Introduction 1 About This Book 1 Foolish Assumptions 2 Icons Used in This Book 2 Beyond the Book 3 Where to Go from Here 3 Part 1: Getting Started with Sat Math 5 Chapter 1: Welcome to SAT Math 7 SAT Math Basics 8 Using the Reference list of formulas 8 Filling answers into the grid 8 Overview of SAT Math Topics 10 Heart of Algebra 10 Problem Solving and Data Analysis 10 Passport to Advanced Math (and Other Topics) 10 SAT Math Strategy 11 Isn''t there some way to get a good SAT Math score without actually knowing math? 11 Is there a penalty for guessing? 11 Are some questions harder than others? 12 Do I have to answer every question? 12 So, how many questions should I answer? 13 When''s the latest I can take the SAT and still get into school? 14 Hey wait -- do I even have to take the SAT to go to college? 14 Three SAT Success Stories 15 Jay''s story -- clearing 500 15 Shaun''s story -- breaking solidly beyond 600 15 Amy''s story -- reaching 700 and beyond 16 Chapter 2: Review of Pre-Algebra 17 Sets of Numbers 17 Natural numbers 18 Integers 18 Rational numbers 18 Real numbers 18 Complex numbers 19 Fractions, Ratios, Decimals, and Percentages 19 Review of fractions and ratios 19 Review of decimals and percentages 22 Absolute Value 22 Radicals 23 Understanding radicals 23 Multiplying and dividing radicals 24 Simplifying radicals 25 Adding and subtracting radicals 25 Rationalizing radicals in the denominator 26 Understanding Algebra Terminology 27 Algebra and arithmetic 27 Equations, identities, and inequalities 28 Expressions 28 Polynomial basics 29 Graphing on the xy-Plane 31 Understanding the axes, the origin, and the quadrants 31 Plotting coordinates on the xy-plane 31 Plotting equations on the xy-plane 32 Choosing and Using a Calculator 33 Knowing which calculators to avoid on the SAT 33 Choosing a calculator 33 Knowing some basic calculator moves 34 Getting familiar with a few advanced calculator moves 34 Part 2: Conquering the Heart of Algebra 37 Chapter 3: Algebra I Reboot Part 1: Expressions 39 Evaluating Expressions 40 Simplifying Expressions 40 Combining like terms 41 Distributing to remove parentheses 41 FOILing to multiply the contents of parentheses 42 Factoring Expressions 43 GCF Factoring 43 Difference of squares 44 Sum and difference of cubes 47 Factoring quadratic trinomials 48 Factoring cubic expressions 50 Chapter 4: Algebra I Reboot Part 2: Equations and Inequalities 53 Solving Simple and Intermediate Algebra Equations 54 Solving basic algebra equations 54 Working with equations that have more than one variable 55 Solving More Difficult Equations 58 Solving quadratic equations 58 Solving rational equations 62 Solving Inequalities 64 Using equation-solving skills with inequalities 64 Knowing when to flip the inequality sign 65 Lining up inequalities to solve systems 65 Chapter 5: Linear Functions 67 Interpreting Linear Functions as Words, Tables, Graphs, and Equations 68 Understanding linear functions in four complementary ways 68 Answering SAT questions about linear functions 70 Linear Function Basics 71 Slope-intercept form 72 Standard form 73 Using Two Formulas to Find the Slope 77 Measuring the slope of a graph 77 Measuring slope using two points 79 Solving Linear Function Problems 79 Finding the equation when you have two pieces of information 80 Understanding problems with parallel and perpendicular lines 81 Solving Word Problems 84 Angela''s flowers 84 Peter''s autos 84 Jacqueline''s ascent 85 Chapter 6: Systems of Equations 87 Systems of Linear Equations 87 Solving systems of linear equations 88 Looking for a fast solution 90 Solving word problems with a system of linear equations 92 Working with Problematic Systems of Equations 94 Understanding systems with one solution 94 Troubleshooting problematic systems 95 Understanding what makes a system problematic 97 Answering SAT questions about problematic systems 97 Systems of Linear Inequalities 98 Setting up systems of linear inequalities to solve word problems 98 Graphs with linear inequalities 99 Systems of Non-Linear Equations 102 Part 3: Tackling