ACT Past Papers with Answers

Paper 68 · ACT January 2008 · Form 61B · Math Test

Tasha's Tegular pay is $12.00 per hour for a 40-hour workweek. For each hour over 40 hours she works in a week, she is paid l- timcs her regular houily pay. How much is Tasha paid for a week in which sbe works 49 hours? $642.00 .3. To .attend the.Press Club AnnL]al Banquet, members pay $40 per ticket, while nonmcrnbers pay $50 per ticket. What is the. re.veniie. in dollars. frorn the tickets when .100 member tickets and n nonmember tickets are purchased? n+lOO

Paper 68 · ACT January 2008 · Form 61B · Math Test

If you answered Yes to Question I, did yod ski ¢ross-¢ountry . After completing the poll, Kelly wondered how many of the students polled had skied both cross-country and downhill. How many of the students polled indicated that they had skied both cross-countr an 28 37 45 20

Paper 68 · ACT January 2008 · Form 61B · Math Test

The word average indicates arithmetic mean. l. Ifr=7,b=4,artdg= (r + b- g)(b + s) equal? , what does DO YOUR FIGURING HERE.

Paper 68 · ACT January 2008 · Form 61B · Math Test

Of the 200 parking spaces in a parking lot, 4(Yo of the spaces are reserved for handicapped parking, an the nonhandicapped spaces are suitable for compact cars only. How many spaces that are NOT reserved for hdndicapped parking are suitable for noncompact cars? DO YOUR FIGURING HERE.

Paper 68 · ACT January 2008 · Form 61B · Math Test

The shadows of a fence post and a nearby fla(Tpole (both vertical and on level ground) were nieasured at the same time. The fence post's shadow was 3 ft long, and the flagpole's shadow was 10 ft long. If the fence post is 6 ft tall. about how many feet tall is the flagpole?

Paper 68 · ACT January 2008 · Form 61B · Math Test

-5(1-3 + 84) -25 25

Paper 68 · ACT January 2008 · Form 61B · Math Test

A 5-inch-by-6-inch reLtangle is cut along its diagonal to form 2 trian(Fles. What is the area of each triangle, in square inches?

Paper 68 · ACT January 2008 · Form 61B · Math Test

Franco is riding in a seat on a Ferris wheel. The wheel rotates at a constant late of I revolution every minute. What is the measure of the angle Franco's seat rotates around the center of the Ferris wheel, starting at the bottom, in - minute? ACT-618-SAMPLE 15 GO ON TO THE NEXT PAGE.

Paper 68 · ACT January 2008 · Form 61B · Math Test

Which of the following talculation8 give& the atea, in square centimeters. of .the squar.e below, with sides . 8 centimet¢rs long. . DO YOUR FIGURING HERE.

Paper 68 · ACT January 2008 · Form 61B · Math Test

A recipe foi l. loaf of bread calls for 3- cups of flour. What is the maximum number of suc oaves that can be made with a bag of flour that contains 12- cups of flour?.

Paper 68 · ACT January 2008 · Form 61B · Math Test

The expression (3c - ?d)(2c + d) is equivalent to: 7cd-2d 7cd + 2d' cd-2d' .cd+2d

Paper 68 · ACT January 2008 · Form 61B · Math Test

Eight points With integer coordinates are plotted ill the standard (x,y) coordinate plane below. Which of the plotted points has an anda y-coordinate of at le

Paper 68 · ACT January 2008 · Form 61B · Math Test

.Wben George fell asleep one night, the ternperature was. 28° Fahrenheit. When George awoke the next rnprning, the temperature was -15° Fahrenheit. Which of the following, where + denotes a rise in temperaturc and - denotes a drop in temperature, best illustrates the temperature change from the time George fell asleep until the.time he awoke? +13°F 16 GO ON TO THE NEXT PAGE.

Paper 68 · ACT January 2008 · Form 61B · Math Test

Which of the following is equivalent to (a ) 18 24 DO YOUR FIGURING HERE. 18 30

Paper 68 · ACT January 2008 · Form 61B · Math Test

Ohm's law toi- electricity is I where l is the cur- rent flow in amperes, E is the number of volts, and R is the number of ohms of resistance. A technician has a circuit with a resistance of 34 ohms and a current flow of 7 amperes. Which of the following expressions gives the number of volts for this circuit? 34 34

Paper 68 · ACT January 2008 · Form 61B · Math Test

In the figure beloiv, AC 11 DF, AEBF is isosceles with EB = FB. and ZCBF measures 35° What is the mea- sure of ZDEB ? 35° iiQ

Paper 68 · ACT January 2008 · Form 61B · Math Test

A sequence of 5 nu￿bE￿baS 6 as its first term and 32 as its last term. The first 3 numbers are an ari sequence. The last 3 numbers are a (Feometric sequence with a common rati0j￿￿ What is the common dit'fer- ence among the first 3 terms?

