3 English and 3 math
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Question 1 of 6
2024 Test A English, question 28Passage Champion of the Channel
Champion of the Channel
In 1926 an editor at the London Daily News predicted that Gertrude Ederle, an American swimmer with eighteen world records and three Olympic medals, would fail in her attempt to swim across the English Channel. He claimed that “even the most uncompromising champion of the rights and capacities of women must admit that in contests of physical skill, speed and endurance they must remain forever the weaker sex.” Yet, at only nineteen years old, Ederle not only became the first woman to accomplish this feat, she also broke the men’s record by two hours. Gertrude Ederle’s triumphant swim across the English Channel was a testimony to her determination, innovative spirit, and passion for swimming.
Crossing the English Channel is a daunting task for any swimmer. At its narrowest point, the channel measures twenty-one miles across. Its icy waters hover around sixty degrees Fahrenheit, and its unruly tides and currents toss swimmers about like bobbing corks. Stinging jellyfish, seaweed, and floating debris from shipwrecks and lost cargoes present added hazards.
For decades the channel’s perils have defeated countless swimmers. Ederle, too, failed in her first attempt to cross the channel in 1925. Just six miles short of finishing, she became ill, and her coach had to haul her out of the water. Undeterred, Ederle decided to try again. Ederle knew that if she did not complete the challenge this time, she might never get the opportunity to set this record, because a rival female swimmer was preparing to make her second attempt at the crossing as well.
To prepare for the marathon swim, Ederle found ways to improve her equipment. She and her sister Meg discovered that melted candle wax perfectly sealed goggle edges, effectively waterproofing Ederle’s goggles against hammering waves. The sisters also designed a two-piece silk swimsuit for Ederle. During her first channel-crossing attempt she had worn a standard one-piece swimsuit that, after the lengthy hours of swimming across the channel, had stretched out, filling with water and creating drag, making an already challenging task almost insurmountable. Unlike the cumbersome typical bathing suit, this silk invention weighed little and allowed for easy movement.
On August 6, 1926, Ederle waded into the channel near Cape Gris-Nez, France. At first she shivered in the bone-chilling water even though she had covered her body in eight layers of grease for insulation. Her limbs felt stiff. Her strokes were irregular. Driving forward, she fought to clear her mind and find what she called her “sphere,” a place where the sea became her only companion and the shrieks of gulls and the humming of boat engines faded away. Using a new overhand stroke called the American crawl, Ederle eventually settled into a steady pace, briskly breaking through waves.
Throughout Ederle’s swim, two tugboats accompanied her. One carried newspaper reporters who wired dispatches of her progress to shore. The other, displaying a sign that read “This way, ole kid!” with an arrow pointing forward, transported her coach, family, and friends. Her coach played songs, such as “Yes, We Have No Bananas,” on a phonograph so that Ederle could time her strokes to the rhythm. Using a net, her coach also passed her baby bottles of broth for nourishment.
For hours Ederle swam, dodging debris with an amused smile. However, as she neared the English shore, a sudden fierce storm erupted. The tides and waves forced Ederle backward, and she fought the stubborn swells for several hours. The salty water caused her tongue to swell and inflamed her ears. Yet Ederle felt indescribably happy as she churned through the sea. Finally, as she neared the English shore, the storm abated, and the tide turned. No longer fighting against her, the sea pushed her toward the shore and victory.
After fourteen hours and thirty-one minutes, Ederle, on wobbly legs, stepped onto the English shore. The waiting crowd roared, honked their automobile horns, blasted their tugboat whistles, and set off flares that flashed in the sky. Ederle had swum into history.
When Ederle returned to New York, she received a parade, where thousands of people shouted “Trudy!” Not only were everyday American citizens proud of Ederle, but she also inspired them to be more active. Over the next few years, more than 60,000 people credited her with motivating them to earn their American Red Cross swimming certificates. Gertrude Ederle’s accomplishment proved to the world that with determination and passion, it was possible for a person to achieve his or her goals.
SOLO SWIMS ACROSS THE ENGLISH CHANNEL
|
Earliest Speed Records |
||
| Year | Swimmer | Time |
| 1875 | Matthew Webb (M) | 21 hours, 45 minutes |
| 1923 | Enrico Tiraboschi (M) | 16 hours, 33 minutes |
| 1926 | Gertrude Ederle (F) | 14 hours, 31 minutes |
| 1926 | Arnst Vierkotter (M) | 12 hours, 38 minutes |
| Current Speed Records | ||
| Year | Swimmer | Time |
| 2012 | Trent Grimsey (M) | 6 hours, 55 minutes |
| 2006 | Yvetta Hlavacova (F) | 7 hours, 25 minutes |
Question
Which statement describes how the author’s use of a problem-and-solution structure in paragraph 5 contributes to the development of ideas in the passage?
- ADetailing the challenges presented by the cold channel waters highlights the effectiveness of Ederle’s training.
- BDescribing Ederle’s physical difficulties during her swim provides evidence of the team effort required to ensure her safety.
- CExplaining the difficulties that arose early in the effort helps predict the additional obstacles that occurred during Ederle’s attempt.
- DIllustrating Ederle’s process of blocking out her discomfort shows that swimming the channel was both a mental and a physical challenge.
Show the answer
Correct answer: D
The question asks how a problem-and-solution structure in paragraph 5 contributes to the ideas presented in the passage.
A. Incorrect. The details in paragraph 5 do not provide a connection between the cold temperature of the water and the effectiveness of Ederle’s training.
