Official SAT Practice Test 2006-07 - Mathematics Page

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Official SAT Practice Test2006-07 Taking the Practice TestThe practice test will help you most if you take it under conditions as close as possible to those ofthe actual test. Set aside 3 hours and 20 minutes of uninterrupted timeThat way you can complete the entire test in one sitting. Note: The total testing time is3 hours and 45 minutes, but you save 25 minutes because the unscored section* from thispractice test was omitted. Sit at a desk or table cleared of any other papers or booksYou won’t be able to take a dictionary, books, notes, or scratch paper into the test room. Allow yourself the specified amount of time for each sectionPace yourself by using a watch (without an audible alarm), which is what you are allowedto use on test day. Have a calculator at hand when you take the math sectionsThis will help you determine how much to use a calculator the day of the test. Use acalculator with which you are familiar—preferably the same calculator you will use on testday. Read the test instructions carefullyThey are reprinted from the back cover of the test book. On test day, you will be asked toread them before you begin answering questions. Make sure you use a No. 2 pencilIt is very important that you fill in the entire circle on the answer sheet darkly andcompletely. If you change your response, erase it as completely as possible. It is veryimportant that you follow these instructions when filling out your answer sheet. Record your answers on paper, then score your testUse the answer sheet when completing a practice test on paper to simulate the real testingenvironment. After completing the practice test, you can score the test yourself with“Scoring Your Test,” or you can return to collegeboard.com to enter your answers onlineand receive a score report and answer explanations.*Section 4 is an unscored section and has been omitted on this test because it contains questions that may beused in future editions of the SAT .

Please note: The appearance of the answer sheet in this booklet may differ from the answer sheet you see on test day.SAT Reasoning TestTMUse a No. 2 pencil only. Be sure each mark is dark and completelyfills the intended circle. Completely erase any errors or stray marks.Your Name:1(Print)LastFirstI agree to the conditions on the back of theSAT M.I.test book.DateSignature:Home Address:Number and StreetCityStateZip CodeCenter:(Print)2CityStateLast Name(First 4 Letters)SOCIAL SECURITYNUMBER3YOUR NAME5First Mid.Init. Init.Female000000000Important: Fill in items8 and 9 exactly as shownon the back of test book.SEXTEST FORM9(Copy from back of test book.)MaleFORMCODETEST BOOKSERIAL JJJJ999KKKKLLLLMMMM4MONTHDATE ION NUMBER(Copy from Admission Ticket.)TESTCENTER7(Supplied by Test CenterSupervisor.)410(Copy from front of test book.)(Copy and grid as onback of test Z01234567890123456789FOR OFFICIAL USE ONLY11030-36390 NS114E1800 Printed in U.S.A.Copyright 2004 by College Entrance Examination Board. All rights reserved.College Board, SAT, and the acorn logo are registered trademarks of the College Entrance Examination Board.724843SAT Reasoning Test and SAT Subject Tests are trademarks owned by the College Entrance Examination Board.170232-001:654321ISD5150PLEASE DO NOT WRITE IN THIS AREASERIAL #38SAT Preparation Booklet

SECTIONI grant the College Board the unlimited right to use, reproduce, and publish my essay for any and allpurposes. My name will not be used in any way in conjunction with my essay. I understand that I amfree to mark "No," with no effect on my score.YesNo1Begin your essay on this page. If you need more space, continue on the next page. Do not write outside of the essay box.Page 2Continue on the next page if necessary.SAT Preparation Booklet39

Continuation of ESSAY Section 1 from previous page. Write below only if you need more space.Page 3PLEASE DO NOT WRITE IN THIS AREASERIAL #40SAT Preparation Booklet

Start with number 1 for each new section. If a section has fewer questions than answer spaces, leave the extraanswer spaces blank. Be sure to erase any errors or stray marks tudent-Produced CDEABCDEONLY ANSWERS ENTERED IN THE CIRCLES IN EACH GRID WILL BE SCORED. YOU WILLNOT RECEIVE CREDIT FOR ANYTHING WRITTEN IN THE BOXES ABOVE THE CIRCLES.109 .0001111222233344511 .000111122223333444455556666777889912 .00011112222333344445555666677778888999914. . 2333445. 88888889999999999 .00016 .0001111222233334444555566667778899.17 e the answer spaces in the grids below for Section 2 or Section 3 only if you are told to do soin your test book.CAUTION.11121314151617181920.18 999.Page 4SAT Preparation Booklet41

