## SAT Math For Dummies with Online Practice 2nd Edition

*SAT Math For Dummies:*

Go intoÂ theÂ SAT relaxed and confident byÂ preparing with this straightforward and practical math resourceÂ

A greatÂ mathÂ score on the SATÂ can unlockÂ countlessÂ opportunities, especially in the STEM fields.Â With the help ofÂ SAT MathÂ ForÂ Dummies,Â youâ€™ll have what it takes to succeed on this challenging section of the exam.Â Â This helpful guideÂ offers the tools and techniques youÂ need to hone your strengths, eliminate your weaknesses, and walk into the testingÂ roomÂ poised and preparedÂ to conquer the math sectionÂ of the SAT.

Youâ€™ll learn to tackleÂ basic and advanced algebra,Â geometry, and trigonometryâ€”with and without a calculator,Â just like youâ€™ll need to do on the test.Â The book also offers intuitive reviews of critical math conceptsÂ andÂ skillsÂ â€“Â like evaluating, simplifying, and factoring algebra expressions â€“Â whileÂ preparing you for common pitfalls and traps that ensnare less prepared students.

This up-to-date resource will help you:

- Reduce test anxietyÂ and stress byÂ preparing with resources that mirror the tasks youâ€™ll have to perform on test dayÂ
- Master the time-management and other test-taking strategies youâ€™ll need toÂ get the results you wantÂ
- Prove youâ€™re ready for the test by practicing with online resourcesÂ that include three complete practice testsÂ

Effective practice and preparation are the keysÂ to succeeding on the math sectionÂ of the SAT.Â And withÂ SAT MathÂ ForÂ DummiesÂ in your arsenal, youâ€™llÂ haveÂ theÂ strategies, knowledge, and skillsÂ that make extraordinary results possible.

##### Table of Contents

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

Trigonometry 237

Using SOH-CAH-TOA to understand sines, cosines, and tangents 237

Building a triangle from a single trig ratio 239

Applying trig ratios to special right triangles 240

Remembering the most important SAT identity 241

Radian measure and arc length 242

Chapter 15: Additional SAT Math Topics 245

Imaginary and Complex Numbers 245

The imaginary number i 246

Complex numbers 248

Circles on the xy-Plane 251

Circles in center-radius form 252

Plotting points on a circle on the xy-plane 254

Identifying interior and exterior points on a circle 255

Completing the square to solve difficult circle problems 256

Part 5: Practice Makes Perfect: Sat Math Section Practice Tests 257

Chapter 16: Practice SAT Math Test 1 259

Answer Sheet for Practice SAT Math Test 1 260

Section 3 – No Calculator 261

Section 4 – Calculator 265

Chapter 17: Answers and Explanations for Practice SAT Math Test 1 273

Section 3 – No Calculator 273

Section 4 – Calculator 277

Chapter 18: Practice SAT Math Test 2 289

Answer Sheet for Practice SAT Math Test 2 290

Section 3 – No Calculator 291

Section 4 – Calculator 296

Chapter 19: Answers to Practice SAT Math Test 2 305

Section 3 – No Calculator 305

Section 4 – Calculator 310

Part 6: The Part of Tens 321

Chapter 20: Ten Things You Will Almost Definitely See on Your SAT Math Test 323

Linear Functions 323

Systems of Linear Equations 324

Quadratic Functions 324

Percentages 324

Ratio/Proportion Problems 325

The Mean and the Median 325

The Trig Identity 325

The Quadratic Formula 326

The Imaginary Number i 326

Circles on the Graph 326

Chapter 21: Ten Tips to Improve Your SAT Math Score 327

Study Diligently in Your Math Classes 327

Get Good at Doing Basic Calculations in Your Head 328

Get Good at Using Your Calculator 328

Study SAT-Specific Math Skills 328

Get Comfortable Turning Words into Numbers 329

Take Timed Practice Tests 329

When Taking Practice Tests, Budget Your Time to Maximize Your Score 329

Study from Your Timed Practice Tests 330

Retake Your Timed Practice Tests 330

Take the SAT More than Once 330

Chapter 22: Ten Tips to Be at Your Best on the SAT 331

Do Something Fun the Day Before the Test 331

Don’t Study for More than 20 Minutes the Night Before the Test 331

Pack Everything You Need the Night Before 332

Do Something Relaxing Before Bed 332

Get a Good Night’s Sleep 332

Wear Several Layers of Clothing 333

Arrive at the Test Site Extra Early 333

Spend Your Time Just Before the Test However You Please 333

Remember to Breathe 333

Skip Over Any Questions That Throw You 333

Index 335

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