3 English and 3 math
Here are 6 random questions to try. Takers earning below 75% are unlikely to receive an offer. You have 1 minute 48 seconds per question on the real exam.
Question 1 of 6
2018 Test B English, question 56Passage Invention of the Telegraph
Samuel Morse, an American inventor, is credited with creating the electronic telegraph, a communication device that allows users to send messages using a system of short and long pulses that represent letters, numbers, and punctuation. In 1843 the United States Congress passed the Telegraph Bill, which provided Morse with the funds to build an electric telegraph system.
Invention of the Telegraph
Earlier Signal Systems
Long before Samuel F. B. Morse electrically transmitted his famous message “What hath God wrought?” from Washington to Baltimore on May 24, 1844, there were signaling systems that enabled people to communicate over distances. Most were visual or “semaphore” systems using flags or lights. In the eighteenth century, such systems used an observer who would decipher a signal from a high tower on a distant hill and then send it on to the next station. The young American republic wanted just such a system along its entire Atlantic coast and offered a prize of $30,000 for a workable proposal. The framers of this legislation had no way of knowing that when they used the word “telegraph” to refer to this visual semaphore system, they would be offered an entirely new and revolutionary means of communication—electricity.
The Growth of an Idea
The idea of using electricity to communicate over distance is said to have occurred to Morse during a conversation aboard ship when he was returning from Europe in 1832. Michael Faraday’s recently invented electromagnet was much discussed by the ship’s passengers, and when Morse came to understand how it worked, he speculated that it might be possible to send a coded message over a wire. While a student at Yale College years before, he had written his parents a letter about how interesting he found the lectures on electricity. Despite what he had learned at Yale, Morse found when he began to develop his idea that he had little real understanding of the nature of electricity, and after sporadic attempts to work with batteries, magnets, and wires, he finally turned for help to a colleague at the University of the City of New York, Leonard D. Gale.
Gale was a professor of chemistry and familiar with the electrical work of Princeton’s Joseph Henry, a true pioneer in the new field. Well before Morse had his shipboard idea about a telegraph, Henry rang a bell at a distance by opening and closing an electric circuit. In 1831, he had published an article, of which Morse was unaware, that contained details suggesting the idea of an electric telegraph. Gale’s help and his knowledge of this article proved crucial to Morse’s telegraph system because Gale not only pointed out flaws in the system but showed Morse how he could regularly boost the strength of a signal and overcome the distance problems he had encountered by using a relay system Henry had invented. Henry’s experiments, Gale’s assistance, and, soon after, hiring the young technician Alfred Vail were keys to Morse’s success.
Obstacles and Opportunities
By December 1837, Morse had enough confidence in his new system to apply for the federal government’s appropriation, and during the next year he conducted demonstrations of his telegraph both in New York and Washington.
However, when the economic disaster known as the Panic of 1837 took hold of the nation and caused a long depression, Morse was forced to wait for better times. It was during this period that Morse visited Europe again and tried not only to secure patent protection overseas but to examine competing telegraph systems in England. . . .
By 1843, the country was beginning to recover economically, and Morse again asked Congress for the $30,000 that would allow him to build a telegraph line from Washington to Baltimore, forty miles away. The House of Representatives eventually passed the bill containing the Morse appropriation, and the Senate approved it in the final hours of that Congress’s last session. With President Tyler’s signature, Morse received the cash he needed and began to carry out plans for an underground telegraph line.
Realizing a Great Invention
Morse had hired the ingenious construction engineer Ezra Cornell to lay the pipe carrying the wire, and although Cornell did his job superbly, one of Morse’s partners, Congressman F. O. J. Smith, had purchased wire with defective insulation. Too much time had been wasted laying bad wire, and with the project on a rigid deadline, something had to be done quickly. Cornell suggested that the fastest and cheapest way of connecting Washington and Baltimore was to string wires overhead on trees and poles. The desperate Morse gave the go-ahead, and the line was completed in time for the dramatic and spectacularly successful link between the Supreme Court chamber of the Capitol building and the railroad station in Baltimore.
Soon, as overhead wires connected cities up and down the Atlantic coast, the dots-and-dashes method that recorded messages on a long moving strip of paper was replaced by the operator’s ability to interpret the code in real time. . . . Telegraph lines soon extended westward, and within Morse’s own lifetime they connected the continents of Europe and America.
“Invention of the Telegraph”—Public Domain/Library of Congress
legislation: Telegraph Bill
dots-and-dashes method: the short and long pulses of Morse code that are sent and received by telegraph operators
The first transatlantic electric telegraph message was sent in 1858, and by 1902 the British All-Red Line connected most of the world.
Source: U.S. Bureau of the Census. Historical Statistics of the United States, Colonial Times to 1970, Bicentennial Edition, Part 2. Washington, D.C., 1975.
