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 18Passage 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 sentence is the best summary of the research procedure used in the study in the excerpt?
- AResearchers had a group of non-English-speaking students learn new English vocabulary by matching words and images on a computer screen, and also by analyzing words in context; some students exercised and some students sat still while learning.
- BResearchers first divided non-English-speaking students into two groups, with one group exercising before and while studying English and the other group studying English without exercising; then, after instruction, student learning was assessed.
- CResearchers first had non-English-speaking students sit on stationary bikes and pedal for 20 minutes before instruction and 15 minutes during instruction; then, after a rest period, students indicated whether English sentences made sense.
- DResearchers asked non-English-speaking students to study English while sitting or biking; then the students’ vocabulary skills were assessed after a short break period and also after a break of a full month without their having studied any of the materials.
Show the answer
Correct answer: B
The question asks for the best summary of the research procedure used in the study in the excerpt.
A. Incorrect. This summary says that students learned new words by matching words and images and “also by analyzing words in context,” but this last method was how the researchers assessed students, not how the students learned words; the summary is therefore inaccurate.
B. CORRECT. The summary includes the most important information, which is that one group of non-English-speaking students exercised before and during the English lessons, while the other group did not, and that the students’ learning was assessed afterward.
C. Incorrect. This summary is incomplete because it never mentions the control group—that is, the students who studied English without exercising—which was essential to the study so that results could be compared.
D. Incorrect. This summary includes unnecessary details, such as that students were assessed after a short break and also assessed after a month of no studying; it also neglects to mention important points: that one group exercised both before and during learning, while the other group did not exercise at all.
Question analysis
This summary question asks which of four long sentences best sums up how the researchers ran the study of exercise and English vocabulary learning. Each choice packs in real details about bikes, screens, quizzes and timing, so students must check both whether every detail is accurate and whether anything essential to the study’s design has been left out.
- Grade level
- Grade 8 reading and task
- Compared with grade 7
- Above grade 7 Grade 7 students summarize texts, usually choosing among short summaries. Here each choice runs about forty words packed with accurate details from several paragraphs, and students must judge which keeps the study’s essential design, not merely which details are true.
- 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 understand
- What makes it hard
- A very close wrong answer major
- Evidence in several places moderate
- A lot to read moderate
- Evidence
- Answered from several paragraphs or stanzas
- Reading level
- Passage: about grade 11, 764 words; question and choices: about grade 16+, 157 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
Most of what the wrong summaries say is true, which makes this a test of completeness and weight rather than of accuracy. One summary describes only the cyclists, another slips the sentence quiz into how words were taught, and the most tempting one is accurate but leaves out that the cyclists pedaled before the lesson as well as during it. The right summary is plainer than its rivals: two groups, one exercising, then a test.
A very close wrong answer major Choosing the answer
The sitting-or-biking summary is accurate and names both conditions, as the right one does, but it spends its words on the short rest and the month-later test instead of when the cyclists rode. (Embretson & Wetzel, 1987; Gorin & Embretson, 2006; Ascalon et al., 2007)
Evidence in several places moderate Working it out
The procedure runs from the recruiting in paragraph 6 through the groups, bikes, lessons and quiz in paragraphs 7–12 to the final test in paragraph 15, so it must be gathered before any summary is judged. (Kirsch & Mosenthal, 1990; Gorin & Embretson, 2006)
A lot to read moderate Understanding the question
Each summary is a 32- to 40-word sentence packed with real details, the 20 minutes of pedaling, the rest period, the month without study, so the four together form a dense passage of their own. (Kintsch, 1998; Gorin & Embretson, 2006; Freedle & Kostin, 1993)
Strategy: Before reading the choices, note in a few words how the study was set up and how learning was checked. Then test each summary for accuracy and for anything essential it leaves out.
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.
The wrong answers, classified
A Twists what the text says (King et al., 2004)
Adds that students learned “by analyzing words in context,” but judging sentences was part of the quiz after each lesson, while the words were taught with pictures on large screens.
C Too narrow (King et al., 2004)
Follows the cyclists’ routine accurately, 20 minutes before and during the lesson, but leaves out the group that studied without exercise, so the comparison at the heart of the study disappears.
D Too narrow (King et al., 2004)
Is drawn by accurate details about the short rest and the month-later test, but it builds the summary around them and leaves out that the cyclists rode before the lessons too.
