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

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

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 2: What is the meaning of the word 'abundant' in 'The garden had an abundant supply of vegetables'?

• Expensive
• Rotten
• Plentiful (Correct answer)
• Scarce

Correct answer: Plentiful

'Abundant' means existing in large quantities, or plentiful.

Question 3: 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 4: Cesar Chavez was an influential leader for farmworkers. He fought for their rights and better working conditions. Chavez led many strikes that angered farm owners. Eventually he succeeded in getting increased wages and better living situations for farmworkers. The passage indicates that Chavez changed lives by

• fighting for the rights of farm owners
• improving the conditions for farmworkers (Correct answer)
• helping to end the farmworkers’ strikes
• working on the farms every day

Correct answer: improving the conditions for farmworkers

The passage explicitly states that Cesar Chavez "fought for their rights and better working conditions" for farmworkers. It concludes by saying he "succeeded in getting increased wages and better living situations for farmworkers." These statements directly indicate that his actions led to an improvement in the overall conditions for these workers.

Question 5: When you cross the street in the middle of the block, this is an example of jaywalking.

• You cross the street in the middle of the block, this
• When you cross the street in the middle of the block, this
• Crossing the street in the middle of the block (Correct answer)
• The fact that you cross the street in the middle of the block

Correct answer: Crossing the street in the middle of the block

The original sentence is wordy and somewhat indirect. Replacing the clause 'When you cross the street in the middle of the block, this' with the concise gerund phrase 'Crossing the street in the middle of the block' makes the sentence more direct and grammatically efficient. It clearly identifies the action as jaywalking without unnecessary words.

Question 6: What is 1/4 + 0.5 expressed as a decimal?

• 0.25
• 0.75 (Correct answer)
• 1.5
• 0.55

Correct answer: 0.75

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

Question 7: Rose was about to fall asleep when, suddenly, the first meteor streaked across the sky. Keeping the same meaning, rewrite this sentence beginning with: The first meteor streaked across the sky,

• but Rose continued falling asleep
• but Rose was wide awake
• awakening Rose from her near slumber (Correct answer)
• but Rose fell asleep

Correct answer: awakening Rose from her near slumber

The original sentence describes Rose being about to fall asleep when the meteor streaked across the sky. The meteor's appearance was a sudden event that interrupted her near sleep. The rewritten sentence, 'The first meteor streaked across the sky,' needs to show its effect on Rose. 'Awakening Rose from her near slumber' accurately captures this interruption and preserves the meaning.

Question 8: A pizza pie has eight slices. Some of the slices have extra toppings of either pepperoni, mushroom, or both, while some slices have no extra toppings. The customer specified that <sup>1<\/sup>&frasl;<sub>2<\/sub> of the pie must contain pepperoni, <sup>3<\/sup>&frasl;<sub>8<\/sub> of the pie must contain mushrooms, and <sup>1<\/sup>&frasl;<sub>4<\/sub> of the pie must contain both pepperoni and mushrooms. What fraction of the pie does not contain any extra topping?

• <sup>1<\/sup>&frasl;<sub>2<\/sub>
• <sup>3<\/sup>&frasl;<sub>8<\/sub> (Correct answer)
• <sup>2<\/sup>&frasl;<sub>8<\/sub>
• <sup>1<\/sup>&frasl;<sub>3<\/sub>

Correct answer: <sup>3<\/sup>&frasl;<sub>8<\/sub>

A pizza has 8 slices. Pepperoni (P) is 1/2 of 8 = 4 slices. Mushrooms (M) is 3/8 of 8 = 3 slices. Both (P and M) is 1/4 of 8 = 2 slices. To find slices with any topping, use the formula: P + M - (P and M) = 4 + 3 - 2 = 5 slices. The number of slices with no extra topping is the total slices minus slices with any topping: 8 - 5 = 3 slices. As a fraction of the pie, this is 3/8.

Question 9: In a passage, a scientist is repeatedly called 'a tireless seeker of truth.' This characterization is meant to make the reader view her as:

• Admirable and dedicated (Correct answer)
• Dishonest
• Lazy and careless
• Indifferent

Correct answer: Admirable and dedicated

Calling her tireless and truth-seeking presents her positively.

Question 10: "Are you sure you don't want to __________ before we leave?"

