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This text, written by best-selling developmental mathematics author Pat McKeague, features a more streamlined review of elementary algebra, allowing for earlier coverage of intermediate topics. An early introduction to graphing presents the foundation for a wide variety of graphing problems throughout the text. Early coverage of functions helps students feel comfortable with the many examples and graphs of functions that occur in later chapters. The first ten chapters of this book cove the topics usually found in a college-level algebra course. The last three chapters cover the essential topics from trigonometry. Optional technology sections and integrated throughout text as a way for students to better understand the material being discussed.
Author Bio
McKeague, Charles P. : Cuesta College
R. BASIC PROPERTIES AND DEFINITIONS.
Fundamental Definitions and Notation.
Properties of Real Numbers.
Arithmetic with Real Numbers.
Exponents and Scientific Notation.
Polynomials, Sums, Differences, and Products.
Factoring.
Special Factoring.
Recognizing Patterns.
Summary. Review.
Test.
Projects.
1. EQUATIONS AND INEQUALITIES IN ONE VARIABLE.
Linear and Quadratic Equations in One Variable.
Formulas.
Applications.
Linear Equalities in One Variable.
Equations with Absolute Value.
Inequalities Involving Absolute Value.
Summary.
Review.
Test.
Cumulative Review.
Projects.
2. EQUATIONS AND INEQUALITIES IN TWO VARIABLES.
Paired Data and the Rectangular Coordinate System.
The Slope of a Line.
The Equation of a Line.
Linear Inequalities in Two Variables.
Introduction to Functions.
Function Notation.
Algebra with Functions.
Variation.
Summary.
Review. Test.
Cumulative Review.
Projects.
3. SYSTEMS OF LINEAR EQUATIONS AND INEQUALITIES.
Systems of Linear Equations in Two Variables.
Systems of Linear Equations in Three Variables.
Introduction to Determinants. CramerÆs Rule.
Applications.
Systems of Linear Inequalities.
Summary.
Review.
Test.
Cumulative Review.
Projects.
4. RATIONAL EXPRESSIONS AND RATIONAL FUNCTIONS.
Basic Properties and Reducing to Lower Terms.
Division of Polynomials.
Multiplication and Division of Rational Expressions.
Complex Fractions.
Equations Involving Rational Expressions.
Applications.
Summary.
Review.
Test. Cumulative Review.
Projects.
5. RATIONAL EXPONENTS AND ROOTS.
Rational Exponents.
More Expressions Involving Rational Exponents.
Simplified Form for Radicals.
Addition and Subtraction of Radical Expressions.
Multiplication and Division of Radical Expressions.
Equations with Radicals.
Complex Numbers.
Summary.
Review.
Test.
Cumulative Review.
Projects.
6. QUADRATIC FUNCTIONS.
Completing the Square.
The Quadratic Formula.
Additional Items Involving Solutions to Equations. Equations in Quadratic Form.
Graphing Parabolas.
Quadratic Inequalities.
Summary.
Review.
Test.
Cumulative Review. Projects.
7. EXPONENTIAL AND LOGARITHMIC FUNCTIONS.
Exponential Functions.
The Inverse of a Function.
Logarithms Are Exponents.
Properties of Logarithms.
Common Logarithms and Natural Logarithms.
Exponential Equations and Change of Base.
Summary.
Review.
Test.
Cumulative Review.
Projects.
8. SEQUENCES AND SERIES.
Sequences.
Series.
Arithmetic Sequences.
Geometric Sequences.
The Binomial Expansion .
Summary.
Review.
Test.
Cumulative Review.
Projects.
9. CONIC SECTIONS.
The Circle.
Ellipses and Hyperbolas.
Second-Degree Inequalities and Nonlinear Systems.
Summary. Review.
Test.
Cumulative Review.
Projects.
10. INTRODUCTION TO TRIGONOMETRY.
Degrees, Radians, and Special Triangles. Trigonometric Functions.
Trigonometric Functions and Calculators.
Graphing 1: Amplitude and Period.
Graphing II: Phase Shift.
Finding an Equation from Its Graph.
Inverse Trigonometric Functions.
Summary.
Review.
Test.
Cumulative Review.
Projects.
11. TRIGONOMETRIC IDENTITIES AND EQUATIONS.
Introduction to Identities.
Proving Identities.
Sum and Difference Formulas.
Double-Angle and Half-Angle Formulas.
Solving Trigonometric Equations.
Summary.
Review. Test.
Cumulative Review.
Projects.
12. TRIANGLES.
Definition II: Right Triangle Trigonometry.
The Law of Sines. The Ambiguous Case.
The Law of Cosines.
Summary.
Review.
Test.
Cumulative Review.
Projects.
APPENDIXES.
A: Synthetic Division.
B: Matrix Solutions to Linear Systems.
C: Conditional Statements.
D: Answers to Odd-Numbered Problems, Chapter Reviews, Chapter Tests, and Cumulative Reviews.