Working it out, step by step
Figure out what the question asks
You need the best summary of how the study was done. A summary gives the main parts in a few words. It must be accurate, and it can’t leave out anything important. Small details can be skipped.
Find the main parts of the study
- Paragraph 7: “The researchers then divided the students into two groups.”
- Paragraphs 8 and 9: one group rode bikes “beginning 20 minutes before the start of the lessons and continuing throughout the 15 minutes or so of instruction.” The other group sat still.
- Paragraph 11: then all the students took a quiz.
So the key parts are two groups, one that exercised, and a test afterward. The group that sat still matters. It lets the researchers compare.
Check each choice
- B has it all: two groups, one exercising “before and while studying,” then a test.
- A says students learned by “analyzing words in context.” But judging sentences was part of the quiz, not the lessons.
- C describes only the bike riders. It leaves out the group that sat still, so nothing gets compared.
- D spends its words on small details: the short break and the test a month later. It leaves out that the bike riders started 20 minutes before the lesson.
Pick the answer
Watch out: D is tempting because everything in it is true. But a summary should give the main parts, not the side details. So the answer is B.
Why this answer and not the closest wrong one
D is the closest wrong answer. Its facts are accurate, and it names both groups. But it builds the summary around the break and the month-later test. It never says the cyclists rode before the lessons too. B gives the main plan plainly: two groups, one exercising, then a test of learning.
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
2024 Test A English, question 55Passage Excerpt from “It’s Time to Stop Thinking That All Non-Native Species Are Evil”
Excerpt from “It’s Time to Stop Thinking That All Non-Native Species Are Evil”
by Emma Marris
The author of this opinion article attended a symposium, or conference, in Missoula, Montana, at which biologists and other scientists discussed species of plants and animals that are not native to the areas in which they live.
Invasive species are scary. It was ecologist Charles Elton, back in the 1950s, who introduced the militaristic “invasion” metaphor to describe exotic plants and animals—but there’s no question some can be extremely destructive.
The brown tree snake has eaten a dozen kinds of forest birds in Guam to extinction; zebra mussels clog pipes around the Great Lakes; the common house cat turns out to be, in Australia, a mercilessly effective killer of cute, fluffy marsupials like the bilby and the numbat.
As scientists have sounded the alarm about these pests, the public has gotten the message. Citizen groups rip out non-native plants. Native gardens have become increasingly popular, both as ways to celebrate the unique flora of each region and as tiny hot spots of diversity. Native trees provide food for native bugs, which feed native birds. Food chains developed over thousands of years of co-evolution unfold in our backyards. . . .
So we’ve learned, scientists and laypeople alike, that native species are good and non-natives are bad.
Julian Olden, a biologist at the University of Washington, Seattle, who co-organized the symposium, recently polled nearly 2,000 ecologists. Among his findings: a substantial number of them said they would immediately eradicate a hypothetical non-native forest plant, even if it were shown to have no effect on the forest. Olden calls this the “guilty even when proven innocent” approach.
That kind of approach is not very useful on a rapidly changing planet.
Exotics Are Everywhere
Climate change is making it harder even to decide who the invaders are.
How, scientists at the symposium wondered, do you define “native” on a warming planet, when plants and animals are already moving toward the poles or up mountainsides in search of climate conditions they can tolerate? Should we consider them “invasive” in their new homes? Regardless of what we label them, conservationists will be reluctant to remove them from their new environs—to do so would stymie1 their chances of adapting to the warmer future we’re creating.
And then there are the non-natives that we actually like. Most domestic crops are exotic in most of the places they’re grown, but there are even wild exotics that “do good,” forming useful relationships with native species.
Edwin Grosholz of the University of California, Davis, told the recent symposium about one such relationship. On beaches in his state, non-native spartina grass has become important habitat for the endangered California clapper rail, a plump shorebird with a downward curving bill more at home on land than in the air. A project to rip out and poison the spartina—which grows in dense swaths that exclude many other shorebirds—saw clapper rail numbers go tumbling downward.
There are other examples like that. The endangered southwestern willow flycatcher nests in “invasive” tamarisk shrubs. Many native (and beautiful) Hawaiian flowers are now pollinated by the Japanese white-eye bird—because the native pollinators have been driven extinct by other non-native species.
