What does "section-adaptive" mean on the PSAT?

Section-adaptive means each PSAT section has two modules, and your performance on the first determines the difficulty of the second. The first module (the routing module) is a mix of easy, medium, and hard questions. Answering more correctly in module 1 routes you to a harder module 2, which is required to earn the very top section scores.

How is the PSAT/NMSQT scored?

Your total score ranges from 320 to 1520 and is the sum of your Reading and Writing section score and your Math section score, each from 160 to 760. There is no pass/fail and no penalty for wrong answers, so always answer every question. Scores also include percentiles and a National Merit Selection Index.

What score do I need for National Merit?

National Merit uses a Selection Index: (Reading & Writing score × 2 + Math score) ÷ 10, ranging from 48 to 228 (Reading & Writing counts twice). The nationwide Commended cutoff is usually around 207–209, while Semifinalist cutoffs vary by state, typically in the ~208–223 range. Only juniors who take the PSAT/NMSQT can qualify.

When is the PSAT/NMSQT offered and who takes it?

The PSAT/NMSQT is given in October each year, on weekdays during the testing window plus select Saturdays, and is administered through your high school. It is taken mainly by juniors (the only students eligible for National Merit), with many sophomores taking it for practice. You sign up through your school, not directly with the College Board.

Can I retake the PSAT/NMSQT?

The PSAT/NMSQT is given only once a year, in October, so you can't retake it within the same testing window. You can take it again in a later school year, but only the score you earn as a junior counts toward the National Merit Scholarship Program. Many students take the related PSAT 10 in spring or use full-length SAT practice to keep improving between October administrations.

What's the best way to study for the PSAT?

The best way to study for the PSAT is taking full-length practice tests that mirror the digital, section-adaptive Bluebook format, then drilling your weaker section — usually Math. Pair these with our free PSAT study guide, flashcards, and cheat sheet to reinforce algebra, advanced math, and the Reading & Writing question types between practice rounds.

In a passage about a historical event, the author uses the phrase "a turning point" to describe a specific moment. What is the intended effect of this phrase on the reader?

To indicate a significant change in direction

To emphasize a small but important detail

To suggest an outcome is inevitable

An author uses parallel structure to emphasize a point. Which of the following is an example of parallel structure?

"To strive, to seek, to find, and not to yield."

"The sunset was vibrant, breathtaking, and beautiful."

If an author includes a scene that describes a character's nightmare, what might the author be trying to convey to the reader?

The character's internal fears or anxieties

The plot's climax and resolution

A symbol of peace and tranquility

A representation of the character's hopes and dreams

An author uses foreshadowing to hint at an event that will occur later in the story. Which of the following is an example of foreshadowing?

A storm begins brewing in the distance as the characters argue

A character gives a long speech about their background

An animal appears to communicate with the protagonist

The story's setting is described in great detail

An author uses an unreliable narrator to tell a story. What is the primary purpose of using an unreliable narrator?

To create ambiguity and encourage readers to question the truth

To provide a detailed, factual account of events

To add humor and lightheartedness to the story

To establish a clear perspective and structure

An author uses anachronism in a historical novel. What does this term refer to?

Insertion of something that does not fit the time period

A contradiction in terms or events

A change in chronological order

An error in historical accuracy

An author uses dramatic irony to create tension in a play. What is dramatic irony?

When the audience knows something that the characters do not

When events take an unexpected turn

When dialogue contains hidden meanings

When a character says one thing but means another

In a speech, the speaker uses rhetorical questions. What is the primary purpose of using rhetorical questions in a speech?

To engage the audience and encourage reflection

To confuse and mislead the audience

To emphasize an important point

To reduce the length of the speech

In a literary analysis, a critic discusses the use of imagery to create a mood. What does imagery refer to in literature?

Descriptive language that appeals to the senses

A recurring theme or motif throughout the text

The emotional tone created by the author

The specific structure or arrangement of the text

What is the best way to combine the following sentences? "The car was red. It was the fastest model in the dealership."

The fastest model in the dealership, the car was red.

The car was red, and it was the fastest model in the dealership.

The fastest model in the dealership was red; it was a car.

It was the fastest model in the dealership, and the car was red.

In which of the following sentences is the use of the passive voice most appropriate?

The cake was eaten by the children before their parents arrived home.

The children ate the cake before their parents arrived home.

The parents arrived home before the children could eat the cake.

The cake that the children ate was made by their grandmother.

Which of the following is the most concise way to express the idea in this sentence? "The teacher explained the concept of photosynthesis in great detail."

The teacher explained photosynthesis.

The teacher elaborated on photosynthesis.

The teacher explained photosynthesis in detail.

The teacher detailed photosynthesis at length.

Which of the following sentences contains correct subject-verb agreement?

Neither John nor his friends were ready for the test.

Neither John nor his friends was ready for the test.

Neither John nor his friends is ready for the test.

Neither John nor his friends are ready for the test.

Which of the following sentences uses parallel structure?

She enjoys reading, writing, and playing music.

She enjoys reading, writing, and to play music.

She enjoys to read, to write, and to play music.

She enjoys reading, to write, and to play music.

Which of the following sentences demonstrates correct use of commas in a list?

The cake was made with flour, sugar, eggs, and butter.

The cake was made with flour, sugar, eggs and butter.

The cake was made with flour sugar, eggs, and butter.

The cake was made with flour, sugar, eggs, and, butter.

What is the best way to correct the following sentence fragment? "Because she was late for school."

Because she was late for school, she missed the first period.

She arrived late because of traffic.

Because she was late, she got in trouble.

Which of the following sentences uses proper punctuation for direct speech?

"I will go to the store," said John.

"I will go to the store" said John.

I will go to the store, John said.

"I will go to the store", said John.

Which of the following sentences demonstrates correct usage of a semicolon?

I like apples; however, I don't like oranges.

I like apples, but I don't like oranges.

I like apples; oranges are too tart.

What is the best way to correct this dangling modifier? "Running down the street, the car nearly hit me."

Running down the street, I was nearly hit by the car.

The car nearly hit me while running down the street.

I was running down the street, and the car nearly hit me.

Running down the street, the car nearly hit me while I was walking.

Which of the following sentences uses a colon correctly?

There were three items in the bag: a book, a pen, and a key.

The bag contained: a book, a pen, and a key.

The bag: contained a book, a pen, and a key.

The bag had a book, a pen, and a key: in it.

What is the best way to correct the following sentence? "The report was written, edited, and then it was printed."

The report was written, edited, and printed.

The report was written and edited; it was then printed.

The report was written, it was edited, and it was printed.

The report was written; then, it was edited and printed.

Your FREE PSAT/NMSQT Practice Test 2026 – 450+ Q&A

Q: How is the digital PSAT/NMSQT structured?

The PSAT/NMSQT has two sections: Reading and Writing (54 questions, two 32-minute modules) and Math (44 questions, two 35-minute modules), for 98 questions administered in 2 hours and 14 minutes with a 10-minute break between sections. Of the 98, 90 are scored and 8 are unscored pretest items. Each section is two-stage module-adaptive — your performance on the first module determines the difficulty of the second.

Q: How much does the PSAT/NMSQT cost?

The PSAT/NMSQT base fee is $18 for the 2025–26 school year, but many schools pay it for their students, so the cost to you may be lower or free. Fee waivers are available for eligible 11th graders from low-income families. Because the test is ordered and administered by your school, ask your counselor about the exact fee at your school.

Prepare with realistic, digital PSAT-style questions — take a full practice test or drill Reading & Writing or Math, the two sections of the adaptive PSAT/NMSQT.

Master questions to boost your scoreMaster questions to raise your exam readiness score

How ready are you?

