ACT Past Papers with Answers

Paper 81

ACT December 2003

Form 61E · Math Test · 60 questions

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Paper 81 · ACT December 2003 · Form 61E · Math Test

lffustra廿ve figuresare NOT n氐essali/y drawn toscale

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Paper 81 · ACT December 2003 · Form 61E · Math Test

The A·l Cab Company中江ges $2.60 for the f"u-st I - rnilc ofa cabride "泊＄1.25 for each additional 2 l . 2 －呻•• reg釭dless ofhow many people 正它江 the cab. Tua stude沁sh釭e • cab ride from the b心江忒ion to I theircollege dormitory, a distance of2¾ mile,. If they 2 share the cost of the cab equally, how mo吐is each pcrsoo's sh江e?

A$7.60B$6.50C$5.10D$3.85E$3.80

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Paper 81 · ACT December 2003 · Form 61E · Math Test

Sam received scores of 86, 81, 82, 80, and 71 on 0 equally weighted tests. Which ofthe followingis洹s mean score?

A83B82C81D80E79

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Paper 81 · ACT December 2003 · Form 61E · Math Test

Three fri皿ds will ron a race. If there are no ties, in how manydistinct orders can these 3 friends finish the race? ACT4nE 14 but some of the problems may best be done without usinga calculator. Note: Unless otheJWise stated, all of!he following should beassumed.

A2B3C4D5E6

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Paper 81 · ACT December 2003 · Form 61E · Math Test

Source question 5. Refer to the source image.

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Paper 81 · ACT December 2003 · Form 61E · Math Test

How many triangles that have integer side lengths匹 si.tnilar 10也e mangle sb叩巾比low? 且telymaoy:

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Paper 81 · ACT December 2003 · Form 61E · Math Test

Whena=7,b=-3,andc=4, bac-ad'-ab=1 C、-49 A rec血gle h玉a w;dth of(3x一2) feet anda length of (4工＋3) feel Which of the following expressions rep resents the a.ea. ins千立c fee� oftherec心gle? Wbatis4% of7.34x对？ g: l·詈5 Due to gravitation,J diffc,cnc«加IWCCD the Moon and Ear山．扛旺tronaut who weighs 198 poUDds on Earth w,ig比， proportionally, 33 p叩血S OD tbe Mooa. How many po心ds would aa,stro立ut who weighs !20po叩ds叩Earth weigb on the Moon? 氐45 What is tbe perimet立h me丘，ofasq吐re having a11 江ea of4 square meters? ... 2

A-217B一175C7D217EI记一66I立＋er-671记＋cr+68I记－ l?工＋691记＋17工－ 610293,6001129.36012过36136141815201633

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Paper 81 · ACT December 2003 · Form 61E · Math Test

Source question 8. Refer to the source image.

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Paper 81 · ACT December 2003 · Form 61E · Math Test

Source question 9. Refer to the source image.

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Paper 81 · ACT December 2003 · Form 61E · Math Test

Source question 10. Refer to the source image.

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Paper 81 · ACT December 2003 · Form 61E · Math Test

24 Tu.is month. Heather sold 75 figurines in 2 size,. Toe large figurines sold for $15 each.础d the small figwincs sold for $10euh. The tptal amotiot ofmoney received for the large figurines was the s&IllC as中e total rccciv吐for the snull figurines. How many large figurines did Heather sell this month? EL 37 J星 45 吓at are the 2 pos;tivo integers su吐'th社thc,quarc oot of thefr snm is S aud如squ釭e root of thou-prod ,ct is 12? ,_ 2血d 3 :. 3 and 4 :. 5 and 144

A48B56C80D25E30650

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Paper 81 · ACT December 2003 · Form 61E · Math Test

Source question 12. Refer to the source image.

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Paper 81 · ACT December 2003 · Form 61E · Math Test

In如, figure below、AB i CD、 LBCDm竺ures65° · 扛id LBCA measures 6I•. Whatdoes LBAC me,这ore?