Should we impose further risk on already endangered natives by severing these relationships? Or should we admire the resilience of nature and let such “well-behaved” exotics stay? . . .
Leave them alone, more and more conservationists are arguing, and stop focusing obsessively on categorizing species as native or non-native. Mark Davis, an ecologist at Macalester College in St. Paul, Minnesota, once considered himself an “invasion biologist”—but not anymore. “I am actively trying to get the field to retire the invader narrative,” he said in Missoula.
A Good Thing, Not the Only Thing
After all, nativeness is just one environmental value, and arguably not as important as preventing extinctions and preserving biodiversity. In some cases we can best serve biodiversity by leaving the non-natives alone or even—brace yourself, now—introducing them on purpose.
This is the thinking behind, for example, installing the Aldabra tortoise on the islands of Mauritius. The islands lost their own large tortoises, and the fruiting plants that formerly had their seeds moved around by these fruit-loving reptiles have been on the decline. A tortoise that’s related to the island’s large tortoises—a non-native from the Seychelles in the Indian Ocean that was intentionally introduced in 2004—is now handling some of that work.
Most of the time, for the time being, conserving species still means focusing on supporting them in their historical habitats, planting natives and removing non-natives. We can and should do that in places where it is feasible and important to us.
From “It’s Time to Stop Thinking That All Non-Native Species Are Evil” by Emma Marris from NATIONAL GEOGRAPHIC MAGAZINE, July 24, 2014. Copyright © 2014 by National Geographic Society.
1stymie: hinder or interfere with
Question
The details in the section “A Good Thing, Not the Only Thing” convey a central idea of the excerpt by suggesting that
- Asome non-native species can replace native species that are unable to survive on their own.
- Bdecisions about whether to keep non-native species should be considered on an individual basis.
- Cthe scientists who study rapidly changing ecosystems agree that non-native species enhance biodiversity.
- Da natural habitat that is healthy should be able to support a blend of native and non-native species.
Show the answer
Correct answer: B
The question asks how the details in the section “A Good Thing, Not the Only Thing” convey a central idea of the excerpt.
A. Incorrect. While paragraph 15 does discuss introducing non-native Aldabra tortoises to replace native tortoises that no longer exist, the real point of this section is to show that non-native species can sometimes help support native species that still exist but are struggling. In this case, the Aldabra tortoises are now moving seeds around for the fruiting plants on the islands where the tortoises have been introduced.
B. CORRECT. This section discusses situations in which non-native species should be kept (as in the example of the Aldabra tortoises in paragraph 15) but also asserts that “most of the time . . . conserving species still means focusing on supporting them in their historical habitats, planting natives and removing non-natives” (paragraph 16). This section makes the point that the issue of non-natives needs to be considered on a case-by-case basis.
C. Incorrect. This section does not claim that non-native species always or even usually enhance biodiversity; rather, it states that “in some cases we can best serve biodiversity by leaving the non-natives alone or even—brace yourself, now—introducing them on purpose” (paragraph 14), later adding that “most of the time . . . conserving species still means focusing on supporting them in their historical habitats, planting natives and removing non-natives” (paragraph 16).
D. Incorrect. While the section happens to give a good example of a habitat that supports both native and non-native species (the islands of Mauritius), it never suggests that being able to do so is a defining characteristic of healthy habitats.
Question analysis
This central-idea question asks how the details in the final section of an article on non-native species, titled “A Good Thing, Not the Only Thing,” convey a central idea of the excerpt. Students must sum up the section as a whole, including its example of a tortoise brought to the islands of Mauritius, and match it to the article's larger argument.
- Grade level
- Grade 8 reading and task
- Compared with grade 7
- Above grade 7 Explaining how a section conveys a central idea is grade 7 work, but this section mixes an argument, an example and a closing paragraph, and the choices differ in how far they generalize from it, which demands more than typical.
- Estimated difficulty
- Hard: combines ideas, needs a plan, and has more than one tempting wrong answer.
