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 31Passage Serpent Mound
Serpent Mound
The Great Serpent Mound, located in Adams County, Ohio, is a human-made mound of earth that researchers believe was created between 300 B.C. and A.D. 1100 by an indigenous culture.
Ohio, 1846
Brush Creek stood low when the museum men came
with their measuring tapes and sketchbooks.
It was winter. Fringed with ice,
the creek doubled back on itself
as if it had forgotten something.
Pa was in Cincinnati, or else on his way home,
so Ma told me to lead the men
into the marshy low grounds. It being winter,
there was little underbrush to speak of—
in the summer there would have been
briars, poison ivy, biting flies. I listened
for the swish of a beaver’s heavy tail,
the chitter of a chickadee, or the cry of a hawk,
but the winter silence of the creek pressed
down on all of us like a weight.
The humps in the ground were all but
invisible until you were right up on them. The figure
was even less obvious: the sinuous body,
the tail coiled three times around,
and at the other end, the mouth wide open.
In the summer the creek bottom was crowded
with so much life that you could trip over
the ridges of earth before you saw
anything at all. In winter you could climb
a tree and get some idea of the whole thing:
the serpent’s body undulating, slithering
silently across the ancient
earth. At the mouth end, there was an oval mound
as if the snake were about to swallow an egg—
as snakes sometimes did in our rickety
henhouse—my Pa always said, or
as if swallowing the sun, one of the museum
men suggested, taking notes with his quill pen,
an old-style inkhorn slung at his side.
I liked that: swallowing the sun,
just the sort of thing a snake might do,
might want to do. When, later, I told my sister Ruth,
she disagreed. It is singing to the sun,
she insisted. That is why its mouth
is wide open. She said, “Sometimes I think
I hear it on summer nights. Not swallowing, singing.”
Question
What impact do the words “swish,” “chitter,” and “cry” in lines 12–13 have in the poem?
- AThey illustrate how lively the mound’s surroundings are during the summer.
- BThey show how the mound disrupts natural life in the marsh.
- CThey indicate the variety of wildlife found in the area around the mound.
- DThey suggest that the speaker prefers the mound’s appearance in winter.
Show the answer
Correct answer: A
The question asks what impact the words “swish,” “chitter,” and “cry” in lines 12–13 have in the poem.
A. CORRECT. The words highlight the sounds of the animals that visit the mound in the summer: the “swish of a beaver’s heavy tail” (line 12), the “chitter of a chickadee” (line 13), and the “cry of a hawk” (line 13). These words help contrast the quiet stillness of the setting around the mound in the winter.
B. Incorrect. While the words in lines 12–13 convey the sounds certain animals make in the summer, the sounds of the animals that live near the mound are a natural part of life in the area, not a disruption.
C. Incorrect. The speaker is contrasting the sounds of the animals around the mound during the rest of the year with the silence of the winter months, not merely indicating the variety of wildlife.
D. Incorrect. The speaker expresses the idea that the mound is more visible in the winter because of the lack of brush (“It being winter, / there was little underbrush to speak of” [lines 8–9]). Then lines 12–13 describe sounds, not the appearance of the mound in winter.
Question analysis
This question about word choice asks what impact the sound words “swish,” “chitter” and “cry” in lines 12–13 of “Serpent Mound” have in the poem. They belong to a beaver, a chickadee and a hawk near the creek, and more than one choice sounds like a fair account of them, so students must read the surrounding lines closely.
- Grade level
- Grade 8 reading and task
- Compared with grade 7
- Above grade 7 Grade 7 students often explain what sensory words add to a description. These three words sit inside a long sentence that runs across several lines, so their effect has to be worked out from the lines around them, beyond 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 analyze
- What makes it hard
- A very close wrong answer major
- Reading between the lines moderate
- Complex sentences minor
- Evidence
- Answered from one paragraph or stanza
- Reading level
- Passage: 354 words (a poem; reading level not measured); question and choices: about grade 6, 61 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
Three vivid animal sounds invite the easy reading that the poem is showing off the creek’s wildlife, and that choice is true as far as it goes. The words matter because they are missing: the speaker listens for them, and “the winter silence” answers. Students must also accept that the key’s “during the summer” comes from the poem’s later picture of a crowded summer creek, not from lines 12–13 themselves.