Question
The idea that, in the mid-nineteenth century, the United States was mostly unaware of the possibilities of electricity is illustrated in the passage mainly through the
- Adescription of the government’s initial desire to expand a semaphore signaling system that used either flags or lights along the Atlantic Coast.
- Bdelay by the House of Representatives to pass the bill funding Morse’s telegraph line six years after he first applied for the appropriation.
- Cdiscussions of the newly invented electromagnet that sparked the idea of sending codes through wires.
- Ddescription of how an electric circuit could be closed to ring a bell at a distance.
Show the answer
Correct answer: A
The question asks for information that conveys the idea that the United States was mostly unaware of the possibilities of electricity in the mid-nineteenth century. The passage states that most signaling systems at the time were “visual or ‘semaphore’ systems using flags or lights” (paragraph 1) and that the United States was looking for “just such a system along its entire Atlantic coast” (paragraph 1).
Option A is correct because waving lights and flags reveals how limiting and simple the system of the time was, and Option A states that the United States wanted to expand this system, not improve upon it.
Option B is incorrect because the delay in funding had to do with the Panic of 1837 and the “long depression” (paragraph 5), not because the House of Representatives was not aware or ready for innovation in the use of electricity.
Option C is incorrect because it focuses on what prompted Morse to consider an electronic wire-based communications system.
Option D is incorrect because it describes a basic aspect of an early electrical discovery that demonstrated the interest of scientists in the possibilities of electricity, not the United States as a whole.
Question analysis
Students identify how “Invention of the Telegraph” mainly illustrates the idea that, in the mid-1800s, the United States was largely unaware of what electricity could do. The idea is implied rather than stated, so students must decide which detail truly reveals the nation’s thinking at the time.
- Grade level
- Grade 8 reading and task
- Compared with grade 7
- Above grade 7 Grade 7 evidence questions often match a stated idea to a sentence. This idea is only implied, so students must infer what a historical detail reveals about a whole nation’s understanding, closer to grade 8 inference.
- Estimated difficulty
- Hard: combines ideas, needs a plan, and has more than one tempting wrong answer.
- Thinking it demands
- Depth of knowledge 3, strategic thinking · mainly evaluate
- What makes it hard
- Reading between the lines moderate
- Evidence in several places moderate
- Hard words minor
- Evidence
- Answered from one paragraph or stanza
- Reading level
- Passage: about grade 11, 910 words; question and choices: about grade 12, 102 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 stem asks about a whole nation’s understanding, so details about individuals with electrical interests, the ship’s passengers and Henry, show the opposite of what is needed. The real trap is the funding delay, which looks like official indifference but has an economic cause the passage states. Students who remember that the semaphore plan came with a remark about not knowing electricity was coming find the answer.
Reading between the lines moderate Working it out
The idea is implied: wanting a semaphore system shows unawareness only alongside paragraph 1’s comment that its framers “had no way of knowing” they would be offered electricity. (Graesser, Singer & Trabasso, 1994; Kintsch, 1998)
Evidence in several places moderate Working it out
The choices point to four separate places, paragraph 1’s semaphore plan, the funding delay of paragraphs 4 to 6, the shipboard talk in paragraph 2 and Henry’s bell in paragraph 3, and each must be checked there. (Kirsch & Mosenthal, 1990; Gorin & Embretson, 2006)
Hard words minor Understanding the question
“Semaphore” and “appropriation” are uncommon words, and the passage defines “semaphore” only in passing, as systems “using flags or lights.” (Perfetti, 2007; Freedle & Kostin, 1993)
Strategy: For each choice, find the detail in the passage and ask whether the author uses it to show what the country did or did not understand about electricity.
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.
- Supports only part of the claim: In a question about evidence: a line that backs one half of the claim but not the other, or a related point rather than the claim itself.
The wrong answers, classified
B Twists what the text says (King et al., 2004)
Reads the long wait for funding as doubt about electricity, but the passage gives a different cause, the Panic of 1837 and the “long depression” that followed.
C Supports only part of the claim (King et al., 2004; Thissen, Steinberg & Fitzpatrick, 1989)
The ship’s passengers did discuss the new electromagnet, but that shows a few people interested in electricity, not a country unaware of what it could do.
D Supports only part of the claim (King et al., 2004; Thissen, Steinberg & Fitzpatrick, 1989)
Henry’s bell rung at a distance is a real detail, but it shows a scientist exploring electricity’s uses, the opposite of unawareness, and says nothing about the nation.
Working it out, step by step
Figure out what the question asks
This asks which part of the passage best shows an idea. The idea is that in the mid-1800s, the United States mostly did not know what electricity could do. Look for a detail about the country as a whole, not about one scientist.
Find the detail in paragraph 1
Paragraph 1 says most early systems were visual, or semaphore, “systems using flags or lights.” Then it says, “The young American republic wanted just such a system along its entire Atlantic coast.” The next sentence explains that its lawmakers “had no way of knowing” they would be offered “an entirely new and revolutionary means of communication—electricity.”
