ACT Past Papers with Answers

Paper 69 · ACT December 2007 · Form 65E · Math Test

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Paper 69 · ACT December 2007 · Form 65E · Math Test

. As shown in rhe fiL7ure beloiy, ￿"Ith anules a5 tnarked. a pole casts a shado￿. that 15 14 feel lontr Which of ihe followin¢7 is closest to Ihe h¢icpht of ihe pole. in feet? 60, k-14--4

Paper 69 · ACT December 2007 · Form 65E · Math Test

The word average indicates arithmetic mean. l. In the diaoram below, B is ihe rnidpoini of AC and C is the midpoint of AD. The len¢yih of BC is 14 cm. What is Ihe lenoth. in cenlimeiers, of AD ? DO,YOUR FIGURING HERE. -14cm4

Paper 69 · ACT December 2007 · Form 65E · Math Test

Which of the following are Ehe coordinales of the unlabeled vercex of the parallelogram shown in the siandard (i.y) coordinate plane below? DO YOUR FIGURING HERE. (0.5) (4,5) (1.3)

Paper 69 · ACT December 2007 · Form 65E · Math Test

Natiya's moiher's aoe in whole years is 4 titnes ati)a's aoe in whole years. The sum of these 2 aDes is 35 years.-What is Natiya's rnothcr's atre in whole

Paper 69 · ACT December 2007 · Form 65E · Math Test

If £.4BC is a rioht ancrle and D is in the interior of ZABC. Nv"hich of the follo￿.intr CANNOT be the measure of ZDBC ? 60, 80, loo,

Paper 69 · ACT December 2007 · Form 65E · Math Test

Jick has a blue sweaishirt, a black sweatshirt. and a tan sw'eatshirt. He also has a pair ot blue pants, a pair ot black pants, and a pair of ian pants. How maay different s￿'ea1$h1rt-panES combinations does Jack ha%e iih exacily I sw'eatshirl and I pair of panls in each cotn.bination.

Paper 69 · ACT December 2007 · Form 65E · Math Test

507G of 8 is equal io ?iC7c of u'hai nutnber. AC i -DiC 15 GO ON TO THE NEXT PAGE.

Paper 69 · ACT December 2007 · Form 65E · Math Test

All 30 siudenls in a history class look 2 lesES. Of ihese siudents, 28 passed the firsl lest and 25 passed the second test. What is the maximum possible number of students who passed both tests? .H. 27 DO YOUR FIGURING HERE.

Paper 69 · ACT December 2007 · Form 65E · Math Test

IVh21 is the largesi I'alue of x for ￿'hICh Ihere e.KÉ£lS a real value of J such that x + y 3?4? 18

Paper 69 · ACT December 2007 · Form 65E · Math Test

An adi'ertisement shows a stereo system at reoular price of S675. An 8C70 sales tax ￿.111 be applied to the sale pricc of the system. A customer bu}'ino Ihe stereo sysiem gives ihe sales clerk.S500. How much chanoe. if any, should the customer receive. off the S86

Paper 69 · ACT December 2007 · Form 65E · Math Test

Ivhich of rhe followinty numbers is l%:OT a Teal number. 25 27 25 -2)

Paper 69 · ACT December 2007 · Form 65E · Math Test

Which of ihe follo￿,1￿(? is a facior=d form of ihe expression 36x 36 49 12 hCT*5E GO ON TO THE NEXT PAGE. li. Each square in the grid below measures l unit on a side. Each vertex of Ihe shaded polygon is an inierseciion of 2 grid line5. Whai is Ihe area, in square unils, of Ihe shaded polyvon. DO YOUR FIGURING HERE. ¥J

Paper 69 · ACT December 2007 · Form 65E · Math Test

Source question 15. Refer to the source image.

Paper 69 · ACT December 2007 · Form 65E · Math Test

Th¥ heiuhi, h. of a projectile, itl feel above ihe ground, is given by the function h(r) -4t + 401 where t iepiesents time. in seconds. How many feel above the oround is the projeciiEe when t= 5 ? 160

Paper 69 · ACT December 2007 · Form 65E · Math Test

A 5-pound bau of onions CO>lS. Sl.9i at Grocery Gaiden. A 2-pound bao of th= 5&ine iype of onions cost) SO.88 at Food Fair. HokN" much cheaper, p- poiind, are Ihe Grocery, Garden onions Ihan Ihe Food Fair onions?

