SHSAT Sunset

Six SHSAT Questions

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.

RefreshNew TestYour practice tests

Question 1 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 2 of 6

2026 Practice Test B English, question 28
Passage Looking for the Smallest Spark of Everything

Looking for the Smallest Spark of Everything

Located underground near Geneva, Switzerland, the Large Hadron Collider (LHC) helps scientists study and understand how the smallest particles of matter interact with one another. The LHC propels atomic particle beams along a 17-mile-long ring.

There are the things the world is made of,
things we can see and feel, and then
there are the things even smaller, things that seem
to exist only when we are looking right at them.

So beneath the level of molecules are atoms,
and beneath the level of atoms, we find
protons, electrons, neutrons; and beneath that—
what, exactly? Because we are talking about
everything here: your fingernail,
the candy at the back of your mouth,
the coffee your teacher drank this morning,
your little sister, and the stuffed dog
she used to carry around with her everywhere.
And everywhere.

Everything and everywhere
are made up of the same stuff, whatever
it is. How do we find it? We can listen for it
in the wavelengths from deep space,
talking back to us from unimaginable
distances. Or we can build long,
deep circular tunnels beneath the surface
of this Earth and race particles
(like racing cars, only very tiny cars
flashing along at close to the speed of light)
until everything we think we know
bangs against everything else we know.

And there, in the explosion, in the darkness,
briefly incandescent, they appear:
the quarks, the leptons, and the bosons;
the baryons and the mesons. Their names
sound like dinosaurs or maybe bands
playing terrible music in someone’s garage.

The one thing we know for sure
is that they spin. This is how gravity
enters our world, how our world is held
both together and apart, what keeps
together the pencil in your hand right now
as well as separate from, say,
Jupiter. They spin, and it is only down there
in the darkness—in the vast garage
where physicists jot down
what they can, whatever seems most real—
that they let us perceive their wild dancing,
combusting to the music they make.

Question

Read lines 39–44 from the poem.

They spin, and it is only down there
in the darkness—in the vast garage
where physicists jot down
what they can, whatever seems most real—
that they let us perceive their wild dancing,
combusting to the music they make.

The lines reveal the speaker’s

  • Afrustration with the research facilities physicists use.
  • Bbelief that physicists are frantically working toward a new discovery.
  • Cinterest in physicists and their study of particles.
  • Dcertainty that physicists are working in secrecy.
Show the answer

Correct answer: C

The question asks what lines 39–44 reveal about the speaker.

A. Incorrect. While the discoveries are made “in the darkness” (line 40), the imagery conveys the speaker’s positive tone through descriptions like “perceive their wild dancing” (line 43) and “combusting to the music they make” (line 44), not frustration.

B. Incorrect. In lines 39–44, the imagery of energetic movement (“They spin,” “their wild dancing,” and “combusting to the music they make”) is used to describe the particles, not the physicists.

C. CORRECT. The speaker uses the phrases “only down there” (line 39), “physicists jot down … whatever seems most real” (lines 41–42), and “they let us perceive” (line 43) to convey that the physicists have a rare role in studying the mysteries of the universe and that the speaker appreciates and is interested in their work.

D. Incorrect. While the description of the experiments occurring “in the darkness” (line 40) may create a sense of secrecy, the secrets that the darkness refers to are the mysteries of subatomic particles, not the work processes that the physicists use.

Question analysis

The final six lines of “Looking for the Smallest Spark of Everything” describe particles spinning in the darkness of a “vast garage” where physicists work. This question asks what those lines reveal about the speaker. The long sentence is broken by dashes and mixes images of the particles with images of the scientists, so students must sort out which words describe which.

NYS standards
  • 7R6 point of view and author position
  • 7R4 word meaning and choice
Grade level
Grade 8 reading and task
Compared with grade 7
Above grade 7 Grade 7 students infer a speaker’s attitude, usually from a clear statement. These six lines form one sentence broken by dashes, students must keep track of who does what, and the attitude is never stated, so the task is above typical grade 7 work.
Estimated difficulty
Hard: combines ideas, needs a plan, and has more than one tempting wrong answer.
Evidence
Answered from one paragraph or stanza
Reading level
Passage: 346 words (a poem; reading level not measured); question and choices: about grade 8, 82 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 sentence is the hardest part: the physicists appear in a clause set off by dashes, and the two uses of “they” around them refer to different subjects. Students who attach “wild dancing” to the physicists see frantic work, and those who stop at “in the darkness” see secrecy. The right choice is mild and general, so it is easy to pass over, yet it fits because the speaker lingers on the scene with evident fascination and nothing in the lines expresses frustration or certainty.

