Your FREE ACCUPLACER Practice Test 2026 – 450+ Q&A

ACCUPLACER Practice Questions

1. Read the sentence: "The new intern's diligent work ethic impressed her supervisor, who noted that she completed every assignment ahead of schedule." The word "diligent" most nearly means
   • Hardworking
   • Careless
   • Occasional
   • Reluctant

   Correct answer: Hardworking

   Hardworking is correct because finishing every assignment early demonstrates steady, persistent effort, which is what diligent means. Careless and reluctant contradict that effort, and occasional does not fit someone who completes all work ahead of schedule.

2. Read the sentence: "Rather than confront the problem, the manager chose to circumvent it by quietly reassigning the troublesome account." The word "circumvent" most nearly means
   • Solve directly
   • Find a way around
   • Publicly announce
   • Make worse

   Correct answer: Find a way around

   Find a way around is correct because quietly reassigning the account instead of confronting the issue shows the manager avoided it by going around it, which is what circumvent means. Solving it directly and announcing it contradict the quiet avoidance, and making it worse is not implied.

3. Read the sentence: "The critic praised the novel's prose but lamented its tedious middle chapters, which dragged on without purpose." The word "tedious" most nearly means
   • Thrilling
   • Brief
   • Boring
   • Elegant

   Correct answer: Boring

   Boring is correct because chapters that "dragged on without purpose" and drew a complaint describe dull, wearisome reading, which is what tedious means. Thrilling and elegant would invite praise, not a lament, and brief contradicts chapters that dragged on.

4. Read the sentence: "Witnesses described the storm's aftermath as utter desolation, with not a single building left standing." The word "desolation" most nearly means
   • Celebration
   • Mild damage
   • Rapid rebuilding
   • Complete ruin and emptiness

   Correct answer: Complete ruin and emptiness

   Complete ruin and emptiness is correct because no building left standing signals total devastation, which is what desolation means. Celebration and rebuilding contradict the destruction, and mild damage understates a scene where nothing remains.

5. Read the sentence: "The chef was known for her frugal use of ingredients, wasting nothing and stretching every dollar." The word "frugal" most nearly means
   • Thrifty
   • Wasteful
   • Lavish
   • Reckless

   Correct answer: Thrifty

   Thrifty is correct because wasting nothing and stretching every dollar describes careful, economical use, which is what frugal means. Wasteful, lavish, and reckless all describe the opposite of someone who avoids waste.

6. Read the sentence: "His apology seemed perfunctory, delivered in a flat voice without a hint of genuine remorse." The word "perfunctory" most nearly means
   • Heartfelt
   • Done with little care
   • Lengthy
   • Angry

   Correct answer: Done with little care

   Done with little care is correct because a flat, unfeeling apology lacking genuine remorse is one offered as a routine gesture, which is what perfunctory means. Heartfelt contradicts the lack of remorse, and the sentence does not suggest the apology was lengthy or angry.

7. Read the sentence: "The detective remained skeptical of the witness's account, which kept changing each time she retold it." The word "skeptical" most nearly means
   • Convinced
   • Amused
   • Doubtful
   • Fearful

   Correct answer: Doubtful

   Doubtful is correct because a story that changes with each retelling would prompt doubt, and skeptical means inclined to question or disbelieve. Convinced is the opposite, and amused or fearful are not supported by the detective's questioning attitude.

8. Read the sentence: "The volunteers worked tirelessly, their efforts proving indispensable to the relief effort's success." The word "indispensable" most nearly means
   • Optional
   • Harmful
   • Temporary
   • Absolutely essential

   Correct answer: Absolutely essential

   Absolutely essential is correct because efforts that the relief effort's success depended on could not be done without, which is the meaning of indispensable. Optional is the opposite, and the sentence gives no sense that the efforts were harmful or temporary.

9. Read the sentence: "Once a vibrant gathering place, the plaza now stood derelict, its fountains dry and its benches broken." The word "derelict" most nearly means
   • Abandoned and run-down
   • Crowded
   • Newly built
   • Beautifully restored

   Correct answer: Abandoned and run-down

   Abandoned and run-down is correct because dry fountains and broken benches describe a neglected, deteriorating space, which is what derelict means. Crowded contradicts the emptiness, and newly built or restored conflict with the decay described.

10. Read the sentence: "Her remarks were so ambiguous that listeners could not agree on what she had actually proposed." The word "ambiguous" most nearly means
    • Perfectly clear
    • Open to more than one interpretation
    • Extremely long
    • Deliberately rude

    Correct answer: Open to more than one interpretation

    Open to more than one interpretation is correct because listeners' disagreement about her meaning shows the remarks could be understood in different ways, which is what ambiguous means. Perfectly clear is the opposite, and the sentence does not address length or rudeness.

11. Read the sentence: "The coach praised the rookie's tenacity, noting that he refused to quit even when the game seemed lost." The word "tenacity" most nearly means
    • Talent
    • Speed
    • Persistence
    • Luck

    Correct answer: Persistence

    Persistence is correct because refusing to quit when the game seemed lost shows determined, unyielding effort, which is what tenacity means. Talent, speed, and luck describe other qualities not implied by the refusal to give up.

12. Read the sentence: "The lawyer's argument was compelling, drawing even the most doubtful jurors toward her conclusion." The word "compelling" most nearly means
    • Confusing
    • Lengthy
    • Humorous
    • Convincing

    Correct answer: Convincing

    Convincing is correct because an argument that draws doubtful jurors toward a conclusion is persuasive and forceful, which is what compelling means. Confusing would push jurors away, and the sentence says nothing about length or humor.

13. A passage about deep-sea creatures states: "In waters where sunlight never reaches, many animals generate their own light to lure prey and find mates." Based on this sentence, the reader can conclude that
    • Self-produced light serves practical survival purposes for these animals
    • All deep-sea animals are blind
    • Sunlight reaches the deepest oceans
    • Deep-sea animals do not need to eat

    Correct answer: Self-produced light serves practical survival purposes for these animals

    Self-produced light serves practical survival purposes for these animals is correct because the sentence states the light is used to lure prey and attract mates, both survival functions. The other choices add unsupported claims about blindness, sunlight reaching the depths, or animals not needing to eat.

14. A passage notes: "The museum reopened with free admission on weekends, and within a month attendance had tripled compared with the previous year." Which conclusion does the passage best support?
    • The museum lost money by reopening
    • Removing the weekend fee likely increased visitor numbers
    • Visitors disliked the museum's exhibits
    • The museum will close again soon

    Correct answer: Removing the weekend fee likely increased visitor numbers

    Removing the weekend fee likely increased visitor numbers is correct because attendance tripled right after free weekend admission began, linking the change to higher turnout. The passage provides no evidence of lost money, disliked exhibits, or an upcoming closure.

15. A character in a story "checked the locks twice, peered out the window, and kept the phone within arm's reach all night." These details most strongly suggest that the character feels
    • Bored
    • Joyful
    • Anxious
    • Confident

    Correct answer: Anxious

    Anxious is correct because repeatedly checking locks, watching the window, and keeping the phone close are protective behaviors that reveal worry or fear. Boredom, joy, and confidence do not match such cautious, on-edge actions.

16. A passage explicitly states: "The factory installed new filters in March, and by June local air-quality readings had improved noticeably." According to the passage, what happened first?
    • Air quality improved
    • The factory closed
    • Residents filed complaints
    • The filters were installed

    Correct answer: The filters were installed

    The filters were installed is correct because the passage places the March installation before the June improvement, making it the earlier event. Air quality improving comes afterward, and the passage never mentions a closure or complaints.

17. A passage describes a forest where, after wolves were reintroduced, deer grazing decreased, young trees recovered, and riverbanks grew more stable. The central idea of this passage is that
    • A single species can influence an entire ecosystem
    • Wolves are dangerous to humans
    • Removing a single species had no effect on the forest
    • Deer are the most important forest animal

    Correct answer: A single species can influence an entire ecosystem

    A single species can influence an entire ecosystem is correct because the passage traces how reintroducing wolves changed grazing, trees, and riverbanks throughout the forest. The other choices focus on danger, deny any effect, or overstate the role of deer.

18. A passage explains that learning a second language can improve memory, delay cognitive decline, and broaden career options. Which statement best captures the central idea?
    • Second languages are only useful for travel
    • Learning another language offers several wide-ranging benefits
    • Memory cannot be improved by any activity
    • Most people find languages impossible to learn

    Correct answer: Learning another language offers several wide-ranging benefits

    Learning another language offers several wide-ranging benefits is correct because it unites the cognitive and career advantages the passage lists. The other options limit the value to travel, deny that memory can improve, or claim languages are impossible, none of which is the passage's point.

19. A poem repeatedly describes seeds buried in winter soil, buds breaking through snow, and a single green shoot rising from ash. These images together most strongly develop a theme about
    • The inevitability of failure
    • The dangers of cold weather
    • Renewal and the persistence of life
    • The importance of farming

    Correct answer: Renewal and the persistence of life

    Renewal and the persistence of life is correct because seeds, buds breaking through snow, and a shoot rising from ash all suggest new life emerging despite harsh conditions. Failure, cold-weather danger, and farming are not the unifying idea behind these images of growth.

20. Which choice best states the central idea of a passage describing how a city reduced traffic by expanding bus routes, adding bike lanes, and building park-and-ride lots?
    • Cars are the only practical way to travel
    • Public transportation is too expensive to build
    • Bike lanes are dangerous for cyclists
    • The city used several coordinated strategies to ease traffic

    Correct answer: The city used several coordinated strategies to ease traffic

    The city used several coordinated strategies to ease traffic is correct because it ties together the three measures the passage credits with reducing congestion. The other options dismiss alternatives to cars, call transit unaffordable, or raise a danger the passage does not discuss.

21. A passage states: "As temperatures rise, glaciers melt; as glaciers melt, sea levels climb; and as seas climb, coastal communities face greater flooding." Which best summarizes this relationship?
    • A linked chain in which each event triggers the next
    • A comparison of two unrelated regions
    • A definition of several scientific terms
    • A persuasive call to relocate cities

    Correct answer: A linked chain in which each event triggers the next

    A linked chain in which each event triggers the next is correct because rising temperatures lead to melting, which leads to higher seas, which leads to flooding. The passage is not a comparison, a set of definitions, or a relocation argument.

22. A passage reads: "Unlike the gradual erosion that shapes most coastlines over centuries, a tsunami can reshape a shoreline in a matter of minutes." The relationship the sentence establishes is one of
    • Cause and effect
    • Contrast between two rates of change
    • A step-by-step procedure
    • A list of examples

    Correct answer: Contrast between two rates of change

    Contrast between two rates of change is correct because the word "unlike" sets slow, centuries-long erosion against a tsunami's near-instant reshaping. The sentence does not trace a cause to an effect, lay out steps, or list examples.

23. A passage describes a recipe: "Combine the dry ingredients, then fold in the wet mixture, and finally bake until golden." Which summary best captures the passage?
    • It compares two kinds of baking
    • It argues that baking is difficult
    • It lists ordered steps for preparing a dish
    • It defines the word 'fold'

    Correct answer: It lists ordered steps for preparing a dish

    It lists ordered steps for preparing a dish is correct because "then" and "finally" mark a sequence of actions for making the food. The passage does not compare baking methods, make an argument, or define a term.

24. A passage about two scientists notes that "both pursued the same discovery, yet one worked in lavishly funded laboratories while the other relied on borrowed equipment." This sentence primarily highlights
    • A step-by-step research method
    • The definition of a laboratory
    • A warning about scientific failure
    • A similarity in goals alongside a difference in resources

    Correct answer: A similarity in goals alongside a difference in resources

    A similarity in goals alongside a difference in resources is correct because the sentence pairs a shared aim ("the same discovery") with contrasting means (lavish funding versus borrowed equipment). It does not describe a method, define a term, or issue a warning.

25. A writer describes a winter morning as having "air so sharp it seemed to bite at exposed skin." The word "bite" is used here to
    • Convey how painfully cold the air felt
    • Describe an actual animal attack
    • Explain how snow forms
    • Praise the beauty of winter

    Correct answer: Convey how painfully cold the air felt

    Convey how painfully cold the air felt is correct because "bite" is figurative, comparing the sting of cold air to a physical bite to stress its intensity. It is not a literal attack, an explanation of snow, or praise for winter's beauty.

26. An author writes that a politician "peddled empty promises to a hopeful crowd." The word "peddled" mainly serves to
    • Praise the politician's generosity
    • Suggest the promises were sold cheaply and dishonestly
    • Describe a literal marketplace
    • Explain election procedures

    Correct answer: Suggest the promises were sold cheaply and dishonestly

    Suggest the promises were sold cheaply and dishonestly is correct because "peddled," paired with "empty promises," casts the politician as hawking worthless goods, a critical word choice. It does not praise generosity, depict a real market, or explain procedures.

27. A nature writer calls a mountain stream "a ribbon of silver threading through the valley." This description is intended primarily to
    • Give the stream's exact depth
    • Warn hikers about the water
    • Create a vivid, graceful image of the stream
    • List the valley's wildlife

    Correct answer: Create a vivid, graceful image of the stream

    Create a vivid, graceful image of the stream is correct because comparing the water to a silver ribbon threading the valley paints an elegant visual picture. The phrase gives no measurements, no warning, and no list of wildlife.

28. An author describes a crowded subway car as "a sea of weary faces swaying in unison with every lurch." The phrase "sea of weary faces" mainly emphasizes
    • The cleanliness of the subway
    • The speed of the train
    • The cost of a ticket
    • The vast number of tired passengers

    Correct answer: The vast number of tired passengers

    The vast number of tired passengers is correct because comparing the faces to a "sea" stresses how many people there are, and "weary" stresses their tiredness. The phrase says nothing about cleanliness, speed, or fares.

29. A passage first explains how photosynthesis works, then describes how cellular respiration works, and finally points out how the two processes mirror each other. This text is organized primarily by
    • Explaining two processes and then comparing them
    • Listing events in the order they occurred
    • Arguing for a single solution to a problem
    • Describing objects by their physical location

    Correct answer: Explaining two processes and then comparing them

    Explaining two processes and then comparing them is correct because the passage presents each process and concludes by examining how they relate. It is not arranged by chronological time, by a problem-solution argument, or by spatial location.

30. A passage begins with a startling statistic about food waste, then explains the causes, and ends by proposing community composting. The opening statistic most likely functions to
    • Conclude the discussion
    • Grab the reader's attention and introduce the topic
    • List the steps of composting
    • Contradict the proposed solution

    Correct answer: Grab the reader's attention and introduce the topic

    Grab the reader's attention and introduce the topic is correct because a striking statistic at the start of a passage draws readers in and frames the issue to follow. It does not conclude the passage, list steps, or contradict the later solution.

31. A passage about a river is arranged by following the water from its mountain source, through the valley towns, and out to the coastal delta. This organization is best described as
    • Chronological order
    • Comparison and contrast
    • Spatial order that follows a physical path
    • Problem and solution

    Correct answer: Spatial order that follows a physical path

    Spatial order that follows a physical path is correct because the passage moves along the river's course from source to delta, organizing by location. It is not based on time, on comparing items, or on solving a problem.

32. Within an essay, a paragraph beginning "For instance," follows a general claim that exercise improves mood. This transition signals that the paragraph will
    • Contradict the claim about exercise
    • Change the topic to nutrition
    • Summarize the entire essay
    • Provide a specific example supporting the claim

    Correct answer: Provide a specific example supporting the claim

    Provide a specific example supporting the claim is correct because "for instance" introduces an illustration of the preceding general statement. The transition does not signal contradiction, a topic change, or a summary.

33. A memoir is written entirely in the first person, recounting events as "the day I left home" and "what I learned along the way." This point of view allows the reader to
    • Experience events through the narrator's personal perspective
    • See the thoughts of every character equally
    • Read an objective, fact-only report
    • View the story from a distant outsider

    Correct answer: Experience events through the narrator's personal perspective

    Experience events through the narrator's personal perspective is correct because first-person narration filters the story through one individual's experiences and reflections. It does not give equal access to every character's mind, an objective report, or an outsider's distant view.

34. A passage about recycling closes: "Every bottle you sort today is a gift to the generation that inherits this planet." The author's primary purpose is to
    • Entertain readers with a joke
    • Motivate readers to recycle
    • Explain the chemistry of plastics
    • Describe a recycling plant's layout

    Correct answer: Motivate readers to recycle

    Motivate readers to recycle is correct because framing sorting bottles as a gift to future generations is meant to inspire action. The sentence is not a joke, a chemistry lesson, or a description of a plant's layout.

35. A reviewer writes about a film: "The cinematography dazzles, but a hollow script leaves the audience strangely unmoved." The reviewer's overall attitude toward the film is best described as
    • Wholly enthusiastic
    • Completely indifferent
    • Mixed, with both praise and criticism
    • Openly hostile from start to finish

    Correct answer: Mixed, with both praise and criticism

    Mixed, with both praise and criticism is correct because the reviewer admires the cinematography yet faults the hollow script. The attitude is neither wholly enthusiastic nor completely hostile, and indifference is ruled out by the strong opinions expressed.

36. A how-to article on changing a tire is written in short, numbered commands such as "Loosen the lug nuts" and "Lift the car with the jack." The author's main purpose is to
    • Persuade readers to buy new tires
    • Entertain readers with a road-trip story
    • Argue that driving is dangerous
    • Instruct readers how to complete a task

    Correct answer: Instruct readers how to complete a task

    Instruct readers how to complete a task is correct because numbered commands walking through each step are meant to guide readers through changing a tire. The article is not a sales pitch, a story, or an argument about danger.

37. A passage explains the water cycle in neutral, factual language, defining evaporation, condensation, and precipitation without offering any opinion. The author's primary purpose is most likely to
    • Inform readers about a natural process
    • Persuade readers to conserve water
    • Entertain readers with a fictional tale
    • Criticize weather forecasters

    Correct answer: Inform readers about a natural process

    Inform readers about a natural process is correct because neutral, definition-based explanation of the water cycle aims to teach rather than argue or amuse. The passage offers no persuasion, fiction, or criticism.

38. An author writes a humorous, exaggerated account of a disastrous family camping trip, ending with the line, "And that, my friends, is why we now vacation indoors." The author's main purpose is to
    • Instruct readers on camping safety
    • Entertain readers by recounting a funny experience
    • Persuade readers to buy camping gear
    • Report objective weather data

    Correct answer: Entertain readers by recounting a funny experience

    Entertain readers by recounting a funny experience is correct because the exaggerated mishaps and joking closing line are meant to amuse. The passage is not a safety lesson, a sales pitch, or a weather report.

39. An author claims that cities should plant more trees and supports the claim by noting that tree-lined streets lower summer temperatures and reduce cooling costs. The information about temperature and costs functions as
    • A counterargument the author dismisses
    • An unrelated personal anecdote
    • Evidence backing the author's recommendation
    • A definition of the word 'tree'

    Correct answer: Evidence backing the author's recommendation

    Evidence backing the author's recommendation is correct because the cooling and cost data are offered to justify planting more trees. They are not a dismissed counterargument, an unrelated anecdote, or a definition.

40. An author argues that homework should be reduced and acknowledges, "Of course, some practice is valuable," before continuing, "but hours of nightly assignments leave students exhausted." The phrase "some practice is valuable" serves to
    • Abandon the author's main argument
    • Provide statistical proof
    • Introduce an unrelated topic
    • Concede a point before reinforcing the main claim

    Correct answer: Concede a point before reinforcing the main claim

    Concede a point before reinforcing the main claim is correct because the author admits practice has value, then uses "but" to return to the argument against excessive homework. The concession does not abandon the argument, give statistics, or introduce a new topic.

41. An author asserts that a town's new park "has made the community healthier," offering only the observation that the park looks beautiful. A careful reader should recognize that this argument is weak because
    • Beauty does not by itself prove improved health
    • Parks can never affect health
    • The author used too many statistics
    • The claim is about a different town

    Correct answer: Beauty does not by itself prove improved health

    Beauty does not by itself prove improved health is correct because an attractive appearance is not evidence that residents became healthier, leaving the claim unsupported. The argument is not weak because parks never matter, because of excess statistics, or because of a different town.

42. An editorial states: "Opponents warn that the bridge will be costly, and they are right that the price is high; however, the jobs and commerce it creates will repay that cost many times over." The author responds to the opponents by
    • Denying that the bridge costs anything
    • Acknowledging their concern while arguing the benefits outweigh it
    • Agreeing the bridge should not be built
    • Ignoring the cost issue completely

    Correct answer: Acknowledging their concern while arguing the benefits outweigh it

    Acknowledging their concern while arguing the benefits outweigh it is correct because the author grants that the cost is high, then claims the jobs and commerce justify it. The author does not deny the cost, agree against building, or ignore the concern.

43. Passage 1 argues that standardized tests fairly measure student knowledge. Passage 2 contends that such tests favor students who can afford expensive preparation. The relationship between the passages is best described as
    • One passage restating the other
    • Two passages about completely different subjects
    • Two passages presenting conflicting views on the same issue
    • One passage providing data for the other

    Correct answer: Two passages presenting conflicting views on the same issue

    Two passages presenting conflicting views on the same issue is correct because both address standardized testing but disagree about its fairness. Neither restates nor supplies data for the other, and they share a subject rather than being unrelated.

44. Passage 1 is a first-person diary entry from a soldier describing a famous battle. Passage 2 is a textbook account of the same battle with dates and troop numbers. Reading both together would most help a reader
    • Decide which author is more talented
    • Prove the diary entry is fictional
    • Ignore the textbook's facts
    • Understand the battle through both personal experience and factual record

    Correct answer: Understand the battle through both personal experience and factual record

    Understand the battle through both personal experience and factual record is correct because the diary supplies a human viewpoint while the textbook supplies verified facts, together giving a fuller picture. The other choices misuse the pairing by judging talent, disproving, or discarding information.

45. Passage 1 presents data showing that a new medication lowers blood pressure. Passage 2, by a different author, cautions that the same medication has not been tested on older patients. Passage 2 relates to Passage 1 by
    • Identifying a limitation of the findings in Passage 1
    • Repeating Passage 1 word for word
    • Telling an unrelated fictional story
    • Translating Passage 1 into simpler terms

    Correct answer: Identifying a limitation of the findings in Passage 1

    Identifying a limitation of the findings in Passage 1 is correct because Passage 2 points out a gap, the lack of testing on older patients, that qualifies the first passage's positive results. It does not repeat, fictionalize, or merely simplify Passage 1.

46. Read the sentence: "The hikers grew apprehensive as dark clouds gathered and the wind began to howl through the canyon." The word "apprehensive" most nearly means
    • Delighted
    • Uneasy and worried
    • Exhausted
    • Indifferent

    Correct answer: Uneasy and worried

    Uneasy and worried is correct because gathering dark clouds and a howling wind would create anxious anticipation of trouble, which is what apprehensive means. Delighted and indifferent contradict that worry, and exhausted describes tiredness rather than dread.

47. Read the sentence: "The senator's speech was so verbose that many listeners lost track of her actual proposal amid the endless words." The word "verbose" most nearly means
    • Extremely brief
    • Perfectly organized
    • Using too many words
    • Spoken in a whisper

    Correct answer: Using too many words

    Using too many words is correct because listeners lost the proposal "amid the endless words," showing the speech was wordy, which is what verbose means. Extremely brief is the opposite, and the sentence says nothing about organization or volume.

48. Read the sentence: "Despite the team's loss, the coach remained sanguine, certain that the next season would bring victory." The word "sanguine" most nearly means
    • Furious
    • Confused
    • Optimistic
    • Indifferent

    Correct answer: Optimistic

    Optimistic is correct because being "certain that the next season would bring victory" despite a loss shows a hopeful outlook, which is what sanguine means. Furious and confused contradict that calm hope, and indifferent conflicts with the coach's certainty about success.

49. Read the sentence: "The committee reached a unanimous decision, every single member voting the same way without objection." The word "unanimous" most nearly means
    • Decided by one person
    • Agreed upon by everyone
    • Delayed indefinitely
    • Filled with arguments

    Correct answer: Agreed upon by everyone

    Agreed upon by everyone is correct because "every single member voting the same way without objection" describes total agreement, which is what unanimous means. Decided by one person and filled with arguments contradict that agreement, and the vote was not delayed.

50. Read the sentence: "The toddler's curiosity was insatiable; no answer ever seemed to satisfy her endless stream of questions." The word "insatiable" most nearly means
    • Easily satisfied
    • Occasional
    • Quickly tired
    • Impossible to satisfy

    Correct answer: Impossible to satisfy

    Impossible to satisfy is correct because no answer ever satisfied her endless questions, showing a hunger that cannot be filled, which is what insatiable means. Easily satisfied is the opposite, and occasional and quickly tired contradict the endless, persistent curiosity.

51. Read the sentence: "The old contract was rendered obsolete the moment the new technology made its methods completely outdated." The word "obsolete" most nearly means
    • Brand new
    • No longer useful or current
    • Very expensive
    • Highly secret

    Correct answer: No longer useful or current

    No longer useful or current is correct because new technology made the contract's methods "completely outdated," which is what obsolete means. Brand new is the opposite, and the sentence does not mention cost or secrecy.

52. Read the sentence: "Her benevolent nature showed in the countless hours she donated to feeding and sheltering strangers." The word "benevolent" most nearly means
    • Kind and generous
    • Selfish
    • Shy
    • Wealthy

    Correct answer: Kind and generous

    Kind and generous is correct because donating countless hours to help strangers shows goodwill toward others, which is what benevolent means. Selfish is the opposite, and shy and wealthy describe traits the sentence does not support.

53. Read the sentence: "The negotiations finally collapsed when neither side would relinquish its demands, even slightly." The word "relinquish" most nearly means
    • Increase
    • Write down
    • Give up
    • Celebrate

    Correct answer: Give up

    Give up is correct because neither side would let go of its demands, causing the talks to collapse, and relinquish means to surrender or release something. Increase contradicts the idea of yielding, and writing down or celebrating do not fit the failed negotiation.

54. Read the sentence: "The professor's lecture was so esoteric that only a handful of specialists in the room could follow it." The word "esoteric" most nearly means
    • Widely popular
    • Understood by only a few
    • Very loud
    • Completely false

    Correct answer: Understood by only a few

    Understood by only a few is correct because just a handful of specialists could follow the lecture, showing it was meant for a small, knowledgeable group, which is what esoteric means. Widely popular is the opposite, and the sentence does not address volume or truthfulness.

55. Read the sentence: "After the scandal, the company worked hard to placate angry customers with refunds and public apologies." The word "placate" most nearly means
    • Anger further
    • Ignore
    • Investigate
    • Calm or soothe

    Correct answer: Calm or soothe

    Calm or soothe is correct because offering refunds and apologies to angry customers is an effort to pacify them, which is what placate means. Anger further is the opposite, and the sentence describes action rather than ignoring or investigating.

56. Read the sentence: "The witness gave a candid account, admitting her own mistakes without trying to hide anything." The word "candid" most nearly means
    • Dishonest
    • Frightened
    • Honest and open
    • Rehearsed

    Correct answer: Honest and open

    Honest and open is correct because admitting her own mistakes without hiding anything shows frankness, which is what candid means. Dishonest is the opposite, and frightened and rehearsed are not supported by her willingness to be truthful.

