*SAT Math For Dummies®

Table of Contents


About This Book

Conventions Used in This Book

Foolish Assumptions

How This Book Is Organized

Part I: Making Plans for This SATurday: An Overview of SAT Math

Part II: Did They Really Cover This Stuff in School? A Review of Math Skills

Part III: Your Problems Are Solved! SAT Problem-Solving Techniques

Part IV: Practice Makes Perfect: SAT Math Practice Tests

Part V: The Part of Tens

Icons Used in This Book

Where to Go from Here

Part I: Making Plans for This SATurday: An Overview of SAT Math

Chapter 1: SAT Math Basics

Getting an Overview of the SAT Math Sections

Knowing What’s In: The Math You Need for the SAT

Calculating with arithmetic questions

Doing the algebra shuffle

Go figure: Doing geometry

Working with functions and coordinate geometry

Rounding up some grab-bag skills

Knowing What’s Out: A Few Topics Not Covered on the SAT

Building Your Problem-Solving Skills

Solving word problems

Figuring out which tools to use

Chapter 2: Testing 1-2-3: SAT Math Test-Taking Skills

Knowing Both Types of SAT Math Questions

Answering multiple-choice questions

Responding to grid-in questions

Focusing on the Fine Print

Taking note of the Notes: General assumptions

Regarding the Reference Information: Facts and formulas

Getting the Timing Right

Calculating Your Way to Success: Calculators and the SAT

Choosing an acceptable calculator

Reviewing what you should absolutely, positively know how to do on your calculator

Considering other things that are good to know how to do on your calculator

Taking calculations step by step

Knowing the right time to use your calculator

Putting the Flash Back in Flash Cards

Using flash cards effectively

Deciding what to put on flash cards

Part II: Did They Really Cover This Stuff in School? A Review of Math Skills

Chapter 3: The Numbers Game: Arithmetic Review

Maintaining Your Integrity with Integers

Doing Some Digital Computing

The Space Between: Using Number Lines

Dividing and Conquering: Understanding Divisibility, Factors, and Multiples

Testing for divisibility

Factoring in knowledge of factors

Multiplying your understanding of multiples

Understanding Percents

Converting between percents and decimals

Increasing your score (and decreasing your stress) with percent increase/decrease problems

Ratios: Making Comparisons

Treating ratios as fractions

Proportions: Crossing paths with equal ratios

Feeling Powerful with Exponents and Getting Rooted with Roots

Squaring up your knowledge of squares and square roots

Evaluating expressions with exponents and roots

Fractional bases: Raising fractions to powers

Fractional exponents: Combining powers and roots

Practice Problems for Arithmetic Review

Solutions to Practice Problems

Chapter 4: Return of the X-Men: Reviewing Algebra

Knowing the Algebra You Forgot to Remember

Vocab: A few choice words about algebra

It is written: Knowing some algebra shorthand

Expressing Yourself with Algebraic Expressions

Can I get your number? The value of evaluation

Knowing the simple truth about simplifying

Taking the fear out of factoring

Finding a Balance with Algebraic Equations

A lonely letter: Isolating the variable

Doing away with fractions: Cross-multiplying to solve rational equations

Factoring to solve quadratic equations

Solving equations that have exponential variables

Solving equations with radicals (roots)

