3 English and 3 math
Here are 6 random questions to try. Takers earning below 75% are unlikely to receive an offer. You have 1 minute 48 seconds per question on the real exam.
Question 1 of 6
2018 Test B English, question 48Passage Invention of the Telegraph
Samuel Morse, an American inventor, is credited with creating the electronic telegraph, a communication device that allows users to send messages using a system of short and long pulses that represent letters, numbers, and punctuation. In 1843 the United States Congress passed the Telegraph Bill, which provided Morse with the funds to build an electric telegraph system.
Invention of the Telegraph
Earlier Signal Systems
Long before Samuel F. B. Morse electrically transmitted his famous message “What hath God wrought?” from Washington to Baltimore on May 24, 1844, there were signaling systems that enabled people to communicate over distances. Most were visual or “semaphore” systems using flags or lights. In the eighteenth century, such systems used an observer who would decipher a signal from a high tower on a distant hill and then send it on to the next station. The young American republic wanted just such a system along its entire Atlantic coast and offered a prize of $30,000 for a workable proposal. The framers of this legislation had no way of knowing that when they used the word “telegraph” to refer to this visual semaphore system, they would be offered an entirely new and revolutionary means of communication—electricity.
The Growth of an Idea
The idea of using electricity to communicate over distance is said to have occurred to Morse during a conversation aboard ship when he was returning from Europe in 1832. Michael Faraday’s recently invented electromagnet was much discussed by the ship’s passengers, and when Morse came to understand how it worked, he speculated that it might be possible to send a coded message over a wire. While a student at Yale College years before, he had written his parents a letter about how interesting he found the lectures on electricity. Despite what he had learned at Yale, Morse found when he began to develop his idea that he had little real understanding of the nature of electricity, and after sporadic attempts to work with batteries, magnets, and wires, he finally turned for help to a colleague at the University of the City of New York, Leonard D. Gale.
Gale was a professor of chemistry and familiar with the electrical work of Princeton’s Joseph Henry, a true pioneer in the new field. Well before Morse had his shipboard idea about a telegraph, Henry rang a bell at a distance by opening and closing an electric circuit. In 1831, he had published an article, of which Morse was unaware, that contained details suggesting the idea of an electric telegraph. Gale’s help and his knowledge of this article proved crucial to Morse’s telegraph system because Gale not only pointed out flaws in the system but showed Morse how he could regularly boost the strength of a signal and overcome the distance problems he had encountered by using a relay system Henry had invented. Henry’s experiments, Gale’s assistance, and, soon after, hiring the young technician Alfred Vail were keys to Morse’s success.
Obstacles and Opportunities
By December 1837, Morse had enough confidence in his new system to apply for the federal government’s appropriation, and during the next year he conducted demonstrations of his telegraph both in New York and Washington.
However, when the economic disaster known as the Panic of 1837 took hold of the nation and caused a long depression, Morse was forced to wait for better times. It was during this period that Morse visited Europe again and tried not only to secure patent protection overseas but to examine competing telegraph systems in England. . . .
By 1843, the country was beginning to recover economically, and Morse again asked Congress for the $30,000 that would allow him to build a telegraph line from Washington to Baltimore, forty miles away. The House of Representatives eventually passed the bill containing the Morse appropriation, and the Senate approved it in the final hours of that Congress’s last session. With President Tyler’s signature, Morse received the cash he needed and began to carry out plans for an underground telegraph line.
Realizing a Great Invention
Morse had hired the ingenious construction engineer Ezra Cornell to lay the pipe carrying the wire, and although Cornell did his job superbly, one of Morse’s partners, Congressman F. O. J. Smith, had purchased wire with defective insulation. Too much time had been wasted laying bad wire, and with the project on a rigid deadline, something had to be done quickly. Cornell suggested that the fastest and cheapest way of connecting Washington and Baltimore was to string wires overhead on trees and poles. The desperate Morse gave the go-ahead, and the line was completed in time for the dramatic and spectacularly successful link between the Supreme Court chamber of the Capitol building and the railroad station in Baltimore.
Soon, as overhead wires connected cities up and down the Atlantic coast, the dots-and-dashes method that recorded messages on a long moving strip of paper was replaced by the operator’s ability to interpret the code in real time. . . . Telegraph lines soon extended westward, and within Morse’s own lifetime they connected the continents of Europe and America.
“Invention of the Telegraph”—Public Domain/Library of Congress
legislation: Telegraph Bill
dots-and-dashes method: the short and long pulses of Morse code that are sent and received by telegraph operators
The first transatlantic electric telegraph message was sent in 1858, and by 1902 the British All-Red Line connected most of the world.
