# Beginning and Intermediate Algebra

Problem Recognition Exercises—Addition and Subtraction of Real Numbers

1.6 Multiplication and Division of Real NumbersProblem Recognition Exercises—Adding, Subtracting, Multiplying and Dividing Real Numbers

1.7 Properties of Real Numbers and Simplifying ExpressionsChapter 2: Linear Equations and Inequalities 2.1 Addition, Subtraction, Multiplication, and Division Properties of Equality2.2 Solving Linear Equations2.3 Linear Equations: Clearing Fractions and DecimalsProblem Recognition Exercises—Equations vs.Expressions

2.4 Applications of Linear Equations: Introduction to Problem Solving2.5 Applications Involving Percents2.6 Formulas and Applications of Geometry2.7 Mixture Applications and Uniform Motion2.8 Linear InequalitiesChapter 3: Graphing Linear Equations in Two Variables 3.1 Rectangular Coordinate System3.2 Linear Equations in Two Variables3.3 Slope of a Line and Rate of Change3.4 Slope-Intercept Form of a Linear EquationProblem Recognition Exercises-Linear Equations in Two Variables

3.5 Point-Slope Formula3.6 Applications of Linear EquationsChapter 4: Systems of Linear Equations in Two Variables4.1 Solving Systems of Equations by the Graphing Method4.2 Solving Systems of Equations by the Substitution Method4.3 Solving Systems of Equations by the Addition MethodProblem Recognition Exercises: Systems of Equations

4.4 Applications of Linear Equations in Two Variables4.5 Systems of Linear Equations in Three Variables4.6 Applications of Systems of Linear Equations in Three VariablesChapter 5: Polynomials and Properties of Exponents5.1 Multiplying and Dividing Expressions with Common Bases5.2 More Properties of Exponents5.3 Definitions of b^0 and b^-nProblem Recognition Exercises-Properties of Exponents

5.4 Scientific Notation5.5 Addition and Subtraction of Polynomials5.6 Multiplication of Polynomials and Special Products5.7 Division of PolynomialsProblem Recognition Exercises-Operations on Polynomials

Chapter 6: Factoring Polynomials6.1 Greatest Common Factor and Factoring by Grouping6.2 Factoring Trinomials of the Form x^2 + bx + c6.3 Factoring Trinomials: Trial-and-Error Method6.4 Factoring Trinomials: AC-Method6.5 Difference of Squares and Perfect Square Trinomials6.6 Sum and Difference of CubesProblem Recognition Exercises-Factoring Strategy

6.7 Solving Equations Using the Zero Product RuleProblem Recognition Exercises-Polynomial Expressions Versus Polynomial Equations

6.8 Applications of Quadratic EquationsChapter 7: Rational Expressions and Equations 7.1 Introduction to Rational Expressions7.2 Multiplication and Division of Rational Expressions7.3 Least Common Denominator7.4 Addition and Subtraction of Rational ExpressionsProblem Recognition Exercises-Operations of Rational Expressions

7.5 Complex Fractions7.6 Rational EquationsProblem Recognition Exercises-Comparing Rational Equations and Rational Expressions

7.7 Applications of Rational Equations and ProportionsChapter 8: Relations and Functions 8.1 Introduction of Relations8.2 Introduction of Functions8.3 Graphs of FunctionsProblem Recognition Exercises: Characteristics of Relations

8.4 Alebra of Functions and Composition8.5 VariationChapter 9: More Equations and Inequalities9.1 Compound Inequalities9.2 Polynomial and Rational Enequalities9.3 Absolute Value Equations9.4 Absolute Value InequalitiesProblem Recognition Exercises: Equations and Inequalities

9.5 Linear Inequalities and Systems of Linear Inequalities in Two VariablesChapter 10: Radicals and Complex Numbers10.1 Definition of an nth Root10.2 Rational Exponents10.3 Simplifying Radical Expressions10.4 Addition and Subtraction of Radicals10.5 Multiplication of RadicalsProblem Recognition Exercises: Simplifying Radical Expressions

10.6 Division of Radicals and Rationalization10.7 Solving Radical Equations10.8 Complex NumbersChapter 11: Quadratic Equations and Functions11.1 Square Root Property and Completing the Square11.2 Quadratic Formula11.3 Equations in Quadratic FormProblem Recognition Exercises: Quadratic and Quadratic Type Equations

11.4 Graphs of Quadratic Functions11.5 Vertex of a Parabola: Applications and ModelingChapter 12: Exponential and Logarithmic Functions and Applications12.1 Inverse Functions12.2 Exponential Functions12.3 Logarithmic FunctionsProblem Recognition Exercises: Identifying Graphs of Functions

12.4 Properties of Logarithms12.5 The Irrational Number e and change of BaseProblem Recognition Exercises: Formulas and Conic Sections

13.4 Nonlinear Systems of Equation in Two Variables13.5 Nonlinear Inequalities and Systems of Inequalities in Two VariablesChapter 14: Binomial Expansions, Sequences, and Series14.1 Binomial Expansions14.2 Sequences and Series14.3 Arithmetic Sequences and Series14.4 Geometric Sequences and SeriesProblem Recognition Exercises: Identifying Arithmetic and Geometric Series

Chapter 15 (Online): Transformations, Piecewise-Defined Functions, and Probability15.1 Transformations of Graphs and Piecewise-Defined Functions15.2 Fundamentals of Counting15.3 Introduction to ProbabilityAdditional Topics AppendixA.1 Additional FactoringA.2 Mean, Median, and ModeA.3 Introduction to GeometryA.4 Solving Systems of Linear Equations Using MatricesA.5 Determinants and Cramer’s RuleLeaves warehouse in 5 - 8 business days

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