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Six SHSAT Questions

3 English and 3 math

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Question 1 of 6

2024 Test A English, question 46
Passage Excerpt from The Highest Tide

Excerpt from The Highest Tide

by Jim Lynch

The narrator’s summer job is collecting marine specimens in Puget Sound, Washington. In this excerpt, he is looking for specimens in the mudflats before daybreak. Mudflats, or flats, are coastal landforms created when sediment and silt from tides are deposited as the tides recede.

I rounded the oyster beds, to the far side. . . . It was low tide by then, and I saw the water hesitating at its apex, neither leaving nor returning, patiently waiting for the gravitational gears to shift. Dozens of anxious clams started squirting in unison like they did whenever vibrating grains of sand warned them predators were approaching. I stopped and waited with them, to actually see the moment when the tide started returning with its invisible buffet of plankton for the clams, oysters, mussels and other filter feeders. It was right then, ankle deep in the Sound, feet numbing, eyes relaxed, that I saw the nudibranch.1

In all my time on the flats I’d never seen one before. I’d read about them, sure. I’d handled them at aquariums but never in the wild, and I’d never even seen a photo of one this stunning. It was just three inches long but with dozens of fluorescent, orange-tipped hornlike plumes jutting from the back of its see-through body that appeared to be lit from within.

Nudibranchs are often called the butterflies of the sea, but even that understates their dazzle. Almost everything else in the northern Pacific is dressed to blend with pale surroundings. Nudibranchs don’t bother, in part because they taste so lousy they don’t need camouflage to survive. But also, I decided right then, because their beauty is so startling it earns them a free pass, the same way everyday life brakes for peacocks, parade floats. . . .

The dark mudflats loomed like wet, flattened dunes stretching deep into Skookumchuck Bay in front of our house. From a distance, they looked too barren to support sea life. Up close, they still did, unless you knew where to find the hearty clams, worms and tiny creatures that flourish in mud. . . . I’m not sure why I decided to take a look. It was still an hour before sunrise, and I knew exactly what the bars2 looked like in the moonlight, but for some reason, I couldn’t resist.

I heard it long before I saw it. It was an exhale, a release of sorts, and I instantly wondered if a whale was stranded again. We had a young minke3 stuck out there two summers prior, and it made similar noises until the tide rose high enough for rescuers to help free it. . . . I looked for a hulking silhouette but couldn’t find one. I waited, but there were no more sounds. Still, I went toward what I thought I’d heard, avoiding stepping into the mud until I had to. I knew the flats well enough to know I could get stuck just about anywhere. The general rule was you didn’t venture out past the shells and gravel with an incoming tide. I sank up to my knees twice, and numbing water filled my boots.

. . . I kept stepping toward the one sound I’d heard, a growing part of me hoping I’d find nothing at all. When I stopped to rest and yank up my socks, my headlamp crossed it. My first thought? A giant octopus.

Puget Sound has some of the biggest octopi in the world. They often balloon to a hundred pounds. Even the great Jacques Cousteau4 himself came to study them. But when I saw the long tubular shape of its upper body and the tangle of tentacles below it, I knew it was more than an octopus. I came closer, within fifty feet, close enough to see its large cylindrical siphon5 quiver. I couldn’t tell if it was making any sounds at that point, because it was impossible to hear anything over the blood in my ears. . . .

The creature’s body came to a triangular point above narrow fins that lay flat on the mud like wings, but it was hard to be sure exactly where it all began or ended, or how long its tentacles truly were, because I was afraid to pry my eyes off its jumble of arms for more than half a second. I didn’t know whether I was within reach, and its arms were as big around as my ankle and lined with suckers the size of half-dollars. If they even twitched I would have run. So, I was looking at it and not looking at it while my heart spangled my vision. I saw fragments, pieces, and tried to fuse them in my mind but couldn’t be certain of the whole. I knew what it had to be, but I wouldn’t allow myself to even think the two words. Then I gradually realized the dark shiny disc in the middle of the rubbery mass was too perfectly round to be mud or a reflection.

It was too late to smother my scream. Its eye was the size of a hubcap.6

From THE HIGHEST TIDE by Jim Lynch. Copyright © 2005 by Jim Lynch. Used by permission of Bloomsbury USA. All rights reserved.

1nudibranch: type of sea slug

2bars: sandbars

3minke: species of small whale

4Jacques Cousteau: renowned French oceanographer

5siphon: tube-like organ that is used for drawing in or removing fluids

6hubcap: removable cap over the end of a wheel axle

Question

How does the setting affect the plot of the excerpt?

  • AThe darkness of the mudflats before sunrise causes the narrator to pay close attention to his surroundings.
  • BThe rugged terrain of the mudflats makes it more difficult for the narrator to do his job.
  • CThe slow return of the tide along the mudflats forces the narrator to be patient during his journey.
  • DThe barren appearance of the mudflats creates a sense of mystery that unsettles the narrator.
Show the answer

Correct answer: A

The question asks how the setting affects the plot of the excerpt.

A. CORRECT. In paragraph 4, the narrator says that it is an hour before sunrise. It is difficult to see because the mudflats are dark, so the narrator, while familiar with the terrain of the mudflats, is cautious.

B. Incorrect. While the terrain of the mudflats is challenging because of the “wet, flattened dunes” (paragraph 4), the narrator is familiar with the terrain and moves carefully. In addition, the excerpt focuses on the narrator’s curiosity and enjoyment as he explores the mudflats, not on his work collecting specimens.

