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ACT Exam Questions
Page 4 of 26
61.
Read the passage then answer the following question.
What question is raised by the passage but never answered?
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What kind of work is done by the contractors?
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How many contractors' claims were examined?
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How many claims were in compliance?
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Approximately how much money was improperly paid?
At no point in the passage does the author state what business the contractors are in.
From the passage: ...audit review of 400 sampled claims for four contractors, it was identified that only 97 claims were in accordance with company documentation requirements...improperly allowed payment for $271 million...
62.
Given that sin x = r/t, what is cot x?
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√(t² − r²)/r
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t/√(r² − t²)
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√(r² − t²)/t
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r/√(t² − r²)
Correct answer: √(t² − r²)/r
When sin x = r/t, we consider a right triangle where the opposite side is r and the hypotenuse is t. The adjacent side is determined by the Pythagorean theorem.
Adjacent side = √(t² − r²)
cot x = 1/tan x = (Adjacent side)/ (Opposite side) = √(t² − r²)/r.
63.
Read the passage, and then answer the following question.
The fact that crows who were not born at the time of the experiment attacked the scientists indicates that:
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Crows can pass warnings down through subsequent generations
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Crows have psychic abilities
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Crows find all human faces threatening
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Crows have longer memories than other birds
In similar studies, scientists have observed that crows apparently pass such warnings down through subsequent generations, insuring that future crows learn that masked men mean danger.
In the last sentence of the passage, the author states that other studies indicate crows have passed down knowledge of threats to other generations. The exact method of how this occurs is unknown, and leaves the door open for future research.
64.
Find the surface area of a box whose length is 4 inches, width is 6 inches, and height is 5 inches.
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148 square inches
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120 square inches
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60 square inches
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80 square inches
Correct answer: 148 square inches
The length = 4 inches, width = 6 inches and height = 5 inches.
The surface area = 2(4 × 6) + 2(4 × 5) + 2(5 × 6) = 148 square inches.
65.
Express as one fraction:
1/x − 2/x²
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(x − 2)/x²
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2/x²
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(2 − x)/x²
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(x − 2)/x
Correct answer: (x - 2)/x²
1/x − 2/x²
The Lowest Common Multiple of the denominators is x², since x² can be divided by both x and x². Therefore:
1/x − 2/x² = x/x² − 2/x² = (x − 2)/x².
66.
Choose the option that represents the best way to write the underlined portion of the sentence below.
Each of the students was prepared to give a speech.
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No change
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All of the students
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Each of the student
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All of the student
Each of the students was prepared to give a speech.
The subject, "each," is singular. Therefore, to ensure subject-verb agreement, the verb phrase "was prepared" must be used.
67.
View the supporting details to answer the following question.
Find the product of the two matrices.
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-5 -2
4 2
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-4 -2
4 2
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1 0
0 2
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-1 0
2 2
Correct answer:
-5 -2
4 2
The rule of multiplication is that a row is multiplied by a column. The result will be a 2 x 2 matrix.
Top-left value: (1 × -1) + (-2 × 2) = -5
Top-right value: (1 × 0) + (-2 × 1) = -2
Bottom-left value: (0 × -1) + (2 × 2) = 4
Bottom-right value: (0 × 0) + (2 × 1) = 2
The final matrix is:
-5 -2
4 2
68.
Read the passage, and then answer the following question.
Which of the following is a health benefit of drinking alcohol?
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It raises good cholesterol
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It strengthens joints
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It improves eyesight
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It reduces the chances of cancer
Alcohol itself has been shown to help raise good cholesterol and inhibit the formation of blood clots.
The second paragraph states that alcohol raises good cholesterol. It also prevents the formation of blood clots, making the consumption of alcohol in moderation a healthy choice.
69.
Evaluate without using tables or a calculator:
(2cos 30)²
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3
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2√3
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9
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√3
Correct answer: 3
Using trigonometric ratios of special angles, cos 30 = √3/2.
Hence, (2cos 30)² = (2 × √3/2)² = (√3)² = 3.
70.
Find the radius of the circle passing through (7,9) whose center is (2,3).
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7.8 units
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8.1 units
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2.2 units
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6.6 units
Correct answer: 7.8 units
Using the distance formula, we have the following:
Radius =√[(3 − 9)² + (2 − 7)²] = √61 = 7.810 units.