Paper 68 · ACT January 2008 · Form 61B · Math Test

Water in Lake Forman is frozen at Celsius tem era- tures at or be103L.O.°_ Which of the lowin(T expres- sions represents all the Celsius temperatures, T, at which water is frozen in Lake Forman? ACT-61 B-SAMPLE 17 GO ON TO THE NEXT PAGE.

Paper 68 · ACT January 2008 · Form 61B · Math Test

Source question 20. Refer to the source image.

Paper 68 · ACT January 2008 · Form 61B · Math Test

. Sarahi switAs tn a rertangular-shaped swimming pool 18 feet wide and 24 feet long. About how many feet long is a diagonal of the surface of the water in the pool? DO YOUR FIGURING HERE.

Paper 68 · ACT January 2008 · Form 61B · Math Test

What value of x makes th¢ equation 7x- 3(2x_ 4) = 10 true? -12 13 22 13

Paper 68 · ACT January 2008 · Form 61B · Math Test

Which of the following (x,y) pairs is the soIution for the system of equations x + 2y = 5 and-2r + y= 10 ? 35 10

Paper 68 · ACT January 2008 · Form 61B · Math Test

For nonzero numbers x and y, whicb of the following expressions is NOT equivalent to - Ty 18 GO ON TO THE NEXT PAGL ..sides is partitione.d into smaller squares with l-inch sides. The interior of the small square at the Center of the figure and the interiors of all of the small squares that share at least l Side with the large square are haikd. What perccnt of the interior of the lar is sbaded? e square DO YOUR FIGURING HERE. 17% 50%

Paper 68 · ACT January 2008 · Form 61B · Math Test

cos 6 feet for some angle e that satisfies 0° < 0 < 90°. What is the length, in feet,. of the longest side of the triangle? . 59. .FoT all nonzero x) y, and z such that x.= the following must be equivalent to xy ? yz, which of AeT.8t&SAMPLE. GO.ON TO THE NEXT PAGE

Paper 68 · ACT January 2008 · Form 61B · Math Test

A re.searcher observed the growth of a certain colony of bacteria and recorded the data shown below. Number of cells in the colony 100 295 898 2,705 8,194 For the days observed, which of the following expres- sions best approximates the number of cells in the colony on th¢ nth day.

Paper 68 · ACT January 2008 · Form 61B · Math Test

Srniley the Clown charges 10 for schedulin . and $5 pei hour after arrivin a party app arge er but docs not have a charge for sc art . The graph below ows wa es, wi as the number of hours worked foi a par For what range of hours worke.d for a party does Ha the ake as Inueh nr more. than Smiley the. 40 Q30 10 hours worked make as much or more than Smiley the Clown. . GO ON TO THE NEXT PAG& DO YOUR FI￿TrINGHERE. passts through tbé point8 (1,-2) and (4,7) in the stan- dard (x,y) coordinate plane? 17

Paper 68 · ACT January 2008 · Form 61B · Math Test

Source question 28. Refer to the source image.

Paper 68 · ACT January 2008 · Form 61B · Math Test

In the figwe below, A, C, and E are collinear. ￿ABc and LADC are as. shown;. and angle rneasures are as marked. What is the value of p 55 55°

Paper 68 · ACT January 2008 · Form 61B · Math Test

. The diametei of a circle is 10 centimeters. What is its circumference, in centimeters? 10 20 25

Paper 68 · ACT January 2008 · Form 61B · Math Test

A day care cent¢r has 160 feet of fenc¢ that was donated to construct a fence around a play area. The area is to. be rectangular with its length 12 feet longer than its width. Assuming all of the fence is ￿sed, what will be'the apptoximate dixnensions, in feet, of the play area? .

Paper 68 · ACT January 2008 · Form 61B · Math Test

.All" angle. in a right triangle has measure (x. If 24 .thencosu= 25. 527 25 GO ON TO.THE NEXT PAGE.