Explain what the detail shows
A semaphore system sends signals people can see, like waving flags. The country asked for that old kind of system. It did not ask for an electric one, because it did not know one was possible. “Revolutionary” means bringing a huge change. So the government’s plan shows how unaware the nation was of what electricity could do.
Check each choice
- A fits. The government wanted to spread flags and lights, not electric signals.
- B is wrong. The delay had a money cause. The Panic of 1837 “caused a long depression.” It was not about electricity.
- C is wrong. Passengers talking about the electromagnet shows interest in electricity, the opposite of not knowing about it.
- D is wrong. Henry ringing a bell shows one scientist exploring electricity. It says nothing about the whole country.
Choose the answer
The country’s wish for a flags-and-lights system shows it did not yet see what electricity could do. So the answer is A, the description of the government’s plan for a semaphore system along the Atlantic Coast.
Why this answer and not the closest wrong one
B is the closest trap, because a long wait for money can look like doubt about electricity. But paragraph 5 gives the real cause, the Panic of 1837 and the hard times after it. A is backed by the passage’s own words: the lawmakers “had no way of knowing” electricity was coming.
More questions like this
The original DOE question
The passage “Invention of the Telegraph” as printed (pages 146–148)
Question 2 of 6
2026 Practice Test C English, question 31Passage Serpent Mound
Serpent Mound
The Great Serpent Mound, located in Adams County, Ohio, is a human-made mound of earth that researchers believe was created between 300 B.C. and A.D. 1100 by an indigenous culture.
Ohio, 1846
Brush Creek stood low when the museum men came
with their measuring tapes and sketchbooks.
It was winter. Fringed with ice,
the creek doubled back on itself
as if it had forgotten something.
Pa was in Cincinnati, or else on his way home,
so Ma told me to lead the men
into the marshy low grounds. It being winter,
there was little underbrush to speak of—
in the summer there would have been
briars, poison ivy, biting flies. I listened
for the swish of a beaver’s heavy tail,
the chitter of a chickadee, or the cry of a hawk,
but the winter silence of the creek pressed
down on all of us like a weight.
The humps in the ground were all but
invisible until you were right up on them. The figure
was even less obvious: the sinuous body,
the tail coiled three times around,
and at the other end, the mouth wide open.
In the summer the creek bottom was crowded
with so much life that you could trip over
the ridges of earth before you saw
anything at all. In winter you could climb
a tree and get some idea of the whole thing:
the serpent’s body undulating, slithering
silently across the ancient
earth. At the mouth end, there was an oval mound
as if the snake were about to swallow an egg—
as snakes sometimes did in our rickety
henhouse—my Pa always said, or
as if swallowing the sun, one of the museum
men suggested, taking notes with his quill pen,
an old-style inkhorn slung at his side.
I liked that: swallowing the sun,
just the sort of thing a snake might do,
might want to do. When, later, I told my sister Ruth,
she disagreed. It is singing to the sun,
she insisted. That is why its mouth
is wide open. She said, “Sometimes I think
I hear it on summer nights. Not swallowing, singing.”
Question
What impact do the words “swish,” “chitter,” and “cry” in lines 12–13 have in the poem?
- AThey illustrate how lively the mound’s surroundings are during the summer.
- BThey show how the mound disrupts natural life in the marsh.
- CThey indicate the variety of wildlife found in the area around the mound.
- DThey suggest that the speaker prefers the mound’s appearance in winter.
Show the answer
Correct answer: A
The question asks what impact the words “swish,” “chitter,” and “cry” in lines 12–13 have in the poem.
A. CORRECT. The words highlight the sounds of the animals that visit the mound in the summer: the “swish of a beaver’s heavy tail” (line 12), the “chitter of a chickadee” (line 13), and the “cry of a hawk” (line 13). These words help contrast the quiet stillness of the setting around the mound in the winter.
B. Incorrect. While the words in lines 12–13 convey the sounds certain animals make in the summer, the sounds of the animals that live near the mound are a natural part of life in the area, not a disruption.
C. Incorrect. The speaker is contrasting the sounds of the animals around the mound during the rest of the year with the silence of the winter months, not merely indicating the variety of wildlife.
D. Incorrect. The speaker expresses the idea that the mound is more visible in the winter because of the lack of brush (“It being winter, / there was little underbrush to speak of” [lines 8–9]). Then lines 12–13 describe sounds, not the appearance of the mound in winter.
Question analysis
This question about word choice asks what impact the sound words “swish,” “chitter” and “cry” in lines 12–13 of “Serpent Mound” have in the poem. They belong to a beaver, a chickadee and a hawk near the creek, and more than one choice sounds like a fair account of them, so students must read the surrounding lines closely.
- Grade level
- Grade 8 reading and task
- Compared with grade 7
- Above grade 7 Grade 7 students often explain what sensory words add to a description. These three words sit inside a long sentence that runs across several lines, so their effect has to be worked out from the lines around them, beyond typical grade 7 work.
