COMPASS Placement Assessment — Questions and Answers

Question 1: Determine whether the underlined portion of the sentence below is correct or whether it needs to be revised. Most of my favorite movies contain s̲l̲a̲p̲s̲t̲i̲c̲k̲ ̲h̲u̲m̲o̲r̲, ̲h̲o̲w̲e̲v̲e̲r̲ ̲p̲h̲y̲s̲i̲c̲a̲l̲ ̲c̲o̲m̲e̲d̲y̲ ̲i̲s̲ ̲n̲o̲t̲ the only way to make me laugh.

slapstick humor, but it is not physical comedy that is
slapstick humor; physical comedy is not
slapstick humor, however physical comedy is not
slapstick humor, and physical comedy is not
slapstick humor, but physical comedy is not (Correct answer)

Correct answer: slapstick humor, but physical comedy is not

The original sentence creates a comma splice by using 'however' with only a comma to join two independent clauses. 'However' is a conjunctive adverb, not a coordinating conjunction, and requires a semicolon or a period before it when connecting independent clauses. Option B correctly uses the coordinating conjunction 'but' with a comma to properly join the two independent clauses.

Question 2: Choose the correct verb form: 'He _____ to school every day.'

going
go
goes (Correct answer)
gone

Correct answer: goes

Third-person singular subjects in simple present tense require the verb with '-s': goes.

Question 3: Determine whether the underlined portion of the sentence below is correct or whether it needs to be revised. Learning a new language can be difficult for people a̲f̲t̲e̲r̲ ̲o̲n̲e̲ ̲r̲e̲a̲c̲h̲e̲s̲ ̲a̲ ̲c̲e̲r̲t̲a̲i̲n̲ ̲a̲g̲e̲ abilities needed to retain and apply new linguistic information deteriorate with time.

after they reach a certain age (Correct answer)
after it reaches a certain age
after they reaches certain ages
after you reach a certain age
after one reaches a certain age

Correct answer: after they reach a certain age

The original sentence has a pronoun-antecedent agreement error: 'people' is plural, but the pronoun 'one' is singular. Option B corrects this by using the plural pronoun 'they' to match the plural subject 'people.' This ensures consistency and grammatical correctness throughout the sentence.

Question 4: Determine whether the underlined portion of the sentence below is correct or whether it needs to be revised. Y̲e̲s̲t̲e̲r̲d̲a̲y̲ ̲I̲ ̲f̲e̲l̲l̲ ̲d̲o̲w̲n̲ ̲t̲h̲e̲ ̲s̲t̲a̲i̲r̲s̲ ̲a̲n̲d̲ ̲t̲h̲e̲n̲ tried to act like I did so on purpose.

I fell down the stairs yesterday, I
Yesterday I fell down the stairs and then (Correct answer)
After I fell down the stairs yesterday; I
Yesterday I fell down the stairs, I
Falling down the stairs; I

Correct answer: Yesterday I fell down the stairs and then

The original sentence is grammatically correct and clearly links two sequential actions: falling down the stairs and then trying to act like it was intentional. The conjunction 'and then' appropriately connects these two events in a chronological and logical manner. No revision is necessary as it maintains clarity and proper sentence structure.

Question 5: A tangent line to a circle:

Is always parallel to a diameter
Passes through the center of the circle
Touches the circle at exactly one point (Correct answer)
Intersects the circle at two distinct points

Correct answer: Touches the circle at exactly one point

A tangent line touches a circle at exactly one point and is perpendicular to the radius drawn to that point.

Question 6: If a car travels 180 miles in 3 hours, what is its average speed?

55 mph
60 mph (Correct answer)
75 mph
45 mph

Correct answer: 60 mph

Speed = distance ÷ time = 180 ÷ 3 = 60 mph.

Question 7: Determine whether the underlined portion of the sentence below is correct or whether it needs to be revised. There are many reasons to see I Heart H̲u̲c̲k̲a̲b̲e̲e̲s̲, ̲J̲a̲s̲o̲n̲ ̲S̲c̲h̲w̲a̲r̲t̲z̲m̲a̲n̲'s̲ ̲p̲e̲r̲f̲o̲r̲m̲a̲n̲c̲e̲ ̲b̲e̲i̲n̲g̲ ̲o̲n̲e̲ ̲r̲e̲a̲s̲o̲n̲.

