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 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 2 of 6
2026 Practice Test B English, question 33Passage Using Fire to Keep a Prairie Healthy
Using Fire to Keep a Prairie Healthy
Inside the 40,000-acre Joseph H. Williams Tallgrass Prairie Preserve in northern Oklahoma, herds of bison roam on the scenic land that is home to hundreds of different species of plants and animals. While one of the greatest threats to the prairie is wildfire, the use of controlled fires is actually an effective way to protect this idyllic landscape.
Fires that are started by lightning or other natural circumstances are inevitable, and the results can be disastrous. However, hundreds of years ago the American Indian people who inhabited the Great Plains area between Minnesota and Texas realized that these fires could also be helpful. The bison in the area seemed to prefer grazing on tender new grass on the recently burned land rather than on grass in the unburned areas. The American Indian people began to deliberately burn areas of land for bison to graze on, which enticed the herds away from the people’s crops.
Today conservationists at the Tallgrass Prairie Preserve and farmers in the Great Plains continue to use controlled burns for land management. Intentionally burning a portion of land can dramatically improve the quality of the vegetation that regrows there. The fires burn away weedy undergrowth and help limit the overcrowding of shrubs and trees in the burn area, creating less competition for water and nutrients. Additionally, the process of burning excess plant matter adds nitrogen, an essential element for plant growth, to the soil.
One common target of controlled burns at the preserve and the surrounding area is the invasive red cedar tree. A single red cedar tree can consume up to 40 gallons of water per day, taking this vital resource away from other plant life. These tall trees also cast shade that prevents sunlight from reaching the plants beneath them. The fast-growing red cedar trees tend to crowd out prairie grasses, the primary food source for wild and domestic animals that make the prairie their home. An imbalance in one component of the prairie’s ecosystem affects the entire web of life. Controlled burns help maintain this ecosystem’s delicate balance.
Of course, these controlled fires are intended to burn only a portion of an area. A total burn, which is a risk with an uncontrolled wildfire, would destroy all wildlife as well as the crops farmers plant for income. The key to using controlled fires is knowing which areas of land to burn and when. Conservation experts at the preserve employ the “patch-burn” approach, meaning they rotate which portion of land is burned each year. They study the land to find out which areas would most benefit from being burned, and then they arrange about a dozen burns over one-third of the land. This patch burning contains the fire within a specific area and allows animals in the burn area to safely relocate. The following year, conservationists will burn a different section of the preserve, while the land burned the previous year regrows healthier than before.
Researchers have tracked and studied the variety of plant species and animals that live on the preserve, and their studies show that the patch-burn approach has restored biodiversity to the area by promoting the growth of species that were at risk of being crowded out. The patch-burn system is so successful that the conservationists at the preserve provide training to prairie farmers about conducting controlled burns on their own land. Burning land to make it healthy may seem counterintuitive, but strategic controlled fires have helped the prairie sustain life for hundreds of years and, with careful management, will continue to do so.

Question
Read this sentence from paragraph 6.
Burning land to make it healthy may seem counterintuitive, but strategic controlled fires have helped the prairie sustain life for hundreds of years and, with careful management, will continue to do so.
The words “counterintuitive” and “strategic” in the sentence convey the idea that
- Athe safest methods are sometimes the least effective at solving complex challenges.
- Bthorough investigation of uncommon methodologies can lead to beneficial results.
- Cdetailed planning can ensure that a potentially destructive action has a positive impact.
- Dplans that entail a certain amount of risk almost always result in success.
Show the answer
Correct answer: C
The question asks which idea the words “counterintuitive” and “strategic” convey in the last sentence in paragraph 6 in the passage.
A. Incorrect. Though the author states in paragraph 6 that conservationists have used safe and “strategic” methods, those methods have not been ineffective, since “the patch-burn system is so successful that the conservationists at the preserve provide training to prairie farmers about conducting controlled burns on their own land” (paragraph 6). Therefore, the words “counterintuitive” and “strategic” in the last sentence of paragraph 6 do not convey the idea that the safest methods are sometimes the least effective at solving complex challenges.