C. Incorrect. In paragraph 1, the narrator watches the water “hesitating at its apex” and “patiently waiting for the gravitational gears to shift.” This illustrates that the narrator is already familiar with the changes in his surroundings, that the tide is slow to move in, and that he can move carefully through the mudflats without the threat of rising water.

D. Incorrect. While the narrator is on the mudflats for the entire excerpt, the phrase “eyes relaxed” in paragraph 1 indicates that the narrator feels comfortable there. The narrator does not show fear until paragraph 6, when a growing fear about the unknown creature arises.

Question analysis

Set on the mudflats of Puget Sound before daybreak, this excerpt from the novel The Highest Tide is the basis for a question about how setting affects plot. Students must link features of the place and time to what the narrator does across the whole excerpt, and each choice pairs a real feature of the setting with an effect that may or may not be in the text.

NYS standards
  • 7R3 plot elements and ideas
  • 7R1 textual evidence and inferences
Grade level
Grade 8 reading and task
Compared with grade 7
Above grade 7 Analyzing how setting shapes plot is a grade 7 literary standard, but the excerpt never states the link: the effect must be inferred from scattered details, and every choice names a genuine feature of the flats, which is beyond typical work.
Estimated difficulty
Hard: combines ideas, needs a plan, and has more than one tempting wrong answer.
Evidence
Answered from the whole text
Reading level
Passage: about grade 6, 902 words; question and choices: about grade 8, 77 words.
Corrected from the DOE handbook
  • A statement in the explanation that contradicted the excerpt’s introduction 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 a real feature of the mudflats, so the question turns on which feature the excerpt actually shows shaping events. The darkness never gets a sentence of its own; it is felt in a sound heard before anything is seen, a silhouette that cannot be found and a headlamp beam. The barren look of the flats is the strongest pull, because the scene is eerie, but the narrator knows life hides in the mud and his unease comes from the creature.

  1. Reading between the lines major Working it out

    The excerpt never says the darkness changes anything; the effect must be assembled from the hour before sunrise, the sound heard “long before I saw it”, the missing silhouette and the headlamp that finally finds the creature. (Graesser, Singer & Trabasso, 1994; Kintsch, 1998)

  2. The right answer is reworded moderate Choosing the answer

    The right choice uses no words from the text, while the wrong ones echo it: the “barren” look of the flats, the water “patiently waiting”, the narrator's summer job. (Freedle & Kostin, 1993; Kirsch & Mosenthal, 1990)

  3. Evidence in several places moderate Working it out

    The darkness is established in paragraph 4 and felt in paragraphs 5, 6 and 8, so no single passage shows the setting at work. (Kirsch & Mosenthal, 1990; Gorin & Embretson, 2006)

Strategy: Collect the details of time, place and conditions across the excerpt, then for each choice ask whether the text shows that feature of the setting actually changing what the narrator does.

Traps

  • 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.
  • Reads too much in: A reasonable-sounding conclusion that goes further than the text allows.

The wrong answers, classified

What was corrected from the DOE handbook, and why

  • Explanation: In rejecting choice B, the handbook says “the excerpt shows that the narrator explores the mudflats for curiosity and enjoyment, not work.” But the introduction says the narrator’s summer job is collecting marine specimens and that “in this excerpt, he is looking for specimens in the mudflats before daybreak.” The explanation now says the excerpt focuses on his curiosity and enjoyment as he explores the mudflats, not on his work collecting specimens. That keeps the handbook’s point (the excerpt is not about the terrain making his job harder) without contradicting the introduction.

How the questions are analyzed, and the research behind it

Working it out, step by step

  1. Know what setting and plot mean

    The setting is where and when a story happens. The plot is the chain of events. This asks which part of the setting changes what happens or what the narrator does.

  2. Find the time of day

    Paragraph 4 says, “It was still an hour before sunrise.” The narrator is out on the mudflats in the dark. The only light comes from the moon and his headlamp.

  3. See how the dark shapes events

    Because it is dark, he must rely on sounds and small clues. He says, “I heard it long before I saw it.” He looks for “a hulking silhouette,” a dark outline, but can’t find one. He spots the creature only when “my headlamp crossed it.” Then he stares hard, trying to make out its shape. The darkness keeps him alert and watching closely.

  4. Check each choice

    • A fits: the dark makes him pay close attention to everything around him.
    • B is wrong because the excerpt follows a strange sound and never shows the ground making his job harder.
    • C is wrong because in paragraph 1 he chooses to stop and watch the tide, and nothing forces him.
    • D is wrong because he knows life hides in the mud, and what scares him is the creature.

    Watch out: D feels right because the scene is eerie. But the flats’ empty look never troubles him.

  5. Choose the answer

    The darkness before sunrise is what keeps the narrator listening and looking so carefully. So the answer is A.

Why this answer and not the closest wrong one

D comes closest, because the dark flats do feel spooky. But the narrator says they only look “too barren to support sea life” from far away, and he knows better. His fear comes from the creature. The darkness, though, shapes every step: he hears before he sees and must watch closely.