  1. Complex sentences major Understanding the question

    Lines 39–44 are one sentence broken by a dash clause, and its two uses of “they” point different ways: “what they can” means the physicists, “they let us perceive” the spinning particles. (Abedi & Lord, 2001; Freedle & Kostin, 1993; Messick, 1989)

  2. Figurative or literary language moderate Understanding the question

    The particles’ “wild dancing,” “combusting to the music they make,” and the lab as “the vast garage” are images whose tone, delight rather than complaint, students must judge. (Graesser, Singer & Trabasso, 1994; Kintsch, 1998)

  3. Reading between the lines moderate Working it out

    No line states the speaker’s attitude; interest has to be read from how closely the speaker follows the work of physicists who “jot down / what they can, whatever seems most real.” (Graesser, Singer & Trabasso, 1994; Kintsch, 1998)

Strategy: Untangle the sentence in lines 39–44 by finding who spins, who jots things down and who lets us perceive, then decide what the description reveals about how the speaker regards the scene.

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.
  • Wrong tone or attitude: Misjudges the tone, attitude or point of view, such as reading admiration as criticism, or taking a character's or subject's feelings for the author's.
  • Reads too much in: A reasonable-sounding conclusion that goes further than the text allows.

The wrong answers, classified

How the questions are analyzed, and the research behind it

Working it out, step by step

  1. Figure out what the question asks

    This asks what lines 39–44 show about the speaker. The lines are one long sentence. It uses the word “they” for two different groups. So first sort out who is doing what.

  2. Sort out who does what

    • “They spin” means the particles spin.
    • “physicists jot down / what they can” means the physicists write down what they can. Here “they” is the physicists.
    • “they let us perceive their wild dancing” means the particles let us see their dance. Perceive means notice or see. Here “they” is the particles again.

  3. Put the sentence in plain words

    The part between the dashes describes the place. It is the huge tunnel, “the vast garage,” where physicists take notes. Without that part, the sentence says this: only down there do the particles let us see their wild dance. Combusting means bursting into flame. It is a lively, joyful picture.

  4. Decide what it shows about the speaker

    The speaker brings the physicists into the scene and shows their careful work. They write down “whatever seems most real.” The speaker also shows that all of us see the particles only through this research. The speaker cares about the physicists and what they study. That is interest.

  5. Check each choice

    • A does not fit. “The vast garage” is playful, and the lines end in delight. There is no complaint.
    • B does not fit. The wild motion belongs to the particles. The physicists only “jot down / what they can.”
    • C fits. The speaker follows the physicists’ work and the particles they study.
    • D does not fit. It is dark because the tunnel is underground. Nothing suggests the work is secret.

    Watch out: B is tempting because the lines sound frantic, or wild and rushed. But “they let us perceive” means the particles, so the dancing is theirs, not the physicists’.

  6. Choose the answer

    The lines show the speaker paying close attention to physicists and the particles they study. So the answer is C, “interest in physicists and their study of particles.”

Why this answer and not the closest wrong one

B is the closest wrong choice. The words “wild dancing” and “combusting” do sound frantic. But they describe the particles. In “they let us perceive,” “they” means the particles. The physicists just “jot down / what they can.” So the lines do not show physicists rushing. They show the speaker’s interest, which is C.

More questions like this

The original DOE question
Question 28 as shown on the DOE’s digital test, page 39 of its printable version.
As printed in the DOE’s printable version of 2026 Practice Test B English, page 39, question 28.
The passage “Looking for the Smallest Spark of Everything” as printed (pages 32–33)The passage “Looking for the Smallest Spark of Everything” as printed on page 32 of the DOE handbook.The passage “Looking for the Smallest Spark of Everything” as printed on page 33 of the DOE handbook.

Question 3 of 6

2026 Practice Test C English, question 39
Passage Excerpt from “Growing Peppers on the ISS Is Just the Start of Space Farming”

Excerpt from “Growing Peppers on the ISS Is Just the Start of Space Farming”

by Melanie Canales

The author, Melanie Canales, is a first-generation Peruvian American farmer and beekeeper based in Virginia’s Shenandoah Valley, on lands of the indigenous Monacan and Manahoac tribes. Her work focuses on creating healthy relationships between people and their surrounding ecosystems.

Unburdened by the constraints of gravity, red and green peppers jut out at 45-degree angles inside the Advanced Plant Habitat (APH), a sort of space terrarium not much larger than a microwave. Four chile pepper plants stand effortlessly upright, despite the dozens of glossy fruits weighing them down. These plants have lived entirely in space; their leaves have never been chewed on by insects or rustled by a summer breeze, [and] their stems are unfamiliar with bending toward the sun’s arc across the sky. Scissors glint under the tank’s white and blue lights as astronaut Mark Vande Hei and his team snip the stems of those that are ready for harvest. The peppers whirl around their heads until the astronauts catch them and tape them against a board to photograph.

Back on Earth, the Plant Habitat-04 team of engineers and plant scientists are observing and conferring with the astronauts. Of the 26 peppers in this batch, only the 14 finest will stay on the International Space Station [ISS] for consumption. The rest will be wrapped in foil, sealed in a Ziploc bag, then frozen at a brisk −80 degrees, until they can come roaring back to Earth in the next cargo capsule to be studied later. Now, after a 137-day growth cycle, the astronauts remove the plants from the module and trash them. Project Plant Habitat-04 is complete. It’s taco night on the ISS.

