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 25Passage Looking for the Smallest Spark of Everything
Looking for the Smallest Spark of Everything
Located underground near Geneva, Switzerland, the Large Hadron Collider (LHC) helps scientists study and understand how the smallest particles of matter interact with one another. The LHC propels atomic particle beams along a 17-mile-long ring.
There are the things the world is made of,
things we can see and feel, and then
there are the things even smaller, things that seem
to exist only when we are looking right at them.
So beneath the level of molecules are atoms,
and beneath the level of atoms, we find
protons, electrons, neutrons; and beneath that—
what, exactly? Because we are talking about
everything here: your fingernail,
the candy at the back of your mouth,
the coffee your teacher drank this morning,
your little sister, and the stuffed dog
she used to carry around with her everywhere.
And everywhere.
Everything and everywhere
are made up of the same stuff, whatever
it is. How do we find it? We can listen for it
in the wavelengths from deep space,
talking back to us from unimaginable
distances. Or we can build long,
deep circular tunnels beneath the surface
of this Earth and race particles
(like racing cars, only very tiny cars
flashing along at close to the speed of light)
until everything we think we know
bangs against everything else we know.
And there, in the explosion, in the darkness,
briefly incandescent, they appear:
the quarks, the leptons, and the bosons;
the baryons and the mesons. Their names
sound like dinosaurs or maybe bands
playing terrible music in someone’s garage.
The one thing we know for sure
is that they spin. This is how gravity
enters our world, how our world is held
both together and apart, what keeps
together the pencil in your hand right now
as well as separate from, say,
Jupiter. They spin, and it is only down there
in the darkness—in the vast garage
where physicists jot down
what they can, whatever seems most real—
that they let us perceive their wild dancing,
combusting to the music they make.
Question
Read lines 27–28 from the poem.
And there, in the explosion, in the darkness,
briefly incandescent, they appear:
The imagery in the lines reveals that the speaker
- Aenvies the physicists who research colliding particles.
- Bhas personally observed colliding particles.
- Cadmires the powerful reactions that occur when particles collide.
- Dhas a simplistic understanding of how particles collide.
Show the answer
Correct answer: C
The question asks what the imagery in lines 27–28 reveals about the speaker.
A. Incorrect. The physicists mentioned in the fifth stanza (lines 33–44) are described as mere observers: they “jot down / what they can” (lines 41–42). In lines 27–28, the speaker is focused on the reaction between the colliding particles, not on the physicists who study them.
B. Incorrect. The speaker describes the particle collision in detail, but the text does not imply that the speaker has personally witnessed a collision. The speaker implies that his or her understanding of the collision is based on the experiences of the physicists observing the phenomenon (“They spin, and it is only down there / in the darkness—in the vast garage / where physicists jot down / what they can, whatever seems most real— / that they let us perceive their wild dancing” [lines 39–43]).
C. CORRECT. The word “explosion” and the phrase “briefly incandescent” create a picture of rapid changes and short bursts of bright light, revealing how powerful the new particles are. The language the speaker uses is positive, revealing that the speaker admires the power of the reaction and stands in awe of the new particles.
D. Incorrect. The poem reveals the speaker’s deep knowledge about subatomic particles. For example, the speaker is able to name the new particles discovered—“the quarks, the leptons, and the bosons; / the baryons and the mesons” (lines 29–30)—and is able to use imagery to create a powerful picture that reveals the complexity of a scientific process that humans have never been able to see.
Question analysis
This imagery question asks what lines 27–28 of “Looking for the Smallest Spark of Everything” reveal about the poem’s speaker, as particles appear “briefly incandescent” in an explosion inside a particle collider. Students must infer what a vivid image says about the person describing it. The word “incandescent” may be unfamiliar, and the choices are about very different things.
- Grade level
- Grade 8 reading and task
- Compared with grade 7
- Above grade 7 Grade 7 students infer a speaker’s attitude from imagery, but these two lines turn on the uncommon word “incandescent,” state nothing about the speaker outright, and the choices range over the speaker’s knowledge, experience and feelings, which is harder than typical grade 7 work.
- Estimated difficulty
- Hard: combines ideas, needs a plan, and has more than one tempting wrong answer.
- Thinking it demands
- Depth of knowledge 2, skills and concepts · mainly analyze
- What makes it hard
- Reading between the lines major
- Hard words moderate
- Figurative or literary language minor
- Evidence
- Answered from one paragraph or stanza
- Reading level
- Passage: 346 words (a poem; reading level not measured); question and choices: about grade 9, 55 words.
- Students, last 30 days
- Not enough answers yet to show (it takes 10).
Why it is hard, traps and wrong answers (shows the answer)
Why it is hard
Nothing in the two lines names a feeling, so students must judge the speaker’s attitude from the image alone, and its key word is uncommon. The vividness is itself a trap: a scene described this sharply can seem to be one the speaker watched, though the poem says the particles are perceived only through the physicists’ work. The choices range over envy, experience, admiration and understanding, so each must be tested against the lines rather than against an overall impression.
Reading between the lines major Working it out
The lines describe particles, not the speaker, and contain no word of feeling; admiration has to be inferred from the drama of “the explosion” and the glow of “briefly incandescent.” (Graesser, Singer & Trabasso, 1994; Kintsch, 1998)
Hard words moderate Understanding the question
“Incandescent,” glowing with heat and light, is the word that makes the image dazzling, and a student who does not know it sees only an explosion in the dark. (Perfetti, 2007; Freedle & Kostin, 1993)
Figurative or literary language minor Understanding the question
The two lines are pure imagery, a burst of light in darkness as the particles “appear,” and the question asks what that picture reveals about the person painting it. (Graesser, Singer & Trabasso, 1994; Kintsch, 1998)
Strategy: Picture the scene in lines 27–28, including what “incandescent” means, decide what the description suggests about the speaker, and test each choice against these two lines.