Source: U.S. Bureau of the Census. Historical Statistics of the United States, Colonial Times to 1970, Bicentennial Edition, Part 2. Washington, D.C., 1975.
Question
Which statement describes how the author’s use of problem-solution in paragraph 2 contributes to the development of ideas in the passage?
- AMorse’s discussion on a ship about Faraday’s electromagnet reminded him of the Yale College lectures on electricity, which he had enjoyed but had not fully understood, inspiring him to learn more about electricity from his colleague Gale.
- BMorse’s discouragement over his lack of knowledge of electricity prompted him to experiment with batteries, magnets, and wires, which led to the development of a new long-distance communication system.
- CMorse’s difficulty in understanding how Faraday’s electromagnet worked was frustrating, and it pushed him to create a system for sending signals over wires.
- DMorse’s longtime fascination was not enough to make up for his lack of knowledge about electricity, so he eventually sought help from Gale.
Show the answer
Correct answer: D
The question asks for the best explanation of how the use of problem-solution in paragraph 2 helps develop the ideas in the passage. Option D is correct because it explains that Morse realized his problem was that he was not knowledgeable enough to continue his experimentation without help, so the solution was to seek help from a colleague.
Option A is incorrect because, while the discussion on the ship fascinated Morse and reminded him of the lectures he had attended at Yale College, it was his failed attempts with electricity that caused him to reach out to Gale for help.
Option B is incorrect because, while “Morse found when he began to develop his idea that he had little real understanding of the nature of electricity” (paragraph 2), the paragraph does not state that he was discouraged; it was his failed experimentation that resulted in him first realizing that he needed help.
Option C is incorrect because the paragraph states that “Morse came to understand how [Faraday’s electromagnet] worked,” and that understanding is what caused him to think about sending messages over a wire. Also, Morse’s difficulty was in understanding the properties of electricity in general once he began his experimentation.
Question analysis
In this text structure question about “Invention of the Telegraph,” students explain how the problem-and-solution pattern in paragraph 2 develops ideas about Samuel Morse. All four choices are long sentences built from real details about the ship, Yale and Gale, so students must check each one’s account of what led to what.
- Grade level
- Grade 8 reading and task
- Compared with grade 7
- Above grade 7 Identifying problem and solution is familiar from earlier grades, but these choices are long, detail-packed chains in which a single misplaced cause makes an option wrong, which demands closer checking than typical grade 7 items.
- 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
- Every choice must be checked major
- A very close wrong answer moderate
- The right answer is reworded moderate
- A lot to read moderate
- How, not what minor
- Evidence
- Answered from one paragraph or stanza
- Reading level
- Passage: about grade 11, 910 words; question and choices: about grade 16, 132 words.
- Corrected from the DOE handbook
- A wrong paragraph number in the explanation was corrected.
- A misspelled name in the explanation was corrected.
- A punctuation slip in the explanation was corrected.
- Students, last 30 days
- Not enough answers yet to show (it takes 10).
Why it is hard, traps and wrong answers (shows the answer)
Why it is hard
Every choice is assembled from things the paragraph really mentions, so recognition is useless and only the order of causes decides. The most tempting wrong choice ends with Gale, the right solution, but invents a reminder of the Yale lectures to get there; others turn the failed experiments into the solution or reverse what Morse understood. The question rewards reading each long choice clause by clause, which costs time.
Every choice must be checked major Choosing the answer
Each choice is a chain of two or three causes built from real details, the ship, Faraday, Yale, the batteries and wires, Gale, so every link has to be checked against paragraph 2’s order of events. (Embretson & Wetzel, 1987)
A very close wrong answer moderate Choosing the answer
The Yale-reminder choice and the key both join Morse’s enjoyment of electricity, his weak grasp of it and his turn to Gale; they part on one detail, the claim that the shipboard talk “reminded him” of Yale, which the paragraph never makes. (Embretson & Wetzel, 1987; Gorin & Embretson, 2006; Ascalon et al., 2007)
The right answer is reworded moderate Choosing the answer
The key turns the Yale letter and the shipboard speculation into “longtime fascination,” a phrase the passage never uses, while the wrong choices repeat its names and phrases and so look better supported. (Freedle & Kostin, 1993; Kirsch & Mosenthal, 1990)
A lot to read moderate Understanding the question
The four choices run to about 110 words, the longest 37, and paragraph 2 itself packs a voyage, a college letter, failed experiments and a colleague into four sentences. (Kintsch, 1998; Gorin & Embretson, 2006; Freedle & Kostin, 1993)
How, not what minor Working it out
Students must name the paragraph’s problem, too little understanding of electricity, and its solution, Gale, before judging which account of the pattern is accurate. (Anderson & Krathwohl, 2001)
Strategy: Name the problem and the solution in paragraph 2 in a few words each, then choose the option whose sequence of events matches the paragraph exactly.