- Thinking it demands
- Depth of knowledge 3, strategic thinking · mainly understand
- What makes it hard
- The right answer is reworded moderate
- Evidence in several places moderate
- Evidence
- Answered from several paragraphs or stanzas
- Reading level
- Passage: about grade 11, 815 words; question and choices: about grade 11, 82 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 section's most memorable content is an example, the Aldabra tortoise doing the work of the islands' lost tortoises, and a choice built on it is the strongest pull. The central idea sits instead in the qualifiers at the start and end of the section: some cases favor non-natives, most still call for removing them. Students who summarize all three paragraphs in a sentence, including the last, arrive at the case-by-case reading.
The right answer is reworded moderate Choosing the answer
The right choice's “on an individual basis” appears nowhere in the section, while the wrong choices echo it: a non-native standing in for natives, “biodiversity”, natives alongside non-natives. (Freedle & Kostin, 1993; Kirsch & Mosenthal, 1990)
Evidence in several places moderate Working it out
The case-by-case idea comes only from joining paragraph 14's “In some cases” to paragraph 16's “Most of the time” and “where it is feasible and important to us”. (Kirsch & Mosenthal, 1990; Gorin & Embretson, 2006)
Strategy: Sum up the section's three paragraphs in one sentence of your own, including its example and its final paragraph, then compare that sentence with each choice.
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.
- Too broad or too strong: A choice overstates, generalizes, or uses absolute words the text does not support.
- Reads too much in: A reasonable-sounding conclusion that goes further than the text allows.
The wrong answers, classified
A Too narrow (King et al., 2004)
Builds on the Aldabra tortoise standing in for Mauritius's lost tortoises, a single example, and misses the closing point that most conservation still means removing non-natives.
C Too broad or too strong (King et al., 2004)
Turns “In some cases” into a consensus that non-natives enhance biodiversity, though the section limits the claim and the article shows ecologists divided over it.
D Reads too much in (Graesser, Singer & Trabasso, 1994)
Draws a rule about healthy habitats from the Mauritius example, though the section never defines a healthy habitat or says it should hold a mix of species.
Working it out, step by step
Know what the question asks
A section is a part of an article under its own heading. This one runs from paragraph 14 to paragraph 16. You need to sum up the whole section, including its last paragraph. Then match that summary to a central idea.
Read paragraph 14
It says that “in some cases” we help nature most “by leaving the non-natives alone.” We might even bring them in “on purpose.” The words “in some cases” are the key. They mean sometimes, not always.
Read the example and the ending
Paragraph 15 gives an example. A non-native tortoise was brought to Mauritius to spread the seeds of fruiting plants. Then paragraph 16 says that “most of the time,” saving species still means “planting natives and removing non-natives.” We should do that “where it is feasible and important to us.” Feasible means possible.
Put the section together
Sometimes it is best to keep a non-native species. Most of the time it is best to remove it. So each case has to be judged on its own. That is what “on an individual basis” means.
Check each choice
- B fits: deciding case by case matches both “in some cases” and “most of the time.”
- A is wrong because the tortoise is one example, and the section ends by saying removal is still the usual choice.
- C is wrong because the section never says scientists agree, and “in some cases” is far from always.
- D is wrong because the section never says what a healthy habitat should hold.
Watch out: A is built on the section’s most memorable detail. But the main idea comes from the words that limit the claim.
Choose the answer
The section says to keep non-natives in some cases and remove them in others. So the answer is B.
Why this answer and not the closest wrong one
A comes closest, because the Aldabra tortoise really does take over work the lost tortoises once did. But that is one case. The section ends by saying that most of the time we still remove non-natives. B covers both sides: some cases call for keeping them, and others call for removing them.
More questions like this
The original DOE question
The passage “Excerpt from “It’s Time to Stop Thinking That All Non-Native Species Are Evil”” as printed (pages 68–70)
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
2026 Practice Test C Math, question 35Question
If , what is the value of a in terms of b?
Enter your answer in the space provided. Enter only your answer.
On the test you build the answer on an on-screen keypad; here, type it. Use ^ for a power, sqrt( ) or √ for a root, pi for π, and <= or >= for ≤ and ≥.
Show the answer
Correct answer: a = 10b
To find the value of a in terms of b, solve for a. Begin by distributing 4 on the left side of the equation:
Then, get the a terms on one side and the b terms on the other:
Solve for the value of a in terms of b by combining like terms and then dividing each side by 2:
Question analysis
An algebra question gives an equation with a and b on both sides, one side written as 4 times a sum in parentheses, and students type a in terms of b after a printed "a =". It tests the distributive property and solving linear equations. The answer is typed, so a slip in distributing or moving terms is not caught by any choices.
