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 8Passage Find Time to Volunteer
Find Time to Volunteer
(1) Many people believe that they gain a greater sense of purpose by giving their time to serve others. (2) These are the people who spend their free time volunteering at various places within the community. (3) Those who are served benefit from the work of these volunteers. (4) However, research shows that those who volunteer also receive benefits.
(5) For many students, this proposition may sound impossible. (6) Schoolwork can require hours of study each week. (7) Volunteering at a retirement center or homeless shelter requires both time and energy. (8) Extracurricular activities fill up after-school time. (9) Family obligations and part-time jobs often have to be worked into the schedule, too. (10) However, if students can find time to volunteer, even for a few hours a month, they may find that the benefits outweigh the scheduling difficulties.
(11) To begin with, students who engage in volunteer activities acquire valuable skills and experience, which can help them focus on potential fields of study and career options. (12) Furthermore, when students list volunteer work on college applications, admissions counselors see applicants who care about making their community and college campus a better place.
(13) Volunteerism benefits more than students applying to college. (14) This type of experience is equally important for students moving directly into the workforce after high school. (15) Volunteering demonstrates initiative, dedication, and a strong work ethic, qualities that companies value in a potential employee. (16) In a CareerBuilder study, 60 percent of managers regarded volunteerism as a significant asset when considering applicants.
(17) Students who volunteer undoubtedly make a positive investment in their future, but they also affect their present quality of life. (18) Studies have shown that volunteering is good for both the mind and the body. (19) Volunteering can boost mood levels and reduce anxiety. (20) According to the Mayo Clinic,1 the feeling of doing something meaningful and the appreciation received from that action can reduce stress.
(21) Even the busiest of students can find a way to donate some time to a worthy cause. (22) Though managing different commitments may seem overwhelming at times, students are sure to feel a sense of fulfillment in volunteerism.
1Mayo Clinic: a nonprofit medical organization dedicated to treatment and research
Question
Which of these would best follow sentence 12 and support the ideas presented in the third paragraph (sentences 11–12)?
- AThese students show that they are likely to be responsible, reliable, and helpful young adults. Admissions counselors know that character traits like these will benefit the applicants as well as whomever they interact with.
- BVolunteering can help students meet new people who can provide references and advice to the students when they are applying to colleges. It can also be an invaluable opportunity for students to meet possible future employers.
- CThe counselors hope that young adults who demonstrate this behavior will go on to volunteer during their college years, working on campus in student government and leadership programs or serving in the community at hospitals, schools, and homeless shelters.
- DMany colleges are looking for students who are not just academically successful but who also work well with others and care about improving and serving surrounding communities.
Show the answer
Correct answer: D
The question asks which option would best follow sentence 12 to support the ideas presented in the third paragraph (sentences 11–12).
A. Incorrect. The subject of the main clause in sentence 12 is “admissions counselors.” Although the second sentence in the option mentions “admissions counselors,” it does not support the ideas in the paragraph, because the statement that “admissions counselors know that character traits like these will benefit the applicants” focuses on how students benefit, while sentence 12 focuses on how these traits benefit the community.
B. Incorrect. While sentence 11 discusses the potential academic and professional connections that can be made through volunteering, sentence 12 moves on to the topic of college admissions. Since the sentences in the option revert back to the topic of connections, they do not support and logically follow a sentence about how college admissions counselors view students with volunteering experience.
C. Incorrect. Although the sentence in the option continues on the subject of admissions counselors and follows the idea in sentence 12 that these counselors tend to favor students who “care about making their community and college campus a better place,” the sentence focuses on what students will do while in college rather than on how volunteering helps them get into college. Therefore, the sentence does not best follow sentence 12 and support the ideas presented in the third paragraph.
D. CORRECT. In sentence 12, the author states that college admissions counselors view students who list volunteer work on admissions applications as “applicants who care about making their community and college campus a better place.” The sentence in the option best follows sentence 12 and supports the ideas in the third paragraph because it provides additional details about why admissions counselors look beyond academics when considering students for admissions and the positive qualities assigned to those who have volunteering experience.
