Table of Contents
How This Workbook Is Organized
Where to Go for Additional Help
Chapter 1: Signing on with Signed Numbers
Placing Real Numbers on the Number Line
Using the Absolute Value Operation
Multiplying and Dividing Signed Numbers
Chapter 2: Recognizing Algebraic Properties and Notation
Applying Traditional Grouping Symbols
Introducing Some Non-Traditional Grouping Symbols
Distributing Multiplication over Addition and Subtraction
Associating Terms Differently with the Associative Property
Rearranging with the Commutative Property
Applying More Than One Property to an Expression
Chapter 3: Working with Fractions and Decimals
Adding and Subtracting Fractions
Adding and Subtracting Decimals
Changing Fractions to Decimals
Changing Decimals to Fractions
Chapter 4: Making Exponential Expressions and Operations More Compatible
Multiplying and Dividing Exponentials with the Same Base
Combining Different Operations on Exponentials
Changing the Base to Perform an Operation
Working with Scientific Notation
Simplifying Radical Expressions
Using Fractional Exponents for Radicals
Evaluating Expressions with Fractional Exponents
Operating on Factors with Fractional Exponents
Chapter 6: Creating More User-Friendly Algebraic Expressions
Adding and Subtracting Like Terms
Multiplying and Dividing Factors
Simplifying Expressions Using Order of Operations
Evaluating Expressions Using Order of Operations
Chapter 7: Multiplying by One or More Terms
Distributing One Term Over Sums and Differences
Multiplying Binomials Using Distributing
Multiplying Binomials Using FOIL
Distributing Binomials Over Trinomials
Raising Binomials to the Third Power
Finding Special Products of Binomials and Trinomials
Chapter 8: Dividing Algebraic Expressions
Dividing with Monomial Divisors
Monomial Divisors and Remainders
Using Long Division to Divide with Binomials
Dividing with Binomials Using Synthetic Division
Dividing with Higher Power Divisors
Finding Divisors Using Rules of Divisibility
Reducing Fractions with a Common GCF
Chapter 10: Factoring Binomials
Factoring the Difference of Perfect Squares
Factoring the Sum or Difference of Two Perfect Cubes
Chapter 11: Factoring Quadratic Trinomials
Factoring Out the GCF of a Trinomial
Factoring Trinomials into the Products of Binomials
Factoring Quadratic-Like Expressions
Factoring Completely Using More Than One Technique
Chapter 12: Other Factoring Techniques
Combining Other Factoring Techniques with Grouping
Using Multiple Factoring Methods
Chapter 13: Solving Linear Equations
Solving Linear Equations Using Basic Operations
Dealing with Fractions in Linear Equations
Chapter 14: Taking on Quadratic Equations
Applying the Square Root Rule to Quadratic Equations
Solving Quadratic Equations Using Factoring
Applying the Quadratic Formula to Quadratic Equations
Completing the Square to Solve Quadratic Equations
Writing Complex Numbers in the Standard a + bi Form
Finding Complex Solutions Using the Quadratic Formula
Chapter 15: Solving Polynomials with Powers Three and Higher
Applying Descartes's Rule of Signs to Count Real Roots
Applying the Rational Root Theorem to List Roots
Determining Whether Numbers Are Roots
Solving for the Roots of Polynomials
Chapter 16: Reining in Radical and Absolute Value Equations
Solving Basic Radical Equations
Squaring Both Sides of Equations Twice
Solving Radicals with Roots Other Than Square Roots
Solving Absolute Value Equations
Handling Absolute Value Equations with No Solution
Chapter 17: Making Inequalities More Fair
Performing Operations on Inequalities
Writing Inequalities Using Interval Notation
Changing Interval Notation to Inequality Notation
Taking on Compound Inequalities
Solving Quadratic Inequalities
Finding Solutions of Nonlinear Inequalities
Rewriting and Solving Absolute Value Inequalities
Delving into Complex Inequalities
Chapter 18: Using Established Formulas
Getting Interested in Interest Problems
Heating It Up with Temperature Problems
Going the Distance with the Distance Formula
Getting the Inside Scoop with Sums of Interior Angles
Summing the Squares of Numbers
Finding the Terms of a Sequence
Adding the Terms in an Arithmetic Sequence
Using the Formula for the Sum of Cubes
Compounding the Problems Involving Compound Interest
Chapter 19: Using Formulas in Geometric Story Problems
Working around the Perimeter of Rectangles
Using the Area Formula for a Trapezoid
Tackling Area and Perimeter of a Square
Solving Problems Using the Perimeter of a Triangle
Working with the Area and Perimeter of a Rectangle
Using the Formula for the Area of a Hexagon
Getting Pythagoras Involved in the Area of a Triangle
Making Use of the Volume of a Box
Working with the Volume of a Cylinder
Changing Radians to Degrees and Degrees to Radians
Determining the Height of an Object
Working with Heron's Formula for the Area of a Triangle
Chapter 20: Tackling Traditional Story Problems
Working with Consecutive Integers
Getting the Job Done on Work Problems
Counting on Quality and Quantity Problems
Plotting Points on the Coordinate System
Determining the Quadrant of a Point
Finding the Intercepts of a Line
Calculating the slope of a line from two points
Determining a Line's Slope from Its Equation
Sketching the Graph of a Line from Its Equation
Sketching Lines Using Two Points
Chapter 22: Using the Algebra of Lines
Writing Equations of Lines Using the Slope and a Point
Writing the Equation of a Line Using Two Points
Dealing with Slopes of Parallel and Perpendicular Lines
Finding Equations of Lines Parallel or Perpendicular to One Given
Computing the Distance Between Points
Chapter 23: Other Graphing Topics
Graphing to Find the Intersection of Two Lines
Sketching the Graph of a Circle
Creating the Graph of a Parabola