ACT Past Papers with Answers

Paper 85 · ACT December 2001 · Form 58E · Math Test

Two liii¢S intcrsLcL at an an&pl¥ of 89° shown bclow, Whilt 1.8 thL' miasurL of the angle indicaicd wilh a ques- lion m,Irk'? 89° Fl. 90°

Paper 85 · ACT December 2001 · Form 58E · Math Test

In ￿ABC. the sum of ihe Tnea5ures of ZA and ZB 15 68° What is the measure of ZC ?

Paper 85 · ACT December 2001 · Form 58E · Math Test

What is the value of 3x 14 5xwhenx- ACT.58E 14 GO ON TO THE NEXT PAGE. S. On a particular road map, inch represents 18 rnilcs, About how many mil¢s apart arc 2 towns that are inchcs apart on this map. DO YOUR FIGURING HERE. and d are any 4 inlegers, then a+b+c=a+c+dislrueonlyifwhichofthefol- lowing is true?

Paper 85 · ACT December 2001 · Form 58E · Math Test

Source question 5. Refer to the source image.

Paper 85 · ACT December 2001 · Form 58E · Math Test

Source question 6. Refer to the source image.

Paper 85 · ACT December 2001 · Form 58E · Math Test

Suppos¢ that rcp141cing an old elcctric watcr hcatcr wilh a new, energy-efficicni electric watcr hcatcr will rcduce a home's averqc gL monthly clLclric bill by 20%. It. thi old clcLtric water hc41tcr in & honiL With (I currLnt ftv¢ra¥yc monthly clectric bill of $ 110 its rcplacLd by o nLw cnLrby-cfficient one, whai will bc ihe hom¥'S new nvcr41bTC Inoil Ihly elLciric bi I l? A, S 22.00

Paper 85 · ACT December 2001 · Form 58E · Math Test

0 cubic meters per second and the weight of water is 9,790 newtons per cubic meier?

Paper 85 · ACT December 2001 · Form 58E · Math Test

You have agre¢d with an automoblle dealership to pur- chase a car for $3.400, which includes lax and all mis- cellaneous costs. You give the dealership $400 as a down payment and get a car loan for thc rcst. If you pay off your loan by making 24 monthly payments of $150 each, the total of all your payments will be how much more than the actual purchase PTice of the car? ACT. 15 GO ON TO THE NEXT PAGE.

Paper 85 · ACT December 2001 · Form 58E · Math Test

The monihly rents for single rooms at 5 collegL)s are $350. $310, $360, $320. and $310, rcspectivcly. What is thc mcan of thes¢ monthly renLS? DO YOUR FIGURING HERE.

Paper 85 · ACT December 2001 · Form 58E · Math Test

3+x+y D, 3x+y 32, Forall xandy. xy 16=7

Paper 85 · ACT December 2001 · Form 58E · Math Test

Ir 9111 + 57= 87. then 9(m + 6)= 9 36 93 13, If id¥nticAI cylindrical Clills i& rc packed 12 cans to an 18" x 24" rcciangulsir carton, as shown bLlow, what is IhL approximalc radiu.s, in inchcs, of each of the cans? +++4 +++4 18" 24" 14, Poinis A, B, C, and D are collinear such that A is between C and B, and D is between A and B. Which of the following statements about thc distances betwccn these points must be true? 16 GO ON TO THE NEXT PAGE.

Paper 85 · ACT December 2001 · Form 58E · Math Test

Source question 13. Refer to the source image.

Paper 85 · ACT December 2001 · Form 58E · Math Test

Source question 14. Refer to the source image.

Paper 85 · ACT December 2001 · Form 58E · Math Test

The power that a hydroelectric dam generatcs can bc modclcd using thc formula DO YOUR FIGURING HERE. Qliy I.(KK),000 whcr¢ P is the power the dam generaies, in megawatis; Q is thc flow rale of the river, in cubic meters per second; h is the height of the dam, in meters; and y is thc wcighi pcr unit volume of water, in newions per cubic meter. According to ihis model, which of the following is closest to the power, in megawaits, gener- ated by a dam that is 25 mcters high if the flow rate is

Paper 85 · ACT December 2001 · Form 58E · Math Test

Kay collected data from 5 friends who have jobs. She plotted the data on a graph to compare the numbcr of hours hLr friends work'¢d to tlieir toial earnings in dol- 14rs, as shown below. According 10 the graph, which of hcr 5 friLndi earned the most per hoiir ? Bonit16 Ana Ch¥n Dainian limc worked in hours

Paper 85 · ACT December 2001 · Form 58E · Math Test

On thc lot at Quality Used Cars, there arc only 15 cars wilh aulomatic transmission and only l2 cars wilh bucket seats. The number of cars on the lol wilh both automatic transmission and bucket seats is: exactly 3. at least 3. no more than 3, no more than 12.

