ACCUPLACER Exam — Questions and Answers

Question 1: Knowledge of another language fosters greater awareness of cultural diversity among the peoples of the world. Individuals who have foreign language skills can appreciate more readily other peoples’ values and ways of life. How are the two sentences related?

They repeat the same idea. (Correct answer)
They present problems and solutions
They contradict each other
They establish a contrast.

Correct answer: They repeat the same idea.

Both sentences convey the same core message: learning another language leads to a greater understanding and appreciation of diverse cultures. The second sentence rephrases and reinforces the idea presented in the first, stating that foreign language skills enable individuals to 'appreciate more readily other peoples’ values and ways of life.' They essentially express the same concept in slightly different words.

Question 2: Graph of f(x) crosses the x-axis at x = −2 and x = 4. Which is a possible equation?

f(x) = (x + 2)(x + 4)
f(x) = (x + 2)(x − 4) (Correct answer)
f(x) = (x − 2)(x − 4)
f(x) = (x − 2)(x + 4)

Correct answer: f(x) = (x + 2)(x − 4)

Setting x + 2 = 0 gives x = −2 and x − 4 = 0 gives x = 4, matching both x-intercepts.

Question 3: A bag contains 3 red, 5 blue, and 2 green marbles. What is the probability of randomly selecting a blue marble?

3/10
1/5
2/5
1/2 (Correct answer)

Correct answer: 1/2

There are 5 blue marbles out of 10 total, giving a probability of 5/10 = 1/2.

Question 4: Choose the correct word: "Neither the manager nor the employees ___ aware of the change."

has been
were (Correct answer)
was
is

Correct answer: were

With "neither/nor," the verb agrees with the nearer subject "employees," which is plural.

Question 5: Many people own different pets. Dogs, cats, birds, and fish are common household pets. Others pets are considered to be exotic animals. These include snakes, lizards, and hedgehogs. According to the passage, snakes are

likely to be found in a household with dogs
uncommon pets (Correct answer)
found only in zoos
not allowed in people’s homes

Correct answer: uncommon pets

The passage categorizes dogs, cats, birds, and fish as "common household pets." It then states that "Other pets are considered to be exotic animals. These include snakes, lizards, and hedgehogs." By classifying snakes as "exotic animals" and contrasting them with "common household pets," the passage implies that snakes are not common pets.

Question 6: What is the period of the function y = cos(πx)?

1
π
2π
2 (Correct answer)

Correct answer: 2

Period = 2π ÷ B = 2π ÷ π = 2.

Question 7: Solve the system: 2x + y = 7 and x − y = 2.

x = 4, y = −1
x = 1, y = 5
x = 3, y = 1 (Correct answer)
x = 2, y = 3

Correct answer: x = 3, y = 1

Add the two equations to eliminate y: 3x = 9, so x = 3; then y = 7 − 2(3) = 1.

Question 8: Simplify: (x³ · x²) ÷ x⁴

x³
x⁴
x²
x (Correct answer)

Correct answer: x

Multiply exponents in the numerator: x³ · x² = x⁵, then x⁵ ÷ x⁴ = x¹ = x.

Question 9: A function is defined as f(x) = −2x + 7. Over which interval is f(x) > 0?

x > 7
x < 7/2 (Correct answer)
x < −7/2
x > 7/2

Correct answer: x < 7/2

Set −2x + 7 > 0 → −2x > −7 → x < 7/2 (inequality flips when dividing by a negative).

Question 10: If a passage's main idea is implied rather than stated, the reader must:

Ignore the supporting facts
Infer it from details (Correct answer)
Find it in the title only
Skip the passage

Correct answer: Infer it from details

An implied main idea is drawn from clues across the passage.

Question 11: Solve for x: 5x − 3 = 2x + 9

x = 4 (Correct answer)
x = 2
x = 3
x = 6

Correct answer: x = 4

Subtract 2x from both sides to get 3x − 3 = 9, then add 3 and divide by 3 to find x = 4.

Question 12: A data set has values 4, 7, 7, 9, 13. What is the median?

7 (Correct answer)
7.5
9
8

Correct answer: 7

When values are arranged in order, the middle value of five numbers is the third one, which is 7.

Question 13: Select the correct word: "The effect of the new policy ___ noticeable immediately."

have been
were
was (Correct answer)
are

Correct answer: was

The singular subject "effect" takes the singular verb "was."

Question 14: Identify the sentence type: "Although she was tired, she finished the race."

Compound
Simple
Run-on
Complex (Correct answer)

Correct answer: Complex

It joins a dependent clause and an independent clause, making it complex.

Question 15: What is the best version of the underlined part of this sentence? One of the choices involves leaving the sentence as it is written. Because of his fame in the music industry, Tupac was able to become starring in various films<\/u>, before his death in 1996.

become the star of various films (Correct answer)
become starring in various films
starring variously in films
various films becomes the star

Correct answer: become the star of various films

The phrase 'become starring in various films' is grammatically awkward and incorrect. To express that Tupac took on leading roles in films, a more appropriate and grammatically correct phrasing is needed. Option A, 'become the star of various films,' clearly and correctly conveys that he achieved a starring role or status in films.

