ACT Past Papers with Answers

The statement AABC= LDEF is true. Which of the following .staternents iiiust be true? ZA-ZF

A group of students was surveyed about what types ol musiL c(Ich had listened to during the previous week. Students could choose 1, 2, 01 3 types of music (Rap. Rock, or Country), or they could respond "none of these music types., Only l O student% responded with 'none of these music type.s,' and 18 stLidents responded that they had listened to all 3 types. In the figure below, the 8 regions show tlie numbers of responses in each category. DO YOUR FIGURING HERE. Rap Rock 12 10 14 Country 10 One region had exactly 8 re8ponses. What typ¢(s) of mu%ic did those 8 gtudents re.8pond they had li%tened to during the prevÈous week? Rc1P only Rap and Rock only

Whatisthevalueof 212-91 3(4+2) ? 15

Portions of the graphs represented by the functions -2x+v= and x + 1: = 5 are 8liown in the standard (x,vl coordinate plane below. Although oiily a portion of each graph is shown, the domain of each function is all real numbers. If it Ccin be detei"niined, at what point do the graphs inter%ect? ACT-74H 15 GO ON TO THE NEXT PAGE.

011 Li niap, inch represents 10 actual miles. Two DO YOUR FIGURING HERE. towns that are 4- inches apart on this map are how mLilly LlCtIlLiI mile% 2¢ pai t,?

The cost ot" a lono_distaiicL call to a certain city is $1 .05 for the first minute and $0.15 for each additional minute oi" pai"t tliereot. Wliat is the co8t of a 15-minute call t() thi% city

Tamm)I will draft I player at random from a list of 20 playei's toi" her fantaqy football team. Each player in the list plays onl), J po.%ition. The number of players who play a particular position is given in the table below. WIIQL t is the probability that the player Tammy dral:t% will be a kicker or a receivei P Number of players Position Kicker Linebacker Qiiill-terback Recciver ?£ ACT-74H 16 GO ON TO THE NEXT PAG

Ben is saving money to buy a TV that costs $495, includino tax. Ben opens a savings account with a depo8lt of $75 and deposits $65 at the end of each month. What is the minimum number of months Ben will need io make deposits until he has enoiigh money in hi% account to buy the TV ? DO YOUR FIGURING HERE.

What is the slope of HM, shown in the standard (x,),) coordinate plane below? H(_2,2) K(O,-l ) M(2,-4)

The polynomial 45x- + 261 - is equivalent to the product of (5x + 4) and which of the following binomials? 9x+ 4

Given that sin-x= 13 what is cos x ? 13 13 ACT.74H GO ON TO THE NEXT PAGE.

In the figure below, all of the srnall squares are equal in area, and the area of rectangle ABCD is I square unit. Which of the following expressions represents tlie area, in square units, of the shaded region? DO YOUR FIGURING HERE.

In the standard (x,y} coordinate plane, the line represented by which of the following equations goes through (0.7) and is parallel to the line represented by -2x+7 ACT-74H 18 GO ON TO THE NEXT PAGE.

In the standard (x,y) coordinate plane, the graph of the line 3.r - d passes through the point (-5,6). What is the value ol- d ? -39 38

Given u and v such that (a~ positive a, what is a. for all 10 16 20 ACT-74H 19 GO ON TO THE NEXT PAGE.

In the standard (x,v) coordinate plane, a translation mL1PS a point (x,),) to its image (x- 5, y + 3). To what image does this translation map (-3,-2) 9 DO YOUR FIGURING HERE.

Given x = 4a+b which of the following expressions is equivalent to b ?

Matt purchased a 60-foot-long i'oll of chain-link fence. He used the entire roll of fence to construct a rectangular pen for his dog. Given that the pen is 12 feet wide, what is its length, in feet?

Angle IJKL is shown below with the given lengths in coordinate units. What is the measure of ZJKL in radians? 37C 23[ 120° K 3 L 43[

A rectangle is 3f5 meters wide and 5<5 meters long. Wliat is the area, in square meters, of the rectangle? 8<5 ACT-74H 20 GO ON TO THE NEXT PA

In Westville on Tuesday, the high temperature was 30°C and the low temperalure was 20°C. What was the difference between the high and low temperatures, in degrees Fahrenheit ? (Notc.. The relationship between the temperature c, in degrees Celsius, and the temperature f, in degrees Fahrenheit, is given by c - (f- 32).) IO°F

A conimittee will be selected from a group of 12 women and 18 men. The committee will consist of 5 wonien and 5 men. Which of the following expressions givcs the number of different committees that could be selected from these 30 people? PI)(18P5)

Which of the following expressions is equal to 4-<5 12-3<5 21 12+f15 li 12+3<5 li ACT-74H 21 GO ON TO THE NEXT PAGE. DO YOUR FIGURING HERE. Use the following information to answer questions 32-34. When it wa8 constructed 4,500 years aiFO, the Great Pyrainid in Egypt had a height of 147 meters and contained roiiolily 2._3 rnillion .stone blnck,8. It is estimated that

Wheii written in scientific n()tation. which of the rollowing expressions is equal to the number of blocks Lised to construct the pyramidg 93 x l{) 78 x 10-,

The perimeter of the pyramid's base W<iS 920 meters wlien construLliOli was completed. At that time, wliich ol the tollowiiigi values is closest to the length, in InetLI-s. ot L'ach diaiional of the base? 3(1 40

