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 D English, question 26Passage Ode to Fireworks
Ode to Fireworks
In autumn my mother drove us to the edge of the field
where the fair was set up year after year:
the carousel, the bumper cars, the long, low sheds
filled with prizewinning animals.
We—my sister, my cousin, and I—were ready for bed,
already in our pajamas. This was a treat we waited
all year for. We waited in the darkness
for the first low, dull thwumps, like someone
beating an old, filthy rug hung on a wash line.
Then we counted the seconds between the lightning
and thunder, as we also used to do, until the sky
lit up: red, blue, green, gold. In my mind’s eye
I can still see the straggly, ancient oak whose branches
reached up past the exhibition halls, silhouetted
against the spectrum of stars that cascaded behind it.
It was one thing to look up into the sky
and imagine yourself in it or to make out pictures
among the clouds, which my sister liked to do.
No, I would tell her, that cloud
does not look like an elephant, a hat, an umbrella.
But it was another thing to see
the sky at night written upon
with those jewels. (We lived in the country:
night was night.) All around us, crickets
stridulated in the stubble of what had been
somebody’s cornfield, their song rising and falling.
You could smell winter on the air’s edge.
Now, in the city, when the sky dips into shadow
at New Year’s or on the Fourth of July, I find myself
craning my neck upward at odd moments.
The city sky is always lit up. This is where we live now,
and it is how we live now, awash in light
of every hue. Everything is a constant celebration:
picking up washing at the cleaner’s or stopping by
the corner market for a loaf of heavy bread.
And the music around me is the music of people,
their voices rising and falling in a hundred languages.
But beneath the yellowish glow deep in the sky
of all our city lights pelting out into the universe,
I remember the feel of the pickup truck bumping
across the ridged field, as I kept waiting for those
childhood bursts, watching as they escorted us home.
Question
The fireworks in the poem represent the speaker’s
- Awish to return to a simpler way of living.
- Bbittersweet feelings about leaving the past behind.
- Chigh expectations for everyday life.
- Dreflections on past interactions with relatives.
Show the answer
Correct answer: B
The question asks what the fireworks in the poem represent about the speaker.
A. Incorrect. While the speaker misses elements of the past, the speaker is also positive about the present, with comparisons to a “constant celebration” (line 33) and descriptions of “the music of people” (line 36). The speaker does not indicate a desire to return to a simpler way of living.
B. CORRECT. The speaker misses the experience of watching the fireworks display with family and friends but understands that time has progressed and that life is now different. The lines “This was a treat we waited / all year for” (lines 6–7) highlight the significance of the memory of waiting for and watching the fireworks. In the speaker’s present, the lines “I remember the feel of the pickup truck bumping / across the ridged field” (lines 40–41) emphasize the key details from the experience that stand out in the speaker’s mind when something in the current environment reminds the speaker of the past.
C. Incorrect. While the speaker does share details about the present and the tone is generally positive, the fireworks do not suggest that the speaker has high expectations for how everyday life should be. The third stanza (lines 28–42) describes the speaker’s daily life in the city, but the speaker does not form expectations from these everyday moments.
D. Incorrect. While the speaker does mention discussing cloud shapes with a family member in lines 19–20, the fireworks serve as a more general reminder of the speaker’s past life. Viewing the bright lights of the city makes the speaker recall memories of the speaker’s past and the feelings of anticipation before the fireworks show.
Question analysis
This question about symbolism asks what the fireworks represent in “Ode to Fireworks,” a 42-line poem in which an adult speaker remembers watching fireworks at a country fair as a child. Students must weigh all three stanzas to decide what the central image stands for, and the choices name abstract feelings and wishes that are close to one another.
- Grade level
- Grade 8 reading and task
- Compared with grade 7
- Above grade 7 Grade 7 students interpret symbols, usually where the text makes their meaning fairly clear. Here they must hold a 42-line poem in mind and choose among four abstract feelings, two of them very close, which goes 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 3, strategic thinking · mainly analyze
- What makes it hard
- Figurative or literary language moderate
- A very close wrong answer moderate
- Evidence in several places moderate
- Evidence
- Answered from the whole text
- Reading level
- Passage: 379 words (a poem; reading level not measured); question and choices: about grade 8, 35 words.
- Corrected from the DOE handbook
- The explanation of C misdescribed the third stanza; one sentence was corrected.
- Students, last 30 days
- Not enough answers yet to show (it takes 10).
Why it is hard, traps and wrong answers (shows the answer)
Why it is hard
This symbol question asks students to hold the whole 42-line poem in mind and weigh two feelings at once: the speaker misses the fireworks of childhood but speaks warmly of city life. Readers who notice only the longing choose a wish to go back, and readers who fix on one detail choose the relatives or the city’s “constant celebration.” The key’s “bittersweet” is the one word that holds both halves, which is why it is easy to pass over for a choice that states only one.
Figurative or literary language moderate Understanding the question
The fireworks are never explained; they are “jewels” in stanza 2 and the “childhood bursts” that “escorted us home” in stanza 3, so their meaning as a symbol must be built from images. (Graesser, Singer & Trabasso, 1994; Kintsch, 1998)
A very close wrong answer moderate Choosing the answer
The wish-to-return choice and the key both read the fireworks as feelings about the past; they differ in whether the speaker wants that past back or has accepted leaving it. (Embretson & Wetzel, 1987; Gorin & Embretson, 2006; Ascalon et al., 2007)
Evidence in several places moderate Working it out
The answer needs all three stanzas: the treat “we waited / all year for,” the dark country night, and the city stanza’s “This is where we live now,” which shows acceptance beside longing. (Kirsch & Mosenthal, 1990; Gorin & Embretson, 2006)
Strategy: Note how the speaker describes the fireworks in each stanza and how the speaker feels about the present in the last one, then choose the feeling that fits all three stanzas, not only the first.
