3 English and 3 math
Here are 6 random questions to try. Takers earning below 75% are unlikely to receive an offer. You have 1 minute 48 seconds per question on the real exam.
Question 1 of 6
2026 Practice Test B English, question 28Passage 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.
- 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.
- Thinking it demands
- Depth of knowledge 2, skills and concepts · mainly analyze
- What makes it hard
- Complex sentences major
- Figurative or literary language moderate
- Reading between the lines moderate
- 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.
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)
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)
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
A Wrong tone or attitude (Graesser, Singer & Trabasso, 1994)
Links “the vast garage” to the garage bands’ “terrible music” of line 32 and hears a complaint, though the lines end on the delighted image of “wild dancing.”
B Twists what the text says (King et al., 2004)
Gives the particles’ “wild dancing” and “combusting” to the physicists, misled by the pronouns around them, though the physicists only “jot down / what they can.”
D Reads too much in (Graesser, Singer & Trabasso, 1994)
Reads “only down there / in the darkness” as a sign of hidden work, though the darkness belongs to the underground tunnel, and nothing in the lines suggests secrecy.
Working it out, step by step
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.
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.
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.
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.
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’.
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
The passage “Looking for the Smallest Spark of Everything” as printed (pages 32–33)
Question 2 of 6
2026 Practice Test D English, question 17Passage Wolves of the Sea
Wolves of the Sea
The cool and misty landscape of the Great Bear Rainforest can be found along the coast of British Columbia, Canada, and its nearby islands, from Vancouver Island to the Alaskan border. Within this protected area, wolves roam the forests, islands, and beaches. When biologist Chris Darimont began to study these wolves, he wanted to confer with local First Nations groups, as aboriginal Canadians are known, in order to learn what they knew about these wolves. He spoke with Chester Starr, an elder of the Heiltsuk Nation that has occupied the Great Bear Rainforest for thousands of years. What Starr had to say about the wolves changed Darimont’s perception of the animals.
Starr asked Darimont which wolves he and his team were going to study—the timber wolves (mainland wolves) or the coastal wolves on the islands. The question took Darimont by surprise. Biologists had always believed that the wolves that are sometimes spotted swimming between islands and eating salmon are the same wolves that live on the mainland. Darimont was intrigued by Starr’s classification of the wolves as two different groups. At first, he was hesitant to accept the idea. The distances between the mainland and the islands are small, less than a mile. Why would the wolves on the islands be any different from the wolves on the mainland? To find out, Darimont and his research team studied the wolves on the islands and in the densely forested territory of the Great Bear Rainforest for ten years.
Throughout the study, Darimont recorded several significant, observable differences between the “sea wolves,” as they are nicknamed, and the mainland wolves. Compared with the mainland wolves, the sea wolves are smaller in size and are strong swimmers. In 1996 sea wolves were spotted on an island nearly eight miles from any other land formation. While mainland wolves almost exclusively eat meat, such as deer and elk, and teach their young to hunt for land animals, sea wolves get as much as 90 percent of their nutrition from the sea and teach their young to dig for clams and to catch fish. Sea wolves regularly swim between islands and have been known to sneak up on a seal sunning itself on a rock and make a leaping attack from the water. Some salmon-eating mainland wolves come and go from the islands with the fish-spawning season, but the sea wolves are full-time island residents. Darimont suspects that some sea wolves live their entire life on the islands.
The sea wolves displayed not only physical and behavioral differences but also genetic variations from the mainland wolves. After collecting and analyzing the DNA in 800 samples of gray fur and wolf waste, researchers could produce hard biological evidence that sea wolves had genetic markers that made them distinct from the mainland wolves. A genetic marker is a variation in a DNA sequence that can be used to identify individuals or a species because it is passed down to offspring. Darimont hypothesizes that a change in habitat led to the eventual genetic differences between sea wolves and mainland wolves. Many years ago, loss of habitat and food sources forced some mainland wolves out to the islands. They learned to eat everything from kelp and fish eggs to the remains of sea creatures that washed up on the beach. Wolves living on the islands and mainland wolves became more isolated and rarely mated with each other. Over time the two types of wolves became more distinct.
It turned out that Chester Starr was right all along. “It sounded totally bizarre at first,” admits Darimont, “that there could be two versions of the species.” But he now realizes that this skepticism “definitely reflected my ignorance of indigenous knowledge at the time.” Learning to trust the wisdom of the Heiltsuk people opened Darimont up to knowledge accumulated over millennia and positioned him so that he could gather new scientific evidence about one of British Columbia’s most elusive species, the sea wolf.