Question 16: What is 1/4 + 0.5 expressed as a decimal?

0.55
0.75 (Correct answer)
1.5
0.25

Correct answer: 0.75

1/4 = 0.25, and 0.25 + 0.5 = 0.75.

Question 17: A jacket originally $80 is now $60. What is the percent decrease?

15%
20%
25% (Correct answer)
30%

Correct answer: 25%

The decrease is $20, and $20 / $80 = 0.25, or 25%.

Question 18: Subtract: 1,002 - 487.

525
505
615
515 (Correct answer)

Correct answer: 515

1,002 minus 487 equals 515.

Question 19: What is the sum of 1/2 and 1/3?

2/5
1/6
2/6
5/6 (Correct answer)

Correct answer: 5/6

Using a common denominator of 6: 3/6 + 2/6 = 5/6.

Question 20: 1.4 + 0.06 + 0.522 =

2.522
1.542
1.982 (Correct answer)
2.144

Correct answer: 1.982

To add decimals, align the numbers vertically by their decimal points. It's helpful to add trailing zeros so all numbers have the same number of decimal places: 1.400 + 0.060 + 0.522. Then, add each column from right to left, carrying over when necessary. The sum of these numbers is 1.982.

Question 21: According to the American Sleep Disorders Association, the average teenager needs around 9.5 hours of sleep per night, possibly because critical growth hormones are released during sleep. The average adult requires between six and eight hours of sleep per night for optimal health and productivity. How do the two sentences relate?

They establish a contrast. (Correct answer)
They contradict each other.
They reinforce each other.
They provide a problem and solution

Correct answer: They establish a contrast.

The two sentences present different sleep requirements for two distinct demographic groups: teenagers and adults. By highlighting these differing needs (9.5 hours for teenagers vs. 6-8 hours for adults), they draw a clear comparison that emphasizes their differences. This comparison serves to establish a contrast between the two groups.

Question 22: If y = 2x + 5 and x = −3, what is y?

−1 (Correct answer)
1
11
−11

Correct answer: −1

Substitute x = −3: y = 2(−3) + 5 = −6 + 5 = −1.

Question 23: A bag contains 30 colored marbles that have either a rough or smooth texture. Exactly 1<\/sup>&frasl;2<\/sub> of the marbles are blue, 1<\/sup>&frasl;3<\/sub> are green, and the rest are yellow. Exactly 2<\/sup>&frasl;3<\/sub> of the marbles are smooth. If half of the rough marbles are green, then what fraction of the total bag is rough green marbles?

1<\/sup>&frasl;5<\/sub>
1<\/sup>&frasl;6<\/sub> (Correct answer)
2<\/sup>&frasl;3<\/sub>
2<\/sup>&frasl;5<\/sub>

Correct answer: 1<\/sup>&frasl;6<\/sub>

First, calculate the total number of rough marbles: 2/3 of the 30 marbles are smooth, meaning 1/3 are rough. So, (1/3) * 30 = 10 rough marbles. If half of these rough marbles are green, then there are (1/2) * 10 = 5 rough green marbles. To find the fraction of the total bag that is rough green marbles, divide the number of rough green marbles by the total number of marbles: 5/30, which simplifies to 1/6.

Question 24: With varying success, many women around the world today struggle for equal rights. Historically, women have achieved greater equality with men during periods of social adversity. The following factors initiated the greatest number of improvements for women: violent revolution, world war, and the rigors of pioneering in an undeveloped land. In all three cases, the essential element that improved the status of women was a shortage of men, which required women to perform many of society’s vital tasks. We can conclude from the information in this passage that

historically, women have only achieved equality through force
women today are highly successful in winning equal rights
only pioneer women have been considered equal to men
historically, the principle of equality alone has not been enough to secure women equal rights (Correct answer)

Correct answer: historically, the principle of equality alone has not been enough to secure women equal rights

The passage explicitly states that women achieved greater equality during periods of social adversity, and the 'essential element' was a shortage of men, requiring women to perform vital tasks. This indicates that practical necessity, rather than the inherent principle of equality, was the driving force behind historical gains for women. Thus, the principle of equality alone was insufficient to secure these rights.

Question 25: What is the y-intercept of the function f(x) = 3x² − 4x + 2?

3
2 (Correct answer)
−4
0

Correct answer: 2

The y-intercept occurs at x = 0: f(0) = 3(0) − 4(0) + 2 = 2.

Question 26: Follow my directions exactly and you should have no trouble finding the old barn. Keeping the same meaning, rewrite this sentence beginning with: You should have no trouble finding the old barn

if you forget about my directions
if you don’t deviate from my directions (Correct answer)
if you follow my directions somewhat
if you don’t follow my directions

Correct answer: if you don’t deviate from my directions

The original sentence states that following directions 'exactly' will prevent trouble. The rewritten sentence, 'You should have no trouble finding the old barn,' needs a condition that reflects this exactness. 'If you don’t deviate from my directions' means following them precisely without straying, which perfectly matches the original meaning.

Question 27: Evaluate: log₂(32)

6
8
5 (Correct answer)
4

Correct answer: 5

2⁵ = 32, so log₂(32) = 5.

