3 English and 3 math
Here are 6 random questions to try. Takers earning below 75% are unlikely to receive an offer. You have 1 minute 48 seconds per question on the real exam.
Question 1 of 6
2026 Practice Test A English, question 39Passage Massachusetts: Lowell National Historical Park
Massachusetts: Lowell National Historical Park
During the first half of the 19th century, Lowell, Massachusetts, quickly transformed itself from a farm town to a bustling industrial city. In time, Lowell became a model of industry, gaining global recognition for its state-of-the-art technology, innovative canal and dam system, mill architecture, boardinghouses, churches, and ethnic neighborhoods. Young Yankee women, immigrant families, and European tourists all flocked to Lowell to find work at one of the many textile mills, or visit the industrious city that was becoming a popular tourist destination. As one Scottish traveler observed during his visit to America, “Niagara and Lowell are the two objects I will longest remember in my American journey, the one the glory of American scenery, the other of American industry.” Today, Lowell National Historical Park welcomes visitors to enjoy the sights of Lowell and learn about the history of one of America’s most significant industrial cities.
The Boston merchants who founded Lowell in 1821 and named it after Francis Cabot Lowell chose to locate the town along Massachusetts’s Merrimack River to take advantage of the kinetic energy offered by the Pawtucket waterfalls. Over six miles of canals powered the waterwheels of Lowell’s mills, whose massive five- and six-story brick buildings dominated the city’s landscape. . . . The most recognized of these buildings are the Lowell Manufacturing Company chartered in 1821, the Suffolk or Wannalancit Mill completed around the 1880s, the Boott Mill Company established in 1835, and the Boott Mill Boardinghouse that opened in 1838. By the 1850s, 40 textile mills employing over 10,000 workers stretched for about a mile along the river. . . .
The city’s female workforce was significant in the history of Lowell. From the early to mid-1800s, women left the constricted lifestyle of small rural towns and rural areas for independent industrial city life. Most were young single Yankee girls, who were tired of the limited opportunities offered by their domestic work. Women found that Lowell’s mills offered monthly wages for their services and provided them room and board. Although these women gained economic independence in Lowell, the mill boardinghouse keepers constantly supervised their social activities, for which they hardly had any time, considering their daily 12- to 14-hour work schedules. At the end of the day, the factory bell signaled the “mill girls” to return to their boardinghouses. They were expected to adhere to the strict code of conduct respecting curfew and attending church.
Yankee “mill girls” continued to dominate the Lowell workforce until the 1840s, when the city began to find it difficult to compete with the growing industrial development in other New England communities. As profits fell, the mill industry cut wages. These wage cuts, deteriorating working conditions, and long workdays led the “mill girls” to protest and organize strikes. When their demands went unheard, the women left Lowell, and immigrant groups replaced them in the workforce. Despite the low wages and unhealthy work conditions, immigrants were eager to find work.
The immigrants replacing the Yankee “mill girls” during the 1840s were predominantly Irish Catholics, who traveled to America during the Great Potato Famine. Although Lowell received an influx of Irish families during this time, the Irish were a part of the city’s history from its birth, and before the “mill girls” arrived, they built Lowell’s historic canals, mills, and boardinghouses. Initially, Lowell’s Protestant community was slow to welcome Irish immigrants, but the hostility between Yankee Protestants and Irish Catholics eventually disappeared. Irish immigrants dominated the industrial scene until the Civil War, when other immigrant groups began to work in the city mills.
Like the Irish, the French-Canadians, Greeks, Poles, Portuguese, Russian Jews, and Armenians who came to work in Lowell’s mills faced long work hours, low wages, and poor living conditions in the city’s crowded tenements. By the time Lowell’s industry declined, the city had become an ethnic melting pot, where each group claimed its own distinct neighborhood, like the Irish immigrants’ “New Dublin” or “Acre,” and the French-Canadians’ “Little Canada.” The city officially began to close down its mills in the 1920s and ’30s after Lowell’s outdated mills could no longer compete against the state-of-the-art cotton mills in other communities and working conditions continued to decline as Lowell’s companies stopped reinvesting in their mills. . . . Despite a brief resurgence during World War II, the city shut down its last surviving mill by the mid-1950s.
From “Massachusetts: Lowell National Historical Park”—Public Domain/National Park Service
Yankee: native to New England
Niagara: a town in northwestern New York State well known as the location of Niagara Falls, a series of waterfalls on the Canadian border
domestic work: household duties like cooking and cleaning
Question
Read this sentence from paragraph 3.
From the early to mid-1800s, women left the constricted lifestyle of small rural towns and rural areas for independent industrial city life.
Which statement best describes how the sentence fits into the overall structure of the passage?
- AIt provides a transition from a description of the mills to a description of the workforce in those mills.
- BIt indicates a shift in tone from positive and hopeful to negative and dissatisfied with working conditions at the mill.
- CIt summarizes a challenge that led many women to leave their hometown and seek work in urban areas.
- DIt begins a comparison of the mill workforce between the mid-1800s and the late 1800s.
Show the answer
Correct answer: A
The question asks which statement best describes how the sentence in paragraph 3 fits into the overall structure of the passage.
A. CORRECT. The sentence in paragraph 3 provides a transition from the overall description of the city and the mills to a description of the women who made up the workforce in the mills. The idea that women left domestic life in favor of working in the mills is important in the passage, and the sentence serves to connect that idea to the previous discussion about the mills.
B. Incorrect. While the mill girls’ dissatisfaction with their working conditions is addressed later in the passage (“These wage cuts, deteriorating working conditions, and long workdays led the ‘mill girls’ to protest and organize strikes” [paragraph 4]), the sentence in paragraph 3 does not indicate a shift in tone from positive to negative. The sentence provides a transition to the discussion of the women who worked in the mills.
