Algebra Foundations: Prealgebra, Introductory Algebra, & Intermediate Algebra, 1st edition

  • Elayn Martin-Gay

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Elayn Martin-Gay's developmental math program is motivated by her firm belief that every student can succeed. The new All in One, Algebra Foundations: Prealgebra, Introductory Algebra, & Intermediate Algebra offers everything needed to teach the full developmental math sequence in one flexible course solution. Martin-Gay's focus on the student shapes her clear, accessible writing, inspires her constant pedagogical innovations, and contributes to the popularity and effectiveness of her video resources. This new All in One continues her focus on students and what they need to be successful.

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Table of contents

1. The Whole Numbers

1.1 Study Skill Tips for Success in Mathematics

1.2 Place Value, Names for Numbers, and Reading Tables

1.3 Adding and Subtracting Whole Numbers, and Perimeter

1.4 Rounding and Estimating

1.5 Multiplying Whole Numbers and Area

1.6 Dividing Whole Numbers

            Integrated Review–Operations on Whole Numbers

1.7 Exponents and Order of Operations

1.8 Introduction to Variables, Algebraic Expressions, and Equations


2. Integers and Introduction to Solving Equations

2.1 Introduction to Integers

2.2 Adding Integers

2.3 Subtracting Integers

2.4 Multiplying and Dividing Integers

            Integrated Review–Integers

2.5 Order of Operations

2.6 Solving Equations: The Addition and Multiplication Properties


3. Solving Equations and Problem Solving

3.1 Simplifying Algebraic Expressions

3.2 Solving Equations: Review of the Addition and Multiplication Properties

            Integrated Review–Expressions and Equations

3.3 Solving Linear Equations in One Variable

3.4 Linear Equations in One Variable and Problem Solving


4. Fractions and Mixed Numbers

4.1 Introduction to Fractions and Mixed Numbers

4.2 Factors and Simplest Form

4.3 Multiplying and Dividing Fractions

4.4 Adding and Subtracting Like Fractions, Least Common Denominator, and Equivalent Fractions

4.5 Adding and Subtracting Unlike Fractions

            Integrated Review–Summary on Fractions and Operations on Fractions

4.6 Complex Fractions and Review of Order of Operations

4.7 Operations on Mixed Numbers

4.8 Solving Equations Containing Fractions


5. Decimals

5.1 Introduction to Decimals

5.2 Adding and Subtracting Decimals

5.3 Multiplying Decimals and Circumference of a Circle

5.4 Dividing Decimals

            Integrated Review–Operations on Decimals

5.5 Fractions, Decimals, and Order of Operations

5.6 Solving Equations Containing Decimals

5.7 Decimal Applications: Mean, Median, and Mode


6. Ratio, Proportion, and Percent

6.1 Ratio and Proportion

6.2 Percents, Decimals, and Fractions

6.3 Solving Percent Problems with Equations

6.4 Solving Percent Problems with Proportions

            Integrated Review–Ratio, Proportion, and Percent

6.5 Applications of Percent

6.6 Percent and Problem Solving: Sales Tax, Commission, and Discount

6.7 Percent and Problem Solving: Interest


7. Graphs and Triangle Applications

7.1 Reading Pictographs, Bar Graphs, Histograms, and Line Graphs

7.2 Reading and Drawing Circle Graphs

Integrated Review–Reading Graphs

7.3 Square Roots and the Pythagorean Theorem

7.4 Congruent and Similar Triangles

7.5 Counting and Introduction to Probability


8. Geometry and Measurement

8.1 Lines and Angles

8.2 Perimeter

8.3 Area, Volume, and Surface Area

            Integrated Review–Geometry Concepts

8.4 Linear Measurement

8.5 Weight and Mass

8.6 Capacity

8.7 Temperature and Conversions Between the U.S. and Metric Systems


9. Equations, Inequalities, and Problem Solving

9.1 Symbols and Sets of Numbers

9.2 Properties of Real Numbers

9.3 Further Solving Linear Equations

            Integrated Review–Real Numbers and Solving Linear Equations

9.4 Further Problem Solving

9.5 Formulas and Problem Solving

9.6 Linear Inequalities and Problem Solving


10. Graphing

10.1 Reading Graphs and the Rectangular Coordinate System

10.2 Graphing Linear Equations

10.3 Intercepts

10.4 Slope and Rate of Change

            Integrated Review–Summary on Slope and Graphing Linear Equations

10.5 Equation of Lines

10.6 Functions


11. Solving Systems of Linear Equations

11.1 Solving Systems of Linear Equations by Graphing

11.2 Solving Systems of Linear Equations by Substitution

11.3 Solving Systems of Linear Equations by Addition

            Integrated Review–Solving Systems of Equations

11.4 Solving Systems of Linear Equations in Three Variables

11.5 Systems of Linear Equations and Problem Solving


