Part VI Final Preparation 
Comprehensive Final Practice Exam (Approx. 2 Hours) 
Practice Final Exam
Answer Key