ACT Past Papers with Answers

Paper 62 · ACT April 2009 · Form 66F · Math Test

TITe cost of a ¥ym membership is a onetime fet of $140, plus a monthly fee of $40. Brendan wrote a $500 check to pay his gym &membership for a certain number of Jnonths, illLluding the onetime fee. How Inany monihs of membership did he pay for,?

Paper 62 · ACT April 2009 · Form 66F · Math Test

. To the nearest tenth of an hour, whaE is the average number of hours for Ihe 20 suivey responses? ACTé6F 21 GO ON TO THE NEXT PAGE.

Paper 62 · ACT April 2009 · Form 66F · Math Test

A museum offers a 2-hour guided uroup tour. For groups wilh fewer than 25 people the cosi is $9.25 per rson; for groups with 25 people or more the cost is r8.50 per person. The 27 people in the 9.,00 a,m. iour group each paid S9.25 in advance. What is the total refund that the museum owes the 9:00 a.m. trroup. ACT-66F 14 GO ON TO THE NEXT PAGE. The 13-member math club needs to choose a student government representative. They decide that Ihe representative, who will be chosen ai random, CANNOT be any of Ihe 3 officers of the club. What LS Ihe probability thai Samara, who is a meniber of the club but NOT an otficer. will be chosen. DO YOUR FIGURING HERE. 13 10 13

Paper 62 · ACT April 2009 · Form 66F · Math Test

Source question 5. Refer to the source image.

Paper 62 · ACT April 2009 · Form 66F · Math Test

What 15 th¢ perimeier, in centimeters, of a rectan(Tle with lengih 15 cm and width 6 cm ?

Paper 62 · ACT April 2009 · Form 66F · Math Test

Tickets for a community theater production cost $6 each when bought in advance and S8 each when boutrht at the door. The theaier sroup's (yoal is at least S2,000 in tickei sales for opening night. The theater <yroup sold 142 openin(y-nioht tickets in advance. Whai is Ihe rninkmum number of tickets they need to sell at the door on openinty'nioht'io make their ooal? A, 143

Paper 62 · ACT April 2009 · Form 66F · Math Test

For what value of r is the equation 10 12

Paper 62 · ACT April 2009 · Form 66F · Math Test

If 12(.I I i ) 15, Ihenx= 49 13 39 15 GO ON TO THE NEXT PAGE. ACTQGF

Paper 62 · ACT April 2009 · Form 66F · Math Test

In the fi¢yure below, A, D, C, and E are collinear, AD, BD, and BC are all ihe sanie length, and Ihe anvle ' Ineiqsure of ZABD is as niarked. What i.s ihe deoree measure of ZBCE ? DO YOUR FIGURING HE'RE. 50°

Paper 62 · ACT April 2009 · Form 66F · Math Test

Iff(x)- 9x' + 5x- 8, thenf(-2)= 9 -54 18 18 38

Paper 62 · ACT April 2009 · Form 66F · Math Test

Wliat is the leas¢ common multiple of 30, 20, and 70 ? 40 42 120 420

Paper 62 · ACT April 2009 · Form 66F · Math Test

While doing a problem on his ca,culaior, Tom nieant 10 divide 2 number by 2, but instead he accidetjlally multiplied the number by 2. Which of the following calculations could Torn then do to ihe result on the calculator screen 10 obtain ihe result he originally wanted?

Paper 62 · ACT April 2009 · Form 66F · Math Test

4 i5. Which ot the followin<y is an irrational number that is a solulion zo the equation 27 GO ON TO THE NEXT PAGE. ACT.66F

Paper 62 · ACT April 2009 · Form 66F · Math Test

In LABC, ZA measures greatei than 43° and ZB measures exactly 90° Which of the following phrases best describes Ilie measure of IC ? E, Less than 47° DO YOUR FIGURING HERE.