More questions like this

The original DOE question
Question 46 as printed on page 66 of the DOE handbook.
As printed in the DOE’s NYC Guide to the Specialized High Schools Admissions Test (SHSAT) for 2025 Admissions, page 66, question 46. Open page 66 of the handbook (PDF) The handbook letters this question’s choices E–H; here they are A–D (E = A, F = B, G = C, H = D). This is the DOE’s version, before the corrections listed in the analysis.
The passage “Excerpt from The Highest Tide” as printed (pages 64–65)The passage “Excerpt from The Highest Tide” as printed on page 64 of the DOE handbook.The passage “Excerpt from The Highest Tide” as printed on page 65 of the DOE handbook.

Question 2 of 6

2026 Practice Test A English, question 37
Passage 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.

NYS standards
  • 7R2 theme or central idea
  • 7R5 structure and genre features
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.
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.

  1. 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)

  2. 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)

  3. 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)

  4. 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

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.”

How the questions are analyzed, and the research behind it

Working it out, step by step

  1. 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.

  2. 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.

  3. 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.

  4. 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.

  5. 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
Question 37 as shown on the DOE’s digital test, page 52 of its printable version.
As printed in the DOE’s printable version of 2026 Practice Test A English, page 52, question 37. This is the DOE’s version, before the corrections listed in the analysis.
The passage “Massachusetts: Lowell National Historical Park” as printed (page 50)The passage “Massachusetts: Lowell National Historical Park” as printed on page 50 of the DOE handbook.

Question 3 of 6

2026 Practice Test C English, question 8
Passage Excerpt from “Niagara Falls”

Excerpt from “Niagara Falls”

by Rupert Brooke

The real secret of the beauty and terror of the Falls is not their height or width, but the feeling of colossal power and of unintelligible disaster caused by the plunge of that vast body of water. If that were taken away, there would be little visible change, but the heart would be gone.

The American Falls do not inspire this feeling in the same way as the Canadian. It is because they are less in volume, and because the water does not fall so much into one place. By comparison their beauty is almost delicate and fragile. They are extraordinarily level, one long curtain of lacework and woven foam. Seen from opposite, when the sun is on them, they are blindingly white, and the clouds of spray show dark against them. With both Falls the colour of the water is the ever-altering wonder. Greens and blues, purples and whites, melt into one another, fade, and come again, and change with the changing sun. Sometimes they are as richly diaphanous1^1 as a precious stone, and glow from within with a deep, inexplicable light. Sometimes the white intricacies of dropping foam become opaque and creamy. And always there are the rainbows. If you come suddenly upon the Falls from above, a great double rainbow, very vivid, spanning the extent of spray from top to bottom, is the first thing you see. If you wander along the cliff opposite, a bow springs into being in the American Falls, accompanies you courteously on your walk, dwindles and dies as the mist ends, and awakens again as you reach the Canadian tumult. And the bold traveller who attempts the trip under the American Falls sees, when he dare open his eyes to anything, tiny baby rainbows, some four or five yards in span, leaping from rock to rock among the foam, and gambolling beside him, barely out of hand’s reach, as he goes. One I saw in that place was a complete circle, such as I have never seen before, and so near that I could put my foot on it. It is a terrifying journey, beneath and behind the Falls. The senses are battered and bewildered by the thunder of the water and the assault of wind and spray; or rather, the sound is not of falling water, but merely of falling; a noise of unspecified ruin. So, if you are close behind the endless clamour, the sight cannot recognise liquid in the masses that hurl past. You are dimly and pitifully aware that sheets of light and darkness are falling in great curves in front of you. Dull omnipresent foam washes the face. Farther away, in the roar and hissing, clouds of spray seem literally to slide down some invisible plane of air.

Beyond the foot of the Falls the river is like a slipping floor of marble, green with veins of dirty white, made by the scum that was foam. It slides very quietly and slowly down for a mile or two, sullenly exhausted. Then it turns to a dull sage green, and hurries more swiftly, smooth and ominous. As the walls of the ravine close in, trouble stirs, and the waters boil and eddy. These are the lower rapids, a sight more terrifying than the Falls, because less intelligible. Close in its bands of rock the river surges tumultuously forward, writhing and leaping as if inspired by a demon. It is pressed by the straits into a visibly convex form. Great planes of water slide past. Sometimes it is thrown up into a pinnacle of foam higher than a house, or leaps with incredible speed from the crest of one vast wave to another, along the shining curve between, like the spring of a wild beast. Its motion continually suggests muscular action. The power manifest in these rapids moves one with a different sense of awe and terror from that of the Falls. Here the inhuman life and strength are spontaneous, active, almost resolute. . . . A place of fear.

One is drawn back, strangely, to a contemplation of the Falls, at every hour, and especially by night, when the cloud of spray becomes an immense visible ghost, straining and wavering high above the river, white and pathetic and translucent. The Victorian lies very close below the surface in every man. There one can sit and let great cloudy thoughts of destiny and the passage of empires drift through the mind; for such dreams are at home by Niagara. I could not get out of my mind the thought of a friend, who said that the rainbows over the Falls were like the arts and beauty and goodness, with regard to the stream of life—caused by it, thrown upon its spray, but unable to stay or direct or affect it, and ceasing when it ceased. In all comparisons that rise in the heart, the river, with its multitudinous waves and its single current, likens itself to a life, whether of an individual or of a community. A man’s life is of many flashing moments, and yet one stream; a nation’s flows through all its citizens, and yet is more than they. In such places, one is aware, with an almost insupportable and yet comforting certitude, that both men and nations are hurried onwards to their ruin or ending as inevitably as this dark flood. Some go down to it unreluctant, and meet it, like the river, not without nobility. And as incessant, as inevitable, and as unavailing as the spray that hangs over the Falls, is the white cloud of human crying. . . . With some such thoughts does the platitudinous2^2 heart win from the confusion and thunder of a Niagara peace that the quietest plains or most stable hills can never give.