Traps
- Reads too much in: A reasonable-sounding conclusion that goes further than the text allows.
- Word match: Repeats striking words or phrases from the text, so it looks supported, but its meaning does not fit the question.
- Too narrow: A single detail offered as the central idea or a summary, or a summary that keeps minor details and leaves out an essential part.
The wrong answers, classified
A Reads too much in (Graesser, Singer & Trabasso, 1994)
Takes the poem’s fond memories of the country as a wish to go back, though the speaker accepts “where we live now” and never asks to return.
C Word match (Freedle & Kostin, 1993)
Links the fireworks to line 33’s “Everything is a constant celebration,” then turns that into high expectations for daily life, which the poem never mentions.
D Too narrow (King et al., 2004)
Fixes on the mother, sister and cousin of the first stanza, real details, but the fireworks stand for a whole period of the speaker’s life, not time with relatives.
What was corrected from the DOE handbook, and why
- Explanation: Rejecting C, the handbook's explanation calls the third stanza (lines 28–42) “the speaker’s imaginings” and “fantasies”. The stanza describes the speaker's real life in the city now: “This is where we live now”, picking up washing at the cleaner's, stopping by the corner market. It now says the stanza describes the speaker's daily life in the city. The answer, B, is unchanged.
Working it out, step by step
Figure out what the question asks
This asks what the fireworks represent, or stand for. A thing in a poem that stands for a bigger idea is called a symbol. Look at the fireworks in all three stanzas. Then see how the speaker feels about the past and the present.
Look at the past
Stanza 1 shows how special the fireworks were: “This was a treat we waited / all year for.” Stanza 2 calls them “jewels.” In stanza 3 the speaker still remembers them: “I remember the feel of the pickup truck bumping / across the ridged field.” So the speaker misses that time.
Look at the present
The speaker also accepts city life: “This is where we live now, / and it is how we live now.” The city is “a constant celebration,” full of “the music of people.” So the speaker is not unhappy now. The speaker misses the past but has moved on. That feeling is bittersweet: happy and sad at the same time.
Check each choice
- A is wrong. The speaker never says they want to go back to the country.
- B is right. The fireworks stand for a loved past the speaker has left behind. The feeling is both warm and sad.
- C is wrong. The “constant celebration” describes city life. Nothing shows high expectations.
- D is wrong. Relatives appear in stanza 1. But the fireworks stand for a whole time of life, not just time with family.
Watch out: A notices only the longing. It misses that the speaker accepts “where we live now.”
Choose the answer
The fireworks hold both the joy of the past and the sadness of leaving it. So the answer is B, “bittersweet feelings about leaving the past behind.”
Why this answer and not the closest wrong one
A is the closest wrong answer. Both A and B are about feelings for the past. But A says the speaker wants to return, and the poem never says that. The speaker calls the city “a constant celebration” and accepts “where we live now.” Missing the past while accepting the present is bittersweet. That is B.
More questions like this
The original DOE question
The passage “Ode to Fireworks” as printed (page 32)
Question 2 of 6
2024 Test A English, question 46Passage Excerpt from The Highest Tide
Excerpt from The Highest Tide
by Jim Lynch
The narrator’s summer job is collecting marine specimens in Puget Sound, Washington. In this excerpt, he is looking for specimens in the mudflats before daybreak. Mudflats, or flats, are coastal landforms created when sediment and silt from tides are deposited as the tides recede.
I rounded the oyster beds, to the far side. . . . It was low tide by then, and I saw the water hesitating at its apex, neither leaving nor returning, patiently waiting for the gravitational gears to shift. Dozens of anxious clams started squirting in unison like they did whenever vibrating grains of sand warned them predators were approaching. I stopped and waited with them, to actually see the moment when the tide started returning with its invisible buffet of plankton for the clams, oysters, mussels and other filter feeders. It was right then, ankle deep in the Sound, feet numbing, eyes relaxed, that I saw the nudibranch.1
In all my time on the flats I’d never seen one before. I’d read about them, sure. I’d handled them at aquariums but never in the wild, and I’d never even seen a photo of one this stunning. It was just three inches long but with dozens of fluorescent, orange-tipped hornlike plumes jutting from the back of its see-through body that appeared to be lit from within.
Nudibranchs are often called the butterflies of the sea, but even that understates their dazzle. Almost everything else in the northern Pacific is dressed to blend with pale surroundings. Nudibranchs don’t bother, in part because they taste so lousy they don’t need camouflage to survive. But also, I decided right then, because their beauty is so startling it earns them a free pass, the same way everyday life brakes for peacocks, parade floats. . . .
The dark mudflats loomed like wet, flattened dunes stretching deep into Skookumchuck Bay in front of our house. From a distance, they looked too barren to support sea life. Up close, they still did, unless you knew where to find the hearty clams, worms and tiny creatures that flourish in mud. . . . I’m not sure why I decided to take a look. It was still an hour before sunrise, and I knew exactly what the bars2 looked like in the moonlight, but for some reason, I couldn’t resist.
I heard it long before I saw it. It was an exhale, a release of sorts, and I instantly wondered if a whale was stranded again. We had a young minke3 stuck out there two summers prior, and it made similar noises until the tide rose high enough for rescuers to help free it. . . . I looked for a hulking silhouette but couldn’t find one. I waited, but there were no more sounds. Still, I went toward what I thought I’d heard, avoiding stepping into the mud until I had to. I knew the flats well enough to know I could get stuck just about anywhere. The general rule was you didn’t venture out past the shells and gravel with an incoming tide. I sank up to my knees twice, and numbing water filled my boots.
. . . I kept stepping toward the one sound I’d heard, a growing part of me hoping I’d find nothing at all. When I stopped to rest and yank up my socks, my headlamp crossed it. My first thought? A giant octopus.