B. Incorrect. The difficulties Ederle encountered were only partially relieved by her team, and her team’s efforts to ensure Ederle’s safety are not explained in the passage.
C. Incorrect. The paragraph does not focus on the relationship between the problems Ederle encountered at the start of her swim and the problems she encountered during or near the end of her swim.
D. CORRECT. The paragraph describes how the water’s temperature made Ederle uncomfortable and made it difficult for her to regulate her stroke. The paragraph continues with the explanation of how she overcame these issues by focusing her mind on the sea and tuning out the distractions in her surroundings (“the sea became her only companion and the shrieks of gulls and the humming of boat engines faded away” [paragraph 5]).
Question analysis
Gertrude Ederle's cold, stiff first hours in the English Channel are told as problem and solution, and this text-structure question asks what that pattern adds to the passage's ideas. Students must spot the troubles she met in the cold water and how she handled them, then pick the abstract statement that accounts for both halves of the pattern.
- Grade level
- Grade 8 reading and task
- Compared with grade 7
- Above grade 7 A problem-and-solution question about one paragraph is familiar grade 7 fare, yet these four answers are general claims about the swim, each tied to a real hardship, so students need a clear map of the paragraph before judging them.
- 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
- How, not what major
- Every choice must be checked moderate
- Figurative or literary language minor
- Evidence
- Answered from one paragraph or stanza
- Reading level
- Passage: about grade 9, 790 words; question and choices: about grade 14, 95 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 opening halves of the choices are all accurate, which moves the whole decision onto their second halves. Readers who notice only the physical side of the paragraph, the cold and the stiffness, reach for training, teamwork or foreshadowing to explain it. The paragraph's turning point is a mental one, clearing her mind until the noise faded, and only the statement that names both a mental and a physical challenge accounts for the problem and the solution together.
How, not what major Working it out
The question asks what paragraph 5's pairing of problems (bone-chilling water, stiff limbs, irregular strokes) with solutions (finding her “sphere”, the American crawl) does for the passage, so retelling the hardships earns nothing. (Anderson & Krathwohl, 2001)
Every choice must be checked moderate Choosing the answer
Each choice opens with a fair description of paragraph 5, the cold water, her physical difficulties, the early struggle, so only what each claims that description shows can be tested. (Embretson & Wetzel, 1987)
Figurative or literary language minor Understanding the question
The mental half of the solution is told in images, a place where “the sea became her only companion” and gulls and engines “faded away”, which must be read as blocking out discomfort. (Graesser, Singer & Trabasso, 1994; Kintsch, 1998)
Strategy: Sort paragraph 5 into two lists, what went wrong for Ederle early in the swim and what she did about it, then ask what that pairing shows about the swim as a whole.
Traps
- Wrong purpose or structure: Names a purpose, structure or effect that the part does not serve, or describes what a part says when the question asks what it does.
- Outside knowledge: A choice is plausible in the real world but not supported by this text.
- Wrong part of the text: A choice is true of another paragraph, stanza or speaker than the one asked about.
The wrong answers, classified
A Outside knowledge (King et al., 2004; Recht & Leslie, 1988)
Assumes that coping with icy water proves good training, a natural idea from sports, but paragraph 5 never mentions training and credits her focus and her stroke.
B Wrong part of the text (Kirsch & Mosenthal, 1990)
Brings in the tugboat crew of paragraph 6, the coach passing broth and playing songs, though paragraph 5 shows Ederle coping alone and never raises her safety.
C Wrong purpose or structure (Anderson & Krathwohl, 2001)
Treats the early shivering and stiffness as a setup for the storm of paragraph 7, a link the paragraph never makes, since it resolves its own problems with a steady pace.
Working it out, step by step
Learn what the question asks
A problem-and-solution structure tells about a difficulty and then how someone deals with it. The question asks what this pattern in paragraph 5 adds to the ideas of the passage. So first sort the paragraph into problems and solutions.
List the problems in paragraph 5
When Ederle waded in, “she shivered in the bone-chilling water.” Next, “Her limbs felt stiff. Her strokes were irregular.” Limbs are arms and legs. Irregular means uneven, not steady. All of these are troubles with her body.
List her solutions
Ederle “fought to clear her mind.” She looked for what she called her “sphere.” There, “the sea became her only companion and the shrieks of gulls and the humming of boat engines faded away.” In other words, she shut out the noise and her discomfort. Then, using the American crawl, she “settled into a steady pace.”
Connect problems and solutions
The problems were physical, which means of the body. A big part of the fix was mental, which means of the mind. She calmed her thoughts so her body could keep working. So the paragraph shows that the swim tested her mind as well as her body.
Check each choice
- D fits: blocking out her discomfort shows the swim was “both a mental and a physical challenge.”
- A is wrong because paragraph 5 never mentions her training.
- B is wrong because her team on the tugboats appears in paragraph 6, and her safety is never discussed.
- C is wrong because the early troubles are solved inside this paragraph instead of setting up later ones.
Watch out: A storm does hit in paragraph 7, so C may look right. But paragraph 5 does not point ahead to it.
Choose the answer
Only D explains both the problem and the way Ederle solved it. So the answer is D.
Why this answer and not the closest wrong one
C is tempting, since a storm really does strike in paragraph 7. But paragraph 5 never hints at it. The paragraph ends with its problem solved, as Ederle is “briskly breaking through waves.” D explains both halves of the pattern: troubles of the body, eased by the mind.
More questions like this
The original DOE question
The passage “Champion of the Channel” as printed (pages 56–57)
Question 2 of 6
2024 Test B English, question 1Question
What is the best way to combine these sentences to clarify the relationship between ideas?