PSAT Practice Questions

In the passage, the author implies that technology's rapid advancements pose what kind of challenge to society?
- Ethical
- Financial
- Logistical
- Cultural
Correct answer: Ethical
Correct answer: Ethical. Explanation: The author mentions concerns about privacy and data security, indicating that the challenge posed by technological advancements is primarily ethical.
According to the passage, what is the main reason for the decline in bee populations?
- Climate change
- Pesticide use
- Habitat loss
- Disease
Correct answer: Pesticide use
Correct answer: Pesticide use. Explanation: The passage discusses how certain pesticides are harmful to bees, leading to a decline in their populations.
Based on the passage, the author's view on the new environmental policy is best described as:
- Supportive
- Critical
- Neutral
- Uncertain
Correct answer: Critical
Correct answer: Critical. Explanation: The author critiques various aspects of the new policy, suggesting that it does not go far enough to address environmental concerns.
In the context of the passage, what is the primary effect of automation on the job market?
- Increased productivity
- Job displacement
- Improved safety
- Lower costs
Correct answer: Job displacement
Correct answer: Job displacement. Explanation: The passage discusses the impact of automation on workers, emphasizing job displacement as a key issue.
What does the author suggest is the main cause of the recent increase in extreme weather events?
- Industrial pollution
- Deforestation
- Climate change
- Urbanization
Correct answer: Climate change
Correct answer: Climate change. Explanation: The passage correlates climate change with a noticeable increase in extreme weather events.
In the passage, the character's decision to leave the city is motivated by which factor?
- Family
- Career opportunities
- Financial troubles
- Desire for a simpler life
Correct answer: Desire for a simpler life
Correct answer: Desire for a simpler life. Explanation: The passage describes the character's longing for a quieter, simpler lifestyle, leading to the decision to leave the city.
According to the passage, which factor most significantly contributed to the growth of the tech industry in the past decade?
- Venture capital investment
- Government subsidies
- Technological innovation
- Globalization
Correct answer: Venture capital investment
Correct answer: Venture capital investment. Explanation: The passage attributes the rapid growth of the tech industry to an increase in venture capital investments.
The author's perspective on the role of social media in modern communication can best be described as:
- Ambivalent
- Positive
- Negative
- Optimistic
Correct answer: Ambivalent
Correct answer: Ambivalent. Explanation: The author acknowledges the benefits of social media but also discusses its negative impacts, suggesting a mixed view.
What does the passage suggest is the primary challenge facing the education system today?
- Budget cuts
- Outdated curricula
- Teacher shortages
- Student disengagement
Correct answer: Student disengagement
Correct answer: Student disengagement. Explanation: The passage highlights issues of student motivation and engagement as a central challenge within the education system.
According to the passage, the primary motivation for the author's journey was:
- Academic research
- Family tradition
- Personal growth
- Professional advancement
Correct answer: Personal growth
Correct answer: Personal growth. Explanation: The passage explores the author's journey as a quest for self-discovery and personal growth, rather than for academic or professional reasons.
Based on the passage, what is the primary reason for the community's opposition to the proposed development project?
- Environmental concerns
- Economic factors
- Aesthetic reasons
- Traffic congestion
Correct answer: Environmental concerns
Correct answer: Environmental concerns. Explanation: The passage discusses how the proposed project could negatively impact the local environment, leading to significant community opposition.
In the passage, what is the most significant factor that led to the successful implementation of the new business strategy?
- Team collaboration
- Strong leadership
- Market analysis
- Customer feedback
Correct answer: Strong leadership
Correct answer: Strong leadership. Explanation: The passage credits the successful business strategy to the effective leadership and vision of the company's CEO.
According to the passage, what is the underlying reason for the author's shift in career focus?
- Family obligations
- Changing interests
- Health concerns
- Job redundancy
Correct answer: Changing interests
Correct answer: Changing interests. Explanation: The passage describes how the author's interests evolved, leading to a change in career direction.
What does the author imply is the primary cause of the declining popularity of traditional media?
- Rise of digital platforms
- Increased competition
- Decreased quality of content
- Changing consumer behavior
Correct answer: Rise of digital platforms
Correct answer: Rise of digital platforms. Explanation: The passage emphasizes the shift towards digital platforms, contributing to a decline in traditional media's popularity.
According to the passage, what is the main reason for the author's preference for independent film over mainstream cinema?
- Artistic freedom
- Smaller budgets
- Unconventional storytelling
- Limited distribution
Correct answer: Unconventional storytelling
Correct answer: Unconventional storytelling. Explanation: The passage highlights the unique and unconventional storytelling techniques used in independent films, leading to the author's preference for them.
In a passage discussing the role of technology in modern education, which of the following statements best captures the author's tone?
- Skeptical and critical
- Enthusiastic and optimistic
- Neutral and objective
- Cautious and tentative
Correct answer: Cautious and tentative
Correct answer: Cautious and tentative. Explanation: The author's tone is cautious and tentative because they express both the benefits and potential drawbacks of technology in education, using words and phrases that indicate uncertainty and the need for further exploration.
In a passage about a historical event, the author uses the phrase "a turning point" to describe a specific moment. What is the intended effect of this phrase on the reader?
- To indicate a significant change in direction
- To emphasize a small but important detail
- To introduce a counterargument
- To suggest an outcome is inevitable
Correct answer: To indicate a significant change in direction
Correct answer: To indicate a significant change in direction. Explanation: The phrase "a turning point" typically indicates a significant shift or change in direction, emphasizing that the historical event marked a new phase or outcome.
Which of the following rhetorical devices is used when an author presents an exaggerated description of an event to create a humorous effect?
- Hyperbole
- Irony
- Understatement
- Allusion
Correct answer: Hyperbole
Correct answer: Hyperbole. Explanation: Hyperbole is a rhetorical device involving deliberate exaggeration for emphasis or humorous effect, often used to create a vivid or over-the-top impression.
If an author writes, "The storm came in like a lion, fierce and unforgiving," which of the following literary techniques is being used?
- Simile
- Metaphor
- Personification
- Alliteration
Correct answer: Simile
Correct answer: Simile. Explanation: A simile is a figure of speech that compares two different things using "like" or "as." In this sentence, the storm is compared to a lion using "like."
In a story where the protagonist discovers an old diary, which of the following literary elements does the diary represent?
- Symbol
- Foreshadowing
- Irony
- Motif
Correct answer: Symbol
Correct answer: Symbol. Explanation: A symbol is an object, person, or event that represents a larger idea or concept. The diary in this context can symbolize the past, memory, or hidden knowledge.
An author uses parallel structure to emphasize a point. Which of the following is an example of parallel structure?
- "The sunset was vibrant, breathtaking, and beautiful."
- "To strive, to seek, to find, and not to yield."
- "She was fast like a cheetah."
- "It rained cats and dogs."
Correct answer: "To strive, to seek, to find, and not to yield."
Correct answer: "To strive, to seek, to find, and not to yield.". Explanation: Parallel structure involves using the same pattern of words to show that two or more ideas have the same level of importance. In this example, the repeated use of "to" followed by verbs creates a parallel structure.
If an author includes a scene that describes a character's nightmare, what might the author be trying to convey to the reader?
- The character's internal fears or anxieties
- The plot's climax and resolution
- A symbol of peace and tranquility
- A representation of the character's hopes and dreams
Correct answer: The character's internal fears or anxieties
Correct answer: The character's internal fears or anxieties. Explanation: A nightmare scene often reveals a character's internal fears or anxieties, providing insight into their emotional state or past experiences.
An author uses foreshadowing to hint at an event that will occur later in the story. Which of the following is an example of foreshadowing?
- A storm begins brewing in the distance as the characters argue
- A character gives a long speech about their background
- An animal appears to communicate with the protagonist
- The story's setting is described in great detail
Correct answer: A storm begins brewing in the distance as the characters argue
Correct answer: A storm begins brewing in the distance as the characters argue. Explanation: Foreshadowing involves suggesting or hinting at events that will occur later in the story. The brewing storm symbolizes rising tension, indicating that conflict or dramatic events may follow.
An author uses an unreliable narrator to tell a story. What is the primary purpose of using an unreliable narrator?
- To create ambiguity and encourage readers to question the truth
- To provide a detailed, factual account of events
- To add humor and lightheartedness to the story
- To establish a clear perspective and structure
Correct answer: To create ambiguity and encourage readers to question the truth
Correct answer: To create ambiguity and encourage readers to question the truth. Explanation: An unreliable narrator is one whose credibility is questionable, often leading to ambiguity and encouraging readers to question what is real and what is not. This technique adds complexity to the narrative.
If an author describes a character as having "a heart of stone," which of the following rhetorical devices is being used?
- Metaphor
- Simile
- Irony
- Hyperbole
Correct answer: Metaphor
Correct answer: Metaphor. Explanation: A metaphor is a figure of speech that directly compares two different things without using "like" or "as." Describing someone as having "a heart of stone" suggests they are unemotional or unkind.
An author uses anachronism in a historical novel. What does this term refer to?
- Insertion of something that does not fit the time period
- A contradiction in terms or events
- A change in chronological order
- An error in historical accuracy
Correct answer: Insertion of something that does not fit the time period
Correct answer: Insertion of something that does not fit the time period. Explanation: Anachronism is when something that doesn't fit within a specific historical period is included, creating a sense of inconsistency or inaccuracy. It is often used to draw attention or create humor.
In a passage describing a character's appearance, the author writes, "She moved with the grace of a swan." Which of the following literary devices is this?
- Simile
- Metaphor
- Personification
- Hyperbole
Correct answer: Simile
Correct answer: Simile. Explanation: A simile is a comparison between two different things using "like" or "as." The description "with the grace of a swan" compares the character's movement to that of a swan, emphasizing elegance and grace.
An author uses dramatic irony to create tension in a play. What is dramatic irony?
- When the audience knows something that the characters do not
- When events take an unexpected turn
- When dialogue contains hidden meanings
- When a character says one thing but means another
Correct answer: When the audience knows something that the characters do not
Correct answer: When the audience knows something that the characters do not. Explanation: Dramatic irony occurs when the audience has more information about a situation than the characters, creating tension or anticipation as the audience waits for the characters to discover the truth.
In a speech, the speaker uses rhetorical questions. What is the primary purpose of using rhetorical questions in a speech?
- To engage the audience and encourage reflection
- To confuse and mislead the audience
- To emphasize an important point
- To reduce the length of the speech
Correct answer: To engage the audience and encourage reflection
Correct answer: To engage the audience and encourage reflection. Explanation: Rhetorical questions are questions not intended for a direct answer. They are used to engage the audience, encourage them to think, and reflect on the points being made in the speech.
In a literary analysis, a critic discusses the use of imagery to create a mood. What does imagery refer to in literature?
- Descriptive language that appeals to the senses
- A recurring theme or motif throughout the text
- The emotional tone created by the author
- The specific structure or arrangement of the text
Correct answer: Descriptive language that appeals to the senses
Correct answer: Descriptive language that appeals to the senses. Explanation: Imagery involves the use of descriptive language to create vivid mental images, often appealing to the senses. It is commonly used to establish a specific mood or atmosphere in literature.
What is the best way to combine the following sentences? "The car was red. It was the fastest model in the dealership."
- The fastest model in the dealership, the car was red.
- The car was red, and it was the fastest model in the dealership.
- The fastest model in the dealership was red; it was a car.
- It was the fastest model in the dealership, and the car was red.
Correct answer: The fastest model in the dealership, the car was red.
Correct answer: The fastest model in the dealership, the car was red. Explanation: This option combines both sentences in a clear, concise manner, with correct punctuation and structure. The other options either misrepresent the original sentences' meaning or use awkward phrasing.
In which of the following sentences is the use of the passive voice most appropriate?
- The cake was eaten by the children before their parents arrived home.
- The children ate the cake before their parents arrived home.
- The parents arrived home before the children could eat the cake.
- The cake that the children ate was made by their grandmother.
Correct answer: The cake was eaten by the children before their parents arrived home.
Correct answer: The cake was eaten by the children before their parents arrived home. Explanation: In this context, the passive voice emphasizes the action rather than the subject performing the action, which aligns with the focus of the sentence.
Which of the following is the most concise way to express the idea in this sentence? "The teacher explained the concept of photosynthesis in great detail."
- The teacher explained photosynthesis.
- The teacher elaborated on photosynthesis.
- The teacher explained photosynthesis in detail.
- The teacher detailed photosynthesis at length.
Correct answer: The teacher explained photosynthesis.
Correct answer: The teacher explained photosynthesis. Explanation: This option removes unnecessary words while preserving the meaning, creating a concise and clear sentence.
What is the most appropriate transition between these two sentences? "Maria always loved science. She decided to major in biology in college."
- However
- Therefore
- In addition
- Nonetheless
Correct answer: Therefore
Correct answer: Therefore. Explanation: "Therefore" is the most appropriate transition, indicating a cause-and-effect relationship between Maria's love for science and her decision to major in biology.
Which of the following sentences contains correct subject-verb agreement?
- Neither John nor his friends was ready for the test.
- Neither John nor his friends were ready for the test.
- Neither John nor his friends is ready for the test.
- Neither John nor his friends are ready for the test.
Correct answer: Neither John nor his friends were ready for the test.
Correct answer: Neither John nor his friends were ready for the test. Explanation: When using "neither/nor," the verb agrees with the nearest noun. Since "friends" is the nearest noun, "were" is the correct verb form.
Which of the following sentences uses parallel structure?
- She enjoys reading, writing, and to play music.
- She enjoys reading, writing, and playing music.
- She enjoys to read, to write, and to play music.
- She enjoys reading, to write, and to play music.
Correct answer: She enjoys reading, writing, and playing music.
Correct answer: She enjoys reading, writing, and playing music. Explanation: Parallel structure requires similar grammatical forms in a list. This answer uses gerunds consistently, while the other options mix gerunds and infinitives.
Which of the following sentences demonstrates correct use of commas in a list?
- The cake was made with flour, sugar, eggs, and butter.
- The cake was made with flour, sugar, eggs and butter.
- The cake was made with flour sugar, eggs, and butter.
- The cake was made with flour, sugar, eggs, and, butter.
Correct answer: The cake was made with flour, sugar, eggs, and butter.
Correct answer: The cake was made with flour, sugar, eggs, and butter. Explanation: The correct use of the Oxford comma (or serial comma) requires a comma before "and" in a list. This sentence correctly uses it, while the others have errors.
What is the best way to correct the following sentence fragment? "Because she was late for school."
- She was late for school.
- She arrived late because of traffic.
- Because she was late for school, she missed the first period.
- Because she was late, she got in trouble.
Correct answer: Because she was late for school, she missed the first period.
Correct answer: Because she was late for school, she missed the first period. Explanation: Sentence fragments lack a complete thought. This correction provides a complete independent clause, explaining the consequence of her lateness.
Which of the following sentences uses proper punctuation for direct speech?
- "I will go to the store," said John.
- "I will go to the store" said John.
- I will go to the store, John said.
- "I will go to the store", said John.
Correct answer: "I will go to the store," said John.
Correct answer: "I will go to the store," said John. Explanation: Direct speech should have a comma before closing the quotation mark when followed by an attribution. This option uses proper punctuation, while others are incorrect.
Which of the following sentences demonstrates correct usage of a semicolon?
- I like apples; however, I don't like oranges.
- I like apples; and oranges.
- I like apples, but I don't like oranges.
- I like apples; oranges are too tart.
Correct answer: I like apples; however, I don't like oranges.
Correct answer: I like apples; however, I don't like oranges. Explanation: Semicolons can connect two related independent clauses with a transition. This answer uses a semicolon and "however" correctly, while others misuse or avoid semicolons.
What is the best way to correct this dangling modifier? "Running down the street, the car nearly hit me."
- Running down the street, I was nearly hit by the car.
- The car nearly hit me while running down the street.
- I was running down the street, and the car nearly hit me.
- Running down the street, the car nearly hit me while I was walking.
Correct answer: Running down the street, I was nearly hit by the car.
Correct answer: Running down the street, I was nearly hit by the car. Explanation: A dangling modifier occurs when it's unclear who is performing the action. This answer clarifies that the person running down the street was nearly hit by the car, correcting the ambiguity.
Which of the following sentences uses a colon correctly?
- There were three items in the bag: a book, a pen, and a key.
- The bag contained: a book, a pen, and a key.
- The bag: contained a book, a pen, and a key.
- The bag had a book, a pen, and a key: in it.
Correct answer: There were three items in the bag: a book, a pen, and a key.
Correct answer: There were three items in the bag: a book, a pen, and a key. Explanation: Colons are used to introduce a list after a complete independent clause. This answer uses a colon correctly to list the bag's contents, while the other options misuse colons.
What is the best way to correct the following sentence? "The report was written, edited, and then it was printed."
- The report was written, edited, and printed.
- The report was written and edited; it was then printed.
- The report was written, it was edited, and it was printed.
- The report was written; then, it was edited and printed.
Correct answer: The report was written, edited, and printed.
Correct answer: The report was written, edited, and printed. Explanation: This option simplifies the sentence by removing redundant phrases, creating a concise sentence with a parallel structure.
Which of the following sentences uses correct tense consistency?
- She studies hard and passed the exam.
- She studies hard and has passed the exam.
- She studied hard and passes the exam.
- She studies hard and will pass the exam.
Correct answer: She studies hard and will pass the exam.
Correct answer: She studies hard and will pass the exam. Explanation: Tense consistency requires verbs in the same clause or related clauses to maintain consistent tenses. This option uses the present tense and future tense logically, while the other options mix different tenses inappropriately.
What is the best way to correct the following sentence? "While reading the book, the story captivated me."
- The book's story captivated me while I was reading.
- The story captivated me while I was reading the book.
- While I was reading the book, the story captivated me.
- The story captivated me; while reading, the book was in my hand.
Correct answer: While I was reading the book, the story captivated me.
Correct answer: While I was reading the book, the story captivated me. Explanation: This correction resolves the ambiguity of the dangling modifier, indicating that the speaker, not the book, was doing the reading and captivated by the story.
Which of the following sentences is grammatically correct?
- The group of students enjoys their break during summer.
- Neither of the candidates were available for the meeting.
- The family went on its annual vacation to the beach.
- None of the books are suitable for reading in class.
Correct answer: The family went on its annual vacation to the beach.
Correct answer: The family went on its annual vacation to the beach. Explanation: The singular noun "family" takes a singular possessive "its." All other options have subject-verb agreement errors or incorrect pluralization.
In which of the following sentences is the verb tense consistent?
- When she had finished the report, she sends it to her supervisor.
- By the time the movie starts, they had already eaten dinner.
- After they cooked dinner, they cleaned the kitchen.
- After he calls the client, he will write the report.
Correct answer: After they cooked dinner, they cleaned the kitchen.
Correct answer: After they cooked dinner, they cleaned the kitchen. Explanation: This option maintains consistent past tense throughout. Other options mix past and present tense or other inconsistencies.
Which of the following sentences contains correct punctuation?
- John's car; which was new, was already experiencing issues.
- My favorite hobbies include reading: writing, and cooking.
- The conference attendees had to bring their IDs, laptops, and business cards.
- She said that she wasn't going; but she did anyway.
Correct answer: The conference attendees had to bring their IDs, laptops, and business cards.
Correct answer: The conference attendees had to bring their IDs, laptops, and business cards. Explanation: This option correctly uses commas to separate items in a list. The other options misuse semicolons or colons, or contain incorrect punctuation.
Which of the following sentences uses a correct comparative form?
- This is the most easiest problem in the set.
- She is more happy than her sister.
- This restaurant serves better food than the one down the street.
- He is the least happiest person in the office.
Correct answer: This restaurant serves better food than the one down the street.
Correct answer: This restaurant serves better food than the one down the street. Explanation: This option uses the correct comparative form "better." Other options use redundant or incorrect comparative structures.
Which of the following sentences uses an appropriate transition word?
- However, the team reached the finals for the first time.
- Moreover, the city is known for its natural beauty, not its pollution.
- Consequently, she always tried to avoid success.
- Instead, he enjoyed all the homework assigned to him.
Correct answer: However, the team reached the finals for the first time.
Correct answer: However, the team reached the finals for the first time. Explanation: This option uses the correct transition word to indicate a contrasting idea. Other options use transition words that do not logically fit with the context.
Which of the following sentences demonstrates correct pronoun usage?
- Everyone should do their best to improve.
- Neither of the teachers gave their opinion.
- The coach distributed water bottles to all of us players.
- Each student needs to bring their book to class.
Correct answer: The coach distributed water bottles to all of us players.
Correct answer: The coach distributed water bottles to all of us players. Explanation: This option uses the correct pronoun "us." Other options contain incorrect singular/plural pronoun agreements or unclear references.
Which of the following sentences uses correct subject-verb agreement?
- The data was analyzed by the scientists.
- Each of the participants were given a survey.
- The committee have decided to postpone the meeting.
- Neither of the answers seem correct.
Correct answer: Neither of the answers seem correct.
Correct answer: Neither of the answers seem correct. Explanation: This option has correct subject-verb agreement. Other options contain subject-verb agreement errors due to collective nouns or pluralization.
Which of the following sentences uses the correct adjective form?
- She is more taller than her brother.
- The sunset was more beautiful than any he had ever seen.
- The weather became coldest as the night fell.
- It was the most smallest town in the state.
Correct answer: The sunset was more beautiful than any he had ever seen.
Correct answer: The sunset was more beautiful than any he had ever seen. Explanation: This option uses the correct comparative adjective form "more beautiful." Other options use redundant or incorrect adjective forms.
Which of the following sentences uses a correct idiomatic expression?
- He is quite interested to sports.
- She excelled on her math test.
- The company is keen on exploring new markets.
- He is not that bad than expected.
Correct answer: The company is keen on exploring new markets.
Correct answer: The company is keen on exploring new markets. Explanation: This option uses a correct idiomatic expression "keen on." Other options contain incorrect idiomatic expressions or prepositions.
Which of the following sentences uses the correct parallel structure?
- He likes to read, write, and painting.
- She enjoys singing, dancing, and to travel.
- The committee discussed the budget, planned the event, and they finalized the schedule.
- The team needs to practice, strategize, and execute.
Correct answer: The team needs to practice, strategize, and execute.
Correct answer: The team needs to practice, strategize, and execute. Explanation: This option uses correct parallel structure with consistent verb forms. Other options contain mixed verb forms or structures that break the parallelism.
Which of the following sentences uses the correct form of a possessive noun?
- The Smith's have a new car.
- The cars doors were damaged.
- The children's playground was closed.
- The cat's are asleep in the sunroom.
Correct answer: The children's playground was closed.
Correct answer: The children's playground was closed. Explanation: This option uses the correct form of a plural possessive noun "children's." Other options have incorrect possessive forms or unnecessary apostrophes.
Which of the following sentences uses correct punctuation?
- The book, which I borrowed from you is really interesting.
- The cat's tail was stuck in the door, so it couldn't move.
- She said "I'll be there in five minutes."
- I can't believe it; she finally graduated!
Correct answer: I can't believe it; she finally graduated!
Correct answer: I can't believe it; she finally graduated!. Explanation: This option uses correct punctuation with a semicolon to separate two independent clauses. Other options contain punctuation errors with commas or quotation marks.
Which of the following sentences uses correct punctuation and structure?
- The report's conclusions were, however, inconclusive.
- John said "I'll be back in an hour."
- She asked me if I could help her with her homework and I agreed.
- After the meeting, we went out to lunch; I had a great time.
Correct answer: After the meeting, we went out to lunch; I had a great time.
Correct answer: After the meeting, we went out to lunch; I had a great time. Explanation: This option uses correct punctuation with a semicolon separating two independent clauses. Other options contain incorrect punctuation with commas or quotation marks.
Which of the following sentences uses correct parallel structure?
- The report contained observations, conclusions, and suggestive recommendations.
- She wanted to sing, dance, and played the guitar.
- The professor's class was difficult, but informative, and engaging.
- The team needs to practice, strategize, and execute.
Correct answer: The team needs to practice, strategize, and execute.
Correct answer: The team needs to practice, strategize, and execute. Explanation: This option uses consistent verb forms in parallel structure. Other options contain mixed verb forms or other errors in structure.
Solve for x: 3x + 7 = 22.
- X = 3
- X = 5
- X = 6
- X = 4
Correct answer: X = 5
Correct answer: x = 5. Explanation: To isolate x, subtract 7 from 22, resulting in 15, then divide by 3, yielding x = 5.
If 2x + 3 = 11, what is x?
- X = 4
- X = 5
- X = 3
- X = 2
Correct answer: X = 4
Correct answer: x = 4. Explanation: Isolate x by subtracting 3 from 11, resulting in 8, then divide by 2 to yield x = 4.
Solve for x: x2 - 6x + 8 = 0.
- X = 2 or x = 4
- X = -2 or x = -4
- X = 1 or x = 5
- X = 3 or x = 7
Correct answer: X = 2 or x = 4
Correct answer: x = 2 or x = 4. Explanation: Factoring x2 - 6x + 8, the factors are (x - 2)(x - 4). This leads to the solutions x = 2 or x = 4.
Find x when 4x + 5 = 25.
- X = 7
- X = 6
- X = 4
- X = 5
Correct answer: X = 5
Correct answer: x = 5. Explanation: Subtract 5 from 25 to get 20, then divide by 4 to get x = 7.
Find the value of y when 2y + 10 = 30.
- Y = 12
- Y = 10
- Y = 6
- Y = 5
Correct answer: Y = 10
Correct answer: y = 10. Explanation: Subtract 10 from 30, resulting in 20. Divide by 2 to get y = 10.
If 3x - 7 = 11, what is x?
- X = 5
- X = 6
- X = 7
- X = 4
Correct answer: X = 6
Correct answer: x = 6. Explanation: Add 7 to 11 to get 18, then divide by 3 to yield x = 6.
Given that y = 3x + 2, find x when y = 11.
- X = 4
- X = 3
- X = 2
- X = 1
Correct answer: X = 3
Correct answer: x = 3. Explanation: Substitute y = 11 into the equation, getting 3x + 2 = 11. Subtraction gives 9, then dividing by 3 gives x = 3.
Solve for x: x - 4 = 3.
- X = 7
- X = 8
- X = 6
- X = 5
Correct answer: X = 7
Correct answer: x = 7. Explanation: Add 4 to 3 to get x = 7.
Given that y = 2x - 1, what is x when y = 9?
- X = 4
- X = 5
- X = 3
- X = 6
Correct answer: X = 5
Correct answer: x = 5. Explanation: Substitute y = 9 into the equation, resulting in 2x - 1 = 9. Adding 1 to 9, then dividing by 2, leads to x = 5.
Solve for x: x - 7 = -4.
- X = 2
- X = 3
- X = 4
- X = 7
Correct answer: X = 3
Correct answer: x = 3. Explanation: Add 7 to -4 to get x = 3.
What is the solution for x: 5x - 2 = 18?
- X = 4
- X = 3
- X = 6
- X = 5
Correct answer: X = 4
Correct answer: x = 4. Explanation: By isolating x, add 2 to 18, resulting in 20. Divide by 5 to get x = 4.
If y = 4x + 1, what is x when y = 17?
- X = 4
- X = 6
- X = 5
- X = 7
Correct answer: X = 4
Correct answer: x = 4. Explanation: Substitute y = 17, resulting in 4x + 1 = 17. Subtraction yields 16, then divide by 4, leading to x = 4.
Find x when x - 5 = 3.
- X = 6
- X = 9
- X = 10
- X = 8
Correct answer: X = 8
Correct answer: x = 8. Explanation: Add 5 to 3, yielding x = 8.
Given 2x + 8 = 24, what is x?
- X = 7
- X = 8
- X = 6
- X = 10
Correct answer: X = 8
Correct answer: x = 8. Explanation: To isolate x, subtract 8 from 24, yielding 16. Divide by 2 to get x = 8.
If 3x - 4 = 17, what is x?
- X = 6
- X = 7
- X = 5
- X = 8
Correct answer: X = 7
Correct answer: x = 7. Explanation: To isolate x, add 4 to 17 to get 21, then divide by 3, yielding x = 7.
If the sum of two numbers is 10 and their product is 21, what is the value of the smaller number?
- 3
- 4
- 5
- 6
Correct answer: 3
Correct answer: 3. Explanation: If the numbers are x and y, then x + y = 10 and x × y = 21. These are the roots of x² − 10x + 21 = 0, which factors as (x − 3)(x − 7) = 0. The smaller root is 3.
The function g(x) = 2log(x) + 3. What is the value of g(100)?
- 5
- 7
- 9
- 11
Correct answer: 7
Correct answer: 7. Explanation: The logarithm log(x) gives the power to which 10 must be raised to obtain x. Since log(100) = 2, the value of g(100) = 2 × 2 + 3 = 7.
A rectangle has a length of 2x + 3 and a width of x - 1. If its perimeter is 34, what is x?
- 7
- 5
- 9
- 6
Correct answer: 5
Correct answer: 5. Explanation: Perimeter of a rectangle is $2 \times (\text{length} + \text{width})$ . Given the perimeter is 34, the equation is $2 \times ((2x + 3) + (x - 1)) = 34$ . Simplifying, we get $2 \times (3x + 2) = 34$ , resulting in $3x + 2 = 17$ , yielding $3x = 15$ . Thus, $x = 5$ .
If x2 - y2 = 21, what is the value of x - y?
- 7
- 5
- 3
- 2
Correct answer: 7
Correct answer: 7. Explanation: Rewrite x2 - y2 = 21 as (x + y)(x - y) = 21. The factors of 21 are 1, 3, 7, 21. If x - y = 7, then x + y = 3, leading to consistent integer values for x and y.
A sphere has a volume of 36π. What is the radius of the sphere?
- 3
- 4
- 6
- 2
Correct answer: 3
Correct answer: 3. Explanation: The volume of a sphere is V = (4 ÷ 3)πr³. Given V = 36π, solve r³ = (36π × 3) ÷ (4π) = 27, so r = ∛27 = 3.
A right triangle has legs of length 5 and 12. What is the length of the hypotenuse?
- 13
- 14
- 15
- 16
Correct answer: 13
Correct answer: 13. Explanation: By the Pythagorean theorem, the hypotenuse c is given by c2 = 52 + 122 = 25 + 144 = 169. Taking the square root, c = 13.
If x3 - x = k, what is the value of x when k = 6?
- 2
- 3
- 1
- 0
Correct answer: 2
Correct answer: 2. Explanation: With k = 6, the equation becomes x3 - x - 6 = 0. Testing potential roots, x = 2 solves the equation, as 23 - 2 = 6.
A quadratic equation is given as ax2 + bx + c = 0. If a = 2, b = -8, and c = 6, what is the larger solution x?
- 3
- 1
- 2
- 6
Correct answer: 3
Correct answer: 3. Explanation: Using the quadratic formula x = (−b ± √(b² − 4ac)) ÷ (2a) with a = 2, b = −8, and c = 6 gives x = (8 ± √(64 − 48)) ÷ 4, so x = 3 and x = 1. The larger solution is 3.
If the geometric series has the first term a1 = 2 and a common ratio r = 3, what is the fourth term in the series?
- 54
- 6
- 12
- 18
Correct answer: 54
Correct answer: 54. Explanation: The general term of a geometric series is aₙ = a₁ × r⁽ⁿ⁻¹⁾. For the fourth term (n = 4), a₄ = 2 × 3³ = 54.
A bag contains 8 red, 6 blue, and 10 green marbles. If 2 marbles are drawn at random, what is the probability that both are red?
- 0.127
- 0.071
- 0.055
- 0.101
Correct answer: 0.101
Correct answer: 0.101. Explanation: The total number of ways to choose 2 marbles from 24 is C(24, 2) = (24 × 23) ÷ 2 = 276. The number of ways to choose 2 red marbles is C(8, 2) = (8 × 7) ÷ 2 = 28. The probability that both are red is 28 ÷ 276 ≈ 0.101.
If a graph has a linear trend with a slope of -3 and a y-intercept of 12, what is the x-coordinate when the y-coordinate is 0?
- 4
- -4
- 3
- -3
Correct answer: 4
Correct answer: 4. Explanation: Given the equation y = -3x + 12, setting y = 0 leads to 0 = -3x + 12. Solving for x, we get x = (12)/(3) = 4.
A test score has a mean of 80 with a standard deviation of 5. What is the score at the 95th percentile?
- 90
- 88
- 95
- 85
Correct answer: 88
Correct answer: 88. Explanation: The 95th percentile of a normal distribution has a Z-score of about 1.645. Using Z = (X − mean) ÷ standard deviation, X = 1.645 × 5 + 80 ≈ 88.
If the correlation coefficient between two variables is -0.75, what is the coefficient of determination?
- 0.56
- 0.5625
- 0.75
- -0.75
Correct answer: 0.5625
Correct answer: 0.5625. Explanation: The coefficient of determination is r2, so for r = -0.75, r2 = 0.5625.
In a linear relationship, if the x-intercept is -4 and the slope is 2, what is the y-intercept?
- -8
- 8
- 4
- -2
Correct answer: 8
Correct answer: 8. Explanation: Using the linear equation $y = mx + c$ , where $m = 2$ , and given $x = -4$ , setting $y = 0$ , we get $0 = 2 \times -4 + c$ . This leads to $c = 8$ .
If the median of a dataset is 40 and the range is 30, what is the maximum value in the dataset if the minimum value is 25?
- 65
- 70
- 55
- 75
Correct answer: 55
Correct answer: 55. Explanation: The range is defined as the difference between the maximum and minimum values. If the minimum value is 25 and the range is 30, then the maximum value can be found by adding the range to the minimum value: 25 + 30 = 55.
A graph shows a linear trend with a y-intercept of 7 and a slope of -5. At what x-coordinate does the graph cross the x-axis?
- -1.4
- 1.4
- 7
- -7
Correct answer: 1.4
Correct answer: 1.4. Explanation: Using the linear equation $y = -5x + 7$ , we set $y = 0$ to find the $x$ -intercept: $0 = -5 \times x + 7$ . Solving for $x$ , we get $x = \frac{7}{5} \approx 1.4$ .
An investor buys a stock at USD 50 per share. It appreciates by 25 percent and then depreciates by 20 percent. What is the final price per share?
- USD 50
- USD 52
- USD 48
- USD 60
Correct answer: USD 50
Correct answer: USD 50. Explanation: A 25 percent appreciation raises the price from USD 50 to USD 50 × 1.25 = USD 62.50. A 20 percent depreciation then lowers it to USD 62.50 × 0.80 = USD 50. So the final price per share is USD 50.
A triangle has angles measuring 40 degrees and 75 degrees. What is the measure of the third angle?
- 65 degrees
- 55 degrees
- 45 degrees
- 90 degrees
Correct answer: 65 degrees
Correct answer: 65 degrees. Explanation: The sum of the angles in a triangle is 180 degrees. The third angle is found by subtracting the sum of the given angles from 180 degrees. 180 - 40 - 75 = 65.
If the circumference of a circle is 31.4 units, what is the approximate diameter?
- 5 units
- 8 units
- 10 units
- 20 units
Correct answer: 10 units
Correct answer: 10 units. Explanation: The circumference is C = πd, where d is the diameter. So d = 31.4 ÷ π ≈ 10 units.
In a right triangle, one angle is 45 degrees. If the hypotenuse is 10 units, what is the length of each of the other two sides?
- 7.07 units
- 8 units
- 5 units
- 10 units
Correct answer: 7.07 units
Correct answer: 7.07 units. Explanation: In a 45-45-90 triangle the two legs are equal and the hypotenuse is √2 times a leg. With a hypotenuse of 10 units, each leg is 10 ÷ √2 ≈ 7.07 units.
A regular hexagon has a side length of 6 units. What is the perimeter of the hexagon?
- 30 units
- 36 units
- 42 units
- 48 units
Correct answer: 36 units
Correct answer: 36 units. Explanation: A regular hexagon has six equal sides, so the perimeter is the side length times the number of sides: 6 × 6 = 36 units.
What is the area of a circle with a radius of 7 units?
- 154 square units
- 100 square units
- 49 square units
- 78 square units
Correct answer: 154 square units
Correct answer: 154 square units. Explanation: The area of a circle is A = πr². Using π ≈ 3.14, the area is 3.14 × 7² = 3.14 × 49 ≈ 154 square units.
A triangle has sides measuring 7 units, 24 units, and 25 units. What type of triangle is this?
- Right triangle
- Acute triangle
- Obtuse triangle
- Equilateral triangle
Correct answer: Right triangle
Correct answer: Right triangle. Explanation: To determine if a triangle is a right triangle, use the Pythagorean theorem. If a2 + b2 = c2, then it is a right triangle. Given sides 7, 24, and 25, where 25 is the hypotenuse, 72 + 242 = 252, confirming it is a right triangle.
An equilateral triangle has a side length of 12 units. What is the area of the triangle?
- 62.35 square units
- 90 square units
- 124 square units
- 50 square units
Correct answer: 62.35 square units
Correct answer: 62.35 square units. Explanation: The area of an equilateral triangle is (√3 ÷ 4) × s². With a side length of 12 units, the area is (√3 ÷ 4) × 144 ≈ 62.35 square units.
What is the measure of each interior angle in a regular octagon?
- 135 degrees
- 140 degrees
- 150 degrees
- 165 degrees
Correct answer: 135 degrees
Correct answer: 135 degrees. Explanation: Each interior angle of a regular polygon is ((n − 2) × 180) ÷ n. For an octagon (n = 8), that is ((8 − 2) × 180) ÷ 8 = 135 degrees.
What is the total surface area of a cube with an edge length of 6 units?
- 150 square units
- 216 square units
- 72 square units
- 360 square units
Correct answer: 216 square units
Correct answer: 216 square units. Explanation: The total surface area of a cube is given by $6 \times s^2$ . Given an edge length of 6 units, the total surface area is $6 \times (6 \times 6) = 216$ square units.
The following is from a science article about urban wildlife. Across many large cities, biologists have documented coyotes living undetected in parks, golf courses, and the margins of busy neighborhoods. Rather than abandoning these areas during the day, the animals shift their activity to nighttime, slipping through alleys and storm drains while residents sleep. This behavioral flexibility allows coyotes to exploit food and shelter in places that would seem, at first glance, entirely unsuited to a wild predator. Which choice best states the main idea of the text?
- Storm drains and alleys provide coyotes with their primary source of food.
- Coyotes have adapted their behavior to survive in urban environments that seem inhospitable to wild predators.
- Biologists have struggled to track coyotes because the animals are active at night.
- Coyotes pose a growing danger to residents of large cities.
Correct answer: Coyotes have adapted their behavior to survive in urban environments that seem inhospitable to wild predators.
The main idea is that coyotes have adapted their behavior to survive in seemingly inhospitable urban environments. The passage centers on the animals' behavioral flexibility, shifting activity to night and using city features, to thrive where a predator would not be expected. To find the main idea, look for the point every sentence supports rather than a single detail. The claims about danger, tracking difficulty, and drains as a food source are not stated and are too narrow to capture the whole text.
The following is from an essay about volunteer record-keeping. For decades, amateur birdwatchers have logged the species they spot, the dates, and the locations in personal notebooks. Once treated as a private hobby, these scattered records have become surprisingly valuable: when pooled into large databases, they let scientists track how bird populations and migration timing shift across years. What began as casual note-taking now contributes meaningfully to climate and conservation research. Which choice best states the central idea of the text?
- Climate research depends entirely on the notebooks of birdwatchers.
- Birdwatching is a popular hobby that has existed for many decades.
- Amateur birdwatchers' casual records have become a valuable resource for scientific research.
- Scientists prefer amateur records over data collected by professionals.
Correct answer: Amateur birdwatchers' casual records have become a valuable resource for scientific research.
The central idea is that amateur birdwatchers' casual records have become a valuable scientific resource. The text traces a shift from private hobby notebooks to pooled databases that aid climate and conservation research. A central idea unifies the passage; the longevity of the hobby is a supporting detail, and the claims that scientists prefer amateur data or depend on it entirely overstate what the text says.
The following is from a passage about a historical printing technique. Before photography, illustrators reproduced detailed images using wood engraving, in which an artist carved a design into the dense end-grain of a hardwood block. Because the raised surface could be inked and pressed alongside movable type, a single page could combine text and pictures in one printing. Newspapers of the 1800s relied heavily on this method to bring battlefield scenes and portraits to readers who had never seen a photograph. Which choice best describes the function of the second sentence in the overall text?
- It introduces a problem that photography would later solve.
- It explains why wood engraving was practical for printing images together with text.
- It questions whether wood engraving produced accurate images.
- It compares wood engraving to other forms of artistic carving.
Correct answer: It explains why wood engraving was practical for printing images together with text.
The second sentence explains why wood engraving was practical for printing images together with text: its raised, inkable surface could be pressed alongside movable type on one page. The sentence supports the passage's account of how the technique worked and why newspapers used it. It does not raise a problem, question accuracy, or compare carving methods.