Question analysis
This supporting-details question asks which addition would best follow the volunteering essay’s sentence about how college admissions counselors view applicants who list volunteer work. Every option mentions college and sounds reasonable on its own, so students must decide which one develops the paragraph’s point rather than drifting to a related idea.
- NYS standards
- 7W1b supporting claims with evidence
- Grade level
- Grade 8 reading and task
- Compared with grade 7
- Above grade 7 Grade 7 students choose evidence that supports a claim. Here the options are one or two full sentences, all of them about college, and the right fit depends on the precise idea in sentence 12, a finer judgment than usual.
- Estimated difficulty
- Hard: combines ideas, needs a plan, and has more than one tempting wrong answer.
- Thinking it demands
- Depth of knowledge 2, skills and concepts · mainly evaluate
- What makes it hard
- A very close wrong answer major
- How sentences fit together moderate
- A lot to read minor
- Evidence
- Answered from one paragraph or stanza
- Reading level
- Passage: about grade 11, 354 words; question and choices: about grade 13, 153 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 option stays on the subject of college, so the work is matching sentence 12’s exact idea: counselors see applicants who care about making their community a better place. The near miss also explains what counselors value, but it swaps caring for the community for a new set of traits and ends on what those traits do for the applicants. Students who restate sentence 12 before reading the options can hear that the right one simply widens it, from community service to what colleges want beyond grades.
A very close wrong answer major Choosing the answer
The right sentence and the two-sentence option about responsible, reliable, helpful students both explain why volunteers impress admissions; only the right one keeps sentence 12’s point, caring about improving communities. (Embretson & Wetzel, 1987; Gorin & Embretson, 2006; Ascalon et al., 2007)
How sentences fit together moderate Working it out
The new sentence must extend sentence 12’s specific idea, what admissions counselors see in volunteers, rather than return to sentence 11’s skills and careers or move on to college life. (Halliday & Hasan, 1976)
A lot to read minor Understanding the question
The options run 27 to 39 words, two of them two sentences long, and all four are about college, so topic alone rules none of them out. (Kintsch, 1998; Gorin & Embretson, 2006; Freedle & Kostin, 1993)
Strategy: Restate sentence 12 in your own words, then ask of each option whether it explains or extends that exact point about what admissions counselors value.
Traps
- Off the point: Adds or keeps something that does not support the paragraph's or the passage's focus, or an introduction or conclusion that misses the main point.
The wrong answers, classified
A Off the point (Halliday & Hasan, 1976)
Follows the admissions counselors from sentence 12 but replaces caring for the community with new traits, responsibility and reliability, and turns to how those traits help the applicants.
B Off the point (Halliday & Hasan, 1976)
Is drawn by “applying to colleges,” but networking for references and future employers is a new benefit that neither sentence 11 nor sentence 12 develops.
C Off the point (Halliday & Hasan, 1976)
Stays with the counselors and picks up “college campus” from sentence 12, but jumps ahead to what students might do in college instead of explaining admission decisions.
Working it out, step by step
Figure out what the question asks
You need the sentence that best follows sentence 12. A good next sentence adds to the same idea. It does not jump to a new point. Example: after Dogs make loyal pets, the sentence They stay by their owners’ side fits. Dogs come in many colors drifts away. So first put sentence 12 in your own words.
Restate sentence 12
Sentence 12 says that “when students list volunteer work on college applications, admissions counselors see applicants who care about making their community and college campus a better place.” Admissions counselors are the people who choose which students get into a college. So the idea is this: colleges like volunteers because volunteers care about their communities.
Check each choice
- D says colleges want students who are “not just academically successful.” That means more than good grades. They also want students who “care about improving and serving surrounding communities.” That explains sentence 12 and builds on it.
