ACT Past Papers with Answers

Paper 24

ACT April 2019

Form Z15 · Math Test · 60 questions

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Paper 24 · ACT April 2019 · Form Z15 · Math Test

2cm 0,6 cm4 30° 90°

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A60°BChoice B — see source imageCChoice C — see source imageDChoice D — see source imageEChoice E — see source image

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Paper 24 · ACT April 2019 · Form Z15 · Math Test

Jeralyn purchases I box of grdnola bars and 6 boxes of chocolate bars foT a lotal price of $22.00, The price of each box of granola bars 18 $2.50, and the price of each box of chocolate bars is n dc)Ilars. Which of the followring equations models Jeralyn's purchase?

A2.50 + 22.W- 6nB2.50n + 22.00- 6nC2.50(6n) = 22.00 22.00D2.50n + 6n- 22.00

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Paper 24 · ACT April 2019 · Form Z15 · Math Test

In AABC ghown below, AC = BC and the measure of L4 is 48°. What is the measure of ZC ? 48° 48°

A84°B90°C96°D132°

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Paper 24 · ACT April 2019 · Form Z15 · Math Test

A 4quare has a perimeter of 20 feel. What is the area, in square feet, ot the square? GO ON TO THE NEXT PAGE. ACT-Z15

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A25B40C80DChoice J — see source imageEChoice K — see source image

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Paper 24 · ACT April 2019 · Form Z15 · Math Test

A bag contains exactly 21 solid-colored buttons: 3 red, 6 blue, and 12 white. What is thc probability of randomly selecling I button that is NOT white.) DO YOUR FIGURING HERE.

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Paper 24 · ACT April 2019 · Form Z15 · Math Test

Whatis the value of 1-71 |7- 291 -29 29

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Paper 24 · ACT April 2019 · Form Z15 · Math Test

A store's revenue is the amount of money received for goods 801d. A store's cost is the amount of money the store pays for the goods plus all the store'% operating costs like rent, utilities, wages, etc. A store's net profit is the difference between revenue and cost. During I mollth, a grocery store pdid $30,000 for goods that were sold for $39,500. With operating c08tg as shown below. what was the store's net profit for that month? Opcrating costs Rent, utilities, and telephone Taxes and insurance Interest on business loan Grocer's own wages Wages for p(Lrl-tirne help Misccllaneous Atnouni $2,500 $ 370 $ 400 $4,500 $ 630 $ 400

A$ 700B$ 800C$ 900D$1,000E$1,100

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Paper 24 · ACT April 2019 · Form Z15 · Math Test

When Jorge began a driving trip, his car's odometer read 42 tniles. After Jorge drove for 3 hours, the odometeT read 165 miles. Which of the following values is closest to Jorge's average driving speed. in miles per hour, during those 3 hours? ACT-21S 15 GO ON TO THE NEXT PAGE.

A36B41C54D55E62

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Paper 24 · ACT April 2019 · Form Z15 · Math Test

Melinda and JeriLho are painting a room in the city recreation center. They started with 5 gallotL% of paint. On the first day, Melinda used gallon of paint and Jericho used 2- gallons of paint. How many gallons of DO YOUR FIGURING HERE. paint were left after the first day .

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Paper 24 · ACT April 2019 · Form Z15 · Math Test

What valuc of x makes the equation below true? 25

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Paper 24 · ACT April 2019 · Form Z15 · Math Test

For functions f(x) - 5 . 2, and g(x) - lox: thc Ydlue of A(3) g(3) is. 10 70 970

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A1.030BChoice B — see source imageCChoice C — see source imageDChoice D — see source imageEChoice E — see source image

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Paper 24 · ACT April 2019 · Form Z15 · Math Test

Tanisha, a manager at a stale park, Lounted the money in the c8sh register at the end of her shift, and then she deposited the money in the bank. When she went back to her office, she accidentally shredded thc deposit slip. She remembered that there werc only $5 and $10 bills. She also recalled that there were 27 bills totaliiig $205. How many $5 bills were in Tanisha % cash register at the end of her shift? 16 GO ON TO THE NEXT PAGE. ACT_Z15

A13B14C16D23E32

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Paper 24 · ACT April 2019 · Form Z15 · Math Test

In the standard (x,y) coordinaic plan¢. a line intersects the y-axis at (0,2) and contains the point (8,3). What is the slope of the line? DO YOUR FIGURING HERE.