Paper 68 · ACT January 2008 · Form 61B · Math Test

What is and (8,10) in th& standard (X9y) coordinate plane? DO YOUR FIGURING HERE. 32 One of the following is the slope of th¢ line graphed in the stattdard (x,y) coordinate plane below. Which one is it? (I, o) 4-2Q' 2 4 6 8

Paper 68 · ACT January 2008 · Form 61B · Math Test

Source question 34. Refer to the source image.

Paper 68 · ACT January 2008 · Form 61B · Math Test

A lormula for the area of a trapezoid is A = (b, + b2)h, where A is the area, bi and b2 are the lengths of the bases, and h is the h¢ight of the trapezoid. Irt terms of bi+b bi+b

Paper 68 · ACT January 2008 · Form 61B · Math Test

.Which. of the following equations has the pressure P varying direcll inversely as t as the square of the teMPerat￿e T and e volume V ? lov cc 10 GO ON TO THE NEXT PAGE. 16z? DO YOUP FIGUryNG HERE. .38. What is thc sine of (x in the right triangle shown in the standard (Xgy).¢oordinat¢ pla]J¢ b¢lc)w? 13 12 12 13 12 12 13

Paper 68 · ACT January 2008 · Form 61B · Math Test

Source question 37. Refer to the source image.

Paper 68 · ACT January 2008 · Form 61B · Math Test

Source question 38. Refer to the source image.

Paper 68 · ACT January 2008 · Form 61B · Math Test

In the figure below. AE and BD intersect at C, and the measure of ZE is twice the measure of ZD. The mea- sure of ZA is 40:.. and the measure of is 32°. What is the measure of ZE ? 40° 32 40° .40. In the figure below, the measure of ZBAC is greater than the measure of ZDAC and AB = AD. Which of the following statements must.be tru.e? GO ON TO THE NEXT. PAGE.

Paper 68 · ACT January 2008 · Form 61B · Math Test

Source question 40. Refer to the source image.

Paper 68 · ACT January 2008 · Form 61B · Math Test

In a math course, a student scored 100 on one test, 97 on another test, and 88 on each of the other tests. The student s test average for the course, where each test is weighted equally, is exactly 91. What is the total number of math tests that the student has taken in the course? DO YOUR FIGURING HERE.

Paper 68 · ACT January 2008 · Form 61B · Math Test

An equation of a particular circle is (x - 3), + y 10. What are the coordinates of this circle's center and what is the length, in coordinate units, of this circle's radius? Center Radius 'K. (3,0) 10

Paper 68 · ACT January 2008 · Form 61B · Math Test

The point (3,-4) is the mid oint of the line segment in the standard (x,y) coor inate plane joining the point (8,-11) and the point (a,b). Which of the following is (a,b) ?

Paper 68 · ACT January 2008 · Form 61B · Math Test

If AC- 10 feet and BD - 12 feet in the rhombus ABCD shown below, what is its area, in square feet? 11 60 ACT-61 B-SAMPLE 23 GO ON TO THE NEXT PAGE. DO YOUR FIGURING HERE. wide, and 3 feet tall is shown below. What is its volutne, in Fubic feet? 4ft Use the following information to answer questlons 46-49. A balloonist collecting data on pollutants at various levels above the ground takes off at 8.00 A.M. When the balloon is in motion, it moves only straight up or straight down and at a constant speed within each hour-long interval. The balloon is at an altitude that is a multiplc of 100 mcters at the begin- ning o.f each hour. The balloon lands at 2:00 p.m. at the same spot from which it took off. The altitude of the balloon. in meters above th¢ ground. is shown in the fIg￿e below. 500 400 VAII 200 8:(X) 9:(x) 10:(M) 11:(X) 12:IK) I:IXI 2.110 M. KM. AM AM..IMTh P. tllne

Paper 68 · ACT January 2008 · Form 61B · Math Test

Source question 45. Refer to the source image.