B. Incorrect. Although the author points out in paragraph 6 that researchers’ studies have shown “that the patch-burn approach has restored biodiversity to the area by promoting the growth of species that were at risk of being crowded out,” the author does not suggest that the methodologies conservationists used to conduct the patch burns are uncommon, since the methods were used by “the American Indian people [who] began to deliberately burn areas of land for bison to graze on” (paragraph 2). Therefore, the words “counterintuitive” and “strategic” in the last sentence of paragraph 6 do not convey the idea that thorough investigation of uncommon methodologies can lead to beneficial results.
C. CORRECT. In paragraph 1, the author states that “one of the greatest threats to the prairie is wildfire,” so the idea of conducting controlled burns suggests risk and runs “counter,” or contrary, to people’s common expectations, or “intuition,” about the dangers of fires. Thus, the words “counterintuitive” and “strategic” in the last sentence of paragraph 6 convey the idea that detailed planning can ensure that a potentially destructive action has a positive impact.
D. Incorrect. The author states in paragraph 6 that “the patch-burn system is so successful that the conservationists at the preserve provide training to prairie farmers.” This statement supports the idea of the action being “strategic” in order to achieve success. However, the statement does not suggest that because the process is “counterintuitive,” or unexpected, it involves a certain amount of risk to achieve that success. Therefore, the words “counterintuitive” and “strategic” in the last sentence of paragraph 6 do not convey the idea that plans that entail a certain amount of risk almost always result in success.
Question analysis
This vocabulary question takes the last sentence of the prairie article, which says burning land to make it healthy may seem counterintuitive, and asks what the words “counterintuitive” and “strategic” convey together. Students need the meaning of a hard word built from a prefix, then must match the pair to a general statement, and the choices are worded abstractly.
- Grade level
- Grade 8 reading and task
- Compared with grade 7
- Above grade 7 A typical grade 7 vocabulary question asks what one word means in context. This one pairs a hard word, “counterintuitive,” with “strategic” and asks for the idea they express together, with four abstract general statements to weigh.
- 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 moderate
- Hard words moderate
- Combines ideas minor
- Evidence
- Answered from one sentence or line
- Reading level
- Passage: about grade 11, 598 words; question and choices: about grade 11, 97 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
Students first need the meaning of “counterintuitive,” then must see what it says here: that burning land to heal it seems backward because fire destroys. “Strategic” supplies the other half, careful planning. The most tempting wrong answer gets the planning right but misreads the first word as “uncommon,” and others turn the pair into a rule about risk or a warning about safe methods. The question rewards translating each word before reading the abstract choices.
A very close wrong answer moderate Choosing the answer
The choice about “thorough investigation of uncommon methodologies” follows the key’s pattern, planning that leads to a good result, and differs only in calling the method uncommon instead of potentially destructive. (Embretson & Wetzel, 1987; Gorin & Embretson, 2006; Ascalon et al., 2007)
Hard words moderate Understanding the question
“Counterintuitive,” contrary to what one would expect, is an uncommon word, and the choices add “methodologies” and “entail,” so the options are as hard to read as the sentence. (Perfetti, 2007; Freedle & Kostin, 1993)
Combines ideas minor Working it out
The two words point different ways, one to burning that seems harmful and one to careful planning, and the answer must join both into a single general statement. (Embretson, 1998; Daniel & Embretson, 2010)
Strategy: Break “counterintuitive” into its parts, counter and intuitive, decide what each of the two words says about burning land, then find the statement that joins both meanings without adding claims of its own.
Traps
- Half right: One half of a two-part choice is right and the other is not.
- Too broad or too strong: A choice overstates, generalizes, or uses absolute words the text does not support.
- 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)
Reads “counterintuitive” as a hint that the safe choice fails, but the sentence praises carefully managed fire and never says safer methods are less effective.
B Half right (King et al., 2004; Thissen, Steinberg & Fitzpatrick, 1989)
Matches “strategic” to thorough investigation, since the experts “study the land,” but takes “counterintuitive” to mean uncommon, though the passage traces burning back hundreds of years.
D Too broad or too strong (King et al., 2004)
Hears risk in “counterintuitive” and success in “strategic” but turns them into a rule that risky plans “almost always” succeed, far more than one sentence about the prairie claims.
