Precalculus © 2017

Chapter R:Review of Prerequisites

SectionR.1Sets and the Real Number LineSectionR.2Exponents and RadicalsSectionR.3Polynomials and Factoring Obj 8Factor Expressions Containing Negative and Rational ExponentsProblem Recognition Exercises Simplifying Algebraic ExpressionsSectionR.4Rational Expressions and More Operations on RadicalsSectionR.5EquationsSection R.6Complex Numbers and Equations with Complex SolutionsSectionR.7Linear, Compound, and Absolute Value InequalitiesSectionR.8Applications of Equations and Inequalities

Chapter 1:Functions and Relations

Section1.1The Rectangular Coordinate System and Graphing UtilitiesSection1.2CirclesSection1.3Functions and RelationsSection1.4Linear Equations in Two Variables and Linear FunctionsSection1.5Applications of Linear Equations and ModelingProblem Recognition Exercises Comparing Graphs of EquationsSection1.6Transformations of GraphsSection1.7Analyzing Graphs of Functions and Piecewise-Defined FunctionsSection1.8Algebra of Functions and Function Composition

Chapter 2:Polynomial and Rational Functions

Section2.1Quadratic Functions and ApplicationsSection2.2Introduction to Polynomial FunctionsSection2.3Division of Polynomials and the Remainder and Factor TheoremsSection2.4Zeros of PolynomialsSection2.5Rational FunctionsProblem Recognition Exercises Polynomial and Rational FunctionsSection2.6Polynomial and Rational InequalitiesProblem Recognition Exercises Solving Equations and InequalitiesSection2.7Variation

Chapter 3:Exponential and Logarithmic Functions

Section3.1Inverse FunctionsSection3.2Exponential FunctionsSection3.3Logarithmic FunctionsProblem Recognition Exercises Analyzing FunctionsSection3.4Properties of LogarithmsSection3.5Exponential and Logarithmic EquationsSection3.6Modeling with Exponential and Logarithmic Functions

Chapter 4:Trigonometric Functions

Section4.1Angles and Their Measure and Special TrianglesSection4.2Trigonometric Functions Defined on the Unit CircleSection4.3Trigonometric Functions Defined on Right TrianglesSection4.4Graphs of the Sine and Cosine Functions Section4.5Graphs of Other Trigonometric FunctionsProblem Recognition Exercises Comparing Graphical Characteristics of Trigonometric FunctionsSection4.6Inverse Trigonometric Functions

Chapter 5:Analytic Trigonometry

Section5.1Trigonometric IdentitiesSection5.2Sum and Difference FormulasSection5.3Double-Angle and Half-Angle FormulasSection5.4Product-to-Sum and Sum-to-Product FormulasSection5.5Trigonometric Equations

Chapter 6:Applications of Trigonometric Functions

Section6.1Applications of Right TrianglesSection6.2The Law of SinesSection6.3The Law of CosinesProblem Recognition Exercises Solving Triangles Using a Variety of ToolsSection6.4Harmonic Motion and Combinations of Trigonometric Functions

Chapter 7:Trigonometry Applied to Rectangular and Polar Coordinate Systems and Vectors

Section7.1Polar CoordinatesSection7.2Graphs of Polar EquationsProblem Recognition Exercises Comparing Equations in Polar and Rectangular FormSection 7.3Complex Numbers in Polar FormSection7.4VectorsSection7.5Dot Product

Chapter 8:Systems of Equations and Inequalities

Section8.1Systems of Linear Equations in Two Variables and ApplicationsSection8.2Systems of Linear Equations in Three Variables and ApplicationsSection8.3Partial Fraction DecompositionSection8.4Systems of Nonlinear Equations in Two VariablesSection8.5Inequalities and Systems of Inequalities in Two VariablesProblem Recognition Exercises Equations and Inequalities in Two VariablesSection8.6Linear Programming

Chapter 9:Matrices and Determinants and Applications

Section9.1Solving Systems of Linear Equations Using MatricesSection9.2Inconsistent Systems and Dependent EquationsSection9.3Operations on MatricesSection9.4Inverse Matrices and Matrix EquationsSection9.5Determinants and Cramer's RuleProblem Recognition Exercises Using Multiple Methods to Solve Systems of Linear Equations

Chapter 10:Analytic Geometry

Section10.1The EllipseSection10.2The HyperbolaSection10.3The ParabolaProblem Recognition Exercises Comparing Equations of Conic Sections and the General EquationSection10.4Rotation of AxesSection10.5Polar Equations of ConicsSection10.6Plane Curves and Parametric Equations

Chapter 11:Sequences, Series, Induction, and Probability

Section11.1Sequences and SeriesSection11.2Arithmetic Sequences and SeriesSection11.3Geometric Sequences and SeriesProblem Recognition Exercises Comparing Arithmetic and Geometric Sequences and SeriesSection11.4Mathematical InductionSection11.5The Binomial TheoremSection11.6Principles of CountingSection11.7Introduction to Probability

Online:Chapter 12:Preview of Calculus

Section12.1Introduction to Limits through Tables and GraphsSection12.2Algebraic Properties of LimitsProblem Recognition Exercises Using a Variety of Methods to Evaluate LimitsSection12.3Derivatives: The Tangent ProblemSection12.4Integrals: The Area Problem