Traps
- Reversed relationship: Cause and effect, or the order of events, turned around.
- Half right: One half of a two-part choice is right and the other is not.
The wrong answers, classified
A Half right (King et al., 2004; Thissen, Steinberg & Fitzpatrick, 1989)
Ends correctly with Morse learning from Gale, but invents its cause: the paragraph never says the shipboard talk reminded Morse of Yale, and it skips the failed experiments that sent him to Gale.
B Reversed relationship (King et al., 2004)
Reverses cause and effect: the “sporadic attempts” with batteries, magnets and wires exposed Morse’s weak grasp of electricity and sent him to Gale, rather than flowing from discouragement and producing the system.
C Twists what the text says (King et al., 2004)
Says Morse struggled to understand Faraday’s electromagnet, but the paragraph states that he “came to understand how it worked,” and that understanding is what gave him the idea.
What was corrected from the DOE handbook, and why
- Explanation: The handbook places the sentence “Morse found when he began to develop his idea that he had little real understanding of the nature of electricity” in paragraph 3. It is in paragraph 2, the paragraph the question is about, so the site now says “(paragraph 2).”
- Explanation: The handbook spells Leonard Gale’s name “Gail.” The passage spells it “Gale,” and so does the site now.
- Explanation: The handbook capitalizes “Also” after a semicolon (“over a wire; Also, Morse’s difficulty…”). The site starts a new sentence instead: “over a wire. Also, Morse’s difficulty…”
Working it out, step by step
Figure out what the question asks
This asks about problem-solution in paragraph 2. Problem-solution is a way to organize writing. First you learn about a problem, then how someone solved it. Find the problem and the solution. Then pick the choice that tells them in the right order.
Find the problem in paragraph 2
Paragraph 2 starts with “The idea of using electricity to communicate over distance.” It says Morse had enjoyed the electricity lectures at Yale. But then comes the problem: “Morse found when he began to develop his idea that he had little real understanding of the nature of electricity.”
Find the solution
The same sentence goes on: “after sporadic attempts to work with batteries, magnets, and wires, he finally turned for help to a colleague.” “Sporadic” means now and then, not steady. A colleague is a coworker. So Morse was interested in the subject, tried on his own, and did not succeed. His interest was not enough. His solution was to ask Gale for help.
Check each choice
- A is wrong. It ends with Gale, but the paragraph never says the ship talk “reminded him” of Yale. It also skips the failed tries.
- B is wrong. It has the order backward. The experiments showed the problem. They did not build the system.
- C is wrong. The paragraph says Morse “came to understand how it worked,” meaning the electromagnet.
- D fits. Long interest was not enough, so he got help from Gale.
Choose the answer
The problem was Morse’s weak grasp of electricity, and the solution was Gale. So the answer is D, “Morse’s longtime fascination was not enough to make up for his lack of knowledge about electricity, so he eventually sought help from Gale.”
Why this answer and not the closest wrong one
A is the closest trap. Like D, it mentions Yale, Morse’s weak grasp of electricity and Gale. But it adds a link the paragraph never makes, that the ship talk reminded him of Yale. With long choices, check every part. One made-up link makes the whole choice wrong.
More questions like this
The original DOE question
The passage “Invention of the Telegraph” as printed (pages 146–148)
Question 2 of 6
2018 Test B English, question 31Passage 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
With which statement would the author of this excerpt most likely agree?
- AA sense of ease and assurance comes with accepting one’s fate.
- BNo matter where one’s path goes in life, one will always have regrets.
- CThe best way to overcome fear is to recognize it and then defy it.
- DReason will die out with humanity, but art will remain immortal.
Show the answer
Correct answer: A
The question asks for the statement the author would agree with most. In paragraph 4, the author states that the Falls make a person feel “with an almost insupportable and yet comforting certitude, that both men and nations are hurried onwards to their ruin or ending.” Later, the final sentence says, “With some such thoughts does the platitudinous heart win from the confusion and thunder of a Niagara peace.” This sentence supports the author’s belief that a person can find peace in accepting the certainty of his or her own ending, as expressed in Option A.
Option B is incorrect because the author does not discuss regrets in the excerpt.
