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
2024 Test B English, question 22Passage Excerpt from “How Exercise Could Help You Learn a New Language”
Excerpt from “How Exercise Could Help You Learn a New Language”
by Gretchen Reynolds
Many scientists suspect that exercise alters the biology of the brain in ways that make it more malleable and receptive to new information, a process that scientists refer to as plasticity.
But many questions have remained unanswered about movement and learning, including whether exercise is most beneficial before, during or after instruction and how much and what types of exercise might be best.
So for a new study, which was published recently in PLOS One, researchers in China and Italy decided to home in on language learning and the adult brain.
Language learning is interesting. As young children, almost all of us picked up our first language easily. We didn’t have to be formally taught; we simply absorbed words and concepts.
But by early adulthood, the brain generally begins to lose some of its innate language capability. It displays less plasticity in areas of the brain related to language. As a result, for most of us, it becomes harder to learn a second language after childhood.
To see what effects exercise might have on this process, the researchers first recruited 40 college-age Chinese men and women who were trying to learn English. The students had some facility with this second language but were far from proficient.
The researchers then divided the students into two groups. Those in one group would continue to learn English as they had before, primarily while seated in rote vocabulary-memorization sessions.
The others would supplement these sessions with exercise.
Specifically, the students would ride exercise bikes at a gentle pace (about 60 percent of their maximum aerobic capacity) beginning 20 minutes before the start of the lessons and continuing throughout the 15 minutes or so of instruction.
Both groups learned their new vocabulary by watching words projected onto large screens, together with comparable pictures, such as “apple” and a Red Delicious. They were shown 40 words per session, with the sequence repeated several times.
Afterward, the students all rested briefly and then completed a vocabulary quiz, using computer keys to note as quickly as possible whether a word was with its correct picture. They also responded to sentences using the new words, marking whether the sentences were accurate or, in the case of “The apple is a dentist,” nonsensical. Most linguists1 feel that understanding sentences shows greater mastery of a new language than does simple vocabulary improvement.
The students completed eight vocabulary sessions over the course of two months.
And at the end of each lesson, the students who had ridden bikes performed better on the subsequent vocabulary tests than did the students who sat still.
They also became more proficient at recognizing proper sentences than the sedentary students, although that difference did not emerge until after several weeks of instruction.
Perhaps most interesting, the gains in vocabulary and comprehension lingered longest for the cyclists. When the researchers asked the students to return to the lab for a final round of testing a month after the lessons—without practicing in the meantime—the cyclists remembered words and understood them in sentences more accurately than did the students who had not moved.
“The results suggest that physical activity during learning improves that learning,” says Simone Sulpizio, a professor of psychology and linguistics at the University Vita-Salute San Raffaele in Milan, Italy, and a study co-author.
These improvements extend beyond simply aiding in memorization, she added. The exercise also deepened language learners’ grasp of how to use their newly acquired words.
This study involved college students performing relatively light exercise, though, and cannot tell us whether other people completing other types of exercise would achieve the same results.
It also offers no clues about what is occurring inside the brain that might be contributing to the benefits of the exercise. But many past studies have shown that exercise prompts the release of multiple neurochemicals in the brain that increase the number of new brain cells and the connections between neurons, Dr. Sulpizio says. These effects improve the brain’s plasticity and augment the ability to learn.
From a real-world standpoint, the study’s implications might seem at first to be impractical. Few classrooms are equipped with stationary bicycles. But specialized equipment is probably unnecessary, Dr. Sulpizio says.
“We are not suggesting that schools or teachers buy lots of bicycles,” she says. “A simpler take-home message may be that instruction should be flanked by physical activity.”
From “How Exercise Could Help You Learn a New Language” by Gretchen Reynolds from THE NEW YORK TIMES, August 16, 2017. Copyright © 2017 The New York Times Company.
1linguists: scientists who study language
Question
Which evidence from the excerpt is most relevant to the author’s claim that there are many unanswered questions about the relationship between movement and learning?
- Athe method of the study using one type of exercise and people from one age group
- Bthe statement from Sulpizio explaining past studies on neurochemicals in the brain
- Cthe finding of the study that exercise helps people recall information over a long period of time
- Dthe statement from Sulpizio describing how the results of the study can be applied
Show the answer
Correct answer: A
The question asks which evidence from the excerpt is most relevant to the author’s claim that there are many unanswered questions about the relationship between movement and learning.
A. CORRECT. While the study revealed that the college students who used exercise bikes did better in their language learning, paragraph 18 indicates that we cannot know “whether other people completing other types of exercise would achieve the same results,” suggesting that there are many unknowns about the relationship between movement and learning.
B. Incorrect. Rather than supporting the claim that there are many unanswered questions about the relationship between movement and learning, this statement offers a possible explanation as to why exercise might improve learning.
C. Incorrect. The finding that exercise helps people retain their language learning longer (paragraph 15) adds to our understanding of the relationship between movement and learning rather than supporting the claim that there are still many unanswered questions.
D. Incorrect. Sulpizio’s statement that the study suggests that “ ‘instruction should be flanked by physical activity’ ” (paragraph 21) does not in any way address the issue of unanswered questions about movement and learning.
Question analysis
This evidence question asks which part of the exercise and language-learning article is most relevant to the author’s early claim that many questions about movement and learning remain unanswered. The choices describe parts of the article in general terms rather than quoting them, so students must locate each one and judge how it bears on that claim.
- Grade level
- Grade 8 reading and task
- Compared with grade 7
- Above grade 7 Grade 7 students trace claims and judge whether evidence is relevant. Here the claim appears early, the evidence is described in summary rather than quoted, and students must see an indirect link across the article, which demands more than usual.
- 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 evaluate
- What makes it hard
- Reading between the lines moderate
- Evidence in several places moderate
- Evidence
- Answered from several paragraphs or stanzas
- Reading level
- Passage: about grade 11, 764 words; question and choices: about grade 11, 84 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 choices describe evidence instead of quoting it, so each must first be located and then weighed against a claim made near the start of the article. The trap is the neurochemical statement: its paragraph begins by admitting what the study cannot show, but the statement itself offers an answer from past research. The key is easy to undervalue because it sounds like a plain description of the method, until it is linked to paragraph 18’s account of what the study cannot tell us.