- Estimated difficulty
- Hard: combines ideas, needs a plan, and has more than one tempting wrong answer.
- Thinking it demands
- Depth of knowledge 2, skills and concepts · mainly analyze
- What makes it hard
- A very close wrong answer major
- Reading between the lines moderate
- Complex sentences minor
- Evidence
- Answered from one paragraph or stanza
- Reading level
- Passage: 354 words (a poem; reading level not measured); question and choices: about grade 6, 61 words.
- Students, last 30 days
- Not enough answers yet to show (it takes 10).
Why it is hard, traps and wrong answers (shows the answer)
Why it is hard
Three vivid animal sounds invite the easy reading that the poem is showing off the creek’s wildlife, and that choice is true as far as it goes. The words matter because they are missing: the speaker listens for them, and “the winter silence” answers. Students must also accept that the key’s “during the summer” comes from the poem’s later picture of a crowded summer creek, not from lines 12–13 themselves.
A very close wrong answer major Choosing the answer
The variety choice is literally true, since a beaver, a chickadee and a hawk are three kinds of animal; it differs from the key in missing why the sounds are named, as a contrast with winter. (Embretson & Wetzel, 1987; Gorin & Embretson, 2006; Ascalon et al., 2007)
Reading between the lines moderate Working it out
The speaker listens for these sounds and does not hear them, so students must infer that they stand for the creek’s life in warmer months, which lines 21–22 call “crowded / with so much life.” (Graesser, Singer & Trabasso, 1994; Kintsch, 1998)
Complex sentences minor Understanding the question
The three words sit in one sentence that runs from “I listened” in line 11 to “like a weight” in line 15 and turns on “but,” so their point arrives only at its end. (Abedi & Lord, 2001; Freedle & Kostin, 1993; Messick, 1989)
Strategy: Read the full sentence that holds these words, from “I listened” in line 11 to the end of line 15, then decide what the three sound words add to the scene.
Traps
- True but not the answer: A choice says something accurate about the text that does not answer this question.
- Wrong part of the text: A choice is true of another paragraph, stanza or speaker than the one asked about.
The wrong answers, classified
B Twists what the text says (King et al., 2004)
Notices that the beaver, chickadee and hawk go unheard but blames the mound for the hush, though line 14 calls it “the winter silence of the creek.”
C True but not the answer (King et al., 2004; Embretson & Wetzel, 1987)
Rightly counts three different animals in lines 12–13, but the speaker listens for them in vain, so the point is their absence in winter, not the range of species.
D Wrong part of the text (Kirsch & Mosenthal, 1990)
Remembers from lines 8–9 and 24–25 that winter makes the mound easier to see, but lines 12–13 are about sounds and state no preference for either season.
Working it out, step by step
Figure out what the question asks
This asks what three sound words do in the poem. They are “swish,” “chitter” and “cry,” in lines 12–13. Read the whole sentence they sit in. It starts at “I listened” in line 11 and ends with “like a weight” in line 15.
Read the full sentence
Lines 11–15 say “I listened / for the swish of a beaver’s heavy tail, / the chitter of a chickadee, or the cry of a hawk, / but the winter silence of the creek pressed / down on all of us like a weight.” A chickadee is a small bird, and a chitter is its quick, chirping sound. The speaker listens for these sounds. But the word “but” tells you they never come. Only silence answers.
Work out why the sounds are named
A beaver, a chickadee and a hawk are signs of a creek full of life. The speaker hears none of them in winter. Later lines tell you when the creek is lively. Lines 21–22 say “In the summer the creek bottom was crowded / with so much life.” So the missing sounds remind you how lively the place is in summer. They also make the winter silence feel even emptier.
Check each choice
- A fits. The sounds stand for the busy life around the mound in the warm months.
- B does not fit. The quiet comes from the season: “the winter silence of the creek.” The mound does not cause it.
- C does not fit. There are three kinds of animals, but the point is that their sounds are missing.
- D does not fit. These lines are about sounds. The speaker says nothing about liking how the mound looks in winter.
Watch out: C is true as far as it goes. But it misses why the speaker names the sounds at all: to set them against the silence.
Choose the answer
The sounds the speaker listens for, and doesn’t hear, show how lively the creek is in summer. So the answer is A, “They illustrate how lively the mound’s surroundings are during the summer.”
Why this answer and not the closest wrong one
C is the closest wrong choice, because a beaver, a chickadee and a hawk really are three kinds of wildlife. But the speaker listens for them and hears nothing. The word “but” turns the sentence to “the winter silence.” The sounds matter because they are missing. They show the creek in its lively season, which line 21 names as summer.
More questions like this
The original DOE question
The passage “Serpent Mound” as printed (page 40)
Question 3 of 6
2026 Practice Test B English, question 25Passage 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 27–28 from the poem.
