Algebra Foundations: Basic Mathematics, Introductory Algebra, and Intermediate Algebra, 1st edition

Published by Pearson (April 10, 2015) © 2015

  • Marvin L. Bittinger Indiana University Indianapolis
  • Judith A. Beecher Indiana University Indianapolis
  • Barbara L. Johnson Indiana University Indianapolis
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1. Whole Numbers

1.1 Standard Notation

1.2 Addition

1.3 Subtraction

1.4 Multiplication

1.5 Division

            Mid-Chapter Review

1.6 Rounding and Estimating; Order

1.7 Solving Equations

1.8 Applications and Problem Solving

            Translating for Success

1.9 Exponential Notation and Order of Operations

            Summary and Review

            Test

 

2. Fraction Notation: Multiplication and Division

2.1 Factorizations

2.2 Divisibility

2.3 Fractions and Fraction Notation

2.4 Multiplication and Applications

2.5 Simplifying

            Mid-Chapter Review

2.6 Multiplying, Simplifying, and Applications

2.7 Division and Applications

            Translating for Success

            Summary and Review

            Test

 

3. Fraction Notation and Mixed Numerals

3.1 Least Common Multiples

3.2 Addition and Applications

3.3 Subtraction, Order, and Applications

            Translating for Success

3.4 Mixed Numerals

            Mid-Chapter Review

3.5 Addition and Subtraction Using Mixed Numerals; Applications

3.6 Multiplication and Division Using Mixed Numerals; Applications

            Translating for Success

3.7 Order of Operations, Complex Fractions, and Estimation

            Summary and Review

            Test

            Cumulative Review

 

4. Decimal Notation

4.1 Decimal Notation, Order, and Rounding

4.2 Addition and Subtraction

4.3 Multiplication

4.4 Division

            Mid-Chapter Review

4.5 Converting from Fraction Notation

to Decimal Notation

4.6 Estimating

4.7 Applications and Problem Solving

            Translating for Success

            Summary and Review

            Test

            Cumulative Review

 

5. Ratio and Proportion

5.1 Introduction to Ratios

5.2 Rates and Unit Prices

5.3 Proportions

            Mid-Chapter Review

5.4 Applications of Proportions

            Translating for Success

5.5 Geometric Applications

            Summary and Review

            Test

            Cumulative Review

 

6. Percent Notation

6.1 Percent Notation

6.2 Percent Notation and Fraction Notation

6.3 Solving Percent Problems Using Percent Equations

6.4 Solving Percent Problems Using Proportions

            Mid-Chapter Review

6.5 Applications of Percent

            Translating for Success

6.6 Sales Tax, Commission, and Discount

6.7 Simple Interest and Compound Interest; Credit Cards

            Summary and Review

            Test

            Cumulative Review

 

7. Data, Graphs, and Statistics

7.1 Averages, Medians, and Modes

7.2 Interpreting Data from Tables and Graphs

            Mid-Chapter Review

7.3 Interpreting and Drawing Bar Graphs and Line Graphs

7.4 Interpreting and Drawing Circle Graphs

            Translating for Success

            Summary and Review

            Test

            Cumulative Review

 

8. Measurement

8.1 Linear Measures: American Units

8.2 Linear Measures: The Metric System

8.3 Converting Between American Units and Metric Units

            Mid-Chapter Review

8.4 Weight and Mass; Medical Applications

8.5 Capacity: Medical Applications

8.6 Time and Temperature

8.7 Converting Units of Area

            Translating for Success

            Summary and Review

            Test

            Cumulative Review

 

9. Geometry

9.1 Perimeter

9.2 Area

9.3 Circles

            Mid-Chapter Review

9.4 Volume

9.5 Angles and Triangles

9.6 Square Roots and the Pythagorean Theorem

            Translating for Success

            Summary and Review

            Test

            Cumulative Review

 

10. Introduction to Real Numbers and Algebraic Expressions

10.1 Introduction to Algebra

10.2 The Real Numbers

10.3 Addition of Real Numbers

10.4 Subtraction of Real Numbers

            Mid-Chapter Review

10.5 Multiplication of Real Numbers

10.6 Division of Real Numbers

10.7 Properties of Real Numbers

10.8 Simplifying Expressions;

Order of Operations

            Summary and Review

            Test

 

11. Solving Equations and Inequalities

11.1 Solving Equations: The Addition Principle

11.2 Solving Equations: The Multiplication Principle

11.3 Using the Principles Together

11.4 Formulas

            Mid-Chapter Review

11.5 Applications of Percent

11.6 Applications and Problem Solving

            Translating for Success

11.7 Solving Inequalities

11.8 Applications and Problem Solving with Inequalities

            Summary and Review

            Test

            Cumulative Review

 