Working it out, step by step
Figure out what the question asks
This question asks about two words in the last sentence: “counterintuitive” and “strategic.” You need the idea the two words give together. So first figure out what each word means here.
Break down “counterintuitive”
Counter means against. Intuitive means what you would naturally expect. So counterintuitive means the opposite of what you would expect. The sentence says “Burning land to make it healthy may seem counterintuitive.” Fire usually destroys things. So burning land to help it seems backward. Paragraph 1 even calls wildfire “one of the greatest threats to the prairie.”
Figure out “strategic”
Strategic means carefully planned to reach a goal. Paragraph 5 shows that planning. The experts “study the land to find out which areas would most benefit from being burned.” Then they burn only part of the land each year. Put the two words together. Fire seems harmful, but careful planning makes it helpful.
Check each choice
- A is wrong. The sentence doesn’t say safe methods fail. It praises a method that works.
- B is wrong. It treats counterintuitive as if it meant uncommon. But burning isn’t new. Paragraph 2 says people did it “hundreds of years ago.”
- C is right. Strategic matches detailed planning. Counterintuitive matches an action that could destroy, fire, which turns out to help.
- D is wrong. “Almost always” is far too strong. The sentence is about prairie fires, not all risky plans.
Watch out: B gets strategic right, since the experts study the land. But counterintuitive doesn’t mean uncommon. It means against what you would expect.
Choose the answer
Fire seems destructive, but a careful plan makes it helpful. So the answer is C: “detailed planning can ensure that a potentially destructive action has a positive impact.”
Why this answer and not the closest wrong one
B is the closest wrong answer, because its first part, careful study, fits strategic. But its second part calls the method uncommon, and people have burned the prairie for hundreds of years. C fits both words: careful planning, and an action that seems harmful but helps.
More questions like this
The original DOE question

The passage “Using Fire to Keep a Prairie Healthy” as printed (page 41)

Question 3 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.
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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 4 of 6
2024 Test B Math, question 25Question
Which number line represents the values of x that satisfy the inequality ?
- A

- B

- C

- D

Show the answer
Correct answer: B
Split the compound inequality into two inequalities.
and
For each inequality, subtract 1 from each side.
and
For each inequality, divide both sides by −3. Note that dividing each side of an inequality by a negative number changes the direction of the inequality.
and
Combining the pieces gives the compound inequality .
The solution is that x is greater than or equal to −1 and less than or equal to 2, so choose the number line with filled circles at −1 and 2, with the filled segment between the circles.
Question analysis
An inequality question: choose the number line that shows the solutions of the compound inequality −5 ≤ 1 − 3x ≤ 4. Students solve an inequality whose x term has a negative coefficient, then match the endpoints, open or closed circles, and shading to one of four graphs.
- Grade level
- Grade 7 content, by NYS standard
- Compared with grade 7
- Above grade 7 Grade 7 students solve and graph two-step inequalities one at a time. This compound inequality needs two solved together and a division by a negative number, which reverses the signs, a step many grade 7 classes only touch on.
- Estimated difficulty
- Hard: combines ideas, needs a plan, and has more than one tempting wrong answer.
- Thinking it demands
- Depth of knowledge 1, recall and reproduction · mainly apply
- What makes it hard
- Error-prone arithmetic moderate
- A very close wrong answer moderate
- Reading a figure, table or graph minor
- Solution
- 4 steps
- Reading level
- Question and choices: about grade 12, 13 words.
- Students, last 30 days
- Not enough answers yet to show (it takes 10).
Why it is hard, traps and wrong answers (shows the answer)
Why it is hard
The question stacks two classic traps: reversing the inequality signs when dividing by −3, and matching filled or open circles to ≤. All four graphs use the endpoints −1 and 2, so finding those numbers proves little; the choice turns on the circles and the direction of the shading. Testing x = 0, x = 3 and the endpoint x = 2 in the original inequality checks both decisions in under a minute.