Since 2014, NASA1 has experimented with growing lettuces, brassicas,2 and zinnias3 in space, an endeavor that relies on highly specialized technology over 50 years in the making. [Fall 2021’s] two successful pepper harvests . . . will provide data on the nutritional and psychological benefits of growing vegetables on-craft, as well as a crop’s ability to reliably produce long-term in microgravity. While controlled environmental agriculture is not new, the APH experiment represents an evolution in specialized growth habitats. It doesn’t aim to re-create Earth’s conditions, but to perfect each isolated variable of plant growth in the clinical environment of a spaceship.

“The Advanced Plant Habitat is the most complex plant growth system on orbit today,” says Lashelle Spencer, a plant scientist at NASA’s Kennedy Space Center. Its more than 180 sensors control and monitor temperature, humidity, and carbon dioxide. The astronauts can adjust the color and intensity of the light, and how much moisture the plants’ roots are getting. It waters itself.

It’s the day after Thanksgiving, and Spencer has been at Kennedy since 5 a.m. to facilitate the peppers’ final harvest. As part of the project team, she played a crucial role in preparing the seeds that were sent hurtling into space in June and guiding the astronauts through maintaining the plants in orbit. . . . Though astronauts can spend upwards of 100 days in space, their on-mission meals come dehydrated and pre-packaged; their vitamins and minerals are isolated in supplements, which lose nutritional value the longer they’re stored. Spencer’s goal is to create the conditions necessary for cultivating healthy plants in space, so those plants can sustain healthy astronauts on long-term missions. Astronaut food is great, she says—“especially the shrimp cocktail. But you’re missing that crunch. You’re missing that fresh pop of flavor, the green flavor that’s not there in that packaged food.”

The sensory experience of growing productive crops can also help mitigate4 the psychological effects of long-term space travel. . . . Spencer says the team cracked open the door of the APH every day to observe their vegetable companions with all the tenderness of home gardeners. When harvest day came, they batted their bounty around the ISS, taking selfies and delighting in watching the fruits pirouetting around the spacecraft. . . .

“We were thinking no heat, so that [the peppers] wouldn’t be dangerous, but maybe the astronauts need a little spice in their life,” says Paul Bosland, who along with his colleagues at the Chile Pepper Institute genetically engineered5 the NuMex Española Improved chile pepper seeds grown in Plant Habitat-04. . . .

Working with NASA, Bosland cultivated a variety that could accommodate both the nutritional needs of astronauts as well as the logistics of growing a plant in space. . . .

. . . The experiment is helping gather the data necessary to determine the nutritional content of crops grown in space, and therefore how many people they can feed, and for how long. Though much is still unknown, Spencer is certain of one thing that future astronauts will need to do: “I think in an optimal world, a scientist like me would say that they would be growing plants from day one. From the day they left to the day they came back, they would be growing them.”

From “Growing Peppers on the ISS Is Just the Start of Space Farming” by Melanie Canales from WIRED, December 21, 2021. Copyright © 2021 Condé Nast. All rights reserved.

1NASA: National Aeronautics and Space Administration

2brassicas: a large genus of herbs, such as broccoli and cabbage

3zinnias: a genus of herbs and low shrubs that have flowers at their heads

4mitigate: to make something less severe or harmful

5genetically engineered: combined parts of DNA from different plants to produce a new plant

Question

The description in paragraph 5 of Lashelle Spencer’s goal develops a central idea of the excerpt by

  • Aillustrating that certain types of packaged foods available in space lack particular flavors.
  • Bsupporting the notion that spending more than 100 days in space is detrimental to astronauts’ health.
  • Coffering an example of how the limited selection of on-mission meals becomes less appealing over time.
  • Dmaking an important point about the astronauts’ current reliance on supplements for vitamins and minerals.
Show the answer

Correct answer: D

The question asks how the description of Lashelle Spencer’s goal in paragraph 5 develops a central idea of the excerpt.

A. Incorrect. Although Spencer mentions how astronauts miss certain eating experiences like the “fresh pop” and “green flavor” not found in packaged and dehydrated food, a central idea of the excerpt is that there is a need to provide fresh, healthy foods for long missions, not that food flavor should be improved.

B. Incorrect. While the excerpt focuses on how spending more than 100 days in space affects nutrition, it does not discuss specific ways in which spending long periods of time in space is detrimental to the health of astronauts.

C. Incorrect. Although paragraph 5 states that astronauts “can spend upwards of 100 days in space,” the excerpt does not develop a central idea that existing meals in space become less appealing over time.

D. CORRECT. The paragraph explains that astronauts currently rely on supplements for vitamins and minerals, which lose their nutritional value over time. Spencer’s goal for growing plants in space is to “sustain healthy astronauts,” supporting a central idea that astronauts need more nutritionally valuable food to sustain them while in space for long periods of time.

Question analysis

Lashelle Spencer’s goal for growing plants in space is described in paragraph 5 of the WIRED excerpt, and this central-idea question asks how that description develops a central idea of the whole excerpt. Students must connect a single sentence about a scientist’s aim to the article’s larger point, and every choice draws on details from that same paragraph.

