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ACT Exam Questions
Page 2 of 26
21.
Read the passage, and then answer the following question.
Which of the following correctly summarizes the second paragraph of this passage?
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Diamonds are valued for their beauty and excellent appearance
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Diamonds are often used in cutting tools
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Colored diamonds are rare and more valuable than clear diamonds
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Diamonds are formed over thousands of years
Diamonds have outstanding optical characteristics. The rigid lattice of a diamond permits it to be contaminated by very few types of impurities. This results in the clear, colorless appearance of most natural diamonds. Minor flaws color diamonds blue, yellow, brown, green, purple, pink, orange, or red. Diamonds also have comparatively high optical dispersal, which results in its characteristic sheen. Exceptional optical and mechanical assets make the diamond the most admired gemstone in the world.
The first sentence of the second paragraph in this passage states that diamonds are visually appealing, which summarizes the rest of the paragraph. The remainder of the paragraph elaborates on the specific reasons diamonds are highly regarded and considered to be so beautiful.
22.
Determine a value of x that will satisfy the following equation:
|2x − 4| = 10
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-3
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-7
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3
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14
Correct answer: -3
From the definition of absolute numbers, |2x − 4| = 10 implies that 2x − 4 = 10 and 2x − 4 = -10.
For 2x − 4 = 10, we get 2x = 14; x = 7.
For 2x − 4 = -10, we get 2x = -6; x = -3.
From the answer choices, x = -3
23.
Choose the option that represents the best way to write the underlined portion of the sentence below.
Ken Burns, who is famous for his documentaries, is an excellent filmmaker.
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No change
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who is famous, for his documentaries
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who is famous for his documentaries;
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who is famous for his documentaries
Ken Burns, who is famous for his documentaries, is an excellent filmmaker.
The phrase "who is famous for his documentaries" is a parenthetical phrase. Parenthetical phrases are always set off by commas.
24.
Choose the option that represents the best way to write the underlined portion of the sentence below.
With a shiny new coat of red paint, my mother drove the convertible through town.
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My mother drove the convertible, with a shiny new coat of red paint, through town.
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No change
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With a shiny new coat of red paint; my mother drove the convertible through town.
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With a shiny new coat of red paint: my mother drove the convertible through town.
My mother drove the convertible, with a shiny new coat of red paint, through town.
The phrase "with a shiny new coat of red paint" is an appositive phrase which refers to the car. The way the sentence is written it sounds like the writer's mother has a shiny new coat of red paint rather than the car.
25.
Choose the option that represents the best way to write the underlined portion of the sentence below.
I don't know how to install the software, it didn't come with a manual.
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software; it
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No change
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software it,
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software it:
I don't know how to install the software; it didn't come with a manual.
This sentence consists of two independent clauses, which should be joined using a semicolon. As it is written, it contains a comma splice, which is incorrect.
26.
Determine the value of cot(-60) × sin(480).
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-1/2
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√3/2
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-√3/2
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-1/√3
Correct answer: -1/2
cot(-60) × sin(480) = 1/tan(-60) × sin(480 − 360) = -1/tan(60) × sin(120)
120 is an angle in the second quadrant, so its sine will be positive sin (180 − 120) = sin(60) = -1/tan(60) × sin(60).
Using trigonometric ratios of special angles, we have the following:
-1/tan(60) × sin(60) = -1/√3 × √3/2 = -1/2
27.
Identify the value of the missing number in the following pattern:
2 ,3 ,6 ,11 ,18, ___, 38
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27
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26
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24
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25
Correct answer: 27
Consider the differences between each set of consecutive terms:
3 − 2 = 1; 6 − 3 = 3; 11 − 6 = 5; 18 − 11 = 7
These differences are odd numbers, and are in a sequence of 1, 3, 5, 7. The next difference should be 9.
Thus, the next missing number is 18 + 9 = 27.
28.
Simplify without using tables or calculators:
cos(60) − sin(30) tan(45)
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0
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1/4
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(√3 - 1)/2
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1/2
Correct answer: 0
Using trigonometric ratios for special angles, we have:
cos(60) − sin(30) tan(45) = 1/2 − (1/2)(1) = 1/2 − 1/2 = 0
29.
Read the passage then answer the following question.
The author is willing to pay for the more expensive clubs because:
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He thinks he will at least look good with them
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He wants his friends to be jealous
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He thinks they will make him a better player
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He has wanted them for a long time
The author states that even if doesn't play golf well, he would at least look good with the new clubs.
