Cliffsquickreview Precalculus

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Cliffsquickreview Precalculus

Format:  Paperback,

216 pages

Publisher: Houghton Mifflin Harcourt

Publish Date: Feb 2004

ISBN-13: 9780764539848

ISBN-10: 0764539841

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Book Information

The following content was provided by the publisher.
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 asArithmetic and algebraic skillsFunctions and their graphsPolynomials, including binomial expansionRight and oblique angle trigonometryEquations and graphs of conic sectionsMatrices and their application to systems of equations

"CliffsQuickReview Precalculus" acts as a supplement to your textbook and to classroom lectures. Use this reference in any way that fits your personal style for study and review -- you decide what works best with your needs. You can either read the book from cover to cover or just look for the information you want and put it back on the shelf for later. What's more, you canUse the free Pocket Guide full of essential informationGet a glimpse of what you'll gain from a chapter by reading through the Chapter Check-In at the beginning of each chapterUse the Chapter Checkout at the end of each chapter to gauge your grasp of the important information you need to knowTest your knowledge more completely in the CQR Review and look for additional sources of information in the CQR Resource CenterUse the glossary to find key terms fast.

With titles available for all the most popular high school and college courses, CliffsQuickReview guides are a comprehensive resource that can help you get the best possible grades.

Specifications

Publisher: Houghton Mifflin Harcourt
Publish Date: Feb 2004
ISBN-13: 9780764539848
ISBN-10: 0764539841
Format: Paperback
Number of Pages: 216
Shipping Weight (in pounds): 0.5
Product in Inches (L x W x H): 5.5 x 8.5 x 0.75
Walmart No.: 764539841