Option C is incorrect because, while the excerpt discusses fear when looking at the power of the Falls, the excerpt does not support the idea that one should defy fear.
Option D is incorrect because the excerpt states in paragraph 4 that art and beauty are “caused by” the stream of life and end with it, “ceasing when it ceased.”
Question analysis
This question asks students to infer which statement about life the author of “Niagara Falls” would most likely agree with, based on the reflections that close his essay. It is hard because the evidence sits in long, abstract sentences of century-old prose and must be pieced together from more than one place in the final paragraph.
- Grade level
- Grade 9 reading and task
- Compared with grade 7
- Above grade 7 Grade 7 point-of-view questions usually rest on a clearly stated opinion. Here the author’s view must be pieced together from abstract reflection on lives, nations and the river, with words like “insupportable” and “platitudinous,” which is closer to high school reading.
- 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
- Complex sentences major
- The right answer is reworded moderate
- Hard words moderate
- Evidence
- Answered from one paragraph or stanza
- Reading level
- Passage: about grade 9, 987 words; question and choices: about grade 6, 61 words.
- Corrected from the DOE handbook
- A misreading of a word in the passage was corrected in the explanation.
- Students, last 30 days
- 47% right, of 15 answers
Why it is hard, traps and wrong answers (shows the answer)
Why it is hard
This question asks for the author’s outlook, which he reaches only in the closing sentences of a long, abstract paragraph. The mood there is gloomy, with ruin, a dark flood and human crying, so students who read the mood but not the argument choose regret. The comfort and peace he finds in that certainty are easy to miss in the inverted final sentence, and they are exactly what the answer rests on.
Reading between the lines major Working it out
The author never states a belief; students must combine “comforting certitude,” people who meet their end “unreluctant” and “not without nobility,” and the closing “peace” into an attitude of accepting fate. (Graesser, Singer & Trabasso, 1994; Kintsch, 1998)
Complex sentences major Understanding the question
The last sentence inverts normal order, “With some such thoughts does the platitudinous heart win from the confusion and thunder of a Niagara peace,” so its subject and object are hard to find. (Abedi & Lord, 2001; Freedle & Kostin, 1993; Messick, 1989)
The right answer is reworded moderate Choosing the answer
The right statement uses none of the passage’s words, turning “certitude” into “assurance” and “peace” into “ease,” while wrong choices pick up “fear” and “art.” (Freedle & Kostin, 1993; Kirsch & Mosenthal, 1990)
Hard words moderate Understanding the question
“Certitude,” “unreluctant,” “unavailing” and “platitudinous” carry the author’s attitude, and the glossary defines only the last of them. (Perfetti, 2007; Freedle & Kostin, 1993)
Strategy: Reread the second half of paragraph 4 slowly, translating each long sentence into plain words, then choose the statement those lines support without adding ideas the author never mentions.
Traps
- Outside knowledge: A choice is plausible in the real world but not supported by this text.
- Reads too much in: A reasonable-sounding conclusion that goes further than the text allows.
The wrong answers, classified
B Reads too much in (Graesser, Singer & Trabasso, 1994)
Reads “the white cloud of human crying” and the dark flood as a claim about lifelong regret, though the author never mentions regret and finds comfort in the end.
C Outside knowledge (King et al., 2004; Recht & Leslie, 1988)
Falls back on familiar advice about facing fears, prompted by the excerpt’s talk of terror, but the author recommends accepting what is inevitable, not defying it.
D Twists what the text says (King et al., 2004)
Reverses the friend’s rainbow comparison: art and beauty are “caused by” the stream of life and end with it, “ceasing when it ceased,” so art is not immortal.
What was corrected from the DOE handbook, and why
- Explanation: The handbook rejects Option D because paragraph 4 says art is “unable to stay.” In the passage, art and beauty are “unable to stay or direct or affect” the stream of life: “stay” means to stop or hold back the stream, not to last. What shows that art is not immortal is that it is “caused by” the stream of life and ends with it, “ceasing when it ceased,” which the site now quotes.
How 15 answers split, last 30 days
- A47%
- B7%
- C20%
- D27%
Working it out, step by step
Figure out what the question asks
This asks which statement the author would most likely agree with. He never states his belief outright, so you must infer it from his words, especially at the end of paragraph 4.
Find what he says about endings
In paragraph 4, he says that at Niagara one feels “with an almost insupportable and yet comforting certitude” that people and nations reach an end. He adds: “Some go down to it unreluctant, and meet it, like the river, not without nobility.” His last sentence says the heart can “win from the confusion and thunder of a Niagara peace.”