- A swaps in new traits: “responsible, reliable, and helpful.” Then it says those traits help the applicants and the people around them. It drops caring for the community.
- B brings in a new benefit: meeting people who can give advice or jobs. Neither sentence 11 nor sentence 12 talks about that.
- C jumps ahead to what students might do in college. It doesn’t explain how volunteering helps them get in.
Pick the answer
Watch out: A is the most tempting. It is about what counselors value, just like the right answer. But it changes the reason they value it. Only D keeps sentence 12’s idea of caring for the community. So the answer is D.
Why this answer and not the closest wrong one
A is the closest wrong answer. Like D, it explains why admissions counselors like volunteers. But A’s reasons are new ones, such as being responsible and reliable. D keeps sentence 12’s exact idea, caring about the community, and adds that colleges want more than good grades. So D supports the paragraph best.
More questions like this
The original DOE question
The passage “Find Time to Volunteer” as printed (page 163)
Question 2 of 6
2026 Practice Test B English, question 32Passage 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
Which sentence supports the idea that farmers and people who manage land may be concerned about using fire as a way to benefit the land?
- A“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.” (paragraph 1)
- B“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.” (paragraph 2)
- C“This patch burning contains the fire within a specific area and allows animals in the burn area to safely relocate.” (paragraph 5)
- D“The following year, conservationists will burn a different section of the preserve, while the land burned the previous year regrows healthier than before.” (paragraph 5)
Show the answer
Correct answer: A
The question asks which sentence supports the idea that farmers and people who manage land may be concerned about using fire as a way to benefit the land.
A. CORRECT. The sentence from paragraph 1 supports the idea that farmers and people who manage land may be concerned about using fire as a way to benefit the land because it acknowledges that “one of the greatest threats to the prairie is wildfire.”
B. Incorrect. Although the sentence from paragraph 2 relates how American Indians “began to deliberately burn areas of land for bison to graze on” and to protect people’s crops, the sentence does not support the idea that farmers and people who manage land may be concerned about using fire as a way to benefit the land. Instead, it focuses on the cause-and-effect relationship between bison and newly burned areas.
C. Incorrect. The sentence from paragraph 5 provides details about how “patch burning contains the fire” and “allows animals in the burn area to safely relocate,” but it does not adequately support the idea that farmers and people who manage land may be concerned about using fire as a way to benefit the land, because it does not mention that wildfires can be a threat to the prairie.
D. Incorrect. While the sentence from paragraph 5 does explain how “conservationists will burn a different section of the preserve” in order to rotate the process year after year so that the burned land has time to regrow, the sentence does not support the idea that farmers and people who manage land may be concerned about using fire as a way to benefit the land because it does not mention the potential for total burns.
Question analysis
This evidence question asks which sentence from the article on controlled prairie burns supports the idea that farmers and others who manage land may be concerned about using fire to benefit it. The passage never states that concern directly, so students must infer it, and all four quoted sentences, taken from across the article, talk about burning land in some way.
- Grade level
- Grade 8 reading and task
- Compared with grade 7
- Above grade 7 Grade 7 evidence questions usually ask for support of an idea the text states. This idea, that people who manage land may worry about using fire, is never stated outright, so students must infer which sentence implies it, 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 evaluate
- What makes it hard
- Reading between the lines major
- A very close wrong answer moderate
- Every choice must be checked minor
- Evidence
- Answered from one sentence or line
- Reading level
- Passage: about grade 11, 598 words; question and choices: about grade 13, 123 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 idea to support is about people’s feelings, yet none of the four sentences mentions farmers worrying, so students have to decide what would justify such worry. The opening sentence does it by naming wildfire as a great threat before praising controlled fire, a concession many students read past as background. The strongest pull is the sentence on containing the fire, which implies caution but presents patch burning as the answer, not the concern.