Question 28: What is the domain of f(x) = 1/(x − 4)?

x > 4
x ≠ 4 (Correct answer)
x ≠ −4
All real numbers

Correct answer: x ≠ 4

The function is undefined when the denominator equals zero, i.e., when x = 4, so the domain is all real numbers except 4.

Question 29: Which percentage is equivalent to the fraction 5<\/sup>&frasl;8<\/sub>?

62.50% (Correct answer)
72.50%
65.50%
67.50%

Correct answer: 62.50%

To convert a fraction to a percentage, divide the numerator by the denominator and then multiply the result by 100. For the fraction 5/8, dividing 5 by 8 yields 0.625. Multiplying 0.625 by 100 gives 62.5%, making 62.50% the equivalent percentage.

Question 30: Choose the correct word(s) for the blank in this sentence: When we removed the old carpet in the second floor of our house, I was dismayed to find a hole that reached all the way ____ to the lower floor.

through (Correct answer)
away from
around
inside

Correct answer: through

The hole 'reached all the way ____ to the lower floor,' indicating a passage or connection from one floor to the other. 'Through' accurately describes this movement or extension from one side or level to another. It implies the hole completely penetrated the floor.

Question 31: Which of the following is the inverse function of f(x) = 3x − 6?

f⁻¹(x) = 3x + 6
f⁻¹(x) = (x − 6)/3
f⁻¹(x) = x/3 − 6
f⁻¹(x) = (x + 6)/3 (Correct answer)

Correct answer: f⁻¹(x) = (x + 6)/3

Swap x and y in y = 3x − 6, then solve for y: x = 3y − 6 → y = (x + 6)/3.

Question 32: The wheel is considered one of the most important mechanical inventions of all time. Many technologies since the invention of the wheel have been based on its principles, and since the industrial revolution, the wheel has been a basic element of nearly every machine constructed by humankind. No one knows the exact time and place of the invention of the wheel, but its beginnings can be seen across many ancient civilizations. The passage suggests that the wheel is an important invention because it

forms the basis of so many later inventions (Correct answer)
is one the world’s most famous inventions
can be traced to many ancient cultures
is one of the world’s oldest inventions

Correct answer: forms the basis of so many later inventions

The passage emphasizes the wheel's importance by stating that 'Many technologies since the invention of the wheel have been based on its principles' and that it is a 'basic element of nearly every machine constructed by humankind.' This highlights its foundational role in subsequent mechanical innovations. Its significance stems from its influence on countless later inventions.

Question 33: An author writes mostly about the harmful effects of a new law, then briefly notes one benefit. What is the author's primary purpose?

To praise the law
To criticize the law (Correct answer)
To define the law
To compare two laws

Correct answer: To criticize the law

Emphasis on harmful effects shows the purpose is to criticize.

Question 34: A car travels 180 miles in 3 hours. At the same rate, how far will it travel in 5 hours?

360 miles
300 miles (Correct answer)
270 miles
320 miles

Correct answer: 300 miles

The speed is 60 mph; in 5 hours the car travels 60 × 5 = 300 miles.

Question 35: In 'The old bridge groaned under the weight of traffic,' the word 'groaned' is an example of:

Personification (Correct answer)
Simile
Irony
Metaphor

Correct answer: Personification

Giving the bridge a human action (groaning) is personification.

Question 36: What does the word 'reluctant' mean in 'He was reluctant to share his opinion'?

Eager
Loud
Unwilling (Correct answer)
Happy

Correct answer: Unwilling

'Reluctant' means hesitant or unwilling to do something.

Question 37: What are the solutions to x² − 5x + 6 = 0?

x = −2 and x = −3
x = 1 and x = 6
x = −1 and x = −6
x = 2 and x = 3 (Correct answer)

Correct answer: x = 2 and x = 3

Factor as (x − 2)(x − 3) = 0, giving x = 2 and x = 3.

Question 38: Which of the following is the least?

0.015
0.15 (Correct answer)
0.501
0.105

Correct answer: 0.15

To compare decimals, align them by their decimal points and compare digits from left to right, starting with the tenths place. For 0.105, 0.501, 0.015, and 0.150 (adding a zero to 0.15 for easier comparison), 0.015 has a 0 in the tenths place, which is smaller than the 1 in 0.105 and 0.150, and the 5 in 0.501. Therefore, 0.015 is the least. Option D (0.15) is greater than 0.015.

Question 39: What is 1/5 written as a decimal?

0.05
0.15
0.5
0.2 (Correct answer)

Correct answer: 0.2

1 ÷ 5 = 0.2.

Question 40: Linda has a bag that is filled 2<\/sup>&frasl;3<\/sub> of the way with candy. If she takes out 1<\/sup>&frasl;4<\/sub> of the candy and gives it to her brother, what fraction of the bag will be filled with candy?

1<\/sup>&frasl;3<\/sub>
1<\/sup>&frasl;2<\/sub> (Correct answer)
5<\/sup>&frasl;6<\/sub>
1<\/sup>&frasl;4<\/sub>

Correct answer: 1<\/sup>&frasl;2<\/sub>

Linda's bag is 2/3 full. She takes out 1/4 *of the candy*, meaning 1/4 of the 2/3. So, the amount taken out is (1/4) * (2/3) = 2/12 = 1/6 of the bag. To find the remaining candy, subtract the amount taken out from the initial amount: 2/3 - 1/6. Convert 2/3 to 4/6, then 4/6 - 1/6 = 3/6, which simplifies to 1/2. Thus, 1/2 of the bag will be filled with candy.