• ate
• eaten
• eating
• eat (Correct answer)

Correct answer: eat

The phrase "want to" is followed by an infinitive verb, which is the base form of the verb. In this case, "eat" is the correct base form. Options like "ate," "eaten," or "eating" are incorrect verb forms to follow "want to" in this construction.

Question 11: 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 12: What is 12% of 120?

• 14.4
• 10 (Correct answer)
• 28.8
• 18.4

Correct answer: 10

To calculate a percentage of a number, convert the percentage to a decimal by dividing by 100, then multiply by the number. So, 12% of 120 is calculated as 0.12 × 120. Performing this multiplication yields 14.4. Therefore, 12% of 120 is 14.4, not 10.

Question 13: What does the WritePlacer test primarily assess?

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

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 14: Before giving first aid to an accident victim, you should obtain his or her consent. Asking for consent takes a simple question. Say to the victim, “I know first aid, and I can help until an ambulance arrives. Is that okay?” According to the passage, it is wrong to

• use first aid on an accident victim without medical training
• call for an ambulance instead of helping the victim
• help a victim before an ambulance arrives
• attempt to help an accident victim without permission (Correct answer)

Correct answer: attempt to help an accident victim without permission

The passage explicitly states, "Before giving first aid to an accident victim, you should obtain his or her consent." It then provides an example of how to ask for consent. This directly implies that proceeding to give first aid without first obtaining permission from the victim is the wrong action to take.

Question 15: Read: 'The detective examined every clue meticulously.' What does 'meticulously' mean?

• Rarely
• Carelessly
• Quickly
• Very carefully (Correct answer)

Correct answer: Very carefully

'Meticulously' means with great attention to detail and care.

Question 16: Derek will ____________ this July with an engineering degree in computer engineering.

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

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 17: If 2x – 3(x + 4) = –5, then x =

• 17
• 7
• –7 (Correct answer)
• –17

Correct answer: –7

To solve 2x – 3(x + 4) = –5, first distribute the –3: 2x – 3x – 12 = –5. Combine like terms to get –x – 12 = –5. Add 12 to both sides, resulting in –x = 7. Finally, multiply by –1 to find x = –7.

Question 18: Which of the following is a zero of f(x) = x³ − x² − 6x?

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

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

• 19
• 49
• 13
• 37 (Correct answer)

Correct answer: 37

g(3) = 6, then f(6) = 6² + 1 = 37.

Question 20: 25.6 x 10.42 is closest to which of the following?

• 260 (Correct answer)
• 2600
• 2650
• 200

Correct answer: 260

To estimate the product of 25.6 x 10.42, round each number to a convenient whole number. 25.6 can be rounded to 26, and 10.42 can be rounded to 10. Multiplying these rounded numbers gives 26 x 10 = 260. This estimate is closest to the actual product, making 260 the correct answer.

Question 21: Choose the correct word for the blank in this sentence: I looked up and found an old bird’s nest ____ my window in the gutter on the roof.

• above (Correct answer)
• around
• below
• along

Correct answer: above

The sentence states 'I looked up' and the nest was 'in the gutter on the roof.' Gutters on a roof are always positioned higher than a window. Therefore, 'above' correctly indicates the nest's position relative to the window.

Question 22: The word 'meticulous' most nearly means:

• Very careful about details (Correct answer)
• Generous
• Loud and forceful
• Careless and rushed

Correct answer: Very careful about details

'Meticulous' describes someone extremely precise and detail-oriented.

Question 23: Which scatterplot description indicates a strong negative correlation?

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

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 24: Choose the correct word(s) for the blank in this sentence: Tanya ____ lots of new bicycle equipment, when she acquired her first sponsorship, because of her great abilities as a rider.

• was given (Correct answer)
• gave
• was giving
• was gave

Correct answer: was given

The sentence implies that Tanya *received* the equipment due to her abilities and sponsorship, rather than her giving it away. This requires the passive voice, where the subject is the recipient of the action. 'Was given' correctly forms the past tense passive voice, indicating that the equipment was provided to her by someone else.

Question 25: A data set has values 4, 7, 7, 9, 13. What is the median?

• 7 (Correct answer)
• 8
• 7.5
• 9

Correct answer: 7

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

Question 26: Choose the best word: "The instructions were so _____ that no one could follow them."