Puget Sound has some of the biggest octopi in the world. They often balloon to a hundred pounds. Even the great Jacques Cousteau4 himself came to study them. But when I saw the long tubular shape of its upper body and the tangle of tentacles below it, I knew it was more than an octopus. I came closer, within fifty feet, close enough to see its large cylindrical siphon5 quiver. I couldn’t tell if it was making any sounds at that point, because it was impossible to hear anything over the blood in my ears. . . .
The creature’s body came to a triangular point above narrow fins that lay flat on the mud like wings, but it was hard to be sure exactly where it all began or ended, or how long its tentacles truly were, because I was afraid to pry my eyes off its jumble of arms for more than half a second. I didn’t know whether I was within reach, and its arms were as big around as my ankle and lined with suckers the size of half-dollars. If they even twitched I would have run. So, I was looking at it and not looking at it while my heart spangled my vision. I saw fragments, pieces, and tried to fuse them in my mind but couldn’t be certain of the whole. I knew what it had to be, but I wouldn’t allow myself to even think the two words. Then I gradually realized the dark shiny disc in the middle of the rubbery mass was too perfectly round to be mud or a reflection.
It was too late to smother my scream. Its eye was the size of a hubcap.6
From THE HIGHEST TIDE by Jim Lynch. Copyright © 2005 by Jim Lynch. Used by permission of Bloomsbury USA. All rights reserved.
1nudibranch: type of sea slug
2bars: sandbars
3minke: species of small whale
4Jacques Cousteau: renowned French oceanographer
5siphon: tube-like organ that is used for drawing in or removing fluids
6hubcap: removable cap over the end of a wheel axle
Question
How does the setting affect the plot of the excerpt?
- AThe darkness of the mudflats before sunrise causes the narrator to pay close attention to his surroundings.
- BThe rugged terrain of the mudflats makes it more difficult for the narrator to do his job.
- CThe slow return of the tide along the mudflats forces the narrator to be patient during his journey.
- DThe barren appearance of the mudflats creates a sense of mystery that unsettles the narrator.
Show the answer
Correct answer: A
The question asks how the setting affects the plot of the excerpt.
A. CORRECT. In paragraph 4, the narrator says that it is an hour before sunrise. It is difficult to see because the mudflats are dark, so the narrator, while familiar with the terrain of the mudflats, is cautious.
B. Incorrect. While the terrain of the mudflats is challenging because of the “wet, flattened dunes” (paragraph 4), the narrator is familiar with the terrain and moves carefully. In addition, the excerpt focuses on the narrator’s curiosity and enjoyment as he explores the mudflats, not on his work collecting specimens.
C. Incorrect. In paragraph 1, the narrator watches the water “hesitating at its apex” and “patiently waiting for the gravitational gears to shift.” This illustrates that the narrator is already familiar with the changes in his surroundings, that the tide is slow to move in, and that he can move carefully through the mudflats without the threat of rising water.
D. Incorrect. While the narrator is on the mudflats for the entire excerpt, the phrase “eyes relaxed” in paragraph 1 indicates that the narrator feels comfortable there. The narrator does not show fear until paragraph 6, when a growing fear about the unknown creature arises.
Question analysis
Set on the mudflats of Puget Sound before daybreak, this excerpt from the novel The Highest Tide is the basis for a question about how setting affects plot. Students must link features of the place and time to what the narrator does across the whole excerpt, and each choice pairs a real feature of the setting with an effect that may or may not be in the text.
- Grade level
- Grade 8 reading and task
- Compared with grade 7
- Above grade 7 Analyzing how setting shapes plot is a grade 7 literary standard, but the excerpt never states the link: the effect must be inferred from scattered details, and every choice names a genuine feature of the flats, which is beyond typical work.
- Estimated difficulty
- Hard: combines ideas, needs a plan, and has more than one tempting wrong answer.
- Thinking it demands
- Depth of knowledge 3, strategic thinking · mainly analyze
- What makes it hard
- Reading between the lines major
- The right answer is reworded moderate
- Evidence in several places moderate
- Evidence
- Answered from the whole text
- Reading level
- Passage: about grade 6, 902 words; question and choices: about grade 8, 77 words.
- Corrected from the DOE handbook
- A statement in the explanation that contradicted the excerpt’s introduction was corrected.
- Students, last 30 days
- Not enough answers yet to show (it takes 10).
Why it is hard, traps and wrong answers (shows the answer)
Why it is hard
Every choice names a real feature of the mudflats, so the question turns on which feature the excerpt actually shows shaping events. The darkness never gets a sentence of its own; it is felt in a sound heard before anything is seen, a silhouette that cannot be found and a headlamp beam. The barren look of the flats is the strongest pull, because the scene is eerie, but the narrator knows life hides in the mud and his unease comes from the creature.
Reading between the lines major Working it out
The excerpt never says the darkness changes anything; the effect must be assembled from the hour before sunrise, the sound heard “long before I saw it”, the missing silhouette and the headlamp that finally finds the creature. (Graesser, Singer & Trabasso, 1994; Kintsch, 1998)
The right answer is reworded moderate Choosing the answer
The right choice uses no words from the text, while the wrong ones echo it: the “barren” look of the flats, the water “patiently waiting”, the narrator's summer job. (Freedle & Kostin, 1993; Kirsch & Mosenthal, 1990)
Evidence in several places moderate Working it out
The darkness is established in paragraph 4 and felt in paragraphs 5, 6 and 8, so no single passage shows the setting at work. (Kirsch & Mosenthal, 1990; Gorin & Embretson, 2006)
Strategy: Collect the details of time, place and conditions across the excerpt, then for each choice ask whether the text shows that feature of the setting actually changing what the narrator does.
Traps
- Twists what the text says: Uses the text's topic and ideas but changes what it says: who did it, how much, when, or why.
- Reads too much in: A reasonable-sounding conclusion that goes further than the text allows.