Question 41: Which value of x satisfies 2^(x+1) = 16?

x = 5
x = 2
x = 3 (Correct answer)
x = 4

Correct answer: x = 3

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

Question 42: In the sentence 'The ancient manuscript was fragile and crumbled at the slightest touch,' what does 'fragile' most nearly mean?

Easily broken (Correct answer)
Colorful
Heavy
Valuable

Correct answer: Easily broken

'Fragile' means delicate and easily broken, supported by 'crumbled at the slightest touch.'

Question 43: A concluding paragraph in a WritePlacer essay should:

Ask readers a question without providing an answer
Restate the thesis in different words and summarize key points (Correct answer)
Introduce new evidence and arguments not covered earlier
Simply repeat the introduction word for word

Correct answer: Restate the thesis in different words and summarize key points

A strong conclusion restates the thesis using different wording and summarizes the essay's main points, giving the reader a sense of closure without introducing new ideas.

Question 44: There are 3 people who work full-time and are to work together on a project, but their total time on the project is to be equivalent to that of only one person working full-time. If one of the people is budgeted for 1 of his time to the project 2 and a second person for 1 3 of her time, what part of the third worker’s time should be budgeted to this project?

3\/5
1\/3
1\/6 (Correct answer)
1\/8

Correct answer: 1\/6

The total project time is equivalent to one full-time person, represented as 1. The first two workers contribute 1/2 + 1/3 of their time. To add these fractions, find a common denominator (6), resulting in 3/6 + 2/6 = 5/6. To find the third worker's contribution, subtract this sum from the total: 1 - 5/6 = 6/6 - 5/6 = 1/6.

Question 45: It became clear that the celebration was getting out of hand when Uncle Dwayne arrived on the dance floor. Keeping the meaning the same, rewrite this sentence beginning with: When Uncle Dwayne arrived on the dance floor,

the celebration was clearly out of hand (Correct answer)
the hand was out at the celebration
clearly the out of hand celebration was happening
the hand was a clear celebration

Correct answer: the celebration was clearly out of hand

The original sentence implies that Uncle Dwayne's arrival was the turning point when the celebration became unruly. The rewritten sentence correctly places this event as the trigger, stating 'the celebration was clearly out of hand' immediately after his arrival. This accurately reflects the cause-and-effect relationship presented in the original.

Question 46: Read: 'Unlike his brother, Tom enjoys quiet evenings at home.' What does 'unlike' signal?

Sequence
Similarity
Contrast (Correct answer)
Cause

Correct answer: Contrast

'Unlike' shows a contrast between Tom and his brother.

Question 47: Which scatterplot description indicates a strong negative correlation?

Points cluster along a line sloping upward
Points are randomly scattered
Points form a U shape
Points cluster tightly along a line sloping downward (Correct answer)

Correct answer: Points cluster tightly along a line sloping downward

A strong negative correlation means data points fall close to a downward-sloping line.

Question 48: (-3)(2+6)⁄4 - 2 =

-6
-8 (Correct answer)
6
4

Correct answer: -8

Following the order of operations (PEMDAS/BODMAS), first solve the expression inside the parentheses: 2 + 6 = 8. Next, perform the multiplication in the numerator: (-3)(8) = -24. Then, divide by 4: -24 / 4 = -6. Finally, subtract 2 from the result: -6 - 2 = -8.

Question 49: Choose the word that best completes: "The movie was so _____ that many people fell asleep."

scary
exciting
boring (Correct answer)
funny

Correct answer: boring

People falling asleep signals the movie was "boring."

Question 50: What does the WritePlacer test primarily assess?

Your ability to write an essay in response to a prompt (Correct answer)
Your ability to solve math problems
Your knowledge of grammar rules in isolation
Your reading speed and comprehension

Correct answer: Your ability to write an essay in response to a prompt

The WritePlacer test evaluates your ability to produce a written essay in response to a given prompt, assessing your overall writing competency.

Question 51: John is repainting the outside of his shed. The front and back of the shed are rectangles, 10 feet long and 8 feet high. The sides of the shed are also rectangular, but they are 12 feet long and 8 feet high. If one bucket of paint can cover exactly 50 square feet of the shed, how many buckets of paint should he have to buy to ensure the entire shed is painted and to have the smallest amount left over?

7 buckets
8 buckets (Correct answer)
9 buckets
6 buckets

Correct answer: 8 buckets

First, calculate the total surface area to be painted. The front and back are 10x8 feet, so 2 * (10*8) = 160 sq ft. The two sides are 12x8 feet, so 2 * (12*8) = 192 sq ft. The total area is 160 + 192 = 352 square feet. Since one bucket covers 50 square feet, divide the total area by the coverage per bucket: 352 / 50 = 7.04 buckets. To ensure the entire shed is painted, John must buy 8 buckets, as he cannot buy a fraction of a bucket.