(1) The International Space Station has been inhabited by crew members since 2000.
(2) Tourists will soon be allowed to pay for visits to the space station.
(3) Because the cost is $52–$58 million round trip, few people will be able to take advantage of the opportunity to have a vacation in outer space.
- AThe International Space Station has been inhabited by crew members since 2000, but tourists will soon be allowed to pay for visits to the space station, which cost $52–$58 million round trip, so few people will be able to take advantage of the opportunity to have a vacation in outer space.
- BThe International Space Station has been inhabited by crew members since 2000 and will soon allow tourists to pay for visits, but because the cost is $52–$58 million round trip, few people will be able to take advantage of the opportunity to have a vacation in outer space.
- CThe International Space Station has been inhabited by crew members since 2000, but tourists will soon be allowed to pay for visits to the space station, though the cost is $52–$58 million round trip, so few people will be able to take advantage of the opportunity to have a vacation in outer space.
- DThe International Space Station has been inhabited by crew members since 2000, and tourists will soon be allowed to pay for visits to the space station because the cost is $52–$58 million round trip, therefore few people will be able to take advantage of the opportunity to have a vacation in outer space.
Show the answer
Correct answer: B
The question asks for the best way to combine the sentences.
A. Incorrect. Although the option combines the sentences in a way that accurately reflects the meaning of each individual sentence, the combined sentence is a string of clauses that do not effectively cohere. Because it is poorly structured, the combined sentence does not clarify the relationship of ideas as effectively as the correct response does. The sentence incorrectly uses “but tourists,” and “which cost” modifies “the space station” but does not modify the trip. Compared with the correct response, the combined sentence in this option is also imprecise and unnecessarily wordy.
B. CORRECT. The option uses a complex sentence to present ideas clearly and precisely, and it shows the relationship between the ideas in the original sentences. In the first part of the sentence, the conjunction “and” correctly joins the first and second sentences by indicating a relationship, rather than a contrast, between the two. In the second part of the sentence, the conjunction “but” adds additional emphasis to the fact that while tourists will be allowed to visit the space station, the cost of the trip will likely prohibit most people from visiting.
C. Incorrect. Although the option combines the sentences in a way that accurately reflects the meaning of each individual sentence, the combined sentence is a string of clauses that do not effectively cohere. Because it is so poorly structured, the combined sentence does not clarify the relationship of ideas as effectively as the correct response does. Compared with the correct response, the combined sentence in this option is also imprecise and unnecessarily wordy.
D. Incorrect. The combination of the sentences contains an illogical relationship between ideas with the statement that tourists will be allowed to pay for visits to the space station because the cost is $52–$58 million round trip. The connection between the idea that “tourists will soon be allowed to pay for visits” and the subsequent “therefore few people will be able to take advantage of the opportunity” is also illogical.
Question analysis
This sentence-combining question gives three sentences about the International Space Station, its crew and the high price of a tourist trip, and asks for the best way to join them into one. Every version keeps the same facts, so students must judge which connecting words show how the ideas relate while the sentences stay long and nearly identical.
- Grade level
- Grade 8 reading and task
- Compared with grade 7
- Above grade 7 Grade 7 students practice joining two short sentences with a fitting conjunction. Here three sentences become one long sentence in four nearly identical versions, so students must weigh every connecting word and clause rather than spot one error.
- 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 major
- Complex sentences moderate
- Every choice must be checked moderate
- Evidence
- Answered from one sentence or line
- Reading level
- Question and choices: about grade 15, 261 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
None of the wrong versions drops a fact, and two of them are loose rather than plainly ungrammatical, so the ear is little help. Students lose the point by accepting the smoothest chain of clauses without asking what each connector claims: whether the crew and the tourists really contrast, what the price belongs to, and what the price explains. The question rewards deciding the three links before reading the versions, then checking them one connector at a time.
How sentences fit together major Working it out
Sentence 2 simply adds to sentence 1, while sentence 3’s price works against the tourist plan and explains why few will go, so every “but,” “though,” “because” or “so” in a version must fit one of those links. (Halliday & Hasan, 1976)
Complex sentences moderate Understanding the question
Each version is one sentence of 48 to 53 words with four clauses, and at that length a “which cost” hanging on the wrong noun or a comma before “therefore” is easy to read past. (Abedi & Lord, 2001; Freedle & Kostin, 1993; Messick, 1989)
Every choice must be checked moderate Choosing the answer
All four versions keep the same facts in the same order and share most of their words, so none can be ruled out by content; each connecting word has to be tested in turn. (Embretson & Wetzel, 1987)
Strategy: Before reading the choices, decide how each sentence relates to the next: added fact, contrast, or cause and result. Then check every connecting word in each version against those links.
Traps
- Misplaced modifier: A describing word or phrase that attaches to the wrong word, or to nothing in the sentence.
- Wordy, vague or informal: A revision is grammatical but wordy, imprecise or too casual for the passage.
- Wrong transition: A connecting word or phrase that signals the wrong relationship, such as contrast where the idea continues.
The wrong answers, classified
A Misplaced modifier (Connors & Lunsford, 1988)
Keeps the price as the reason few can go, marked by “so,” but misses that “which cost” hangs on “the space station” and that “but” sets crew against tourists.
C Wordy, vague or informal (Connors & Lunsford, 1988)
Keeps every fact in order, but stacking “but,” “though” and “so” in one sentence turns the price into an aside instead of plainly the reason few people will go.
