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For college-level courses of combined introductory and intermediate algebra.
Elayn Martin-Gay's success as a developmental math author and teacher starts with a strong focus on mastering the basics through well-written explanations, innovative pedagogy and a meaningful, integrated program of learning resources. The revisions provide new pedagogy and resources to build student confidence, help students develop basic skills and understand concepts, and provide the highest level of instructor and adjunct support.
Martin-Gay's series is well known and widely praised for an unparalleled ability to:
Martin-Gay believes that every student can succeed, and with each successive edition enhances her pedagogy and learning resources to provide evermore relevant and useful tools to help students and instructors achieve success.
1. Review of Real Numbers
1.1 Tips for Success in Mathematics
1.2 Symbols and Sets of Numbers
1.3 Fractions
1.4 Introduction to Variable Expressions and Equations
1.5 Adding Real Numbers
1.6 Subtracting Real Numbers
1.7 Multiplying and Dividing Real Numbers
Integrated Review--Operations on Real Numbers
1.8 Properties of Real Numbers
2. Equations and Problem Solving
2.1 Simplifying Expressions
2.2 The Addition and Multiplication Properties of Equality
2.3 Solving Linear Equations
Integrated Review--Solving Linear Equations
2.4 An Introduction to Problem Solving
2.5 Formulas and Problem Solving
2.6 Further Problem Solving
2.7 Solving Linear Inequalities
3. Graphing
3.1 Reading Graphs and the Rectangular Coordinate System
3.2 Graphing Linear Equations
3.3 Intercepts
3.4 Slope and Rate of Change
Integrated Review--Summary on Slope and Graphing Linear Equations
3.5 The Slope-Intercept Form
3.6 The Point Slope Form
3.7 Functions
4. Systems of Linear Equations
4.1 Solving Systems of Linear Equations by Graphing
4.2 Solving Systems of Linear Equations by Substitution
4.3 Solving Systems of Linear Equations by Addition
4.4 Solving Systems of Linear Equations in Three Variables
Integrated Review--Systems of Equations
4.5 Systems of Linear Equations and Problem Solving
5. Exponents and Polynomials
5.1 Exponents
5.2 Polynomial Functions and Adding and Subtracting Polynomials
5.3 Multiplying Polynomials
5.4 Special Products
Integrated Review--Exponents and Operations on Polynomials
5.5 Negative Exponents and Scientific Notation
5.6 Dividing Polynomials
5.7 Synthetic Division and the Remainder Theorem
6. Factoring Polynomials
6.1 The Greatest Common Factor and Factoring by Grouping
6.2 Factoring Trinomials of the Form x2 + bx + c
6.3 Factoring Trinomials of the Form ax2 + bx + c
6.4 Factoring Binomials
Integrated Review--Choosing a Factoring Strategy
6.5 Solving Quadratic Equations by Factoring
6.6 Quadratic Equations and Problem Solving
7. Rational Expressions
7.1 Rational Functions and Simplifying Rational Expressions
7.2 Multiplying and Dividing Rational Expressions
7.3 Adding and Subtracting Rational Expressions with Common Denominators and Least Common Denominator
7.4 Adding and Subtracting Rational Expressions with Unlike Denominators
7.5 Solving Equations Containing Rational Expressions
Integrated Review--Summary on Rational Expressions
7.6 Proportion and Problem Solving with Rational Equations
7.7 Simplifying Complex Fractions
8. Functions and Graphs
8.1 Graphing and Writing Linear Functions
8.2 Graphing Nonlinear Functions
Integrated Review--Summary on Functions
8.3 The Algebra of Functions; Composite Functions
8.4 Variation and Problem Solving
9. Inequalities and Absolute Value
9.1 Compound Inequalities
9.2 Absolute Value Equations
9.3 Absolute Value Inequalities
Integrated Review--Solving Equations and Inequalities