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 develops, usually through a plainly stated example. Here the goal’s connection to the central idea runs through the sentences around it, and the choices are abstract restatements, which asks more than typical grade 7 work.
Estimated difficulty
Hard: combines ideas, needs a plan, and has more than one tempting wrong answer.
Evidence
Answered from several paragraphs or stanzas
Reading level
Passage: about grade 10, 890 words; question and choices: about grade 12, 75 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 choice draws on paragraph 5, and none mentions growing plants, which leaves students looking for the goal without finding it. The flavor quotation that follows the goal is the most memorable detail and the easiest wrong pick. The key works only through context: the goal answers the problem the previous sentence sets out, crews depending on supplements that weaken in storage, which is why it serves the article’s case for fresh food on long missions.

  1. Reading between the lines moderate Working it out

    Spencer’s goal names healthy plants and healthy astronauts but no supplements; its link to the key runs through the sentence before it, where vitamins sit in supplements that “lose nutritional value the longer they’re stored.” (Graesser, Singer & Trabasso, 1994; Kintsch, 1998)

  2. Every choice must be checked moderate Choosing the answer

    No choice restates the goal of growing plants itself, so none can be matched at a glance; each must be tested for whether it ties the goal to the excerpt’s concern with nutrition on long missions. (Embretson & Wetzel, 1987)

  3. How, not what minor Working it out

    The question asks how the description develops a central idea, its role in the article, so knowing what Spencer wants is only the first step toward the answer. (Anderson & Krathwohl, 2001)

  4. Evidence in several places minor Working it out

    The central idea must come from the whole excerpt: paragraph 3’s “nutritional and psychological benefits,” paragraph 8’s “nutritional needs of astronauts” and paragraph 9’s “nutritional content of crops.” (Kirsch & Mosenthal, 1990; Gorin & Embretson, 2006)

Strategy: State a central idea of the whole excerpt in your own words, reread Spencer’s goal with the sentences around it in paragraph 5, and pick the option that connects the goal to that central idea.

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.
  • 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

How the questions are analyzed, and the research behind it

Working it out, step by step

  1. Figure out what the question asks

    A central idea is a main point the whole article keeps coming back to. This question asks how Spencer’s goal, in paragraph 5, helps build one of those main points. So first, find the goal. Then connect it to the big idea.

  2. Find the goal and the sentence before

    Paragraph 5 says: “Spencer’s goal is to create the conditions necessary for cultivating healthy plants in space, so those plants can sustain healthy astronauts on long-term missions.” Cultivating means growing. The sentence just before it shows why she has this goal. Astronauts’ “vitamins and minerals are isolated in supplements, which lose nutritional value the longer they’re stored.”

  3. Connect the goal to the big idea

    Today astronauts get vitamins from pills, called supplements. Those pills lose their health value as they sit. Spencer wants fresh plants grown in space to keep astronauts healthy instead. So her goal points to a problem: relying on weak pills. The article returns to food and health again and again. Paragraph 8 mentions “the nutritional needs of astronauts.” Nutritional means having to do with healthy food.

  4. Check each choice

    • A is wrong. The “fresh pop of flavor” line comes after the goal. It is about taste, a side point.
    • B is wrong. The article never says long trips in space harm astronauts’ health.
    • C is wrong. It is the stored supplements that lose value over time, not meals that get less tasty.
    • D is right. The goal answers a problem: astronauts depend on supplements that weaken in storage. That ties to the article’s idea that astronauts need healthy fresh food on long trips.

    Watch out: Spencer’s flavor quote is the most memorable line nearby, so A pulls hard. But her goal is about health, not taste.

  5. Choose the answer

    Spencer wants healthy plants because pills are not enough. So the answer is D, “making an important point about the astronauts’ current reliance on supplements for vitamins and minerals.” Reliance means depending on something.

Why this answer and not the closest wrong one

A is the closest wrong answer. Spencer really does miss the crunch and flavor of fresh food. But her goal is to “sustain healthy astronauts,” which is about health. Health is the big idea the article keeps returning to. D connects the goal to that idea through the supplements that lose value.

More questions like this

The original DOE question
Question 39 as shown on the DOE’s digital test, page 57 of its printable version.
As printed in the DOE’s printable version of 2026 Practice Test C English, page 57, question 39.
The passage “Excerpt from “Growing Peppers on the ISS Is Just the Start of Space Farming”” as printed (pages 50–51)The passage “Excerpt from “Growing Peppers on the ISS Is Just the Start of Space Farming”” as printed on page 50 of the DOE handbook.The passage “Excerpt from “Growing Peppers on the ISS Is Just the Start of Space Farming”” as printed on page 51 of the DOE handbook.

Question 4 of 6

2026 Practice Test C Math, question 15

Question

A grocery store sells 1-gallon containers of milk for $3.99. The store also sells orange juice in a 6-pack of 5.5-fluid-ounce bottles for $1.79. Suppose the store wants to sell its orange juice in gallon containers instead. To the nearest dollar, how much more would a gallon of orange juice cost than a gallon of milk?

Enter your answer in the space.

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

Show the answer

Correct answer: 3

To determine the cost of a gallon of orange juice, begin by finding the total number of ounces in the 6-pack of bottles:

5.5 oz×6=33 oz5.5\text{ oz} \times 6 = 33\text{ oz}

So, 33 oz of orange juice costs $1.79.