Traps
- Taking figurative language literally: A choice reads a figure of speech or image at face value.
- Reads too much in: A reasonable-sounding conclusion that goes further than the text allows.
The wrong answers, classified
A Reads too much in (Graesser, Singer & Trabasso, 1994)
Reasons that someone so drawn to the scene must envy the physicists who study it, though the physicists appear only in lines 39–44 and nothing in the poem hints at envy.
B Taking figurative language literally (Graesser, Singer & Trabasso, 1994)
Takes the vivid scene of particles that “appear” in a glow as something the speaker witnessed, though lines 39–43 place that sight “down there,” where physicists record what they can.
D Reads too much in (Graesser, Singer & Trabasso, 1994)
Treats the poem’s playful comparisons, racing cars and garage bands, as a sign of shallow knowledge, though the next lines have the speaker naming quarks, leptons, bosons, baryons and mesons.
Working it out, step by step
Figure out what the question asks
This asks what the imagery in lines 27–28 shows about the speaker. Imagery is language that helps you see, hear or feel a scene. The lines describe particles, not the speaker. So you must infer, or figure out from clues, how the speaker feels.
Read lines 27–28
The lines say “And there, in the explosion, in the darkness, / briefly incandescent, they appear:” Briefly means for a short time. Incandescent means glowing with heat and light. So picture a burst of bright light flashing in the dark. The particles have just crashed into each other, or collided. In that flash, the tiny particles appear.
Decide how the speaker feels
The words are bold and bright: “explosion,” “incandescent,” “appear.” The speaker makes the moment sound dramatic and amazing. People describe something this way when they are in awe of it. So the speaker admires, or looks up to, the power of the crash.
Check each choice
- A does not fit. Physicists come up only later, in line 41. Nothing shows envy, or wanting what they have.
- B does not fit. Nothing says the speaker was there. Lines 39–42 place the sight “down there,” where “physicists jot down / what they can.”
- C fits. The glowing burst in the dark shows the speaker’s wonder.
- D does not fit. Right after, the speaker names quarks, leptons, bosons, baryons and mesons. That is not a simple understanding.
Watch out: B is tempting because the scene is so vivid. But a writer can picture something without seeing it in person.
Choose the answer
The bright, explosive picture shows a speaker who is amazed by the crash. So the answer is C, “admires the powerful reactions that occur when particles collide.”
Why this answer and not the closest wrong one
B is the closest wrong choice, because the scene feels like an eyewitness report. But the lines never say the speaker was in the tunnel. What they do show is a feeling. Words like “explosion” and “briefly incandescent” make the moment thrilling. That is admiration, so C fits.
More questions like this
The original DOE question
The passage “Looking for the Smallest Spark of Everything” as printed (pages 32–33)
Question 2 of 6
2026 Practice Test C English, question 11Passage Excerpt from “Niagara Falls”
Excerpt from “Niagara Falls”
by Rupert Brooke
The real secret of the beauty and terror of the Falls is not their height or width, but the feeling of colossal power and of unintelligible disaster caused by the plunge of that vast body of water. If that were taken away, there would be little visible change, but the heart would be gone.
The American Falls do not inspire this feeling in the same way as the Canadian. It is because they are less in volume, and because the water does not fall so much into one place. By comparison their beauty is almost delicate and fragile. They are extraordinarily level, one long curtain of lacework and woven foam. Seen from opposite, when the sun is on them, they are blindingly white, and the clouds of spray show dark against them. With both Falls the colour of the water is the ever-altering wonder. Greens and blues, purples and whites, melt into one another, fade, and come again, and change with the changing sun. Sometimes they are as richly diaphanous as a precious stone, and glow from within with a deep, inexplicable light. Sometimes the white intricacies of dropping foam become opaque and creamy. And always there are the rainbows. If you come suddenly upon the Falls from above, a great double rainbow, very vivid, spanning the extent of spray from top to bottom, is the first thing you see. If you wander along the cliff opposite, a bow springs into being in the American Falls, accompanies you courteously on your walk, dwindles and dies as the mist ends, and awakens again as you reach the Canadian tumult. And the bold traveller who attempts the trip under the American Falls sees, when he dare open his eyes to anything, tiny baby rainbows, some four or five yards in span, leaping from rock to rock among the foam, and gambolling beside him, barely out of hand’s reach, as he goes. One I saw in that place was a complete circle, such as I have never seen before, and so near that I could put my foot on it. It is a terrifying journey, beneath and behind the Falls. The senses are battered and bewildered by the thunder of the water and the assault of wind and spray; or rather, the sound is not of falling water, but merely of falling; a noise of unspecified ruin. So, if you are close behind the endless clamour, the sight cannot recognise liquid in the masses that hurl past. You are dimly and pitifully aware that sheets of light and darkness are falling in great curves in front of you. Dull omnipresent foam washes the face. Farther away, in the roar and hissing, clouds of spray seem literally to slide down some invisible plane of air.