Reading between the lines major Working it out
No sentence mentions worry; students must see that calling wildfire “one of the greatest threats to the prairie” gives landowners a reason to fear fire, and that “actually” answers that fear. (Graesser, Singer & Trabasso, 1994; Kintsch, 1998)
A very close wrong answer moderate Choosing the answer
The patch-burn sentence about containing the fire “within a specific area” also hints at fire’s danger; it differs from the right one by describing the safeguard without ever naming a threat. (Embretson & Wetzel, 1987; Gorin & Embretson, 2006; Ascalon et al., 2007)
Every choice must be checked minor Choosing the answer
The four sentences come from paragraphs 1, 2 and 5, and each is about burning land, so each must be tested for a hint of risk rather than for its topic. (Embretson & Wetzel, 1987)
Strategy: Before rereading the choices, decide what a sentence would need to say to show that landowners have reason to be wary of fire, then test each quoted sentence for exactly that.
Traps
- Supports only part of the claim: In a question about evidence: a line that backs one half of the claim but not the other, or a related point rather than the claim itself.
- True but not the answer: A choice says something accurate about the text that does not answer this question.
The wrong answers, classified
B True but not the answer (King et al., 2004; Embretson & Wetzel, 1987)
Links “the people’s crops” to farmers, but the sentence tells how early burns drew bison away from the crops and shows no worry about fire itself.
C Supports only part of the claim (King et al., 2004; Thissen, Steinberg & Fitzpatrick, 1989)
Sees caution in containing the fire “within a specific area,” but the sentence explains how patch burning keeps animals safe and never says fire threatens the land.
D Supports only part of the claim (King et al., 2004; Thissen, Steinberg & Fitzpatrick, 1989)
Takes the yearly rotation as a careful precaution, but the sentence describes the schedule and land that “regrows healthier than before,” which backs the benefit, not the worry.
Working it out, step by step
Figure out what the question asks
This is an evidence question. Evidence is the words in a text that back up an idea. The idea here is that farmers might worry about using fire to help land. No sentence says farmers are worried. So look for a sentence that gives them a reason to fear fire.
Decide what the evidence needs
A sentence that supports this idea must show that fire can be dangerous. If fire can harm land, people have a reason to be careful with it. So test each sentence with one question: does it say fire is a threat?
Look closely at paragraph 1
Choice A quotes paragraph 1. Its first half says “one of the greatest threats to the prairie is wildfire.” That is a reason to fear fire. Its second half says controlled fires are “actually” helpful. The word “actually” pushes back against that fear. It means: you might expect fire to hurt the land, but here it helps.
Check each choice
- A is right. It names wildfire as a great threat. That gives farmers a reason to worry about fire.
- B is wrong. It tells how early burns drew bison away from crops. It shows no danger from fire.
- C is wrong. It tells how patch burning keeps the fire in one area. It describes a safety step but never names a threat.
- D is wrong. It describes burning a new section each year. It shows a benefit: land that “regrows healthier than before.”
Watch out: C hints that fire must be contained, or kept in, so it sounds careful. But it describes the solution, not the danger.
Choose the answer
Only one sentence names fire as a danger. So the answer is A, the sentence from paragraph 1: “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.” Idyllic means peaceful and lovely.
Why this answer and not the closest wrong one
C is the closest wrong answer, because keeping fire “within a specific area” suggests caution. But C only explains how patch burning works. It never says fire can harm the prairie. A does, by calling wildfire one of the greatest threats.
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 B English, question 1Question
What is the best way to combine these sentences to clarify the relationship between ideas?
(1) The International Space Station has been inhabited by crew members since 2000.
(2) Tourists will soon be allowed to pay for visits to the space station.
(3) Because the cost is $52–$58 million round trip, few people will be able to take advantage of the opportunity to have a vacation in outer space.
- AThe International Space Station has been inhabited by crew members since 2000, but tourists will soon be allowed to pay for visits to the space station, which cost $52–$58 million round trip, so few people will be able to take advantage of the opportunity to have a vacation in outer space.