Reading between the lines moderate Working it out
The right choice names a method, not a question; students must see that one light exercise tried on college students leaves open paragraph 2’s “what types of exercise might be best,” as paragraph 18 says. (Graesser, Singer & Trabasso, 1994; Kintsch, 1998)
Evidence in several places moderate Working it out
The claim sits in paragraph 2, and the choices are short labels that must be traced to paragraphs 15, 18, 19 and 21 before any of them can be judged. (Kirsch & Mosenthal, 1990; Gorin & Embretson, 2006)
Strategy: Reread the claim in paragraph 2, then find where each choice’s material appears in the article and ask how directly it bears on that claim.
Traps
- True but not the answer: A choice says something accurate about the text that does not answer this question.
- Supports only part of the claim: In a question about evidence: a line that backs one half of the claim but not the other, or a related point rather than the claim itself.
The wrong answers, classified
B Supports only part of the claim (King et al., 2004; Thissen, Steinberg & Fitzpatrick, 1989)
Comes from paragraph 19, which opens with something the study cannot explain, but Sulpizio’s point about neurochemicals offers an answer from past research, not an open question.
C True but not the answer (King et al., 2004; Embretson & Wetzel, 1987)
Reads the claim as being about how movement and learning are related and picks a key finding, but lasting recall answers a question rather than showing one remains open.
D True but not the answer (King et al., 2004; Embretson & Wetzel, 1987)
Remembers Sulpizio’s practical advice to flank lessons with activity, a real statement that applies the findings and says nothing about what is still unknown.
Working it out, step by step
Figure out what the question asks
The author claims there are many unanswered questions about movement and learning. You need the evidence that best supports that claim. Evidence is the facts that back up a point. So look for something that shows a question is still open, not something that answers one.
Find the claim
Paragraph 2 says “many questions have remained unanswered about movement and learning.” It names some. One is whether exercise helps most “before, during or after instruction.” Another is “how much and what types of exercise might be best.” Instruction means teaching.
Find what the study left open
The study used one kind of exercise, light biking. It also used one age group, college students. Paragraph 18 says the study “cannot tell us whether other people completing other types of exercise would achieve the same results.” So the question of “what types of exercise” work best is still open. That is what choice A describes.
Check the other choices
- B: in paragraph 19, Sulpizio says past studies show exercise releases “neurochemicals,” or brain chemicals, that help learning. That offers an answer, not an open question.
- C: the finding in paragraph 15, that cyclists remembered words longer, answers a question.
- D: Sulpizio’s advice in paragraph 21 says how to use the results. It says nothing about what is still unknown.
Watch out: Paragraph 19 begins with something the study can’t explain, so B is tempting. But Sulpizio’s statement itself gives an explanation.
Pick the answer
Only the study’s narrow method shows that big questions remain. So the answer is A.
Why this answer and not the closest wrong one
B is the closest wrong answer, because its paragraph starts by admitting the study “offers no clues” about the brain. But Sulpizio then fills that gap with what past studies found. A points to what is truly still unknown: whether other people and other kinds of exercise would get the same results.
More questions like this
The original DOE question
The passage “Excerpt from “How Exercise Could Help You Learn a New Language”” as printed (pages 171–172)
Question 2 of 6
2026 Practice Test B English, question 22Passage Excerpt from In Search of the Unknown
Excerpt from In Search of the Unknown
by Robert W. Chambers
It was at that time the policy of the trustees and officers of the Zoological Gardens neither to employ collectors nor to send out expeditions in search of specimens. The society decided to depend upon voluntary contributions, and I was always busy, part of the day, in dictating answers to correspondents who wrote offering their services as hunters of big game, collectors of all sorts of fauna, trappers, snarers, and also to those who offered specimens for sale, usually at exorbitant rates.
To the proprietors of . . . mangy lynxes, moth-eaten coyotes, and dancing bears I returned courteous but uncompromising refusals—of course, first submitting all such letters, together with my replies, to Professor Farrago.
One day towards the end of May, however, just as I was leaving Bronx Park to return to town, Professor Lesard, of the reptilian department, called out to me that Professor Farrago wanted to see me a moment; so I . . . retraced my steps to the temporary, wooden building occupied by Professor Farrago, general superintendent of the Zoological Gardens. The professor, who was sitting at his desk before a pile of letters and replies submitted for approval by me, pushed his glasses down and looked over them at me with a whimsical smile that suggested amusement, impatience, annoyance, and perhaps a faint trace of apology.
“Now, here’s a letter,” he said, with a deliberate gesture towards a sheet of paper impaled on a file—“a letter that I suppose you remember.” He disengaged the sheet of paper and handed it to me.
“Oh yes,” I replied, with a shrug; “of course the man is mistaken—or—”
“Or what?” demanded Professor Farrago, tranquilly, wiping his glasses.
“—Or a liar,” I replied.
After a silence he leaned back in his chair and bade me read the letter to him again, and I did so with a contemptuous tolerance for the writer, who must have been either a very innocent victim or a very stupid swindler. I said as much to Professor Farrago, but, to my surprise, he appeared to waver.
“I suppose,” he said, with his near-sighted, embarrassed smile, “that nine hundred and ninety-nine men in a thousand would throw that letter aside and condemn the writer as a liar or a fool?”
“In my opinion,” said I, “he’s one or the other.”
“He isn’t—in mine,” said the professor, placidly.
“What!” I exclaimed. “Here is a man living all alone on a strip of rock and sand between the wilderness and the sea, who wants you to send somebody to take charge of a bird that doesn’t exist!”
“How do you know,” asked Professor Farrago, “that the bird in question does not exist?”
“It is generally accepted,” I replied, sarcastically, “that the great auk has been extinct for years. Therefore I may be pardoned for doubting that our correspondent possesses a pair of them alive.”