Huckabees, Jason Schwartzman's performance being one reason.
Huckabees, Jason Schwartzman's performance is only one of them.
Huckabees, the performance of Jason Schwartzman is one of them.
Huckabees, including Jason Schwartzman's performance. (Correct answer)
Huckabees; Jason Schwartzman's performance, for one.

Correct answer: Huckabees, including Jason Schwartzman's performance.

The phrase 'the reason...is because' is redundant because 'because' inherently means 'for the reason that.' This creates a grammatical error. Option C corrects this by using the more concise and grammatically correct phrasing 'the reason...is that,' and also improves the awkward 'her being a fan' to the more direct 'she is a fan.'

Question 8: If x = y, what does 4(x-y) + 7 =?

11x - 11y
7 (Correct answer)
4x - 4y + 7
4xy + 7

Correct answer: 7

Given that x = y, the term (x-y) in the expression becomes (x-x) or (y-y), which simplifies to 0. Substituting this into the expression, we get 4(0) + 7. This simplifies further to 0 + 7, which equals 7.

Question 9: What is 2/5 of 75?

35
30 (Correct answer)
25
15

Correct answer: 30

2/5 × 75 = 150/5 = 30.

Question 10: Determine whether the underlined portion of the sentence below is correct or whether it needs to be revised. H̲i̲g̲h̲ ̲s̲c̲h̲o̲o̲l̲ ̲r̲e̲u̲n̲i̲o̲n̲s̲ ̲a̲r̲e̲ ̲u̲s̲u̲a̲l̲l̲y̲ ̲l̲o̲o̲k̲e̲d̲ ̲f̲o̲r̲w̲a̲r̲d̲ ̲t̲o̲ ̲b̲y̲ ̲a̲l̲u̲m̲n̲i̲ ̲t̲h̲a̲t̲ ̲h̲a̲v̲e̲ ̲w̲o̲r̲k̲e̲d̲ ̲h̲a̲r̲d̲ ̲s̲i̲n̲c̲e̲ ̲g̲r̲a̲d̲u̲a̲t̲i̲o̲n̲ ̲a̲n̲d̲ ̲n̲o̲w̲ ̲c̲o̲n̲s̲i̲d̲e̲r̲ ̲t̲h̲e̲m̲s̲e̲l̲v̲e̲s̲ ̲s̲u̲c̲c̲e̲s̲s̲f̲u̲l̲.

Alumni who have worked hard since graduation and now consider themselves successful usually look forward to high school reunions. (Correct answer)
High school reunions are usually looked forward to by alumni that have worked hard since graduation and now consider themselves successful.
High school reunions are usually looked forward to by alumni who have worked hard since graduation and now consider themselves successful.
Alumnus that have worked hard since graduation and now consider themselves successful usually look forward to high school reunions.
High school reunions are usually looked forward to by alumni that have worked hard since graduation and now consider yourselves successful.

Correct answer: Alumni who have worked hard since graduation and now consider themselves successful usually look forward to high school reunions.

The original sentence uses the passive voice ('are usually looked forward to by'). Option C revises the sentence to the active voice, making it more direct and concise by placing the doers of the action ('Alumni who have worked hard...') as the subject. Additionally, 'who' is the correct relative pronoun for referring to people, not 'that'.

Question 11: Determine whether the underlined portion of the sentence below is correct or whether it needs to be revised. Since the work force is becoming increasingly competitive in light of technological advances and outsourcing, t̲h̲e̲r̲e̲f̲o̲r̲e̲, ̲i̲t̲ ̲i̲s̲ ̲e̲v̲e̲n̲ ̲m̲o̲r̲e̲ ̲b̲a̲s̲i̲c̲ ̲f̲o̲r̲ ̲s̲t̲u̲d̲e̲n̲t̲s̲ ̲t̲o̲ ̲c̲o̲m̲p̲l̲e̲t̲e̲ ̲h̲i̲g̲h̲ ̲s̲c̲h̲o̲o̲l̲ ̲a̲n̲d̲ ̲a̲t̲t̲a̲i̲n̲ ̲a̲t̲ ̲l̲e̲a̲s̲t̲ ̲a̲ ̲b̲a̲c̲h̲e̲l̲o̲r̲’s̲ ̲d̲e̲g̲r̲e̲e̲.

it is even more basic for students to complete high school and attain at least a bachelor’s degree. (Correct answer)
but, it is even more basic for students to complete high school and attain at least a bachelor’s degree.
therefore, it is even more basic for students to complete high school and attain at least a bachelor’s degree.
it is even more basic for students to complete high school and attain at least a bachelor’s degree.
moreover, it is even more basic for students to complete high school and attain at least a bachelor’s degree.

Correct answer: it is even more basic for students to complete high school and attain at least a bachelor’s degree.

The original sentence incorrectly uses 'therefore' after an introductory clause beginning with 'Since.' 'Since' already establishes a cause-and-effect relationship, making 'therefore' redundant and grammatically incorrect in this context. Option E correctly removes the unnecessary 'therefore,' allowing the main clause to logically follow the introductory 'Since' clause without repetition or grammatical error.

Question 12: Select the passive voice sentence:

The chef cooked the meal.
The chef is cooking the meal.
The chef had cooked the meal.
The meal was cooked by the chef. (Correct answer)

Correct answer: The meal was cooked by the chef.

Passive voice puts the object first and uses 'to be + past participle'; the agent follows 'by'.

Question 13: What is the square root of 144?

14
11
13
12 (Correct answer)

Correct answer: 12

√144 = 12 because 12 × 12 = 144.

Question 14: Two vertical angles are formed when two lines intersect. If one angle measures 65°, the vertical angle measures:

115°
65° (Correct answer)
25°
130°

Correct answer: 65°

Vertical angles are always congruent, so both measure 65°.

Question 15: Which number is a prime number?

33
29 (Correct answer)
21
27

Correct answer: 29

29 is prime because it has no factors other than 1 and itself.

Question 16: What is the degree of the polynomial 4x³ − 2x² + x − 7?

3 (Correct answer)
2
4
1

Correct answer: 3

The degree is the highest exponent of the variable, which is 3.

Question 17: Read the following passage and answer the question But man is not destined to vanish. He can be killed, but he cannot be destroyed, because his soul is deathless and his spirit is irrepressible. Therefore, though the situation seems dark in the context of the confrontation between the superpowers, the silver lining is provided by amazing phenomenon that the very nations which have spent incalculable resources and energy for the production of deadly weapons are desperately trying to find out how they might never be used. They threaten each other, intimidate each other and go to the brink, but before the total hour arrives they withdraw from the brink. 'Irrepressible' in the second line means

unrestrainable (Correct answer)
incompatible
unspirited
oppressive
strong

Correct answer: unrestrainable

The passage states, 'He can be killed, but he cannot be destroyed, because his soul is deathless and his spirit is irrepressible.' 'Irrepressible' means not able to be controlled, restrained, or kept down. In this context, it emphasizes the enduring and unconquerable nature of the human spirit, suggesting it cannot be suppressed or held back.

Question 18: Which conic section is described by the equation x² + y² = 25?

Circle (Correct answer)
Hyperbola
Parabola
Ellipse

Correct answer: Circle

An equation of the form x² + y² = r² represents a circle with radius r.

Question 19: Which transformation shifts y = f(x) up by 3 units?

y = f(x + 3)
y = f(x) − 3
y = f(x) + 3 (Correct answer)
y = 3f(x)

Correct answer: y = f(x) + 3

Adding a constant outside the function shifts the graph vertically upward.

Question 20: If f(x) = x + 9, which of the following is a solution of f(5a) + 3 = f(3a) + 11? In other words, what might be the value of ‘a’?

6
8
5/3
There are no solutions
4 (Correct answer)

Correct answer: 4

Substituting both 5a and 3a into f(x) and then using the second equation, we get 5a + 9 + 3 = 3a + 9 + 11 . This simplifies to 5a + 12 = 3a + 20, and then we get 2a = 8 . Finally, we get a = 4. This is response E.

Question 21: Solve: |2x − 3| = 7

x = 5 or x = −2 (Correct answer)
x = 5 or x = 2
x = 4 or x = −2
x = −5 or x = 2

Correct answer: x = 5 or x = −2

Set up two cases: 2x − 3 = 7 (x = 5) and 2x − 3 = −7 (x = −2).

Question 22: Simplify: (3x²y)(4xy³)

12x²y³
12x³y⁴ (Correct answer)
7x³y⁴
12x³y³

Correct answer: 12x³y⁴

Multiply coefficients (3 × 4 = 12) and add exponents: x²⁺¹ = x³, y¹⁺³ = y⁴.

Question 23: Solve for x: 3x + 7 = 22

3
4
6
5 (Correct answer)

Correct answer: 5

Subtract 7 from both sides: 3x = 15, then divide by 3: x = 5.

Question 24: Which of the following is a solution to x² − 5x + 6 = 0?

x = 2 (Correct answer)
x = 5
x = 1
x = −2

Correct answer: x = 2

The equation factors as (x − 2)(x − 3) = 0, giving solutions x = 2 and x = 3.

Question 25: What is 15% of 240?

24
32
36 (Correct answer)
40

Correct answer: 36

15% of 240 = 0.15 × 240 = 36.

Question 26: Which statement is true about a rectangle?

The diagonals are perpendicular to each other
All four sides are equal in length
Opposite sides are parallel and equal in length (Correct answer)
All interior angles measure 60°

Correct answer: Opposite sides are parallel and equal in length

A rectangle has opposite sides that are both parallel and equal, with all four angles measuring 90°.

Question 27: A store sells pens at 3 for $1.50. How much do 10 pens cost?

$4.50
$5.00 (Correct answer)
$6.00
$5.50

Correct answer: $5.00

Each pen costs $0.50, so 10 pens cost 10 × $0.50 = $5.00.

Question 28: What is the area of a trapezoid with bases of length 6 and 10 and a height of 4?

48
40
32 (Correct answer)
24

Correct answer: 32

Area = ½(b₁ + b₂) × h = ½(6 + 10) × 4 = ½ × 16 × 4 = 32.

Question 29: Which sentence uses the correct article?

She is a honest woman.
She is honest woman.
She is the honest woman.
She is an honest woman. (Correct answer)

Correct answer: She is an honest woman.

Use 'an' before words beginning with a vowel sound; 'honest' starts with a silent 'h' giving a vowel sound.

Question 30: Determine whether the underlined portion of the sentence below is correct or whether it needs to be revised. Natural disasters h̲a̲v̲e̲ ̲b̲e̲e̲n̲ ̲i̲n̲c̲r̲e̲a̲s̲i̲n̲g̲l̲y̲ ̲e̲f̲f̲e̲c̲t̲i̲n̲g̲ nearly every part of the world in the past decade with catastrophic tornadoes, hurricanes and tsunamis.

have been increasingly affecting (Correct answer)
have been increasingly effecting
will be increasingly effecting
will be increasingly affecting
has been increasingly effecting

Correct answer: have been increasingly affecting

The word 'effecting' is incorrect here; 'effect' is primarily a noun meaning result, while 'affect' is a verb meaning to influence or impact. Natural disasters *affect* parts of the world. Additionally, 'Natural disasters' is plural, so the verb 'have' is correct for subject-verb agreement.

Question 31: What is the y-intercept of the line y = 3x − 4?

0
4
−4 (Correct answer)
3

Correct answer: −4

In slope-intercept form y = mx + b, the y-intercept is b = −4.

Question 32: Simplify: |−7| + |−3|

10 (Correct answer)
4
−10
−4

Correct answer: 10

Absolute value makes each term positive: 7 + 3 = 10.

Question 33: Determine whether the underlined portion of the sentence below is correct or whether it needs to be revised. The argument b̲e̲t̲w̲e̲e̲n̲ ̲P̲a̲a̲r̲i̲n̲ ̲a̲n̲d̲ ̲m̲e̲ ̲a̲b̲o̲u̲t̲ ̲t̲h̲e̲ ̲d̲e̲n̲t̲ ̲i̲n̲ ̲h̲i̲s̲ ̲c̲a̲r̲ ̲c̲o̲n̲t̲i̲n̲u̲e̲d̲ until the early morning.

on the dent in his car between Paarin and me continued
about the dent in his car continued for Paarin and I
between Paarin and I about the dent in his car continued
between Paarin and me about the dent in his car continued (Correct answer)
between Paarin and I on the dent in his car continued

Correct answer: between Paarin and me about the dent in his car continued

The preposition 'between' requires objective case pronouns as its objects. In the original sentence, 'Paarin and me' correctly uses the objective pronoun 'me.' Using 'I' (a subjective pronoun) after a preposition, as seen in other options, would be grammatically incorrect.

Question 34: Simplify: 18/24

6/8
5/8
3/4 (Correct answer)
2/3

Correct answer: 3/4

The GCF of 18 and 24 is 6, so 18/24 = 3/4.

Question 35: Evaluate: 3⁻² as a fraction

1/9 (Correct answer)
9
−1/9
−9

Correct answer: 1/9

A negative exponent means take the reciprocal: 3⁻² = 1/3² = 1/9.

Question 36: If f(x) = 2x² − 3x + 1, what is f(2)?

5
1
3 (Correct answer)
7

Correct answer: 3

f(2) = 2(4) − 3(2) + 1 = 8 − 6 + 1 = 3.

Question 37: What is the value of 3/4 + 1/6?

5/12
4/10
7/12
11/12 (Correct answer)

Correct answer: 11/12

To add fractions, find the LCD (12): 9/12 + 2/12 = 11/12.

Question 38: What is the least common multiple (LCM) of 8 and 12?

24 (Correct answer)
96
48
16

Correct answer: 24

The LCM of 8 and 12 is 24 because 24 is the smallest number divisible by both.

Question 39: Find the zeros of f(x) = x³ − x

x = 1, −1
x = 0, 1
x = 0, 1, −1 (Correct answer)
x = 0, −1

Correct answer: x = 0, 1, −1

Factor: x(x² − 1) = x(x − 1)(x + 1) = 0, giving x = 0, 1, −1.

Question 40: Determine whether the underlined portion of the sentence below is correct or whether it needs to be revised. Study the ancient fighting art of Hapkido and you will learn to avoid directly matching y̲o̲u̲r̲ ̲s̲t̲r̲e̲n̲g̲t̲h̲ ̲a̲g̲a̲i̲n̲s̲t̲ ̲y̲o̲u̲r̲ ̲o̲p̲p̲o̲n̲e̲n̲t̲'s̲.

your strength against your opponent's.
your strength with your opponent.
your strength against your opponent.
your strength against your opponent's. (Correct answer)
your opponent's strength against one's own.

Correct answer: your strength against your opponent's.

The original sentence is grammatically correct. The possessive form 'opponent's' is used correctly to imply 'opponent's strength,' avoiding redundant repetition of the word 'strength.' This construction is concise and maintains clarity in the comparison.

Question 41: What is the range of f(x) = x²?

y ≥ 0 (Correct answer)
y ≤ 0
y > 0
All real numbers

Correct answer: y ≥ 0

x² is always non-negative, so the range is y ≥ 0.

Question 42: Solve: 2^(x+1) = 16

5
3 (Correct answer)
2
4

Correct answer: 3

16 = 2⁴, so 2^(x+1) = 2⁴ means x + 1 = 4, giving x = 3.

Question 43: Solve the inequality: 2x − 5 > 9

x ≥ 7
x < 7
x > 7 (Correct answer)
x > 4

Correct answer: x > 7

Add 5: 2x > 14, then divide by 2: x > 7.

Question 44: Read the following passage and answer the question Greek mythology is a vehicle that uses mythological characters and creatures to teach people about the dangers, beauties and possible outcomes of life. In many myths, characters face moral dilemmas involving honor and practicality. The protagonists of epics face creatures that represent values and challenges such as respect, temptation and redemption. How has Greek mythology inevitably evolved with time and new story tellers? Scholars that have interpreted Greek mythology seek to maintain the universal values conveyed in these stories, while ensuring the validity of adapting these stories to their own distinct cultures. It is up to each reader to seek their own truths and learn from epic Greek mythology as best they can. According to the author’s description, which of the following is most likely to be a message from Greek mythology?

Passing down Greek mythology has taken on a new form since oral records faded.
Love is difficult, but it will last if the lovers are meant to be together.
It is not the fastest, but the longest lasting that wins the race.
Resisting temptation and immediate gratification will lead to ultimate success. (Correct answer)
It is important to keep track of your personal history.

Correct answer: Resisting temptation and immediate gratification will lead to ultimate success.

The passage states that 'protagonists of epics face creatures that represent values and challenges such as respect, temptation and redemption.' This directly indicates that Greek myths often involve characters confronting and overcoming temptation. The implication is that successfully navigating these challenges, like resisting temptation, is a path to positive outcomes or 'ultimate success' within the narrative's moral framework.

Question 45: A toll is $2 for a car and the driver and 75 cent for each additional passenger. If the toll comes to $4.25, how many total people are in the car?

4 (Correct answer)
3
6
5

Correct answer: 4

First, subtract the base toll for the car and driver ($2.00) from the total toll ($4.25) to find the cost for additional passengers, which is $2.25. Then, divide this amount by the cost per additional passenger ($0.75) to find that there are 3 additional passengers. Finally, add the driver to the additional passengers (1 + 3) to get a total of 4 people in the car.

Question 46: The line in the xy-coordinate system is the graph of the equation y=mx+b. Which of the following must be true?

m = -b
b
mb = 1
mb (Correct answer)
mb = 0

Correct answer: mb

The slope and y -intercept of the graph of y=mx+b are m and b respectively. From the graph, it can be seen that the line has a negative slope and a positive y-intercept. Therefore, m<0 and b>0 so mb<0.

Question 47: If log(x) = 3, what is x?

300
30
100
1000 (Correct answer)

Correct answer: 1000

log₁₀(x) = 3 means 10³ = x = 1000.

Question 48: Simplify: log(100) + log(10)

2
1
4
3 (Correct answer)

Correct answer: 3

log(100) = 2 and log(10) = 1, so 2 + 1 = 3.

Question 49: Determine whether the underlined portion of the sentence below is correct or whether it needs to be revised. For every song that is a hit, it is critical to have a quality “beat” and quality lyrics; h̲o̲w̲e̲v̲e̲r̲ music companies hire professional producers and song writers.

nevertheless
and
yet
therefore (Correct answer)
however

Correct answer: therefore

The first part of the sentence states that quality beat and lyrics are critical for a hit song. The second part describes music companies hiring professionals. This relationship is one of cause and effect: because quality is critical, companies *therefore* hire professionals to achieve it. 'However' implies a contrast, which is not present here.

Question 50: Two lines that lie in the same plane and never intersect are called:

Parallel lines (Correct answer)
Concurrent lines
Transversal lines
Perpendicular lines

Correct answer: Parallel lines

Parallel lines remain the same distance apart and never meet, no matter how far they extend.

Question 51: Two sides of a triangle have sides 4 and 8. The length of the third side must be greater than_ and less than.

4, 8
2, 3
0, 12
4, 12 (Correct answer)

Correct answer: 4, 12

The third side of the triangle must be greater than the smallest side (4) and less than the sum of the two sides (4+8=12)

Question 52: What is the slope of a horizontal line?

0 (Correct answer)
−1
Undefined
1

Correct answer: 0

A horizontal line has no vertical change (rise = 0), so slope = rise/run = 0.

Question 53: What is the vertex of the parabola y = (x − 3)² + 2?

(3, −2)
(−3, 2)
(3, 2) (Correct answer)
(2, 3)

Correct answer: (3, 2)

In vertex form y = (x − h)² + k, the vertex is (h, k) = (3, 2).

Question 54: Determine whether the underlined portion of the sentence below is correct or whether it needs to be revised. I̲n̲ ̲m̲a̲n̲y̲ ̲c̲u̲l̲t̲u̲r̲e̲s̲ ̲t̲h̲e̲y̲ ̲c̲o̲n̲s̲i̲d̲e̲r̲ ̲f̲i̲s̲h̲ ̲e̲g̲g̲s̲ ̲a̲ ̲d̲e̲l̲i̲c̲a̲c̲y̲.

In many cultures fish eggs are considered a delicacy. (Correct answer)
They consider fish eggs to be a delicacy in many cultures.
In many cultures a delicacy is considered to be fish eggs.
Fish eggs, a delicacy in many cultures.
In many cultures they consider fish eggs a delicacy.