- BThe International Space Station has been inhabited by crew members since 2000 and will soon allow tourists to pay for visits, but because the cost is $52–$58 million round trip, few people will be able to take advantage of the opportunity to have a vacation in outer space.
- CThe International Space Station has been inhabited by crew members since 2000, but tourists will soon be allowed to pay for visits to the space station, though the cost is $52–$58 million round trip, so few people will be able to take advantage of the opportunity to have a vacation in outer space.
- DThe International Space Station has been inhabited by crew members since 2000, and tourists will soon be allowed to pay for visits to the space station because the cost is $52–$58 million round trip, therefore few people will be able to take advantage of the opportunity to have a vacation in outer space.
Show the answer
Correct answer: B
The question asks for the best way to combine the sentences.
A. Incorrect. Although the option combines the sentences in a way that accurately reflects the meaning of each individual sentence, the combined sentence is a string of clauses that do not effectively cohere. Because it is poorly structured, the combined sentence does not clarify the relationship of ideas as effectively as the correct response does. The sentence incorrectly uses “but tourists,” and “which cost” modifies “the space station” but does not modify the trip. Compared with the correct response, the combined sentence in this option is also imprecise and unnecessarily wordy.
B. CORRECT. The option uses a complex sentence to present ideas clearly and precisely, and it shows the relationship between the ideas in the original sentences. In the first part of the sentence, the conjunction “and” correctly joins the first and second sentences by indicating a relationship, rather than a contrast, between the two. In the second part of the sentence, the conjunction “but” adds additional emphasis to the fact that while tourists will be allowed to visit the space station, the cost of the trip will likely prohibit most people from visiting.
C. Incorrect. Although the option combines the sentences in a way that accurately reflects the meaning of each individual sentence, the combined sentence is a string of clauses that do not effectively cohere. Because it is so poorly structured, the combined sentence does not clarify the relationship of ideas as effectively as the correct response does. Compared with the correct response, the combined sentence in this option is also imprecise and unnecessarily wordy.
D. Incorrect. The combination of the sentences contains an illogical relationship between ideas with the statement that tourists will be allowed to pay for visits to the space station because the cost is $52–$58 million round trip. The connection between the idea that “tourists will soon be allowed to pay for visits” and the subsequent “therefore few people will be able to take advantage of the opportunity” is also illogical.
Question analysis
This sentence-combining question gives three sentences about the International Space Station, its crew and the high price of a tourist trip, and asks for the best way to join them into one. Every version keeps the same facts, so students must judge which connecting words show how the ideas relate while the sentences stay long and nearly identical.
- Grade level
- Grade 8 reading and task
- Compared with grade 7
- Above grade 7 Grade 7 students practice joining two short sentences with a fitting conjunction. Here three sentences become one long sentence in four nearly identical versions, so students must weigh every connecting word and clause rather than spot one error.
- Estimated difficulty
- Hard: combines ideas, needs a plan, and has more than one tempting wrong answer.
- Thinking it demands
- Depth of knowledge 2, skills and concepts · mainly evaluate
- What makes it hard
- How sentences fit together major
- Complex sentences moderate
- Every choice must be checked moderate
- Evidence
- Answered from one sentence or line
- Reading level
- Question and choices: about grade 15, 261 words.
- Students, last 30 days
- Not enough answers yet to show (it takes 10).
Why it is hard, traps and wrong answers (shows the answer)
Why it is hard
None of the wrong versions drops a fact, and two of them are loose rather than plainly ungrammatical, so the ear is little help. Students lose the point by accepting the smoothest chain of clauses without asking what each connector claims: whether the crew and the tourists really contrast, what the price belongs to, and what the price explains. The question rewards deciding the three links before reading the versions, then checking them one connector at a time.