D Wrong transition (Halliday & Hasan, 1976)
Keeps sentence 3’s “because the cost is” word for word, but here it explains why tourists are allowed, and “therefore” after a comma splices on the result.
Working it out, step by step
Figure out what the question asks
You need to join three sentences into one. The best version shows clearly how the ideas connect. Joining words do that job. A conjunction is a joining word, like and, but, so or because. Each one tells the reader something. And adds a fact. But shows a contrast (two ideas that pull against each other). Because and so show a cause and its result.
Decide how the three sentences connect
Sentence 1 says crews have lived on the station since 2000. Sentence 2 adds a new fact: tourists will soon be able to visit. That is not a contrast, so it needs and. Sentence 3 works against sentence 2. The trip costs “$52–$58 million round trip.” That price is also the reason few people will go. So you need a contrast and a reason. Example: The pool is open to all, but because it costs $90, few kids swim there.
Test each choice
- B uses “and will soon allow tourists” to add the new fact. Then “but because the cost is” shows the contrast and the reason. Every link is right.
- A joins sentence 2 with “but tourists,” as if crews and tourists were opposites. Also, “which cost” comes right after “the space station.” So it sounds like the station costs that much, not the trip.
- C stacks “but,” “though” and “so” in one long chain. The price turns into a side note instead of the clear reason.
- D says tourists may visit “because the cost is” so high. That makes no sense. And “therefore” after a comma joins two sentences the wrong way.
Pick the answer
Watch out: A is the most tempting. It keeps the price as the reason, with “so.” But its “but” and its “which” send the reader the wrong way. Only one choice links every idea correctly. So the answer is B.
Why this answer and not the closest wrong one
A is the closest wrong answer. Like B, it says the price keeps most people away. But A sets crews against tourists with “but tourists.” Its “which cost” also seems to give the price of the station. B uses and for the added fact and but because for the price, so each link is clear.
More questions like this
The original DOE question
Question 3 of 6
2026 Practice Test A English, question 18Passage Excerpt from A Voice in the Wilderness
Excerpt from A Voice in the Wilderness
by Grace Livingston Hill
With a lurch the train came to a dead stop and Margaret Earle, hastily gathering up her belongings, hurried down the aisle and got out into the night.
It occurred to her, as she swung her heavy suit-case down the rather long step to the ground, and then carefully swung herself after it, that it was strange that neither conductor, brakeman, nor porter had come to help her off the train, when all three had taken the trouble to tell her that hers was the next station; but she could hear voices up ahead. Perhaps something was the matter with the engine that detained them and they had forgotten her for the moment.
The ground was rough where she stood, and there seemed no sign of a platform. Did they not have platforms in this wild Western land, or was the train so long that her car had stopped before reaching it?
She strained her eyes into the darkness, and tried to make out things from the two or three specks of light that danced about like fireflies in the distance. She could dimly see moving figures away up near the engine, and each one evidently carried a lantern. The train was tremendously long. A sudden feeling of isolation took possession of her. Perhaps she ought not to have got out until some one came to help her. Perhaps the train had not pulled into the station yet and she ought to get back on it and wait. Yet if the train started before she found the conductor she might be carried on somewhere and he justly blame her for a fool.
There did not seem to be any building on that side of the track. It was probably on the other, but she was standing too near the cars to see over. She tried to move back to look, but the ground sloped and she slipped and fell in the cinders, bruising her knee and cutting her wrist.
In sudden panic she arose. She would get back into the train, no matter what the consequences. They had no right to put her out here, away off from the station, at night, in a strange country. If the train started before she could find the conductor she would tell him that he must back it up again and let her off. He certainly could not expect her to get out like this.
She lifted the heavy suit-case up the high step that was even farther from the ground than it had been when she came down, because her fall had loosened some of the earth and caused it to slide away from the track. Then, reaching to the rail of the step, she tried to pull herself up, but as she did so the engine gave a long snort and the whole train, as if it were in league against her, lurched forward crazily, shaking off her hold. She slipped to her knees again, the suit-case, toppled from the lower step, descending upon her, and together they slid and rolled down the short bank, while the train . . . ran giddily off into the night.
The horror of being deserted helped the girl to rise in spite of bruises and shock. She lifted imploring hands to the unresponsive cars as they hurried by her—one, two, three, with bright windows, each showing a passenger, comfortable and safe inside, unconscious of her need.
A moment of useless screaming, running, trying to attract some one’s attention, a sickening sense of terror and failure, and the last car slatted itself past with a mocking clatter, as if it enjoyed her discomfort.
Margaret stood dazed, reaching out helpless hands, then dropped them at her sides and gazed after the fast-retreating train, the light on its last car swinging tauntingly, blinking now and then with a leer in its eye, rapidly vanishing from her sight into the depth of the night.
She gasped and looked about her for the station that but a short moment before had been so real to her mind; and, lo! on this side and on that there was none!
The night was wide like a great floor shut in by a low, vast dome of curving blue set with the largest, most wonderful stars she had ever seen. Heavy shadows of purple-green, smoke-like, hovered over earth darker and more intense than the unfathomable blue of the night sky. It seemed like the secret nesting-place of mysteries wherein no human foot might dare intrude. It was incredible that such could be but common sage-brush, sand, and greasewood wrapped about with the beauty of the lonely night.
No building broke the inky outlines of the plain, nor friendly light streamed out to cheer her heart. Not even a tree was in sight, except on the far horizon, where a heavy line of deeper darkness might mean a forest. Nothing, absolutely nothing, in the blue, deep, starry dome above and the bluer darkness of the earth below save one sharp shaft ahead like a black mast throwing out a dark arm across the track.