Question
Read this sentence from paragraph 4.
After collecting and analyzing the DNA in 800 samples of gray fur and wolf waste, researchers could produce hard biological evidence that sea wolves had genetic markers that made them distinct from the mainland wolves.
The phrase “hard biological evidence” conveys that the goal of the research team was to
- Adevelop a procedure in order to ensure their study yielded plentiful data about the wolves.
- Bseek definitive scientific proof of the number of wolf species present in the area of the study.
- Cconduct a study to evaluate multiple theories about the diets of different wolf species.
- Ddiscover if the new data would provide information different from that of previous studies.
Show the answer
Correct answer: B
The question asks what the phrase “hard biological evidence” in the sentence from paragraph 4 conveys about the goal of the research team.
A. Incorrect. Although the research team followed a labor-intensive procedure, the phrase “hard biological evidence” refers to the product of their scientific research (the genetic markers revealed within the DNA samples), not the process by which they collected it. Their goal was not to develop a procedure for data collection but to determine precisely how many species of wolf were present in the area.
B. CORRECT. The research team wanted to prove or disprove the theory that two separate groups of wolves were present in the area, an idea that was already supported by the observations of scientists and local indigenous people. The phrase “hard biological evidence” conveys that the scientists wanted to bolster their observations of the wolves with concrete scientific data about the wolves’ biological makeup. The goal of the researchers was to use the data to prove how many species of wolf were present in the area of the study.
C. Incorrect. The research team gathered extensive data during their study (“After collecting and analyzing the DNA in 800 samples of gray fur and wolf waste” [paragraph 4]), and their goal in doing so was to evaluate a single theory about the wolves: that the wolves had evolved into two separate and genetically distinct species. The research team did not conduct the study in order to evaluate multiple theories about the diets of the wolves.
D. Incorrect. The phrase “hard biological evidence” does not suggest that the research team was hoping to discover if the new data would provide information that was different from previous studies. In fact, the goal of the research team was to use the genetic data to supplement their initial sources of information about the wolves and their own observations from the field.
Question analysis
This word-in-context question quotes a sentence from paragraph 4 of “Wolves of the Sea” about DNA taken from 800 samples of gray fur and wolf waste, and asks what the phrase “hard biological evidence” shows about the research team’s goal. Students must work out what the phrase says about the evidence and then turn that into a statement of purpose, choosing among four plausible aims for a study.
- Grade level
- Grade 8 reading and task
- Compared with grade 7
- Above grade 7 Grade 7 students regularly interpret a phrase in context. Here the phrase must be turned into a claim about the team’s purpose, which the passage never states outright, and the four choices are abstract research goals that each sound reasonable.
- 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 understand
- What makes it hard
- Reading between the lines moderate
- Hard words moderate
- Evidence in several places minor
- Evidence
- Answered from several paragraphs or stanzas
- Reading level
- Passage: about grade 10, 662 words; question and choices: about grade 10, 114 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 asks for a purpose, but the phrase it quotes describes a result, so students have to reason from the kind of evidence produced to what the team wanted it for. Readers who take “hard” as difficult drift toward a goal about procedure, and those who remember that biologists had long thought the wolves were one group are drawn to a goal of overturning earlier studies. The key’s “number of wolf species” is looser than the passage’s “two versions of the species,” which can make careful readers hesitate.
Reading between the lines moderate Working it out
The passage never states the team’s goal, so students must work back from “hard biological evidence” to the question paragraph 2 set up: whether island and mainland wolves are really two groups. (Graesser, Singer & Trabasso, 1994; Kintsch, 1998)
Hard words moderate Understanding the question
“Hard” here means solid and conclusive, as in hard evidence, not difficult; students who know only the everyday sense connect it to the labor of analyzing 800 samples of fur and waste. (Perfetti, 2007; Freedle & Kostin, 1993)
Evidence in several places minor Working it out
The goal the phrase points to lies two paragraphs back, in Starr’s two-group question and Darimont’s ten-year study “to find out,” not in the sentence the stem quotes. (Kirsch & Mosenthal, 1990; Gorin & Embretson, 2006)
Strategy: Replace “hard” with a word that fits evidence produced by DNA analysis, then ask what the team wanted that kind of evidence for, recalling the question Darimont set out to answer.
Traps
- Dictionary meaning, not meaning here: A common meaning of the word that does not fit its use in this text.
- Reads too much in: A reasonable-sounding conclusion that goes further than the text allows.
- Wrong part of the text: A choice is true of another paragraph, stanza or speaker than the one asked about.
