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 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 2 of 6
2026 Practice Test B English, question 41Passage Letter from Brooklyn
Letter from Brooklyn
by Jacob Scheier
I can already see how this will end.
How I will grow tired of the bridge’s
steep incline, and the absent-minded tourists
wandering into the bicycle path.
The weather will turn cold.
But that all happens later.
For now it is the early edge of fall,
leaves green still while the air narrows,
is slightly crisp, almost grazing
the hair of my arm like a passing stranger,
as though the air has been forced into intimacy
by the brevity of daylight.
But when it starts darkening at 4,
this closeness, I know, will be a felt distance,
like someone drawing your attention
to their lack of intimacy.
These days I am still walking at a cathedral pace
beneath the branches bending across avenues,
brownstones like rows of lived-in chapels,
like a pop-up picture book I could have had as a child,
but didn’t. How Brooklyn makes me nostalgic
for the moment I am walking inside of.
These late afternoons filled
with a loneliness that makes me feel
distinctly myself, and an awareness
of how rare that is.
“Letter from Brooklyn” from LETTER FROM BROOKLYN: POEMS by Jacob Scheier, published by ECW Press. Copyright © 2013 by Jacob Scheier All rights reserved.
brevity: briefness
cathedral: meditative
chapels: private places of prayer or worship
nostalgic: yearning for the past
Question
Read these lines from the poem.
I can already see how this will end. (line 1)
How Brooklyn makes me nostalgic
for the moment I am walking inside of. (lines 21–22)
The lines develop a central idea of the poem by
- Asuggesting the speaker’s desire to find a way to break free from the repetitive pattern of daily life.
- Brevealing the speaker’s feelings of disappointment over the predictable change in season.
- Cemphasizing the speaker’s awareness of the future significance of the present moment in the setting.
- Dshowing the speaker’s anticipation of specific emotions caused by an intimate knowledge of the setting.
Show the answer
Correct answer: C
The question asks how line 1 and lines 21–22 develop a central idea of the poem.
A. Incorrect. Although these lines suggest that life is governed by repetitive patterns, such as the change of seasons, they do not suggest that the speaker wishes to break free from these natural cycles of change, and a desire for freedom is not a central idea of the poem.
B. Incorrect. Although the speaker acknowledges that colder weather will inevitably bring disappointment, the speaker does not suggest in these lines that the predictability of changing weather is itself disappointing. Rather, the speaker recognizes the value of enjoying the present moment.
C. CORRECT. These lines connect the present warmer weather with the future colder weather and develop the central idea that the present “moment I am walking inside of” must be embraced because the speaker will be “nostalgic” for it in the future.
D. Incorrect. In these lines, the speaker is aware that specific emotions will occur in the future, during cold weather, but this awareness is only part of the more complex central idea of the poem, which is that current emotions and feelings must be recognized, experienced, and appreciated.
Question analysis
This central-idea question pairs the first line of “Letter from Brooklyn” with lines 21–22, where Brooklyn makes the speaker nostalgic “for the moment I am walking inside of,” and asks how they develop a central idea of the poem. Students must link excerpts from opposite ends of the poem, untangle a paradoxical image and choose among four abstract statements.
- Grade level
- Grade 8 reading and task
- Compared with grade 7
- Above grade 7 Grade 7 students analyze how lines develop a central idea. Here two excerpts twenty lines apart must be read together, one of them built on a paradox, and the four choices are long and abstract, well beyond typical grade 7 work.
- Estimated difficulty
- Among the hardest on the SHSAT: a non-obvious approach, heavy reading, or a well-hidden trap.
- Thinking it demands
- Depth of knowledge 3, strategic thinking · mainly analyze
- What makes it hard
- Figurative or literary language major
- A very close wrong answer moderate
- Evidence in several places moderate
- Evidence
- Answered from several paragraphs or stanzas
- Reading level
- Passage: 217 words (a poem; reading level not measured); question and choices: about grade 7, 99 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
This is among the hardest questions in the set because the two excerpts must be joined through a paradox and then matched to four long, abstract statements. Line 1 foresees an ending; lines 21–22 miss a moment while it is still happening, so both look at now from the future. Students who see only the foresight pick the choice about anticipated emotions, while those who hear gloom in “how this will end” settle on disappointment or a wish to escape.