• obvious
• confusing (Correct answer)
• simple
• helpful

Correct answer: confusing

If no one could follow them, the instructions must have been "confusing."

Question 27: Which of the following lists the given numbers in order from least to greatest?

• 0.058 < 0.42 < 0.48 < 0.405
• 0.405 < 0.058 < 0.48 < 0.42
• 0.48 < 0.42 <0.405 < 0.058
• 0.058 < 0.405 < 0.42 < 0.48 (Correct answer)

Correct answer: 0.058 < 0.405 < 0.42 < 0.48

To order decimals from least to greatest, compare the digits from left to right, starting with the tenths place. 0.058 is the smallest because it has a 0 in the tenths place. For 0.405, 0.42, and 0.48, all have 4 in the tenths place; comparing the hundredths place (0, 2, 8 respectively) shows the correct order is 0.405 < 0.42 < 0.48. Thus, the complete order is 0.058 < 0.405 < 0.42 < 0.48.

Question 28: 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)
• 6 buckets
• 9 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 29: People have different ways of learning. Some are better at making mental pictures of new ideas. Others are more comfortable with writing lists of things to memorize. Certain people can learn best when listening to music, while others need silence to concentrate. Which of the following is the main idea of the passage?

• Mental pictures help many to learn
• Some people prefer lists to making mental pictures.
• Different individuals have different ways of acquiring information (Correct answer)
• To learn well you need to be comfortable.

Correct answer: Different individuals have different ways of acquiring information

The passage explicitly states, "People have different ways of learning." It then provides several examples: making mental pictures, writing lists, listening to music, or needing silence. Each example illustrates a distinct method of learning, directly supporting the main idea that individuals vary in their preferred and most effective approaches to acquiring information.

Question 30: The Institute for Public Learning (IPL) was founded in the late 20th century. Which year might the IPL have been founded?

• 1950
• 1898
• 1985 (Correct answer)
• 2010

Correct answer: 1985

The 20th century spans from the year 1901 to 2000. The 'late 20th century' refers to the latter decades of this period. Among the given options, 1985 falls within this timeframe, specifically in the latter half of the century.

Question 31: Choose the correct word(s) for the blank in this sentence: Jane, the ____ of the four sisters, is Head of Emergency Nursing at the local hospital.

• oldest (Correct answer)
• more older
• most old
• older

Correct answer: oldest

When comparing three or more items or people, the superlative form of an adjective is used. Since there are 'four sisters,' we need the superlative form of 'old,' which is 'oldest.' This indicates Jane is the most senior among all four.

Question 32: If a passage's tone is described as 'sardonic,' the author is being:

• Mockingly sarcastic (Correct answer)
• Deeply sorrowful
• Warmly sincere
• Strictly neutral

Correct answer: Mockingly sarcastic

'Sardonic' means grimly mocking or cynically sarcastic.

Question 33: Simplify: (x³ · x²) ÷ x⁴

• x³
• x⁴
• x (Correct answer)
• x²

Correct answer: x

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

Question 34: Which word best completes the sentence: 'Despite the ___ evidence, the jury reached a quick verdict'?

• abundant
• overwhelming
• clear
• scant (Correct answer)

Correct answer: scant

'Despite' signals contrast, so little evidence still led to a quick verdict.

Question 35: Which is NOT a helping verb?

• talk (Correct answer)
• will
• can
• am

Correct answer: talk

Helping verbs (also called auxiliary verbs) assist the main verb in expressing tense, mood, or voice. 'Can,' 'will,' and 'am' are all common helping verbs that precede a main verb (e.g., 'I can run,' 'She will sing,' 'I am eating'). 'Talk,' however, is a main action verb itself, not a verb used to assist another verb.

Question 36: What percentage of 128 is 96?

• 70%
• 75% (Correct answer)
• 80%
• 65%

Correct answer: 75%

To find what percentage of 128 is 96, divide the part (96) by the whole (128) and then multiply by 100%. The fraction 96/128 simplifies to 3/4 by dividing both numerator and denominator by their greatest common divisor, 32. Converting 3/4 to a decimal gives 0.75, and multiplying by 100% yields 75%. Thus, 96 is 75% of 128.