Question 52: What is the best summary of: 'Exercise improves health, boosts mood, and increases energy'?

Exercise has many benefits (Correct answer)
Exercise wastes time
Exercise is expensive
Exercise is difficult

Correct answer: Exercise has many benefits

The sentence lists several positive effects, so exercise has many benefits.

Question 53: What is the value of 4³ ÷ 2²?

16 (Correct answer)
32
4
8

Correct answer: 16

4³ = 64 and 2² = 4, so 64 ÷ 4 = 16.

Question 54: Simplify: √(75)

15√3
5√15
5√3 (Correct answer)
3√5

Correct answer: 5√3

75 = 25 × 3, so √75 = √25 · √3 = 5√3.

Question 55: Choose the word that best completes: "The scientist's theory was _____ after years of testing."

forgotten
ignored
confirmed (Correct answer)
rejected

Correct answer: confirmed

Years of testing leading to acceptance means the theory was "confirmed."

Question 56: A recipe uses 2.5 cups of flour for 12 cookies. How many cups are needed for 36 cookies?

6 cups
7.5 cups (Correct answer)
7 cups
8 cups

Correct answer: 7.5 cups

36 ÷ 12 = 3, so multiply 2.5 × 3 = 7.5 cups.

Question 57: Estimate 48 × 21 by rounding each number.

800
900
1200
1000 (Correct answer)

Correct answer: 1000

Rounding to 50 × 20 gives 1000.

Question 58: Which of the following words is a gerund in the following sentence? Swimming is a pleasurable hobby.

swimming (Correct answer)
pleasurable
is
hobby

Correct answer: swimming

A gerund is a verb form ending in '-ing' that functions as a noun in a sentence. In the sentence 'Swimming is a pleasurable hobby,' 'swimming' acts as the subject, performing the role of a noun. Therefore, it is the gerund.

Question 59: While most people think of dogs as pets, some dogs are bred and trained specifically for certain types of work. The bloodhound’s acute sense of smell and willing personality make it ideal for tracking lost objects or people. What does the second sentence do?

It gives an example. (Correct answer)
It states an effect.
It restates an idea found in the first.
It makes a contrast.

Correct answer: It gives an example.

The first sentence makes a general statement about dogs being trained for work. The second sentence then provides a specific instance of this by describing the bloodhound's abilities and its suitability for tracking lost objects or people. This serves as a concrete illustration or example of the general point made in the first sentence.

Question 60: 1<\/sup>&frasl;3<\/sub> of 250 is approximately ____.

85 (Correct answer)
50
100
70

Correct answer: 85

To find 1/3 of 250, divide 250 by 3. The calculation 250 ÷ 3 results in approximately 83.33. Among the given options, 85 is the closest approximation to this value. Therefore, 1/3 of 250 is approximately 85.

Question 61: What is the mode of the data set: 5, 8, 3, 8, 7, 5, 8?

5
7
3
8 (Correct answer)

Correct answer: 8

The number 8 appears three times, more than any other value, making it the mode.

Question 62: A store sells a jacket for $120 after applying a 20% discount. What was the original price?

$140
$150 (Correct answer)
$160
$144

Correct answer: $150

If $120 is 80% of the original price, divide $120 by 0.80 to get $150.

Question 63: What does 'inevitable' mean in 'With such heavy traffic, being late was inevitable'?

Pleasant
Surprising
Unavoidable (Correct answer)
Avoidable

Correct answer: Unavoidable

'Inevitable' means certain to happen and impossible to avoid.

Question 64: Which sentence uses a transition word that signals an addition of information?

Although it rained, we went.
Instead, they left.
Furthermore, costs increased. (Correct answer)
However, the plan failed.

Correct answer: Furthermore, costs increased.

'Furthermore' adds more information to a previous point.

Question 65: What is the vertex of the parabola y = (x − 3)² + 5?

(3, −5)
(3, 5) (Correct answer)
(−3, −5)
(−3, 5)

Correct answer: (3, 5)

In vertex form y = (x − h)² + k, the vertex is (h, k) = (3, 5).

Question 66: Dogs and cats make very different types of pets. Before deciding whether to buy or adopt a dog or a cat, prospective owners need to carefully consider their own lifestyles and personalities. Dogs may make more affectionate companions, but they require more care and attention. They must be taken out several times a day and should not be left alone for more than a few hours. Larger dogs require significant exercise to remain fit and healthy. Cats are usually more independent in nature and interact less with their owners. Also, a cat can be left on its own all day, or even for several days, as long as it has food and clean water to drink. From this passage a reader can conclude that

owning a cat requires less work than owning a dog (Correct answer)
people who like to play with their pets should own a cat
owning a cat is more responsibility than owning a dog
people who are away from home during the day should not own a cat

Correct answer: owning a cat requires less work than owning a dog

The passage contrasts the care requirements for dogs and cats. It states that dogs "require more care and attention," need to be "taken out several times a day," and "should not be left alone for more than a few hours." In contrast, cats are "more independent" and "can be left on its own all day, or even for several days, as long as it has food and clean water." This comparison clearly indicates that cats generally demand less daily attention and effort from their owners.

