جبر II (راهنمای احمق‌ها)

Perhaps no subject strikes so much fear in the hearts of high school and college students as Algebra I, except of course its older, meaner sibling, Algebra II! Starting with reinforcing concepts from Algebra I and with lots of practice and tips along the way, Idiot's Guides: Algebra II eases you into second-year algebra to help you master your academic goals. With Common Core instruction in mind, students get: &; A natural transition from Algebra I , with a review of relevant concepts and operations. &; An in-depth review and expansion of polynomials. &; Easy guidance on solving complex rational expressions and radical functions. &; Instructions on how to perform operations on polynomials and factoring. &; An exploration of exponential and logarithmic functions. &; Tips on solving matrices and determinants. &; Special sidebars pointing out the reasoning behind the techniques, which is an essential part of Common Core instruction. &; Separate workbook section of extra Algebra practice problems &; like getting two books in one. Contents iii Part 1: Foundations 1 1 Building Blocks from Algebra I 3 The Real Numbers 3 Simplifying Expressions 5 Order of Operations Example 5 Order of Operations with Variables 6 Solving Equations and Inequalities 7 Linear Equations 7 Linear Inequalities 8 Graphing Lines 9 Slope 10 Finding the Points for a Line 10 Writing a Linear Equation 12 FOIL and Factoring 13 Factoring a Quadratic Trinomial 14 Factoring When the Coefficient of x2 Isn’t 1 15 2 Functions 17 Relations and Functions 17 Function Notation 18 Building New Functions 19 Function Arithmetic 20 Composition 22 Inverses 24 Parent Functions and Transformations 27 Rigid Transformations 28 Nonrigid Transformations 31 Creating Families of Functions 32 Part 2: Linear Relationships 35 3 Linear Functions 37 Inequalities in Two Variables 37 Graphing an Inequality in Slope-Intercept Form 38 Graphing an Inequality in Standard Form 39 Fitting Equations to Data 41 Piecewise Functions 45 Graphing a Piecewise Function 46 A Well-Known Piecewise Function 47 4 Absolute Value 49 Absolute Value Equations 49 Absolute Value Inequalities 51 How Absolute Value Inequalities Work 51 Solving Absolute Value Inequalities 52 Absolute Value Functions 53 5 Solving Systems Algebraically 61 Systems of Equations 61 Graphing 62 Substitution 63 Elimination 65 Systems with Three Variables 66 Using Substitution 67 Using Elimination 69 Systems of Inequalities 71 Linear Programming 74 6 Systems and Matrices 79 Matrices and Matrix Arithmetic 79 Addition and Subtraction 80 Multiplication 81 Determinants 82 Representing a System by Matrices 84 Cramer’s Rule 85 Solving Systems by Row Operations 86 Solving Systems by Inverse Matrices 88 Finding an Inverse Matrix 89 Solving a System by Inverses 90 Part 3: Quadratic Relationships 93 7 Roots and Radicals 95 Rational Exponents 95 Simplifying Radical Expressions 97 Rationalizing More Complex Denominators 98 Solving Radical Equations 99 Graphing Radical Functions 102 8 Quadratics 107 Quadratic Equations 107 Square Root Method 108 Completing the Square 109 Quadratic Formula 111 Complex Numbers and Their Arithmetic 114 Graphing Quadratic Functions 116 Quadratic Modeling 119 9 Conics 123 Parabolas 123 Vertex Form Equation 125 Graphing a Parabola 126 Circles 128 Ellipses 129 Standard Form Equation 130 Graphing an Ellipse 132 Hyperbolas 134 Standard Form Equation 135 Graphing a Hyperbola 136 Quadratic Systems 138 Part 4: Polynomial and Rational Functions 143 10 Polynomials 145 Polynomial Equations and Functions 145 Factors and Solutions 146 Rational Zeros Theorem 147 Descartes’ Rule of Signs 148 Finding the Solutions 149 Long Division 150 Synthetic Division 152 Polynomial Inequalities 156 Graphs of Polynomial Functions 157 11 Rational Functions 161 Rational Expressions and Their Arithmetic 161 Simplifying Rational Expressions 162 Adding and Subtracting 163 Multiplying Rational Expressions 165 Dividing by a Rational Expression 166 Complex Fractions 167 Solving Rational Equations 169 Cross-Multiplying 169 Multiplying Through 171 How to Graph Rational Functions 172 Domain 172 Asymptotes 173 Intercepts 176 Part 5: Calculating and Counting 181 12 Exponential and Logarithmic Functions 183 Logarithms 183 Properties of Logarithms 185 Expanding an Expression 185 Condensing an Expression 186 Solving Exponential Equations 188 Powers of the Same Base 188 Log of Both Sides 188 Quadratic Form 191 Solving Log Equations 192 Log Equals Constant 192 Log Equals Log 193 How to Graph Exponential and Logarithmic Functions 195 Growth and Decay 199 13 Probability 203 Basic Counting Principle 203 Combinations and Permutations 206 Pascal’s Triangle 208 Calculating Probability 209 Dependent vs Independent Events 210 Disjoint vs Connected Events 211 Binomial Theorem 212 Part 6: Extra Practice 217 14 Extra Practice Questions 219 A Glossary 233 B Resources 245 C Checkpoint Answers 247 D Extra Practice Answers 295 Index 339 Perhaps no subject strikes so much fear in the hearts of high school and college students as Algebra I, except of course its older, meaner sibling, Algebra II! Starting with reinforcing concepts from Algebra I and with lots of practice and tips along the way, __Idiot's Guides: Algebra II__ eases you into second-year algebra to help you master your academic goals. With Common Core instruction in mind, students get: