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June 2023 F12 - act

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Pre-Calculus

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© 2023 by ACT, Inc. All rights reserved. NOTE: This test material is the condential copyrighted property of ACT, Inc., and may not be copied, reproduced, sold, scanned, emailed, or otherwise transferred without the prior express written permission of ACT, Inc. Violators of ACT’s copyrights are subject to civil and criminal penalties.

2022

l

2023
Form F

####### (June 2023)

In response to your request for Test Information Release materials, this booklet contains the test questions, scoring keys, and conversion tables used in determining your ACT scores. Enclosed with this booklet is a report that lists each of your answers, shows whether your answer was correct, and, if your answer was not correct, gives the correct answer.

ACT owns the test questions and responses, and you may not share them with anyone in any form.

This booklet contains tests in English, mathematics, reading, and science. These tests measure skills and abilities highly related to high school course work and success in college. Calculators may be used on the mathematics test only.

The questions in each test are numbered, and the suggested answers for each question are lettered. On the answer document, the rows of ovals are numbered to match the questions, and the ovals in each row are lettered to correspond to the suggested answers.

For each question, rst decide which answer is best. Next, locate on the answer document the row of ovals numbered the same as the question. Then, locate the oval in that row lettered the same as your answer. Finally, ll in the oval completely. Use a soft lead pencil and make your marks heavy and black. Do not use ink or a mechanical pencil.

Mark only one answer to each question. If you change your mind about an answer, erase your rst mark thoroughly before marking your new answer. For each question, make certain that you mark in the row of ovals with the same number as the question.

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Lay your pencil down immediately when time is called at the end of each test. You may not for any reason ll in or alter ovals for a test after time is called for that test. To do so will disqualify you from the examination.

Do not fold or tear the pages of your test booklet.

DO NOT OPEN THIS BOOKLET UNTIL TOLD TO DO SO.

Directions

[2]

Nevertheless, I eked out my first news story,

which was about a boy who received a typewriter from his

grandmother on his birthday. [B] The story didn’t even fill

half a page, but I handed it to my grandmother with pride.

After she read it, she squinted at me from behind her

glasses. [C] “But news writing is about telling your

readers something they need to know. Enlighten them.”

[3]

The next morning I scoured the

neighborhood empty notebook in hand,

dejected. [D] I was surrounded by adults who

already seemed to know everything. Who was I

to judge what people needed to know?

[4]

Then, as I approached the park at the end of my

block, I heard a small squeal coming from the direction

of the swings. I ran over to find a girl standing there,

brushing dirt from her jeans. The seat of the nearest swing

dangled from one chain while the other chain swayed back

and forth, unattached. No one else had witnessed what I

had; I realized I’d found my story.

[5]

Later that day, while I hand-delivered copies of my

broken swing story to every house on the block. Someone

repaired the swing the very next day. Regardless, my

grandmother attributed its quick repair to my story.

  1. A. NO CHANGE B. neighborhood, empty notebook in hand, C. neighborhood, empty notebook in hand D. neighborhood empty notebook in hand

  2. F. NO CHANGE G. forth for it was H. forth, it was J. forth being

  3. A. NO CHANGE B. while hand-delivering C. I hand-delivered D. hand-delivering

  4. F. NO CHANGE G. Of course, H. However, J. Instead,

  5. A. NO CHANGE B. designated C. assigned D. referred

7

8

9

10

11

[6]

Now, fifteen years later, I’ve moved past writing about

broken playground equipment. But whatever I write,

whenever I write, my grandmother’s voice still guides

me. “Anthony,” she says, “tell them something they

need to know.”

  1. The essay writer is considering adding the following sentence to the essay: “This is a good start, Anthony,” she said. The sentence would most logically be placed at: F. Point A in Paragraph 1. G. Point B in Paragraph 2. H. Point C in Paragraph 2. J. Point D in Paragraph 3.