The following is from a report on community gardens. A neighborhood association converted a vacant lot into a shared vegetable garden, expecting mainly to grow food. Organizers soon noticed an unplanned effect: neighbors who had rarely spoken began meeting weekly to water plots and trade seedlings, and several said they finally knew the people on their block. The harvest mattered, but the strengthened relationships proved just as significant. Which choice best states the main idea of the text?
- The garden produced an unexpected social benefit alongside the food it grew.
- Neighbors disagreed about how to manage the shared garden.
- Vacant lots are best used for purposes other than gardening.
- Growing vegetables in a city requires careful organization.
Correct answer: The garden produced an unexpected social benefit alongside the food it grew.
The main idea is that the garden produced an unexpected social benefit alongside the food it grew. The passage explicitly contrasts the expected harvest with the unplanned strengthening of relationships, calling the latter just as significant. Identifying the main idea means capturing this dual outcome; the choices about organization, disagreement, or alternative lot uses introduce ideas the text does not assert.
The following is from a passage about deep-sea exploration. Researchers lowering cameras into ocean trenches once assumed that little could survive in the crushing pressure and total darkness of the deepest waters. Yet footage from these expeditions has repeatedly revealed thriving communities of fish, crustaceans, and microbes. ______ the harsh conditions, life appears not merely to persist but to flourish at depths researchers long considered nearly barren. Which choice completes the text so that it conforms to the conventions of Standard English?
- Despite
- Because of
- In addition to
- As a result of
Correct answer: Despite
"Despite" correctly completes the sentence because it signals the contrast the passage builds: harsh conditions would seem to prevent life, yet life flourishes anyway. The logic of the text turns on this unexpected outcome. "Because of" and "As a result of" wrongly imply the conditions caused the flourishing, and "In addition to" fails to mark any contrast.
The following is from an article about an archaeological discovery. Excavating a riverbank, archaeologists uncovered a row of wooden posts arranged in a wide circle. The posts had long since rotted, but the dark stains they left in the soil preserved their exact positions. From the spacing and diameter of these stains, the team concluded that a large circular building had once stood on the site. Based on the text, which choice best describes what the soil stains allowed the archaeologists to do?
- Identify the people who constructed the building.
- Recover intact wooden posts from the riverbank.
- Date the building using chemical analysis of the wood.
- Determine the original arrangement of a structure even though its wood had decayed.
Correct answer: Determine the original arrangement of a structure even though its wood had decayed.
The soil stains allowed the archaeologists to determine the original arrangement of a structure even though its wood had decayed. The text states the posts had rotted but their stains preserved exact positions, letting the team infer a circular building from spacing and diameter. The wood was not recovered intact, and the passage mentions no dating analysis or identification of builders.
The following is from a passage about a marine biologist's field notes. Dr. Okafor had expected the reef to look as it had on her first visit a decade earlier. Instead, stretches that once burst with color now stood pale and brittle. She lingered at each bleached section, photographing it carefully, and wrote little in her notebook beyond the dates and depths. Which choice best describes the main idea of the text?
- Dr. Okafor doubts that the reef has changed since her last visit.
- Dr. Okafor encounters a reef visibly degraded from the vibrant one she remembered.
- Dr. Okafor prefers photography to written field notes.
- Dr. Okafor is conducting her first survey of an unfamiliar reef.
Correct answer: Dr. Okafor encounters a reef visibly degraded from the vibrant one she remembered.
The main idea is that Dr. Okafor encounters a reef visibly degraded from the vibrant one she remembered. The passage contrasts her expectation, the colorful reef of a decade ago, with the pale, brittle reality she now documents. This is not a first visit, her sparse notes are a detail rather than a stated preference, and the text shows change rather than doubt about it.
The following is from a passage about sleep research. A team studying memory had participants learn a list of word pairs, then split them into two groups. One group slept for eight hours; the other stayed awake the same length of time. When both groups were tested afterward, those who had slept recalled noticeably more pairs than those who had remained awake. Which choice most logically completes the text?
- These results suggest that learning word pairs is easier than other tasks.
- These results suggest that eight hours is the ideal amount of sleep.
- These results suggest that sleep helps strengthen newly formed memories.
- These results suggest that the awake group was less motivated to study.
Correct answer: These results suggest that sleep helps strengthen newly formed memories.
The most logical completion is that sleep helps strengthen newly formed memories. The study isolated sleep as the only difference between the groups, and the sleepers recalled more pairs, so the conclusion should connect sleep to better memory. The other options introduce claims the experiment did not test, task difficulty, motivation, or an optimal sleep duration.
The following is from a passage about a small business. The bakery's owner tracked which pastries sold out first and which lingered in the case until closing. After several weeks, she quietly stopped baking the two slowest sellers and doubled her morning batch of the most popular item. Within a month, daily waste had dropped sharply and revenue had edged upward. Based on the text, which choice best describes why the owner changed what she baked?
- She wanted to introduce entirely new pastries to attract customers.
- She preferred baking the items that were simplest to prepare.
- She used her sales observations to match production to customer demand.
- She was forced to cut items because of rising ingredient costs.
Correct answer: She used her sales observations to match production to customer demand.
The owner changed what she baked because she used her sales observations to match production to customer demand. The text shows her tracking what sold out versus what lingered, then dropping slow sellers and increasing the popular item, with reduced waste and higher revenue as the result. The passage gives no evidence of new pastries, rising costs, or a preference for easy recipes.
The following text is followed by data. A city compared average commute times for residents who drove alone versus those who took the new express bus line during morning rush hour. Mode of travel | Average morning commute (minutes) Drive alone | 38 Express bus | 29 Which choice best uses data from the table to support the claim that the express bus saved commuters time?
- Both modes of travel produced morning commutes of roughly the same length.
- Those who drove alone averaged 38 minutes, fewer than the 29 minutes for bus riders.
- Express bus riders averaged 29 minutes, 9 minutes less than the 38-minute average for those who drove alone.
- Express bus riders averaged 29 minutes, while drivers averaged a comparable 38 minutes.
Correct answer: Express bus riders averaged 29 minutes, 9 minutes less than the 38-minute average for those who drove alone.
The data-supported statement is that express bus riders averaged 29 minutes, 9 minutes less than the 38-minute average for drivers. This accurately reads the table and shows a time savings, which is what command-of-evidence quantitative questions on the PSAT ask you to do: pick the option whose numbers are both correct and relevant to the claim. The other choices either reverse which mode was faster, call a 9-minute gap comparable, or wrongly say the times were equal.
The following text is followed by data. A researcher recorded how many hours per week students in three grade levels spent reading for pleasure. Grade | Average hours reading for pleasure per week 6th | 4.5 8th | 3.2 10th | 1.8 A student claims that time spent reading for pleasure declined as grade level increased. Which choice best uses data from the table to support this claim?
- Tenth graders read for pleasure more than sixth graders did.
- Weekly reading fell from 4.5 hours in 6th grade to 3.2 in 8th and 1.8 in 10th.
- Eighth graders read for the fewest hours of any grade measured.
- Weekly reading rose steadily from 6th grade through 10th grade.
Correct answer: Weekly reading fell from 4.5 hours in 6th grade to 3.2 in 8th and 1.8 in 10th.
The supporting statement is that weekly reading fell from 4.5 hours in 6th grade to 3.2 in 8th and 1.8 in 10th. Command of evidence with data requires choosing the option whose figures match the table and back the stated claim of decline. The numbers drop steadily across grades, so the choices saying reading rose, that 10th graders read most, or that 8th graders read least all contradict the table.
The following is from a passage about an experiment with plants. A gardener grew two trays of identical seedlings under the same light and water but played recorded music to only one tray. After three weeks, she measured the plants in both trays and found no meaningful difference in their height or leaf count. Which choice most logically completes the text?
- The results suggest the gardener measured the plants incorrectly.
- The results confirm that music significantly accelerates plant growth.
- The results provide no support for the idea that music affected the seedlings' growth.
- The results show that light is unnecessary for healthy seedlings.
Correct answer: The results provide no support for the idea that music affected the seedlings' growth.
The logical completion is that the results provide no support for the idea that music affected the seedlings' growth. Because the trays differed only in exposure to music yet grew alike, the data show no detectable effect. Claiming music accelerated growth contradicts the finding, and the conclusions about light or measurement error introduce issues the experiment did not address.
The following is from a passage about an inventor. Granville Woods filed dozens of patents in the late nineteenth century, many of them improving how trains and telegraph systems shared information. One of his best-known inventions let moving trains and station operators send messages to one another, reducing collisions on crowded rail lines. Railroad companies that adopted his system gained a safer way to coordinate traffic. Which choice best states the main idea of the text?
- Telegraph systems were more important to railroads than trains themselves.
- Railroad collisions were primarily caused by faulty station equipment.
- Granville Woods invented systems that improved communication and safety on railroads.
- Granville Woods filed more patents than any other inventor of his era.
Correct answer: Granville Woods invented systems that improved communication and safety on railroads.
The main idea is that Granville Woods invented systems that improved communication and safety on railroads. The passage describes his patents for train-to-station messaging and the resulting reduction in collisions. The text never claims he held the most patents of his era, never ranks telegraphs above trains, and never identifies station equipment as the main cause of collisions.
The following is from a passage about glaciers. As a glacier creeps downhill over thousands of years, it grinds rock into a fine powder and carries boulders far from where they formed. When the ice finally melts, these out-of-place boulders, called erratics, are left stranded on the landscape. Geologists can trace an erratic back to its source and so reconstruct the path the vanished glacier once followed. Based on the text, which choice best explains how erratics are useful to geologists?
- They show the chemical composition of melting ice.
- They indicate how quickly a glacier is currently advancing.
- They mark places where new glaciers are likely to form.
- They reveal the route a glacier traveled before it melted.
Correct answer: They reveal the route a glacier traveled before it melted.
Erratics are useful because they reveal the route a glacier traveled before it melted. The text explains that glaciers carry boulders far from their origin, and tracing a stranded erratic to its source lets geologists reconstruct the glacier's path. The passage does not connect erratics to a glacier's current speed, the chemistry of ice, or where new glaciers will form.
The following is from a passage about an author's working habits. The novelist insisted that her best ideas came not while sitting at her desk but during long, aimless walks. She kept a small notebook in her coat pocket, and friends grew used to her stopping mid-conversation to jot down a phrase. Only later, back at home, would she shape these fragments into chapters. Which choice best describes the main idea of the text?
- The novelist generated her ideas while walking and developed them into writing afterward.
- The novelist rarely recorded her ideas before they faded.
- The novelist wrote her best chapters directly at her desk.
- The novelist disliked the company of friends while she worked.
Correct answer: The novelist generated her ideas while walking and developed them into writing afterward.
The main idea is that the novelist generated her ideas while walking and developed them into writing afterward. The passage shows her capturing phrases on walks in a pocket notebook, then shaping those fragments into chapters at home. The other choices contradict the text, which mentions friends without dislike, locates idea generation away from the desk, and shows her diligently recording ideas rather than losing them.
Marine biologist Dr. Lena Ortiz argued that coral reefs are not the fragile, passive systems they are often portrayed to be. Reefs, she noted, are remarkably ______ ecosystems, able to recover from storms and bleaching events when conditions improve and given enough time. Which choice completes the text with the most logical and precise word or phrase?
- Isolated
- Temporary
- Decorative
- Resilient
Correct answer: Resilient
"Resilient" is correct because the sentence describes reefs as the opposite of fragile and emphasizes their ability to recover from damage, which is exactly what resilient means. "Decorative," "isolated," and "temporary" do not capture the idea of bouncing back from harm, and "temporary" actually contradicts the recovery the passage describes. This is a Words in Context question, which asks you to choose the word whose meaning best fits the logic of the surrounding sentence.
Although critics initially dismissed the young composer's symphony as derivative, later scholars came to regard it as strikingly ______: it borrowed almost nothing from earlier works and introduced harmonies audiences had never encountered before. Which choice completes the text with the most logical and precise word or phrase?
- Original
- Conventional
- Melodic
- Repetitive
Correct answer: Original
"Original" is correct because the second half of the sentence explains that the symphony borrowed almost nothing from earlier works and introduced new harmonies, which defines originality. The word also creates the intended contrast with the critics who called it "derivative." "Conventional" and "repetitive" both mean the opposite of what the evidence supports, and "melodic" describes pleasantness, not newness. In Words in Context items, the blank must agree with the textual evidence, not just sound positive.
The following text is from a passage about urban planning. The author begins by describing a single crowded intersection where pedestrians, cyclists, and cars constantly compete for space. She then explains how this small scene reflects a citywide failure to plan for multiple kinds of travelers, and she ends by proposing a network of dedicated lanes that would separate these groups. Which choice best describes the overall structure of the text?
- It compares two cities and argues that one is better managed than the other.
- It defines a technical term and then traces the history of that term.
- It presents a specific example, broadens it into a general problem, and offers a solution.
- It lists several unrelated complaints about a city without connecting them.
Correct answer: It presents a specific example, broadens it into a general problem, and offers a solution.
The structure moves from a specific example (one intersection) to a general problem (a citywide planning failure) and then to a proposed solution (dedicated lanes), so the description naming that example-to-problem-to-solution progression is correct. The text is not a list of unrelated complaints, a comparison of two cities, or a history of a term. Text Structure questions reward tracking how the parts of a passage build on one another.
The following text is from a science article. For decades, researchers assumed that the deep ocean floor was nearly lifeless. Recent expeditions, however, have revealed dense communities of worms, crabs, and microbes clustered around hydrothermal vents. These findings have forced scientists to reconsider where, and under what conditions, life can thrive. Which choice best states the main purpose of the text?
- To describe the daily behavior of a single deep-sea organism
- To present new evidence that overturns a long-held assumption about deep-sea life
- To argue that deep-ocean expeditions are too expensive to continue
- To explain how hydrothermal vents form on the ocean floor
Correct answer: To present new evidence that overturns a long-held assumption about deep-sea life
The main purpose is to present new evidence that overturns a long-held assumption, because the passage contrasts the old belief that the deep ocean was lifeless with recent discoveries that forced scientists to reconsider. The text does not explain how vents form, argue about expedition costs, or focus on one organism's daily behavior. Main Purpose questions ask what the author is mainly trying to accomplish across the whole passage, not just one detail.
Text 1: Economist Priya Nair contends that remote work permanently benefits employees, citing surveys in which most workers report shorter commutes, greater flexibility, and higher job satisfaction. Text 2: Management scholar David Cole acknowledges those reported gains but warns that they may fade over time. He points to evidence that fully remote employees are promoted less often and feel increasingly disconnected from their teams. Based on the texts, how would David Cole (Text 2) most likely respond to the view presented in Text 1?
- By acknowledging the reported benefits but cautioning that they may not last
- By arguing that commutes are the only factor that matters to workers
- By denying that remote workers report any satisfaction at all
- By agreeing fully that remote work is permanently beneficial for all employees
Correct answer: By acknowledging the reported benefits but cautioning that they may not last
Cole would most likely acknowledge the reported benefits while cautioning that they may not last, because Text 2 explicitly accepts the survey gains yet warns they "may fade over time" and notes drawbacks like fewer promotions and disconnection. He does not fully agree, deny that workers report satisfaction, or claim commutes are the only thing that matters. Cross-Text Connections questions ask you to infer how one author would react to the other based on each text's stated position.
The engineer described the bridge's design as deceptively ______: though its sweeping arches looked effortless and graceful, each one required years of calculation to keep the structure standing. Which choice completes the text with the most logical and precise word or phrase?
- Simple
- Modern
- Colorful
- Expensive
Correct answer: Simple
"Simple" is correct because the word "deceptively" signals a contrast between appearance and reality, and the sentence explains that the arches looked effortless yet actually demanded years of calculation. Something that appears easy but is hard is deceptively simple. "Expensive," "modern," and "colorful" do not connect to the gap between effortless appearance and difficult reality. The structural cue word "deceptively" is the key to this Words in Context item.
The following text is from a historical account. The author opens by stating a claim: that the printing press did more to reshape Europe than any single invention before it. She then supports this claim with three developments it enabled, the spread of literacy, the rise of newspapers, and the rapid exchange of scientific ideas. Which choice best describes the overall structure of the text?
- It defines two opposing viewpoints and refuses to choose between them.
- It states a claim and then offers supporting examples.
- It poses a question and leaves it deliberately unanswered.
- It tells a story in strict chronological order from birth to death.
Correct answer: It states a claim and then offers supporting examples.
The structure states a claim (the printing press reshaped Europe more than any prior invention) and then supports it with examples (literacy, newspapers, scientific exchange), so the claim-then-support description is correct. The passage answers rather than leaves a question open, is organized by supporting points rather than a life story, and presents one viewpoint rather than two opposing ones. Recognizing a claim-and-evidence pattern is central to identifying text structure.
The committee praised the volunteer's ______ contribution to the shelter: over twelve years she had quietly cooked thousands of meals without ever seeking recognition or thanks. Which choice completes the text with the most logical and precise word or phrase?
- Selfless
- Occasional
- Reluctant
- Profitable
Correct answer: Selfless
"Selfless" is correct because the sentence describes someone who served for years without seeking recognition or thanks, which is the defining trait of selflessness. "Reluctant" contradicts twelve years of steady service, "occasional" contradicts "thousands of meals," and "profitable" contradicts working without reward. Words in Context items require matching the blank to the concrete behavior the sentence reports.
The following text is from an essay about language. The writer first defines a "loanword" as a term borrowed from one language into another. He then gives familiar examples, such as "safari" from Swahili and "piano" from Italian. Finally, he argues that loanwords are not signs of a language's weakness but evidence of its openness and vitality. Which choice best describes the function of the final sentence in the overall structure of the text?
- It provides a list of additional languages unrelated to the essay's point.
- It introduces a new term that the rest of the passage will define.
- It offers the writer's main argument, building on the definition and examples that came before.
- It contradicts the examples by claiming they are not really loanwords.
Correct answer: It offers the writer's main argument, building on the definition and examples that came before.
The final sentence offers the writer's main argument, building on the earlier definition and examples, because after defining a loanword and illustrating it, the writer uses those foundations to make his central claim that loanwords reflect vitality. It does not introduce a new term, contradict the examples, or list unrelated languages. Specific Purpose questions ask what one part of a text accomplishes within the whole.
Text 1: Astronomer Wei Chen argues that funding should prioritize large ground-based telescopes, which she says deliver the most observations per dollar and can be upgraded over decades. Text 2: Astronomer Marcus Hale agrees that cost matters but favors space-based telescopes. Earth's atmosphere, he notes, blurs and blocks much of the light that ground instruments try to capture, no matter how large they are. Which choice best describes a key difference between the two astronomers' positions?
- Chen emphasizes cost efficiency on the ground, while Hale stresses a limitation of ground-based observation.
- Both reject the idea that telescopes are worth funding at all.
- Chen ignores cost entirely, while Hale considers it the only factor.
- Chen and Hale fully agree that space-based telescopes are superior.
Correct answer: Chen emphasizes cost efficiency on the ground, while Hale stresses a limitation of ground-based observation.
The key difference is that Chen emphasizes cost efficiency of ground-based telescopes while Hale stresses a limitation of ground observation, namely the atmosphere blurring and blocking light. Both authors consider cost, so it is wrong to say Chen ignores it; neither rejects telescope funding; and they do not fully agree. Cross-Text Connections questions reward pinpointing exactly where two informed authors diverge.
The following text is from a passage about photography. The author describes how an old photograph of her grandmother sat unnoticed in a drawer for years. She recalls the moment she finally framed it, and she reflects on how a single image can suddenly make a distant relative feel close and real. Which choice best states the main purpose of the text?
- To explain the technical process of developing photographs
- To argue that physical photographs are better than digital ones
- To convey how a photograph can transform a viewer's sense of connection to the past
- To list the items the author keeps in her drawers
Correct answer: To convey how a photograph can transform a viewer's sense of connection to the past
The main purpose is to convey how a photograph can transform a viewer's sense of connection to the past, because the passage centers on how framing one image made a distant relative feel close and real. It does not explain developing photographs, argue physical versus digital, or catalog drawer contents. Main Purpose questions focus on the central effect the author is reaching for, not incidental details.
In the report, the inspector noted that the factory's safety claims were ______ at best: official records showed three serious accidents in the past year, directly contradicting the company's statement that no injuries had occurred. Which choice completes the text with the most logical and precise word or phrase?
- Generous
- Dubious
- Detailed
- Permanent
Correct answer: Dubious
"Dubious" is correct because records of three serious accidents directly contradict the company's claim of no injuries, making the safety claims doubtful or questionable. "Generous," "detailed," and "permanent" do not capture the idea that a claim is untrustworthy in light of contradicting evidence. In Words in Context items, the surrounding evidence, here the contradiction, determines the precise meaning required.
The following text is from an article about migration. The writer presents a puzzle: how do monarch butterflies, which live only a few weeks, complete a multi-generation journey of thousands of miles? She then walks through current research suggesting the butterflies inherit navigational cues. She closes by admitting that much about the process remains unexplained. Which choice best describes the overall structure of the text?
- It raises a puzzle, examines proposed explanations, and acknowledges remaining uncertainty.
- It ranks butterfly species from most to least impressive.
- It compares butterflies to birds and declares birds superior navigators.
- It argues that monarch migration has been fully explained by science.
Correct answer: It raises a puzzle, examines proposed explanations, and acknowledges remaining uncertainty.
The structure raises a puzzle (how short-lived butterflies complete a long journey), examines proposed explanations (inherited navigational cues), and acknowledges remaining uncertainty, so that three-part description is correct. The text does not rank species, claim the question is fully solved, or compare butterflies to birds. Identifying text structure means following how a passage frames, develops, and qualifies its central question.
Despite the storm's intensity, the captain remained ______, calmly issuing orders and reassuring the crew even as waves crashed over the deck. Which choice completes the text with the most logical and precise word or phrase?
- Frantic
- Composed
- Silent
- Careless
Correct answer: Composed
"Composed" is correct because the sentence shows the captain staying calm, issuing orders, and reassuring the crew during a violent storm, which describes someone composed under pressure. "Frantic" and "careless" contradict the calm behavior described, and "silent" contradicts the issuing of orders and reassurances. Words in Context items ask you to read the behavior in the sentence and select the word that matches it precisely.
The following text is from a passage about a community garden. The author notes that before the garden existed, neighbors rarely spoke to one another. She describes how planting and harvesting together gradually built friendships. The passage ends with residents organizing a shared autumn festival. Which choice best describes the overall structure of the text?
- It lists the vegetables grown in the garden in order of size.
- It argues that gardens are the cheapest form of food production.
- It defines the word "neighbor" and explores its origins.
- It traces a change over time, from isolation to community.
Correct answer: It traces a change over time, from isolation to community.
The structure traces a change over time, from neighbors who rarely spoke to residents organizing a shared festival, so the isolation-to-community description is correct. The passage is not an economic argument, a list of vegetables, or a definition of a word. A before-and-after progression is a common text structure, and recognizing it answers the question.
Text 1: Nutritionist Ana Reyes recommends that people eat a wide variety of vegetables, arguing that different colors of produce supply different nutrients the body needs. Text 2: Dietitian Sam Whitlock generally supports variety but adds an important qualification: for people on certain medications, some vegetables can interfere with treatment, so variety should be guided by a doctor's advice. Based on the texts, how does Text 2 relate to Text 1?
- Text 2 completely rejects the advice given in Text 1.
- Text 2 accepts Text 1's general advice but introduces an important exception.
- Text 2 claims that vegetables have no nutritional value.
- Text 2 repeats Text 1's advice without adding anything.
Correct answer: Text 2 accepts Text 1's general advice but introduces an important exception.
Text 2 accepts Text 1's general advice but introduces an important exception, because Whitlock supports variety yet warns that some vegetables can interfere with certain medications. He does not reject the advice, simply repeat it, or deny that vegetables are nutritious. Cross-Text Connections questions often hinge on spotting a qualification or exception that one author adds to another's claim.
The reviewer called the novel's plot ______: events that seemed unrelated in early chapters turned out to be carefully linked, and every loose thread was tied together by the final page. Which choice completes the text with the most logical and precise word or phrase?
- Brief
- Predictable
- Careless
- Intricate
Correct answer: Intricate
"Intricate" is correct because the sentence describes seemingly unrelated events that prove carefully linked, with every loose thread tied together, which is the mark of an intricate, complexly constructed plot. "Predictable" misses the surprise of the hidden links, "careless" contradicts "carefully linked," and "brief" addresses length rather than complexity. Words in Context requires matching the word to the structural detail the sentence emphasizes.
The following text is from an opinion essay. The writer spends the first half of the essay describing how convenient smartphones have made everyday tasks. Then, at the midpoint, he shifts: he argues that this same convenience has quietly eroded people's patience and attention. The remainder of the essay develops that concern. Which choice best describes the overall structure of the text?
- It gives step-by-step instructions for using a smartphone.
- It presents a benefit, then pivots to a drawback that it develops.
- It compares two brands of smartphones feature by feature.
- It maintains a single, unchanging tone of praise throughout.
Correct answer: It presents a benefit, then pivots to a drawback that it develops.
The structure presents a benefit (smartphone convenience) and then pivots at the midpoint to a drawback (eroded patience and attention) that the rest of the essay develops, so the benefit-then-drawback description is correct. The tone does not stay uniformly positive, the text gives no instructions, and it compares no brands. Noticing a clearly marked pivot or shift is essential when answering text structure questions.
Many migratory songbirds navigate at night using the stars as a compass. Researchers raised young indigo buntings inside a planetarium, exposing them only to an artificial sky that rotated around a false pole star. _____ when these birds were later tested, they oriented their flight relative to the false pole rather than the true one. Which choice completes the text with the most logical transition?
- Nevertheless,
- In contrast,
- For example,
- Tellingly,
Correct answer: Tellingly,
"Tellingly" is correct because the second sentence presents the experiment's outcome as meaningful evidence that the birds learned the artificial sky, reinforcing the first sentence rather than opposing it. "In contrast" and "Nevertheless" both signal opposition, which does not fit, and "For example" wrongly frames the result as one instance among many rather than the key finding.
On the digital PSAT/NMSQT, the Expression of Ideas portion of the Reading and Writing section asks students to revise a text so it better meets a stated rhetorical goal. A student reviewing study materials wants to know what skills this portion covers. Which statement most accurately describes the Expression of Ideas questions on the PSAT?
- They ask students to identify the main idea of a long literary passage
- They test only spelling, capitalization, and punctuation rules
- They test revising texts for effective written expression, including transitions and rhetorical synthesis
- They require students to write a multi-paragraph persuasive essay
Correct answer: They test revising texts for effective written expression, including transitions and rhetorical synthesis
The correct description is that Expression of Ideas questions test revising texts for effective written expression, including transitions and rhetorical synthesis. This domain measures rhetorical revision skills, not the mechanics of capitalization and punctuation (those fall under Standard English Conventions). The PSAT contains no essay, and main-idea identification belongs to the Information and Ideas domain.
A transition word or phrase is a connector that signals the logical relationship between ideas, such as addition, contrast, cause, or sequence. A student is unsure what counts as a transition word. Which of the following is functioning as a transition?
- "Mountain" naming a physical place
- "Quickly" describing how someone ran
- "However" linking a claim to a contrasting point
- "Beautiful" describing a sunset
Correct answer: "However" linking a claim to a contrasting point
"However" is the transition because it connects two clauses by signaling a contrast in logic between them. Transition words express relationships like contrast, addition, or cause between ideas. "Beautiful," "quickly," and "mountain" are an adjective, an adverb, and a noun that describe or name things rather than linking ideas, so none of them serves a transitional function.
The deep-sea anglerfish lures prey with a glowing growth on its head. This light is not produced by the fish itself. _____ it comes from colonies of bioluminescent bacteria that live inside the lure and receive shelter in return. Which choice completes the text with the most logical transition?
- Therefore,
- Likewise,
- Instead,
- Meanwhile,
Correct answer: Instead,
"Instead" is correct because the second sentence corrects the implied assumption by stating the actual source of the light after the first sentence rules out the fish itself. "Likewise" signals similarity and "Therefore" signals a conclusion, neither of which fits a corrective relationship. "Meanwhile" indicates simultaneous events in time, which is not the logic here.
While researching a presentation, a student took these notes: Honeybees communicate the location of food through a movement called the waggle dance. The angle of the dance relative to vertical indicates the direction of the food. The duration of the waggle indicates the distance to the food. Other bees follow the dancer to learn the route. The student wants to emphasize how a single dance conveys two distinct pieces of information. Which choice most effectively uses relevant information from the notes to accomplish this goal?
- Honeybees perform a movement called the waggle dance to communicate.
- In the waggle dance, the dance's angle encodes direction while the waggle's duration encodes distance.
- Other bees follow the dancer in order to learn the route to food.
- The waggle dance is one of several behaviors honeybees use.
Correct answer: In the waggle dance, the dance's angle encodes direction while the waggle's duration encodes distance.
The choice naming both the angle as direction and the duration as distance is correct because it combines exactly the two notes that show one dance carrying two distinct messages, matching the rhetorical goal. The option about bees following the dancer and the one calling it a movement to communicate each convey only general or single facts, and the claim about several behaviors adds information not supported by the notes.
Volcanic ash can disrupt air travel for thousands of miles. _____ the 2010 eruption of Iceland's Eyjafjallajokull grounded flights across much of Europe even though the volcano itself caused little local damage. Which choice completes the text with the most logical transition?
- As a result,
- In conclusion,
- For instance,
- Conversely,
Correct answer: For instance,
"For instance" is correct because the second sentence offers the Eyjafjallajokull eruption as a specific example illustrating the general claim that volcanic ash disrupts distant air travel. "Conversely" would signal an opposite case, and "As a result" would make the eruption a consequence of the first sentence rather than an illustration. "In conclusion" signals a summary ending, which does not fit a single supporting example.
A student researching coral reefs compiled these notes: Coral polyps are tiny animals that build hard skeletons. Many corals host algae called zooxanthellae in their tissues. The algae photosynthesize and supply most of the coral's energy. When water grows too warm, corals expel the algae, an event called bleaching. The student wants to explain why bleaching threatens a coral's survival. Which choice most effectively uses the notes to accomplish this goal?
- Because the expelled algae normally supply most of the coral's energy, bleaching can starve the coral.
- Zooxanthellae are a kind of algae that live inside coral tissues.
- Bleaching happens when ocean water becomes too warm for corals.
- Coral polyps are tiny animals that build hard skeletons over time.
Correct answer: Because the expelled algae normally supply most of the coral's energy, bleaching can starve the coral.
The choice linking the loss of the energy-supplying algae to the coral's starvation is correct because it connects the bleaching note with the energy note to explain the threat, fulfilling the goal. The statements about polyps building skeletons, algae living in tissues, and warm water causing bleaching are accurate but describe what or when, not why bleaching endangers survival.
For decades, scientists assumed that adult human brains could not grow new neurons. _____ studies in the late twentieth century found evidence of new neuron formation in a region tied to memory. Which choice completes the text with the most logical transition?
- Furthermore,
- However,
- Consequently,
- Similarly,
Correct answer: However,
"However" is correct because the second sentence contradicts the long-held assumption stated in the first sentence, marking a contrast. "Furthermore" and "Similarly" would signal that the second sentence adds to or agrees with the first, but it overturns it. "Consequently" would make the new findings a result of the old assumption, which reverses the actual logic.
The painter Artemisia Gentileschi achieved fame in seventeenth-century Italy, a period when few women worked as professional artists. Her dramatic use of light and shadow drew on the style of Caravaggio. _____ she developed compositions and subjects that were distinctly her own. Which choice completes the text with the most logical transition?
- In other words,
- Therefore,
- For example,
- Still,
Correct answer: Still,
"Still" is correct because it concedes her debt to Caravaggio while emphasizing that she nevertheless created original work, a contrast-with-concession relationship. "Therefore" and "For example" imply the third sentence follows from or illustrates the second, which it does not. "In other words" signals a restatement, but the sentence introduces new, contrasting information rather than rephrasing.
A student gathered these notes for an article: The Antikythera mechanism is an ancient Greek device recovered from a shipwreck. It dates to roughly the second century BCE. It used dozens of bronze gears to model the motions of the sun and moon. No comparably complex geared device is known for over a thousand years afterward. The student wants to stress how technologically advanced the mechanism was for its era. Which choice most effectively uses the notes to accomplish this goal?
- The Antikythera mechanism dates to roughly the second century BCE.
- Built around the second century BCE, the gear-driven Antikythera mechanism had no known equal in complexity for more than a thousand years.
- The Antikythera mechanism was recovered from an ancient shipwreck near Greece.
- The Antikythera mechanism used bronze gears to model the sun and moon.
Correct answer: Built around the second century BCE, the gear-driven Antikythera mechanism had no known equal in complexity for more than a thousand years.
The choice pairing the device's date with the fact that nothing as complex appeared for over a thousand years is correct because it combines those two notes to dramatize how far ahead of its time the mechanism was. The notes about the shipwreck, the bronze gears alone, and the date alone each state a single fact without establishing the comparison that conveys advancement.
Desert plants face long periods without rain. The saguaro cactus survives these droughts by storing water in its thick, pleated stem. _____ its shallow but wide-spreading roots let it absorb large amounts of water quickly during brief rainstorms. Which choice completes the text with the most logical transition?
- However,
- In addition,
- Therefore,
- Instead,
Correct answer: In addition,
"In addition" is correct because the third sentence presents a second water-survival adaptation alongside the stem-storage strategy from the second sentence, an additive relationship. "However" and "Instead" signal contrast or replacement, but both adaptations work together. "Therefore" would make the roots a consequence of the stem storage, which misrepresents the parallel structure of the two traits.
A student preparing a report assembled these notes: Lichens are organisms formed from a fungus and an alga or cyanobacterium living together. They can grow on bare rock where few other organisms survive. They slowly break down rock into soil. This soil allows mosses and later plants to take root. The student wants to explain the role lichens play in beginning the formation of an ecosystem on bare rock. Which choice most effectively uses the notes to accomplish this goal?
- Lichens are made of a fungus paired with an alga or cyanobacterium.
- By breaking bare rock into soil, lichens prepare the ground for mosses and plants to follow.
- Lichens can grow on bare rock where few other organisms survive.
- Mosses and plants eventually take root in newly formed soil.
Correct answer: By breaking bare rock into soil, lichens prepare the ground for mosses and plants to follow.
The choice describing lichens breaking rock into soil so mosses and plants can follow is correct because it links the soil-forming note to the colonization note, capturing the pioneering role the goal requires. The definition of lichens, the fact that they grow on bare rock, and the note about mosses taking root each give a partial piece but do not connect lichens' action to the ecosystem's start.
The novelist used short, clipped sentences throughout the chase scene. _____ she switched to long, flowing sentences in the quiet passages that followed, slowing the reader's pace. Which choice completes the text with the most logical transition?
- Accordingly,
- Likewise,
- By contrast,
- In summary,
Correct answer: By contrast,
"By contrast" is correct because the second sentence sets the long, slow sentences against the short, fast ones from the first sentence, highlighting an opposition in style. "Likewise" would wrongly signal that the two passages share the same approach. "Accordingly" implies a cause-and-effect result, and "In summary" signals a concluding recap, neither of which matches the contrast being drawn.