Figurative or literary language major Understanding the question
Lines 21–22 are a paradox: “nostalgic,” glossed as yearning for the past, is aimed at “the moment I am walking inside of,” so the speaker already feels the present as a future memory. (Graesser, Singer & Trabasso, 1994; Kintsch, 1998)
A very close wrong answer moderate Choosing the answer
The choice about anticipating “specific emotions” shares the key’s link between future and present; it differs by tracing those feelings to knowing the setting well, which neither excerpt says. (Embretson & Wetzel, 1987; Gorin & Embretson, 2006; Ascalon et al., 2007)
Evidence in several places moderate Working it out
The excerpts are the poem’s first line and lines 21–22, twenty lines apart, and what joins them, the speaker looking ahead at the present, shows only when they are read side by side. (Kirsch & Mosenthal, 1990; Gorin & Embretson, 2006)
Strategy: Paraphrase each excerpt on its own, using the glossary's meaning of “nostalgic,” then decide what the first line and the last two share and match that to a choice.
Traps
- Half right: One half of a two-part choice is right and the other is not.
- 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.
- Reads too much in: A reasonable-sounding conclusion that goes further than the text allows.
The wrong answers, classified
A Reads too much in (Graesser, Singer & Trabasso, 1994)
Links “how this will end” and growing tired of the bridge to a dull routine and imagines a wish to escape it, which the poem never expresses.
B Wrong tone or attitude (Graesser, Singer & Trabasso, 1994)
Hears resignation in “I can already see how this will end” and reads it as disappointment with the seasons, missing that the speaker treasures the present walk.
D Half right (King et al., 2004; Thissen, Steinberg & Fitzpatrick, 1989)
Rightly sees the speaker foreseeing feelings in line 1, but traces them to an “intimate knowledge of the setting,” while lines 21–22 long for the present moment itself.
Working it out, step by step
Figure out what the question asks
This question gives two pieces of the poem: line 1 and lines 21–22. You need the central idea they build together. A central idea is the main point the poem keeps working toward. Read each piece alone first, then join them.
Read line 1
Line 1 says “I can already see how this will end.” The speaker looks ahead. Lines 2–5 then list what will come: growing tired of the bridge, and the cold. So the speaker already pictures the future while living in the present.
Read lines 21–22
The lines say “How Brooklyn makes me nostalgic / for the moment I am walking inside of.” The glossary says nostalgic means “yearning for the past.” Yearning means longing. But the speaker longs for now, a moment still happening. That is a paradox, an idea that seems impossible but makes sense. The speaker knows this walk will be a precious memory.
Join the two pieces
Both pieces look at the present from the future. In line 1, the speaker sees the end coming. In lines 21–22, the speaker already misses the walk. So the speaker knows this present moment will matter later. Significance means importance.
Check each choice
- A is wrong. The speaker never wants to break free from daily routine.
- B is wrong. Line 1 can sound gloomy. But the speaker isn’t upset with the seasons. The speaker treasures the walk.
- C is right. The speaker sees that this moment in Brooklyn will be precious later.
- D is wrong. The speaker does foresee feelings. But neither piece says they come from knowing the place well.
Watch out: D gets the looking-ahead part of line 1 right. But lines 21–22 long for the moment itself, not for feelings caused by knowing the city.
Choose the answer
So the answer is C: “emphasizing the speaker’s awareness of the future significance of the present moment in the setting.”
Why this answer and not the closest wrong one
D is the closest wrong answer, because line 1 does show the speaker foreseeing feelings. But D says they come from an “intimate knowledge of the setting.” Neither piece says that. Lines 21–22 miss the moment while it is still happening. C captures that: the present will matter in the future.
More questions like this
The original DOE question
The passage “Letter from Brooklyn” as printed (page 50)
Question 3 of 6
2026 Practice Test A English, question 37Passage 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
A central idea that Lowell was “one of America’s most significant industrial cities” (paragraph 1) is conveyed in the passage primarily through a description of the
- Acanals, mills, and boardinghouses that were built by immigrants.
- Bmill girls and immigrants who comprised Lowell’s workforce.
- Cdevelopment of the mills and the workforce established to support them.
- Dcultural diversity of the people who lived in the area.
Show the answer
Correct answer: C
The question asks which description conveys the central idea that Lowell was “one of America’s most significant industrial cities” (paragraph 1).
A. Incorrect. While the passage does state that the city’s canals, mills, and boardinghouses were built by early immigrants from Ireland, these details do not contribute to the development of the overall idea that Lowell was a significant industrial city.
