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Precalculus

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ISBN-10: 0764539841

ISBN-13: 9780764539848

Edition: 2004

Authors: W. Michael Kelley

List price: $10.99
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Description:

CliffsQuickReview course guides cover the essentials of your toughest classes. You're sure to get a firm grip on core concepts and key material and be ready for the test with this guide at your side. Whether you're new to functions, analytic geometry, and matrices or just brushing up on those topics, CliffsQuickReview Precalculus can help. This guide introduces each topic, defines key terms, and walks you through each sample problem step-by-step. In no time, you'll be ready to tackle other concepts in this book such as Arithmetic and algebraic skills Functions and their graphs Polynomials, including binomial expansion Right and oblique angle trigonometry Equations and graphs of conic…    
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Book details

List price: $10.99
Copyright year: 2004
Publisher: Houghton Mifflin Harcourt Publishing Company
Publication date: 2/27/2004
Binding: Paperback
Pages: 240
Size: 5.50" wide x 8.50" long x 0.75" tall
Weight: 0.484
Language: English

Introduction
Why You Need This Book
How to Use This Book
Visit Our Web Site
Precalculus Prerequisites
Classifying Numbers
Interval Notation
Bounded intervals
Unbounded intervals
Algebraic Properties
The associative property
The commutative property
The distributive property
Identity elements
Inverse properties
Exponential Expressions
Radical Expressions
Properties of radicals
Simplifying radicals
Operations with radicals
Rationalizing expressions
Polynomial Expressions
Classifying polynomials
Adding and subtracting polynomials
Multiplying polynomials
Rational Expressions
Adding and subtracting rational expressions
Multiplying rational expressions
Simplifying complex fractions
Equations and Inequalities
Solving equations
Solving linear inequalities
Solving absolute value inequalities
Special inequality cases
Finding Linear Equations
Functions
Relations vs. Functions
Understanding relations
Defining functions
Writing functions
Function Graphs
The vertical line test
Finding symmetry
Calculating intercepts
Determining domain and range
Eight Key Function Graphs
Basic Function Transformations
Vertical and horizontal shifts
Reflections
Stretching and squishing
Multiple transformations
Combining and Composing Functions
Arithmetic combinations
The composition of functions
Inverse Functions
What is an inverse function?
Graphs of inverse functions
Finding inverse functions
Polynomial and Rational Functions
Factoring Polynomials
Greatest common factors
Factoring by grouping
Factoring quadratic trinomials
Special factor patterns
Solving Quadratic Equations
Factoring
The quadratic formula
Completing the square
Polynomial Division
Long division
Synthetic division
Important Root-Finding Theorems
The remainder theorem
The factor theorem
Calculating Roots
The Fundamental Theorem of Algebra
Descartes' Rule of Signs
The Rational Root Test
Determining roots
Advanced Graphing Techniques
The Leading Coefficient Test
Finding rational asymptotes
Exponential and Logarithmic Functions
Exponential Functions
Natural exponential function
Graphs of exponential functions
Logarithmic Functions
Natural and common logs
Inverse relationship
Graphs of logarithmic functions
Change of base formula
Properties of Logarithms
Solving Exponential and Logarithmic Equations
Exponential equations
Logarithmic equations
Exponential Word Problems
Compound interest
Growth and decay
Trigonometry
Measuring Angles
Characteristics of angles
Degrees and radians
Angle pairs
Coterminal angles
The Unit Circle
Right Triangle Trigonometry
Oblique Triangle Trigonometry
Reference angles
Calculating trigonometric ratios
Graphs of Sine and Cosine
Periodic graphs
Transforming sine and cosine
Other Trigonometric Function Graphs
Inverse Trigonometric Functions
Analytic Trigonometry
Trigonometric Identities
Four types of identities
Simplifying expressions with identities
Proving Trigonometric Identities
Solving Trigonometric Equations
Simple equations
Quadratic equations
Equations requiring identities
Equations requiring squaring
Functions of multiple angles
Sum and Difference Identities
Additional Identities
Double-angle formulas
Half-angle formulas
Sum-product formulas
Product-sum formulas
Oblique Triangle Laws
Law of Sines
Law of Cosines
Calculating Triangle Area
Given Side-Angle-Side
Given side-side-side
Vectors and the Trigonometry of Complex Numbers
Vectors in the Coordinate Plane
Standard form of a vector
Unit vectors
Basic vector operations
Dot Products
Properties of the dot product
Measuring angles between vectors
Orthogonal vectors
Complex Numbers and Trigonometry
Basic operations with complex numbers
Trigonometric form of a complex number
Multiplying and dividing complex numbers
Roots and Powers of Complex Numbers
DeMoivre's Theorem
Calculating nth roots of complex numbers
Analytic Geometry
Conic Sections
Circles
Parabolas
Ellipses
Standard form
Eccentricity
Hyperbolas
Standard form
Graphing hyperbolas
Equations of asymptote lines
Identifying Conic Sections
Parametric Equations
Graphing parametric equations
Rewriting parametric equations
Polar Coordinates
Converting between polar and rectangular coordinates
Converting between polar and rectangular equations
Matrices and Systems of Equations
Systems of Equations
Two-Variable Linear Systems
Substitution method
Elimination method
Nonlinear Systems of Equations
Characteristics of Matrices
Basic Matrix Operations
Adding matrices
Scalar multiplication
Subtracting matrices
Multiplying matrices
Solving Systems of Equations with Matrices
Gaussian and Gauss-Jordan elimination
Matrix row operations
Systems with infinitely many solutions
Inverse Matrices
Calculating inverse matrices
Solving matrix equations
Determinants
Determinants of 2 x 2 matrices
Minors and cofactors
Determinants of square matrices
Cramer's Rule
Graphs of Two-Variable Inequalities
Single inequalities
Systems of inequalities
Linear Programming
Additional Topics
Binomial Expansion
Pascal's Triangle
Factorials
The Binomial Theorem
Ordered Number Lists
Sequences
Series
CQR Resource Center
Glossary for CQR Precalculus
Index