Paper 69 · ACT December 2007 · Form 65E · Math Test

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Paper 69 · ACT December 2007 · Form 65E · Math Test

Delon set his car's Irip odomeier EO 0.0 rniles before he Cra&'eled to i'isil a friend. He Ira¥'eled ai an averaue speed of 6) mph for ?.) hours and then look a 30-minuie bleak. Then he irav=led at an ai"eratre speed of 5) mph until his irip odomller read ?4i.O mil= HOKI, Tnany hourb did D>lon trai'el ati=r his break? GO ON TO THE NEXT PAGE. ?0. In ihe standard (x.y). coordinate plane. A has coordinates (0.3) and B has coordinates (-6,9). What arc ihe coordinates of the midpoint of AB ? DO YOUR FIGURING HERE.

Paper 69 · ACT December 2007 · Form 65E · Math Test

Source question 20. Refer to the source image.

Paper 69 · ACT December 2007 · Form 65E · Math Test

Andre has a rectanoular oarden in his backyard. He is preparing to put fencinu along the edoe of Ihe garden, which is 12 feel bN' 10 feet. One long side of ihe garden is alonG his house, so he ￿1]1 only need to fence 3 sides. How many feet of fencino w'ill Andie need9 22 44 ?2. Il'hat is the slope of Ihe line represenied by ihe equation 4v - 8.r -

Paper 69 · ACT December 2007 · Form 65E · Math Test

Source question 22. Refer to the source image.

Paper 69 · ACT December 2007 · Form 65E · Math Test

At 6:00 A.M. Ihe iemperature was JO.6°C ai Ehe Sleepy oround. At 12..00 tjoon the temperaiure ￿'aS Bear Camp¥

Paper 69 · ACT December 2007 · Form 65E · Math Test

Source question 24. Refer to the source image.

Paper 69 · ACT December 2007 · Form 65E · Math Test

Source question 25. Refer to the source image.

Paper 69 · ACT December 2007 · Form 65E · Math Test

A daca sei has i daia poinis. For Ihis daia sei, the tnean, Ihe m- -dian, and the tnode are each equal to 10., Four ol Ihe J POLnti are 8. 10. 10..and li. %l'"hikn-h OF Ihe tolIo¥i"incr is the 5Lh dat￿ poini? . 17 ??. In a ceriain number Siquence. each cletnent afier the I si elemenl 15 Ihe resuli of muliipls'intr Ihe previous elemenl b and addintr ? 10 Ihat produci. The Iid elemetLE in Ihe sequence is i3. Nl'hat is the 1st elemenl.. )? ￿'haI are Ihe possible N'alues for x ? -40 and 14 -?4 and 24 -?4 and 40 -8and 8 ?4 and 40 ?9. For 211 real niitnbers IL.. -T, }, and such Ihai .r+i"+ li ind SL. < i-. iihiLh of the followinLY statements is true. 73 73 '<7i <73 ACTffj5 GO ON TO THE NEXT PAGE.

Paper 69 · ACT December 2007 · Form 65E · Math Test

Source question 27. Refer to the source image.

Paper 69 · ACT December 2007 · Form 65E · Math Test

Source question 28. Refer to the source image.

Paper 69 · ACT December 2007 · Form 65E · Math Test

Source question 29. Refer to the source image.

Paper 69 · ACT December 2007 · Form 65E · Math Test

In the figure below. line q is parallel to line r, C is ihe cenier of the circle. AE and BD both tro through C, q is tancvent to the circle at B. F lies on AD, and ihe measure of ZFAC is 145° Whac is Ihe measure of ZBCE ? DO YOUR FIGURING HERE. l45° 145° 55°

Paper 69 · ACT December 2007 · Form 65E · Math Test

8°C. If Ihe temperature rose at a constant rate, at ,hat lime thal mornintr w'as it 31.0°C ? 7:00 A.M. 8:00 A.M. I 1:00 A.M. ?4. The expression gii?en belo￿. is equii'alent to which of Ihe follourinc expressions.

