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Gruber’s Complete SAT Guide 2011

What the Media is saying :

“Gary Gruber is the most prominent guru of SAT preparation.”—Chicago Tribune
“His methods make the questions seem amazingly simple to solve.”—Library Journal
“Dr. Gruber knows the ins and outs of the SAT.”—Los Angeles Times

What Students, Parents, and Educators Are Saying:

“The work that Gary Gruber does should be given to every student and every teacher.”—Dr. Shirley Thornton, former deputy superintendent, California State Department of Education
“I’ve gone through almost all the SAT books I can get ahold of, and so far the best is the Gruber’s SAT book. I wish I could have found it earlier.”—Online review
“With the aid of your books, my scores improved so dramatically that I am now anticipating acceptance into schools that I was reluctant to even apply to.”—Lauren Frasciello, Princeton, New Jersey
“In regards to the breadth and quality of material offered, the difference between Gruber’s and other publications is quite astonishing. Indeed, only Gruber’s deserves the highest recommendation in SAT preparation.”—Online review

Get the Skills that Unlock the Answers

With the explanation to a question, you can answer that one question. With the Gruber strategies, you can answer thousands of questions! These strategies show you how to think about problems instead of trying to solve each one individually and can be used consistently on every SAT test.

Use the Most Trusted Method

Table of Contents

Table of Contents

INTRODUCTION xiii

I. Important Facts About the SAT / xiii
II. The Inside Track on How SAT Questions Are Developed and How They Vary from Test to Test / xx
III. What Are Critical Thinking Skills? / xxi
IV. Strategies for Women / xxiii
V. Multi-Level Approaches to the Solution of Problems / xxiv
VI. A Four-Hour Study Program for the SAT / xxvii
VII. Longer-Range Study Program and Helpful Steps for Using This Book / xxviii
VIII. Format of the SAT / xxix

PART 1

STRATEGY DIAGNOSTIC TEST FOR THE SAT 1

Directions for Taking the Diagnostic Test / 2

Strategy Diagnostic Test Answer Sheet / 3

Section 1:Verbal Ability / 4

Section 2:Math Ability / 12

Strategy Diagnostic Test Answer and Diagnostic Table (Keyed to Strategies in Book) / 18

PART 2

THE shortest sat test—18 QUESTIONS to approximate your sat score 23

Verbal (Critical Reading) / 24

Math / 25

Writing / 26

Answers / 27

Shortest SAT Test: What You Did Wrong, Explanatory Answers, and Scoring, Strategies, and Basic Skills Needed to Improve / 28