“Oh, you young fellows,” said the professor, smiling wearily, “you embark on a theory for destinations that don’t exist.”
He leaned back in his chair, his amused eyes searching space for the imagery that made him smile.
“Like swimming squirrels, you navigate with the help of Heaven and a stiff breeze, but you never land where you hope to—do you?”
Rather red in the face, I said: “Don’t you believe the great auk to be extinct?”
“Audubon saw the great auk.”
“Who has seen a single specimen since?”
“Nobody—except our correspondent here,” he replied, laughing.
I laughed, too, considering the interview at an end, but the professor went on, coolly:
“Whatever it is that our correspondent has—and I am daring to believe that it is the great auk itself—I want you to secure it for the society.”
When my astonishment subsided my first conscious sentiment was one of pity. Clearly, Professor Farrago was on the verge of dotage—ah, what a loss to the world!
I believe now that Professor Farrago perfectly interpreted my thoughts, but he betrayed neither resentment nor impatience. I drew a chair up beside his desk—there was nothing to do but to obey, and this fool’s errand was none of my conceiving.
Together we made out a list of articles necessary for me and itemized the expenses I might incur, and I set a date for my return, allowing no margin for a successful termination to the expedition.
“Never mind that,” said the professor. “What I want you to do is to get those birds here safely. Now, how many men will you take?”
“None,” I replied, bluntly; “it’s a useless expense, unless there is something to bring back. If there is I’ll wire you, you may be sure.”
“Very well,” said Professor Farrago, good-humoredly, “you shall have all the assistance you may require. Can you leave to-night?”
The old gentleman was certainly prompt. I nodded, half-sulkily, aware of his amusement.
“So,” I said, picking up my hat, “I am to start north to find a place called Black Harbor, where there is a man named Halyard who possesses, among other household utensils, two extinct great auks—”
We were both laughing by this time. I asked him why on earth he credited the assertion of a man he had never before heard of.
“I suppose,” he replied, with the same half-apologetic, half-humorous smile, “it is instinct. I feel, somehow, that this man Halyard has got an auk—perhaps two. I can’t get away from the idea that we are on the eve of acquiring the rarest of living creatures. It’s odd for a scientist to talk as I do; doubtless you’re shocked—admit it, now!”
But I was not shocked; on the contrary, I was conscious that the same strange hope that Professor Farrago cherished was beginning, in spite of me, to stir my pulses, too.
“If he has—” I began, then stopped.
The professor and I looked hard at each other in silence.
“Go on,” he said, encouragingly.
But I had nothing more to say, for the prospect of beholding with my own eyes a living specimen of the great auk produced a series of conflicting emotions within me which rendered speech profanely superfluous.
From IN SEARCH OF THE UNKNOWN by Robert W. Chambers—Public Domain
Audubon: John James Audubon, an ornithologist and artist who created scientific illustrations of birds
dotage: a loss of reasoning brought about by old age
Question
How does the author develop the contrast between the narrator’s point of view and the professor’s point of view?
- Aby providing both the narrator’s and professor’s thoughts on how age and experience influence each other’s reasoning
- Bby using the conversation between the narrator and the professor to emphasize their reactions to the letter
- Cby describing the professor’s persistent efforts to change the narrator’s mind about the letter
- Dby including dialogue that explains why the professor is the supervisor and the narrator is his subordinate
Show the answer
Correct answer: B
The question asks how the author develops the contrast between the narrator’s point of view and the professor’s point of view.
A. Incorrect. The excerpt does not describe the narrator’s thoughts about how age and experience influence the professor’s reasoning in enough detail to fully contrast them against the thoughts about the narrator that the professor expresses in paragraphs 15–17. The narrator’s idea that the professor might be “on the verge of dotage” (paragraph 24) is meant in a humorous way.
B. CORRECT. The primary conflict of the excerpt revolves around the narrator’s disagreement with the professor about whether the letter about the great auks could be true. As the two men converse, their contrasting attitudes toward the letter become clear: the narrator dismisses the possibility of great auks out of hand (“ ‘of course the man is mistaken’ ” [paragraph 5]; “ ‘here is a man . . . who wants you to send somebody to take charge of a bird that doesn’t exist!’ ” [paragraph 12]), while the professor calmly admits that although “ ‘nine hundred and ninety-nine men in a thousand would throw that letter aside and condemn the writer’ ” (paragraph 9), he himself believes that the writer could be telling the truth (“ ‘How do you know,’ asked Professor Farrago, ‘that the bird in question does not exist?’ ” [paragraph 13]).
C. Incorrect. The professor explains why he disagrees with the narrator (paragraphs 19–21), but he does not make persistent efforts to convince the narrator to change his mind about the letter. Instead he states that the narrator will go on an expedition to retrieve “ ‘whatever it is that our correspondent has’ ” (paragraph 23), thereby requiring the narrator to go collect the great auks whether the narrator believes in them or not.
D. Incorrect. The point of the dialogue is not to explain the subordinate-supervisor relationship between the narrator and the professor but rather to contrast what each character believes about the contents of the letter.
Question analysis
This point-of-view question asks how Robert W. Chambers develops the contrast between the narrator’s outlook and Professor Farrago’s in the excerpt from In Search of the Unknown. Students must step back from single lines and judge the author’s method across the whole excerpt. The choices describe techniques in general terms, and several connect to real moments in the story.
- Grade level
- Grade 8 reading and task
- Compared with grade 7
- Above grade 7 Analyzing how an author contrasts two characters’ points of view is the grade 7 standard itself, but here students must judge the main method across the whole excerpt, and each choice names an abstract method that touches something in the text.
- 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
- A very close wrong answer moderate
- Evidence in several places moderate
- Evidence
- Answered from the whole text
- Reading level
- Passage: about grade 9, 1066 words; question and choices: about grade 11, 84 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 right choice is plain enough to seem too obvious, so students look for something more specific. The excerpt offers a candidate: the professor teases “you young fellows,” and the narrator decides the old man is near “dotage,” which makes age look like the method. Those remarks are passing jokes, while the men’s opposite reactions to Halyard’s letter run through the whole conversation. The question rewards judging what carries the contrast from start to end rather than what is most striking.