B. Incorrect. The details about the women and immigrants who worked in the mills are important to the passage, but these details alone do not show that Lowell was a significant industrial city.
C. CORRECT. The details throughout the passage about the development of the mills and the people who worked in them convey the significance of Lowell in early American industry. Paragraph 2 shares details about the businesses that started in the 1800s and contributed to the development of industry in the region (“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”). Then paragraphs 3–6 provide specific details about the people who worked in the mills at different points in time.
D. Incorrect. Although the passage references Lowell’s culturally diverse community (“Young Yankee women, immigrant families, and European tourists all flocked to Lowell to find work at one of the many textile mills” [paragraph 1]), these groups alone are not what marked Lowell as a significant industrial city.
Question analysis
This central idea question asks which kind of description in an article about the Massachusetts mill city of Lowell does most to show that it was one of America's most significant industrial cities. Students need a map of all six paragraphs, because every choice names something the passage really describes, and the question turns on which description does the main work.
- Grade level
- Grade 8 reading and task
- Compared with grade 7
- Above grade 7 Grade 7 students trace how a central idea is developed, usually through a few supporting details. Here the strands to weigh run through six dense paragraphs of dates, mills and worker groups, and the stem is long and passive, so it asks 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 3, strategic thinking · mainly analyze
- What makes it hard
- A very close wrong answer major
- Evidence in several places moderate
- A lot to read minor
- Complex sentences minor
- Evidence
- Answered from the whole text
- Reading level
- Passage: about grade 15, 764 words; question and choices: about grade 10, 63 words.
- Corrected from the DOE handbook
- A grammatical error in the explanation was corrected.
- An inaccurate detail in the explanation was corrected.
- 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
Every choice names something the passage really describes, so truth rules nothing out; the question turns on which description carries the claim that Lowell mattered as an industrial city. Because four of the six paragraphs follow the workers, the workforce alone looks like the passage's main thread, and students who forget paragraph 2's mills take the half for the whole. Diversity and the immigrant builders are real themes too, but neither says anything about Lowell's industrial standing.
A very close wrong answer major Choosing the answer
The workforce choice is the key with one half removed: both describe the people who worked the mills, but only the key also names the development of the mills, which paragraph 2 builds with dates and numbers. (Embretson & Wetzel, 1987; Gorin & Embretson, 2006; Ascalon et al., 2007)
Evidence in several places moderate Working it out
The industrial picture is built in two stages, the canals and mills of paragraph 2 and the successive workforces of paragraphs 3 to 6, so each choice must be measured against the whole passage. (Kirsch & Mosenthal, 1990; Gorin & Embretson, 2006)
A lot to read minor Understanding the question
Six paragraphs pack in mill names, dates from 1821 to the 1950s and a string of worker groups, from Yankee mill girls to Irish, French-Canadian and Greek immigrants. (Kintsch, 1998; Gorin & Embretson, 2006; Freedle & Kostin, 1993)
Complex sentences minor Understanding the question
The stem is a long passive sentence that quotes paragraph 1 inside it and holds the real question, “primarily through a description of the,” until its last words. (Abedi & Lord, 2001; Freedle & Kostin, 1993; Messick, 1989)
Strategy: Note in a phrase what each of the six paragraphs is about, then test each choice against the stem's claim: would that description make a reader see Lowell as a major industrial city?
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.
- True but not the answer: A choice says something accurate about the text that does not answer this question.
The wrong answers, classified
A Too narrow (King et al., 2004)
Seizes on paragraph 5's clause that Irish workers built the canals, mills and boardinghouses, one fact about construction rather than the account of mills and workers that shows Lowell's importance.
B Too narrow (King et al., 2004)
Sees that paragraphs 3 to 6 follow the mill girls and the immigrants who replaced them, but leaves out the mills themselves, the heart of paragraph 2's industrial picture.
D True but not the answer (King et al., 2004; Embretson & Wetzel, 1987)
Recalls paragraph 6's “ethnic melting pot” and paragraph 1's “ethnic neighborhoods,” which are real, but the city's diversity says nothing about its standing as an industrial city.
What was corrected from the DOE handbook, and why
- Explanation: The handbook’s explanation of Option B says “The details about the women and immigrants who worked in the mills is important to the passage.” The subject is “details,” so the site now says “are important.”
- Explanation: The handbook’s explanation of Option C says paragraph 2 describes “the businesses that started in the early 1800s,” but the sentence it then quotes includes “the Suffolk or Wannalancit Mill completed around the 1880s,” late in the century. The site now says “the businesses that started in the 1800s.”
Working it out, step by step
Figure out what the question asks
This is a central idea question. A central idea is a main point that the whole passage builds. The point here is that Lowell was “one of America’s most significant industrial cities.” Significant means important. You need the description that does the most to show this.
Map the six paragraphs
- Paragraph 1: Lowell grows from a farm town into a famous industrial city.
- Paragraph 2: The mills: canals, huge brick buildings, mills started across the 1800s, and by the 1850s, “40 textile mills employing over 10,000 workers.”
- Paragraphs 3 and 4: The Yankee “mill girls” who worked in the mills.
- Paragraphs 5 and 6: The Irish and other immigrants who took their place.
See how the picture is built
The passage shows Lowell’s importance in two parts. First it describes the mills: how they were built and how big they grew. Then it follows the workers who ran them, group after group. Together, the mills and the workforce show a major industrial city. Workforce means all the people who do the work. Either part alone tells only half the story.
Check each choice
- A is wrong. Paragraph 5 does say the Irish built the canals, mills and boardinghouses. But that is one fact in one sentence, not the main description.
- B is wrong. The mill girls and immigrants fill paragraphs 3 to 6. But this choice leaves out the mills themselves, the heart of paragraph 2.
- C is right. It covers both parts: how the mills grew and the workers who kept them running.
- D is wrong. Lowell did become an “ethnic melting pot.” But a mix of cultures doesn’t show that a city was an industrial leader.
Watch out: Four of the six paragraphs are about workers, so B looks like the main thread. It is only half of it.
Choose the answer
The central idea is carried by the growth of the mills plus the workforce gathered to run them. So the answer is C.
Why this answer and not the closest wrong one
B is the closest wrong answer. It matches the second half of C, the people who worked in the mills. But it drops the mills, with their six miles of canals and, by the 1850s, 40 mills. Workers alone don’t make a city an industrial giant. C keeps both halves, so it fits the whole passage.
More questions like this
The original DOE question
The passage “Massachusetts: Lowell National Historical Park” as printed (page 50)
Question 4 of 6
2024 Test B Math, question 17Question
A bowl contains 12 green candies, 4 yellow candies, and some red candies. The probability of choosing a green candy at random is twice as great as the probability of choosing a red candy at random. What is the probability of choosing a yellow candy at random?
- A
- B
- C
- D
Show the answer
Correct answer: A
The probability of choosing a green candy is twice as great as the probability of choosing a red candy. There are 12 green candies. Let r = the number of red candies.
So there are 6 red candies. 12 green candies + 4 yellow candies + 6 red candies = 22 total candies.
There are 4 yellow candies out of a total of 22 candies. So the probability of choosing a yellow candy is
.
Question analysis
A probability question about a bowl of 12 green candies, 4 yellow candies and an unknown number of red ones. A green candy is twice as likely to be picked as a red one, and students find the chance of picking a yellow candy. The missing red count has to be worked out before any probability can be found.
- Grade level
- Grade 6 content, by NYS standard
- Compared with grade 7
- Above grade 7 Simple probability is grade 6 content in New York, and grade 7 problems usually give every count. Working backward from a comparison of two probabilities to a missing count, then forward to a third probability, is 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 2, skills and concepts · mainly apply
- What makes it hard
- Turning words into math moderate
- Combines ideas moderate
- Solution
- 3 steps
- Reading level
- Question and choices: about grade 7, 49 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 withholds the red count, and everything depends on recovering it from the comparison of probabilities. Students who cannot make that step tend to leave red out altogether, while those who find 6 red candies can still slip at the end by using the wrong total or the wrong color. Writing all three counts and the total of 22 before forming any fraction prevents both endings.
Turning words into math moderate Understanding the question
“Twice as great as the probability of choosing a red candy” must become 12 = 2 × the red count, which works only because both probabilities share one total. (Hegarty, Mayer & Monk, 1995; Koedinger & Nathan, 2004)
Combines ideas moderate Working it out
An unknown count has to be found from a ratio before any probability can be written, joining proportional reasoning with probability as a part over the total. (Embretson, 1998; Daniel & Embretson, 2010)
Strategy: Turn twice as likely into a statement about numbers of candies to find the red count, add all three colors for the total, then put the yellow count over that total and simplify.