From LETTERS FROM AMERICA by Rupert Brooke—Public Domain

1^1diaphanous: sheer, translucent

2^2platitudinous: clichéd, common

Question

Read this sentence from paragraph 3.

These are the lower rapids, a sight more terrifying than the Falls, because less intelligible.

Which statement best describes how the sentence fits into the overall structure of the excerpt?

  • AIt signals a change from the positive aspects of the Falls to the negative aspects.
  • BIt indicates a progression from the literal description of the water to a discussion of timeless truths.
  • CIt reinforces a shift from the qualities of the Falls to the qualities of the river.
  • DIt introduces a contrast between the obvious and the hidden features of the rapids.
Show the answer

Correct answer: C

The question asks for the statement that best describes how the sentence from paragraph 3 fits into the overall structure of the excerpt.

A. Incorrect. Although in paragraph 2 the author describes the beauty of the Falls as both an “ever-altering wonder” and an “assault of wind and spray,” in paragraph 3 the author does not signal a change from the positive aspects of the Falls to the negative aspects. Instead, the author provides a description of the river and the rapids below the Falls.

B. Incorrect. While the author compares the water of the river to “a slipping floor of marble, green with veins of dirty white, made by the scum that was foam” in paragraph 3, the statement that the lower rapids are “more terrifying than the Falls, because less intelligible” does not indicate a progression from the literal description of the water to a discussion of timeless truths. Instead, the author is merely describing all aspects of the rapids, both literally and figuratively.

C. CORRECT. The first sentence of paragraph 3 moves the description “beyond the foot of the Falls” to “the river” and then the paragraph begins to describe this location in further detail (“a dull sage green,” “hurries more swiftly,” “smooth and ominous,” “waters boil and eddy”) before reinforcing this shift by confirming it again with the words “These are the lower rapids, a sight more terrifying than the Falls.”

D. Incorrect. Although the author states that the waters of the rapids “boil and eddy” and suggests that the rapids are “less intelligible,” these statements do not introduce a contrast between the obvious and the hidden features of the rapids. They merely describe a feature and the sight of the lower rapids.

Question analysis

This text structure question quotes a sentence from paragraph 3 of Rupert Brooke’s “Niagara Falls,” in which the lower rapids are called “more terrifying than the Falls,” and asks how it fits the excerpt’s overall organization. It rewords a question from the 2018 handbook’s Test B. Every choice describes a turn the essay could plausibly take, so students need a clear picture of what each paragraph covers.

NYS standards
  • 7R5 structure and genre features
Grade level
Grade 8 reading and task
Compared with grade 7
Above grade 7 A typical grade 7 structure question asks what one paragraph adds. This one asks where a sentence from the middle of paragraph 3 fits in the whole essay, which means summing up four long paragraphs of century-old prose.
Estimated difficulty
Hard: combines ideas, needs a plan, and has more than one tempting wrong answer.
What makes it hard
Evidence
Answered from several paragraphs or stanzas
Reading level
Passage: about grade 9, 987 words; question and choices: about grade 8, 97 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

A sentence that compares the rapids with the Falls is easy to misplace, because both of its subjects appear elsewhere in the excerpt. The strongest pull is a real turn in the essay, from describing water to musing on destiny, that comes a paragraph later, while “more terrifying” draws students who forget that terror runs through the excerpt from its first sentence. The 2026 verb “reinforces” rewards those who saw that paragraph 3 had already left the Falls with “Beyond the foot of the Falls the river.”

  1. How, not what major Working it out

    The task is to place one sentence in the essay’s plan, and the sentence pulls the wrong way: it mentions “the Falls” and “more terrifying,” though its job is to confirm that paragraph 3 has already moved downstream to the rapids. (Anderson & Krathwohl, 2001)

  2. Much to keep track of moderate Working it out

    Placing the sentence takes a summary of all four long paragraphs at once: the Falls’ power, the two Falls’ beauty and the trip behind them, the river below, and the night thoughts on destiny. (Sweller, 1988; Carpenter, Just & Shell, 1990)

  3. Hard words moderate Understanding the question

    “Less intelligible” means harder to make sense of; a student who takes it as harder to see is led toward a contrast between obvious and hidden features of the rapids. (Perfetti, 2007; Freedle & Kostin, 1993)

Strategy: Sum up each of the four paragraphs in a few words, find where this sentence sits in that outline, and choose the description of the essay’s movement at exactly that point.

Traps

The wrong answers, classified

How the questions are analyzed, and the research behind it

Working it out, step by step

  1. Figure out what the question asks

    This is a text structure question. Structure is the plan of a piece of writing: what each part does and how the parts connect. You get one sentence from paragraph 3. You must decide what job it does in the plan of the whole excerpt. So first sum up what each of the four paragraphs is about.

  2. Sum up the four paragraphs

    • Paragraph 1: the real secret of the Falls is “the feeling of colossal power.” Colossal means huge.
    • Paragraph 2: the two Falls, their colors, the rainbows, and the scary trip behind the water.
    • Paragraph 3: the river below the Falls and its wild rapids.
    • Paragraph 4: the author goes back to the Falls at night and thinks about life and destiny, or what happens in the end.