PASSAGE II

Animals Over, Under, and Above All

[1]

In northwest Montana, more than thirty species of

animals, ranging from otters to elk, travel across a busy

fifty-six-mile stretch of US Highway 93 via overpasses,

bridges, and tunnels. These structures comprise the most

expensive and innovative wildlife-centered highway design

project in the United States. [A]

  1. F. NO CHANGE G. passed writing about H. passed writing for J. past writing for

  2. The essay writer is considering deleting the underlined portion. Should the underlined portion be kept or deleted? A. Kept, because it introduces the grandmother’s voice to the narrative. B. Kept, because it reiterates the main theme of the narrative. C. Deleted, because it fails to explain how the grand- mother is qualified to give the narrator advice. D. Deleted, because it takes the focus away from the narrator’s writing technique.

  3. Suppose the essay writer’s primary purpose had been to provide a brief overview of the narrator’s fifteen- year career as a news writer. Would this essay accom- plish that purpose? A. Yes, because it describes the narrator’s most sig- nificant news stories and how they shaped him as a writer. B. Yes, because it focuses on the news stories the nar- rator wrote when he was nine years old. C. No, because it instead focuses on the narrator’s grandmother’s experiences as a news writer and how those experiences shaped her career. D. No, because it instead describes a single story that marked the beginning of the narrator’s interest in news writing.

Questions 14 and 15 ask about the preceding passage as a whole.

12

13

13

It guides bears and moose from the highway for

the other half of their natural habitat range.

[4]

This highway project helps protect

both humans and animals. Surveillance

cameras have captured animals

seeming to teach their young how to use

the structures. A mother black bear nudges

her cub as it climbs onto the overpass; then

the two walk ahead quickly so her cub will follow

her. White-tailed does lie down (in a culvert) as their

fawns run back and forth in it, and then they all walk

through the culvert together. With thousands of deer

having bounded over one new bridge, animals seem

to be learning that they have found safe passage.

  1. The writer is considering adding the following sen- tence to the essay: If the road were widened conventionally, crossing it would become even more danger- ous, and animals would eventually be trapped in haphazard fragments of their natural habitat. If the writer were to add this sentence, it would most logically be placed at: A. Point A in Paragraph 1. B. Point B in Paragraph 2. C. Point C in Paragraph 2. D. Point D in Paragraph 3.

  2. A. NO CHANGE B. with the highway toward C. over the highway to D. on the highway at

  3. Which statement most effectively introduces this paragraph? F. NO CHANGE G. The very highways that allow people to move freely often block the movement of animals. H. So far, these wildlife crossings appear to be doing what they were designed to do. J. Safe, carefully placed fencing seems to help ani- mals use the crossings.

  4. A. NO CHANGE B. that record nearby activities have C. recording animals have D. have recorded and

  5. F. NO CHANGE G. are seeming H. while seem J. seem

  6. A. NO CHANGE B. she walks C. they walk D. it walks

  7. F. NO CHANGE G. down, in a culvert, H. down, in a culvert J. down in a culvert

  8. Suppose the writer’s primary purpose had been to describe the process by which a few groups worked together to achieve a common goal. Would this essay accomplish that purpose? F. Yes, because the essay makes clear that groups worked together in the 1980s to prevent the redesign of several historic two-lane roads in Montana. G. Yes, because the essay describes the organized group protests by tribes, engineers, and scientists that led to the animal crossings being built. H. No, because although the essay states that groups worked together to create animal crossings, the essay focuses on describing the benefits of the structures. J. No, because the essay instead focuses on provid- ing data to show the number of animal deaths that a road redesign project has prevented.

Questions 29 and 30 ask about the preceding passage as a whole.