How sentences fit together major Working it out
Sentence 2 simply adds to sentence 1, while sentence 3’s price works against the tourist plan and explains why few will go, so every “but,” “though,” “because” or “so” in a version must fit one of those links. (Halliday & Hasan, 1976)
Complex sentences moderate Understanding the question
Each version is one sentence of 48 to 53 words with four clauses, and at that length a “which cost” hanging on the wrong noun or a comma before “therefore” is easy to read past. (Abedi & Lord, 2001; Freedle & Kostin, 1993; Messick, 1989)
Every choice must be checked moderate Choosing the answer
All four versions keep the same facts in the same order and share most of their words, so none can be ruled out by content; each connecting word has to be tested in turn. (Embretson & Wetzel, 1987)
Strategy: Before reading the choices, decide how each sentence relates to the next: added fact, contrast, or cause and result. Then check every connecting word in each version against those links.
Traps
- Misplaced modifier: A describing word or phrase that attaches to the wrong word, or to nothing in the sentence.
- Wordy, vague or informal: A revision is grammatical but wordy, imprecise or too casual for the passage.
- Wrong transition: A connecting word or phrase that signals the wrong relationship, such as contrast where the idea continues.
The wrong answers, classified
A Misplaced modifier (Connors & Lunsford, 1988)
Keeps the price as the reason few can go, marked by “so,” but misses that “which cost” hangs on “the space station” and that “but” sets crew against tourists.
C Wordy, vague or informal (Connors & Lunsford, 1988)
Keeps every fact in order, but stacking “but,” “though” and “so” in one sentence turns the price into an aside instead of plainly the reason few people will go.
D Wrong transition (Halliday & Hasan, 1976)
Keeps sentence 3’s “because the cost is” word for word, but here it explains why tourists are allowed, and “therefore” after a comma splices on the result.
Working it out, step by step
Figure out what the question asks
You need to join three sentences into one. The best version shows clearly how the ideas connect. Joining words do that job. A conjunction is a joining word, like and, but, so or because. Each one tells the reader something. And adds a fact. But shows a contrast (two ideas that pull against each other). Because and so show a cause and its result.
Decide how the three sentences connect
Sentence 1 says crews have lived on the station since 2000. Sentence 2 adds a new fact: tourists will soon be able to visit. That is not a contrast, so it needs and. Sentence 3 works against sentence 2. The trip costs “$52–$58 million round trip.” That price is also the reason few people will go. So you need a contrast and a reason. Example: The pool is open to all, but because it costs $90, few kids swim there.
Test each choice
- B uses “and will soon allow tourists” to add the new fact. Then “but because the cost is” shows the contrast and the reason. Every link is right.
- A joins sentence 2 with “but tourists,” as if crews and tourists were opposites. Also, “which cost” comes right after “the space station.” So it sounds like the station costs that much, not the trip.
- C stacks “but,” “though” and “so” in one long chain. The price turns into a side note instead of the clear reason.
- D says tourists may visit “because the cost is” so high. That makes no sense. And “therefore” after a comma joins two sentences the wrong way.
Pick the answer
Watch out: A is the most tempting. It keeps the price as the reason, with “so.” But its “but” and its “which” send the reader the wrong way. Only one choice links every idea correctly. So the answer is B.
Why this answer and not the closest wrong one
A is the closest wrong answer. Like B, it says the price keeps most people away. But A sets crews against tourists with “but tourists.” Its “which cost” also seems to give the price of the station. B uses and for the added fact and but because for the price, so each link is clear.
More questions like this
The original DOE question
Question 4 of 6
2024 Test A Math, question 39Question
Raquel is cutting out pieces of cardboard to make a pyramid. She will use a square piece for the base and identical triangular pieces for the sides. The figure above shows the dimensions of the triangle for each side. What will be the total surface area, in square inches, of the pyramid, including the square base?
- A280
- B295
- C340
- D360
Show the answer
Correct answer: C
Surface area is found by calculating the area of each side, including the base, and adding them all together.
The base of the pyramid measures 10 inches on each side, so the area of the base is
Each triangular face has a base of 10 inches and a height of 12 inches, so the area of each face is
There are 4 triangular faces (because the square base has 4 edges, each of which will have a triangular face). So the total surface area of the pyramid is the sum of the areas of 4 triangles and 1 square.