12. Graphs of Linear Equations

12.1 Introduction to Graphing

12.2 Graphing Linear Equations

12.3 More with Graphing and Intercepts

            Visualizing for Success

            Mid-Chapter Review

12.4 Slope and Applications

            Summary and Review

            Test

            Cumulative Review

 

13. Polynomials: Operations

13.1 Integers as Exponents

13.2 Exponents and Scientific Notation

13.3 Introduction to Polynomials

13.4 Addition and Subtraction of Polynomials

            Mid-Chapter Review

13.5 Multiplication of Polynomials

13.6 Special Products

            Visualizing for Success

13.7 Operations with Polynomials in Several Variables

13.8 Division of Polynomials

            Summary and Review

            Test

            Cumulative Review

 

14. Polynomials: Factoring

14.1 Introduction to Factoring

14.2 Factoring Trinomials of the Type x2 + bx + c

14.3 Factoring ax2 + bx + c, a ≠ 1: The FOIL Method

14.4 Factoring ax2 + bx + c, a ≠ 1: The ac-Method

            Mid-Chapter Review

14.5 Factoring Trinomial Squares and Differences of Squares

14.6 Factoring Sums or Differences of Cubes

14.7 Factoring: A General Strategy

14.8 Solving Quadratic Equations by Factoring

14.9 Applications of Quadratic Equations

            Translating for Success

            Summary and Review

            Test

            Cumulative Review

 

15. Rational Expressions and Equations

15.1 Multiplying and Simplifying Rational Expressions

15.2 Division and Reciprocals

15.3 Least Common Multiples and Denominators

15.4 Adding Rational Expressions

15.5 Subtracting Rational Expressions

            Mid-Chapter Review

15.6 Complex Rational Expressions

15.7 Solving Rational Equations

15.8 Applications Using Rational Equations and Proportions

            Translating for Success

15.9 Variation and Applications

            Summary and Review

            Test

            Cumulative Review

 

16. Graphs, Functions, and Applications

16.1 Functions and Graphs

16.2 Finding Domain and Range

            Mid-Chapter Review

16.3 Linear Functions: Graphs and Slope

16.4 More on Graphing Linear Equations

            Visualizing for Success

16.5 Finding Equations of Lines; Applications

            Summary and Review

            Test

            Cumulative Review

 

17. Systems of Equations

17.1 Systems of Equations in Two Variables

17.2 Solving by Substitution

17.3 Solving by Elimination

17.4 Solving Applied Problems: Two Equations

            Translating for Success

            Mid-Chapter Review

17.5 Systems of Equations in Three Variables

17.6 Solving Applied Problems: Three Equations

            Summary and Review

            Test

            Cumulative Review

 

18. More on Inequalities

18.1 Sets, Inequalities, and Interval Notation

            Translating for Success

18.2 Intersections, Unions, and Compound Inequalities

            Mid-Chapter Review

18.3 Absolute-Value Equations and inequalities

18.4 Systems of Inequalities in Two Variables

            Visualizing for Success

            Summary and Review

            Test

            Cumulative Review

 

19. Radical Expressions, Equations, and Functions

19.1 Radical Expressions and Functions

19.2 Rational Numbers as Exponents

19.3 Simplifying Radical Expressions

19.4 Addition, Subtraction, and More Multiplication

            Mid-Chapter Review

19.5 More on Division of Radical Expressions

19.6 Solving Radical Equations

19.7 Applications Involving Powers and Roots

            Translating for Success

19.8 The Complex Numbers

            Summary and Review

            Test

            Cumulative Review

 

20. Quadratic Equations and Functions

20.1 The Basics of Solving Quadratic Equations

20.2 The Quadratic Formula

20.3 Applications Involving Quadratic Equations

            Translating for Success

20.4 More on Quadratic Equations

            Mid-Chapter Review

20.5 Graphing f(x) = a(x - h)2 + k

20.6 Graphing f(x) = ax2 + bx + c

            Visualizing for Success

20.7 Mathematical Modeling with Quadratic functions

20.8 Polynomial Inequalities and Rational Inequalities

            Summary and Review

            Test

            Cumulative Review

 

21. Exponential Functions and Logarithmic Functions

21.1 Exponential Functions

21.2 Composite Functions and Inverse Functions

21.3 Logarithmic Functions

21.4 Properties of Logarithmic Functions

            Mid-Chapter Review

21.5 Natural Logarithmic Functions

            Visualizing for Success

21.6 Solving Exponential Equations and Logarithmic Equations

21.7 Mathematical Modeling with Exponential Functions and Logarithmic Functions

            Translating For Success

            Summary and Review

            Test

            Cumulative Review

 

Appendices

A. Synthetic Division

B. Determinants and Cramer’s Rule

C. Elimination Using Matrices

D. The Algebra of Functions

E. Distance, Midpoints, and Circles

 

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