Start with number 1 for each new section. If a section has fewer questions than answer spaces, leave the extraanswer spaces blank. Be sure to erase any errors or stray marks completely.123SECTION CDEABCDE123SECTION tingauqe4, thenticeoictacrpSesof ABCDEABCDEABCDEABCDEABCDEABCDEABCDEABCDEUse the answer spaces in the grids below for Section 4 or Section 5 only if you are told todo so in your test book.CAUTIONStudent-Produced ResponsesONLY ANSWERS ENTERED IN THE CIRCLES IN EACH GRID WILL BE SCORED. YOU WILLNOT RECEIVE CREDIT FOR ANYTHING WRITTEN IN THE BOXES ABOVE THE CIRCLES.109 .0001111222233344511 .0001111222233334444555566667778899. .00011112222333344445555666677778888999914. . 2333445. 88888889999999999 .00016 .0001111222233334444555566667778899.17 18 999.Page 542SAT Preparation Booklet

Start with number 1 for each new section. If a section has fewer questions than answer spaces, leave the extraanswer spaces blank. Be sure to erase any errors or stray marks tudent-Produced Responses CDEABCDEABCDEABCDE0001111222233344511 223333444455556666777889912 .00011112222333344445555666677778888999914Page CDEABCDEABCDEABCDEABCDEABCDEABCDEABCDEABCDEONLY ANSWERS ENTERED IN THE CIRCLES IN EACH GRID WILL BE SCORED. YOU WILLNOT RECEIVE CREDIT FOR ANYTHING WRITTEN IN THE BOXES ABOVE THE CIRCLES.109. . 2333445. 88888889999999999 .00016 .0001111222233334444555566667778899.17 e the answer spaces in the grids below for Section 6 or Section 7 only if you are told todo so in your test book.CAUTION.11121314151617181920.18 999.PLEASE DO NOT WRITE IN THIS AREASERIAL #SAT Preparation Booklet43

Start with number 1 for each new section. If a section has fewer questions than answer spaces, leave the extraanswer spaces blank. Be sure to erase any errors or stray marks completely.123SECTION CDEABCDE123SECTION CDEABCDE123SECTION DEABCDEABCDEABCDEABCDEABCDEABCDEABCDEABCDEPage 744SAT Preparation Booklet

YOUR NAME (PRINT)LASTFIRSTMITEST CENTERNUMBERNAME OF TEST CENTERROOM NUMBERSAT Reasoning Test — General DirectionsTiming You will have 3 hours and 45 minutes to work on this test.There are ten separately timed sections:䉴 One 25-minute essay䉴 Six other 25-minute sections䉴 Two 20-minute sections䉴 One 10-minute sectionYou may work on only one section at a time.The supervisor will tell you when to begin and end each section.If you finish a section before time is called, check your work on that section.You may NOT turn to any other section.Work as rapidly as you can without losing accuracy. Don’t waste time onquestions that seem too difficult for you.IMPORTANT: The codes below are unique toyour test book. Copy them on your answer sheetin boxes 8 and 9 and fill in the correspondingcircles exactly as shown.TEST FORM98(Copy from back of test book.)FORM CODE(Copy and grid as onback of test book.)Marking Answers Be sure to mark your answer sheet 5GGGG666HHHH777IIII888Using Your Test BookJJJJ999 KKKK You must use a No. 2 pencil.Carefully mark only one answer for each question.Make sure you fill the entire circle darkly and completely.Do not make any stray marks on your answer sheet.If you erase, do so completely. Incomplete erasures may be scored asintended answers.Use only the answer spaces that correspond to the question numbers.You may use the test book for scratchwork, but you will not receive creditfor anything written there.After time has been called, you may not transfer answers to your answersheet or fill in circles.You may not fold or remove pages or portions of a page from this book,or take the book or answer sheet from the testing room.Scoring For each correct answer, you receive one point.For questions you omit, you receive no points.For a wrong answer to a multiple-choice question, you lose one-fourth ofa point.䉴 If you can eliminate one or more of the answer choices as wrong,you increase your chances of choosing the correct answer andearning one point.䉴 If you can’t eliminate any choice, move on. You can return to thequestion later if there is time.For a wrong answer to a student-produced response (“grid-in”) mathquestion, you don’t lose any points.Multiple-choice and student-produced response questions are machinescored.The essay is scored on a 1 to 6 scale by two different readers. The totalessay score is the sum of the two readers’ scores.Off-topic essays, blank essays, and essays written in ink will receive ascore of WWWXXXXYYYYZZZZThe passages for this test have been adapted from published material.The ideas contained in them do not necessarily represent the opinions of the College Board.DO NOT OPEN THIS BOOK UNTIL THESUPERVISOR TELLS YOU TO DO SO.SAT Preparation Booklet45