57. Read the sentence: "The reviewer dismissed the sequel as a mediocre imitation, neither bad enough to mock nor good enough to praise." The word "mediocre" most nearly means
    • Outstanding
    • Only average or ordinary
    • Extremely original
    • Deeply moving

    Correct answer: Only average or ordinary

    Only average or ordinary is correct because a work that is neither bad enough to mock nor good enough to praise is unremarkable, which is what mediocre means. Outstanding, original, and deeply moving all describe quality the reviewer denies the sequel.

58. Read the sentence: "The mountain trail was so precarious that one wrong step could send a hiker tumbling down the cliff." The word "precarious" most nearly means
    • Perfectly safe
    • Dangerously unstable
    • Very wide
    • Well lit

    Correct answer: Dangerously unstable

    Dangerously unstable is correct because a single wrong step risking a fall off the cliff describes a risky, insecure trail, which is what precarious means. Perfectly safe is the opposite, and the sentence says nothing about width or lighting.

59. Read the sentence: "The diplomat's tactful reply avoided offense while still making the nation's position perfectly clear." The word "tactful" most nearly means
    • Careful to avoid giving offense
    • Rude
    • Extremely long
    • Easily angered

    Correct answer: Careful to avoid giving offense

    Careful to avoid giving offense is correct because the reply avoided offending anyone while still being clear, which is exactly what tactful means. Rude and easily angered are opposites, and the sentence does not comment on length.

60. A passage states: "Because the bakery began composting its scraps and switched to reusable containers, the amount of trash it sent to the landfill dropped sharply." Based on this sentence, the reader can conclude that
    • The bakery's changes reduced its waste
    • The bakery went out of business
    • Composting increased the bakery's trash
    • Customers complained about the containers

    Correct answer: The bakery's changes reduced its waste

    The bakery's changes reduced its waste is correct because the sentence directly links composting and reusable containers to a sharp drop in landfill trash. The passage gives no evidence the bakery closed, that trash rose, or that customers complained.

61. A narrator describes a man who "slid the unopened bills into a drawer, avoided his ringing phone, and crossed the street to dodge his landlord." These details most strongly suggest that the man is
    • Struggling with money troubles
    • Celebrating good fortune
    • Planning a long vacation
    • Searching for a new job offer

    Correct answer: Struggling with money troubles

    Struggling with money troubles is correct because hiding bills, dodging the phone, and avoiding the landlord all point to debt he cannot pay. Celebrating fortune contradicts the avoidance, and nothing suggests a vacation or a job search.

62. A passage explicitly states: "The library extended its hours in September, hired two additional staff members in October, and reported record book checkouts in November." According to the passage, which event happened last?
    • Hours were extended
    • Staff members were hired
    • Record checkouts were reported
    • The library closed for repairs

    Correct answer: Record checkouts were reported

    Record checkouts were reported is correct because the passage places November, the month of record checkouts, after the September and October events. Extending hours and hiring staff came earlier, and a closure is never mentioned.

63. A passage notes: "The remote village had no paved roads, yet every household owned a smartphone and relied on solar panels for power." From this, the reader can reasonably infer that
    • The village rejected all modern technology
    • Modern technology can reach places without traditional infrastructure
    • The village had abandoned electricity entirely
    • No one in the village could communicate

    Correct answer: Modern technology can reach places without traditional infrastructure

    Modern technology can reach places without traditional infrastructure is correct because the village had smartphones and solar power despite lacking paved roads. The other choices contradict the smartphones, solar panels, and communication the passage describes.

64. A passage describes how a small town's mural project brought neighbors together to paint, raised local pride, and drew tourists who spent money downtown. The central idea of this passage is that
    • A community art project produced several positive effects
    • Painting is a difficult skill to learn
    • Tourists rarely visit small towns
    • Murals fade quickly in the sun

    Correct answer: A community art project produced several positive effects

    A community art project produced several positive effects is correct because it unites the social, civic, and economic benefits the passage credits to the mural. The other choices focus on painting's difficulty, doubt tourism, or raise fading, none of which is the main point.

65. A passage explains that regular sleep strengthens immunity, sharpens focus, and stabilizes mood. Which statement best captures the central idea?
    • Sleep only matters for athletes
    • People rarely need more than a few hours of sleep
    • Focus cannot be improved by rest
    • Adequate sleep supports several aspects of health

    Correct answer: Adequate sleep supports several aspects of health

    Adequate sleep supports several aspects of health is correct because it gathers the immune, mental, and emotional benefits the passage lists. The other options limit sleep to athletes, minimize how much is needed, or deny that rest aids focus.

66. A short story follows a stubborn farmer who refuses help all season, watches his lone crop fail, and finally joins a cooperative the next spring. The story's theme is best described as
    • The superiority of working alone
    • The danger of changing your mind
    • The value of working together
    • The importance of fast machinery

    Correct answer: The value of working together

    The value of working together is correct because the farmer's solitary failure followed by success in a cooperative shows the benefits of cooperation. The other choices praise isolation, warn against change, or focus on machinery, none of which the story endorses.

67. Which choice best states the central idea of a passage describing how a hospital cut wait times by adding online check-in, opening more exam rooms, and retraining its front desk?
    • Hospitals can never reduce wait times
    • Online tools always frustrate patients
    • The hospital combined several measures to shorten patient waits
    • Exam rooms are expensive to build

    Correct answer: The hospital combined several measures to shorten patient waits

    The hospital combined several measures to shorten patient waits is correct because it ties together the three steps the passage credits with reducing waits. The other options deny progress, criticize online tools, or focus narrowly on cost.

68. A passage reads: "When the dam released too much water, the river flooded; when the river flooded, the fields were ruined; and when the fields were ruined, the harvest failed." Which best summarizes this relationship?
    • A comparison of two rivers
    • A list of unrelated facts
    • A set of step-by-step instructions
    • A chain in which each event leads to the next

    Correct answer: A chain in which each event leads to the next

    A chain in which each event leads to the next is correct because the released water causes flooding, which ruins the fields, which fails the harvest. The passage is not a comparison, an unrelated list, or a how-to procedure.

69. A passage reads: "Whereas the older model required hours of manual setup, the newer device configures itself in seconds." The relationship the sentence establishes is one of
    • Cause and effect
    • A numbered procedure
    • A definition of a term
    • Contrast between two devices

    Correct answer: Contrast between two devices

    Contrast between two devices is correct because "whereas" sets the slow manual older model against the fast self-configuring newer one. The sentence does not trace a cause to an effect, give numbered steps, or define a word.

70. A passage states: "First gather the documents, next verify each signature, then scan the pages, and finally upload the file." Which summary best captures the passage?
    • It argues that paperwork is unnecessary
    • It compares two filing systems
    • It lists ordered steps for completing a task
    • It defines the word 'signature'

    Correct answer: It lists ordered steps for completing a task

    It lists ordered steps for completing a task is correct because "first," "next," "then," and "finally" mark a sequence of actions. The passage makes no argument, comparison, or definition.

71. A passage notes that "the drought reduced the wheat supply, and as a result, bread prices in the region climbed steadily for months." The relationship the sentence establishes is one of
    • Cause and effect
    • Comparison of two crops
    • Spatial description
    • An unrelated list

    Correct answer: Cause and effect

    Cause and effect is correct because the drought reducing supply is the cause and the phrase "as a result" introduces the climbing bread prices as the effect. The sentence does not compare crops, describe locations, or list unrelated items.

72. A writer describes a busy newsroom where "phones erupted, keyboards clattered, and reporters shouted across a maze of desks." The word "erupted" is used here mainly to
    • Describe an actual volcano
    • Explain how telephones are built
    • Praise the quiet of the office
    • Convey the sudden, overwhelming burst of ringing

    Correct answer: Convey the sudden, overwhelming burst of ringing

    Convey the sudden, overwhelming burst of ringing is correct because "erupted" is figurative, likening the phones' sudden noise to an explosion to stress its intensity. It is not a literal volcano, an explanation of phone design, or praise for quiet.

73. An author writes that the executive "devoured every report on his desk before lunch." The word "devoured" mainly serves to
    • Describe an actual meal
    • Explain the rules of business
    • Emphasize how eagerly and quickly he read them
    • Criticize his table manners

    Correct answer: Emphasize how eagerly and quickly he read them

    Emphasize how eagerly and quickly he read them is correct because "devoured," applied to reports, figuratively compares his fast, hungry reading to eating. It does not describe a real meal, explain business rules, or comment on manners.

74. A travel writer calls a desert sunset "a slow fire spreading across the western sky." This description is intended primarily to
    • Create a vivid image of the glowing colors
    • Warn travelers of a wildfire
    • Give the sky's exact temperature
    • List the desert's plants

    Correct answer: Create a vivid image of the glowing colors

    Create a vivid image of the glowing colors is correct because comparing the sunset to a slow-spreading fire paints a striking picture of its warm, blazing hues. The phrase is not a wildfire warning, a temperature, or a list of plants.

75. An author describes a long meeting as "an endless desert of slides and droning voices." The phrase "endless desert" mainly emphasizes
    • The comfort of the meeting room
    • The dry, tedious, drawn-out nature of the meeting
    • The cost of the projector
    • The speed of the presentation

    Correct answer: The dry, tedious, drawn-out nature of the meeting

    The dry, tedious, drawn-out nature of the meeting is correct because comparing it to an endless desert stresses how dull and seemingly unending it felt. The phrase does not address comfort, cost, or speed.

76. A passage first describes the problem of plastic waste in the ocean, then presents a new biodegradable packaging as a remedy. This text is organized primarily by
    • Listing events in time order
    • Stating a problem and then offering a solution
    • Describing objects by location
    • Comparing two unrelated topics

    Correct answer: Stating a problem and then offering a solution

    Stating a problem and then offering a solution is correct because the passage names the ocean plastic problem and follows it with biodegradable packaging as a fix. It is not arranged by chronology, by spatial location, or by comparing unrelated topics.

77. A passage ends with the sentence, "In short, these three reforms together rebuilt the school's reputation." This concluding sentence most likely functions to
    • Introduce a brand-new topic
    • List the steps of a science experiment
    • Sum up the main points of the passage
    • Contradict everything stated earlier

    Correct answer: Sum up the main points of the passage

    Sum up the main points of the passage is correct because "in short" signals a wrap-up that pulls the three reforms together into a closing statement. It does not introduce a new topic, list experiment steps, or contradict the passage.

78. An article about a house tour is arranged by describing the front porch, then the living room, then the kitchen, then the upstairs bedrooms. This organization is best described as
    • Chronological order
    • Cause and effect
    • Problem and solution
    • Spatial order that moves through the house

    Correct answer: Spatial order that moves through the house

    Spatial order that moves through the house is correct because the article guides readers room by room according to physical location. It is not based on time, on cause and effect, or on solving a problem.

79. Within an essay, a paragraph opens with the word "However," right after a paragraph praising electric cars. This transition signals that the new paragraph will
    • Repeat the previous praise
    • Summarize the whole essay
    • Introduce a contrasting point or drawback
    • List the parts of a car

    Correct answer: Introduce a contrasting point or drawback

    Introduce a contrasting point or drawback is correct because "however" signals a shift away from the preceding praise toward an opposing idea. It does not repeat the praise, summarize the essay, or list car parts.

80. A novel is told by a narrator who knows the private thoughts and feelings of every character in every scene. This point of view is best described as
    • Third-person omniscient, with access to all characters' minds
    • First-person, limited to one character
    • Second-person, addressing the reader directly
    • An objective report with no thoughts revealed

    Correct answer: Third-person omniscient, with access to all characters' minds

    Third-person omniscient, with access to all characters' minds is correct because the narrator knows every character's private thoughts across scenes. It is not limited first person, second-person address, or a thought-free objective report.

81. A passage about voting closes: "So mark your calendar, find your polling place, and let your voice be heard this November." The author's primary purpose is to
    • Explain the history of elections
    • Urge readers to vote
    • Describe a voting machine's parts
    • Entertain readers with a funny story

    Correct answer: Urge readers to vote

    Urge readers to vote is correct because the direct commands to mark the calendar, find the polling place, and be heard are meant to spur readers to action. The passage is not a history, a description of machinery, or a comic story.

82. A critic writes of a restaurant: "The service charmed us and the dessert delighted, yet the bland main course nearly spoiled the evening." The critic's overall attitude is best described as
    • Entirely glowing
    • Mixed, blending praise with disappointment
    • Completely negative
    • Totally uninterested

    Correct answer: Mixed, blending praise with disappointment

    Mixed, blending praise with disappointment is correct because the critic praises the service and dessert but faults the bland main course. The attitude is neither entirely glowing nor completely negative, and the strong reactions rule out being uninterested.

83. A pamphlet on fire safety lists short directives such as "Test your smoke alarms monthly" and "Plan two escape routes from every room." The author's main purpose is to
    • Tell an exciting fire-rescue story
    • Sell readers a brand of smoke alarm
    • Argue that homes are too dangerous
    • Instruct readers how to stay safe

    Correct answer: Instruct readers how to stay safe

    Instruct readers how to stay safe is correct because the directives walk readers through specific safety actions to take. The pamphlet is not a story, a sales pitch, or an argument about danger.

84. A passage describes the layers of the Earth using neutral, factual language, defining the crust, mantle, and core without expressing any opinion. The author's primary purpose is most likely to
    • Inform readers about the planet's structure
    • Persuade readers to study geology
    • Entertain readers with a tall tale
    • Complain about science textbooks

    Correct answer: Inform readers about the planet's structure

    Inform readers about the planet's structure is correct because the neutral, definition-based description of Earth's layers aims to teach rather than persuade or amuse. The passage contains no persuasion, fiction, or complaint.

85. An author writes a lighthearted, exaggerated tale about a cat that supposedly runs the household, ending, "And so we humans simply do as we are told." The author's main purpose is to
    • Amuse readers with a playful story
    • Instruct readers on pet care
    • Persuade readers to adopt cats
    • Report scientific facts about cats

    Correct answer: Amuse readers with a playful story

    Amuse readers with a playful story is correct because the exaggerated, joking account of a cat ruling the house is meant to entertain. It is not a care guide, an adoption appeal, or a scientific report.

86. An author argues that schools should start later and supports the claim by citing studies showing that teenagers who sleep longer earn higher grades. The studies about sleep and grades function as
    • An unrelated personal story
    • Evidence supporting the author's recommendation
    • A counterargument the author rejects
    • A definition of the word 'school'

    Correct answer: Evidence supporting the author's recommendation

    Evidence supporting the author's recommendation is correct because the studies link more sleep to better grades, backing the call for later start times. They are not an anecdote, a rejected counterargument, or a definition.

87. An author argues that a city should ban gas-powered leaf blowers and writes, "Admittedly, they save landscapers time, but their noise and fumes harm entire neighborhoods." The phrase "they save landscapers time" serves to
    • Abandon the author's argument
    • Provide statistical proof
    • Change the subject to gardening
    • Concede a point before reasserting the main claim

    Correct answer: Concede a point before reasserting the main claim

    Concede a point before reasserting the main claim is correct because the author grants a benefit, then uses "but" to return to the case against leaf blowers. The concession does not abandon the argument, supply statistics, or change the subject.

88. An author claims that a new app "clearly makes people happier" but offers only the fact that many people downloaded it. A careful reader should recognize that this argument is weak because
    • Downloading an app does not prove it makes users happier
    • Apps can never affect emotions
    • The author included far too much data
    • The claim is about a different app

    Correct answer: Downloading an app does not prove it makes users happier

    Downloading an app does not prove it makes users happier is correct because download numbers measure interest, not emotional impact, leaving the happiness claim unsupported. The flaw is not that apps never affect emotions, that there was too much data, or that a different app was discussed.

89. Passage 1 argues that working from home boosts productivity by removing commutes. Passage 2 contends that working from home weakens teamwork because colleagues rarely meet in person. The relationship between the passages is best described as
    • One passage restating the other
    • Two passages on entirely different topics
    • One passage supplying data for the other
    • Two passages offering opposing views on the same issue

    Correct answer: Two passages offering opposing views on the same issue

    Two passages offering opposing views on the same issue is correct because both discuss working from home but disagree about its effects. Neither restates nor supplies data for the other, and they share a topic rather than differing.

90. Passage 1 is a journalist's eyewitness report of a city festival, full of sights and sounds. Passage 2 is an official city document listing the festival's budget and attendance figures. Reading both together would most help a reader
    • Decide which writer is funnier
    • Understand the festival through both vivid experience and hard data
    • Prove the festival never happened
    • Ignore the official figures entirely

    Correct answer: Understand the festival through both vivid experience and hard data

    Understand the festival through both vivid experience and hard data is correct because the report gives a sensory account while the document supplies numbers, together forming a fuller picture. The other choices misuse the pairing by judging humor, disproving, or discarding data.

91. Passage 1 presents research suggesting a new fertilizer increases crop yields. Passage 2, by a different author, warns that the same fertilizer may pollute nearby streams. Passage 2 relates to Passage 1 by
    • Repeating Passage 1 word for word
    • Telling an unrelated story
    • Restating Passage 1 in simpler words
    • Pointing out a potential drawback of the finding in Passage 1

    Correct answer: Pointing out a potential drawback of the finding in Passage 1

    Pointing out a potential drawback of the finding in Passage 1 is correct because Passage 2 raises a pollution concern that qualifies the first passage's positive yield results. It does not repeat, fictionalize, or merely simplify Passage 1.

92. An independent clause is best described as a group of words that
    • Begins with a relative pronoun and modifies a noun
    • Always requires a comma to attach to a main clause
    • Lacks a finite verb but expresses a partial idea
    • Contains a subject and verb and can stand alone as a complete sentence

    Correct answer: Contains a subject and verb and can stand alone as a complete sentence

    Containing a subject and verb that can stand alone is correct because an independent clause expresses a complete thought without needing another clause. A relative pronoun begins a dependent clause, attachment punctuation is a separate matter, and a group lacking a finite verb is a phrase, not a clause.

93. Which sentence corrects the comma splice while subordinating one idea? "The trail was steep, the hikers paused often."
    • The trail was steep, the hikers paused often as a result.
    • Because the trail was steep, the hikers paused often.
    • The trail was steep the hikers paused often.
    • The trail was steep, however the hikers paused often.

    Correct answer: Because the trail was steep, the hikers paused often.

    Beginning with "Because the trail was steep" is correct because it turns the first clause into a dependent clause, eliminating the splice and showing cause. Adding "as a result" leaves the splice intact, removing the comma creates a run-on, and "however" without a semicolon still splices the clauses.

94. Which revision corrects the dangling modifier? "To qualify for the scholarship, an essay must be submitted by March."
    • To qualify for the scholarship, the deadline is in March for the essay.
    • An essay must be submitted by March, to qualify for the scholarship.
    • To qualify for the scholarship the essay must be submitted by March.
    • To qualify for the scholarship, applicants must submit an essay by March.

    Correct answer: To qualify for the scholarship, applicants must submit an essay by March.

    Naming "applicants" right after the opening phrase is correct because the action "to qualify" must attach to people who can qualify, not to an essay. The other versions leave the phrase modifying the deadline or the essay, or merely shift word order without supplying a logical subject.

95. Which group of words is a sentence fragment rather than a complete sentence?
    • A scientist who studies coral reefs in warm waters.
    • The orchestra rehearsed late into the evening.
    • Snow fell steadily throughout the night.
    • The audience applauded loudly after the encore.

    Correct answer: A scientist who studies coral reefs in warm waters.

    "A scientist who studies coral reefs in warm waters" is correct because the relative clause leaves the noun without a main verb, making it a fragment. The other three each pair a subject with a complete predicate and express a full thought on their own.

96. Which sentence keeps parallel structure across its three verb phrases?
    • The intern was responsible for sorting mail, answering phones, and to greet visitors.
    • The intern was responsible for sorting mail, answering phones, and greeting visitors.
    • The intern was responsible for sorting mail, to answer phones, and greeting visitors.
    • The intern was responsible for sorting mail, phone answers, and greeting visitors.

    Correct answer: The intern was responsible for sorting mail, answering phones, and greeting visitors.

    Listing "sorting," "answering," and "greeting" is correct because all three duties appear as gerunds, keeping the series parallel. The other versions mix a gerund with an infinitive or substitute a noun phrase, breaking the grammatical balance.

97. Read the sentence: "Rushing to catch the bus, the wallet slipped from his pocket." Which revision fixes the modifier?
    • Rushing to catch the bus, his wallet slipped from his pocket.
    • Rushing to catch the bus, he felt his wallet slip from his pocket.
    • The wallet slipped from his pocket, rushing to catch the bus.
    • Rushing to catch the bus the wallet slipped from his pocket.

    Correct answer: Rushing to catch the bus, he felt his wallet slip from his pocket.

    Naming "he" after the introductory phrase is correct because the person, not the wallet, was rushing to catch the bus. The versions tied to "his wallet" still let the phrase modify the wallet, and moving or unpunctuating the phrase does not give it a logical subject.

98. Which sentence combines the ideas to emphasize the result rather than the cause? "The river flooded. Several roads were closed."
    • The river flooded, several roads were closed.
    • The river flooded and roads.
    • The river flooded; although several roads were closed.
    • When the river flooded, several roads were closed.

    Correct answer: When the river flooded, several roads were closed.

    Opening with "When the river flooded" is correct because it subordinates the cause and leaves the road closures as the emphasized main clause. The comma-only version is a splice, the third choice is incomplete, and the semicolon version strands a dependent clause after it.

99. Read the sentence: "The professor explained the theory clearly and then she answers questions from the class." Which revision corrects the inconsistent verb tense?
    • The professor explains the theory clearly and then she answered questions from the class.
    • The professor explained the theory clearly and then answering questions from the class.
    • The professor explained the theory clearly and then she answer questions from the class.
    • The professor explained the theory clearly and then answered questions from the class.

    Correct answer: The professor explained the theory clearly and then answered questions from the class.

    Pairing "explained" with "answered" is correct because both actions happened in the past and must share the past tense. Mixing present with past, using a participle, or leaving an unconjugated "answer" all break the tense agreement between the two verbs.

100. Which sentence places the modifier so that it is clear the report, not the manager, was incomplete?
     • The manager returned the report to the analyst that was incomplete.
     • Incomplete, the manager returned the report to the analyst.
     • The manager returned the incomplete report to the analyst.
     • The manager, incomplete, returned the report to the analyst.

     Correct answer: The manager returned the incomplete report to the analyst.

     Placing "incomplete" directly before "report" is correct because a modifier belongs next to the noun it describes, making clear the report was incomplete. The other versions let the modifier attach to the analyst or the manager, distorting the intended meaning.

101. Which sentence avoids a run-on by correctly joining two independent clauses?
     • The deadline approached the team worked through the weekend.
     • The deadline approached, so the team worked through the weekend.
     • The deadline approached, the team worked through the weekend.
     • The deadline approached so, the team worked through the weekend.

     Correct answer: The deadline approached, so the team worked through the weekend.

     Using a comma plus "so" is correct because a coordinating conjunction with a comma properly joins two independent clauses. Omitting punctuation creates a run-on, a comma alone makes a splice, and misplacing the comma after "so" disrupts the join.

102. Which sentence corrects the faulty parallelism in the paired comparison? "The new method is not only faster but also it costs less."
     • The new method is not only faster but also less expensive.
     • The new method not only is faster but also it costs less.
     • The new method is not only faster but it also costing less.
     • The new method is faster not only but also it costs less.

     Correct answer: The new method is not only faster but also less expensive.

     Pairing "faster" with "less expensive" is correct because the correlative "not only...but also" must join matching adjective phrases. The other versions follow the second half with a clause or an unconjugated form, breaking the parallel structure the construction requires.

103. Which choice corrects the underlined word? "The committee will choose among the three finalists, but I think their is one clear leader."
     • They're
     • Theyre
     • Theirs
     • There

     Correct answer: There

     Choosing "there" is correct because the sentence needs the word that signals existence in "there is one clear leader." "Their" is possessive, "they're" means "they are," "theyre" is a misspelling, and "theirs" is a possessive pronoun that does not fit.

104. Which choice corrects the underlined word? "The amount of students enrolled this semester broke the previous record."
     • Quantity of
     • Amounts of
     • Number of
     • Sum of

     Correct answer: Number of

     Choosing "number of" is correct because "students" are countable, and countable nouns take "number" rather than "amount." "Amount" and "quantity" suit uncountable masses, "amounts of" repeats the error, and "sum of" applies to figures being added.

105. Which sentence uses "lie" and "lay" correctly?
     • Please lay down for a few minutes before dinner.
     • He lay the book on the table and left the room.
     • She laid the blanket on the grass before the picnic.
     • The dog likes to lay in the sun all afternoon.

     Correct answer: She laid the blanket on the grass before the picnic.

     "She laid the blanket on the grass" is correct because "laid" is the past tense of "lay," the transitive verb that takes an object such as "blanket." The other sentences misuse "lay" where the intransitive "lie" (to recline, with no object) is required.

106. Which choice corrects the underlined word? "Between the two candidates, she is clearly the better speaker, and her ideas are good as well."
     • Is the best speaker
     • Is the more better speaker
     • Is the better speaker
     • Is a better speaker than

     Correct answer: Is the better speaker

     Keeping "the better speaker" is correct because the comparative form is used when comparing exactly two people. The superlative "best" applies to three or more, "more better" doubles the comparative, and "better speaker than" leaves the comparison without its second element.

107. Which choice corrects the underlined words? "Neither of the proposals were accepted by the board."
     • Neither of the proposals are
     • Neither of the proposals being
     • Neither of the proposals was
     • Neither of the proposal were

     Correct answer: Neither of the proposals was

     Choosing "Neither of the proposals was" is correct because "neither" is singular and governs the verb, regardless of the plural "proposals" in the prepositional phrase. The plural "are" and "were" disagree, "being" leaves no finite verb, and "proposal" creates a new mismatch.

108. Which choice corrects the underlined word? "By next June, she will have worked here for ten years, and her colleagues plan to congratulate her then."
     • Will have worked
     • Will work
     • Had worked
     • Has worked

     Correct answer: Will have worked

     Keeping "will have worked" is correct because the future perfect shows an action that will be completed before a future point, "next June." The simple future loses the completion, while "had worked" and "has worked" place the action in the past rather than the future.

109. Which choice corrects the underlined word? "The new intern works real hard to meet every deadline."
     • Real hardly
     • Really hard
     • Real harder
     • Realer hard

     Correct answer: Really hard

     Choosing "really hard" is correct because the adverb "really" is needed to modify "hard," not the adjective "real." "Real hardly" changes the meaning, while "real harder" and "realer hard" are nonstandard forms.

110. Which choice corrects the underlined word? "The chef prepared the meal as if he were cooking for royalty, careful to season everything just write."
     • Rite
     • Wright
     • Writ
     • Right

     Correct answer: Right

     Choosing "right" is correct because the sentence needs the word meaning correctly or properly. "Write" means to put words on paper, while "rite," "wright," and "writ" are unrelated words that do not fit the meaning.