Put his words in plain English
“Certitude” means being sure. “Insupportable” means too hard to bear. So knowing that everything ends is hard, yet it is also comforting. “Unreluctant” means willing. Some people meet their end willingly, with dignity. And the Falls give the heart peace. Put together: accepting what must happen brings calm.
Check each choice
- A is right. He finds comfort and peace in accepting fate. That is “ease and assurance.”
- B is wrong. He never mentions regrets.
- C is wrong. He talks about accepting what must happen, not about fighting fear.
- D is wrong. Art and beauty are “caused by” life and end with it, “ceasing when it ceased.” So art does not last forever.
Watch out: “The white cloud of human crying” sounds sad, so B may tempt you. But sadness is not regret, and the author ends on peace.
Choose the answer
The author finds calm and comfort in accepting what must come. So the answer is A.
Why this answer and not the closest wrong one
B is the closest wrong answer, because paragraph 4 mentions human crying and ruin. But the author never talks about regret. He calls the certainty of an ending “comforting,” and the essay closes on the word “peace.” Feeling calm by accepting fate is what A says.
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 44Passage 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
Which word should be added to the beginning of sentence 8 to provide a better transition to the third paragraph (sentences 8–11)?
Move the correct answer to the box.
(8) ____ Opportunity continued to provide valuable data about craters and other surface features.
On the test you drag one of the tiles into the box; here, choose it.
- AOverall,
- BFurthermore,
- CMeanwhile,
- DConsequently,
Show the answer
Correct answer: C
The question asks for the word that should be added to the beginning of sentence 8 to provide a better transition to the third paragraph (sentences 8–11).
“Overall,” is incorrect and should not be added. While sentence 8 is a more general statement than sentence 7, the word “Overall” would imply that all of the third paragraph features general information about the Opportunity rover. Instead, paragraphs 2 and 3 both describe specific accomplishments of the Opportunity rover (the discovery of possible water on Mars and the distance the rover traveled), so these paragraphs require a word between them that does not transition from the specific to the general.
“Furthermore,” is incorrect and should not be added. The word “Furthermore” would suggest that the author is making an argument in paragraph 2 that is further developed by the statement in sentence 8 and the rest of paragraph 3. Because this is not the case, the word “Furthermore” is not a suitable transition from one paragraph to the next.
“Meanwhile,” is correct and should be added. The word “Meanwhile” is an appropriate transition to add to the beginning of sentence 8, since the actions of the Opportunity rover in paragraph 2 (taking photographs) and in paragraph 3 (traveling long distances) happened at the same time and both served critical functions to the overall mission.
“Consequently,” is incorrect and should not be added. The word “Consequently” would create a cause-and-effect relationship that does not exist between the paragraphs. The passage gives no indication that the rover’s actions in the third paragraph (traveling a far distance) resulted from the actions in the second paragraph (taking photographs).
Question analysis
In this transition question, sentence 8 opens the third paragraph of the Opportunity rover passage with a blank, and on the test students move one of four word tiles into the box. The paragraph before ends with the “blueberries,” small round rocks that hinted at water, so students must decide how the rover's further work relates to that discovery.
- NYS standards
- 7W2d transitions in informative writing
- Grade level
- Grade 7 reading and task
- Compared with grade 7
- Above grade 7 Choosing a transition is regular grade 7 writing work, but this one links two paragraphs, and two of the four words fit the sentence's grammar and sound natural, so the choice turns on exactly how the paragraphs relate.
- 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
- A very close wrong answer moderate
- How sentences fit together moderate
- Reading between the lines minor
- Evidence
- Answered from several paragraphs or stanzas
- Reading level
- Passage: about grade 11, 337 words; question and choices: about grade 9, 43 words.
- Students, last 30 days
- 27% right, of 11 answers
Why it is hard, traps and wrong answers (shows the answer)
Why it is hard
Two tiles sound natural in the blank, and the one most students reach for first is an all-purpose adding word. The key goes a step further: it marks the rover’s work in paragraph 3 as happening alongside the photographs of paragraph 2, a relationship the word “continued” supports. Students who test each tile against how the paragraphs relate, rather than against the sound of the sentence, also rule out a summing-up word and a cause word.