The wrong answers, classified
A Dictionary meaning, not meaning here (Perfetti, 2007)
Reads “hard” as difficult and ties it to the labor of analyzing 800 samples, so takes the goal to be a thorough procedure rather than conclusive proof.
C Wrong part of the text (Kirsch & Mosenthal, 1990)
Brings in the diet differences of paragraph 3, clams, fish and seals, as theories under test, though the DNA work in paragraph 4 asked whether two groups exist.
D Reads too much in (Graesser, Singer & Trabasso, 1994)
Knows that biologists “had always believed” the wolves were one group and assumes the team set out to contradict earlier studies, which the phrase about solid proof does not suggest.
Working it out, step by step
Figure out what the question asks
This asks what a phrase shows about the team’s goal. A goal is what you are trying to get. The phrase names the kind of evidence the team got. Work back from that to what they wanted it for.
Read the sentence with the phrase
In paragraph 4, the team studied “800 samples of gray fur and wolf waste.” Then they “could produce hard biological evidence that sea wolves had genetic markers that made them distinct from the mainland wolves.” A genetic marker is a small difference in the DNA that parents pass to their young. Distinct means clearly different.
Work out what “hard” means
Here “hard” does not mean difficult. Hard evidence is solid proof that is tough to argue with. Biological means it comes from living things and their bodies. So the team wanted firm proof from the wolves’ own bodies.
Connect the proof to the question
What did they want to prove? Go back to paragraph 2. Starr said there were two groups of wolves. Darimont was unsure. “To find out,” his team studied the wolves. The DNA gave a firm answer: the sea wolves really are a separate group. So the goal was solid proof of how many groups of wolves live there.
Check each choice
- A is wrong. It reads “hard” as hard work. The phrase is about how firm the proof is, not about a procedure.
- B is right. Definitive means final and settled. The team wanted settled proof of how many groups of wolves live there. B says “species,” which goes further than the passage. Darimont speaks only of “two versions of the species.”
- C is wrong. Diets come up in paragraph 3. The DNA work tested whether there were two groups.
- D is wrong. The phrase says nothing about earlier studies.
Watch out: D is tempting because biologists “had always believed” the wolves were one group. But “hard” evidence is about firm proof, not about beating old studies.
Choose the answer
“Hard biological evidence” shows the team wanted firm, scientific proof. So the answer is B, “seek definitive scientific proof of the number of wolf species present in the area of the study.”
Why this answer and not the closest wrong one
D is the closest wrong answer. Biologists had thought the wolves were one group, so D can seem to fit. But the phrase “hard biological evidence” is about how firm the proof is. It says nothing about earlier studies. B matches that: the team wanted settled proof of how many groups there were.
More questions like this
The original DOE question
The passage “Wolves of the Sea” as printed (pages 23–24)
Question 3 of 6
2024 Test A English, question 24Passage At Dusk
At Dusk
by Natasha Trethewey
At first I think she is calling a child,
my neighbor, leaning through her doorway
at dusk, street lamps just starting to hum
the backdrop of evening. Then I hear
the high-pitched wheedling1 we send out
to animals who know only sound, not
the meanings of our words—here here—
nor how they sometimes fall short.
In another yard, beyond my neighbor’s
sight, the cat lifts her ears, turns first
toward the voice, then back
to the constellation of fireflies flickering
near her head. It’s as if she can’t decide
whether to leap over the low hedge,
the neat row of flowers, and bound
onto the porch, into the steady circle
of light, or stay where she is: luminous
possibility—all that would keep her
away from home—flitting before her.
I listen as my neighbor’s voice trails off.
She’s given up calling for now, left me
to imagine her inside the house waiting,
perhaps in a chair in front of the TV,
or walking around, doing small tasks;
left me to wonder that I too might lift
my voice, sure of someone out there,
send it over the lines stitching here
to there, certain the sounds I make
are enough to call someone home.
“At Dusk” from NATIVE GUARD by Natasha Trethewey, published by Houghton Mifflin Company. Copyright © 2006 by Natasha Trethewey. All rights reserved.
1wheedling: speaking in a flattering manner
Question
How does the setting affect the events of the poem?
- AIt enables the speaker to regularly overhear the neighbor calling for her cat at dusk.
- BIt allows the speaker to observe the neighbor quietly without interacting with her.
- CIt shows how living in close proximity helps the speaker feel connected to the neighbor.
- DIt shows how feeling isolated causes the speaker to imagine interactions with the neighbor.