Paper 85 · ACT December 2001 · Form 58E · Math Test

Which of the following describes the solutions to the equation x 8x~48=07 I real number and l imaginary number . ACT.$8E 17 GO ON TO THE NEXT PAGE.

Paper 85 · ACT December 2001 · Form 58E · Math Test

Lee walked for 20 minutes on a motorized trcadmill that was sei at a consiant speed of 4 miles per hour. About how mLiny miles dtd Lee walk on the ireadmill? DO YOUR FIGURING HERE. and I

Paper 85 · ACT December 2001 · Form 58E · Math Test

In the figure below, P is on AB, and E is on PD. Polygon ABCDEF, with dimensions in inches as marked, has an area of 122 square inches. What IS Lhc area of LPEB, in square inchcs9 15 13

Paper 85 · ACT December 2001 · Form 58E · Math Test

(3xy + 21xy 7y) - (5xy + Ilyy 3y) is equivalent to: -8xy + 9xy 4y -8xy + 33xy - loy -2xy + 9xy' _ 4y -24, + 9xy - loy -2xy + 33xy loy 18 GO ON TO THE NEXT PAGE.

Paper 85 · ACT December 2001 · Form 58E · Math Test

Chasc Ciiy is 12 milcs dircctly cast of Red Oak, and Wylliesburg is 8 miles directly norih of Red Oak. If you could travcl in a straight line from Wylliesburg directly to ch.isc City, about how many milLs would you iravcl? DO YOUR FIGURING HERE.

Paper 85 · ACT December 2001 · Form 58E · Math Test

In which of the following are ascending orderg and arranged in

Paper 85 · ACT December 2001 · Form 58E · Math Test

The orea of an cllipsc miy bc found by using the exprcssion Xab, whcrL a is Ihc l¥ngth of thi minor axis, Wha¢ is the Icngih of ihc major axis 14 nd b is the arca, in squarc uniis, of thc largcst ellipsc .thaL can bc inscribcd in a rcctanglc with Icngth 10 unils and width 6 units?

Paper 85 · ACT December 2001 · Form 58E · Math Test

If thenx= 12

Paper 85 · ACT December 2001 · Form 58E · Math Test

Erin had 6 slips of pa er, numbered I through 6, Erik rcnumbcrs them once y adding 3 to each odd number and subiraciing I from each even number. When 2 renurnbered slips of paper are chosen ai random, what is the hi8hcst sutn possible? DO YOUR FIGURING HERE.

Paper 85 · ACT December 2001 · Form 58E · Math Test

Water drips from 2 faucets at different rates. The first faucei drips I drop every l2 seconds, and the second faucei drips I drop every 18 seconds. If you see thesc "faucets drip simulianeously. the next time they drip simulianeously will be in how many seconds?

Paper 85 · ACT December 2001 · Form 58E · Math Test

Looking out his apartmcnt window that is 20 feet above the ground and direcily over the front door. Han could see a red flower on the sidewalk. As shown below, the angle formed by the building and Han's line of sight to the flower is 35° Approximately how many feet from the front door is the flower? (Note: tan 35° .70 cos 35° .82 sin 35° .57) window 35° 2(Y door flower 20 GO ON TO THE NEXT PAGE.

Paper 85 · ACT December 2001 · Form 58E · Math Test

In thc figure below, AB11 FC, 2A measures 41° ZC measures I IO. and ZADB measures 122° What is the measurc of 2CBD ? DO YOUR FIGURING HERE. 122, 41°

Paper 85 · ACT December 2001 · Form 58E · Math Test

The coordinates of the endpoints of JK, in the Slandard (x,y) coordinaie plane, are (-2,-6) and (4,6). What is the x-coordinate of the midpoint of JK

Paper 85 · ACT December 2001 · Form 58E · Math Test

What is the cxponcnt on a in ihc produci 2a, a 3aV ?