Paper 68 · ACT January 2008 · Form 61B · Math Test

, Which of the following is closest to the total distance, in meters, that the balloonist traveled from IO=OO A.M. to 1:00 p.m. ? 47: What was the total time, in hours and minutC8. that thc balloon wa.s at least 200 meters above the gIound? AGT:,61&SAMPLE. GO ON TO THE NEXT PAGE. ' abgolute value of the ballo.on's velocity, in me.ters per Iw)Jr, between 8:00 A.M. and 2.00 p.m. ? .tNot¢" Ignore accel¢ration and deceleration..) 500 400 DO YOUR FIGURING HERE. . 8:(K> 10:00 12:LK) 2'1X) noon P.M. ' ' 11.IIVAVIlAII 8:00 10:(N) 12:(K) 2:(K) noo P.M. time 500 200 ' 11:IIIVJqVAII 8:00 10:00 12:00 2Q) noon PM. time 500 ,Q3C)ea 40Q ,' IIIIIVJkirAIII , JkJTAIIIIIIII 8:(Kh 10:00 12:QLI IIN) P.M. time 5(X) 100 8:00 10:00 12:CM) 2: noon time PM

Paper 68 · ACT January 2008 · Form 61B · Math Test

Source question 47. Refer to the source image.

Paper 68 · ACT January 2008 · Form 61B · Math Test

Source question 48. Refer to the source image.

Paper 68 · ACT January 2008 · Form 61B · Math Test

.. Which of the following phrases best describes the bal- loon s motion between 10:30 A.M. and 12:00 noon? D: Ascended, and then descended mo.re quickly . GO ONTO THE NEXT PAGE. . 50: In the .standard (z,y) coordinate plane shown below, ABC has vertices at A(-2,3), B(-2,1), and C(-I,l). A translation is performed on ￿ABC, and the image of each point P with coordinates (Xgy) is the point P, with coordinates (x',y') where x, _ x + 3 and y, _ y - 2. The vertices of £&A'B'C' are in which quadrant(s)? DO YOUR FIGURING HERE. quadrants of the standard (x,y) coordinate plane li Quadrant I only

Paper 68 · ACT January 2008 · Form 61B · Math Test

Source question 50. Refer to the source image.

Paper 68 · ACT January 2008 · Form 61B · Math Test

In the figure below, AB - CD. Fred wants to apply the Side-Angle-Side (SAS) congruence theorem to prove that ￿ABD = ACDB. Which of the following congru- ences, if established. is sufficient?

Paper 68 · ACT January 2008 · Form 61B · Math Test

A camper at Site C sends a distress signal. The signal is received by both Ranger Station A and Ranger Sta- tion B. As. s'hown below, RangeI Station A is 6 miles directly west of Ranger Station B. Ranger Station A is directly. south of Site C. The entire region is flat and Icvcl. On a map. thc anglc formed at Ranger Statioii B by drawing straight lines from Ranger Station B to Site C and to Ranger Station A measures 57° About how many miles away from Site C is the closer of the 2 ranger stations? Site C sin 57° Ranger Station A Ranger Station B ACT.-61WMPLE . 26 GO ON TO THE NEXT PAGL

Paper 68 · ACT January 2008 · Form 61B · Math Test

If th¢ dlaiiteter of a clrcle is tripled, the area of the resulting circle is how rnany times the area of the orig- inal. circle? . DO YOUR FIGURING HERE.

Paper 68 · ACT January 2008 · Form 61B · Math Test

Only tenth-, ¢lev¢nth-, and twelfth-grade students attend Washington High School. The ratio of tenth graders to the school's total student population is

Paper 68 · ACT January 2008 · Form 61B · Math Test

When x and y are nonzero r¢al nurnb¢rs such that -x and | y | = y, which of the folIowing must be positiv¢7 x+y

Paper 68 · ACT January 2008 · Form 61B · Math Test

If x+y 27 GO ON TO THE NEXT PAGE. 57: Kelly askèd,. 120."studEnt&. qiie8tions aboJ]t skiing. Th¢ results of the poll are shown in tbe..table below. Question Yes l. Hav.e you skied either cross-couDtry . or downhill?. DO YOUR FIGURING HERE. 65 55 ou answered Yes 10 Question I, you ski downhill?

Paper 68 · ACT January 2008 · Form 61B · Math Test

Source question 57. Refer to the source image.

Paper 68 · ACT January 2008 · Form 61B · Math Test

A right trianglc bas legs of length 25 sin 6 feet and

Paper 68 · ACT January 2008 · Form 61B · Math Test

Source question 59. Refer to the source image.

Paper 68 · ACT January 2008 · Form 61B · Math Test

Wheo-3 g x g 4 and -1 £ y g 2, what is the least possi- ble value for x - y ? DO YQUR FIGURING HERE.. END OF TEST 2 STOPI DO NOT TURN THE PAGE UNTIL TOLD TO DO SO. DO NOT RÉTURN TO THE PREVIOUS TEST.