- NYS standards
- Grade level
- Grade 8 content, by NYS standard
- Compared with grade 7
- Above grade 7 Grade 7 students solve equations like 4(x + 2) = 28 with numbers. This one has letters on both sides, needs the distributive property and like terms, and asks for a in terms of b, which is grade 8 algebra.
- 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
- Variables instead of numbers moderate
- Many steps moderate
- An answer in an unexpected form minor
- Solution
- 3 steps
- Reading level
- Question and choices: about grade 4, 23 words.
- Students, last 30 days
- Not enough answers yet to show (it takes 10).
Why it is hard, traps and wrong answers (shows the answer)
Why it is hard
Every step is routine, yet there are four of them, each with a classic slip, and the typed answer catches none. Multiplying the 4 into only the a, or carrying 8b across without changing its sign, gives another whole multiple of b that looks finished. Testing b = 1, where 4(a + 2) and 28 + 2a must come out equal, confirms an entry quickly.
Variables instead of numbers moderate Understanding the question
Both letters appear on both sides, and the answer must stay a multiple of b, so there is no number to check an entry against unless students invent one. (Koedinger & Nathan, 2004; Enright, Morley & Sheehan, 2002)
Many steps moderate Working it out
Four moves run in a chain, distributing the 4, gathering the a terms, gathering the b terms and dividing by 2, and an error at any one carries into the typed result. (Daniel & Embretson, 2010; Enright, Morley & Sheehan, 2002)
An answer in an unexpected form minor Choosing the answer
The answer is typed after a printed “a =”, with no choices, so 20b, the line before dividing by 2, can be entered without anything on screen questioning it. (Enright, Morley & Sheehan, 2002)
Strategy: Distribute the 4 to both terms in the parentheses, gather the a terms on one side and the b terms on the other, then divide by the coefficient of a.
Traps
- 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.
- Stops one step early: A choice is a number from partway through the solution.
The wrong answers, classified
13b A faulty procedure (Brown & Burton, 1978; Tatsuoka, 1983)
Multiplies only the a by 4, writing 4a + 2b = 28b + 2a, so 2a = 26b and a = 13b.
18b A faulty procedure (Brown & Burton, 1978; Tatsuoka, 1983)
Distributes correctly but moves 8b to the right without changing its sign, so 2a = 28b + 8b = 36b and a = 18b.
20b Stops one step early (King et al., 2004; Gierl et al., 2017)
Reaches 2a = 20b correctly and enters 20b, stopping before dividing both sides by 2 to get a alone.
Worked solution, step by step
Formulas used
- Distributive property
- k is the number outside the parentheses. x and y are the terms inside. The number outside multiplies every term inside, not just the first one. It works because 4 groups of (x + y) hold 4 x’s and 4 y’s.
- Doing the same thing to both sides
- A and B are the two equal sides of an equation. C is any amount. Taking the same amount from both sides, or dividing both by the same number, keeps them equal, like a balanced scale.
Sort out the question
The equation is . You need a in terms of b. That means a alone on one side, with only b and numbers on the other.
The answer box already shows a =, so you type only what comes after it.
Multiply out the parentheses
Use the distributive property. The 4 multiplies both terms inside:
Watch out: multiplying only the a by 4 gives 4a + 2b. That leads to the wrong answer 13b.
Gather the a terms
Like terms are terms with the same letter, such as 4a and 2a. Put the a terms on the left. Subtract 2a from both sides:
Gather the b terms
Now subtract 8b from both sides:
Watch out: moving 8b without changing its sign gives . That leads to 18b, which is wrong.
Divide both sides by 2
2a means 2 times a. Divide both sides by 2 to get a alone:
Watch out: 20b is equal to 2a, not a. Do not stop there.
Enter it after the printed a =
On the test, the box already shows a =. Press 1, then 0, then the b key. You do not need a times sign. Do not type a = again. On this site, type 10b in the box.
So you would enter 10b, which makes a = 10b.
Check your answer
Pick b = 1, so a = 10. The left side is . The right side is . The sides match, so 10b works.