Error-prone arithmetic moderate Working it out
Dividing all three parts of −6 ≤ −3x ≤ 3 by −3 reverses both signs and the order, giving 2 ≥ x ≥ −1, which must be rewritten as −1 ≤ x ≤ 2. (Brown & Burton, 1978; Junker & Sijtsma, 2001)
A very close wrong answer moderate Choosing the answer
Two graphs share the endpoints −1 and 2 and the shading between them; only the circles, filled for ≤ and open for <, separate them. (Embretson & Wetzel, 1987; Gorin & Embretson, 2006; Ascalon et al., 2007)
Reading a figure, table or graph minor Understanding the question
Each graph must be read for three things at once: the endpoints, the fill of each circle, and whether the shading runs between them or outward. (Lesh, Post & Behr, 1987; Kirsch & Mosenthal, 1990)
Strategy: Subtract 1 from all three parts, divide all three by −3 while reversing both inequality signs, then rewrite the result from smallest to largest before matching circles and shading.
Traps
- Negatives and direction: Arithmetic with negative numbers, the order of a subtraction, or direction on a number line. (Moving a term across the equals sign without changing its sign is a faulty procedure.)
- Counting the ends: Inclusive or exclusive ends, fence posts, consecutive numbers: an answer that is one too many or too few, or an endpoint drawn open where it belongs closed (or the reverse).
The wrong answers, classified
A Counting the ends (Brown & Burton, 1978)
Solves for the right endpoints and shading but draws open circles, as if ≤ excluded −1 and 2 instead of including them.
C Negatives and direction (Brown & Burton, 1978)
Divides by −3 without reversing the signs, so the solutions seem to lie outside −1 and 2; with open circles, this graph shows exactly the values that fail.
D Negatives and direction (Brown & Burton, 1978)
Shades outward as if the signs had not reversed, but mixes the circles, filled at −1 and open at 2, which no single reading of ≤ gives.
Worked solution, step by step
Formulas used
- Subtracting from every part
- a and b are the two sides of an inequality, and c is any number. Subtracting the same number from every part keeps the inequality true. The sign does not change.
- Dividing by a negative number
- a and b are numbers, and c is a positive number, so −c is negative. When you divide both sides by a negative number, the inequality sign flips. For example, 2 is less than 3, but −2 is greater than −3.
Sort out the question
The inequality says that is between −5 and 4. The sign ≤ means less than or equal to. So −5 and 4 themselves are allowed. You need the number line that shows every x that works. To find them, get x alone in the middle.
Subtract 1 from every part
First take away the 1 in the middle. Subtract 1 from all three parts.
Divide by −3 and flip
Now x is multiplied by −3. Divide all three parts by −3. Dividing by a negative number flips each sign.
Watch out: if you forget to flip, x seems to lie outside −1 and 2. That leads to choices C and D, which are shaded outward.Read the result
Turn it around so the smaller number is on the left. It means the same thing.
So x can be any number from −1 to 2. The ends, −1 and 2, are included, because the signs are ≤.
Pick the number line
On a number line, a closed (filled-in) circle means the end number is included. An open circle means it is not. So you need closed circles at −1 and 2, with the part between them shaded. Watch out: choice A has the right shading but open circles, which leave out −1 and 2.
So the answer is B.
Check your answer
Test a few numbers in . For x = 0 you get 1, which is between −5 and 4, and 0 is shaded. For x = 2 you get −5, which is allowed, so the circle at 2 is filled in. For x = 3 you get −8, which is too small, so 3 is not shaded.
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The original DOE question

Question 5 of 6
2024 Test B Math, question 14Question
Karen reads at the rate of 60 pages per day. Martina reads 25% more pages per day than Karen. If the two students begin 1,500-page reading assignments on the same day, how many days sooner will Martina complete the assignment than Karen?
- A4
- B5
- C7
- D15
Show the answer
Correct answer: B
First, determine the rate at which Martina reads, in pages per day, using the rate at which Karen reads, 60 pages per day.
Next, determine the number of days it will take each person to complete the 1,500-page reading assignment.
Karen:
Martina:
Finally, determine the difference between the two numbers of days.
So Martina will complete the assignment 5 days sooner than Karen.
Question analysis
A reading-rate word problem: Karen reads 60 pages a day, and Martina reads 25% more pages a day. Both start a 1,500-page assignment on the same day, and students find how many days sooner Martina finishes. It combines a percent increase with rates and times, and asks for a difference in days.