Show the answer
Correct answer: B
The question asks how the setting affects the events discussed in the poem.
A. Incorrect. In line 2, the speaker refers to the woman calling for her cat as “my neighbor,” which clearly suggests that the speaker lives next door to the woman. However, although the two live next door to each other, line 1 suggests that perhaps the speaker does not regularly overhear the neighbor because the speaker initially thinks that the neighbor is “calling a child” and only later realizes the neighbor is calling to a cat. Although the setting places the speaker and the neighbor in close proximity, the poem does not indicate the frequency or regularity with which the speaker overhears the neighbor.
B. CORRECT. In the first four lines, the speaker observes the actions of the neighbor as the neighbor leans out to call for the cat at dusk. Despite the speaker’s observation of the neighbor, there is no indication that the neighbor notices the speaker. The reader can conclude that because of the time of day and the speaker being in the house next door, the speaker can observe the neighbor without being observed by her or having to interact with her.
C. Incorrect. The setting of the poem is a neighborhood at nightfall, as indicated by “at dusk” in line 3, the reference to “another yard” in line 9, and the flickering fireflies in line 12. However, while the speaker is close enough to the neighbor to overhear her calling to the cat, there is no indication that the speaker feels connected to the neighbor. Instead, the speaker expresses curiosity about the neighbor after the neighbor goes inside, and the speaker is “left . . . / to imagine her inside the house waiting” (lines 21–22). The fact the speaker initially thought that the neighbor was calling a child indicates that the speaker is not familiar with the neighbor and her habits, and there is no indication that the speaker feels connected to the neighbor.
D. Incorrect. In lines 22–24, the speaker imagines what the neighbor may be doing while the neighbor is waiting inside for the cat to return, but the speaker is imagining the neighbor’s solitary experience after the neighbor has momentarily “given up” on calling to the cat (line 21). The speaker does not imagine personally interacting with the neighbor but rather briefly imagines what the neighbor is doing at home while the cat is away.
Question analysis
This reading question asks how the setting of At Dusk, a neighborhood at nightfall where a woman leans from her doorway to call her cat, affects the events of the poem. Because so little happens, students must infer the setting's role from small details, and several choices sound reasonable without being supported by the poem.
- Grade level
- Grade 8 reading and task
- Compared with grade 7
- Above grade 7 Grade 7 students analyze how setting shapes events, usually in a story with a clear plot. This poem has almost no action, so the student must reason from a handful of details about place and time, 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 3, strategic thinking · mainly analyze
- What makes it hard
- A very close wrong answer major
- Reading between the lines moderate
- Evidence
- Answered from the whole text
- Reading level
- Passage: 236 words (a poem; reading level not measured); question and choices: about grade 8, 67 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
Little happens in this poem, so the setting's role must be built from small details: a neighbor at her doorway at dusk, a cat in another yard, a speaker who hears and watches but never speaks. The strongest wrong answer is right about overhearing and wrong only in claiming it happens regularly, which the speaker's first mistaken guess argues against. The other choices supply a feeling of closeness or of isolation that the poem never states.
A very close wrong answer major Choosing the answer
The overhearing choice describes what the setting allows almost as well as the right one and fails on a single word, “regularly,” since the poem records one evening and the speaker first mistakes the call. (Embretson & Wetzel, 1987; Gorin & Embretson, 2006; Ascalon et al., 2007)
Reading between the lines moderate Working it out
The setting's effect is never stated; it has to be inferred from the speaker hearing and watching from nearby while the neighbor, “leaning through her doorway,” never seems to notice anyone. (Graesser, Singer & Trabasso, 1994; Kintsch, 1998)
Strategy: Picture the scene from the speaker's position, then check each choice word by word against the poem and reject any that claims something the poem never states.
Traps
- Too broad or too strong: A choice overstates, generalizes, or uses absolute words the text does not support.
- Reads too much in: A reasonable-sounding conclusion that goes further than the text allows.
- Twists what the text says: Uses the text's topic and ideas but changes what it says: who did it, how much, when, or why.
The wrong answers, classified
A Too broad or too strong (King et al., 2004)
Rightly sees that living next door lets the speaker overhear the call, but “regularly” is unsupported, and the first guess about a child suggests the call is unfamiliar.
C Reads too much in (Graesser, Singer & Trabasso, 1994)
Connects living close by with the poem's interest in connection and the speaker's “I too,” but the speaker never claims to feel close to the neighbor.
D Twists what the text says (King et al., 2004)
Notices the speaker picturing the neighbor indoors and calls it imagined interaction, but the speaker pictures her alone, waiting or doing small tasks, and never mentions feeling isolated.