A54°B56°C61°D63°E65°

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Paper 81 · ACT December 2003 · Form 61E · Math Test

巨tisba坛starting aworko1lt rootinc.立面t中y she plans to jo: I mil..讫ch day after如•t. she pl扭s to I 让crca.,c her distance by -!- mile口lil she is jo邸让g 4 2血cs per中y. Then she plans to continue jo严g 2 miles <'ery day. If巨匹ha b中心h:: worko立rou tine tod•y, bow many miles will she jog in中0 fust 7中,ys? 压．The home plate of a baseball中amond比illustta1ed below. T比interior angles that .. re not right angles江e congruent. What is止e measu� of each of中cse ·5. 130° 人．61E 丿 16 DO YOUR FIGURING HERE. GO ON TO THE NEXT PAGE. 2 ^ ＾卒^ ＾＾＾＾＾ 2 6. (4a+3b+2c)一（2a+功－1c) is equiv斗cot IO !ff仁）=-2:?--:出．thcn/(-2) = 7

A7-!- 2B11-!- 2C12-l- 4D14E286ugles?7125°8135°9140°10145°112a+ b-5c122a+ b+9c132a+5b-5c14位＋5b+9c1512abc168

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Paper 81 · ACT December 2003 · Form 61E · Math Test

Source question 15. Refer to the source image.

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Paper 81 · ACT December 2003 · Form 61E · Math Test

Source question 16. Refer to the source image.

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Paper 81 · ACT December 2003 · Form 61E · Math Test

Source question 17. Refer to the source image.

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Paper 81 · ACT December 2003 · Form 61E · Math Test

Source question 18. Refer to the source image.

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Paper 81 · ACT December 2003 · Form 61E · Math Test

Source question 19. Refer to the source image.

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Paper 81 · ACT December 2003 · Form 61E · Math Test

Source question 20. Refer to the source image.

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Paper 81 · ACT December 2003 · Form 61E · Math Test

Source question 21. Refer to the source image.

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Paper 81 · ACT December 2003 · Form 61E · Math Test

What江．the distance比tweenthe points叩th coordi 凹．tcs (3．4)..d (-2.7) in the standard (z,J) coonlin让e plane? 公＾亡亡丛 00 YOUR FIGURING HERE. 2 23_ tossmg darts a1 aboard中at duplicates part of the江还 dard (x,y) coordmate pl压e. A ballooo is釭口cbed 0 中c board at c江b point (x,y) such中a口indy a:rc血• gers. If a p切er brcaJcs 3 balloons atUcbed to adjacent 血釭pom氐山eplayerWlDS中e歹扭dpmz. SbeUa broken中e balloons皇1 coord呾1es (--4.2)印d l).W邱士of山e folio吨g正血coordio血＄ofa ooo Sheilacould bro吐m w江山e gr心d产？ (-3, 3) (-4, I) (-5, 0) (4,-2) (2, 4) 认．lo tu.BC shown belo中，the measure of乙A is 30° , LACS is a right angle. D江on五．aDd宽bisects LACB.｀"立is中• measure of乙CDB. ill de歹ees? D A 三三氐105° 18 GO ON TO THE NEXT PAGE. 2 乙心乙亡亡

A顷BVC岔D洹E熘645°760°875°990•

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Paper 81 · ACT December 2003 · Form 61E · Math Test

Source question 23. Refer to the source image.

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Paper 81 · ACT December 2003 · Form 61E · Math Test

Source question 24. Refer to the source image.

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Paper 81 · ACT December 2003 · Form 61E · Math Test

One of tho following cqo吐ions, io slope-intercept form, is the equation of the line shown below ill the S组ndard(工,y) coordin毗plane. Which one? 三二一二工．；一 ,＇，· 1 ; ：，： -,... , ： , l , 3 B. y=--fx-2 5 5 C. y=－－工一 2 3 5 3 亡乙心八 DO YOUR FIGURINGHERE. 2 坏．Each of土c fignm. below can be divided into 3 squares: one with side lengths 6 cm, 四oth忒 with 忒北lengths 4 cm.=dthe血d with sidelengths 2cm. Which figure h旺 the great心t pcrimc虹？勹二] J 厂 k 丿 � L 1 1 , 三 `CT.“E ,9 GO ON TO THE NEXT PAGE. 2^ 么^ ＾＾ ^ ^ ＾＾ 2 27. When a banl: pay>闷inter~t, co工pouaded 扫nually, a I deposit of SP increases to SP(J十面ratthe end of y years, whuey is a w加le number. Lon initially depos虹＄600 in an account如t pays