A very close wrong answer moderate Choosing the answer
“Furthermore” and “Meanwhile” both let paragraph 3 add to paragraph 2; only “Meanwhile” also says the rover’s further work went on during the same mission, as “continued” implies. (Embretson & Wetzel, 1987; Gorin & Embretson, 2006; Ascalon et al., 2007)
How sentences fit together moderate Working it out
The tile must link the “blueberries” of paragraph 2 to the craters and miles of paragraph 3, so students must decide how two paragraphs relate, not just two sentences. (Halliday & Hasan, 1976)
Reading between the lines minor Working it out
The timing is never stated; it comes from “During the rover’s mission” in sentence 4 and “continued” in sentence 8, which place both kinds of work in the same years. (Graesser, Singer & Trabasso, 1994; Kintsch, 1998)
Strategy: State in your own words how what the rover did in paragraph 2 relates to what it did in paragraph 3, then test the relationship each tile signals against that.
Traps
- Wrong transition: A connecting word or phrase that signals the wrong relationship, such as contrast where the idea continues.
The wrong answers, classified
A Wrong transition (Halliday & Hasan, 1976)
Treats sentence 8 as a summing up because it is broader than sentence 7, though paragraph 3 goes on to give new specifics such as the 28.06 miles.
B Wrong transition (Halliday & Hasan, 1976)
Adds paragraph 3 as one more achievement, which sounds natural, but “Furthermore” signals a point being built up, not two kinds of work carried on during one mission.
D Wrong transition (Halliday & Hasan, 1976)
Hears “continued” as a result of the blueberry discovery and adds a cause-and-effect link, though nothing says the rover’s later work followed from its photographs.
How 11 answers split, last 30 days
- A36%
- B36%
- C27%
- D0%
Working it out, step by step
Figure out what the question asks
On the test, you move one word tile into the box at the start of sentence 8. The word is a transition, a word that shows how two ideas connect. Some transitions add an idea, some show a result, some sum up, and some show time. You need the one that links paragraph 2 to paragraph 3.
Compare the two paragraphs
Paragraph 2 begins “During the rover’s mission.” It tells how the camera found the round rocks called “blueberries.” Paragraph 3 begins “Opportunity continued to provide valuable data about craters and other surface features.” Craters are bowl-shaped holes in the ground. So paragraph 3 tells about other work the rover kept doing in those same years.
Test each transition
- Overall sums things up. But paragraph 3 gives new facts, like the 28.06 miles.
- Furthermore adds one more reason to an argument, as in Dogs are loyal. Furthermore, they are fun. But paragraph 2 isn’t arguing a point. It tells what the rover did.
- Meanwhile means during that same time. It links things that go on together.
- Consequently means as a result. But the photos didn’t cause the rover’s later work.
See why “Meanwhile” fits
While the camera was finding blueberries, the rover was also studying craters and driving many miles. The word “continued” in sentence 8 shows that the work kept going. “Meanwhile” tells the reader these jobs happened during the same mission.
Watch out: “Furthermore” sounds natural in the blank, so many students choose B. But it only says here is one more point. It doesn’t show two kinds of work going on at the same time.
Choose the answer
With the tile in place, sentence 8 reads: Meanwhile, Opportunity continued to provide valuable data about craters and other surface features. So the answer is C: move the tile “Meanwhile,” into the box.
Why this answer and not the closest wrong one
B, “Furthermore,” is the closest wrong answer, because it also adds information. But it treats paragraph 2 as one point in an argument. The passage just tells what the rover did. “Meanwhile” links the two paragraphs in time, and it matches the word “continued.”
More questions like this
The original DOE question
The passage “The End of an Era” as printed (page 60)
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
- 50% right, of 20 answers
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.
How 20 answers split, last 30 days
- Right50%
- Wrong50%
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
2018 Test A Math, question 40Question
In the set of consecutive integers from 12 to 30, inclusive, there are four integers that are multiples of both 2 and 3. How many integers in this set are multiples of neither 2 nor 3?
- A5
- B6
- C13
- D15
Show the answer
Correct answer: B
The question asks for integers from 12 to 30 that are not divisible by 2 or 3. The set of consecutive integers is
{12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30}
Since all even numbers are divisible by 2, eliminate all even numbers, leaving the odd numbers in the set:
{13, 15, 17, 19, 21, 23, 25, 27, 29}
Eliminate those integers that are multiples of 3 (15, 21, and 27). The remaining integers are:
{13, 17, 19, 23, 25, 29}
Therefore, there are 6 numbers in the set that are multiples of neither 2 nor 3.
Question analysis
This number properties question takes the integers from 12 to 30, inclusive, and asks how many are multiples of neither 2 nor 3. Students must count the whole set, remove multiples of 2 and of 3 without removing any number twice, and count what remains. Inclusive endpoints and the overlap make it easy to miscount.
