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Chương trình dạy toán theo chứng chỉ SAT của Mỹ đang triển khai trong các kỳ thi tốt nghiệp THPT. Chương trình bám sát trọng tâm chương trình TOÁN học THPT. Chương trình dạy toán theo chứng chỉ SAT của Mỹ đang triển khai trong các kỳ thi tốt nghiệp THPT. Chương trình bám sát trọng tâm chương trình TOÁN học THPT
BOXMATH.VN Petersons.com/publishing Check out our Web site at www.petersons.com/publishing to see if there is any new information regarding the test and any revisions or corrections to the content of this book. We’ve made sure the information in this book is accurate and up-to-date; however, the test format or content may have changed since the time of publication. BOXMATH.VN BOXMATH.VN About Thomson Peterson’s Thomson Peterson’s (www.petersons.com) is a leading provider of education information and advice, with books and online resources focusing on education search, test preparation, and financial aid. Its Web site offers searchable databases and interactive tools for contacting educational institu- tions, online practice tests and instruction, and planning tools for securing financial aid. Peterson’s serves 110 million education consumers annually. For more information, contact Peterson’s, 2000 Lenox Drive, Lawrenceville, NJ 08648; 800-338- 3282; or find us on the World Wide Web at www.petersons.com/about. ® 2005 Thomson Peterson’s, a part of The Thomson Corporation Thomson Learning TM is a trademark used herein under license. Editor: Wallie Walker Hammond; Production Editor: Alysha Bullock; Manufacturing Manager: Judy Coleman; Composition Manager: Melissa Ignatowski; Cover Design: Greg Wuttke ALL RIGHTS RESERVED. No part of this work covered by the copyright herein may be repro- duced or used in any form or by any means—graphic, electronic, or mechanical, including photo- copying, recording, taping, Web distribution, or information storage and retrieval systems—without the prior written permission of the publisher. For permission to use material from this text or product, submit a request online at www.thomsonrights.com Any additional questions about permissions can be submitted by email to thomsonrights@thomson.com ISBN: 0-7689-1717-4 Printed in the United States of America 10 9 8 7 6 5 4 3 2 07 06 05 BOXMATH.VN v Contents About the SAT vii 1. Operations with Whole Numbers and Decimals 1 Diagnostic Test • Addition of Whole Numbers • Subtraction of Whole Numbers • Multiplication of Whole Numbers • Division of Whole Numbers • Addition or Subtraction of Decimals • Multiplication of Decimals • Division of Decimals • The Laws of Arithmetic • Estimating Answers • Retest • Solutions to Practice Exercises 2. Operations with Fractions 19 Diagnostic Test • Addition and Subtraction • Multiplication and Division • Simplifying Fractions • Operations with Mixed Numbers • Comparing Fractions • Retest • Solutions to Practice Exercises 3. Verbal Problems Involving Fractions 39 Diagnostic Test • Part of a Whole • Finding Fractions of Fractions • Finding Whole Numbers • Solving with Letters • Retest • Solutions to Practice Exercises 4. Variation 53 Diagnostic Test • Ratio and Proportion • Direct Variation • Inverse Variation • Retest • Solutions to Practice Exercises 5. Percent 69 Diagnostic Test • Fractional and Decimal Equivalents of Percents • Finding a Percent of a Number • Finding a Number When a Percent Is Given • To Find What Percent One Number Is of Another • Percents Greater Than 100 • Retest • Solutions to Practice Exercises 6. Verbal Problems Involving Percent 85 Diagnostic Test • Percent of Increase or Decrease • Discount • Commission • Profit and Loss • Taxes • Retest • Solutions to Practice Exercises 7. Averages 103 Diagnostic Test • Simple Average • To Find a Missing Number When an Average Is Given • Weighted Average • Retest • Solutions to Practice Exercises 8. Concepts of Algebra—Signed Numbers and Equations 115 Diagnostic Test • Signed Numbers • Solution of Linear Equations • Simultaneous Equations in Two Unknowns • Quadratic Equations • Equations Containing Radicals • Retest • Solutions to Practice Exercises 9. Literal Expressions 133 Diagnostic Test • Communication with Letters • Retest • Solutions to Practice Exercises BOXMATH.VN Contents vi www.petersons.com 10. Roots and Radicals 143 Diagnostic Test • Addition and Subtraction of Radicals • Multiplication and Division of Radicals • Simplifying Radicals Containing a Sum or Difference • Finding the Square Root of a Number • Retest • Solutions to Practice Exercises 11. Factoring and Algebraic Fractions 155 Diagnostic Test • Simplifying Fractions • Addition or Subtraction of Fractions • Multiplication or Division of Fractions • Complex Algebraic Fractions • Using Factoring to Find Missing Values • Retest • Solutions to Practice Exercises 12. Problem Solving in Algebra 171 Diagnostic Test • Coin Problems • Consecutive Integer Problems • Age Problems • Investment Problems • Fraction Problems • Mixture Problems • Motion Problems • Work Problems • Retest • Solutions to Practice Exercises 13. Geometry 197 Diagnostic Test • Areas • Perimeter • Right Triangles • Coordinate Geometry • Parallel Lines • Triangles • Polygons • Circles • Volumes • Similar Polygons • Retest • Solutions to Practice Exercises 14. Inequalities 231 Diagnostic Test • Algebraic Inequalities • Geometric Inequalities • Retest • Solutions to Practice Exercises 15. Numbers and Operations, Algebra, and Fractions 243 16. Additional Geometry Topics, Data Analysis, and Probability 273 Practice Test A 313 Practice Test B 319 Practice Test C 327 Solutions to Practice Tests 333 BOXMATH.VN vii About the SAT PURPOSE OF THE SAT The SAT is a standardized exam used by many colleges and universities in the United States and Canada to help them make their admissions decisions. The test is developed and administered by Educational Testing Service (ETS) for the Col- lege Entrance Examination Board. The SAT consists of two different types of exams designated SAT and SAT II. The SAT tests verbal and mathematical reasoning skills — your ability to under- stand what you read, to use language effectively, to reason clearly, and to apply fundamental mathematical principles to unfamiliar problems. SAT II tests mastery of specific subjects such as Chemistry or French or World History. TAKING THE SAT The SAT is offered on one Saturday morning in October, November, December, January, March, May, and June. When you apply to a college, find out whether it requires you to take the SAT and if so when scores are due. To make sure your scores arrive in time, sign up for a test date that’s at least six weeks before the school’s deadline for test scores. Registration forms for the SAT are available in most high school guidance of- fices. You can also get registration forms and any other SAT information from: College Board SAT Program P.O. Box 6200 Princeton, NJ 08541-6200 609-771-7600 Monday through Friday, 8:30 a.m. to 9:30 p.m. Eastern Time www.collegeboard.com Along with your registration form you will receive a current SAT Student Bulletin. The bulletin includes all necessary information on procedures, exceptions and spe- cial arrangements, times and places, and fees. BOXMATH.VN About the SAT viii www.petersons.com FORMAT OF THE NEW SAT The new SAT is a three-hour, mostly multiple-choice examination divided into sections as shown in the chart below. One of the sections is experimental. Your score on the six nonexperimental sections is the score colleges use to evaluate your application. The critical reading sections of the SAT use Sentence Completions to measure your knowledge of the meanings of words and your understanding of how parts of sentences go together, and Critical Reading questions (short and long passages) to measure your ability to read and think carefully about the information presented in passages. The mathematical sections use Standard Multiple-Choice Math, Quantitative Comparisons, and Student-Produced Response Questions to test your knowledge of arithmetic, algebra, and geometry. Many of the formulas that you need will be given in the test instructions. You are not required to memorize them. SAT math questions are designed to test your skill in applying basic math principles you already know to unfamiliar situations. The experimental section of SAT may test