Problem Solving and Data Analysis 105 Chapter 7: Ratios, Proportions, and Percentages 107 Understanding Ratios and Proportions 107 Understanding ratios 108 Creating proportional equations 108 Using Ratios and Proportions to Solve SAT Word Problems 109 Solving unit conversion problems 109 Using population density in a proportional equation 110 Answering questions involving similar triangles 111 Understanding direct proportionality 112 Using Percentages to Answer SAT Questions 113 Setting up equations to solve percentage problems 113 Solving percent increase and percent decrease problems 114 Chapter 8: Statistics and Probability 119 Statistics 119 Statistical calculations 120 Collecting data and interpreting statistics 122 Probability 125 Understanding the probability formula 125 Answering SAT probability questions 125 Answering table-based SAT probability questions 126 Chapter 9: Understanding Data and Information from Tables and Graphs 129 Reading Information from Tables 129 Understanding Bar Graphs, Histograms, and Dot Plots 130 Bar graphs 131 Histograms 132 Dot plots 132 Working with Line Graphs and Scatterplots 134 Mapping time with line graphs 134 Understanding scatterplots 134 Part 4: Your Passport to Advanced Math 137 Chapter 10: Functions 139 Understanding Function Notation 139 Evaluating a function by plugging in a number 140 Evaluating a function plus or minus a value 140 Evaluating a function times or divided by a value 141 Evaluating a function by plugging in a variable or an expression 142 Working with Function Notation 143 Combining functions 143 Compositions of functions 145 Inverse functions 146 Using the Vertical Line Test for Functions 147 Knowing Some Key Parent Functions 149 Polynomial functions 149 Other important parent functions 151 Transforming Functions 154 Clarifying vertical and horizontal transformations 154 Understanding stretch-compress-flip transformations 158 Working with all three types of transformations 160 Chapter 11: Polynomials 163 Knowing Polynomial Basics 163 Looking at the leading term 164 Using the constant term to find the y -intercept 167 Identifying Odd and Even Polynomials 167 Identifying odd and even functions 167 Spotting end behavior as x approaches 168 Finding the x -Intercepts of Polynomials 169 Knowing a few names for x -intercepts 169 Finding the x -intercepts of a polynomial in factored form 170 Finding the x -intercepts of a polynomial in standard form 170 Sketching the Graph of a Polynomial 171 Sketching a polynomial from its factored form 171 Sketching "bounce" x -intercepts 173 Sketching a polynomial from its standard form 175 Equivalent Polynomials 177 Recalling Synthetic Division for Polynomials 178 Chapter 12: Quadratic Functions 179 The Quadratic Function in Standard Form 180 Understanding standard-form quadratic functions 180 Sketching a parabola from standard form 184 The Quadratic Function in Vertex Form 186 Understanding vertex form quadratic functions 186 Sketching a parabola from vertex form 191 Connecting Standard and Vertex Forms 194 Changing vertex form to standard form 194 Changing standard form to vertex form 195 Finding the Roots of a Quadratic Function 198 Distinguishing quadratic functions from quadratic equations 198 Identifying quadratic functions with 2, 1, and no x -intercepts 199 Using the discriminant to count x -intercepts 200 Finding the roots of a quadratic function 201 Using quadratic equations to solve word problems about projectiles 203 Chapter 13: Exponential and Radical Equations 207 Solving Exponential Equations 207 Using exponential identities 208 Solving exponential equations 209 Answering SAT Math Questions Using Exponential Functions 211 Understanding exponential growth 211 Working with exponential decay 214 Graphing Exponential Functions 217 Radical Equations and Functions 220 Solving radical equations 220 Graphing radical functions 221 Chapter 14: Geometry and Trigonometry 225 Geometry 225 Geometric formulas for success 226 Knowing the angles 227 Isosceles triangles 229 Similar triangles 231 Working with right triangles 231 Trigono.