ACT Past Papers with Answers

Paper 50

ACT December 2012

Form 71A · Math Test · 60 questions

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Paper 50 · ACT December 2012 · Form 71A · Math Test

Illustrative figures are NOT necessarily drawn to scale.

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Paper 50 · ACT December 2012 · Form 71A · Math Test

What is the le邸t co血oo deno而nator of the fraction 4 1 3 扭d 15'6' 4 ？

A20B60C90D120E360

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Paper 50 · ACT December 2012 · Form 71A · Math Test

Malik is building a frame for a recta11gular picture that he paiutcd, and hc needs to know theterimctcr ofthe picture. The length of tbe picture is 36 inches and the width is 24 inches. What is 山e perimeter, in inches, of the picture?

A60B84C96D. 120E864

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Paper 50 · ACT December 2012 · Form 71A · Math Test

The word a四rage lndlcates arithmetic mean. DO YOUR FIGURING HERE. GO ON TO THE NEXT PAGE. ． 1 S. On a map, -;} inch represents 10 miles. How many 4 inches on this map represent250 miles? I B. 6- 4 6, The 2 cubes shown below have diagonals茂and峦、 respectively. The side lengths given are in feet. What is the ratio of 由e length of刀和othe.length of峦？ DO YOUR FIGURING HERE. 乡 A B I •• I , ．`、· I 、蛔、 I 蝎，户一一---寸－．：7D ,＇ ,＇． 3 12

A2+ 2B2SC40D62¾ 2E.．｀＇、．蜘61:471:1684:1916:11064;1

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Paper 50 · ACT December 2012 · Form 71A · Math Test

Source question 5. Refer to the source image.

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Paper 50 · ACT December 2012 · Form 71A · Math Test

Source question 6. Refer to the source image.

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Paper 50 · ACT December 2012 · Form 71A · Math Test

Wb.at is the value of -x +y +z for x"'-1. y= -3, and z=2?

A-6B－2C0D4E6

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Paper 50 · ACT December 2012 · Form 71A · Math Test

If9 + 3x== 21, 山en 五＝？

A6B12C15D18E24

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Paper 50 · ACT December 2012 · Form 71A · Math Test

A woman purchased 100 shares of stock at $5.00 per share. If each share rose S0.10 the first month, decreased $0.08 the second mo.nth, aod gained $0.03 the third month, what is lhe value of 由e woman's investment? T 荨 www.loviact.com 15 GO ON TO THE NEXT PAGE.

A$ 505B$ 520C$ 525D$1,505E$1,545

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Paper 50 · ACT December 2012 · Form 71A · Math Test

At Acme Manufacturing Company, each employee' I annual salary for oext y也r will be 3¼% more than血s 2 year's annual salary. An employee whose annual sal江y this year is $32,000.00 will have what annual salary next year? DO YOUR FIGURING HERE.

A$32,003.50B$32,035.00C$32,350.00D$33,120.00E$41,600.00

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Paper 50 · ACT December 2012 · Form 71A · Math Test

Vat 1, Vat 2,血Vat.3, when full, each hold the same amount of water. At the present time, Vat l is full, 1 1 Vat 2 is 一 full, and Vat 3 is ¾ full. Water will be 12 3 tr缸sferred between the vats so山at each of tbe 3 vats contains the same amount of water. After the transfer, each ofthe 3 vats will比what fraction full? 气 C l • 9 12

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Paper 50 · ACT December 2012 · Form 71A · Math Test

Which of the following graphs shows the solution set for the inequality 4x -2 之 6 ? 一2 。 2 X G, 。 x I _ 2 3 0 f 0 2 x -喊嘈贮 l X ．一2 ＿。 X 荨 www.loviact.com 16 GO ON TO THE NEXT PAGE.