12. Exponents and Polynomials

12.1 Exponents

12.2 Polynomial Functions and Adding and Subtracting Polynomials

12.3 Multiplying Polynomials

12.4 Special Products

            Integrated Review–Exponents and Operations on Polynomials

12.5 Negative Exponents and Scientific Notation

12.6 Dividing Polynomials

12.7 Synthetic Division and the Remainder Theorem


13. Factoring Polynomials

13.1 The Greatest Common Factor and Factoring by Grouping

13.2 Factoring Trinomials of the Form x2 + bx + c

13.3 Factoring Trinomials of the Form ax2 + bx + c and Perfect Square Trinomials

13.4 Factoring Trinomials of the Form ax2 + bx + c by Grouping

13.5 Factoring Binomials

            Integrated Review–Choosing a Factoring Strategy

13.6 Solving Quadratic Equations by Factoring

13.7 Quadratic Equations and Problem Solving


14. Rational Expressions

14.1 Rational Functions and Simplifying Rational Expressions

14.2 Multiplying and Dividing Rational Expressions

14.3 Adding and Subtracting Rational Expressions with Common Denominators and Least Common Denominator

14.4 Adding and Subtracting Rational Expressions with Unlike Denominators

14.5 Solving Equations Containing Rational Expressions

            Integrated Review–Summary on Rational Expressions

14.6 Problem Solving with Proportions and Rational Equations

14.7 Simplifying Complex Fractions


15. More on Functions and Graphs

15.1 Graphing and Writing Linear Functions

15.2 Reviewing Function Notation and Graphing Nonlinear Functions

            Integrated Review–Summary on Functions and Equations of Lines

15.3 Graphing Piecewise-Defined Functions and Shifting and Reflecting Graphs of Functions

15.4 Variation and Problem Solving


16. Inequalities and Absolute Value

16.1 Compound Inequalities

16.2 Absolute Value Equations

16.3 Absolute Value Inequalities

            Integrated Review–Solving Compound Inequalities and Absolute Value Equations and Inequalities

16.4 Graphing Linear Inequalities in Two Variables and Systems of Linear Inequalities


17. Rational Exponents, Radicals, and Complex Numbers

17.1 Radicals and Radical Functions

17.2 Rational Exponents

17.3 Simplifying Radical Expressions

17.4 Adding, Subtracting, and Multiplying Radical Expressions

17.5 Rationalizing Denominators and Numerators of Radical Expressions

            Integrated Review–Radicals and Rational Exponents

17.6 Radical Equations and Problem Solving

17.7 Complex Numbers


18. Quadratic Equations and Functions

18.1 Solving Quadratic Equations by Completing the Square

18.2 Solving Quadratic Equations by the Quadratic Formula

18.3 Solving Equations by Using Quadratic Methods

            Integrated Review–Summary on Solving Quadratic Equations

18.4 Nonlinear Inequalities in One Variable

18.5 Quadratic Functions and Their Graphs

18.6 Further Graphing of Quadratic Functions


19. Exponential and Logarithmic Functions

19.1 The Algebra of Functions: Composite Functions

19.2 Inverse Functions

19.3 Exponential Functions

19.4 Exponential Growth and Decay Functions

19.5 Logarithmic Functions

19.6 Properties of Logarithms

            Integrated Review–Functions and Properties of Logarithms

19.7 Common Logarithms, Natural Logarithms, and Change of Base

19.8 Exponential and Logarithmic Equations and Problem Solving


20. Conic Sections

20.1 The Parabola and the Circle

20.2 The Ellipse and the Hyperbola

            Integrated Review–Graphing Conic Sections

20.3 Solving Nonlinear Systems of Equations

20.4 Nonlinear Inequalities and Systems of Inequalities


21. Sequences, Series, and the Binomial Theorem

21.1 Sequences

21.2 Arithmetic and Geometric Sequences

21.3 Series

            Integrated Review–Sequences and Series

21.4 Partial Sums of Arithmetic and Geometric Sequences

21.5 The Binomial Theorem



Appendix A    Tables

A.1 Table of Geometric Figures

A.2 Table of Percents, Decimals, and Fraction Equivalents

A.3 Table on Finding Common Percents of a Number

A.4 Table of Squares and Square Roots

A.5 Geometric Formulas


Appendix B      Review of Algebra Topics

B.1 Equations (Linear and Quadratic Solved by Factoring)

B.2 Mixture and Uniform Motion Problem Solving

B.3 Graphing

B.4 Polynomials and Factoring

B.5 Rational Expressions


Appendix C. Stretching and Compressing Graphs of Absolute Value Functions

Appendix D. An Introduction to Using a Graphing Utility

Appendix E. Solving Systems of Equations by Matrices

Appendix F. Solving Systems of Equations by Determinants

    Student Resources

    Study Skills Builders

    Bigger Picture-Study Guide Outline

    Practice Final Exam

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Published by Pearson (August 17th 2017) - Copyright © 2015