ESSAYTime — 25 minutesTurn to page 2 of your answer sheet to write your ESSAY.The essay gives you an opportunity to show how effectively you can develop and express ideas. You should, therefore, takecare to develop your point of view, present your ideas logically and clearly, and use language precisely.Your essay must be written on the lines provided on your answer sheet— you will receive no other paper on which to write.You will have enough space if you write on every line, avoid wide margins, and keep your handwriting to a reasonable size.Remember that people who are not familiar with your handwriting will read what you write. Try to write or print so that whatyou are writing is legible to those readers.Important Reminders: A pencil is required for the essay. An essay written in ink will receive a score of zero. Do not write your essay in your test book. You will receive credit only for what you write on youranswer sheet. An off-topic essay will receive a score of zero.You have twenty-five minutes to write an essay on the topic assigned below.Think carefully about the issue presented in the following excerpt and the assignment below.Nowadays nothing is private: our culture has become too confessional and self-expressive.People think that to hide one’s thoughts or feelings is to pretend not to have those thoughtsor feelings. They assume that honesty requires one to express every inclination and impulse.Adapted from J. David Velleman, “The Genesis of Shame”Assignment:Should people make more of an effort to keep some things private? Plan and write an essay in which youdevelop your point of view on this issue. Support your position with reasoning and examples taken fromyour reading, studies, experience, or observations.BEGIN WRITING YOUR ESSAY ON PAGE 2 OF THE ANSWER SHEET.If you finish before time is called, you may check your work on this section only.Do not turn to any other section in the test.46SAT Preparation Booklet

SECTION 2Time — 25 minutes20 QuestionsTurn to Section 2 (page 4) of your answer sheet to answer the questions in this section.Directions: For this section, solve each problem and decide which is the best of the choices given. Fill in the correspondingcircle on the answer sheet. You may use any available space for scratchwork.1. If 10 x is 5 more than 10, what is the value of 2x ?(A)(B)(C)(D)(E) 551025502. The result when a number is divided by 2 is equal tothe result when that same number is divided by 4.What is that number?(A) - 4(B) -2(C) 0(D) 2(E) 4SAT Preparation Booklet47

3. If this page was folded along the dotted line in thefigure above, the left half of the letter W wouldexactly coincide with the right half of W. Which ofthe following letters, as shown, CANNOT be foldedalong a vertical line so that its left half would coincidewith its right half?xy-2-30316294155. Which of the following equations is satisfied by thefive pairs of numbers listed in the table above?(A) y x 33(B) y 3 x 3(A)(C) y -3 x 6(B)(C)(D) y x2 6(E) y x2-7(D)(E)6. The circle graph above shows how David’s monthlyexpenses are divided. If David spends 450 per monthfor food, how much does he spend per month on hiscar?4. In the figure above, lines and k intersect at point Q.If m 40 and p 25, what is the value of x ?(A)(B)(C)(D)(E)481520254065SAT Preparation Booklet(A)(B)(C)(D)(E) 200 320 360 400 450