9.4 Graphing Linear Inequalities in Two Variables and Systems of Linear Inequalities
10. Radicals, Rational Exponents, and Complex Numbers
10.1 Radicals and Radical Functions
10.2 Rational Exponents
10.3 Simplifying Radical Expressions
10.4 Adding and Subtracting and Multiplying Radical Expressions
10.5 Rationalizing Denominators and Numerators of Radical Expressions
Integrated Review-- Radicals and Rational Exponents
10.6 Radical Equations and Problem Solving
10.7 Complex Numbers
11. Quadratic Equations and Functions
11.1 Solving Quadratic Equations by Completing the Square
11.2 Solving Quadratic Equations by the Quadratic Formula
11.3 Solving Equations by Using Quadratic Methods
Integrated Review--Summary on Solving Quadratic Equations
11.4 Nonlinear Inequalities in One Variable
11.5 Quadratic Functions and Their Graphs
11.6 Further Graphing of Quadratic Functions
12. Exponential and Logarithmic Functions
12.1 Inverse Functions
12.2 Exponential Functions
12.3 Logarithmic Functions
12.4 Properties of Logarithms
Integrated Review--Functions and Properties of Logarithms
12.5 Common Logarithms, Natural Logarithms, and Change of Base
12.6 Exponential and Logarithmic Equations and Applications
13. Conic Sections
13.1 The Parabola and the Circle
13.2 The Ellipse and the Hyperbola
Integrated Review--Graphing Conic Sections
13.3 Solving Nonlinear Systems of Equations
13.4 Nonlinear Inequalities and Systems of Inequalities
14. Sequences, Series, and the Binomial Theorem
14.1 Sequences
14.2 Arithmetic and Geometric Sequences
14.3 Series
Integrated Review--Sequences and Series
14.4 Partial Sums of Arithmetic and Geometric Sequences
14.5 The Binomial Theorem
Appendix A - Review of Algebra Topics
1. Equations and Inequalities
2. Problem Solving
3. Graphing
4. Polynomials and Factoring
5. Rational Expressions
Appendix B - Solving Systems of Equations by Matrices
Appendix C - Solving Systems of Equations by Determinants
For college-level courses of combined introductory and intermediate algebra.
Elayn Martin-Gay's success as a developmental math author and teacher starts with a strong focus on mastering the basics through well-written explanations, innovative pedagogy and a meaningful, integrated program of learning resources. The revisions provide new pedagogy and resources to build student confidence, help students develop basic skills and understand concepts, and provide the highest level of instructor and adjunct support.
Martin-Gay's series is well known and widely praised for an unparalleled ability to:
Martin-Gay believes that every student can succeed, and with each successive edition enhances her pedagogy and learning resources to provide evermore relevant and useful tools to help students and instructors achieve success.
Table of Contents
1. Review of Real Numbers
1.1 Tips for Success in Mathematics
1.2 Symbols and Sets of Numbers
1.3 Fractions
1.4 Introduction to Variable Expressions and Equations
1.5 Adding Real Numbers
1.6 Subtracting Real Numbers
1.7 Multiplying and Dividing Real Numbers
Integrated Review--Operations on Real Numbers
1.8 Properties of Real Numbers
2. Equations and Problem Solving
2.1 Simplifying Expressions
2.2 The Addition and Multiplication Properties of Equality
2.3 Solving Linear Equations
Integrated Review--Solving Linear Equations
2.4 An Introduction to Problem Solving
2.5 Formulas and Problem Solving
2.6 Further Problem Solving
2.7 Solving Linear Inequalities
3. Graphing
3.1 Reading Graphs and the Rectangular Coordinate System
3.2 Graphing Linear Equations
3.3 Intercepts
3.4 Slope and Rate of Change
Integrated Review--Summary on Slope and Graphing Linear Equations
3.5 The Slope-Intercept Form
3.6 The Point Slope Form
3.7 Functions
4. Systems of Linear Equations
4.1 Solving Systems of Linear Equations by Graphing