C. Incorrect. Although the sentence in paragraph 3 mentions that women became interested in working in the mills because of the “constricted lifestyle of small rural towns,” structurally the sentence does not function as a summary because, instead of expanding on the idea of the difficulties or challenges of life in small rural towns and rural areas, the paragraph goes on to describe the advantages and disadvantages of life in the city for these women.
D. Incorrect. The sentence in paragraph 3 focuses on the choices women made to leave rural towns to work in the city in the early to mid-1800s, not the mid-1800s to the late 1800s. The sentence does not create a comparison between the workforce in the mid-1800s and that in the late 1800s.
Question analysis
A sentence from the start of paragraph 3 of the Lowell article, about women leaving the limited life of rural towns for the city, is the focus of this text-structure question. Students decide how it fits into the structure of the passage as a whole, so they must place it within the order of all six paragraphs instead of judging it by itself.
- NYS standards
- 7R5 structure and genre features
- Grade level
- Grade 8 reading and task
- Compared with grade 7
- Above grade 7 Grade 7 structure questions often ask what a paragraph does. This one asks how a single sentence serves a six-paragraph history and offers four abstract roles, so the student must hold the passage's whole plan in mind, more than typical grade 7 work.
- Estimated difficulty
- Hard: combines ideas, needs a plan, and has more than one tempting wrong answer.
- Thinking it demands
- Depth of knowledge 3, strategic thinking · mainly analyze
- What makes it hard
- How, not what moderate
- Evidence in several places moderate
- Reading between the lines minor
- Evidence
- Answered from the whole text
- Reading level
- Passage: about grade 15, 764 words; question and choices: about grade 9, 116 words.
- Students, last 30 days
- Not enough answers yet to show (it takes 10).
Why it is hard, traps and wrong answers (shows the answer)
Why it is hard
The answer depends on seeing the passage's plan, mills first and then the people who ran them, and placing this sentence at the seam. Its wording invites a content answer instead, since it really does describe a hardship that drove women to the city, and the later strikes tempt students to see a darker tone beginning here. The fit of the key is also imperfect, because the paragraph's opening sentence starts the turn, so students must choose the best description rather than an exact one.
How, not what moderate Working it out
The question asks what the sentence does in the passage, and its content, women escaping a “constricted lifestyle,” is easy to restate, which makes a summary of that content feel like an answer. (Anderson & Krathwohl, 2001)
Evidence in several places moderate Working it out
The sentence's role shows only from its neighbors: paragraph 2 ends with 40 mills and 10,000 workers, and paragraph 3 then follows the women who left rural towns to work in them. (Kirsch & Mosenthal, 1990; Gorin & Embretson, 2006)
Reading between the lines minor Working it out
Paragraph 3's first sentence, “The city's female workforce was significant,” already names the new subject, so students must see this second sentence as part of the turn rather than a fresh point. (Graesser, Singer & Trabasso, 1994; Kintsch, 1998)
Strategy: Sum up each paragraph in a few words, then look at what comes just before and just after this sentence and decide what role it plays at that point in the passage.
Traps
- Wrong purpose or structure: Names a purpose, structure or effect that the part does not serve, or describes what a part says when the question asks what it does.
- Wrong tone or attitude: Misjudges the tone, attitude or point of view, such as reading admiration as criticism, or taking a character's or subject's feelings for the author's.
The wrong answers, classified
B Wrong tone or attitude (Graesser, Singer & Trabasso, 1994)
Expects a turn toward complaint because the mill girls later strike, but this sentence is hopeful about “independent industrial city life,” and the protests wait until paragraph 4.
C Wrong purpose or structure (Anderson & Krathwohl, 2001)
Restates what the sentence says, women escaping a “constricted lifestyle,” instead of what it does, and the paragraph goes on to life in Lowell rather than rural hardship.
D Wrong purpose or structure (Anderson & Krathwohl, 2001)
Sees the dates “early to mid-1800s” and expects a then-and-later contrast, though the sentence opens the mill girls' story and the passage sets up no such comparison.
Working it out, step by step
Figure out what the question asks
This is a structure question. Structure is how a passage is put together. You need to say what job this sentence does in the whole passage. Don’t just restate what it says. Ask what comes before it and what comes after it.
Look at what comes before
Paragraph 2 is all about the mills. It ends with “40 textile mills employing over 10,000 workers.” Then paragraph 3 begins: “The city’s female workforce was significant in the history of Lowell.” Workforce means the people who do the work. The sentence in the question comes right after that: “From the early to mid-1800s, women left the constricted lifestyle of small rural towns and rural areas for independent industrial city life.”
Look at what comes after
Constricted means tight and limited. So women left small, limited farm towns to live on their own in the city. After this, the passage stays with the workers. Paragraphs 3 and 4 tell about the mill girls’ wages, rules, strikes and leaving. Paragraphs 5 and 6 tell about the immigrants who replaced them. So the passage turns here, from the mills to the people who worked in them.
Check each choice
- A is right. The sentence helps carry the reader from the mills to the workforce in those mills.
- B is wrong. The tone isn’t negative here. “Independent industrial city life” sounds hopeful. The protests and strikes don’t come until paragraph 4.
- C is wrong. It tells what the sentence says, not what it does. And the paragraph goes on to life in Lowell, not to more about hard times back home.
- D is wrong. The passage never compares workers of the mid-1800s with workers of the late 1800s.
Watch out: C sounds right because the sentence really does describe a limited life that women wanted to leave. But the question asks about its role, not its content.