A very close wrong answer major Choosing the answer
The variety choice is literally true, since a beaver, a chickadee and a hawk are three kinds of animal; it differs from the key in missing why the sounds are named, as a contrast with winter. (Embretson & Wetzel, 1987; Gorin & Embretson, 2006; Ascalon et al., 2007)
Reading between the lines moderate Working it out
The speaker listens for these sounds and does not hear them, so students must infer that they stand for the creek’s life in warmer months, which lines 21–22 call “crowded / with so much life.” (Graesser, Singer & Trabasso, 1994; Kintsch, 1998)
Complex sentences minor Understanding the question
The three words sit in one sentence that runs from “I listened” in line 11 to “like a weight” in line 15 and turns on “but,” so their point arrives only at its end. (Abedi & Lord, 2001; Freedle & Kostin, 1993; Messick, 1989)
Strategy: Read the full sentence that holds these words, from “I listened” in line 11 to the end of line 15, then decide what the three sound words add to the scene.
Traps
- True but not the answer: A choice says something accurate about the text that does not answer this question.
- Wrong part of the text: A choice is true of another paragraph, stanza or speaker than the one asked about.
The wrong answers, classified
B Twists what the text says (King et al., 2004)
Notices that the beaver, chickadee and hawk go unheard but blames the mound for the hush, though line 14 calls it “the winter silence of the creek.”
C True but not the answer (King et al., 2004; Embretson & Wetzel, 1987)
Rightly counts three different animals in lines 12–13, but the speaker listens for them in vain, so the point is their absence in winter, not the range of species.
D Wrong part of the text (Kirsch & Mosenthal, 1990)
Remembers from lines 8–9 and 24–25 that winter makes the mound easier to see, but lines 12–13 are about sounds and state no preference for either season.
Working it out, step by step
Figure out what the question asks
This asks what three sound words do in the poem. They are “swish,” “chitter” and “cry,” in lines 12–13. Read the whole sentence they sit in. It starts at “I listened” in line 11 and ends with “like a weight” in line 15.
Read the full sentence
Lines 11–15 say “I listened / for the swish of a beaver’s heavy tail, / the chitter of a chickadee, or the cry of a hawk, / but the winter silence of the creek pressed / down on all of us like a weight.” A chickadee is a small bird, and a chitter is its quick, chirping sound. The speaker listens for these sounds. But the word “but” tells you they never come. Only silence answers.
Work out why the sounds are named
A beaver, a chickadee and a hawk are signs of a creek full of life. The speaker hears none of them in winter. Later lines tell you when the creek is lively. Lines 21–22 say “In the summer the creek bottom was crowded / with so much life.” So the missing sounds remind you how lively the place is in summer. They also make the winter silence feel even emptier.
Check each choice
- A fits. The sounds stand for the busy life around the mound in the warm months.
- B does not fit. The quiet comes from the season: “the winter silence of the creek.” The mound does not cause it.
- C does not fit. There are three kinds of animals, but the point is that their sounds are missing.
- D does not fit. These lines are about sounds. The speaker says nothing about liking how the mound looks in winter.
Watch out: C is true as far as it goes. But it misses why the speaker names the sounds at all: to set them against the silence.
Choose the answer
The sounds the speaker listens for, and doesn’t hear, show how lively the creek is in summer. So the answer is A, “They illustrate how lively the mound’s surroundings are during the summer.”
Why this answer and not the closest wrong one
C is the closest wrong choice, because a beaver, a chickadee and a hawk really are three kinds of wildlife. But the speaker listens for them and hears nothing. The word “but” turns the sentence to “the winter silence.” The sounds matter because they are missing. They show the creek in its lively season, which line 21 names as summer.
