Intermediate Algebra

Chapter R Review of Basic Algebra

Part 1 Operations

R.1 The Set of Real Numbers

R.2 Operations with Real Numbers

R.3 Exponential Notation and Order of Operations

Part 2 Manipulations

R.4 Introduction to Algebraic Expressions

R.5 Equivalent Algebraic Expressions

R.6 Simplifying Algebraic Expressions

R.7 Properties of Exponents and Scientific Notation

 

Chapter 1 Solving Linear Equations and Inequalities

1.1 Solving Equations

1.2 Formulas and Applications

1.3 Applications and Problem Solving

1.4 Sets, Inequalities, and Interval Notation

1.5 Intersections, Unions, and Compound Inequalities

1.6 Absolute-Value Equations and Inequalities

 

Chapter 2 Graphs, Functions, and Applications

2.1 Graphs of Equations

2.2 Functions and Graphs

2.3 Finding Domain and Range

2.4 Linear Functions: Graphs and Slope

2.5 More on Graphing Linear Equations

2.6 Finding Equations of Lines: Applications

 

Chapter 3 Systems of Equations

3.1 Systems of Equations in Two Variables

3.2 Solving by Substitution

3.3 Solving by Elimination

3.4 Solving Applied Problems: Two Equations

3.5 Systems of Equations in Three Variables

3.6 Solving Applied Problems: Three Equations

3.7 Systems of Inequalities in Two Variables

3.8 Business and Economics Applications

 

Chapter 4 Polynomials and Polynomial Functions

4.1 Introduction to Polynomials and Polynomial Functions

4.2 Multiplication of Polynomials

4.3 Introduction to Factoring

4.4 Factoring Trinomials: x2 + bx + c

4.5 Factoring Trinomials: ax2 + bx + c, a ≠ 1

4.6 Special Factoring

4.7 Factoring: A General Strategy

4.8 Applications of Polynomial Equations and Functions

 

Chapter 5 Rational Expressions, Equations, and Functions

5.1 Rational Expressions and Functions:  Multiplying, Dividing, and Simplifying

5.2 LCMs, LCDs, Addition, and Subtraction

5.3 Division of Polynomials

5.4 Complex Rational Expressions

5.5 Solving Rational Equations

5.6 Applications and Proportions

5.7 Formulas and Applications

5.8 Variation and Applications

 

Chapter 6 Radical Expressions, Equations, and Functions

6.1 Radical Expressions and Functions

6.2 Rational Numbers as Exponents

6.3 Simplifying Radical Expressions

6.4 Addition, Subtraction, and More Multiplication

6.5 More on Division of Radical Expressions

6.6 Solving Radical Equations

6.7 Applications Involving Powers and Roots

6.8 The Complex Numbers

 

Chapter 7 Quadratic Equations and Functions

7.1 The Basics of Solving Quadratic Equations

7.2 The Quadratic Formula

7.3 Applications Involving Quadratic Equations

7.4 More on Quadratic Equations

7.5 Graphing f(x) = a(x — h)2 + k

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

7.7 Mathematical Modeling with Quadratic Functions

7.8 Polynomial and Rational Inequalities

 

Chapter 8 Exponential and Logarithmic Functions

8.1 Exponential Functions

8.2 Inverse and Composite Functions

8.3 Logarithmic Functions

8.4 Properties of Logarithmic Functions

8.5 Natural Logarithmic Functions

8.6 Solving Exponential and Logarithmic Equations

8.7 Mathematical Modeling with Exponential and Logarithmic Functions

 

Chapter 9 Conic Sections

9.1 Parabolas and Circles

9.2 Ellipses

9.3 Hyperbolas

9.4 Nonlinear Systems of Equations     

 

Appendixes    

A Handling Dimension Symbols

B Determinants and Cramer’s Rule

C Elimination Using Matrices

D The Algebra of Functions