How, not what major Working it out
The question asks for the author’s method across the whole excerpt, and every choice names an abstract technique, so students must step back from single lines to see that the dialogue carries the contrast. (Anderson & Krathwohl, 2001)
A very close wrong answer moderate Choosing the answer
The choice about age and experience and the right one both describe the two men’s opposed views as they come out in the excerpt; they part on the subject, their ages or the letter. (Embretson & Wetzel, 1987; Gorin & Embretson, 2006; Ascalon et al., 2007)
Evidence in several places moderate Working it out
The contrast builds from the narrator’s “of course the man is mistaken” in paragraph 5 to the professor’s appeal to “instinct” in paragraph 33, so no single passage shows the method. (Kirsch & Mosenthal, 1990; Gorin & Embretson, 2006)
Strategy: For each choice, find where the excerpt does what the choice describes, and ask whether that method carries the contrast through the whole excerpt or appears only once or twice.
Traps
- Too narrow: A single detail offered as the central idea or a summary, or a summary that keeps minor details and leaves out an essential part.
- Twists what the text says: Uses the text's topic and ideas but changes what it says: who did it, how much, when, or why.
- Wrong 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.
The wrong answers, classified
A Too narrow (King et al., 2004)
Notices the jab at “you young fellows” and the narrator’s thought of “dotage,” but two passing remarks about age are not how the author builds the contrast across the excerpt.
C Twists what the text says (King et al., 2004)
Overstates the professor’s role, since he asks a few calm questions and then simply assigns the trip, never working to win the narrator over.
D Wrong purpose or structure (Anderson & Krathwohl, 2001)
Knows that the professor is the superior, but no line of dialogue explains how either man got his position; the talk is about the letter, not their ranks.
Working it out, step by step
Figure out what the question asks
This asks about the author’s method. How does the author show that the two men see things differently? Look at how the whole excerpt is built, not just one line.
Notice how the excerpt is told
Most of the excerpt is a conversation. The two men talk back and forth about the letter. Each answer shows how one man reacts to it. So their reactions to the letter are where the contrast shows up. A contrast is a clear difference between two things.
Find the two reactions
The narrator says “of course the man is mistaken” (paragraph 5). He laughs at the idea of “a bird that doesn’t exist!” (paragraph 12). The professor stays open. In paragraph 13 he asks how the narrator can be sure “that the bird in question does not exist.” In paragraph 23, he is “daring to believe” it is the great auk.
Check each choice
- A does not fit. Age comes up only twice: “you young fellows” and the narrator’s thought about “dotage.” Two short remarks do not build the contrast.
- B fits. The talk about the letter shows their opposite reactions.
- C does not fit. The professor asks a few calm questions and then simply sends the narrator. He does not keep trying to change his mind.
- D does not fit. No line explains how either man got his job.
Watch out: A is tempting because those remarks about age are real. But they are passing moments, not the author’s main method.
Choose the answer
The author builds the contrast through the two men’s talk about the letter. So the answer is B, “by using the conversation between the narrator and the professor to emphasize their reactions to the letter.”
Why this answer and not the closest wrong one
A is the closest wrong choice. The professor does tease “you young fellows,” and the narrator does think of “dotage.” But those are two quick remarks. From paragraph 5 to paragraph 33, the two men keep reacting to the letter in opposite ways. That steady back-and-forth builds the contrast, so B fits.
More questions like this
The original DOE question
The passage “Excerpt from In Search of the Unknown” as printed (page 21)
Question 3 of 6
2024 Test A English, question 8Passage The Free College Debate
The Free College Debate
(1) A college degree has become an essential tool in an increasingly competitive job market. (2) Yet the price of higher education, at both private and public universities, continues to rise. (3) Helping students cover the cost of attending college is an important issue.
(4) Many people agree that a college education should be a financially realistic option for those who aspire to obtain a degree. (5) For example, in 2017, the New York State legislature passed a bill creating a program to cover the tuition costs for nearly one million students. (6) The state of Tennessee also has a program that offers all students scholarships and mentoring services if they attend one of the state’s community colleges. (7) Proponents generally believe that these programs are a step in the right direction for making college affordable for students who would have had to take out loans or who would have decided not to pursue higher education at all.
(8) On the other hand, some people oppose bills like the ones in New York and Tennessee because they believe “free” college programs are unsustainable. (9) In order to implement these types of programs, a state pays the college on behalf of the students using funds from the state’s budget, which primarily comes from state taxes. (10) As more students choose to attend college, more funds will be needed to cover the costs. (11) Additionally, many students do not finish college within four years because they switch majors or because they have to work. (12) Critics believe that these circumstances will inevitably lead to an increase in taxes, a decline in the quality of the education offered by the schools, or both. (13) They think narrower college-affordability efforts that target the students who need the most support, such as first-generation college students, may be more effective and viable solutions.
(14) Faculty and students at higher-education institutions can work to keep costs down. (15) In light of increased access to computers, mobile devices, and the Internet, there are more opportunities for students to take courses online, thus reducing the need for and cost of maintaining physical classrooms. (16) Additionally, colleges should account for experience by allowing students to demonstrate their knowledge in order to avoid having to pay to sit through classes on subjects they have already mastered. (17) Similarly, college-bound high school students need to be prepared for college-level work so that they do not have to spend money on remedial classes.
(18) The solutions to the problems associated with rising college costs are not simple. (19) Passing legislation that boosts college affordability will take time, input from experts with different ideas, and careful planning.
Question
Which phrase should be added before sentence 14 to best transition to the ideas in the fourth paragraph (sentences 14–17)?