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A◄ ． I 一．一一－· ►BChoice H — see source imageCChoice J — see source imageDChoice K — see source image

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Paper 50 · ACT December 2012 · Form 71A · Math Test

Thc Hope-A.LotFoundationis mailin.g brochures to 4,000 prospective donors. The foundation's goal is to have procceds of $l,500 af[er p . aying $900 for the mailing. Accordjng to past mailings, the average donation was $20 per donor. Assuming this average, how many of the prospective donors need to donate to reach the goal? DO YOUR FIGURING HERE. 七 < <

A30B45C120D200EJ,SOO

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Paper 50 · ACT December 2012 · Form 71A · Math Test

Lines BC and DE are paralJeJ, and transversals BD � ． and CE iotersect at A, as shown in the figure below. Given that AABC is an equilateral triangle,.r =? A 30 60 120 130 150 ．．． E G H j k

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Paper 50 · ACT December 2012 · Form 71A · Math Test

What is 小e positive solution to the equation 16x2 = 30? 30 l6 I.., \10/ • 30 E 30 - 16 l6. IfKusum uses l pound of gras$ se“per 800 , uare feet to比seeded, how many pounds of grass seed will she use to seed the region shown below? l l 4 3 E 30ft 20ft - 昌 K 5 T 荨 www.loviact.com 17 GO ON TO THE NEXT PAGE. DO YOUR FIGURING HERE. Use the following information to answer questions 17-20. An organization promoting good nutritionaJ habits collected data on fat calories in foods from 9 fast-food restaurants in Mesa City. The values in the list below represent the number of fat cal.odes in a small order of frencb fries at each of these fast-food 氏staurants. 160, 106, 104, 113, 160, 103. 161. 89, 96

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AChoice A — see source imageBChoice B — see source imageC16D/ 16E4 40ft, ...641 100ft 474¾

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Paper 50 · ACT December 2012 · Form 71A · Math Test

Source question 16. Refer to the source image.

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Paper 50 · ACT December 2012 · Form 71A · Math Test

Based on the daca listed, what is the median num比r of fat calories in a small order of french fries at these 9 restaurants? 18, Which of the following b叮 graphs most accurately represents the data on the number of.fat calories in a -small order of frcncb fries at the 9 fast•food restaurants? 于 3 2 1 g - s g b q 日 n u 4 3 l 3 月 n 3 馆 U K o 5 Q E u G numberof fat calori心 4 3 2 1 竺 m m e 1 S 3 y0 g E n u l numberof fatcalorics - 4 3 2 l 包 m m 3 8 J J o J g u k ． numberof fatcalories numberof 住tcalories 4 1 3 月月一只 J o 』必 E n u H ， number of fatcalories ．． T 荨 www.loviact.com 18 GO ON TO THE NEXT PAGE. 10 11 1,092+l'+y 1,092+x+2 9+x+y l,092+x+y II

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A106B108C125D128E1606932+x+y7932+x+y8Choice H — see source image9Choice J — see source image10Choice K — see source image

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Paper 50 · ACT December 2012 · Form 71A · Math Test

Source question 18. Refer to the source image.

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Paper 50 · ACT December 2012 · Form 71A · Math Test

Of the 9 fast-food restaurants, Hungry Henry's has the lowest num比r of fat calories in a small order of freach fries. At Henry's, 43% of rbe total. number of calories in frcncb fries are fat calories. Which of the following values is closest to the total number of calories in a small order of Henry's freacb fries? o. 207

A127B132C139D223

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Paper 50 · ACT December 2012 · Form 71A · Math Test

The organization collects data from 2 additional restaurants and includes tbe new data io. tbe list Tbc number of fat calories in a small order of french fries at each of the 2 additional restaurants is designated by x and y, respectively. Which of the following expression gives the average of this larger list of values?