Beyond the foot of the Falls the river is like a slipping floor of marble, green with veins of dirty white, made by the scum that was foam. It slides very quietly and slowly down for a mile or two, sullenly exhausted. Then it turns to a dull sage green, and hurries more swiftly, smooth and ominous. As the walls of the ravine close in, trouble stirs, and the waters boil and eddy. These are the lower rapids, a sight more terrifying than the Falls, because less intelligible. Close in its bands of rock the river surges tumultuously forward, writhing and leaping as if inspired by a demon. It is pressed by the straits into a visibly convex form. Great planes of water slide past. Sometimes it is thrown up into a pinnacle of foam higher than a house, or leaps with incredible speed from the crest of one vast wave to another, along the shining curve between, like the spring of a wild beast. Its motion continually suggests muscular action. The power manifest in these rapids moves one with a different sense of awe and terror from that of the Falls. Here the inhuman life and strength are spontaneous, active, almost resolute. . . . A place of fear.
One is drawn back, strangely, to a contemplation of the Falls, at every hour, and especially by night, when the cloud of spray becomes an immense visible ghost, straining and wavering high above the river, white and pathetic and translucent. The Victorian lies very close below the surface in every man. There one can sit and let great cloudy thoughts of destiny and the passage of empires drift through the mind; for such dreams are at home by Niagara. I could not get out of my mind the thought of a friend, who said that the rainbows over the Falls were like the arts and beauty and goodness, with regard to the stream of life—caused by it, thrown upon its spray, but unable to stay or direct or affect it, and ceasing when it ceased. In all comparisons that rise in the heart, the river, with its multitudinous waves and its single current, likens itself to a life, whether of an individual or of a community. A man’s life is of many flashing moments, and yet one stream; a nation’s flows through all its citizens, and yet is more than they. In such places, one is aware, with an almost insupportable and yet comforting certitude, that both men and nations are hurried onwards to their ruin or ending as inevitably as this dark flood. Some go down to it unreluctant, and meet it, like the river, not without nobility. And as incessant, as inevitable, and as unavailing as the spray that hangs over the Falls, is the white cloud of human crying. . . . With some such thoughts does the platitudinous heart win from the confusion and thunder of a Niagara peace that the quietest plains or most stable hills can never give.
From LETTERS FROM AMERICA by Rupert Brooke—Public Domain
diaphanous: sheer, translucent
platitudinous: clichéd, common
Question
In paragraph 4, the idea that human life and history ultimately end in the same way is illustrated mainly through
- Athe discussion of how the rainbows visible in the Falls are like the art and beauty created by humankind.
- Bthe comparison between the movement of water in the Falls and the human experience.
- Cthe inclusion of details that show that every observer’s experience with the Falls is different.
- Dthe acknowledgment that contemplating the Falls at night sparks an awareness of humankind’s destiny.
Show the answer
Correct answer: B
The question asks how paragraph 4 of the excerpt mainly illustrates the idea that human life and history ultimately end in the same way.
A. Incorrect. In paragraph 4, the author compares the rainbows visible in the Falls to “the arts and beauty,” which share the rainbows’ dependence on “the stream of life”—that is, they are “caused by it, thrown upon its spray, but unable to stay or direct or affect it, and ceasing when it ceased.” This comparison does not illustrate the idea that human life and history ultimately end in the same way but rather that art and beauty, like human beings, are unable to “stay or direct or affect” their ultimate fate.
B. CORRECT. The author concludes in paragraph 4 that the movement of the Falls can be compared to people and history when he writes, “both men and nations are hurried onwards to their ruin or ending as inevitably as this dark flood.” This comparison illustrates the idea that human life and history ultimately end in the same way.
C. Incorrect. Although in paragraph 4 the author states that “One is drawn back, strangely, to a contemplation of the Falls” and provides an account of “a friend, who said that the rainbows over the Falls were like the arts and beauty and goodness, with regard to the stream of life,” the author does not provide details to show that every observer’s experience with the Falls is different. Rather, the author explains that “the Victorian lies very close below the surface in every man” (paragraph 4).
D. Incorrect. While the setting at night does provide a place of contemplation, the author notes the “dark flood” as the overall illustration of the human experience.
Question analysis
In this question on the closing paragraph of Rupert Brooke’s “Niagara Falls,” students identify the main way the author illustrates the idea that human life and history ultimately end in the same way. It is a lightly reworded version of a 2018 Test B question. The paragraph is long and reflective, mixing several images with abstract thoughts, so students must decide which of them actually illustrates this particular idea.
- Grade level
- Grade 8 reading and task
- Compared with grade 7
- Above grade 7 Most grade 7 work asks how an idea is shown in plain modern prose. This paragraph is a century-old reflection in long sentences with words like “certitude” and “unavailing,” and several of its images could each seem to carry the idea.
- 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
- The right answer is reworded moderate
- Hard words minor
- Evidence
- Answered from one paragraph or stanza
- Reading level
- Passage: about grade 9, 987 words; question and choices: about grade 11, 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
Paragraph 4 offers three pictures, the spray as a night ghost, the friend’s rainbows and the river as a life, and only one of them shows people and nations meeting an end. The 2026 stem’s “ultimately end” makes the rainbows’ “ceasing when it ceased” more tempting, and the night-time “thoughts of destiny” sound like the idea itself. Students who ask what the paragraph uses to show the idea, rather than where it mentions endings or destiny, land on the dark flood.
Complex sentences major Understanding the question
The idea sits inside a hedged sentence, “one is aware, with an almost insupportable and yet comforting certitude, that both men and nations are hurried onwards to their ruin or ending,” and the comparison comes last: “as inevitably as this dark flood.” (Abedi & Lord, 2001; Freedle & Kostin, 1993; Messick, 1989)
The right answer is reworded moderate Choosing the answer
The key sums up the paragraph’s river-and-life likeness in its own words, “movement of water” and “human experience,” while the other choices borrow the paragraph’s vocabulary: “rainbows,” “art and beauty,” “night” and “destiny.” (Freedle & Kostin, 1993; Kirsch & Mosenthal, 1990)
Hard words minor Understanding the question
“Multitudinous,” “certitude,” “insupportable” and “unavailing” all sit in the lines that carry the idea, and the footnoted “platitudinous” closes the paragraph, so the comparison has to be read through them. (Perfetti, 2007; Freedle & Kostin, 1993)
Strategy: Find the sentence in paragraph 4 that actually states the idea about life and history ending, then ask how that very sentence makes its point and match a choice to it.