The wrong answers, classified
B Reads too much in (Graesser, Singer & Trabasso, 1994)
Combines the introduction's specimen job with his sinking to his knees to infer a harder workday, though the excerpt follows a strange sound and never shows his work suffering.
C Twists what the text says (King et al., 2004)
Borrows paragraph 1's water “patiently waiting” at low tide and has the tide force the narrator to wait, when he chose to stop and watch it turn.
D Twists what the text says (King et al., 2004)
Joins the flats' barren look from a distance to his later fear, but he knows life hides in the mud, and what unsettles him is the creature, not the landscape.
What was corrected from the DOE handbook, and why
- Explanation: In rejecting choice B, the handbook says “the excerpt shows that the narrator explores the mudflats for curiosity and enjoyment, not work.” But the introduction says the narrator’s summer job is collecting marine specimens and that “in this excerpt, he is looking for specimens in the mudflats before daybreak.” The explanation now says the excerpt focuses on his curiosity and enjoyment as he explores the mudflats, not on his work collecting specimens. That keeps the handbook’s point (the excerpt is not about the terrain making his job harder) without contradicting the introduction.
Working it out, step by step
Know what setting and plot mean
The setting is where and when a story happens. The plot is the chain of events. This asks which part of the setting changes what happens or what the narrator does.
Find the time of day
Paragraph 4 says, “It was still an hour before sunrise.” The narrator is out on the mudflats in the dark. The only light comes from the moon and his headlamp.
See how the dark shapes events
Because it is dark, he must rely on sounds and small clues. He says, “I heard it long before I saw it.” He looks for “a hulking silhouette,” a dark outline, but can’t find one. He spots the creature only when “my headlamp crossed it.” Then he stares hard, trying to make out its shape. The darkness keeps him alert and watching closely.
Check each choice
- A fits: the dark makes him pay close attention to everything around him.
- B is wrong because the excerpt follows a strange sound and never shows the ground making his job harder.
- C is wrong because in paragraph 1 he chooses to stop and watch the tide, and nothing forces him.
- D is wrong because he knows life hides in the mud, and what scares him is the creature.
Watch out: D feels right because the scene is eerie. But the flats’ empty look never troubles him.
Choose the answer
The darkness before sunrise is what keeps the narrator listening and looking so carefully. So the answer is A.
Why this answer and not the closest wrong one
D comes closest, because the dark flats do feel spooky. But the narrator says they only look “too barren to support sea life” from far away, and he knows better. His fear comes from the creature. The darkness, though, shapes every step: he hears before he sees and must watch closely.
More questions like this
The original DOE question
The passage “Excerpt from The Highest Tide” as printed (pages 64–65)
Question 3 of 6
2026 Practice Test D English, question 5Passage A Memory Revolution
A Memory Revolution
A high school senior logs on to a computer at the library to double-check the application due date listed on a college admissions website. Nearby, a librarian helps a group of biology students use a database to search for recent studies about mammals. In the past few decades, the Internet has become an integral component of daily life for many people. The seemingly limitless power of search engines made the Internet search extremely common, and today people increasingly rely on the Internet’s vast accumulation of sources to access all types of information. Scientists are beginning to examine how this reliance is modifying the strategies people use to store and prioritize information in their mind.
A Dependable and Valuable Asset
Psychologist Benjamin Storm from the University of California, Santa Cruz, and researchers Sean Stone and Aaron Benjamin devised an experiment to study students’ tendency to depend on the Internet for facts. To begin, the scientists divided sixty participants into multiple groups, including an “Internet” group and a “memory” group, and placed them in front of computers. The Internet group was required to use the search engine Google to answer eight challenging trivia questions. In contrast, participants in the memory group were permitted to use only their personal knowledge to answer the questions. In the second round, the researchers administered notably easier questions. This time, they allowed each group the option of using Google as they answered. Their results showed that 83 percent of the Internet group continued to consult Google in the second round, while only 63 percent of the memory group chose to do so.
People’s growing inclination to rely on the Internet in order to retrieve information, particularly facts and figures, is called cognitive offloading. Canadian researcher Evan F. Risko and British researcher Sam Gilbert, who have written extensively about the topic, say a similar process has been taking place for centuries. In the past, people used resources like encyclopedias to assist their memories; however, today the Internet, serving as a vast extended memory, allows people to digitally access and retrieve much larger volumes of information. Consequently, people’s minds are free for other cognitive feats, such as connecting data, learning new information, or solving problems.
Filing Information Away
The use of the Internet also appears to be modifying the strategies people use to store information in their mind. Researchers Betsy Sparrow from Columbia University, Jenny Liu from the University of Wisconsin-Madison, and Daniel Wegner from Harvard University conducted several studies to discover how people efficiently manage their information intake.
To begin, the researchers examined how people evaluate which information deserves their effort to remember. For this experiment, participants read forty trivia facts, such as “An ostrich’s eye is bigger than its brain,” and typed the statements into a computer file. Half the participants had been previously told the file would be saved, while half believed it would be erased. Next, the participants wrote down every fact they could recall. Those who believed the information would be erased and no longer available could recall 40 percent more facts than those who thought the information would be saved.
In another experiment, the same researchers tested the ability of study participants to remember where to access information. For this trial, participants read and typed trivia statements, which they saved in folders with generic names such as “Facts” and “Items.” After spending ten minutes writing down all the facts they could recall from memory, participants were asked which folder contained a particular fact based on a keyword. For example, “Which folder has the fact about ostriches?” Overall, participants recalled the information’s location more often than the content itself, correctly identifying 49 percent of the folders for specific facts while remembering only 23 percent of the actual trivia. The researchers concluded that our memory is adapting to the Internet age by prioritizing where to locate information even when the specific details are forgotten. According to Sparrow, the Internet has become an important form of transactive memory, an external source of the recollections and associative networks that constitute memory.