- Grade level
- Grade 7 content, by NYS standard
- Compared with grade 7
- Above grade 7 Grade 7 percent problems usually stop after one increase or decrease. This one turns the percent into a new rate, finds two finishing times and compares them, four steps that go beyond a typical grade 7 task.
- 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
- Many steps moderate
- Combines ideas moderate
- Turning words into math minor
- Solution
- 4 steps
- Reading level
- Question and choices: about grade 6, 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
Each step is easy on its own; the difficulty is in carrying the chain to the end. Three of the choices are numbers a student meets or makes along the way: the extra pages per day, a quotient of two rates, or a rate built on 25 pages instead of 25%. Writing both finishing times down before subtracting keeps the target, a number of days, in view.
Many steps moderate Working it out
Four operations chain together: 25% of 60, Martina's 75 pages, the two finishing times 1,500 ÷ 60 and 1,500 ÷ 75, and finally their difference. (Daniel & Embretson, 2010; Enright, Morley & Sheehan, 2002)
Combines ideas moderate Working it out
A percent increase in a daily rate has to be turned into a change in days, and 25% more pages a day does not mean 25% fewer days. (Embretson, 1998; Daniel & Embretson, 2010)
Turning words into math minor Understanding the question
“25% more pages per day than Karen” makes Martina's rate 1.25 × 60, and “how many days sooner” asks for a difference of two times, not of two rates. (Hegarty, Mayer & Monk, 1995; Koedinger & Nathan, 2004)
Strategy: Increase 60 by 25% to get Martina's daily pages, divide 1,500 by each girl's daily rate to get her number of days, then subtract the two numbers of days.
Traps
- Stops one step early: A choice is a number from partway through the solution.
- 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.
- Numbers taken from the question: Combines the numbers in the question without a model of the situation, or is simply a number that appears in the question.
The wrong answers, classified
A Numbers taken from the question (Hegarty, Mayer & Monk, 1995)
Divides Karen's 60 pages a day by Martina's 15 extra pages a day, combining two rates without finding how long either girl takes.
C Misunderstands the concept (Smith, diSessa & Roschelle, 1993; De Bock et al., 1998; Ni & Zhou, 2005)
Adds 25 pages instead of 25%, giving Martina 85 pages a day, so she needs 1,500 ÷ 85 ≈ 17.6, or 18 days, and 25 − 18 = 7.
D Stops one step early (King et al., 2004; Gierl et al., 2017)
Finds that Martina reads 25% of 60 = 15 more pages each day and stops there, giving a number of pages instead of days.
Worked solution, step by step
Formulas used
- Percent increase
- Old is the starting amount, and p is the percent it grows by. First find p percent of the old amount. That is the extra. Then add the extra to the old amount to get the new amount.
- Time from a rate
- Total pages is the whole assignment. Pages per day is how fast someone reads. Dividing tells how many days of reading fit into the whole job.
Sort out what you know
Karen reads 60 pages per day. Martina reads 25% more pages per day than Karen. Each girl must read 1,500 pages. You need how many days sooner Martina finishes. That is the difference between their numbers of days.
Find Martina’s pages per day
25% more means Karen’s 60 pages plus 25% of 60.
Martina reads 75 pages per day. Watch out: 15 is extra pages, not days. Stopping here gives 15, choice D. Adding 25 pages instead of 25% gives 85 pages and leads to 7, choice C.
Find each girl’s number of days
Divide the whole assignment by each girl’s pages per day.
Karen needs 25 days, and Martina needs 20 days.
Subtract the days
“How many days sooner” asks for the difference.
Martina finishes 5 days sooner. Watch out: dividing 60 by 15 mixes two rates and gives 4, choice A.
So the answer is B, 5.
Check your answer
Multiply back. Karen: pages. Martina: pages. Both read all 1,500 pages, and 25 days is 5 days more than 20 days.
More questions like this
The original DOE question

Question 6 of 6
2018 Test A Math, question 30Question
Today, Tien’s age is of Jordan’s age. In 2 years, Tien’s age will be of Jordan’s age. How old is Jordan today?
- A4 years old
- B6 years old
- C12 years old
- D16 years old
Show the answer
Correct answer: D
First, set up an equation to express Tien’s age () and Jordan’s age () today:
Two years from now, Tien’s age will be , and Jordan’s age will be .
