Intermediate Algebra for College Students

1. Algebra, Mathematical Models, and Problem Solving

1.1 Algebraic Expressions, Real Numbers, and Interval Notation

1.2 Operations with Real Numbers and Simplifying Algebraic Expressions

1.3 Graphing Equations

1.4 Solving Linear Equations

            Mid-Chapter Check Point

1.5 Problem Solving and Using Formulas

1.6 Properties of Integral Exponents

1.7 Scientific Notation

 

2. Functions and Linear Functions

2.1 Introduction to Functions

2.2 Graphs of Functions

2.3 The Algebra of Functions

            Mid-Chapter Check Point

2.4 Linear Functions and Slope

2.5 The Point-Slope Form of the Equation of a Line

 

3. Systems of Linear Equations

3.1 Systems of Linear Equations in Two Variables

3.2 Problem Solving and Business Applications Using Systems of Equations

3.3 Systems of Linear Equations in Three Variables

            Mid-Chapter Check Point

3.4 Matrix Solutions to Linear Systems

3.5 Determinants and Cramer’s Rule

 

4. Inequalities and Problem Solving

4.1 Solving Linear Inequalities

4.2 Compound Inequalities

4.3 Equations and Inequalities Involving Absolute Value

            Mid-Chapter Check Point

4.4 Linear Inequalities in Two Variables

4.5 Linear Programming

 

5. Polynomials, Polynomial Functions, and Factoring

5.1 Introduction to Polynomials and Polynomial Functions

5.2 Multiplication of Polynomials

5.3 Greatest Common Factors and Factoring by Grouping

5.4 Factoring Trinomials

            Mid-Chapter Check Point

5.5 Factoring Special Forms

5.6 A General Factoring Strategy

5.7 Polynomial Equations and Their Applications

 

6. Rational Expressions, Functions, and Equations

6.1 Rational Expressions and Functions; Multiplying and Dividing

6.2 Adding and Subtracting Rational Expressions

6.3 Complex Rational Expressions

6.4 Division of Polynomials

            Mid-Chapter Check Point

6.5 Synthetic Division and the Remainder Theorem

6.6 Rational Equations

6.7 Formulas and Applications of Rational Equations

6.8 Modeling Using Variation

 

7. Radicals, Radical Functions, and Rational Exponents

7.1 Radical Expressions and Functions

7.2 Rational Exponents

7.3 Multiplying and Simplifying Radical Expressions

7.4 Adding, Subtracting, and Dividing Radical Expressions

            Mid-Chapter Check Point

7.5 Multiplying with More Than One Term and Rationalizing Denominators

7.6 Radical Equations

7.7 Complex Numbers

 

8. Quadratic Equations and Functions

8.1 The Square Root Property and Completing the Square

8.2 The Quadratic Formula

8.3 Quadratic Functions and Their Graphs

            Mid-Chapter Check Point

8.4 Equations Quadratic in Form

8.5 Polynomial and Rational Inequalities

 

9. Exponents and Logarithmic Functions

9.1 Exponential Functions

9.2 Composite and Inverse Functions

9.3 Logarithmic Functions

9.4 Properties of Logarithms

            Mid-Chapter Check Point

9.5 Exponential and Logarithmic Equations

9.6 Exponential Growth and Decay; Modeling Data

 

10. Conic Sections and Systems of Nonlinear Equations

10.1 Distance and Midpoint Formulas; Circles

10.2 The Ellipse

10.3 The Hyperbola

            Mid-Chapter Check Point

10.4 The Parabola; Identifying Conic Sections

10.5 Systems of Nonlinear Equations in Two Variables

 

11. Sequences, Series, and the Binomial Theorem

11.1 Sequences and Summation Notation

11.2 Arithmetic Sequences

11.3 Geometric Sequences and Series

            Mid-Chapter Check Point

11.4 The Binomial Theorem