  3. See where paragraph 3 begins

    Paragraph 3 opens with “Beyond the foot of the Falls the river is like a slipping floor of marble.” Beyond the foot means past the bottom. So the author has already left the Falls. He follows the river as it “hurries more swiftly” and the waters “boil and eddy,” or swirl. Then comes the sentence: “These are the lower rapids, a sight more terrifying than the Falls, because less intelligible.” Rapids are a stretch of fast, rough water. Less intelligible means harder to make sense of.

  4. Decide what the sentence does

    The sentence names the new place: the lower rapids. It also sets the rapids against the Falls. That tells you again that the essay has moved from the Falls to the river below them. To reinforce something is to make it stronger. The sentence reinforces a shift, or change of subject, that the paragraph’s first sentence began.

  5. Check each choice

    • A does not fit. Terror is not new here. Paragraph 1 already speaks of “unintelligible disaster,” and paragraph 2 calls the trip behind the Falls “a terrifying journey.”
    • B does not fit. The essay does turn to big, timeless ideas, but in paragraph 4, not here.
    • C fits. The sentence confirms the move from the Falls to the river.
    • D does not fit. The rapids are in plain sight. “Less intelligible” means harder to understand, not hidden.

    Watch out: B names a real turn in the essay. But it comes one paragraph later, with “thoughts of destiny and the passage of empires.”

  6. Choose the answer

    The sentence names the rapids and compares them with the Falls. That confirms the essay has moved downstream. So the answer is C, “It reinforces a shift from the qualities of the Falls to the qualities of the river.”

Why this answer and not the closest wrong one

B is the closest wrong choice, because the essay really does move from describing water to big ideas about life. But that move comes in paragraph 4, at night. The sentence in paragraph 3 is still describing water. Its job is to name the rapids and confirm that the essay has left the Falls for the river.

More questions like this

The original DOE question
Question 8 as shown on the DOE’s digital test, page 16 of its printable version.
As printed in the DOE’s printable version of 2026 Practice Test C English, page 16, question 8.
The passage “Excerpt from “Niagara Falls”” as printed (pages 134–135)The passage “Excerpt from “Niagara Falls”” as printed on page 134 of the DOE handbook.The passage “Excerpt from “Niagara Falls”” as printed on page 135 of the DOE handbook.

Question 4 of 6

2024 Test A Math, question 39

Question

Triangle with its two slanted sides each labeled 13 in. and its base labeled 10 in. Beside it, a vertical arrow as tall as the triangle, from its base to its top vertex, is labeled 12 in.

Raquel is cutting out pieces of cardboard to make a pyramid. She will use a square piece for the base and identical triangular pieces for the sides. The figure above shows the dimensions of the triangle for each side. What will be the total surface area, in square inches, of the pyramid, including the square base?

  • A280
  • B295
  • C340
  • D360
Show the answer

Correct answer: C

Surface area is found by calculating the area of each side, including the base, and adding them all together.

The base of the pyramid measures 10 inches on each side, so the area of the base is

10×10=10010 \times 10 = 100

Each triangular face has a base of 10 inches and a height of 12 inches, so the area of each face is

12×10×12=60\frac{1}{2} \times 10 \times 12 = 60

There are 4 triangular faces (because the square base has 4 edges, each of which will have a triangular face). So the total surface area of the pyramid is the sum of the areas of 4 triangles and 1 square.

(4×60)+100=240+100(4 \times 60) + 100 = 240 + 100

So the total surface area is 340 square inches.

Question analysis

This surface area word problem shows one triangular face, with sides of 13 inches, a base of 10 inches and a height of 12 inches, that Raquel will use to build a cardboard pyramid with a square base. Students find the total area of the base and all the triangular sides. Picturing the solid and choosing the right measurements from the figure are the tricky parts.

NYS standards
  • 7.G.6 area, surface area, and volume
  • 6.G.4 nets and surface area
  • 6.G.1 area of polygons
Grade level
Grade 7 content, by NYS standard
Compared with grade 7
Above grade 7 Grade 7 students find the surface area of a pyramid from a drawn net or solid. Here only one triangular face is shown, so students must picture the whole pyramid, count its faces, and choose which labeled length belongs in the area formula.
Estimated difficulty
Hard: combines ideas, needs a plan, and has more than one tempting wrong answer.
Solution
4 steps
Reading level
Question and choices: about grade 6, 56 words.
Corrected from the DOE handbook
  • A wrong unit 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

Students have to build the pyramid in their heads from one flat triangle, then choose the right measurement from three labels. The 13-inch sides look like the natural height, and using them gives a listed total; picturing a pyramid with three sloping faces gives another. Sketching the square base with a triangle on each edge, and marking 12 as the height, settles both the face count and the formula.

  1. Reading a figure, table or graph moderate Understanding the question

    The figure gives one triangle with three length labels, 13, 13 and 10, and puts its height, 12, on a separate arrow beside it, where it is easy to overlook. (Lesh, Post & Behr, 1987; Kirsch & Mosenthal, 1990)

  2. Combines ideas moderate Working it out

    The solid is never drawn: students must see that the square's side equals the triangle's 10-inch base, count four triangles, and add triangle and square areas. (Embretson, 1998; Daniel & Embretson, 2010)

  3. Something you must already know minor Working it out

    A triangle's area uses its perpendicular height, not a slanted side, and a pyramid on a square base has four triangular faces; neither fact is given. (Anderson & Krathwohl, 2001)

Strategy: Sketch the pyramid: a square base whose side is the triangle's base, and one triangular face on each side of the square. Find each area with the matching formula, then add them all.