Correct answer: In many cultures fish eggs are considered a delicacy.

The original sentence uses the vague pronoun 'they' without a clear antecedent, making the subject unclear. Option B corrects this by using the passive voice, making 'fish eggs' the clear subject of the sentence. This revision improves clarity and conciseness by directly stating what is considered a delicacy.

Question 55: All cabbages are red. Which of the following statements shows that the statement is FALSE?

Keisha is eating a green cabbage. (Correct answer)
Alice is not eating a red cabbage.
Ted is eating a red cabbage.
David is eating a red apple.
Bill is eating a green apple.

Correct answer: Keisha is eating a green cabbage.

Hint: you need a statement that mentions a cabbage which isn’t red.

Question 56: Which quadrilateral has all four sides equal in length AND all four angles equal to 90°?

Trapezoid
Rectangle
Square (Correct answer)
Rhombus

Correct answer: Square

A square satisfies both conditions: four equal sides and four right angles.

Question 57: What is the period of y = cos(2x)?

π (Correct answer)
π/2
2π
4π

Correct answer: π

The period of y = cos(bx) is 2π/b = 2π/2 = π.

Question 58: Solve the system: x + y = 8 and x − y = 2

x = 5, y = 3 (Correct answer)
x = 3, y = 5
x = 6, y = 2
x = 4, y = 4

Correct answer: x = 5, y = 3

Adding the equations: 2x = 10, so x = 5; substituting back: y = 3.

Question 59: Determine whether the underlined portion of the sentence below is correct or whether it needs to be revised. A consummate gentleman S̲t̲e̲f̲a̲n̲'s̲ ̲e̲t̲i̲q̲u̲e̲t̲t̲e̲ ̲a̲n̲d̲ ̲s̲o̲c̲i̲a̲l̲ ̲g̲r̲a̲c̲e̲ ̲w̲a̲s̲ ̲u̲n̲m̲a̲t̲c̲h̲e̲d̲.

Stefan's social grace was matched only by his etiquette.
Stefan's etiquette and social grace was unmatched.
Stefan's etiquette and social grace were unmatched.
Stefan possessed unmatched etiquette and social grace. (Correct answer)

Correct answer: Stefan possessed unmatched etiquette and social grace.

The original sentence suffers from a dangling modifier, as 'A consummate gentleman' incorrectly modifies 'Stefan's etiquette and social grace' instead of Stefan himself. Additionally, 'etiquette and social grace' is a compound subject requiring the plural verb 'were,' not 'was.' Option C corrects both issues by making Stefan the direct subject and clearly stating what he possessed, thus eliminating the dangling modifier and the subject-verb agreement error.

Question 60: (x+3)(x+5) = A. x2+16x +8 B. x2+16x+15 C. x2+8x+15 D. x2+8x+8

C (Correct answer)
B
A
D

Correct answer: C

Use the FOIL method (First, Outside, Inside, Last) to solve. X2 +3x +5x + 3x5

Question 61: A farmer can pick 12 cabbages in 1 hour. Working at the same rate, how long in hours would it take two farmers to pick 48 cabbages?

8
4
1
2 (Correct answer)
6

Correct answer: 2

First, determine the combined work rate of two farmers. If one farmer picks 12 cabbages in 1 hour, two farmers working at the same rate will pick 2 * 12 = 24 cabbages in 1 hour. To find out how long it would take them to pick 48 cabbages, divide the total number of cabbages by their combined rate: 48 cabbages / 24 cabbages/hour = 2 hours. Therefore, it would take two farmers 2 hours to pick 48 cabbages.

Question 62: If 5(x − 2) = 3x + 4, what is x?

7 (Correct answer)
1
3
5

Correct answer: 7

Expand: 5x − 10 = 3x + 4; subtract 3x: 2x = 14; x = 7.

COMPASS Placement Assessment

The COMPASS (Computer-Adaptive Placement Assessment and Support System) by ACT is an untimed, computer-adaptive college placement test covering math, reading, and writing skills to determine appropriate course placement.

Questions

150 min

Time Limit

65%

To Pass

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Exam Rules

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Unanswered questions count as wrong — answer everything
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