Question 67: Solve the equation for x, given y = 3 9x−12+y2 = 5

x = 5⁄7
x = 4⁄9
x = 3⁄2
x = 8⁄9 (Correct answer)

Correct answer: x = 8⁄9

First, substitute the value of y=3 into the equation: 9x - 12 + (3)^2 = 5. This simplifies to 9x - 12 + 9 = 5. Combine the constant terms: 9x - 3 = 5. Add 3 to both sides to isolate the x term: 9x = 8. Finally, divide by 9 to solve for x: x = 8/9.

Question 68: Which of the following correctly lists the numbers in order from greatest to least?ub>2

3⁄4 > 5⁄2 > − 1⁄2 > −1⁄4
-1⁄4> − 1⁄2 > 3⁄4 > 5⁄2
5⁄2 > 3⁄4 > − 1⁄4 > −1⁄2 (Correct answer)
5⁄2 >3⁄4 > − 1⁄2 > − 1⁄4

Correct answer: 5⁄2 > 3⁄4 > − 1⁄4 > −1⁄2

To order the numbers, it's helpful to convert them to decimals: 5/2 = 2.5, 3/4 = 0.75, -1/4 = -0.25, and -1/2 = -0.5. Arranging these from greatest to least gives 2.5 > 0.75 > -0.25 > -0.5. This corresponds to 5/2 > 3/4 > -1/4 > -1/2.

Question 69: If f(x) = x² + 1 and g(x) = 2x, what is f(g(3))?

19
13
37 (Correct answer)
49

Correct answer: 37

g(3) = 6, then f(6) = 6² + 1 = 37.

Question 70: 3<\/sup>&frasl;4<\/sub> is equivalent to which of the following?

18<\/sup>&frasl;24<\/sub> (Correct answer)
0.7
6<\/sup>&frasl;9<\/sub>
8<\/sup>&frasl;10<\/sub>

Correct answer: 18<\/sup>&frasl;24<\/sub>

To find an equivalent fraction, you can multiply or divide both the numerator and denominator by the same non-zero number. For 3/4, let's check option A) 18/24. If you divide both 18 and 24 by their greatest common divisor, 6, you get 18 ÷ 6 = 3 and 24 ÷ 6 = 4. Thus, 18/24 simplifies to 3/4, making it equivalent.

Question 71: Which expression is equivalent to (2x³y²)²?

2x⁶y⁴
4x⁵y⁴
4x⁶y⁴ (Correct answer)
4x⁶y²

Correct answer: 4x⁶y⁴

Square each factor: 2² = 4, (x³)² = x⁶, (y²)² = y⁴, giving 4x⁶y⁴.

Question 72: Which word is an antonym for 'generous'?

Wealthy
Helpful
Stingy (Correct answer)
Kind

Correct answer: Stingy

'Stingy' means unwilling to give, the opposite of 'generous.'

Question 73: Read: 'The author begins each chapter with a question to engage readers.' Why does the author do this?

To capture readers' interest (Correct answer)
To list facts
To confuse readers
To end the book

Correct answer: To capture readers' interest

Starting with a question is a technique to engage and interest readers.

Question 74: Derek will ____________ this July with an engineering degree in computer engineering.

be graduate
was graduating
be graduating (Correct answer)
have graduating

Correct answer: be graduating

The phrase 'this July' indicates a future event that will be in progress or completed around that specific time. The future continuous tense, 'will be graduating,' is used to describe an action that will be ongoing at a particular point in the future. This tense correctly conveys that Derek's graduation process will be happening around July.

Question 75: What is the remainder when x³ − 2x + 4 is divided by (x − 1)?

1
2
0
3 (Correct answer)

Correct answer: 3

By the Remainder Theorem, substitute x = 1: 1 − 2 + 4 = 3.

Question 76: What is the best version of the underlined part of this sentence? One of the choices involves leaving the sentence as it is written. Doris feels that she<\/u> is the ideal candidate for the job because she is experienced, dedicated, and persistent.

Doris felt that she is
Doris felt that she was
Doris feels that she is (Correct answer)
Doris, feeling that she is,

Correct answer: Doris feels that she is

The original sentence uses consistent present tense verbs ('feels,' 'is,' 'is experienced, dedicated, and persistent'), which correctly expresses Doris's current belief and her current qualities. Options A and B introduce inconsistent past tenses, while option D changes the sentence structure, making it less direct than the clear statement of current facts in the original.

Question 77: A passage begins, 'Imagine a world without honeybees.' This opening is meant to:

Summarize the conclusion
Engage the reader's interest (Correct answer)
Cite a statistic
Define a term

Correct answer: Engage the reader's interest

A vivid hypothetical opening is a hook to draw the reader in.

Question 78: Which of the following is closest to 27.8 × 9.6?

280
3,000
2,800
300 (Correct answer)

Correct answer: 300

To estimate the product of 27.8 × 9.6, round each number to a convenient value. Rounding 27.8 up to 30 and 9.6 up to 10 gives an estimated product of 30 × 10 = 300. While 280 (from 28 x 10) is numerically closer to the exact product (266.88), 300 is a common estimation result when rounding both factors up to the nearest multiple of ten, making it the intended answer among the choices.

