Beginning and Intermediate Algebra : The Language and Symbolism of Mathematics

by Hall, James W.; Mercer, Brian A.

• ISBN13: 9780073229713
• ISBN10: 0073229717
• Edition: 2nd
• Format: Hardcover
• Copyright: 2007-01-19
• Publisher: McGraw-Hill Science/Engineering/Math

Summary

Intended for schools that want a single text covering the standard topics from Beginning and Intermediate Algebra. Topics are organized by using the principles of the AMATYC standards as a guide, giving strong support to teachers using the text. The book's organization and pedagogy are designed to workfor studentswith a variety of learning styles and for teachers with varied experiences and backgrounds. The inclusion of multiple perspectives -- verbal, numerical, algebraic, and graphical -- has proven popular with a broad cross section of students. Use of a graphing calculator is assumed. BEGINNING AND INTERMEDIATE ALGEBRA: THE LANGUAGE AND SYMBOLISM OF MATHEMATICS is a reform-oriented book.

Table of Contents

Operations with Real Numbers

Preparing for an Algebra Class

The Real Number Line

Addition of Real Numbers

Subtraction of Real Numbers

Multiplication of Real Numbers and Natural Number Exponents

Division of Real Numbers

Order of Operations

Linear Equations and Patterns

The Rectangular Coordinate System and Arithmetic Sequences

Function Notation and Linear Functions

Graphs of Linear Equations in Two Variables

Solving Linear Equations in One Variable by Using the Addition-Subtraction Principle

Solving Linear Equations in One Variable by Using the Multiplication-Division Principle

Using and Rearranging Formulas

Proportions and Direct Variation

More Applications of Linear Equations

Lines and Systems of Linear Equations in Two Variables

Slope of a Line and Applications of Slope

Special Forms of Linear Equations in Two Variables

Solving Systems of Linear Equations in Two Variables Graphically and Numerically

Solving Systems of Linear Equations in Two Variables by the Substitution Method

Solving Systems of Linear Equations in Two Variables by the Addition Method

More Applications of Linear Systems Cumulative Review of Chapters 1-3

Linear Inequalities and Systems of Linear Inequalities

Solving Linear Inequalities by Using the Addition-Subtraction Principle

Solving Linear Inequalities by Using the Multiplication-Divison Principle

Solving Compound Inequalities

Solving Absolute Value Equations and Inequalities

Graphing Systems of Linear Inequalities in Two Variables

Exponents and Operations with Polynomials

Product and Power Rules for Exponents

Quotient Rule and Zero Exponents

Negative Exponents and Scientific Notation

Adding and Subtracting Polynomials

Multiplying Polynomials

Special Products of Binomials

Dividing Polynomials Diagonostic Review of Beginning Algebra

Factoring Polynomials

An Introduction to Factoring Polynomials

Factoring Trinomials of the Form x2 + bxy + cy2

Factoring Trinomials of the Form ax2 + bxy + cy2

Factoring Special Forms

Factoring by Grouping and a General Strategy for Factoring Polynomials

Solving Equations by Factoring

Functions: Linear, Absolute Value, and Quadratic

Functions and Representations of Functions

Linear and Absolute Value Functions

Linear and Quadratic Functions and Curve Fitting

Using the Quadratic Formula to find Real Solutions

The Vertex of a Parabola and Max-Min Applications

More Applications of Quadratic Equations

Complex Numbers and Solving Quadratic Equations with Complex Solutions

Rational Functions

Graphs of Rational Functions and Reducing Rational Expressions

Multiplying and Dividing Rational Expressions

Adding and Subtracting Rational Expressions

Combining Operations and Simplifying Complex Rational Expressions

Solving Equations Containing Rational Expressions

Inverse and Joint Variation and Other Applications Yielding Equations with Fractions Cumulative Review of Chapters 1-8

Square Root and Cube Root Functions and Rational Exponents

Evaluating Radical Expressions and Graphs of Square Root and Cube Root Functions

Adding and Subtracting Radical Expressions

Multiplying and Dividing Radical Expressions

Solving Equations Containing Radical Expressions

Rational Exponents and Radicals

Exponential and Logarithmic Functions

Geometric Sequences Graphs of Exponential Functions

Inverse Functions

Logarithmic Functions

Evaluating Logarithms

Properties of Logarithms

Solving Exponential and Logarithmic Equations

Exponential Curve Fitting and Other Applications of Exponential and Logarithmic Equations Cumulative Review of Chapters 1-10

A Preview of College Algebra

Solving Systems of Linear Equations by Using Augmented Matrices

Systems of Linear Equations in Three Variables

Horizontal and Vertical Translations of the Graphs of Functions

Stretching, Shrinking and Reflecting Graphs of Functions

Algebra of Functions

Sequences, Series and Summation Notation

Conic Sections

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