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Paper 24 · ACT April 2019 · Form Z15 · Math Test

For an anglc with measure tx in a righi triangle, 15 15 17 and titn (X - What is ihe value of cos (x 17 15 17 161 514

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Paper 24 · ACT April 2019 · Form Z15 · Math Test

The expression 28 3W7 is equal to: 3V21

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A12BChoice B — see source imageCChoice C — see source imageDChoice D — see source imageEChoice E — see source image

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Paper 24 · ACT April 2019 · Form Z15 · Math Test

In the figure below, XW illtersects VZ at Y, the measure of ZXYV is (3x + 5)°, and the nieasure of ZZYW is (4x - 6)° What is the measure of ZXYZ g {31 + 5}° (4x- 6)° 83° 142° ACT-Z15 GO ON TO THE NEXT PAGE.

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A104°BChoice G — see source imageCChoice H — see source imageDChoice J — see source imageEChoice K — see source image

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Paper 24 · ACT April 2019 · Form Z15 · Math Test

The table below shows the letter grades 60 studenls earned on the final exam in Amcric&n Literature. The highcst possible grade is A: the lowesi possible griide DO YOUR FIGURING HERE. Final exam grade Number of students 10 26 18 A student from this group will be chosen at random, What is the probability that the student's final exam grade is C or higher.

A0.3B0.4C0.6D0.7E0.9

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Paper 24 · ACT April 2019 · Form Z15 · Math Test

For wh&t value of n does the quadratic equation 2x + n - O have solutions of x- 4 and x-

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Paper 24 · ACT April 2019 · Form Z15 · Math Test

The circumference of a circle is 12ff incbes. What is the area of the circle, in square inchcs?

A4B9C127rDl6JtE36

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Paper 24 · ACT April 2019 · Form Z15 · Math Test

The applicalion for a license plate statcs that the license plate number has 3 letters followed by a 3-digit number, for example, AEE123. The leiiers O and l and the digit O cannot be part of the license plate number. Any of the other letters and digits may be used up io 3 times. Which of the following expressions represents how many different license plate numbers are possible?

A24(23)(22)(9)(8)(7}B24(23)(22){10)(10)(10)C24(24)(24)(9)(9)(9)D26{25)(24)(10)(9)(8)E26(26)(26)(10)(10)(10)

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Paper 24 · ACT April 2019 · Form Z15 · Math Test

Which of the following expressions 1% equiv&lent to 3(a+b)-2(a-5b)? 9b 7b 4b a+13b 18 GO ON TO THE NEXT PAGE ACT-Z15

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Aa+ 8bBChoice B — see source imageCChoice C — see source imageDChoice D — see source imageEChoice E — see source image

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Paper 24 · ACT April 2019 · Form Z15 · Math Test

In the figure below, all of the small squares are equal in area, and the area of reciangle ABCD is I square unit. Which of the following expres8ions represents the area. in square units, of the shaded region. DO YOUR FIGURING HERE.

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Paper 24 · ACT April 2019 · Form Z15 · Math Test

Marie 18 building a kite. In a drawing of her kite shown below. AB= BC, AD - DC, the measure of £ABC is 80° and the measurc of ZADC is 50° Whal is the measure of ZBAD ? 65°

A50°B90°C115°D130°

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Paper 24 · ACT April 2019 · Form Z15 · Math Test

The triangles below are similar (ZsABC - ADEF). Which of the following is an expression foT the area of ABC. in square inches? (2+4){3+x) (2)(3) (2)(3){2) xin (2) (4)(6) 4in D 2in F

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Paper 24 · ACT April 2019 · Form Z15 · Math Test

The interior of a rectangular .shipping crate has dimen8Rons 2 ft by 3 ft by 6 ft. Tbe crate wilE be filled with cube-shaped boxes whose exteriors havc dimensions 12 in by 12 in by 12 in. Given that no box can cxtend beyond the dimensions of the crate's interior. what is the maximum nuTnber (Jf boxes ihe crate can hold? ACT.I15 19 GO ON TO THE NEXT PAGE. DO YOUR FIGURING HERE. Uso the following information to answer questions 26-29. Shasta is parlicipating in a bike ride for charity. The graph of speed (s} versus time (t) for the first 20 Seconds of her bike iide is shown in the coordinate plane below. The graph is composed of 2 line segments for which the endpoints are at (O,0}, (10,5), and (20,3). Shasta traveled 25 meters in ihe first 10 second%. (10,5) (20.3) 10 20 seconds Beginning at /- 20 seconds, Shasta slow5 down as shc approaches a familiar group of riders ahead of her and then travels at a constant speed with the group after joining thcm.

