1. The Elements of Algebra
1.1 Writing and Translating Algebraic Expressions: Tile Equations (p402)
1.1 Writing and Translating Algebraic Expressions: Tile Equations (p402)
Writing an Algebraic Expression
Writing a More Complex Algebraic Expression
Writing an Expression from a Table
Creating a Table to Help Write an Algebraic Expression
Applying a Formula
Distance, Speed and Time
Order of Operations
Order of Operations and Algebraic Expressions
The Communicative Properties
The Associative Properties
Identities and Inverses
Distributive Property
Distributing Negative Numbers
Substitution, Reflexive, Symmetric, and Translative Properties
Definitions of Exponents
Exponent Examples
Sample Problem: Order of Operations with Exponents
Exponents, Negative Numbers, and Variables
Product of Powers
Quotient of Powers
Negative Exponents
Zero as an Exponent
Negative Exponents and Rules of Exponents
Negative Exponents in the Denominator
Power of Product
Power of Quotient
Radical Expressions
Square Roots of Perfect Squares
Cube Roots
Product Rule for Radicals
Simplifying Radicals Using the Product Rule
Simplifying Radicals
Multiplying and Simplifying Radical Expressions
Quotient Rule for Radicals
Dividing Radicals
Rationalizing the Denominator
Simplifying the Square Root of a Fraction with a Variable in the Denominator
Adding and Subtracting Like Radicals
Writing Numbers in Scientific Notation
Multiplying Numbers in Scientific Notation
Dividing Numbers in Scientific Notation
Applications for Scientific Notation
2. Writing and Solving Linear Equations and Inequalities
Addition Property of Equality
Multiplication Property of Equality
Negative Coefficients
Solving Linear Equations with a Variable
Combining Like Terms
Combining Like Terms to Solve an Equation
Solving an Equation Using the Distributive Property
Distributing Negative Numbers and Solving Equations
Number of Solutions to an Equation
Equations with Fractions
Equations with Decimals
What Is a Proportion?
Application: Estimating Wildlife Populations
Application: Similar Triangles
Rates
Rates in a Proportion
Basic Problem Solving Skills
Consecutive Number Problems
Money Problems
Tax Applications
Solutions to Inequalities
Graphing Inequalities on the Number Line
The Addition Property of Inequality
The Multiplication Property of Inequality
Sample Problem: Solving and Checking an Inequality
Conjunctions of Inequalities
Disjunctions of Inequalities
Solving a Compound Inequality
3. Graphing Linear Equations and Inequalities
3.1 Graphing Linear Equations: Plotting Points of Linear Equations (p403)
3.8 Modeling Linear Functions: Finding the Rate of Change (p405)
3.8 Modeling Linear Functions: Finding the Rate of Change (p405)
3.8 Modeling Linear Functions: Finding the Rate of Change (p405)
3.8 Modeling Linear Functions: Comparing Costs (p405)
3.8 Modeling Linear Functions: Comparing Costs (p405)
Determining If a Point Is a Solution to an Equation
Linear and Nonlinear Equations
Graphing the Equation of a Line
Sample Problem: Graphing y = −¾x − 1
Application: Burning Calories
Graphing Horizontal and Vertical Lines
The Slope of a Line
Formula for Slope
What Is the Role of m in y = mx + b?
Slope and the Steepness of a Line
Determining When Lines Are Parallel
Determining When Lines Are Perpendicular
What Is the Role of b in y = mx + b?
Graphing Equations in Slope-Intercept Form
Graphing Linear Equations in General Form
Finding an Equation with Slope and One Point
Finding an Equation from Two Points
Writing an Equation for a Parallel Line
Writing an Equation for a Perpendicular Line
Function Basics
Relations and Functions
Using Function Notation
Graph of a Linear Function
Graph of a Nonlinear Function
Determining the Domain and Range from a Graph
Determining If a Graph Represents a Function
4. Inequalities, Absolute Value, Piecewise and Stepwise Functions
4.1 Graphing Linear Inequalities: Graphing Practice (p406)
4.2 Absolute Value Inequalities and Graphing on the Number Line: Determine the Conjunction (p406)
4.2 Absolute Value Inequalities and Graphing on the Number Line: Determine the Disjunction (p406)
4.4 Graphing Absolute Value Functions: Adding a Constant (p407)
Solutions to Linear Inequalities
Graphing Linear Inequalities
Inequalities with Absolute Values
4.5 Solving Absolute Value Equations Algebraically Equations with Absolute Value
Solving an Absolute Value Equation
5. Systems of Linear Equations and Inequalities
5.1 Solving Systems of Linear Equations by Graphing (p407)
5.1 Solving Systems of Linear Equations by Graphing (p407)
Solving by Graphing
Number of Solutions to Systems of Linear Equations
Solve by Substitution
Application: Racing Cyclists
Sample Problem: How Old Are Adam and Ben?