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.
- Numbers taken from the question: Combines the numbers in the question without a model of the situation, or is simply a number that appears in the question.
The wrong answers, classified
B Misunderstands the concept (Smith, diSessa & Roschelle, 1993; De Bock et al., 1998; Ni & Zhou, 2005)
Finds the 6 red candies but compares the 4 yellow with the 18 green and red ones, 4/18, a part-to-part ratio instead of part to whole.
C Numbers taken from the question (Hegarty, Mayer & Monk, 1995)
Leaves out the red candies, whose number is not given, and divides the 4 yellow by the 16 green and yellow candies.
D Answers a different question (King et al., 2004; Hegarty, Mayer & Monk, 1995)
Finds the 6 red candies and the total of 22 correctly but gives the chance of red, 6/22 = 3/11, instead of yellow.
Worked solution, step by step
Formulas used
- Probability
- P is the probability, the chance that something happens. The top is how many candies are the kind you want. The bottom is how many candies there are in all. Each candy is just as likely to be picked, so this fraction gives the chance.
Sort out what you know
The bowl has 12 green candies, 4 yellow candies and some red candies. You are not told how many are red. Let r be the number of red candies.
The chance of picking green is twice the chance of picking red. You need the probability (the chance) of picking yellow.
Compare green and red
Write each chance with the probability formula.
Green and red have the same bottom number, the total number of candies. So if the chance of green is twice the chance of red, there are twice as many green candies as red ones.
Find the red candies and the total
There are 6 red candies. Now add up all the candies.
There are 22 candies in all. Watch out: do not leave out the red candies just because their number was not given. Using 16 as the total gives 1/4, choice C.
Find the chance of yellow
There are 4 yellow candies out of 22.
Divide the top and the bottom by 2 to simplify. Watch out: the question asks for yellow, not red. 6/22 = 3/11 is the chance of red, choice D. The bottom must be all 22 candies. Using 18 gives 2/9, choice B.
So the answer is A, .
Check your answer
Check the clue. The chance of green is , and the chance of red is . Twelve is twice 6, so green is twice as likely. Also, the three chances add up to 1: .
More questions like this
The original DOE question
Question 5 of 6
2026 Practice Test D Math, question 36Question
Leah has set a goal to read a total of 500 pages of a textbook. The table shows the book page numbers for the reading she did during three days.
DAILY READING LOG
| Day | Pages Read |
|---|---|
| 1 | pages 45–90, inclusive |
| 2 | pages 100–135, inclusive |
| 3 | pages 145–190, inclusive |
What percentage of her 500-page goal did Leah read on these three days? Round your answer to the nearest tenth.
Enter your answer in the space.
Fill-in question: work out the answer and type it as a number.
Show the answer
Correct answer: 25.6%
First, determine the number of pages read each day. Since the pages per assignment are inclusive, subtract the first page from the last page assigned and then add 1 to determine the pages read for each day.
Day 1: pages
Day 2: pages
Day 3: pages
Leah read a total of 128 pages, since .
To determine the percent, express 128 pages out of 500 pages as a fraction.
Question analysis
Leah's daily reading log lists three ranges of textbook pages, each marked inclusive, and her goal is 500 pages. This percent question asks what percentage of the goal she read over the three days, rounded to the nearest tenth and typed in. Counting the pages in each inclusive range correctly is the tricky step before the percent.
- Grade level
- Grade 7 content, by NYS standard
- Compared with grade 7
- Above grade 7 Finding what percent one number is of another is grade 6 and 7 work. This adds three inclusive page ranges to count, which takes more care than subtracting, then a rounding step, all typed with no choices to check against.
- 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
- Something you must already know moderate
- Many steps moderate
- An answer in an unexpected form minor
- Solution
- 4 steps
- Reading level
- Question and choices: about grade 3, 66 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
Counting pages in a range is the whole difficulty; the percent at the end is routine once the total is right. Subtracting first from last feels natural, and here it even rewards the student with a round 25%, so nothing looks wrong. Checking the rule on a tiny range, pages 1 to 3, which is 3 pages and not 2, fixes the count, and the instruction to round to the nearest tenth hints that the answer is not a whole number.