Working it out, step by step
Figure out what the question asks
The setting is where and when a story or poem takes place. You need to see how the setting shapes what happens in the poem.
Picture the setting
It is “dusk” (line 3), the dim time just after sunset. The neighbor is “leaning through her doorway” (line 2). The cat is “In another yard” (line 9). The speaker is close enough to hear and watch it all. But the speaker never speaks to the neighbor. Nothing shows the neighbor notices the speaker.
Work out the effect
Living next door puts the speaker close by. In the fading light, the speaker can watch quietly. So the speaker sees the neighbor and the cat without joining in. The whole poem is what the speaker sees, hears and imagines from there.
Check each choice
- A is wrong. The word “regularly” is the problem. The poem shows one evening.
- B is right. The speaker watches from nearby and never talks with the neighbor.
- C is wrong. The speaker never says they feel close to the neighbor.
- D is wrong. The poem never says the speaker feels lonely. The speaker pictures the neighbor alone inside, not the two of them talking.
Watch out: A is almost right, since living nearby does let the speaker overhear. One word makes it wrong.
Choose the answer
The setting lets the speaker watch quietly from close by. So the answer is B.
Why this answer and not the closest wrong one
A is the closest wrong answer. Living next door does let the speaker hear the call. But nothing says it happens often. The poem tells about one evening. At first the speaker even thinks a child is being called. B fits what the poem shows: the speaker watches without ever talking to the neighbor.
More questions like this
The original DOE question
The passage “At Dusk” as printed (page 48)
Question 4 of 6
2018 Test A Math, question 44Question
On the number line above, points , , , and are integers, and . What is the value of ?
- A8
- B11
- C12
- D18
Show the answer
Correct answer: C
Convert the ratios into fractions of . Use the sum of the ratios for the denominator.
The part of that is is the sum of those fractions:
Find the length of :
The value of is .
Question analysis
This number line question places integer points W, X, Y and Z on a line and gives the ratio of the segments WX, XY and YZ as 4 to 2 to 3. Students find the whole length from W to Z, split it by the ratio, and add the parts that make up WY. Mixing up a part with the whole is the main risk.
- Grade level
- Grade 7 content, by NYS standard
- Compared with grade 7
- Above grade 7 Grade 7 students find distances on a number line and use part-to-whole ratios, usually separately. This item joins them: a negative endpoint, a three-term ratio and a choice of which segments to combine.
- 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
- Reading a figure, table or graph moderate
- Many steps minor
- Solution
- 3 steps
- Reading level
- Question and choices: about grade 10, 21 words.
- Corrected from the DOE handbook
- Equations in the explanation that mixed up a fraction of a length with the length itself were 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
Each step is routine, but the question keeps asking for a different piece of the line: the whole WZ, the part WX, and finally WY, which is two parts added together. Two of the wrong choices are exactly those other pieces. Students who mark the actual positions, X at −2 and Y at 2, can check the ratio before answering.
Combines ideas moderate Working it out
A three-part ratio, 4:2:3, must be applied to a length found from a negative endpoint, 8 − (−10) = 18, joining ratio and number-line distance. (Embretson, 1998; Daniel & Embretson, 2010)
Reading a figure, table or graph moderate Understanding the question
Only W at −10 and Z at 8 are labeled, and the drawing is not to scale: Y is drawn nearer 5 than 2, so reading WY from the picture fails. (Lesh, Post & Behr, 1987; Kirsch & Mosenthal, 1990)
Many steps minor Working it out
Find WZ, split it into 9 equal parts of 2, then add the 4 parts of WX and the 2 parts of XY. (Daniel & Embretson, 2010; Enright, Morley & Sheehan, 2002)
Strategy: Find the length WZ from the endpoints on the number line, divide it by the total number of ratio parts, and multiply by the parts from W to Y.
Traps
- Stops one step early: A choice is a number from partway through the solution.
- Answers a different question: A choice is right for another quantity: the other unknown, the rest instead of the part, the part instead of the whole.
- Counting the ends: Inclusive or exclusive ends, fence posts, consecutive numbers: an answer that is one too many or too few, or an endpoint drawn open where it belongs closed (or the reverse).
The wrong answers, classified
A Stops one step early (King et al., 2004; Gierl et al., 2017)
Finds WX, 4/9 of 18 = 8, and stops without adding XY's 4 to reach Y; 8 also matches Z's label.