Positive thoughts: Feeling confident with absolute value

Solving Problems with More Than One Variable

Solving an equation in terms of other variables

Solving equations with extra variables

Solving a system of equations

Solving Inequalities

Solving basic inequalities

Solving inequalities with absolute value

Symbol Secrets: Working with New Notations

Practice Problems for Algebra

Solutions to Practice Problems

Chapter 5: Picture Perfect: Reviewing Geometry

Working All the Angles

Crossing over with vertical angles

Supplementary angles: Doing a one-eighty

Going ninety: Right angles and complementary angles

Making matches: Parallel lines and corresponding angles

Sum of the angles in a triangle

Putting Triangles to the Test

Touching base on the area of a triangle

Keeping right triangles cornered

Side shows: The triangle inequality

Getting familiar looks: Congruent and similar triangles

Going for Four: Quadrilaterals




Rolling Along with Circles

From center stage: Radius and diameter

Finding the area of a circle

Getting around to the circumference

Not quite full circle: Finding arc length

Touching on tangent lines

Solidifying Your Understanding of Solid Geometry

Volume of a rectangular solid

Volumes of a cylinder

Pyramids and cones

Improving Your Geometric Perception

Getting your head around rotations

Adding a dimension: Getting other views of 3-D objects

Folding in information about surfaces

Practice Problems for Geometry

Solutions to Practice Problems

Chapter 6: Functions and Coordinate Geometry

Knowing How Mathematical Functions Function

Understanding the basic idea of a function

Solving functions with an input-output table

Using function notation

Functioning within certain limits: Finding the domain and the range

Coordinating Your Grasp of Coordinate Geometry

Getting to the point

Lining things up

Feeling inclined to measure slope

Graphing Linear Functions

Quadratic Functions

Solving quadratic equations

Graphing quadratic functions

Transformations: Moving and Flipping Graphs

Reflecting on reflections

Shift happens: Moving left, right, up, or down

Practice Problems on Functions and Coordinate Geometry

Solutions to Practice Problems

Chapter 7: From the Grab Bag: A Variety of Other SAT Math Skills

Lining Things Up with Sequences

Setting up for Success: Set Theory

Understanding union and intersection

Knowing a few important sets of numbers

Intersections: Showing overlap with Venn diagrams

Thinking Logically: Logic Questions

Statistically Speaking: Understanding Averages

Knowing the three M’s: Mean, median, and mode

Weighs and means: Finding weighted averages

Finding the mean of algebraic expressions

Figuring the Odds: Problems in Probability

Possible outcomes: Using your counting skills

What are the odds? Calculating probability

On target: Visualizing geometric probability

Seeing Is Believing: Interpreting Data from Graphs

Raising the bar with a bar graph

Picturing data with a pictogram

Getting a slice of the pie chart

Lining up information with a line graph

Unscattering data with a scatterplot

Practice Problems for Grab-Bag Skills

Solutions to Practice Problems

Part III : Your Problems Are Solved! SAT Problem-Solving Techniques

Chapter 8: What’s in a Word? SAT Word Problems

Solving Word Problems Using Equations

Getting the groupings right: Translations with parentheses

Translating equations that involve fractions

Choosing a variable to avoid fractions

Writing systems of equations: Using more than one variable

Charting a Course: Drawing Charts to Solve Word Problems

Picturing Success: Sketching to Solve Word Problems

Distance drawings: Moving with a purpose

Timelines: Avoiding algebra with a number line

Spacing out: Uncovering hidden geometry

Practice Word Problems

Solutions to Practice Problems

Chapter 9: SAT Math Strategy

Performing SA-Triage: How Difficult Is This Problem?