And there, in the explosion, in the darkness,
briefly incandescent, they appear:
The imagery in the lines reveals that the speaker
- Aenvies the physicists who research colliding particles.
- Bhas personally observed colliding particles.
- Cadmires the powerful reactions that occur when particles collide.
- Dhas a simplistic understanding of how particles collide.
Show the answer
Correct answer: C
The question asks what the imagery in lines 27–28 reveals about the speaker.
A. Incorrect. The physicists mentioned in the fifth stanza (lines 33–44) are described as mere observers: they “jot down / what they can” (lines 41–42). In lines 27–28, the speaker is focused on the reaction between the colliding particles, not on the physicists who study them.
B. Incorrect. The speaker describes the particle collision in detail, but the text does not imply that the speaker has personally witnessed a collision. The speaker implies that his or her understanding of the collision is based on the experiences of the physicists observing the phenomenon (“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” [lines 39–43]).
C. CORRECT. The word “explosion” and the phrase “briefly incandescent” create a picture of rapid changes and short bursts of bright light, revealing how powerful the new particles are. The language the speaker uses is positive, revealing that the speaker admires the power of the reaction and stands in awe of the new particles.
D. Incorrect. The poem reveals the speaker’s deep knowledge about subatomic particles. For example, the speaker is able to name the new particles discovered—“the quarks, the leptons, and the bosons; / the baryons and the mesons” (lines 29–30)—and is able to use imagery to create a powerful picture that reveals the complexity of a scientific process that humans have never been able to see.
Question analysis
This imagery question asks what lines 27–28 of “Looking for the Smallest Spark of Everything” reveal about the poem’s speaker, as particles appear “briefly incandescent” in an explosion inside a particle collider. Students must infer what a vivid image says about the person describing it. The word “incandescent” may be unfamiliar, and the choices are about very different things.
- Grade level
- Grade 8 reading and task
- Compared with grade 7
- Above grade 7 Grade 7 students infer a speaker’s attitude from imagery, but these two lines turn on the uncommon word “incandescent,” state nothing about the speaker outright, and the choices range over the speaker’s knowledge, experience and feelings, which is harder than typical grade 7 work.
- Estimated difficulty
- Hard: combines ideas, needs a plan, and has more than one tempting wrong answer.
- Thinking it demands
- Depth of knowledge 2, skills and concepts · mainly analyze
- What makes it hard
- Reading between the lines major
- Hard words moderate
- Figurative or literary language minor
- Evidence
- Answered from one paragraph or stanza
- Reading level
- Passage: 346 words (a poem; reading level not measured); question and choices: about grade 9, 55 words.
- Students, last 30 days
- Not enough answers yet to show (it takes 10).
Why it is hard, traps and wrong answers (shows the answer)
Why it is hard
Nothing in the two lines names a feeling, so students must judge the speaker’s attitude from the image alone, and its key word is uncommon. The vividness is itself a trap: a scene described this sharply can seem to be one the speaker watched, though the poem says the particles are perceived only through the physicists’ work. The choices range over envy, experience, admiration and understanding, so each must be tested against the lines rather than against an overall impression.
Reading between the lines major Working it out
The lines describe particles, not the speaker, and contain no word of feeling; admiration has to be inferred from the drama of “the explosion” and the glow of “briefly incandescent.” (Graesser, Singer & Trabasso, 1994; Kintsch, 1998)
Hard words moderate Understanding the question
“Incandescent,” glowing with heat and light, is the word that makes the image dazzling, and a student who does not know it sees only an explosion in the dark. (Perfetti, 2007; Freedle & Kostin, 1993)
Figurative or literary language minor Understanding the question
The two lines are pure imagery, a burst of light in darkness as the particles “appear,” and the question asks what that picture reveals about the person painting it. (Graesser, Singer & Trabasso, 1994; Kintsch, 1998)
Strategy: Picture the scene in lines 27–28, including what “incandescent” means, decide what the description suggests about the speaker, and test each choice against these two lines.
Traps
- Taking figurative language literally: A choice reads a figure of speech or image at face value.
- Reads too much in: A reasonable-sounding conclusion that goes further than the text allows.
The wrong answers, classified
A Reads too much in (Graesser, Singer & Trabasso, 1994)
Reasons that someone so drawn to the scene must envy the physicists who study it, though the physicists appear only in lines 39–44 and nothing in the poem hints at envy.
B Taking figurative language literally (Graesser, Singer & Trabasso, 1994)
Takes the vivid scene of particles that “appear” in a glow as something the speaker witnessed, though lines 39–43 place that sight “down there,” where physicists record what they can.
D Reads too much in (Graesser, Singer & Trabasso, 1994)
Treats the poem’s playful comparisons, racing cars and garage bands, as a sign of shallow knowledge, though the next lines have the speaker naming quarks, leptons, bosons, baryons and mesons.