A student researching renewable energy took these notes: Tidal power plants generate electricity from the rise and fall of ocean tides. Tides are highly predictable years in advance. Wind and solar output vary with unpredictable weather. Some engineers favor tidal power for grid planning. The student wants to explain why some engineers consider tidal power especially useful for planning a stable electricity grid. Which choice most effectively uses the notes to accomplish this goal?
- Because tides are predictable years ahead, tidal power offers grid planners a reliability that variable wind and solar cannot.
- Wind and solar power output changes with the weather from day to day.
- Some engineers favor using tidal power for planning the electricity grid.
- Tidal power plants generate electricity from the rise and fall of the tides.
Correct answer: Because tides are predictable years ahead, tidal power offers grid planners a reliability that variable wind and solar cannot.
The choice contrasting predictable tides with variable wind and solar is correct because it draws on the predictability and variability notes to explain the planning advantage the goal calls for. The note defining tidal plants, the one about weather-dependent output, and the bare statement that engineers favor tidal power each omit the contrast that makes tidal power valuable for stable grid planning.
Early maps of the ocean floor showed it as a flat, featureless plain. _____ sonar surveys in the twentieth century revealed towering mountain ranges, deep trenches, and vast underwater volcanoes. Which choice completes the text with the most logical transition?
- In reality,
- As a result,
- Therefore,
- Similarly,
Correct answer: In reality,
"In reality" is correct because the second sentence corrects the mistaken early picture by revealing what sonar actually found, an opposition between belief and fact. "As a result" and "Therefore" would make the sonar findings a consequence of the flat-map belief, which is illogical. "Similarly" would signal agreement, but the findings overturn the earlier view rather than echoing it.
A student writing about urban design compiled these notes: Green roofs are rooftops planted with vegetation. They absorb rainwater that would otherwise overwhelm city drains. They insulate buildings, lowering heating and cooling costs. They also provide habitat for insects and birds. The student wants to convey that green roofs offer multiple distinct benefits to a city. Which choice most effectively uses the notes to accomplish this goal?
- Green roofs absorb rainwater that would otherwise overwhelm city drains.
- Green roofs benefit cities in several ways at once, easing drainage, cutting building energy costs, and supporting wildlife.
- Green roofs are rooftops that have been planted with vegetation.
- Green roofs can lower a building's heating and cooling costs.
Correct answer: Green roofs benefit cities in several ways at once, easing drainage, cutting building energy costs, and supporting wildlife.
The choice listing drainage relief, energy savings, and wildlife support together is correct because it gathers three separate benefit notes to show the multiple distinct advantages the goal specifies. The definition of green roofs and the single notes about drainage or energy costs each present only one fact and do not establish the range of benefits.
Octopuses can change the color and texture of their skin almost instantly. _____ they are colorblind, perceiving the world in shades of brightness rather than hue. How they match colors so precisely remains a puzzle. Which choice completes the text with the most logical transition?
- Consequently,
- For example,
- Surprisingly,
- In addition,
Correct answer: Surprisingly,
"Surprisingly" is correct because the fact that color-matching octopuses are themselves colorblind is unexpected and creates the puzzle the third sentence names. "Consequently" would make colorblindness a result of color-changing, which is backward. "For example" frames it as an illustration, and "In addition" treats it as a simple addition, but neither captures the striking tension between the two abilities.
A student researching food history gathered these notes: Chocolate comes from the seeds of the cacao tree. The Maya and Aztec peoples prepared cacao as a bitter, spiced drink. They sometimes used cacao seeds as a form of currency. Sweetened solid chocolate did not appear until centuries later in Europe. The student wants to highlight that cacao once held value beyond being a food. Which choice most effectively uses the notes to accomplish this goal?
- Sweetened solid chocolate first appeared centuries later in Europe.
- The Maya and Aztec prepared cacao as a bitter, spiced drink.
- Among the Aztec and Maya, cacao seeds served not only as a drink but also as money.
- Chocolate is made from the seeds of the cacao tree.
Correct answer: Among the Aztec and Maya, cacao seeds served not only as a drink but also as money.
The choice noting that cacao served as both a drink and money is correct because it combines the beverage and currency notes to show value beyond food, exactly as the goal requires. The notes that chocolate comes from cacao seeds, that it was a bitter drink, and that solid chocolate came later each describe cacao only as a food or trace its history, missing the non-food value.
Most stars spend billions of years steadily fusing hydrogen into helium. _____ the most massive stars burn through their fuel in only a few million years before collapsing. Which choice completes the text with the most logical transition?
- Moreover,
- Therefore,
- By comparison,
- For instance,
Correct answer: By comparison,
"By comparison" is correct because the second sentence sets the brief lifespans of massive stars against the billions of years of ordinary stars, drawing a contrast. "Moreover" and "For instance" would signal addition or illustration of the first idea, but the sentence opposes it. "Therefore" would make the short lifespans a consequence of the slow fusion, which contradicts the meaning.
A student preparing a biology article took these notes: The axolotl is a salamander that keeps its larval features for life. Unlike most amphibians, it never fully transforms into a land-dwelling adult. It can regrow lost limbs, parts of its heart, and even portions of its brain. Scientists study it to understand tissue regeneration. The student wants to explain why scientists are especially interested in studying the axolotl. Which choice most effectively uses the notes to accomplish this goal?
- The axolotl is able to regrow lost limbs and parts of its heart.
- The axolotl is a salamander that keeps its larval features throughout its life.
- Unlike most amphibians, the axolotl never fully transforms into an adult.
- Scientists study the axolotl because its ability to regrow limbs, heart, and brain tissue may reveal how regeneration works.
Correct answer: Scientists study the axolotl because its ability to regrow limbs, heart, and brain tissue may reveal how regeneration works.
The choice connecting the axolotl's broad regenerative ability to scientists' goal of understanding regeneration is correct because it joins the regeneration note with the research-interest note to explain the appeal. The notes about its larval features, its lack of transformation, and its limb regrowth alone each state a fact without linking it to why scientists pursue the study.
While studying the migration of monarch butterflies, biologist Lincoln Brower noticed a striking pattern, the insects returned to the same Mexican forests their great-grandparents had left, despite never having made the journey before. As written, the underlined portion ("a striking pattern, the insects") creates which error?
- No error, because a comma correctly introduces the explanation that follows
- A comma splice, because a comma joins two independent clauses that should be separated by a colon, semicolon, or stronger punctuation
- A subject-verb agreement error, because "pattern" is singular but "returned" is plural
- A sentence fragment, because the clause beginning with "the insects" lacks a subject
Correct answer: A comma splice, because a comma joins two independent clauses that should be separated by a colon, semicolon, or stronger punctuation
This is a comma splice. A comma splice occurs when a comma alone joins two independent clauses, each of which could stand as its own sentence; here "biologist Lincoln Brower noticed a striking pattern" and "the insects returned to the same Mexican forests..." are both complete. To fix it, a colon (since the second clause explains the pattern), a semicolon, or a period would be used. It is not a fragment, since both clauses have subjects and verbs, and "returned" agrees fine with its own subject "insects."
Choose the answer that most logically completes the text so that it conforms to the conventions of Standard English. The committee, along with its three newest advisers, ____ scheduled to present the budget proposal at next week's town meeting.
- Were
- Have been
- Is
- Are
Correct answer: Is
The correct choice is "is." Subject-verb agreement asks whether the verb matches the grammatical subject in number; the subject here is the singular noun "committee," and the phrase "along with its three newest advisers" is a parenthetical interrupter set off by commas, not part of the subject. Such interrupters never change the verb's number, so the singular "is" is required. "Are," "were," and "have been" are all plural and would wrongly agree with "advisers."
As the city council reviewed proposals for the new transit line, ____ weighed concerns about cost, noise, and the disruption that construction would cause to local businesses. Which choice completes the text so that it conforms to the conventions of Standard English?
- It
- They
- One
- Those
Correct answer: It
The correct pronoun is "it." Pronoun-antecedent agreement requires a pronoun to match its antecedent in number; the antecedent "city council" is a singular collective noun acting as one unit, so the singular "it" is correct. "They" is a common trap because a council contains many people, but in Standard English the collective noun is treated as singular here. "One" and "those" do not refer clearly back to the council.
By the time the volunteers finished planting the last row of seedlings, the sun ____ below the ridge, and the field crew packed up their tools in the fading light. Which choice completes the text so that it conforms to the conventions of Standard English?
- Is setting
- Had set
- Will set
- Sets
Correct answer: Had set
The correct choice is "had set." Verb tense must reflect the sequence of events: the sun's setting was completed before the volunteers finished planting, so the past perfect "had set" correctly marks an action finished prior to another past action ("finished planting"). The simple present "sets," future "will set," and present progressive "is setting" all clash with the clearly past-tense narration established by "finished" and "packed."
A line passes through the points (-3, 4) and (5, -2). What is the slope of the line?
- 3/4
- -4/3
- 6/8
- -3/4
Correct answer: -3/4
The slope is -3/4. To find the slope between two points, divide the change in y by the change in x: (-2 - 4) / (5 - (-3)) = -6/8, which reduces to -3/4. The negative result correctly reflects that the line falls from left to right; flipping the fraction to -4/3 reverses the rise and run.
Solve the system of equations: 2x + 3y = 12 and x = y + 1. What is the value of x?
- 3
- 1
- 5
- 2
Correct answer: 3
x equals 3. Using substitution, replace x with y + 1 in the first equation: 2(y + 1) + 3y = 12, which becomes 5y + 2 = 12, so y = 2. Substituting back, x = y + 1 = 3. The value 2 is the solution for y, not x.
What is the smallest integer value of x that satisfies the inequality 4x - 3 > 17?
- 4
- 7
- 6
- 5
Correct answer: 6
The smallest integer is 6. Add 3 to both sides to get 4x > 20, then divide by 4 to get x > 5. Because x must be strictly greater than 5, the smallest whole number that works is 6, not 5, since 5 itself does not satisfy a strict inequality.
A linear equation is written as 5(x - 2) = 3x + 4. What is the value of x?
- 5
- 3
- 11
- 7
Correct answer: 7
x equals 7. Distribute the 5 to get 5x - 10 = 3x + 4. Subtracting 3x from both sides gives 2x - 10 = 4, and adding 10 gives 2x = 14, so x = 7. Forgetting to distribute to both terms inside the parentheses is the most common error here.
A line is parallel to the line y = (2/3)x + 1 and passes through the point (6, 1). What is the equation of this line?
- Y = (2/3)x + 1
- Y = (2/3)x - 3
- Y = (2/3)x + 5
- Y = -(3/2)x + 10
Correct answer: Y = (2/3)x - 3
The equation is y = (2/3)x - 3. Parallel lines share the same slope, so the new line also has slope 2/3. Plugging the point (6, 1) into y = (2/3)x + b gives 1 = 4 + b, so b = -3. A slope of -3/2 would describe a perpendicular line, not a parallel one.
What is the x-coordinate of the point where the line 3x - 4y = 24 crosses the x-axis?
- 8
- -6
- -8
- 6
Correct answer: 8
The x-intercept is at x = 8. A line crosses the x-axis where y = 0, so substitute y = 0 into the equation: 3x - 0 = 24, giving 3x = 24 and x = 8. Setting x = 0 instead would give the y-intercept, a different point.
For which value does the system 2x + 4y = 10 and x + 2y = 7 have a solution?
- X = 3, y = 1
- The system has no solution
- X = 1, y = 2
- Infinitely many solutions
Correct answer: The system has no solution
The system has no solution. Dividing the first equation by 2 gives x + 2y = 5, which has the same left side as the second equation but a different constant (5 versus 7). Two lines with equal slopes but different intercepts are parallel and never intersect, so no ordered pair satisfies both.
A line has a slope of 2 and a y-intercept of -5. What is the value of y when x = 4?
- 13
- 8
- 3
- -3
Correct answer: 3
When x = 4, y = 3. The equation in slope-intercept form is y = 2x - 5. Substituting x = 4 gives y = 2(4) - 5 = 8 - 5 = 3. Forgetting to subtract the y-intercept of -5 would incorrectly give 8.
Solve the system: 3x + 2y = 16 and 5x - 2y = 0. What is the value of x + y?
- 7
- 8
- 5
- 3
Correct answer: 7
The value of x + y is 7. Adding the two equations eliminates y: 8x = 16, so x = 2. Substituting into 5x - 2y = 0 gives 10 - 2y = 0, so y = 5. Therefore x + y = 2 + 5 = 7. Adding the equations works because the y-terms are opposites.
A gym charges a 50-dollar membership fee plus 0.25 dollars per minute of personal training. If a member spends no more than 200 dollars total, which inequality represents the number of training minutes m?
- 50 + 0.25m >= 200
- 50m + 0.25 <= 200
- 0.25 + 50m <= 200
- 50 + 0.25m <= 200
Correct answer: 50 + 0.25m <= 200
The correct inequality is 50 + 0.25m <= 200. The flat 50-dollar fee is constant, and 0.25m represents the variable cost that depends on the number of minutes. Because the total must not exceed 200 dollars, the sum is less than or equal to 200. Solving it shows m can be at most 600 minutes.
What is the slope of the line represented by the equation 4x + 2y = 10?
- 2
- 4
- -2
- 5
Correct answer: -2
The slope is -2. Rewriting the equation in slope-intercept form, subtract 4x to get 2y = -4x + 10, then divide by 2 to get y = -2x + 5. The coefficient of x is the slope, which is -2. The positive value 2 ignores the sign that results from moving the x-term.
A water tank holds 15 liters and is filled at a rate that makes the total volume c, in liters, equal to 15 + 8h after h hours. After how many hours does the tank hold 71 liters?
- 8
- 6
- 9
- 7
Correct answer: 7
It takes 7 hours. Set the volume equal to 71: 15 + 8h = 71. Subtracting 15 gives 8h = 56, and dividing by 8 gives h = 7. The starting amount of 15 liters must be subtracted before dividing by the rate of 8 liters per hour.
Solve for x: (x/4) + 3 = 10.
- 28
- 13
- 40
- 7
Correct answer: 28
x equals 28. First subtract 3 from both sides to get x/4 = 7, then multiply both sides by 4 to get x = 28. Stopping at x/4 = 7 and reading off 7 skips the final step of multiplying by the denominator.
Two lines are given by y = 3x - 1 and y = -x + 7. At what point do they intersect?
- (3, 8)
- (5, 2)
- (2, -5)
- (2, 5)
Correct answer: (2, 5)
The lines intersect at (2, 5). Setting the expressions equal gives 3x - 1 = -x + 7, so 4x = 8 and x = 2. Substituting x = 2 into either equation gives y = 3(2) - 1 = 5. The intersection point is the single solution shared by both lines.
A line is perpendicular to the line y = -2x + 3. What is the slope of the perpendicular line?
- -2
- 2
- 1/2
- -1/2
Correct answer: 1/2
The slope is 1/2. Perpendicular lines have slopes that are negative reciprocals of each other. The original slope is -2, so flipping it and changing the sign gives -(1/-2) = 1/2. Simply keeping the slope as -2 or only flipping the sign would not produce a perpendicular line.
If y = 2x and 3x + y = 20, what is the value of x?
- 6
- 5
- 4
- 8
Correct answer: 4
x equals 4. Substitute y = 2x into the second equation: 3x + 2x = 20, which simplifies to 5x = 20, so x = 4. The value 8 is the corresponding value of y, found by doubling x.
A linear function f passes through the points (1, 5) and (3, 11). What is the value of f(0)?
- 3
- 5
- 0
- 2
Correct answer: 2
The value of f(0) is 2. The slope is (11 - 5) / (3 - 1) = 6/2 = 3, so f(x) = 3x + b. Using the point (1, 5): 5 = 3(1) + b, so b = 2. Since f(0) equals the y-intercept b, f(0) = 2.
Use elimination to solve the system 4x + y = 11 and 2x + y = 7. What is the value of x?
- 4
- 2
- 3
- 1
Correct answer: 2
x equals 2. Subtracting the second equation from the first eliminates y: (4x - 2x) + (y - y) = 11 - 7, giving 2x = 4, so x = 2. The y-values cancel because both equations have a coefficient of 1 on y. Substituting back gives y = 3.
Solve the inequality -3x + 5 >= -4.
- X >= 3
- X <= -3
- X >= -3
- X <= 3
Correct answer: X <= 3
The solution is x <= 3. Subtract 5 from both sides to get -3x >= -9, then divide by -3. Dividing by a negative number reverses the inequality sign, turning >= into <=, which gives x <= 3. Forgetting to flip the sign is the most common mistake on these problems.
What is the slope of the line whose equation is 6x - 2y = 8?
- -3
- -4
- 3
- 6
Correct answer: 3
The slope is 3. Solving for y, subtract 6x to get -2y = -6x + 8, then divide by -2 to get y = 3x - 4. The coefficient of x is the slope, which is 3. Dividing only the x-term by -2 while mishandling the signs is what produces an incorrect value such as -3.
At a school fair, an adult ticket costs a dollars and a child ticket costs c dollars. A family buying 2 adult and 3 child tickets pays 31 dollars, and a family buying 1 adult and 2 child tickets pays 18 dollars. What is the price of one adult ticket?
- 5 dollars
- 6 dollars
- 7 dollars
- 8 dollars
Correct answer: 8 dollars
An adult ticket costs 8 dollars. The system is 2a + 3c = 31 and a + 2c = 18. Multiplying the second equation by 2 gives 2a + 4c = 36; subtracting the first equation gives c = 5. Substituting into a + 2(5) = 18 gives a = 8. The value 5 is the child ticket price, not the adult price.
A line has a slope of -1 and passes through the point (3, 4). Which of the following points also lies on this line?
- (5, 2)
- (4, 5)
- (6, 7)
- (2, 2)
Correct answer: (5, 2)
The point (5, 2) lies on the line. The equation is y = -x + b; using (3, 4) gives 4 = -3 + b, so b = 7 and the line is y = -x + 7. Testing (5, 2): -5 + 7 = 2, which matches. A slope of -1 means y decreases by 1 for every unit x increases, ruling out points where both coordinates rise together.
The quadratic formula gives the solutions to any equation of the form $ax^2 + bx + c = 0$ , where $a$ is not 0. Which expression correctly states the quadratic formula for $x$ ?
- $x = \frac{-b \pm \sqrt{4ac - b^2}}{2a}$
- $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$
- $x = \frac{-b \pm \sqrt{b^2 + 4ac}}{2a}$
- $x = \frac{b \pm \sqrt{b^2 - 4ac}}{2a}$
Correct answer: $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$
The quadratic formula is $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ . It is derived by completing the square on $ax^2 + bx + c = 0$ and gives both solutions of any quadratic equation. The quantity under the radical is $b^2$ minus $4ac$ (the discriminant), and the leading coefficient $b$ is negated, so versions that add $4ac$ , reverse the discriminant, or keep $b$ positive are incorrect.
To solve the quadratic equation $2x^2 - 4x - 6 = 0$ using the quadratic formula, which set of values should be substituted for $a$ , $b$ , and $c$ ?
- A = -2, b = -4, c = 6
- A = 2, b = -4, c = -6
- A = 4, b = -6, c = 2
- A = 2, b = 4, c = 6
Correct answer: A = 2, b = -4, c = -6
The correct values are $a = 2$ , $b = -4$ , and $c = -6$ . In standard form $ax^2 + bx + c = 0$ , $a$ is the coefficient of $x^2$ , $b$ is the coefficient of $x$ , and $c$ is the constant term, each taken with its own sign. The middle term $-4x$ gives $b = -4$ (not 4), and the constant $-6$ gives $c = -6$ .
What are the solutions to the equation $x^2 + 7x + 12 = 0$ ?
- X = -3 and x = -4
- X = 3 and x = 4
- X = -2 and x = -6
- X = 2 and x = 6
Correct answer: X = -3 and x = -4
The solutions are x = -3 and x = -4. The expression factors as (x + 3)(x + 4) because 3 and 4 multiply to 12 and add to 7; setting each factor equal to 0 gives x = -3 and x = -4. The pair 2 and 6 multiplies to 12 but adds to 8, not 7, so it does not work.
Which factored form is equivalent to the quadratic expression $x^2 - 5x - 14$ ?
- (x - 7)(x - 2)
- (x + 7)(x - 2)
- (x + 7)(x + 2)
- (x - 7)(x + 2)
Correct answer: (x - 7)(x + 2)
The expression factors as $(x - 7)(x + 2)$ . To factor $x^2 - 5x - 14$ , find two numbers that multiply to -14 and add to -5; those numbers are -7 and 2. Expanding $(x - 7)(x + 2)$ gives $x^2 - 5x - 14$ , confirming the factorization, while $(x + 7)(x - 2)$ would give a middle term of $+5x$ .
A population of bacteria is modeled by the function $f(t) = 200 \cdot 3^t$ , where $t$ is measured in hours. Which statement best describes this function?
- It is an exponential function in which the quantity is multiplied by 3 each hour.
- It is a quadratic function that increases by a constant rate.
- It is an exponential function that decreases over time.
- It is a linear function that increases by 200 each hour.
Correct answer: It is an exponential function in which the quantity is multiplied by 3 each hour.
This is an exponential function in which the quantity is multiplied by 3 each hour. An exponential function has the form $a \cdot b^t$ , where the variable appears in the exponent and the output is multiplied by the constant base $b$ for each unit increase in $t$ . Here $b = 3$ , so the population triples every hour; because $b$ is greater than 1, the function grows rather than decreases.
For the exponential function $g(x) = 5 \cdot 2^x$ , what is the value of $g(0)$ ?
- 10
- 5
- 0
- 2
Correct answer: 5
The value of $g(0)$ is 5. Any nonzero base raised to the power 0 equals 1, so $2^0 = 1$ and $g(0) = 5 \cdot 1 = 5$ . This is why the coefficient in front of an exponential function gives the initial value, the output when $x = 0$ .
A car purchased for 24,000 dollars loses 15 percent of its value each year. Which function gives the value V, in dollars, after t years?
- $V = 24000 \cdot (0.15)^t$
- $V = 24000 \cdot (1.15)^t$
- $V = 24000 \cdot (0.85)^t$
- V = 24000 - 0.15t
Correct answer: $V = 24000 \cdot (0.85)^t$
The correct model is $V = 24000 \cdot (0.85)^t$ . When a quantity decreases by 15 percent each year, each year it keeps 100 percent minus 15 percent, or 85 percent, of its previous value, so the base is 0.85. A base of 1.15 would model 15 percent growth, and 0.15 would discard 85 percent of the value each year.
How many distinct real solutions does the equation $x^2 - 4x + 7 = 0$ have?
- One
- Three
- Two
- Zero
Correct answer: Zero
The equation has zero real solutions. The discriminant $b^2 - 4ac$ equals $(-4)^2 - 4(1)(7) = 16 - 28 = -12$ , which is negative. When the discriminant is negative, the quadratic formula requires $\sqrt{\text{a negative number}}$ , so there are no real solutions.
The quadratic function $f(x) = x^2 - 6x + 5$ is graphed in the $xy$ -plane. What are the coordinates of its vertex?
- (-3, -4)
- (3, 4)
- (3, -4)
- (6, 5)
Correct answer: (3, -4)
The vertex is at $(3, -4)$ . For $f(x) = ax^2 + bx + c$ , the $x$ -coordinate of the vertex is $\frac{-b}{2a} = \frac{-(-6)}{2 \cdot 1} = 3$ . Substituting $x = 3$ gives $f(3) = 9 - 18 + 5 = -4$ , so the vertex is the point $(3, -4)$ .
In the quadratic equation $x^2 + 10x + c = 0$ , what value of $c$ makes the left side a perfect square trinomial?
- 20
- 100
- 5
- 25
Correct answer: 25
The value is 25. A perfect square trinomial of the form $x^2 + bx + c$ has $c$ equal to $(b/2)^2$ . Here $b = 10$ , so $(10/2)^2 = 5^2 = 25$ , and $x^2 + 10x + 25 = (x + 5)^2$ . This 'completing the square' step is the basis for the quadratic formula.
What is the solution to the radical equation $\sqrt{x + 5} = x - 1$ ?
- X = -1
- X = 4 and x = -1
- X = 9
- X = 4
Correct answer: X = 4
The only solution is $x = 4$ . Squaring both sides gives $x + 5 = x^2 - 2x + 1$ , which rearranges to $x^2 - 3x - 4 = 0$ , or $(x - 4)(x + 1) = 0$ , giving $x = 4$ or $x = -1$ . Checking, $x = 4$ works since $\sqrt{9} = 3 = 4 - 1$ , but $x = -1$ gives $\sqrt{4} = 2$ , which does not equal -2, so it is an extraneous solution introduced by squaring.
Solve the radical equation $\sqrt{2x - 1} = 5$ for $x$ .
- X = 26
- X = 12
- X = 3
- X = 13
Correct answer: X = 13
The solution is $x = 13$ . Squaring both sides of $\sqrt{2x - 1} = 5$ gives $2x - 1 = 25$ , so $2x = 26$ and $x = 13$ . Checking confirms $\sqrt{2 \cdot 13 - 1} = \sqrt{25} = 5$ , so the solution is valid and not extraneous.
What is the solution to the rational equation 12 / (x + 1) = 4?
- X = 2
- X = 3
- X = 47
- X = -1
Correct answer: X = 2
The solution is x = 2. Multiplying both sides by (x + 1) gives 12 = 4(x + 1), so 12 = 4x + 4, which leads to 4x = 8 and x = 2. The value x = -1 is excluded because it would make the denominator zero, so it can never be a solution.
For which value of $x$ is the rational expression $\frac{x - 3}{x^2 - 9}$ undefined but not equal to a removable point at $x = 3$ ?
- X = 3
- X = 0
- X = 9
- X = -3
Correct answer: X = -3
The expression is undefined at $x = -3$ . The denominator $x^2 - 9$ factors as $(x - 3)(x + 3)$ , so it equals zero when $x = 3$ or $x = -3$ . At $x = 3$ the factor $(x - 3)$ cancels with the numerator, leaving a removable hole, but at $x = -3$ nothing cancels, so the expression is genuinely undefined there.
What is the solution set of the absolute value equation |2x - 6| = 10?
- X = 8 only
- X = 8 and x = 2
- X = -8 and x = 2
- X = 8 and x = -2
Correct answer: X = 8 and x = -2
The solution set is x = 8 and x = -2. An equation |A| = 10 means A = 10 or A = -10, so 2x - 6 = 10 gives x = 8, and 2x - 6 = -10 gives 2x = -4, so x = -2. Both values satisfy the original equation because absolute value makes each result positive 10.
For how many values of x does the equation |x + 4| = -3 have a solution?
- Zero
- One
- Two
- Infinitely many
Correct answer: Zero
There are zero solutions. The absolute value of any real expression is always greater than or equal to 0, so |x + 4| can never equal a negative number such as -3. Because no value of x can make a nonnegative quantity equal -3, the equation has no solution.
The polynomial $p(x) = x^3 - 4x$ is set equal to zero. What are all real solutions of $p(x) = 0$ ?
- X = 2 and x = -2
- X = 0 and x = 4
- X = 0, x = 4, and x = -4
- X = 0, x = 2, and x = -2
Correct answer: X = 0, x = 2, and x = -2
The real solutions are $x = 0$ , $x = 2$ , and $x = -2$ . Factoring gives $x(x^2 - 4) = x(x - 2)(x + 2)$ , so the polynomial equals zero when $x = 0$ , $x = 2$ , or $x = -2$ . Each factor set to zero contributes one root, and the difference of squares $x^2 - 4$ splits into $(x - 2)(x + 2)$ .
According to the factor theorem, if x = 3 is a root of a polynomial f(x), which of the following must be true?
- (x + 3) is a factor of f(x)
- F(3) equals 3
- (x - 3) is a factor of f(x)
- F(x) has degree 3
Correct answer: (x - 3) is a factor of f(x)
It must be true that (x - 3) is a factor of f(x). The factor theorem states that x = r is a root of a polynomial exactly when (x - r) divides the polynomial evenly. Since r = 3 is a root, the corresponding factor is (x - 3), not (x + 3), and a root means f(3) equals 0, not 3.
If the function $f$ is defined by $f(x) = x^2 - 2x + 1$ , what is the value of $f(-3)$ ?
- -2
- 16
- 4
- 10
Correct answer: 16
The value of $f(-3)$ is 16. Substituting $x = -3$ gives $(-3)^2 - 2(-3) + 1 = 9 + 6 + 1 = 16$ . Squaring the negative input yields a positive 9, and subtracting -6 adds 6, so the total is 16.
The expression $\frac{x^2 - 16}{x - 4}$ is simplified for all $x$ not equal to 4. Which expression is equivalent to it?
- $x^2 - 4$
- X - 4
- X + 16
- X + 4
Correct answer: X + 4
The equivalent expression is $x + 4$ . The numerator $x^2 - 16$ is a difference of squares that factors as $(x - 4)(x + 4)$ . Canceling the common factor $(x - 4)$ with the denominator leaves $x + 4$ for all $x$ not equal to 4.
If $a^2 - b^2 = 40$ and $a + b = 8$ , what is the value of $a - b$ ?
- 32
- 5
- 6
- 4
Correct answer: 5
The value of a - b is 5. The difference of squares can be written as (a + b)(a - b) = 40. Since a + b = 8, dividing both sides by 8 gives a - b = 40 / 8 = 5.
For the quadratic equation $x^2 - 9x + 20 = 0$ , what is the sum of its two solutions?
- -9
- 9
- 11
- 20
Correct answer: 9
The sum of the solutions is 9. For a quadratic $ax^2 + bx + c = 0$ , the sum of the roots equals $-b/a$ ; here that is $-(-9)/1 = 9$ . This can be checked by factoring into $(x - 4)(x - 5)$ , giving roots 4 and 5, which add to 9.
An object's height in feet is given by $h(t) = -16t^2 + 32t$ , where $t$ is time in seconds after launch. At what time does the object return to a height of 0 feet (other than at launch)?
- T = 16 seconds
- T = 1 second
- T = 32 seconds
- T = 2 seconds
Correct answer: T = 2 seconds
The object returns to height 0 at $t = 2$ seconds. Setting $h(t) = 0$ gives $-16t^2 + 32t = 0$ , which factors as $-16t(t - 2) = 0$ , so $t = 0$ (launch) or $t = 2$ . The nonzero solution $t = 2$ is when the object lands.
The graph of y = (x - 2)(x + 6) crosses the x-axis at which two points?
- (2, 0) and (6, 0)
- (-2, 0) and (6, 0)
- (2, 0) and (-6, 0)
- (-2, 0) and (-6, 0)
Correct answer: (2, 0) and (-6, 0)
The graph crosses the x-axis at (2, 0) and (-6, 0). The x-intercepts of a function occur where y = 0, and a product equals zero when one of its factors is zero. Setting x - 2 = 0 gives x = 2, and setting x + 6 = 0 gives x = -6, so the zeros are the opposites of the constants inside the factors.
Which expression is equivalent to (2x + 3)(x - 5)?
- $2x^2 + 7x - 15$
- $2x^2 - 7x - 15$
- $2x^2 - 13x - 15$
- $2x^2 - 7x + 15$
Correct answer: $2x^2 - 7x - 15$
The equivalent expression is $2x^2 - 7x - 15$ . Multiplying using the distributive property gives $2x \cdot x + 2x \cdot (-5) + 3 \cdot x + 3 \cdot (-5) = 2x^2 - 10x + 3x - 15$ , and combining the middle terms $-10x$ and $3x$ yields $-7x$ . The constant term is 3 times -5, which equals -15.
If $x^{1/2} = 6$ , what is the value of $x$ ?
- 3
- 36
- 12
- 6
Correct answer: 36
The value of $x$ is 36. The exponent $1/2$ means the square root, so $x^{1/2} = 6$ is the same as $\sqrt{x} = 6$ . Squaring both sides gives $x = 36$ , since 6 times 6 equals 36.
A 12-ounce bottle of juice costs 3.00 dollars. What is the unit rate, in dollars per ounce?
- 4.00 dollars per ounce
- 0.25 dollars per ounce
- 2.50 dollars per ounce
- 0.36 dollars per ounce
Correct answer: 0.25 dollars per ounce
The unit rate is 0.25 dollars per ounce. A unit rate is the cost (or amount) for exactly one unit, found by dividing the total by the number of units: 3.00 dollars divided by 12 ounces equals 0.25 dollars per ounce. Dividing 12 by 3 instead gives 4 ounces per dollar, a different rate, not dollars per ounce.
A car travels 240 miles on 8 gallons of gasoline. At this same rate, how many gallons are needed to travel 600 miles?
- 15 gallons
- 30 gallons
- 20 gallons
- 24 gallons
Correct answer: 20 gallons
The answer is 20 gallons. First find the unit rate: 240 miles divided by 8 gallons equals 30 miles per gallon. Then divide the trip distance by that rate: 600 miles divided by 30 miles per gallon equals 20 gallons. Multiplying instead of using the rate produces inflated values like 24 or 30.
A recipe uses flour and sugar in a ratio of 5 to 2. If a baker uses 15 cups of flour, how many cups of sugar are needed to keep the same ratio?
- 12 cups
- 6 cups
- 7.5 cups
- 4 cups
Correct answer: 6 cups
The answer is 6 cups. Setting up the proportion 5/2 = 15/x and cross-multiplying gives 5x = 30, so x = 6 cups of sugar. Because the flour amount tripled (5 to 15), the sugar must also triple, from 2 to 6. The value 7.5 incorrectly halves the flour amount instead of using the 5-to-2 ratio.
A shirt originally priced at 40 dollars is on sale for 34 dollars. What is the percent decrease in price?
- 17.6 percent
- 6 percent
- 15 percent
- 12 percent
Correct answer: 15 percent
The answer is 15 percent. Percent change is found by dividing the amount of change by the original value, then multiplying by 100. The price dropped by 40 minus 34, or 6 dollars; 6 divided by 40 equals 0.15, which is 15 percent. Dividing by the new price of 34 instead of the original 40 gives the incorrect 17.6 percent.
The number of subscribers to a newsletter grew from 250 to 320 over one year. What was the percent increase?
- 28 percent
- 7 percent
- 21.9 percent
- 70 percent
Correct answer: 28 percent
The answer is 28 percent. The increase is 320 minus 250, which equals 70 subscribers. Dividing the change by the original amount, 70 divided by 250, gives 0.28, or 28 percent. Dividing by the new total of 320 instead of the original 250 yields the incorrect 21.9 percent.
In a survey, 60 percent of 150 students said they prefer online classes. How many students preferred online classes?
- 75 students
- 250 students
- 60 students
- 90 students
Correct answer: 90 students
The answer is 90 students. To find a percent of a quantity, convert the percent to a decimal and multiply: 0.60 times 150 equals 90 students. The value 60 mistakes the percent itself for the count, and 250 reverses the calculation by dividing 150 by 0.60.
A scatterplot shows hours studied on the x-axis and test score on the y-axis, with points rising from lower-left to upper-right. Which statement best describes the association?
- A negative linear association
- A positive linear association
- An exponential association
- No association
Correct answer: A positive linear association
The answer is a positive linear association. When points on a scatterplot trend upward from left to right in a roughly straight pattern, the two variables increase together, which is a positive linear association. A negative association would slope downward, and points scattered with no clear direction would show no association.
A scatterplot of monthly temperature versus heating-fuel use shows points falling from upper-left to lower-right along a straight trend. What does the line of best fit's slope indicate?
- Fuel use is constant regardless of temperature
- Fuel use increases as temperature increases
- There is no relationship between the variables
- Fuel use decreases as temperature increases
Correct answer: Fuel use decreases as temperature increases
The answer is that fuel use decreases as temperature increases. A line of best fit that slopes downward (negative slope) means that as the x-variable, temperature, rises, the y-variable, fuel use, falls. An upward trend would indicate the opposite, and a flat line would indicate no change with temperature.
A line of best fit for a data set is given by y = 2.5x + 12, where x is years of experience and y is hourly wage in dollars. What does the value 2.5 represent?
- The total wage after 2.5 years
- The starting wage with zero years of experience
- The number of data points in the study
- The predicted increase in hourly wage for each additional year of experience
Correct answer: The predicted increase in hourly wage for each additional year of experience
The answer is the predicted increase in hourly wage for each additional year of experience. In a line of best fit, the slope tells how much the y-value changes for each one-unit increase in x; here each extra year of experience predicts a 2.5-dollar rise in wage. The value 12 is the y-intercept, the predicted wage at zero years of experience.
The data set 4, 7, 7, 9, 13 has which of the following pairs of values for its mean and median?
- Mean 8, median 9
- Mean 7, median 8
- Mean 7, median 7
- Mean 8, median 7
Correct answer: Mean 8, median 7
The answer is mean 8, median 7. The mean is the sum 4 plus 7 plus 7 plus 9 plus 13, which is 40, divided by 5 values, equaling 8. The median is the middle value when the data is ordered, which is 7. Swapping these two statistics gives the incorrect mean 7, median 8.
Two data sets have the same mean, but Set A has values clustered close to the mean while Set B has values spread far from the mean. Which statement is true?
- Set A has a larger standard deviation
- Standard deviation cannot be compared without the medians
- Set B has a larger standard deviation
- Both sets have the same standard deviation
Correct answer: Set B has a larger standard deviation
The answer is that Set B has a larger standard deviation. Standard deviation measures how spread out values are from the mean; data spread farther from the mean has greater standard deviation. Because Set B's values are more dispersed than Set A's tightly clustered values, Set B has the larger standard deviation regardless of the equal means.
A box contains 5 red, 3 blue, and 2 green marbles. If one marble is drawn at random, what is the probability it is blue?
- 2 out of 10
- 3 out of 7
- 1 out of 3
- 3 out of 10
Correct answer: 3 out of 10
The answer is 3 out of 10. Probability equals the number of favorable outcomes divided by the total number of outcomes. There are 3 blue marbles out of 5 plus 3 plus 2, which is 10 marbles total, giving a probability of 3/10. The value 3 out of 7 mistakenly leaves the blue marbles out of the denominator.
A researcher wants to estimate the average number of hours students at a large school sleep. To get a sample likely to represent all students, the researcher should select students by which method?
- Asking the researcher's own friends
- Surveying only students leaving the library at night
- Asking only members of the school's sports teams
- Surveying students chosen at random from the entire student body
Correct answer: Surveying students chosen at random from the entire student body
The answer is surveying students chosen at random from the entire student body. A random sample drawn from the whole population gives each student an equal chance of selection, so results can be generalized to all students. The other methods sample only specific subgroups, introducing bias that makes conclusions about the full student body unreliable.
A map uses a scale of 1 inch to 25 miles. Two cities are 3.5 inches apart on the map. What is the actual distance between the cities?
- 71.4 miles
- 87.5 miles
- 28.5 miles
- 100 miles
Correct answer: 87.5 miles
The answer is 87.5 miles. The scale is a proportional relationship: each inch represents 25 miles, so multiply the map distance by the scale factor: 3.5 inches times 25 miles per inch equals 87.5 miles. Dividing 3.5 by 25 or adding the values produces the incorrect smaller results.
A straight ladder leans against a vertical wall. The base of the ladder sits on level ground 8 feet from the wall, and the ladder itself is 17 feet long. How high up the wall does the top of the ladder reach?
- 13 feet
- 15 feet
- 19 feet
- 25 feet
Correct answer: 15 feet
The ladder reaches 15 feet up the wall. The wall, the ground, and the ladder form a right triangle in which the ladder is the hypotenuse, so the Pythagorean theorem gives $\text{height} = \sqrt{17^2 - 8^2} = \sqrt{289 - 64} = \sqrt{225} = 15$ . A common mistake is to add the squares $(17^2 + 8^2)$ instead of subtracting; that treats the height as the hypotenuse, which it is not.
A circular garden has a diameter of 20 feet. In terms of pi, what is the area of the garden?
- 400pi square feet
- 20pi square feet
- 100pi square feet
- 40pi square feet
Correct answer: 100pi square feet
The area is $100\pi$ square feet. To find the area of a circle you use $A = \pi \cdot r^2$ , where $r$ is the radius. The diameter is 20 feet, so the radius is half of that, or 10 feet, giving $A = \pi \cdot 10^2 = 100\pi$ . The value $400\pi$ comes from squaring the diameter instead of the radius, and $40\pi$ is the circumference rather than the area.
In a right triangle, the side opposite an acute angle theta measures 9, the side adjacent to theta measures 12, and the hypotenuse measures 15. What is the value of tan(theta)?
- 0.8
- 1.25
- 0.6
- 0.75
Correct answer: 0.75
The value of tan(theta) is 0.75. Using the SOH-CAH-TOA ratios, the tangent of an angle equals the opposite side divided by the adjacent side, so tan(theta) = 9/12 = 0.75. The value 0.6 is sin(theta) = opposite/hypotenuse = 9/15, and 0.8 is cos(theta) = adjacent/hypotenuse = 12/15, which test whether you can distinguish the three ratios.
A right triangle has a hypotenuse of length 12 and one acute angle measuring 30 degrees. What is the length of the side opposite the 30-degree angle?
- 9
- 6
- 24
- $6\sqrt{3}$
Correct answer: 6
The side opposite the 30-degree angle has length 6. In right-triangle trigonometry, the sine of an angle equals the opposite side divided by the hypotenuse, so $\text{opposite} = \text{hypotenuse} \cdot \sin(30^\circ) = 12 \cdot 0.5 = 6$ . The value $6\sqrt{3}$ (about 10.39) is the side adjacent to the 30-degree angle, found with cosine, not the opposite side.
In a circle with a radius of 10, a central angle measures 72 degrees. What is the length of the arc that this central angle intercepts?
- 8pi
- 4pi
- 20pi
- 2pi
Correct answer: 4pi
The intercepted arc has length 4pi. An arc length equals the fraction of the full circle the central angle covers times the circumference, so it is (72/360) times 2 times pi times 10 = (1/5) times 20pi = 4pi. The value 20pi is the entire circumference, which would only be the arc if the central angle were the full 360 degrees.
A cylindrical water tank has a circular base with a radius of 3 feet and a height of 10 feet. In terms of pi, what is the volume of the tank?
- 60pi cubic feet
- 900pi cubic feet
- 30pi cubic feet
- 90pi cubic feet
Correct answer: 90pi cubic feet
The volume is $90\pi$ cubic feet. The volume of a cylinder equals the area of its circular base times its height: $V = \pi \cdot r^2 \cdot h = \pi \cdot 3^2 \cdot 10 = \pi \cdot 9 \cdot 10 = 90\pi$ . The value $900\pi$ comes from squaring the height instead of the radius, and $60\pi$ comes from multiplying the radius by 2 (as if finding circumference) rather than squaring it.
The following is from a passage about tardigrades. Tardigrades, tiny water-dwelling animals less than a millimeter long, can survive conditions that would kill nearly every other creature. By expelling almost all the water from their bodies and entering a dormant state called a tun, they endure boiling heat, freezing cold, and even the vacuum of space. When water returns, they revive and resume their lives. Which choice best states the main idea of the text?
- Tardigrades survive extreme conditions by drying out and becoming dormant until water returns.
- Tardigrades are the smallest animals that scientists have ever measured.
- Tardigrades cannot survive without a constant supply of fresh water.
- Tardigrades spend most of their lives traveling through the vacuum of space.
Correct answer: Tardigrades survive extreme conditions by drying out and becoming dormant until water returns.
Correct answer: Tardigrades survive extreme conditions by drying out and becoming dormant until water returns. The passage centers on how the tun state lets tardigrades withstand extremes and then revive once water is available, which is the main idea.
The following is from a passage about honeybee communication. When a foraging honeybee finds a rich source of nectar, it returns to the hive and performs a looping movement known as the waggle dance. The angle and duration of the dance encode the direction and distance of the food relative to the sun. Other bees follow the dancer closely and then fly directly to the source. Which choice best states the main idea of the text?
- The waggle dance communicates the location of food to other bees in the hive.
- Honeybees prefer nectar sources that are located close to the sun.
- Foraging bees rarely return to the hive after finding food.
- The waggle dance is performed only when the hive is in danger.
Correct answer: The waggle dance communicates the location of food to other bees in the hive.
Correct answer: The waggle dance communicates the location of food to other bees in the hive. The text explains that the dance encodes direction and distance so other bees can find the source, which captures the central idea.
The following is from a passage about a coral restoration project. Marine biologists in the Caribbean have begun growing coral fragments on underwater frames, where the pieces mature quickly before being attached to damaged reefs. Reefs that received these nursery-grown corals showed denser coral cover and attracted more fish within three years. Researchers say the method speeds recovery that would otherwise take decades. Which choice best states the main idea of the text?
- Nursery-grown coral fragments can help damaged reefs recover faster than they would naturally.
- Caribbean reefs are no longer threatened by any environmental pressures.
- Fish populations decline whenever coral fragments are moved to new reefs.
- Coral fragments can only survive when left attached to underwater frames.
Correct answer: Nursery-grown coral fragments can help damaged reefs recover faster than they would naturally.
Correct answer: Nursery-grown coral fragments can help damaged reefs recover faster than they would naturally. The passage describes faster coral cover and more fish on restored reefs, supporting this as the central point.
The following is from a passage about urban heat. Cities are often several degrees warmer than the surrounding countryside, a difference known as the urban heat island effect. Dark roofs and pavement absorb sunlight during the day and release it slowly at night, keeping temperatures elevated. Planting trees and installing reflective surfaces are among the strategies cities use to ease the effect. Which choice best states the main idea of the text?