4.2 Solving Systems of Linear Equations by Substitution
4.3 Solving Systems of Linear Equations by Addition
4.4 Solving Systems of Linear Equations in Three Variables
Integrated Review--Systems of Equations
4.5 Systems of Linear Equations and Problem Solving
5. Exponents and Polynomials
5.1 Exponents
5.2 Polynomial Functions and Adding and Subtracting Polynomials
5.3 Multiplying Polynomials
5.4 Special Products
Integrated Review--Exponents and Operations on Polynomials
5.5 Negative Exponents and Scientific Notation
5.6 Dividing Polynomials
5.7 Synthetic Division and the Remainder Theorem
6. Factoring Polynomials
6.1 The Greatest Common Factor and Factoring by Grouping
6.2 Factoring Trinomials of the Form x2 + bx + c
6.3 Factoring Trinomials of the Form ax2 + bx + c
6.4 Factoring Binomials
Integrated Review--Choosing a Factoring Strategy
6.5 Solving Quadratic Equations by Factoring
6.6 Quadratic Equations and Problem Solving
7. Rational Expressions
7.1 Rational Functions and Simplifying Rational Expressions
7.2 Multiplying and Dividing Rational Expressions
7.3 Adding and Subtracting Rational Expressions with Common Denominators and Least Common Denominator
7.4 Adding and Subtracting Rational Expressions with Unlike Denominators
7.5 Solving Equations Containing Rational Expressions
Integrated Review--Summary on Rational Expressions
7.6 Proportion and Problem Solving with Rational Equations
7.7 Simplifying Complex Fractions
8. Functions and Graphs
8.1 Graphing and Writing Linear Functions
8.2 Graphing Nonlinear Functions
Integrated Review--Summary on Functions
8.3 The Algebra of Functions; Composite Functions
8.4 Variation and Problem Solving
9. Inequalities and Absolute Value
9.1 Compound Inequalities
9.2 Absolute Value Equations
9.3 Absolute Value Inequalities
Integrated Review--Solving Equations and Inequalities
9.4 Graphing Linear Inequalities in Two Variables and Systems of Linear Inequalities
10. Radicals, Rational Exponents, and Complex Numbers
10.1 Radicals and Radical Functions
10.2 Rational Exponents
10.3 Simplifying Radical Expressions
10.4 Adding and Subtracting and Multiplying Radical Expressions
10.5 Rationalizing Denominators and Numerators of Radical Expressions
Integrated Review-- Radicals and Rational Exponents
10.6 Radical Equations and Problem Solving
10.7 Complex Numbers
11. Quadratic Equations and Functions
11.1 Solving Quadratic Equations by Completing the Square
11.2 Solving Quadratic Equations by the Quadratic Formula
11.3 Solving Equations by Using Quadratic Methods
Integrated Review--Summary on Solving Quadratic Equations
11.4 Nonlinear Inequalities in One Variable
11.5 Quadratic Functions and Their Graphs
11.6 Further Graphing of Quadratic Functions
12. Exponential and Logarithmic Functions
12.1 Inverse Functions
12.2 Exponential Functions
12.3 Logarithmic Functions
12.4 Properties of Logarithms
Integrated Review--Functions and Properties of Logarithms
12.5 Common Logarithms, Natural Logarithms, and Change of Base
12.6 Exponential and Logarithmic Equations and Applications
13. Conic Sections
13.1 The Parabola and the Circle
13.2 The Ellipse and the Hyperbola
Integrated Review--Graphing Conic Sections
13.3 Solving Nonlinear Systems of Equations
13.4 Nonlinear Inequalities and Systems of Inequalities
14. Sequences, Series, and the Binomial Theorem
14.1 Sequences
14.2 Arithmetic and Geometric Sequences
14.3 Series
Integrated Review--Sequences and Series
14.4 Partial Sums of Arithmetic and Geometric Sequences
14.5 The Binomial Theorem
Appendix A - Review of Algebra Topics
1. Equations and Inequalities
2. Problem Solving
3. Graphing
4. Polynomials and Factoring
5. Rational Expressions
Appendix B - Solving Systems of Equations by Matrices
Appendix C - Solving Systems of Equations by Determinants