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Paper 50 · ACT December 2012 · Form 71A · Math Test

A bag contains 8 red marbles, 5 yellow marbles, and 11 green marbles. How many add;itional red marbles must be added to the 24 marbles already in the bag so 小at the probability of randomly druwing a red marble . 3 lS - 5 ？ ZZ. The sum of (3x3 +4x2 一 3x+ l) and which of the 》olynomj +7x-3)? E －五乓肛2 一10x+4 G,．记一 8:c + lOx-4 3 + lOx + 2 3 + 4x - 2 DO YOUR FIGURING HERE. 、． T 荨 www.loviact.com 19 GO ON TO THE NEXT PAGE.

A11B16C20D24E3262x78x81Sx3- 1釭－2 lx-3

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Paper 50 · ACT December 2012 · Form 71A · Math Test

Source question 22. Refer to the source image.

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Paper 50 · ACT December 2012 · Form 71A · Math Test

The table below gives the _price to mail a single package through theUnited 忒如 Postal Scrvice on August 30, 2007. The price depended on the weight of the package. DO YOUR FIGURING HERE. 酗．． Weight in pounds Price O<x<2 $4.60 2Sx<3 $5.05

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Paper 50 · ACT December 2012 · Form 71A · Math Test

What is the value of/(-4)given/(x)= 5斗妇10? 2S. AU of the following monomials are factors, over the in比gers, of1Sx2 y + 1记y仁矿y 欧CEPT: D,. 12./ T 荨 www.loviact.com 20 GO ON TO THE NEXT PAGE.

A一 382B-62C82D98E4186673x82x29x2y

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Paper 50 · ACT December 2012 · Form 71A · Math Test

Source question 25. Refer to the source image.

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Paper 50 · ACT December 2012 · Form 71A · Math Test

Josh is standing in a pool and Joo幻ng up at his f rieod Olivia. Olivia is lying on her stomach on the diving board looking at Josh. The horizontal and vertical 如tanccs, in meters, between Josh 血d Olivia are given in the diagrambelow. What is the me丛urc ofthe angle ofelevation, 8, ofJosh's line ofsight.? (Note: Drawing is NOT to scale.) DO YOUR FIGURING HERE. 3 ,＇bi_｀＿

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Paper 50 · ACT December 2012 · Form 71A · Math Test

Avari traveled the 2-mile trail from her bouse to Big Lake on herbicycle. She then traveled 3 times aro皿d the Big 巨ke Loop and returned bomeby the 2-mile 呻． At tbe end ofbcrbjcrcleride, the lrip odomcter showed that she bad 廿aveled 22 miles. Which of the followjng equations, when solved, gives 山e distance Avari traveled oncearound Big 巨比 Loop, d miles?

A2+ d=22B2+3d=22C4-3d= 22D4+ d=22E4+3d=22

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Paper 50 · ACT December 2012 · Form 71A · Math Test

In the standard (x,y) coordinate plane, wh11t is the slope of the line with equation 3x + Sy= 6 7 3 s 5 ．． 3 T 荨 www.loviact.com 21 GO ON TO THE NEXT PAGE. 29, What is 如 solution to the equationbelow? 3(:c-4) - 2(x- 3) =5(-x - 3) +6 DO YOUR FIGURING HERE. 3 - 2 9 - 2 ｀．

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A立B_lC2D2,E26气 -.:..7Choice B — see source image8Choice C — see source image9Choice D — see source image10Choice E — see source image

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Paper 50 · ACT December 2012 · Form 71A · Math Test

Source question 29. Refer to the source image.

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Paper 50 · ACT December 2012 · Form 71A · Math Test

If O<x<l, and k is a positive integer, 中en what must 比 true about tbe value ofxt ? G．一l<x•<o <1 d 3 a 3 a 3 a 3 a 1 1 - － - - l Q J a 4 4 3 5 0 3 4 3 4 4 A B C D E

A:I＜一1BO<:IC:I>1D·.:c企＝0

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Paper 50 · ACT December 2012 · Form 71A · Math Test

Source question 31. Refer to the source image.