Paper 62 · ACT April 2009 · Form 66F · Math Test

Among the following arithmeiie operalions, which could the symbol Q represent piven that the equation (2 & 1), + {6 0 3} 10 is Erue? l. Addition II. SubiracEion III, Division

Paper 62 · ACT April 2009 · Form 66F · Math Test

One of the followkng is'an equation of the linear relation ghown in the standard (x,).) coordinate plane belo￿1 Which equation is il? 12 10

Paper 62 · ACT April 2009 · Form 66F · Math Test

An iiiteger. ii, is added to 4. That sum i< then multiplied by 8. This result is 10 less ihan twice the original inte<7er. Which of the following equations represents this relationship. 10 n+4x8-211 10 17 GO ON TO THE NEXT PAGE. AGT-66F

Paper 62 · ACT April 2009 · Form 66F · Math Test

Two workers were hired to beoiii Kvoi'k ai tlie S2ln¢ time. Worker A's contracl called foi a stariiiio salai'y of $20,000 Vdiili an increase of $800 dfier eacli ycar of employn)enl. Worker B's coi)Iract called for a Siarti21iY salary of $15,200 with ali inci'ease of S?:000 afier each year of employnienr. If x represenis the nuiiiber of full years, employmeiit (Iliat is. Ihe nuiTJbei- of )iearly increases each worker has received), whicl) of ilie following equations could be solved to deiermiiie Ihe number of years until B's yearly sAlary equals A's yearly salary. DO YOUR FIGURING HERE.

Paper 62 · ACT April 2009 · Form 66F · Math Test

A ramp for loadinLY trucks is 13 feel loncr and cover8 12 feel along the level ground, as shown beloiv. How many feet high is the highesi point on the ramp. 13 12

Paper 62 · ACT April 2009 · Form 66F · Math Test

The expression 7(x + 3) - 3(2x- 2) 15 equivalent to: x+15 +19 .Y+23

Paper 62 · ACT April 2009 · Form 66F · Math Test

Ifx+i,-32, andx-y- 12, Ilien J-

Paper 62 · ACT April 2009 · Form 66F · Math Test

.When (2.Y

Paper 62 · ACT April 2009 · Form 66F · Math Test

What is the area, in square feet, of the figure below? 25 feel DO YOUR FIGURING HERE. 5 feet 15 feet IS feet 60

Paper 62 · ACT April 2009 · Form 66F · Math Test

The table below gives the values of 2 functions, f and 8, for various values of x. One of the functions exprcsses a linear relationship. What is the value of that function at x- f(x) g(x)

Paper 62 · ACT April 2009 · Form 66F · Math Test

What is the slope of the line reprtsented by the equ&tÉon 6y- 14x- 14 14

Paper 62 · ACT April 2009 · Form 66F · Math Test

What is the sum of the 2 solutions of the equation x-+.¥- 12 AGf-66F 19 GO ON TO THE NEXT PAGE.

Paper 62 · ACT April 2009 · Form 66F · Math Test

Two siiiiilar trianoles have perinietei's in the raiio 3.5. The sides of the smaller Iri2ngle measure 3 cm, 5 cm: 2nd 7 ci)I, respectively. Wh-at is the periineter, in centimeters, of the larger triangle? DO YOUR FIGURING HERE.

Paper 62 · ACT April 2009 · Form 66F · Math Test

At a certain location, the low iemperatures, in degrees Fahrenheit, for each of 7 consecutkve days in January were -2°F, 4°F, -3°F, l°F, 2°F, ~5°F, 2nd -6°F. What was ihe median of ihese low temperalures? .30. When asked his age, the algebra teacher said, 'If you square my aoc, then subtract 23 times my age, Ihe result is 50., How old is he? F, 23 .J. 46

Paper 62 · ACT April 2009 · Form 66F · Math Test

Source question 30. Refer to the source image.

Paper 62 · ACT April 2009 · Form 66F · Math Test

The digiance, d, an accelerating objeci travels in t s¢corJds can be modcled by the equation d ar where a is Ihe acceleration rate, in meters per second per second. If. a car accelerates from a stop at the rate of 20 meters per second per seiond and travels a disiance of 80 meters, aboui how many seconds did the car Iravel?

Paper 62 · ACT April 2009 · Form 66F · Math Test

Lei d, b, c, and d be distinct posilive integers. Whai is the 4th term of the geomelTiC sequence below? bcd, abc d, a bc d, ACT.6SF 20 GO ON TO THE NEXT HAGE. DO YOUR FIGURING HERE. Use the following information to answer questions 33-35. survey in a study skills class asked Ihe 20 studeats enrolled in the class how maiiy hours (rounded to tlie nearest hour) they had spent studyino on the previous evening. The 20 responses are summarized by Ihe histooram btlow. 0 1 2 3 4 5 hours

Paper 62 · ACT April 2009 · Form 66F · Math Test

Whai fraciion of the studenLS responded that they had spent less than 3 hours Studyinoy? io 13 20 20

Paper 62 · ACT April 2009 · Form 66F · Math Test

The teacher decides to show ihe daia in a clrcle trraph (pie chart). Whai should be the measure of the central angle of ihe sector for 3 hours?