23

24

24

25

26

27

28

PASSAGE III

Eva Zeisel’s Playful Search for Beauty

[1]

Speaking at an event held to honor her nearly

eighty years as a ceramics designer, artist Eva Zeisel

said her focus had always been the same; a playful

search for beauty. [A] The Hungarian-born artist’s

search began following a 1925 trip to the World’s

Fair in Paris, France. [B] There she had visited

row after row of exhibitions not only by

the world’s preeminent new architects but

also by creators of fashion mannequins.

Zeisel felt that many of the featured

designs, stressing stark, geometric shapes

and angular lines, fundamentally

too cold. B For Zeisel, the only

emotion they conveyed was “leave me alone.”

[2]

Zeisel herself personally thought and believed

that items to be used in the home, where people

gather most often and most closely, should be warm

and inviting. Working in simple white ceramic,

for creating her dinnerware sets of plates, bowls,

cups, and saucers and exhibiting them at local fairs.

  1. A. NO CHANGE B. same: a playful C. same a playful: D. same a playful

  2. Given that all the choices are accurate, which one best provides a foundation for the essay’s discussion of Zeisel’s artistic focus? F. NO CHANGE G. graphic artists, many of whom were from Poland. H. leading designers of objects for the home. J. prominent French perfume makers.

  3. A. NO CHANGE B. were C. also D. DELETE the underlined portion.

  4. Which of the following true statements, if added here, would best connect the preceding sentence to the last sentence in the paragraph? F. They didn’t remind her of anything she had cre- ated as an apprentice potter. G. She did, however, appreciate that the designs were not at all flowery or frilly. H. She still appreciated all that she had taken in at the World’s Fair. J. They didn’t express a sense of joy or humanity.

  5. A. NO CHANGE B. emotion, they conveyed, C. emotion they conveyed: D. emotion they conveyed,

  6. F. NO CHANGE G. Zeisel, who was a ceramics designer for nearly eighty years, H. Zeisel, who attended the 1925 World’s Fair in Paris, J. Zeisel

  7. A. NO CHANGE B. she began creating C. the creation of her D. while creating

31

32

33

35

36

37

PASSAGE IV

Berry Sweet

Dark red and containing one seed, the berry of

Synsepalum dulcificum, called miracle fruit, may not

seem particularly impressive at first. Its mildly sweet

tang is often compared to that of a cranberry. But within

this small fruit lays miraculin, a natural protein with the

power to trick the tongue by making even the sourest

flavors taste remarkably sweet.

Eating a miracle fruit allows miraculin

molecules that bind to the sweetness receptors

on the tongue’s taste buds. Then, when a food

containing acid (which generally causes a sour taste)

is consumed, this molecular bond intensifies. This

reaction, in turn, transmits a signal indicating sweetness

to the brain. Thus, acidic foods with sour or bitter flavors

register as sweet. Raw lemon slices taste like candy.

  1. The writer is considering adding the following sen- tence to the essay: Many of Zeisel’s first designs to be mass- manufactured had been critically acclaimed by art enthusiasts and museums, but she wanted her dinnerware pieces to be enjoyed by people in the home. If the writer were to add this sentence, it would most logically be placed at: A. Point A in Paragraph 1. B. Point B in Paragraph 1. C. Point C in Paragraph 2. D. Point D in Paragraph 3.

  2. Given that all the choices are accurate, which one pro- vides the most specific description of the berry’s appearance? F. NO CHANGE G. about the size and shape of an almond, H. cultivated primarily in warm climates, J. grown on a shrub with dense foliage,

  3. A. NO CHANGE B. dulcificum called, miracle fruit, C. dulcificum called miracle fruit, D. dulcificum, called miracle fruit

  4. F. NO CHANGE G. lies H. laid J. lie

  5. A. NO CHANGE B. molecules, which then bind C. molecules, binding them D. molecules to bind

Question 45 asks about the preceding passage as a whole.

46

47

48

49

With tart vinegar, you taste apple juice. Sour cream

tastes like pudding. The effect takes anywhere from

fifteen minutes to an hour to compress.

