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Beginning and Intermediate Algebra: Connecting Concepts Through Applications, 2nd Edition
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Overview
“Beginning and Intermediate Algebra: Connecting Concepts Through Applications,” 2e, helps students build algebra skills through meaningful applications and a deeper grasp of key ideas. The content develops mathematical thinking by connecting algebraic concepts to realistic problem-solving instead of focusing on procedures alone. Updated applications, current data, expanded support, and integrated learning tools help students strengthen problem-solving, communication, and critical-thinking skills while making clear connections between algebra and the real world.
R. Review of Prealgebra.
Operations with Integers. Operations with Fractions. Operations with Decimals. Operations with Percents. The Real Number System.
1. Building Blocks of Algebra.
Exponents, Order of Operations, and Properties of Real Numbers Exponents. Algebra and Working with Variables. Simplifying Expressions. Graphs and the Rectangular Coordinate System.
2. Linear Equations and Inequalities With One Variable.
Addition and Subtraction Properties of Equality. Multiplication and Division Properties of Equality. Solving Equations with Variables on Both Sides. Solving and Graphing Linear Inequalities on a Number Line.
3. Linear Equations With Two Variables.
Graphing Equations with Two Variables. Finding and Interpreting Slope. Slope-Intercept Form of Lines. Linear Equations and Their Graphs. Finding Equations of Lines.
4. Systems of Linear Equations.
Identifying Systems of Linear Equations. Solving Systems Using the Substitution Method. Solving Systems Using the Elimination Method. Solving Linear Inequalities in Two Variables Graphically.
5. Exponents and Polynomials.
Rules for Exponents. Negative Exponents and Scientific Notation. Adding and Subtracting Polynomials. Multiplying Polynomials. Dividing Polynomials.
6. Factoring and Quadratic Equations.
What It Means to Factor. Factoring Trinomials. Factoring Special Forms. Solving Quadratic Equations by Factoring.
7. Rational Expressions and Equations.
The Basics of Rational Expressions and Equations. Multiplication and Division of Rational Expressions. Addition and Subtraction of Rational Expressions. Solving Rational Equations. Proportions, Similar Triangles, and Variation.
8. Modeling Data and Functions.
Solving Linear Applications. Functions and Function Notation. Using Data to Create Scatterplots. Finding Linear Models. Combining Functions. Composing Functions.
9. Inequalities and Absolute Values.
Absolute Value Equations and Inequalities. Non-Linear Inequalities in One Variable. Solving Systems of Linear Inequalities.
10. Radical Functions.
From Squaring a Number to Roots and Radicals. Basic Operations with Radical Expressions. Multiplying and Dividing Radical Expressions. Radical Functions. Solving Radical Equations. Complex Numbers.
11. Quadratic Functions.
Quadratic Functions and Parabolas. Graphing Quadratics in Vertex Form. Finding Quadratic Models. Solving Quadratic Equations by Square Root Property and Completing the Square. Solving Quadratic Equations by Using the Quadratic Formula. Graphing Quadratics from Standard Form.
12. Exponential Functions.
Exponential Functions: Patterns of Growth and Decay. Solving Equations Using Exponent Rules. Graphing Exponential Functions. Finding Exponential Models. Exponential Growth and Decay Rates and Compounding Interest.
13. Logarithmic Functions.
Functions and Their Inverses. Logarithmic Functions. Graphing Logarithmic Functions. Properties of Logarithms. Solving Exponential Equations. Solving Logarithmic Equations.
14. Conic Sections, Sequences And Series.
Parabolas and Circles. Ellipses and Hyperbolas. Arithmetic Sequences. Geometric Sequences. Series
Appendix A: Matrices.
Appendix B: Using the Graphing Calculator.
Appendix C: Answers to Practice Problems.
Appendix D: Answers to Selected Exercises.
Operations with Integers. Operations with Fractions. Operations with Decimals. Operations with Percents. The Real Number System.
1. Building Blocks of Algebra.
Exponents, Order of Operations, and Properties of Real Numbers Exponents. Algebra and Working with Variables. Simplifying Expressions. Graphs and the Rectangular Coordinate System.
2. Linear Equations and Inequalities With One Variable.
Addition and Subtraction Properties of Equality. Multiplication and Division Properties of Equality. Solving Equations with Variables on Both Sides. Solving and Graphing Linear Inequalities on a Number Line.
3. Linear Equations With Two Variables.
Graphing Equations with Two Variables. Finding and Interpreting Slope. Slope-Intercept Form of Lines. Linear Equations and Their Graphs. Finding Equations of Lines.
4. Systems of Linear Equations.
Identifying Systems of Linear Equations. Solving Systems Using the Substitution Method. Solving Systems Using the Elimination Method. Solving Linear Inequalities in Two Variables Graphically.
5. Exponents and Polynomials.
Rules for Exponents. Negative Exponents and Scientific Notation. Adding and Subtracting Polynomials. Multiplying Polynomials. Dividing Polynomials.
6. Factoring and Quadratic Equations.
What It Means to Factor. Factoring Trinomials. Factoring Special Forms. Solving Quadratic Equations by Factoring.
7. Rational Expressions and Equations.
The Basics of Rational Expressions and Equations. Multiplication and Division of Rational Expressions. Addition and Subtraction of Rational Expressions. Solving Rational Equations. Proportions, Similar Triangles, and Variation.
8. Modeling Data and Functions.
Solving Linear Applications. Functions and Function Notation. Using Data to Create Scatterplots. Finding Linear Models. Combining Functions. Composing Functions.
9. Inequalities and Absolute Values.
Absolute Value Equations and Inequalities. Non-Linear Inequalities in One Variable. Solving Systems of Linear Inequalities.
10. Radical Functions.
From Squaring a Number to Roots and Radicals. Basic Operations with Radical Expressions. Multiplying and Dividing Radical Expressions. Radical Functions. Solving Radical Equations. Complex Numbers.
11. Quadratic Functions.
Quadratic Functions and Parabolas. Graphing Quadratics in Vertex Form. Finding Quadratic Models. Solving Quadratic Equations by Square Root Property and Completing the Square. Solving Quadratic Equations by Using the Quadratic Formula. Graphing Quadratics from Standard Form.
12. Exponential Functions.
Exponential Functions: Patterns of Growth and Decay. Solving Equations Using Exponent Rules. Graphing Exponential Functions. Finding Exponential Models. Exponential Growth and Decay Rates and Compounding Interest.
13. Logarithmic Functions.
Functions and Their Inverses. Logarithmic Functions. Graphing Logarithmic Functions. Properties of Logarithms. Solving Exponential Equations. Solving Logarithmic Equations.
14. Conic Sections, Sequences And Series.
Parabolas and Circles. Ellipses and Hyperbolas. Arithmetic Sequences. Geometric Sequences. Series
Appendix A: Matrices.
Appendix B: Using the Graphing Calculator.
Appendix C: Answers to Practice Problems.
Appendix D: Answers to Selected Exercises.
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