7. If n and k are positive integers and 8n 2k , what isnthe value of ?k1(A)4(B)13(C)1248. In a certain store, the regular price of a refrigerator is 600. How much money is saved by buying this refrigerator at 20 percent off the regular price rather thanbuying it on sale at 10 percent off the regular pricewith an additional discount of 10 percent off the saleprice?(A)(B)(C)(D)(E) 6 12 24 54 609. If the function f is defined by f ( x) 3 x 4,then 2 f ( x ) 4 0045,00075,00080,00012. If a positive integer n is picked at random from thepositive integers less than or equal to 10, what is theprobability that 5n 3 14 ?(D) 3(E)11. A total of 120,000 votes were cast for 2 opposingcandidates, Garcia and Pérez. If Garcia won by a ratioof 5 to 3, what was the number of votes cast for Pérez? 4 8 4 8 1210. What is the greatest possible area of a triangle withone side of length 7 and another side of length 10 ?(A) 17(B) 34(C) 35(D) 70(E) 140(A)0(B)110(C)15(D)310(E)25213. If t is a number greater than 1, then t is how muchgreater than t ?(A)(B)(C)(D)(E)12tt (t 1)(t 1) (t 1)14. The height of a right circular cylinder is 5 and thediameter of its base is 4. What is the distance from thecenter of one base to a point on the circumference ofthe other base?(A) 3(B) 5(C) 29 (approximately 5.39)(D) 33 (approximately 5.74)41 (approximately 6.40)(E)SAT Preparation Booklet49

15. If p and n are integers such that p n 0 andp 2 - n2 12, which of the following can be thevalue of p - n ?I. 1II. 2III. 4(A)(B)(C)(D)(E)I onlyII onlyI and II onlyII and III onlyI, II, and IIIQuestions 16-18 refer to the following figure andinformation.16. What is the m-distance of the building at W from thefirehouse?(A) 2(B) 212(C) 3121(E) 42(D) 317. What is the total number of different routes that a firetruck can travel the m-distance from F to Z ?(A)(B)(C)(D)(E)SixFiveFourThreeTwo18. All of the buildings in the town that are an m-distanceof 3 from the firehouse must lie on aThe grid above represents equally spaced streets in atown that has no one-way streets. F marks the cornerwhere a firehouse is located. Points W, X, Y, and Zrepresent the locations of some other buildings. Thefire company defines a building’s m-distance as theminimum number of blocks that a fire truck must travelfrom the firehouse to reach the building. For example,the building at X is an m-distance of 2, and the1building at Y is an m-distance of from the2firehouse.50SAT Preparation Booklet(A)(B)(C)(D)(E)circlesquareright isosceles trianglepair of intersecting linesline

19. If x and y are positive integers, which of thefollowing is equivalent to 2 x(A)2x2yyx(C)2xy2x(D)2xy4x y(E)2xy2x(B) 23x3y2xy?20. If j , k , and n are consecutive integers such that0 j k n and the units (ones) digit of the productjn is 9, what is the units digit of k ?(A)(B)(C)(D)(E)y2y101234131STOPIf you finish before time is called, you may check your work on this section only.Do not turn to any other section in the test.SAT Preparation Booklet51

SECTION 3Time — 25 minutes24 QuestionsTurn to Section 3 (page 4) of your answer sheet to answer the questions in this section.Directions: For each question in this section, select the best answer from among the choices given and fill in the correspondingcircle on the answer sheet.Each sentence below has one or two blanks, each blankindicating that something has been omitted. Beneaththe sentence are five words or sets of words labeled Athrough E. Choose the word or set of words that, wheninserted in the sentence, best fits the meaning of thesentence as a whole.Example:Hoping to ------- the dispute, negotiators proposeda compromise that they felt would be ------- to bothlabor and management.(A)(B)(C)(D)(E)enforce . . usefulend . . divisiveovercome . . unattractiveextend . . satisfactoryresolve . . acceptable1. Many private universities depend heavily on -------, thewealthy individuals who support them with gifts andbequests.(A) instructors(B) administrators(C) monitors(D) accountants(E) benefactors2. One of the characters in Milton Murayama’s novelis considered ------- because he deliberately defiesan oppressive hierarchical society.(A) rebellious(B) impulsive(C) artistic(D) industrious(E) tyrannical52SAT Preparation Booklet3. Nightjars possess a camouflage perhaps unparalleledin the bird world: by day they roost hidden in shadywoods, so ------- with their surroundings that they arenearly impossible to -------.(A)(B)(C)(D)(E)vexed . . dislodgeblended . . discernharmonized . . interruptimpatient . . distinguishintegrated . . classify4. Many economists believe that since resources arescarce and since human desires cannot all be -------,a method of ------- is needed.(A)(B)(C)(D)(E)indulged . . apportionmentverified . . distributionusurped . . expropriationexpressed . . reparationanticipated . . advertising5. The range of colors that homeowners could use on theexterior of their houses was ------- by the community’sstringent rules regarding upkeep of property.(A) circumscribed(C) embellished(E) cultivated(B) bolstered(D) insinuated