Paper 85 · ACT December 2001 · Form 58E · Math Test

Source question 32. Refer to the source image.

Paper 85 · ACT December 2001 · Form 58E · Math Test

A high school sells student tickets for a band concert for S2 each and nonstudent tickets for $4 each. How many student tickets did the high school sell if the high school sold 220 iickets worth a total of $640 ? 40 A¢T.18E 21 GO ON TO THE NEXT PAGE.

Paper 85 · ACT December 2001 · Form 58E · Math Test

The Irapezoid bclow, with dimensions given in inches, has an arLa of 36 Sqil&irc inches. What arc ihc Icngths, in inchcs, of ihc bascs of thc irapczoid? h(b + b2) is a formula for the area of a DO YOUR FIGURING HERE. (Note: A trapezoid.) IK. 9and 9 3S. Wh;11 is thL valul of x in thc soluiion to thc systcm of cqu'itions bLlow? 2x+y=2a

Paper 85 · ACT December 2001 · Form 58E · Math Test

Source question 35. Refer to the source image.

Paper 85 · ACT December 2001 · Form 58E · Math Test

Every integer is in l and only l of ihe following sets: 15,-10.-5, 0, 5. 10, 15, }, denot¢d [0] 14, -9.4, 1,6, 11, 16. .},denoted [1] -8,-3, 2, 7, 12. 17. . }, denoled [2]

Paper 85 · ACT December 2001 · Form 58E · Math Test

The avcragc dcnsity of. an object is defined as thc object's ¢lvcf41gc weight per unli volume. A slab of building material is a rectangular solid that is 8 fcct long, 2 feel wide, and - foot high. If the slab weighs 250 pounds, about what is its average densiiy in pounds per cubic foot? 24,4 DO YOUR FIGURING HERE.

Paper 85 · ACT December 2001 · Form 58E · Math Test

Consider Iwo gLometric sequences. dcnoted Si and S S has 40 as its Ist Icrm, and S has 100 as its Ist term. For both Si and S each ierm after Ihe I si term is thc term preccding it. Which term of S2 will have thc same value as Ihe 4th ierm of S ? 2nd 3rd 51h

Paper 85 · ACT December 2001 · Form 58E · Math Test

In thc st¥iiidard (x,y) coordinaic pl¢1ne, whai Is ih perimclLr. in coordin&llc units, of an i.sosccles tri41nglL having vcrticcs A(-2,-1), B(3,11), and C{8,-1) 9 JJ. 33

Paper 85 · ACT December 2001 · Form 58E · Math Test

In the standiird (x,).) coordinatc plane, a circlc with its cenier at (6,9) and a radius of 5 units has which of thc following a5 ils equation? 25

Paper 85 · ACT December 2001 · Form 58E · Math Test

For oll real x * O, 15 4x 4+x 5x+ 12 4+x 3x+20 ACT.)8E 23 GO ON TO THE NEXT PAGE.

Paper 85 · ACT December 2001 · Form 58E · Math Test

What is (he area, in square units, of a circlc that has a circumference I8￿ units long. 9n 18 36 81 DO YOUR FIGURING HERE.

Paper 85 · ACT December 2001 · Form 58E · Math Test

If a ship continues on ils current heading, il will hil a rock 3,000 feet ahead at point X. as shown below. Which of ihc following equations will givc thc angle of the course correction needed so the ship will clear .point X by 100 feet? ship 100 ri 3,000 fi cosA 100 sccA cotA

Paper 85 · ACT December 2001 · Form 58E · Math Test

Whai is che soluiion set for the equation Ix- 11 2 ? ACTQ8 24 GO ON TO THE NEXT PAGE.

Paper 85 · ACT December 2001 · Form 58E · Math Test

The linc graphed in Lhc standard (x,y) coordinale planc bclow is also represented by one of the following Cqualions. Which equation is i(? DO YOUR FIGURING HERE. .r+6

Paper 85 · ACT December 2001 · Form 58E · Math Test

Which of the followinbv is ihc graph of thc rcgion l < x + y < 2 in thc standard (x,y) coordinate plancg Acf.5eE 25 GO ON TO THE NEXT PAGE.