As soon as she sighted it she picked up her baggage and made her painful way toward it, for her knees and wrist were bruised and her baggage was heavy.
A soft drip, drip greeted her as she drew nearer; something plashing down among the cinders by the track. Then she saw the tall column with its arm outstretched, and looming darker among the sage-brush the outlines of a water-tank. It was so she recognized the engine’s drinking-tank, and knew that she had mistaken a pause to water the engine for a regular stop at a station.
cinders: track bed made from the residue of burnt coal
From A VOICE IN THE WILDERNESS by Grace Livingston Hill—Public Domain
Question
How does Margaret’s experience in paragraph 9 emphasize a theme of the excerpt?
- AIt confirms Margaret’s understanding that she cannot rely on help from anyone else.
- BIt leads Margaret to realize that her desire to change her situation is impractical.
- CIt causes Margaret to believe that her own actions led to an unfavorable outcome.
- DIt reinforces Margaret’s frustration about her lack of control over her surroundings.
Show the answer
Correct answer: A
The question asks about the relationship between the theme and paragraph 9, where Margaret desperately tries to get someone on the train to notice her.
A. CORRECT. One important theme of this excerpt concerns Margaret’s willingness to take action to ensure that she reaches her destination. This determination, described in Option A, is why she gathers her belongings together without help, gets off the train without being assisted by employees, and then attempts to climb back on while the train employees are busy examining the engine.
B. Incorrect. While the narrator describes her screaming as useless, she does not feel that her efforts overall are useless, and she does not give up until paragraph 10.
C. Incorrect. While Margaret is feeling a sense of “failure” in paragraph 9, she does not condemn herself as the train moves away.
D. Incorrect. Margaret expresses “terror” in paragraph 9 over being unable to catch someone’s attention, not frustration about her lack of control over her surroundings.
Question analysis
This theme question asks how Margaret’s experience in paragraph 9 of A Voice in the Wilderness, as she screams and runs while the train pulls away, emphasizes a theme of the excerpt. It is a lightly reworded version of an earlier handbook question. Every choice describes a believable reaction to being left behind, so the answer depends on the excerpt’s larger pattern.
- Grade level
- Grade 8 reading and task
- Compared with grade 7
- Above grade 7 Typical grade 7 theme questions trace a given theme through a text. Here students must decide which theme one frantic paragraph supports, and all four choices describe reactions that fit the scene, so the decision draws on the whole excerpt.
- Estimated difficulty
- Among the hardest on the SHSAT: a non-obvious approach, heavy reading, or a well-hidden trap.
- Thinking it demands
- Depth of knowledge 3, strategic thinking · mainly analyze
- What makes it hard
- Reading between the lines major
- Evidence in several places moderate
- Evidence
- Answered from the whole text
- Reading level
- Passage: about grade 8, 981 words; question and choices: about grade 10, 65 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
Each choice names a feeling a stranded traveler might have, and two lean on the paragraph’s own words, “useless” and “failure,” so the paragraph alone cannot decide it. Paragraph 9 must be read as the last link in a chain of trainmen, passengers and a departing train that all leave her to herself. Students who judge from that one paragraph often decide she has given up, though she soon picks up her bags and walks toward the dark shaft by the track.
Reading between the lines major Working it out
The theme is never stated; it must be drawn from paragraph 9’s cries that no one answers and from the passengers “comfortable and safe inside, unconscious of her need” in paragraph 8. (Graesser, Singer & Trabasso, 1994; Kintsch, 1998)
Evidence in several places moderate Working it out
The pattern begins in paragraph 2, when no trainman helps her off, and runs through the train lurching away “as if it were in league against her” in paragraph 7. (Kirsch & Mosenthal, 1990; Gorin & Embretson, 2006)
Strategy: Sum up in a phrase what keeps happening to Margaret from the start of the excerpt to its end, then check which choice paragraph 9’s own words most clearly add to.
Traps
- Too broad or too strong: A choice overstates, generalizes, or uses absolute words the text does not support.
- Wrong tone or attitude: Misjudges the tone, attitude or point of view, such as reading admiration as criticism, or taking a character's or subject's feelings for the author's.
The wrong answers, classified
B Too broad or too strong (King et al., 2004)
Stretches the “useless screaming” of one moment into a judgment that changing her situation is impractical, though she soon gathers her bags and sets off toward the shaft ahead.
C Reads too much in (Graesser, Singer & Trabasso, 1994)
Turns the “sense of terror and failure” into self-blame, though Margaret never says that her own choice to step off the train caused her trouble.
D Wrong tone or attitude (Graesser, Singer & Trabasso, 1994)
Fits the indifferent train, but names frustration over control where paragraph 9 stresses terror at being ignored by everyone aboard.
Working it out, step by step
Figure out what the question asks
This asks about a theme: a big idea a story keeps coming back to. How does what happens in paragraph 9 point to a theme? The right choice should fit a pattern across the whole excerpt.
Read paragraph 9
Paragraph 9 describes “A moment of useless screaming, running, trying to attract some one’s attention, a sickening sense of terror and failure.” Margaret screams and runs, trying to get someone to notice her. No one does. The last car rolls past “as if it enjoyed her discomfort.”
Find the same thing earlier
This is not the first time. In paragraph 2, none of the workers “had come to help her off the train.” In paragraph 8, the passengers sit “comfortable and safe inside, unconscious of her need.” That means they don’t know she needs help. Paragraph 9 is one more time when nobody comes. She will have to count on herself.