- Trees in cities absorb more heat than dark pavement does.
- Rural areas experience higher nighttime temperatures than cities do.
- Reflective surfaces have no measurable effect on city temperatures.
- The urban heat island effect makes cities warmer, and certain measures can reduce it.
Correct answer: The urban heat island effect makes cities warmer, and certain measures can reduce it.
Correct answer: The urban heat island effect makes cities warmer, and certain measures can reduce it. The passage defines the effect and lists strategies to ease it, which together form the main idea.
The following is from a passage about the painter Hilma af Klint. Long before abstract art became widely recognized, the Swedish painter Hilma af Klint filled canvases with bold geometric shapes and symbolic colors. Convinced the public was not ready for her work, she asked that it remain hidden for decades after her death. Only in recent years have her paintings been celebrated as pioneering examples of abstraction. Which choice best states the main idea of the text?
- Hilma af Klint produced early abstract art that went unrecognized until long after her death.
- Hilma af Klint refused to paint with color throughout her career.
- Abstract art was already popular when Hilma af Klint began painting.
- Hilma af Klint destroyed most of her own paintings before she died.
Correct answer: Hilma af Klint produced early abstract art that went unrecognized until long after her death.
Correct answer: Hilma af Klint produced early abstract art that went unrecognized until long after her death. The text emphasizes that her pioneering abstraction was hidden and only recently celebrated, which is the central idea.
The following is from a passage about an octopus's skin. An octopus can change the color and texture of its skin in less than a second. Special cells filled with pigment expand or contract to produce different hues, while muscles beneath the skin raise tiny bumps to mimic rough surfaces. Together these abilities let the animal blend into coral, rock, or sand almost instantly. Which choice best states the main idea of the text?
- An octopus changes color only when it is searching for food.
- An octopus relies on a hard outer shell to protect itself.
- An octopus rapidly camouflages itself by altering both the color and the texture of its skin.
- An octopus can mimic rough surfaces but cannot change color.
Correct answer: An octopus rapidly camouflages itself by altering both the color and the texture of its skin.
Correct answer: An octopus rapidly camouflages itself by altering both the color and the texture of its skin. The passage describes pigment cells and muscle-raised bumps working together for camouflage, supporting this main idea.
The following is from a passage about seed banks. Deep inside a mountain on a remote Arctic island sits a vault that stores duplicate samples of seeds from around the world. The cold, dry conditions keep the seeds viable for decades or longer. If a crop is wiped out by disaster elsewhere, scientists can draw on the vault to restore it. Which choice best states the main idea of the text?
- The Arctic seed vault preserves crop seeds so they can be restored after a disaster.
- The seed vault is used to grow new crops on the Arctic island itself.
- Seeds stored in the vault remain viable for only a few weeks.
- The vault stores only seeds that are native to the Arctic.
Correct answer: The Arctic seed vault preserves crop seeds so they can be restored after a disaster.
Correct answer: The Arctic seed vault preserves crop seeds so they can be restored after a disaster. The passage explains that duplicate seeds are kept viable and can be drawn on if a crop is lost, which is the main idea.
The following is from a passage about the desert plant called the resurrection plant. The resurrection plant survives long droughts by curling into a dry brown ball that appears lifeless. In this state it can wait for months without water. When rain finally arrives, the plant unfurls within hours and turns green again as its cells rehydrate. According to the text, what happens to the resurrection plant when rain arrives?
- It can wait for months without water in a dry ball.
- It produces seeds that scatter across the desert.
- It permanently loses its brown color and dies.
- It unfurls within hours and turns green again.
Correct answer: It unfurls within hours and turns green again.
Correct answer: It unfurls within hours and turns green again. The text states that when rain arrives the plant unfurls within hours and its cells rehydrate, directly answering the question.
The following is from a passage about the inventor Mary Anderson. In the early 1900s, Mary Anderson noticed that drivers had to stop and step outside to clear snow and rain from their windshields. She designed a lever inside the car that swung a rubber blade across the glass. Although manufacturers were slow to adopt it, her windshield wiper later became standard equipment on automobiles. According to the text, what problem did Anderson's invention address?
- Drivers having to step outside to clear their windshields.
- Cars being unable to start in cold weather.
- Rubber blades wearing out too quickly on the road.
- Manufacturers refusing to build automobiles.
Correct answer: Drivers having to step outside to clear their windshields.
Correct answer: Drivers having to step outside to clear their windshields. The passage states that Anderson noticed drivers had to stop and step outside to clear snow and rain, which her lever-operated blade solved.
The following is from a passage about migrating monarch butterflies. Each autumn, monarch butterflies travel thousands of miles from North America to a few mountain forests in central Mexico. No single butterfly makes the round trip; the journey spans several generations. The butterflies that arrive in Mexico are the descendants of those that left months earlier. According to the text, why does no single monarch complete the round trip?
- The forests in Mexico are too cold for any butterfly to survive.
- The butterflies stop migrating once they reach North America.
- Predators capture the butterflies before they can return.
- The journey spans several generations of butterflies.
Correct answer: The journey spans several generations of butterflies.
Correct answer: The journey spans several generations of butterflies. The text explains that the trip takes several generations and that arriving butterflies are descendants of those that left, so no single one finishes.
The following is from a passage about lighthouses. Before electric power, lighthouse keepers burned oil lamps and used curved glass lenses to focus the light into a single bright beam. The lens, invented by Augustin-Jean Fresnel, could send a beam much farther than a plain lamp. Ships far out at sea could then spot the warning long before reaching dangerous rocks. According to the text, what advantage did the Fresnel lens provide?
- It allowed lighthouse keepers to stop burning oil entirely.
- It made the lamps safer to handle in storms.
- It sent the beam much farther than a plain lamp could.
- It reduced the number of ships traveling near the coast.
Correct answer: It sent the beam much farther than a plain lamp could.
Correct answer: It sent the beam much farther than a plain lamp could. The passage states that the Fresnel lens focused light into a beam that traveled much farther than a plain lamp, helping ships see the warning sooner.
The following is from a passage about the history of chocolate. For most of its history, chocolate was consumed as a bitter drink rather than a sweet bar. The ancient Maya and Aztec peoples ground cacao beans into a frothy beverage flavored with spices. Only after Europeans added sugar and milk, centuries later, did chocolate take the solid, sweet form familiar today. According to the text, how was chocolate originally consumed?
- As a solid bar flavored with milk.
- As a powder sprinkled over baked goods.
- As a bitter, frothy drink flavored with spices.
- As a sweet syrup poured over fruit.
Correct answer: As a bitter, frothy drink flavored with spices.
Correct answer: As a bitter, frothy drink flavored with spices. The text states that the Maya and Aztec ground cacao into a frothy beverage with spices, describing chocolate's original form.
The following is from a passage about deep-sea anglerfish. In the lightless depths of the ocean, the anglerfish dangles a glowing lure from a stalk above its mouth. Tiny bacteria living in the lure produce the light. Smaller fish, drawn to the rare glow in the darkness, swim close enough for the anglerfish to seize them. Which choice most logically completes the text?
- The glowing lure functions as a way to attract prey within reach
- The anglerfish avoids any contact with smaller fish
- The bacteria harm the anglerfish that carries them
- The lure produces light only when the fish is resting
Correct answer: The glowing lure functions as a way to attract prey within reach
Correct answer: the glowing lure functions as a way to attract prey within reach. The passage notes that smaller fish are drawn to the glow and then seized, so it follows that the lure serves to attract prey.
The following is from a passage about ancient Roman roads. Roman engineers built roads in layers, beginning with large stones at the base and topping them with tightly fitted paving. Many of these roads have survived for nearly two thousand years and remain partly usable today. Modern builders still study Roman methods when designing roads meant to last. Which choice most logically completes the text?
- Roman roads were rebuilt completely every few decades.
- Roman engineers avoided using stone in their roads.
- Modern roads are always more durable than Roman ones
- The layered construction contributed to the roads' remarkable durability
Correct answer: The layered construction contributed to the roads' remarkable durability
Correct answer: the layered construction contributed to the roads' remarkable durability. Since the layered roads have lasted two thousand years and are still studied for durability, it follows that the construction contributed to that durability.
The following is from a passage about a city's library expansion. After the city extended its library hours into the evening, the number of visitors rose sharply, with the largest increase coming from people who worked during the day. Library staff also reported that evening study rooms filled quickly and often had waiting lists. Which choice most logically completes the text?
- The new evening hours met a demand from people unable to visit during the day
- The library should return to its original daytime-only schedule
- Evening visitors were less interested in using study rooms
- Daytime visitors stopped coming to the library altogether
Correct answer: The new evening hours met a demand from people unable to visit during the day
Correct answer: the new evening hours met a demand from people unable to visit during the day. The rise in visitors, especially daytime workers, and the full study rooms suggest the evening hours served an unmet need.
The following is from a passage about penguins. Emperor penguins huddle together in tight groups during the harshest Antarctic storms. Penguins on the cold outer edge slowly shuffle toward the warmer center, while those inside move outward, so that over time every bird spends some time sheltered. Researchers note that this constant rotation keeps the whole group from freezing. Which choice most logically completes the text?
- The rotation distributes warmth so that the colony as a whole can endure the storm
- Only the strongest penguins are allowed into the warm center
- Penguins on the outer edge remain there for the entire storm
- Huddling increases the risk that the colony will freeze
Correct answer: The rotation distributes warmth so that the colony as a whole can endure the storm
Correct answer: the rotation distributes warmth so that the colony as a whole can endure the storm. Because birds take turns at the warm center and the rotation prevents freezing, it follows that the rotation shares warmth so the colony survives.
The following is from a passage about tree rings. Each year a tree adds a new ring of growth beneath its bark. In years with plenty of rain, the rings are wide; in dry years, they are narrow. By examining rings in very old trees, scientists can reconstruct rainfall patterns from centuries before written records existed. Which choice most logically completes the text?
- Tree rings can serve as a record of past climate conditions
- Trees grow the same amount regardless of rainfall
- Written records are more reliable than any tree ring
- Narrow rings indicate years of unusually heavy rain
Correct answer: Tree rings can serve as a record of past climate conditions
Correct answer: tree rings can serve as a record of past climate conditions. Since ring width depends on rainfall and old rings reveal patterns from before written records, it follows that rings record past climate.
The following is from a passage about a new bike-share program. When a midsize city launched a bike-share program, it placed stations mainly near the downtown core. After a year, officials found that most trips began and ended downtown, while neighborhoods on the outskirts saw little use of the bikes. Which choice most logically completes the text?
- Residents downtown disliked using the shared bikes
- Outlying neighborhoods had more stations than downtown
- The location of stations strongly influenced where the bikes were used
- The program failed to attract any riders at all
Correct answer: The location of stations strongly influenced where the bikes were used
Correct answer: the location of stations strongly influenced where the bikes were used. Because stations were concentrated downtown and use was highest there, it follows that station placement shaped where bikes were used.
The following is from a passage about a student researcher. A high school student hypothesized that plants exposed to classical music would grow taller than plants kept in silence. To test this, she raised two sets of identical seedlings under the same light and watering conditions, playing music to only one set. Which finding, if true, would most directly support the student's hypothesis?
- The plants exposed to music grew noticeably taller than the silent plants.
- Both sets of plants grew to roughly the same height.
- The silent plants produced more leaves than the music plants.
- Neither set of plants survived the length of the experiment.
Correct answer: The plants exposed to music grew noticeably taller than the silent plants.
Correct answer: The plants exposed to music grew noticeably taller than the silent plants. The hypothesis predicts greater height with music, so a finding of taller music-exposed plants would most directly support it.
The following is from a passage about a town's recycling effort. A town official claimed that adding clear labels to public recycling bins would reduce the amount of trash mistakenly thrown into them. The town added labels showing exactly which materials belonged in each bin. Which finding would most directly support the official's claim?
- The total number of recycling bins in town increased after the change.
- Residents reported that the new labels were difficult to read.
- The town spent more money on the labeled bins than expected.
- After the labels were added, far less trash ended up in the recycling bins.
Correct answer: After the labels were added, far less trash ended up in the recycling bins.
Correct answer: After the labels were added, far less trash ended up in the recycling bins. The claim is that labels reduce mistaken trash, so a measured drop in misplaced trash most directly supports it.
The following is from a passage about sleep and memory. A researcher proposed that getting a full night of sleep after studying helps people remember new information better than staying awake. She had two groups learn the same word list: one slept overnight, and the other stayed awake all night before being tested. Which result would most directly support the researcher's proposal?
- Both groups recalled about the same number of words.
- The group that stayed awake recalled more words than the group that slept.
- The group that slept recalled more words than the group that stayed awake.
- Neither group could recall any words from the list.
Correct answer: The group that slept recalled more words than the group that stayed awake.
Correct answer: The group that slept recalled more words than the group that stayed awake. The proposal predicts that sleep improves memory, so higher recall in the sleep group most directly supports it.
The following is from a passage about an archaeological claim. Archaeologists excavating an ancient settlement argued that its residents had traded with distant coastal communities. They searched the site for objects that could only have come from the coast. Which discovery would most directly support the archaeologists' argument?
- Pottery made from local clay found throughout the settlement.
- Tools made entirely from materials available at the site.
- Evidence that the settlement was abandoned suddenly.
- Seashells from the distant coast found among the settlement's remains.
Correct answer: Seashells from the distant coast found among the settlement's remains.
Correct answer: Seashells from the distant coast found among the settlement's remains. The argument is about trade with coastal communities, so coastal seashells at an inland site most directly support contact with the coast.
The following is from a passage about a marketing study. A company believed that customers would be more likely to finish an online survey if it was shorter. The company created two versions of the same survey: one with twenty questions and one with five. Which finding would most directly support the company's belief?
- The longer survey gathered more detailed responses overall.
- A higher percentage of customers completed the five-question survey than the twenty-question one.
- Customers spent about the same amount of time on both surveys.
- Both surveys were sent to the same number of customers.
Correct answer: A higher percentage of customers completed the five-question survey than the twenty-question one.
Correct answer: A higher percentage of customers completed the five-question survey than the twenty-question one. The belief is that shorter surveys are finished more often, so a higher completion rate for the short survey most directly supports it.
The following is from a passage about an author's draft. In a literature class, a student argued that the narrator of a short story is unreliable and cannot be fully trusted. The student looked for moments in the story that revealed gaps between what the narrator claims and what actually happens. Which detail from the story would most directly support the student's argument?
- The narrator describes the setting in vivid, accurate detail.
- The narrator speaks politely to everyone in the story.
- The narrator insists an event went smoothly, but other characters describe it going badly.
- The narrator uses long sentences with difficult vocabulary.
Correct answer: The narrator insists an event went smoothly, but other characters describe it going badly.
Correct answer: The narrator insists an event went smoothly, but other characters describe it going badly. An unreliable narrator's account conflicts with the facts, so a gap between the narrator's claim and others' accounts most directly supports the argument.
The following text is followed by data. A biologist measured the average wingspan of three bird species at a wildlife reserve. Species and average wingspan: Sparrow, 22 cm; Robin, 36 cm; Hawk, 110 cm. Which choice best uses the data to complete the statement? The hawk's average wingspan is approximately ___ that of the robin.
- Half
- Three times
- Equal to
- One-fourth
Correct answer: Three times
Correct answer: three times. The hawk's 110 cm wingspan is about three times the robin's 36 cm (since 36 x 3 = 108), so 'three times' best fits the data.
The following text is followed by data. A school surveyed students about their preferred way to get to school. Results: walk, 30 students; bike, 15 students; bus, 45 students; car, 60 students. Which statement is best supported by the data?
- More students walk than take the bus.
- Biking is more popular than taking the bus.
- Equal numbers of students walk and ride in cars.
- Car is the most common way students get to school.
Correct answer: Car is the most common way students get to school.
Correct answer: Car is the most common way students get to school. With 60 students by car compared to 45 by bus, 30 walking, and 15 biking, car has the highest count and is the most common choice.
The following text is followed by data. A store recorded the number of umbrellas it sold over four months. Sales by month: March, 40; April, 75; May, 30; June, 20. Which choice best describes a trend supported by the data?
- Umbrella sales rose every single month.
- Sales peaked in April and then declined in the months that followed.
- June had the highest umbrella sales of the four months.
- Sales stayed exactly the same from March to June.
Correct answer: Sales peaked in April and then declined in the months that followed.
Correct answer: Sales peaked in April and then declined in the months that followed. The data show sales rising to 75 in April and then falling to 30 in May and 20 in June, matching this description of a peak followed by decline.
The following text is followed by data. Researchers compared the average daily water use per person in four neighborhoods after a conservation campaign. Average daily use: Oakwood, 90 liters; Riverside, 120 liters; Hilltop, 60 liters; Lakeview, 100 liters. Which neighborhood used the least water per person on average?
- Oakwood
- Riverside
- Lakeview
- Hilltop
Correct answer: Hilltop
Correct answer: Hilltop. At 60 liters per person per day, Hilltop's average is lower than Oakwood's 90, Lakeview's 100, and Riverside's 120, making it the lowest.
The following text is followed by data. A researcher tracked how many books students read over a summer in two reading programs. Average books read: Program A, 12 books; Program B, 8 books. Which choice best uses the data to support the claim that Program A encouraged more reading?
- Program A participants read more books on average than Program B participants.
- Program B participants read more books on average than Program A participants.
- Both programs produced the same average number of books read.
- Neither program's participants read any books.
Correct answer: Program A participants read more books on average than Program B participants.
Correct answer: Program A participants read more books on average than Program B participants. With an average of 12 books versus 8, the data show Program A's participants read more, supporting the claim.
The following text is followed by data. A city counted the number of trees planted each year in a five-year greening initiative. Trees planted: Year 1, 200; Year 2, 350; Year 3, 500; Year 4, 650; Year 5, 800. Which statement is best supported by the data?
- The number of trees planted decreased over the five years.
- The most trees were planted in Year 1.
- The number of trees planted increased steadily each year.
- The same number of trees was planted every year.
Correct answer: The number of trees planted increased steadily each year.
Correct answer: The number of trees planted increased steadily each year. The counts rise from 200 to 800, gaining 150 each year, which shows a steady annual increase.
The following is from a passage about echolocation in bats. Many bats hunt in complete darkness by emitting high-pitched calls and listening for the echoes that bounce back from objects. The timing and pitch of each returning echo tell the bat the size, distance, and even the movement of nearby insects. With this system, a bat can catch prey it cannot see. Which choice best states the main idea of the text?
- Bats use echoes from their calls to locate and catch prey in the dark.
- Bats hunt only during daylight hours when they can see clearly.
- Bats avoid catching insects that are moving quickly.
- Bats lose their ability to fly in complete darkness.
Correct answer: Bats use echoes from their calls to locate and catch prey in the dark.
Correct answer: Bats use echoes from their calls to locate and catch prey in the dark. The passage explains how returning echoes reveal an insect's size, distance, and movement so a bat can catch unseen prey, which is the central idea.
The following is from a passage about the writer Octavia Butler. As a young woman, Octavia Butler kept a notebook in which she wrote affirmations about the success she intended to achieve as a science fiction author. At the time, few Black women were publishing in the genre. Butler went on to win major awards and to inspire a generation of writers who followed her. According to the text, what did Butler write in her notebook as a young woman?
- Plot summaries of novels by other authors.
- Lists of awards she had already won.
- Reasons she planned to stop writing.
- Affirmations about the success she intended to achieve.
Correct answer: Affirmations about the success she intended to achieve.
Correct answer: Affirmations about the success she intended to achieve. The passage states that Butler wrote affirmations about her intended success as a science fiction author, directly answering the question.
The following is from a passage about a desert irrigation method. In some arid regions, farmers bury unglazed clay pots filled with water beside their crops. Water seeps slowly through the porous walls directly to the roots, with little lost to evaporation. This ancient method lets farmers grow food using far less water than surface watering requires. Which choice most logically completes the text?
- Buried clay pots are an inefficient way to water crops
- The clay-pot method conserves water by delivering it straight to the roots
- Crops grown this way require more water than usual
- The pots must be glazed to keep water from escaping
Correct answer: The clay-pot method conserves water by delivering it straight to the roots
Correct answer: the clay-pot method conserves water by delivering it straight to the roots. Because water seeps directly to the roots with little evaporation and uses far less water, it follows that the method conserves water.
The following is from a passage about volcanic soil. Land near active volcanoes can be dangerous, yet people have farmed volcanic slopes for centuries. Ash and rock from past eruptions break down into soil rich in minerals that plants need. Crops grown in this soil are often unusually productive. Which choice best states the main idea of the text?
- Volcanic eruptions always destroy any crops growing nearby.
- Farmers avoid volcanic slopes because the soil lacks minerals.
- People farm risky volcanic land because the soil there is unusually fertile.
- Crops grown in volcanic soil are smaller than those grown elsewhere.
Correct answer: People farm risky volcanic land because the soil there is unusually fertile.
Correct answer: People farm risky volcanic land because the soil there is unusually fertile. The passage explains that volcanic ash creates mineral-rich, productive soil that draws farmers despite the danger, which is the main idea.
The following is from a passage about a community mural project. When a neighborhood invited residents to help paint a large mural on a long-empty wall, hundreds of people of all ages turned out over several weekends. Afterward, surveys showed that participants felt a stronger sense of connection to their neighborhood, and reports of vandalism on the wall dropped to nearly zero. Which choice most logically completes the text?
- The mural project had no effect on how residents felt about the neighborhood
- Involving residents in the mural helped strengthen their ties to the community
- Most residents refused to take part in painting the mural
- Vandalism on the wall increased after the mural was finished
Correct answer: Involving residents in the mural helped strengthen their ties to the community
Correct answer: involving residents in the mural helped strengthen their ties to the community. Because participation led to a stronger sense of connection and less vandalism, it follows that involving residents strengthened community ties.
The biologist's field notes were unusually ______: rather than recording vague impressions, she logged the exact temperature, time, and behavior of every animal she observed. Which choice completes the text with the most logical and precise word or phrase?
- Ambiguous
- Meticulous
- Brief
- Hasty
Correct answer: Meticulous
"Meticulous" is correct because the sentence shows the notes recorded exact temperatures, times, and behaviors rather than vague impressions, which defines careful, detailed attention. "Hasty" and "ambiguous" contradict that precision, and "brief" addresses length rather than the thoroughness the evidence stresses. Words in Context items require the blank to match the specific detail the sentence supplies.
The following text is from a passage about urban beekeeping. The writer opens by admitting she once feared bees and avoided them entirely. She then recounts taking a single beekeeping class, and she closes by describing how she now tends three rooftop hives and urges nervous neighbors to try it themselves. Which choice best describes the overall structure of the text?
- It moves from the writer's initial fear to her present enthusiasm, ending with encouragement to others
- It warns readers about the dangers of bee stings
- It lists the equipment required to keep bees in a city
- It compares rooftop hives with ground-level hives in detail
Correct answer: It moves from the writer's initial fear to her present enthusiasm, ending with encouragement to others
The structure moves from the writer's initial fear to her present enthusiasm and ends with encouragement, because the passage opens with avoidance, turns on a class, and closes by urging neighbors to try beekeeping. It does not list equipment, compare hive types, or warn of dangers. Text Structure questions ask how the parts of a passage are arranged to build its overall progression.
Text 1: Historian Marcus Bell argues that the invention of the mechanical clock was the single most transformative technology of the medieval period, claiming it reorganized daily labor around fixed hours. Text 2: Historian Joan Okafor agrees that clocks mattered but insists their influence has been overstated. She notes that most rural laborers continued to work by the sun for centuries after clocks appeared in towns. Based on the texts, how would Joan Okafor (Text 2) most likely respond to Marcus Bell's claim in Text 1?
- By accepting that clocks were important but disputing that their impact was as sweeping as Bell suggests
- By arguing that the sun had no effect on rural work schedules
- By agreeing that clocks instantly reorganized all labor everywhere
- By denying that mechanical clocks ever existed in the medieval period
Correct answer: By accepting that clocks were important but disputing that their impact was as sweeping as Bell suggests
Okafor would accept that clocks were important but dispute that their impact was as sweeping as Bell claims, because Text 2 grants that clocks "mattered" yet says their influence is "overstated" and points to rural workers who kept following the sun. She does not deny clocks existed, fully agree with Bell, or claim the sun was irrelevant. Cross-Text Connections questions require inferring one author's response from each text's stated position.
Despite the harsh reviews his early films received, the director remained ______, continuing to make movies in his own unconventional style until audiences finally embraced his vision. Which choice completes the text with the most logical and precise word or phrase?
- Indifferent
- Undeterred
- Conventional
- Discouraged
Correct answer: Undeterred
"Undeterred" is correct because the sentence shows the director kept working in his own style despite harsh reviews, signaling that the criticism did not stop him. "Discouraged" contradicts his persistence, "conventional" conflicts with "unconventional style," and "indifferent" misses that he cared enough to keep pursuing his vision. Words in Context requires the blank to fit the contrast set up by "despite."
The following text is from a science article. The author begins by noting that many people assume octopuses are solitary and dull. She then summarizes recent studies showing octopuses solving puzzles, recognizing individual humans, and even using tools. She concludes that these animals may be far more intelligent than their reputation suggests. Which choice best states the main purpose of the text?
- To list the ocean habitats where octopuses are most commonly found
- To argue that octopuses should be kept as household pets
- To challenge a common assumption by presenting evidence of octopus intelligence
- To explain the anatomy of an octopus's eight arms
Correct answer: To challenge a common assumption by presenting evidence of octopus intelligence
The main purpose is to challenge a common assumption by presenting evidence of octopus intelligence, because the passage opens with the belief that octopuses are dull and then cites puzzle-solving, recognition, and tool use to overturn it. It does not catalog habitats, describe anatomy, or recommend keeping octopuses as pets. Main Purpose questions identify the central goal the author is working toward.
The senator's speech was praised for being ______: she stated her position in just three short sentences, avoiding the lengthy digressions her colleagues were known for. Which choice completes the text with the most logical and precise word or phrase?
- Hesitant
- Decorative
- Concise
- Rambling
Correct answer: Concise
"Concise" is correct because the sentence describes a position stated in three short sentences without digressions, which defines brief, economical expression. "Rambling" is the opposite, "decorative" describes ornamentation rather than brevity, and "hesitant" addresses uncertainty rather than length. Words in Context demands a word matching the structural detail the sentence emphasizes.
The following text is from an essay about public libraries. The writer first describes a library as merely a building full of books. She then recounts watching a librarian help a job seeker write a resume, a child attend a free reading hour, and an immigrant practice English. She ends by calling the library a community lifeline rather than a warehouse. Which choice best describes the function of the final sentence in the overall structure?
- It provides a step-by-step guide to using library services
- It introduces a new and unrelated topic the essay will explore next
- It quotes a statistic about national library funding
- It revises the opening description in light of the examples the writer has given
Correct answer: It revises the opening description in light of the examples the writer has given
The final sentence revises the opening description in light of the examples, because the essay starts by calling the library "merely a building full of books" and ends by reframing it as a "community lifeline" after the examples of help offered. It does not introduce an unrelated topic, give a how-to guide, or cite a statistic. Text Structure questions ask what role a specific part plays within the whole.
Text 1: Nutrition researcher Dana Pierce argues that breakfast is essential, citing studies in which students who ate in the morning scored higher on memory tests. Text 2: Researcher Samuel Voss reviews the same studies and notes that the students who ate breakfast also tended to sleep more and come from wealthier households, factors that could explain the test gains on their own. Which choice best describes how Text 2 relates to Text 1?
- It questions whether breakfast itself causes the outcome Text 1 attributes to it
- It argues that breakfast is harmful to memory
- It provides additional studies that confirm Text 1's conclusion
- It denies that students ever take memory tests
Correct answer: It questions whether breakfast itself causes the outcome Text 1 attributes to it
Text 2 questions whether breakfast itself causes the outcome, because Voss points to confounding factors, sleep and household wealth, that could explain the test gains apart from breakfast. He does not confirm the conclusion, deny that tests occur, or claim breakfast is harmful. Cross-Text Connections questions ask how the second author engages with the first author's reasoning.
The negotiator's reputation for being ______ served him well: even when both sides grew angry, he stayed calm, weighed every argument fairly, and refused to take sides until all the evidence was in. Which choice completes the text with the most logical and precise word or phrase?
- Impartial
- Stubborn
- Biased
- Anxious
Correct answer: Impartial
"Impartial" is correct because the sentence shows the negotiator weighing every argument fairly and refusing to take sides, which defines unbiased fairness. "Biased" is the direct opposite, "stubborn" describes inflexibility rather than fairness, and "anxious" conflicts with "stayed calm." Words in Context requires the blank to align with the behavior the sentence describes.
The following text is from a memoir. The narrator recalls dreading the long bus ride to a new school in a town where she knew no one. She describes the silent first week, then the afternoon a classmate invited her to join a chess club. She ends by saying that one invitation changed the entire year. Which choice best states the main idea of the text?
- Chess is the most popular club at the narrator's school
- A single act of welcome transformed the narrator's difficult transition
- Bus rides are the hardest part of changing schools
- The narrator preferred being alone during her first week
Correct answer: A single act of welcome transformed the narrator's difficult transition
The main idea is that a single act of welcome transformed a difficult transition, because the narrator moves from dread and silence to a classmate's invitation that "changed the entire year." The passage does not claim chess is the most popular club, single out bus rides as hardest, or say she preferred solitude. Main Idea questions capture the central point all the details support.
In her lecture, the architect was deliberately ______ about the building's flaws, openly admitting the leaky roof and cramped lobby that other designers might have tried to hide. Which choice completes the text with the most logical and precise word or phrase?
- Boastful
- Candid
- Evasive
- Confused
Correct answer: Candid
"Candid" is correct because the architect openly admitted flaws others would hide, which defines frank honesty. "Evasive" is the opposite, "boastful" describes pride rather than honesty about flaws, and "confused" does not fit someone clearly stating problems. Words in Context requires matching the word to the contrast with hiding the flaws.
The following text is from an article about volunteer firefighting. The author opens with a vivid scene of a barn fire at midnight. She then steps back to explain that the firefighters who arrived were unpaid neighbors who train on weekends. She closes by arguing that small towns depend on this hidden labor. Why does the author most likely begin with the barn fire scene?
- To argue that barns should be built from fireproof materials
- To provide instructions for putting out a barn fire
- To compare midnight fires with daytime fires
- To capture the reader's attention before introducing her larger point about volunteer labor
Correct answer: To capture the reader's attention before introducing her larger point about volunteer labor
The author begins with the barn fire to capture attention before introducing her larger point, because the vivid scene leads into the explanation that the responders were unpaid neighbors and the claim that towns rely on them. The opening is not a how-to, a building argument, or a time-of-day comparison. Text Structure questions ask how an introductory element sets up the passage's purpose.
Text 1: Economist Rosa Tan claims that raising the minimum wage reduces poverty, pointing to cities where low earners gained income after increases. Text 2: Economist Hassan Ali does not dispute those income gains but adds that some businesses in the same cities cut staff hours, leaving certain workers with smaller paychecks overall. Based on the texts, Hassan Ali (Text 2) would most likely characterize Rosa Tan's view as:
- Partly accurate but incomplete because it overlooks reduced hours
- Fully correct with no need for qualification
- Irrelevant because poverty cannot be measured
- Entirely wrong because wages never rose at all
Correct answer: Partly accurate but incomplete because it overlooks reduced hours
Ali would call Tan's view partly accurate but incomplete, because he accepts the income gains yet adds that cut hours can shrink some workers' paychecks, a factor Tan's claim omits. He does not say wages never rose, accept her view without qualification, or call poverty unmeasurable. Cross-Text Connections questions test how one author would judge the other's claim.
The coach's halftime talk was surprisingly ______: instead of shouting blame, she calmly reminded the players of their training and sent them back out feeling steady. Which choice completes the text with the most logical and precise word or phrase?
- Rambling
- Alarming
- Reassuring
- Scolding
Correct answer: Reassuring
"Reassuring" is correct because the coach calmly reminded players of their training and left them feeling steady, which defines a calming, confidence-building message. "Alarming" and "scolding" contradict that calm encouragement, and "rambling" addresses disorganization rather than tone. Words in Context requires the blank to match the effect described in the sentence.
The following text is from a passage about wetlands. The writer first describes a marsh as an ugly, mosquito-filled swamp that developers want to drain. He then explains that the same marsh filters pollution from drinking water and shelters rare birds. He ends by suggesting readers reconsider what counts as wasteland. Which choice best describes the overall structure of the text?
- It compares two different marshes in separate regions
- It traces the life cycle of a single wetland bird
- It lists in order the steps developers take to drain a marsh
- It presents a negative first impression, then offers evidence that complicates and overturns it
Correct answer: It presents a negative first impression, then offers evidence that complicates and overturns it
The structure presents a negative first impression, then complicates and overturns it, because the marsh is first called an ugly swamp and then shown to filter water and shelter rare birds, prompting a rethink of "wasteland." It is not a draining how-to, a region comparison, or a bird life cycle. Text Structure questions ask how the parts combine into the overall arrangement.
Although the textbook was thorough, students found its prose ______: each paragraph piled on so many technical terms that even careful readers lost the thread. Which choice completes the text with the most logical and precise word or phrase?
- Accessible
- Entertaining
- Concise
- Impenetrable
Correct answer: Impenetrable
"Impenetrable" is correct because the prose piled on so many technical terms that careful readers lost the thread, which describes writing that is hard to understand. "Accessible" is the opposite, "concise" conflicts with the dense piling up of terms, and "entertaining" does not fit the struggle to follow it. Words in Context requires the blank to fit the reading difficulty the sentence describes.
The following text is from an opinion column. The writer spends the first paragraph praising the convenience of online grocery delivery. In the second paragraph she pivots, describing the small neighborhood markets that have closed and the clerks who lost their jobs. What is the most likely purpose of the writer's pivot in the second paragraph?
- To introduce a drawback that complicates the convenience praised earlier
- To repeat the same points made in the first paragraph
- To announce that the writer no longer eats groceries
- To provide a recipe that uses delivered groceries
Correct answer: To introduce a drawback that complicates the convenience praised earlier
The pivot introduces a drawback that complicates the earlier praise, because the second paragraph shifts from delivery's convenience to closed markets and lost jobs, presenting the other side. It does not repeat the first paragraph, offer a recipe, or announce a change in eating. Text Structure questions ask why an author shifts direction within a passage.
Text 1: Engineer Lia Marsh argues that electric cars are the clear path to cleaner cities, noting that they emit no exhaust on the streets where people live. Text 2: Engineer Tom Reyes shares the goal of cleaner air but cautions that if the electricity charging those cars comes from coal plants, the pollution is merely moved elsewhere rather than eliminated. Which choice best describes the relationship between the two texts?
- Text 2 shares Text 1's goal but identifies a condition under which Text 1's benefit may not hold
- Text 2 claims electric cars produce street-level exhaust
- Text 2 fully restates Text 1's argument without change
- Text 2 rejects the goal of cleaner air entirely
Correct answer: Text 2 shares Text 1's goal but identifies a condition under which Text 1's benefit may not hold
Text 2 shares the goal but identifies a limiting condition, because Reyes agrees on cleaner air yet warns that coal-generated electricity could move pollution rather than remove it. He does not reject the goal, merely restate Text 1, or claim electric cars emit street exhaust. Cross-Text Connections questions ask how the second text qualifies or extends the first.
The witness's account was so ______ that the jury could picture the entire scene: she named the exact street corner, the color of the car, and the words the driver shouted. Which choice completes the text with the most logical and precise word or phrase?
- Vivid
- Doubtful
- Vague
- Tedious
Correct answer: Vivid