More questions like this
The original DOE question
Question 5 of 6
2026 Practice Test C Math, question 15Question
A grocery store sells 1-gallon containers of milk for $3.99. The store also sells orange juice in a 6-pack of 5.5-fluid-ounce bottles for $1.79. Suppose the store wants to sell its orange juice in gallon containers instead. To the nearest dollar, how much more would a gallon of orange juice cost than a gallon of milk?
Enter your answer in the space.
Fill-in question: work out the answer and type it as a number.
Show the answer
Correct answer: 3
To determine the cost of a gallon of orange juice, begin by finding the total number of ounces in the 6-pack of bottles:
So, 33 oz of orange juice costs $1.79.
There are 128 oz in 1 gallon. Set up a proportion using the $1.79 cost per 33 oz of orange juice and the unknown cost (x) per 1 gallon of orange juice:
Cross multiply to solve for x in the proportion:
So, the orange juice costs $6.94 per gallon, and the milk costs $3.99 per gallon.
Subtract the cost per gallon of milk from the cost per gallon of orange juice.
Round the difference to the nearest dollar.
$2.95 rounds to $3.
Question analysis
A store sells milk by the gallon for $3.99 and orange juice in six-packs of 5.5-fluid-ounce bottles for $1.79. Students work out what a gallon of the juice would cost at the same price per ounce and how much more that is than the milk, to the nearest dollar. The ounces in a gallon must be known, and several steps involve decimals.
- Grade level
- Grade 7 content, by NYS standard
- Compared with grade 7
- Above grade 7 Unit prices are grade 6 and 7 work, but this chains five steps with decimals and needs a fact the question does not give, the number of fluid ounces in a gallon. Typing a rounded difference, with no choices, adds risk.
- Estimated difficulty
- Hard: combines ideas, needs a plan, and has more than one tempting wrong answer.
- Thinking it demands
- Depth of knowledge 2, skills and concepts · mainly apply
- What makes it hard
- Something you must already know moderate
- Many steps moderate
- Error-prone arithmetic minor
- An answer in an unexpected form minor
- Solution
- 5 steps
- Reading level
- Question and choices: about grade 5, 60 words.
- Corrected from the DOE handbook
- A rounded value in the explanation is now marked as approximate (≈ instead of =).
- 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 calculation is long, and its key fact is missing from the page. Students who know the 128 fluid ounces still face a division by 33 that does not come out evenly, which tempts them to round the price per ounce to 5 cents and lose about 50 cents a gallon. Keeping the exact quotient to the end, or scaling 33 ounces up by about 3.9, keeps the difference near $2.95, which rounds to 3.
Something you must already know moderate Working it out
The question never says that a gallon holds 128 fluid ounces, yet the whole comparison depends on it; the 6-pack holds only 6 × 5.5 = 33 ounces. (Anderson & Krathwohl, 2001)
Many steps moderate Working it out
Five moves follow one another: the ounces in a pack, the scale-up to 128 ounces, the division by 33, the subtraction of $3.99 and the rounding to a whole dollar. (Daniel & Embretson, 2010; Enright, Morley & Sheehan, 2002)
Error-prone arithmetic minor Working it out
1.79 × 128 = 229.12 and 229.12 ÷ 33 are long decimal calculations without a calculator, and a slip in either moves the price of a gallon. (Brown & Burton, 1978; Junker & Sijtsma, 2001)
An answer in an unexpected form minor Choosing the answer
The rounded difference is typed with no choices, so an unrounded $2.95, or a figure rounded too soon, looks just as finished as the whole-dollar answer. (Enright, Morley & Sheehan, 2002)
Strategy: Find the ounces in one six-pack, scale its price up to the 128 fluid ounces in a gallon, subtract the milk's price, and round only at the end.
Traps
- Stops one step early: A choice is a number from partway through the solution.
- Rounds too early: Rounds a value partway through, or rounds the wrong way, so the final answer drifts from the exact one.
- Misreads the question: Misses or misreads a condition or a word in the question: "at least", "each", "remaining", "not".
The wrong answers, classified
7 Stops one step early (King et al., 2004; Gierl et al., 2017)
Finds the juice's cost per gallon, about $6.94, rounds it to $7, and enters that without subtracting the $3.99 price of the milk.
