Algebra 1 Companion Website

Select the chapter title below to access activities and videos.

1. The Elements of Algebra

• Videos
  1.1 Writing and Translating Algebraic Expressions

  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

  1.2 Translating and Writing Formulas

  Applying a Formula
  Distance, Speed and Time

  1.4 Evaluating Algebraic Expressions and Formulas

  Order of Operations
  Order of Operations and Algebraic Expressions

  1.5 Algebraic Properties

  The Communicative Properties
  The Associative Properties
  Identities and Inverses
  Distributive Property
  Distributing Negative Numbers
  Substitution, Reflexive, Symmetric, and Translative Properties

  1.6 Exponents

  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

  1.7 Roots and Radicals

  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

  1.8 Scientific Notation, Significant Digits, Precision, and Accuracy

  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

• Videos
  2.1 Solving Linear Equations

  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

  2.2 Solve for a Variable in Literal Equations

  Solving for a Variable

  2.3 Rates, Ratios, and Proportions

  What Is a Proportion?
  Application: Estimating Wildlife Populations
  Application: Similar Triangles
  Rates
  Rates in a Proportion

  2.4 Modeling with Linear Equations

  Basic Problem Solving Skills
  Consecutive Number Problems
  Money Problems
  Tax Applications

  2.5 Solving Linear Inequalities

  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

• Videos
  3.1 Graphing Linear Equations

  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

  3.2 Direct Variation

  Direct Variation

  3.3 The Slope of a Line

  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

  3.4 Graphing and Writing Linear Equations Using the Slope-Intercept and Point-Slope Forms

  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

  3.5 Functions

  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

• Videos
  4.1 Solving Linear Equations

  Solutions to Linear Inequalities
  Graphing Linear Inequalities

  4.2 Absolute Value Inequalities and Graphing on the Number Line

  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

• Videos
  5.1 Solving Systems of Linear Equations by Graphing

  Solving by Graphing
  Number of Solutions to Systems of Linear Equations

  5.2 Solving Systems of Linear Equations by Substitution

  Solve by Substitution
  Application: Racing Cyclists
  Sample Problem: How Old Are Adam and Ben?
  Application: Making a Necklace

  5.3 Solving Systems of Linear Equations by Elimination

  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

• Videos
  6.1 Adding and Subtracting Polynomials

  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

  6.2 Multiplying a Monomial by a Monomial

  Power of Power
  Sample Problems: Power of Power
  Multiplying Monomials

  6.3 Multiplying a Polynomial by a Monomial

  Multiplying a Binomial by a Monomial

  6.4 Multiplying a Polynomial by a Polynomial

  Multiplying Polynomials Using the Distributive Property
  Multiplying Binomials: FOIL

  6.5 Special Products of Binomials

  Squares of Binomials
  Product of the Sum and Difference of Two Terms

  6.6 Negative Integers as Exponents

  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

• Videos
  7.1 Greatest Common Factors

  Common Factors

  7.3 Factoring Trinomials

  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

  7.4 Factoring Completely

  Greatest Common Factor

8. Quadratic Equations and Functions

• Videos
  8.1 Standard Form of the Quadratic Equation

  Quadratic Equations

  8.2 Solving Quadratic Equations Algebraically

  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

  8.3 Solving Quadratic Equations by Completing the Square

  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

  8.4 Solving Quadratic Equations from the Graph

  Graphing a Parabola
  Solving Quadratic Equations Graphically
  Finding the x-intercepts of a Parabola

  8.5 Graphing Quadratic Functions

  Graphing a Parabola
  Graphing a Parabola of the Form f(x) = ax²
  Finding the x-intercepts of a Parabola

  8.8 The Quadratic Formula and the Discriminant

  The Quadratic Formula
  Applying the Quadratic Formula
  Summary: Solving Quadratic Equations

9. Exponents and Exponential Functions

• Videos
  9.2 Graphing Exponential Functions

  Exponential Functions
  Exponential Function Graphs
  The Shapes of Graphs of Exponential Functions

  9.3 Modeling Exponential Growth and Decay

  Application: Interest Compounded Annually
  Application: Bacteria and Doubling
  Application: An Interesting Question

  9.4 Sequences and Arithmetic Sequences

  Arithmetic Sequences
  Explicit Formula for an Arithmetic Sequence

  9.5 Geometric Sequences

  Geometric Sequences
  Explicit Formula for a Geometric Sequence
  What Type of Sequence?

10. Interpreting Quantitative and Categorical Data

• Videos
  10.1 Simple Single-Count Statistics

  Dot Plots
  Histograms
  Scales and Graphs

  10.2 Measure of a Central Tendency

  Calculating Mean, Median, and Mode

  10.3 Single-Count Statistics with Dispersion

  Standard Deviation
  Calculating Standard Deviation
  Box-and-Whisker Plots
  Outliers