Something you must already know moderate Working it out
Every row says inclusive, but nothing says that pages 45 to 90 hold 90 − 45 + 1 = 46 pages; subtracting alone loses one page on each of the three days. (Anderson & Krathwohl, 2001)
Many steps moderate Working it out
Three page counts, a sum, a division by 500 and a change to a percent come in sequence, and a one-page error in each count carries through to the end. (Daniel & Embretson, 2010; Enright, Morley & Sheehan, 2002)
An answer in an unexpected form minor Choosing the answer
The answer is typed with no choices, and the miscounted total, 125 pages, gives a tidy 25% that looks more finished than the right value with its tenth. (Enright, Morley & Sheehan, 2002)
Strategy: Count each day's pages carefully, testing your method on a short range such as pages 1–3, add the three days, divide by 500, and write the result as a percent to the nearest tenth.
Traps
- 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).
- Stops one step early: A choice is a number from partway through the solution.
- Misreads the question: Misses or misreads a condition or a word in the question: "at least", "each", "remaining", "not".
The wrong answers, classified
25 Counting the ends (Brown & Burton, 1978)
Subtracts the first page from the last for each day, 45 + 35 + 45 = 125 pages, forgetting that an inclusive range counts both end pages, so 125 ÷ 500 = 25%.
0.256 Stops one step early (King et al., 2004; Gierl et al., 2017)
Counts the 128 pages and divides by 500 correctly, then enters the decimal 0.256, one step short of multiplying by 100 to make a percent.
26 Misreads the question (Hegarty, Mayer & Monk, 1995)
Finds 25.6% correctly but rounds it to the nearest whole percent, overlooking the instruction to round to the nearest tenth.
Worked solution, step by step
Formulas used
- Counting pages in an inclusive range
- Inclusive means the first and last pages are both read. Subtracting counts the steps from the first page to the last. That misses one page, so add 1. Test it: pages 1 to 3 are 3 pages, and 3 − 1 + 1 = 3.
- Percent of a total
- The part is the amount you have, here the pages read. The whole is the amount you compare with, here the 500-page goal. Dividing gives a decimal. Multiplying by 100 turns it into a percent, a number out of 100.
Sort out the question
Leah’s goal is 500 pages. The log shows three days:
- Day 1: pages 45 to 90
- Day 2: pages 100 to 135
- Day 3: pages 145 to 190
Each range is inclusive. You need the percent of 500 pages she read, rounded to the nearest tenth.
Count the pages each day
Use the rule for an inclusive range: last page minus first page, plus 1.
Watch out: subtracting alone gives 45, 35 and 45 pages. That is 125 pages, which is exactly 25%. A round answer like that can hide the mistake.
Add the three days
Add the pages from all three days to get her total:
Leah read 128 pages in all. This is the part you compare with the goal.
Change to a percent
Divide the pages read by the goal, then multiply by 100:
Leah read 25.6% of her goal. That already ends in tenths, so no rounding is needed.
Watch out: 0.256 is a decimal, not a percent. And 26 rounds to a whole number, not to the nearest tenth.
Enter the answer
The box has no % sign, but the question asks for a percentage, so the number in the box is the percent. Type it with its decimal point. Typing 25.6% also counts on this site. So you would enter 25.6.
Check your answer
Estimate. 10% of 500 pages is 50 pages. 128 pages is a bit more than 2 × 50 = 100, so the answer is between 20% and 30%. Then check exactly: pages. It matches.
More questions like this
The original DOE question
Question 6 of 6
2018 Test A Math, question 1Question
In the figure above, PQRS is a parallelogram. What is the value of ?
Grid-in question: work out the answer and enter it as a number.
Show the answer
Correct answer: 162
First, find the measure of angle PQR. The measure of angle PQR is equal to the measure of angle PSR.
m∠PSR = 180 − 72 = 108.
So, the measure of angle PQR is also 108.
108 + 90 + x = 360
198 + x = 360
x = 162
Question analysis
A grid-in geometry question about angles around a parallelogram PQRS. A 72° angle sits outside corner S on the extended base, and at corner Q a right angle and the unknown angle x complete the turn around the point. Students chain three angle facts, and the angle asked for lies outside the shape, not inside it.
- NYS standards
- Grade level
- Grade 8 content, by NYS standard
- Compared with grade 7
- Above grade 7 Grade 7 angle work usually applies one or two facts, such as supplementary or vertical angles, to find an angle. This chains three, and needs the equal opposite angles of a parallelogram, which rest on grade 8 parallel-line facts.