More questions like this
The original DOE question
The passage “Serpent Mound” as printed (page 40)
Question 2 of 6
2024 Test B English, question 48Passage Snowy Mountains
Snowy Mountains
by John Gould Fletcher
Higher and still more high,
Palaces made for cloud,
Above the dingy city-roofs
Blue-white like angels with broad wings,
Pillars of the sky at rest
The mountains from the great plateau
Uprise.
But the world heeds them not;
They have been here now for too long a time.
The world makes war on them,
Tunnels their granite cliffs,
Splits down their shining sides,
Plasters their cliffs with soap-advertisements,
Destroys the lonely fragments of their peace.
Vaster and still more vast,
Peak after peak, pile after pile,
Wilderness still untamed,
To which the future is as was the past,
Barrier spread by Gods,
Sunning their shining foreheads,
Barrier broken down by those who do not need
The joy of time-resisting storm-worn stone,
The mountains swing along
The south horizon of the sky;
Welcoming with wide floors of blue-green ice
The mists that dance and drive before the sun.
“Snowy Mountains” by John Gould Fletcher—Public Domain
Question
How do the details in the third stanza (lines 15–26) most contribute to the development of a theme of the poem?
- Aby reflecting nature’s capacity to resist change
- Bby showing that nature is capable of influencing human will
- Cby exposing how a lack of awareness leads to nature’s ruin
- Dby explaining why people must respect nature
Show the answer
Correct answer: A
The question asks how the details in the third stanza most contribute to the development of a theme of the poem.
A. CORRECT. In the third stanza, phrases such as “Wilderness still untamed” (line 17), “time-resisting storm-worn stone” (line 22), and “The mountains swing along” (line 23) convey the message that in spite of the destruction described in the second stanza, the mountains manage to maintain their wild magnificence.
B. Incorrect. While the phrase “Barrier broken down” (line 21) conveys the idea that people can have some effect on the natural landscape, it does not convey how nature affects people.
C. Incorrect. The phrase “those who do not need” (line 21) implies a choice to damage nature and not a lack of awareness or understanding.
D. Incorrect. The third stanza is not a call to humanity to respect the mountains but a description of the untamed, welcoming mountains and the joy they provide for those who appreciate them.
Question analysis
Students trace how the details of the third and final stanza of “Snowy Mountains,” lines 15–26, most contribute to developing a theme of the poem. Because the stanza is a single sentence that runs from line 15 to the poem’s last word, students must keep its whole movement in mind before deciding what it adds.
- Grade level
- Grade 8 reading and task
- Compared with grade 7
- Above grade 7 Grade 7 theme questions usually rest on a few clear details. Here students must hold a twelve-line stanza of inverted, piled-up phrases in mind and pick among four reasonable lessons about nature, a heavier load closer to grade 8.
- 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
- Complex sentences moderate
- Figurative or literary language moderate
- Evidence in several places moderate
- Evidence
- Answered from one paragraph or stanza
- Reading level
- Passage: 161 words (a poem; reading level not measured); question and choices: about grade 7, 55 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 final stanza holds both endurance and damage, and the stem’s “most” asks which of the two its details build. Students who fix on the broken barrier choose ruin, a reading the second stanza seems to confirm, while those who tally the stanza’s details find untamed wilderness, time-resisting stone and mountains swinging at ease. Because the stanza is one long, inverted sentence, that tally is slow, which is what makes the question hard.
Complex sentences moderate Understanding the question
Lines 15–26 are one sentence in which phrase after phrase, from “Vaster and still more vast” to “storm-worn stone,” comes before its subject, “The mountains,” in line 23. (Abedi & Lord, 2001; Freedle & Kostin, 1993; Messick, 1989)
Figurative or literary language moderate Understanding the question
The message of endurance is carried by personification: the peaks have “shining foreheads,” are “spread by Gods,” and “swing along” the horizon welcoming the mists. (Graesser, Singer & Trabasso, 1994; Kintsch, 1998)
Evidence in several places moderate Working it out
The theme has to be assembled from details scattered over twelve lines, “Wilderness still untamed,” “the future is as was the past,” “time-resisting,” and weighed against the single line of damage. (Kirsch & Mosenthal, 1990; Gorin & Embretson, 2006)
Strategy: Read lines 15–26 as one long sentence, find its main subject and verb, and sum up its message in a phrase; then check each choice against the whole stanza, not a single line.