This text, written by best-selling developmental mathematics author Pat McKeague, features a more streamlined review of elementary algebra, allowing for earlier coverage of intermediate topics. An early introduction to graphing presents the foundation for a wide variety of graphing problems throughout the text. Early coverage of functions helps students feel comfortable with the many examples and graphs of functions that occur in later chapters. The first ten chapters of this book cove the topics usually found in a college-level algebra course. The last three chapters cover the essential topics from trigonometry. Optional technology sections and integrated throughout text as a way for students to better understand the material being discussed.
Author Bio
McKeague, Charles P. : Cuesta College
Table of Contents
R. BASIC PROPERTIES AND DEFINITIONS.
Fundamental Definitions and Notation.
Properties of Real Numbers.
Arithmetic with Real Numbers.
Exponents and Scientific Notation.
Polynomials, Sums, Differences, and Products.
Factoring.
Special Factoring.
Recognizing Patterns.
Summary. Review.
Test.
Projects.
1. EQUATIONS AND INEQUALITIES IN ONE VARIABLE.
Linear and Quadratic Equations in One Variable.
Formulas.
Applications.
Linear Equalities in One Variable.
Equations with Absolute Value.
Inequalities Involving Absolute Value.
Summary.
Review.
Test.
Cumulative Review.
Projects.
2. EQUATIONS AND INEQUALITIES IN TWO VARIABLES.
Paired Data and the Rectangular Coordinate System.
The Slope of a Line.
The Equation of a Line.
Linear Inequalities in Two Variables.
Introduction to Functions.
Function Notation.
Algebra with Functions.
Variation.
Summary.
Review. Test.
Cumulative Review.
Projects.
3. SYSTEMS OF LINEAR EQUATIONS AND INEQUALITIES.
Systems of Linear Equations in Two Variables.
Systems of Linear Equations in Three Variables.
Introduction to Determinants. CramerÆs Rule.
Applications.
Systems of Linear Inequalities.
Summary.
Review.
Test.
Cumulative Review.
Projects.
4. RATIONAL EXPRESSIONS AND RATIONAL FUNCTIONS.
Basic Properties and Reducing to Lower Terms.
Division of Polynomials.
Multiplication and Division of Rational Expressions.
Complex Fractions.
Equations Involving Rational Expressions.
Applications.
Summary.
Review.
Test. Cumulative Review.
Projects.
5. RATIONAL EXPONENTS AND ROOTS.
Rational Exponents.
More Expressions Involving Rational Exponents.
Simplified Form for Radicals.
Addition and Subtraction of Radical Expressions.
Multiplication and Division of Radical Expressions.
Equations with Radicals.
Complex Numbers.
Summary.
Review.
Test.
Cumulative Review.
Projects.
6. QUADRATIC FUNCTIONS.
Completing the Square.
The Quadratic Formula.
Additional Items Involving Solutions to Equations. Equations in Quadratic Form.
Graphing Parabolas.
Quadratic Inequalities.
Summary.
Review.
Test.
Cumulative Review. Projects.
7. EXPONENTIAL AND LOGARITHMIC FUNCTIONS.
Exponential Functions.
The Inverse of a Function.
Logarithms Are Exponents.
Properties of Logarithms.
Common Logarithms and Natural Logarithms.
Exponential Equations and Change of Base.
Summary.
Review.
Test.
Cumulative Review.
Projects.
8. SEQUENCES AND SERIES.
Sequences.
Series.
Arithmetic Sequences.
Geometric Sequences.
The Binomial Expansion .
Summary.
Review.
Test.
Cumulative Review.
Projects.
9. CONIC SECTIONS.
The Circle.
Ellipses and Hyperbolas.
Second-Degree Inequalities and Nonlinear Systems.
Summary. Review.
Test.
Cumulative Review.
Projects.
10. INTRODUCTION TO TRIGONOMETRY.
Degrees, Radians, and Special Triangles. Trigonometric Functions.
Trigonometric Functions and Calculators.
Graphing 1: Amplitude and Period.
Graphing II: Phase Shift.
Finding an Equation from Its Graph.
Inverse Trigonometric Functions.
Summary.
Review.
Test.
Cumulative Review.
Projects.
11. TRIGONOMETRIC IDENTITIES AND EQUATIONS.
Introduction to Identities.
Proving Identities.
Sum and Difference Formulas.
Double-Angle and Half-Angle Formulas.
Solving Trigonometric Equations.
Summary.
Review. Test.
Cumulative Review.
Projects.
12. TRIANGLES.
Definition II: Right Triangle Trigonometry.
The Law of Sines. The Ambiguous Case.
The Law of Cosines.
Summary.
Review.
Test.
Cumulative Review.
Projects.
APPENDIXES.
A: Synthetic Division.
B: Matrix Solutions to Linear Systems.
C: Conditional Statements.
D: Answers to Odd-Numbered Problems, Chapter Reviews, Chapter Tests, and Cumulative Reviews.