B Counting the ends (Brown & Burton, 1978)
Places Y at 2 but counts the integers strictly between −10 and 2, which are −9 through 1, getting 11 instead of the distance 12.
D Answers a different question (King et al., 2004; Hegarty, Mayer & Monk, 1995)
Gives the whole length WZ, 8 − (−10) = 18, instead of the part from W to Y.
What was corrected from the DOE handbook, and why
- Explanation: The handbook writes WX = 4/9, XY = 2/9 and WY = 2/3, and then says “The value of WY is 2/3(18) = 12”. Those fractions are parts of WZ, not the lengths themselves (WX is 8 and WY is 12), so WY cannot be both 2/3 and 12. The lines now read WX = 4/9 WZ, XY = 2/9 WZ and WY = 2/3 WZ. The method and the answer are unchanged.
Worked solution, step by step
Formulas used
- Distance on a number line
- d is the distance between two points. b is the point on the right and a is the point on the left. Subtracting left from right always gives a positive distance. It works even when a is negative.
- Size of one part of a ratio
- u is the size of one part. L is the whole length being shared. p is the total number of parts, found by adding the numbers in the ratio. Every part is the same size, so you share the length equally.
Sort out what you know
W is at −10 and Z is at 8. X and Y are between them. The ratio 4:2:3 means WX is 4 parts, XY is 2 parts and YZ is 3 parts. All the parts are the same size.
You need the length WY, from W to Y. The drawing is not exact, so use the numbers, not the picture.
Find the whole length WZ
WZ is 18 units long. Subtracting a negative number is the same as adding.
Find the size of one part
Add the ratio numbers to get the number of parts:
Share the 18 units equally among 9 parts:
Each part is 2 units long.
Find WY
WY is WX and XY together, so it has 4 + 2 = 6 parts:
Watch out: WX alone is 4 × 2 = 8, which is choice A. And 18 is the whole line, choice D. So the answer is C, 12.
Check your answer
Place the points. W is at −10. X is 8 units to the right, at −2. Y is 4 more, at 2. Z is 6 more, at 8, which matches its label. And the distance from −10 to 2 is 2 − (−10) = 12.
More questions like this
The original DOE question
Question 5 of 6
2018 Test A Math, question 1Question
In the figure above, PQRS is a parallelogram. What is the value of ?
Grid-in question: work out the answer and enter it as a number.
Show the answer
Correct answer: 162
First, find the measure of angle PQR. The measure of angle PQR is equal to the measure of angle PSR.
m∠PSR = 180 − 72 = 108.
So, the measure of angle PQR is also 108.
108 + 90 + x = 360
198 + x = 360
x = 162
Question analysis
A grid-in geometry question about angles around a parallelogram PQRS. A 72° angle sits outside corner S on the extended base, and at corner Q a right angle and the unknown angle x complete the turn around the point. Students chain three angle facts, and the angle asked for lies outside the shape, not inside it.
- NYS standards
- Grade level
- Grade 8 content, by NYS standard
- Compared with grade 7
- Above grade 7 Grade 7 angle work usually applies one or two facts, such as supplementary or vertical angles, to find an angle. This chains three, and needs the equal opposite angles of a parallelogram, which rest on grade 8 parallel-line facts.
- Estimated difficulty
- Hard: combines ideas, needs a plan, and has more than one tempting wrong answer.
- Thinking it demands
- Depth of knowledge 2, skills and concepts · mainly apply
- What makes it hard
- Reading a figure, table or graph major
- Combines ideas moderate
- An answer in an unexpected form minor
- Solution
- 3 steps
- Reading level
- Question and choices: about grade 7, 14 words.
- Students, last 30 days
- Not enough answers yet to show (it takes 10).
Why it is hard, traps and wrong answers (shows the answer)
Why it is hard
The arithmetic is two subtractions; the difficulty is seeing which angles the marks refer to. Students lose points by treating the 72° as the parallelogram's own angle at S, or by stopping at angle PQR, the most natural number to grid. The question rewards tracing a route from S to Q before computing anything, and checking at the end that x is the angle outside the shape that the arc marks.
Reading a figure, table or graph major Understanding the question
The 72° is marked outside the parallelogram, between side SR and the base extended past S, and x sits outside corner Q, between QP and a vertical ray that meets QR at a right-angle mark. (Lesh, Post & Behr, 1987; Kirsch & Mosenthal, 1990)
Combines ideas moderate Working it out
Three angle facts have to be chained: a straight line gives the angle inside S, opposite angles of a parallelogram carry it to Q, and the angles around Q make a full 360° turn. (Embretson, 1998; Daniel & Embretson, 2010)
An answer in an unexpected form minor Choosing the answer
As a grid-in there are no choices to check against, so a student who stops at angle PQR, inside the parallelogram, gets no signal that the job is unfinished. (Enright, Morley & Sheehan, 2002)
Strategy: Use the straight line at S to find the parallelogram's angle there, carry it to the opposite corner Q, then take that angle and the right angle away from 360.