Choose the answer
Paragraph 3’s first sentence names the new subject. This sentence carries it forward by telling where the workers came from. Together they move the passage from mills to people. So the answer is A.
Why this answer and not the closest wrong one
C is the closest wrong answer. It is true that women wanted to escape a “constricted lifestyle.” But C describes what the sentence says, not the job it does. The paragraph then moves on to life in Lowell. A names the job: the sentence links the story of the mills to the story of the mill workers.
More questions like this
The original DOE question
The passage “Massachusetts: Lowell National Historical Park” as printed (page 50)
Question 2 of 6
2026 Practice Test B English, question 45Passage The End of an Era
The End of an Era
(1) In 2004, the National Aeronautics and Space Administration (NASA) landed a rover, or robotic vehicle, named Opportunity on the surface of Mars. (2) The rover’s mission was to search for evidence of water and life on the planet. (3) The rover was designed to gather data on Mars for about 90 days, but Opportunity’s assignment did not come to an end until nearly 15 years later in 2019.
(4) During the rover’s mission, a high-resolution camera on the rover’s robotic arm took magnified photographs of the surface of Mars. (5) The photographs revealed small round rocks scattered across the surface of the planet. (6) The scientists nicknamed these rocks “blueberries” based on the rocks’ resemblance to the fruit. (7) These rocks were important because their spherical shape suggested that liquid water may have flowed over them for a substantial amount of time.
(8) Opportunity continued to provide valuable data about craters and other surface features. (9) Throughout the mission, the rover traveled a total of 28.06 miles across Mars’ surface. (10) When Opportunity had traveled nearly the length of a marathon, scientists celebrated the accomplishment by naming the valley that the rover was in Marathon Valley. (11) However, in 2018, a dust storm spread all over the planet, putting the rover’s progress on hold.
(12) Prior to this planet-wide dust storm, minor dust storms had periodically deposited a layer of dust onto the solar panels of the rover. (13) These prevented it from charging its batteries. (14) Scientists then had to rely on the passing winds and dust devils to clean off the solar panels. (15) After the massive 2018 dust storm subsided, scientists expected to be able to reestablish communication with Opportunity. (16) They made repeated attempts but to no avail. (17) In 2019, NASA finally declared Opportunity’s mission complete.
(18) Opportunity was an important asset in scientists’ study of Mars; it returned valuable data about our neighbor planet and survived powerful dust storms. (19) NASA described the mission of Opportunity as “one of the most successful and enduring feats of interplanetary exploration.” (20) Even though this rover’s journey ended, other rovers still roam the surface of Mars.
Question
Which revision of sentence 11 best maintains the formal style established in the passage?
- AHowever, in 2018, a dust storm covered the planet, bringing the rover’s progress to a standstill.
- BHowever, in 2018, a dust storm shrouded the planet, impermanently halting the rover’s progress.
- CHowever, in 2018, a dust storm enveloped the whole of the planet, arresting the rover’s progress for a time.
- DHowever, in 2018, a dust storm covered up the whole planet, which quickly brought a stop to the progress of the rover.
Show the answer
Correct answer: A
The question asks for the revision of sentence 11 that best maintains the formal style established in the passage.
A. CORRECT. This sentence uses clear and formal writing throughout. The phrase “covered the planet” is accurate and formal without being overly poetic, and “standstill” is a precise word for putting something “on hold,” as expressed by the original sentence, while maintaining the formal style of the passage.
B. Incorrect. Although the sentence is formal in style, the word “shrouded” is overly poetic, and the phrase “impermanently halting” is too stilted and formal for the style and tone of the passage.
C. Incorrect. Although the sentence is formal in style, the words “enveloped” and “arresting” are overly poetic, especially when used in the same sentence, and the phrases “the whole of the planet” and “for a time” are needlessly wordy and imprecise, compared with the formal scientific language of the passage.
D. Incorrect. The phrases “covered up the whole planet” and “quickly brought a stop to the progress of the rover” are less formal and unnecessarily wordy, compared with the formal style established by the rest of the passage.
Question analysis
This style question asks which revision of sentence 11, about the 2018 dust storm that covered Mars and stopped the Opportunity rover, best maintains the formal style of the passage. All four versions say the same thing, so students must compare word choice and wordiness and decide which one reads like the rest of the passage.
- Grade level
- Grade 8 reading and task
- Compared with grade 7
- Above grade 7 Keeping a formal style is grade 7 writing work, usually tested by spotting slang or casual wording. Here all four revisions keep the meaning and differ in register by degrees, so students must judge the passage's own style closely, more than typical.
- Estimated difficulty
- Hard: combines ideas, needs a plan, and has more than one tempting wrong answer.
- Thinking it demands
- Depth of knowledge 2, skills and concepts · mainly evaluate
- What makes it hard
- Something you must already know moderate
- Every choice must be checked moderate
- Hard words minor
- Evidence
- Answered from one sentence or line
- Reading level
- Passage: about grade 11, 337 words; question and choices: about grade 9, 80 words.
- Students, last 30 days
- Not enough answers yet to show (it takes 10).
Why it is hard, traps and wrong answers (shows the answer)
Why it is hard
The question turns on what “formal” means. Many students equate it with impressive words and choose the revision with “enveloped” and “arresting,” or the one with “shrouded,” missing that both are more poetic than a passage that reports dates and distances. The casual revision is easy to reject, so the real test is preferring the plainest formal sentence to the grandest one.