Paper 62 · ACT April 2009 · Form 66F · Math Test

Source question 35. Refer to the source image.

Paper 62 · ACT April 2009 · Form 66F · Math Test

Forall.¥>?I, (1- + 81"* 7)(.1- 3) ?l)(.i + l) DO YOUR FIGURING HERE. .¥*3 ,r+l 4(x-i) A+J

Paper 62 · ACT April 2009 · Form 66F · Math Test

The boiioni of ihe baskei of a hoi-37r balloon is parallel lo Ihe Icvtl ground. One t2Ut tether line 144 feel lono is attached to ihe cenier of ihe boitom of ihe basket and is anchored to the uround ai an antsle of 72° as shown in Ihe figure below. Ivhich of Ihe following expressions gives ihe dist2nce, in feet, from ihe center of ihe boiiom of the basket to th¢ oround? cos 72° sin 729 zeiher line 144 fi 72°

Paper 62 · ACT April 2009 · Form 66F · Math Test

The coordinates of ihe endpoinis of GH, in ihe szandard (x,y) coord'inaie plane, are (-8,-3) and (2,3). What is the x-coordinate of the midpoint of GTh ?

Paper 62 · ACT April 2009 · Form 66F · Math Test

On a map in Ihe siandard (X•y) coordinate plane, Ihe iowns of Arlin8lon and Belelwood are represenied by Ihe points (-2,-3) and (-6,-7), respectively. Each unit on ihe map represents an actual disiance of 10 miles. Which of Ihe following is closest to the distance, in miles, between ihese 2. lowns? ACT4fjF 22 GO ON TO THE NEXT PAGE.

Paper 62 · ACT April 2009 · Form 66F · Math Test

Which of the followin(y statements is true aboui rational . andlor irrational numbers? DO YOUR FIGURING HERE.

Paper 62 · ACT April 2009 · Form 66F · Math Test

For th¢ complex number i and an iRleoer x. which of the followintr is a possible value of i, ?

Paper 62 · ACT April 2009 · Form 66F · Math Test

Consider the equaiion y - (x - 3) + 2 where x and y are boih real numbers. The table below Gives Ihe values of ) for selected values of x. 83 51 27 For the.equation above, which of ihe following values of x (Fives the least value of y

Paper 62 · ACT April 2009 · Form 66F · Math Test

The heighi and radius of the righi circular cylinder below are oiven in meiers. What is the volume, in cubic meters, of the cylinder? 30 31TC C, 150 23 GO ON TO THE NEXT PAGE. ACT.66F 44, Lines l and l? inierseci eacli oiher and 3 parallel lilies, I;, l . and If:.at the poinis shown in ilie fitsure below. The ralio of Ihe perimeter of LABC io ihe periiiieleT of AFG 1% 1.3. The raiio of DEio fG is 2.3. Wliat is tlie ratio of AC to CE ? DO YOUR FIGURING HERE. .45. A rocket lified off from a launch pad and traveled verlically 30 kilometers, Ihen Iraveled 40 kilometers at 30° from the vertical, and ilien traveled l 00 kilomelers ai 45° from the vertical, as shown in ihe figure below. .Ai Ihat poini, Ihe iockel was how many kilomeiers above ihe heioht of ihe launch pad? Iookm 40km 30km. C, 190

Paper 62 · ACT April 2009 · Form 66F · Math Test

Source question 44. Refer to the source image.

Paper 62 · ACT April 2009 · Form 66F · Math Test

Source question 45. Refer to the source image.

Paper 62 · ACT April 2009 · Form 66F · Math Test

In Ihe siandard (x,i) coordinale plane, what is the 2re2 of Ihe circlex +y 16 ? 16 64 ACT.86F 24 GO ON TO THE NEXT PAGE.

Paper 62 · ACT April 2009 · Form 66F · Math Test

In the standard (x,y) coordinate plane below, I side of a rectanule is on The .r-axis, and the Yertices of ihe opposite side of the rectangle are oll the graph ol the parabola ! Lei a represent any value of x such that O < x < <3. Which of the followin4J is an expression in terms of a for Ihe aTea, in square coordinate units, of any such rectanole? DO YOUR FIGURING HERE. 6-2a Illk -4a + 12a -4a + 4a+12 ?4a +36

Paper 62 · ACT April 2009 · Form 66F · Math Test

If n is a positive intever, which of the following expressions must be an odd inteoer?