The passages below are followed by questions based on their content; questions following a pair of related passages may alsobe based on the relationship between the paired passages. Answer the questions on the basis of what is stated or implied in thepassages and in any introductory material that may be provided.Questions 6-9 are based on the following passages.Passage 1I know what your e-mail in-box looks like, and itisn’t pretty: a babble of come-ons and lies from huckstersand con artists. To find your real e-mail, you must wadeLine through the torrent of fraud and obscenity known politely5 as “unsolicited bulk e-mail” and colloquially as “spam.”In a perverse tribute to the power of the online revolution,we are all suddenly getting the same mail: easy weightloss, get-rich-quick schemes, etc. The crush of these messages is now numbered in billions per day. “It’s becoming10 a major systems and engineering and network problem,”says one e-mail expert. “Spammers are gaining control ofthe Internet.”Passage 2Many people who hate spam assume that it is protectedas free speech. Not necessarily so. The United States15 Supreme Court has previously ruled that individualsmay preserve a threshold of privacy. “Nothing in theConstitution compels us to listen to or view any unwantedcommunication, whatever its merit,” wrote Chief JusticeWarren Burger in a 1970 decision. “We therefore categori20 cally reject the argument that a vendor has a right to sendunwanted material into the home of another.” With regardto a seemingly similar problem, the Telephone ConsumerProtection Act of 1991 made it illegal in the United Statesto send unsolicited faxes; why not extend the act to include25 unsolicited bulk e-mail?6. The primary purpose of Passage 1 is to(A)(B)(C)(D)(E)make a comparisondispute a hypothesissettle a controversyjustify a distinctionhighlight a concern7. The primary purpose of Passage 2 is to(A)(B)(C)(D)(E)confirm a widely held beliefdiscuss the inadequacies of a rulingdefend a controversial technologyanalyze a widespread social problemlay the foundation for a course of action8. What would be the most likely reaction by the authorof Passage 1 to the argument cited in lines 16-21 ofPassage 2 (“Nothing . . . another”) ?(A) Surprise at the assumption that freedom of speechis indispensable to democracy(B) Dismay at the Supreme Court’s vigorous defenseof vendors’ rights(C) Hope that the same reasoning would be appliedto all unsolicited e-mail(D) Concern for the plight of mass marketers facingsubstantial economic losses(E) Appreciation for the political complexity ofthe debate about spam9. Unlike the author of Passage 1, the author of Passage 2(A)(B)(C)(D)(E)criticizes a practiceoffers an exampleproposes a solutionstates an opinionquotes an expertSAT Preparation Booklet53