Question 79: 7.86 × 4.6 =

351.56
36.216 (Correct answer)
361.56
36.156

Correct answer: 36.216

To multiply decimals, first multiply the numbers as if they were whole numbers (786 × 46 = 36156). Then, count the total number of decimal places in the original factors (two in 7.86 and one in 4.6, for a total of three). Place the decimal point three places from the right in the product, resulting in 36.156. Option B (36.216) is incorrect, indicating a calculation error in the multiplication process.

Question 80: A survey of 200 students found that 60 prefer math. What percentage prefer math?

20%
30% (Correct answer)
25%
40%

Correct answer: 30%

(60 ÷ 200) × 100 = 30%.

Question 81: Which sentence uses the apostrophe correctly?

The dog's bowl's was empty.
The dogs bowl was empty.
The dogs' was empty bowl.
The dog's bowl was empty. (Correct answer)

Correct answer: The dog's bowl was empty.

"Dog's" shows singular possession of the bowl.

Question 82: What is 7/8 − 1/2?

1/4
1/2
6/6
3/8 (Correct answer)

Correct answer: 3/8

1/2 = 4/8, so 7/8 - 4/8 = 3/8.

Question 83: 6<\/sup>&frasl;7<\/sub> + 5<\/sup>&frasl;4<\/sub> =

46<\/sup>&frasl;7<\/sub>
2 1<\/sup>&frasl;2<\/sub>
59<\/sup>&frasl;28<\/sub> (Correct answer)
21<\/sup>&frasl;28<\/sub>

Correct answer: 59<\/sup>&frasl;28<\/sub>

To add fractions with different denominators, first find a common denominator. For 6/7 and 5/4, the least common multiple of 7 and 4 is 28. Convert the fractions: 6/7 becomes 24/28 (multiply numerator and denominator by 4), and 5/4 becomes 35/28 (multiply numerator and denominator by 7). Now, add the new fractions: 24/28 + 35/28 = 59/28. This is an improper fraction and can be left as such or converted to a mixed number (2 3/28).

Question 84: Read: 'The scientist's theory was eventually proven correct after years of testing.' What does 'eventually' suggest?

By accident
Never
Immediately
After a period of time (Correct answer)

Correct answer: After a period of time

'Eventually' means after some time has passed.

Question 85: (x2+ 8x + 15)⁄(x + 3) =

(x+5) (Correct answer)
(x+2)
(x−5)
(x−3)

Correct answer: (x+5)

To simplify this rational expression, factor the quadratic in the numerator. We need two numbers that multiply to 15 and add to 8, which are 3 and 5. So, x^2 + 8x + 15 factors into (x+3)(x+5). Now, the expression becomes [(x+3)(x+5)] / (x+3). Since (x+3) is in both the numerator and denominator, they cancel out, leaving (x+5).

Question 86: Rory couldn’t remember the steps to make a peanut butter sandwich, often ending up with peanut butter smeared all over the bread. Keeping the meaning the same, rewrite this sentence beginning with: Rory smeared peanut butter all over the bread

making the steps to a peanut butter sandwich
because he couldn’t remember the steps to make a peanut butter sandwich (Correct answer)
as he remembers the steps to make a peanut butter sandwich
remembering the steps to make a peanut butter sandwich

Correct answer: because he couldn’t remember the steps to make a peanut butter sandwich

The original sentence establishes a cause-and-effect relationship: Rory's inability to remember steps led to smeared peanut butter. The rewritten sentence correctly uses 'because' to explicitly state this causal link. This maintains the original meaning by clearly identifying the reason for Rory's messy sandwich-making.

Question 87: Choose the word that best completes: "The witness gave an _____ account that matched the evidence exactly."

accurate (Correct answer)
false
doubtful
vague

Correct answer: accurate

An account that matches evidence exactly is "accurate."

Question 88: Which of the following is equivalent to the expression 3x² − 12x?

3(x² − 4x)
Both A and B (Correct answer)
3x(x − 4)
3x(x + 4)

Correct answer: Both A and B

Factor out 3x to get 3x(x − 4), which equals 3(x² − 4x), so both A and B are correct.

Question 89: Which inequality is represented by the statement 'twice a number is at most 14'?

2n < 14
2n > 14
2n ≤ 14 (Correct answer)
2n ≥ 14

Correct answer: 2n ≤ 14

'At most 14' means less than or equal to 14, so the inequality is 2n ≤ 14.

Question 90: What is the amplitude of y = 4sin(2x)?

π
4 (Correct answer)
8
2

Correct answer: 4

The amplitude of y = A·sin(Bx) is |A|, which is 4.

Question 91: Some stores are testing a new checkout system that allows shoppers to use their mobile phones to scan items as they walk through stores and pay at self-service kiosks, skipping the cashiers’ lines. The new mobile checkout system reduces long lines and customer wait times in stores. What does the second sentence do?

It contrasts with the first.
It expands on the first
It gives an example.
It states an effect. (Correct answer)

Correct answer: It states an effect.

The first sentence describes a new checkout system. The second sentence then explains a direct positive outcome or consequence of implementing this system: it 'reduces long lines and customer wait times in stores.' This clearly describes an effect of the system detailed in the first sentence.