Formulas for Success: Working with Math Formulas

Knowing the right formulas

Answering formula questions

Plotting a Course to Answer Tough Questions

Tips and Tricks: Looking for Fast, Easy Approaches

Using the five resources at your service

Putting your brain to work

Part IV: Practice Makes Perfect: SAT Math Practice Tests

Chapter 10: Practice Test 1

Chapter 11: Answers and Explanations for Practice Test 1

Solutions to Section 1 Questions

Solutions to Section 2 Questions

Solutions to Section 3 Questions

Answer Key

Chapter 12: Practice Test 2

Section 2

Section 3

Chapter 13: Answers and Explanations for Practice Test 2

Solutions to Section 1 Questions

Solutions to Section 2 Questions

Solutions to Section 3 Questions

Answer Key

Chapter 14: Practice Test 3

Section 2

Section 3

Chapter 15: Answers and Explanations for Practice Test 3

Solutions to Section 1 Questions

Solutions to Section 2 Questions

Solutions to Section 3 Questions

Answer Key

Part V: The Part of Tens

Chapter 16: Ten Tips to Improve Your SAT Math Score

Study Diligently in Your Math Classes

Get Good at Doing Basic Calculations in Your Head

Get Good at Using Your Calculator

Study SAT-Specific Math Skills

Study SAT-Specific Problem-Solving Skills

Get Comfortable Turning Words into Numbers

Take Timed Practice Tests

Study from Your Timed Practice Tests

Retake Your Timed Practice Tests

Take the SAT More Than Once

Chapter 17: Ten Tips to Be at Your Best on the SAT

Do Something Fun the Day Before the Test

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

Pack Everything You Need the Night Before

Do Something Relaxing before Bed

Get a Good Night’s Sleep

Wear Several Layers of Clothing

Arrive at the Test Site Extra Early

Spend Your Time Just before the Test However You Please

Remember to Breathe

Skip Over Any Questions That Throw You

*SAT Math For Dummies®

Mark Zegarelli


About the Author

Mark Zegarelli is the author of LSAT Logic Games For Dummies (Wiley) plus four other For Dummies books on basic math and pre-algebra, Calculus II, and logic. He holds degrees in both English and math from Rutgers University and is an SAT teacher and tutor.

Mark lives in Long Branch, New Jersey, and San Francisco, California.


This is for my dear friend Simon Stanley Marcus, with much gratitude for your boundless wisdom and presence.

Author’s Acknowledgments

This is my sixth For Dummies book, and again I enjoy the privilege of working with an editorial team that continues to inspire and call me to my best. Thank you to my Wiley editors: Chrissy Guthrie, Danielle Voirol, and Lindsay Lefevere. More thanks for my technical editors, Amy Nicklin and Benjamin Wyss, for setting me on a better course whenever 2 + 2 = 5.

I really don’t know how to express proper gratitude for all of the wonderful people in my life who surround me with constant love, support, encouragement, and joy. But I want you to know that I feel truly blessed and fortunate to make my home here on Earth with all of you. So a very deep thank you to my family: Alan and Mary Lou Cary, Joe, Jasmine, and Jacob Cianflone, Deseret Moctezuma, Janet Rackham, Anthony and Christine Zegarelli, and Tami Zegarelli. And one more to my family of friends: Pete Apito, Bradley Averill, Joel Cohen, Chip DeCraene, Mark Dembrowski, Chris Demers, David Feaster, Rick Kawala, Michael Konopko, Al LeGoff, Brian London, Stephen McAllister, Lou Natale, Tom Nicola, Mark O’Malley, Tim O’Rourke, Christian Romo, Robert Rubin, Alison Sigethy, Rachel Silber, and Ken Wolfe.

And again, I must pay tribute to the kind folks at Maxfield’s House of Caffeine for providing a seemingly endless supply of coffee, bagels, bananas, and carrot juice.

Publisher’s Acknowledgments

We’re proud of this book; please send us your comments through our online registration form located at For other comments, please contact our Customer Care Department within the U.S. at 877-762-2974, outside the U.S. at 317-572-3993, or fax 317-572-4002.

Some of the people who helped bring this book to market include the following:

Acquisitions, Editorial, and Media Development

Senior Project Editor: Christina Guthrie

Senior Acquisitions Editor: Lindsay Lefevere

Senior Copy Editor: Danielle Voirol

Assistant Editor: Erin Calligan Mooney

Senior Editorial Assistant: David Lutton

Technical Editors: Amy L. Nicklin, Benjamin Wyss

Editorial Manager: Christine Meloy Beck

Editorial Assistants: Rachelle Amick, Jennette ElNaggar

Cover Photos: © iStock / Keith Bishop

Cartoons: Rich Tennant (

Composition Services

Project Coordinator: Patrick Redmond

Layout and Graphics: Carrie A. Cesavice, Nikki Gately, Erin Zeltner

Proofreader: Henry Lazarek

Indexer: BIM Indexing & Proofreading Services

Publishing and Editorial for Consumer Dummies

Diane Graves Steele, Vice President and Publisher, Consumer Dummies

Kristin Ferguson-Wagstaffe, Product Development Director, Consumer Dummies

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Kelly Regan, Editorial Director, Travel

Publishing for Technology Dummies

Andy Cummings, Vice President and Publisher, Dummies Technology/General User

Composition Services

Debbie Stailey, Director of Composition Services


Just like the senior prom or getting a driver’s license, the SAT is one of those milestones in the life of a high school student. I wish I could say it was as much fun as those other things, but if I did, you probably wouldn’t believe anything else I say in the rest of the book.