Questions 10-16 are based on the following passage.The following passage is adapted from a novel set inthe early twentieth century. Mr. Beebe, a clergyman, isspeaking with Cecil Vyse about a mutual acquaintance,Lucy Honeychurch. Miss Honeychurch has recentlyreturned from a journey with her older cousin andchaperone, Miss Bartlett.Line5101520253035404554“Lucy Honeychurch has no faults,” said Cecil,with grave sincerity.“I quite agree. At present she has none.”“At present?”“I’m not cynical. I’m only thinking of my pet theoryabout Miss Honeychurch. Does it seem reasonable thatshe should play piano so wonderfully, and live so quietly?I suspect that someday she shall be wonderful in both.The water-tight compartments in her will break down,and music and life will mingle. Then we shall have herheroically good, heroically bad —too heroic, perhaps,to be good or bad.”Cecil found his companion interesting.“And at present you think her not wonderful as faras life goes?”“Well, I must say I’ve only seen her at TunbridgeWells, where she was not wonderful, and at Florence.She wasn’t wonderful in Florence either, but I kepton expecting that she would be.”“In what way?”Conversation had become agreeable to them, andthey were pacing up and down the terrace.“I could as easily tell you what tune she’ll play next.There was simply the sense that she found wings andmeant to use them. I can show you a beautiful picturein my diary. Miss Honeychurch as a kite, Miss Bartlettholding the string. Picture number two: the string breaks.”The sketch was in his diary, but it had been made afterwards, when he viewed things artistically. At the time hehad given surreptitious tugs to the string himself.“But the string never broke?”“No. I mightn’t have seen Miss Honeychurch rise,but I should certainly have heard Miss Bartlett fall.”“It has broken now,” said the young man in low,vibrating tones.Immediately he realized that of all the conceited,ludicrous, contemptible ways of announcing an engagement this was the worst. He cursed his love of metaphor;had he suggested that he was a star and that Lucy wassoaring up to reach him?“Broken? What do you mean?”“I meant,” Cecil said stiffly, “that she is goingto marry me.”The clergyman was conscious of some bitterdisappointment which he could not keep out of hisvoice.SAT Preparation Booklet“I am sorry; I must apologize. I had no idea youwere intimate with her, or I should never have talkedin this flippant, superficial way. You ought to have50 stopped me.” And down in the garden he saw Lucyherself; yes, he was disappointed.Cecil, who naturally preferred congratulationsto apologies, drew down the corner of his mouth. Wasthis the reaction his action would get from the whole55 world? Of course, he despised the world as a whole;every thoughtful man should; it is almost a test ofrefinement.“I’m sorry I have given you a shock,” he saiddryly. “I fear that Lucy’s choice does not meet with60 your approval.”10. Cecil’s remark in line 1 (“Lucy . . . faults”) is madein a tone of(A)(B)(C)(D)(E)great convictionstudied neutralityplayful ironygenuine surpriseweary cynicism11. Mr. Beebe asks the question in lines 6-7 (“Does . . .quietly”) primarily in order to(A)(B)(C)(D)(E)raise an urgent concernanticipate a possible objectionchallenge a widely accepted theorynote an apparent inconsistencycriticize a popular pastime12. Mr. Beebe’s statement, “The water-tight . . . bad”(lines 9-11), suggests that Lucy will(A) ultimately become a famous and respectedmusician(B) eventually play music in a less disciplinedfashion(C) one day begin to live with great passion(D) soon regret an impetuous decision(E) someday marry a man who will be thecause of her undoing

13. In line 24, “sense” most nearly lityconsensusimpression14. For Mr. Beebe, “Picture number two” (line 27)represents(A)(B)(C)(D)(E)a misleading occurrencea dangerous gamblean unlikely developmentan anticipated outcomean avoidable difficulty15. Ultimately, Cecil views his remark in line 34(“It . . . now”) as(A)(B)(C)(D)(E)singularly poeticparticularly memorableembarrassingly inaptexcessively criticalregrettably underhanded16. The question in lines 39-40 (“had . . . him ”) suggeststhat Cecil fears that Mr. Beebe will(A)(B)(C)(D)(E)detect the lack of originality in his thinkingconsider him to be vaintell Lucy of his inappropriate remarkdistrust him as a confidantattempt to block his engagement to LucySAT Preparation Booklet55

Questions 17-24 are based on the following passage.The following passage is adapted from a book published in1999.Line51015202530354045Calling it a cover-up would be far too dramatic. But formore than half a century—even in the midst of some ofthe greatest scientific achievements in history—physicistshave been quietly aware of a dark cloud looming on adistant horizon. The problem is this: There are twofoundational pillars upon which modern physics rests.One is general relativity, which provides a theoreticalframework for understanding the universe on the largestof scales: stars, galaxies, clusters of galaxies, and beyondto the immense expanse of the universe itself. The otheris quantum mechanics, which provides a theoreticalframework for understanding the universe on the smallest of scales: molecules, atoms, and all the way down tosubatomic particles like electrons and quarks. Throughyears of research, physicists have experim

Official SAT Practice Test 2006-07 Taking the Practice Test The practice test will help you most if you take it under conditions as close as possible to those of the actual test. Set aside 3 hours and 20 minutes of uninterrupted time That way you can complete the entire test in one sitting. Note: The total testing time is