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.
- Outside knowledge: A choice is plausible in the real world but not supported by this text.
- Reversed relationship: Cause and effect, or the order of events, turned around.
The wrong answers, classified
B Reversed relationship (King et al., 2004)
Turns the influence around: in this stanza people break down the barrier while the peaks endure, and nothing shows the mountains shaping what people want.
C Too narrow (King et al., 2004)
Builds on line 21’s “Barrier broken down,” the stanza’s one line of damage, and lets it stand for twelve lines that mostly celebrate the mountains as wild and lasting.
D Outside knowledge (King et al., 2004; Recht & Leslie, 1988)
States the lesson a nature poem is expected to teach, that people must respect nature, but the stanza describes the mountains and never tells readers what to do.
Working it out, step by step
Figure out what the question asks
This asks about theme, the big message of the poem. You need to see what the details of the third stanza, lines 15 to 26, add to that message. The word “most” matters. Pick the idea that most of the details support, not just one line.
Gather the details in lines 15 to 26
The peaks grow “Vaster and still more vast” (line 15). They are a “Wilderness still untamed” (line 17). For them, the future is “as was the past” (line 18). Their stone is “time-resisting” (line 22). In the last four lines, “The mountains swing along” the sky and welcome the mists. Only line 21 shows damage: the barrier is “broken down.”
Find what the details share
Untamed means still wild, not controlled by people. If the future is the same as the past, the mountains are not changing. Time-resisting means they hold out against the years. And at the end of the stanza, they are still moving along at ease. Nearly every detail shows the same thing. The mountains last and stay wild, which is nature’s power to resist change.
Check each choice
- A fits. Wild, unchanging, time-resisting mountains show nature holding out against change.
- B does not fit. It turns things around. In this stanza, people affect the mountains. Nothing shows the mountains changing what people want.
- C does not fit. Line 21 shows damage, but it is one line out of twelve. The stanza does not end in ruin either: the mountains still swing along and welcome the mists.
- D does not fit. These lines paint a picture of the peaks. They give readers no orders and no reasons to behave a certain way.
Choose the answer
Most of the third stanza shows mountains that stay wild and lasting. So the answer is A.
Why this answer and not the closest wrong one
C is the closest trap, because line 21 does show the barrier “broken down,” and the second stanza is full of harm. But this question is about the third stanza, and it asks what the details most add. Most of the other lines there show mountains that are vast, wild and lasting. That builds A, not ruin.
More questions like this
The original DOE question
The passage “Snowy Mountains” as printed (page 142)
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
2018 Test A Math, question 30Question
Today, Tien’s age is of Jordan’s age. In 2 years, Tien’s age will be of Jordan’s age. How old is Jordan today?
- A4 years old
- B6 years old
- C12 years old
- D16 years old
Show the answer
Correct answer: D
First, set up an equation to express Tien’s age () and Jordan’s age () today:
Two years from now, Tien’s age will be , and Jordan’s age will be .
Set up an equation about the relationship between Tien’s age and Jordan’s age in two years:
Solve the above equation for :
Now set the two equations equal to each other and solve for :
Question analysis
This age word problem says Tien is one fourth of Jordan's age today and will be one third of Jordan's age in two years, then asks for Jordan's current age. Students must turn two fractional relationships into equations and solve them together. Both people age by the same two years, and it is easy to solve for the wrong person.
- NYS standards
- Grade level
- Grade 8 content, by NYS standard
- Compared with grade 7
- Above grade 7 Grade 7 equations have one unknown on one side, like 3x + 5 = 20. This one links two unknown ages with fractional coefficients and leads to a variable on both sides, which is grade 8 algebra.
- 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 major
- Error-prone arithmetic moderate
- Solution
- 4 steps
- Reading level
- Question and choices: about grade 1, 31 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 difficulty is in the setup: two fractional relationships at two different times, with both people aging. Once the equations are right, the algebra is short, but it ends with two ages and only one is asked for. Testing the choices against both conditions is a reliable alternative that avoids the algebra entirely.