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Ay=－扣＋2By= 3 �x+2Cy = 5 �x+2D·EChoice H — see source image

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Paper 81 · ACT December 2003 · Form 61E · Math Test

Source question 26. Refer to the source image.

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Paper 81 · ACT December 2003 · Form 61E · Math Test

Source question 27. Refer to the source image.

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Paper 81 · ACT December 2003 · Form 61E · Math Test

Tbenu呻er迈ismnonal池decimal叩sent,ll00 neithe, te-～ nor ～尸心．Howm江l, of the fol Iowmg 4 «al numben江e imuional? (\/守，（'v'S·V孔6'\12.仅可＋句 29, W妇i is让e沁latioa立tfor the eq凹tion :?--12, + 36 =4? E, [7, 10)

A0BIC2D3E46[-8.-4)7I一2, 8)8{4,8)9{5,81

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Paper 81 · ACT December 2003 · Form 61E · Math Test

Source question 29. Refer to the source image.

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Paper 81 · ACT December 2003 · Form 61E · Math Test

For all real nombers •·中h;ch of the following is 宁心ntto 声？心T.“' 20 00 YOUR FIGURING HERE. GO ON TO THE NEXT PAGE. 2^ 31, Whi中ofthe following is NOT平val中tto 80% ofn? 乙＾＾心乙乙/乙 DO YOUR FIGURING HERE. 2 5 JOO

A1B石Cl•IDolEo`6O.BOn78(0.l凸）84n94(y)10，尺

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Paper 81 · ACT December 2003 · Form 61E · Math Test

Source question 31. Refer to the source image.

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Paper 81 · ACT December 2003 · Form 61E · Math Test

碑ch of the following ;, the slope of the line with equation 3x + 2y � 7 in the standard (x,y) coordin血 pl印e? 2 G. －了．， § 3 2 7 3 l

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Paper 81 · ACT December 2003 · Form 61E · Math Test

The function g(x) is defmed for aU real numbera工 Some of the fuoction v斗ues盯e given in the table 加low. One of th, following丐uations defines the function g(x). Which o立，'it? g;) j:1:I_:1:l1: D, g(x)＝左－3 s 丸If90" < 8 < 180". 扭dsinB=一中eecosB =? 13" 13 12 耳 l2 13 13 12 K －旦 5 E A2T4E1芒 21 GO ON TO THE NE灯PAGE. 12 Li | 乙公乙 Use the following information to an郅er questions 35-38. 心公心乙乙 DO YOUR FIGURINGHERE. 2 In the United States, contribu丘ens 10 8 ca匕gories of c缸斗 table organizations totaled $143.5 billion in 1997, The bar !!"'P_h _ _below _ sho _ ws the di _ stri_b血on of th� contributions, in billio匹of dollars, to the 8 categories. II also gives the percent_ of change in 1997 contribution, comp江cd to 1996 contributions for eacll catcgo巧－ 1997 Cliarltable Contributions Cg叩Cootnbutions (c加ngcfrom 1996)(billiOIIS ofdo止）碑郓on(+6％）11'11喟汕＂叩叨隔闺70.25 Ed此立on(+l2%)圈圈膛21.S1 Health(+!%）匮国14.03 Human=ices(+4％)国匮12.66 H皿皿ities(－选）圈1062 Publicservices(+ll%）墨I 8.38 氐呴onme立(+7%) !14.09 worldaff玉(+15%) 11.96

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Ag（工）= X -3Bg(.r)=2x -3Cg（工）＝ >!-+!Dg(,c)＝玉－IE56Choice J — see source image

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Paper 81 · ACT December 2003 · Form 61E · Math Test

Source question 34. Refer to the source image.