Question 37: "Many parents use Child Benefit income to __________ their entire household budget."

• supporting
• support as
• support (Correct answer)

Correct answer: support

The phrase "to" preceding the blank indicates an infinitive of purpose, which requires the base form of the verb. "Support" is the correct base form, indicating the action parents take with the Child Benefit income. "Supporting" is a gerund and "support as" is grammatically incorrect in this context.

Question 38: A function is defined as f(x) = −2x + 7. Over which interval is f(x) > 0?

• x > 7
• x > 7/2
• x < 7/2 (Correct answer)
• 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 39: A student writes three body sentences each beginning with 'First... Second... Third...' without elaboration. What revision would MOST improve this?

• Add more items to extend the list further
• Develop each point with specific details and explanation rather than just listing (Correct answer)
• Remove all the transitions to make the paragraph flow better
• Change 'first, second, third' to 'one, two, three'

Correct answer: Develop each point with specific details and explanation rather than just listing

Simply listing points without development is a weak writing pattern; effective WritePlacer responses develop each point with specific evidence, examples, and explanation.

Question 40: Which of the following is equivalent to the expression 3x² − 12x?

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

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

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

Correct answer: 30%

(60 ÷ 200) × 100 = 30%.

Question 42: Which of the following correctly lists the numbers in order from greatest to least?

• 7\/8 > 0.605 > 0.5 > 65%
• 7\/8 > 0.605 > 65% > 0.5
• 0.605 > 7\/8 > 0.5 > 65%
• 7\/8 > 65% > 0.605 > 0.5 (Correct answer)

Correct answer: 7\/8 > 65% > 0.605 > 0.5

To compare numbers in different formats, convert them all to decimals. 7/8 is 0.875, 65% is 0.65, 0.605 is already a decimal, and 0.5 is 0.500. Arranging these from greatest to least gives 0.875 (7/8), 0.65 (65%), 0.605, and 0.5 (0.5). Therefore, the correct order is 7/8 > 65% > 0.605 > 0.5.

Question 43: Which BEST describes the 'focus' criterion in WritePlacer scoring?

• The essay is exactly the required minimum length
• The essay consistently stays on the assigned topic and supports its thesis (Correct answer)
• The essay uses a narrow vocabulary to maintain consistency
• The essay discusses many different topics to show broad knowledge

Correct answer: The essay consistently stays on the assigned topic and supports its thesis

Focus in WritePlacer scoring means the essay consistently addresses the assigned prompt and maintains a clear central argument throughout without straying to unrelated topics.

Question 44: The mean of five numbers is 10. Four of the numbers are 8, 11, 9, and 12. What is the fifth number?

• 8
• 11
• 12
• 10 (Correct answer)

Correct answer: 10

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

Question 45: Which expression is equivalent to (2x³y²)²?

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

Correct answer: 4x⁶y⁴

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

Question 46: What is the period of the function y = cos(πx)?

• 2π
• 2 (Correct answer)
• 1
• π

Correct answer: 2

Period = 2π ÷ B = 2π ÷ π = 2.

Question 47: Choose the best word: "The library must remain _____ so students can concentrate."

• quiet (Correct answer)
• crowded
• noisy
• dark

Correct answer: quiet

Concentration requires a "quiet" environment.

Question 48: A bag contains 3 red, 5 blue, and 2 green marbles. What is the probability of randomly selecting a blue marble?

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

Correct answer: 1/2

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

Question 49: Simplify: √(75)

• 5√15
• 15√3
• 5√3 (Correct answer)
• 3√5

Correct answer: 5√3

75 = 25 × 3, so √75 = √25 · √3 = 5√3.

Question 50: What is the mode of the data set: 5, 8, 3, 8, 7, 5, 8?

• 3
• 5
• 8 (Correct answer)
• 7

Correct answer: 8

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

Question 51: \t In the words of Thomas De Quincey, “It is notorious that the memory strengthens as you lay burdens upon it.” If, like most people, you have trouble recalling the names of those you have just met, try this: The next time you are introduced, plan to remember the names. Say to yourself, “I’ll listen carefully; I’ll repeat each person’s name to be sure I have it, and I will remember.” You’ll discover how effective this technique is and probably recall those names for the rest of your life. The passage suggests that people remember names best when they

• meet new people
• . are interested in people
• decide to do so (Correct answer)
• are intelligent

Correct answer: decide to do so

The passage directly advises readers to 'plan to remember the names' and to consciously decide to listen, repeat, and actively intend to recall them. It suggests that this deliberate decision and mental commitment are the keys to improving memory for names. Therefore, remembering names best occurs when people make a conscious choice to do so.