111. Read the sentence: "Each student must submit their own project, and each must defend it before the panel." Which revision keeps the pronoun consistent with the singular antecedent in formal usage?
     • Each student must submit his or her own project
     • Each student must submit there own project
     • Each student must submit our own project
     • Each student must submit its own project

     Correct answer: Each student must submit his or her own project

     Choosing "his or her" is correct because the singular "each student" takes a singular possessive in formal usage. "There" indicates place, "our" shifts to first person, and "its" is used for things, none of which agrees with a singular person.

112. Which choice corrects the underlined word? "The proposal was excepted by the committee after a brief discussion."
     • Expected
     • Accepted
     • Exempted
     • Acception

     Correct answer: Accepted

     Choosing "accepted" is correct because the sentence needs the verb meaning to receive or approve. "Excepted" means left out, "expected" means anticipated, "exempted" means freed from a rule, and "acception" is not a standard word.

113. Which sentence uses the comparative and superlative forms correctly?
     • Of all the routes we tried, the coastal road was the most scenic.
     • Of all the routes we tried, the coastal road was the more scenic.
     • Of all the routes we tried, the coastal road was more scenic than any.
     • Of all the routes we tried, the coastal road was scenicest.

     Correct answer: Of all the routes we tried, the coastal road was the most scenic.

     Choosing "the most scenic" is correct because the superlative is used when comparing more than two items, here "all the routes." The comparative "more scenic" suits only two, the third choice is illogical, and "scenicest" is a nonstandard form.

114. Read the sentence: "The principle reason for the policy change was budget pressure." Which revision corrects the error?
     • The principled reason for the policy change was budget pressure.
     • The principals reason for the policy change was budget pressure.
     • The principal reason for the policy change was budget pressure.
     • The principel reason for the policy change was budget pressure.

     Correct answer: The principal reason for the policy change was budget pressure.

     Choosing "principal" is correct because here it means main or primary, the adjective the sentence needs. "Principle" means a rule or belief, "principled" means having strong morals, "principals" is a plural noun, and "principel" is a misspelling.

115. Which choice corrects the underlined word? "She felt the criticism was unfair, but she decided to take it in stride, regardless of how others might of reacted."
     • Might had
     • Might have
     • Might off
     • May of

     Correct answer: Might have

     Choosing "might have" is correct because the standard form combines the modal "might" with "have," not the sound-alike "of." "Might had," "might off," and "may of" are all nonstandard substitutions for "might have."

116. Which sentence correctly uses commas to set off a nonrestrictive appositive?
     • The river the longest in the region floods every spring.
     • The river the longest in the region, floods every spring.
     • The river, the longest in the region floods every spring.
     • The river, the longest in the region, floods every spring.

     Correct answer: The river, the longest in the region, floods every spring.

     Enclosing "the longest in the region" in two commas is correct because a nonrestrictive appositive that renames the noun is set off on both sides. Using one comma or none fails to mark the appositive and runs the elements together.

117. Which sentence correctly uses a colon after an independent clause to introduce a list?
     • For the trip, remember to pack: sunscreen, a hat, and water.
     • Remember to pack three essentials: sunscreen, a hat, and water.
     • Remember: to pack sunscreen, a hat, and water.
     • Remember to pack sunscreen, a hat, and water:

     Correct answer: Remember to pack three essentials: sunscreen, a hat, and water.

     Placing the colon after "Remember to pack three essentials" is correct because a colon introduces a list only after a complete independent clause. Putting the colon right after "pack," after "Remember," or at the end of the sentence misplaces it.

118. Which sentence correctly forms the possessive of a singular noun ending in s?
     • The boss's schedule was posted on Monday.
     • The boss schedule was posted on Monday.
     • The bosss schedule was posted on Monday.
     • The bosses schedule was posted on Monday.

     Correct answer: The boss's schedule was posted on Monday.

     Writing "boss's" is correct because a singular noun, even one ending in s, typically forms the possessive by adding an apostrophe plus s. "Boss" shows no possession, "bosss" is not a valid form, and "bosses" is a plural with no apostrophe.

119. Which sentence correctly uses a semicolon to separate two independent clauses linked by a conjunctive adverb?
     • Attendance was low, therefore the event was rescheduled.
     • Attendance was low therefore; the event was rescheduled.
     • Attendance was low; therefore the event was rescheduled,
     • Attendance was low; therefore, the event was rescheduled.

     Correct answer: Attendance was low; therefore, the event was rescheduled.

     Placing a semicolon before "therefore" and a comma after it is correct because a conjunctive adverb joining two independent clauses takes that punctuation. A comma alone creates a splice, and the other versions misplace the semicolon or drop the comma.

120. Which sentence correctly punctuates a restrictive (essential) clause without commas?
     • Students, who fail to register, will lose their seats.
     • Students who fail to register will lose their seats.
     • Students who fail to register, will lose their seats.
     • Students, who fail to register will lose their seats.

     Correct answer: Students who fail to register will lose their seats.

     Leaving "who fail to register" without commas is correct because the clause is essential to identify which students lose their seats. Setting it off with commas would wrongly mark it as nonessential, implying all students fail to register.

121. Which sentence uses quotation marks and end punctuation correctly?
     • "Have you finished the report"? she asked.
     • "Have you finished the report?", she asked.
     • "Have you finished the report? she asked."
     • "Have you finished the report?" she asked.

     Correct answer: "Have you finished the report?" she asked.

     Placing the question mark inside the closing quotation mark and following with "she asked" is correct because the question mark belongs to the quoted question. The other versions put the mark outside, add an extra comma, or enclose the speaker tag inside the quotation.

122. Read the sentence: "My sister who lives in Denver is visiting next week and I cannot wait." Where should a comma be added to join the two independent clauses?
     • After "sister"
     • After "week"
     • After "Denver"
     • After "visiting"

     Correct answer: After "week"

     Adding a comma after "week" is correct because it precedes the coordinating conjunction "and" that joins two independent clauses. A comma after "sister," "Denver," or "visiting" would fall inside the first clause and fail to mark the join between the two clauses.

123. Which sentence correctly uses an apostrophe to indicate plural possession?
     • The employees lounge was renovated over the weekend.
     • The employees' lounge was renovated over the weekend.
     • The employee's lounge was renovated over the weekend.
     • The employees's lounge was renovated over the weekend.

     Correct answer: The employees' lounge was renovated over the weekend.

     Writing "employees'" is correct because a plural noun ending in s forms the possessive by adding only an apostrophe after the s. "Employees" shows no possession, "employee's" is singular possessive, and "employees's" doubles the marking.

124. Which sentence correctly uses commas to set off an interrupting nonessential phrase?
     • The novel, despite mixed reviews became a bestseller.
     • The novel despite mixed reviews, became a bestseller.
     • The novel, despite mixed reviews, became a bestseller.
     • The novel despite mixed reviews became a bestseller.

     Correct answer: The novel, despite mixed reviews, became a bestseller.

     Enclosing "despite mixed reviews" in two commas is correct because the interrupting nonessential phrase is set off on both sides. Using one comma or none fails to separate the phrase from the main clause and disrupts the sentence.

125. Which sentence correctly uses a colon to introduce a formal quotation after an independent clause?
     • The mayor closed with: these words "Our city will rebuild stronger than before."
     • The mayor closed with these words: "Our city will rebuild stronger than before."
     • The mayor: closed with these words "Our city will rebuild stronger than before."
     • The mayor closed with these words "Our city will rebuild stronger than before":

     Correct answer: The mayor closed with these words: "Our city will rebuild stronger than before."

     Placing the colon after the complete clause "The mayor closed with these words" is correct because a colon introduces a formal quotation after an independent clause. The other versions split the clause or strand the colon at the end, where it introduces nothing.

126. Which sentence correctly uses a comma to separate two coordinate adjectives?
     • She wore a bright, cheerful scarf to the party.
     • She wore a bright cheerful, scarf to the party.
     • She wore a, bright cheerful scarf to the party.
     • She wore a bright cheerful scarf, to the party.

     Correct answer: She wore a bright, cheerful scarf to the party.

     Placing the comma between "bright" and "cheerful" is correct because two coordinate adjectives that each modify the noun are separated by a comma. The other versions misplace the comma between an adjective and the noun or after the phrase.

127. A writer wants to add a sentence supporting the claim that the new tutoring center improved student grades. Which sentence best provides that support?
     • The center is located on the second floor of the library.
     • Many students say they enjoy visiting the center.
     • Average math grades rose by a full letter among students who attended weekly.
     • Tutoring centers are common at colleges across the country.

     Correct answer: Average math grades rose by a full letter among students who attended weekly.

     Citing the full-letter rise in grades is correct because the specific result directly supports the claim that grades improved. The center's location, students' enjoyment, and the general fact about other colleges do not show an effect on grades.

128. In a paragraph arguing that telecommuting boosts productivity, which sentence should be removed because it does not support the focus?
     • Remote workers report fewer interruptions during the day.
     • Studies show telecommuters complete tasks faster on average.
     • The company's parking lot was repaved last summer.
     • Working from home eliminates long, tiring commutes.

     Correct answer: The company's parking lot was repaved last summer.

     Removing the sentence about the repaved parking lot is correct because it has nothing to do with telecommuting and productivity, breaking the paragraph's focus. The sentences on fewer interruptions, faster task completion, and eliminated commutes all support the productivity claim.

129. Which sentence would serve best as a clear thesis for an essay arguing that cities should expand public parks?
     • Parks have existed in cities for centuries.
     • My neighborhood has a small park nearby.
     • Expanding public parks improves residents' health, strengthens communities, and raises property values.
     • Some people use parks more often than others do.

     Correct answer: Expanding public parks improves residents' health, strengthens communities, and raises property values.

     Stating that expanding parks improves health, strengthens communities, and raises property values is correct because it offers a focused, arguable claim with clear supporting points. The other sentences give background facts or personal details that do not establish a thesis.

130. A writer wants to add a concrete detail to support the claim that the festival drew a large crowd. Which addition is most effective?
     • Festivals are popular events in many towns.
     • The festival featured food, music, and crafts.
     • Planning the festival took several months of effort.
     • Organizers counted more than twelve thousand visitors over the weekend.

     Correct answer: Organizers counted more than twelve thousand visitors over the weekend.

     Reporting more than twelve thousand visitors is correct because the specific count directly supports the claim of a large crowd. The general remark about festivals, the list of features, and the planning detail do not provide evidence of crowd size.

131. Which revision best sharpens this vague topic sentence? "There are a few things to like about the new app."
     • The new app loads quickly, organizes notes clearly, and syncs across devices.
     • The new app is a pretty good thing overall.
     • People have lots of opinions about the new app.
     • There are good and bad sides to the new app.

     Correct answer: The new app loads quickly, organizes notes clearly, and syncs across devices.

     Naming that the app loads quickly, organizes notes, and syncs across devices is correct because it gives specific reasons for the paragraph to develop. The other revisions remain vague, mention mixed feelings, or shift to general opinions.

132. A paragraph claims that the volunteer program reduced neighborhood litter. Which sentence best develops that claim with relevant detail?
     • Volunteers wore matching green shirts each Saturday.
     • The program was announced at a community meeting.
     • Litter is a problem in many cities around the world.
     • Reported litter complaints fell by half within three months of the program's start.

     Correct answer: Reported litter complaints fell by half within three months of the program's start.

     Reporting that litter complaints fell by half is correct because the detail directly develops the claim that litter was reduced. The volunteers' shirts, the announcement, and the general fact about cities do not show a change in litter.

133. A student drafting an introduction wants a sentence that previews the body paragraphs' three reasons. Which sentence does this best?
     • This essay covers a topic worth thinking about.
     • There is a lot that could be said about school calendars.
     • School calendars have changed over the years.
     • Year-round schooling reduces summer learning loss, eases family scheduling, and uses buildings efficiently.

     Correct answer: Year-round schooling reduces summer learning loss, eases family scheduling, and uses buildings efficiently.

     Listing reduced learning loss, easier scheduling, and efficient building use is correct because it previews three concrete reasons the body will develop. The other sentences offer vague promises or background that does not preview specific points.

134. A writer needs a transition sentence to move from a paragraph describing a problem to one proposing several solutions. Which sentence works best?
     • Fortunately, several practical steps can address these difficulties.
     • Problems like this appear in the news every day.
     • The weather that week was unusually mild.
     • People often disagree about current events.

     Correct answer: Fortunately, several practical steps can address these difficulties.

     Writing that several practical steps can address these difficulties is correct because it links the established problem to the upcoming solutions. The other sentences are too general or unrelated to bridge the two paragraphs.

135. Which transition word best signals that the writer is adding emphasis to a point just made? "The plan cuts costs. ___, it does so without reducing service."
     • Otherwise
     • Indeed
     • Conversely
     • Instead

     Correct answer: Indeed

     Beginning with "Indeed" is correct because it emphasizes and strengthens the preceding point about cutting costs. "Otherwise," "conversely," and "instead" all signal contrast or an alternative, which does not fit reinforcing the same idea.

136. These sentences are out of order. Which sequence is most logical? (1) Therefore, the city installed new filters at the plant. (2) Residents complained that the tap water tasted strange. (3) Tests revealed high levels of minerals in the supply.
     • 1, 2, 3
     • 3, 2, 1
     • 2, 3, 1
     • 2, 1, 3

     Correct answer: 2, 3, 1

     The order complaint, then testing, then installing filters is correct because it follows cause and effect: residents complained, tests found the cause, and the city responded "therefore." Any other order places a response before the problem it addresses, contradicting the logical cues.

137. Which transition best signals that the following sentence offers an example of the preceding general statement? "The museum offers many hands-on exhibits. ___, visitors can build a small bridge and test its strength."
     • For example
     • However
     • In conclusion
     • Nevertheless

     Correct answer: For example

     Beginning with "For example" is correct because it introduces a specific instance of the general statement about hands-on exhibits. "However" and "nevertheless" signal contrast, and "in conclusion" signals a closing, none of which fits an example.

138. A paragraph lists the steps of conducting a survey. Which sentence belongs first to give the clearest starting point?
     • Next, distribute the questionnaire to the chosen group.
     • Then, tally the responses and look for patterns.
     • Begin by deciding what question the survey should answer.
     • Finally, write a report summarizing the findings.

     Correct answer: Begin by deciding what question the survey should answer.

     Leading with deciding the survey's question is correct because "begin" marks the first logical action before distributing or analyzing anything. The steps beginning with "next," "then," and "finally" all signal later stages of the process.

139. Which sentence would best follow a main claim to introduce the first of several supporting reasons in an organized way?
     • In conclusion, the change is overdue.
     • On the other hand, critics disagree strongly.
     • To begin, the policy lowers waiting times for patients.
     • Meanwhile, a different hospital tried another approach.

     Correct answer: To begin, the policy lowers waiting times for patients.

     Beginning with "To begin, the policy lowers waiting times" is correct because "to begin" clearly introduces the first reason in an organized list. "In conclusion" signals a close, "on the other hand" introduces opposition, and "meanwhile" shifts to a different subject.

140. Which transition best signals that the writer is acknowledging a point before countering it? "___ the plan has clear benefits, it overlooks the cost to small businesses."
     • Although
     • Because
     • Therefore
     • Likewise

     Correct answer: Although

     Beginning with "Although" is correct because it concedes the benefits while setting up the contrasting drawback in the main clause. "Because" signals cause, "therefore" signals result, and "likewise" signals similarity, none of which fits a concession and counter.

141. A writer is arranging events from earliest to latest. Which opening phrase best signals the latest event in the sequence?
     • At first, the company sold only handmade goods.
     • Shortly afterward, it opened a second small shop.
     • In its earliest days, it had a single employee.
     • Years later, it operated factories on three continents.

     Correct answer: Years later, it operated factories on three continents.

     Choosing "Years later, it operated factories on three continents" is correct because it marks the latest point in the chronological sequence. "At first," "shortly afterward," and "in its earliest days" all point to earlier stages and would not signal the final event.

142. Which revision best eliminates the redundancy? "The two ideas are similar and alike in many of the same ways."
     • The two ideas are similar in many ways.
     • The two ideas are alike and similar in the same ways.
     • The two ideas are quite similar and very alike in many ways.
     • In many of the same ways, the two ideas are similar and alike.

     Correct answer: The two ideas are similar in many ways.

     Reducing it to "The two ideas are similar in many ways" is correct because "similar," "alike," and "the same" repeat one idea, so keeping a single term removes the redundancy. The other revisions retain or rearrange the duplicated words.

143. Which sentence uses the most precise verb to describe water moving slowly through a crack?
     • Water seeped through the crack in the foundation.
     • Water went through the crack in the foundation.
     • Water happened through the crack in the foundation.
     • Water did stuff through the crack in the foundation.

     Correct answer: Water seeped through the crack in the foundation.

     Choosing "seeped" is correct because it precisely conveys slow movement through a small opening. "Went" is vague, while "happened" and "did stuff" are imprecise and do not describe the manner of movement.

144. A writer wants a formal tone for an academic essay. Which revision is most appropriate? "The experiment was a total flop and didn't work at all."
     • The experiment was a big flop and a total bust.
     • The experiment did not produce the expected results.
     • The experiment totally bombed and failed bad.
     • The experiment was a flop, plain and simple.

     Correct answer: The experiment did not produce the expected results.

     Writing "The experiment did not produce the expected results" is correct because it reports the outcome in measured, formal language suited to an essay. "Flop," "bust," "bombed," and "failed bad" are casual and imprecise expressions.

145. Which revision best replaces the cliché with clearer wording? "The team gave it 110 percent to finish the project."
     • The team gave it their all and then some to finish the project.
     • The team worked intensely to finish the project.
     • The team went above and beyond, giving 110 percent to finish the project.
     • The team gave 110 percent and left it all on the field to finish.

     Correct answer: The team worked intensely to finish the project.

     Replacing the cliché with "worked intensely" is correct because it states the idea directly without a worn-out expression. The other revisions substitute another cliché or pile on additional stock phrases.

146. Which choice best replaces the underlined wordy phrase? "In order to save time, the staff automated the report."
     • For the purpose of saving
     • With the goal in mind of saving
     • In an effort that would save
     • To

     Correct answer: To

     Replacing "In order to" with "To" is correct because the single word conveys the same purpose concisely. The other choices are longer, roundabout phrasings that add words without adding meaning.

147. A writer wants an objective tone in a news report. Which revision best removes the loaded language? "The careless mayor pushed through a wasteful, reckless budget."
     • The mayor approved a budget that drew criticism over its spending.
     • The reckless mayor approved a wasteful budget.
     • The careless mayor approved a questionable budget.
     • The mayor pushed through a wasteful and reckless budget.

     Correct answer: The mayor approved a budget that drew criticism over its spending.

     Writing that the budget "drew criticism over its spending" is correct because it reports the situation without emotionally charged judgments. "Careless," "wasteful," "reckless," and "questionable" all inject bias unsuited to an objective report.

148. Which sentence is the most concise version without losing meaning? "She made the decision to postpone the meeting until a later date."
     • She decided to postpone the meeting.
     • She made the decision to postpone the meeting to a later time.
     • She came to the decision that the meeting should be postponed later.
     • She made a decision to push the meeting back to later on.

     Correct answer: She decided to postpone the meeting.

     Writing "She decided to postpone the meeting" is correct because "decided" replaces "made the decision to" and "postpone" already means to move to a later date, making "until a later date" redundant. The other versions keep the wordy phrase or the redundant time reference.

149. A writer wants the most precise word to describe a brief, sudden burst of laughter from the audience. Which choice is best?
     • The remark drew a noise from the audience.
     • The remark drew a reaction from the audience.
     • The remark drew a chuckle from the audience.
     • The remark drew a thing from the audience.

     Correct answer: The remark drew a chuckle from the audience.

     Choosing "chuckle" is correct because it precisely names a brief, quiet burst of laughter. "Noise," "reaction," and "thing" are vague and do not specify laughter at all.

150. Which revision corrects the misplaced modifier? "The waiter served a steak to the customer that was cooked rare."
     • The waiter served a steak cooked rare to the customer.
     • The waiter served a steak to the customer cooked rare.
     • Cooked rare, the customer was served a steak by the waiter.
     • The waiter, cooked rare, served a steak to the customer.

     Correct answer: The waiter served a steak cooked rare to the customer.

     Placing "cooked rare" right after "steak" is correct because a modifier belongs next to the noun it describes, making clear the steak, not the customer, was cooked rare. The other versions leave the phrase attached to the customer or the waiter.

151. Which sentence keeps parallel structure across its list of nouns?
     • The course covers reading, writing, and how to speak in public.
     • The course covers reading, writing, and public speaking.
     • The course covers reading, to write, and public speaking.
     • The course covers reading, writing skills, and to speak publicly.

     Correct answer: The course covers reading, writing, and public speaking.

     Listing "reading," "writing," and "public speaking" is correct because all three items appear as nouns, keeping the series parallel. The other versions mix a clause or an infinitive into the list, breaking the grammatical balance.

152. Which sentence corrects the comma splice by using a semicolon correctly? "The museum closed early, the staff needed to install a new exhibit."
     • The museum closed early the staff; needed to install a new exhibit.
     • The museum closed early; because the staff needed to install a new exhibit.
     • The museum closed early; the staff needed to install a new exhibit.
     • The museum closed early, the staff; needed to install a new exhibit.

     Correct answer: The museum closed early; the staff needed to install a new exhibit.

     Placing a semicolon between the two independent clauses is correct because a semicolon can join closely related clauses that could each stand alone. The other versions add a subordinator after the semicolon or misplace it inside a clause.

153. Read the sentence: "The recipe calls for fresh herbs, and it requiring careful timing." Which revision corrects the verb form?
     • The recipe calling for fresh herbs, and it requiring careful timing.
     • The recipe calls for fresh herbs, and it require careful timing.
     • The recipe calls for fresh herbs, and it requiring careful timing carefully.
     • The recipe calls for fresh herbs, and it requires careful timing.

     Correct answer: The recipe calls for fresh herbs, and it requires careful timing.

     Using "requires" is correct because the second clause needs a finite verb that agrees with the singular "it." The participle "requiring" leaves no main verb, "require" disagrees in number, and the last choice removes the finite verb from both clauses.

154. Which group of words is a complete sentence rather than a fragment?
     • The conductor signaled the departure.
     • Running quickly toward the closing gate.
     • Whenever the train arrives at the crowded station.
     • A long delay caused by the morning storm.

     Correct answer: The conductor signaled the departure.

     "The conductor signaled the departure" is correct because it pairs the subject "conductor" with the verb "signaled" and expresses a complete thought. The other choices are a dependent clause or phrases that lack a finite verb and a complete idea.

155. Which sentence correctly joins the two clauses with a subordinating conjunction to show contrast? "The forecast predicted rain. The afternoon stayed dry."
     • The forecast predicted rain, the afternoon stayed dry.
     • Although the forecast predicted rain, the afternoon stayed dry.
     • The forecast predicted rain the afternoon stayed dry.
     • The forecast predicted rain, so the afternoon stayed dry.

     Correct answer: Although the forecast predicted rain, the afternoon stayed dry.

     Opening with "Although" is correct because it subordinates the first clause and signals the contrast between the prediction and the outcome. The comma-only version is a splice, the third is a run-on, and "so" wrongly implies cause and effect.

156. Which choice best combines the two sentences into one without changing the meaning? "The library extended its hours. Students could study later into the night."
     • The library extended its hours, students could study later into the night.
     • The library extended its hours; students could study, later into the night.
     • The library extended its hours so students could study later into the night.
     • The library extended its hours and students could study; later into the night.

     Correct answer: The library extended its hours so students could study later into the night.

     Using "so" to link the clauses is correct because it joins the ideas smoothly and shows the purpose of the extended hours. The comma-only version splices the clauses, and the other two misplace punctuation that fractures the sentence.

157. Which sentence corrects the faulty parallelism? "She likes hiking, swimming, and to ride her bike on weekends."
     • She likes to hike, swimming, and riding her bike on weekends.
     • She likes hiking, to swim, and to ride her bike on weekends.
     • She likes hiking, swims, and to ride her bike on weekends.
     • She likes hiking, swimming, and riding her bike on weekends.

     Correct answer: She likes hiking, swimming, and riding her bike on weekends.

     Listing "hiking," "swimming," and "riding" is correct because all three activities appear as gerunds, keeping the series parallel. The other versions mix gerunds with infinitives or a conjugated verb, breaking the grammatical balance.

158. Which choice corrects the underlined word? "The effect of the new schedule on attendance was immediate, but no one could explain it."
     • Effect
     • Effects
     • Affects
     • Affect

     Correct answer: Effect

     Keeping "effect" is correct because the sentence needs the noun meaning a result, the thing the schedule produced. "Affect" is usually a verb meaning to influence, and the plural forms do not fit the singular subject of the sentence.

159. Which choice corrects the underlined words? "Each of the volunteers have signed the attendance sheet."
     • Each of the volunteers having
     • Each of the volunteers has
     • Each of the volunteer have
     • Each of the volunteers are

     Correct answer: Each of the volunteers has

     Choosing "Each of the volunteers has" is correct because "each" is singular and governs the verb despite the plural "volunteers" in the prepositional phrase. The plural "have" and "are" disagree, "having" leaves no finite verb, and "volunteer" creates a new mismatch.

160. Which choice corrects the underlined word? "The teacher gave the assignment to Marco and I before the bell rang."
     • To me and Marco
     • To Marco and myself
     • To Marco and me
     • To I and Marco

     Correct answer: To Marco and me

     Choosing "to Marco and me" is correct because the pronoun is the object of the preposition "to" and requires the objective form "me." The subjective "I" is wrong as an object, "myself" needs an antecedent, and reordering does not fix the case.

161. Which sentence uses "fewer" and "less" correctly?
     • There were less cars on the road and fewer traffic this morning.
     • There were fewer cars on the road and fewer traffic this morning.
     • There were less cars on the road and less traffic this morning.
     • There were fewer cars on the road and less traffic this morning.

     Correct answer: There were fewer cars on the road and less traffic this morning.

     Pairing "fewer cars" with "less traffic" is correct because "fewer" modifies the countable "cars" and "less" modifies the uncountable "traffic." The other versions misapply one or both words to nouns of the wrong type.

162. Which choice corrects the underlined word? "The drought had a serious affect on the region's crops this year."
     • Effect
     • Affects
     • Effects
     • Affecting

     Correct answer: Effect

     Choosing "effect" is correct because the sentence needs the noun meaning a result, the impact the drought had. "Affect" is normally a verb, "affects" and "effects" are plural, and "affecting" is a participle that does not fit after "a serious."

163. Which choice corrects the underlined word? "The two researchers shared the prize equal between them."
     • Equality
     • Equally
     • More equal
     • Equalest

     Correct answer: Equally

     Choosing "equally" is correct because an adverb is needed to modify the verb "shared," describing how they divided the prize. "Equal" is an adjective, "equality" is a noun, and the comparative and superlative forms do not fit the action.