This rounds to 7.8 units.
71.
Read the passage, and then answer the following question.
John Doerr and Wayne Kartchner were:
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Naturalists
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Park rangers
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Mountain climbers
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Explorers
It was not until the 1930s that the Old Man of the Lake was studied by naturalists. John Doerr and Wayne Kartchner documented the stump’s movements over a three-month period.
In the first two sentences of the third paragraph, the author of the passage states that the Old Man of the Lake was studied by naturalists, and identifies these naturalists as John Doerr and Wayne Kartchner.
72.
Factor the following expression:
6st − s²t − 3t²s
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st(6 − s − 3t)
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st(6 − s − 3)
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2st(3 − 2s)
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2st(3 + 2s)
Correct answer: st(6 − s − 3t)
Upon factoring out st, we have:
6st − s²t − 3t²s = st(6 − s − 3t).
73.
Which of the following algebraic expressions divides evenly into 2x² + 5x − 3?
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x + 3
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x − 3
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x − 2
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2x + 1
Correct answer: x + 3
We need to factor the expression 2x² + 5x − 3 so that we can identify its divisor.
Expanding the middle term, we have:
2x² + 5x − 3 = 2x² + 6x − x − 3 = 2x(x + 3) − 1(x + 3)
(2x − 1)(x + 3)
The factors 2x − 1 and x + 3 divide 2x² + 5x − 3 evenly.
Thus, the correct answer is x + 3.
74.
If g varies directly with p, find the expression relating g and p.
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g = kp
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g = k/p
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g = p
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gp = k
Correct answer: g = kp
If g varies directly with p, then when one increases, the other increases too. And when one decreases, the other decreases too. Thus, we write g ∝ p. Using k as the constant of proportionality, we have g = kp.
75.
View the supporting details to answer the following question.
Identify the element represented by A(2,1) in the matrix.
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3
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-1
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2
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0
Correct answer: 3
A(2,1) is the element in the second row and first column. The element is 3.
76.
Read the passage, and then answer the following question.
According to the passage, frankincense is often associated with which historical figures?
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The three magi
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The ancient Persians
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Ferdinand and Isabella
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The ancient Egyptians
Many people associate frankincense with the gifts of the three kings, but there is much more to know about frankincense than its ancient association with the magi.
In the second sentence of the passage, the author states that frankincense is often associated with the magi. However, frankincense is used for many other reasons and is considered quite valuable in some areas of the world.
77.
Choose the option that represents the best way to write the underlined portion of the sentence below.
Riding in the car with my father, a historian, can be interesting as he stops to read every historic marker along the highway.
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No change
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a historian;
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a historian
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a historian:
Riding in the car with my father, a historian, can be interesting as he stops to read every historic marker along the highway.
Commas are used to set off a phrase that interferes with the flow of a sentence. In this case, "a historian" should be set off by commas.
78.
Choose the option that represents the best way to write the underlined portion of the sentence below.
To raise money for charity, the principal wore a chicken costume for an entire day.
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No change
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wore a chicken costume, for an entire day
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wore a chicken costume for an entire, day
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wore a chicken costume; for an entire day
To raise money for charity, the principal wore a chicken costume for an entire day.
There is no need for punctuation in this phrase. The correct usage should be "wore a chicken costume for an entire day."
79.
Read the passage, and then answer the following question.
The Old Man of the Lake has been documented since:
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1896
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1901
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1918
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1946
There has been a record of the Old Man for at least as long as the lake was first documented in 1896.
In the second sentence of the second paragraph, the author states that the Old Man of the Lake has been documented since 1896. Though it may have existed before this date, this is the earliest known written documentation of its existence.
80.
Read the passage, and then answer the following question.
According to the passage, pregnant women ingest frankincense in order to:
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Ensure that they have a smart baby
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Ensure that they have a healthy baby
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Ensure that they have a large baby
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Ensure that they have a girl
Omanis ingest frankincense to sweeten the breath, to settle the stomach, and some pregnant Omani women continue the ancient tradition of chewing frankincense to ensure a smart baby.
Near the end of the second paragraph, the author of the passage states that some Omani women chew frankincense to ensure a smart baby.