2 Rounds too early (King et al., 2004)
Rounds the price per ounce, 1.79 ÷ 33 ≈ 0.054, to $0.05, so a gallon costs $6.40 and the difference, $2.41, rounds to 2.
2.95 Misreads the question (Hegarty, Mayer & Monk, 1995)
Works out the difference of $2.95 correctly but enters it as it stands, though the question asks for it to the nearest dollar.
What was corrected from the DOE handbook, and why
- Explanation: The DOE’s explanation goes from 33x = $229.12 to “x = $6.94”. But 229.12 ÷ 33 = 6.9430…, so $6.94 is the cost per gallon rounded to the cent. The site writes x ≈ $6.94. Nothing else changes: $6.94 − $3.99 = $2.95, which rounds to $3, and the unrounded cost gives the same answer.
Worked solution, step by step
Formulas used
- Fluid ounces in a gallon
- A gallon holds 128 fluid ounces. This is a fact you must know, because the question does not give it. A fluid ounce measures an amount of liquid. Multiply gallons by 128 to change them into fluid ounces.
- Cross-multiplying a proportion
- A proportion says two ratios are equal. Here each ratio is ounces over dollars. a and c are the tops, and b and d are the bottoms. Multiply each top by the other bottom, and the two products are equal. That turns the proportion into an equation.
Sort out the question
Milk costs $3.99 for 1 gallon. Orange juice comes in a 6-pack of 5.5-fluid-ounce bottles for $1.79. You need how much more a gallon of juice would cost than a gallon of milk. Round to the nearest dollar.
The question doesn’t say how big a gallon is. You must know this fact: 1 gallon is 128 fluid ounces.
Find the ounces in a 6-pack
Each of the 6 bottles holds 5.5 fluid ounces:
So $1.79 buys 33 fluid ounces of juice.
Set up a proportion
Let x be the cost in dollars of a gallon, 128 fluid ounces, of juice. The price per ounce stays the same. So ounces over dollars is the same for the pack and the gallon:
Cross-multiply:
Find the cost of a gallon
Divide both sides by 33:
The sign ≈ means about equal. The exact value is 6.943…, so a gallon of juice costs about $6.94.
Watch out: don’t round too early. One ounce costs about $0.054. Rounding that to $0.05 makes a gallon $6.40, and your answer becomes 2.
Subtract the milk’s price
Find how much more the juice costs:
A gallon of juice costs $2.95 more than a gallon of milk.
Watch out: entering 7, the juice’s price, forgets to subtract the milk.
Round and enter it
The question asks for the nearest dollar. $2.95 is between $2 and $3. Its cents, 95, are 50 or more, so it rounds up to $3. Do not enter 2.95.
Type only the number in the box. So you would enter 3.
Check your answer
Estimate. 128 ounces is almost 4 packs, since . Four packs cost dollars, so a gallon costs a bit less than that. Milk costs about $4. About $7 minus $4 is $3, which matches.
More questions like this
The original DOE question
Question 6 of 6
2026 Practice Test B Math, question 24Question
A chemical decays in such a way that the amount left at the end of each week is 20% less than the amount at the beginning of that same week. What percentage of the original amount is left after two weeks?
- A40%
- B60%
- C64%
- D80%
Show the answer
Correct answer: C
Let x be the original amount of the chemical. It loses 20% after each week, which means 80% of the chemical remains at the end of each week. End of first week:
At the end of the second week, 80% of the amount left at the end of the first week remains.
End of second week: or 64%
Question analysis
A chemical loses 20% of the amount present at the start of each week, and students find what percentage of the original amount is left after two weeks. It tests applying a percent decrease more than once. The question turns on which amount each week's loss is measured against.
- NYS standards
- 7.RP.3 multistep ratio and percent problems
- Grade level
- Grade 7 content, by NYS standard
- Compared with grade 7
- Above grade 7 A typical grade 7 percent task applies one increase or decrease to one amount. This one applies a weekly decrease twice in a row, an early form of exponential decay that goes beyond typical grade 7 work.
- Estimated difficulty
- Hard: combines ideas, needs a plan, and has more than one tempting wrong answer.
- Thinking it demands
- Depth of knowledge 2, skills and concepts · mainly apply
- What makes it hard
- A very close wrong answer major
- Turning words into math moderate
- Variables instead of numbers minor
- Solution
- 2 steps
- Reading level
- Question and choices: about grade 8, 40 words.