PART 3

THE 101 MOST IMPORTANT MATH QUESTIONS YOU NEED TO KNOW HOW TO SOLVE 29

101 Math Questions Answer Sheet / 30

101 Math Questions Test / 32

101 Math Questions: Answers, Diagnosis, Solutions, Generalizations, Rules / 43

101 Math Questions: Answers / 44

Basic Skills Math Diagnosis / 46

Solutions, Generalizations, Rules / 47

PART 4

STRATEGY SECTION 57

5 General Strategies / 58

35 Easy-to-Learn Strategies / 60

How to Learn the Strategies / 60

Important Note on the Allowed Use of Calculators on the SAT / 60

Important Note on Math Questions on the SAT / 61

The Grid-Type Math Question / 61

Use of a Calculator in the Grid-Type Question / 65

19 Math Strategies / 67

16 Verbal (Critical Reading) Strategies / 115

4 Sentence Completion Strategies / 116

Critical Reading Strategies / 123

What Reading Comprehension Questions Ask / 123

Getting Involved with the Passage / 123

Introductory Passage 1 / 124

Breakdown and Underlining of Passage / 124

How to Answer Reading Comprehension Questions Most Effectively / 125

Introductory Passage 2 / 126

Introductory Passage 3 / 128

Summary / 130

About the Double-Reading Passages / 130

9 Reading Comprehension Strategies / 131

3 Vocabulary Strategies / 146

PART 5

MINI-MATH REFRESHER 153

Algebra and Arithmetic / 154

Geometry / 157

PART 6

COMPLETE SAT MATH REFRESHER 163

Algebra and Arithmetic / 154

Geometry / 157

Session #1—Fractions, Decimals, Percentages, etc. / 166

Fractions, Decimals, Percentages / 166

Deviations / 169

Ratios and Proportions / 170

Variations / 171

Comparison of Fractions / 172

Practice Test 1 / 174

Answer Key for Practice Test 1 / 183

Answers and Solutions for Practice Test 1 / 183

Session #2—Rate Problems / 188

Word Problem Setup / 188

Distance and Time / 190

Work / 191

Mixture / 192

Cost / 192

Practice Test 2 / 194

Answer Key for Practice Test 2 / 203

Answers and Solutions for Practice Test 2 / 203

Session #3—Area, Perimeter, and Volume Problems / 214

Area, Perimeter, and Volume / 214

Practice Test 3 / 222

Answer Key for Practice Test 3 / 231

Answers and Solutions for Practice Test 3 / 231

Session #4—Algebra Problems / 238

Algebraic Properties / 238

Fundamental Laws of Our Number System / 238

Algebraic Expressions / 239

Equations / 239

Algebra of Graphs / 241

Inequalities / 248

Exponents and Roots / 253

Practice Test 4 / 254

Answer Key for Practice Test 4 / 262

Answers and Solutions for Practice Test 4 / 262

Session #5—Geometry Problems / 268

Basic Definitions / 268

Triangles / 270

Properties of Triangles / 271

Four-Sided Figures / 274

Many-Sided Figures / 275

Circles / 275

Practice Test 5 / 278

Answer Key for Practice Test 5 / 287

Answers and Solutions for Practice Test 5 / 287

Session #6—Miscellaneous Problems / 298

Averages, Medians, and Modes / 298

Series / 299

Properties of Integers / 300

Approximations / 302

Combinations / 303

Probability / 304

The Absolute Value Sign / 305

Functions / 305

Practice Test 6 / 306

Answer Key for Practice Test 6 / 314

Answers and Solutions for Practice Test 6 / 314

Session #7—Tables, Charts, and Graphs / 320

Charts and Graphs / 320

Tables and Charts / 320

Graphs / 321

Bar Graphs / 322

Circle Graphs / 323

Line Graphs / 324

Practice Test 7 and Solutions / 325

Session #8—Modern Math / 332

Sets / 332

Relations / 333

Solution Sets / 333

Axioms / 334

Closed Sets / 334

Mathematical Symbols / 334

Practice Test 8 and Solutions / 335

PART 7

VOCABULARY BUILDING THAT IS GUARANTEED TO RAISE YOUR SAT SCORE 343

Knowing Word Meanings Is Essential for a Higher SAT Score / 344

8 Steps to Word Power / 345

The Gruber Prefix-Root-Suffix List That Gives You the Meanings of Over 150,000 Words / 348