Check each choice
- A fits. Her cries go unanswered, just as before. She cannot rely on anyone else.
- B does not fit. Impractical means not sensible or workable. Her screaming fails, but she never decides that trying to change things is pointless. In paragraph 14 she “picked up her baggage” and set off again.
- C does not fit. She feels “failure,” but she never blames herself.
- D does not fit. The paragraph shows terror at being ignored, not frustration about having no control over her surroundings.
Choose the answer
Paragraph 9 adds one more moment where no one helps Margaret. So the answer is A.
Why this answer and not the closest wrong one
B is the closest wrong choice, because paragraph 9 calls her screaming “useless.” But one failed moment does not mean she gives up. Soon she takes her bags and walks toward the tall dark shape ahead. What stays true from paragraph 2 to paragraph 9 is that no one helps her. That is A.
More questions like this
The original DOE question
The passage “Excerpt from A Voice in the Wilderness” as printed (pages 128–129)
Question 4 of 6
2018 Test A Math, question 5Question
The sum of two consecutive integers is −15. If 1 is added to the smaller integer and 2 is subtracted from the larger integer, what is the product of the two resulting integers?
Grid-in question: work out the answer and enter it as a number.
Show the answer
Correct answer: 63
If x is the smaller consecutive integer, then
is the larger consecutive integer. Use their sum (−15) to find x:
The two consecutive integers are −8 and −7. One is added to the smaller integer:
and 2 is subtracted from the larger integer:
Find the product:
Question analysis
A grid-in problem about two consecutive integers whose sum is −15. Students find the two integers, add 1 to the smaller and subtract 2 from the larger, then multiply the results. Deciding which negative integer is the smaller one, and keeping signs straight through every step, are what make it tricky.
- Grade level
- Grade 7 content, by NYS standard
- Compared with grade 7
- Above grade 7 A typical grade 7 task solves one two-step equation or multiplies signed numbers. This links both: set up a consecutive-integer equation, solve it with negatives, adjust each integer, and multiply, with no choices to check against.
- Estimated difficulty
- Hard: combines ideas, needs a plan, and has more than one tempting wrong answer.
- Thinking it demands
- Depth of knowledge 2, skills and concepts · mainly apply
- What makes it hard
- Error-prone arithmetic moderate
- Turning words into math moderate
- Many steps moderate
- Solution
- 4 steps
- Reading level
- Question and choices: about grade 9, 30 words.
- Students, last 30 days
- Not enough answers yet to show (it takes 10).
Why it is hard, traps and wrong answers (shows the answer)
Why it is hard
Every step is routine, yet the question collects most of the ways students lose points with negatives. The crucial judgment is which of −8 and −7 is the smaller; a student who picks −7 still produces a tidy, wrong product. Gridding the product of the original pair, or giving a negative product, are the other usual losses. Writing each intermediate pair down, rather than holding them in mind, protects against all three.
Error-prone arithmetic moderate Working it out
Every number in play is negative: −8 and −7, then −7 and −9, and a product of two negatives that must come out positive. (Brown & Burton, 1978; Junker & Sijtsma, 2001)
Turning words into math moderate Understanding the question
"1 is added to the smaller integer and 2 is subtracted from the larger" depends on knowing that −8, not −7, is the smaller, since it lies farther below zero. (Hegarty, Mayer & Monk, 1995; Koedinger & Nathan, 2004)
Many steps moderate Working it out
Four linked steps: set up x + (x + 1) = −15, solve for x, adjust each integer, then multiply; an error early in the chain carries through to the product. (Daniel & Embretson, 2010; Enright, Morley & Sheehan, 2002)
Strategy: Halve the sum to see which two integers sit on either side of it, remember that the smaller negative is farther from zero, then adjust each and multiply.
Traps
- Negatives and direction: Arithmetic with negative numbers, the order of a subtraction, or direction on a number line. (Moving a term across the equals sign without changing its sign is a faulty procedure.)
- Misreads the question: Misses or misreads a condition or a word in the question: "at least", "each", "remaining", "not".
The wrong answers, classified
60 Negatives and direction (Brown & Burton, 1978)
Takes −7 as the smaller integer because 7 is less than 8, so adjusts to −7 + 1 = −6 and −8 − 2 = −10, and multiplies to 60.
56 Misreads the question (Hegarty, Mayer & Monk, 1995)
Finds −8 and −7 and multiplies them to get 56, skipping the sentence that adds 1 to one integer and subtracts 2 from the other.
-63 Negatives and direction (Brown & Burton, 1978)
Finds the adjusted integers −7 and −9 correctly but gives their product a negative sign, gridding −63.
Worked solution, step by step
Formulas used
- Consecutive integers
- Integers are whole numbers and their opposites, like −2, −1, 0, 1 and 2. Consecutive integers come one right after another. If n is the smaller one, the next one is n + 1, because each step up the number line adds 1.
- Multiplying two negative numbers
- a and b are positive numbers, so −a and −b are negative. When you multiply two negative numbers, the answer is positive. The two minus signs cancel out.
Sort out the question
Two consecutive integers add up to −15. Integers are whole numbers and their negatives. Consecutive means one comes right after the other, like 4 and 5. You need to do three things:
- Find the two integers.
- Add 1 to the smaller one. Subtract 2 from the larger one.
- Find the product of the two new numbers. The product is the answer when you multiply.
Find the two integers
Call the smaller integer n. Then the larger one is n + 1. Their sum is −15.