- ABecause college affordability is a complicated issue,
- BWith so many opinions about how to make college affordable,
- CUntil college becomes more affordable,
- DAlthough some college affordability programs have been successful,
Show the answer
Correct answer: C
The question asks which phrase should be added before sentence 14 to best transition to the ideas in the fourth paragraph (sentences 14–17).
A. Incorrect. Sentence 13 summarizes the viewpoint of opponents, who believe that targeted approaches to funding education “may be more effective and viable solutions,” and sentence 14 serves to introduce how “faculty and students at higher-education institutions can work to keep costs down.” Affordability is “a complicated issue,” but the use of the word “Because” suggests that the ideas that follow in sentences 14–17 will explain a cause-and-effect relationship. However, sentences 14–17 discuss ways faculty and students should work together to keep the cost of college down while waiting for a long-term solution to the problem, not a causal relationship.
B. Incorrect. Sentences 4–13 provide information about the viewpoint of proponents, who believe that “a college education should be a financially realistic option for those who aspire to obtain a degree” (sentence 4), and opponents, who believe free college programs are “unsustainable” (sentence 8). Although the phrase in this option mentions “opinions,” it indicates that the fourth paragraph will discuss why the number of opinions makes affordability a debatable issue. Instead, the fourth paragraph discusses ways faculty and students can help keep costs down until a solution is reached.
C. CORRECT. Sentence 13 summarizes the viewpoint of opponents, who believe that targeted approaches to funding education “may be more effective and viable solutions,” while proponents “generally believe that these [government] programs are a step in the right direction for making college affordable” (sentence 7). However, sentences 14–17 offer three possible solutions that could alleviate the problem in the meantime. Therefore, the phrase in this option should be added before sentence 14 to best transition to the ideas in the fourth paragraph because it suggests that until the issue of affordability is resolved, alternatives are available to help make a college education more affordable.
D. Incorrect. This phrase mentions “college affordability,” a topic discussed in the fourth paragraph. However, the ideas introduced in the phrase do not logically lead into the ideas discussed in sentences 14–17, because the phrase mentions “programs [that] have been successful,” whereas the paragraph states that “faculty and students at higher-education institutions can work to keep costs down” (sentence 14) and that colleges “should account for experience by allowing students to demonstrate their knowledge in order to avoid having to pay to sit through classes on subjects they have already mastered” (sentence 16). Use of the words “can” and “should” in these sentences indicates that the actions or programs mentioned in the paragraph have not been completed.
Question analysis
This revising question asks which introductory phrase should begin the fourth paragraph of a passage on college affordability, linking the debate over state tuition programs to the cost-saving ideas that follow. All four phrases sound natural, so students must work out the relationship between the paragraphs and choose the phrase that signals it accurately.
- NYS standards
- 7W2d transitions in informative writing
- Grade level
- Grade 8 reading and task
- Compared with grade 7
- Above grade 7 Grade 7 transition work usually links two sentences with a word such as however. Here the choices are whole phrases that set up an entire paragraph, and judging them needs a grasp of the full argument, which asks more than typical grade 7 work.
- Estimated difficulty
- Hard: combines ideas, needs a plan, and has more than one tempting wrong answer.
- Thinking it demands
- Depth of knowledge 3, strategic thinking · mainly evaluate
- What makes it hard
- How sentences fit together major
- Reading between the lines moderate
- Every choice must be checked minor
- Evidence
- Answered from several paragraphs or stanzas
- Reading level
- Passage: about grade 12, 427 words; question and choices: about grade 10, 48 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 phrase sounds like a reasonable bridge, and the right one can even seem odd at first, since cutting costs is itself a way to make college affordable. The key is seeing paragraph 4 as what campuses can do while the debate over state programs goes on, a reading the passage confirms only at its end. Students who link back to the many opinions, or accept a causal “Because,” have found real ideas from the passage but not the relationship between these two paragraphs.
How sentences fit together major Working it out
The phrase must link paragraph 3's case against state programs to paragraph 4's steps that “can work to keep costs down,” steps that make sense only as help in the meantime. (Halliday & Hasan, 1976)
Reading between the lines moderate Working it out
Nothing says paragraph 4's ideas are stopgaps; that has to be inferred from sentences 18 and 19, which say the solutions “are not simple” and “will take time.” (Graesser, Singer & Trabasso, 1994; Kintsch, 1998)
Every choice must be checked minor Choosing the answer
All four phrases are grammatical and about affordability, so each must be read into sentence 14 and judged by the relationship its first word signals. (Embretson & Wetzel, 1987)
Strategy: Sum up paragraphs 3 and 4 in a few words each, decide how the second relates to the first, then test the relationship each phrase's opening word signals.
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)
Agrees that affordability is complicated, as sentence 18 says, but “Because” makes the complexity the reason faculty and students can cut costs, a cause the paragraph never gives.
B Wrong transition (Halliday & Hasan, 1976)
Rightly looks back to the clashing views of paragraphs 2 and 3, but offers the disagreement as the ground for the steps instead of marking them as help until a solution arrives.
D Wrong transition (Halliday & Hasan, 1976)
Hears “Although” as a natural turn to a new idea, but the passage never says any program has succeeded, and paragraph 4 does not set its steps against such programs.
Working it out, step by step
Figure out what the question asks
You need a phrase to start sentence 14. It should work as a transition: a word or phrase that shows how two ideas connect. Words like “because,” “although” and “until” each show a different link. So first work out how paragraph 4 connects to what came before.
Compare paragraphs 3 and 4
Paragraph 3 ends with the critics’ view of state programs. People still disagree, so there is no fix everyone accepts yet. Paragraph 4 then says “Faculty and students at higher-education institutions can work to keep costs down.” Faculty means teachers. The paragraph lists ways to do it: online classes, skipping classes you’ve mastered, and getting ready in high school.
Use the ending as a clue
Sentences 18 and 19 say the solutions “are not simple” and “will take time.” So a big fix is still far off. That makes paragraph 4’s ideas things to do in the meantime, while people wait. The phrase “Until college becomes more affordable” says exactly that.