Roots / 349

Prefixes / 351

Suffixes / 352

A List of SAT Words Appearing More Than Once on Actual SAT Exams / 353

The Most Important/Frequently Used SAT Words and Their Opposites / 355

The Gruber SAT 3,400 Word List / 359

100 Tests to Strengthen Your Vocabulary / 408

Answers to Vocabulary Tests / 451

PART 8

GRAMMAR AND USAGE REFRESHER 455

The Parts of Speech / 457

Clauses and Phrases / 460

The Sentence and Its Parts / 463

Verbs / 469

Nouns and Pronouns / 473

Subject-Verb Relationship / 480

Tense / 483

Verbals / 487

Mood and Voice / 491

Modifiers—Adjectives, Adjective Phrases, and Clauses / 494

Modifiers (continued)—Adverbs, Adverbial Phrases, and Clauses / 500

Connectives / 504

Correct Usage—Choosing the Right Word / 509

Grammar and Usage Index / 513

PART 9

THE SAT WRITING TEST 517

The SAT Writing Section / 518

Content of the Writing Test / 518

The Essay on the SAT Writing Test / 519

The SAT Essay Scoring Guide / 522

The Writing Sample / 523

Sample Essays / 523

Important Tips on How to Write the Best Essay / 525

Other Types of Questions on the SAT Writing Test / 533

Identifying Errors / 533

Sample Questions with Answers / 533

Improving Sentences / 536

Sample Questions with Answers / 536

Improving Paragraphs / 540

Sample Test with Answers / 542

PART 10

FIVE SAT PRACTICE TESTS 545

Five Important Reasons for Taking These Practice Tests / 546

10 Tips for Taking the Practice Tests / 547

Answer Sheet for Practice Test 1 / 549

SAT Practice Test 1 / 555

How Did You Do on This Test? / 601

Answer Key for Practice Test 1 / 602

SAT Score Conversion Table / 607

Chart for Self-Appraisal Based on the Practice Test You Have Just Taken / 610

Explanatory Answers for Practice Test 1 / 613

What You Must Do Now to Raise Your SAT Score / 645

Answer Sheet for Practice Test 2 / 647

SAT Practice Test 2 / 653

How Did You Do on This Test? / 701

Answer Key for Practice Test 2 / 702

SAT Score Conversion Table / 707

Chart for Self-Appraisal Based on the Practice Test You Have Just Taken / 710

Explanatory Answers for Practice Test 2 / 713

What You Must Do Now to Raise Your SAT Score / 744

Answer Sheet for Practice Test 3 / 746

SAT Practice Test 3 / 752

How Did You Do on This Test? / 799

Answer Key for Practice Test 3 / 800

SAT Score Conversion Table / 805

Chart for Self-Appraisal Based on the Practice Test You Have Just Taken / 808

Explanatory Answers for Practice Test 3 / 811

What You Must Do Now to Raise Your SAT Score / 844

Answer Sheet for Practice Test 4 / 846

SAT Practice Test 4 / 852

How Did You Do on This Test? / 899

Answer Key for Practice Test 4 / 900

SAT Score Conversion Table / 905

Chart for Self-Appraisal Based on the Practice Test You Have Just Taken / 908

Explanatory Answers for Practice Test 4 / 911

What You Must Do Now to Raise Your SAT Score / 940

Answer Sheet for Practice Test 5 / 942

SAT Practice Test 5 / 948

How Did You Do on This Test? / 995

Answer Key for Practice Test 5 / 996

SAT Score Conversion Table / 1001

Chart for Self-Appraisal Based on the Practice Test You Have Just Taken / 1004

Explanatory Answers for Practice Test 5 / 1007

What You Must Do Now to Raise Your SAT Score / 1039

Appendixes

Appendix A: Hot Prefixes and Roots / 1041

Appendix B: Words Commonly Mistaken for Each Other / 1046

Excerpt

Excerpt

The Author Has Something Important to Tell You About How to Raise Your SAT Score

What Are Critical Thinking Skills?
First of all, I believe that intelligence can be taught. Intelligence, simply defined, is the aptitude or ability to reason things out. I am convinced that you can learn to think logically and figure things out better and faster, particularly in regard to SAT Math and Verbal problems. But someone must give you the tools. Let us call these tools strategies. And that’s what Critical Thinking Skills are all about—strategies.

Learn the Strategies to Get More Points
The Critical Thinking Skills (beginning on page 57) will sharpen your reasoning ability so that you can increase your score up to 300 points on each part of the SAT.
These Critical Thinking Skills—5 General Strategies, 19 Math Strategies, and 16 Verbal Strategies—course right through this book. The Explanatory Answers for the 5 Practice Tests in the book direct you to those strategies that may be used to answer specific types of SAT questions. We can readily prove that the strategies in Part 4 of this book are usable for more than 90 percent of the questions that will appear on your SAT. Each additional correct answer gives you approximately 10 points. It is obvious, then, that your learning and using the 40 easy-to-understand strategies in this book will very likely raise your SAT score substantially.

Are the Practice Tests in This Book Like an Actual SAT?
If you compare any one of the 5 Practice Tests in this book with an actual SAT, you will find the book test very much like the actual test in regard to format, question types, and level of difficulty. Compare our book tests with one of the official tests, published by the College Board!

Building Your Vocabulary Can Make a Big Difference on Your Test
Although Antonyms no longer appear on the SAT, Vocabulary will still be tested, especially on Sentence Completions, and Reading Comprehension. This book includes five vital sections to build your vocabulary:

1. 3,400 Word List
2. 100 Vocabulary Tests
3. Latin and Greek Roots, Prefixes, and Suffixes
4. The Most Important/Frequently Used SAT Words
5. The Hot Prefixes and Roots

If you have time, it is important for you to study this word-building instructional material. You will find that many, many words in the 3,400 Word List will actually show up in the Sentence Completion and Reading Comprehension sections of the Verbal part of your SAT. We repeat that each additional correct answer adds approximately 10 points to your score. Knowing the meanings of the words in the 3,400 Word List will, therefore, help you considerably to “rake in” those precious points.

Study the Latin and Greek Roots, Prefixes, and Suffixes
We have developed a list of roots, prefixes, and suffixes that contains the 50 prefixes and roots that give you the meaning of more than 150,000 words. Learning all 366 will increase your vocabulary immensely. You may also wish to study the Hot Prefixes and Roots in Appendix A.

Study the Most Important/Frequently Used SAT Words
We have developed a list of the most frequently used words and their opposites related to specific categories for easy memorization. Study these words.

Study the Mini-Math Refresher
If you believe you are weak in the basic math skills area, study the Mini-Math Refresher. The material in the section is keyed to the Complete Math Refresher section for more complete instruction.

Take the 101 Most Important Math Questions Test
To see what are your weak basic math skills areas, take the 101 Most Important Math Questions Test and look at the solutions to the questions. The questions are keyed to the Complete Math Refresher so you can further brush up on your weak areas by referring to those pages in the Complete Math Refresher part for those questions you missed.

The Explanatory Answers to Questions Are Keyed to Specific Strategies and Basic Skills
The Explanatory Answers in this book are far from skimpy—so unlike those of other SAT books. Our detailed answers will direct you to the strategy that will help you to arrive at a correct answer quickly. In addition, the Math solutions in the book refer directly to the Math Refresher section, particularly useful in case your Math skills are “rusty.”

Lift That SAT Score
By using the material in this book, that is, by taking the tests, learning the specific strategies, refreshing your basic skills, etc., as described above, you should increase your SAT score substantially.

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