There are 128 oz in 1 gallon. Set up a proportion using the $1.79 cost per 33 oz of orange juice and the unknown cost (x) per 1 gallon of orange juice:

33 oz$1.79=128 ozx\frac{33\text{ oz}}{\$1.79} = \frac{128\text{ oz}}{x}

Cross multiply to solve for x in the proportion:

(33)×(x)=($1.79)×(128)(33) \times (x) = (\$1.79) \times (128)

33x=$229.1233x = \$229.12

x≈$6.94x \approx \$6.94

So, the orange juice costs $6.94 per gallon, and the milk costs $3.99 per gallon.

Subtract the cost per gallon of milk from the cost per gallon of orange juice.

$6.94−$3.99=$2.95\$6.94 - \$3.99 = \$2.95

Round the difference to the nearest dollar.

$2.95 rounds to $3.

Question analysis

A store sells milk by the gallon for $3.99 and orange juice in six-packs of 5.5-fluid-ounce bottles for $1.79. Students work out what a gallon of the juice would cost at the same price per ounce and how much more that is than the milk, to the nearest dollar. The ounces in a gallon must be known, and several steps involve decimals.

NYS standards
  • 7.RP.3 multistep ratio and percent problems
  • 6.RP.3d converting measurement units
Grade level
Grade 7 content, by NYS standard
Compared with grade 7
Above grade 7 Unit prices are grade 6 and 7 work, but this chains five steps with decimals and needs a fact the question does not give, the number of fluid ounces in a gallon. Typing a rounded difference, with no choices, adds risk.
Estimated difficulty
Hard: combines ideas, needs a plan, and has more than one tempting wrong answer.
Solution
5 steps
Reading level
Question and choices: about grade 5, 60 words.
Corrected from the DOE handbook
  • A rounded value in the explanation is now marked as approximate (≈ instead of =).
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 calculation is long, and its key fact is missing from the page. Students who know the 128 fluid ounces still face a division by 33 that does not come out evenly, which tempts them to round the price per ounce to 5 cents and lose about 50 cents a gallon. Keeping the exact quotient to the end, or scaling 33 ounces up by about 3.9, keeps the difference near $2.95, which rounds to 3.

  1. Something you must already know moderate Working it out

    The question never says that a gallon holds 128 fluid ounces, yet the whole comparison depends on it; the 6-pack holds only 6 × 5.5 = 33 ounces. (Anderson & Krathwohl, 2001)

  2. Many steps moderate Working it out

    Five moves follow one another: the ounces in a pack, the scale-up to 128 ounces, the division by 33, the subtraction of $3.99 and the rounding to a whole dollar. (Daniel & Embretson, 2010; Enright, Morley & Sheehan, 2002)

  3. Error-prone arithmetic minor Working it out

    1.79 × 128 = 229.12 and 229.12 ÷ 33 are long decimal calculations without a calculator, and a slip in either moves the price of a gallon. (Brown & Burton, 1978; Junker & Sijtsma, 2001)

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

    The rounded difference is typed with no choices, so an unrounded $2.95, or a figure rounded too soon, looks just as finished as the whole-dollar answer. (Enright, Morley & Sheehan, 2002)

Strategy: Find the ounces in one six-pack, scale its price up to the 128 fluid ounces in a gallon, subtract the milk's price, and round only at the end.

Traps

  • Stops one step early: A choice is a number from partway through the solution.
  • Rounds too early: Rounds a value partway through, or rounds the wrong way, so the final answer drifts from the exact one.
  • Misreads the question: Misses or misreads a condition or a word in the question: "at least", "each", "remaining", "not".

The wrong answers, classified

What was corrected from the DOE handbook, and why

  • Explanation: The DOE’s explanation goes from 33x = $229.12 to “x = $6.94”. But 229.12 ÷ 33 = 6.9430…, so $6.94 is the cost per gallon rounded to the cent. The site writes x ≈ $6.94. Nothing else changes: $6.94 − $3.99 = $2.95, which rounds to $3, and the unrounded cost gives the same answer.

How the questions are analyzed, and the research behind it

Worked solution, step by step

Formulas used

Fluid ounces in a gallon
fluid ounces=128×gallons\text{fluid ounces} = 128 \times \text{gallons}
A gallon holds 128 fluid ounces. This is a fact you must know, because the question does not give it. A fluid ounce measures an amount of liquid. Multiply gallons by 128 to change them into fluid ounces.
Cross-multiplying a proportion
ab=cd means a×d=b×c\frac{a}{b} = \frac{c}{d} \text{ means } a \times d = b \times c
A proportion says two ratios are equal. Here each ratio is ounces over dollars. a and c are the tops, and b and d are the bottoms. Multiply each top by the other bottom, and the two products are equal. That turns the proportion into an equation.

  1. Sort out the question

    Milk costs $3.99 for 1 gallon. Orange juice comes in a 6-pack of 5.5-fluid-ounce bottles for $1.79. You need how much more a gallon of juice would cost than a gallon of milk. Round to the nearest dollar.