Traps

  • Misreads the figure: Reads a value, label or tick spacing in a figure, table or graph wrongly.
  • Information you don't need: The question gives numbers or facts that play no part in the answer.
  • Misunderstands the concept: A wrong belief about a concept: that percents can be added, that area grows like length, that averages can be averaged, that a bigger denominator means a bigger fraction.

The wrong answers, classified

What was corrected from the DOE handbook, and why

  • Explanation: The handbook ends “So the total surface area is 340 square feet.” The triangle’s dimensions are in inches and the question asks for square inches, so the site now reads “340 square inches.”

How the questions are analyzed, and the research behind it

Worked solution, step by step

Formulas used

Area of a triangle
A=12×b×hA = \frac{1}{2} \times b \times h
A is the area. b is the base, the side the triangle sits on. h is the height: the straight-up distance from the base to the top corner, at a right angle to the base. You take half because a triangle is half of a rectangle with the same base and height.
Area of a square
A=s×sA = s \times s
A is the area and s is the length of one side. All four sides of a square are equal, so the area is side times side.
Surface area
surface area=sum of the areas of all the faces\text{surface area} = \text{sum of the areas of all the faces}
A face is one flat side of a solid shape. The surface area is the total area of the outside. Picture unfolding the solid into flat pieces. Then add up the area of every piece.

  1. Sort out the question

    Raquel’s pyramid has a square base. Each side is a triangle like the one in the figure. The triangle’s base is 10 in. Its two slanted sides are 13 in. Its height, the arrow beside it, is 12 in. You need the total surface area, including the square base, in square inches.

  2. Picture the pyramid

    Surface area is the total area of all the flat sides, called faces. Each triangle stands on one edge of the square. So each edge of the square is 10 inches, the same as the triangle’s base. A square has 4 edges, so the pyramid has 4 triangles.

    surface area=sum of the areas of all the faces\text{surface area} = \text{sum of the areas of all the faces}

    Here that is 4 triangles plus 1 square. Watch out: counting only 3 triangles gives 280, choice A.

  3. Find the area of one triangle

    A=12×b×hA = \frac{1}{2} \times b \times h

    A=12×10×12=60A = \frac{1}{2} \times 10 \times 12 = 60

    Each triangle is 60 square inches. Watch out: the height is 12 in., the straight-up arrow. It is not 13 in., the slanted side. Using 13 gives 65 for each triangle and 360 in all, choice D.

  4. Find the area of the base

    The base is a square with sides of 10 inches, the same as each triangle’s base.

    A=s×sA = s \times s

    A=10×10=100A = 10 \times 10 = 100

    The square base is 100 square inches.

  5. Add all five faces

    surface area=4×60+100=240+100=340\text{surface area} = 4 \times 60 + 100 = 240 + 100 = 340

    The four triangles and the square together cover 340 square inches.

    So the answer is C, 340 square inches.

Check your answer

Each triangle is half of a 10 by 12 rectangle, which has an area of 120. So two triangles make 120, and four make 240. Add the base: 240+100=340240 + 100 = 340. The units fit too: inches times inches gives square inches.

More questions like this

The original DOE question
Question 96 as printed on page 86 of the DOE handbook.
As printed in the DOE’s NYC Guide to the Specialized High Schools Admissions Test (SHSAT) for 2025 Admissions, page 86, question 96. Open page 86 of the handbook (PDF) The handbook letters this question’s choices E–H; here they are A–D (E = A, F = B, G = C, H = D). This is the DOE’s version, before the corrections listed in the analysis.

Question 5 of 6

2018 Test B Math, question 8

Question

M=3N=P4=Q+5=R7>0M=3N=\frac{P}{4}=Q+5=\frac{R}{7}> 0

Based on the statement above, which variable has the greatest value?

  • AMM
  • BNN
  • CPP
  • DRR
Show the answer

Correct answer: D

Break the equations apart to each equal MM:

M=3NM=3N

M=P4M=\frac{P}{4}

M=Q+5M=Q+5

M=R7M=\frac{R}{7}

Pick a number to substitute into the equations, and solve the equations to find the values of MM, NN, PP, QQ, and RR.

Let M=2M=2. Since all the equations are equal to 2, substitute 2 to find each variable.

M=3NM=3N

2=3N2=3N

23=N\frac{2}{3}=N

M=P4M=\frac{P}{4}

2=P42=\frac{P}{4}

8=P8=P

M=Q+5M=Q+5

2=Q+52=Q+5

−3=Q-3=Q

M=R7M=\frac{R}{7}

2=R72=\frac{R}{7}

14=R14=R

Variable RR has the greatest value.

Question analysis

This algebra question sets five expressions equal to one another and to a positive number, then asks which variable has the greatest value. It tests whether students can rewrite each variable in terms of one shared value and compare them. What makes it tricky is that there are no numbers to compute, so each variable's size has to be reasoned out.