Something you must already know moderate Working it out
Students must know that a formal informational style is plain and precise, so words such as “shrouded,” “enveloped” and “arresting” are too ornate for a passage that reports miles and dates. (Anderson & Krathwohl, 2001)
Every choice must be checked moderate Choosing the answer
All four revisions keep the meaning of sentence 11 and differ only in register and length, so each must be heard against the passage’s voice rather than checked for errors. (Embretson & Wetzel, 1987)
Hard words minor Understanding the question
“Impermanently,” “shrouded” and “arresting,” in its sense of stopping, are uncommon words, and students must judge how they sound in the passage, not only what they mean. (Perfetti, 2007; Freedle & Kostin, 1993)
Strategy: Reread a few sentences around sentence 11 to hear the passage's voice, then check each revision for casual phrasing, needless words and words that would sound out of place in that voice.
Traps
- Wordy, vague or informal: A revision is grammatical but wordy, imprecise or too casual for the passage.
The wrong answers, classified
B Wordy, vague or informal (Connors & Lunsford, 1988)
Equates formal with elevated, so “shrouded” and “impermanently halting” seem best, though both are stilted and poetic beside the passage’s plain reporting of facts.
C Wordy, vague or informal (Connors & Lunsford, 1988)
Avoids casual words, but “enveloped” and “arresting” are poetic, and “the whole of the planet” and “for a time” add words the plain version does without.
D Wordy, vague or informal (Connors & Lunsford, 1988)
Keeps the meaning, but the casual “covered up” and the roundabout “brought a stop to the progress of the rover” make it wordier and less formal.
Working it out, step by step
Figure out what the question asks
This question asks which version of sentence 11 keeps the passage’s formal style. Formal writing is serious and clear, like a textbook. It avoids slang and casual words. But formal doesn’t mean fancy. Formal writing about science uses plain, exact words. For example, The game got called off is casual. The contest was halted indefinitely is too fancy. The game was canceled is formal and plain.
Hear the passage’s voice
Sentence 9 says “the rover traveled a total of 28.06 miles across Mars’ surface.” Sentence 12 says minor storms “deposited a layer of dust onto the solar panels.” The words are exact and plain. The passage gives dates and numbers. It doesn’t paint poetic pictures.
Check each revision
- A is right. “Covered the planet” is plain and exact. A standstill is a complete stop, a clear way to say “on hold.”
- B is wrong. “Shrouded” is poetic. A shroud is a cloth wrapped around a body. “Impermanently halting” sounds stiff and odd.
- C is wrong. “Enveloped” and “arresting” are fancy words. Here arresting means stopping. “The whole of the planet” and “for a time” add extra words.
- D is wrong. “Covered up” is casual. “Brought a stop to the progress of the rover” is wordy, or longer than it needs to be.
Watch out: Many students think formal means big words, so they choose C. But a passage of dates and miles calls for plain words.
Choose the answer
Only A is both formal and plain, like the rest of the passage. So the answer is A: “However, in 2018, a dust storm covered the planet, bringing the rover’s progress to a standstill.”
Why this answer and not the closest wrong one
C is the closest wrong answer, because it has no slang and sounds serious. But “enveloped” and “arresting” are poetic, and “the whole of the planet” is wordy. The passage reports facts in plain words. A says the same thing in the plainest formal way.
More questions like this
The original DOE question
The passage “The End of an Era” as printed (page 60)
Question 3 of 6
2026 Practice Test C English, question 24Passage Bird Talk
Bird Talk
by Carl Sandburg
And now when the branches were beginning to be heavy,
It was the time when they once had said, “This is the
beginning of summer.”
The shrilling of the frogs was not so shrill as in the
first weeks after the broken winter;
The birds took their hops and zigzags a little more
anxious; a home is a home; worms are worms.
The yellow spreads of the dandelions and buttercups
reached across the green pastures.
Tee whee and tee whee came on the breezes, and the grackles
chuzzled their syllables.
And it was the leaves with a strong soft wind over them
that talked most of all and said more than any others
though speaking the fewest words.
It was the green leaves trickling out the gaunt nowhere
of winter, out on the gray hungry branches—
It was the leaves on the branches, beginning to be heavy,
who said as they said one time before, “This is the be-
ginning of summer.”
We shall never blame the birds who come
where the river and the road make the Grand Crossing
and talk there, sitting in circles talking bird talk.
If they ask in their circles as to who is here
and as to who is not here and who used to be here,
Or if instead of counting up last year as against
this year, they count up this year as against next
year, and have their bird chatter about who is here
this year who won’t be here next year,
We shall never blame the birds.
If I have put your face among leaf faces, child,
Or if I have put your voice among bird voices,
Blame me no more than the bluejays.
“Bird Talk” by Carl Sandburg—Public domain.
Question
Throughout the poem, the poet conveys the speaker’s point of view by
- Agradually moving the speaker’s attention from one element of nature to another.
- Bproviding the speaker’s motivation for describing the landscape in great detail.
- Chighlighting the speaker’s emotional response as each season passes.
- Dshifting the speaker’s focus from external observations to personal reflection.
Show the answer
Correct answer: D
This question asks for an explanation of how the poet conveys the speaker’s point of view on the natural world and the change of seasons as presented in the poem.
A. Incorrect. Though in the first stanza the speaker describes various elements of nature such as branches, frogs, birds, flowers, and leaves, these elemental shifts are not precisely gradual and occur only in the first stanza. Further, the first stanza, though appreciative of the natural world, is primarily descriptive and does not develop the speaker’s perspective to the degree that other parts of the poem do.
B. Incorrect. While it may be inferred that the speaker describes the landscape to such a degree because it has revealed a seasonal shift, that this is indeed the speaker’s motivation is never explicitly conveyed by the poet.