164. Which sentence uses the correct verb form to agree with a compound subject joined by "and"?
     • The coach and the captain disagrees about the lineup.
     • The coach and the captain disagreeing about the lineup.
     • The coach and the captain disagree about the lineup.
     • The coach and the captain has disagreed about the lineup.

     Correct answer: The coach and the captain disagree about the lineup.

     Choosing "disagree" is correct because two subjects joined by "and" form a plural that takes a plural verb. The singular "disagrees" and "has disagreed" do not match the plural subject, and "disagreeing" leaves no finite verb.

165. Which choice corrects the underlined word? "If she had studied earlier, she would of passed the certification exam."
     • Would off
     • Would had
     • Would of had
     • Would have

     Correct answer: Would have

     Choosing "would have" is correct because the standard form combines the modal "would" with "have," not the sound-alike "of." "Would had," "would of had," and "would off" are all nonstandard substitutions for "would have."

166. Which sentence correctly uses a dash to set off an interrupting explanation?
     • The final score - an unexpected upset - shocked the crowd.
     • The final score an unexpected upset, shocked the crowd.
     • The final score - an unexpected upset shocked the crowd.
     • The final score, an unexpected upset shocked the crowd.

     Correct answer: The final score - an unexpected upset - shocked the crowd.

     Setting off "an unexpected upset" with a dash on each side is correct because a pair of dashes marks an interrupting explanation. Using one dash or commas inconsistently fails to enclose the inserted element on both sides.

167. Which sentence correctly uses commas to set off a nonessential clause beginning with "which"?
     • The bridge which was built in 1920 is closed for repairs.
     • The bridge, which was built in 1920, is closed for repairs.
     • The bridge which was built in 1920, is closed for repairs.
     • The bridge, which was built in 1920 is closed for repairs.

     Correct answer: The bridge, which was built in 1920, is closed for repairs.

     Enclosing "which was built in 1920" in two commas is correct because a nonessential clause adding extra information is set off on both sides. Using one comma or none fails to mark the clause as nonessential.

168. Which sentence correctly uses a comma after an introductory dependent clause?
     • When the alarm sounded the workers calmly left the building.
     • When the alarm, sounded the workers calmly left the building.
     • When the alarm sounded, the workers calmly left the building.
     • When the alarm sounded the workers, calmly left the building.

     Correct answer: When the alarm sounded, the workers calmly left the building.

     Placing the comma after "sounded" is correct because an introductory dependent clause is followed by a comma before the main clause. Omitting it or misplacing it inside a clause fails to mark the boundary between the two clauses.

169. Which sentence correctly uses commas to separate items in a series?
     • The kit includes bandages, scissors tape, and, gloves.
     • The kit includes bandages scissors, tape and gloves.
     • The kit includes, bandages, scissors, tape, and gloves.
     • The kit includes bandages, scissors, tape, and gloves.

     Correct answer: The kit includes bandages, scissors, tape, and gloves.

     Separating each item with a comma is correct because items in a series are divided by commas, including before the final conjunction. The other versions omit needed commas or add commas where no separation belongs.

170. Which sentence correctly uses an apostrophe to form a contraction?
     • It's going to rain before the parade begins.
     • Its' going to rain before the parade begins.
     • Its going to rain before the parade begins.
     • Its is going to rain before the parade begins.

     Correct answer: It's going to rain before the parade begins.

     Writing "It's" is correct because the contraction of "it is" takes an apostrophe before the s. "Its" is the possessive form, "its'" is not a valid word, and "Its is" is redundant.

171. Read the sentence: "My coworker who organized the fundraiser deserves the credit and we should thank her." Where should a comma be added to join the two independent clauses?
     • After "coworker"
     • After "credit"
     • After "fundraiser"
     • After "thank"

     Correct answer: After "credit"

     Adding a comma after "credit" is correct because it precedes the coordinating conjunction "and" that joins two independent clauses. A comma after "coworker," "fundraiser," or "thank" would fall inside a clause and fail to mark the join.

172. Which sentence correctly uses a colon to introduce an explanation after an independent clause?
     • The reason: for the delay was simple a key supplier missed its deadline.
     • The reason for the delay was: simple a key supplier missed its deadline.
     • The reason for the delay was simple: a key supplier missed its deadline.
     • The reason for the delay was simple a key supplier missed its deadline:

     Correct answer: The reason for the delay was simple: a key supplier missed its deadline.

     Placing the colon after the complete clause "The reason for the delay was simple" is correct because a colon introduces an explanation after an independent clause. The other versions split the clause or strand the colon where it introduces nothing.

173. A paragraph describes how to plant a seedling. Which sentence belongs last to give the clearest closing step?
     • First, dig a hole twice as wide as the root ball.
     • Next, place the seedling gently into the hole.
     • Then, fill the hole with soil and press it down.
     • Finally, water the seedling thoroughly to help it settle.

     Correct answer: Finally, water the seedling thoroughly to help it settle.

     Ending with watering the seedling is correct because "finally" marks the last logical action after digging, placing, and filling. The steps beginning with "first," "next," and "then" all signal earlier stages of the process.

174. These sentences are out of order. Which sequence is most logical? (1) As a result, the bakery hired three new employees. (2) A popular review brought in many new customers. (3) The owner could no longer keep up with the orders alone.
     • 2, 3, 1
     • 1, 2, 3
     • 3, 2, 1
     • 2, 1, 3

     Correct answer: 2, 3, 1

     The order review, then the owner falling behind, then hiring is correct because it follows cause and effect: the review brought customers, the owner could not keep up, and so she hired help. Any other order places the hiring before the demand that caused it.

175. Which transition best signals that the writer is drawing a conclusion from the preceding evidence? "Sales rose, costs fell, and reviews improved. ___, the new strategy succeeded."
     • Nevertheless
     • Clearly
     • In contrast
     • Meanwhile

     Correct answer: Clearly

     Beginning with "Clearly" is correct because it draws a conclusion from the listed evidence of success. "Nevertheless" and "in contrast" signal opposition, and "meanwhile" signals a simultaneous event, none of which fits a conclusion.

176. A writer needs a transition sentence to move from a paragraph about the causes of a problem to one about its consequences. Which sentence works best?
     • The meeting that week ran longer than expected.
     • Many topics are worth examining in detail.
     • These causes, in turn, lead to several troubling consequences.
     • People hold many opinions on this subject.

     Correct answer: These causes, in turn, lead to several troubling consequences.

     Writing that the causes lead to several troubling consequences is correct because it links the established causes to the upcoming discussion of consequences. The other sentences are too general or unrelated to bridge the two paragraphs.

177. Which transition word best signals a contrast between the two ideas? "The first design was inexpensive. ___, it broke down within a month."
     • Therefore
     • Likewise
     • Furthermore
     • However

     Correct answer: However

     Beginning with "However" is correct because it signals the contrast between the low cost and the early breakdown. "Therefore" shows result, "likewise" shows similarity, and "furthermore" adds a related point, none of which fits a contrast.

178. Which transition best signals that the writer is adding a second supporting reason to one already given? "The bridge is unsafe. ___, repairing it now would cost far less than rebuilding later."
     • In addition
     • On the contrary
     • Until then
     • By contrast

     Correct answer: In addition

     Beginning with "In addition" is correct because it introduces a second supporting reason alongside the first. "On the contrary" and "by contrast" signal opposition, and "until then" signals time, none of which fits adding a reason.

179. A writer wants a formal tone for a research paper. Which revision is most appropriate? "The data was kind of all over the place and pretty confusing."
     • The data was sort of messy and really hard to read.
     • The data showed considerable variation and lacked a clear pattern.
     • The data was all over the place and super confusing.
     • The data was a mess and made no sense at all.

     Correct answer: The data showed considerable variation and lacked a clear pattern.

     Writing "The data showed considerable variation and lacked a clear pattern" is correct because it describes the results in precise, formal language suited to a research paper. "All over the place," "messy," and "super confusing" are casual and imprecise.

180. Which choice best replaces the underlined wordy phrase? "Due to the fact that the road was closed, we took a detour."
     • On account of the fact that
     • Owing to the reason that
     • Because
     • In view of the fact that

     Correct answer: Because

     Replacing the phrase with "Because" is correct because the single word conveys the same cause concisely. The other choices are longer, roundabout phrasings that add words without adding meaning.

181. A writer wants the most precise word to describe a faint, pleasant smell drifting from the kitchen. Which choice is best?
     • A smell came from the kitchen.
     • A thing came from the kitchen.
     • Something came from the kitchen.
     • An aroma drifted from the kitchen.

     Correct answer: An aroma drifted from the kitchen.

     Choosing "aroma" is correct because it precisely names a faint, pleasant smell, especially of food. "Smell" is neutral and vague, while "thing" and "something" do not name a scent at all.

182. A writer wants an objective tone in a report. Which revision best removes the loaded language? "The greedy company ruthlessly slashed its loyal workers' pay."
     • The company reduced its employees' pay.
     • The greedy company cut its loyal workers' pay.
     • The company ruthlessly cut its workers' pay.
     • The heartless company reduced its loyal workers' pay.

     Correct answer: The company reduced its employees' pay.

     Writing that the company "reduced its employees' pay" is correct because it reports the action without emotionally charged judgments. "Greedy," "ruthlessly," "loyal," and "heartless" all inject bias unsuited to an objective report.

183. Which revision best eliminates the redundancy? "The final outcome of the vote was a complete and total victory."
     • The final outcome of the vote was a total and complete victory.
     • The outcome of the vote was a complete victory.
     • The final end outcome of the vote was a complete victory.
     • The final outcome of the vote was a fully complete and total victory.

     Correct answer: The outcome of the vote was a complete victory.

     Reducing it to "The outcome of the vote was a complete victory" is correct because "final" repeats the idea in "outcome" and "total" repeats "complete," so trimming both removes the redundancy. The other revisions keep or rearrange the duplicated words.

184. Which sentence uses the most precise verb to describe a crowd moving quickly and noisily toward the exits?
     • The crowd was by the exits.
     • The crowd moved toward the exits.
     • The crowd surged toward the exits.
     • The crowd did things toward the exits.

     Correct answer: The crowd surged toward the exits.

     Choosing "surged" is correct because it precisely conveys a forceful, rushing movement of a crowd. "Moved" is vague, "was by" describes position rather than motion, and "did things" is imprecise.

185. A paragraph argues that the recycling program saved the city money. Which sentence best supports that claim with relevant detail?
     • Recycling bins were placed on every block downtown.
     • Recycling has become common in cities throughout the state.
     • Many residents say recycling makes them feel responsible.
     • The program cut landfill fees by two hundred thousand dollars last year.

     Correct answer: The program cut landfill fees by two hundred thousand dollars last year.

     Citing the two-hundred-thousand-dollar cut in landfill fees is correct because the specific savings directly support the claim that the city saved money. The bins, residents' feelings, and the general trend do not show a financial effect.

186. In a paragraph about the benefits of a balanced diet, which sentence should be removed because it does not support the focus?
     • The grocery store nearby recently changed its logo.
     • Whole grains supply steady energy throughout the day.
     • Eating a variety of vegetables provides essential vitamins.
     • Lean proteins help the body repair and build tissue.

     Correct answer: The grocery store nearby recently changed its logo.

     Removing the sentence about the store's logo is correct because it has nothing to do with the benefits of a balanced diet, breaking the paragraph's focus. The sentences on vegetables, whole grains, and lean proteins all support the diet's benefits.

187. Which sentence would serve best as a clear thesis for an essay arguing that schools should teach financial literacy?
     • Money is something everyone deals with eventually.
     • Teaching financial literacy helps students avoid debt, build savings, and make informed choices.
     • Some schools already offer a few finance lessons.
     • Financial topics can sometimes seem complicated to students.

     Correct answer: Teaching financial literacy helps students avoid debt, build savings, and make informed choices.

     Stating that financial literacy helps students avoid debt, build savings, and make informed choices is correct because it offers a focused, arguable claim with clear supporting points. The other sentences give background or vague observations that do not establish a thesis.

188. Which revision best sharpens this vague topic sentence? "The new policy has some effects on workers."
     • The new policy affects workers in various ways.
     • The new policy is something workers should know about.
     • The new policy raises overtime pay, shortens shifts, and adds paid sick days.
     • Workers have different feelings about the new policy.

     Correct answer: The new policy raises overtime pay, shortens shifts, and adds paid sick days.

     Naming that the policy raises overtime pay, shortens shifts, and adds sick days is correct because it gives specific effects for the paragraph to develop. The other revisions remain vague or shift to general feelings without concrete detail.

189. A writer wants to add a concrete detail to support the claim that the bakery quickly gained loyal customers. Which addition is most effective?
     • Bakeries can be found in nearly every neighborhood.
     • Opening a bakery requires a great deal of planning.
     • The bakery sells bread, pastries, and coffee each morning.
     • Within two months, more than three hundred people joined its rewards program.

     Correct answer: Within two months, more than three hundred people joined its rewards program.

     Reporting that more than three hundred people joined the rewards program is correct because the specific number directly supports the claim of loyal customers gained quickly. The general remark, the product list, and the planning detail do not show customer loyalty.

190. Which choice corrects the subject-verb agreement error? "The collection of rare coins are kept in a locked vault downtown."
     • The collection of rare coins is kept in a locked vault downtown.
     • The collection of rare coins were kept in a locked vault downtown.
     • The collection of rare coins being kept in a locked vault downtown.
     • The collection of rare coins are keeping in a locked vault downtown.

     Correct answer: The collection of rare coins is kept in a locked vault downtown.

     Choosing "collection ... is kept" is correct because the singular subject "collection" governs the verb, not the plural "coins" inside the prepositional phrase. "Are" and "were" agree with the wrong noun, and "being" leaves no finite verb in the clause.

191. Which sentence correctly uses an em dash to set off a sudden break that adds emphasis?
     • The verdict was finally announced and the courtroom fell silent.
     • The verdict, was finally announced the courtroom fell silent.
     • The verdict was finally announced—and the courtroom fell silent.
     • The verdict was finally—announced and the courtroom fell silent.

     Correct answer: The verdict was finally announced—and the courtroom fell silent.

     Placing the em dash before "and the courtroom fell silent" is correct because the dash marks a dramatic break while keeping the clauses readable. The first version omits punctuation, and the others insert a comma or dash that interrupts the sentence mid-thought.

192. A paragraph argues that the city should add bike lanes. Which sentence best supports that claim with relevant evidence?
     • Bicycles come in many styles and price ranges.
     • Cities with protected bike lanes report sharply fewer cycling injuries.
     • The mayor rides a bicycle to work on warm mornings.
     • Bike lanes are painted in a variety of bright colors.

     Correct answer: Cities with protected bike lanes report sharply fewer cycling injuries.

     Citing fewer cycling injuries in cities with protected lanes is correct because the specific outcome directly backs the claim that the city should add bike lanes. The bicycle styles, the mayor's habit, and the lane colors give no evidence about the benefit of building lanes.

193. Which choice corrects the underlined word? "After the long hike, the campers were so tired that they could hardly affect the climb up the final ridge."
     • Effect
     • Affecting
     • Effected
     • Afect

     Correct answer: Effect

     Choosing "effect" is correct because the sentence needs the verb meaning to bring about or accomplish the climb. "Affect" usually means to influence, "affecting" and "effected" are wrong forms here, and "afect" is a misspelling.

194. Which transition best signals that the following sentence states a result of the preceding cause? "The bridge was closed for repairs. ___, commuters had to find alternate routes."
     • Consequently
     • Similarly
     • In contrast
     • Meanwhile

     Correct answer: Consequently

     Beginning with "Consequently" is correct because it shows that the alternate routes resulted from the bridge closure. "Similarly" signals likeness, "in contrast" signals opposition, and "meanwhile" signals simultaneous action, none of which conveys cause and effect.

195. Which revision best replaces the vague underlined word with precise wording? "The storm caused a lot of bad stuff along the coast."
     • Caused a lot of things along the coast
     • Caused widespread flooding and downed power lines along the coast
     • Caused some issues along the coast
     • Caused various problems and other matters along the coast

     Correct answer: Caused widespread flooding and downed power lines along the coast

     Choosing "widespread flooding and downed power lines" is correct because it names concrete damage in place of the vague "a lot of bad stuff." The other revisions keep imprecise terms like "things," "some issues," and "various problems" that fail to specify the damage.

196. Which sentence correctly joins the two independent clauses with a semicolon? "The recipe looked complicated. The result was surprisingly simple to make."
     • The recipe looked complicated, the result was surprisingly simple to make.
     • The recipe looked complicated; the result was surprisingly simple to make.
     • The recipe looked complicated the result; was surprisingly simple to make.
     • The recipe looked complicated; and the result was surprisingly simple to make.

     Correct answer: The recipe looked complicated; the result was surprisingly simple to make.

     Placing a semicolon between the two clauses is correct because a semicolon joins closely related independent clauses without a conjunction. A comma alone creates a splice, the third choice misplaces the semicolon, and pairing a semicolon with "and" is redundant.

197. These sentences are out of order. Which sequence is most logical? (1) Within a week, green shoots appeared in the soil. (2) She planted the seeds in early spring. (3) By summer, the garden was full of tall sunflowers.
     • 1, 2, 3
     • 3, 1, 2
     • 2, 1, 3
     • 2, 3, 1

     Correct answer: 2, 1, 3

     The order planting, then shoots, then full sunflowers is correct because it follows the time cues from "early spring" to "within a week" to "by summer." Any other arrangement places a later stage of growth before the planting that must come first.

198. Which revision corrects the misplaced modifier? "Covered in chocolate, the child eagerly reached for the strawberries."
     • Covered in chocolate, the strawberries were eagerly reached for by the child.
     • The child eagerly reached for the strawberries covered in chocolate.
     • Covered in chocolate the child eagerly reached for the strawberries.
     • The child, covered in chocolate, eagerly reached for the strawberries.

     Correct answer: The child eagerly reached for the strawberries covered in chocolate.

     Placing "covered in chocolate" next to "strawberries" is correct because the modifier should describe the strawberries, not the child. The opening-phrase versions still attach the phrase to the child, and the last revision states the child, not the fruit, was covered in chocolate.

199. Evaluate $12 + 6 \times 5$.
     • 90
     • 60
     • 23
     • 42

     Correct answer: 42

     The value is $42$. Multiplication is performed before addition, so $6 \times 5 = 30$ is computed first, then $12 + 30 = 42$. Adding $12 + 6$ to get $18$ and then multiplying by $5$ ignores the precedence of multiplication and gives $90$.

200. In the expression $40 - 8 \times 2 + 3$, which operation is performed first?
     • The subtraction $40 - 8$
     • The multiplication $8 \times 2$
     • The addition $2 + 3$
     • Read strictly left to right with no precedence

     Correct answer: The multiplication $8 \times 2$

     The multiplication $8 \times 2$ is performed first. Order of operations places multiplication ahead of addition and subtraction, so $8 \times 2 = 16$ is evaluated before the expression becomes $40 - 16 + 3$. Doing the subtraction or addition first violates the precedence rule.

201. A school orders 32 boxes of pencils with 144 pencils in each box. If 1,200 pencils are handed out, how many pencils are left?
     • 4,608
     • 3,608
     • 3,408
     • 1,236

     Correct answer: 3,408

     There are $3{,}408$ pencils left. The total is $32 \times 144 = 4{,}608$ pencils, and subtracting the $1{,}200$ handed out gives $4{,}608 - 1{,}200 = 3{,}408$. Stopping at the total of $4{,}608$ ignores the pencils that were distributed.

202. Evaluate $48 \div (10 - 4) \times 2$.
     • 4
     • 9.6
     • 12
     • 16

     Correct answer: 16

     The result is $16$. The parentheses are evaluated first $(10 - 4 = 6)$, and then division and multiplication are done left to right: $48 \div 6 = 8$, then $8 \times 2 = 16$. Multiplying before dividing, or dividing by $10$ first, produces an incorrect value.

203. What is the value of $5^2 - 3 \times 4$?
     • 88
     • 28
     • 17
     • 13

     Correct answer: 13

     The value is $13$. The exponent is evaluated first, so $5^2 = 25$, then the multiplication $3 \times 4 = 12$, and finally $25 - 12 = 13$. Subtracting $3$ from $25$ before multiplying, or multiplying before the exponent, gives the wrong result.

204. A factory produces 2,184 parts in one shift and packs them into crates of 8. How many full crates are filled?
     • 263
     • 273
     • 270
     • 2,176

     Correct answer: 273

     The factory fills $273$ full crates. Dividing $2{,}184$ by $8$ gives exactly $273$ with no remainder, so all parts fit into $273$ crates. Subtracting $8$ from $2{,}184$ or adding instead of dividing produces the incorrect choices.

205. Evaluate $(7 + 5) \div 3 + 2^3$.
     • 12
     • 20
     • 14
     • 44

     Correct answer: 12

     The value is $12$. The parentheses give $7 + 5 = 12$, the exponent gives $2^3 = 8$, then the division $12 \div 3 = 4$, and finally $4 + 8 = 12$. Adding before dividing or skipping the exponent step leads to incorrect totals.

206. Add the fractions $\frac{3}{4}$ and $\frac{1}{6}$.
     • $\frac{4}{10}$
     • $\frac{4}{24}$
     • $\frac{1}{2}$
     • $\frac{11}{12}$

     Correct answer: $\frac{11}{12}$

     The sum is $\frac{11}{12}$. Using a common denominator of $12$ gives $\frac{3}{4} = \frac{9}{12}$ and $\frac{1}{6} = \frac{2}{12}$, so $\frac{9}{12} + \frac{2}{12} = \frac{11}{12}$. Adding the numerators and denominators directly to get $\frac{4}{10}$ is not a valid way to add fractions.

207. To divide $\frac{5}{8}$ by $\frac{3}{4}$, what is the correct first step?
     • Multiply $\frac{5}{8}$ by $\frac{4}{3}$
     • Multiply $\frac{5}{8}$ by $\frac{3}{4}$
     • Multiply $\frac{8}{5}$ by $\frac{3}{4}$
     • Add $\frac{5}{8}$ and $\frac{3}{4}$

     Correct answer: Multiply $\frac{5}{8}$ by $\frac{4}{3}$

     The correct first step is multiplying $\frac{5}{8}$ by $\frac{4}{3}$, the reciprocal of $\frac{3}{4}$. Dividing by a fraction is equivalent to multiplying by its reciprocal, giving $\frac{5 \times 4}{8 \times 3} = \frac{20}{24} = \frac{5}{6}$. Multiplying by $\frac{3}{4}$ without flipping, or flipping the wrong fraction, gives an incorrect quotient.

208. A pitcher holds $3\tfrac{1}{3}$ cups of juice. If you pour out $1\tfrac{1}{2}$ cups, how much juice remains?
     • $1\tfrac{5}{6}$ cups
     • $2\tfrac{1}{6}$ cups
     • $1\tfrac{1}{6}$ cups
     • $2\tfrac{5}{6}$ cups

     Correct answer: $1\tfrac{5}{6}$ cups

     The remaining juice is $1\tfrac{5}{6}$ cups. Converting to sixths gives $3\tfrac{2}{6} - 1\tfrac{3}{6}$; borrowing one whole turns $3\tfrac{2}{6}$ into $2\tfrac{8}{6}$, and $2\tfrac{8}{6} - 1\tfrac{3}{6} = 1\tfrac{5}{6}$. Subtracting without borrowing leads to the incorrect choices.

209. Multiply $\frac{2}{3}$ by $\frac{5}{8}$ and express the result in lowest terms.
     • $\frac{7}{11}$
     • $\frac{10}{24}$
     • $\frac{5}{12}$
     • $\frac{16}{15}$

     Correct answer: $\frac{5}{12}$

     The product is $\frac{5}{12}$. Multiplying numerators and denominators gives $\frac{10}{24}$, which reduces by dividing both by $2$ to reach $\frac{5}{12}$. The unreduced $\frac{10}{24}$ has the right value but is not in lowest terms, and $\frac{7}{11}$ comes from incorrectly adding.

210. Which improper fraction is equivalent to the mixed number $4\tfrac{3}{7}$?
     • $\frac{12}{7}$
     • $\frac{31}{7}$
     • $\frac{43}{7}$
     • $\frac{7}{7}$

     Correct answer: $\frac{31}{7}$

     The equivalent improper fraction is $\frac{31}{7}$. Multiplying the whole number $4$ by the denominator $7$ gives $28$, and adding the numerator $3$ gives $31$ over the original denominator $7$. Attaching the digits to form $\frac{43}{7}$ or adding $4$ and $3$ are both incorrect conversions.

211. Add the mixed numbers $2\tfrac{5}{6}$ and $1\tfrac{1}{2}$.
     • $4\tfrac{1}{3}$
     • $3\tfrac{6}{8}$
     • $4\tfrac{2}{3}$
     • $3\tfrac{1}{3}$

     Correct answer: $4\tfrac{1}{3}$

     The sum is $4\tfrac{1}{3}$. Adding the whole numbers gives $3$, and converting the fractions to sixths gives $\frac{5}{6} + \frac{3}{6} = \frac{8}{6} = 1\tfrac{2}{6}$; combining $3 + 1\tfrac{2}{6} = 4\tfrac{2}{6}$, which reduces to $4\tfrac{1}{3}$. Adding numerators and denominators separately gives the invalid result $3\tfrac{6}{8}$.

212. A ribbon is $\frac{5}{6}$ yard long and is cut into pieces that are each $\frac{1}{12}$ yard long. How many pieces are made?
     • 10
     • 5
     • 72
     • 6

     Correct answer: 10

     Ten pieces are made. Dividing $\frac{5}{6}$ by $\frac{1}{12}$ means multiplying $\frac{5}{6}$ by $\frac{12}{1}$, giving $\frac{5 \times 12}{6} = \frac{60}{6} = 10$. Multiplying $\frac{5}{6}$ by $\frac{1}{12}$ instead of dividing gives a tiny fraction rather than a count of pieces.

213. Add the decimals $12.6$ and $3.45$.
     • 15.06
     • 16.5
     • 47.1
     • 16.05

     Correct answer: 16.05

     The sum is $16.05$. Aligning the decimal points and adding gives $12.60 + 3.45 = 16.05$. Failing to line up the place values, such as treating $12.6$ as $12.06$, produces the incorrect totals.

214. How many decimal places will the product of $0.07$ and $0.6$ have?
     • One
     • Two
     • Three
     • Four

     Correct answer: Three

     The product will have three decimal places. The factor $0.07$ has two decimal places and $0.6$ has one, and the number of decimal places in the product equals their sum, so $0.07 \times 0.6 = 0.042$ has three. Reporting fewer places would misplace the decimal point.

215. A chemist measures liquid amounts of $0.85$, $1.2$, and $0.075$ liters. What is the total volume?
     • 2.125 liters
     • 2.215 liters
     • 1.225 liters
     • 2.05 liters

     Correct answer: 2.125 liters

     The total volume is $2.125$ liters. Aligning the decimals and adding $0.850 + 1.200 + 0.075$ gives $2.125$. Misaligning the place values when adding numbers with different lengths leads to the other results.