But any way you slice it, the SAT is still there, scheduled for some Saturday morning a few weeks or months from now. Most colleges require you to submit an SAT score as part of your application process. So because there’s no getting around it and it’s not going away, your best bet is to do some preparation and get the best possible SAT score you can.

That’s where this book comes in. The entire book you have in your hot little hands right now is devoted to refining the math skills you need most to succeed on that all-important SATurday.

About This Book

A lot of SAT prep books divide their attention among all three sections of the SAT: critical reading, writing, and mathematics. This is fine as far as it goes, because you probably want to boost all three scores. But in this book, I focus exclusively on math, math, and more math to help you achieve the best score you can on this — what can I say? — most often dreaded part of the test.

The SAT covers a variety of areas, including arithmetic, algebra, geometry, functions and graphs, and statistics and probability. But it doesn’t require the quadratic formula or anything you’d cover after that in an algebra class, so you don’t need to know trig or calculus. This book focuses on SAT topics and helps you get used to problem-solving so that you can turn facts and formulas into useful tools.

I wrote this book to give you the best possible advantage at achieving a good score on the math portion of your SAT. There’s no shortcut, but most of what you need to work on comes down to four key factors:

Know the basics inside and out.

Get comfortable using your calculator.

Strengthen SAT-specific math skills.

Practice answering SAT questions.

For that last point, every example and problem here is written in SAT format — either as a multiple-choice question or as a student-produced grid-in question. From Chapter 3 to Chapter 8, every chapter contains math skills that are essential to the SAT, with dozens of SAT examples followed by a set of 20 practice problems. And to give you that test-day experience, this book also includes three practice tests. That’s hundreds and hundreds of questions designed to strengthen your “SAT muscle,” so to speak.

Conventions Used in This Book

Following are a few conventions to keep in mind:

New terms introduced in a chapter, as well as variables, are in italics.

Keywords in lists and numbered steps are in boldface.

Any Web sites appear in monofont.

The final answers to problems appear in bold. For multiple-choice questions, that’s a letter from (A) to (E). For grid-in questions, I write the answer as you’d fill it in on the

test. So as a test answer, I give 620854-EQin01.eps as 7/9 or .777 or .778, which are all acceptable ways

to write it on your answer sheet.

Foolish Assumptions

This is an SAT prep book, so my first assumption is that you or someone you love (your son or daughter, mom or granddad, or perhaps your cat) is thinking about taking the SAT sometime in the future. If not, you’re still welcome to buy the book.

My second assumption is that you’re currently taking or have in your life at some point taken an algebra course, even if you feel like it’s all a blur. Now, I wish I could tell you that algebra isn’t very important on the SAT — oh, a mere trifle, hardly a thought. But this would be like saying you can play NFL football without getting rushed at by a bunch of 250-pound guys trying to pulverize you. It just ain’t so.

But don’t worry — this book is all about the blur and, more importantly, what lies beyond it. Read on, walk through the examples, and then try out the practice problems at the end of each chapter. I can virtually guarantee that if you do this, the stuff will start to make sense.

How This Book Is Organized

This book is organized into five parts, taking you from an overview of SAT math through the nitty-gritty skills you need to get the best possible score. Here’s a look at what’s waiting for you in these chapters.

Part I: Making Plans for This SATurday: An Overview of SAT Math

Part I introduces you to the SAT in general and the math sections in particular. Chapter 1 provides you with the most basic and important information about SAT math. You see the general areas of math that you need to focus on: arithmetic, algebra, geometry, coordinate geometry, plus a few additional scattered topics.