C. Incorrect. Multiple seasons do not pass in the poem; only the shift to the “ ‘beginning of summer’ ” (line 3) occurs in an endless cycle. Further, the speaker does not reveal an emotional response; it is the responses of nature that the speaker describes.
D. CORRECT. The first stanza is the speaker’s observations of the natural world embracing a new season. In the second stanza, the speaker begins to reflect on how the natural world, as embodied by the birds, calmly accepts seasonal change in its perpetual sameness. The reflection continues in the third stanza, where it is revealed that the speaker has been addressing these observations to a child.
Question analysis
This point-of-view question asks how the poet of “Bird Talk” conveys the speaker’s point of view throughout the poem. Students must keep in mind the long opening description of early summer and the two shorter stanzas after it, and decide which description of the poet’s method holds from the first line to the last.
- Grade level
- Grade 8 reading and task
- Compared with grade 7
- Above grade 7 Grade 7 point-of-view questions often ask what a speaker thinks. This one asks how the poet conveys that view across all three stanzas of a long free-verse poem, and the choices name methods in general terms, closer to grade 8 work.
- Estimated difficulty
- Hard: combines ideas, needs a plan, and has more than one tempting wrong answer.
- Thinking it demands
- Depth of knowledge 3, strategic thinking · mainly analyze
- What makes it hard
- Evidence in several places moderate
- A very close wrong answer moderate
- How, not what moderate
- Figurative or literary language minor
- Evidence
- Answered from the whole text
- Reading level
- Passage: 296 words (a poem; reading level not measured); question and choices: about grade 10, 54 words.
- Students, last 30 days
- Not enough answers yet to show (it takes 10).
Why it is hard, traps and wrong answers (shows the answer)
Why it is hard
The first stanza takes up 19 of the poem’s 32 lines and moves steadily from branches to frogs, birds, flowers and leaves, so a choice that describes it alone feels right. The point of view shows only when the poem turns to “We” and then to “I” addressing a child, and that third stanza is three hard lines. Students must keep the whole poem’s course in mind and choose the method that holds from first line to last.
Evidence in several places moderate Working it out
The answer depends on all three stanzas at once: the long catalog of the season in lines 1–19, the shift to “We shall never blame the birds,” and the closing “If I have put your face … child.” (Kirsch & Mosenthal, 1990; Gorin & Embretson, 2006)
A very close wrong answer moderate Choosing the answer
The choice about moving from one element of nature to another and the key both describe a shift in the speaker’s attention; they differ in what shifts, nature to nature or the outside world to the speaker’s own thoughts. (Embretson & Wetzel, 1987; Gorin & Embretson, 2006; Ascalon et al., 2007)
How, not what moderate Working it out
The stem asks how the poet conveys a point of view, a method, so a choice must describe what the speaker does across the poem, not what the speaker sees. (Anderson & Krathwohl, 2001)
Figurative or literary language minor Understanding the question
The last stanza is cryptic, “Blame me no more than the bluejays,” and students who miss that the speaker is now talking about putting a child into the poem lose the move to reflection. (Graesser, Singer & Trabasso, 1994; Kintsch, 1998)
Strategy: Write one phrase for what the speaker attends to in each stanza, then keep only a choice that describes the whole sequence, not one stanza.
Traps
- Too narrow: A single detail offered as the central idea or a summary, or a summary that keeps minor details and leaves out an essential part.
- Reads too much in: A reasonable-sounding conclusion that goes further than the text allows.
- Twists what the text says: Uses the text's topic and ideas but changes what it says: who did it, how much, when, or why.
The wrong answers, classified
A Too narrow (King et al., 2004)
Describes the first stanza well, its walk from branches to frogs, birds, flowers and leaves, but misses the later turn to “We” and to the speaker’s own “I.”
B Reads too much in (Graesser, Singer & Trabasso, 1994)
Supplies a reason for all the description, perhaps from the closing words to a child, but the speaker never says why the landscape is described, and the reflection is not a motive.
C Twists what the text says (King et al., 2004)
Sees that the poem follows nature through a change of season but makes it many seasons and hands the creatures’ reactions, such as the birds’ anxious hops, to the speaker as feelings.
Working it out, step by step
Figure out what the question asks
This asks about point of view: how the speaker, the voice talking in the poem, sees things. It also asks how the poet shows that view across the whole poem. So look at what the speaker pays attention to in each of the three stanzas. A stanza is a group of lines set apart by a blank line.
Follow the speaker through the stanzas
- Stanza 1, lines 1–19: the speaker describes the world outside. There are branches, frogs, birds, flowers and leaves at the start of summer.
- Stanza 2, lines 20–29: the speaker starts to judge and think. “We shall never blame the birds.”
- Stanza 3, lines 30–32: the speaker says “I” and talks to a child: “If I have put your face among leaf faces, child.”
Name the change in focus
The poem starts with external observations, or things the speaker sees and hears outside. It ends with personal reflection, or the speaker’s own thoughts. In the last stanza, the speaker admits to putting a child’s face and voice into the poem. The speaker asks to be blamed “no more than the bluejays.” Since “We shall never blame the birds,” that means not at all. This move from looking outward to looking inward is how the speaker’s view comes through.
Check each choice
- A does not fit. Moving from branches to frogs to birds happens only in stanza 1. It misses the turn to “We” and “I.”
- B does not fit. The speaker never says why the landscape is described.
- C does not fit. Only one change of season happens, the start of summer. The anxious feelings belong to the birds, not the speaker.
- D fits. The speaker moves from describing nature to thinking about it.
Watch out: A describes stanza 1 very well. But the question says “Throughout the poem,” so the answer must cover all three stanzas.
Choose the answer
The speaker starts by watching nature and ends by thinking aloud to a child. So the answer is D, “shifting the speaker’s focus from external observations to personal reflection.”