NYS standards
  • 7.EE.2 rewriting expressions to show relationships
  • 6.EE.7 one-step equations
Grade level
Grade 7 content, by NYS standard
Compared with grade 7
Above grade 7 Grade 7 students rewrite expressions to see how quantities relate, usually one equation at a time. This chain of five linked expressions, with no numbers to compute and a positivity condition to use, is a reasoning task beyond routine grade 7 work.
Estimated difficulty
Hard: combines ideas, needs a plan, and has more than one tempting wrong answer.
Solution
3 steps
Reading level
Question and choices: about grade 10, 16 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 rewards a strategy, not a calculation: once the shared value is named, each variable follows in one line and R is clearly largest. Without that step, students judge by how the expressions look, and the look is backwards, since the 3 in 3N makes N small and the 7 under R makes R large. The positivity condition at the end is easy to skip but is what fixes the order.

  1. Variables instead of numbers major Understanding the question

    There are no numbers to compute: five variables are tied together in the one chain M = 3N = P/4 = Q + 5 = R/7, and each must be compared through the shared value. (Koedinger & Nathan, 2004; Enright, Morley & Sheehan, 2002)

  2. No obvious method moderate Working it out

    Nothing says how to compare; the efficient move is to name the common value, or pick one such as 12, and rewrite each variable, which students must think of themselves. (Schoenfeld, 1985)

  3. Much to keep track of minor Working it out

    Five relations and the condition > 0 must be held at once; the condition matters, since with a negative common value the order of M, N, P and R would reverse. (Sweller, 1988; Carpenter, Just & Shell, 1990)

Strategy: Call the shared value k, a positive number, and rewrite each variable as an expression in k; or substitute a convenient positive value such as 12 and compare the results.

Traps

  • Equation written backwards: Writes a comparison the wrong way round, word for word: "six times as many students as professors" as 6S = P. The bigger quantity gets the bigger number.

The wrong answers, classified

How the questions are analyzed, and the research behind it

Worked solution, step by step

Formulas used

Undoing division
ab=c means a=b×c\frac{a}{b} = c \text{ means } a = b \times c
a is the top of the fraction, b is the bottom, and c is the result. Multiplying undoes dividing. So if a divided by b is c, then a is b times c.
Undoing multiplication
b×a=c means a=c÷bb \times a = c \text{ means } a = c \div b
b is the number multiplied by a, and c is the result. Dividing undoes multiplying. So to get a alone, divide c by b.

  1. Understand the chain

    The statement is a chain of equal signs. It says five expressions all have the same value. The last part says that value is greater than 0, so it is positive.

    You need to find which letter has the largest value.

  2. Pick a value to test

    All five expressions are equal, so give them one shared value. Pick a positive number that 3 divides evenly. That way N will be a whole number.

    Let the shared value be 12. Then M=12M = 12, and each of the other four expressions also equals 12.

  3. Solve for each letter

    Undo each operation to find each letter. Divide to undo times. Multiply to undo divide. Subtract to undo plus.

    3N=12, so N=12÷3=43N = 12 \text{, so } N = 12 \div 3 = 4

    P4=12, so P=12×4=48\frac{P}{4} = 12 \text{, so } P = 12 \times 4 = 48

    Q+5=12, so Q=12−5=7Q + 5 = 12 \text{, so } Q = 12 - 5 = 7

    R7=12, so R=12×7=84\frac{R}{7} = 12 \text{, so } R = 12 \times 7 = 84

  4. Compare the values

    The values are M = 12, N = 4, P = 48, Q = 7 and R = 84. R is the largest.

    Watch out: 3N does not make N big. It means 3 times N equals M, so N is only one third of M. That trap points to choice B. Also, P is big, but R is bigger. Check every letter before you pick choice C.

    So the answer is D, R.

Check your answer

Think without numbers. R divided by 7 is M, so R is 7 times M. P is only 4 times M. N is a third of M, and Q is 5 less than M. Since M is positive, 7 times M is the biggest.

More questions like this

The original DOE question
Question 65 as printed on page 154 of the DOE handbook.
As printed in the DOE’s Specialized High Schools Student Handbook 2018–2019, page 154, question 65. Open page 154 of the handbook (PDF)

Question 6 of 6

2026 Practice Test C Math, question 32

Question

A box plot titled MONTHLY HIGH TEMPERATURES IN NEW YORK above a number line labeled Temperature (°F), from 36 to 88 with a labeled tick every 4. The left whisker starts at about 39, just left of the tick for 40. The box runs from 48 to about 78, between the ticks for 76 and 80, with the median line at 64. The right whisker ends at 84.

The box plot shows the average monthly high temperatures in New York City for 12 months. What is the difference between the range and the interquartile range of the temperature data?

Enter your answer in the space.

Fill-in question: work out the answer and type it as a number.

Show the answer

Correct answer: 15

Determine the range by subtracting the minimum value on the box plot from the maximum value on the box plot:

Maximum value =84∘ F= 84^{\circ}\text{ F}, Minimum value =39∘ F= 39^{\circ}\text{ F}

84∘ F−39∘ F=45∘ F84^{\circ}\text{ F} - 39^{\circ}\text{ F} = 45^{\circ}\text{ F}

Determine the interquartile range by subtracting the lower quartile value on the box plot from the upper quartile value on the box plot:

Upper Quartile Value =78∘ F= 78^{\circ}\text{ F}, Lower Quartile Value =48∘ F= 48^{\circ}\text{ F}

78∘ F−48∘ F=30∘ F78^{\circ}\text{ F} - 48^{\circ}\text{ F} = 30^{\circ}\text{ F}

Determine the difference between the range (45° F) and the interquartile range (30° F):

45∘ F−30∘ F=15∘ F45^{\circ}\text{ F} - 30^{\circ}\text{ F} = 15^{\circ}\text{ F}

Question analysis

A box plot of New York City's average monthly high temperatures for 12 months sits above a number line labeled every 4 degrees. Students type the difference between the range and the interquartile range of the data. Two of the plot's values fall between labeled ticks, so careful reading of the scale decides the answer.