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Paper 50 · ACT December 2012 · Form 71A · Math Test

The diameter of Earth is about 1.28 x 104 km. The di血eter of the Moon is about 3.S x lo'km. Which of 如 foUowing is c.Joscst to the difference, inkilometers, between the diameter of Earth and the diameter of the ”[oon? ．．．

A2.2 >< 103B2.2 X 104C9.3 X l02D9.3)(103E9.3 x 104

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Paper 50 · ACT December 2012 · Form 71A · Math Test

ln lhe right triangle shown below, the leogtb of亢is 4mm and tbe length of沉is 3 mm. For LA, the value of which of the following 1rigonometric expressions • 3 lS - 5 ？． B T 荨 www.loviact.com 22 GO ON TO THE NEXT PAGE.

AsinABcosA 3CtanADcscAEcotA C 4 A

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Paper 50 · ACT December 2012 · Form 71A · Math Test

When light shines on a.n obj比t, the intensity of that light, /, in units of light intensity, can be expressed as k d ";i• where d is the distance, in feet, the Ji吵t source i from the object, and k is a proportionality constant. For one light source shini.ng on an object, d::: 12 aod I"" I0. lf d = 6 for the same light source shining on the same object, what is the corresponding value of I ? DO YOUR FIGURING HERE.．．． G. ) l 3 3 0 3 4

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A20BChoice H — see source imageC200D1,440

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Paper 50 · ACT December 2012 · Form 71A · Math Test

A circle in the standard (x,y) coordinate plane has its center at (-2,4) and passes through (3,16). What is the area. iusqu江c coordina比 units, of this circle? D, 289兀

A26JtB34兀C1691tD441兀

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Paper 50 · ACT December 2012 · Form 71A · Math Test

Royce plans to construct a triangular flower 比d on the corner of bis property where a sidewalk forms a d珈亟l.e. The fJower bed and the lengths, in feet, of2 of its sides arc shown in the』figure below. The flower bed will be enclosed by a garden fence that is set up along its entire perimeter. To 山e nearest foot, bow many feet of garden fence will enclose the flower bed? 12 14 16 17 20 ．．． E G H j k flowerbed ．

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Paper 50 · ACT December 2012 · Form 71A · Math Test

lf 2w + 7 = l-21, bow many different values arc possible for w ? T 荨 www.loviact.com 23 GO ON TO THE NEXT PAGE.

A0BlC2D3Elnfinil.e)y many

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Paper 50 · ACT December 2012 · Form 71A · Math Test

Thegraph.oftheparabolawithcauationy=x勹让－8 is shown in the standard (x,y) coordi.nate p血C 氏low. ne of the follow.ing graphs is the graph of th, reflection ofthe parabola over the y-axis. W血hone is it? y DO YOUR FIGURING HERE. ． O• X Fo y y 。 x 。 x y y 。 X X ． x ．

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Paper 50 · ACT December 2012 · Form 71A · Math Test

The points A(12,18) 扭dB(-4，2) lie in the standard (x,y) coordinate plane. What are the coordinates of the midpoint of商？ T 荨 www.loviact.com 24 GO ON TO THE NEXT PAGE.

A(4, 8)B(4,10)C(8, 8)D(8,20)E(16,l6)

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Paper 50 · ACT December 2012 · Form 71A · Math Test

For 丛BC shown bcJow. the Ieng由 of宽is SO mm. Which of the following equations, when solved, will give the Jength, in millimet.ers, of商？ (Note: The law of sines states that given 6XYZ, S屯丛．＝竺＝坐） YZ - XZ - XY ' DO YOUR FIGURING HERE. 50 . AB _ s-in68° 文） AB 50 AB l sin夕$ 0 _ sin68° 50 AB SO AB A ？ 540--; B c

A畔＝血军Bsin58°Csin58° - sin54°D畔＝血立8°

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Paper 50 · ACT December 2012 · Form 71A · Math Test