    The question doesn’t say how big a gallon is. You must know this fact: 1 gallon is 128 fluid ounces.

  2. Find the ounces in a 6-pack

    Each of the 6 bottles holds 5.5 fluid ounces:

    6×5.5=336 \times 5.5 = 33

    So $1.79 buys 33 fluid ounces of juice.

  3. Set up a proportion

    Let x be the cost in dollars of a gallon, 128 fluid ounces, of juice. The price per ounce stays the same. So ounces over dollars is the same for the pack and the gallon:

    331.79=128x\frac{33}{1.79} = \frac{128}{x}

    Cross-multiply:

    33×x=1.79×128=229.1233 \times x = 1.79 \times 128 = 229.12

  4. Find the cost of a gallon

    Divide both sides by 33:

    x=229.12÷33≈6.94x = 229.12 \div 33 \approx 6.94

    The sign ≈ means about equal. The exact value is 6.943…, so a gallon of juice costs about $6.94.

    Watch out: don’t round too early. One ounce costs about $0.054. Rounding that to $0.05 makes a gallon $6.40, and your answer becomes 2.

  5. Subtract the milk’s price

    Find how much more the juice costs:

    6.94−3.99=2.956.94 - 3.99 = 2.95

    A gallon of juice costs $2.95 more than a gallon of milk.

    Watch out: entering 7, the juice’s price, forgets to subtract the milk.

  6. Round and enter it

    The question asks for the nearest dollar. $2.95 is between $2 and $3. Its cents, 95, are 50 or more, so it rounds up to $3. Do not enter 2.95.

    Type only the number in the box. So you would enter 3.

Check your answer

Estimate. 128 ounces is almost 4 packs, since 4×33=1324 \times 33 = 132. Four packs cost 4×1.79=7.164 \times 1.79 = 7.16 dollars, so a gallon costs a bit less than that. Milk costs about $4. About $7 minus $4 is $3, which matches.

More questions like this

The original DOE question
Question 15 as shown on the DOE’s digital test, page 88 of its printable version.
As printed in the DOE’s printable version of 2026 Practice Test C Math, page 88, question 15. This is the DOE’s version, before the corrections listed in the analysis.

Question 5 of 6

2026 Practice Test C Math, question 18

Question

I. s−ts - t
II. st2st^{2}
III. sts^{t}

If s is a positive integer and t is a negative integer, which of the above expressions must be a positive number?

  • AII only
  • BI and II only
  • CII and III only
  • DI, II, and III
Show the answer

Correct answer: D

Each of the three expressions must be considered:

Expression I: s−ts - t, where s is a positive integer and t is a negative integer:

Subtracting a negative integer is the equivalent of adding a positive integer, so s−ts - t is equivalent to finding the value of s+(−t)s + (-t), which must result in a positive number.

Expression II: st2st^{2}, where s is a positive integer and t is a negative integer:

Squaring a negative integer results in a positive integer, so s(−t)2s(-t)^{2} is equivalent to finding the value of st2st^{2}, which must result in a positive number.

Expression III: sts^{t}, where s is a positive integer and t is a negative integer:

A negative exponent results in the reciprocal of the same exponential expression, so sts^{t} is equivalent to finding the value of 1s(−t)\frac{1}{s^{(-t)}}, which must result in a positive number.

Therefore, Expressions I, II, and III must all result in a positive number.

Question analysis

Three expressions, s − t, s times t squared, and s to the power t, are listed, and students decide which must be positive when s is a positive integer and t is a negative integer. It tests sign rules for subtraction and multiplication and the meaning of a negative exponent. Each expression has to be judged for every possible pair, not just one example.

NYS standards
  • 8.EE.1 integer exponent properties
  • 7.NS.1c rational number subtraction
  • 7.NS.2a rational number multiplication
Grade level
Grade 8 content, by NYS standard
Compared with grade 7
Above grade 7 Grade 7 students learn sign rules for subtracting and multiplying signed numbers. Here they reason about letters rather than numbers, decide what must always hold, and handle a negative exponent, a grade 8 idea.
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 5, 42 words.
Corrected from the DOE handbook
  • Two steps of the explanation that treated t as a positive number were corrected.
  • A punctuation error 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

The three expressions test three different sign facts: subtracting a negative, squaring a negative, and raising to a negative power. The last is the trap, since a negative exponent seems to promise a negative result when it really gives a fraction, and that belief alone leads to a listed choice. Trying s = 2 and t = −3 gives 5, 18 and 1/8, all positive, and the rules show why no other pair can change that.

  1. Variables instead of numbers moderate Understanding the question

    No values are given for s and t, only their signs, and must means each expression has to be positive for every such pair, not just for one example. (Koedinger & Nathan, 2004; Enright, Morley & Sheehan, 2002)

  2. Something you must already know moderate Working it out

    Expression III needs the meaning of a negative exponent, s to the power t equals 1 over s to the power −t, a grade 8 rule the question does not state. (Anderson & Krathwohl, 2001)

  3. Every choice must be checked minor Choosing the answer

    Each of the three expressions is judged on its own and the choices combine the verdicts, so one wrong judgment anywhere points to a wrong combination. (Embretson & Wetzel, 1987)

Strategy: Try a pair such as s = 2 and t = −3 in each expression, then explain why its sign could or could not change for any other positive s and negative t.