Paper 62 · ACT April 2009 · Form 66F · Math Test

The value of logs is between which of the following pairs of congecutive iniegers . 25 GO ON TO THE NEXT PAGE. ACT-66F DO YOUR FIGURING HERE. Use the following information to answer queslions 50-52. The table beloiv shoivs tlie Mieekly sales totals (in ihousands of dollars) for 4 departments at Pinky's Nqe(yainarket durin Ihe 5 most recent iiieek5, Daia is mis£in¢Y due io a conipuier 'irus Ihai infecied ihe superniarkei's daiabase. The daia in the table has beeii iierified as bei no accurale. Week nuinber Deparinieni 145 30 54 86 144 156 145 140 Produce Canned goods Dry tFoods 62 82 69 75 77 85 .50. Wliich of the following is closest to the pereent increase in meal deparinient sales for Pinky's MeoamaTket from Week 2 to Iveek 3 ? l.llo

Paper 62 · ACT April 2009 · Form 66F · Math Test

Source question 50. Refer to the source image.

Paper 62 · ACT April 2009 · Form 66F · Math Test

.Prior to Week 3. Ihe manaoer sei ihe 4yoal for meat department sales io averaoe 150 ihousand dollars per week from ihe beginning of Week 3 ihrough ihe end of Week 6. To meet this goal, what musi bc ihe minimum meat department sales for Week 6, in thousands of dollars?

Paper 62 · ACT April 2009 · Form 66F · Math Test

The assisiant manager recalls that produce deparLmenl sales increased at a very high rate durino ihc 5 weeks, due io a projecied shortage of fruit. She says that for each week from Week 2 to Week 5, produce department sales increased l 00/0 froni the previous week. Which of the following values: in thousands of dollars, is c105est to produce department sales for Week 5 9 J, 40 ACTffj6F 26 GO ON TO THE NEXT PAGE.

Paper 62 · ACT April 2009 · Form 66F · Math Test

A irioonometric function with equaiion y - a sin(bx + c), where a, b, and e are real numbers, is graphed in the standard (x,>9 coordinate plane below. The period of this funciion f(x) is the smallest positive number p such Ihai f(x + p) - f(x) for eiery real number x. One of ihe followinu is the period of Ihis funclion. Which one is it? DO YOUR FIGURING HERE. 2n

Paper 62 · ACT April 2009 · Form 66F · Math Test

The buildinu below casts a shadow 24 yards lono, and the angle of elevation from ihe tip of the shadow to the top of the buildino has a sine of What is Ihe height of the building in yards? ACME SINE co. angle of elevaiion 1-24 yards-4

Paper 62 · ACT April 2009 · Form 66F · Math Test

Source question 55. Refer to the source image.

Paper 62 · ACT April 2009 · Form 66F · Math Test

The graph below %how5 the distance Malika is froin a Inotion detector for a period of 10 seconds. A certaiii order of 3 of the folloiviiio actions deseribes Malika s iiioveiiieni iii relation to the position of Ihe niotion detecior. Ivliich order is li? DO YOUR FIGURING HERE, seconds I. Stands still for 5 seconds Il. Walks away ai 4 feet per second III. Walks toward ai 4 feet per second IV. Walks away at 2 feet per second V. Walks toward at 2 feet per second

Paper 62 · ACT April 2009 · Form 66F · Math Test

As shown in the figure below, a clock has a minute hand that measures 5 em from its lip to the center of the clock. To the nearest centimeter, what is the distance Iraveled by the lip of the minuie hand between 2:10 p.m. and 5:30 p.m. ? 12 10 10 68 ACT.66F 28 GO ON TO THE NEXT PAGE.

Paper 62 · ACT April 2009 · Form 66F · Math Test

For li, an anvle whose measure is between 90° and 180°, Which of the followin(y equals sin 24". DO YOUR FIGURING HERE. 24 25 24 25 25 i9. Consider all pairs of posiiive integers w and z whose sum is 5. Foi hoiv many values of i¥, does there exist a posiiive inieger x that satisfie5 both 2" xandx- 64?

Paper 62 · ACT April 2009 · Form 66F · Math Test

Source question 59. Refer to the source image.

Paper 62 · ACT April 2009 · Form 66F · Math Test

A cube with edoes 4 cm lono is inscribed in a sphere, as shown below. What is the radius of the sphere, in cenEimeters? END OF TEST 2 STOP! DO NOT TURN THE PAGE UNTIL TOLD TO DO SO. DO NOT RETURN TO THE PREVIOUS TEST. 29 ACT-66Y