Turning words into math major Understanding the question
The second sentence must become T + 2 = (J + 2)/3; writing J/3, or forgetting that Jordan also ages two years, breaks the equation. (Hegarty, Mayer & Monk, 1995; Koedinger & Nathan, 2004)
Error-prone arithmetic moderate Working it out
Substituting J/4 for T leaves J/4 + 2 = (J + 2)/3, an equation with fractions on both sides that must be cleared, usually by multiplying by 12. (Brown & Burton, 1978; Junker & Sijtsma, 2001)
Strategy: Let Jordan's age be J, write Tien's age as J/4, and set J/4 + 2 equal to one third of (J + 2); or test each choice against both conditions.
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.
The wrong answers, classified
A Answers a different question (King et al., 2004; Hegarty, Mayer & Monk, 1995)
Solves the equations correctly but reports Tien's age today, 4, which is one fourth of Jordan's 16, instead of Jordan's age.
B Answers a different question (King et al., 2004; Hegarty, Mayer & Monk, 1995)
Gives Tien's age two years from now, 4 + 2 = 6, answering for the wrong person and the wrong time.
C Numbers taken from the question (Hegarty, Mayer & Monk, 1995)
Picks 12 because it is a multiple of both 4 and 3, but then Tien would be 3 and later 5, not a third of 14.
Worked solution, step by step
Formulas used
- Distributive property
- a, b and c are any numbers. To multiply a sum by a number, multiply each part of the sum, then add. It works because a groups of (b + c) is the same as a groups of b plus a groups of c.
Sort out what you know
Today, Tien’s age is of Jordan’s age. That means Jordan is 4 times as old as Tien.
In 2 years, both of them will be 2 years older. Then Tien’s age will be of Jordan’s. So Jordan will be 3 times as old as Tien. You need Jordan’s age today.
Name the ages with a letter
Let t stand for Tien’s age today. Jordan is 4 times as old, so his age is 4t, which means 4 times t. Add 2 years to each age:
Person Today In 2 years Tien Jordan Watch out: Jordan gets 2 years older too. Do not forget to add 2 to his age.
Write an equation for later
In 2 years, Jordan’s age will be 3 times Tien’s age. Write that as an equation:
Use the distributive property on the right side. Multiply both t and 2 by 3:
Solve for Tien’s age
Take 3t away from both sides. Doing the same thing to both sides keeps them equal:
Now take 2 away from both sides:
So Tien is 4 years old today. Watch out: 4 is Tien’s age, not Jordan’s. Choice A, 4 years old, is a trap.
Find Jordan’s age
Jordan is 4 times as old as Tien:
So the answer is D, 16 years old.
Check your answer
Put 16 back into the story. Today, Tien is 16 ÷ 4 = 4. In 2 years, Tien is 6 and Jordan is 18. Is 6 one third of 18? Yes, because 18 ÷ 3 = 6. Choice C fails: Tien would be 3, then 5, and 5 is not a third of 14.
More questions like this
The original DOE question
Question 5 of 6
2018 Test B Math, question 44Question
The hash marks on the number line above are evenly spaced. What is the coordinate of point ?
- A
- B
- C
- D
Show the answer
Correct answer: C
There are 5 sections between M and T. To find the length of one of these sections, find the distance between M and T and divide by 5:
R is 3 sections away from M, so add:
R is located at .
Question analysis
Students find the fraction at point R on a number line with evenly spaced hash marks, where M is at −1/4 and T is at 5/8. It tests fraction arithmetic with negative numbers. Working out the size of one gap and counting gaps from M to R takes several careful steps.
- NYS standards
- Grade level
- Grade 7 content, by NYS standard
- Compared with grade 7
- Above grade 7 Grade 7 students place fractions and negatives on number lines, but here they must subtract a negative fraction, divide by five, and then add back. Four fraction steps with unlike denominators make it harder than typical classwork.