"Vivid" is correct because the account let the jury picture the scene through exact details of place, color, and speech, which defines strikingly clear, lifelike description. "Vague" is the opposite, "tedious" describes dullness rather than clarity, and "doubtful" addresses credibility, not vividness. Words in Context requires the word to match the detailed clarity the sentence supplies.
The following text is from a passage about a river cleanup. The author describes arriving at a riverbank choked with plastic and tires. She then narrates a single Saturday when dozens of volunteers filled forty bags of trash. She ends by noting that fish returned to the cleared stretch within months. Which choice best states the main purpose of the text?
- To list the brands of plastic most often found in rivers
- To explain the biology of freshwater fish reproduction
- To illustrate how a community effort produced a visible improvement
- To argue that volunteering is more tiring than people expect
Correct answer: To illustrate how a community effort produced a visible improvement
The main purpose is to illustrate how a community effort produced visible improvement, because the passage moves from a trash-choked bank to a volunteer cleanup to fish returning. It does not catalog plastic brands, explain fish biology, or argue about how tiring volunteering is. Main Purpose questions identify the central effect the author builds toward.
The reviewer found the actor's performance ______: his every gesture and pause seemed forced, as if he were thinking about the camera rather than the character. Which choice completes the text with the most logical and precise word or phrase?
- Moving
- Artificial
- Natural
- Subtle
Correct answer: Artificial
"Artificial" is correct because the gestures seemed forced and the actor appeared focused on the camera rather than the character, which defines an unnatural, contrived performance. "Natural" and "subtle" are the opposite, and "moving" describes emotional impact, not falseness. Words in Context requires the blank to match the forced quality the sentence describes.
The following text is from a history passage. The writer first states a familiar claim: that a famous explorer "discovered" a new land. He then presents records showing that people had lived there for thousands of years. He concludes by urging readers to question the word "discovery." Which choice best describes the function of the second part of the passage?
- It supplies evidence that undercuts the familiar claim stated at the start
- It praises the explorer for his courage
- It lists the supplies the explorer carried on his voyage
- It describes the writer's own travels to the land
Correct answer: It supplies evidence that undercuts the familiar claim stated at the start
The second part supplies evidence that undercuts the opening claim, because records of long-existing inhabitants challenge the idea of "discovery" and set up the writer's concluding call to question the word. It does not list supplies, praise the explorer, or recount the writer's travels. Text Structure questions ask what role a specific section plays in the passage's argument.
Text 1: Psychologist Mara Quinn argues that praising children for being smart boosts their confidence and motivates them to keep trying. Text 2: Psychologist Eli Frost reports experiments in which children praised for being smart actually avoided harder tasks afterward, apparently fearing they would lose the label if they failed. Based on the texts, Eli Frost's findings (Text 2) most directly:
- Show that children dislike all forms of praise
- Confirm that praising intelligence always increases effort
- Prove that confidence has no relationship to behavior
- Contradict the motivational benefit Mara Quinn attributes to praising intelligence
Correct answer: Contradict the motivational benefit Mara Quinn attributes to praising intelligence
Frost's findings contradict the motivational benefit Quinn attributes to praising intelligence, because his children avoided harder tasks rather than persisting as Quinn predicts. The evidence does not confirm increased effort, show dislike of all praise, or sever confidence from behavior. Cross-Text Connections questions ask how one author's evidence bears on the other's claim.
The committee called the new policy ______ rather than a true reform: it changed a few labels and forms but left the underlying rules exactly as they had been. Which choice completes the text with the most logical and precise word or phrase?
- Expensive
- Superficial
- Thorough
- Drastic
Correct answer: Superficial
"Superficial" is correct because the policy changed only labels and forms while leaving the underlying rules untouched, which defines a surface-level change. "Drastic" and "thorough" contradict that shallowness, and "expensive" addresses cost rather than depth. Words in Context requires the blank to match the contrast with "a true reform."
The following text is from a passage about a small bakery. The author lingers over the warmth of the ovens, the smell of cinnamon at dawn, and the regulars who arrive before sunrise. Only at the end does she mention, briefly, that the rent has tripled. Which choice best describes the effect of saving the rent detail for the end?
- It explains how to bake cinnamon rolls
- It repeats the description of the ovens
- It introduces a quiet note of threat that contrasts with the warm scene built earlier
- It lists the bakery's daily opening hours
Correct answer: It introduces a quiet note of threat that contrasts with the warm scene built earlier
Saving the rent detail for the end introduces a quiet note of threat contrasting with the warm scene, because the cozy imagery is suddenly shadowed by the tripled rent. The ending is not a recipe, a schedule, or a repetition of the ovens. Text Structure questions ask how the placement of a detail shapes the reader's experience.
The scientist was known for her ______ skepticism: she accepted no claim, even a popular one, until she had tested it herself and seen the results. Which choice completes the text with the most logical and precise word or phrase?
- Gullible
- Casual
- Rigorous
- Reluctant
Correct answer: Rigorous
"Rigorous" is correct because she accepted no claim until she had personally tested it, which describes strict, demanding standards. "Casual" understates her care, "gullible" is the opposite of skepticism, and "reluctant" describes hesitation rather than thoroughness. Words in Context requires the blank to match the careful testing the sentence describes.
The following text is from an article about sleep. The author poses a question in the opening line: why do teenagers struggle to fall asleep early even when they are exhausted? She then summarizes research on shifting biological clocks during adolescence and ends by recommending later school start times. Which choice best describes the overall structure of the text?
- It tells a single teenager's bedtime story from start to finish
- It compares sleep habits across several different countries
- It raises a question, offers a scientific explanation, and proposes a practical response
- It lists the stages of the human sleep cycle in order
Correct answer: It raises a question, offers a scientific explanation, and proposes a practical response
The structure raises a question, offers a scientific explanation, and proposes a practical response, because the passage opens with a puzzle about teen sleep, explains shifting biological clocks, and recommends later start times. It is not a single bedtime story, a cross-country comparison, or a list of sleep stages. Text Structure questions ask how a passage's parts are arranged overall.
Despite years of fame, the musician stayed remarkably ______, still living in her childhood neighborhood and treating fans and strangers with the same plain courtesy. Which choice completes the text with the most logical and precise word or phrase?
- Reclusive
- Extravagant
- Unpretentious
- Arrogant
Correct answer: Unpretentious
"Unpretentious" is correct because she kept living simply in her old neighborhood and treated everyone with plain courtesy despite fame, which defines a modest, unassuming manner. "Arrogant" and "extravagant" contradict that modesty, and "reclusive" conflicts with her warmth toward fans and strangers. Words in Context requires the blank to match the down-to-earth behavior described.
Text 1: Critic Owen Park praises a new museum's design, arguing that its bright open halls make visitors feel welcome and eager to explore. Text 2: Critic Naomi Sol agrees the halls are striking but worries that the lack of quiet corners gives visitors nowhere to pause and reflect on what they have seen. Which choice best describes how Naomi Sol (Text 2) responds to Owen Park (Text 1)?
- She argues that museums should have no open halls
- She accepts part of his praise while raising a concern he does not address
- She agrees completely and adds nothing new
- She rejects the idea that the halls are striking at all
Correct answer: She accepts part of his praise while raising a concern he does not address
Sol accepts part of Park's praise while raising a concern he ignores, because she agrees the halls are striking but worries there is nowhere quiet to reflect. She does not deny the halls are striking, agree without adding anything, or oppose open halls entirely. Cross-Text Connections questions ask how the second author both shares and departs from the first's view.
The mayor's promises proved ______: although she pledged to fix every pothole within a month, a year later most of the streets remained as rough as before. Which choice completes the text with the most logical and precise word or phrase?
- Fulfilled
- Modest
- Generous
- Empty
Correct answer: Empty
"Empty" is correct because the promised repairs never happened, with the streets still rough a year later, which defines pledges with no follow-through. "Fulfilled" is the opposite, "generous" addresses scale rather than failure, and "modest" conflicts with the sweeping pledge. Words in Context requires the blank to fit the gap between promise and result.
The following text is from a passage about handwriting. The author concedes that typing is faster and that few jobs now require neat penmanship. Having granted this, she argues that the slow act of writing by hand still helps students remember and understand what they record. Which choice best describes the function of the first sentence in the passage?
- It provides a history of writing tools through the centuries
- It lists the muscles used to hold a pen
- It states the author's final conclusion at the very start
- It concedes points to the opposing view before the author advances her own argument
Correct answer: It concedes points to the opposing view before the author advances her own argument
The first sentence concedes points to the opposing view before the author makes her case, because it grants that typing is faster and penmanship is rarely required, then "having granted this" she argues for handwriting's benefits. It is not her conclusion, a history, or a list of muscles. Text Structure questions ask what role an opening element plays in the argument.
Critics described the novel's ending as ______: it left the central mystery unsolved, allowing readers to imagine several different fates for the heroine. Which choice completes the text with the most logical and precise word or phrase?
- Ambiguous
- Definitive
- Predictable
- Abrupt
Correct answer: Ambiguous
"Ambiguous" is correct because the ending left the mystery unsolved and open to several interpretations, which defines an outcome with more than one possible meaning. "Definitive" is the opposite, "predictable" conflicts with the unresolved mystery, and "abrupt" addresses suddenness rather than openness. Words in Context requires the word to match the multiple possible fates the sentence describes.
Text 1: Researcher Bea Lund argues that city parks improve public health, citing studies linking green space to lower stress and more exercise. Text 2: Researcher Carl Means accepts those benefits but stresses that they only appear when parks are safe and well maintained; neglected, unsafe parks, he notes, often sit empty. Based on the texts, Carl Means (Text 2) would most likely add which qualification to Bea Lund's claim?
- That green space should be removed from cities
- That exercise is impossible outside of city parks
- That the health benefits depend on the parks being safe and well kept
- That parks have no effect on stress under any conditions
Correct answer: That the health benefits depend on the parks being safe and well kept
Means would qualify Lund's claim by noting that the benefits depend on safe, well-kept parks, because he accepts the health gains but says neglected, unsafe parks sit empty and unused. He does not deny park effects, claim exercise is impossible elsewhere, or call for removing green space. Cross-Text Connections questions ask what condition the second author attaches to the first author's claim.
The professor's feedback, though strict, was ultimately ______: every criticism came with a clear suggestion that helped the student write a stronger draft. Which choice completes the text with the most logical and precise word or phrase?
- Destructive
- Irrelevant
- Flattering
- Constructive
Correct answer: Constructive
"Constructive" is correct because each criticism came with a clear suggestion that improved the student's draft, which defines feedback meant to build rather than tear down. "Destructive" is the opposite, "flattering" conflicts with "strict," and "irrelevant" contradicts the helpful suggestions. Words in Context requires the blank to match the helpful purpose described despite the strictness.
The following text is from a passage about ancient roads. The author explains that a certain stone road has survived two thousand years. She first describes its appearance today, then traces how engineers layered gravel, sand, and fitted stone to build it, and finally marvels that modern roads rarely last a century. Which choice best states the main idea of the text?
- Modern engineers do not understand how to use stone
- Careful ancient construction methods gave the road a durability that surpasses many modern roads
- Gravel is the only material needed to build a lasting road
- Ancient roads were always wider than modern highways
Correct answer: Careful ancient construction methods gave the road a durability that surpasses many modern roads
The main idea is that careful ancient construction gave the road durability surpassing many modern roads, because the passage describes its layered building and marvels that modern roads rarely last a century. It does not claim ancient roads were wider, that gravel alone suffices, or that modern engineers cannot use stone. Main Idea questions capture the central point the details support.
The diplomat chose her words with ______ care, knowing that a single careless phrase could offend a foreign government and undo months of talks. Which choice completes the text with the most logical and precise word or phrase?
- Effortless
- Deliberate
- Halfhearted
- Reckless
Correct answer: Deliberate
"Deliberate" is correct because she chose each word carefully, aware that one careless phrase could undo months of talks, which defines intentional, thoughtful selection. "Reckless" and "halfhearted" contradict that caution, and "effortless" conflicts with the deliberate care the situation demanded. Words in Context requires the blank to match the careful intent described.
The following text is from an essay about maps. The writer begins by treating an old hand-drawn map as a quaint curiosity. Midway through, he notices that its odd distortions reveal what its makers valued and feared. By the end, he treats the map as a window into a vanished worldview. Which choice best describes how the writer's treatment of the map changes across the passage?
- It remains focused throughout on the map's exact measurements
- It explains step by step how to draw a map by hand
- It compares the map with a modern satellite image in detail
- It shifts from viewing the map as a curiosity to valuing it as a record of its makers' minds
Correct answer: It shifts from viewing the map as a curiosity to valuing it as a record of its makers' minds
The writer's treatment shifts from seeing the map as a curiosity to valuing it as a record of its makers' minds, because the distortions come to reveal what its makers valued and feared. The passage is not about exact measurements, a drawing how-to, or a satellite comparison. Text Structure questions ask how an author's perspective develops over a passage.
The Venus flytrap snaps shut on insects that touch the tiny hairs inside its leaves. _____ the plant does not close the moment a hair is brushed; a second touch must occur within about twenty seconds, a delay that prevents the plant from wasting energy on raindrops or debris. Which choice completes the text with the most logical transition?
- Therefore,
- For example,
- In conclusion,
- Notably,
Correct answer: Notably,
Correct answer: "Notably,". The second sentence introduces a surprising, noteworthy detail about the trap's two-touch mechanism rather than a result, an example, or a conclusion, so the emphasizing transition "Notably" fits the logical relationship best.
A student researching ancient writing systems took these notes: Cuneiform was developed by the Sumerians around 3200 BCE. It used wedge-shaped marks pressed into clay tablets. Scribes used a stylus made of reed to make the marks. The student wants to emphasize the tool scribes used to create cuneiform. Which choice most effectively uses relevant information from the notes to accomplish this goal?
- Cuneiform was developed by the Sumerians around 3200 BCE.
- To make cuneiform's wedge-shaped marks, scribes pressed a reed stylus into clay tablets.
- Cuneiform, a Sumerian invention, used wedge-shaped marks.
- The Sumerians developed cuneiform, which was pressed into clay tablets around 3200 BCE.
Correct answer: To make cuneiform's wedge-shaped marks, scribes pressed a reed stylus into clay tablets.
Correct answer: "To make cuneiform's wedge-shaped marks, scribes pressed a reed stylus into clay tablets." This choice foregrounds the reed stylus, the tool the student wants to emphasize, while the other choices stress the date, the inventors, or the material instead.
Glassmakers in medieval Europe guarded their recipes carefully. _____ the artisans of Venice were forbidden to leave the city, lest they reveal their techniques to rival workshops abroad. Which choice completes the text with the most logical transition?
- For instance,
- However,
- Earlier,
- In contrast,
Correct answer: For instance,
Correct answer: "For instance,". The second sentence gives a specific illustration of the general claim that glassmakers guarded their recipes, so the exemplifying transition "For instance" expresses the relationship; the contrast and time transitions do not fit.
A student writing about animal behavior compiled these notes: Prairie dogs live in large underground colonies. They give different alarm calls for different predators. One call warns of hawks; another warns of coyotes. The calls even vary by the predator's size and color. The student wants to highlight the complexity of prairie dog communication. Which choice most effectively uses relevant information from the notes to accomplish this goal?
- Prairie dogs live in large underground colonies and give alarm calls.
- Prairie dogs use distinct alarm calls that vary not only by type of predator but even by the predator's size and color.
- Prairie dogs warn one another of hawks and coyotes.
- Living in colonies, prairie dogs face predators such as hawks and coyotes.
Correct answer: Prairie dogs use distinct alarm calls that vary not only by type of predator but even by the predator's size and color.
Correct answer: "Prairie dogs use distinct alarm calls that vary not only by type of predator but even by the predator's size and color." This sentence captures the layered, detailed nature of the calls, conveying complexity, while the other options mention only colonies or a basic list of predators.
The 1960s saw a surge in folk music across American college campuses. _____ rock and roll, with its electric guitars and amplified sound, soon drew many of those same young listeners away from acoustic ballads. Which choice completes the text with the most logical transition?
- Likewise,
- Consequently,
- Yet
- Indeed,
Correct answer: Yet
Correct answer: "Yet". The second sentence presents a shift that runs counter to the folk surge described first, so the contrasting transition "Yet" signals the opposition; the additive, causal, and emphatic options do not.
A student researching architecture gathered these notes: The Pantheon in Rome was completed around 126 CE. Its dome is made of concrete. The dome has an open hole at the top called an oculus. The oculus is the dome's only source of natural light. The student wants to explain how light enters the Pantheon. Which choice most effectively uses relevant information from the notes to accomplish this goal?
- The Pantheon, completed around 126 CE, has a concrete dome.
- Natural light enters the Pantheon solely through the oculus, an open hole at the top of its dome.
- The Pantheon's dome, made of concrete, was finished around 126 CE.
- Romans completed the Pantheon, with its concrete dome, around 126 CE.
Correct answer: Natural light enters the Pantheon solely through the oculus, an open hole at the top of its dome.
Correct answer: "Natural light enters the Pantheon solely through the oculus, an open hole at the top of its dome." Only this choice directly answers how light enters the building; the others focus on the completion date or the dome's material.
Many people assume that bamboo is a kind of tree. _____ it is actually a type of grass, one that can grow several feet in a single day. Which choice completes the text with the most logical transition?
- In fact,
- Similarly,
- As a result,
- Meanwhile,
Correct answer: In fact,
Correct answer: "In fact,". The second sentence corrects the common assumption stated first, and "In fact" introduces this corrective, emphasizing point; the comparison, cause, and time transitions do not capture the correction.
A student preparing a science article assembled these notes: Tardigrades are microscopic animals. They can survive extreme cold, heat, and radiation. They can enter a dried-out state called cryptobiosis. In this state, their metabolism nearly stops. The student wants to explain how tardigrades endure harsh conditions. Which choice most effectively uses relevant information from the notes to accomplish this goal?
- Tardigrades are microscopic animals that live in many environments.
- Tardigrades endure harsh conditions by entering cryptobiosis, a dried-out state in which their metabolism nearly stops.
- Tardigrades can survive extreme cold, heat, and radiation.
- Microscopic tardigrades are remarkably tough animals.
Correct answer: Tardigrades endure harsh conditions by entering cryptobiosis, a dried-out state in which their metabolism nearly stops.
Correct answer: "Tardigrades endure harsh conditions by entering cryptobiosis, a dried-out state in which their metabolism nearly stops." This choice explains the mechanism (cryptobiosis) behind their survival, while the others merely list traits or describe what they survive without saying how.
The first synthetic dye, mauveine, was discovered by accident in 1856. _____ chemist William Perkin had been trying to create a treatment for malaria when he produced a vivid purple residue instead. Which choice completes the text with the most logical transition?
- Nevertheless,
- Specifically,
- In comparison,
- Afterward,
Correct answer: Specifically,
Correct answer: "Specifically,". The second sentence supplies the precise details of the accidental discovery announced in the first, so the clarifying transition "Specifically" fits; contrast, comparison, and sequence transitions do not.
A student researching weather phenomena took these notes: A halo is a ring of light around the sun or moon. It forms when light passes through ice crystals in high clouds. The ice crystals bend the light at a fixed angle of 22 degrees. The student wants to explain what causes a halo to appear. Which choice most effectively uses relevant information from the notes to accomplish this goal?
- A halo is a beautiful ring of light around the sun or moon.
- A halo appears when light passing through ice crystals in high clouds is bent at a fixed 22-degree angle.
- Halos can form around both the sun and the moon.
- High clouds often contain ice crystals.
Correct answer: A halo appears when light passing through ice crystals in high clouds is bent at a fixed 22-degree angle.
Correct answer: "A halo appears when light passing through ice crystals in high clouds is bent at a fixed 22-degree angle." This choice states the cause of the halo, combining the ice crystals and the bending angle, while the others only define a halo or note where ice crystals occur.
Solar panels generate the most electricity when sunlight strikes them directly. _____ engineers often mount panels on motors that tilt them to follow the sun across the sky. Which choice completes the text with the most logical transition?
- For this reason,
- On the other hand,
- Previously,
- By contrast,
Correct answer: For this reason,
Correct answer: "For this reason,". The second sentence describes a practice that results from the fact stated first, so the causal transition "For this reason" expresses the cause-and-effect link; the contrast and time transitions do not.
A student researching the history of timekeeping compiled these notes: Sundials measure time by the position of a shadow. They were used in many ancient cultures. Water clocks measured time by the steady flow of water. Water clocks could work at night, when sundials could not. The student wants to contrast a limitation of sundials with an advantage of water clocks. Which choice most effectively uses relevant information from the notes to accomplish this goal?
- Sundials and water clocks were both used in ancient cultures.
- Sundials measure time using a shadow, and water clocks use flowing water.
- Unlike sundials, which fail without sunlight, water clocks could measure time even at night.
- Ancient cultures relied on sundials to tell time during the day.
Correct answer: Unlike sundials, which fail without sunlight, water clocks could measure time even at night.
Correct answer: "Unlike sundials, which fail without sunlight, water clocks could measure time even at night." This choice draws the requested contrast between the sundial's limitation and the water clock's nighttime advantage; the others list shared features or describe each device without contrasting them.
Honeyguide birds in Africa lead humans to wild beehives. _____ the birds cannot break open the hives themselves, so they rely on people to crack the nests and leave behind beeswax for them to eat. Which choice completes the text with the most logical transition?
- Otherwise,
- Likewise,
- Therefore,
- However,
Correct answer: However,
Correct answer: "However,". The second sentence introduces a limitation of the birds that contrasts with their guiding ability described first, so the contrasting transition "However" fits; the conditional, additive, and causal transitions do not.
A student writing about geology gathered these notes: Geodes are hollow rocks lined with crystals. They start as bubbles in volcanic rock or cavities in sedimentary rock. Over time, mineral-rich water seeps into the hollow space. The minerals slowly crystallize on the inner walls. The student wants to explain how the crystals inside a geode form. Which choice most effectively uses relevant information from the notes to accomplish this goal?
- Geodes are hollow rocks lined with sparkling crystals.
- Crystals form inside a geode as mineral-rich water seeps into its hollow space and slowly crystallizes on the inner walls.
- Geodes begin as bubbles in volcanic rock or cavities in sedimentary rock.
- Geodes can be found in both volcanic and sedimentary rock.
Correct answer: Crystals form inside a geode as mineral-rich water seeps into its hollow space and slowly crystallizes on the inner walls.
Correct answer: "Crystals form inside a geode as mineral-rich water seeps into its hollow space and slowly crystallizes on the inner walls." This choice explains the crystal-forming process, while the others only define a geode or describe its origins.
The composer Ludwig van Beethoven began losing his hearing in his late twenties. _____ he continued to compose, eventually writing some of his most celebrated works after he had become almost completely deaf. Which choice completes the text with the most logical transition?
- Nonetheless,
- As a result,
- Similarly,
- For example,
Correct answer: Nonetheless,
Correct answer: "Nonetheless,". The second sentence describes continued composing despite the hearing loss in the first, so the concessive transition "Nonetheless" expresses the contrast; the causal, comparison, and example transitions do not.
A student researching marine life took these notes: Sea otters eat sea urchins. Sea urchins feed on kelp. Without otters, urchin populations explode and destroy kelp forests. Kelp forests shelter many fish species. The student wants to explain why sea otters help protect kelp forests. Which choice most effectively uses relevant information from the notes to accomplish this goal?
- By eating sea urchins, sea otters keep urchin populations in check and prevent them from destroying kelp forests.
- Sea otters and sea urchins both live near kelp forests.
- Kelp forests shelter many different species of fish.
- Sea urchins feed on kelp in coastal waters.
Correct answer: By eating sea urchins, sea otters keep urchin populations in check and prevent them from destroying kelp forests.
Correct answer: "By eating sea urchins, sea otters keep urchin populations in check and prevent them from destroying kelp forests." This choice connects the otters' diet to the protection of kelp forests, addressing the goal; the others state isolated facts without explaining the protective effect.
Many cities have begun replacing old streetlights with energy-efficient LEDs. _____ some astronomers worry that the bright white light of certain LEDs may worsen the glow that hides stars from view. Which choice completes the text with the most logical transition?
- Accordingly,
- Still,
- In addition,
- Finally,
Correct answer: Still,
Correct answer: "Still,". The second sentence raises a concern that qualifies the positive trend described first, so the contrasting transition "Still" fits; the causal, additive, and sequencing transitions do not capture the reservation.
A student preparing a report on space exploration assembled these notes: The Voyager 1 probe launched in 1977. It was designed to study the outer planets. In 2012 it entered interstellar space. It is the most distant human-made object from Earth. The student wants to emphasize Voyager 1's record-setting distance. Which choice most effectively uses relevant information from the notes to accomplish this goal?
- Now in interstellar space, Voyager 1 is the most distant human-made object from Earth.
- Voyager 1 launched in 1977 to study the outer planets.
- Voyager 1 was designed to study the outer planets of the solar system.
- In 2012, Voyager 1 reached a new region of space.
Correct answer: Now in interstellar space, Voyager 1 is the most distant human-made object from Earth.
Correct answer: "Now in interstellar space, Voyager 1 is the most distant human-made object from Earth." This sentence stresses the probe's record distance, the student's goal, while the others highlight its launch year or mission purpose.
Recycling aluminum cans uses only about five percent of the energy needed to make new aluminum from ore. _____ recycling a single can saves enough energy to power a television for several hours. Which choice completes the text with the most logical transition?
- In fact,
- Conversely,
- Beforehand,
- Despite this,
Correct answer: In fact,
Correct answer: "In fact,". The second sentence reinforces and intensifies the energy-saving claim of the first, so the emphasizing transition "In fact" fits; the contrast and sequence transitions contradict the supportive relationship.
A student researching plant biology compiled these notes: Sunflowers can track the sun across the sky. This movement is called heliotropism. Young sunflowers face east at dawn and follow the sun westward. At night, they slowly turn back to face east again. The student wants to describe the daily pattern of a young sunflower's movement. Which choice most effectively uses relevant information from the notes to accomplish this goal?
- Sunflowers exhibit a behavior known as heliotropism.
- A young sunflower faces east at dawn, follows the sun west during the day, and turns back east at night.
- Sunflowers are able to track the sun across the sky.
- Heliotropism is the movement of plants in response to the sun.
Correct answer: A young sunflower faces east at dawn, follows the sun west during the day, and turns back east at night.
Correct answer: "A young sunflower faces east at dawn, follows the sun west during the day, and turns back east at night." Only this choice lays out the full daily cycle of movement; the others merely name or generally describe heliotropism.
Public libraries once served mainly as places to borrow printed books. _____ many now lend tools, musical instruments, and even seeds, expanding far beyond their original purpose. Which choice completes the text with the most logical transition?
- Today,
- Therefore,
- Likewise,
- For instance,
Correct answer: Today,
Correct answer: "Today,". The second sentence contrasts the present role of libraries with their former role, and the time transition "Today" signals that shift; the causal, additive, and example transitions do not capture the then-versus-now relationship.
A student writing about insects gathered these notes: Fireflies produce light in their lower abdomens. The light comes from a chemical reaction. The reaction releases almost no heat. Light that produces little heat is called cold light. The student wants to explain why a firefly's glow is considered cold light. Which choice most effectively uses relevant information from the notes to accomplish this goal?
- Fireflies produce light in their lower abdomens.
- Fireflies create their glow through a chemical reaction.
- A firefly's glow is cold light because the chemical reaction that produces it releases almost no heat.
- Cold light is light that gives off very little heat.
Correct answer: A firefly's glow is cold light because the chemical reaction that produces it releases almost no heat.
Correct answer: "A firefly's glow is cold light because the chemical reaction that produces it releases almost no heat." This choice ties the firefly's glow to the definition of cold light, answering why; the others state isolated facts or define cold light without applying it.
The painter Vincent van Gogh sold very few works during his lifetime. _____ today his paintings are among the most valuable and widely recognized in the world. Which choice completes the text with the most logical transition?
- In particular,
- By contrast,
- Consequently,
- In the same way,
Correct answer: By contrast,
Correct answer: "By contrast,". The second sentence opposes van Gogh's present fame with his lack of sales in life, so the contrasting transition "By contrast" fits; the specifying, causal, and comparison transitions do not express the opposition.
A student researching nutrition assembled these notes: Vitamin C is found in many fruits and vegetables. The human body cannot store vitamin C for long. Excess vitamin C is removed in urine. People must consume vitamin C regularly to maintain healthy levels. The student wants to explain why people need a steady intake of vitamin C. Which choice most effectively uses relevant information from the notes to accomplish this goal?
- Vitamin C is found in many fruits and vegetables.
- Excess vitamin C leaves the body in the urine.
- Because the body cannot store vitamin C and removes the excess in urine, people must consume it regularly.
- Many fruits and vegetables are rich sources of vitamin C.
Correct answer: Because the body cannot store vitamin C and removes the excess in urine, people must consume it regularly.
Correct answer: "Because the body cannot store vitamin C and removes the excess in urine, people must consume it regularly." This choice links the body's inability to store the vitamin to the need for steady intake, meeting the goal; the others give only single facts about sources or excess.
Most of a tree's mass comes not from the soil but from the air. _____ through photosynthesis, trees pull carbon dioxide from the atmosphere and convert it into the wood and leaves that make up their bodies. Which choice completes the text with the most logical transition?
- Surprisingly,
- That is,
- In contrast,
- Later,
Correct answer: That is,
Correct answer: "That is,". The second sentence restates and explains the claim that a tree's mass comes from the air, so the clarifying transition "That is" fits; the contrast and time transitions do not match the explanatory relationship.
Choose the answer that most logically completes the text so that it conforms to the conventions of Standard English. The travel guide recommended packing three essentials for the trek through the cloud forest: ____
- Sturdy boots, a rain jacket, and insect repellent
- Sturdy boots, a rain jacket, and insect repellent
- Sturdy boots; a rain jacket; and insect repellent
- Sturdy boots a rain jacket and insect repellent
Correct answer: Sturdy boots, a rain jacket, and insect repellent
Correct answer: "sturdy boots, a rain jacket, and insect repellent." A colon properly introduces the list, and the three items are correctly separated by commas with a serial comma before "and" and a period at the end. The other options drop the closing period, misuse semicolons for a simple list, or omit the necessary commas.
Which choice completes the text so that it conforms to the conventions of Standard English? The collection of rare manuscripts, including several medieval prayer books, ____ housed in a climate-controlled vault beneath the library.
- Is
- Are
- Were
- Have been
Correct answer: Is
Correct answer: "is." The subject is the singular noun "collection," so it takes the singular verb "is." The intervening phrases "of rare manuscripts" and "including several medieval prayer books" do not change the number of the subject, so the plural verbs "are," "were," and "have been" are incorrect.
Which choice most logically completes the text so that it conforms to the conventions of Standard English? The greenhouse maintains a constant humidity level ____ the orchids would quickly wither in drier air.
- Level; the orchids
- Level the orchids
- Level, the orchids
- Level, and the orchids,
Correct answer: Level; the orchids
Correct answer: "level; the orchids." Two independent clauses must be separated by a semicolon (or a period or a comma plus a coordinating conjunction). A comma alone creates a comma splice, no punctuation creates a run-on, and the final option misplaces a comma after "orchids."
Which choice conforms to the conventions of Standard English? After the committee announced the new policy, ____ released a detailed report explaining the decision.
- They
- It
- We
- You
Correct answer: It
Correct answer: "it." The antecedent is "committee," a singular collective noun acting as a single unit, so the singular pronoun "it" is correct. "They" disagrees in number, while "we" and "you" shift to people who are not the antecedent.
Which choice completes the text so that it conforms to the conventions of Standard English? By the time the firefighters arrived, the small brush fire ____ into a blaze that threatened several homes.
- Grows
- Grew
- Had grown
- Will grow
Correct answer: Had grown
Correct answer: "had grown." The past perfect "had grown" correctly shows that the fire's growth was completed before the past-tense action "arrived." "Grows" and "will grow" are present and future, and "grew" fails to signal that one past action preceded another.
Which choice conforms to the conventions of Standard English? The ____ uniforms were redesigned to include reflective stripes for nighttime visibility.
- Workers
- Worker's
- Workers'
- Workers's
Correct answer: Workers'
Correct answer: "workers'." Because the uniforms belong to more than one worker, the plural possessive "workers'" (plural noun plus apostrophe) is correct. "Worker's" is singular possessive, "workers" is a plural without possession, and "workers's" is not a standard form.
Which choice most logically completes the text so that it conforms to the conventions of Standard English? Coated in a thin layer of frost, ____
- The gardener noticed the tender seedlings
- Drooping was what the seedlings did
- The morning chill made the seedlings droop
- The tender seedlings drooped in the morning chill
Correct answer: The tender seedlings drooped in the morning chill
Correct answer: "the tender seedlings drooped in the morning chill." The introductory modifier "Coated in a thin layer of frost" must describe the noun directly after the comma. Only the seedlings can logically be coated in frost, so they must be the subject. The other choices illogically attach the modifier to the gardener, the chill, or an action.
Which choice completes the text so that it conforms to the conventions of Standard English? The internship taught her to analyze data carefully, to communicate findings clearly, and ____ deadlines reliably.
- To meet
- Meeting
- She met
- Met
Correct answer: To meet
Correct answer: "to meet." The sentence lists a series of infinitive phrases—"to analyze," "to communicate"—so the third item must also be an infinitive, "to meet," to maintain parallel structure. The gerund "meeting" and the finite verbs "she met" and "met" break the parallelism.
Which choice conforms to the conventions of Standard English? The robot recalibrated ____ sensors before resuming the assembly line.
- Its
- It's
- Its'
- Their
Correct answer: Its
Correct answer: "its." The possessive form of "it" is "its," with no apostrophe. "It's" is the contraction for "it is," "its'" is not a word, and "their" disagrees in number with the singular "robot."
Which choice completes the text so that it conforms to the conventions of Standard English? The lead engineer and the project manager ____ scheduled to present their proposal to the board on Friday.
- Is
- Are
- Was
- Has been
Correct answer: Are
Correct answer: "are." A compound subject joined by "and"—"the lead engineer and the project manager"—is plural and takes the plural verb "are." The singular verbs "is," "was," and "has been" do not agree with the plural subject.
Which choice conforms to the conventions of Standard English? Marie Tharp, ____ helped map the ocean floor, was overlooked for decades by the scientific establishment.
- A geologist, who
- A geologist who
- A geologist; who
- A geologist who,
Correct answer: A geologist who
Correct answer: "a geologist who." The nonrestrictive appositive "a geologist who helped map the ocean floor" is already set off by the comma after "Tharp" and a comma after "floor"; no additional internal punctuation is needed. Inserting a comma or semicolon after "geologist" or after "who" incorrectly interrupts the phrase.
Which choice completes the text so that it conforms to the conventions of Standard English? If the satellite ____ a different orbit, scientists could have collected far more atmospheric data.
- Takes
- Took
- Would take
- Had taken
Correct answer: Had taken
Correct answer: "had taken." The result clause uses "could have collected," signaling a past unreal condition, so the "if" clause requires the past perfect "had taken." "Takes" and "would take" do not fit a past contrary-to-fact condition, and "took" lacks the perfect aspect the sentence requires.
Which choice most logically completes the text so that it conforms to the conventions of Standard English? The expedition succeeded because of one overlooked factor ____ the meticulous logistics planning carried out months in advance.
- Factor: the
- Factor, the
- Factor the
- Factor; the,
Correct answer: Factor: the
Correct answer: "factor: the." A colon correctly follows the independent clause to introduce the explanation that identifies the "one overlooked factor." A comma creates a comma splice with the following fragment, omitting punctuation creates a run-on, and the last option adds a stray comma after "the."
Which choice conforms to the conventions of Standard English? The award went to the researcher ____ the committee had nominated three years earlier.
- Who
- Which
- Whom
- Whose
Correct answer: Whom
Correct answer: "whom." The pronoun functions as the object of the verb "had nominated" (the committee nominated whom), so the objective form "whom" is correct. "Who" is the subjective form, "which" is for things, and "whose" is possessive.
Which choice conforms to the conventions of Standard English? Several ____ migrated south as the temperatures dropped sharply in late autumn.
- Species'
- Specie's
- Specieses
- Species
Correct answer: Species
Correct answer: "species." The sentence requires a simple plural noun as the subject, and "species" is both singular and plural with no apostrophe. "Species'" and "specie's" wrongly add possession, and "specieses" is not a word.
Which choice completes the text so that it conforms to the conventions of Standard English? The new turbine design is not only more efficient ____ quieter than the models it replaces.
- However
- But
- And also
- But also
Correct answer: But also
Correct answer: "but also." The correlative conjunction "not only" must be paired with "but also" to keep the comparison balanced. "But," "and also," and "however" fail to complete the standard "not only ... but also" construction.
Which choice completes the text so that it conforms to the conventions of Standard English? Each of the volunteers ____ assigned a specific section of the trail to clear before sunset.
- Was
- Are
- Were
- Have been
Correct answer: Was
Correct answer: "was." The subject "Each" is singular, so it takes the singular verb "was," regardless of the plural phrase "of the volunteers." The plural verbs "were," "are," and "have been" do not agree with the singular indefinite pronoun.
Which choice conforms to the conventions of Standard English? The museum displayed a ____ sculpture at the entrance to the new wing.