Traps
- Supports only part of the claim: In a question about evidence: a line that backs one half of the claim but not the other, or a related point rather than the claim itself.
- Outside knowledge: A choice is plausible in the real world but not supported by this text.
The wrong answers, classified
A Supports only part of the claim (King et al., 2004; Thissen, Steinberg & Fitzpatrick, 1989)
Settles on the friend’s rainbows because they end “ceasing when it ceased,” which echoes the stem’s ending, but the likeness is about art and beauty, not the lives of men and nations.
C Outside knowledge (King et al., 2004; Recht & Leslie, 1988)
Relies on the common idea that every visitor sees the Falls in a personal way, but the paragraph speaks of “one” and “every man” in general and records no differences.
D Supports only part of the claim (King et al., 2004; Thissen, Steinberg & Fitzpatrick, 1989)
Joins the night view to “thoughts of destiny,” both real in paragraph 4, but they tell when and where the reflecting happens, not which picture shows lives and nations sharing an end.
Working it out, step by step
Figure out what the question asks
This asks how an idea is shown in paragraph 4. The idea is that people’s lives and whole nations end in the same way: they all come to an end. You need the picture the author mainly uses to show that idea. Paragraph 4 has several pictures, so find the one tied to this idea.
Find the sentence with the idea
Paragraph 4 says “both men and nations are hurried onwards to their ruin or ending as inevitably as this dark flood.” Men means people. Nations means countries and their history. Inevitably means in a way that can’t be stopped. The “dark flood” is the river’s dark water rushing over the Falls.
See how the comparison works
Just before, the author says “the river, with its multitudinous waves and its single current, likens itself to a life.” Multitudinous means very many. A current is water flowing one way. Likens itself to means seems like. A life has many moments but moves one way, like the river. And just as the water must rush on, people and nations rush toward their end. So the idea is shown by comparing moving water with human life.
Check each choice
- A does not fit. A friend compares the rainbows to “the arts and beauty and goodness.” That picture is about art, not about lives and nations ending.
- B fits. The river’s movement stands for human lives and history.
- C does not fit. The paragraph never says that each visitor sees the Falls differently.
- D does not fit. The night view and the “thoughts of destiny” tell when and where the author thinks. They do not show how lives end.
Watch out: D is tempting because destiny, or what happens in the end, sounds like the idea itself. But the question asks what illustrates the idea, and that is the river.
Choose the answer
The author pictures people and nations rushing to their end like the river’s water. So the answer is B, “the comparison between the movement of water in the Falls and the human experience.”
Why this answer and not the closest wrong one
D is the closest wrong choice. Paragraph 4 really does say the Falls at night stir “great cloudy thoughts of destiny.” But that only tells you the author was thinking about such things. The picture that shows lives and nations ending is the river. They are “hurried onwards to their ruin or ending as inevitably as this dark flood.”
More questions like this
The original DOE question
The passage “Excerpt from “Niagara Falls”” as printed (pages 134–135)
Question 3 of 6
2026 Practice Test B English, question 47Passage The End of an Era
The End of an Era
(1) In 2004, the National Aeronautics and Space Administration (NASA) landed a rover, or robotic vehicle, named Opportunity on the surface of Mars. (2) The rover’s mission was to search for evidence of water and life on the planet. (3) The rover was designed to gather data on Mars for about 90 days, but Opportunity’s assignment did not come to an end until nearly 15 years later in 2019.
(4) During the rover’s mission, a high-resolution camera on the rover’s robotic arm took magnified photographs of the surface of Mars. (5) The photographs revealed small round rocks scattered across the surface of the planet. (6) The scientists nicknamed these rocks “blueberries” based on the rocks’ resemblance to the fruit. (7) These rocks were important because their spherical shape suggested that liquid water may have flowed over them for a substantial amount of time.
(8) Opportunity continued to provide valuable data about craters and other surface features. (9) Throughout the mission, the rover traveled a total of 28.06 miles across Mars’ surface. (10) When Opportunity had traveled nearly the length of a marathon, scientists celebrated the accomplishment by naming the valley that the rover was in Marathon Valley. (11) However, in 2018, a dust storm spread all over the planet, putting the rover’s progress on hold.
(12) Prior to this planet-wide dust storm, minor dust storms had periodically deposited a layer of dust onto the solar panels of the rover. (13) These prevented it from charging its batteries. (14) Scientists then had to rely on the passing winds and dust devils to clean off the solar panels. (15) After the massive 2018 dust storm subsided, scientists expected to be able to reestablish communication with Opportunity. (16) They made repeated attempts but to no avail. (17) In 2019, NASA finally declared Opportunity’s mission complete.
(18) Opportunity was an important asset in scientists’ study of Mars; it returned valuable data about our neighbor planet and survived powerful dust storms. (19) NASA described the mission of Opportunity as “one of the most successful and enduring feats of interplanetary exploration.” (20) Even though this rover’s journey ended, other rovers still roam the surface of Mars.
Question
What is the best way to combine sentences 12 and 13?
- APreventing the rover from charging its batteries, minor dust storms had periodically deposited a layer of dust onto the solar panels of the rover prior to this planet-wide dust storm.
