McGraw-Hill Education Algebra I Review and Workbook

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McGraw-Hill Education Algebra I Review and Workbook

McGraw-Hill Education Algebra I Review and Workbook

Authors: Sandra Luna McCune

Published: January 2019

eISBN: 9781260128956 | ISBN: 9781260128949

Cover

Title Page

Copyright Page

Contents

Chapter 1 Understanding the Real Numbers

Classifying Real Numbers

Rational and Irrational Roots

Chapter 2 Properties of the Real Numbers

Commutative and Associative Properties

Identity and Inverse Properties

Distributive Property

Zero Factor Property

Chapter 3 The Number Line and Comparing Numbers

The Number Line

Comparing Numbers

Chapter 4 Absolute Value

Determining Absolute Value

Properties of Absolute Value

Chapter 5 Performing Operations with Real Numbers

(Algebraic) Addition and Subtraction of Real Numbers

(Algebraic) Multiplication and Division Rules for Real (Signed) Numbers

Chapter 6 Exponents

Positive Integer Exponents

Zero and Negative Integer Exponents

Rules for Negative Exponents

Unit Fraction and Rational Exponents

Rules for Exponents

Chapter 7 Radicals

Expressing Rational Exponents as Radicals

Product and Quotient Rules for Radicals

Transforming Radicals into Simplified Form

Chapter 8 Order of Operations

Grouping Symbols

Order of Operations

Chapter 9 Algebraic Expressions and Formulas

Algebraic Expressions

Formulas

Chapter 10 Polynomial Terminology

Monomials

One-Variable Polynomials

Chapter 11 Adding and Subtracting Polynomials

Adding and Subtracting Monomials

Adding and Subtracting Polynomials

Chapter 12 Multiplying Polynomials

Multiplying Monomials

Multiplying a Polynomial by a Monomial

Multiplying Binomials

Multiplying Two Polynomials

Special Products

Chapter 13 Simplifying Polynomial Expressions

Removing Parentheses by Addition or Subtraction

Removing Parentheses by Multiplication or Raising to a Power

Chapter 14 Dividing Polynomials

Dividing a Polynomial by a Monomial

Dividing a Polynomial by a Polynomial

Chapter 15 Factoring Polynomials

Factoring Out the Greatest Common Factor

Factoring the Difference of Two Squares

Factoring Perfect Trinomial Squares

Factoring the Sum and the Difference of Two Cubes

Factoring General Trinomials

Chapter 16 Fundamental Concepts of Rational Expressions

Definition of a Rational Expression

Reducing Rational Expressions

Building Up the Denominator of a Rational Expression

Chapter 17 Multiplying and Dividing Rational Expressions

Multiplying Rational Expressions

Dividing Rational Expressions

Chapter 18 Adding and Subtracting Rational Expressions

Adding and Subtracting Rational Expressions, Like Denominators

Adding and Subtracting Rational Expressions, Unlike Denominators

Chapter 19 Simplifying Complex Fractions

Writing Complex Fractions as Division Problems to Simplify

Using the LCD to Simplify a Complex Fraction

Chapter 20 One-Variable Linear Equations and Inequalities

Basic Concepts

Solving One-Variable Linear Equations

Solving Linear Equations with Two or More Variables for a Specific Variable

Solving One-Variable Linear Inequalities

Chapter 21 One-Variable Quadratic Equations

Basic Concepts

Solving Quadratic Equations of the Form ax2 + c = 0

Solving Quadratic Equations by Factoring

Solving Quadratic Equations by Completing the Square

Solving Quadratic Equations by Using the Quadratic Formula

Chapter 22 The Cartesian Coordinate Plane

The Coordinate Plane and Ordered Pairs

Quadrants of the Coordinate Plane

Chapter 23 Formulas for the Coordinate Plane

Distance Formula

Midpoint Formula

Slope Formula

Rise and Run

Chapter 24 Graphing Lines in the Plane

Graphing y = mx + b

Graphing Ax + By = C

Chapter 25 Determining the Equation of a Line

Determining the Equation of a Line Given the Slope and y-Intercept

Determining the Equation of a Line Given the Slope and One Point on the Line

Determining the Equation of a Line Given Two Distinct Points on the Line

Chapter 26 Signal Words and Phrases

Common Signal Words and Phrases for Addition

Common Signal Words and Phrases for Subtraction

Common Signal Words and Phrases for Multiplication

Common Signal Words and Phrases for Division

Common Signal Words and Phrases for Equality

Chapter 27 Applying Algebra to Word Problems

Steps in Algebraic Problem-Solving

Be Careful with Units

Chapter 28 Applications

Number Problems

Age Problems

Ratio and Proportion Problems

Mixture Problems

Coin Problems

Rate-Time-Distance Problems

Work Problems

Percentage Problems

Simple Interest Problems

Geometry Problems

Chapter 29 Introduction to Functions

Defining a Function

Evaluating Functions

Chapter 30 Graphs of Functions

Vertical Line Test

Zeros and Intercepts

Increasing, Decreasing, and Constant Behavior

Chapter 31 Common Functions and Their Graphs

Linear Functions

Quadratic Functions

Exponential Functions

Chapter 32 Introduction to Systems of Two-Variable Equations

Definition and Terminology for Systems of Two-Variable Linear Equations

Types of Solutions for Systems of Two-Variable Linear Equations

Chapter 33 Solving Systems of Two-Variable Linear Equations

Solving Systems of Two-Variable Linear Equations by Substitution

Solving Systems of Two-Variable Linear Equations by Elimination

Solving Systems of Two-Variable Linear Equations by Graphing

Chapter 34 Graphing Systems of Two-Variable Inequalities

Graphing Two-Variable Linear Inequalities

Graphing Two-Variable Quadratic Inequalities

Appendix A Measurement Units and Conversions

Appendix B Geometry Formulas

Triangle

Right Triangle

Square

Rectangle

Parallelogram

Circle

Trapezoid

Sphere

Right Prism

Right Rectangular Prism

Cube

Right Circular Cylinder

Right Pyramid

Right Circular Cone

Answer Key