Paper 85 · ACT December 2001 · Form 58E · Math Test

What is the difference between Ihe mean and the Inedian of Lhc SLI {3, 8, 10, 15 } ? DO YOUR FIGURING HERE.

Paper 85 · ACT December 2001 · Form 58E · Math Test

Consider Ihe following system of equations in x and y, where the values of ni and n are NOT Lhc same. ax+by- ax+by= If you correctly graph this sysiem, which of the fol- lowing could be your graph? I solution 2 solutions I solulion no solution infinitc number of solutions

Paper 85 · ACT December 2001 · Form 58E · Math Test

Given f (x) = and g(x) = hat isf(,(' )) ACT48e 26 GO ON TO THE NEXT PAGE. SO. Casey paid $8.56, which included sales lax of 7%, for cassette, Which of thc following. when solved, will give ¢, the beforc-tax price, in doll4irs, of Ihc cassette. c + .07c - 8.56 c{c +.07)= 8.56 DO YOUR FIGURING HERE.

Paper 85 · ACT December 2001 · Form 58E · Math Test

Source question 50. Refer to the source image.

Paper 85 · ACT December 2001 · Form 58E · Math Test

For the rcctangle below, with dimensions in feet, which of the following is an irrational number? ft 3ft iangle onal

Paper 85 · ACT December 2001 · Form 58E · Math Test

In the figure below, AB and AC are tangenl lo the circle ac B and C, rcspccLively. and O is the c¢nter of Ihe circlc. If ZBA C mc41sures 40° how many d¢grees docs 2AOB mcasurc.

Paper 85 · ACT December 2001 · Form 58E · Math Test

Pat sells refrigerators and is paid $200 per week plus $125 commission for each refrigeratol she sells. Which of the following is an expression for thc numbcr of refrigerators she would need io sell in a iven week in order to earn a lotal of P dollars that wee P-2C() 125 P-125 2CVJ 200 211) 125 325 Acf.$8E 27 GO ON TO THE NEXT PAGE.

Paper 85 · ACT December 2001 · Form 58E · Math Test

When x represenLs an inte8cr, the statcment 'Jf x is divisiblc by 4, then x is cvcn" is equivalent to which of Ihc siaicmcnis bLlow'? l. If x is not divisible by 4, Ihen x is not even. II. Irx is even. then x is divisible by 4. IIT. If x is not even, then x is not divisible by 4. IK. I, II. and III DO YOUR FIGURING HERE.

Paper 85 · ACT December 2001 · Form 58E · Math Test

Which of the following number line graphs represents the solution set of the inequality 2x - 7x > 4 ?

Paper 85 · ACT December 2001 · Form 58E · Math Test

A linc in the standard (x,y) coordinatc planc passcs through thL point) (-1.3) and ( I,k). If th¢ slop¢ of the linc is 2. whai is thc valuc ofk ?

Paper 85 · ACT December 2001 · Form 58E · Math Test

In right triangle LJADE shown below, C is on AE. B is on AD, and BC is parallel to DE. The ditnensions given are in centimeters, How many centimcters long isBDg 10 24 25 Acr.JeE 28 GO ON To THE NEXT PAGE.

Paper 85 · ACT December 2001 · Form 58E · Math Test

In thc rcgular heptagon shown below, what is thc sum of the measurcs of the 7 interior anglcs9 DO YOUR FIGURING HERE. 360° 720° 900° 1,080°

Paper 85 · ACT December 2001 · Form 58E · Math Test

The following identities are true whenever x is an angle measure such that 0° < x < 90° sinx cscx cosx secx l. and tanx cotx l. For x such that < x < 90° and sin.r= whai is the value of secx ?

Paper 85 · ACT December 2001 · Form 58E · Math Test

It'p ig a posilivc real nuinbcr und 2 sin x= 2 sin(x + p) for cvery rc4i1 V1& luc of x, whai is the smallest possiblc valuc for i). in d¥grccs9 END OF TEST 2 STOPI DO NOT TURN THE PAGE UNTIL TOLD TO DO SO. DO NOT RETURN TO THE PREVIOUS TEST. ACT.58E 29