As the Internet’s resources continue to expand our “external” memory, some question whether the process may cause people to depend too heavily on technology. However, Steven Pinker, a professor of psychology at Harvard University, says, “Knowledge is increasing exponentially; human brainpower and waking hours are not. Fortunately, the Internet and information technologies are helping us manage, search and retrieve our collective intellectual output at different scales, from Twitter and previews to e-books and online encyclopedias. Far from making us stupid, these technologies are the only things that will keep us smart.”
Question
How does the diagram provide additional support for the topic presented in the passage?
- AIt reveals why human brains must adapt to obtaining information from the Internet as opposed to other sources.
- BIt indicates how people can use the Internet to help improve their long-term recollection of information.
- CIt shows how study participants’ brains distinguished between important and unimportant details.
- DIt depicts the idea that repetition and rehearsal are necessary to recall information when tools such as search engines are unavailable.
Show the answer
Correct answer: D
The question asks how the diagram provides additional support for the topic presented in the passage.
A. Incorrect. While the diagram indicates that the human brain has the ability to maintain different types of memory, the diagram does not show the need for the brain to adapt to obtaining information from the Internet rather than from other sources.
B. Incorrect. The diagram enhances the reader’s understanding of how long-term memories are formed, but it does not provide details about how the Internet can be used to improve long-term recollection of information.
C. Incorrect. The diagram provides an understanding of how details that are important to people can become stored because of an effort made to recall them. However, the diagram does not show how people decide which information is important and which is not.
D. CORRECT. The diagram depicts the connections that the human brain maintains between the different forms of memory. It also illustrates the idea that repetition and rehearsal are important steps in creating memories, as unrehearsed information will be forgotten. This supports the passage by highlighting the idea that access to search engines and other tools leads people to skip rehearsal and repetition steps that create memories, because people know that the information is readily accessible.
Question analysis
This question pairs “A Memory Revolution” with its flow diagram, “How Memory Works,” which follows new information from sensory memory through short-term and long-term memory, and asks how the diagram supports the topic of the passage. Students must read the diagram’s boxes, arrows and notes and relate them to an article about the Internet that never refers to the diagram, so the connection has to be worked out.
- Grade level
- Grade 8 reading and task
- Compared with grade 7
- Above grade 7 Grade 7 students regularly connect a diagram to a text. This flow diagram of memory never mentions the Internet, so students must build the bridge to the article’s studies themselves, and every choice claims something the diagram alone cannot show.
- 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
- Combines ideas moderate
- Reading a figure, table or graph moderate
- Every choice must be checked minor
- Evidence
- Answered from the whole text
- Reading level
- Passage: about grade 14, 763 words; question and choices: about grade 12, 81 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 diagram is a general model of memory, and every choice, even the right one, goes beyond it by bringing in the Internet, search engines or the study participants. The way through is to ask which choice rests on something the diagram really shows, and only one names its rehearsal loop and the forgetting of unrehearsed information. The strongest pull uses the diagram’s long-term memory and retrieval but claims the Internet improves recollection, the opposite of what paragraph 5’s experiment found.
Combines ideas moderate Working it out
The diagram never mentions the Internet and the article never mentions the diagram, so students must join its rehearsal loop to paragraph 5’s finding that people who expected the facts to be saved remembered fewer. (Embretson, 1998; Daniel & Embretson, 2010)
Reading a figure, table or graph moderate Understanding the question
Students must follow the arrows from “Attention” into short-term memory and find the “Rehearsal” loop beside “Information is maintained through repetition,” with “Unrehearsed information is forgotten” on the other side. (Lesh, Post & Behr, 1987; Kirsch & Mosenthal, 1990)
Every choice must be checked minor Choosing the answer
Three choices tie the diagram to the Internet, adaptation or the study participants, and even the key mentions search engines, so each claim must be held against the boxes and arrows actually drawn. (Embretson & Wetzel, 1987)
Strategy: Trace the diagram’s arrows from new information to long-term memory and say what each label shows, then ask which choice links that process to the studies without crediting the diagram with ideas it never shows.
Traps
- 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.
- 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 Reads too much in (Graesser, Singer & Trabasso, 1994)
Credits the diagram with the article’s claim that memory is “adapting to the Internet age” and adds a “must,” though its boxes and arrows show memory in general and never mention the Internet.
B Twists what the text says (King et al., 2004)
Joins the diagram’s long-term memory and retrieval arrow to the Internet as outside memory, though paragraph 5 found that people who expected the facts to be saved recalled fewer of them.
C Wrong part of the text (Kirsch & Mosenthal, 1990)
Reads the “Attention” arrow and the forgotten unrehearsed information as a picture of paragraph 5’s experiment, though the diagram shows no participants and nothing about judging what is important.
Working it out, step by step
Figure out what the question asks
This asks how the diagram supports the article. The diagram is the flow chart called “HOW MEMORY WORKS” at the end of the passage. It never mentions the Internet. So you must find what it shows, then link that to the article.
Follow the arrows in the diagram
Start at the top. An arrow labeled “New Information” goes into the box “Sensory Memory.” The “Attention” arrow leads to “Short-Term Memory.” From there, two things can happen. On the left, a loop labeled “Rehearsal” sits beside the note “Information is maintained through repetition.” On the right, a note says “Unrehearsed information is forgotten.” A “Storage” arrow leads down to “Long-Term Memory,” and a “Retrieval” arrow leads back up.
Explain what the diagram means
To rehearse information is to repeat it, the way you practice lines for a play. To maintain something is to keep it. So the diagram says that information you repeat stays with you. Information you don’t repeat is lost. Repeating takes effort.
Link the diagram to the passage
Paragraph 5 describes people who typed forty facts. Some thought the file would be saved. Others thought it would be erased. Those who thought it would be erased “could recall 40 percent more facts.” They knew they could not look the facts up later. So they made the effort to remember. The diagram shows that effort: rehearsal. When search engines are at hand, people may skip it.