- Students, last 30 days
- Not enough answers yet to show (it takes 10).
Why it is hard, traps and wrong answers (shows the answer)
Why it is hard
Two equal decreases in a row feel like one decrease of twice the size, and that is the trap: 20% and 20% suggest 40% gone. The stem states the rule, each loss measured from that week’s start, in one quick phrase. Working week by week from 100 shows the second loss is 16, not 20, which separates the answer from the choice four points away, while stopping after one week or reporting the loss costs the point more simply.
A very close wrong answer major Choosing the answer
The choices 60% and 64% sit four percentage points apart, so a rough estimate cannot choose between them; only seeing that the second 20% is taken from 80, not 100, does. (Embretson & Wetzel, 1987; Gorin & Embretson, 2006; Ascalon et al., 2007)
Turning words into math moderate Understanding the question
The phrase “the amount at the beginning of that same week” sets each week’s base, so the second week’s 20% is measured from what was left after the first week. (Hegarty, Mayer & Monk, 1995; Koedinger & Nathan, 2004)
Variables instead of numbers minor Understanding the question
No starting amount is given, so students must pick one, such as 100 grams, or work with a percent of a percent, 0.8 × 0.8. (Koedinger & Nathan, 2004; Enright, Morley & Sheehan, 2002)
Strategy: Use a starting amount of 100 so that percents become units, find what remains after the first week, then apply the same 20% loss to that remainder.
Traps
- Percent of the wrong amount: Finding the whole from a part, or a percent change measured from the wrong starting amount.
- Stops one step early: A choice is a number from partway through the solution.
- Answers a different question: A choice is right for another quantity: the other unknown, the rest instead of the part, the part instead of the whole.
The wrong answers, classified
A Answers a different question (King et al., 2004; Hegarty, Mayer & Monk, 1995)
Adds the weekly losses, 20% + 20% = 40%, and gives that figure, which describes the amount lost rather than the percentage still left.
B Percent of the wrong amount (Parker & Leinhardt, 1995)
Subtracts 20% of the original amount twice, 100 − 20 − 20 = 60, though the second week’s 20% comes from the 80% left, not the starting amount.
D Stops one step early (King et al., 2004; Gierl et al., 2017)
Finds that 80% remains after the first week and stops, never taking the second week’s 20% from that remainder.
Worked solution, step by step
Formulas used
- Percent of an amount
- p is the percent, and amount is the whole you take the percent of. Percent means out of 100, so 20% is 20/100. Multiply to find the part. Be sure the amount is the right whole. Here, each week uses the amount at the start of that week.
- Percent left after a loss
- The whole amount is 100%. If 20% goes away, the rest stays. So 80% of each week’s starting amount is left at the end of that week. Keeping 80% is the same as multiplying by 0.8.
Sort out the question
Each week the chemical loses 20% of what it has. The key words are “the amount at the beginning of that same week.” So each week’s 20% comes from that week’s starting amount. No amount is given. You need the percent of the original amount that is left after two weeks.
Pick an easy starting amount
Pretend the chemical starts at 100 grams. With 100, the number of grams left is the same as the percent left. Any starting amount gives the same percent, so choose the easiest one.
Work out the first week
Use the percent formula. The first week starts with 100 grams:
The chemical loses 20 grams, so grams are left. That is 80% after one week.
Watch out: 80% is only the first week. Stopping here gives choice D.
Work out the second week
The second week starts with 80 grams, not 100. So take 20% of 80:
This time the chemical loses only 16 grams, so grams are left.
Watch out: taking away 20 grams again uses the original amount. That gives 60%, choice B. Choice A, 40%, adds the two losses. But the question asks what is left, and only 36% was lost.
Read the answer as a percent
Week Start (grams) Loss (grams) Left (grams) 1 100 20 80 2 80 16 64 Another way: each week keeps 80%, or 0.8, of its start. Two weeks gives , which is 64%.
64 grams out of the original 100 grams is 64%. So the answer is C, 64%.
Check your answer
Think about the size of the second loss. The second week starts with less, so it loses less than 20 grams. That means more than 60% is left. It does lose something, so less than 80% is left. Of the four choices, only 64% is between 60% and 80%.
More questions like this
The original DOE question