- 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
- Error-prone arithmetic major
- Reading a figure, table or graph moderate
- Solution
- 4 steps
- Reading level
- Question and choices: about grade 6, 22 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
Fractions, a negative starting point and a count of spaces all have to come out right together. Students lose points by counting tick marks instead of spaces, by subtracting −1/4 as if it were positive, or by measuring R from 0 instead of from M. Converting both labels to fortieths first, −10/40 and 25/40, makes each gap a whole number of fortieths.
Error-prone arithmetic major Working it out
The gap length needs 5/8 − (−1/4) = 7/8, then 7/8 ÷ 5 = 7/40, then −10/40 + 21/40: negatives and three different denominators meet in one problem. (Brown & Burton, 1978; Junker & Sijtsma, 2001)
Reading a figure, table or graph moderate Understanding the question
The hash marks have to be counted as spaces: five from M to T, with R three spaces past M, while the unlabeled marks outside M and T play no part. (Lesh, Post & Behr, 1987; Kirsch & Mosenthal, 1990)
Strategy: Find the distance from M to T by subtracting their coordinates, divide it by the number of equal gaps, then step from M toward T by the right number of gaps.
Traps
- Stops one step early: A choice is a number from partway through the solution.
- Negatives and direction: Arithmetic with negative numbers, the order of a subtraction, or direction on a number line. (Moving a term across the equals sign without changing its sign is a faulty procedure.)
The wrong answers, classified
A Stops one step early (King et al., 2004; Gierl et al., 2017)
Finds the length of one gap, 7/8 ÷ 5 = 7/40, and gives it as R's coordinate without stepping from M.
B Negatives and direction (Brown & Burton, 1978)
Subtracts as 5/8 − 1/4 = 3/8 instead of adding, gets gaps of 3/40, and counts three gaps from 0.
D Stops one step early (King et al., 2004; Gierl et al., 2017)
Multiplies the 7/40 gap by 3 to get the distance from M to R, then forgets to add it to M's −1/4.
Worked solution, step by step
Formulas used
- Distance on a number line
- The right number is the point farther to the right on the number line. The left number is the other point. Subtracting tells how many units apart they are. Taking the left from the right keeps the answer positive.
- Dividing a fraction by a whole number
- a over b is the fraction, and c is the whole number you divide by. Splitting a fraction into c equal parts makes each part c times smaller. So you multiply the bottom number, b, by c.
Read the number line
M is at and T is at . The hash marks are evenly spaced, so every space is the same length. Count the spaces. From M to T there are 5 spaces. From M to R there are 3 spaces. You need the number at point R.
Find the distance from M to T
Use the distance formula. First write in eighths, as .
Taking away a negative is the same as adding. M and T are apart.
Find the length of one space
The 5 spaces are equal, so divide by 5.
Each space is long.
Watch out: this is the length of one space, not where R is. Stopping here gives choice A.
Step from M to R
R is 3 spaces to the right of M.
Now add that to M. Write as .
Watch out: is how far R is from M, not where R is. Choosing it gives choice D.
Give the answer
Point R is at , a little to the right of 0. So the answer is C, .
Check your answer
Go backward from T instead. T is 2 spaces past R, and . So R is at . Both ways give the same point.
More questions like this
The original DOE question
Question 6 of 6
2018 Test A Math, question 5Question
The sum of two consecutive integers is −15. If 1 is added to the smaller integer and 2 is subtracted from the larger integer, what is the product of the two resulting integers?
Grid-in question: work out the answer and enter it as a number.
Show the answer
Correct answer: 63
If x is the smaller consecutive integer, then
is the larger consecutive integer. Use their sum (−15) to find x:
The two consecutive integers are −8 and −7. One is added to the smaller integer:
and 2 is subtracted from the larger integer:
Find the product:
Question analysis
A grid-in problem about two consecutive integers whose sum is −15. Students find the two integers, add 1 to the smaller and subtract 2 from the larger, then multiply the results. Deciding which negative integer is the smaller one, and keeping signs straight through every step, are what make it tricky.