Check each choice
- A does not fit. The diagram never mentions the Internet. It does not say brains must adapt.
- B does not fit. The diagram shows nothing about using the Internet. Paragraph 5 even found that people remembered less when they expected the facts to be saved.
- C does not fit. The diagram shows memory in general. It shows no study participants and no sorting of important facts.
- D fits. The “Rehearsal” loop shows that repeating information keeps it. Without a tool to look things up, that repeating is what lets you recall.
Watch out: B is tempting because the diagram has “Long-Term Memory” and “Retrieval,” and the article calls the Internet an outside memory. But the diagram is about the brain, not the Internet.
Choose the answer
The diagram shows rehearsal keeping information and unrehearsed information being forgotten. That explains why people who can’t look facts up must work to remember them. So the answer is D, “It depicts the idea that repetition and rehearsal are necessary to recall information when tools such as search engines are unavailable.”
Why this answer and not the closest wrong one
B is the closest wrong choice. It uses the diagram’s “Long-Term Memory” and “Retrieval” labels. But the diagram never shows the Internet improving recall. The passage says the opposite: expecting the facts to be saved made people remember fewer. D rests on what the diagram really shows, the “Rehearsal” loop and the note “Unrehearsed information is forgotten.”
More questions like this
The original DOE question
The passage “A Memory Revolution” as printed (pages 3–4)
Question 4 of 6
2024 Test A Math, question 39Question
Raquel is cutting out pieces of cardboard to make a pyramid. She will use a square piece for the base and identical triangular pieces for the sides. The figure above shows the dimensions of the triangle for each side. What will be the total surface area, in square inches, of the pyramid, including the square base?
- A280
- B295
- C340
- D360
Show the answer
Correct answer: C
Surface area is found by calculating the area of each side, including the base, and adding them all together.
The base of the pyramid measures 10 inches on each side, so the area of the base is
Each triangular face has a base of 10 inches and a height of 12 inches, so the area of each face is
There are 4 triangular faces (because the square base has 4 edges, each of which will have a triangular face). So the total surface area of the pyramid is the sum of the areas of 4 triangles and 1 square.
So the total surface area is 340 square inches.
Question analysis
This surface area word problem shows one triangular face, with sides of 13 inches, a base of 10 inches and a height of 12 inches, that Raquel will use to build a cardboard pyramid with a square base. Students find the total area of the base and all the triangular sides. Picturing the solid and choosing the right measurements from the figure are the tricky parts.
- Grade level
- Grade 7 content, by NYS standard
- Compared with grade 7
- Above grade 7 Grade 7 students find the surface area of a pyramid from a drawn net or solid. Here only one triangular face is shown, so students must picture the whole pyramid, count its faces, and choose which labeled length belongs in the area formula.
- Estimated difficulty
- Hard: combines ideas, needs a plan, and has more than one tempting wrong answer.
- Thinking it demands
- Depth of knowledge 2, skills and concepts · mainly apply
- What makes it hard
- Reading a figure, table or graph moderate
- Combines ideas moderate
- Something you must already know minor
- Solution
- 4 steps
- Reading level
- Question and choices: about grade 6, 56 words.
- Corrected from the DOE handbook
- A wrong unit in the explanation was corrected.
- Students, last 30 days
- Not enough answers yet to show (it takes 10).
Why it is hard, traps and wrong answers (shows the answer)
Why it is hard
Students have to build the pyramid in their heads from one flat triangle, then choose the right measurement from three labels. The 13-inch sides look like the natural height, and using them gives a listed total; picturing a pyramid with three sloping faces gives another. Sketching the square base with a triangle on each edge, and marking 12 as the height, settles both the face count and the formula.
Reading a figure, table or graph moderate Understanding the question
The figure gives one triangle with three length labels, 13, 13 and 10, and puts its height, 12, on a separate arrow beside it, where it is easy to overlook. (Lesh, Post & Behr, 1987; Kirsch & Mosenthal, 1990)
Combines ideas moderate Working it out
The solid is never drawn: students must see that the square's side equals the triangle's 10-inch base, count four triangles, and add triangle and square areas. (Embretson, 1998; Daniel & Embretson, 2010)
Something you must already know minor Working it out
A triangle's area uses its perpendicular height, not a slanted side, and a pyramid on a square base has four triangular faces; neither fact is given. (Anderson & Krathwohl, 2001)
Strategy: Sketch the pyramid: a square base whose side is the triangle's base, and one triangular face on each side of the square. Find each area with the matching formula, then add them all.
Traps
- Misreads the figure: Reads a value, label or tick spacing in a figure, table or graph wrongly.
- Information you don't need: The question gives numbers or facts that play no part in the answer.
- Misunderstands the concept: A wrong belief about a concept: that percents can be added, that area grows like length, that averages can be averaged, that a bigger denominator means a bigger fraction.
The wrong answers, classified
A Misunderstands the concept (Smith, diSessa & Roschelle, 1993; De Bock et al., 1998; Ni & Zhou, 2005)
Counts only three triangular faces, as if the pyramid had a triangular base, so 3 × 60 + 100 = 280.
B Misunderstands the concept (Smith, diSessa & Roschelle, 1993; De Bock et al., 1998; Ni & Zhou, 2005)
Counts three faces and also uses the 13-inch side as each triangle's height: 3 × 65 + 100 = 295.
D Misreads the figure (Lesh, Post & Behr, 1987; Kirsch & Mosenthal, 1990)
Takes the 13-inch slanted side as each triangle's height instead of the 12-inch arrow beside it, so 4 × 65 + 100 = 360.
What was corrected from the DOE handbook, and why
- Explanation: The handbook ends “So the total surface area is 340 square feet.” The triangle’s dimensions are in inches and the question asks for square inches, so the site now reads “340 square inches.”