Al2B36C48D72

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Paper 24 · ACT April 2019 · Form Z15 · Math Test

1¥'hat is Shasta's speed, in meter£ per second, at t = 3 seconds.

A1.5B2.0C2.5D3.0E6.0

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Paper 24 · ACT April 2019 · Form Z15 · Math Test

Shasta's acceleration, over the interval from t= 10 seconds to t- 20 seconds, is equal to the slope of the graph over that interval, measured in meterg per sccond per second. What is the value of a 20 GO ON TO THE NEXT PAGE. ACT-Z15

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Paper 24 · ACT April 2019 · Form Z15 · Math Test

Calen slarted hi.s bike ride earlier than Shasta. During the first 15 seconds of Shasta's ride, Calen was traveling at a constant speed equal to of Shasta's maximum speed during that same t]e PCTiod. How far, in meters, did Calen travel durillg the first 15 seconds of Shasta's ride? DO YOUR FIGURING HERE.

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A25B45C75DChoice J — see source imageEChoice K — see source image

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Paper 24 · ACT April 2019 · Form Z15 · Math Test

Which of the following graphs best rcpicscnts the portion of Shasta's ride beginning at t = 20 seconds? (20,3) (20,3) 20 20 (20,3) (20,3) 20 20 (20,3) 20 30. 10 12 13 30 ACT-Z15 21 GO ON TO THE NEXT PAGE.

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Paper 24 · ACT April 2019 · Form Z15 · Math Test

Source question 30. Refer to the source image.

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Paper 24 · ACT April 2019 · Form Z15 · Math Test

The lengths of 2 adjacent sides of a rectangle are represented by x + 2 feet and 2x + 7 feet. In terms of x. what is the area, in square feet, of the rectangle? DO YOUR FIGURING HERE.

A6x+18B2x'+14C2r'+ 9x+14D2_T +llx+ 9E2x +llx+14

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Paper 24 · ACT April 2019 · Form Z15 · Math Test

Which one of the following inequalities is true?

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A2<<3<4B4<21<5)<5C<3<4<<5DChoice J — see source imageEChoice K — see source image

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Paper 24 · ACT April 2019 · Form Z15 · Math Test

Two tair coins are repeatedly tossed simultaneously. What is the probability that both coins land heads up on the 36th tOS8? 108 36

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Paper 24 · ACT April 2019 · Form Z15 · Math Test

Suppose a student's course grade is determined solely by that siudenl's scores on 8 tests, which are worth 100 points each. If Bane has an average of exactly 88 points on thc first 6 tests, how many points must he average on the last 2 tests to earn exactly a 90-poinl course grade?

A99B96C95D94E92

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Paper 24 · ACT April 2019 · Form Z15 · Math Test

Which of the following operations will produce the largest result whell substituted for the blank in the expression 62 65 22 GO ON TO THE NEXT PAGE. ACT-Z16

AAveraged withBDivid¢d byCMinusDPlusEMultiplied by

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Paper 24 · ACT April 2019 · Form Z15 · Math Test

Given the sets A= {0, 1, 2, 3} and B-.{l. 3, 5. 7} which of the following defines a function f from A ontoB? DO YOUR FIGURING HERE.

Af(x}=2x+lBf(x)=2¥-1Cf(x)=3x-Df(x)-3x-Ef(x)= x+l

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Paper 24 · ACT April 2019 · Form Z15 · Math Test

Ifx= and z- l + I, which of the following oIders x, y, and z from least to greatest? x<y<z z<)i<x

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Paper 24 · ACT April 2019 · Form Z15 · Math Test

Isosceles triangle AABC has an altitude of h inches, a b¢ise of 36 inches, and 2 base angles measuring 76° each, as shown in the figure below. What is the value ofh? 36 sin 76° 76° 76°

A18 sin 76°B18tan76°C36 cot 76°D36 ian 76°

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Paper 24 · ACT April 2019 · Form Z15 · Math Test

The ,least common multiple (LCM) of 2 numbers is

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Paper 24 · ACT April 2019 · Form Z15 · Math Test