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Paper 81 · ACT December 2003 · Form 61E · Math Test

The 1997 contributions in止e hrm叩services 竺rego可 were closest to how many times山e 1997 contributions io the environm匀

A2B3C4D5E6

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Paper 81 · ACT December 2003 · Form 61E · Math Test

What让中e medi扭0f tb亡8 per立nts of change listed antbe罕aph? 丑4

A0.5B3.5C6.5D7.4

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Paper 81 · ACT December 2003 · Form 61E · Math Test

Among the following. which is the closest approxima !ion, in billloos of dollars, 10-the 1996 charitable eon tributions iD出e humanities过egory? A·,,E 22 GO ON TO THE NEXT PAGE. 2^ ＾＾＾＾＾＾ ^ ＾ 2 38. If the given·har graph were converted inlo a circle 罕aph (p;c chart), the sec匹for the reli氐on c血gory would have a central angle me还uring (10 the oearcSI degree) how m扫y de罕Ces? K4345°

A7.43B7.62C10.30DI0.95E13.81670°788'8147°9176'

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Paper 81 · ACT December 2003 · Form 61E · Math Test

Source question 38. Refer to the source image.

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Paper 81 · ACT December 2003 · Form 61E · Math Test

In the right oiangle shown below, wbic• of the follow ing expressions贮ves the earn心v斗ue ofc.江凸chcs? 口，40' ,ln40霾中40° 二夕

A5B5C5D5 cos 40°E5 s让l 40°

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Paper 81 · ACT December 2003 · Form 61E · Math Test

What is the area. ill squ江e江cb氐．ofa吐cle叫th a diameter of 16让汒bes• 'I. 1f仁扑士＝丑for all;;;-, O. lhenp'=? 36 25 12 25 36 A ball is中rown upward from a po江'that is 32 feet aboye the罕ound. The ball缸S扭initial velocity of 16 feel per second. The height, h feet above the ground,【seconds after the ball was thro吓c吐be modeled by the equation h = 32...16r- !6?．心cord ing to this m吐!, bow m>ny seconds让立中e ball is 土rown will it hit the groond? DO YOUR FIGURING HERE_ 23 GO ON TO THE NEXT PAGE. 2A ^ ＾ A A A A ^ ＾2

A8亢B16亢C32元D64兀E· 256兀6I7I8I94102511I1221341481516

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Paper 81 · ACT December 2003 · Form 61E · Math Test

Source question 41. Refer to the source image.

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Paper 81 · ACT December 2003 · Form 61E · Math Test

Source question 42. Refer to the source image.

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Paper 81 · ACT December 2003 · Form 61E · Math Test

The ti即" below shows !:,ABC and its translation 皿age l:,QRS in the standard (%.y) coo咕立匕pl扭.. whereA匕尘!ates to Q, B transla江s toR,己d Ctrans !ates toS. T比length of职釭s the same岱tbelengtb of芯．Which of the following represents this transl• tion,六工，y）？ 00 YOUR FIGURING HERE. s R ＼八产 B 八＼ 5 。 X

AT(乓y)＝(4y，工）B平J)＝（正，2y)CT(动）＝（x+4,y+2)D炬y)=(.r－4.y-2)ET(动）＝（铎）

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Paper 81 · ACT December 2003 · Form 61E · Math Test

The graph below shows the relationship bctw己n tbe time立d归五gbt-line如匹cc• rolles co釭tes car is from the start. Which ofthefoll"志g best dcscri妇 wbat thee盯must ha四 doneb如~n timcs3立d4? g e . ID 中 to cn m 。 g g th 。 g d be an an fr g c c 乎 5 . and g bc d . g st e 千 St 山 th 。 um ert 4 dag : not 皿 d t : OS 了 s I 匡 the ed - pcd 2 gSp - h gan enl 总 be g 飞 8 and ）叩 rea g slo i w e g e Wll e 5 Car car do car 0 e e ow e g c 甘 S 3 3 日且 9 3 目 l s P Th Th sl Th be Tb do Tb s E G 江 L 正 24 GO ON TO THE NEXT PAGE. 2A ^ ^ A ^ ＾＾＾ A2 心．五o wan区IC find tbe叩户叩mato height of a bnild, ing. A, sboW1I.below, when Tito is at ad达tance of 100 feel aloog level gronnd from the building. be es止 males !hat ho m匹t look op at an angle ofso• to see the lo!'of_tbe building. If Tito is 6 feel tall, which of the 血50• 。工50° 1 100 1 +6 +6 + 6 +6