216. Divide $9.6$ by $0.4$.
     • 2.4
     • 24
     • 240
     • 3.84

     Correct answer: 24

     The quotient is $24$. Multiplying both numbers by $10$ clears the decimal in the divisor, turning the problem into $96 \div 4 = 24$. Dividing without adjusting the divisor gives $2.4$, which misplaces the decimal point.

217. Subtract $14.2 - 8.75$.
     • 5.45
     • 6.55
     • 5.55
     • 6.45

     Correct answer: 5.45

     The difference is $5.45$. Writing $14.2$ as $14.20$ and aligning place values gives $14.20 - 8.75 = 5.45$. Subtracting the digits without aligning the decimal points produces incorrect results.

218. A phone plan costs $32.40 per month. What is the total cost for 4 months?
     • $128.16
     • $36.40
     • $129.60
     • $126.40

     Correct answer: $129.60

     The total cost is $129.60. Multiplying $32.40 by $4$ gives $32.40 \times 4 = 129.60$. Adding $32.40 and $4$ instead of multiplying gives $36.40, and rounding errors produce the other amounts.

219. Multiply $2.5$ by $0.04$.
     • 0.1
     • 1.0
     • 0.01
     • 10.0

     Correct answer: 0.1

     The product is $0.1$. Multiplying $25 \times 4$ gives $100$, and since the factors together have three decimal places, the decimal point is placed to yield $0.100$, which is written as $0.1$. Misplacing the decimal point produces $0.01$ or $1.0$.

220. What is $40\%$ of $150$?
     • 110
     • 375
     • 190
     • 60

     Correct answer: 60

     The result is $60$. Finding $40\%$ means multiplying $0.40 \times 150$, which equals $60$. Subtracting $40$ from $150$ to get $110$ confuses a percent of a number with a difference.

221. To find a $20\%$ decrease on a quantity, what factor should you multiply the original amount by?
     • $1.20$
     • $0.20$
     • $0.80$
     • $0.02$

     Correct answer: $0.80$

     You multiply by $0.80$. A $20\%$ decrease leaves $100\%$ minus $20\%$, which is $80\%$ or the factor $0.80$, of the original amount. Multiplying by $0.20$ finds only the amount removed, and $1.20$ represents a $20\%$ increase.

222. A television originally priced at $400 is on sale for $35\%$ off. What is the sale price?
     • $365
     • $140
     • $260
     • $135

     Correct answer: $260

     The sale price is $260. A $35\%$ discount removes $0.35 \times 400 = 140$ dollars, leaving $400 - 140 = 260$ dollars, or equivalently $0.65 \times 400 = 260$ dollars. The value $140 is only the discount, not the final price.

223. A baseball player got $51$ hits in $170$ at-bats. What percent of at-bats resulted in a hit?
     • $25\%$
     • $33\%$
     • $3\%$
     • $30\%$

     Correct answer: $30\%$

     The player got a hit in $30\%$ of at-bats. Dividing $51$ by $170$ gives $0.30$, which equals $30\%$. Subtracting $51$ from $170$ to get $119$ mistakes the number of outs for a percent.

224. A savings account balance fell from $800 to $680. What was the percent decrease?
     • $12\%$
     • $18\%$
     • $20\%$
     • $15\%$

     Correct answer: $15\%$

     The percent decrease is $15\%$. The decrease is $800 - 680 = 120$, and dividing the change by the original amount gives $120 \div 800 = 0.15$, or $15\%$. Dividing by the new balance instead of the original produces an incorrect percent.

225. If $45$ is $75\%$ of a number, what is the number?
     • $33.75$
     • $120$
     • $60$
     • $90$

     Correct answer: $60$

     The number is $60$. Since $45$ represents $75\%$ of the whole, dividing $45$ by $0.75$ recovers the whole: $45 \div 0.75 = 60$. Multiplying $45$ by $0.75$ instead of dividing gives $33.75$, which reverses the operation.

226. A $600 investment earns $6\%$ simple interest in one year. How much will the account hold after that year?
     • $606
     • $960
     • $36
     • $636

     Correct answer: $636

     The account will hold $636. The interest is $0.06 \times 600 = 36$ dollars, and adding it to the original $600 gives $600 + 36 = 636$ dollars. Reporting $36 gives only the interest, while adding $6$ instead of the computed interest gives $606.

227. A coat priced at $120 is discounted $25\%$, and then $10\%$ is taken off the reduced price. What is the final price?
     • $78
     • $81
     • $90
     • $84

     Correct answer: $81

     The final price is $81. The $25\%$ discount leaves $0.75 \times 120 = 90$ dollars, and then the additional $10\%$ off leaves $0.90 \times 90 = 81$ dollars. Adding the two percents to take $35\%$ off at once gives $78, which does not match successive discounts.

228. Which symbol correctly completes the comparison $\frac{5}{8}$ ___ $0.6$?
     • <
     • >
     • =
     • They cannot be compared

     Correct answer: >

     The correct symbol is the greater-than sign. Converting $\frac{5}{8}$ to a decimal gives $0.625$, and $0.625$ is greater than $0.6$, so $\frac{5}{8} > 0.6$. Assuming the decimal must be larger because it is written as a decimal leads to the wrong choice.

229. Which of these numbers is least: $0.7$, $\frac{3}{4}$, $0.68$, or $\frac{7}{10}$?
     • $0.7$
     • $\frac{3}{4}$
     • $0.68$
     • $\frac{7}{10}$

     Correct answer: $0.68$

     The least value is $0.68$. Converting all to decimals gives $\frac{3}{4} = 0.75$, $0.7$, $\frac{7}{10} = 0.70$, and $0.68$, so $0.68$ is the smallest. Note that $0.7$ and $\frac{7}{10}$ are equal, while $0.68$ falls just below both.

230. On a number line, which value lies between $\frac{2}{5}$ and $\frac{3}{5}$?
     • $0.3$
     • $0.5$
     • $0.7$
     • $0.35$

     Correct answer: $0.5$

     The value $0.5$ lies between them. Since $\frac{2}{5} = 0.4$ and $\frac{3}{5} = 0.6$, a number between them must be greater than $0.4$ and less than $0.6$, and $0.5$ satisfies both conditions. The values $0.3$ and $0.35$ are too small, while $0.7$ is too large.

231. Which decimal is equivalent to the fraction $\frac{9}{25}$?
     • $0.925$
     • $0.25$
     • $3.6$
     • $0.36$

     Correct answer: $0.36$

     The equivalent decimal is $0.36$. Dividing $9$ by $25$ gives $0.36$, or equivalently scaling $\frac{9}{25}$ to $\frac{36}{100}$. Reading the numerator and denominator as digits to form $0.925$ ignores the actual division.

232. Order these values from greatest to least: $0.7$, $\frac{3}{4}$, $\frac{7}{10}$.
     • $\frac{7}{10}$, $0.7$, $\frac{3}{4}$
     • $\frac{3}{4}$, $0.7$, $\frac{7}{10}$
     • $0.7$, $\frac{3}{4}$, $\frac{7}{10}$
     • $\frac{3}{4}$, $\frac{7}{10}$, $0.7$

     Correct answer: $\frac{3}{4}$, $0.7$, $\frac{7}{10}$

     The correct order is $\frac{3}{4}$, $0.7$, $\frac{7}{10}$. Converting to decimals gives $\frac{3}{4} = 0.75$, then $0.7$, then $\frac{7}{10} = 0.70$, which arranges from greatest to least. Because $0.7$ and $\frac{7}{10}$ are equal in value, listing $\frac{7}{10}$ ahead of $0.7$ misorders them.

233. Which statement about $-2$ and $-9$ is true?
     • $-9$ is greater than $-2$
     • $-2$ is greater than $-9$
     • $-2$ and $-9$ are equal
     • $-9$ is closer to zero than $-2$

     Correct answer: $-2$ is greater than $-9$

     The true statement is that $-2$ is greater than $-9$. On a number line, values farther to the right are larger, and $-2$ lies to the right of $-9$, so $-2 > -9$. Treating the larger digit $9$ as the larger number ignores the negative sign.

234. What is $2{,}650$ rounded to the nearest thousand?
     • 2,000
     • 2,700
     • 3,000
     • 2,600

     Correct answer: 3,000

     Rounded to the nearest thousand, $2{,}650$ becomes $3{,}000$. The digit in the hundreds place is $6$, which is $5$ or greater, so the thousands digit rounds up from $2$ to $3$. Rounding down to $2{,}000$ ignores that $650$ is closer to $1{,}000$ than to $0$.

235. Why might a shopper round prices to the nearest dollar before adding several items?
     • To get a quick approximate total in their head
     • To find the exact total to the penny
     • Because prices cannot be added in decimal form
     • Because rounding permanently changes each price

     Correct answer: To get a quick approximate total in their head

     Rounding is done to get a quick approximate total in their head. Replacing each price with the nearest dollar makes mental addition easy and yields an estimate close to the true sum. Estimation gives an approximate, not exact, value, so the other statements misstate its purpose.

236. What is $0.0472$ rounded to the nearest hundredth?
     • $0.04$
     • $0.05$
     • $0.047$
     • $0.1$

     Correct answer: $0.05$

     Rounded to the nearest hundredth, $0.0472$ becomes $0.05$. The thousandths digit is $7$, which is $5$ or greater, so the hundredths digit rounds up from $4$ to $5$. Keeping $0.04$ would round down even though $0.0472$ is closer to $0.05$.

237. A diner orders meals costing $11.85, $7.20, and $14.95. About how much should the total be?
     • About $34
     • About $24
     • About $44
     • About $30

     Correct answer: About $34

     The total should be about $34. Rounding each price to $12, $7, and $15 gives an estimate of $12 + 7 + 15 = 34$ dollars, close to the exact total of $34.00. The other estimates come from rounding the prices incorrectly.

238. Estimate the product $38 \times 52$ by rounding each factor to the nearest ten.
     • $1{,}600$
     • $2{,}000$
     • $1{,}500$
     • $2{,}500$

     Correct answer: $2{,}000$

     The estimate is $2{,}000$. Rounding $38$ up to $40$ and $52$ down to $50$ gives $40 \times 50 = 2{,}000$, which is close to the exact product of $1{,}976$. Rounding only one factor or not rounding at all defeats the purpose of a quick estimate.

239. Evaluate $30 - 4 \times 3 + 18 \div 6$.
     • 21
     • 9
     • 16
     • 12

     Correct answer: 21

     The value is $21$. Multiplication and division come before addition and subtraction, so $4 \times 3 = 12$ and $18 \div 6 = 3$, making the expression $30 - 12 + 3$, which evaluates left to right to $18 + 3 = 21$. Working strictly left to right from the start gives the wrong answer.

240. A landscaper covers $\frac{7}{8}$ of a garden bed with mulch. If the bed has an area of $56$ square feet, how many square feet are mulched?
     • 7 square feet
     • 48 square feet
     • 63 square feet
     • 49 square feet

     Correct answer: 49 square feet

     The mulched area is $49$ square feet. Finding $\frac{7}{8}$ of $56$ means multiplying $\frac{7 \times 56}{8} = \frac{392}{8} = 49$. The value $7$ represents the remaining $\frac{1}{8}$ of the bed, not the mulched portion.

241. A stack of $3$ books weighs $4.86$ pounds total. If each book weighs the same, how much does one book weigh?
     • $1.45$ pounds
     • $14.58$ pounds
     • $1.86$ pounds
     • $1.62$ pounds

     Correct answer: $1.62$ pounds

     Each book weighs $1.62$ pounds. Dividing the total of $4.86$ pounds by $3$ gives $4.86 \div 3 = 1.62$. Multiplying $4.86$ by $3$ instead of dividing gives $14.58$, and misplacing the decimal produces the other values.

242. Which fraction is equivalent to 45%?
     • $\frac{4}{5}$
     • $\frac{9}{20}$
     • $\frac{1}{45}$
     • $\frac{45}{10}$

     Correct answer: $\frac{9}{20}$

     The equivalent fraction is $\frac{9}{20}$. Writing 45% as $\frac{45}{100}$ and reducing by dividing both parts by 5 gives $\frac{9}{20}$. Treating 45% as $\frac{4}{5}$ or as $\frac{1}{45}$ misinterprets the percent.

243. A delivery driver travels 178.4 miles in 5.9 hours. Estimate the average speed by rounding to convenient numbers.
     • About 25 miles per hour
     • About 40 miles per hour
     • About 18 miles per hour
     • About 30 miles per hour

     Correct answer: About 30 miles per hour

     The estimate is about 30 miles per hour. Rounding 178.4 to 180 and 5.9 to 6 gives $180 \div 6 = 30$, close to the exact value of about 30.2. The other estimates come from rounding the distance or time in ways that distort the quotient.

244. Which list places the values 0.25, $\frac{1}{3}$, and 0.3 in order from least to greatest?
     • 0.25, 0.3, $\frac{1}{3}$
     • $\frac{1}{3}$, 0.3, 0.25
     • 0.25, $\frac{1}{3}$, 0.3
     • 0.3, 0.25, $\frac{1}{3}$

     Correct answer: 0.25, 0.3, $\frac{1}{3}$

     The correct order is 0.25, 0.3, $\frac{1}{3}$. Converting to decimals gives 0.25, then 0.3, then $\frac{1}{3} \approx 0.333$, which arranges from least to greatest. Leaving the fraction unconverted makes it easy to misplace $\frac{1}{3}$ relative to 0.3.

245. Evaluate $15 + 36 \div 9 - 2 \times 3$.
     • 13
     • 11
     • 19
     • 7

     Correct answer: 13

     The value is 13. Division and multiplication are done before addition and subtraction, so $36 \div 9 = 4$ and $2 \times 3 = 6$ are found first, leaving $15 + 4 - 6$, which evaluates left to right to $19 - 6 = 13$.

246. What is the value of $3^3 - 4 \times (7 - 2)$?
     • 115
     • 7
     • 47
     • 23

     Correct answer: 7

     The value is 7. Work the parentheses first: $7 - 2 = 5$. Then the exponent: $3^3 = 27$. Next the multiplication: $4 \times 5 = 20$. Finally subtract: $27 - 20 = 7$.

247. Evaluate $72 \div (4 + 5) + 6 \times 2$.
     • 8
     • 26
     • 20
     • 18

     Correct answer: 20

     The result is 20. The parentheses give $4 + 5 = 9$, then division and multiplication follow: $72 \div 9 = 8$ and $6 \times 2 = 12$. Finally add: $8 + 12 = 20$.

248. A bakery bakes 936 muffins and packs them into trays of 12. How many full trays are filled?
     • 924
     • 76
     • 82
     • 78

     Correct answer: 78

     The bakery fills 78 trays. Dividing 936 by 12 gives exactly 78 with no remainder, since $78 \times 12 = 936$, so all muffins fit into 78 trays.

249. Evaluate $(6 + 2)^2 - 40 \div 8$.
     • 59
     • 3
     • 8
     • 60

     Correct answer: 59

     The value is 59. Parentheses first: $6 + 2 = 8$. Then the exponent: $8^2 = 64$. Then division: $40 \div 8 = 5$. Finally subtract: $64 - 5 = 59$.

250. A stadium has 64 sections with 350 seats in each section. If 18,500 tickets are sold, how many seats remain empty?
     • 22,400
     • 3,900
     • 4,100
     • 3,500

     Correct answer: 3,900

     There are 3,900 empty seats. First find the total capacity: $64 \times 350 = 22{,}400$. Then subtract the tickets sold: $22{,}400 - 18{,}500 = 3{,}900$.

251. In the expression $5 \times 6 + 48 \div (2 + 4)$, which operation is performed first?
     • The multiplication $5 \times 6$
     • The division $48 \div 2$
     • The addition $2 + 4$ inside the parentheses
     • The final addition of the two results

     Correct answer: The addition $2 + 4$ inside the parentheses

     The first operation is the addition inside the parentheses. Grouping symbols take top priority in the order of operations, so $2 + 4 = 6$ must be computed before the multiplication, division, or final addition.

252. Add the fractions $\frac{3}{8}$ and $\frac{1}{12}$.
     • $\frac{4}{20}$
     • $\frac{1}{5}$
     • $\frac{4}{24}$
     • $\frac{11}{24}$

     Correct answer: $\frac{11}{24}$

     The sum is $\frac{11}{24}$. The least common denominator of 8 and 12 is 24, so $\frac{3}{8} = \frac{9}{24}$ and $\frac{1}{12} = \frac{2}{24}$. Adding gives $\frac{9}{24} + \frac{2}{24} = \frac{11}{24}$, which is already in lowest terms.

253. Multiply the mixed numbers $2\frac{1}{4}$ and $1\frac{1}{3}$.
     • 3
     • $2\frac{7}{12}$
     • $3\frac{1}{12}$
     • $2\frac{1}{2}$

     Correct answer: 3

     The product is 3. Convert to improper fractions: $2\frac{1}{4} = \frac{9}{4}$ and $1\frac{1}{3} = \frac{4}{3}$. Multiply: $\frac{9 \times 4}{4 \times 3} = \frac{36}{12} = 3$.

254. A recipe calls for $\frac{2}{3}$ cup of sugar per batch. How much sugar is needed for 4 batches?
     • $2\frac{1}{3}$ cups
     • $2\frac{2}{3}$ cups
     • 3 cups
     • 2 cups

     Correct answer: $2\frac{2}{3}$ cups

     You need $2\frac{2}{3}$ cups. Multiplying $\frac{2}{3}$ by 4 gives $\frac{2 \times 4}{3} = \frac{8}{3} = 2\frac{2}{3}$ cups.

255. Which improper fraction is equivalent to the mixed number $6\frac{1}{5}$?
     • $\frac{11}{5}$
     • $\frac{61}{5}$
     • $\frac{31}{5}$
     • $\frac{7}{5}$

     Correct answer: $\frac{31}{5}$

     The equivalent improper fraction is $\frac{31}{5}$. Multiply the whole number by the denominator and add the numerator: $6 \times 5 = 30$, then $30 + 1 = 31$, placed over the original denominator 5.

256. Reduce the fraction $\frac{24}{60}$ to lowest terms.
     • $\frac{4}{10}$
     • $\frac{12}{30}$
     • $\frac{6}{15}$
     • $\frac{2}{5}$

     Correct answer: $\frac{2}{5}$

     In lowest terms the fraction is $\frac{2}{5}$. The greatest common factor of 24 and 60 is 12; dividing both by 12 gives $24 \div 12 = 2$ and $60 \div 12 = 5$.

257. Subtract the mixed numbers $7\frac{1}{6}$ and $2\frac{3}{4}$.
     • $4\frac{5}{12}$
     • $5\frac{5}{12}$
     • $4\frac{7}{12}$
     • $5\frac{7}{12}$

     Correct answer: $4\frac{5}{12}$

     The difference is $4\frac{5}{12}$. Using a common denominator of 12, write $7\frac{1}{6}$ as $7\frac{2}{12}$ and borrow to get $6\frac{14}{12}$. Then $6\frac{14}{12} - 2\frac{9}{12} = 4\frac{5}{12}$.

258. A pipe is $12\frac{1}{4}$ feet long. If a section $5\frac{5}{6}$ feet long is removed, how much pipe remains?
     • $7\frac{5}{12}$ feet
     • $6\frac{5}{12}$ feet
     • $6\frac{7}{12}$ feet
     • $7\frac{1}{12}$ feet

     Correct answer: $6\frac{5}{12}$ feet

     There are $6\frac{5}{12}$ feet remaining. With a common denominator of 12, $12\frac{1}{4}$ becomes $12\frac{3}{12}$. Borrowing gives $11\frac{15}{12}$, and $11\frac{15}{12} - 5\frac{10}{12} = 6\frac{5}{12}$ feet.

259. Divide $\frac{7}{8}$ by $\frac{1}{4}$.
     • $\frac{7}{32}$
     • $1\frac{1}{8}$
     • $3\frac{1}{2}$
     • $\frac{2}{8}$

     Correct answer: $3\frac{1}{2}$

     The quotient is $3\frac{1}{2}$. Dividing by $\frac{1}{4}$ means multiplying by its reciprocal $\frac{4}{1}$: $\frac{7}{8} \times \frac{4}{1} = \frac{28}{8} = \frac{7}{2} = 3\frac{1}{2}$.

260. Round the decimal 14.2763 to the nearest thousandth.
     • 14.277
     • 14.28
     • 14.27
     • 14.276

     Correct answer: 14.276

     Rounded to the nearest thousandth the value is 14.276. The digit in the ten-thousandths place is 3, which is less than 5, so the thousandths digit 6 stays the same.

261. Multiply 0.8 by 0.07.
     • 0.056
     • 0.56
     • 5.6
     • 0.0056

     Correct answer: 0.056

     The product is 0.056. Ignoring decimals, $8 \times 7 = 56$. The factors have a total of three decimal places, so the product is 0.056.

262. A hiker records distances of 2.7, 0.45, and 1.875 miles. What is the total distance?
     • 4.925 miles
     • 5.025 miles
     • 5.125 miles
     • 4.025 miles

     Correct answer: 5.025 miles

     The total is 5.025 miles. Aligning decimal points and adding, $2.700 + 0.450 + 1.875 = 5.025$.

263. Divide 5.6 by 0.08.
     • 7
     • 0.7
     • 70
     • 700

     Correct answer: 70

     The quotient is 70. Multiply both numbers by 100 to clear the decimal in the divisor, giving $560 \div 8 = 70$.

264. What is $15 - 9.27$?
     • 6.73
     • 5.83
     • 6.83
     • 5.73

     Correct answer: 5.73

     The difference is 5.73. Write 15 as 15.00 and subtract: $15.00 - 9.27 = 5.73$.

265. One notebook costs $3.45. What is the total cost of 8 notebooks?
     • $27.60
     • $24.60
     • $27.06
     • $28.40

     Correct answer: $27.60

     The total cost is $27.60. Multiplying 3.45 by 8 gives 27.60, since $3 \times 8 = 24$ and $0.45 \times 8 = 3.60$, which sum to 27.60.

266. Which decimal is equal to $\frac{3}{8}$?
     • 0.38
     • 0.375
     • 0.625
     • 0.3

     Correct answer: 0.375

     The decimal equal to $\frac{3}{8}$ is 0.375. Dividing 3 by 8 gives 0.375.

267. What is 75% of 240?
     • 160
     • 200
     • 180
     • 165

     Correct answer: 180

     The result is 180. Converting 75% to the decimal 0.75 and multiplying, $0.75 \times 240 = 180$.

268. To increase a quantity by 25%, what factor should you multiply the original amount by?
     • 0.25
     • 0.75
     • 1.025
     • 1.25

     Correct answer: 1.25

     The factor is 1.25. A 25% increase means keeping 100% of the amount and adding 25% more, which is 100% + 25% = 125%, written as the decimal 1.25.

269. A pair of shoes regularly priced at $80 is on sale for 30% off. What is the sale price?
     • $56
     • $24
     • $50
     • $104

     Correct answer: $56

     The sale price is $56. A 30% discount leaves 70% of the price, so $0.70 \times 80 = 56$.

270. A worker completed 63 of 90 assigned tasks. What percent of the tasks were completed?
     • 63%
     • 70%
     • 75%
     • 72%

     Correct answer: 70%

     The worker completed 70%. Dividing completed by total, $63 \div 90 = 0.70$, which equals 70%.

271. Attendance at an event rose from 250 to 320. What was the percent increase?
     • 22%
     • 30%
     • 28%
     • 25%

     Correct answer: 28%

     The increase was 28%. The growth is $320 - 250 = 70$, and dividing by the original 250 gives $70 \div 250 = 0.28$, or 28%.

272. If 27 is 45% of a number, what is the number?
     • 12.15
     • 72
     • 54
     • 60

     Correct answer: 60

     The number is 60. Since 27 represents 45% of the value, divide 27 by 0.45: $27 \div 0.45 = 60$.

273. A meal costs $60 before a 20% tip. How much is the tip?
     • $12
     • $15
     • $10
     • $9

     Correct answer: $12

     The tip is $12. Multiplying the bill by 20% as the decimal 0.20, $0.20 \times 60 = 12$.

274. Which symbol correctly completes the comparison $\frac{7}{8}$ ___ 0.9?
     • $=$
     • $<$
     • $>$
     • $\ge$

     Correct answer: $<$

     The correct symbol is the less-than sign. Writing $\frac{7}{8}$ as a decimal gives 0.875, and 0.875 is less than 0.9.

275. Which of these numbers is greatest: 0.62, $\frac{5}{8}$, 0.6, or $\frac{3}{5}$?
     • 0.62
     • 0.6
     • $\frac{5}{8}$
     • $\frac{3}{5}$

     Correct answer: $\frac{5}{8}$

     The greatest value is $\frac{5}{8}$. Converting all to decimals, $\frac{5}{8} = 0.625$, $0.62 = 0.620$, $0.6 = 0.600$, and $\frac{3}{5} = 0.600$, so 0.625 is largest.

276. On a number line, which value lies between $\frac{1}{3}$ and $\frac{2}{3}$?
     • $\frac{1}{4}$
     • $\frac{5}{6}$
     • $\frac{1}{6}$
     • $\frac{1}{2}$

     Correct answer: $\frac{1}{2}$

     The value that lies between is $\frac{1}{2}$. As decimals, $\frac{1}{3} \approx 0.333$ and $\frac{2}{3} \approx 0.667$, and $\frac{1}{2} = 0.5$ falls between them, while $\frac{1}{4}$, $\frac{5}{6}$, and $\frac{1}{6}$ do not.

277. Which fraction is equivalent to the decimal 0.16?
     • $\frac{4}{25}$
     • $\frac{16}{10}$
     • $\frac{1}{16}$
     • $\frac{1}{6}$

     Correct answer: $\frac{4}{25}$

     The equivalent fraction is $\frac{4}{25}$. Writing 0.16 as $\frac{16}{100}$ and dividing both parts by the common factor 4 gives $\frac{4}{25}$.

278. Which statement about $-5$ and $-8$ is true?
     • $-8$ is greater than $-5$
     • $-5$ is greater than $-8$
     • $-5$ equals $-8$
     • $-8$ is closer to zero than $-5$

     Correct answer: $-5$ is greater than $-8$

     The true statement is that $-5$ is greater than $-8$. On a number line, $-5$ lies to the right of $-8$, and values farther right are greater.

279. What is 73,481 rounded to the nearest thousand?
     • 74,000
     • 73,500
     • 73,000
     • 70,000

     Correct answer: 73,000

     Rounded to the nearest thousand the value is 73,000. The hundreds digit is 4, which is less than 5, so the thousands digit 3 stays the same.

280. About how much is $412 \times 19$ when each factor is rounded to a convenient number?
     • 4,000
     • 12,000
     • 800
     • 8,000

     Correct answer: 8,000

     The estimate is about 8,000. Rounding 412 to 400 and 19 to 20, the product $400 \times 20 = 8{,}000$.

281. Estimate the quotient $6{,}250 \div 31$ by rounding to compatible numbers.
     • 200
     • 20
     • 2,000
     • 60

     Correct answer: 200

     The estimate is about 200. Rounding 6,250 to 6,000 and 31 to 30 gives compatible numbers, and $6{,}000 \div 30 = 200$.