Why this answer and not the closest wrong one
A is the closest wrong choice. Stanza 1 really does move from one part of nature to another. But that is only 19 of the 32 lines. In stanzas 2 and 3, the speaker turns to “We” and then “I,” and shares personal thoughts. Only D describes the speaker’s path from the first line to the last.
More questions like this
The original DOE question
The passage “Bird Talk” as printed (page 32)
Question 4 of 6
2018 Test A Math, question 40Question
In the set of consecutive integers from 12 to 30, inclusive, there are four integers that are multiples of both 2 and 3. How many integers in this set are multiples of neither 2 nor 3?
- A5
- B6
- C13
- D15
Show the answer
Correct answer: B
The question asks for integers from 12 to 30 that are not divisible by 2 or 3. The set of consecutive integers is
{12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30}
Since all even numbers are divisible by 2, eliminate all even numbers, leaving the odd numbers in the set:
{13, 15, 17, 19, 21, 23, 25, 27, 29}
Eliminate those integers that are multiples of 3 (15, 21, and 27). The remaining integers are:
{13, 17, 19, 23, 25, 29}
Therefore, there are 6 numbers in the set that are multiples of neither 2 nor 3.
Question analysis
This number properties question takes the integers from 12 to 30, inclusive, and asks how many are multiples of neither 2 nor 3. Students must count the whole set, remove multiples of 2 and of 3 without removing any number twice, and count what remains. Inclusive endpoints and the overlap make it easy to miscount.
- NYS standards
- 6.NS.4 common factors and multiples
- Grade level
- Grade 6 content, by NYS standard
- Compared with grade 7
- Above grade 7 Multiples are sixth-grade content, but grade 7 problems rarely ask students to count a set under two overlapping conditions. The inclusive range and the numbers that are multiples of both make this longer and trickier than usual.
- Estimated difficulty
- Hard: combines ideas, needs a plan, and has more than one tempting wrong answer.
- Thinking it demands
- Depth of knowledge 2, skills and concepts · mainly apply
- What makes it hard
- Much to keep track of moderate
- A very close wrong answer moderate
- Solution
- 3 steps
- Reading level
- Question and choices: about grade 9, 30 words.
- Students, last 30 days
- Not enough answers yet to show (it takes 10).
Why it is hard, traps and wrong answers (shows the answer)
Why it is hard
The question gives the overlap, four multiples of both 2 and 3, which invites a subtraction method with three places to go wrong: the count of the set, the overlap, and the final complement. Each of those errors has its own choice. Listing the 19 numbers and crossing out evens and then odd multiples of 3 is slower to describe but faster and safer to do.
Much to keep track of moderate Working it out
Each of the 19 integers must be checked against two conditions, and the four multiples of 6 meet both, so they must be removed once, not twice. (Sweller, 1988; Carpenter, Just & Shell, 1990)
A very close wrong answer moderate Choosing the answer
The choices 5 and 6 differ by one, the result of counting 30 − 12 = 18 integers instead of 19, so only counting the inclusive set exactly separates them. (Embretson & Wetzel, 1987; Gorin & Embretson, 2006; Ascalon et al., 2007)
Strategy: Cross out every even number first, then cross out the odd multiples of 3 that remain, and count the survivors; listing all nineteen numbers is quick enough.
Traps
- Answers a different question: A choice is right for another quantity: the other unknown, the rest instead of the part, the part instead of the whole.
- Counting the ends: Inclusive or exclusive ends, fence posts, consecutive numbers: an answer that is one too many or too few, or an endpoint drawn open where it belongs closed (or the reverse).
The wrong answers, classified
A Counting the ends (Brown & Burton, 1978)
Counts 30 − 12 = 18 integers instead of 19, then subtracts the 13 multiples of 2 or 3 and gets 5.
C Answers a different question (King et al., 2004; Hegarty, Mayer & Monk, 1995)
Counts the integers that are multiples of 2 or 3, the 13 to be crossed out, and gives that count instead of the 6 left over.
D Misreads the question (Hegarty, Mayer & Monk, 1995)
Subtracts only the four multiples of both 2 and 3 from the 19 integers, reading "neither 2 nor 3" as "not both 2 and 3".
Worked solution, step by step
Formulas used
- Counting whole numbers in a list
- a is the first number and b is the last. n is how many whole numbers there are, counting both ends. You add 1 because subtracting counts the gaps, and there is one more number than gaps.
Sort out the question
The set is every integer (whole number) from 12 to 30. “Inclusive” means 12 and 30 are both in.
A multiple of 2 is an even number. A multiple of 3 is a number in the 3 times table. You need the numbers that are neither: not even, and not in the 3 times table.
Count the numbers in the set
There are 19 integers. Watch out: 30 − 12 = 18 forgets one end. That slip leads to choice A, 5.
Cross out the even numbers
Every even number is a multiple of 2, so remove them all. The odd numbers are left:
13, 15, 17, 19, 21, 23, 25, 27, 29
That is 9 numbers.
Cross out the multiples of 3
Check each odd number for 3. A quick test: add its digits. If the sum is in the 3 times table, so is the number. That removes 15, 21 and 27. These are left:
13, 17, 19, 23, 25, 29
Watch out: only 12, 18, 24 and 30 are multiples of both. Removing just those gives 19 − 4 = 15, choice D. “Neither” means you remove every multiple of 2 and every multiple of 3.
Count what is left
Six numbers are left. Watch out: 13 is how many you crossed out, choice C. The question asks for the ones left. So the answer is B, 6.