Question 52: 7.86 × 4.6 =

• 361.56
• 351.56
• 36.156
• 36.216 (Correct answer)

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 53: What is the average of 12, 18, and 30?

• 18
• 20 (Correct answer)
• 22
• 60

Correct answer: 20

(12 + 18 + 30) ÷ 3 = 60 ÷ 3 = 20.

Question 54: What does 'inevitable' mean in 'With such heavy traffic, being late was inevitable'?

• Pleasant
• Avoidable
• Surprising
• Unavoidable (Correct answer)

Correct answer: Unavoidable

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

Question 55: Choose the correct words for the blank in this sentence: My teacher encouraged me to ____ the answer on my own, rather than simply asking him for the solution.

• look in
• looks up
• look up (Correct answer)
• looking for

Correct answer: look up

The phrasal verb 'look up' means to search for and find information, typically in a reference source or by researching. In this context, the teacher encourages the student to independently discover the answer, aligning perfectly with the meaning of 'look up.'

Question 56: Which inequality is represented by the statement 'twice a number is at most 14'?

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

Correct answer: 2n ≤ 14

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

Question 57: Evaluate: log₂(32)

• 5 (Correct answer)
• 8
• 4
• 6

Correct answer: 5

2⁵ = 32, so log₂(32) = 5.

Question 58: Ron could rely on his years of training to get him through even the toughest scenarios. Keeping the same meaning, rewrite this sentence beginning with: Due to his many years of training,

• even the hardest situations didn’t stop Ron (Correct answer)
• Ron was incompetent during many scenarios
• Ron never knew what to do, no matter the scenario
• Ron performed like a rookie in many situations

Correct answer: even the hardest situations didn’t stop Ron

The original sentence states Ron could rely on his training to get him through tough scenarios. The rewritten sentence, starting 'Due to his many years of training,' needs to show the positive outcome of this training. 'Even the hardest situations didn’t stop Ron' effectively conveys that his training enabled him to overcome challenges, preserving the original meaning.

Question 59: A car travels 150 miles on 5 gallons. What is its mileage per gallon?

• 35 mpg
• 750 mpg
• 25 mpg
• 30 mpg (Correct answer)

Correct answer: 30 mpg

150 ÷ 5 = 30 miles per gallon.

Question 60: Solve for x: |2x − 3| = 7

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

Correct answer: x = 5 or x = −2

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

Question 61: Paris, France, is a city that has long been known as a center of artistic and cultural expression. In the 1920s, Paris was home to many famous artists and writers from around the world, such as Picasso and Hemingway. What does the second sentence do?

• It states an effect.
• It reinforces the first (Correct answer)
• It draws a conclusion.
• It provides a contrast.

Correct answer: It reinforces the first

The first sentence asserts that Paris is known as a center of artistic and cultural expression. The second sentence then provides specific historical evidence, mentioning that in the 1920s, Paris was home to many famous artists and writers like Picasso and Hemingway. This specific example strongly supports and confirms the general claim made in the first sentence, thereby reinforcing it.

Question 62: If y = 2x + 5 and x = −3, what is y?

• −1 (Correct answer)
• 11
• 1
• −11

Correct answer: −1

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

Question 63: 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?

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

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

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

Correct answer: Infer it from details

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

Question 65: The first six days of the week are workdays, during which we _______________ to provide food and other essentials.

• worked hard
• work hard (Correct answer)
• worked harder
• working hard

Correct answer: work hard

The sentence describes a general truth or habitual action that occurs during workdays. For such recurring actions, the simple present tense is required. 'Work hard' is the correct simple present tense form, indicating a regular activity performed to achieve a goal.

Question 66: Which percentage is equivalent to the fraction <sup>5<\/sup>&frasl;<sub>8<\/sub>?

• 65.50%
• 62.50% (Correct answer)
• 72.50%
• 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 67: What is the vertex of the parabola y = (x − 3)² + 5?