Check each choice
- A is wrong. “Because” shows a cause. The issue being complicated is not the reason teachers can cut costs.
- B is wrong. It makes the many opinions the reason for the steps. The passage never links them that way.
- C is right. “Until” shows these are steps to take while waiting for a bigger fix.
- D is wrong. The passage never says any program has been successful.
Watch out: B looks back at the many opinions, which really are in the passage. But it doesn’t show how paragraph 4 relates to paragraph 3.
Choose the answer
Sentence 14 would read: Until college becomes more affordable, faculty and students at higher-education institutions can work to keep costs down. So the answer is C.
Why this answer and not the closest wrong one
B is the closest wrong answer, because the passage does share many opinions. But “With so many opinions” makes the opinions sound like the reason for the cost-cutting steps. They are not. C shows the steps are help for now, while the bigger problem waits to be solved.
More questions like this
The original DOE question
The passage “The Free College Debate” as printed (page 38)
Question 4 of 6
2018 Test A Math, question 21Question
In a sample of 10 cards, 4 are red and 6 are blue. If 2 cards are selected at random from the sample, one at a time without replacement, what is the probability that both cards are not blue?
- A
- B
- C
- D
Show the answer
Correct answer: A
The probability that both cards are not blue is the same as the probability that both cards are red. There are 4 red cards out of the 10, so the probability of the first card being red is
Now there are 9 cards left, and 3 of those are red, so the probability of the second card being red is
Multiply the two probabilities to find the probability that both cards are red (not blue):
Question analysis
This probability question draws 2 cards, one at a time and without replacement, from 10 cards: 4 red and 6 blue. Students find the chance that neither card drawn is blue. The second draw has one fewer card, and the word not changes which color to count.
- NYS standards
- Grade level
- Grade 7 content, by NYS standard
- Compared with grade 7
- Above grade 7 Grade 7 compound probability is usually found with a list or tree of equally likely outcomes. Dependent draws without replacement, plus a negative phrasing to translate, go beyond that typical work.
- Estimated difficulty
- Hard: combines ideas, needs a plan, and has more than one tempting wrong answer.
- Thinking it demands
- Depth of knowledge 2, skills and concepts · mainly apply
- What makes it hard
- Something you must already know moderate
- A very close wrong answer moderate
- Turning words into math minor
- An answer in an unexpected form minor
- Solution
- 3 steps
- Reading level
- Question and choices: about grade 5, 39 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 ideas stack here: restating not blue as red, and changing the second draw's numbers after a card is removed. Students who know to multiply but forget the removal reach a listed choice, and so do students who compute both blue. Writing the second fraction explicitly as 3 red out of 9 cards, before multiplying, is what separates right from nearly right.
Something you must already know moderate Working it out
Multiplying the first draw's chance by the second draw's, with the second adjusted for the card already taken, is a rule the test assumes and does not give. (Anderson & Krathwohl, 2001)
A very close wrong answer moderate Choosing the answer
2/15 and 4/25 are about 0.13 and 0.16, too close to tell apart by estimate; only the second draw's fraction, 3 red of 9 cards rather than 4 of 10, separates them. (Embretson & Wetzel, 1987; Gorin & Embretson, 2006; Ascalon et al., 2007)
Turning words into math minor Understanding the question
"Both cards are not blue" has to be restated as both cards red, and the bold not also invites computing the chance that both are blue. (Hegarty, Mayer & Monk, 1995; Koedinger & Nathan, 2004)
An answer in an unexpected form minor Choosing the answer
The product comes out as 12/90, and it has to be reduced to lowest terms before it matches any of the listed fractions. (Enright, Morley & Sheehan, 2002)
Strategy: Restate not blue as red, then multiply the chance of red on the first draw by the chance of red on the second, with one card fewer.
Traps
- Without replacement: In a second pick there is one fewer item, which changes the probability.
- Misreads the question: Misses or misreads a condition or a word in the question: "at least", "each", "remaining", "not".
The wrong answers, classified
B Without replacement (Fischbein & Schnarch, 1997)
Multiplies 4/10 × 4/10 = 16/100 = 4/25, as if the first red card were put back before the second draw.
C Little reason to choose it (Haladyna & Downing, 1993; Rodriguez, 2005)
No standard working gives 3/10: it is not the chance of red or of blue on one draw or on two, so it mostly catches guesses.
D Misreads the question (Hegarty, Mayer & Monk, 1995)
Computes the chance that both cards are blue, 6/10 × 5/9 = 30/90 = 1/3, missing the bold word not.
Worked solution, step by step
Formulas used
- Probability
- P is the probability, the chance that something happens. Favorable is the number of ways to get what you want, here a red card. Total is the number of all possible picks, here all the cards you can pick from. It works when every pick is equally likely.
- Two events in a row
- A is the first event and B is the second. P( ) means the probability of what is inside. The chance that both happen is the first chance times the second. For the second chance, count only what is left after the first event.
Sort out the question
There are 10 cards: 4 red and 6 blue. You pick 2 cards “one at a time without replacement”. That means the first card is not put back. “Both cards are not blue” means both are red, since red is the only other color. You need the probability, or chance, of that.
Find the chance the first card is red
4 of the 10 cards are red. Each card is equally likely to be picked. Use the probability formula.
Find the chance the second card is red
One red card is gone now, and it is not put back. So 9 cards are left, and 3 of them are red.
Watch out: using 4/10 again acts as if the card went back. That gives 4/25, choice B.
Multiply the two chances
Both cards must be red. So multiply the first chance by the second. To multiply fractions, multiply the tops, then multiply the bottoms.
Simplify the fraction
None of the choices is 12/90, so simplify it. Divide the top and the bottom by 6, the biggest number that goes into both.
Watch out: the chance that both are blue is , choice D. The question says not blue. So the answer is A, .
Check your answer
Count the ways. There are ways to pick two cards in order. Red then red has ways. That gives 12/90, or 2/15. The answer is small, which makes sense, because there are fewer red cards than blue ones.