- NYS standards
- 6.NS.4 common factors and multiples
- Grade level
- Grade 6 content, by NYS standard
- Compared with grade 7
- Above grade 7 Multiples are sixth-grade content, but grade 7 problems rarely ask students to count a set under two overlapping conditions. The inclusive range and the numbers that are multiples of both make this longer and trickier than usual.
- 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
- Much to keep track of moderate
- A very close wrong answer moderate
- Solution
- 3 steps
- Reading level
- Question and choices: about grade 9, 30 words.
- Students, last 30 days
- 50% right, of 10 answers
Why it is hard, traps and wrong answers (shows the answer)
Why it is hard
The question gives the overlap, four multiples of both 2 and 3, which invites a subtraction method with three places to go wrong: the count of the set, the overlap, and the final complement. Each of those errors has its own choice. Listing the 19 numbers and crossing out evens and then odd multiples of 3 is slower to describe but faster and safer to do.
Much to keep track of moderate Working it out
Each of the 19 integers must be checked against two conditions, and the four multiples of 6 meet both, so they must be removed once, not twice. (Sweller, 1988; Carpenter, Just & Shell, 1990)
A very close wrong answer moderate Choosing the answer
The choices 5 and 6 differ by one, the result of counting 30 − 12 = 18 integers instead of 19, so only counting the inclusive set exactly separates them. (Embretson & Wetzel, 1987; Gorin & Embretson, 2006; Ascalon et al., 2007)
Strategy: Cross out every even number first, then cross out the odd multiples of 3 that remain, and count the survivors; listing all nineteen numbers is quick enough.
Traps
- Answers a different question: A choice is right for another quantity: the other unknown, the rest instead of the part, the part instead of the whole.
- Counting the ends: Inclusive or exclusive ends, fence posts, consecutive numbers: an answer that is one too many or too few, or an endpoint drawn open where it belongs closed (or the reverse).
The wrong answers, classified
A Counting the ends (Brown & Burton, 1978)
Counts 30 − 12 = 18 integers instead of 19, then subtracts the 13 multiples of 2 or 3 and gets 5.
C Answers a different question (King et al., 2004; Hegarty, Mayer & Monk, 1995)
Counts the integers that are multiples of 2 or 3, the 13 to be crossed out, and gives that count instead of the 6 left over.
D Misreads the question (Hegarty, Mayer & Monk, 1995)
Subtracts only the four multiples of both 2 and 3 from the 19 integers, reading "neither 2 nor 3" as "not both 2 and 3".
How 10 answers split, last 30 days
- A10%
- B50%
- C30%
- D10%
Worked solution, step by step
Formulas used
- Counting whole numbers in a list
- a is the first number and b is the last. n is how many whole numbers there are, counting both ends. You add 1 because subtracting counts the gaps, and there is one more number than gaps.
Sort out the question
The set is every integer (whole number) from 12 to 30. “Inclusive” means 12 and 30 are both in.
A multiple of 2 is an even number. A multiple of 3 is a number in the 3 times table. You need the numbers that are neither: not even, and not in the 3 times table.
Count the numbers in the set
There are 19 integers. Watch out: 30 − 12 = 18 forgets one end. That slip leads to choice A, 5.
Cross out the even numbers
Every even number is a multiple of 2, so remove them all. The odd numbers are left:
13, 15, 17, 19, 21, 23, 25, 27, 29
That is 9 numbers.
Cross out the multiples of 3
Check each odd number for 3. A quick test: add its digits. If the sum is in the 3 times table, so is the number. That removes 15, 21 and 27. These are left:
13, 17, 19, 23, 25, 29
Watch out: only 12, 18, 24 and 30 are multiples of both. Removing just those gives 19 − 4 = 15, choice D. “Neither” means you remove every multiple of 2 and every multiple of 3.
Count what is left
Six numbers are left. Watch out: 13 is how many you crossed out, choice C. The question asks for the ones left. So the answer is B, 6.
Check your answer
Count another way. Of the 19 numbers, 10 are even. Of the 9 odd ones, 3 are multiples of 3. So 10 + 3 = 13 are crossed out, and 19 − 13 = 6 are left. Same answer.
More questions like this
The original DOE question
Question 6 of 6
2024 Test B Math, question 44Question
Which inequality is equivalent to ?
- A
- B
- C
- D
Show the answer
Correct answer: D
Distribute the coefficient −2 on the right-hand side:
Subtract from both sides:
Add 10 to both sides:
Divide both sides by 5:
This is equivalent to
Question analysis
Students choose the simplest equivalent form of a linear inequality that has x on both sides and a negative number multiplied into parentheses. It tests distributing, combining like terms and solving inequalities. Sign errors in the distribution, and reading the direction of the final inequality, are where most mistakes happen.