Traps

  • Misunderstands the concept: A wrong belief about a concept: that percents can be added, that area grows like length, that averages can be averaged, that a bigger denominator means a bigger fraction.
  • 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

What was corrected from the DOE handbook, and why

  • Explanation: The question makes t the negative integer, but two steps of the DOE’s explanation write the negative integer as −t, as if t were positive. For Expression I it says “s − (−t) is equivalent to finding the value of s + t, which must result in a positive number”: s − (−t) is not Expression I, and with the question’s t, s + t need not be positive (s = 1 and t = −2 give −1). For Expression III it says “s^(−t) is equivalent to finding the value of 1/s^t”, about s^(−t) rather than Expression III. The site now says that s − t is equivalent to s + (−t), and that s^t is equivalent to 1/s^(−t). Since t is negative, −t is a positive integer, so s + (−t) is the sum of two positive integers and 1/s^(−t) is the reciprocal of a positive integer: both positive, and the answer, I, II and III, is unchanged. The step for Expression II, s(−t)² = st², is true for any t and is unchanged.
  • Explanation: The DOE’s explanation introduces Expression III as “s^t. where s is a positive integer and t is a negative integer”, with a period where Expressions I and II (and the 2022–23 guide, which first printed this explanation) have a comma. The site has the comma.

How the questions are analyzed, and the research behind it

Worked solution, step by step

Formulas used

Subtracting a number
s−t=s+(−t)s - t = s + (-t)
s and t are integers, and −t is the opposite of t. Subtracting a number is the same as adding its opposite. When t is negative, −t is positive. So subtracting t adds a positive amount.
A negative exponent
st=1s−ts^{t} = \frac{1}{s^{-t}}
s is the base and t is the exponent. When t is negative, −t is positive. So a negative exponent means 1 over the base to a positive exponent. For example, 2 to the power −3 is 1 over 2³, which is 1/8.

  1. Sort out the question

    An integer is a whole number or its opposite, such as −2, 0 or 5. Here s is a positive integer, like 1, 2 or 3. And t is a negative integer, like −1, −2 or −3. Must means always. An expression counts only if it is positive for every such pair.

  2. Try one pair of numbers

    Try s = 2 and t = −3 in each expression:

    • I: 2−(−3)=2+3=52 - (-3) = 2 + 3 = 5
    • II: 2×(−3)2=2×9=182 \times (-3)^{2} = 2 \times 9 = 18
    • III: 2−3=123=182^{-3} = \frac{1}{2^{3}} = \frac{1}{8}

    All three are positive this time. Now see why that always happens.

  3. Explain expression I

    Use the rule for subtracting:

    s−t=s+(−t)s - t = s + (-t)

    t is negative, so its opposite, −t, is positive. So s − t is a positive plus a positive. That is always positive.

    Watch out: subtracting does not always make a number smaller. Subtracting a negative makes it bigger. Missing this leads to choice C.

  4. Explain expression II

    t2t^{2} means t × t. A negative times a negative is positive, so t2t^{2} is always positive. Then s×t2s \times t^{2} is a positive times a positive. That is always positive too.

  5. Explain expression III

    Use the rule for a negative exponent:

    st=1s−ts^{t} = \frac{1}{s^{-t}}

    −t is a positive integer, so s−ts^{-t} is a positive integer. So sts^{t} is 1 over a positive number. That is a positive fraction.

    Watch out: a negative exponent does not make the answer negative. It makes a fraction. Thinking it does leads to choice B, I and II only.

  6. Choose the answer

    Each of the three expressions is positive for every positive s and negative t. None of them can ever be zero or negative.

    So the answer is D, I, II, and III.

Check your answer

Try the values closest to 0: s = 1 and t = −1. I gives 1−(−1)=21 - (-1) = 2. II gives 1×(−1)2=11 \times (-1)^{2} = 1. III gives 1−1=11=11^{-1} = \frac{1}{1} = 1. All three are still positive.

More questions like this

The original DOE question
Question 18 as shown on the DOE’s digital test, page 91 of its printable version.
As printed in the DOE’s printable version of 2026 Practice Test C Math, page 91, question 18. This is the DOE’s version, before the corrections listed in the analysis.

Question 6 of 6

2024 Test B Math, question 53

Question

Which graph represents the solution to |x+1|≥2|x+1|\geq 2?

  • ANumber line from −3 to 3 with a tick at every integer. Closed dots at −3 and 1. The line is shaded from −3 to the left, ending in an arrow, and from 1 to the right, ending in an arrow.
  • BNumber line from −3 to 3 with a tick at every integer. Closed dots at −1 and 1. The line is shaded from −1 to the left, ending in an arrow, and from 1 to the right, ending in an arrow.
  • CNumber line from −3 to 3 with a tick at every integer. Closed dots at −3 and 1, with the segment between them shaded.
  • DNumber line from −3 to 3 with a tick at every integer. Closed dots at −3 and 3. The line is shaded from −3 to the left, ending in an arrow, and from 3 to the right, ending in an arrow.
Show the answer

Correct answer: A

Since |x+1|≥2|x+1|\geq 2, either x+1≤−2x+1\leq -2 or x+1≥2x+1\geq 2.