- BPeriodically depositing a layer of dust onto the solar panels of the rover prior to this planet-wide dust storm, minor dust storms had prevented it from charging its batteries.
- CMinor dust storms, prior to this planet-wide dust storm, prevented the rover from charging its batteries because they had periodically deposited a layer of dust onto the solar panels of the rover.
- DPrior to this planet-wide dust storm, minor dust storms had periodically deposited a layer of dust onto the solar panels of the rover, preventing it from charging its batteries.
Show the answer
Correct answer: D
The question asks for the best way to combine sentences 12 and 13.
A. Incorrect. The phrase “this planet-wide dust storm” in the original sentence 12 makes a direct reference to sentence 11 and therefore acts as a transition that should be kept at the beginning. In this sentence, the transition phrase is placed at the end of the sentence, making the phrase confusing. In addition, the sentence is unnecessarily repetitive and wordy.
B. Incorrect. This combination unnecessarily turns sentence 12 into an overly long participial phrase, making the connection between “it” and its antecedent, “the rover,” unclear and distracting from the subject of the sentence, “minor dust storms.”
C. Incorrect. Not only does this combination move the reference to “this planet-wide dust storm” farther from sentence 11, but it is also unnecessarily wordy, adding “because” and repeating “the rover.”
D. CORRECT. This sentence efficiently and accurately adds sentence 13 to sentence 12 as a participial phrase by changing “These prevented” to “preventing,” while also retaining the meanings of the original sentences 12 and 13.
Question analysis
This sentence-combining question asks for the best way to join two sentences from the rover passage: one saying minor dust storms had periodically coated the rover's solar panels, the other saying this kept it from charging its batteries. The four versions keep the same facts in different orders, so students must judge which is clearest and most concise in context.
- Grade level
- Grade 8 reading and task
- Compared with grade 7
- Above grade 7 Combining two sentences is grade 7 work, usually with one version clearly better. These four are long, keep the same facts and differ in order and wording, so students must weigh clarity and concision across nearly identical sentences, more than typical.
- 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 evaluate
- What makes it hard
- How sentences fit together moderate
- Every choice must be checked moderate
- Complex sentences minor
- Evidence
- Answered from one sentence or line
- Reading level
- Passage: about grade 11, 337 words; question and choices: about grade 13, 129 words.
- Corrected from the DOE handbook
- Two grammar terms in the explanation 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
None of the versions is plainly ungrammatical, so the ear gives little help, and the version with “because” looks best to students who value a clearly stated cause. Its cost is wordiness and a weaker link: the result comes first and the reference back to sentence 11 is buried mid-sentence. The question rewards keeping the original order, cause then effect, and folding sentence 13 in as a short closing phrase.
How sentences fit together moderate Working it out
“Prior to this planet-wide dust storm” points back to sentence 11, so the best version keeps it first; three versions move it later, which loosens the link between the two sentences. (Halliday & Hasan, 1976)
Every choice must be checked moderate Choosing the answer
All four versions keep every fact of sentences 12 and 13 and run 29 to 32 words, so none can be ruled out by content; order, pronouns and repetition decide. (Embretson & Wetzel, 1987)
Complex sentences minor Understanding the question
Each version is one long sentence built around a participial phrase or a “because” clause, and at that length a stranded “it” or a doubled “the rover” is easy to miss. (Abedi & Lord, 2001; Freedle & Kostin, 1993; Messick, 1989)
Strategy: Read sentence 11 first, then compare the versions on how smoothly each connects to it, how many words it uses, and whether every pronoun has a clear antecedent.
Traps
- Wordy, vague or informal: A revision is grammatical but wordy, imprecise or too casual for the passage.
- Unclear pronoun: A pronoun whose reference is vague or ambiguous, or one in the wrong case.
The wrong answers, classified
A Wordy, vague or informal (Connors & Lunsford, 1988)
Opens with the effect as a participial phrase, which pushes “prior to this planet-wide dust storm,” the link to sentence 11, to the end and names “the rover” twice.
B Unclear pronoun (Connors & Lunsford, 1988)
Packs sentence 12 into a 19-word opening phrase, so “it” follows “this planet-wide dust storm” and no longer points clearly to the rover buried inside the phrase.
C Wordy, vague or informal (Connors & Lunsford, 1988)
Likes the clear cause word “because,” but the result now comes first, “the rover” appears twice, and “prior to this planet-wide dust storm” splits the subject from its verb.
What was corrected from the DOE handbook, and why
- Explanation: The DOE’s explanation of Option B says the combination turns sentence 12 into “an overly long dependent clause,” and its explanation of Option D says Option D adds sentence 13 to sentence 12 “as a dependent clause” by changing “These prevented” to “preventing.” Neither is a clause: “Periodically depositing a layer of dust onto the solar panels of the rover prior to this planet-wide dust storm” (Option B) and “preventing it from charging its batteries” (Option D) have no subject or finite verb of their own. Both are participial phrases, and the site now calls them that. The reasoning and the answer, Option D, are unchanged.
Working it out, step by step
Figure out what the question asks
This question asks for the best way to join sentences 12 and 13 into one sentence. The best version keeps the meaning, uses few words and is clear. It should also connect smoothly to sentence 11, the sentence before.
Read the sentences in order
Sentence 11 tells about the giant 2018 dust storm. Sentence 12 begins “Prior to this planet-wide dust storm.” Prior to means before. That phrase points back to sentence 11, so it works best at the start. Sentence 12 says small storms put dust on the solar panels. Sentence 13 gives the result: “These prevented it from charging its batteries.”