Subtract 1 from both sides. Then divide both sides by 2.
So the integers are −8 and −7.
Decide which one is smaller
On a number line, −8 is to the left of −7. Numbers to the left are smaller. So −8 is the smaller integer, and −7 is the larger one. Watch out: 8 is bigger than 7, but −8 is smaller than −7. Mixing them up gives −6 and −10, and the wrong answer 60.
Change each integer
Add 1 to the smaller integer.
Subtract 2 from the larger integer.
The two new numbers are −7 and −9.
Multiply the new numbers
Both numbers are negative, so their product is positive.
Watch out: the answer is not −63, because two negatives make a positive. Also, don’t multiply the first pair, −8 and −7. That gives 56 and skips the changes. So you would grid 63.
Check your answer
Check the pair: , and they are one apart. Half of −15 is −7.5, and −8 and −7 sit on either side of it. Then , and the sign is positive.
More questions like this
The original DOE question
Question 5 of 6
2024 Test B Math, question 52Question
Five numbered balls are placed in two boxes as shown in the figure above. Davina picks one ball at random from Box B and places it in Box A. Then Yusuf picks one ball from Box A without looking. What is the probability that Yusuf will pick a ball with an odd number?
- A
- B
- C
- D
Show the answer
Correct answer: A
The probability of Davina picking an odd-numbered ball from Box B is . If Davina places an odd-numbered ball in Box A, then the probability of Yusuf picking an odd-numbered ball from Box A is . The probability of both of these events happening is the product of the two probabilities.
Question analysis
Two boxes hold five numbered balls, and Davina moves one ball at random from Box B into Box A before Yusuf draws one from Box A. Students find the probability that Yusuf's ball shows an odd number. It tests two-stage probability, and the tricky part is that the second draw depends on which ball was moved.
- NYS standards
- Grade level
- Grade 7 content, by NYS standard
- Compared with grade 7
- Above grade 7 Grade 7 compound probability lists outcomes for independent stages such as coins or spinners. Here the first random move changes what is in the second box, so students must follow two linked stages, a dependence typical grade 7 work does not include.
- Estimated difficulty
- Among the hardest on the SHSAT: a non-obvious approach, heavy reading, or a well-hidden trap.
- Thinking it demands
- Depth of knowledge 3, strategic thinking · mainly analyze
- What makes it hard
- Solution
- 3 steps
- Reading level
- Question and choices: about grade 4, 57 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 chance events are hidden in what reads like a question about a single draw. Every listed wrong answer is a reasonable single-stage answer, either one of the two factors on its own or a count of odd balls across both boxes. Listing the nine equally likely pairs, Davina's ball and then Yusuf's, shows that only two of them end with an odd ball and makes the structure visible without any formula.
No obvious method major Working it out
The stem asks one question about Yusuf's draw, but the answer depends on Davina's earlier random pick; the key is that Box A starts with only even balls, so Yusuf can draw odd only by drawing the ball she moved. (Schoenfeld, 1985)
Something you must already know minor Working it out
Multiplying the chances of the two stages, 2/3 for an odd ball moving and 1/3 for Yusuf then drawing it, is a rule students must bring themselves. (Anderson & Krathwohl, 2001)
Reading a figure, table or graph minor Understanding the question
The numbers appear only in the figure, Box A holding 2 and 6 and Box B holding 3, 4 and 5, so the odd balls have to be spotted there. (Lesh, Post & Behr, 1987; Kirsch & Mosenthal, 1990)
Strategy: List every equally likely pair of a ball moved by Davina and a ball picked by Yusuf, and count the pairs that end with an odd ball.
Traps
- Stops one step early: A choice is a number from partway through the solution.
- Numbers taken from the question: Combines the numbers in the question without a model of the situation, or is simply a number that appears in the question.
The wrong answers, classified
B Stops one step early (King et al., 2004; Gierl et al., 2017)
Finds Yusuf's chance of drawing the odd ball once one is in Box A, 1 out of 3, leaving out the chance that Davina moves an odd ball at all.
C Numbers taken from the question (Hegarty, Mayer & Monk, 1995)
Counts the odd balls in the figure, 3 and 5, over all five balls, 2/5, ignoring that Yusuf draws only from Box A.
D Stops one step early (King et al., 2004; Gierl et al., 2017)
Gives the chance that Davina moves an odd ball, 2 out of 3, the first stage only, without multiplying by Yusuf's 1/3 chance of drawing it.
Worked solution, step by step
Formulas used
- Probability
- P is the probability, the chance that something happens. It is a number from 0 to 1. The top counts the results you want. The bottom counts all the results that can happen. It works when every result is equally likely.
- Chance of events in a row
- A and B are two events that happen one after the other. P(A) is the chance of the first. P(B after A) is the chance of the second, counting only what is left after the first. You multiply because the second must also happen inside the share of times the first did.
Read the figure
Box A holds balls numbered 2 and 6. Box B holds balls numbered 3, 4 and 5.
An odd number does not divide evenly by 2. So the only odd balls are 3 and 5, and both start in Box B. Box A starts with no odd balls at all.
Spot the two chance events
Two things happen by chance, one after the other:
- Davina picks one of the 3 balls in Box B and moves it to Box A.
- Then Yusuf picks one of the 3 balls now in Box A.
Yusuf gets an odd ball only if both go right. Davina must move an odd ball. Then Yusuf must pick that very ball.
The question asks only about Yusuf. But his chance depends on Davina’s pick, which comes first.