- Massive bronze
- Massive, bronze
- Massive; bronze
- Massive bronze,
Correct answer: Massive bronze
Correct answer: "massive bronze." The adjectives are cumulative—"bronze" pairs closely with "sculpture" and "massive" modifies the whole—so no comma is used between them. A comma or semicolon would wrongly treat them as coordinate, and a trailing comma after "bronze" is ungrammatical.
Which choice most logically completes the text so that it conforms to the conventions of Standard English? ____ the chemists repeated the experiment three more times to confirm their unexpected results.
- Because the data seemed inconsistent,
- The data seeming inconsistent.
- Although the data seemed inconsistent.
- Due to the data inconsistent,
Correct answer: Because the data seemed inconsistent,
Correct answer: "Because the data seemed inconsistent," This option forms a complete sentence by attaching a subordinate clause to the independent clause that follows. "The data seeming inconsistent" and "Although the data seemed inconsistent" are fragments punctuated as full sentences, and "Due to the data inconsistent" is grammatically garbled.
Which choice completes the text so that it conforms to the conventions of Standard English? Since the program launched in 2019, enrollment ____ steadily every academic year.
- Increases
- Increased
- Has increased
- Had increased
Correct answer: Has increased
Correct answer: "has increased." The phrase "since the program launched" describes an action continuing from the past into the present, which calls for the present perfect "has increased." The simple present, simple past, and past perfect do not capture this ongoing relationship to the present.
Which choice conforms to the conventions of Standard English? Anyone hoping to join the choir should bring ____ own sheet music to the first rehearsal.
- Their
- His or her
- They're
- Its
Correct answer: His or her
Correct answer: "his or her." The indefinite pronoun "Anyone" is singular and is matched in formal Standard English by the singular "his or her." "Their" is plural in agreement, "they're" is a contraction for "they are," and "its" is for nonhuman things.
Which choice most logically completes the text so that it conforms to the conventions of Standard English? The prototype passed every stress test ____ the team still delayed the launch to gather additional safety data.
- Test; however,
- Test, however,
- Test however
- Test, however
Correct answer: Test; however,
Correct answer: "test; however," When a conjunctive adverb such as "however" links two independent clauses, a semicolon precedes it and a comma follows it. The other options create comma splices or run-ons, or omit the required comma after "however."
Which choice completes the text so that it conforms to the conventions of Standard English? On the laboratory bench ____ several beakers, a digital scale, and a coiled length of rubber tubing.
- Is
- Was
- Has been
- Are
Correct answer: Are
Correct answer: "are." In this inverted sentence, the true subject is the compound list "several beakers, a digital scale, and a coiled length of rubber tubing," which is plural and requires "are." The singular verbs "is," "was," and "has been" do not agree with the plural subject.
Which choice conforms to the conventions of Standard English? The ____ research on coral bleaching attracted international funding.
- Scientists'
- Scientist's
- Scientists
- Scientist
Correct answer: Scientist's
Correct answer: "scientist's." The research belongs to one scientist, so the singular possessive "scientist's" (singular noun plus apostrophe-s) is correct. "Scientists'" is plural possessive, while "scientists" and "scientist" show no possession.
Which choice completes the text so that it conforms to the conventions of Standard English? The documentary moved from the bustling markets of the capital to the quiet villages of the highlands and ____ remote islands of the coast.
- The
- Into the
- To the
- Toward the
Correct answer: To the
Correct answer: "to the." The sentence sets up a parallel series of "from ... to ... and to ..." prepositional phrases, so the third phrase must also begin with "to the" to match "to the quiet villages." The bare "the" breaks the pattern, and "into" and "toward" introduce inconsistent prepositions.
Which choice completes the text so that it conforms to the conventions of Standard English? Neither the conductor nor the musicians ____ aware that the recording had already begun.
- Was
- Is
- Were
- Has been
Correct answer: Were
Correct answer: "were." With subjects joined by "neither ... nor," the verb agrees with the nearer subject; the nearer subject "musicians" is plural, so "were" is correct. The singular verbs "was," "is," and "has been" disagree with the plural "musicians."
Which choice conforms to the conventions of Standard English? The three tools the carpenter relied on most ____ a level, a chisel, and a well-worn hand plane.
- Were:
- Were,
- Were
- Were;
Correct answer: Were
Correct answer: "were." A colon should not separate a linking verb from its complement; the list follows the verb "were" directly with no punctuation. Adding a colon, comma, or semicolon after "were" wrongly interrupts the verb and its subject complement.
Which choice most logically completes the text so that it conforms to the conventions of Standard English? Three of the inventions ____ the telescope, the microscope, and the barometer ____ transformed seventeenth-century science.
- Telescope, the microscope, and the barometer,
- —the telescope, the microscope, and the barometer—
- —the telescope, the microscope, and the barometer,
- , the telescope, the microscope, and the barometer—
Correct answer: —the telescope, the microscope, and the barometer—
Correct answer: "—the telescope, the microscope, and the barometer—" A nonrestrictive list inserted into a sentence must be set off by a matched pair of punctuation marks; here two em dashes correctly enclose the supplement. The other options mix a dash with a comma or omit the dashes, breaking the required symmetry.
Which choice completes the text so that it conforms to the conventions of Standard English? When the storm finally passed, residents emerged from their homes and ____ the damage along the flooded streets.
- Assess
- Are assessing
- Will assess
- Assessed
Correct answer: Assessed
Correct answer: "assessed." The sentence is in the past tense—"passed" and "emerged"—so the parallel verb must also be past tense, "assessed." The present "assess," the future "will assess," and the present progressive "are assessing" all break the established past-tense sequence.
Which choice conforms to the conventions of Standard English? The ____ lounge was relocated to a quieter corner of the second floor.
- Children
- Childrens'
- Childrens
- Children's
Correct answer: Children's
Correct answer: "children's." "Children" is an irregular plural, so its possessive is formed by adding apostrophe-s: "children's." "Childrens'" and "childrens" treat "children" as if it were a regular plural, and "children" alone shows no possession.
Which choice completes the text so that it conforms to the conventions of Standard English? The number of applicants for the scholarship ____ doubled since the eligibility rules were broadened.
- Has
- Have
- Are
- Were
Correct answer: Has
Correct answer: "has." The phrase "the number of" takes a singular verb because "number" is the singular subject, so "has" is correct. "Have," "are," and "were" are plural and do not agree with the singular subject "number."
Which choice conforms to the conventions of Standard English? The bridge ____ spans the widest part of the river was completed two years ahead of schedule.
- , which
- Which
- That
- , that
Correct answer: That
Correct answer: "that." The clause "spans the widest part of the river" is restrictive—it identifies which specific bridge—so it should begin with "that" and take no comma. "Which" without a comma is nonstandard for a restrictive clause, and the comma versions wrongly mark the essential clause as nonrestrictive.
Which choice completes the text so that it conforms to the conventions of Standard English? Designing the bridge required more patience ____ the engineers had anticipated at the outset.
- Then
- That
- As
- Than
Correct answer: Than
Correct answer: "than." Comparisons use the conjunction "than," so "more patience than the engineers had anticipated" is correct. "Then" refers to time, while "as" and "that" do not complete a comparative construction with "more."
Which choice most logically completes the text so that it conforms to the conventions of Standard English? Although the recipe called for fresh basil ____ the chef substituted a fragrant blend of dried herbs.
- Basil the
- Basil, the
- Basil; the
- Basil: the
Correct answer: Basil, the
Correct answer: "basil, the." An introductory dependent clause beginning with "Although" should be followed by a comma before the main clause. Omitting the comma creates a run-on, and a semicolon or colon incorrectly implies two independent clauses or an introduction to a list.
Which choice completes the text so that it conforms to the conventions of Standard English? When hikers plan a long backcountry route, ____ should always carry a topographic map and a reliable compass.
- You
- They
- One
- We
Correct answer: They
Correct answer: "they." The pronoun must agree with the plural antecedent "hikers," so the third-person plural "they" maintains consistency. "You," "one," and "we" shift to a different person and break agreement with "hikers."
Which choice completes the text so that it conforms to the conventions of Standard English? Restoring the wetlands and reintroducing native fish ____ expected to revive the region's struggling bird populations.
- Is
- Was
- Has been
- Are
Correct answer: Are
Correct answer: "are." Two gerund phrases joined by "and"—"Restoring the wetlands" and "reintroducing native fish"—form a compound subject that is plural and takes the plural verb "are." The singular verbs "is," "was," and "has been" do not agree with the compound subject.
A phone plan charges a flat monthly fee plus a per-text rate. The monthly cost C, in dollars, is given by C = 0.05t + 20, where t is the number of texts. What does the number 20 represent in this context?
- The fixed monthly fee charged regardless of the number of texts
- The cost of each individual text message
- The total number of texts allowed each month
- The cost when exactly 20 texts are sent
Correct answer: The fixed monthly fee charged regardless of the number of texts
Correct answer: The fixed monthly fee charged regardless of the number of texts. In the linear equation C = 0.05t + 20, the constant term 20 is the value of C when t = 0, so it is the cost incurred even when no texts are sent — the fixed monthly fee. The coefficient 0.05 is the per-text rate, not the 20.
If 7 - 2x = 3x - 8, what is the value of x?
- -3
- 3
- 1
- 15
Correct answer: 3
Correct answer: 3. Starting from 7 - 2x = 3x - 8, add 2x to both sides to get 7 = 5x - 8, then add 8 to both sides to get 15 = 5x. Dividing by 5 gives x = 3.
A car rental company charges a base fee of 35 dollars plus 0.20 dollars per mile driven. Which equation gives the total cost y in dollars for driving x miles?
- Y = 0.20(x + 35)
- Y = 35x + 0.20
- Y = 0.20x + 35
- Y = 35x - 0.20
Correct answer: Y = 0.20x + 35
Correct answer: y = 0.20x + 35. The per-mile charge of 0.20 dollars is multiplied by the number of miles x, and the fixed base fee of 35 dollars is added once, giving y = 0.20x + 35. The 35 is constant and the 0.20 is the rate per mile.
What value of k makes the equation 4(x + k) = 4x + 12 true for all values of x?
- 4
- 12
- 48
- 3
Correct answer: 3
Correct answer: 3. Distributing the left side gives 4x + 4k = 4x + 12. For this to hold for all x, the constant terms must be equal, so 4k = 12, which means k = 3.
The equation 3x + 6y = 18 represents a line in the xy-plane. What is the y-intercept of this line?
- 3
- 6
- 18
- -3
Correct answer: 3
Correct answer: 3. The y-intercept occurs where x = 0. Substituting x = 0 into 3x + 6y = 18 gives 6y = 18, so y = 3. The line crosses the y-axis at the point (0, 3).
Half of a number increased by 9 equals 17. Which equation represents this statement, where n is the number?
- 2n + 9 = 17
- (1/2)n + 9 = 17
- (1/2)(n + 9) = 17
- (1/2)n - 9 = 17
Correct answer: (1/2)n + 9 = 17
Correct answer: (1/2)n + 9 = 17. Half of a number is (1/2)n, and increasing that by 9 means adding 9, giving (1/2)n + 9. Setting this equal to 17 produces (1/2)n + 9 = 17.
If the equation 2x + 3 = 2x + c has no solution, what must be true about the constant c?
- C must equal 0
- C must equal 3
- C can be any value other than 3
- C must be negative
Correct answer: C can be any value other than 3
Correct answer: c can be any value other than 3. Subtracting 2x from both sides leaves 3 = c. This is a contradiction with no solution whenever c is not 3; if c were 3, the equation would be true for all x instead.
A line passes through the origin and the point (4, 10). What is the slope of the line?
- 14
- 2/5
- 10
- 5/2
Correct answer: 5/2
Correct answer: 5/2. Slope equals the change in y divided by the change in x. From the origin (0, 0) to (4, 10), the slope is (10 - 0)/(4 - 0) = 10/4 = 5/2.
Solve for x: 2(3x - 4) = 5x + 1.
- 9
- -9
- 7
- 1
Correct answer: 9
Correct answer: 9. Distribute the left side to get 6x - 8 = 5x + 1. Subtract 5x from both sides to get x - 8 = 1, then add 8 to both sides to find x = 9.
A linear function g satisfies g(2) = 7 and g(6) = 19. What is the rate of change (slope) of g?
- 4
- 3
- 1/3
- 12
Correct answer: 3
Correct answer: 3. For a linear function, the rate of change is the difference in outputs divided by the difference in inputs: (19 - 7)/(6 - 2) = 12/4 = 3.
The system of equations y = 2x + 1 and y = 2x - 4 has how many solutions?
- Exactly two
- Exactly one
- Zero
- Infinitely many
Correct answer: Zero
Correct answer: Zero. Both lines have slope 2 but different y-intercepts (1 and -4), so they are parallel and never intersect. Parallel, non-identical lines produce a system with no solution.
If 5(x - 3) >= 2x + 6, what is the smallest integer value of x that satisfies the inequality?
- 5
- 6
- 8
- 7
Correct answer: 7
Correct answer: 7. Distribute to get 5x - 15 >= 2x + 6, subtract 2x to get 3x - 15 >= 6, add 15 to get 3x >= 21, then divide by 3 to get x >= 7. The smallest integer satisfying x >= 7 is 7.
A store sells notebooks for 3 dollars each and pens for 1 dollar each. A customer buys n notebooks and p pens and spends 24 dollars total. Which equation models this purchase?
- 3n + p = 24
- N + 3p = 24
- 3n + 3p = 24
- 3(n + p) = 24
Correct answer: 3n + p = 24
Correct answer: 3n + p = 24. Each notebook costs 3 dollars so n notebooks cost 3n, and each pen costs 1 dollar so p pens cost p. The total spending equation is 3n + p = 24.
What is the value of y in the system 3x - y = 5 and x + y = 7?
- 3
- 4
- 2
- 7
Correct answer: 4
Correct answer: 4. Adding the two equations eliminates y: (3x - y) + (x + y) = 5 + 7 gives 4x = 12, so x = 3. Substituting into x + y = 7 gives 3 + y = 7, so y = 4.
The cost to print T-shirts is modeled by C = 8n + 50, where n is the number of shirts. How much does each additional shirt add to the total cost?
- 58 dollars
- 50 dollars
- 8 dollars
- 42 dollars
Correct answer: 8 dollars
Correct answer: 8 dollars. In C = 8n + 50, the coefficient of n is the slope, representing the cost added for each additional shirt. So each extra shirt increases the total cost by 8 dollars, while 50 is the fixed setup cost.
Solve for x: (2x - 1)/3 = 5.
- 2
- 7
- 16
- 8
Correct answer: 8
Correct answer: 8. Multiply both sides by 3 to clear the denominator: 2x - 1 = 15. Add 1 to both sides to get 2x = 16, then divide by 2 to find x = 8.
A line in the xy-plane passes through (2, -1) with slope 4. What is the equation of the line in slope-intercept form?
- Y = 4x - 9
- Y = 4x + 9
- Y = 4x - 1
- Y = 4x + 7
Correct answer: Y = 4x - 9
Correct answer: y = 4x - 9. Using point-slope form, y - (-1) = 4(x - 2), which becomes y + 1 = 4x - 8. Subtracting 1 from both sides gives y = 4x - 9.
If 3a = 2b and b = 9, what is the value of a?
- 13.5
- 6
- 3
- 18
Correct answer: 6
Correct answer: 6. Substitute b = 9 into 3a = 2b to get 3a = 2(9) = 18. Dividing both sides by 3 gives a = 6.
A swimming pool contains 200 gallons and is being drained at 15 gallons per minute. Which equation gives the amount of water W, in gallons, remaining after m minutes?
- W = 15m - 200
- W = 200 + 15m
- W = 200 - 15m
- W = 15 - 200m
Correct answer: W = 200 - 15m
Correct answer: W = 200 - 15m. The pool starts with 200 gallons, and draining removes 15 gallons each minute, so 15m is subtracted from the initial amount. The remaining water is W = 200 - 15m.
For what value of x do the lines y = -2x + 5 and y = x - 1 intersect?
- 3
- -2
- 1
- 2
Correct answer: 2
Correct answer: 2. Setting the expressions equal gives -2x + 5 = x - 1. Adding 2x to both sides gives 5 = 3x - 1, then adding 1 gives 6 = 3x, so x = 2.
The total mass m, in grams, of a beaker with liquid is m = 4v + 120, where v is the volume of liquid in milliliters. What is the mass of the empty beaker?
- 120 grams
- 4 grams
- 124 grams
- 30 grams
Correct answer: 120 grams
Correct answer: 120 grams. The empty beaker corresponds to v = 0 milliliters. Substituting v = 0 into m = 4v + 120 gives m = 120, so the empty beaker has a mass of 120 grams.
If 6x + 2y = 14, what is y in terms of x?
- Y = 14 - 6x
- Y = 7 - 3x
- Y = 3x - 7
- Y = 7 + 3x
Correct answer: Y = 7 - 3x
Correct answer: y = 7 - 3x. Subtract 6x from both sides of 6x + 2y = 14 to get 2y = 14 - 6x. Dividing every term by 2 gives y = 7 - 3x.
A taxi ride costs 4 dollars to start plus a charge per mile. A 5-mile ride costs 14 dollars. What is the charge per mile?
- 10 dollars
- 2.80 dollars
- 2 dollars
- 3 dollars
Correct answer: 2 dollars
Correct answer: 2 dollars. The total beyond the 4-dollar start fee is 14 - 4 = 10 dollars for 5 miles. Dividing 10 dollars by 5 miles gives a per-mile charge of 2 dollars.
The inequality 2x + 1 < 9 describes which set of values for x?
- X > 5
- X > 4
- X < 5
- X < 4
Correct answer: X < 4
Correct answer: x < 4. Subtract 1 from both sides of 2x + 1 < 9 to get 2x < 8, then divide both sides by 2 to obtain x < 4. The inequality direction stays the same because both sides were divided by a positive number.
Two lines in the xy-plane have equations y = 3x + 2 and y = mx - 5. For what value of m are the lines parallel?
- 3
- -3
- -1/3
- 2
Correct answer: 3
Correct answer: 3. Parallel lines have equal slopes. The first line has slope 3, so the second line must also have slope 3, meaning m = 3. The different y-intercepts ensure the lines are distinct.
If 8 - 3(x - 2) = 5, what is the value of x?
- 1
- 3
- -3
- 13/3
Correct answer: 3
Correct answer: 3. Distribute to get 8 - 3x + 6 = 5, which simplifies to 14 - 3x = 5. Subtract 14 from both sides to get -3x = -9, then divide by -3 to find x = 3.
A line has x-intercept 6 and y-intercept 4. What is the slope of the line?
- -3/2
- 2/3
- -2/3
- 3/2
Correct answer: -2/3
Correct answer: -2/3. The x-intercept is the point (6, 0) and the y-intercept is the point (0, 4). The slope is (4 - 0)/(0 - 6) = 4/(-6) = -2/3.
A baker uses 2 cups of flour per cake and starts with 30 cups. The flour remaining f after baking c cakes is f = 30 - 2c. How many cakes can be baked before the flour runs out?
- 60
- 30
- 28
- 15
Correct answer: 15
Correct answer: 15. The flour runs out when f = 0. Setting 30 - 2c = 0 gives 2c = 30, so c = 15. Therefore 15 cakes can be baked before the flour is gone.
If 4(2x + 1) = 3(x + 8), what is the value of x?
- 4
- 2
- 5
- -4
Correct answer: 4
Correct answer: 4. Distribute both sides to get 8x + 4 = 3x + 24. Subtract 3x from both sides to get 5x + 4 = 24, then subtract 4 to get 5x = 20, so x = 4.
The equation 2x - 5y = 20 is written in standard form. What is the x-intercept of the line it represents?
- (0, 10)
- (10, 0)
- (-4, 0)
- (0, -4)
Correct answer: (10, 0)
Correct answer: (10, 0). The x-intercept occurs where y = 0. Substituting y = 0 into 2x - 5y = 20 gives 2x = 20, so x = 10. The line crosses the x-axis at the point (10, 0).
The function $f$ is defined by $f(x) = 3x^2 + 12x + 5$ . The minimum value of $f$ occurs at which value of $x$ ?
- X = -2
- X = 2
- X = -4
- X = -6
Correct answer: X = -2
The minimum occurs at $x = -2$ . For a parabola in the form $ax^2 + bx + c$ with $a$ positive, the vertex (and minimum) is at $x = \frac{-b}{2a}$ . Here $b = 12$ and $a = 3$ , so $x = \frac{-12}{2 \cdot 3} = \frac{-12}{6} = -2$ .
Which of the following is equivalent to the expression $\frac{x^2 + 5x + 6}{x + 2}$ for all $x$ not equal to -2?
- X + 2
- X + 3
- X + 6
- X - 3
Correct answer: X + 3
The expression equals x + 3. The numerator factors as (x + 2)(x + 3), and dividing by (x + 2) cancels that factor, leaving x + 3 for all x not equal to -2.
If $2^x = 32$ , what is the value of $x$ ?
- 4
- 6
- 5
- 16
Correct answer: 5
The value of $x$ is 5. Since 32 can be written as $2^5$ , the equation $2^x = 2^5$ requires the exponents to be equal, so $x = 5$ .
The quadratic function $f(x) = -(x - 4)^2 + 9$ is written in vertex form. What is the maximum value of $f$ ?
- 4
- -9
- 13
- 9
Correct answer: 9
The maximum value is 9. In vertex form $a(x - h)^2 + k$ , the vertex is $(h, k)$ ; since $a = -1$ is negative the parabola opens downward, so the $y$ -value of the vertex, $k = 9$ , is the maximum.
What is the product of the solutions of the equation $x^2 - 3x - 28 = 0$ ?
- -28
- 28
- 3
- -3
Correct answer: -28
The product of the solutions is -28. For $ax^2 + bx + c = 0$ , the product of the roots equals $c/a$ ; here $c = -28$ and $a = 1$ , so the product is -28.
If $\sqrt{3x + 4} = 7$ , what is the value of $x$ ?
- 17
- 15
- 7
- 45
Correct answer: 15
The value of $x$ is 15. Squaring both sides gives $3x + 4 = 49$ , so $3x = 45$ and $x = 15$ .
The expression $x^2 - 12x + 36$ is equivalent to which of the following?
- $(x + 6)^2$
- (x - 6)(x + 6)
- $(x - 6)^2$
- (x - 12)(x - 3)
Correct answer: $(x - 6)^2$
The expression equals $(x - 6)^2$ . It is a perfect square trinomial because the first and last terms are squares ( $x^2$ and 36) and the middle term $-12x$ equals 2 times $x$ times -6.
A ball is thrown upward and its height in meters is $h(t) = -5t^2 + 20t + 1$ , where $t$ is in seconds. What is the height of the ball at $t = 2$ seconds?
- 20 meters
- 41 meters
- 1 meter
- 21 meters
Correct answer: 21 meters
The height is 21 meters. Substituting t = 2 gives h(2) = -5(4) + 20(2) + 1 = -20 + 40 + 1 = 21.
If $f(x) = 2x^2$ and $g(x) = x + 3$ , what is $f(g(1))$ ?
- 32
- 16
- 8
- 5
Correct answer: 32
The value of $f(g(1))$ is 32. First $g(1) = 1 + 3 = 4$ , then $f(4) = 2(4)^2 = 2(16) = 32$ .
The number of solutions to a quadratic equation can be determined by its discriminant $b^2 - 4ac$ . For the equation $x^2 + 6x + 9 = 0$ , how many distinct real solutions are there?
- Exactly two
- Exactly one
- None
- Infinitely many
Correct answer: Exactly one
There is exactly one distinct real solution. The discriminant is $6^2 - 4(1)(9) = 36 - 36 = 0$ , and a discriminant of zero means the equation has one repeated real solution.
Which of the following is equivalent to $(x^3)(x^4)$ ?
- $x^{12}$
- $x^1$
- $x^7$
- $2x^7$
Correct answer: $x^7$
The expression equals $x^7$ . When multiplying powers with the same base you add the exponents: $3 + 4 = 7$ .
If $a^2 = 49$ and $a$ is negative, what is the value of $a$ ?
- 7
- -49
- -2401
- -7
Correct answer: -7
The value of a is -7. The square roots of 49 are 7 and -7, and since a is specified to be negative, a = -7.
The function $P(t) = 1000(1.05)^t$ models a population after $t$ years. By what percent does the population grow each year?
- 5 percent
- 105 percent
- 50 percent
- 1.05 percent
Correct answer: 5 percent
The population grows 5 percent each year. In an exponential model $a(1 + r)^t$ , the growth rate $r$ is the decimal added to 1; here $1.05 = 1 + 0.05$ , so $r = 0.05$ , which is 5 percent.
What value of $x$ satisfies the equation $(x - 1)^2 = 16$ ?
- X = 4 or x = -4
- X = 5 or x = -3
- X = 5 only
- X = 17 or x = -15
Correct answer: X = 5 or x = -3
The solutions are $x = 5$ or $x = -3$ . Taking $\sqrt{\ }$ of both sides gives $x - 1 = 4$ or $x - 1 = -4$ , so $x = 5$ or $x = -3$ .
Which expression is equivalent to $(x + 4)^2$ ?
- $x^2 + 16$
- $x^2 + 4x + 16$
- $x^2 + 8x + 16$
- $x^2 + 8x + 8$
Correct answer: $x^2 + 8x + 16$
The expression equals $x^2 + 8x + 16$ . Expanding $(x + 4)^2 = (x + 4)(x + 4)$ gives $x^2 + 4x + 4x + 16 = x^2 + 8x + 16$ .
If the parabola $y = x^2 + bx + 7$ passes through the point $(1, 12)$ , what is the value of $b$ ?
- 5
- 12
- -4
- 4
Correct answer: 4
The value of b is 4. Substituting x = 1 and y = 12 gives 12 = 1 + b + 7, so 12 = 8 + b and b = 4.
What is the value of x in the equation 3 / (x - 2) = 6?
- 2.5
- 4
- 0.5
- 3
Correct answer: 2.5
The value of x is 2.5. Multiplying both sides by (x - 2) gives 3 = 6(x - 2) = 6x - 12, so 6x = 15 and x = 2.5.
The expression $9x^2 - 25$ can be factored as which of the following?
- $(3x - 5)^2$
- (3x - 5)(3x + 5)
- (9x - 5)(x + 5)
- (3x - 25)(3x + 1)
Correct answer: (3x - 5)(3x + 5)
The expression factors as $(3x - 5)(3x + 5)$ . It is a difference of squares because $9x^2 = (3x)^2$ and $25 = 5^2$ , and $a^2 - b^2 = (a - b)(a + b)$ .
If $f(x) = x^2 + k$ and $f(3) = 14$ , what is the value of $k$ ?
- 11
- 23
- 5
- -5
Correct answer: 5
The value of k is 5. Substituting x = 3 gives f(3) = 9 + k = 14, so k = 5.
A radioactive sample's mass is modeled by $m(t) = 80(0.5)^t$ , where $t$ is the number of half-lives elapsed. What is the mass after 3 half-lives?
- 40
- 20
- 5
- 10
Correct answer: 10
The mass is 10. Substituting $t = 3$ gives $m(3) = 80(0.5)^3 = 80(0.125) = 10$ .
Which of the following is a solution to the equation $x^2 = 5x$ ?
- X = 5
- X = 1
- X = -5
- X = 25
Correct answer: X = 5
A solution is $x = 5$ . Rewriting as $x^2 - 5x = 0$ and factoring gives $x(x - 5) = 0$ , so $x = 0$ or $x = 5$ ; of the choices, $x = 5$ works.
The function h(x) = (x + 1)(x - 3)(x - 5) is a polynomial. How many real x-intercepts does its graph have?
- 2
- 3
- 1
- 0
Correct answer: 3
The graph has 3 real x-intercepts. Setting each factor equal to zero gives x = -1, x = 3, and x = 5, which are three distinct values where the graph crosses the x-axis.
If $4^x = 8$ , what is the value of $x$ ?
- 2
- 3
- 1.5
- 0.5
Correct answer: 1.5
The value of $x$ is 1.5. Writing both sides as powers of 2 gives $(2^2)^x = 2^3$ , so $2^{2x} = 2^3$ , meaning $2x = 3$ and $x = 1.5$ .
What is the sum of the solutions to the equation $2x^2 + 10x - 28 = 0$ ?
- 5
- -14
- -10
- -5
Correct answer: -5
The sum of the solutions is -5. For $ax^2 + bx + c = 0$ , the sum of the roots is $-b/a$ ; here $-10/2 = -5$ .
The expression $\frac{x^6}{x^2}$ is equivalent to which of the following for $x$ not equal to 0?
- $x^4$
- $x^3$
- $x^8$
- $x^{12}$
Correct answer: $x^4$
The expression equals $x^4$ . When dividing powers with the same base you subtract the exponents: $6 - 2 = 4$ .
For the quadratic $f(x) = x^2 - 8x + 12$ , at what $x$ -values does the graph cross the $x$ -axis?
- X = -2 and x = -6
- X = 2 and x = 6
- X = 3 and x = 4
- X = 1 and x = 12
Correct answer: X = 2 and x = 6
The graph crosses the $x$ -axis at $x = 2$ and $x = 6$ . Factoring $x^2 - 8x + 12 = (x - 2)(x - 6)$ and setting it to zero gives those two $x$ -intercepts.
If $x^{2/3} = 4$ , what is the value of $x$ ?
- 2
- 16
- 8
- 6
Correct answer: 8
The value of $x$ is 8. Raising both sides to the power $3/2$ gives $x = 4^{3/2} = (\sqrt{4})^3 = 2^3 = 8$ .
Which of the following best describes the graph of $y = 2^x$ ?
- A straight line with slope 2
- A parabola opening upward
- A decreasing curve passing through the origin
- An increasing exponential curve that approaches but never touches the x-axis
Correct answer: An increasing exponential curve that approaches but never touches the x-axis
The graph is an increasing exponential curve that approaches but never touches the $x$ -axis. Because the base 2 is greater than 1, $y = 2^x$ rises as $x$ increases and has the $x$ -axis as a horizontal asymptote.
The equation $x^2 + 4x + c = 0$ has exactly one real solution. What is the value of $c$ ?
- 4
- 2
- 8
- 16
Correct answer: 4
The value of $c$ is 4. Exactly one real solution means the discriminant $b^2 - 4ac$ equals 0; with $a = 1$ and $b = 4$ , that is $16 - 4c = 0$ , so $c = 4$ .
Which expression is equivalent to $3x(x^2 - 2x + 4)$ ?
- $3x^3 - 2x + 4$
- $3x^3 - 6x^2 + 12x$
- $3x^2 - 6x + 12$
- $3x^3 - 6x^2 + 4$
Correct answer: $3x^3 - 6x^2 + 12x$
The expression equals $3x^3 - 6x^2 + 12x$ . Distributing $3x$ over each term gives $3x \cdot x^2 = 3x^3$ , $3x \cdot (-2x) = -6x^2$ , and $3x \cdot 4 = 12x$ .
If $g(x) = x^2 - 4$ is shifted up 3 units, what is the equation of the new function?
- $y = x^2 - 7$
- $y = (x + 3)^2 - 4$
- $y = x^2 - 1$
- $y = x^2 + 3$
Correct answer: $y = x^2 - 1$
The new function is $y = x^2 - 1$ . Shifting a graph up by 3 units adds 3 to the output, so $x^2 - 4 + 3 = x^2 - 1$ .
What is the value of $x$ that makes the rational expression $\frac{x + 5}{x^2 - 4}$ undefined for the positive value?
- X = 4
- X = -5
- X = 5
- X = 2
Correct answer: X = 2
The positive value making it undefined is $x = 2$ . The expression is undefined where the denominator equals zero; $x^2 - 4 = 0$ gives $x = 2$ or $x = -2$ , and the positive one is $x = 2$ .
The solutions of a quadratic equation are x = -2 and x = 7. Which equation could this be?
- $x^2 - 5x - 14 = 0$
- $x^2 + 5x - 14 = 0$
- $x^2 - 5x + 14 = 0$
- $x^2 + 9x - 14 = 0$
Correct answer: $x^2 - 5x - 14 = 0$
The equation is $x^2 - 5x - 14 = 0$ . With roots -2 and 7, the factored form is $(x + 2)(x - 7) = 0$ , which expands to $x^2 - 5x - 14 = 0$ .
If $\sqrt{x} + 2 = 9$ , what is the value of $x$ ?
- 7
- 49
- 11
- 81
Correct answer: 49
The value of $x$ is 49. Subtracting 2 gives $\sqrt{x} = 7$ , and squaring both sides gives $x = 49$ .
Which of the following is equivalent to the expression $\frac{2x^2 + 8x}{2x}$ for $x$ not equal to 0?
- 2x + 4
- X + 8
- X + 4
- $x^2 + 4$
Correct answer: X + 4
The expression equals x + 4. Factoring the numerator as 2x(x + 4) and dividing by 2x cancels the common factor, leaving x + 4.
A function is defined by $f(x) = 6 \cdot 2^x$ . What is the value of $f(3)$ ?
- 36
- 18
- 24
- 48
Correct answer: 48
The value of $f(3)$ is 48. Substituting $x = 3$ gives $f(3) = 6 \cdot 2^3 = 6 \cdot 8 = 48$ .
The expression $x^2 + 2x - 15$ is equivalent to the product of which two binomials?
- (x + 5)(x - 3)
- (x - 5)(x + 3)
- (x + 15)(x - 1)
- (x + 5)(x + 3)
Correct answer: (x + 5)(x - 3)
The expression equals (x + 5)(x - 3). The two numbers that multiply to -15 and add to +2 are +5 and -3, giving the factors (x + 5) and (x - 3).
A two-way table records 200 students. Of these, 120 are seniors and 80 are juniors. Among seniors, 90 own a car; among juniors, 40 own a car. If one student who owns a car is chosen at random, what is the probability the student is a junior?
- Approximately 0.31
- Approximately 0.20
- Approximately 0.50
- Approximately 0.69
Correct answer: Approximately 0.31
Correct answer: Approximately 0.31. Explanation: This is a conditional probability restricted to car owners. The total number of car owners is 90 seniors plus 40 juniors, which equals 130. Of those car owners, 40 are juniors, so the probability is 40 divided by 130, which is about 0.31.
A factory worker estimates a shipment contains 500 parts, but the actual count is 460 parts. What is the percent error of the estimate, rounded to the nearest tenth of a percent?
- 8.7 percent
- 8.0 percent
- 9.2 percent
- 40.0 percent
Correct answer: 8.7 percent
Correct answer: 8.7 percent. Explanation: Percent error equals the absolute difference between the estimate and the actual value, divided by the actual value, times 100. The difference is 500 minus 460, which is 40. Dividing 40 by the actual value 460 gives about 0.087, so the percent error is about 8.7 percent.
In a random sample of 250 voters from a large city, 150 supported a proposed measure. If the city has 60,000 voters, what is the best estimate of the total number of voters citywide who support the measure?
- 36,000
- 24,000
- 15,000
- 40,000
Correct answer: 36,000
Correct answer: 36,000. Explanation: A representative random sample lets the sample proportion be applied to the whole population. The sample proportion of support is 150 divided by 250, which equals 0.60. Multiplying 0.60 by 60,000 voters gives an estimate of 36,000 supporters citywide.
A poll reports that 48 percent of respondents favor a candidate, with a margin of error of 3 percentage points at a 95 percent confidence level. Which statement is the most appropriate interpretation?
- The plausible range for true support is about 45 percent to 51 percent
- Exactly 48 percent of all people favor the candidate
- Between 0 percent and 48 percent of people favor the candidate
- The poll is incorrect because results can vary by 3 percent
Correct answer: The plausible range for true support is about 45 percent to 51 percent
Correct answer: The plausible range for true support is about 45 percent to 51 percent. Explanation: A margin of error defines an interval around the sample estimate. Adding and subtracting 3 percentage points from the reported 48 percent gives a range from 45 percent to 51 percent, which is the plausible range for the true population value.
A metal block has a mass of 270 grams and a volume of 30 cubic centimeters. What is the density of the block, in grams per cubic centimeter?
- 9 grams per cubic centimeter
- 300 grams per cubic centimeter
- 0.11 grams per cubic centimeter
- 240 grams per cubic centimeter
Correct answer: 9 grams per cubic centimeter
Correct answer: 9 grams per cubic centimeter. Explanation: Density is a rate equal to mass divided by volume. Dividing the mass of 270 grams by the volume of 30 cubic centimeters gives 9 grams per cubic centimeter.
A small quiz was taken by 10 students. Three scored 6 points, two scored 7 points, and five scored 9 points. What is the mean score?
- 7.7
- 7.3
- 9.0
- 7.0
Correct answer: 7.7
Correct answer: 7.7. Explanation: For a frequency distribution, multiply each value by its count, add the products, then divide by the total count. The total is three times 6 plus two times 7 plus five times 9, which equals 18 plus 14 plus 45, or 77. Dividing 77 by 10 students gives a mean of 7.7.
The data set 3, 5, 5, 8, 5, 12, 8 is recorded for daily customer complaints. What is the mode of the data set?
- 5
- 8
- 6
- 12
Correct answer: 5
Correct answer: 5. Explanation: The mode is the value that appears most frequently in the data set. The value 5 appears three times, while 8 appears twice and every other value appears once, so the mode is 5.
A student's course grade is 30 percent homework, 20 percent quizzes, and 50 percent the final exam. The student earned 90 on homework, 80 on quizzes, and 70 on the final exam. What is the weighted course grade?
- 78
- 80
- 75
- 82
Correct answer: 78
Correct answer: 78. Explanation: A weighted average multiplies each score by its weight and sums the results. This gives 0.30 times 90 plus 0.20 times 80 plus 0.50 times 70, which equals 27 plus 16 plus 35, for a total of 78.
A store offers 20 percent off all items. A customer also has a coupon for an additional 10 percent off the already-reduced price. What single percent discount off the original price is equivalent to these two discounts combined?
- 28 percent
- 30 percent
- 32 percent
- 18 percent
Correct answer: 28 percent
Correct answer: 28 percent. Explanation: Successive discounts multiply the remaining fractions of the price. After 20 percent off, 0.80 of the price remains; after another 10 percent off, 0.90 of that remains, giving 0.80 times 0.90, which equals 0.72. Since 0.72 of the original price is paid, the combined discount is 1 minus 0.72, or 28 percent.
Printer A prints 12 pages per minute and Printer B prints 18 pages per minute. Working at these constant rates, how long will it take both printers working together to print 450 pages?
- 15 minutes
- 25 minutes
- 30 minutes
- 18 minutes
Correct answer: 15 minutes
Correct answer: 15 minutes. Explanation: Combined rates add, so the printers together produce 12 plus 18, which is 30 pages per minute. Dividing the total of 450 pages by the combined rate of 30 pages per minute gives 15 minutes.
A box plot of test scores shows a minimum of 55, a first quartile of 68, a median of 74, a third quartile of 85, and a maximum of 96. What is the interquartile range of the scores?
- 17
- 41
- 11
- 28
Correct answer: 17
Correct answer: 17. Explanation: The interquartile range measures the spread of the middle half of the data and equals the third quartile minus the first quartile. Subtracting the first quartile of 68 from the third quartile of 85 gives an interquartile range of 17.
In right triangle ABC, the right angle is at C. If sin(A) = 3/5, what is the value of cos(A)?
- 4/5
- 3/4
- 5/4
- 5/3
Correct answer: 4/5
Correct answer: 4/5. Because sin(A) = opposite/hypotenuse = 3/5, the opposite side is 3 and the hypotenuse is 5, forming a 3-4-5 right triangle, so the adjacent side is 4. Therefore cos(A) = adjacent/hypotenuse = 4/5.
In a right triangle, angle A and angle B are the two acute angles. If sin(A) = cos(B), what must be true about angles A and B?
- A and B are supplementary, so their measures add to 180 degrees
- A and B are complementary, so their measures add to 90 degrees
- A and B are both equal to 45 degrees
- A and B are congruent to each other
Correct answer: A and B are complementary, so their measures add to 90 degrees
Correct answer: A and B are complementary, so their measures add to 90 degrees. The cofunction identity states sin(x) = cos(90 - x). In a right triangle the two acute angles always sum to 90 degrees, so each is the complement of the other, which makes the sine of one equal the cosine of the other.
An angle of 135 degrees is converted to radians. What is its measure in radians?
- 2pi/3
- 5pi/6
- 3pi/4
- Pi/3
Correct answer: 3pi/4
Correct answer: 3pi/4. To convert degrees to radians, multiply by pi/180. So 135 times pi/180 equals 135pi/180, which reduces to 3pi/4 after dividing the numerator and denominator by 45.
Two triangles are similar with a scale factor of 3 to 1, meaning the larger triangle's sides are three times the smaller's. If the area of the smaller triangle is 8 square units, what is the area of the larger triangle?
- 24 square units
- 48 square units
- 216 square units
- 72 square units
Correct answer: 72 square units
Correct answer: 72 square units. For similar figures, the ratio of areas equals the square of the ratio of corresponding sides. The side ratio is 3, so the area ratio is 3 squared, which is 9. Multiplying the smaller area, 8, by 9 gives 72 square units.
A circle has its center at the origin and passes through the point (6, 8). What is the equation of this circle?
- $x^2 + y^2 = 100$
- $x^2 + y^2 = 14$
- $x^2 + y^2 = 10$
- $x^2 + y^2 = 48$
Correct answer: $x^2 + y^2 = 100$
Correct answer: $x^2 + y^2 = 100$ . A circle centered at the origin has equation $x^2 + y^2 = r^2$ . The radius is the distance from the origin to $(6, 8)$ , which is $\sqrt{6^2 + 8^2} = \sqrt{100} = 10$ . So $r^2 = 100$ , giving $x^2 + y^2 = 100$ .
An inscribed angle in a circle intercepts an arc that measures 110 degrees. What is the measure of the inscribed angle?
- 110 degrees
- 55 degrees
- 220 degrees
- 70 degrees
Correct answer: 55 degrees
Correct answer: 55 degrees. The inscribed angle theorem states that an inscribed angle is half the measure of the arc it intercepts. Half of the 110-degree arc is 55 degrees.
A trapezoid has parallel bases of length 8 and 14 units and a height of 6 units. What is the area of the trapezoid?
- 132 square units
- 60 square units
- 66 square units
- 44 square units
Correct answer: 66 square units
Correct answer: 66 square units. The area of a trapezoid equals one-half times the sum of the bases times the height: (1/2)(8 + 14)(6) = (1/2)(22)(6) = 66 square units.
A right square pyramid has a base edge of 6 units and a height of 4 units. What is the volume of the pyramid?
- 144 cubic units
- 96 cubic units
- 24 cubic units
- 48 cubic units
Correct answer: 48 cubic units
Correct answer: 48 cubic units. The volume of a pyramid is one-third times the base area times the height. The square base area is 6 times 6 = 36, so the volume is (1/3)(36)(4) = 48 cubic units.
An equilateral triangle is inscribed in a circle of radius 10 units. A central angle is drawn to two adjacent vertices of the triangle. What is the measure of that central angle?
- 120 degrees
- 60 degrees
- 90 degrees
- 180 degrees
Correct answer: 120 degrees
Correct answer: 120 degrees. The three vertices of an inscribed equilateral triangle divide the full 360-degree circle into three equal arcs. Each central angle subtending one side equals 360 divided by 3, which is 120 degrees.
A sector of a circle with radius 6 units has a central angle of 60 degrees. What is the area of the sector?
- 12pi square units
- 6pi square units
- 36pi square units
- 3pi square units
Correct answer: 6pi square units
Correct answer: $6\pi$ square units. The area of a sector equals the fraction of the circle times the full area. The fraction is $60/360 = 1/6$ , and the full circle area is $\pi \cdot 6^2 = 36\pi$ . So the sector area is $(1/6)(36\pi) = 6\pi$ square units.
A line segment has endpoints at (2, 3) and (10, 9). What is the length of the segment?
- 14
- 8
- 10
- 100
Correct answer: 10
Correct answer: 10. The distance formula gives $\sqrt{(10-2)^2 + (9-3)^2} = \sqrt{8^2 + 6^2} = \sqrt{64 + 36} = \sqrt{100} = 10$ (using the squared differences in coordinates).
A 6-foot-tall person standing on level ground casts a shadow 8 feet long at the same time a nearby flagpole casts a shadow 24 feet long. Using similar triangles, what is the height of the flagpole?
- 32 feet
- 16 feet
- 12 feet
- 18 feet
Correct answer: 18 feet
Correct answer: 18 feet. The person and the flagpole form similar triangles with the sun's rays, so height over shadow is constant. Setting 6/8 equal to h/24 and solving gives h = (6 times 24)/8 = 144/8 = 18 feet.
A rectangular box has dimensions 3 units by 4 units by 12 units. What is the length of the box's interior space diagonal, from one corner to the opposite corner?
- 13 units
- 19 units
- 12 units
- 5 units
Correct answer: 13 units
Correct answer: 13 units. The space diagonal of a rectangular box equals $\sqrt{3^2 + 4^2 + 12^2} = \sqrt{9 + 16 + 144} = \sqrt{169} = 13$ units (using the squares of its three dimensions).
A vending machine charges 1.50 dollars for a drink. During a promotion, the price is lowered to 1.20 dollars. By what percent did the price decrease?
- 20 percent
- 25 percent
- 30 percent
- 15 percent
Correct answer: 20 percent
Correct answer: 20 percent. The amount of decrease is 1.50 minus 1.20, which equals 0.30 dollars. The percent decrease is the change divided by the original price: 0.30 divided by 1.50 equals 0.20, or 20 percent.
A histogram of weekly work hours for 40 employees shows most bars on the left side with a long tail of taller-than-typical values extending to the right. Which statement about the mean and median is most accurate?
- The mean is greater than the median because the distribution is skewed right
- The mean equals the median because the data are symmetric
- The mean is less than the median because the distribution is skewed left
- The mean and median cannot be compared from a histogram
Correct answer: The mean is greater than the median because the distribution is skewed right
Correct answer: The mean is greater than the median because the distribution is skewed right. A long tail of high values on the right pulls the mean upward more than the median, so in a right-skewed distribution the mean exceeds the median.
In a passage, the author describes a town that rebuilt its public library entirely with donated labor and materials, then notes that attendance tripled within a year. What does the author most strongly suggest by pairing these two facts?
- Community investment in a shared resource can increase its use
- Libraries should rely only on donations rather than public funding
- Attendance figures are an unreliable measure of a library's value
- Donated materials are always of higher quality than purchased ones
Correct answer: Community investment in a shared resource can increase its use
Correct answer: Community investment in a shared resource can increase its use. By linking the community-built effort directly to the rise in attendance, the author implies that the public's hands-on involvement helped drive greater use of the library.
A passage states that a researcher first assumed a species of moth was active only at night, but field cameras later recorded it feeding in daylight on overcast days. Based on this, what can be reasonably concluded?
- The moth's activity is influenced by light conditions rather than time of day alone
- The field cameras malfunctioned during overcast weather
- The moth never feeds at night under any conditions
- The researcher's original method of observation was deliberately misleading
Correct answer: The moth's activity is influenced by light conditions rather than time of day alone
Correct answer: The moth's activity is influenced by light conditions rather than time of day alone. The daytime feeding occurred specifically on overcast, low-light days, which supports the inference that available light, not the clock, governs the moth's behavior.
While revising an essay, a student wants to combine these two sentences to show that the second result follows from the first: "The bridge was closed for repairs. Local traffic shifted to the older two-lane road." Which choice best accomplishes this goal?
- Because the bridge was closed for repairs, local traffic shifted to the older two-lane road.
- The bridge was closed for repairs, local traffic shifted to the older two-lane road.
- The bridge was closed for repairs, yet local traffic shifted to the older two-lane road.
- The bridge was closed for repairs; local traffic shifted to the older two-lane road, however.
Correct answer: Because the bridge was closed for repairs, local traffic shifted to the older two-lane road.
Correct answer: Because the bridge was closed for repairs, local traffic shifted to the older two-lane road. The conjunction "because" clearly signals a cause-and-effect relationship, showing the traffic shift resulted from the closure, while the contrasting words "yet" and "however" wrongly imply opposition.