Learn the tool: a participial phrase
A participial phrase is a group of words built on a verb form, often an -ing word. It describes something, but it has no subject and can’t stand alone. Example: The dog ran to the door. It wagged its tail. becomes The dog ran to the door, wagging its tail. Choice D does this. It turns “These prevented” into “preventing.”
Check each choice
- A is wrong. It starts with the result. It moves “prior to this planet-wide dust storm” to the end, far from sentence 11. It also says “the rover” twice.
- B is wrong. Its long opening phrase hides the rover. Then “it” comes after “minor dust storms,” so it is hard to tell what “it” means.
- C is wrong. It adds “because,” puts the result first and says “the rover” twice. It is wordier than D.
- D is right. It keeps the link to sentence 11 first, gives the cause, then adds the result as a short participial phrase.
Watch out: C looks clear because “because” names the cause. But it is longer, and it puts an extra phrase between “Minor dust storms” and its verb.
Choose the answer
So the answer is D: “Prior to this planet-wide dust storm, minor dust storms had periodically deposited a layer of dust onto the solar panels of the rover, preventing it from charging its batteries.”
Why this answer and not the closest wrong one
C is the closest wrong answer, because “because” makes the cause very clear. But C puts the result first and repeats “the rover.” D keeps the original order, cause then result. It also keeps the link to sentence 11 up front, in fewer words.
More questions like this
The original DOE question
The passage “The End of an Era” as printed (page 60)
Question 4 of 6
2026 Practice Test B Math, question 24Question
A chemical decays in such a way that the amount left at the end of each week is 20% less than the amount at the beginning of that same week. What percentage of the original amount is left after two weeks?
- A40%
- B60%
- C64%
- D80%
Show the answer
Correct answer: C
Let x be the original amount of the chemical. It loses 20% after each week, which means 80% of the chemical remains at the end of each week. End of first week:
At the end of the second week, 80% of the amount left at the end of the first week remains.
End of second week: or 64%
Question analysis
A chemical loses 20% of the amount present at the start of each week, and students find what percentage of the original amount is left after two weeks. It tests applying a percent decrease more than once. The question turns on which amount each week's loss is measured against.
- NYS standards
- 7.RP.3 multistep ratio and percent problems
- Grade level
- Grade 7 content, by NYS standard
- Compared with grade 7
- Above grade 7 A typical grade 7 percent task applies one increase or decrease to one amount. This one applies a weekly decrease twice in a row, an early form of exponential decay that 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 2, skills and concepts · mainly apply
- What makes it hard
- A very close wrong answer major
- Turning words into math moderate
- Variables instead of numbers minor
- Solution
- 2 steps
- Reading level
- Question and choices: about grade 8, 40 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
Two equal decreases in a row feel like one decrease of twice the size, and that is the trap: 20% and 20% suggest 40% gone. The stem states the rule, each loss measured from that week’s start, in one quick phrase. Working week by week from 100 shows the second loss is 16, not 20, which separates the answer from the choice four points away, while stopping after one week or reporting the loss costs the point more simply.
A very close wrong answer major Choosing the answer
The choices 60% and 64% sit four percentage points apart, so a rough estimate cannot choose between them; only seeing that the second 20% is taken from 80, not 100, does. (Embretson & Wetzel, 1987; Gorin & Embretson, 2006; Ascalon et al., 2007)
Turning words into math moderate Understanding the question
The phrase “the amount at the beginning of that same week” sets each week’s base, so the second week’s 20% is measured from what was left after the first week. (Hegarty, Mayer & Monk, 1995; Koedinger & Nathan, 2004)
Variables instead of numbers minor Understanding the question
No starting amount is given, so students must pick one, such as 100 grams, or work with a percent of a percent, 0.8 × 0.8. (Koedinger & Nathan, 2004; Enright, Morley & Sheehan, 2002)
Strategy: Use a starting amount of 100 so that percents become units, find what remains after the first week, then apply the same 20% loss to that remainder.
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.
- 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.
The wrong answers, classified
A Answers a different question (King et al., 2004; Hegarty, Mayer & Monk, 1995)
Adds the weekly losses, 20% + 20% = 40%, and gives that figure, which describes the amount lost rather than the percentage still left.
B Percent of the wrong amount (Parker & Leinhardt, 1995)
Subtracts 20% of the original amount twice, 100 − 20 − 20 = 60, though the second week’s 20% comes from the 80% left, not the starting amount.
D Stops one step early (King et al., 2004; Gierl et al., 2017)
Finds that 80% remains after the first week and stops, never taking the second week’s 20% from that remainder.
Worked solution, step by step
Formulas used
- Percent of an amount
- p is the percent, and amount is the whole you take the percent of. Percent means out of 100, so 20% is 20/100. Multiply to find the part. Be sure the amount is the right whole. Here, each week uses the amount at the start of that week.
- Percent left after a loss
- The whole amount is 100%. If 20% goes away, the rest stays. So 80% of each week’s starting amount is left at the end of that week. Keeping 80% is the same as multiplying by 0.8.
Sort out the question
Each week the chemical loses 20% of what it has. The key words are “the amount at the beginning of that same week.” So each week’s 20% comes from that week’s starting amount. No amount is given. You need the percent of the original amount that is left after two weeks.
Pick an easy starting amount
Pretend the chemical starts at 100 grams. With 100, the number of grams left is the same as the percent left. Any starting amount gives the same percent, so choose the easiest one.
Work out the first week
Use the percent formula. The first week starts with 100 grams:
The chemical loses 20 grams, so grams are left. That is 80% after one week.
Watch out: 80% is only the first week. Stopping here gives choice D.
Work out the second week
The second week starts with 80 grams, not 100. So take 20% of 80:
This time the chemical loses only 16 grams, so grams are left.