critical reading or mathematical rea- soning, and it can occur at any point during the test. This section is used solely by the testmakers to try out questions for use in future tests. You won’t know which section it is. So you’ll have to do your best on all of the sections. FORMAT OF A TYPICAL SAT Number of Section #/Content Questions Time (1) Writing 1 essay 25 min. (2) Mathematics 20 25 min. Standard Multiple Choice (3)* “Wild Card” an Experimental Section varies 30 min. (Varies with test) (4) Critical Reading 16 25 min. Sentence Completions 8 (5) Writing 35 25 min. Standard Multiple Choice (6) Mathematics 25 min. Standard Multiple-choice 8 Grid-Ins 10 (7) Critical Reading 19 25 min. Sentence Completions 5 (8) Mathematics 20 min. Standard Multiple Choice 16 (9) Critical Reading 13 20 min. Sentence Completions 6 * Can occur in any section BOXMATH.VN About the SAT ix www.petersons.com THE NEW SAT MATH QUESTIONS The mathematical reasoning sections of the SAT test problem solving in numbers and operations, algebra I and II, geometry, statistics, probability, and data analysis using two question types: • Standard multiple-choice questions give you a problem in arithmetic, algebra, or geometry. Then you choose the correct answer from the five choices. • Grid-Ins do not give you answer choices. You have to compute the answer and then use the ovals on the answer sheet to fill in your solution. Although calculators are not required to answer any SAT math questions, students are encouraged to bring a calculator to the test and to use it wherever it is helpful. Mathematics tests your knowledge of arithmetic, algebra, and geometry. You are to select the correct solution to the problem from the five choices given. Example: If (x + y) 2 = 17, and xy = 3, then x 2 + y 2 = (A) 11 (B) 14 (C) 17 (D) 20 (E) 23 Solution: The correct answer is (A). (x + y) 2 = 17 (x + y)(x + y) = 17 x 2 + 2xy + y 2 = 17 Since xy = 3, x 2 + 2(3) + y 2 = 17 x 2 + 6 + y 2 = 17 x 2 + y 2 = 11 Student-Produced Responses test your ability to solve mathematical problems when no choices are offered. Example: On a map having a scale of 1 4 inch = 20 miles, how many inches should there be between towns that are 70 miles apart? Solution: The correct answer is 7 8 or .875, depending upon whether you choose to solve the problem using fractions or decimals. BOXMATH.VN About the SAT x www.petersons.com Using fractions Using decimals 1 4 20 70 20 70 4 70 4 1 20 7 8 = = = = x x x . . . 25 20 70 20 17 5 875 = = = x x x HOW TO USE THE ANSWER GRID The answer grid for student-produced response (grid-ins) questions is similar to the grid used for your zip code on the personal information section of your answer sheet. An example of the answer grid is shown below. The open spaces above the grid are for you to write in the numerical value of your answer. The first row of ovals has only two ovals in the middle with a “/”. These allow you to enter numbers in fractional form. Since a fraction must have both a numerator and a denominator, it is not possible that the leftmost or rightmost posi- tions could have a “/”. To protect you from yourself, there are no “/s” in those positions. The next row has decimal points. The horizontal bar separates the frac- tion lines and decimal points from the digits 0 to 9. Record your answers to grid-in questions according to the rules that follow. GRID RULES 1. Write your answer in the boxes at the top of the grid. Technically this isn’t required by the SAT. Realistically, it gives you something to follow as you fill in the ovals. Do it—it will help you. 2. Mark the bubbles that correspond to the answer you entered in the boxes. Mark one bubble per column. The machine that scores the test can only read the bubbles, so if you don’t fill them in, you won’t get credit. Just entering your answer in the boxes is not enough. BOXMATH.VN [...]