Check your answer
Count another way. Of the 19 numbers, 10 are even. Of the 9 odd ones, 3 are multiples of 3. So 10 + 3 = 13 are crossed out, and 19 − 13 = 6 are left. Same answer.
More questions like this
The original DOE question
Question 5 of 6
2026 Practice Test D Math, question 48Question
The perimeter of square W is twice the perimeter of equilateral triangle X. What is the ratio of the length of one side of square W to the length of one side of equilateral triangle X?
- A3:8
- B2:3
- C3:2
- D2:1
Show the answer
Correct answer: C
First, set up the ratio of the perimeter of the square to the triangle as 2:1 because the question states that the perimeter of the square is twice the perimeter of the triangle.
Recognizing that the square has 4 equal sides and that an equilateral triangle has 3 sides, use division to find the ratio of the sides.
Perimeter:
Sides:
Question analysis
The perimeter of square W is twice the perimeter of equilateral triangle X, and students find the ratio of a side of the square to a side of the triangle. This ratio question uses perimeters of regular shapes with no lengths given. Turning a comparison of perimeters into one of sides, and keeping the ratio in the order asked, are the tricky parts.
- NYS standards
- Grade level
- Grade 7 content, by NYS standard
- Compared with grade 7
- Above grade 7 Grade 7 ratio problems usually supply numbers to work with. This one gives only a relationship between two perimeters, so students must bring in the number of sides of each shape themselves and keep the ratio in the order asked.
- Estimated difficulty
- Hard: combines ideas, needs a plan, and has more than one tempting wrong answer.
- Thinking it demands
- Depth of knowledge 2, skills and concepts · mainly apply
- What makes it hard
- Turning words into math moderate
- Variables instead of numbers moderate
- A very close wrong answer minor
- Solution
- 3 steps
- Reading level
- Question and choices: about grade 9, 36 words.
- Students, last 30 days
- Not enough answers yet to show (it takes 10).
Why it is hard, traps and wrong answers (shows the answer)
Why it is hard
The question turns a statement about perimeters into a ratio of sides, and the natural guess, that the sides keep the perimeters’ 2 to 1, ignores that the square shares its perimeter among 4 sides and the triangle among 3. Choosing a triangle perimeter such as 12 makes the comparison concrete. The order of the ratio still has to be checked at the end, because its reverse is listed too.
Turning words into math moderate Understanding the question
“The perimeter of square W is twice the perimeter of equilateral triangle X” must become 4s = 2 × 3t, with the 2 on the triangle’s side; written backward, it gives the triangle the larger perimeter. (Hegarty, Mayer & Monk, 1995; Koedinger & Nathan, 2004)
Variables instead of numbers moderate Understanding the question
No side length is given, so students must either work with letters for the two sides or choose a convenient perimeter themselves, such as 12 for the triangle. (Koedinger & Nathan, 2004; Enright, Morley & Sheehan, 2002)
A very close wrong answer minor Choosing the answer
The ratios 3:2 and 2:3 use the same two numbers, so only keeping the square’s side first, as the question orders it, separates the answer from its reverse. (Embretson & Wetzel, 1987; Gorin & Embretson, 2006; Ascalon et al., 2007)
Strategy: Pick an easy side length for the triangle, find its perimeter, double that for the square, divide by the square's number of sides, and write square to triangle.
Traps
- Misunderstands the concept: A wrong belief about a concept: that percents can be added, that area grows like length, that averages can be averaged, that a bigger denominator means a bigger fraction.
- Wrong operation: Adds instead of multiplying, divides the wrong way round, turns a ratio or rate upside down, or undoes a step in the wrong direction (subtracts what should be added back).
- Equation written backwards: Writes a comparison the wrong way round, word for word: "six times as many students as professors" as 6S = P. The bigger quantity gets the bigger number.
The wrong answers, classified
A Equation written backwards (Clement, Lochhead & Monk, 1981)
Writes the comparison backward, 2 × 4s = 3t, giving the triangle the larger perimeter, so the ratio of the sides comes out 3:8.
B Wrong operation (Hegarty, Mayer & Monk, 1995; King et al., 2004)
Finds the right relationship but turns the ratio upside down, giving the triangle’s side to the square’s instead of the square’s side first.
D Misunderstands the concept (Smith, diSessa & Roschelle, 1993; De Bock et al., 1998; Ni & Zhou, 2005)
Assumes the sides are in the same ratio as the perimeters, 2:1, ignoring that the square has 4 sides and the triangle only 3.
Worked solution, step by step
Formulas used
- Perimeter of a square
- P is the perimeter, the distance around the shape. s is the length of one side. A square has 4 equal sides, so its perimeter is 4 times one side.
- Perimeter of an equilateral triangle
- An equilateral triangle has 3 equal sides. t is the length of one side. So its perimeter is 3 times one side.
- Ratio
- A ratio compares two amounts in order. a : b means a compared with b. The order matters, so write the amounts in the order the question names them.
Sort out the question
Square W has a perimeter twice as long as the perimeter of triangle X. Equilateral means all 3 sides of X are equal.
You need the ratio of one side of the square to one side of the triangle, in that order. No lengths are given, so you can pick a size to try.
Pick a size for the triangle
Choose an easy side length for the triangle, such as 2 units. All 3 sides are 2, so its perimeter is:
Find the square’s side
The square’s perimeter is twice the triangle’s:
The square has 4 equal sides, so divide by 4:
Each side of the square is 3 units.
Write the ratio in order
The square comes first, then the triangle. Their sides are 3 and 2, so the ratio is 3 : 2.
Watch out: 2 : 1, choice D, compares the perimeters, not the sides. The square splits its perimeter into 4 sides, the triangle into only 3. Choice B, 2 : 3, puts the triangle first. Choice A, 3 : 8, comes from giving the triangle the bigger perimeter.