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

Correct answer: (3, 5)

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

Question 68: Which of the following is the greatest?

• 0.65
• 0.62
• 0.67 (Correct answer)
• 0.668

Correct answer: 0.67

To compare decimals, align them by their decimal points and compare the digits from left to right. For 0.62, 0.65, 0.67, and 0.668, all start with '0.6'. Comparing the next digit, we have 2, 5, 7, and 6. Since 7 is the largest of these digits, 0.67 is the greatest number among the choices.

Question 69: 36÷1.5=

• 2.8
• 28
• 24 (Correct answer)
• 2.4

Correct answer: 24

To divide 36 by 1.5, it's helpful to eliminate the decimal in the divisor. Multiply both the dividend (36) and the divisor (1.5) by 10 to get 360 ÷ 15. Performing this division, 360 divided by 15 equals 24.

Question 70: Which sentence uses a transition word that signals an addition of information?

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

Correct answer: Furthermore, costs increased.

'Furthermore' adds more information to a previous point.

Question 71: Choose the correct preposition: She is good ___ math.

• at (Correct answer)
• of
• on
• in

Correct answer: at

"Good at" is the standard expression for skill in something.

Question 72: What is the amplitude of y = 4sin(2x)?

• 2
• π
• 4 (Correct answer)
• 8

Correct answer: 4

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

Question 73: A recipe uses 2.5 cups of flour for 12 cookies. How many cups are needed for 36 cookies?

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

Correct answer: 7.5 cups

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

Question 74: What is 2/5 of 35?

• 10
• 12
• 14 (Correct answer)
• 15

Correct answer: 14

35 divided by 5 is 7, and 7 × 2 = 14.

Question 75: 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 expands on the first
• It gives an example.
• It states an effect. (Correct answer)
• It contrasts with the first.

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 76: "Nearly half of all marketers say Twitter is their go-to network for __________ customers, according to social media statistics."

• engage to
• engaging to
• engaging with

The preposition "for" is typically followed by a gerund (verb + -ing) when indicating purpose. Additionally, the verb "engage" commonly takes the preposition "with" when referring to interacting or connecting with people or entities. Therefore, "engaging with" is the correct and idiomatic phrase to describe the marketers' purpose.

Question 77: 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 difficult
• Exercise is expensive

Correct answer: Exercise has many benefits

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

Question 78: Which of the following is the inverse function of f(x) = 3x − 6?

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

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 79: 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 80: Which version correctly fixes the fragment: "Because the bus was late."?

• Because the bus was late, we missed the meeting. (Correct answer)
• Because the bus was late.
• The bus. Because it was late.
• Late was the bus because.

Correct answer: Because the bus was late, we missed the meeting.

Adding an independent clause completes the thought left hanging by the dependent clause.

Question 81: Which equation represents exponential decay?

• y = x²
• y = 3(0.8)ˣ (Correct answer)
• y = 5 + 2x
• 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 82: Dr. Benway looked forward to receiving tenure after he had been teaching at the university for 20 years. What will happen to Dr. Benway’s job when he receives tenure?

• He will be fired.
• He will retire from his job.
• He will get a promotion.
• He will have a greater guarantee of job security. (Correct answer)

Correct answer: He will have a greater guarantee of job security.

In academia, tenure is a status granted to a professor after a probationary period, providing them with permanent employment and significant protection against dismissal. This greatly increases their job security. Therefore, receiving tenure means Dr. Benway will have a greater guarantee of job security.

Question 83: Which value of x satisfies 2^(x+1) = 16?

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

Correct answer: x = 3

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

Question 84: Two passages discuss the same event but draw opposite conclusions. This relationship is best described as:

• Repetition
• Sequential steps
• Cause and effect
• Contrasting viewpoints (Correct answer)

Correct answer: Contrasting viewpoints

Opposite conclusions on one topic show contrasting viewpoints.

Question 85: Which of the following is a rational number?

• π
• √2
• √9 (Correct answer)
• √5

Correct answer: √9

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

Question 86: <sup>1<\/sup>&frasl;<sub>3<\/sub> of 250 is approximately ____.

• 70
• 100
• 85 (Correct answer)
• 50

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 87: Identify the error: "The list of items are on the desk."