The Vert.ices of 6AOB are A(0,6), 0(0,0), and 8(8,0), ?,S shown in the standard (x,y) coordinate plane below. What arc the coordinates ofthe center ofthe circle that circumscribes �AOB ? A(O. X

A(0,3)B(2,1.5)C(4,0)D(4,3)E(7,7) 0(0,0) B(8-�

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Paper 50 · ACT December 2012 · Form 71A · Math Test

Circle P has a. radius of 4 units and is in the s巳nd缸d (x,y) coordinate plane. The set of all points in the coordinate plane that are 3 units fr.om the center of Circle P is a circle tba1: ！．intersects Circle P at 2 points. is internally tangent to Circle P. is externally tan.gent to Circle P.俸 isinterior to and does not intersect Circ1e P. is exterior to and does not intersect Circle P.

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Paper 50 · ACT December 2012 · Form 71A · Math Test

Suppose that x is a positive real number and � is a 釭 2 rational nu.mbc.r. Which of the following statements about xmust be uue? 3 E X=立 • 2 ．． T 荨 www.loviact.com 25 GO ON TO THE NEXT PAGE.

Ax is rationalBxis irrationalCx= lDx= � 2

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Paper 50 · ACT December 2012 · Form 71A · Math Test

The functions／扭dg 血 defined as/(x)_=3x +2 and g(x)＝让－l. What is the value of/(g(-2))? B．一5 k身一 13 DO YOUR FIGURING HERE.

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A20B－4C-9DChoice J — see source imageEChoice K — see source image

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Paper 50 · ACT December 2012 · Form 71A · Math Test

Consider all rectangles with an area of 36 square feet. P is the pcdmeter, in. feet, of at least I of these rectangles if and only if: B, p;;i: 24

Ap之 6Bp之 36CP 之 144DP 之 324

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Paper 50 · ACT December 2012 · Form 71A · Math Test

Carmen. drove from Blairtown to Ore City, a distance of 80 miles. From Ore City she drove on to JancsviJle, and then drove back to Blairtown. The ratio of Carmen's driving times 01:1 the first, second, 印d third segments of the trip, respectively, was 5:2:4, and she drove at thesame average speed on cach se f ment. What was Carmen's to叫 driving 如ance, io 面 cs.for the 3 segments of the trip? R. 2心

A176B.220C360D440

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Paper 50 · ACT December 2012 · Form 71A · Math Test

In b.ABC, themeasureof LA is 43° 皿d the measure of LC is 32° . Which of lhe fo)lowi1.lg inequali[ie involving the lengths ofthe sides of b.ABC is ll'Ue?

AAB>ACBAB>BCCAC>BCDAC>AB+BCEBC>AC

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Paper 50 · ACT December 2012 · Form 71A · Math Test

One of the following functions is graphed in the standard (x,y) coordinate plane below. Which fu.oction is it? y 2 2 2 1 1 - - + ＋－， l l l 2 2 －＋＋－＋ x x x x x ＿＿＿＿＿＿＿＿＿＿ y y y y y Fo G H j k x (1,-2) T 荨 www.loviact.com 26 GO ON TO THE NEXT PAGE. 。一X = 16 4 2 =l 16 4 ＋ 4 =l �9. One of the following is an equation of the ellipse shown in Che standard (x,y) coordinate plane below. Which one? (Note: The coordinate unit on the x-axis is the same length as the coordinate unit on the y-a立s.) y

Ax2-y2B(x-8)2+(y-4)2=16C啤－卢D缸十卢＝ 1E�卢 16

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Paper 50 · ACT December 2012 · Form 71A · Math Test

Source question 49. Refer to the source image.