Question 92: Solve for x: |2x − 3| = 7

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

Correct answer: x = 5 or x = −2

Set 2x − 3 = 7 giving x = 5, and 2x − 3 = −7 giving x = −2.

Question 93: "Subtitles are typically shown for the __________ of those who do not understand Latin."

beneficiary
benefit (Correct answer)
disadvantage
hindrance

Correct answer: benefit

Subtitles are provided to assist viewers in understanding content, especially when they don't comprehend the original language. Therefore, they are shown for the "benefit" or advantage of those individuals. "Benefit" correctly expresses this positive purpose, while the other options are either grammatically incorrect or convey the opposite meaning.

Question 94: What is the slope of the line passing through (2, 3) and (6, 11)?

2 (Correct answer)
3
1
4

Correct answer: 2

Slope = (11 − 3) ÷ (6 − 2) = 8 ÷ 4 = 2.

Question 95: What is 100 - 37.5?

72.5
62.5 (Correct answer)
62.0
63.5

Correct answer: 62.5

100 minus 37.5 equals 62.5.

Question 96: Erica bought 3 1 2 yards of fabric. If she uses 2 3 of the fabric to make a curtain, how much will she have left?

two and one third yards
one sixth yard (Correct answer)
one third yard
one and one sixth yards

Correct answer: one sixth yard

Erica bought 3 1/2 yards of fabric, which is equivalent to 7/2 yards. If she uses 2/3 of the fabric, the fraction of fabric she has left is 1 - 2/3 = 1/3. To find the actual amount left, multiply this remaining fraction by the total fabric: (1/3) × (7/2) = 7/6 yards. This is equivalent to 1 and 1/6 yards, not one sixth yard.

Question 97: What is the best version of the underlined part of this sentence? One of the choices involves leaving the sentence as it is written. The search for a new job can be a challenge for anyone, so everyone should know how to write a resume and perform well in an interview<\/u>.

performs well in interviews
perform well in an interview (Correct answer)
performing well in an interview
interview performing well

Correct answer: perform well in an interview

The sentence requires parallel structure for the skills everyone should know: 'how to write a resume' and 'how to perform well in an interview.' The original phrasing 'perform well in an interview' correctly maintains this parallelism, as both phrases are implicitly governed by 'how to.' Options B, C, and D break this grammatical balance by changing the verb form.

Question 98: What is the best version of the underlined part of this sentence? One of the choices involves leaving the sentence as it is written. When my brother and I were children, we found five kittens hided under our porch<\/u>.

he found five kittens hided under our porch
five kittens that were hid under the porch, we found them
we found the five kittens, hiding as they were under the porch
we found five kittens hidden under our porch (Correct answer)

Correct answer: we found five kittens hidden under our porch

The original sentence uses the incorrect past participle 'hided.' The correct past participle of the verb 'to hide' is 'hidden.' Option D, 'we found five kittens hidden under our porch,' correctly uses 'hidden' to describe the state of the kittens, making the sentence grammatically sound and clear.

Question 99: 46.2 × 10–2 =

0.462
462
0.0462
4.62 (Correct answer)

Correct answer: 4.62

Multiplying a number by 10 raised to a negative exponent means moving the decimal point to the left by the number of places indicated by the exponent's absolute value. For 10^-2, the decimal point moves two places to the left. Starting with 46.2, moving the decimal two places left results in 0.462. The provided answer 4.62 would be 46.2 × 10^-1.

Question 100: Which number is largest: 0.7, 0.07, 0.77, or 0.707?

0.77 (Correct answer)
0.07
0.7
0.707

Correct answer: 0.77

Comparing decimals, 0.77 is greater than the others.

Question 101: Which sentence places the modifier "only" correctly to mean she ate nothing but salad?

She only ate the salad.
Only she ate the salad.
She ate only the salad. (Correct answer)
She ate the salad only her.

Correct answer: She ate only the salad.

Placing "only" before "the salad" limits what she ate.

Question 102: Which of the following is a zero of f(x) = x³ − x² − 6x?

x = 1
x = 3 (Correct answer)
x = 4
x = −2

Correct answer: x = 3

Factor: x(x² − x − 6) = x(x − 3)(x + 2), so zeros are x = 0, x = 3, and x = −2.

Question 103: Which equation represents exponential decay?

y = 5 + 2x
y = 3(0.8)ˣ (Correct answer)
y = x²
y = 2(1.5)ˣ

Correct answer: y = 3(0.8)ˣ

A base between 0 and 1 (like 0.8) causes the function to decrease, representing exponential decay.

Question 104: Which of the following is a rational number?

√2
π
√5
√9 (Correct answer)

Correct answer: √9

√9 = 3, which is an integer and therefore a rational number.

Question 105: The mean of five numbers is 10. Four of the numbers are 8, 11, 9, and 12. What is the fifth number?

12
8
10 (Correct answer)
11

Correct answer: 10

The sum must be 5 × 10 = 50; subtracting the four known values: 50 − 40 = 10.

ACCUPLACER Exam

The ACCUPLACER is a computer-adaptive college placement test administered by College Board, used by colleges and universities to assess reading, writing, and math skills for course placement decisions.

105

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120 min

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