Working it out, step by step
Figure out what the question asks
This asks what the imagery in lines 27–28 shows about the speaker. Imagery is language that helps you see, hear or feel a scene. The lines describe particles, not the speaker. So you must infer, or figure out from clues, how the speaker feels.
Read lines 27–28
The lines say “And there, in the explosion, in the darkness, / briefly incandescent, they appear:” Briefly means for a short time. Incandescent means glowing with heat and light. So picture a burst of bright light flashing in the dark. The particles have just crashed into each other, or collided. In that flash, the tiny particles appear.
Decide how the speaker feels
The words are bold and bright: “explosion,” “incandescent,” “appear.” The speaker makes the moment sound dramatic and amazing. People describe something this way when they are in awe of it. So the speaker admires, or looks up to, the power of the crash.
Check each choice
- A does not fit. Physicists come up only later, in line 41. Nothing shows envy, or wanting what they have.
- B does not fit. Nothing says the speaker was there. Lines 39–42 place the sight “down there,” where “physicists jot down / what they can.”
- C fits. The glowing burst in the dark shows the speaker’s wonder.
- D does not fit. Right after, the speaker names quarks, leptons, bosons, baryons and mesons. That is not a simple understanding.
Watch out: B is tempting because the scene is so vivid. But a writer can picture something without seeing it in person.
Choose the answer
The bright, explosive picture shows a speaker who is amazed by the crash. So the answer is C, “admires the powerful reactions that occur when particles collide.”
Why this answer and not the closest wrong one
B is the closest wrong choice, because the scene feels like an eyewitness report. But the lines never say the speaker was in the tunnel. What they do show is a feeling. Words like “explosion” and “briefly incandescent” make the moment thrilling. That is admiration, so C fits.
More questions like this
The original DOE question
The passage “Looking for the Smallest Spark of Everything” as printed (pages 32–33)
Question 4 of 6
2024 Test B Math, question 53Question
Which graph represents the solution to ?
- A
- B
- C
- D
Show the answer
Correct answer: A
Since , either or .
Solving for x gives .
Solving for x gives .
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.
- Thinking it demands
- Depth of knowledge 2, skills and concepts · mainly apply
- What makes it hard
- Something you must already know moderate
- A very close wrong answer moderate
- Reading a figure, table or graph minor
- 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.
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)
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)
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
B Misunderstands the concept (Smith, diSessa & Roschelle, 1993; De Bock et al., 1998; Ni & Zhou, 2005)
Solves x + 1 ≥ 2 to get x ≥ 1, then mirrors it across 0 to x ≤ −1, as if the solution were centered on 0 rather than on −1.
C Negatives and direction (Brown & Burton, 1978)
Finds −3 and 1 but shades between them, the solution of |x + 1| ≤ 2, reversing which side of the boundaries lies at least 2 units from −1.
D Misunderstands the concept (Smith, diSessa & Roschelle, 1993; De Bock et al., 1998; Ni & Zhou, 2005)
Solves x + 1 ≤ −2 to get x ≤ −3, then mirrors it across 0 to x ≥ 3, assuming the boundaries are symmetric about 0.
Worked solution, step by step
Formulas used
- Absolute value as distance
- 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.
Sort out the question
You need the graph of every x that makes 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.
Read it as a distance
Adding 1 is the same as subtracting −1, so . By the formula, is the distance from x to −1.
So the inequality says that x is at least 2 units away from −1.
Find the two boundary points
Start at −1 and go 2 units each way.
At −3 and at 1, the distance is exactly 2. The words or equal to let them count, so they get filled dots.
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 or . These give or .
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 . 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, , and 3 is at least 2. For x = 0, , which is less than 2. For x = −3, , which counts. Graph A agrees with all three.
More questions like this
The original DOE question
Question 5 of 6
2018 Test A Math, question 5Question
The sum of two consecutive integers is −15. If 1 is added to the smaller integer and 2 is subtracted from the larger integer, what is the product of the two resulting integers?
Grid-in question: work out the answer and enter it as a number.
Show the answer
Correct answer: 63
If x is the smaller consecutive integer, then
is the larger consecutive integer. Use their sum (−15) to find x:
The two consecutive integers are −8 and −7. One is added to the smaller integer:
and 2 is subtracted from the larger integer:
Find the product:
Question analysis
A grid-in problem about two consecutive integers whose sum is −15. Students find the two integers, add 1 to the smaller and subtract 2 from the larger, then multiply the results. Deciding which negative integer is the smaller one, and keeping signs straight through every step, are what make it tricky.
- Grade level
- Grade 7 content, by NYS standard
- Compared with grade 7
- Above grade 7 A typical grade 7 task solves one two-step equation or multiplies signed numbers. This links both: set up a consecutive-integer equation, solve it with negatives, adjust each integer, and multiply, with no choices to check against.
- Estimated difficulty
- Hard: combines ideas, needs a plan, and has more than one tempting wrong answer.