Worked solution, step by step
Formulas used
- Area of a triangle
- A is the area. b is the base, the side the triangle sits on. h is the height: the straight-up distance from the base to the top corner, at a right angle to the base. You take half because a triangle is half of a rectangle with the same base and height.
- Area of a square
- A is the area and s is the length of one side. All four sides of a square are equal, so the area is side times side.
- Surface area
- A face is one flat side of a solid shape. The surface area is the total area of the outside. Picture unfolding the solid into flat pieces. Then add up the area of every piece.
Sort out the question
Raquel’s pyramid has a square base. Each side is a triangle like the one in the figure. The triangle’s base is 10 in. Its two slanted sides are 13 in. Its height, the arrow beside it, is 12 in. You need the total surface area, including the square base, in square inches.
Picture the pyramid
Surface area is the total area of all the flat sides, called faces. Each triangle stands on one edge of the square. So each edge of the square is 10 inches, the same as the triangle’s base. A square has 4 edges, so the pyramid has 4 triangles.
Here that is 4 triangles plus 1 square. Watch out: counting only 3 triangles gives 280, choice A.
Find the area of one triangle
Each triangle is 60 square inches. Watch out: the height is 12 in., the straight-up arrow. It is not 13 in., the slanted side. Using 13 gives 65 for each triangle and 360 in all, choice D.
Find the area of the base
The base is a square with sides of 10 inches, the same as each triangle’s base.
The square base is 100 square inches.
Add all five faces
The four triangles and the square together cover 340 square inches.
So the answer is C, 340 square inches.
Check your answer
Each triangle is half of a 10 by 12 rectangle, which has an area of 120. So two triangles make 120, and four make 240. Add the base: . The units fit too: inches times inches gives square inches.
More questions like this
The original DOE question
Question 5 of 6
2026 Practice Test D Math, question 19Question
A store manager purchases a piece of furniture for $456.00. To determine the selling price, the manager increases the purchase cost by 125%. A customer buys the furniture and pays an additional 8% sales tax. How much does the customer pay for the furniture?
- A$615.60
- B$627.48
- C$1,108.08
- D$1,846.80
Show the answer
Correct answer: C
Given a purchase price of $456.00, the 125% increase in price is calculated as:
The selling price equals the purchase price plus the increase, or:
The sales tax on the selling price is:
The customer pays the selling price plus the sales tax:
Question analysis
A store manager buys a piece of furniture for $456.00 and raises the price by 125% to set the selling price, and the customer also pays 8% sales tax. Students find the total the customer pays. It tests percent increase and sales tax in sequence, and reading an increase of more than 100% correctly is the main challenge.
- NYS standards
- Grade level
- Grade 7 content, by NYS standard
- Compared with grade 7
- Above grade 7 Grade 7 students find markups and sales tax, usually with increases under 100%. An increase of more than 100% is unusual and easy to misread, and two percent changes must be applied in order, which goes beyond routine 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
- Turning words into math moderate
- Many steps moderate
- Error-prone arithmetic minor
- Solution
- 4 steps
- Reading level
- Question and choices: about grade 7, 41 words.
- Students, last 30 days
- Not enough answers yet to show (it takes 10).
Why it is hard, traps and wrong answers (shows the answer)
Why it is hard
A percent above 100 is unusual in grade 7 work, and it is the center of the question: the markup more than doubles the price. Students who treat “by 125%” as “125% of” still find a listed answer after adding tax, and so do students who add $125. A rough check helps: the selling price must be more than twice $456, about $1,000, and the tax adds less than a tenth of that.
Turning words into math moderate Understanding the question
“Increases the purchase cost by 125%” adds 125% of $456 to the $456 itself, a multiplier of 2.25; reading it as 125% of the cost leaves the original price out. (Hegarty, Mayer & Monk, 1995; Koedinger & Nathan, 2004)
Many steps moderate Working it out
Four steps in a row, the increase, the selling price, the tax and the total, each depend on the one before, and two of them are easy to merge or skip. (Daniel & Embretson, 2010; Enright, Morley & Sheehan, 2002)
Error-prone arithmetic minor Working it out
Taking 8% of $1,026 means multiplying by 0.08, and a decimal point one place off, 0.8, makes the tax ten times too large. (Brown & Burton, 1978; Junker & Sijtsma, 2001)
Strategy: Turn each percent change into a multiplier, remembering that an increase by a percent is added to the original amount, apply the markup and then the tax, and estimate to check the size.
Traps
- Stops one step early: A choice is a number from partway through the solution.
- 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.
- An arithmetic slip: The right method with a plausible arithmetic error: a digit, a place value or a times-table fact.
The wrong answers, classified
A Stops one step early (King et al., 2004; Gierl et al., 2017)
Finds the increase, 125% of $456 = $570, and uses it as the selling price without adding back the $456 cost, then adds 8% tax.
B Misunderstands the concept (Smith, diSessa & Roschelle, 1993; De Bock et al., 1998; Ni & Zhou, 2005)
Reads the 125% increase as $125, a fixed amount, so the selling price is $581, and then adds 8% tax correctly to reach $627.48.
D An arithmetic slip (Junker & Sijtsma, 2001)
Finds the $1,026 selling price correctly but writes 8% as 0.8, adding $820.80 in tax instead of $82.08.
Worked solution, step by step
Formulas used
- Percent of a number
- n is the starting amount, and p is the percent. Percent means out of 100, so 125% is 125/100 = 1.25 and 8% is 8/100 = 0.08. Multiply n by that decimal to find the part.
- Price after an increase
- The old price is what you start with. The increase is the amount added on. To increase by a percent, find that percent of the old price, then add it to the old price. Sales tax is added the same way.
Sort out the question
The manager pays $456.00 for the furniture. The selling price is that cost increased by 125%. The customer then pays 8% sales tax on top. Sales tax is an extra charge, a percent of the price. You need the total the customer pays.