Find the chance for Davina’s pick
Box B has 3 balls, and 2 of them, the 3 and the 5, are odd.
If she moves the 4 instead, Box A holds only even balls. Then Yusuf can’t get an odd ball at all.
Find the chance for Yusuf’s pick
Say Davina moved an odd ball. Box A now holds 3 balls: the 2, the 6 and that one odd ball.
Watch out: alone is choice B. It forgets that Davina might move the 4.
Multiply the two chances
Both events must happen, so use the rule for events in a row.
Watch out: alone, choice D, stops after Davina’s pick. , choice C, counts 2 odd balls out of all 5. But Yusuf picks only from Box A.
So the answer is A, .
Check your answer
List all 9 equally likely outcomes. Davina can move 3, 4 or 5. Then Yusuf picks one of 3 balls.
| Ball moved | Box A then | Odd picks |
|---|---|---|
| 3 | 2, 6, 3 | 1 |
| 4 | 2, 6, 4 | 0 |
| 5 | 2, 6, 5 | 1 |
That is 2 odd picks out of 9, or .
More questions like this
The original DOE question
Question 6 of 6
2018 Test B Math, question 8Question
Based on the statement above, which variable has the greatest value?
- A
- B
- C
- D
Show the answer
Correct answer: D
Break the equations apart to each equal :
Pick a number to substitute into the equations, and solve the equations to find the values of , , , , and .
Let . Since all the equations are equal to 2, substitute 2 to find each variable.
Variable has the greatest value.
Question analysis
This algebra question sets five expressions equal to one another and to a positive number, then asks which variable has the greatest value. It tests whether students can rewrite each variable in terms of one shared value and compare them. What makes it tricky is that there are no numbers to compute, so each variable's size has to be reasoned out.
- Grade level
- Grade 7 content, by NYS standard
- Compared with grade 7
- Above grade 7 Grade 7 students rewrite expressions to see how quantities relate, usually one equation at a time. This chain of five linked expressions, with no numbers to compute and a positivity condition to use, is a reasoning task 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 3, strategic thinking · mainly analyze
- What makes it hard
- Variables instead of numbers major
- No obvious method moderate
- Much to keep track of minor
- Solution
- 3 steps
- Reading level
- Question and choices: about grade 10, 16 words.
- Students, last 30 days
- Not enough answers yet to show (it takes 10).
Why it is hard, traps and wrong answers (shows the answer)
Why it is hard
The question rewards a strategy, not a calculation: once the shared value is named, each variable follows in one line and R is clearly largest. Without that step, students judge by how the expressions look, and the look is backwards, since the 3 in 3N makes N small and the 7 under R makes R large. The positivity condition at the end is easy to skip but is what fixes the order.
Variables instead of numbers major Understanding the question
There are no numbers to compute: five variables are tied together in the one chain M = 3N = P/4 = Q + 5 = R/7, and each must be compared through the shared value. (Koedinger & Nathan, 2004; Enright, Morley & Sheehan, 2002)
No obvious method moderate Working it out
Nothing says how to compare; the efficient move is to name the common value, or pick one such as 12, and rewrite each variable, which students must think of themselves. (Schoenfeld, 1985)
Much to keep track of minor Working it out
Five relations and the condition > 0 must be held at once; the condition matters, since with a negative common value the order of M, N, P and R would reverse. (Sweller, 1988; Carpenter, Just & Shell, 1990)
Strategy: Call the shared value k, a positive number, and rewrite each variable as an expression in k; or substitute a convenient positive value such as 12 and compare the results.
Traps
- Equation written backwards: Writes a comparison the wrong way round, word for word: "six times as many students as professors" as 6S = P. The bigger quantity gets the bigger number.
The wrong answers, classified
A Equation written backwards (Clement, Lochhead & Monk, 1981)
Reads P/4 and R/7 as a quarter and a seventh of M, the reverse of the truth, so M looks largest of all.
B Equation written backwards (Clement, Lochhead & Monk, 1981)
Reads the 3 in 3N as making N three times as large, when 3N = M actually makes N one third of M.
C Stops one step early (King et al., 2004; Gierl et al., 2017)
Correctly sees that P is four times M but stops there without checking R, which at seven times M is larger.
Worked solution, step by step
Formulas used
- Undoing division
- a is the top of the fraction, b is the bottom, and c is the result. Multiplying undoes dividing. So if a divided by b is c, then a is b times c.
- Undoing multiplication
- b is the number multiplied by a, and c is the result. Dividing undoes multiplying. So to get a alone, divide c by b.
Understand the chain
The statement is a chain of equal signs. It says five expressions all have the same value. The last part says that value is greater than 0, so it is positive.
You need to find which letter has the largest value.
Pick a value to test
All five expressions are equal, so give them one shared value. Pick a positive number that 3 divides evenly. That way N will be a whole number.
Let the shared value be 12. Then , and each of the other four expressions also equals 12.
Solve for each letter
Undo each operation to find each letter. Divide to undo times. Multiply to undo divide. Subtract to undo plus.
Compare the values
The values are M = 12, N = 4, P = 48, Q = 7 and R = 84. R is the largest.
Watch out: 3N does not make N big. It means 3 times N equals M, so N is only one third of M. That trap points to choice B. Also, P is big, but R is bigger. Check every letter before you pick choice C.
So the answer is D, R.
Check your answer
Think without numbers. R divided by 7 is M, so R is 7 times M. P is only 4 times M. N is a third of M, and Q is 5 less than M. Since M is positive, 7 times M is the biggest.
More questions like this
The original DOE question