- NYS standards
- Grade level
- Grade 8 content, by NYS standard
- Compared with grade 7
- Above grade 7 Grade 7 inequalities have the form px + q < r. This one has x on both sides and a negative factor to distribute across a subtraction, steps that belong to grade 8 equation work, so it is harder than typical grade 7 practice.
- Estimated difficulty
- Hard: combines ideas, needs a plan, and has more than one tempting wrong answer.
- Thinking it demands
- Depth of knowledge 1, recall and reproduction · mainly apply
- What makes it hard
- Error-prone arithmetic moderate
- A very close wrong answer moderate
- Many steps minor
- Solution
- 4 steps
- Reading level
- Question and choices: about grade 16+, 10 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 move is standard algebra, but the inequality is built so that small slips change the answer completely. The −2 has to reach both terms in the parentheses, and once the boundary −2 is found its direction still has to be read correctly, since the variable ends up on the right as −2 < x. Rewriting that as x > −2, or substituting x = 0 into the original, catches the trap.
Error-prone arithmetic moderate Working it out
Distributing −2 over (5 − 3x) gives −10 + 6x, two sign decisions in one move, and the x terms then sit on both sides of the inequality. (Brown & Burton, 1978; Junker & Sijtsma, 2001)
A very close wrong answer moderate Choosing the answer
x < −2 and x > −2 share the boundary and differ only in direction, which depends on reading −2 < x correctly or flipping the sign when dividing by a negative. (Embretson & Wetzel, 1987; Gorin & Embretson, 2006; Ascalon et al., 2007)
Many steps minor Working it out
Four moves follow one another, distributing, collecting 5x + 6x, moving the x terms and dividing by 5, and a slip at any of them changes the result. (Daniel & Embretson, 2010; Enright, Morley & Sheehan, 2002)
Strategy: Distribute the −2 to both terms in the parentheses, combine the x terms on the right, then gather the x terms on the side that keeps their coefficient positive.
Traps
- Order of operations: Working left to right, or distributing a minus sign wrongly, gives a choice.
- 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.)
- A faulty procedure: A systematic but wrong procedure: adding fractions straight across, applying an exponent to each term of a sum, dropping a sign when moving a term.
The wrong answers, classified
A A faulty procedure (Brown & Burton, 1978; Tatsuoka, 1983)
Treats 5 − 3x as 2, combining a number with an x term, so the right side becomes 5x − 4 and the solution x < 16.
B Order of operations (Brown & Burton, 1978)
Multiplies the −2 by the 5 but not by the −3x, writing 5x − 10 − 3x, which leads to 4x < 10 and x < 5/2.
C Negatives and direction (Brown & Burton, 1978)
Finds the boundary −2 but points the inequality the wrong way, by misreading −2 < x or by not flipping the sign after dividing by −5.
Worked solution, step by step
Formulas used
- Distributive property
- a is the number outside the parentheses. b and c are the terms inside. Multiply a by each one. A minus sign inside counts as a negative term, so 5 − 3x is 5 + (−3x). A negative times a negative is positive.
- Keeping an inequality true
- a and b are the two sides, and c is any number. Adding or subtracting the same number on both sides keeps the inequality true. Dividing both sides by a positive number also keeps it true. Only multiplying or dividing by a negative number flips the sign.
Sort out the question
An inequality compares two sides with a sign like <, which means is less than. To solve it, you get x alone on one side.
You need the short inequality that has the same answers as the long one.
Distribute the −2
Multiply −2 by both terms inside the parentheses, 5 and −3x.
A negative times a negative is positive, so the second part is +6x. Watch out: If the −2 multiplies only the 5, you end up with , choice B.
Combine the x terms
The right side is now 5x − 10 + 6x. Put the x terms together: 5x + 6x = 11x.
Gather the x terms on one side
Subtract 6x from both sides. That leaves the x terms on the right, where they stay positive.
Get x by itself
Add 10 to both sides. Then divide both sides by 5.
You divided by a positive 5, so the sign does not flip.
Read it with x first
says −2 is less than x. That is the same as saying x is greater than −2, just as 3 < 5 means 5 > 3.
Watch out: , choice C, has the same number but points the wrong way.
So the answer is D, .
Check your answer
Test x = 0, which is greater than −2. The left side is . The right side is . And −20 < −10 is true. Now test x = −3. The left side is −38 and the right side is −43. That is false, as it should be.
More questions like this
The original DOE question