Find the increase
Find 125% of $456. As a decimal, 125% is 1.25, which is 1 and a quarter. A quarter of 456 is 114:
The increase is $570.
Find the selling price
Increases by means the increase is added to the cost:
The selling price is $1,026.
Watch out: $570 is only the increase. Using it as the price gives $615.60, choice A. And 125% is a percent, not $125. Adding $125 leads to $627.48, choice B.
Find the sales tax
As a decimal, 8% is 0.08. Find 8% of the selling price:
The tax is $82.08.
Watch out: 8% is 0.08, not 0.8. Using 0.8 makes the tax ten times too big and gives $1,846.80, choice D.
Add the tax to the price
The customer pays the selling price plus the tax:
So the answer is C, $1,108.08.
Check your answer
Estimate. The price more than doubles: $456 plus $570 is about $1,000. Tax of 8% adds about $80. So the total should be a bit over $1,080, and only $1,108.08 is close. Or multiply in one go: 456 × 2.25 × 1.08 = 1,108.08.
More questions like this
The original DOE question
Question 6 of 6
2024 Test A Math, question 6Question
Mr. Jones has 550 goats, which is 10% more than Mr. King has. How many more goats does Mr. Jones have than Mr. King?
- A50
- B55
- C495
- D500
Show the answer
Correct answer: A
First, set up a proportion to determine x, the number of goats Mr. King has.
Then solve the proportion for x.
Finally, determine the difference between the number of goats Mr. Jones has, 550, and the number of goats Mr. King has, 500.
Mr. Jones has 50 more goats than Mr. King.
Question analysis
A percent word problem: Mr. Jones has 550 goats, which is 10% more than Mr. King has, and students find how many more goats Mr. Jones has. It asks students to work with a percent increase when only the larger amount is known. The tricky part is deciding which amount the 10% is taken of.
- Grade level
- Grade 7 content, by NYS standard
- Compared with grade 7
- Above grade 7 Grade 7 students usually find a percent increase from a known original amount. This runs the task backward: the increased amount is given, and the original must be recovered before the difference can be found, a step many do not expect.
- Estimated difficulty
- Hard: combines ideas, needs a plan, and has more than one tempting wrong answer.
- Thinking it demands
- Depth of knowledge 2, skills and concepts · mainly apply
- What makes it hard
- Turning words into math major
- A very close wrong answer moderate
- Solution
- 2 steps
- Reading level
- Question and choices: about grade 1, 22 words.
- Students, last 30 days
- Not enough answers yet to show (it takes 10).
Why it is hard, traps and wrong answers (shows the answer)
Why it is hard
The arithmetic is one division and one subtraction, so the question is really about the base of a percent. The sentence gives the bigger number and calls it 10% more, and the reflex is to take 10% of the number on the page. That shortcut lands on a listed choice five goats from the answer. Students who find King's herd first, 550 ÷ 1.1, still have to remember that the question wants the difference, not the herd.
Turning words into math major Understanding the question
The clause "which is 10% more than" makes King's unknown herd the base of the 10%, so 550 is 110% of his number rather than the amount the 10% is taken of. (Hegarty, Mayer & Monk, 1995; Koedinger & Nathan, 2004)
A very close wrong answer moderate Choosing the answer
The choices 50 and 55 are only 5 goats apart, and both are 10% of a herd; only taking the percent of King's 500 rather than of 550 separates them. (Embretson & Wetzel, 1987; Gorin & Embretson, 2006; Ascalon et al., 2007)
Strategy: Mr. Jones's 550 is 110% of Mr. King's number, so divide 550 by 1.10 to find Mr. King's goats, then subtract that from 550.
Traps
- Percent of the wrong amount: Finding the whole from a part, or a percent change measured from the wrong starting amount.
- Stops one step early: A choice is a number from partway through the solution.
The wrong answers, classified
B Percent of the wrong amount (Parker & Leinhardt, 1995)
Takes 10% of 550, measuring the increase from Jones's herd instead of from King's smaller herd, which is the amount the 10% is based on.
C Percent of the wrong amount (Parker & Leinhardt, 1995)
Takes 10% off 550 to get King's herd, 550 − 55 = 495, using the wrong base, then gives that herd instead of the difference.
D Stops one step early (King et al., 2004; Gierl et al., 2017)
Finds King's herd correctly, 550 ÷ 1.1 = 500, then stops there instead of subtracting it from 550 to get how many more.
Worked solution, step by step
Formulas used
- Percent increase
- The original is the amount you start from, the one the percent is taken of. p is the percent of increase. The new amount is all of the original, which is 100%, plus p% more. For 10% more, you multiply by 1.10.
Sort out the question
Mr. Jones has 550 goats. That is “10% more than Mr. King has”. You need how many more goats Mr. Jones has than Mr. King. That is the difference between the two herds, not the size of a herd.
Decide what the 10% is of
The words “10% more than Mr. King” mean the 10% is a part of Mr. King’s herd. So Mr. King’s herd is the original. Mr. Jones has all of Mr. King’s goats, 100%, plus 10% more. That is 110% of Mr. King’s herd. Watch out: do not take 10% of 550. That gives 55, choice B. It uses the wrong herd. Taking those 55 away from 550 gives 495, choice C, which is also wrong.
Find Mr. King’s herd
Call Mr. King’s number of goats K. Use the percent increase formula with p = 10. The new amount is 550.
Mr. King has 500 goats. Watch out: 500 is Mr. King’s herd, choice D. It is not the difference.
Find the difference
Mr. Jones has 50 more goats than Mr. King. So the answer is A, 50.
Check your answer
Check the 10%. 10% of 500 is , and , Mr. Jones’s herd. So 550 really is 10% more than 500. If King had 495, then 10% more would be about 545, not 550.
More questions like this
The original DOE question