Watch out: taking away 20 grams again uses the original amount. That gives 60%, choice B. Choice A, 40%, adds the two losses. But the question asks what is left, and only 36% was lost.
Read the answer as a percent
Week Start (grams) Loss (grams) Left (grams) 1 100 20 80 2 80 16 64 Another way: each week keeps 80%, or 0.8, of its start. Two weeks gives , which is 64%.
64 grams out of the original 100 grams is 64%. So the answer is C, 64%.
Check your answer
Think about the size of the second loss. The second week starts with less, so it loses less than 20 grams. That means more than 60% is left. It does lose something, so less than 80% is left. Of the four choices, only 64% is between 60% and 80%.
More questions like this
The original DOE question
Question 5 of 6
2024 Test A Math, question 16Question
A truck rental company charges a one-time fee of $40 plus $1 per mile driven. Dalia rented a truck and used a coupon for 20% off the total rental cost. After the coupon was applied, she spent a total of $60. How many miles did she drive?
- A8
- B20
- C32
- D35
Show the answer
Correct answer: D
Let m equal the miles driven during Dalia’s rental. The total cost, c, can be expressed as an equation.
Dalia spent a total of $60, which included a 20% off coupon. Find the cost before the coupon by dividing the final cost ($60) by the percentage paid (80%):
Use $75 as the total cost to find m.
Dalia drove 35 miles.
Question analysis
A multistep word problem about a truck rental that costs a $40 fee plus $1 per mile, with a 20% off coupon applied to the total. Given that Dalia paid $60 after the coupon, students find how many miles she drove. Undoing the discount correctly before removing the fixed fee is the hard part.
- Grade level
- Grade 7 content, by NYS standard
- Compared with grade 7
- Above grade 7 Grade 7 students solve two-step equations and work with discounts, usually separately. This combines them and makes students undo a 20% discount starting from the price paid, a reversal many grade 7 students have not practised.
- 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
- Combines ideas moderate
- A very close wrong answer moderate
- Solution
- 3 steps
- Reading level
- Question and choices: about grade 5, 43 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
Two ordinary skills, undoing a discount and solving a two-step equation, are stacked, and the first runs in reverse. The natural way to undo 20% off is to add 20% back, which gives $72 instead of $75 and a choice three miles from the answer. Students who check by applying the coupon to the full cost of 40 + 35 = 75 dollars see at once that 80% of it is 60.
Turning words into math moderate Understanding the question
The sentence "After the coupon was applied, she spent a total of $60" makes 60 the price after 20% off, so it is 80% of the full cost, 40 + m. (Hegarty, Mayer & Monk, 1995; Koedinger & Nathan, 2004)
Combines ideas moderate Working it out
A percent discount has to be undone before the fee-plus-mileage equation can be solved: 60 ÷ 0.8 = 75, then 75 − 40 = 35 miles. (Embretson, 1998; Daniel & Embretson, 2010)
A very close wrong answer moderate Choosing the answer
The choices 32 and 35 are three miles apart, too close to tell apart by estimate; only dividing 60 by 0.8, rather than adding 20% of 60, separates them. (Embretson & Wetzel, 1987; Gorin & Embretson, 2006; Ascalon et al., 2007)
Strategy: Since $60 is 80% of the full cost, divide 60 by 0.80 to find the cost before the coupon, then subtract the $40 fee to get the miles.
Traps
- Percent of the wrong amount: Finding the whole from a part, or a percent change measured from the wrong starting amount.
- Misreads the question: Misses or misreads a condition or a word in the question: "at least", "each", "remaining", "not".
The wrong answers, classified
A Wrong operation (Hegarty, Mayer & Monk, 1995; King et al., 2004)
Takes 20% off the $60 again, 60 × 0.8 = 48, instead of undoing the discount, then subtracts the $40 fee to get 8 miles.
B Misreads the question (Hegarty, Mayer & Monk, 1995)
Ignores the coupon and treats the $60 as the full cost, so it subtracts the $40 fee and gets 20 miles.
C Percent of the wrong amount (Parker & Leinhardt, 1995)
Undoes the coupon by adding 20% of $60 to get $72, though the 20% was taken of the larger pre-coupon cost, then subtracts the $40 fee.
Worked solution, step by step
Formulas used
- Rental cost
- c is the full cost in dollars, before any coupon. 40 is the one-time fee, paid once no matter how far you drive. m is the number of miles, and each mile costs 1 dollar.
- Price after a discount
- The full cost is the price before the discount. p is the percent taken off. You pay what is left: 100% minus p%. For 20% off you pay 80%, so you multiply by 0.80.
Sort out the question
The truck costs a $40 fee, plus $1 for each mile. Dalia’s coupon took 20% off the total. After the coupon, she paid $60. You need how many miles she drove. The $60 is the price after the discount, not the full cost.
Write what she paid
20% off means she paid what was left of the full cost.
As a decimal, 80% is 0.80.
Undo the discount
To undo times 0.80, divide by 0.80. Move the decimal point one place in both numbers to make it easier.
The full cost was $75. Watch out: the 20% was taken off the full cost, not off $60. Adding 20% of $60 gives $72 and leads to 32 miles, choice C. Taking 20% off $60 again leads to 8 miles, choice A.
Find the miles
She drove 35 miles. Watch out: do not skip the coupon. Using $60 as the full cost gives 20 miles, choice B. So the answer is D, 35.
Check your answer
Go forward. 35 miles cost $35. Add the $40 fee to get $75. The coupon takes off 20% of $75, which is dollars. Then . That is exactly what she paid.