Which of thc follow'ing cxpre%sions is equal to the length, in meters: of DC ? 147 sii) 19° 147 LC)5 39° 147 .%in 79" 147 ACT-74H 22 GO ON TO THE NEXT PAG

In AABC, AB= 6 cm, AC= 12 cm, 7iiZA= 60,, and AC is the longest side. Which of the following statements about the ineasures of the angles in AABC niii.st be true? DO YOUR FIGURING HERE. (Note: Inzx dcnotes the measui'e of angle X.) IZA = i?IZB = MZC In£B > niZA > iiilc yi1ZB Inzc > niZA n?ZB > inZC- MZA n?ZC > inZA > MZB

Erika is landscaping her front yard. The y{￿d, which is level, haq the %hape of a rectangle thcil is 60 feet wide by 80 teet long. To cover the yard with a layer of topsoil having a uniform depth of 4 inches fool Ei'ik1t Iieeds to use how many Lubic feet of topsoil'P

Suzanne and Chad are going to bake and deliver cookies to college students during lÈnal exan] week. They estimate it will cost $4 for the ingredients to make each batch of cookies and $50 to buy the mixer, bowls: and other utensils they will need. They decide to sell the cookies for $5 per batch. Assume they have no otlier expen%es. Which of the followin(T equations represcnts the profit, P dollars, they will make on b batches of cookies? -b+50 b-50

The Sum of the measures of ZA and ZB is 90° The sum of the measure8 of ZA and ZC is 180° The %um of the nieasures of ZB and ZD is 180°. What is the sum ot the measures of ZC and ZD ? 45° ACT-74H 23 GO ON TO THE NEXT PAGE. DO YOUR FIGURING HERE. Use the following information to answer questions 39-41. The figure below shows the top view of the Santana family's house and yard. The Santanas, rectangular house is 40 feet wide and 30 feet long, and their rectangular yard is 75 feet wide and 100 feet long. The Santanas have a rectangular garden in the back corner of their yard that is 30 feet wide and 25 feet long. The garden currently contains 48 flower bulbs: 10 tulip bulbs, 18 daffodil bulbs, and 20 crocus bulbs. 25 garden 30 yard 30 house

The area of the garden is what percent of the area of the yard? 25go

Beginning next year, Mr. Santana will increase the number of bulbs in the garden each year so that tlie numbers form a geometric sequence. In 3 years, there will be 162 bulbs in the garden. By what factor will the number of bulbs be multiplied each year?

Suspended from the ceiling is a weight on a large spring that is oscillating up and down. The digtance, d inches, between the location of the center of the mass of the weight after tseconds and the weight's equilibrium location at t - O 1% modeled by the function d- 5 sin(47ct). What is the amplitudc of the function? DO YOUR FIGURING HERE.

Given that i l and that k is a positive integer, what is the value of i14k + 21 ?

For all real numbers a, b, and c, which of the followino expressions is equal to | a |a+b+cl |a+b- -a+b+c ACT-74H 25 GO ON TO THE NEXT PAGE.

Given g{x) = which of the following expressions is equal to g(x- l) for all x in its domain x+l DO YOUR FIGURING HERE. 2x+l 1+1

A circle with radius 10 cm is divided into 3 congruent arcs. What Es the length, in centimeters, of each of the 3 arcg? 10 20 40

Consider all posilive integers that are multiples of 20 and that are less than or equal to 300. Whal fraction of those integers are multiples of 15 ? 15 15 15

The fraction is equivalent to 0.285714. What is the digit in the I,OOlst decimal place of 0.285714 ? DO YOUR FIGURING HERE. (Note: The digit in the 4th decimal place of 0.285714

At what point in the standard (x,y) coordinate plane do the asymptotes of the function y- 2x(x + 2} graphed below, intersect? 45 40 35 30 25 20 15 10 2 4 6 8 10 12 14 10 15 ,10 ACT-74H 27 GO ON TO THE NEXT PAGE.

The employees at a hotel i'eservation center as.sign an %-digit confirmation number (CN) to each customer miikinrF a reservation. The first digit in each CN is 8. I'he othei" 7 di(rits can be any digit O through 9. and diirits may repeat. How many po8sÈble 8-digit CNS are DO YOUR FIGURING HERE. i ()'

Which of thc follom'ing number line graphs i'epre%eii(s all Vcilucs Én the domain of the function logiiilx-

What is the determiiiant of the matrix shown below? 34

At Wal"er Technologies, identification codes each conqist of the following sequence: I digit, 4 letters, I digit. Foi any I code, the digits (0-9) may be thc %ame, but the letters, each from the English alphabet, Inu%t (ill be ditferent. Which of the following expressions gives the probability that a randomly selected identification code contains the word MATH, spelled correLtIy. 10 (26,) 10 10'(261(?5)(24){?3) io, i 0(9)1261(25)(94)(23) 10 (4)(3)(?)( i ) 10"(26') 10 (41(3)(2)(1) 10{26)(25)(24)(23) ACT-74H 28 GO ON TO THE NEXT PAG

What is the distai)ce, Én cooi"dinate units, between 2 + 61 and -4 + li in the complex plane? DO YOUR FIGURING HERE. 45

What 1% the minimum valiie of .f(A)- |-(.r l?) + kl q toi. each set of po.%itive real numbers, h, k, and q

Which of the following data sets ha8 the greatest standard deviation? 1,2,3,4,5,6 ? 6,6, 10. 10, 12