More questions like this
The original DOE question
Question 5 of 6
2024 Test A Math, question 39Question
Raquel is cutting out pieces of cardboard to make a pyramid. She will use a square piece for the base and identical triangular pieces for the sides. The figure above shows the dimensions of the triangle for each side. What will be the total surface area, in square inches, of the pyramid, including the square base?
- A280
- B295
- C340
- D360
Show the answer
Correct answer: C
Surface area is found by calculating the area of each side, including the base, and adding them all together.
The base of the pyramid measures 10 inches on each side, so the area of the base is
Each triangular face has a base of 10 inches and a height of 12 inches, so the area of each face is
There are 4 triangular faces (because the square base has 4 edges, each of which will have a triangular face). So the total surface area of the pyramid is the sum of the areas of 4 triangles and 1 square.
So the total surface area is 340 square inches.
Question analysis
This surface area word problem shows one triangular face, with sides of 13 inches, a base of 10 inches and a height of 12 inches, that Raquel will use to build a cardboard pyramid with a square base. Students find the total area of the base and all the triangular sides. Picturing the solid and choosing the right measurements from the figure are the tricky parts.
- Grade level
- Grade 7 content, by NYS standard
- Compared with grade 7
- Above grade 7 Grade 7 students find the surface area of a pyramid from a drawn net or solid. Here only one triangular face is shown, so students must picture the whole pyramid, count its faces, and choose which labeled length belongs in the area formula.
- Estimated difficulty
- Hard: combines ideas, needs a plan, and has more than one tempting wrong answer.
- Thinking it demands
- Depth of knowledge 2, skills and concepts · mainly apply
- What makes it hard
- Reading a figure, table or graph moderate
- Combines ideas moderate
- Something you must already know minor
- Solution
- 4 steps
- Reading level
- Question and choices: about grade 6, 56 words.
- Corrected from the DOE handbook
- A wrong unit in the explanation was corrected.
- Students, last 30 days
- Not enough answers yet to show (it takes 10).
Why it is hard, traps and wrong answers (shows the answer)
Why it is hard
Students have to build the pyramid in their heads from one flat triangle, then choose the right measurement from three labels. The 13-inch sides look like the natural height, and using them gives a listed total; picturing a pyramid with three sloping faces gives another. Sketching the square base with a triangle on each edge, and marking 12 as the height, settles both the face count and the formula.
Reading a figure, table or graph moderate Understanding the question
The figure gives one triangle with three length labels, 13, 13 and 10, and puts its height, 12, on a separate arrow beside it, where it is easy to overlook. (Lesh, Post & Behr, 1987; Kirsch & Mosenthal, 1990)
Combines ideas moderate Working it out
The solid is never drawn: students must see that the square's side equals the triangle's 10-inch base, count four triangles, and add triangle and square areas. (Embretson, 1998; Daniel & Embretson, 2010)
Something you must already know minor Working it out
A triangle's area uses its perpendicular height, not a slanted side, and a pyramid on a square base has four triangular faces; neither fact is given. (Anderson & Krathwohl, 2001)
Strategy: Sketch the pyramid: a square base whose side is the triangle's base, and one triangular face on each side of the square. Find each area with the matching formula, then add them all.
Traps
- Misreads the figure: Reads a value, label or tick spacing in a figure, table or graph wrongly.
- Information you don't need: The question gives numbers or facts that play no part in the answer.
- Misunderstands the concept: A wrong belief about a concept: that percents can be added, that area grows like length, that averages can be averaged, that a bigger denominator means a bigger fraction.
The wrong answers, classified
A Misunderstands the concept (Smith, diSessa & Roschelle, 1993; De Bock et al., 1998; Ni & Zhou, 2005)
Counts only three triangular faces, as if the pyramid had a triangular base, so 3 × 60 + 100 = 280.
B Misunderstands the concept (Smith, diSessa & Roschelle, 1993; De Bock et al., 1998; Ni & Zhou, 2005)
Counts three faces and also uses the 13-inch side as each triangle's height: 3 × 65 + 100 = 295.
D Misreads the figure (Lesh, Post & Behr, 1987; Kirsch & Mosenthal, 1990)
Takes the 13-inch slanted side as each triangle's height instead of the 12-inch arrow beside it, so 4 × 65 + 100 = 360.
What was corrected from the DOE handbook, and why
- Explanation: The handbook ends “So the total surface area is 340 square feet.” The triangle’s dimensions are in inches and the question asks for square inches, so the site now reads “340 square inches.”
Worked solution, step by step
Formulas used
- Area of a triangle
- A is the area. b is the base, the side the triangle sits on. h is the height: the straight-up distance from the base to the top corner, at a right angle to the base. You take half because a triangle is half of a rectangle with the same base and height.
- Area of a square
- A is the area and s is the length of one side. All four sides of a square are equal, so the area is side times side.
- Surface area
- A face is one flat side of a solid shape. The surface area is the total area of the outside. Picture unfolding the solid into flat pieces. Then add up the area of every piece.
Sort out the question
Raquel’s pyramid has a square base. Each side is a triangle like the one in the figure. The triangle’s base is 10 in. Its two slanted sides are 13 in. Its height, the arrow beside it, is 12 in. You need the total surface area, including the square base, in square inches.
Picture the pyramid
Surface area is the total area of all the flat sides, called faces. Each triangle stands on one edge of the square. So each edge of the square is 10 inches, the same as the triangle’s base. A square has 4 edges, so the pyramid has 4 triangles.
Here that is 4 triangles plus 1 square. Watch out: counting only 3 triangles gives 280, choice A.
Find the area of one triangle
Each triangle is 60 square inches. Watch out: the height is 12 in., the straight-up arrow. It is not 13 in., the slanted side. Using 13 gives 65 for each triangle and 360 in all, choice D.
Find the area of the base
The base is a square with sides of 10 inches, the same as each triangle’s base.
The square base is 100 square inches.
Add all five faces
The four triangles and the square together cover 340 square inches.
So the answer is C, 340 square inches.