Application: Making a Necklace
Solving by Elimination
Sample Problem: A Problem with Numbers
Sample Problem: A Problem for the Ages
Solving by Elimination: Multiplication and Division
Sample Problem: Solving by Multiplying Equations by a Constant and Eliminating
Application: Chips and Juice
Systems with Many or No Solutions
6. Operations with Polynomials
6.1 Adding and Subtracting Polynomials: Combining Like Terms (p409)
6.1 Adding and Subtracting Polynomials: Combining Like Terms (p409)
6.1 Adding and Subtracting Polynomials: Combining Like Terms (p409)
Monomials
Polynomials
Polynomials: Descending Order
Like Terms
Standard Form of a Polynomial
Adding Polynomials: Horizontal Method
Adding Polynomials: Vertical Method
Subtracting Polynomials: Horizontal Method
Subtracting Polynomials: Vertical Method
Power of Power
Sample Problems: Power of Power
Multiplying Monomials
Multiplying a Binomial by a Monomial
6.4 Multiplying a Polynomial by a Polynomial Multiplying Polynomials Using the Distributive Property
Multiplying Binomials: FOIL
Squares of Binomials
Product of the Sum and Difference of Two Terms
Applying Power Rules with Negative Exponents
6.7 Dividing Polynomials Dividing a Monomial by a Monomial
Dividing a Polynomial by a Monomial
7. Special Products and Factoring
7.3 Factoring Trinomials: Factor Tiles- Activity 1 (p409)
7.3 Factoring Trinomials: Factor Tiles- Activity 2 (p410)
7.3 Factoring Trinomials: Factor Tiles a≠1- Activity 3 (p410)
Factoring Perfect-Square Trinomials
Factoring x² + bx + c
Factoring x² + bx + c, with c Negative
Factoring x² + bx + c, b Is Negative, c Is Positive
Summary: Factoring a Trinomial x² + bx + c
Factoring a Trinomial with ax² Term, a ≠ 1
8. Quadratic Equations and Functions
8.5 Graphing Quadratic Functions: Locate the Vertex with Given X-Coordinates (p411)
8.5 Graphing Quadratic Functions: Locate the Vertex with Given X-Coordinates (p411)
8.6 Quadratic Functions in Vertex Form: Locate the Vertex with Vertex Form (p411)
8.6 Quadratic Functions in Vertex Form: Locate the Vertex with Vertex Form (p411)
8.7 Transformations of Quadratic Formula: Horizontal and Vertical Transformations (p413)
8.11 Graphing Cubic and Root Functions: Experimenting with Translations and Dilations (p413)
Solving by Factoring: Common Factors
Solving by Factoring: Trinomials
Sample Problems: Solving by Factoring
Solving by Factoring: Difference of Two Squares
The Square Root Principle
Quadratic Equations with Irrational Solutions
Solving an Equation with a Squared Expression
Using the Square Root Principle
Complete the Square
Solving a Quadratic Equation
Complete the Square: a > 1
Complete the Square: a < 0
Graphing a Parabola
Solving Quadratic Equations Graphically
Finding the x-intercepts of a Parabola
Graphing a Parabola
Graphing a Parabola of the Form f(x) = ax²
Finding the x-intercepts of a Parabola
The Quadratic Formula
Applying the Quadratic Formula
Summary: Solving Quadratic Equations
9. Exponents and Exponential Functions
9.2 Graphing Exponential Functions: Match the Exponential Function (p414)
9.4 Sequences and Arithmetic Sequences: Shapes and Patterns- Activity 1 (p415)
9.4 Sequences and Arithmetic Sequences: Shapes and Patterns- Activity 2 (p415)
9.4 Sequences and Arithmetic Sequences: Shapes and Patterns- Activity 3 (p415)
9.4 Sequences and Arithmetic Sequences: The Geometric Frog- Activity 1 (p415)
9.4 Sequences and Arithmetic Sequences: The Geometric Frog- Activity 2 (p415)
9.5 Geometric Sequences: Shapes and Patterns- Activity 4 (p416)
9.5 Geometric Sequences: Shapes and Patterns- Activity 5 (p416)
9.5 Geometric Sequences: The Geometric Frog- Activity 3 (p416)
9.5 Geometric Sequences: The Geometric Frog- Activity 4 (p416)
Exponential Functions
Exponential Function Graphs
The Shapes of Graphs of Exponential Functions
Application: Interest Compounded Annually
Application: Bacteria and Doubling
Application: An Interesting Question
Arithmetic Sequences
Explicit Formula for an Arithmetic Sequence
Geometric Sequences
Explicit Formula for a Geometric Sequence
What Type of Sequence?
10. Interpreting Quantitative and Categorical Data
Dot Plots
Histograms
Scales and Graphs
Calculating Mean, Median, and Mode
10.3 Single-Count Statistics with Dispersion Standard Deviation
Calculating Standard Deviation
Box-and-Whisker Plots
Outliers