In the standard (x,li) coordinate plane, given Parabola A with equation ) 3x , Parabola B is the image of Parabola A afÈer & shift of 7 coordinate units to the left and 4 coordinate units down. Parabola B has which of the following equations? ACT-215 23 GO ON TO THE NEXT PAGE. DO YOUR FIGURING HERE. Use the following information to answer questions 41-43. In 2012, pollsters for the Gallup Organizaiion asked a r.andom samplc of 1,014 adults. 'On the average, about how much doe5 your farnily spelld on food each week?" The table below lists the percent of the sample that gave each response. For example, approximately 21¢Yo of adults in the samplc rcsponded that, on average, they spcnd no le%s than $200 but no more than $299 on food each week. Average amount spent Less than S50 S50 to $99 $100 10 $124 $125 to $149 $150 to $199 $200 to $299 $300 or rnore Did not give an amount Percent of sample 8qo 17q 22% 4Yo 15(Yc 21Yo 3oYo

A}=3(x-4)' 7By-3(x-7)'_4C)'=3(x-7}'+4Dy-3(x+7)'Ey-3(x+7} +4

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Paper 24 · ACT April 2019 · Form Z15 · Math Test

Which of the following expressions is equal to the approximate number of adlllts from the sample that said Ihey spend an average of less than $100 each week on food?

A1,014(22}B1,014(25)C1,014(47)D1,014(0.22)E1,014(0.25)

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Paper 24 · ACT April 2019 · Form Z15 · Math Test

What percent of adults in ihe sample responded that thcy spend, on average, at least $150 each week on food? F, 15%

A46YB49%C51YD66Y

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Paper 24 · ACT April 2019 · Form Z15 · Math Test

A pollster will crcate a Circle graph using the information in the table. One sector of thc circle graph will represent the percent of adults in the sample who said they gpend an average of $300 or more on food each week. What will be the measure of the central angle for that scctor? 24 GO ON TO THE NEXT PAGE ACT-Z15

A10°B13°C36°D45°E47°

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Paper 24 · ACT April 2019 · Form Z15 · Math Test

A sphcrical droplet of ink strikeq a iiertical wall, as odeled in the figure below. The angle of impact ig indicated by O in the figure. DO YOUR FIGURING HERE. ink droplet wall The stain the droplet Jeai'es on the wall is oval-shaped. Scientists Lan measure the maximum length and maximum width of the Stain to determine ihe angle of impact according to the tormula sin 8 - maximum width MaXiuln length ' The ligure below models such a stain. Whal wag the impact angle of the droplet thai leti this stain? m(Iximum width maximum length

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Paper 24 · ACT April 2019 · Form Z15 · Math Test

The giaph below shows the disiribution of a data set consisting of 16 positive integers. Which of the following SLatemcnt.S (ibout the mean, tnedian, and mode of the data set is irueg 1 2 3 4 5 6 7 8 integer is less than the mean. equal to the median. less Ihan the median. is Icss than the Mode. is equal to the mode. ACT-215 25 GO ON TO THE NEXT PAGE.

AThe mode is Iess than the median, and the medianBThe mode is less than the mean, and the mean isCThe mode is equal to thc n]ean, and the niean isDThe mean is less Lhan the median, and the medianEThe mean is equal to the median, and the median

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Paper 24 · ACT April 2019 · Form Z15 · Math Test

Yolanda collects trading cards, and she has started her younger brothers, XavieT and Zach, collecting cards a well. As of today, Zach owns 5 more cards than Xavier, and Yolanda owns twice as many cards as Xavier and Zach combined. Which of the following equations expresges the relationship between y, the number of cards Yolanda owns, and x, the number of cards Xavier owns? DO YOUR FIGURING HERE. x+5 v-4x-10

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Ay-4x+lOBChoice G — see source imageCChoice H — see source imageDChoice J — see source imageEChoice K — see source image

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Paper 24 · ACT April 2019 · Form Z15 · Math Test

What is the distance. in coordinate units, between the points {-2,1) and (1,10) in the standard (x,y) coordinate plane? 72 82 90 12

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Paper 24 · ACT April 2019 · Form Z15 · Math Test

A rectangular solid has a volume of 100 cubic ullils. If the length, width, and height of the solid are each doubled, what will the volume, in cubic units, ot the new solid be? 21Kb 400 600 800

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A2,700BChoice G — see source imageCChoice H — see source imageDChoice J — see source imageEChoice K — see source image

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Paper 24 · ACT April 2019 · Form Z15 · Math Test

The set of all values of x that satisfies Ix- the same as the set of all values of x that satisfies.. O<x<5 O<x<9 -5<x<5 -5<x<9 -9<x<9

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Paper 24 · ACT April 2019 · Form Z15 · Math Test

The fifth power of a number is 380,204,032. The number is between: 1,000 and 100,000. 26 GO ON TO THE NEXT PAGE. ACT-ZI 5

Al and 10.B10 and 100.CLOO and 1,000.D100,000 and 100,000,000.