282. What is 0.0834 rounded to the nearest hundredth?
     • 0.09
     • 0.08
     • 0.083
     • 0.1

     Correct answer: 0.08

     Rounded to the nearest hundredth the value is 0.08. The thousandths digit is 3, which is less than 5, so the hundredths digit 8 stays the same.

283. A shopper buys items costing $6.10, $12.85, and $4.95. About how much should the total be?
     • About $20
     • About $30
     • About $24
     • About $26

     Correct answer: About $24

     The total should be about $24. Rounding each price to $6, $13, and $5 gives an estimate of $6 + 13 + 5 = 24$ dollars, close to the exact total of $23.90.

284. Estimate the product $47 \times 63$ by rounding each factor to the nearest ten.
     • 2,400
     • 3,500
     • 2,800
     • 3,000

     Correct answer: 3,000

     The estimate is 3,000. Rounding 47 up to 50 and 63 down to 60 gives $50 \times 60 = 3{,}000$, which is close to the exact product of 2,961.

285. What is the value of $|6| + |-2|$?
     • 8
     • 4
     • -8
     • 12

     Correct answer: 8

     The value is 8. Each absolute value is taken first, giving $|6| = 6$ and $|-2| = 2$, and then $6 + 2 = 8$. Treating $|-2|$ as $-2$ and computing $6 + (-2)$ would wrongly give 4.

286. Evaluate the expression $-4 - 6 + 3$.
     • 1
     • -7
     • -13
     • 5

     Correct answer: -7

     The result is -7. Working left to right, $-4 - 6$ equals $-10$, and $-10 + 3$ equals $-7$. Adding the negatives as if they canceled would give an incorrect positive value.

287. What is the quotient of $-\frac{3}{8}$ divided by $\frac{3}{4}$?
     • $-\frac{9}{32}$
     • -2
     • $-\frac{1}{2}$
     • $\frac{1}{2}$

     Correct answer: $-\frac{1}{2}$

     The quotient is $-\frac{1}{2}$. Dividing by $\frac{3}{4}$ means multiplying by its reciprocal $\frac{4}{3}$, so $-\frac{3}{8} \times \frac{4}{3} = -\frac{12}{24}$, which reduces to $-\frac{1}{2}$. Multiplying the two fractions directly without flipping the divisor would give $-\frac{9}{32}$.

288. Which value is greater than $-\frac{2}{5}$ but less than 0?
     • $-\frac{1}{2}$
     • $\frac{1}{5}$
     • $-\frac{3}{5}$
     • $-\frac{1}{10}$

     Correct answer: $-\frac{1}{10}$

     The value $-\frac{1}{10}$ fits. Expressed as decimals, $-\frac{2}{5}$ is $-0.4$ and the value must lie between $-0.4$ and 0, and $-\frac{1}{10}$ equals $-0.1$, which falls in that interval. The choice $-\frac{1}{2}$ equals $-0.5$, which is less than $-0.4$, not greater.

289. A submarine sits at -120 feet relative to sea level, then rises 45 feet. What is its new depth relative to sea level?
     • -75 feet
     • -165 feet
     • 75 feet
     • 165 feet

     Correct answer: -75 feet

     The new depth is -75 feet. Rising 45 feet adds 45 to the position, so $-120 + 45 = -75$ feet, still below sea level. Subtracting 45 instead of adding it would push the depth lower to -165 feet.

290. A factory produces 252 parts in 6 hours. At this rate, how many parts are produced per hour?
     • 246 parts
     • 42 parts
     • 1,512 parts
     • 36 parts

     Correct answer: 42 parts

     The factory produces 42 parts per hour. A unit rate divides total parts by hours, so $252 \div 6 = 42$. Multiplying 252 by 6 instead of dividing would give an unreasonably large total.

291. The ratio of teachers to students at a school is 1 to 18. If there are 540 students, how many teachers are there?
     • 522 teachers
     • 9,720 teachers
     • 30 teachers
     • 60 teachers

     Correct answer: 30 teachers

     There are 30 teachers. Setting up the proportion $\frac{1}{18} = \frac{x}{540}$ and cross multiplying gives $18x = 540$, so $x = 30$. Multiplying 540 by 18 instead of dividing would overstate the number of teachers.

292. How many centimeters are in 2.4 meters, given that 1 meter equals 100 centimeters?
     • 24 centimeters
     • 0.024 centimeters
     • 102.4 centimeters
     • 240 centimeters

     Correct answer: 240 centimeters

     There are 240 centimeters. Each meter is 100 centimeters, so $2.4 \times 100 = 240$. Adding 100 to 2.4 treats the conversion factor as a sum rather than a multiplier.

293. A 16-ounce bottle of juice costs $2.88, and a 24-ounce bottle costs $4.08. Which bottle has the lower cost per ounce?
     • The 24-ounce bottle at $0.17 per ounce
     • The 16-ounce bottle at $0.18 per ounce
     • The 16-ounce bottle at $0.17 per ounce
     • Both cost the same per ounce

     Correct answer: The 24-ounce bottle at $0.17 per ounce

     The 24-ounce bottle is cheaper at $0.17 per ounce. Dividing price by ounces gives $2.88 $\div 16 =$ $0.18 for the small bottle and $4.08 $\div 24 =$ $0.17 for the large bottle. Comparing only the total prices ignores the difference in sizes.

294. A model train is built at a scale where 3 inches represents 24 feet. How many feet does 7 inches represent?
     • 168 feet
     • 56 feet
     • 31 feet
     • 84 feet

     Correct answer: 56 feet

     Seven inches represents 56 feet. Since 3 inches stands for 24 feet, each inch stands for 8 feet, and $7 \times 8 = 56$ feet. Multiplying 7 by 24 directly ignores that the scale is set by 3 inches, not 1.

295. What is the value of $4^3$?
     • 12
     • 16
     • 64
     • 81

     Correct answer: 64

     The value is 64. The exponent means 4 is used as a factor three times: $4 \times 4 \times 4 = 64$. Multiplying the base by the exponent to get 12 treats the power as ordinary multiplication.

296. Simplify the expression $(x^3)^4$.
     • $x^{7}$
     • $x^{81}$
     • $x^{64}$
     • $x^{12}$

     Correct answer: $x^{12}$

     The result is $x^{12}$. When a power is raised to another power, the exponents are multiplied, so $(x^3)^4 = x^{3 \times 4} = x^{12}$. Adding the exponents to get $x^7$ applies the rule for multiplying like bases instead.

297. Write the number 6,200,000 in scientific notation.
     • $6.2 \times 10^{6}$
     • $62 \times 10^{5}$
     • $6.2 \times 10^{5}$
     • $6.2 \times 10^{-6}$

     Correct answer: $6.2 \times 10^{6}$

     In scientific notation, 6,200,000 is $6.2 \times 10^6$. The decimal point moves six places to the left to form 6.2, which requires a positive exponent of 6 for a number greater than ten. Writing $62 \times 10^5$ is not proper because the leading factor must be between 1 and 10.

298. What is the value of $\sqrt[3]{27}$?
     • 9
     • 3
     • 13.5
     • 6

     Correct answer: 3

     The value of $\sqrt[3]{27}$ is 3. The cube root asks for the number that, used as a factor three times, gives 27, and $3 \times 3 \times 3 = 27$. Dividing 27 by 3 to get 9 confuses taking a root with simple division.

299. Simplify the radical expression for $\sqrt{98}$ in simplest form.
     • $49\sqrt{2}$
     • $2\sqrt{7}$
     • $7\sqrt{2}$
     • $14\sqrt{7}$

     Correct answer: $7\sqrt{2}$

     The simplified form is $7\sqrt{2}$. Factoring 98 as $49 \times 2$ lets the perfect square 49 leave the radical as 7, giving $7\sqrt{2}$. Leaving $2\sqrt{7}$ reverses which factor is the perfect square.

300. A bacterium measures about $2 \times 10^{-5}$ meters across. Written as a standard decimal, how many meters is this?
     • 0.0002 meters
     • 200,000 meters
     • 0.000002 meters
     • 0.00002 meters

     Correct answer: 0.00002 meters

     The width is 0.00002 meters. The exponent $-5$ means the decimal point moves five places to the left of the 2, producing 0.00002. A positive exponent would instead make the number very large.

301. Simplify the expression $6m + 2 - 9m + 7$.
     • -3m + 9
     • 3m + 9
     • -3m - 5
     • 15m + 9

     Correct answer: -3m + 9

     The simplified expression is $-3m + 9$. Combining the like terms $6m$ and $-9m$ gives $-3m$, and combining the constants 2 and 7 gives 9. Adding the variable terms instead of subtracting would wrongly give $15m$.

302. Expand the expression $-2(5x - 3)$.
     • -10x - 3
     • -10x + 6
     • -10x - 6
     • 10x + 6

     Correct answer: -10x + 6

     The expanded form is $-10x + 6$. Distributing $-2$ to each term gives $-2 \times 5x = -10x$ and $-2 \times (-3) = +6$. Treating the product of two negatives as negative would incorrectly yield $-6$.

303. Evaluate the expression $4x^2 - 7$ when $x = 2$.
     • 1
     • 57
     • 9
     • 25

     Correct answer: 9

     The value is 9. Substituting $x = 2$ gives $4(2^2) - 7$, and order of operations means squaring first: $4 \times 4 - 7 = 16 - 7 = 9$. Squaring after multiplying by 4, as in $(4 \times 2)^2$, would produce an incorrect larger value.

304. Which expression is equivalent to $3(4y - 1) - 5y$?
     • 7y - 1
     • 12y - 3
     • 17y - 3
     • 7y - 3

     Correct answer: 7y - 3

     The equivalent expression is $7y - 3$. Distributing 3 gives $12y - 3$, and subtracting the separate $5y$ leaves $7y - 3$. Forgetting to combine $12y$ with $-5y$ would leave an incorrect coefficient.

305. Solve the linear equation $7x - 4 = 24$.
     • X = 4
     • X = 2.86
     • X = 20
     • X = -4

     Correct answer: X = 4

     The solution is $x = 4$. Adding 4 to both sides gives $7x = 28$, and dividing both sides by 7 gives $x = 4$. Dividing 24 by 7 directly without first adding 4 would give an incorrect value.

306. Solve for x: $3(2x - 1) = x + 12$.
     • X = 5
     • X = 3
     • X = -3
     • X = 2.2

     Correct answer: X = 3

     The solution is $x = 3$. Distributing gives $6x - 3 = x + 12$, subtracting x from both sides leaves $5x - 3 = 12$, so $5x = 15$ and $x = 3$. Failing to distribute the 3 to the $-1$ would change the constant and the result.

307. Solve the system of equations: $3x + 2y = 14$ and $y = 2x$.
     • X = 4, y = 8
     • X = 1, y = 2
     • X = 2, y = 4
     • X = 3, y = 6

     Correct answer: X = 2, y = 4

     The solution is $x = 2$ and $y = 4$. Substituting $y = 2x$ into the first equation gives $3x + 2(2x) = 14$, so $7x = 14$ and $x = 2$, which makes $y = 2(2) = 4$. Treating y as equal to x rather than $2x$ would lead to the wrong values.

308. Solve for x: $\frac{2x - 1}{5} = 3$.
     • X = 7
     • X = 16
     • X = 2
     • X = 8

     Correct answer: X = 8

     The solution is $x = 8$. Multiplying both sides by 5 gives $2x - 1 = 15$, adding 1 gives $2x = 16$, and dividing by 2 gives $x = 8$. Dividing by 2 before clearing the denominator would change the order of operations and give a wrong value.

309. The sum of two numbers is 50, and one number is 14 more than the other. What is the larger number?
     • 32
     • 18
     • 36
     • 25

     Correct answer: 32

     The larger number is 32. Letting the smaller be n, the equation $n + (n + 14) = 50$ gives $2n + 14 = 50$, so $2n = 36$ and $n = 18$, making the larger number $18 + 14 = 32$. Stopping at 18 reports the smaller number instead of the larger.

310. What is the slope of the line passing through the points (1, -3) and (5, 9)?
     • -3
     • 3
     • $\frac{1}{3}$
     • 12

     Correct answer: 3

     The slope is 3. Slope equals the change in y over the change in x, so $\frac{9 - (-3)}{5 - 1} = \frac{12}{4} = 3$. Inverting the ratio to compute change in x over change in y would give the reciprocal $\frac{1}{3}$.

311. What is the y-intercept of the line $y = -5x + 7$?
     • -5
     • -7
     • 7
     • 5

     Correct answer: 7

     The y-intercept is 7. In slope-intercept form $y = mx + b$, the constant term b is the y-intercept, so the line crosses the y-axis at 7. Reading the coefficient $-5$ as the intercept confuses the slope with where the line crosses the axis.

312. A line is perpendicular to a line with slope $\frac{1}{4}$. What is the slope of the perpendicular line?
     • $\frac{1}{4}$
     • 4
     • $-\frac{1}{4}$
     • -4

     Correct answer: -4

     The perpendicular slope is $-4$. Perpendicular lines have slopes that are negative reciprocals, so flipping $\frac{1}{4}$ to 4 and changing its sign gives $-4$. Only flipping without changing the sign would leave 4, which is not perpendicular.

313. A streaming service charges a $5 activation fee plus $12 per month. Which equation models the total cost y after x months?
     • Y = 12x + 5
     • Y = 5x + 12
     • Y = 17x
     • Y = 12x - 5

     Correct answer: Y = 12x + 5

     The correct equation is $y = 12x + 5$. The monthly $12 charge multiplies the number of months x, and the one-time $5 activation fee is the constant added once. Switching the roles of 5 and 12 would charge the activation fee every month.

314. A line has a slope of -2 and passes through the point (0, 4). Which point also lies on this line?
     • (1, 6)
     • (1, 2)
     • (2, 4)
     • (-1, 2)

     Correct answer: (1, 2)

     The point (1, 2) lies on the line. The equation is $y = -2x + 4$, and substituting $x = 1$ gives $y = -2(1) + 4 = 2$, matching the point (1, 2). Adding the slope instead of subtracting it would land on the wrong point.

315. A spinner has 10 equal sections numbered 1 through 10. What is the probability of landing on a number less than 4?
     • $\frac{1}{10}$
     • $\frac{2}{5}$
     • $\frac{3}{10}$
     • $\frac{4}{10}$

     Correct answer: $\frac{3}{10}$

     The probability is $\frac{3}{10}$. The numbers less than 4 are 1, 2, and 3, giving 3 favorable outcomes out of 10 equally likely sections, so the probability is $\frac{3}{10}$. Including 4 itself would wrongly add a fourth outcome.

316. A drawer holds 5 black socks, 3 white socks, and 4 gray socks. If one sock is drawn at random, what is the probability it is NOT white?
     • $\frac{3}{12}$
     • $\frac{1}{4}$
     • $\frac{9}{12}$
     • $\frac{3}{4}$

     Correct answer: $\frac{3}{4}$

     The probability is $\frac{3}{4}$. There are 12 socks total and 3 white, so 9 are not white, and $\frac{9}{12}$ reduces to $\frac{3}{4}$. Reporting the probability of drawing white instead of not white would give $\frac{1}{4}$.

317. A fair coin is flipped three times. What is the probability of getting heads on all three flips?
     • $\frac{1}{8}$
     • $\frac{1}{2}$
     • $\frac{1}{6}$
     • $\frac{3}{8}$

     Correct answer: $\frac{1}{8}$

     The probability is $\frac{1}{8}$. The flips are independent, so the probabilities multiply: $\frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} = \frac{1}{8}$. Adding the three probabilities instead of multiplying would wrongly give $\frac{3}{2}$, which is impossible.

318. Set A contains {1, 3, 5, 7, 9} and set B contains {2, 3, 5, 8}. What is the union of A and B?
     • {3, 5}
     • {1, 2, 3, 5, 7, 8, 9}
     • {1, 7, 9}
     • {2, 8}

     Correct answer: {1, 2, 3, 5, 7, 8, 9}

     The union is {1, 2, 3, 5, 7, 8, 9}. The union contains every element that appears in either set, listing each distinct value once. Listing only the values found in both sets describes the intersection, not the union.

319. A box contains 4 winning tickets and 16 losing tickets. One ticket is drawn and kept, and it is a winner. What is the probability that a second ticket drawn is also a winner?
     • $\frac{4}{20}$
     • $\frac{1}{5}$
     • $\frac{3}{19}$
     • $\frac{4}{19}$

     Correct answer: $\frac{3}{19}$

     The probability is $\frac{3}{19}$. After removing one winning ticket, 3 winners remain out of 19 total tickets, so the conditional probability is $\frac{3}{19}$. Using the original counts of 4 out of 20 ignores that the first ticket was not replaced.

320. A number cube numbered 1 through 6 is rolled once. What is the probability of rolling a factor of 6?
     • $\frac{1}{6}$
     • $\frac{1}{2}$
     • $\frac{5}{6}$
     • $\frac{2}{3}$

     Correct answer: $\frac{2}{3}$

     The probability is $\frac{2}{3}$. The factors of 6 between 1 and 6 are 1, 2, 3, and 6, giving 4 favorable outcomes out of 6, so $\frac{4}{6}$ reduces to $\frac{2}{3}$. Counting only some of the factors would understate the favorable outcomes.

321. The values 6, 10, 14, 14, and 21 make up a data set. What is the mean?
     • 13
     • 14
     • 12
     • 15

     Correct answer: 13

     The mean is 13. Adding the values gives $6 + 10 + 14 + 14 + 21 = 65$, and dividing by the 5 values gives $65 \div 5 = 13$. Choosing the most frequent value of 14 reports the mode rather than the mean.

322. What is the median of the data set 30, 12, 45, 18, 27, and 33?
     • 27
     • 28.5
     • 30
     • 29.2

     Correct answer: 28.5

     The median is 28.5. Ordering the six values as 12, 18, 27, 30, 33, 45 leaves two middle numbers, 27 and 30, and their average is $\frac{27 + 30}{2} = 28.5$. Picking just one of the two middle values would not give the true center for an even-sized set.

323. A histogram shows weekly sales for five stores: 22, 18, 35, 27, and 18. What is the mode of these values?
     • 35
     • 24
     • 18
     • 27

     Correct answer: 18

     The mode is 18. The mode is the value that appears most often, and 18 occurs twice while every other value appears once. Choosing the largest value of 35 confuses the maximum with the most frequent value.

324. A data set has a mean of 15 across 6 values. If a new value of 50 is added, raising the count to 7, what is the new mean?
     • 15
     • 32.5
     • 25
     • 20

     Correct answer: 20

     The new mean is 20. The original six values total $6 \times 15 = 90$, adding 50 gives 140, and dividing by 7 values gives $140 \div 7 = 20$. Averaging only 15 and 50 to get 32.5 ignores the other five values.

325. A scatterplot of daily temperature versus hot-cocoa sales shows points trending downward as temperature rises. What does this pattern indicate?
     • A negative correlation
     • A positive correlation
     • No correlation
     • An exact proportional relationship

     Correct answer: A negative correlation

     This indicates a negative correlation. When one variable increases while the other decreases, the points trend downward and the relationship is negative. A positive correlation would instead show sales rising as temperature rises.

326. On a box plot, the minimum is marked at 20 and the maximum is marked at 95. What is the range of the data?
     • 57.5
     • 75
     • 115
     • 95

     Correct answer: 75

     The range is 75. On a box plot the whiskers reach the minimum and maximum, so the range equals $95 - 20 = 75$. Adding the two endpoints or reading only the maximum does not measure the spread of the data.

327. A trapezoid has parallel bases of 8 inches and 12 inches and a height of 5 inches. What is its area?
     • 100 square inches
     • 240 square inches
     • 50 square inches
     • 25 square inches

     Correct answer: 50 square inches

     The area is 50 square inches. The area of a trapezoid equals one-half the sum of the bases times the height, so $\frac{1}{2}(8 + 12)(5) = \frac{1}{2}(20)(5) = 50$. Forgetting to take half of the base sum would double the area to 100.

328. A circle has a diameter of 10 centimeters. Using 3.14 for pi, what is its approximate circumference?
     • 78.5 centimeters
     • 62.8 centimeters
     • 15.7 centimeters
     • 31.4 centimeters

     Correct answer: 31.4 centimeters

     The circumference is about 31.4 centimeters. Circumference equals $\pi$ times the diameter, so $3.14 \times 10 = 31.4$. Using $\pi$ times the radius squared would instead give the area of the circle.

329. A right triangle has legs of length 9 and 12. What is the length of the hypotenuse?
     • 15
     • 21
     • 225
     • 21.6

     Correct answer: 15

     The hypotenuse is 15. By the Pythagorean theorem, the square of the hypotenuse equals $9^2 + 12^2 = 81 + 144 = 225$, and $\sqrt{225} = 15$. Adding the legs to get 21 ignores that the relationship involves squares, not sums.

330. A cylinder has a base radius of 3 inches and a height of 10 inches. Using 3.14 for pi, what is its approximate volume?
     • 94.2 cubic inches
     • 282.6 cubic inches
     • 188.4 cubic inches
     • 30 cubic inches

     Correct answer: 282.6 cubic inches

     The volume is about 282.6 cubic inches. The volume of a cylinder equals $\pi$ times the radius squared times the height, so $3.14 \times 3^2 \times 10 = 3.14 \times 9 \times 10 = 282.6$. Using the radius instead of the radius squared would give too small a result.

331. What is the value of $-15 + |-9|$?
     • -6
     • -24
     • 6
     • 24

     Correct answer: -6

     The value is -6. The absolute value is evaluated first, so $|-9|$ equals 9, and then $-15 + 9 = -6$. Treating $|-9|$ as $-9$ and computing $-15 + (-9)$ would wrongly give -24.

332. What is the product of $-\frac{2}{3}$ and $-\frac{9}{4}$?
     • $-\frac{3}{2}$
     • $\frac{3}{2}$
     • $-\frac{11}{12}$
     • $\frac{6}{4}$

     Correct answer: $\frac{3}{2}$

     The product is $\frac{3}{2}$. Multiplying the numerators and denominators gives $\frac{18}{12}$, the negatives cancel to a positive, and $\frac{18}{12}$ reduces to $\frac{3}{2}$. Keeping a negative sign would ignore that a negative times a negative is positive.

333. Which list orders the numbers $-0.5$, $-\frac{3}{4}$, $0.2$, and $-\frac{1}{8}$ from least to greatest?
     • $-\frac{1}{8}$, $-0.5$, $-\frac{3}{4}$, $0.2$
     • $0.2$, $-\frac{1}{8}$, $-0.5$, $-\frac{3}{4}$
     • $-\frac{3}{4}$, $-0.5$, $-\frac{1}{8}$, $0.2$
     • $-0.5$, $-\frac{3}{4}$, $-\frac{1}{8}$, $0.2$

     Correct answer: $-\frac{3}{4}$, $-0.5$, $-\frac{1}{8}$, $0.2$

     The correct order is $-\frac{3}{4}, -0.5, -\frac{1}{8}, 0.2$. Converting to decimals gives $-0.75$, $-0.5$, $-0.125$, and $0.2$, which increase in that sequence. Listing the most negative number last reverses the order.

334. Evaluate the expression $-20 - (-7)$.
     • 27
     • -27
     • 13
     • -13

     Correct answer: -13

     The result is -13. Subtracting a negative is the same as adding its opposite, so $-20 - (-7)$ becomes $-20 + 7 = -13$. Treating the double negative as further subtraction would give -27.

335. A bank account has a balance of -$48. After a deposit, the balance becomes $35. By how much did the balance change?
     • $83
     • $13
     • -$13
     • $48

     Correct answer: $83

     The change is $83. The change equals the final balance minus the starting balance, so $35 - (-48) = 35 + 48 = 83$. Subtracting 48 from 35 instead would ignore that the starting balance was negative.

336. A car travels 360 miles using 12 gallons of gasoline. What is its fuel efficiency in miles per gallon?
     • 348 miles per gallon
     • 30 miles per gallon
     • 4,320 miles per gallon
     • 0.03 miles per gallon

     Correct answer: 30 miles per gallon

     The car gets 30 miles per gallon. A unit rate divides miles by gallons, so $360 \div 12 = 30$. Dividing gallons by miles would instead give an unreasonably tiny value.

337. A recipe uses 3 cups of flour for every 2 cups of sugar. If a baker uses 15 cups of flour, how many cups of sugar are needed?
     • 22.5 cups
     • 30 cups
     • 10 cups
     • 14 cups

     Correct answer: 10 cups

     The baker needs 10 cups of sugar. Setting up the proportion $\frac{3}{2} = \frac{15}{x}$ and cross multiplying gives $3x = 30$, so $x = 10$. Multiplying 15 by 2 and ignoring the 3 would overstate the sugar.

338. A runner completes a race in 1.5 hours. How many minutes is this, given that 1 hour equals 60 minutes?
     • 61.5 minutes
     • 150 minutes
     • 40 minutes
     • 90 minutes

     Correct answer: 90 minutes

     The time is 90 minutes. Each hour is 60 minutes, so $1.5 \times 60 = 90$. Adding 60 to 1.5 treats the conversion factor as a sum rather than a multiplier.

339. A printer prints 5 pages every 8 seconds. At this rate, how many pages does it print in 2 minutes?
     • 75 pages
     • 16 pages
     • 10 pages
     • 192 pages

     Correct answer: 75 pages

     The printer prints 75 pages. Two minutes is 120 seconds, and printing 5 pages per 8 seconds gives $120 \div 8 = 15$ sets of 8 seconds, so $15 \times 5 = 75$. Forgetting to convert minutes to seconds would undercount the pages.

340. A map uses a scale where 2 centimeters represents 50 kilometers. How many kilometers does a distance of 7 centimeters represent?
     • 100 kilometers
     • 175 kilometers
     • 350 kilometers
     • 57 kilometers

     Correct answer: 175 kilometers

     Seven centimeters represents 175 kilometers. Since 2 centimeters stands for 50 kilometers, each centimeter stands for 25 kilometers, and $7 \times 25 = 175$. Multiplying 7 by 50 ignores that the scale is set by 2 centimeters.

341. Simplify the expression $x^9$ divided by $x^2$.
     • $x^{11}$
     • $x^{4.5}$
     • $x^{7}$
     • $x^{18}$

     Correct answer: $x^{7}$

     The result is $x^7$. When like bases are divided, the exponents are subtracted, so $x^9 \div x^2 = x^{9-2} = x^7$. Adding the exponents to get $x^{11}$ applies the rule for multiplication instead.

342. What is the value of $5^{-2}$ written as a fraction?
     • -10
     • $\frac{1}{10}$
     • -25
     • $\frac{1}{25}$

     Correct answer: $\frac{1}{25}$

     The value is $\frac{1}{25}$. A negative exponent means the reciprocal of the positive power, so $5^{-2} = \frac{1}{5^2} = \frac{1}{25}$. Treating the negative exponent as making the result negative would give an incorrect -25.

343. Write the number 0.00047 in scientific notation.
     • $4.7 \times 10^{-4}$
     • $4.7 \times 10^{4}$
     • $47 \times 10^{-5}$
     • $4.7 \times 10^{-3}$

     Correct answer: $4.7 \times 10^{-4}$

     In scientific notation, 0.00047 is $4.7 \times 10^{-4}$. The decimal point moves four places to the right to form 4.7, which requires a negative exponent of 4 for a number less than one. Writing $47 \times 10^{-5}$ is improper because the leading factor must be between 1 and 10.