- 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
- Reading a figure, table or graph major
- Combines ideas moderate
- An answer in an unexpected form minor
- Solution
- 3 steps
- Reading level
- Question and choices: about grade 7, 14 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 arithmetic is two subtractions; the difficulty is seeing which angles the marks refer to. Students lose points by treating the 72° as the parallelogram's own angle at S, or by stopping at angle PQR, the most natural number to grid. The question rewards tracing a route from S to Q before computing anything, and checking at the end that x is the angle outside the shape that the arc marks.
Reading a figure, table or graph major Understanding the question
The 72° is marked outside the parallelogram, between side SR and the base extended past S, and x sits outside corner Q, between QP and a vertical ray that meets QR at a right-angle mark. (Lesh, Post & Behr, 1987; Kirsch & Mosenthal, 1990)
Combines ideas moderate Working it out
Three angle facts have to be chained: a straight line gives the angle inside S, opposite angles of a parallelogram carry it to Q, and the angles around Q make a full 360° turn. (Embretson, 1998; Daniel & Embretson, 2010)
An answer in an unexpected form minor Choosing the answer
As a grid-in there are no choices to check against, so a student who stops at angle PQR, inside the parallelogram, gets no signal that the job is unfinished. (Enright, Morley & Sheehan, 2002)
Strategy: Use the straight line at S to find the parallelogram's angle there, carry it to the opposite corner Q, then take that angle and the right angle away from 360.
Traps
- Stops one step early: A choice is a number from partway through the solution.
The wrong answers, classified
108 Stops one step early (King et al., 2004; Gierl et al., 2017)
Finds angle PSR = 180 − 72 = 108 and carries it to angle PQR, then grids that interior angle instead of the angle x outside it.
198 Misreads the figure (Lesh, Post & Behr, 1987; Kirsch & Mosenthal, 1990)
Reads the 72° as the parallelogram's interior angle at S, so takes angle PQR as 72 and grids 360 − 90 − 72 = 198.
252 Misreads the figure (Lesh, Post & Behr, 1987; Kirsch & Mosenthal, 1990)
Overlooks the right-angle mark at Q and subtracts only the 108° angle PQR from 360, giving 252.
Worked solution, step by step
Formulas used
- Angles on a straight line
- a and b are two angles side by side on a straight line. Together they make a half turn, so they always add up to 180 degrees. Use it when an angle you need shares a straight line with an angle you know.
- Opposite angles of a parallelogram
- The symbol ∠ means angle. ∠PQR is the angle at corner Q, between sides QP and QR. ∠PSR is the angle at the opposite corner, S. In a parallelogram, opposite corners always have equal angles, because the shape leans the same way at both.
- Angles around a point
- a, b and c are angles that fit around one point with no gaps and no overlaps. Going all the way around is a full turn, which is 360 degrees. So the angles add up to 360.
Sort out what the figure shows
PQRS is a parallelogram. That is a four-sided shape whose opposite sides are parallel, which means they never meet. You need the value of x, in degrees.
Look closely at the marks. The 72° angle is outside the shape, at S. It sits between side SR and the base line, which keeps going past S. At Q, a vertical line meets side QR. The small square means a right angle, 90°. The angle x is outside the shape too. It runs from that vertical line around to side QP.
Find the angle inside corner S
Angle PSR is the shape’s own angle at S. It sits right next to the 72° angle, on the same straight base line. So the two angles add up to 180°.
So angle PSR is 108°. Watch out: 72° is not the inside angle at S. Using 72 as the inside angle leads to the wrong answer 198.
Carry the angle over to Q
Corners Q and S are opposite each other. In a parallelogram, opposite angles are equal. So angle PQR matches angle PSR.
So angle PQR is 108°. Watch out: this is not x. Angle PQR is inside the shape, and x is outside it. Stopping here and gridding 108 is the most common mistake.
Add the angles around Q
Three angles fill the space all the way around point Q. They are the right angle (90°), angle PQR (108°) and x. Together they make a full turn.
Watch out: don’t skip the right angle at Q. Leaving out the 90 gives 252.
Solve for x
Subtract 198 from 360 to find what is left for x.
So x is 162°. So you would grid 162.
Check your answer
Add the three angles at Q: . That is a full turn. Also, the arc for x is wider than a right angle but not as wide as a straight line. So x should be between 90° and 180°, and 162° is.
More questions like this
The original DOE question