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Paper 24 · ACT April 2019 · Form Z15 · Math Test

Given A- 20 3 1 5 -2 ,andC- if it is DO YOUR FIGURING HERE. possible to calculitte C + AB, which of ihe following matrice5 is the resultg 22-4 11 6

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AIt is not possible to caIculate C + AB.BChoice B — see source imageCChoice C — see source imageDChoice D — see source imageEChoice E — see source image

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Paper 24 · ACT April 2019 · Form Z15 · Math Test

Given O < x < 8 and y > 18, what is the greatest value if it call be determined? 13 13

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ACannot be determined from the given inforinationBChoice G — see source imageCChoice H — see source imageDChoice J — see source imageEChoice K — see source image

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Paper 24 · ACT April 2019 · Form Z15 · Math Test

The graph below gives the spced. in knots (nautical miles per hour), of a cruise ship during a 5-hour period. Which of the following values is closest to thc rate of change, in knots per hour, of the speed of the ship between hours 2 and 4 ? 25 20 15 hour ACT.Z1S 27 GO ON TO THE NEXT PAGE.

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AloB25CChoice C — see source imageDChoice D — see source imageEChoice E — see source image

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Paper 24 · ACT April 2019 · Form Z15 · Math Test

A fair spinner wilh 4 equally sized regions and an arrow has regions numbered 1, 2, 3, and 4, respectively, <illd a second fair spinner with 5 equally sized regions and an aTTOW has regiong numbered 1, 2, 3, 4, and 5, respectiTr ely. The arrows are both spun at the satne time, and the numbers ihe 2 arrows land on are multiplied together. What is the probability that this product is an odd numberg DO YOUR FIGURING HERE. io

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Paper 24 · ACT April 2019 · Form Z15 · Math Test

The bottom of a swimming pool, shown below, has an area of 630 square feet and a perimeter of 114 ft. The sivimming pool has a uniform depth of 5 ft of water, and Ihe given lengths are in feet. If it can be deterTnined, what is the volume of water, in cubic feet, that the pool contains. 16 44

A3.150B3,335C3,520D3,720ECannot be determined from the gii'en infonnation

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Paper 24 · ACT April 2019 · Form Z15 · Math Test

For all positiv¢ integeTS a and b, Ihe expression (a !) is cquivalent to one of the following expressions. Which one? K, [a(a- lJ{a 2} (1)], 28 GO ON TO THE NEXT PAGE. ACT.ZI5

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A(a'}!B{ab)ICb(a!)DChoice J — see source imageEChoice K — see source image

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Paper 24 · ACT April 2019 · Form Z15 · Math Test

The standard normal probability distribution function (kL= O and (s- 1) is graphed in the standard (x,y) coordinate plane below. Whi¢h of the following percentages is closest to the percent of thc data poinls that are within 2 standard deviations of the Tnean in dny normal dibtribution? DO YOUR FIGURING HERE.

A50%B68C90%D95CyoE99%

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Paper 24 · ACT April 2019 · Form Z15 · Math Test

For what value of b will the determinant of the mairix have a value of 18 ? io

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A15BChoice G — see source imageCChoice H — see source imageDChoice J — see source imageEChoice K — see source image

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Paper 24 · ACT April 2019 · Form Z15 · Math Test

What are the solutions to x 2x+17-0? -3and5

Ai +132)1B1+41C1+81D2+81

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Paper 24 · ACT April 2019 · Form Z15 · Math Test

Shown below are the top, front, and right side views of a stack of l-centimeter cubes. The labels T, F, and R specify where the top, fiont, and right sides are located with respect to the view. What is the volume, in cubic centimeters, of the stack of cubes? top front righi ,sidc END OF TEST 2 STOP! DO NOT TURN THE PAGE UNTIL TOLD TO DO SO. DO NOT RETURN TO THE PREVIOUS TEST. ACT.Z15 29

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A12B14CChoice H — see source imageDChoice J — see source imageEChoice K — see source image

Form Z15 · Math Test · 60 questions

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