More questions like this
The original DOE question
Question 6 of 6
2026 Practice Test D Math, question 36Question
Leah has set a goal to read a total of 500 pages of a textbook. The table shows the book page numbers for the reading she did during three days.
DAILY READING LOG
| Day | Pages Read |
|---|---|
| 1 | pages 45–90, inclusive |
| 2 | pages 100–135, inclusive |
| 3 | pages 145–190, inclusive |
What percentage of her 500-page goal did Leah read on these three days? Round your answer to the nearest tenth.
Enter your answer in the space.
Fill-in question: work out the answer and type it as a number.
Show the answer
Correct answer: 25.6%
First, determine the number of pages read each day. Since the pages per assignment are inclusive, subtract the first page from the last page assigned and then add 1 to determine the pages read for each day.
Day 1: pages
Day 2: pages
Day 3: pages
Leah read a total of 128 pages, since .
To determine the percent, express 128 pages out of 500 pages as a fraction.
Question analysis
Leah's daily reading log lists three ranges of textbook pages, each marked inclusive, and her goal is 500 pages. This percent question asks what percentage of the goal she read over the three days, rounded to the nearest tenth and typed in. Counting the pages in each inclusive range correctly is the tricky step before the percent.
- Grade level
- Grade 7 content, by NYS standard
- Compared with grade 7
- Above grade 7 Finding what percent one number is of another is grade 6 and 7 work. This adds three inclusive page ranges to count, which takes more care than subtracting, then a rounding step, all typed with no choices to check against.
- Estimated difficulty
- Hard: combines ideas, needs a plan, and has more than one tempting wrong answer.
- Thinking it demands
- Depth of knowledge 2, skills and concepts · mainly apply
- What makes it hard
- Something you must already know moderate
- Many steps moderate
- An answer in an unexpected form minor
- Solution
- 4 steps
- Reading level
- Question and choices: about grade 3, 66 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
Counting pages in a range is the whole difficulty; the percent at the end is routine once the total is right. Subtracting first from last feels natural, and here it even rewards the student with a round 25%, so nothing looks wrong. Checking the rule on a tiny range, pages 1 to 3, which is 3 pages and not 2, fixes the count, and the instruction to round to the nearest tenth hints that the answer is not a whole number.
Something you must already know moderate Working it out
Every row says inclusive, but nothing says that pages 45 to 90 hold 90 − 45 + 1 = 46 pages; subtracting alone loses one page on each of the three days. (Anderson & Krathwohl, 2001)
Many steps moderate Working it out
Three page counts, a sum, a division by 500 and a change to a percent come in sequence, and a one-page error in each count carries through to the end. (Daniel & Embretson, 2010; Enright, Morley & Sheehan, 2002)
An answer in an unexpected form minor Choosing the answer
The answer is typed with no choices, and the miscounted total, 125 pages, gives a tidy 25% that looks more finished than the right value with its tenth. (Enright, Morley & Sheehan, 2002)
Strategy: Count each day's pages carefully, testing your method on a short range such as pages 1–3, add the three days, divide by 500, and write the result as a percent to the nearest tenth.
Traps
- 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).
- Stops one step early: A choice is a number from partway through the solution.
- Misreads the question: Misses or misreads a condition or a word in the question: "at least", "each", "remaining", "not".
The wrong answers, classified
25 Counting the ends (Brown & Burton, 1978)
Subtracts the first page from the last for each day, 45 + 35 + 45 = 125 pages, forgetting that an inclusive range counts both end pages, so 125 ÷ 500 = 25%.
0.256 Stops one step early (King et al., 2004; Gierl et al., 2017)
Counts the 128 pages and divides by 500 correctly, then enters the decimal 0.256, one step short of multiplying by 100 to make a percent.
26 Misreads the question (Hegarty, Mayer & Monk, 1995)
Finds 25.6% correctly but rounds it to the nearest whole percent, overlooking the instruction to round to the nearest tenth.
Worked solution, step by step
Formulas used
- Counting pages in an inclusive range
- Inclusive means the first and last pages are both read. Subtracting counts the steps from the first page to the last. That misses one page, so add 1. Test it: pages 1 to 3 are 3 pages, and 3 − 1 + 1 = 3.
- Percent of a total
- The part is the amount you have, here the pages read. The whole is the amount you compare with, here the 500-page goal. Dividing gives a decimal. Multiplying by 100 turns it into a percent, a number out of 100.
Sort out the question
Leah’s goal is 500 pages. The log shows three days:
- Day 1: pages 45 to 90
- Day 2: pages 100 to 135
- Day 3: pages 145 to 190
Each range is inclusive. You need the percent of 500 pages she read, rounded to the nearest tenth.
Count the pages each day
Use the rule for an inclusive range: last page minus first page, plus 1.
Watch out: subtracting alone gives 45, 35 and 45 pages. That is 125 pages, which is exactly 25%. A round answer like that can hide the mistake.
Add the three days
Add the pages from all three days to get her total:
Leah read 128 pages in all. This is the part you compare with the goal.
Change to a percent
Divide the pages read by the goal, then multiply by 100:
Leah read 25.6% of her goal. That already ends in tenths, so no rounding is needed.
Watch out: 0.256 is a decimal, not a percent. And 26 rounds to a whole number, not to the nearest tenth.
Enter the answer
The box has no % sign, but the question asks for a percentage, so the number in the box is the percent. Type it with its decimal point. Typing 25.6% also counts on this site. So you would enter 25.6.
Check your answer
Estimate. 10% of 500 pages is 50 pages. 128 pages is a bit more than 2 × 50 = 100, so the answer is between 20% and 30%. Then check exactly: pages. It matches.
More questions like this
The original DOE question