Solving x+1≤−2x+1\leq -2 for x gives x≤−3x\leq -3.

Solving x+1≥2x+1\geq 2 for x gives x≥1x\geq 1.

A filled circle on a number line represents “or equal to.” So the correct number line representation has filled circles at −3 and 1, with the number line filled to the left of −3 for “less than” and to the right of 1 for “greater than.”

Question analysis

Students choose the number line graph that shows every solution of an inequality in which x + 1 sits inside absolute value bars. It tests absolute value as distance and graphing inequalities. The tricky part is turning one absolute value statement into two pieces and placing each boundary point and shaded ray correctly.

NYS standards
Grade level
Grade 7 content, by NYS standard
Compared with grade 7
Above grade 7 Grade 7 students solve and graph two-step inequalities and know absolute value as distance. An inequality with an absolute value has to be split into two cases, which is outside the grade 6 to 8 standards and well above typical 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 9, 7 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

Reading |x + 1| as the distance from x to −1 makes this quick: the points 2 units away are −3 and 1, and greater than or equal means outside them. Students who solve only one case and mirror it across 0 land on graphs centered on 0, and students who find both endpoints may still shade between them. The graphs differ in just one dot or one shading choice, so each must be read carefully.

  1. Something you must already know moderate Working it out

    Solving |x + 1| ≥ 2 needs two cases, x + 1 ≤ −2 or x + 1 ≥ 2, joined by or; absolute value inequalities go beyond grade 7, and the stem gives no hint. (Anderson & Krathwohl, 2001)

  2. A very close wrong answer moderate Choosing the answer

    The right graph and the segment from −3 to 1 share both filled endpoints, so only deciding between outside and between the boundaries separates them. (Embretson & Wetzel, 1987; Gorin & Embretson, 2006; Ascalon et al., 2007)

  3. Reading a figure, table or graph minor Understanding the question

    Four number lines must be read for filled dots and arrow directions, and two of them differ from the right one only in where a single dot sits. (Lesh, Post & Behr, 1987; Kirsch & Mosenthal, 1990)

Strategy: Read the absolute value as distance from −1 on the number line, find the points exactly 2 units away, and decide whether the solutions lie between or outside them.

Traps

  • Misunderstands the concept: A wrong belief about a concept: that percents can be added, that area grows like length, that averages can be averaged, that a bigger denominator means a bigger fraction.
  • 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

How the questions are analyzed, and the research behind it

Worked solution, step by step

Formulas used

Absolute value as distance
|x−a|=distance from x to a|x - a| = \text{distance from } x \text{ to } a
x and a are points on the number line. The bars mean absolute value. |x − a| is how far apart the two points are, which is never negative. Since x + 1 = x − (−1), |x + 1| is the distance from x to −1.

  1. Sort out the question

    You need the graph of every x that makes |x+1|≥2|x + 1| \geq 2 true. The sign ≥ means greater than or equal to. The bars mean absolute value.

    On a number line, a filled dot means that point counts. A thick line with an arrow means all the numbers that way count too.

  2. Read it as a distance

    Adding 1 is the same as subtracting −1, so x+1=x−(−1)x + 1 = x - (-1). By the formula, |x+1||x + 1| is the distance from x to −1.

    So the inequality says that x is at least 2 units away from −1.

  3. Find the two boundary points

    Start at −1 and go 2 units each way.

    −1−2=−3-1 - 2 = -3

    −1+2=1-1 + 2 = 1

    At −3 and at 1, the distance is exactly 2. The words or equal to let them count, so they get filled dots.

  4. Decide which side to shade

    Being at least 2 away means being farther out. Numbers between −3 and 1 are too close to −1. For example, 0 is only 1 unit away. So shade to the left of −3 and to the right of 1.

    In algebra, that is x+1≤−2x + 1 \leq -2 or x+1≥2x + 1 \geq 2. These give x≤−3x \leq -3 or x≥1x \geq 1.

  5. Match the graph

    Choice A has filled dots at −3 and 1, with arrows going outward. That matches.

    Watch out: Choice C shades between −3 and 1. Those are the points within 2 of −1, the answer to |x+1|≤2|x + 1| \leq 2. Choices B and D are centered on 0, but the center here is −1.

    So the answer is A, the graph shaded outward from −3 and 1.

Check your answer

Test a point from each part. For x = 2, |2+1|=3|2 + 1| = 3, and 3 is at least 2. For x = 0, |0+1|=1|0 + 1| = 1, which is less than 2. For x = −3, |−3+1|=2|-3 + 1| = 2, which counts. Graph A agrees with all three.

More questions like this

The original DOE question
Question 110 as printed on page 214 of the DOE handbook.
As printed in the DOE’s NYC Guide to the Specialized High Schools Admissions Test (SHSAT) for 2025 Admissions, page 214, question 110. Open page 214 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).

Sample #487765