- Thinking it demands
- Depth of knowledge 2, skills and concepts · mainly apply
- What makes it hard
- Error-prone arithmetic moderate
- Turning words into math moderate
- Many steps moderate
- Solution
- 4 steps
- Reading level
- Question and choices: about grade 9, 30 words.
- Students, last 30 days
- Not enough answers yet to show (it takes 10).
Why it is hard, traps and wrong answers (shows the answer)
Why it is hard
Every step is routine, yet the question collects most of the ways students lose points with negatives. The crucial judgment is which of −8 and −7 is the smaller; a student who picks −7 still produces a tidy, wrong product. Gridding the product of the original pair, or giving a negative product, are the other usual losses. Writing each intermediate pair down, rather than holding them in mind, protects against all three.
Error-prone arithmetic moderate Working it out
Every number in play is negative: −8 and −7, then −7 and −9, and a product of two negatives that must come out positive. (Brown & Burton, 1978; Junker & Sijtsma, 2001)
Turning words into math moderate Understanding the question
"1 is added to the smaller integer and 2 is subtracted from the larger" depends on knowing that −8, not −7, is the smaller, since it lies farther below zero. (Hegarty, Mayer & Monk, 1995; Koedinger & Nathan, 2004)
Many steps moderate Working it out
Four linked steps: set up x + (x + 1) = −15, solve for x, adjust each integer, then multiply; an error early in the chain carries through to the product. (Daniel & Embretson, 2010; Enright, Morley & Sheehan, 2002)
Strategy: Halve the sum to see which two integers sit on either side of it, remember that the smaller negative is farther from zero, then adjust each and multiply.
Traps
- Negatives and direction: Arithmetic with negative numbers, the order of a subtraction, or direction on a number line. (Moving a term across the equals sign without changing its sign is a faulty procedure.)
- Misreads the question: Misses or misreads a condition or a word in the question: "at least", "each", "remaining", "not".
The wrong answers, classified
60 Negatives and direction (Brown & Burton, 1978)
Takes −7 as the smaller integer because 7 is less than 8, so adjusts to −7 + 1 = −6 and −8 − 2 = −10, and multiplies to 60.
56 Misreads the question (Hegarty, Mayer & Monk, 1995)
Finds −8 and −7 and multiplies them to get 56, skipping the sentence that adds 1 to one integer and subtracts 2 from the other.
-63 Negatives and direction (Brown & Burton, 1978)
Finds the adjusted integers −7 and −9 correctly but gives their product a negative sign, gridding −63.
Worked solution, step by step
Formulas used
- Consecutive integers
- Integers are whole numbers and their opposites, like −2, −1, 0, 1 and 2. Consecutive integers come one right after another. If n is the smaller one, the next one is n + 1, because each step up the number line adds 1.
- Multiplying two negative numbers
- a and b are positive numbers, so −a and −b are negative. When you multiply two negative numbers, the answer is positive. The two minus signs cancel out.
Sort out the question
Two consecutive integers add up to −15. Integers are whole numbers and their negatives. Consecutive means one comes right after the other, like 4 and 5. You need to do three things:
- Find the two integers.
- Add 1 to the smaller one. Subtract 2 from the larger one.
- Find the product of the two new numbers. The product is the answer when you multiply.
Find the two integers
Call the smaller integer n. Then the larger one is n + 1. Their sum is −15.
Subtract 1 from both sides. Then divide both sides by 2.
So the integers are −8 and −7.
Decide which one is smaller
On a number line, −8 is to the left of −7. Numbers to the left are smaller. So −8 is the smaller integer, and −7 is the larger one. Watch out: 8 is bigger than 7, but −8 is smaller than −7. Mixing them up gives −6 and −10, and the wrong answer 60.
Change each integer
Add 1 to the smaller integer.
Subtract 2 from the larger integer.
The two new numbers are −7 and −9.
Multiply the new numbers
Both numbers are negative, so their product is positive.
Watch out: the answer is not −63, because two negatives make a positive. Also, don’t multiply the first pair, −8 and −7. That gives 56 and skips the changes. So you would grid 63.
Check your answer
Check the pair: , and they are one apart. Half of −15 is −7.5, and −8 and −7 sit on either side of it. Then , and the sign is positive.
More questions like this
The original DOE question
Question 6 of 6
2026 Practice Test B Math, question 31Question
A pizza shop offers a choice of 3 sizes (small, medium, and large) and 7 different toppings. Different pizzas can be created by changing the size and the choice of toppings. If Cody wants to order a pizza with exactly 2 different toppings, how many different pizzas can he create?
- A6
- B21
- C63
- D126
Show the answer
Correct answer: C
Figure out how many different topping pairs are possible. Use 1, 2, 3, 4, 5, 6, 7 to represent the toppings, and create a list of possible pairs:
1,2; 1,3; 1,4; 1,5; 1,6; 1,7
2,3; 2,4; 2,5; 2,6; 2,7
3,4; 3,5; 3,6; 3,7
4,5; 4,6; 4,7
5,6; 5,7
6,7
So there are 21 different topping combinations for one pizza.