A100B100C100 sin 50°D100 cos so• + 6E100血50°

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Paper 81 · ACT December 2003 · Form 61E · Math Test

Source question 45. Refer to the source image.

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Paper 81 · ACT December 2003 · Form 61E · Math Test

Po江t A is吐the cemer of the circle, ri:ctangle, and 工hombus in the fill= below. The 归rtices of rectangle BCDE lie on the circle and the vertices of rhombus FGHI are the midpo吐of the sides of r立－丘ugleBCDE. Ifthe radi匹ofthe C虹比i, 2foeL how比ngi, asideof the中ombas, in foct1 瓦4 25 DO YOUR FIGURING HERE. GO ON TO THE NEXT PAGE. 2A A A A ^ ＾ ^ ＾＾2 47. Thecircle（工＋3)'+()'．一9)'= JO is SDOWILin the S血－ d叩（工;y) coordin�比pl血e below. Which of the fol Iowini: is皿cq血OD of如血e that让血gent to出e 改rclc社出epoint(0,10) 1 DO YOUR FIGURING HERE. 1 c. y= －；；－ 10 3 1 D. y= ¾；；＋10 3 y : 』妞Points M, N, X, and Y are colline扛，Mis tbemi中oint of对，and Nis the midpoint of匹．w垣tis the ratio of如length of对to the length of欢？

AIB叶C2D3Ey=-3工一 106J=-3.r+!O7y= 3.r+!O81:291:3101:4113:1123:4

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Paper 81 · ACT December 2003 · Form 61E · Math Test

Source question 47. Refer to the source image.

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Paper 81 · ACT December 2003 · Form 61E · Math Test

Source question 48. Refer to the source image.

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Paper 81 · ACT December 2003 · Form 61E · Math Test

W比tare the re斗solutions forx, ifany, to the勺吐don （因一如I - b) = O ifa and b are positiveintegers?

A±aand土bB-amd -bCaaod b-DYaand讶ETh= are uoreal solutions.

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Paper 81 · ACT December 2003 · Form 61E · Math Test

A叩C四be cousists of8 small cubes as shown比low. Each s平吐cub• has an edge !,ngtb of 2工cbcs. If 1 small cube is remov吐how docs th• surface 云－ in sqn江e inc比s, of th• original large cube comp江e to that ofthen,m刁ininirsolid? 言 2 2 匹atban them二吐血gsolid. 釭eathan the rem吐血g solid. ,.,.m和oini: solid. face江eathan the rem昢血gsolid. face ar..th扭theremai血gsoud. 26 GO ON TO THE NEXT PAGE 2A ^ ＾丛＾ 51. Suppose/(;;c)砬d g(x) arc血cti叩5 dcfin吐for all real number,x,血d/(,:) is the.inverse function ofg(x). Ifr is a real number皿df(r) = 0, then g(O) = ? 2 立．The polynomial，，－kx mi,l（工＋匀血d础other low江g让the江tegorvalue

ATheoriginal cube h邸24 s叩are i皿hes leas surfaceBToe original cube b还12 square inches less surfaceCThe original cube缸s the s扛ae s画缸'.,.....邸theDToe original cube has 12 square in土es ll10re surEThe original cube h压24 sq立e inches m忒e sur6071829工10r11-1112-613I1461511

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Paper 81 · ACT December 2003 · Form 61E · Math Test

Source question 51. Refer to the source image.

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Paper 81 · ACT December 2003 · Form 61E · Math Test

Source question 52. Refer to the source image.