Traps
- Stops one step early: A choice is a number from partway through the solution.
The wrong answers, classified
108 Stops one step early (King et al., 2004; Gierl et al., 2017)
Finds angle PSR = 180 − 72 = 108 and carries it to angle PQR, then grids that interior angle instead of the angle x outside it.
198 Misreads the figure (Lesh, Post & Behr, 1987; Kirsch & Mosenthal, 1990)
Reads the 72° as the parallelogram's interior angle at S, so takes angle PQR as 72 and grids 360 − 90 − 72 = 198.
252 Misreads the figure (Lesh, Post & Behr, 1987; Kirsch & Mosenthal, 1990)
Overlooks the right-angle mark at Q and subtracts only the 108° angle PQR from 360, giving 252.
Worked solution, step by step
Formulas used
- Angles on a straight line
- a and b are two angles side by side on a straight line. Together they make a half turn, so they always add up to 180 degrees. Use it when an angle you need shares a straight line with an angle you know.
- Opposite angles of a parallelogram
- The symbol ∠ means angle. ∠PQR is the angle at corner Q, between sides QP and QR. ∠PSR is the angle at the opposite corner, S. In a parallelogram, opposite corners always have equal angles, because the shape leans the same way at both.
- Angles around a point
- a, b and c are angles that fit around one point with no gaps and no overlaps. Going all the way around is a full turn, which is 360 degrees. So the angles add up to 360.
Sort out what the figure shows
PQRS is a parallelogram. That is a four-sided shape whose opposite sides are parallel, which means they never meet. You need the value of x, in degrees.
Look closely at the marks. The 72° angle is outside the shape, at S. It sits between side SR and the base line, which keeps going past S. At Q, a vertical line meets side QR. The small square means a right angle, 90°. The angle x is outside the shape too. It runs from that vertical line around to side QP.
Find the angle inside corner S
Angle PSR is the shape’s own angle at S. It sits right next to the 72° angle, on the same straight base line. So the two angles add up to 180°.
So angle PSR is 108°. Watch out: 72° is not the inside angle at S. Using 72 as the inside angle leads to the wrong answer 198.
Carry the angle over to Q
Corners Q and S are opposite each other. In a parallelogram, opposite angles are equal. So angle PQR matches angle PSR.
So angle PQR is 108°. Watch out: this is not x. Angle PQR is inside the shape, and x is outside it. Stopping here and gridding 108 is the most common mistake.
Add the angles around Q
Three angles fill the space all the way around point Q. They are the right angle (90°), angle PQR (108°) and x. Together they make a full turn.
Watch out: don’t skip the right angle at Q. Leaving out the 90 gives 252.
Solve for x
Subtract 198 from 360 to find what is left for x.
So x is 162°. So you would grid 162.
Check your answer
Add the three angles at Q: . That is a full turn. Also, the arc for x is wider than a right angle but not as wide as a straight line. So x should be between 90° and 180°, and 162° is.
More questions like this
The original DOE question
Question 6 of 6
2026 Practice Test D Math, question 48Question
The perimeter of square W is twice the perimeter of equilateral triangle X. What is the ratio of the length of one side of square W to the length of one side of equilateral triangle X?
- A3:8
- B2:3
- C3:2
- D2:1
Show the answer
Correct answer: C
First, set up the ratio of the perimeter of the square to the triangle as 2:1 because the question states that the perimeter of the square is twice the perimeter of the triangle.
Recognizing that the square has 4 equal sides and that an equilateral triangle has 3 sides, use division to find the ratio of the sides.
Perimeter:
Sides:
Question analysis
The perimeter of square W is twice the perimeter of equilateral triangle X, and students find the ratio of a side of the square to a side of the triangle. This ratio question uses perimeters of regular shapes with no lengths given. Turning a comparison of perimeters into one of sides, and keeping the ratio in the order asked, are the tricky parts.
- NYS standards
- Grade level
- Grade 7 content, by NYS standard
- Compared with grade 7
- Above grade 7 Grade 7 ratio problems usually supply numbers to work with. This one gives only a relationship between two perimeters, so students must bring in the number of sides of each shape themselves and keep the ratio in the order asked.