Paper 69 · ACT December 2007 · Form 65E · Math Test

The figure below represenis a certain race alono a siraighL course. The race staited at S and finished at F. A certain runner parlicipaiino in Ihis race clocked elapsed times r rg. fc. ID, and rF minutes from S 10 poinis A, B, C. D, and F, ielpecijirely. If BC. for example, denoies the disiance beEween poinis B and C, and all distances are measured in kilometers, which of Ihe followino expressions necessarily represenis ihe runner's aK'erage speed for this race, in kilomeiers per minute? elapsed lime SA SB sc SD SF rF ACT-SS 20 GO ON TO THE NEXT PAGE.

Paper 69 · ACT December 2007 · Form 65E · Math Test

The trian(Tle shown below has a hypotenuse wilh a lengih of 10 meiers. The measure of IA is 25° and the measure of ZB is 65° Which of the followin(T is closest to the lentyth. in rneters. of AC ? (Noie: sin 25° 0.42?6 cos 25° 0.9063 tan ? j,

Paper 69 · ACT December 2007 · Form 65E · Math Test

Nvhat IS the value of - -henx-3andv=

Paper 69 · ACT December 2007 · Form 65E · Math Test

Source question 35. Refer to the source image.

Paper 69 · ACT December 2007 · Form 65E · Math Test

In the diaoram beloN4'. AABC is isosceles. The measure of ZABC is 3 tim=s the measure of ZCAB. What is ihe rneasure of ZDCB '? 36° ios, ACT-S> 21 GO ON TO THE NEXT PAGE. DO YOUR FIGURING HERE. Use the following information to answer questions 37-39. The coordinates of the N'CTtices of ZIABO are sl)own in Ihe standard (x,)) coordinate plane below. Square CDEO 15 shown shaded. Point C lies on BO. point D lies on AB, and point E lies on AO. A(0,3) 10(o,o) c B(5.0)

Paper 69 · ACT December 2007 · Form 65E · Math Test

Whai is ihe slope of AB ?

Paper 69 · ACT December 2007 · Form 65E · Math Test

Which of Ihe follow'incr is closesi 10 the perimeter, in coordinate uniis, of AABO ?

Paper 69 · ACT December 2007 · Form 65E · Math Test

What is the value of tan(ZEAD) 34 ACT-85& 22 GO ON TO THE NEXT PAGE.

Paper 69 · ACT December 2007 · Form 65E · Math Test

A quality control inspecior at a factory (ook a sample of b items frotn a pioduction line and found rhal a of the itcms w¢rc defeciive. Which of the followin￿ is a oeneral expression for the fraction of the sample thai was NOT defeclive? DO YOUR FIGURING HERE.

Paper 69 · ACT December 2007 · Form 65E · Math Test

IlTrich of the followinv number line graphs shows Ihe solution set of 3(x + 2) + 1 < 4.r + 15 9 -12 -8 4? A r￿CtanCrular prism Ns-iih ili dimensions in ceniimeters is show'n in ihe figure below. NN'hai is the pristn s lolal surface area, in square cenlimeiers? ACT& 23 GO ON TOTHE NEXT PAGE.

Paper 69 · ACT December 2007 · Form 65E · Math Test

Source question 42. Refer to the source image.

Paper 69 · ACT December 2007 · Form 65E · Math Test

In ihe figure below, AE is parallel to BC. the measure of ZD is 72°. and the measure of ZE is 40° Whai is Ihe measure of £BCD ? DO YOUR FIGURING HERE. 72°

Paper 69 · ACT December 2007 · Form 65E · Math Test

What is Ihe area of ihe trapezoid below, in square inches? 6 inches 4 inches l? inches Il'hai is Ihe soluiion sei of ACT.65t 24 GO ON TO THE NEXT PAGE.

Paper 69 · ACT December 2007 · Form 65E · Math Test

Source question 45. Refer to the source image.

Paper 69 · ACT December 2007 · Form 65E · Math Test

A pond's length. represented by AB. is determined by sin(t right triangle &ABC. shown in the figure below. The distance from A to C is 40 meiers and Ihe measure of £CBA is 28° Which of the following expressions reprcsenls the lenoth, in meters. of the pond? DO YOUR FIGURING HERE. 40 sin ?8° 4D cos 28° 40 40 sÈn 28°

Paper 69 · ACT December 2007 · Form 65E · Math Test

The ) POSltive inte(yers x, x. x. ), and z have an aNeraoe of x. Nvhich of the lollowino equations must be true.