NYS standards
  • 7.SP.1 box plots and interquartile range
  • 6.SP.5c range, center, and overall pattern
Grade level
Grade 7 content, by NYS standard
Compared with grade 7
Above grade 7 Reading a box plot and finding its interquartile range are grade 7 skills. Here two of the five values fall between ticks spaced 4 apart, and the range, the IQR and their difference must all be found and typed with no choices.
Estimated difficulty
Hard: combines ideas, needs a plan, and has more than one tempting wrong answer.
Solution
3 steps
Reading level
Question and choices: about grade 7, 36 words.
Students, last 30 days
Not enough answers yet to show (it takes 10).
Why it is hard, traps and wrong answers (shows the answer)

Why it is hard

The method is standard, but the key rests on reading the scale between its labels. The axis is ticked only every 4 degrees, and the minimum and the upper quartile land off the ticks, so rounding either one to the nearest label moves the result by a degree or two with nothing to flag it. Students who find the range correctly can also stop there, entering 45, the larger of the two spreads, instead of the difference the question asks for.

  1. Reading a figure, table or graph major Understanding the question

    Two of the five values fall between ticks spaced 4 degrees apart: the left whisker ends just short of the 40 tick, at 39, and the box’s right edge sits midway between 76 and 80, at 78. (Lesh, Post & Behr, 1987; Kirsch & Mosenthal, 1990)

  2. Many steps minor Working it out

    Four values are read and combined in three subtractions, the range, the interquartile range and then their difference, so one misread value changes the final entry. (Daniel & Embretson, 2010; Enright, Morley & Sheehan, 2002)

  3. Something you must already know minor Working it out

    Neither measure is defined on the page: the range spans the whiskers, and the interquartile range is the width of the box, the upper quartile minus the lower. (Anderson & Krathwohl, 2001)

  4. An answer in an unexpected form minor Choosing the answer

    The result is typed with no choices to compare, so an entry one or two degrees off, from rounding a value to the nearest tick, looks just as finished as the right one. (Enright, Morley & Sheehan, 2002)

Strategy: Read the minimum, both quartiles and the maximum, judging where each mark falls between the ticks, then subtract for the range and for the IQR, and subtract those two results.

Traps

The wrong answers, classified

How the questions are analyzed, and the research behind it

Worked solution, step by step

Formulas used

Range
range=maximum−minimum\text{range} = \text{maximum} - \text{minimum}
The maximum is the greatest value, at the right end of the right whisker. The minimum is the least value, at the left end of the left whisker. The range tells how far the whole set of data spreads.
Interquartile range (IQR)
IQR=Q3−Q1\text{IQR} = Q_3 - Q_1
Q3 is the upper quartile, the right edge of the box. Q1 is the lower quartile, the left edge of the box. The IQR is the width of the box. It tells how far the middle half of the data spreads.

  1. Sort out the question

    A box plot shows data with five numbers. The two whiskers are the lines on each side of the box. Their ends are the minimum, the least value, and the maximum, the greatest. The box runs from the lower quartile to the upper quartile. These are the middles of the lower half and the upper half of the data. The line inside the box is the median, the middle value.

    You need the range minus the interquartile range (IQR), in degrees.

  2. Read the values between the ticks

    The ticks on the number line are 4 degrees apart. So each degree is one quarter of the space between two ticks. Three values sit right on ticks: the box’s left edge at 48, the median at 64, and the right whisker’s end at 84.

    • The left whisker starts just left of the 40 tick. It sits about one quarter of the way back toward 36. So the minimum is 40−1=3940 - 1 = 39 degrees.
    • The box’s right edge is halfway between 76 and 80. Halfway is 78 degrees.

  3. Find the range

    Use the range formula:

    range=84−39=45\text{range} = 84 - 39 = 45

    The data spread over 45 degrees.

    Watch out: rounding the minimum to the 40 tick gives a range of 44. Then the final answer comes out 14, which is wrong.

  4. Find the IQR

    Use the IQR formula with the two edges of the box:

    IQR=78−48=30\text{IQR} = 78 - 48 = 30

    The middle half of the data spreads over 30 degrees.

    Watch out: reading the box’s right edge as 76 gives an IQR of 28. Then the final answer comes out 17.

  5. Subtract the IQR from the range

    The question asks for the difference between the two:

    45−30=1545 - 30 = 15

    Watch out: 45 is only the range. Do not stop there. Type only the number, with no degree sign.

    So you would enter 15.

Check your answer

The range covers the whole plot, and the IQR covers only the box. So their difference is the two whiskers added together. The left whisker is 48−39=948 - 39 = 9 degrees long. The right whisker is 84−78=684 - 78 = 6 degrees long. 9+6=159 + 6 = 15, which matches.

More questions like this

The original DOE question
Question 32 as shown on the DOE’s digital test, page 105 of its printable version.
As printed in the DOE’s printable version of 2026 Practice Test C Math, page 105, question 32.

Sample #714297