344. Simplify the radical expression for $\sqrt{72}$ in simplest form.
     • $36\sqrt{2}$
     • $6\sqrt{2}$
     • $2\sqrt{6}$
     • $8\sqrt{3}$

     Correct answer: $6\sqrt{2}$

     The simplified form is $6\sqrt{2}$. Factoring 72 as $36 \times 2$ lets the perfect square 36 leave the radical as 6, giving $6\sqrt{2}$. Choosing $8\sqrt{3}$ uses factors that do not multiply back to 72.

345. What is the product of $4 \times 10^3$ and $2 \times 10^5$, written in scientific notation?
     • $8 \times 10^{15}$
     • $6 \times 10^{8}$
     • $8 \times 10^{8}$
     • $8 \times 10^{2}$

     Correct answer: $8 \times 10^{8}$

     The product is $8 \times 10^8$. Multiplying the leading factors gives $4 \times 2 = 8$, and adding the exponents gives $10^{3+5} = 10^8$. Multiplying the exponents instead of adding them would wrongly give $10^{15}$.

346. Simplify the expression $8a - 3b + 2a + 5b$.
     • 12ab
     • 6a + 8b
     • 10a + 8b
     • 10a + 2b

     Correct answer: 10a + 2b

     The simplified expression is $10a + 2b$. Combining the like terms $8a$ and $2a$ gives $10a$, and combining $-3b$ and $5b$ gives $2b$. Subtracting the a terms or adding unlike terms together would produce an incorrect result.

347. Expand the expression $4(2x + 3) - 5x$.
     • 3x + 12
     • 13x + 12
     • 3x + 7
     • 8x + 12

     Correct answer: 3x + 12

     The result is $3x + 12$. Distributing 4 gives $8x + 12$, and subtracting the separate $5x$ leaves $3x + 12$. Forgetting to combine $8x$ with $-5x$ would leave an incorrect coefficient.

348. Evaluate the expression $2x^2 + 3x$ when $x = -3$.
     • -9
     • 9
     • 27
     • -27

     Correct answer: 9

     The value is 9. Substituting $x = -3$ gives $2(-3)^2 + 3(-3)$, and squaring first gives $2(9) - 9 = 18 - 9 = 9$. Treating $(-3)^2$ as $-9$ would change the sign and give the wrong total.

349. Which expression is equivalent to $5(x + 2) + 3(x - 4)$?
     • 2x - 2
     • 8x + 22
     • 8x - 2
     • 8x - 14

     Correct answer: 8x - 2

     The equivalent expression is $8x - 2$. Distributing gives $5x + 10$ and $3x - 12$, and combining like terms yields $8x$ and $10 - 12 = -2$. Adding the constants instead of accounting for the negative would give the wrong constant.

350. Solve the linear equation $5x + 9 = 2x - 6$.
     • X = -1
     • X = 5
     • X = 1
     • X = -5

     Correct answer: X = -5

     The solution is $x = -5$. Subtracting $2x$ from both sides gives $3x + 9 = -6$, then subtracting 9 gives $3x = -15$, so $x = -5$. Adding 9 to both sides instead of subtracting would lead to a wrong value.

351. Solve for x: $-3(x - 4) = 18$.
     • X = -2
     • X = 2
     • X = 10
     • X = -10

     Correct answer: X = -2

     The solution is $x = -2$. Distributing gives $-3x + 12 = 18$, subtracting 12 gives $-3x = 6$, and dividing by $-3$ gives $x = -2$. Forgetting to divide by the negative sign would give the wrong sign on the answer.

352. Solve the system of equations: $x + y = 10$ and $x - y = 4$.
     • X = 3, y = 7
     • X = 7, y = 3
     • X = 6, y = 4
     • X = 5, y = 5

     Correct answer: X = 7, y = 3

     The solution is $x = 7$ and $y = 3$. Adding the two equations eliminates y, giving $2x = 14$ so $x = 7$, and substituting back gives $y = 3$. Swapping the values would not satisfy $x - y = 4$.

353. Solve the proportion $\frac{x}{6} = \frac{15}{9}$ for x.
     • X = 9
     • X = 22.5
     • X = 10
     • X = 3.6

     Correct answer: X = 10

     The solution is $x = 10$. Cross multiplying gives $9x = 90$, and dividing both sides by 9 gives $x = 10$. Multiplying 6 by 15 without dividing by 9 would overstate the value.

354. Three times a number decreased by 8 equals 19. What is the number?
     • 3.67
     • 11
     • 27
     • 9

     Correct answer: 9

     The number is 9. The equation $3n - 8 = 19$ leads to $3n = 27$, so $n = 9$. Adding instead of the correct steps, or dividing 19 by 3 before adding 8, would give a wrong value.

355. What is the slope of the line passing through the points (-2, 5) and (4, -7)?
     • -2
     • 2
     • $-\frac{1}{2}$
     • 12

     Correct answer: -2

     The slope is -2. Slope equals the change in y over the change in x, so $\frac{-7 - 5}{4 - (-2)} = \frac{-12}{6} = -2$. Inverting the ratio would give the reciprocal instead of the slope.

356. A line is parallel to the line $y = 3x - 1$. What is the slope of the parallel line?
     • $-\frac{1}{3}$
     • 3
     • -3
     • $\frac{1}{3}$

     Correct answer: 3

     The parallel slope is 3. Parallel lines have equal slopes, so any line parallel to $y = 3x - 1$ also has a slope of 3. Using the negative reciprocal $-\frac{1}{3}$ would describe a perpendicular line instead.

357. What is the x-intercept of the line $2x + 5y = 10$?
     • (0, 5)
     • (2, 0)
     • (5, 0)
     • (0, 2)

     Correct answer: (5, 0)

     The x-intercept is (5, 0). At the x-intercept y equals 0, so $2x = 10$ gives $x = 5$. Setting x to 0 instead would find the y-intercept rather than the x-intercept.

358. A taxi charges a $3 base fare plus $2 per mile. How many miles correspond to a total fare of $19?
     • 16 miles
     • 11 miles
     • 9.5 miles
     • 8 miles

     Correct answer: 8 miles

     The trip is 8 miles. The equation $2m + 3 = 19$ gives $2m = 16$, so $m = 8$. Dividing 19 by 2 without subtracting the base fare first would give a wrong distance.

359. A line passes through (0, -2) with a slope of 4. What is its equation in slope-intercept form?
     • Y = 4x - 2
     • Y = -2x + 4
     • Y = 4x + 2
     • Y = -4x - 2

     Correct answer: Y = 4x - 2

     The equation is $y = 4x - 2$. Slope-intercept form is $y = mx + b$, where the slope 4 is m and the point (0, -2) shows the y-intercept b is -2. Swapping the slope and intercept would give the wrong equation.

360. A bag contains 6 red, 4 blue, and 2 green marbles. If one marble is drawn at random, what is the probability it is blue?
     • $\frac{1}{2}$
     • $\frac{1}{3}$
     • $\frac{1}{6}$
     • $\frac{2}{3}$

     Correct answer: $\frac{1}{3}$

     The probability is $\frac{1}{3}$. There are 12 marbles total and 4 blue, so $\frac{4}{12}$ reduces to $\frac{1}{3}$. Using only the count of non-blue marbles would give the probability of the wrong event.

361. Two fair number cubes are rolled. What is the probability that both show a 5?
     • $\frac{2}{12}$
     • $\frac{1}{6}$
     • $\frac{1}{36}$
     • $\frac{1}{12}$

     Correct answer: $\frac{1}{36}$

     The probability is $\frac{1}{36}$. The two rolls are independent, so the probabilities multiply: $\frac{1}{6} \times \frac{1}{6} = \frac{1}{36}$. Adding the probabilities instead would wrongly give $\frac{2}{6}$.

362. Set A is {2, 4, 6, 8, 10} and set B is {3, 6, 9, 12}. What is the intersection of A and B?
     • {2, 4, 8, 10}
     • {2, 3, 4, 6, 8, 9, 10, 12}
     • {3, 9, 12}
     • {6}

     Correct answer: {6}

     The intersection is {6}. The intersection contains only elements found in both sets, and 6 is the single value appearing in A and B. Listing all elements of both sets describes the union instead.

363. In a class of 30 students, 18 play a sport and 12 do not. If one student is chosen at random, what is the probability the student plays a sport?
     • $\frac{3}{5}$
     • $\frac{2}{5}$
     • $\frac{2}{3}$
     • $\frac{1}{2}$

     Correct answer: $\frac{3}{5}$

     The probability is $\frac{3}{5}$. There are 18 sport-playing students out of 30, so $\frac{18}{30}$ reduces to $\frac{3}{5}$. Using the 12 students who do not play would give the probability of the opposite event.

364. A jar holds 7 cherry candies and 13 lemon candies. One candy is eaten and it is lemon, leaving 19 candies. What is the probability the next candy drawn is also lemon?
     • $\frac{13}{20}$
     • $\frac{12}{19}$
     • $\frac{12}{20}$
     • $\frac{7}{19}$

     Correct answer: $\frac{12}{19}$

     The probability is $\frac{12}{19}$. After removing one lemon candy, 12 lemon candies remain out of 19 total, so the conditional probability is $\frac{12}{19}$. Using the original count of 13 out of 20 ignores that one candy was already eaten.

365. A spinner is divided into 8 equal sections, 3 of which are shaded. What is the probability the spinner does NOT land on a shaded section?
     • $\frac{1}{8}$
     • $\frac{3}{8}$
     • $\frac{5}{8}$
     • $\frac{1}{2}$

     Correct answer: $\frac{5}{8}$

     The probability is $\frac{5}{8}$. With 3 of 8 sections shaded, 5 sections are unshaded, so the probability of not landing on shaded is $\frac{5}{8}$. Reporting $\frac{3}{8}$ would give the probability of landing on shaded instead.

366. The test scores 88, 92, 75, 88, and 67 make up a data set. What is the mean score?
     • 85
     • 88
     • 80
     • 82

     Correct answer: 82

     The mean is 82. Adding the scores gives $88 + 92 + 75 + 88 + 67 = 410$, and dividing by the 5 scores gives $410 \div 5 = 82$. Choosing the most frequent value of 88 reports the mode rather than the mean.

367. What is the range of the data set 14, 9, 22, 31, 18, and 9?
     • 22
     • 31
     • 13
     • 9

     Correct answer: 22

     The range is 22. The range is the largest value minus the smallest, so $31 - 9 = 22$. Reporting the maximum value of 31 alone does not measure the spread of the data.

368. A scatterplot of hours studied versus exam score shows points rising as hours increase. What does this pattern indicate?
     • A negative correlation
     • A positive correlation
     • No correlation
     • A causation guarantee

     Correct answer: A positive correlation

     This indicates a positive correlation. When both variables increase together, the points trend upward and the relationship is positive. A negative correlation would instead show scores falling as study hours rise.

369. On a box plot of quiz scores, the median is drawn at 74. What does this value represent?
     • The most common score
     • The average of all the scores
     • The middle of the data set
     • The largest score

     Correct answer: The middle of the data set

     The median represents the middle of the data set. On a box plot, the line inside the box marks the median, which is the value separating the lower half from the upper half. The median is not the average, the mode, or the maximum.

370. A data set of 5 numbers has a mean of 12. Four of the numbers are 8, 10, 15, and 11. What is the fifth number?
     • 12
     • 11
     • 14
     • 16

     Correct answer: 16

     The fifth number is 16. A mean of 12 across 5 numbers means the total is $5 \times 12 = 60$, and the four known values sum to 44, so the fifth is $60 - 44 = 16$. Dividing or averaging the known values would not recover the missing term.

371. Factor the trinomial $x^2 + 7x + 12$ completely.
     • $(x + 6)(x + 2)$
     • $(x + 3)(x + 4)$
     • $(x + 12)(x + 1)$
     • $(x - 3)(x - 4)$

     Correct answer: $(x + 3)(x + 4)$

     The factorization is $(x + 3)(x + 4)$. The two numbers must multiply to 12 and add to 7, and 3 and 4 satisfy both conditions. The pair 6 and 2 multiplies to 12 but adds to 8, giving the wrong middle term.

372. Factor $9x^2 - 25$ completely.
     • $(9x - 5)(x + 5)$
     • $(3x - 5)(3x + 5)$
     • $(3x - 5)^2$
     • $(3x + 5)^2$

     Correct answer: $(3x - 5)(3x + 5)$

     The factorization is $(3x - 5)(3x + 5)$. This is a difference of squares with the first term being $(3x)^2 = 9x^2$ and the second being $5^2 = 25$. Writing it as a squared binomial would introduce a middle term that the original lacks.

373. Factor $5x^3 + 10x^2$ by removing the greatest common factor.
     • $5x(x^2 + 2x)$
     • $x^2(5x + 10)$
     • $5x^2(x + 2)$
     • $5(x^3 + 2x^2)$

     Correct answer: $5x^2(x + 2)$

     The complete factorization is $5x^2(x + 2)$. The greatest common factor of $5x^3$ and $10x^2$ is $5x^2$, and dividing each term by it leaves $x + 2$. Pulling out a smaller factor such as $5x$ or $x^2$ alone leaves terms that still share a common factor.

374. Factor the trinomial $x^2 - 9x + 20$ completely.
     • $(x - 4)(x - 5)$
     • $(x - 2)(x - 10)$
     • $(x + 4)(x + 5)$
     • $(x - 1)(x - 20)$

     Correct answer: $(x - 4)(x - 5)$

     The factorization is $(x - 4)(x - 5)$. The two numbers must multiply to 20 and add to $-9$, and $-4$ and $-5$ satisfy both. The pair $-2$ and $-10$ multiplies to 20 but adds to $-12$, producing the wrong middle term.

375. Factor by grouping: $x^3 + 3x^2 + 2x + 6$.
     • $(x^2 + 3)(x + 2)$
     • $(x + 3)(x^2 + 2)$
     • $(x + 2)(x^2 + 3x)$
     • $(x + 6)(x^2 + 1)$

     Correct answer: $(x + 3)(x^2 + 2)$

     The factorization is $(x + 3)(x^2 + 2)$. Grouping the first two terms gives $x^2(x + 3)$ and the last two give $2(x + 3)$, so factoring out the common binomial $(x + 3)$ leaves $x^2 + 2$. Grouping the terms in a different pairing fails to produce a shared binomial factor.

376. Solve the quadratic equation $x^2 - x - 12 = 0$ by factoring.
     • $x = 4$ or $x = -3$
     • $x = -4$ or $x = 3$
     • $x = 6$ or $x = -2$
     • $x = 12$ or $x = -1$

     Correct answer: $x = 4$ or $x = -3$

     The solutions are $x = 4$ or $x = -3$. Factoring gives $(x - 4)(x + 3) = 0$, so setting each factor to zero yields $x = 4$ and $x = -3$. Reversing the signs would give the form $(x + 4)(x - 3)$, producing a middle term of $+x$ rather than $-x$.

377. Solve $(x - 2)^2 = 49$.
     • $x = 51$ or $x = -47$
     • $x = 7$ or $x = -7$
     • $x = 9$ or $x = -5$
     • $x = 9$ only

     Correct answer: $x = 9$ or $x = -5$

     The solutions are $x = 9$ or $x = -5$. Taking the $\sqrt{\ }$ of both sides gives $x - 2 = 7$ or $x - 2 = -7$, so $x = 9$ or $x = -5$. Considering only the positive root would drop the solution $x = -5$.

378. Using the quadratic formula, solve $x^2 + 4x + 1 = 0$.
     • $x = 2 \pm \sqrt{3}$
     • $x = -4 \pm \sqrt{3}$
     • $x = -2 \pm \sqrt{3}$
     • $x = -2 \pm \sqrt{5}$

     Correct answer: $x = -2 \pm \sqrt{3}$

     The solutions are $x = -2 \pm \sqrt{3}$. With $a = 1$, $b = 4$, and $c = 1$, the discriminant is $16 - 4 = 12$, so the formula gives $(-4 \pm \sqrt{12})/2 = (-4 \pm 2\sqrt{3})/2 = -2 \pm \sqrt{3}$. Failing to simplify $\sqrt{12}$ to $2\sqrt{3}$ before dividing causes errors.

379. What is the discriminant of the quadratic equation $2x^2 + 3x + 5 = 0$, and what does it indicate?
     • 49; two real solutions
     • -31; no real solutions
     • -31; one real solution
     • 9; two real solutions

     Correct answer: -31; no real solutions

     The discriminant is $-31$, indicating no real solutions. Using $b^2 - 4ac$ with $a = 2$, $b = 3$, and $c = 5$ gives $9 - 40 = -31$, and a negative discriminant means the parabola does not cross the x-axis. A positive value would be required for real solutions.

380. A ball is thrown upward and its height in feet is given by $h = -16t^2 + 32t$. At what time $t$ does the ball return to the ground (height 0), other than $t = 0$?
     • $t = 2$
     • $t = 1$
     • $t = 4$
     • $t = 16$

     Correct answer: $t = 2$

     The ball returns to the ground at $t = 2$ seconds. Setting $-16t^2 + 32t = 0$ and factoring gives $-16t(t - 2) = 0$, so $t = 0$ or $t = 2$, and the nonzero solution is $t = 2$. Dividing out the $t$ factor at the start would discard the meaningful return time.

381. Given $f(x) = 3x - 7$, what is $f(5)$?
     • 15
     • -7
     • 22
     • 8

     Correct answer: 8

     The value is 8. Substituting 5 for $x$ gives $f(5) = 3(5) - 7 = 15 - 7 = 8$. Subtracting before multiplying, or forgetting the constant term, would produce an incorrect result.

382. If $f(x) = 2x + 1$ and $g(x) = x - 4$, what is $(f + g)(x)$?
     • $3x - 3$
     • $2x - 3$
     • $3x + 5$
     • $x - 3$

     Correct answer: $3x - 3$

     The sum is $3x - 3$. Adding the two functions combines like terms: $2x + x$ gives $3x$, and $1 + (-4)$ gives $-3$. Multiplying the functions instead of adding them would change the operation requested.

383. What is the domain of the function $f(x) = \sqrt{x - 3}$?
     • $x > 3$
     • $x \le 3$
     • All real numbers
     • $x \ge 3$

     Correct answer: $x \ge 3$

     The domain is $x \ge 3$. The expression under a square root must be greater than or equal to zero, so $x - 3 \ge 0$ requires $x \ge 3$. Using a strict inequality would wrongly exclude $x = 3$, where the radicand equals zero and the function is defined.

384. The graph of $g(x) = (x - 4)^2 - 1$ is the graph of $f(x) = x^2$ transformed in which way?
     • 4 units left and 1 unit up
     • 4 units right and 1 unit up
     • 4 units right and 1 unit down
     • 4 units left and 1 unit down

     Correct answer: 4 units right and 1 unit down

     The graph moves 4 units right and 1 unit down. Replacing $x$ with $(x - 4)$ shifts the parabola right by 4, and subtracting 1 outside the squared term shifts it down by 1. Treating the inside subtraction as a leftward move reverses the horizontal direction.

385. What is the range of the function $f(x) = x^2 - 6$?
     • $y \ge -6$
     • $y \le -6$
     • All real numbers
     • $y \ge 6$

     Correct answer: $y \ge -6$

     The range is $y \ge -6$. The parabola opens upward, so its minimum output occurs at $x = 0$ where $f(0) = -6$, and all other outputs are larger. Treating the parabola as opening downward would incorrectly suggest a maximum at $-6$.

386. Given the table where $f(1) = 4$, $f(2) = 7$, $f(3) = 10$, and $f(4) = 13$, the function is linear. What is $f(0)$?
     • 0
     • 3
     • 1
     • 4

     Correct answer: 1

     The value $f(0)$ is 1. The outputs increase by 3 for each increase of 1 in the input, so the slope is 3, and working backward from $f(1) = 4$ gives $f(0) = 4 - 3 = 1$. Assuming $f(0)$ equals zero ignores the constant term of the linear pattern.

387. For the function $g(x) = -2(x - 1)^2 + 5$, what are the coordinates of the vertex?
     • $(-1, 5)$
     • $(1, -5)$
     • $(-1, -5)$
     • $(1, 5)$

     Correct answer: $(1, 5)$

     The vertex is $(1, 5)$. In vertex form $a(x - h)^2 + k$, the vertex is the point $(h, k)$, so $(x - 1)$ gives $h = 1$ and the added 5 gives $k = 5$. Reversing the sign of $h$ or $k$ would misread the vertex coordinates.

388. Solve the radical equation $\sqrt{x + 7} = 5$.
     • $x = 25$
     • $x = 32$
     • $x = 12$
     • $x = 18$

     Correct answer: $x = 18$

     The solution is $x = 18$. Squaring both sides removes the radical to give $x + 7 = 25$, so $x = 18$. Forgetting to square the right side and setting $x + 7$ equal to 5 would give a much smaller incorrect value.

389. Solve the rational equation $\frac{1}{x} + \frac{1}{2} = \frac{3}{4}$.
     • $x = 1$
     • $x = 2$
     • $x = \frac{1}{4}$
     • $x = 4$

     Correct answer: $x = 4$

     The solution is $x = 4$. Subtracting $\frac{1}{2}$ from both sides gives $\frac{1}{x} = \frac{3}{4} - \frac{2}{4} = \frac{1}{4}$, so $x = 4$. Adding the fractions on the left as if they shared a common variable denominator would misrepresent the equation.

390. Solve for $x$: $\sqrt{x + 12} = x$.
     • $x = 4$ or $x = -3$
     • $x = -3$
     • $x = 4$
     • $x = 12$

     Correct answer: $x = 4$

     The solution is $x = 4$. Squaring both sides gives $x + 12 = x^2$, which rearranges to $x^2 - x - 12 = 0$ and factors as $(x - 4)(x + 3) = 0$. The value $x = -3$ makes the radical equal a negative number, so it is extraneous and must be rejected.

391. Simplify the rational expression $\frac{x^2 - 16}{x - 4}$ for $x \ne 4$.
     • $x - 4$
     • $x - 16$
     • $x + 4$
     • $x^2 - 4$

     Correct answer: $x + 4$

     The simplified expression is $x + 4$. The numerator is a difference of squares that factors into $(x - 4)(x + 4)$, and canceling the common factor $(x - 4)$ leaves $x + 4$. Subtracting the constants directly without factoring would give an incorrect result.

392. Solve the rational equation $\frac{6}{x - 1} = 2$.
     • $x = 2$
     • $x = 3$
     • $x = 4$
     • $x = 7$

     Correct answer: $x = 4$

     The solution is $x = 4$. Multiplying both sides by $(x - 1)$ gives $6 = 2(x - 1)$, which expands to $6 = 2x - 2$, so $2x = 8$ and $x = 4$. Dividing 6 by 2 to get 3 without accounting for the subtracted 1 would give the wrong value.

393. Add the rational expressions $\frac{2}{x} + \frac{3}{x}$.
     • $\frac{5}{2x}$
     • $\frac{6}{x}$
     • $\frac{5}{x}$
     • $\frac{5}{x^2}$

     Correct answer: $\frac{5}{x}$

     The sum is $\frac{5}{x}$. Because the two fractions already share the common denominator $x$, the numerators add directly to give $2 + 3 = 5$ over $x$. Multiplying the denominators together or adding them would incorrectly change the shared denominator.

394. Subtract the polynomials $(5x^2 + 2x - 1) - (2x^2 - 3x + 4)$.
     • $3x^2 - x + 3$
     • $3x^2 + 5x - 5$
     • $7x^2 - x + 3$
     • $3x^2 - 5x - 5$

     Correct answer: $3x^2 + 5x - 5$

     The difference is $3x^2 + 5x - 5$. Distributing the negative sign gives $5x^2 + 2x - 1 - 2x^2 + 3x - 4$, and combining like terms yields $3x^2 + 5x - 5$. Forgetting to distribute the subtraction to every term in the second polynomial is a common error.

395. Multiply the binomials $(2x + 3)(x - 4)$.
     • $2x^2 + 11x - 12$
     • $2x^2 - 5x - 12$
     • $2x^2 - 5x + 12$
     • $2x^2 - x - 12$

     Correct answer: $2x^2 - 5x - 12$

     The product is $2x^2 - 5x - 12$. Using the distributive method gives $2x \times x = 2x^2$, the outer and inner terms $-8x$ and $3x$ combine to $-5x$, and $3 \times -4 = -12$. Failing to combine the two middle terms would leave the wrong coefficient.

396. What is the degree of the polynomial $4x^3 - 2x^5 + x - 9$?
     • 3
     • 9
     • 4
     • 5

     Correct answer: 5

     The degree is 5. The degree of a polynomial is the highest exponent present, which is the 5 in the term $-2x^5$, even though that term is not written first. Reading the first listed term's exponent rather than scanning for the largest exponent gives a wrong answer.

397. Solve the polynomial equation $x^3 - 4x^2 = 0$.
     • $x = 4$ only
     • $x = 0$ or $x = -4$
     • $x = -4$ only
     • $x = 0$ or $x = 4$

     Correct answer: $x = 0$ or $x = 4$

     The solutions are $x = 0$ or $x = 4$. Factoring out $x^2$ gives $x^2(x - 4) = 0$, so either $x^2 = 0$ giving $x = 0$, or $x - 4 = 0$ giving $x = 4$. Dividing both sides by $x^2$ at the outset would discard the valid solution $x = 0$.

398. Expand the product $(x - 6)(x + 6)$.
     • $x^2 - 36$
     • $x^2 + 36$
     • $x^2 - 12x - 36$
     • $x^2 - 12x + 36$

     Correct answer: $x^2 - 36$

     The expansion is $x^2 - 36$. Multiplying conjugate binomials follows the pattern $(a - b)(a + b) = a^2 - b^2$, giving $x^2 - 6^2 = x^2 - 36$. The middle terms $-6x$ and $+6x$ cancel, so any answer with a remaining $x$ term is incorrect.

399. When the polynomial $x^2 + 5x + 6$ is divided by $x + 2$, what is the quotient?
     • $x + 4$
     • $x + 3$
     • $x + 2$
     • $x + 6$

     Correct answer: $x + 3$

     The quotient is $x + 3$. The dividend factors as $(x + 2)(x + 3)$, so dividing by $x + 2$ leaves $x + 3$ with no remainder. Selecting $x + 6$ mistakes the constant term of the dividend for the quotient rather than performing the division.

400. Solve the exponential equation $2^x = 32$.
     • $x = 16$
     • $x = 5$
     • $x = 4$
     • $x = 6$

     Correct answer: $x = 5$

     The solution is $x = 5$. Because 32 equals 2 raised to the fifth power, the exponents must be equal when the bases match, so $x = 5$. Dividing 32 by 2 to get 16 treats the exponential relationship as ordinary division.