- Grade level
- Grade 7 content, by NYS standard
- Compared with grade 7
- Above grade 7 A typical grade 7 task solves one two-step equation or multiplies signed numbers. This links both: set up a consecutive-integer equation, solve it with negatives, adjust each integer, and multiply, 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
- Error-prone arithmetic moderate
- Turning words into math moderate
- Many steps moderate
- Solution
- 4 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
Every step is routine, yet the question collects most of the ways students lose points with negatives. The crucial judgment is which of −8 and −7 is the smaller; a student who picks −7 still produces a tidy, wrong product. Gridding the product of the original pair, or giving a negative product, are the other usual losses. Writing each intermediate pair down, rather than holding them in mind, protects against all three.
Error-prone arithmetic moderate Working it out
Every number in play is negative: −8 and −7, then −7 and −9, and a product of two negatives that must come out positive. (Brown & Burton, 1978; Junker & Sijtsma, 2001)
Turning words into math moderate Understanding the question
"1 is added to the smaller integer and 2 is subtracted from the larger" depends on knowing that −8, not −7, is the smaller, since it lies farther below zero. (Hegarty, Mayer & Monk, 1995; Koedinger & Nathan, 2004)
Many steps moderate Working it out
Four linked steps: set up x + (x + 1) = −15, solve for x, adjust each integer, then multiply; an error early in the chain carries through to the product. (Daniel & Embretson, 2010; Enright, Morley & Sheehan, 2002)
Strategy: Halve the sum to see which two integers sit on either side of it, remember that the smaller negative is farther from zero, then adjust each and multiply.
Traps
- Negatives and direction: Arithmetic with negative numbers, the order of a subtraction, or direction on a number line. (Moving a term across the equals sign without changing its sign is a faulty procedure.)
- Misreads the question: Misses or misreads a condition or a word in the question: "at least", "each", "remaining", "not".
The wrong answers, classified
60 Negatives and direction (Brown & Burton, 1978)
Takes −7 as the smaller integer because 7 is less than 8, so adjusts to −7 + 1 = −6 and −8 − 2 = −10, and multiplies to 60.
56 Misreads the question (Hegarty, Mayer & Monk, 1995)
Finds −8 and −7 and multiplies them to get 56, skipping the sentence that adds 1 to one integer and subtracts 2 from the other.
-63 Negatives and direction (Brown & Burton, 1978)
Finds the adjusted integers −7 and −9 correctly but gives their product a negative sign, gridding −63.
Worked solution, step by step
Formulas used
- Consecutive integers
- Integers are whole numbers and their opposites, like −2, −1, 0, 1 and 2. Consecutive integers come one right after another. If n is the smaller one, the next one is n + 1, because each step up the number line adds 1.
- Multiplying two negative numbers
- a and b are positive numbers, so −a and −b are negative. When you multiply two negative numbers, the answer is positive. The two minus signs cancel out.
Sort out the question
Two consecutive integers add up to −15. Integers are whole numbers and their negatives. Consecutive means one comes right after the other, like 4 and 5. You need to do three things:
- Find the two integers.
- Add 1 to the smaller one. Subtract 2 from the larger one.
- Find the product of the two new numbers. The product is the answer when you multiply.
Find the two integers
Call the smaller integer n. Then the larger one is n + 1. Their sum is −15.
Subtract 1 from both sides. Then divide both sides by 2.
So the integers are −8 and −7.
Decide which one is smaller
On a number line, −8 is to the left of −7. Numbers to the left are smaller. So −8 is the smaller integer, and −7 is the larger one. Watch out: 8 is bigger than 7, but −8 is smaller than −7. Mixing them up gives −6 and −10, and the wrong answer 60.
Change each integer
Add 1 to the smaller integer.
Subtract 2 from the larger integer.
The two new numbers are −7 and −9.
Multiply the new numbers
Both numbers are negative, so their product is positive.
Watch out: the answer is not −63, because two negatives make a positive. Also, don’t multiply the first pair, −8 and −7. That gives 56 and skips the changes. So you would grid 63.
Check your answer
Check the pair: , and they are one apart. Half of −15 is −7.5, and −8 and −7 sit on either side of it. Then , and the sign is positive.
More questions like this
The original DOE question