Set up an equation about the relationship between Tien’s age and Jordan’s age in two years:
Solve the above equation for :
Now set the two equations equal to each other and solve for :
Question analysis
This age word problem says Tien is one fourth of Jordan's age today and will be one third of Jordan's age in two years, then asks for Jordan's current age. Students must turn two fractional relationships into equations and solve them together. Both people age by the same two years, and it is easy to solve for the wrong person.
- NYS standards
- Grade level
- Grade 8 content, by NYS standard
- Compared with grade 7
- Above grade 7 Grade 7 equations have one unknown on one side, like 3x + 5 = 20. This one links two unknown ages with fractional coefficients and leads to a variable on both sides, 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 2, skills and concepts · mainly apply
- What makes it hard
- Turning words into math major
- Error-prone arithmetic moderate
- Solution
- 4 steps
- Reading level
- Question and choices: about grade 1, 31 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 difficulty is in the setup: two fractional relationships at two different times, with both people aging. Once the equations are right, the algebra is short, but it ends with two ages and only one is asked for. Testing the choices against both conditions is a reliable alternative that avoids the algebra entirely.
Turning words into math major Understanding the question
The second sentence must become T + 2 = (J + 2)/3; writing J/3, or forgetting that Jordan also ages two years, breaks the equation. (Hegarty, Mayer & Monk, 1995; Koedinger & Nathan, 2004)
Error-prone arithmetic moderate Working it out
Substituting J/4 for T leaves J/4 + 2 = (J + 2)/3, an equation with fractions on both sides that must be cleared, usually by multiplying by 12. (Brown & Burton, 1978; Junker & Sijtsma, 2001)
Strategy: Let Jordan's age be J, write Tien's age as J/4, and set J/4 + 2 equal to one third of (J + 2); or test each choice against both conditions.
Traps
- Answers a different question: A choice is right for another quantity: the other unknown, the rest instead of the part, the part instead of the whole.
The wrong answers, classified
A Answers a different question (King et al., 2004; Hegarty, Mayer & Monk, 1995)
Solves the equations correctly but reports Tien's age today, 4, which is one fourth of Jordan's 16, instead of Jordan's age.
B Answers a different question (King et al., 2004; Hegarty, Mayer & Monk, 1995)
Gives Tien's age two years from now, 4 + 2 = 6, answering for the wrong person and the wrong time.
C Numbers taken from the question (Hegarty, Mayer & Monk, 1995)
Picks 12 because it is a multiple of both 4 and 3, but then Tien would be 3 and later 5, not a third of 14.
Worked solution, step by step
Formulas used
- Distributive property
- a, b and c are any numbers. To multiply a sum by a number, multiply each part of the sum, then add. It works because a groups of (b + c) is the same as a groups of b plus a groups of c.
Sort out what you know
Today, Tien’s age is of Jordan’s age. That means Jordan is 4 times as old as Tien.
In 2 years, both of them will be 2 years older. Then Tien’s age will be of Jordan’s. So Jordan will be 3 times as old as Tien. You need Jordan’s age today.
Name the ages with a letter
Let t stand for Tien’s age today. Jordan is 4 times as old, so his age is 4t, which means 4 times t. Add 2 years to each age:
Person Today In 2 years Tien Jordan Watch out: Jordan gets 2 years older too. Do not forget to add 2 to his age.
Write an equation for later
In 2 years, Jordan’s age will be 3 times Tien’s age. Write that as an equation:
Use the distributive property on the right side. Multiply both t and 2 by 3:
Solve for Tien’s age
Take 3t away from both sides. Doing the same thing to both sides keeps them equal:
Now take 2 away from both sides:
So Tien is 4 years old today. Watch out: 4 is Tien’s age, not Jordan’s. Choice A, 4 years old, is a trap.
Find Jordan’s age
Jordan is 4 times as old as Tien:
So the answer is D, 16 years old.
Check your answer
Put 16 back into the story. Today, Tien is 16 ÷ 4 = 4. In 2 years, Tien is 6 and Jordan is 18. Is 6 one third of 18? Yes, because 18 ÷ 3 = 6. Choice C fails: Tien would be 3, then 5, and 5 is not a third of 14.
More questions like this
The original DOE question