In its native West Africa, given that miracle

fruit has been used as a sweetener for centuries. Yet,

due in part to its fragility and short shelf life, the fruit

is not widely known in the Western world. Growers

such as Curtis Mozie, who began growing miracle fruit in

Florida as a hobby over two decades ago, is attempting to

increase awareness and consumption of the fruit. To avoid

difficulties in shipping the delicate berries, his company

sells them in frozen and dried forms and it also sells them

in powder, gum, and lollipops. X

  1. Which choice best maintains the stylistic pattern estab- lished in the preceding sentence and continued in the sentence that follows? F. NO CHANGE G. An apple juice taste replaces one of tart vinegar. H. Vinegar that is tart tastes like apple juice instead. J. Tart vinegar tastes like apple juice.

  2. A. NO CHANGE B. downgrade. C. diminish. D. constrict.

  3. F. NO CHANGE G. a region in which H. where J. DELETE the underlined portion.

  4. A. NO CHANGE B. Consequently, C. Moreover, D. That is,

  5. F. NO CHANGE G. are attempting H. has attempted J. attempts

  6. A. NO CHANGE B. forms, additionally, it sells them C. forms, the berries are also sold D. forms, as well as

  7. At this point, the writer is considering adding the fol- lowing true statement: Mozie has said that his favorite foods to eat with miracle fruit include green mangoes and oysters with lemon juice. Should the writer make this addition here? F. Yes, because it offers an informed opinion on a subject with which many people may be unfamiliar. G. Yes, because it provides examples of acidic foods that pair well with miracle fruit. H. No, because it is only loosely related to the para- graph’s focus on efforts to expand awareness of and access to miracle fruit. J. No, because it gives the false impression that mira- cle fruit is widely available.

50

51

52

53

54

55

She speaks no words, however, instead relaying the ancient

story through the expressive art of dance native to Hawai‘i:

hula. [A] Her performance marks the start of the world’s

most prestigious hula competition, held each spring at the

Merrie Monarch Festival in Hilo, Hawai‘i. [B]

[2]

Founded in 1964 as an endeavor to

accomplish a boost in Hilo’s economy, the

festival, named for a nineteenth-century Hawaiian

king known for patronizing the arts, initially

struggled to gain interest. [C] It wasn’t until festival

organizer Dottie Thompson and respected hula master,

“Uncle” George Na‘ope introduced hula competitions

in 1971 that attendance was invigorated.

It’s renewed focus on celebrating hula and

other aspects of authentic Hawaiian culture

attracted both locals and visitors alike.

[3]

Thompson and Na‘ope believed all elements of hula

tradition, both ancient (referring to hula predating 1893)

and modern, need to be preserved and shared. [D] Kahiko,

or ancient hula, involves chanting and little instrumental

accompaniment. ‘Auana (modern hula), on the other hand,

having been influenced by Western music, is generally

accompanied by guitar or ukulele. Due in part to

Na‘ope’s efforts to revive male hula, when a men’s

division was added in 1976.

  1. F. NO CHANGE G. dance—native to Hawai‘i, H. dance, native to Hawai‘i, J. dance native to Hawai‘i;

  2. A. NO CHANGE B. a way of trying to help out with C. an attempt to bolster D. an effort to amp up

  3. F. NO CHANGE G. organizer, Dottie Thompson, and respected hula master H. organizer, Dottie Thompson and respected hula master, J. organizer Dottie Thompson and respected hula master

  4. A. NO CHANGE B. so that C. when D. DELETE the underlined portion.

  5. F. NO CHANGE G. The festival’s H. They’re J. One’s

  6. A. NO CHANGE B. has a need C. does need D. needs

  7. F. NO CHANGE G. he had H. so J. DELETE the underlined portion.

65

66

67

68

69

70

64

65

The festival’s competitive hula events, which had grown

so popular by then that they were relocated from a small

auditorium to a larger venue, where they have taken

place ever since.