Check your answer
Each triangle is half of a 10 by 12 rectangle, which has an area of 120. So two triangles make 120, and four make 240. Add the base: . The units fit too: inches times inches gives square inches.
More questions like this
The original DOE question
Question 6 of 6
2018 Test A Math, question 1Question
In the figure above, PQRS is a parallelogram. What is the value of ?
Grid-in question: work out the answer and enter it as a number.
Show the answer
Correct answer: 162
First, find the measure of angle PQR. The measure of angle PQR is equal to the measure of angle PSR.
m∠PSR = 180 − 72 = 108.
So, the measure of angle PQR is also 108.
108 + 90 + x = 360
198 + x = 360
x = 162
Question analysis
A grid-in geometry question about angles around a parallelogram PQRS. A 72° angle sits outside corner S on the extended base, and at corner Q a right angle and the unknown angle x complete the turn around the point. Students chain three angle facts, and the angle asked for lies outside the shape, not inside it.
- NYS standards
- Grade level
- Grade 8 content, by NYS standard
- Compared with grade 7
- Above grade 7 Grade 7 angle work usually applies one or two facts, such as supplementary or vertical angles, to find an angle. This chains three, and needs the equal opposite angles of a parallelogram, which rest on grade 8 parallel-line facts.
- Estimated difficulty
- Hard: combines ideas, needs a plan, and has more than one tempting wrong answer.
- Thinking it demands
- Depth of knowledge 2, skills and concepts · mainly apply
- What makes it hard
- Reading a figure, table or graph major
- Combines ideas moderate
- An answer in an unexpected form minor
- Solution
- 3 steps
- Reading level
- Question and choices: about grade 7, 14 words.
- Students, last 30 days
- Not enough answers yet to show (it takes 10).
Why it is hard, traps and wrong answers (shows the answer)
Why it is hard
The arithmetic is two subtractions; the difficulty is seeing which angles the marks refer to. Students lose points by treating the 72° as the parallelogram's own angle at S, or by stopping at angle PQR, the most natural number to grid. The question rewards tracing a route from S to Q before computing anything, and checking at the end that x is the angle outside the shape that the arc marks.
Reading a figure, table or graph major Understanding the question
The 72° is marked outside the parallelogram, between side SR and the base extended past S, and x sits outside corner Q, between QP and a vertical ray that meets QR at a right-angle mark. (Lesh, Post & Behr, 1987; Kirsch & Mosenthal, 1990)
Combines ideas moderate Working it out
Three angle facts have to be chained: a straight line gives the angle inside S, opposite angles of a parallelogram carry it to Q, and the angles around Q make a full 360° turn. (Embretson, 1998; Daniel & Embretson, 2010)
An answer in an unexpected form minor Choosing the answer
As a grid-in there are no choices to check against, so a student who stops at angle PQR, inside the parallelogram, gets no signal that the job is unfinished. (Enright, Morley & Sheehan, 2002)
Strategy: Use the straight line at S to find the parallelogram's angle there, carry it to the opposite corner Q, then take that angle and the right angle away from 360.
Traps
- Stops one step early: A choice is a number from partway through the solution.
The wrong answers, classified
108 Stops one step early (King et al., 2004; Gierl et al., 2017)
Finds angle PSR = 180 − 72 = 108 and carries it to angle PQR, then grids that interior angle instead of the angle x outside it.
198 Misreads the figure (Lesh, Post & Behr, 1987; Kirsch & Mosenthal, 1990)
Reads the 72° as the parallelogram's interior angle at S, so takes angle PQR as 72 and grids 360 − 90 − 72 = 198.
252 Misreads the figure (Lesh, Post & Behr, 1987; Kirsch & Mosenthal, 1990)
Overlooks the right-angle mark at Q and subtracts only the 108° angle PQR from 360, giving 252.
Worked solution, step by step
Formulas used
- Angles on a straight line
- a and b are two angles side by side on a straight line. Together they make a half turn, so they always add up to 180 degrees. Use it when an angle you need shares a straight line with an angle you know.
- Opposite angles of a parallelogram
- The symbol ∠ means angle. ∠PQR is the angle at corner Q, between sides QP and QR. ∠PSR is the angle at the opposite corner, S. In a parallelogram, opposite corners always have equal angles, because the shape leans the same way at both.
- Angles around a point
- a, b and c are angles that fit around one point with no gaps and no overlaps. Going all the way around is a full turn, which is 360 degrees. So the angles add up to 360.
Sort out what the figure shows
PQRS is a parallelogram. That is a four-sided shape whose opposite sides are parallel, which means they never meet. You need the value of x, in degrees.
Look closely at the marks. The 72° angle is outside the shape, at S. It sits between side SR and the base line, which keeps going past S. At Q, a vertical line meets side QR. The small square means a right angle, 90°. The angle x is outside the shape too. It runs from that vertical line around to side QP.
Find the angle inside corner S
Angle PSR is the shape’s own angle at S. It sits right next to the 72° angle, on the same straight base line. So the two angles add up to 180°.
So angle PSR is 108°. Watch out: 72° is not the inside angle at S. Using 72 as the inside angle leads to the wrong answer 198.
Carry the angle over to Q
Corners Q and S are opposite each other. In a parallelogram, opposite angles are equal. So angle PQR matches angle PSR.
So angle PQR is 108°. Watch out: this is not x. Angle PQR is inside the shape, and x is outside it. Stopping here and gridding 108 is the most common mistake.
Add the angles around Q
Three angles fill the space all the way around point Q. They are the right angle (90°), angle PQR (108°) and x. Together they make a full turn.
Watch out: don’t skip the right angle at Q. Leaving out the 90 gives 252.
Solve for x
Subtract 198 from 360 to find what is left for x.
So x is 162°. So you would grid 162.
Check your answer
Add the three angles at Q: . That is a full turn. Also, the arc for x is wider than a right angle but not as wide as a straight line. So x should be between 90° and 180°, and 162° is.
More questions like this
The original DOE question