In Chapter 2, I talk about the two types of questions you face on the SAT: multiple-choice questions and grid-in questions. I go over some of the “fine print” information that the test-makers, in their infinite wisdom, provide to make the test fair. I also touch upon the list of formulas that you don’t have to memorize because you’ll have them on the test. I discuss when and how to use your calculator, and I provide some advice on strengthening a few mental math skills so you can answer questions quickly and confidently.

Part II: Did They Really Cover This Stuff in School? A Review of Math Skills

In Part II, I review the basic skills you need to remember from your math classes before sitting for your SAT. I also provide lots of practice problems in SAT style so that you can strengthen these skills.

In Chapter 3, I discuss topics in arithmetic, such as integers, digits, the number line, divisibility, percents, ratios, and more. Chapter 4 covers algebra, from simplifying and factoring to solving systems of equations, working with inequalities, and answering SAT questions that give you new, unfamiliar notations to work with. In Chapter 5, the focus is on geometry, including the basics about lines, angles, circles, and the ever-important right triangle. To finish up, I give you a few important formulas in solid geometry and tips on questions that test your geometric perception. In Chapter 6, you look at functions and coordinate geometry, which is geometry on the xy-plane.

Chapter 7 is a grab bag of topics you’ll probably see on your SAT but that don’t fit neatly into any of the other chapters. It includes number sequences, set theory, statistics, graphs of data, and more.

Part III: Your Problems Are Solved! SAT Problem-Solving Techniques

Part III takes a step forward, showing you how to pull together the set of skills from Part II to answer more-complicated SAT questions. In Chapter 8, you concentrate on word problems.

Chapter 9 takes a wide view of SAT strategy, giving you a few perspectives on how to approach the questions. I discuss how problems are arranged by difficulty and show you how to match the skills in your math toolbox to each question as you face it. I also show you how to read a question and anticipate the formulas that may be helpful to answer it.

Part IV: Practice Makes Perfect: SAT Math Practice Tests

Part IV gives you three opportunities to practice your SAT skills under timed conditions. Each practice test also comes with an accompanying chapter that provides the answers to the questions, along with explanations to help you understand why the correct answers are correct.

Part V: The Part of Tens

In this part, I give you the best ways to utilize your study time between now and the big day. I also identify ten smart but simple things you can do just before the test to help boost your score.

Icons Used in This Book

In this book, I use these four icons to signal what’s most important along the way:

remember.eps This icon points out important information that you need to focus on. Make sure you understand this information fully before moving on. You can skim through these icons when reading a chapter to make sure you remember the highlights.

tip.eps Tips are hints that can help speed you along when answering a question. See whether you find them useful when working on practice problems.

warning_bomb.eps This icon flags common mistakes that students make if they’re not careful. Take note and proceed with caution!

example_gre.eps Each example is a formal SAT-style question followed by a step-by-step solution. Work through these examples and then refer to them to help you solve the practice problems at the end of the chapter.

Where to Go from Here

This book is organized so that you can safely jump around and dip into every chapter in whatever order you like. You can strengthen skills you feel confident in or work on those that need some attention.

If this is your first introduction to SAT math, I strongly recommend that you start out by reading Chapters 1 and 2. There, you find some simple but vital SAT-specific information that you need to know before you sit down with pencil in hand to take the test.

If it’s been a while since you’ve taken a math course, read the math-skills chapters (Chapter 3 to Chapter 7) in order. Chapter 3, which focuses on arithmetic, can get your math brain moving again, and you may find that a lot of this stuff looks familiar as you go along.

Finally, if you read through a few chapters and feel that the book is moving more quickly than you’d like, go ahead and pick up my earlier book, Basic Math & Pre-Algebra For Dummies (Wiley). There, I adopt a more leisurely pace and spend more time filling in any gaps in understanding you may find along the way.

Part I

Making Plans for This SATurday: An Overview of SAT Math


In this part . . .

Part I gives you an overview of SAT math. I introduce you to multiple-choice and grid-in questions, discuss when and how to use your calculator, and give you some time-saving mental math skills.