Chapter outline

Introductionp. 1
Why You Need This Bookp. 1
How to Use This Bookp. 2
Visit Our Web Sitep. 2
Precalculus Prerequisitesp. 3
Classifying Numbersp. 3
Interval Notationp. 5
Bounded intervalsp. 5
Unbounded intervalsp. 6
Algebraic Propertiesp. 7
The associative propertyp. 7
The commutative propertyp. 8
The distributive propertyp. 8
Identity elementsp. 9
Inverse propertiesp. 9
Exponential Expressionsp. 9
Radical Expressionsp. 12
Properties of radicalsp. 12
Simplifying radicalsp. 12
Operations with radicalsp. 13
Rationalizing expressionsp. 14
Polynomial Expressionsp. 14
Classifying polynomialsp. 15
Adding and subtracting polynomialsp. 15
Multiplying polynomialsp. 16
Rational Expressionsp. 17
Adding and subtracting rational expressionsp. 17
Multiplying rational expressionsp. 18
Simplifying complex fractionsp. 18
Equations and Inequalitiesp. 19
Solving equationsp. 19
Solving linear inequalitiesp. 20
Solving absolute value inequalitiesp. 21
Special inequality casesp. 22
Finding Linear Equationsp. 23
Functionsp. 26
Relations vs. Functionsp. 26
Understanding relationsp. 26
Defining functionsp. 27
Writing functionsp. 28
Function Graphsp. 30
The vertical line testp. 31
Finding symmetryp. 31
Calculating interceptsp. 33
Determining domain and rangep. 33
Eight Key Function Graphsp. 34
Basic Function Transformationsp. 36
Vertical and horizontal shiftsp. 37
Reflectionsp. 38
Stretching and squishingp. 39
Multiple transformationsp. 40
Combining and Composing Functionsp. 41
Arithmetic combinationsp. 41
The composition of functionsp. 42
Inverse Functionsp. 43
What is an inverse function?p. 43
Graphs of inverse functionsp. 44
Finding inverse functionsp. 44
Polynomial and Rational Functionsp. 47
Factoring Polynomialsp. 47
Greatest common factorsp. 48
Factoring by groupingp. 48
Factoring quadratic trinomialsp. 49
Special factor patternsp. 50
Solving Quadratic Equationsp. 50
Factoringp. 51
The quadratic formulap. 51
Completing the squarep. 52
Polynomial Divisionp. 53
Long divisionp. 53
Synthetic divisionp. 55
Important Root-Finding Theoremsp. 56
The remainder theoremp. 56
The factor theoremp. 57
Calculating Rootsp. 58
The Fundamental Theorem of Algebrap. 58
Descartes' Rule of Signsp. 58
The Rational Root Testp. 60
Determining rootsp. 60
Advanced Graphing Techniquesp. 62
The Leading Coefficient Testp. 62
Finding rational asymptotesp. 64
Exponential and Logarithmic Functionsp. 67
Exponential Functionsp. 67
Natural exponential functionp. 68
Graphs of exponential functionsp. 68
Logarithmic Functionsp. 70
Natural and common logsp. 71
Inverse relationshipp. 71
Graphs of logarithmic functionsp. 71
Change of base formulap. 73
Properties of Logarithmsp. 73
Solving Exponential and Logarithmic Equationsp. 76
Exponential equationsp. 76
Logarithmic equationsp. 77
Exponential Word Problemsp. 79
Compound interestp. 79
Growth and decayp. 80
Trigonometryp. 83
Measuring Anglesp. 83
Characteristics of anglesp. 83
Degrees and radiansp. 84
Angle pairsp. 86
Coterminal anglesp. 87
The Unit Circlep. 88
Right Triangle Trigonometryp. 91
Oblique Triangle Trigonometryp. 94
Reference anglesp. 95
Calculating trigonometric ratiosp. 96
Graphs of Sine and Cosinep. 98
Periodic graphsp. 98
Transforming sine and cosinep. 99
Other Trigonometric Function Graphsp. 101
Inverse Trigonometric Functionsp. 103
Analytic Trigonometryp. 106
Trigonometric Identitiesp. 106
Four types of identitiesp. 107
Simplifying expressions with identitiesp. 108
Proving Trigonometric Identitiesp. 110
Solving Trigonometric Equationsp. 111
Simple equationsp. 113
Quadratic equationsp. 113
Equations requiring identitiesp. 114
Equations requiring squaringp. 115
Functions of multiple anglesp. 115
Sum and Difference Identitiesp. 116
Additional Identitiesp. 117
Double-angle formulasp. 117
Half-angle formulasp. 118
Sum-product formulasp. 119
Product-sum formulasp. 120
Oblique Triangle Lawsp. 120
Law of Sinesp. 121
Law of Cosinesp. 123
Calculating Triangle Areap. 124
Given Side-Angle-Sidep. 125
Given side-side-sidep. 125
Vectors and the Trigonometry of Complex Numbersp. 128
Vectors in the Coordinate Planep. 128
Standard form of a vectorp. 129
Unit vectorsp. 130
Basic vector operationsp. 131
Dot Productsp. 134
Properties of the dot productp. 134
Measuring angles between vectorsp. 135
Orthogonal vectorsp. 136
Complex Numbers and Trigonometryp. 137
Basic operations with complex numbersp. 138
Trigonometric form of a complex numberp. 140
Multiplying and dividing complex numbersp. 141
Roots and Powers of Complex Numbersp. 142
DeMoivre's Theoremp. 142
Calculating nth roots of complex numbersp. 143
Analytic Geometryp. 145
Conic Sectionsp. 145
Circlesp. 146
Parabolasp. 148
Ellipsesp. 153
Standard formp. 153
Eccentricityp. 156
Hyperbolasp. 158
Standard formp. 159
Graphing hyperbolasp. 160
Equations of asymptote linesp. 162
Identifying Conic Sectionsp. 163
Parametric Equationsp. 163
Graphing parametric equationsp. 163
Rewriting parametric equationsp. 164
Polar Coordinatesp. 165
Converting between polar and rectangular coordinatesp. 167
Converting between polar and rectangular equationsp. 168
Matrices and Systems of Equationsp. 171
Systems of Equationsp. 171
Two-Variable Linear Systemsp. 172
Substitution methodp. 173
Elimination methodp. 174
Nonlinear Systems of Equationsp. 175
Characteristics of Matricesp. 176
Basic Matrix Operationsp. 177
Adding matricesp. 177
Scalar multiplicationp. 178
Subtracting matricesp. 178
Multiplying matricesp. 179
Solving Systems of Equations with Matricesp. 180
Gaussian and Gauss-Jordan eliminationp. 181
Matrix row operationsp. 182
Systems with infinitely many solutionsp. 184
Inverse Matricesp. 185
Calculating inverse matricesp. 186
Solving matrix equationsp. 187
Determinantsp. 189
Determinants of 2 x 2 matricesp. 189
Minors and cofactorsp. 189
Determinants of square matricesp. 190
Cramer's Rulep. 192
Graphs of Two-Variable Inequalitiesp. 194
Single inequalitiesp. 194
Systems of inequalitiesp. 196
Linear Programmingp. 198
Additional Topicsp. 201
Binomial Expansionp. 201
Pascal's Trianglep. 202
Factorialsp. 204
The Binomial Theoremp. 204
Ordered Number Listsp. 205
Sequencesp. 206
Seriesp. 206
CQR Resource Centerp. 208
Glossary for CQR Precalculusp. 210
Indexp. 217

Book 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 sections
  • Matrices and their application to systems of equations

CliffsQuickReview Precalculus acts as a supplement to your textbook and to classroom lectures. Use this reference in any way that fits your personal style for study and review — you decide what works best with your needs. You can either read the book from cover to cover or just look for the information you want and put it back on the shelf for later. What's more, you can

  • Use the free Pocket Guide full of essential information
  • Get a glimpse of what you’ll gain from a chapter by reading through the Chapter Check-In at the beginning of each chapter
  • Use the Chapter Checkout at the end of each chapter to gauge your grasp of the important information you need to know
  • Test your knowledge more completely in the CQR Review and look for additional sources of information in the CQR Resource Center
  • Use the glossary to find key terms fast.

With titles available for all the most popular high school and college courses, CliffsQuickReview guides are a comprehensive resource that can help you get the best possible grades.

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