Paper 69 · ACT December 2007 · Form 65E · Math Test

11'hich of rhe follo￿,Intr pairs of functions, f(.r) and g{.r). ¥orm rhe composite functionf Ig(.r))- f (.r) 8(x)

Paper 69 · ACT December 2007 · Form 65E · Math Test

One day. Jill and Mati began at the same point, bui ran around the track in opposite directions. Jill ran at a consiani speed Ihai was 2 rneiers per second fasier Ihan Mail's constant speed. Jill passed Mail for the first lime in 40 seconds. Jill ran at a conslant rate of how many meler5 per second? >0. Today, Jill averaoed 70 seconds per lap uniil she bec*an the la>l lap. She ihen SIO￿.ed down. She averaued 72 seconds pei lap for her daily run. How manv seconds did Jill take to run the last lap. l. Matl ran 4 laps in J niinuies. Ai ￿'hat ai'era(ye raie, in meters per second, did Matt run these 4 laps. >? A circle in the standard (.r.i') coordinate plane is 12noeni 10 Ihe x-axis and has ils center 21 {2,-2). Where is Ihe poinl (O,-?) locaied? . Cannoi be delermined from Ihe given information ACT-6>E 26 GO ON TO THE NEXT PAGE.

Paper 69 · ACT December 2007 · Form 65E · Math Test

Source question 50. Refer to the source image.

Paper 69 · ACT December 2007 · Form 65E · Math Test

Source question 51. Refer to the source image.

Paper 69 · ACT December 2007 · Form 65E · Math Test

Source question 52. Refer to the source image.

Paper 69 · ACT December 2007 · Form 65E · Math Test

A window is a rectangle wilh a scmicircle whose dKamcter is a side of the rectangle. The ￿'IndoW is shown in the siandard (x.>) coordinaie plane below. where I coordinate unit represents I foot. The coordinates of 5 points on the border of the window are given. Whai is ihe area, in square feet, of the Windo￿.? DO YOUR FIGURING HERE. (0.3) (?.3) (0,0) (?,o)

Paper 69 · ACT December 2007 · Form 65E · Math Test

.4 funclion f(.r) is one-ro-opte if and onl). if each .r i the domain of f(x) corresponds 10 a unique f(x) 2nd each'f(.T) corresponds to a unique x. One of the fvlloivino is the rrraph of a one-to-one funclion f(x). Ithich crraph is it? j {.r) fl.r) f(.r) J (.r) ACT-6i 27 GO ON TO THE NEXT PAGE. >5. What is the distance. in coordinate units. between the points (p. p + l ) and (2p, p - l) in the SEandard (x,I') coordinaie plane? DO YOUR FIGURING HERE. p-+2p+2 i6. In the figure below,. LABC is a right trianole w'ith all sides of different lenryths. What is Ihe value of sinA+sinB? i7. In isosceles Irapezoid ABCD below, E is the inierseciion of ihe dia£onals. The lenoih of AB is 6 inches, the lenirihs of AE and BE are 4 inchcs, the lenoih of CE is 10 inches, and Ihe measures of £CDE and £L)CE are equal. What is the length, in inches, of CD ? 10 ACT.85E 28 GO ON TO THE NEXT PAGE.

Paper 69 · ACT December 2007 · Form 65E · Math Test

Source question 55. Refer to the source image.

Paper 69 · ACT December 2007 · Form 65E · Math Test

Source question 56. Refer to the source image.

Paper 69 · ACT December 2007 · Form 65E · Math Test

Source question 57. Refer to the source image.

Paper 69 · ACT December 2007 · Form 65E · Math Test

Which of the following mairices, when substituted for salisfies the maciix equaiion below? DO YOUR FIGURING HERE.

Paper 69 · ACT December 2007 · Form 65E · Math Test

Source question 59. Refer to the source image.

Paper 69 · ACT December 2007 · Form 65E · Math Test

Ivhal is Ehe ratio ol (he diameter l(> Ehkn cifiumfcrcnct of a cir¥ END OF TEST 2 STOP! DO NOT TURN THE PAGE UNTIL TOLD TO DO SO. DO NOT RETURN TO THE PREVIOUS TEST. ACT.6ig 29