Since there are 3 pizza sizes, multiply the total number of combinations by 3 to get the total number of different pizzas Cody can create: .
Question analysis
Cody orders a pizza with exactly 2 of 7 toppings in one of 3 sizes, and students count how many different pizzas he could create. It tests counting combinations, where the order of the toppings does not matter, combined with a second choice. The challenge is to count every possible pizza exactly once.
- NYS standards
- 7.SP.8b sample spaces for compound events
- Grade level
- Grade 7 content, by NYS standard
- Compared with grade 7
- Above grade 7 In grade 7, compound events are usually ordered pairs, such as a coin with a number cube. Here an unordered pair of toppings is chosen from seven and then matched with three sizes, a combination count beyond typical grade 7 work.
- Estimated difficulty
- Hard: combines ideas, needs a plan, and has more than one tempting wrong answer.
- Thinking it demands
- Depth of knowledge 2, skills and concepts · mainly apply
- What makes it hard
- Combines ideas moderate
- Something you must already know minor
- Solution
- 3 steps
- Reading level
- Question and choices: about grade 8, 47 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 packs two counts into one sentence, each with its own trap. Order does not matter among the toppings, while the size multiplies every pair, and students tend to remember one of these and forget the other. Listing pairs systematically, each topping matched only with later ones, keeps the first count honest, and the stem’s “changing the size and the choice of toppings” is the reminder that size counts too.
Combines ideas moderate Working it out
Two counts are joined: the unordered pairs of toppings from 7, then the 3 sizes each pair can come in, and a mistake in either count changes the total. (Embretson, 1998; Daniel & Embretson, 2010)
Something you must already know minor Working it out
Students must know that a pizza with mushroom and onion is the same as one with onion and mushroom, so the ordered count 7 × 6 has to be halved. (Anderson & Krathwohl, 2001)
Strategy: Number the toppings 1 to 7, list each pair once by matching every topping only with higher-numbered ones, count the list, then bring in the choice of size.
Traps
- Stops one step early: A choice is a number from partway through the solution.
- Overlapping groups: Things in two groups at once are counted twice, or not subtracted.
The wrong answers, classified
A Numbers taken from the question (Hegarty, Mayer & Monk, 1995)
Multiplies the 3 sizes by the 2 toppings Cody wants, using the number of toppings on the pizza instead of the number of possible pairs.
B Stops one step early (King et al., 2004; Gierl et al., 2017)
Lists or counts the 21 pairs of toppings correctly, then stops without giving each pair its 3 possible sizes.
D Overlapping groups (King et al., 2004)
Counts ordered pairs, 7 × 6 = 42, so each pair of toppings appears twice, and then multiplies by the 3 sizes to reach 126.
Worked solution, step by step
Formulas used
- The counting principle
- m is the number of ways to make one choice, and n is the number of ways to make a second choice. Every first choice can go with every second choice, so you multiply. Here, every pair of toppings can come in every size.
- Pairs when order does not matter
- n is the number of items to choose from. There are n ways to pick a first item and n − 1 ways to pick a different second one. That counts each pair twice, once in each order. Dividing by 2 counts each pair once.
Sort out the question
Each of Cody’s pizzas has one size and exactly 2 different toppings. There are 3 sizes and 7 toppings. Pizzas differ by “changing the size and the choice of toppings.” So a small and a large with the same toppings are two different pizzas. You need to count every pizza once.
List the topping pairs
Order does not matter: onion with peppers is the same pizza as peppers with onion. So number the toppings 1 to 7, and pair each one only with bigger numbers. Then no pair shows up twice.
Topping Pairs with Pairs 1 2, 3, 4, 5, 6, 7 6 2 3, 4, 5, 6, 7 5 3 4, 5, 6, 7 4 4 5, 6, 7 3 5 6, 7 2 6 7 1 There are 21 different pairs of toppings.
Check the pairs with the formula
Use the pairs formula with 7 toppings:
Watch out: 7 × 6 = 42 counts every pair twice, once as 1 then 2 and once as 2 then 1. Keeping 42 leads to , choice D.
Bring in the sizes
Each of the 21 topping pairs can come in any of the 3 sizes. Use the counting principle:
Watch out: stopping at 21 leaves out the sizes, which gives choice B. Choice A, 6, multiplies the 3 sizes by the 2 toppings on one pizza. That does not count pizzas.
Give the answer
There are 21 topping pairs, and each one comes in 3 sizes. Cody can create 63 different pizzas. So the answer is C, 63.
Check your answer
Count one size at a time. A small pizza can have any of the 21 pairs, so there are 21 small pizzas. There are also 21 medium and 21 large ones: . That is more than the 21 pairs but fewer than 126, so it is reasonable.
More questions like this
The original DOE question