- Estimated difficulty
- Hard: combines ideas, needs a plan, and has more than one tempting wrong answer.
- Thinking it demands
- Depth of knowledge 2, skills and concepts · mainly apply
- What makes it hard
- Turning words into math moderate
- Variables instead of numbers moderate
- A very close wrong answer minor
- Solution
- 3 steps
- Reading level
- Question and choices: about grade 9, 36 words.
- Students, last 30 days
- Not enough answers yet to show (it takes 10).
Why it is hard, traps and wrong answers (shows the answer)
Why it is hard
The question turns a statement about perimeters into a ratio of sides, and the natural guess, that the sides keep the perimeters’ 2 to 1, ignores that the square shares its perimeter among 4 sides and the triangle among 3. Choosing a triangle perimeter such as 12 makes the comparison concrete. The order of the ratio still has to be checked at the end, because its reverse is listed too.
Turning words into math moderate Understanding the question
“The perimeter of square W is twice the perimeter of equilateral triangle X” must become 4s = 2 × 3t, with the 2 on the triangle’s side; written backward, it gives the triangle the larger perimeter. (Hegarty, Mayer & Monk, 1995; Koedinger & Nathan, 2004)
Variables instead of numbers moderate Understanding the question
No side length is given, so students must either work with letters for the two sides or choose a convenient perimeter themselves, such as 12 for the triangle. (Koedinger & Nathan, 2004; Enright, Morley & Sheehan, 2002)
A very close wrong answer minor Choosing the answer
The ratios 3:2 and 2:3 use the same two numbers, so only keeping the square’s side first, as the question orders it, separates the answer from its reverse. (Embretson & Wetzel, 1987; Gorin & Embretson, 2006; Ascalon et al., 2007)
Strategy: Pick an easy side length for the triangle, find its perimeter, double that for the square, divide by the square's number of sides, and write square to triangle.
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.
- Wrong operation: Adds instead of multiplying, divides the wrong way round, turns a ratio or rate upside down, or undoes a step in the wrong direction (subtracts what should be added back).
- Equation written backwards: Writes a comparison the wrong way round, word for word: "six times as many students as professors" as 6S = P. The bigger quantity gets the bigger number.
The wrong answers, classified
A Equation written backwards (Clement, Lochhead & Monk, 1981)
Writes the comparison backward, 2 × 4s = 3t, giving the triangle the larger perimeter, so the ratio of the sides comes out 3:8.
B Wrong operation (Hegarty, Mayer & Monk, 1995; King et al., 2004)
Finds the right relationship but turns the ratio upside down, giving the triangle’s side to the square’s instead of the square’s side first.
D Misunderstands the concept (Smith, diSessa & Roschelle, 1993; De Bock et al., 1998; Ni & Zhou, 2005)
Assumes the sides are in the same ratio as the perimeters, 2:1, ignoring that the square has 4 sides and the triangle only 3.
Worked solution, step by step
Formulas used
- Perimeter of a square
- P is the perimeter, the distance around the shape. s is the length of one side. A square has 4 equal sides, so its perimeter is 4 times one side.
- Perimeter of an equilateral triangle
- An equilateral triangle has 3 equal sides. t is the length of one side. So its perimeter is 3 times one side.
- Ratio
- A ratio compares two amounts in order. a : b means a compared with b. The order matters, so write the amounts in the order the question names them.
Sort out the question
Square W has a perimeter twice as long as the perimeter of triangle X. Equilateral means all 3 sides of X are equal.
You need the ratio of one side of the square to one side of the triangle, in that order. No lengths are given, so you can pick a size to try.
Pick a size for the triangle
Choose an easy side length for the triangle, such as 2 units. All 3 sides are 2, so its perimeter is:
Find the square’s side
The square’s perimeter is twice the triangle’s:
The square has 4 equal sides, so divide by 4:
Each side of the square is 3 units.
Write the ratio in order
The square comes first, then the triangle. Their sides are 3 and 2, so the ratio is 3 : 2.
Watch out: 2 : 1, choice D, compares the perimeters, not the sides. The square splits its perimeter into 4 sides, the triangle into only 3. Choice B, 2 : 3, puts the triangle first. Choice A, 3 : 8, comes from giving the triangle the bigger perimeter.
So the answer is C, 3:2.
Check your answer
Try a different size. Give the triangle sides of 4. Its perimeter is 12, so the square’s is 24. Each side of the square is . The ratio 6 : 4 simplifies to 3 : 2. The size does not change the ratio.
More questions like this
The original DOE question