[4]

Today, many credit the festival, an annual

event in Hilo, with the widespread revitalization

of hula. The organizers’ ongoing commitment to

promote and preserve Hawaiian culture helps the

art of hula continue to thrive as a “living tradition.”

  1. The writer wants to add the following sentence to the essay: To that end, they established two stylistic cate- gories in the competition. This sentence would most logically be placed at: F. Point A in Paragraph 1. G. Point B in Paragraph 1. H. Point C in Paragraph 2. J. Point D in Paragraph 3.

  2. A. NO CHANGE B. events had grown C. events growing D. events,

  3. The writer is considering revising the underlined por- tion to the following: 5,000-seat stadium, Given that the information is accurate, should the writer make this revision? F. Yes, because it provides a more specific idea of the number of dancers competing in the festival. G. Yes, because it offers a specific detail that better illustrates how popular the events became. H. No, because it is only loosely related to the sen- tence’s discussion of the events’ popularity. J. No, because it repeats information about festival attendance stated earlier in the essay.

  4. A. NO CHANGE B. festival, which hosts the world’s most prestigious hula competition, C. festival, established in 1964, D. festival

  5. Suppose the writer’s primary purpose had been to dis- cuss the revival of a traditional cultural art form. Would this essay accomplish that purpose? A. Yes, because it describes how the Merrie Monarch Festival helped rekindle widespread interest in hula. B. Yes, because it notes significant events in the his- tory of many traditional Hawaiian art forms. C. No, because it focuses instead on describing the various activities that take place at the Merrie Monarch Festival. D. No, because it focuses instead on explaining the origins of hula and its initial impact on Hawaiian culture.

ACT-F12 13

Questions 74 and 75 ask about the preceding passage as a whole.

END OF TEST 1

STOP! DO NOT TURN THE PAGE UNTIL TOLD TO DO SO.

71

72

73

73

  1. Ken is paid a regular hourly wage of $15 per hour, before taxes and benefits are deducted, for working up to and including 40 hours in 1 week. For each additional hour he works in a week, Ken is paid 2 times his regular hourly wage. Ken worked 44 hours this week. What was his pay for this week before taxes and benefits were deducted? F. $0, 630 G. $0, 660 H. $0, 720 J. $0, 930 K. $1,

  2. What is the length, in inches, of the hypotenuse of a right triangle with a leg that is 7 inches long and a leg that is 4 inches long?

A. √•• 22 B. √•• 33 C. √•• 65 D. 000 5. E. 0, 11

  1. Given 3x − 7 = 8 x − 16 is true, x =?

F. −

G. −

H. −

J.

K.

  1. As shown in the figure below, points A, B, and D lie on a line. The measure of angle ABC (m∠ABC) is x°, and m∠CBD is (5x + 4)°.

Which of the following equations is true? A. 0 (5x + 4) = x B. x − (5x + 4) = 90 C. x + (5x + 4) = 90 D. x + (5x + 4) = 180 E. x + (5x + 4) = 360

23 ___ 5 23 ___ 11

23 ___ 11

_ 9 _ 5 _ 9 _ 5

A B

C

D

DO YOUR FIGURING HERE.

DO YOUR FIGURING HERE. 8. A restaurant currently has an outdoor rectangular dining section measuring 30 feet by 40 feet. The shorter sides will be increased by 10 feet each, resulting in a larger rectangular dining section. What is the positive difference, in square feet, between the areas of the resulting and current dining sections? F. 100 G. 300 H. 400 J. 500 K. 600

  1. What is the value of ⎪− 4 ⎪ − ⎪ 6 − 29 ⎪? A. − 31 B. − 27 C. − 19 D. 19 E. 27

  2. Christopher works in a clothing store. He earns $7 per hour, plus 6% of his sales. Which of the following expressions gives Christopher’s earnings, in dollars, when he works x hours and has y dollars in sales? F. 75 x + 6 y G. 75 x + 0 H. 0 7 + 6 y J. 0 7 + 0 K. 0 7 + 0

  3. For RT

↔ shown below, point S is on RT


, the length of

RS


is 8 cm, and the length of ST

is 20 cm. What is the

distance, in centimeters, between T and the midpoint of RS


?