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AChoice F — see source imageBChoice G — see source imageCChoice H — see source imageDChoice J — see source imageEChoice K — see source image

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Paper 81 · ACT December 2003 · Form 61E · Math Test

One of the following匀过ems of in叩斗还es is如wn 红aphed as the shaded rcgi。n in the standard (x,y) ～叫in•仁pl扭• below. Which one i• it? 勹勹鼻x Y> f-3 y> 一五 -3 2 y> 王 -3 2

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Ay< 扛＋3 yBy＜扛＋3Cy > 3工＋3DChoice D — see source imageEChoice E — see source image

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Paper 81 · ACT December 2003 · Form 61E · Math Test

The real number c is positivo and the real nm:nbers a 立db虹such that ab > 0 and a > b. Which ofthe fol lowing江meforall such a.b, andc ? F．旦＜上 C C a b ACT令E 句 ^ ＾ A A2 DO YOUR FIGURING HERE. GOON TO THE NEXT PAGE. 2A A A ^ ＾＾＾＾ A2

A丘＜丘Ba-cCa-cDa+c

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Paper 81 · ACT December 2003 · Form 61E · Math Test

One ofth• follow江g巨aphs in the叩ndard(立y) coor ，， f 血ate p血c is the graph ofthe叫uation 7 +1,= I. 4 9 Which one isit? DO YOUR FIGURING HERE. y 4 0 T 凡正三 D 6 : c ; $ 儿丑

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AChoice A — see source imageBChoice B — see source imageCChoice C — see source imageDChoice D — see source imageEChoice E — see source image

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Paper 81 · ACT December 2003 · Form 61E · Math Test

Giv..th吐a, b, and c釭C吐l po•itive, which oftile fol- lowingis equi吐entto log件）？江玉 loge ]. �)(log约 logc loge ACT-<1E 28 GO ON TO THE NEXT PAGE. 2 ^ ＾＾＾＾＾＾＾＾2 S7. How many cubic ceoc.imete过釭e equal to I cubic meter? (Nate: l meter = I00 ceo立ne比rs) 仓器 C. 10,000 DO YOUR FIGURING HERE.

Aloga+2logb-JogcB2(loga+Jogb)一logeC@ga)(logb?D30,000E1,000,000

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Paper 81 · ACT December 2003 · Form 61E · Math Test

Source question 57. Refer to the source image.

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AChoice A — see source imageBChoice B — see source imageCChoice C — see source imageDChoice D — see source imageEChoice E — see source image

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Paper 81 · ACT December 2003 · Form 61E · Math Test

Mel..ie让belping to paint a reometric d呻"on a school wall The fig,,rc below, with its dimensions ill painL The b心es of the tr11pezoidal元gion江e 10 feet 扭d 12 feet, respective!y.By painting the tra产01dal region, how m扭y芍吐re feet of the wall will M中血 p血t? 66 72 88 96 32 1 E G 江 L K l 10 l l2 1

Source page for act-december-2003-form-61e-math-058

A.t, shows the trapezoidal region Mc血ie agre吐toBChoice G — see source imageCChoice H — see source imageDChoice J — see source imageEChoice K — see source image

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Paper 81 · ACT December 2003 · Form 61E · Math Test

The table below giv;畜 onlered p吐飞;n the s血吐d (r,y)coo记丘a仁plane.互"" 0, which of血following 血e functi叩s goes throu吐all ofthese orderedpairs? I1:I:I:1:I::11 :|：l:｝_：；l:II A. y= sin(沁立）

Ay = as丘（和）By=asin（元）Cy = ，叫护－a)Dy = asi.n（工－引

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Paper 81 · ACT December 2003 · Form 61E · Math Test

At a chess tournamcn� each person played exactly I oame with every other pcrso丘Tw吐勺七ight g立立S were played How many pooplc played in the tonrn召－ ment? 江14 END OFTEST2 STOP! DO NOT TURN THE PAGE UNTIL TOLDTO DO SO. DO NOT RETURN TO THE PREVIOUS TEST. 29

A7B8C28D56

Form 61E · Math Test · 60 questions

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