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Paper 50 · ACT December 2012 · Form 71A · Math Test

A regular pyramid with a square base is shown in the figure below. The slant height is迈units and the length of the base edge is 2 units. What is the total length, in units, ofall 8 edges ofthe pyramid? DO YOUR FIGURING HERE. ．．． -….....… ,.- k令 16 2

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A4V7B4V7+8 /,'___f迈C8D14 ，，，｀＇．EChoice K — see source image

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Paper 50 · ACT December 2012 · Form 71A · Math Test

The solution of the system of equations below is the set of all(x,y) such that 让一 3y=6. What is the value ofk? 9 1 3 6 9 l - A B C D E 18x-27y= 54 6x+ b=-2K ，

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Paper 50 · ACT December 2012 · Form 71A · Math Test

The solution set for the equation zr1+ 1=1 contains: T 荨 www.loviact.com 27 GO ON TO THE NEXT PAGE. 00 YOUR FIGURING HERE. Use the tollowlng Information to answer questions 53,...55_ In the figure below, a large circle with center O bas a diameter兀f that is 40 nun long. Point C lies on the large circle such that themeasureof 乙ABCis 60° . A di扫ueter of the small circle js邓．． A 60° "B

A2imaginary numbers.B2positive real numbers.C1 negative and l positive real number.D1 negative real number only.El re.al number, which is 0. ．

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Paper 50 · ACT December 2012 · Form 71A · Math Test

What is the area, in square millimecer-s, of the small C让clc? 已·．一、

A10冗B2加C40亢D100亢E400兀

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Paper 50 · ACT December 2012 · Form 71A · Math Test

What i＄山eleng小．iomillim吮cs, ofarcAB 1 SS. The figure is placed in the s即nda(d (.-r,y) coordinate plane so that A has coordinates (-20,0) and B bas coordinates (20,0). What.is the: x-coordinateof C ? u. -10 ．． S6. In the figu比沈own below, C, M, and NJie on 山ccircle wbose center js 0, and /.MONis a right nngle. What is tbe sum of tile mcasur心 ofLCMO 皿d乙CNO? M c 。 N T 荨 www.loviact.com 28 GO ON TO THE NEXT PAGE.

A20B20兀C40D40兀E806一15708JO9151090°1167.5°1260°1345°1422.5°

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Paper 50 · ACT December 2012 · Form 71A · Math Test

Source question 55. Refer to the source image.

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Paper 50 · ACT December 2012 · Form 71A · Math Test

Source question 56. Refer to the source image.

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Paper 50 · ACT December 2012 · Form 71A · Math Test

The leog _ th of tbe shorter side of reclaogle ABCD is 4 inches less 小antlle length,L,ofthc 鄂八ide. The length of 小e longer side of rec侐gle WXYZ, which is simil叮 to ABCD, is lOL inches. In terms of L, what is the length of the shorter side of WX辽？

AL-40BL+ 6CJOL- 4DlOL+ 6ElOL-40

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Paper 50 · ACT December 2012 · Form 71A · Math Test

For any integer n > 0, the triangular number T,. is the number of dots in a triangular array wi由 n points on eacb side. The figure below shows the fi 订st 4 triangu)ar numbers. What is the value of T d-4 ? ．．．． T1 = 1 T2 = 3 ． • •• ．．．．． T3 =6 ．．． •••• T4 = 10 ．

A189B192C2,016D2,048E2,080

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Paper 50 · ACT December 2012 · Form 71A · Math Test

For what integer k are both solutions of the勺uation x2 +lex+ 17 = 0 positive integers?

A一18B-16ClD16E18

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Paper 50 · ACT December 2012 · Form 71A · Math Test

In 6XY2, the.measure of LXis 90° ,the measure ofLZ 4 is 8, XY = 12 units, and tan 8 = ;. What is the area of 6XYZ, in square units? DO YOUR FIGURING HERE. ， END OF TEST2 STOPJ DO NOT TURN THE PAGE UNTIL TOLD TO DO SO. DO NOT RETURN TO THE PREVIOUS'!EST. • • ．． T 荨 www.loviact.com 29 GO ON TO THE NEXT PAGE.

A162B324C2瘁D6菹5E12V585

Form 71A · Math Test · 60 questions

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