• Pronoun error
• No error
• Subject-verb agreement (Correct answer)
• Verb tense

Correct answer: Subject-verb agreement

The subject "list" is singular, so the verb should be "is."

Question 88: Social studies classes focus on the complexity of our social environment. The subject combines the study of history and the social sciences and promotes skills in citizenship. What does the second sentence do?

• It states an effect.
• It expands on the first sentence. (Correct answer)
• It proposes a solution.
• It makes a contrast.

Correct answer: It expands on the first sentence.

The first sentence makes a general statement about the focus of social studies classes. The second sentence then elaborates on this by specifying what the subject combines (history and social sciences) and what skills it promotes (citizenship). This provides more detail and depth to the initial statement, thus expanding on it.

Question 89: A class has 30 students and 40% are boys. How many boys are there?

• 18
• 10
• 12 (Correct answer)
• 15

Correct answer: 12

40% of 30 is 0.40 × 30 = 12 boys.

Question 90: (-3)(2+6)⁄4 - 2 =

• -8 (Correct answer)
• 6
• 4
• -6

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 91: Solve for x: 5x − 3 = 2x + 9

• x = 2
• x = 3
• x = 4 (Correct answer)
• 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 92: A store sells a jacket for $120 after applying a 20% discount. What was the original price?

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

Correct answer: $150

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

Question 93: Select the correct verb form: If I ___ rich, I would travel.

• be
• am
• was
• were (Correct answer)

Correct answer: were

"Were" is used in hypothetical conditional sentences with "if."

Question 94: The Midwest is experiencing its worst drought in 15 years. Corn and soybean prices are expected to be very high this year. What does the second sentence do?

• It gives an example.
• It states an effect. (Correct answer)
• It analyzes the statement made in the first.
• It restates the idea found in the first.

Correct answer: It states an effect.

The first sentence describes a drought, which is a cause of agricultural problems. The second sentence then states that 'Corn and soybean prices are expected to be very high this year,' which is a direct consequence or result of the drought. Therefore, the second sentence describes an effect of the situation presented in the first.

Question 95: Solve the system: 2x + y = 7 and x − y = 2.

• x = 3, y = 1 (Correct answer)
• x = 4, y = −1
• x = 1, y = 5
• 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 96: What is 6 × 1 1/2?

• 7 1/2
• 6 1/2
• 9 (Correct answer)
• 8

Correct answer: 9

6 × 3/2 = 18/2 = 9.

Question 97: Read: 'The committee postponed the meeting until further notice.' What does 'postponed' mean?

• Attended
• Started early
• Delayed to a later time (Correct answer)
• Cancelled forever

Correct answer: Delayed to a later time

'Postponed' means to delay an event to a later time.

Question 98: A passage describes a character clenching her fists and speaking in short, clipped sentences. What can the reader infer about her mood?

• She is joyful
• She is angry (Correct answer)
• She is sleepy
• She is bored

Correct answer: She is angry

Clenched fists and clipped speech signal anger or tension.

Question 99: What are the solutions to x² − 5x + 6 = 0?

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

Correct answer: x = 2 and x = 3

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

Question 100: What is the remainder when x³ − 2x + 4 is divided by (x − 1)?

• 0
• 3 (Correct answer)
• 2
• 1

Correct answer: 3

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

Question 101: What is the slope of the line passing through (2, 3) and (6, 11)?

• 1
• 2 (Correct answer)
• 4
• 3

Correct answer: 2

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

Question 102: What is the value of 4³ ÷ 2²?

• 4
• 8
• 16 (Correct answer)
• 32

Correct answer: 16

4³ = 64 and 2² = 4, so 64 ÷ 4 = 16.

Question 103: A car travels 180 miles in 3 hours. At the same rate, how far will it travel in 5 hours?

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

Correct answer: 300 miles

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

Question 104: Which word is an antonym for 'generous'?

• Kind
• Helpful
• Stingy (Correct answer)
• Wealthy

Correct answer: Stingy

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

Question 105: 10 – 2.267 =

• 6.334
• 7.733 (Correct answer)
• 77.33
• 8.233

Correct answer: 7.733

To subtract decimals, align the numbers by their decimal points. You can rewrite 10 as 10.000 to match the number of decimal places in 2.267. Subtracting 2.267 from 10.000 yields 7.733.