401. Evaluate the logarithm $\log_2 16$.
     • 8
     • 2
     • 5
     • 4

     Correct answer: 4

     The value is 4. The logarithm asks for the exponent to which 2 must be raised to produce 16, and since $2^4 = 16$, the answer is 4. Dividing 16 by 2 to get 8 confuses the logarithm with simple division.

402. Rewrite the logarithmic equation $\log_3 81 = 4$ in exponential form.
     • $4^3 = 81$
     • $3^4 = 81$
     • $81^3 = 4$
     • $3^{81} = 4$

     Correct answer: $3^4 = 81$

     The exponential form is $3^4 = 81$. A logarithm of the form $\log_b n = e$ converts to $b^e = n$, so the base 3 raised to 4 produces 81. Swapping the base and exponent would give an untrue statement.

403. A bacteria culture doubles every hour and starts with 50 cells. Which expression gives the number of cells after $h$ hours?
     • $50 + 2h$
     • $2(50)^h$
     • $50h^2$
     • $50(2)^h$

     Correct answer: $50(2)^h$

     The expression is $50(2)^h$. Exponential growth with a starting amount of 50 and a doubling factor of 2 is modeled by the initial value times the growth factor raised to the number of time periods. Adding $2h$ would describe linear rather than doubling growth.

404. Solve for $x$: $5^{x + 1} = 125$.
     • $x = 3$
     • $x = 24$
     • $x = 4$
     • $x = 2$

     Correct answer: $x = 2$

     The solution is $x = 2$. Because 125 equals 5 to the third power, the equation becomes $5^{x + 1} = 5^3$, so the exponents are equal: $x + 1 = 3$, giving $x = 2$. Setting $x + 1$ equal to 125 instead of matching exponents would give a far larger value.

405. Using the property $\log_b(mn) = \log_b m + \log_b n$, which expression equals $\log_2 8 + \log_2 4$?
     • $\log_2 32$
     • $\log_2 12$
     • $\log_4 32$
     • $\log_2 2$

     Correct answer: $\log_2 32$

     The expression equals $\log_2 32$. The sum of two logarithms with the same base equals the logarithm of the product, and $8 \times 4 = 32$. Adding the arguments to get 12 instead of multiplying them misapplies the product rule.

406. In a right triangle, the side opposite an acute angle is 3 and the hypotenuse is 5. What is the sine of that angle?
     • $\frac{4}{5}$
     • $\frac{3}{4}$
     • $\frac{3}{5}$
     • $\frac{5}{3}$

     Correct answer: $\frac{3}{5}$

     The sine is $\frac{3}{5}$. Sine of an angle equals the length of the opposite side divided by the hypotenuse, so 3 divided by 5 gives $\frac{3}{5}$. Using the adjacent side of 4 instead would give the cosine, not the sine.

407. What is the exact value of $\sin 30^\circ$?
     • $\frac{1}{2}$
     • $\frac{\sqrt{3}}{2}$
     • $\frac{\sqrt{2}}{2}$
     • 1

     Correct answer: $\frac{1}{2}$

     The value is $\frac{1}{2}$. The angle of 30 degrees is a standard reference angle whose sine is exactly one-half. The value $\frac{\sqrt{3}}{2}$ is the sine of 60 degrees, so swapping the two common reference angles is a frequent error.

408. Convert the angle 90 degrees to radians.
     • $\frac{\pi}{4}$ radians
     • $\frac{\pi}{3}$ radians
     • $\frac{\pi}{2}$ radians
     • $\pi$ radians

     Correct answer: $\frac{\pi}{2}$ radians

     The measure is $\frac{\pi}{2}$ radians. Multiplying degrees by $\frac{\pi}{180}$ converts to radians, so $90 \times \frac{\pi}{180} = \frac{90\pi}{180}$, which simplifies to $\frac{\pi}{2}$. Multiplying by $\frac{180}{\pi}$ instead would reverse the conversion and not yield radians.

409. For an acute angle, if the tangent equals $\frac{3}{4}$, and the opposite side is 6, what is the length of the adjacent side?
     • 8
     • 4.5
     • 10
     • 2

     Correct answer: 8

     The adjacent side is 8. Tangent equals the opposite divided by the adjacent, so $\frac{3}{4}$ equals 6 divided by the adjacent side, and solving gives an adjacent side of 8. Multiplying 6 by $\frac{3}{4}$ instead of dividing would produce the wrong length.

410. In a right triangle with legs 6 and 8 and hypotenuse 10, what is the cosine of the angle opposite the side of length 6?
     • $\frac{8}{10}$
     • $\frac{6}{10}$
     • $\frac{6}{8}$
     • $\frac{10}{8}$

     Correct answer: $\frac{8}{10}$

     The cosine is $\frac{8}{10}$. For the angle opposite the side of length 6, the adjacent leg is 8 and the hypotenuse is 10, and cosine equals adjacent over hypotenuse. Using the opposite side 6 in the numerator would give the sine of that angle instead.

411. What is the exact value of $\tan 45^\circ$?
     • $\frac{\sqrt{2}}{2}$
     • 1
     • $\sqrt{3}$
     • 0

     Correct answer: 1

     The value is 1. At 45 degrees the opposite and adjacent sides of a right triangle are equal, so their ratio, which defines the tangent, is exactly 1. Confusing tangent with sine or cosine of 45 degrees, which equal $\frac{\sqrt{2}}{2}$, would give a different value.

412. What is the equation of a circle centered at the origin with radius 6?
     • $x^2 + y^2 = 6$
     • $x^2 + y^2 = 36$
     • $(x - 6)^2 + (y - 6)^2 = 36$
     • $x^2 + y^2 = 12$

     Correct answer: $x^2 + y^2 = 36$

     The equation is $x^2 + y^2 = 36$. A circle centered at the origin follows the form $x^2 + y^2 = r^2$, and 6 squared is 36. Writing 6 on the right side rather than its square confuses the radius with the radius squared.

413. What is the distance between the points $(1, 2)$ and $(4, 6)$?
     • 7
     • 5
     • 25
     • $\sqrt{7}$

     Correct answer: 5

     The distance is 5. The distance formula gives the $\sqrt{\ }$ of the squared differences, so $\sqrt{(4 - 1)^2 + (6 - 2)^2} = \sqrt{9 + 16} = \sqrt{25} = 5$. Adding the coordinate differences without squaring would not give the straight-line distance.

414. The parabola $y = x^2 - 6x + 5$ has its vertex at what x-coordinate?
     • $x = 3$
     • $x = 6$
     • $x = -3$
     • $x = 5$

     Correct answer: $x = 3$

     The vertex is at $x = 3$. The x-coordinate of a parabola's vertex is found with the formula $\frac{-b}{2a}$, which gives $\frac{-(-6)}{2(1)} = \frac{6}{2} = 3$. Forgetting the negative sign in the formula would give an incorrect x-coordinate of $-3$.

415. A circle has equation $(x - 2)^2 + (y + 3)^2 = 16$. Does the point $(6, -3)$ lie on the circle?
     • Yes, it lies on the circle
     • No, it lies inside the circle
     • No, it lies outside the circle
     • It cannot be determined

     Correct answer: Yes, it lies on the circle

     Yes, the point lies on the circle. Substituting the coordinates gives $(6 - 2)^2 + (-3 + 3)^2 = 16 + 0 = 16$, which equals the right side, so the point satisfies the equation exactly. A result less than 16 would place the point inside and a result greater than 16 outside.

416. What number must be added to $x^2 + 10x$ to complete the square?
     • 100
     • 5
     • 20
     • 25

     Correct answer: 25

     The number is 25. To complete the square on $x^2 + bx$, you add the square of half the coefficient $b$, and half of 10 is 5, whose square is 25. Using the full coefficient 10 or simply halving it without squaring would give an incorrect value.

417. Factor the trinomial $x^2 + 2x - 15$ completely.
     • $(x + 3)(x - 5)$
     • $(x + 15)(x - 1)$
     • $(x - 5)(x - 3)$
     • $(x - 3)(x + 5)$

     Correct answer: $(x - 3)(x + 5)$

     The factorization is $(x - 3)(x + 5)$. The two numbers must multiply to $-15$ and add to $+2$, and $-3$ and $+5$ satisfy both. The pair $+3$ and $-5$ multiplies to $-15$ but adds to $-2$, producing the wrong middle term.

418. Factor the trinomial $2x^2 + 7x + 3$ completely.
     • $(2x + 3)(x + 1)$
     • $(2x + 3)(x + 3)$
     • $(2x + 1)(x + 3)$
     • $(x + 1)(x + 3)$

     Correct answer: $(2x + 1)(x + 3)$

     The factorization is $(2x + 1)(x + 3)$. The outer and inner products must give $7x$, and $2x$ times 3 plus 1 times $x$ equals $6x + x = 7x$, while the constants 1 and 3 multiply to 3. The pair $(2x + 3)(x + 1)$ gives a middle term of $5x$ instead of $7x$.

419. Factor $4x^2 - 49$ completely.
     • $(4x - 7)(x + 7)$
     • $(2x - 7)^2$
     • $(2x + 7)^2$
     • $(2x - 7)(2x + 7)$

     Correct answer: $(2x - 7)(2x + 7)$

     The factorization is $(2x - 7)(2x + 7)$. This is a difference of squares because $4x^2$ equals $(2x)^2$ and 49 equals $7^2$, so it follows the pattern $a^2 - b^2 = (a - b)(a + b)$. A squared binomial would add a middle term that the original expression does not contain.

420. Factor the expression $x^2 - 12x + 36$ completely.
     • $(x - 6)(x + 6)$
     • $(x - 4)(x - 9)$
     • $(x - 6)^2$
     • $(x + 6)^2$

     Correct answer: $(x - 6)^2$

     The factorization is $(x - 6)^2$. This is a perfect square trinomial because the first and last terms are squares of $x$ and 6, and the middle term $-12x$ equals twice the product of $x$ and $-6$. The difference of squares form would require the constant term to be negative, not $+36$.

421. Factor completely: $3x^2 - 27$.
     • $(3x - 9)(x + 3)$
     • $3(x - 9)(x + 3)$
     • $3(x - 3)(x + 3)$
     • $(x - 3)(3x + 9)$

     Correct answer: $3(x - 3)(x + 3)$

     The complete factorization is $3(x - 3)(x + 3)$. First the greatest common factor 3 is removed to give $3(x^2 - 9)$, and then $x^2 - 9$ factors as the difference of squares $(x - 3)(x + 3)$. Stopping after pulling out 3 would leave the expression not fully factored.

422. Solve the quadratic equation $x^2 + 3x - 10 = 0$ by factoring.
     • $x = 5$ or $x = -2$
     • $x = 5$ or $x = 2$
     • $x = -5$ or $x = -2$
     • $x = -5$ or $x = 2$

     Correct answer: $x = -5$ or $x = 2$

     The solutions are $x = -5$ or $x = 2$. Factoring gives $(x + 5)(x - 2) = 0$, so setting each factor to zero yields $x = -5$ and $x = 2$. Reversing the signs would produce a middle term of $-3x$ rather than $+3x$.

423. Solve $(x + 3)^2 = 25$.
     • $x = 5$ or $x = -5$
     • $x = 22$ or $x = -28$
     • $x = 2$ only
     • $x = 2$ or $x = -8$

     Correct answer: $x = 2$ or $x = -8$

     The solutions are $x = 2$ or $x = -8$. Taking the $\sqrt{\ }$ of both sides gives $x + 3 = 5$ or $x + 3 = -5$, so $x = 2$ or $x = -8$. Considering only the positive root would drop the solution $x = -8$.

424. Using the quadratic formula, solve $x^2 - 6x + 7 = 0$.
     • $x = -3 \pm \sqrt{2}$
     • $x = 6 \pm \sqrt{2}$
     • $x = 3 \pm \sqrt{7}$
     • $x = 3 \pm \sqrt{2}$

     Correct answer: $x = 3 \pm \sqrt{2}$

     The solutions are $x = 3 \pm \sqrt{2}$. With $a = 1$, $b = -6$, and $c = 7$, the discriminant is $36 - 28 = 8$, so the formula gives $\frac{6 \pm \sqrt{8}}{2} = \frac{6 \pm 2\sqrt{2}}{2} = 3 \pm \sqrt{2}$. Failing to simplify $\sqrt{8}$ to $2\sqrt{2}$ before dividing leads to errors.

425. How many real solutions does the equation $x^2 - 4x + 4 = 0$ have, based on its discriminant?
     • Two real solutions
     • One real solution
     • No real solutions
     • Three real solutions

     Correct answer: One real solution

     The equation has one real solution. The discriminant $b^2 - 4ac$ equals $16 - 16 = 0$, and a discriminant of zero means the parabola touches the x-axis at exactly one point. A positive discriminant would be needed for two distinct real solutions.

426. A rectangular garden has a length 2 feet greater than its width, and its area is 48 square feet. If $w$ represents the width, which equation models this situation?
     • $w^2 - 2w - 48 = 0$
     • $2w + 2 = 48$
     • $w^2 + 2w - 48 = 0$
     • $w^2 + 2w + 48 = 0$

     Correct answer: $w^2 + 2w - 48 = 0$

     The correct equation is $w^2 + 2w - 48 = 0$. The length is $w + 2$, so the area $w(w + 2)$ equals 48, which expands to $w^2 + 2w = 48$ and rearranges to $w^2 + 2w - 48 = 0$. Adding 48 instead of subtracting it would place the constant on the wrong side of the equation.

427. What value of $c$ makes $x^2 - 8x + c$ a perfect square trinomial?
     • 64
     • 8
     • 4
     • 16

     Correct answer: 16

     The value is 16. To complete the square on $x^2 + bx$, you add the square of half of $b$, and half of $-8$ is $-4$, whose square is 16. Using the full coefficient 8 or halving it without squaring would give an incorrect constant.

428. Given $f(x) = x^2 - 2x$, what is $f(-3)$?
     • 3
     • 15
     • -3
     • 9

     Correct answer: 15

     The value is 15. Substituting $-3$ for $x$ gives $f(-3) = (-3)^2 - 2(-3) = 9 + 6 = 15$. Treating $(-3)^2$ as $-9$ or mishandling the sign of the $-2x$ term would produce an incorrect result.

429. What is the domain of the rational function $f(x) = \frac{5}{x - 2}$?
     • $x \ne 5$
     • $x > 2$
     • All real numbers
     • $x \ne 2$

     Correct answer: $x \ne 2$

     The domain is $x \ne 2$. A rational function is undefined wherever its denominator equals zero, and $x - 2$ equals zero when $x = 2$, so that value must be excluded. The numerator 5 has no effect on the domain restriction.

430. If $f(x) = 2x - 1$ and $g(x) = x^2$, what is $f(g(2))$?
     • 7
     • 9
     • 3
     • 15

     Correct answer: 7

     The value is 7. First $g(2) = 2^2 = 4$, then $f(4) = 2(4) - 1 = 7$. Evaluating $f$ before $g$, which would give $f(2) = 3$ and then square it, applies the composition in the wrong order.

431. The graph of $g(x) = x^2 + 3$ is the graph of $f(x) = x^2$ transformed in which way?
     • 3 units right
     • 3 units down
     • 3 units left
     • 3 units up

     Correct answer: 3 units up

     The graph moves 3 units up. Adding a constant outside the squared term shifts the entire parabola vertically, and a positive 3 moves it upward. A horizontal shift would require the 3 to appear inside the squared expression with $x$.

432. What is the range of the function $f(x) = -x^2 + 4$?
     • $y \ge 4$
     • All real numbers
     • $y \le 4$
     • $y \le -4$

     Correct answer: $y \le 4$

     The range is $y \le 4$. The negative leading coefficient means the parabola opens downward, so its maximum output occurs at $x = 0$ where $f(0) = 4$, and all other outputs are smaller. Treating the parabola as opening upward would wrongly suggest a minimum at 4.

433. For a linear function, $f(2) = 5$ and $f(6) = 17$. What is the slope of the function?
     • 4
     • 2
     • 3
     • 12

     Correct answer: 3

     The slope is 3. The slope equals the change in output divided by the change in input, which is $(17 - 5)$ divided by $(6 - 2)$ equal to $\frac{12}{4} = 3$. Dividing the input difference by the output difference would invert the ratio.

434. Given $f(x) = 2x + 3$, what is the inverse function $f^{-1}(x)$?
     • $\frac{x + 3}{2}$
     • $2x - 3$
     • $\frac{x - 3}{2}$
     • $\frac{1}{2x + 3}$

     Correct answer: $\frac{x - 3}{2}$

     The inverse is $\frac{x - 3}{2}$. To find the inverse, swap $x$ and $y$ in $y = 2x + 3$ to get $x = 2y + 3$, then solve for $y$ by subtracting 3 and dividing by 2. Taking the reciprocal of the function instead of reversing its operations confuses the inverse with $\frac{1}{f(x)}$.

435. Solve the radical equation $\sqrt{2x - 1} = 3$.
     • $x = 5$
     • $x = 4$
     • $x = 10$
     • $x = 2$

     Correct answer: $x = 5$

     The solution is $x = 5$. Squaring both sides removes the radical to give $2x - 1 = 9$, so $2x = 10$ and $x = 5$. Forgetting to square the right side and setting $2x - 1$ equal to 3 would give a smaller incorrect value.

436. Solve the rational equation $\frac{3}{x + 2} = 1$.
     • $x = 1$
     • $x = 3$
     • $x = 5$
     • $x = -1$

     Correct answer: $x = 1$

     The solution is $x = 1$. Multiplying both sides by $(x + 2)$ gives $3 = x + 2$, so $x = 1$. Subtracting 2 from 3 incorrectly before clearing the denominator would lead to the wrong value.

437. Simplify the rational expression $\frac{x^2 + 5x + 6}{x + 3}$ for $x \ne -3$.
     • $x + 6$
     • $x + 3$
     • $x + 2$
     • $x - 2$

     Correct answer: $x + 2$

     The simplified expression is $x + 2$. The numerator factors as $(x + 3)(x + 2)$, and canceling the common factor $(x + 3)$ leaves $x + 2$. Selecting $x + 6$ mistakes the constant term of the numerator for the simplified result.

438. Multiply the rational expressions $\frac{2}{x} \times \frac{x}{6}$.
     • $\frac{2}{6x}$
     • $\frac{1}{3}$
     • $\frac{2x}{6}$
     • $\frac{12}{x^2}$

     Correct answer: $\frac{1}{3}$

     The product is $\frac{1}{3}$. Multiplying across gives $2x$ in the numerator and $6x$ in the denominator, and canceling the common factor $x$ leaves $\frac{2}{6}$, which simplifies to $\frac{1}{3}$. Adding the fractions instead of multiplying them would change the operation requested.

439. Solve the rational equation $\frac{x}{x - 3} = 4$.
     • $x = 4$
     • $x = 3$
     • $x = 12$
     • $x = -4$

     Correct answer: $x = 4$

     The solution is $x = 4$. Multiplying both sides by $(x - 3)$ gives $x = 4(x - 3)$, which expands to $x = 4x - 12$, so $-3x = -12$ and $x = 4$. Cross-multiplying incorrectly or dropping the distribution of the 4 would give a wrong result.

440. Add the polynomials $(3x^2 - x + 5) + (x^2 + 4x - 2)$.
     • $4x^2 + 3x + 3$
     • $4x^2 - 3x + 3$
     • $4x^2 + 5x + 3$
     • $2x^2 + 3x + 3$

     Correct answer: $4x^2 + 3x + 3$

     The sum is $4x^2 + 3x + 3$. Combining like terms gives $3x^2 + x^2 = 4x^2$, $-x + 4x = 3x$, and $5 + (-2) = 3$. Subtracting the second polynomial instead of adding it would change the signs of its terms.

441. Expand the product $(x + 5)^2$.
     • $x^2 + 25$
     • $x^2 + 10x + 25$
     • $x^2 + 5x + 25$
     • $x^2 + 10x + 10$

     Correct answer: $x^2 + 10x + 25$

     The expansion is $x^2 + 10x + 25$. Squaring a binomial follows the pattern $(a + b)^2 = a^2 + 2ab + b^2$, so the middle term is twice $x$ times 5, which is $10x$, and the last term is $5^2 = 25$. Omitting the middle term mistakenly treats the square as a sum of squares.

442. Multiply the binomial by the trinomial: $(x + 2)(x^2 + 3x + 1)$.
     • $x^3 + 5x^2 + 7x + 2$
     • $x^3 + 3x^2 + x + 2$
     • $x^3 + 5x^2 + 6x + 2$
     • $x^3 + 2x^2 + 7x + 2$

     Correct answer: $x^3 + 5x^2 + 7x + 2$

     The product is $x^3 + 5x^2 + 7x + 2$. Distributing $x$ across the trinomial gives $x^3 + 3x^2 + x$, distributing 2 gives $2x^2 + 6x + 2$, and combining like terms yields $x^3 + 5x^2 + 7x + 2$. Failing to combine the $x^2$ and $x$ terms from both distributions leaves wrong coefficients.

443. What is the leading coefficient of the polynomial $7 - 3x^2 + 5x^4 - x$?
     • 7
     • -3
     • -1
     • 5

     Correct answer: 5

     The leading coefficient is 5. The leading coefficient is the number multiplying the term with the highest exponent, which is $5x^4$, even though that term is not written first. Reading the constant term 7 or the first listed coefficient ignores the need to identify the highest-degree term.

444. Solve the polynomial equation $x^3 - 9x = 0$.
     • $x = 0, 3,$ or $-3$
     • $x = 3$ or $-3$ only
     • $x = 0$ or $9$
     • $x = 9$ only

     Correct answer: $x = 0, 3,$ or $-3$

     The solutions are $x = 0, 3,$ or $-3$. Factoring out $x$ gives $x(x^2 - 9) = 0$, and $x^2 - 9$ factors further as $(x - 3)(x + 3)$, so the three factors set to zero give $x = 0$, $x = 3$, and $x = -3$. Dividing by $x$ first would discard the valid solution $x = 0$.

445. Evaluate the logarithm $\log_5 125$.
     • 3
     • 25
     • 5
     • 2

     Correct answer: 3

     The value is 3. The logarithm asks for the exponent to which 5 must be raised to produce 125, and since $5^3 = 125$, the answer is 3. Dividing 125 by 5 to get 25 confuses the logarithm with simple division.

446. Solve the exponential equation $3^{2x} = 81$.
     • $x = 4$
     • $x = 3$
     • $x = 2$
     • $x = 27$

     Correct answer: $x = 2$

     The solution is $x = 2$. Because 81 equals $3^4$, the equation becomes $3^{2x} = 3^4$, so the exponents are equal: $2x = 4$, giving $x = 2$. Setting $2x$ equal to 81 rather than matching exponents would give a far larger value.

447. Rewrite the exponential equation $2^6 = 64$ in logarithmic form.
     • $\log_6 64 = 2$
     • $\log_2 64 = 6$
     • $\log_{64} 2 = 6$
     • $\log_2 6 = 64$

     Correct answer: $\log_2 64 = 6$

     The logarithmic form is $\log_2 64 = 6$. An exponential statement $b^e = n$ converts to $\log_b n = e$, so base 2 and result 64 give an exponent of 6. Swapping the base and the result would produce an untrue statement.

448. An investment of $1,000 grows by a factor of 1.05 each year. Which expression gives the value after $t$ years?
     • $1000 + 1.05t$
     • $1000(1.05)^t$
     • $1000(1.05)t$
     • $1.05(1000)^t$

     Correct answer: $1000(1.05)^t$

     The expression is $1000(1.05)^t$. Exponential growth with a starting amount of 1000 and an annual growth factor of 1.05 is modeled by the initial value times the growth factor raised to the number of years. Adding $1.05t$ would describe linear rather than compounding growth.

449. Using the property $\log_b\left(\frac{m}{n}\right) = \log_b m - \log_b n$, which expression equals $\log_3 54 - \log_3 2$?
     • $\log_3 27$
     • $\log_3 52$
     • $\log_3 108$
     • $\log_1 27$

     Correct answer: $\log_3 27$

     The expression equals $\log_3 27$. The difference of two logarithms with the same base equals the logarithm of the quotient, and 54 divided by 2 is 27. Subtracting the arguments to get 52 instead of dividing them misapplies the quotient rule.

450. What is the exact value of $\cos 60^\circ$?
     • $\frac{\sqrt{3}}{2}$
     • $\frac{\sqrt{2}}{2}$
     • 1
     • $\frac{1}{2}$

     Correct answer: $\frac{1}{2}$

     The value is $\frac{1}{2}$. The angle of $60^\circ$ is a standard reference angle whose cosine is exactly one-half. The value $\frac{\sqrt{3}}{2}$ is the cosine of $30^\circ$, so swapping the two common reference angles is a frequent error.

451. In a right triangle, the side adjacent to an acute angle is 12 and the hypotenuse is 13. What is the cosine of that angle?
     • $\frac{5}{13}$
     • $\frac{12}{13}$
     • $\frac{13}{12}$
     • $\frac{12}{5}$

     Correct answer: $\frac{12}{13}$

     The cosine is $\frac{12}{13}$. Cosine of an angle equals the length of the adjacent side divided by the hypotenuse, so 12 divided by 13 gives $\frac{12}{13}$. Using the remaining side of 5 in the numerator would give the sine of the angle instead.

452. Convert the angle $60^\circ$ to radians.
     • $\frac{\pi}{2}$ radians
     • $\frac{\pi}{6}$ radians
     • $\frac{\pi}{3}$ radians
     • $\frac{\pi}{4}$ radians

     Correct answer: $\frac{\pi}{3}$ radians

     The measure is $\frac{\pi}{3}$ radians. Multiplying degrees by $\frac{\pi}{180}$ converts to radians, so 60 times $\frac{\pi}{180}$ equals $\frac{60\pi}{180}$, which simplifies to $\frac{\pi}{3}$. Multiplying by $\frac{180}{\pi}$ instead would reverse the conversion and not yield radians.

453. In a right triangle, an acute angle has sine equal to $\frac{5}{13}$ and the hypotenuse is 13. What is the length of the side opposite that angle?
     • 12
     • 5
     • 8
     • 13

     Correct answer: 5

     The opposite side is 5. Sine equals the opposite divided by the hypotenuse, so $\frac{5}{13}$ equals the opposite over 13, which means the opposite side is 5. Using the adjacent side of 12 would describe the cosine rather than the sine.

454. What is the radius of the circle described by the equation $x^2 + y^2 = 49$?
     • 49
     • 7
     • 24.5
     • 14

     Correct answer: 7

     The radius is 7. A circle centered at the origin follows the form $x^2 + y^2 = r^2$, so the radius is $\sqrt{49}$, which is 7. Treating the 49 as the radius itself confuses the radius with the radius squared.

455. What is the midpoint of the segment connecting the points $(2, 4)$ and $(8, 10)$?
     • $(6, 6)$
     • $(5, 7)$
     • $(10, 14)$
     • $(3, 3)$

     Correct answer: $(5, 7)$

     The midpoint is $(5, 7)$. The midpoint formula averages the coordinates, so the x-value is $\frac{2 + 8}{2} = 5$ and the y-value is $\frac{4 + 10}{2} = 7$. Subtracting the coordinates instead of averaging them would describe the differences used in the distance formula, not the midpoint.