Assessment and Learning in Knowledge Spaces is a Web-based, artificially intelligent assessment and learning system. ALEKS uses adaptive questioning to quickly and accurately determine exactly what a student knows and doesn't know in a course. ALEKS then instructs the student on the topics she is most ready to learn. As a student works through a course, ALEKS periodically reassesses the student to ensure that topics learned are also retained. ALEKS courses are very complete in their topic coverage and ALEKS avoids multiple-choice questions. A student who shows a high level of mastery of an ALEKS course will be successful in the actual course she is taking.

# Beginning and Intermediate Algebra 4e

### Chapter 1: Set of Real Numbers

#### 1.1 Fractions

#### 1.2 Introduction to Algebra and the Set of Real Numbers

#### 1.3 Exponents, Square Roots, and Order of Operations

#### 1.4 Addition of Real Numbers

#### 1.5 Subtraction of Real Numbers

Problem Recognition Exercises—Addition and Subtraction of Real Numbers

#### 1.6 Multiplication and Division of Real Numbers

Problem Recognition Exercises—Adding, Subtracting, Multiplying and Dividing Real Numbers

#### 1.7 Properties of Real Numbers and Simplifying Expressions

### Chapter 2: Linear Equations and Inequalities

#### 2.1 Addition, Subtraction, Multiplication, and Division Properties of Equality

#### 2.2 Solving Linear Equations

#### 2.3 Linear Equations: Clearing Fractions and Decimals

Problem Recognition Exercises—Equations vs.Expressions

#### 2.4 Applications of Linear Equations: Introduction to Problem Solving

#### 2.5 Applications Involving Percents

####

#### 2.6 Formulas and Applications of Geometry

#### 2.7 Mixture Applications and Uniform Motion

#### 2.8 Linear Inequalities

### Chapter 3: Graphing Linear Equations in Two Variables

#### 3.1 Rectangular Coordinate System

#### 3.2 Linear Equations in Two Variables

#### 3.3 Slope of a Line and Rate of Change

#### 3.4 Slope-Intercept Form of a Linear Equation

Problem Recognition Exercises-Linear Equations in Two Variables

#### Point-Slope Formula

#### Applications of Linear Equations

### Chapter 4: Systems of Linear Equations

#### 4.1 Solving Systems of Equations by the Graphing Method

#### 4.2 Solving Systems of Equations by the Substitution Method

#### 4.3 Solving Systems of Equations by the Addition Method

Problem Recognition Exercises: Systems of Equations

#### 4.4 Applications of Linear Equations in Three Variables

#### 4.5 Systems of Linear Equations in Three Variables

#### 4.6 Applications of Systems of Linear Equations in Three Variables

### Chapter 5: Polynomials and Properties of Exponents

#### 5.1 Multiplying and Dividing Expressions with Common Bases

#### 5.2 More Properties of Exponents

#### 5.3 Definitions of b^0 and b^-n

Problem Recognition Exercises-Properties of Exponents

#### 5.4 Scientific Notation

#### 5.5 Addition and Subtraction of Polynomials

#### 5.6 Multiplication of Polynomials

#### 5.7 Division of Polynomials

Problem Recognition Exercises-Operations on Polynomials

### Chapter 6: Factoring Polynomials

#### 6.1 Greatest Common Factor and Factoring by Grouping

#### 6.2 Factoring Trinomials of the Form x^2 + bx + c

#### 6.3 Factoring Trinomials: Trial-and-Error Method

#### 6.4 Factoring Trinomials: AC-Method

#### 6.5 Difference of Squares and Perfect Square Trinomials

#### 6.6 Sum and Difference of Cubes

Problem Recognition Exercises-Factoring Strategy

#### 6.7 Solving Equations Using the Zero Product Rule

Problem Recognition Exercises-Polynomial Expressions and Polynomial Equations

#### 6.8 Applications of Quadratic Equations

### Chapter 7: Rational Expressions and Equations

#### 7.1 Introduction of Rational Expressions

#### 7.2 Multiplication and Division of Rational Expressions

#### 7.3 Least Common Denominator

#### 7.4 Addition and Subtraction of Rational Expressions

Problem Recognition Exercises-Operations of Rational Expressions

#### 7.5 Complex Fractions

#### 7.6 Rational Equations

Problem Recognition Exercises-Comparing Rational Equations and Rational Expressions

#### 7.7 Applications of Rational Equations and Proportions

### Chapter 8: Relations and Functions

#### 8.1 Introduction of Relations

#### 8.2 Introduction of Functions

#### 8.3 Graphs of Functions

Problem Recognition Exercises: Characteristics of Relations

#### 8.4 Alebra of Functions and Composition

#### 8.5 Variation

### Chapter 9: More Equations and Inequalities

#### 9.1 Compound Inequalities

#### 9.2 Polynomial and Rational Enequalities

#### 9.3 Absolute Value Equations

#### 9.4 Absolute Value Inequalities

Problem Recognition Exercises: Equations and Inequalities

#### 9.5 Linear and Compound Inequalities in Two Variables

### Chapter 10: Radicals and Complex Numbers

#### 10.1 Definition of an nth Root

#### 10.2 Rational Exponents

#### 10.3 Simplifying Radical Expressions

#### 10.4 Addition and Subtraction of Radicals

#### 10.5 Multiplication of Radical

Problem Recognition Exercises: Simplifying Radical Expressions

#### 10.6 Division of Radicals and Rationalization

#### 10.7 Solving Radical Equations

#### 10.8 Complex Numbers

### Chapter 11: Quadratic Equations, Functions and Inequalities

#### 11.1 Square Root Property and Completing the Square

#### 11.2 Quadratic Formula

#### 11.3 Equations in Quadratic Form

Problem Recognition Exercises: Quadratic and Quadratic Type Equations

#### 11.4 Graphs of Quadratic Functions

#### 11.5 Vertex of a Parabola: Applications and Modeling

### Chapter 12: Exponential and Logarithmic Functions and Applications

#### 12.1 Inverse Functions

#### 12.2 Exponential Functions

#### 12.3 Logarithmic Functions

Problem Recognition Exercises: Logarithmic and Exponential Forms

#### 12.4 Properties of Logarithms

#### 12.5 The Irrational Number and change of Base

#### 12.6 Logarithmic and Exponential Equations and Applications

### Chapter 13: Conic Sections

#### 13.1 Distance Formula, Midpoint Formula, and Circles

#### 13.2 More on the Parabola

#### 13.3 The Ellipse and Hyperbola

Problem Recognition Exercises: Formulas and Conic Sections

#### 13.4 Nonlinear Systems of Equation in Two Variables

#### 13.5 Nonlinear Inequalities and Systems of Inequalities

### Chapter 14: Binomial Expansions, Sequences, and Series

#### 14.1 Binomial Expansions

#### 14.2 Sequences and Series

#### 14.3 Arithmetic Sequences and Series

#### 14.4 Geometric Sequences and Series

Problem Recognition Exercises: Identifying Arithmetic and Geometric Series

### Additional Topics Appendix

#### A.1 Mean, Median, and Mode

#### A.2 Introduction to Geometry

#### A.3 Solving Systems of Linear Equations Using Matrices

#### A.4 Determinants and Cramer’s Rule