So the answer is C, 3:2.
Check your answer
Try a different size. Give the triangle sides of 4. Its perimeter is 12, so the square’s is 24. Each side of the square is . The ratio 6 : 4 simplifies to 3 : 2. The size does not change the ratio.
More questions like this
The original DOE question
Question 6 of 6
2024 Test A Math, question 16Question
A truck rental company charges a one-time fee of $40 plus $1 per mile driven. Dalia rented a truck and used a coupon for 20% off the total rental cost. After the coupon was applied, she spent a total of $60. How many miles did she drive?
- A8
- B20
- C32
- D35
Show the answer
Correct answer: D
Let m equal the miles driven during Dalia’s rental. The total cost, c, can be expressed as an equation.
Dalia spent a total of $60, which included a 20% off coupon. Find the cost before the coupon by dividing the final cost ($60) by the percentage paid (80%):
Use $75 as the total cost to find m.
Dalia drove 35 miles.
Question analysis
A multistep word problem about a truck rental that costs a $40 fee plus $1 per mile, with a 20% off coupon applied to the total. Given that Dalia paid $60 after the coupon, students find how many miles she drove. Undoing the discount correctly before removing the fixed fee is the hard part.
- Grade level
- Grade 7 content, by NYS standard
- Compared with grade 7
- Above grade 7 Grade 7 students solve two-step equations and work with discounts, usually separately. This combines them and makes students undo a 20% discount starting from the price paid, a reversal many grade 7 students have not practised.
- Estimated difficulty
- Hard: combines ideas, needs a plan, and has more than one tempting wrong answer.
- Thinking it demands
- Depth of knowledge 2, skills and concepts · mainly apply
- What makes it hard
- Turning words into math moderate
- Combines ideas moderate
- A very close wrong answer moderate
- Solution
- 3 steps
- Reading level
- Question and choices: about grade 5, 43 words.
- Students, last 30 days
- Not enough answers yet to show (it takes 10).
Why it is hard, traps and wrong answers (shows the answer)
Why it is hard
Two ordinary skills, undoing a discount and solving a two-step equation, are stacked, and the first runs in reverse. The natural way to undo 20% off is to add 20% back, which gives $72 instead of $75 and a choice three miles from the answer. Students who check by applying the coupon to the full cost of 40 + 35 = 75 dollars see at once that 80% of it is 60.
Turning words into math moderate Understanding the question
The sentence "After the coupon was applied, she spent a total of $60" makes 60 the price after 20% off, so it is 80% of the full cost, 40 + m. (Hegarty, Mayer & Monk, 1995; Koedinger & Nathan, 2004)
Combines ideas moderate Working it out
A percent discount has to be undone before the fee-plus-mileage equation can be solved: 60 ÷ 0.8 = 75, then 75 − 40 = 35 miles. (Embretson, 1998; Daniel & Embretson, 2010)
A very close wrong answer moderate Choosing the answer
The choices 32 and 35 are three miles apart, too close to tell apart by estimate; only dividing 60 by 0.8, rather than adding 20% of 60, separates them. (Embretson & Wetzel, 1987; Gorin & Embretson, 2006; Ascalon et al., 2007)
Strategy: Since $60 is 80% of the full cost, divide 60 by 0.80 to find the cost before the coupon, then subtract the $40 fee to get the miles.
Traps
- Percent of the wrong amount: Finding the whole from a part, or a percent change measured from the wrong starting amount.
- Misreads the question: Misses or misreads a condition or a word in the question: "at least", "each", "remaining", "not".
The wrong answers, classified
A Wrong operation (Hegarty, Mayer & Monk, 1995; King et al., 2004)
Takes 20% off the $60 again, 60 × 0.8 = 48, instead of undoing the discount, then subtracts the $40 fee to get 8 miles.
B Misreads the question (Hegarty, Mayer & Monk, 1995)
Ignores the coupon and treats the $60 as the full cost, so it subtracts the $40 fee and gets 20 miles.
C Percent of the wrong amount (Parker & Leinhardt, 1995)
Undoes the coupon by adding 20% of $60 to get $72, though the 20% was taken of the larger pre-coupon cost, then subtracts the $40 fee.
Worked solution, step by step
Formulas used
- Rental cost
- c is the full cost in dollars, before any coupon. 40 is the one-time fee, paid once no matter how far you drive. m is the number of miles, and each mile costs 1 dollar.
- Price after a discount
- The full cost is the price before the discount. p is the percent taken off. You pay what is left: 100% minus p%. For 20% off you pay 80%, so you multiply by 0.80.
Sort out the question
The truck costs a $40 fee, plus $1 for each mile. Dalia’s coupon took 20% off the total. After the coupon, she paid $60. You need how many miles she drove. The $60 is the price after the discount, not the full cost.
Write what she paid
20% off means she paid what was left of the full cost.
As a decimal, 80% is 0.80.
Undo the discount
To undo times 0.80, divide by 0.80. Move the decimal point one place in both numbers to make it easier.
The full cost was $75. Watch out: the 20% was taken off the full cost, not off $60. Adding 20% of $60 gives $72 and leads to 32 miles, choice C. Taking 20% off $60 again leads to 8 miles, choice A.
Find the miles
She drove 35 miles. Watch out: do not skip the coupon. Using $60 as the full cost gives 20 miles, choice B. So the answer is D, 35.
Check your answer
Go forward. 35 miles cost $35. Add the $40 fee to get $75. The coupon takes off 20% of $75, which is dollars. Then . That is exactly what she paid.
More questions like this
The original DOE question
