# Beginning and Intermediate Algebra

Problem Recognition Exercisesâ€”Addition and Subtraction of Real Numbers1.6 Multiplication and Division of Real Numbers

Problem Recognition Exercisesâ€”Adding, Subtracting, Multiplying and Dividing Real Numbers1.7 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 Decimals

Problem Recognition Exercisesâ€”Equations vs.Expressions2.4 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 Equation

Problem Recognition Exercises-Linear Equations in Two VariablesPoint-Slope FormulaApplications of Linear EquationsChapter 4: Systems of Linear Equations 4.1 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 Method

Problem Recognition Exercises: Systems of Equations4.4 Applications of Linear Equations in Three 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^-n

Problem Recognition Exercises-Properties of Exponents5.4 Scientific Notation5.5 Addition and Subtraction of Polynomials5.6 Multiplication of Polynomials5.7 Division of Polynomials

Problem Recognition Exercises-Operations on PolynomialsChapter 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 Cubes

Problem Recognition Exercises-Factoring Strategy6.7 Solving Equations Using the Zero Product Rule

Problem Recognition Exercises-Polynomial Expressions and Polynomial Equations6.8 Applications of Quadratic EquationsChapter 7: Rational Expressions and Equations 7.1 Introduction of Rational Expressions7.2 Multiplication and Division of Rational Expressions7.3 Least Common Denominator7.4 Addition and Subtraction of Rational Expressions

Problem Recognition Exercises-Operations of Rational Expressions7.5 Complex Fractions7.6 Rational Equations

Problem Recognition Exercises-Comparing Rational Equations and Rational Expressions7.7 Applications of Rational Equations and ProportionsChapter 8: Relations and Functions 8.1 Introduction of Relations8.2 Introduction of Functions8.3 Graphs of Functions

Problem Recognition Exercises: Characteristics of Relations8.4 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 Inequalities

Problem Recognition Exercises: Equations and Inequalities9.5 Linear and Compound 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 Radical

Problem Recognition Exercises: Simplifying Radical Expressions10.6 Division of Radicals and Rationalization10.7 Solving Radical Equations10.8 Complex NumbersChapter 11: Quadratic Equations, Functions and Inequalities11.1 Square Root Property and Completing the Square11.2 Quadratic Formula11.3 Equations in Quadratic Form

Problem Recognition Exercises: Quadratic and Quadratic Type Equations11.4 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 Functions

Problem Recognition Exercises: Logarithmic and Exponential Forms12.4 Properties of Logarithms12.5 The Irrational Number and change of Base12.6 Logarithmic and Exponential Equations and ApplicationsChapter 13: Conic Sections13.1 Distance Formula, Midpoint Formula, and Circles13.2 More on the Parabola13.3 The Ellipse and Hyperbola

Problem Recognition Exercises: Formulas and Conic Sections13.4 Nonlinear Systems of Equation in Two Variables13.5 Nonlinear Inequalities and Systems of InequalitiesChapter 14: Binomial Expansions, Sequences, and Series14.1 Binomial Expansions14.2 Sequences and Series14.3 Arithmetic Sequences and Series14.4 Geometric Sequences and Series

Problem Recognition Exercises: Identifying Arithmetic and Geometric SeriesAdditional Topics AppendixA.1 Mean, Median, and ModeA.2 Introduction to GeometryA.3 Solving Systems of Linear Equations Using MatricesA.4 Determinants and Cramerâ€™s Rule

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