... Working diligently through each chapter in this manner will strengthen your weaknesses and prepare you to get your best score on the three Practice new SAT Math Tests at the end of this book—and on your actual SAT Good luck www.petersons.com xv BOXMATH.VN BOXMATH.VN 1 Operations with Whole Numbers and Decimals DIAGNOSTIC TEST Directions: Work out each problem Circle the letter that appears before your... the test, all SAT scores are reported on a scale of 200 to 800 The scores are based on the nonexperimental sections and are broken down into separate math and verbal scores Five or six weeks after the exam, your scores will be sent to the colleges you have named on your registration form, to your high school, and to you www.petersons.com BOXMATH.VN About the SAT HOW TO USE THIS BOOK The math review that... example, if a question asks for a prime number between 5 and 13, the answer could be 7 or 11 Grid 7 or grid 11, but don’t put in both answers www.petersons.com BOXMATH.VN About the SAT CALCULATORS AND THE SAT Calculators are allowed on the SAT You may bring to your exam any of the following types of calculators: • four-function • scientific • graphing You may not bring calculators of the following types:... www.petersons.com xiii BOXMATH.VN xiv About the SAT Here is a problem for which a calculator would not be useful: Example: Joshua travels a distance of d miles in t - 6 hours At this rate, how many miles will he travel in t2 - 36 hours? (A) d(t + 6) (B) d(t - 6) (C) (D) (E) d t+6 d t−6 t+6 d Solution: The correct answer is (A) distance time d Joshua's rate = t−6 rate = To calculate his new distance, use distance... (C) 400 (D) 4000 (E) 40,000 (B) Add 6.43 + 46.3 + 346 (A) 14.52 (B) 53.779 (C) 53.392 (D) 53.076 (E) 1452 1 2 8317×91 217×.8 ? BOXMATH.VN 2 Chapter 1 In preparing for the mathematics section of your college entrance examination, it is most important to overcome any fear of mathematics The level of this examination extends no further than relatively simple geometry Most problems can be solved using only...BOXMATH.VN About the SAT 3 Start your answer in any column, if space permits Unused columns should be left blank Don’t put in zeroes Look at this example: Here are two ways to enter an answer of “150.” 4 Work with... your high school, and to you www.petersons.com BOXMATH.VN About the SAT HOW TO USE THIS BOOK The math review that follows is designed as a self-teaching text to help you prepare for the mathematics sections of the SAT At the beginning of each chapter, you will find a ten-question diagnostic test Try this test before you read the chapter Check your answers with the solutions provided at the end of the... unless they don’t fit in 4 the answer grid For example, you can grid 10 , but you can’t grid 12 because 16 3 you’d need five spaces So, you would simplify it and grid 4 www.petersons.com xi BOXMATH.VN xii About the SAT 5 Express a mixed number as a decimal or as an improper fraction 3 If you tried to grid 1 4 , it would be read as 13 , which would give you a wrong 4 7 answer Instead you should grid this... d = (t + 6)(t − 6) t − 6 = d (t + 6) This is an algebra problem Using a calculator would not be helpful SCORING THE SAT Every correct answer is worth one point If you leave an answer blank, you score no point For incorrect answers to all verbal questions and to regular mathematics questions, you lose one-fourth of a point For incorrect answers to quantitative comparisons, you lose one-third... + 5 + 8 – 3 = 18 ) 3000 + 1000 10 (A) Estimate 6000 30 = 4000 180, 000 = 0 2, which is closest to 02 .361 8.7 + 43.17 52.231 5 (E) 6 5 1 0 9 1 0 (C) – 2 3 1 7 2 7 7 3 4 8 www.petersons.com 17 BOXMATH.VN BOXMATH.VN 2 Operations with Fractions DIAGNOSTIC TEST Directions: Work out each problem Circle the letter that appears before your answer Answers are at the end of the chapter 1 The sum of (A) (B) . Completions 6 * Can occur in any section BOXMATH.VN About the SAT ix www.petersons.com THE NEW SAT MATH QUESTIONS The mathematical reasoning sections of the SAT test problem solving in numbers and. you to get your best score on the three Practice new SAT Math Tests at the end of this book—and on your actual SAT. Good luck. BOXMATH.VN BOXMATH.VN 1 1 Operations with Whole Numbers and Decimals DIAGNOSTIC. them. SAT math questions are designed to test your skill in applying basic math principles you already know to unfamiliar situations. The experimental section of SAT may test critical reading or mathematical