From the passage: These clubs looked a lot better than the cheap set, and I thought that if I could not play well, then at least I would look good.
30.
Find the y-intercept of the following equation:
y = t³ − 6t² + 11t − 6
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-6
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-1
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-2
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3
Correct answer: -6
At the y-intercept, t = 0. Substituting 0 for t, we get:
y = (0)³ − 6(0)² + 11(0) − 6 = -6.
31.
Read the passage then answer the following question.
What is the author's level of experience with golf?
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He has never played before
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He was once a professional golfer
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He played occasionally as a teenager
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He used to play regularly, but hasn't in a long time
At the beginning of the passage, the author states that he has never played "real" golf, only miniature golf.
From the passage: I’m not much of a golf player. In fact, I have never played. Sure, I have played miniature golf and have hit a few “holes in one,” but I have never been out on a true golf course.
32.
Find the value of sec 405° without using tables or a calculator.
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√2
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-1/√2
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1/√2
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1
Correct answer: √2
sec 405° = sec (405 − 360°) = sec 45° = 1/(cos 45°).
Applying the trigonometric ratios of special angles, we have:
1/(cos 45°) = 1/(1/√2) = √2
33.
It takes a car an average of two hours to move from Town A to Town B. If Town C is twice as far from B as A is from B, how long does it take the same car traveling at the same average speed to reach C from A?
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6 hours
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5 hours
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4 hours
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5.5 hours
Correct answer: 6 hours
From A to B; distance = AB; time = 2 hours.
From C to B; distance = 2AB.
From A to C; distance = AB + 2AB = 3AB.
Since AB takes 2 hours, 3AB takes 2 × 3 = 6 hours.
34.
Choose the option that represents the best way to write the underlined portion of the sentence below.
Kelly and Gerald are married and he has been married for fifteen years.
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they have been
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No change
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she has been
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we have been
Kelly and Gerald are married and they have been married for fifteen years.
"Kelly and Gerald" is plural, but "he" is singular. Therefore, the correct usage would be "they have been."
35.
Choose the option that represents the best way to write the underlined portion of the sentence below.
Neither Carla nor Jessica had completed their applications by the deadline.
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No change
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had completed theirs
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had completed his
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had completed its
Neither Carla nor Jessica had completed their applications by the deadline.
"Carla nor Jessica" is plural, therefore a plural pronoun must be used in order for it to agree with the antecedent. In this case, the correct pronoun is "their."
36.
Read the passage then answer the following question.
How much does Bryan's employer reimburse him for tuition?
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$6,000
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$10,000
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$1,500
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$800
The first paragraph states that Bryan's company reimburses $6,000 of his tuition.
From the passage: Bryan’s employer reimburses $6,000 per year through the company's tuition reimbursement program...
37.
Read the passage then answer the following question.
Most employers prefer that employees attend college:
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Online
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Only in the summers
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Out of state
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In art-related fields
The second paragraph states that many businesses ask employees to take courses online or during non-scheduled hours.
From the passage: Most organizations are asking that their employees find ways to complete course work online or attend college classes during non-scheduled hours.
38.
Find the range of values of x that satisfy x² − 9 > 0.
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x < -3 and x > 3
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x > -3
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x > -3 and x > 3
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x < 3
Correct answer: x < -3 and x > 3
Since x² − 9 > 0, we add 9 on both sides of the inequality to get x² > 9.
Determining the square root on both sides, we have x > 3 and x < -3. We test for the validity of each case.
When x = 4, x² − 9 = 7 > 0; thus x > 3 is valid.
When x = -4, x² − 9 = 7 > 0; thus x < -3 is valid.
Therefore, the solution is x < -3 and x > 3.
39.
Choose the option that represents the best way to write the underlined portion of the sentence below.
A refund was given to me by the store manager.
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The store manager gave me a refund.
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No change
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The refund was given unto me by the store manager.
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A store refund was given to me by the manager.
The store manager gave me a refund.
As it is written, the sentence is in the passive voice and is unnecessarily wordy. The correct usage should be "The store manager gave me a refund."
40.
Evaluate -2(-4 − (-2)) + 1.
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5
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-3
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-11
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13
Correct answer: 5
-2(-4 − (-2)) + 1 = -2 ( -4 + 2) + 1 = -2 (-2) + 1 = 4 + 1 = 5