A. 14 B. 18 C. 20 D. 24 E. 28

  1. A conference presenter earned $48 for attending a conference and $15 per hour for the hours she spent preparing for her presentation. Let y be the amount of money, in dollars, earned by the presenter when she spent x hours preparing for her presentation. Which of the following equations gives the relationship between x and y? F. y = 15 G. y = 33 H. y = 63 J. y = 15 + 48. K. y = 48 + 15.

R 8 S 20 T

17. Which of the following matrices is equal to 4 3 4?

A. 3 −8 12 4

B. 3
C. 3

D.

3 4

E. 3
  1. Point P(5,−1), which is graphed in the standard (x,y) coordinate plane below, will be reflected across the x-axis. What will be the coordinates of the image of P?

F. (−5,−1) G. (−5, 1) H. (−1, 5) J. ( 5,−1) K. ( 5, 1)

  1. Given that x ≤ 2 and x + y ≥ 6, what is the LEAST value that y can have? A. − 8 B. − 4 C. 0 D. 4 E. 8

  2. A square vegetable garden is built in a rectangular 50-meter-by-40-meter lawn. The lengths of the sides of the garden are 5 meters. What area of the lawn, in square meters, is outside of the vegetable garden? F. 1, G. 1, H. 1, J. 1, K. 2,

16 − 12

2 4 10 1

− _ 1 _ 2

0

− _ 3 _ 2 − _ 3 _ 4 − 8 0

24 − 12

y

x P(5,−1)

O

6 − 3

− 2 0 DO YOUR FIGURING HERE.

  1. The distance of the longest jump of each of the participants in a long jump competition is given in the stem-and-leaf plot below.

What is the probability that a long jump participant chosen at random from the competition will have jumped at least 75 inches?

A.

B.

C.

D.

E.

  1. In the figure below, DE

↔ i GF

↔ , point A lies on DE


,

points C and B lie on GF


, m∠GCA = 120°, and

m∠GBA = 50°. What is m∠CAB?

(Note: The figure is NOT drawn to scale. The degree measure of ∠STU is denoted m∠STU.)

F. 10° G. 20° H. 50° J. 60° K. 70°

  1. Gabe will use 1 fluid ounce of fertilizer for every 30 square feet of soil. At this rate, how much fertilizer, to the nearest 0 gallon, will Gabe use for 0 acres of soil? (Note: 1 acre = 43,560 square feet; 1 gallon = 128 fluid ounces) A. 0 0. B. 0 0. C. 0 9. D. 14. E. 24.

__ 3 _ 13 __ 7 _ 13 __ 3 _ 10 __ 4 _ 10 __ 6 _ 10

A

B F

D E

G C

Stem Leaf

6 8 9 7 1 4 7 8 9 8 0 1 2

Key: 7 3 = 73 inches

DO YOUR FIGURING HERE.

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June 2023 F12 - act

Topic: Functions

Subject: Pre-Calculus

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©2023 by ACT, Inc. All rights reserved.
NOTE: This test material is the confidential copyrighted property of ACT, Inc., and may not be copied,
reproduced, sold, scanned, emailed, or otherwise transferred without the prior express written permission
of ACT, Inc. Violators of ACT’s copyrights are subject to civil and criminal penalties.
2022
l
2023
Form F12
(June 2023)
In response to your request for Test Information
Release materials, this booklet contains the test
questions, scoring keys, and conversion tables used
in determining your ACT scores. Enclosed with this
booklet is a report that lists each of your answers,
shows whether your answer was correct, and, if your
answer was not correct, gives the correct answer.
ACT owns the test questions and responses, and
you may not share them with anyone in any form.

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