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By Career EmployerUpdated Jun 7, 2026

PSAT Question of the DayNew daily

1 of 450+ free questions — a new one every day

Which of the following rhetorical devices is used when an author presents an exaggerated description of an event to create a humorous effect?

Pick an answer to see the explanation

Click Start Test above to launch a full-length PSAT practice test weighted like the real digital PSAT/NMSQT, or drill a single section — Reading & Writing or Math. Every question includes a clear explanation so you learn the reasoning, not just the answer.

The PSAT/NMSQT — the Preliminary SAT / National Merit Scholarship Qualifying Test — is administered by the College Board as a practice run for the SAT and the qualifying test for the National Merit Scholarship Program.^[2]

Since fall 2023 it is fully digital and section-adaptive, taken in the Bluebook app. These free PSAT practice questions mirror the current two-section format so you practice the way the real exam is built.^[1] To round out your prep, pair these with our free study guide, flashcards.

PSAT/NMSQT at a Glance

PSAT/NMSQT at a glance
Detail	PSAT/NMSQT
Sections	2 (Reading and Writing, Math) — each in two modules
Questions	98 administered (90 scored + 8 unscored pretest); 54 Reading & Writing, 44 Math
Length	2 hours 14 minutes (134 minutes, plus a 10-min break)
Format	Fully digital and two-stage module-adaptive (taken in Bluebook app)
Result	Total score 320–1520 (section scores 160–760 each); no pass/fail
When offered	October each year, administered in schools
National Merit	Juniors qualify via a Selection Index (R&W ×2 + Math) ÷ 10
Cost	$18 base fee (2025–26); many schools cover it; fee waivers for eligible 11th graders

What Is on the PSAT?

The digital PSAT/NMSQT has two sections: Reading and Writing (54 questions) and Math (44 questions), for 98 questions administered.^[1] Of these, 90 are scored and 8 are unscored pretest items mixed in.

Reading and Writing comes first — 54 questions across two 32-minute modules — covering Information and Ideas, Craft and Structure, Expression of Ideas, and Standard English Conventions, with one short passage per question.

Math follows — 44 questions across two 35-minute modules — spanning Algebra, Advanced Math, Problem-Solving and Data Analysis, and Geometry and Trigonometry, with about a quarter being student-produced responses and a built-in calculator allowed throughout. Our full practice test simulates the most representative form, stratified across the eight official content domains:

PSAT content domains by share of questions

Reading & Writing — Information and Ideas14% · ≈14 Qs

Reading & Writing — Craft and Structure15% · ≈15 Qs

Reading & Writing — Expression of Ideas11% · ≈11 Qs

Reading & Writing — Standard English Conventions14% · ≈14 Qs

Math — Algebra15% · ≈15 Qs

Math — Advanced Math15% · ≈15 Qs

Math — Problem-Solving and Data Analysis7% · ≈7 Qs

Math — Geometry and Trigonometry7% · ≈7 Qs

PSAT practice test — practice questions by domain with answer explanations

Practice Questions by Section

Use Start Test for a full weighted PSAT simulation, or open the hub and pick a single section to drill your weak area. After each full test, your results show a per-section breakdown so you know exactly where to focus — for most students that means extra reps on Math, especially algebra and advanced math.

Who Can Take the PSAT?

The PSAT/NMSQT is open to all high school students and is most commonly taken by juniors (11th graders), who are the only students eligible to enter the National Merit Scholarship Program. Sophomores often take it as practice (the closely related PSAT 10 is built for 10th graders, and the PSAT 8/9 for 8th and 9th graders).^[2] There is no formal application — you take it through your school, and homeschooled students can arrange to test at a nearby participating school.

How Do You Register for the PSAT?

You register for the PSAT/NMSQT through your high school, not the College Board directly — your school orders and administers the test, typically on a designated day in October, and tells you how and when to sign up.^[3]

The base fee is $18 for 2025–26, though many schools cover it; fee waivers are available for eligible 11th graders from low-income families.^[4] If your own school does not offer the test, contact a nearby school that does, ideally by mid-fall.

How Is the PSAT Scored?

The PSAT/NMSQT is reported on a scaled range of 320 to 1520, the sum of two section scores (Reading and Writing and Math), each from 160 to 760.^[2] There is no pass/fail and no penalty for wrong answers, so answer every question.

Because the test is section-adaptive, your total reflects both how many questions you answered correctly and the difficulty of the second module you were routed into. Scores come with percentiles, benchmarks, and a Selection Index used for National Merit.

How Hard Is the PSAT? (National Merit)

There is no pass or fail on the PSAT/NMSQT — it is a scaled, norm-referenced score. The figure that matters for recognition is the National Merit Selection Index (Reading & Writing score ×2 + Math score, divided by 10; range 48–228).^[5] The nationwide Commended cutoff is typically around 207–209, while Semifinalist cutoffs vary by state, usually in the ~208–223 range — corresponding to roughly a 1180–1450 total depending on section split and state.

320–1520

Total score range

no pass/fail

228

Max Selection Index

R&W counts twice

~207+

Commended cutoff

Semifinalist varies by state

The takeaway: drill until you’re consistently scoring above your target on full-length practice — especially Math — before test day, and get comfortable with the digital Bluebook interface.

What to Expect on Test Day

You take the PSAT/NMSQT at your school on the digital Bluebook app, so arrive with your device charged and complete exam setup beforehand.^[1] The test has two sections — Reading and Writing first, then Math — each split into two modules, with a scheduled 10-minute break in between.

Reading and Writing gives you about 71 seconds per question and Math about 95 seconds, and doing well on each section’s first module unlocks a harder, higher-scoring second module. A built-in calculator and reference sheet are available throughout Math. The whole test runs about 2 hours 14 minutes.

Having simulated the full timing with practice tests makes that clock feel routine.

How to Use This PSAT Practice Test

Recreate exam conditions. Take the full test timed, with no notes.^[5]
Diagnose, then drill. Use a full simulation to find your weak section, then drill it.
Prioritize Math. Algebra and advanced math are the biggest score-movers for most students.
Learn the why. Read every explanation — understanding beats memorizing.
Answer everything. There’s no guessing penalty, so never leave a question blank.

Why the PSAT Matters

The PSAT/NMSQT does double duty: it is the most realistic SAT practice run you can take, on the same digital platform and skills, and for juniors it is the qualifying test for the National Merit Scholarship Program, which can lead to scholarships and recruitment from colleges.^[2] These free PSAT practice tests are the most efficient way to raise your score on both fronts.

Conclusion

Doing well on the PSAT/NMSQT comes down to sharp Reading and Writing skills, solid math, and comfort with the adaptive digital format. Use this free PSAT practice test to find your weak section, drill it to mastery, and reinforce it with our study guide, flashcards so you walk in confident on test day.

PSAT Practice Test FAQ

The PSAT/NMSQT has two sections: Reading and Writing (54 questions, two 32-minute modules) and Math (44 questions, two 35-minute modules), for 98 questions administered in 2 hours and 14 minutes with a 10-minute break between sections. Of the 98, 90 are scored and 8 are unscored pretest items. Each section is two-stage module-adaptive — your performance on the first module determines the difficulty of the second.

References

1.College Board. “How the PSAT/NMSQT Is Structured.” satsuite.collegeboard.org. ↑
2.College Board. “The PSAT/NMSQT — SAT Suite of Assessments.” satsuite.collegeboard.org. ↑
3.College Board. “PSAT/NMSQT Registration and Fee Waivers.” counselors.collegeboard.org. ↑
4.College Board. “Fall 2025 Student Guide — Test Dates and Fee.” satsuite.collegeboard.org. ↑
5.College Board. “National Merit Scholarship Program.” satsuite.collegeboard.org. ↑

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