So the total surface area is 340 square inches.
Question analysis
This surface area word problem shows one triangular face, with sides of 13 inches, a base of 10 inches and a height of 12 inches, that Raquel will use to build a cardboard pyramid with a square base. Students find the total area of the base and all the triangular sides. Picturing the solid and choosing the right measurements from the figure are the tricky parts.
- Grade level
- Grade 7 content, by NYS standard
- Compared with grade 7
- Above grade 7 Grade 7 students find the surface area of a pyramid from a drawn net or solid. Here only one triangular face is shown, so students must picture the whole pyramid, count its faces, and choose which labeled length belongs in the area formula.
- Estimated difficulty
- Hard: combines ideas, needs a plan, and has more than one tempting wrong answer.
- Thinking it demands
- Depth of knowledge 2, skills and concepts · mainly apply
- What makes it hard
- Reading a figure, table or graph moderate
- Combines ideas moderate
- Something you must already know minor
- Solution
- 4 steps
- Reading level
- Question and choices: about grade 6, 56 words.
- Corrected from the DOE handbook
- A wrong unit in the explanation was corrected.
- Students, last 30 days
- Not enough answers yet to show (it takes 10).
Why it is hard, traps and wrong answers (shows the answer)
Why it is hard
Students have to build the pyramid in their heads from one flat triangle, then choose the right measurement from three labels. The 13-inch sides look like the natural height, and using them gives a listed total; picturing a pyramid with three sloping faces gives another. Sketching the square base with a triangle on each edge, and marking 12 as the height, settles both the face count and the formula.
Reading a figure, table or graph moderate Understanding the question
The figure gives one triangle with three length labels, 13, 13 and 10, and puts its height, 12, on a separate arrow beside it, where it is easy to overlook. (Lesh, Post & Behr, 1987; Kirsch & Mosenthal, 1990)
Combines ideas moderate Working it out
The solid is never drawn: students must see that the square's side equals the triangle's 10-inch base, count four triangles, and add triangle and square areas. (Embretson, 1998; Daniel & Embretson, 2010)
Something you must already know minor Working it out
A triangle's area uses its perpendicular height, not a slanted side, and a pyramid on a square base has four triangular faces; neither fact is given. (Anderson & Krathwohl, 2001)
Strategy: Sketch the pyramid: a square base whose side is the triangle's base, and one triangular face on each side of the square. Find each area with the matching formula, then add them all.
Traps
- Misreads the figure: Reads a value, label or tick spacing in a figure, table or graph wrongly.
- Information you don't need: The question gives numbers or facts that play no part in the answer.
- Misunderstands the concept: A wrong belief about a concept: that percents can be added, that area grows like length, that averages can be averaged, that a bigger denominator means a bigger fraction.
The wrong answers, classified
A Misunderstands the concept (Smith, diSessa & Roschelle, 1993; De Bock et al., 1998; Ni & Zhou, 2005)
Counts only three triangular faces, as if the pyramid had a triangular base, so 3 × 60 + 100 = 280.
B Misunderstands the concept (Smith, diSessa & Roschelle, 1993; De Bock et al., 1998; Ni & Zhou, 2005)
Counts three faces and also uses the 13-inch side as each triangle's height: 3 × 65 + 100 = 295.
D Misreads the figure (Lesh, Post & Behr, 1987; Kirsch & Mosenthal, 1990)
Takes the 13-inch slanted side as each triangle's height instead of the 12-inch arrow beside it, so 4 × 65 + 100 = 360.
What was corrected from the DOE handbook, and why
- Explanation: The handbook ends “So the total surface area is 340 square feet.” The triangle’s dimensions are in inches and the question asks for square inches, so the site now reads “340 square inches.”
Worked solution, step by step
Formulas used
- Area of a triangle
- A is the area. b is the base, the side the triangle sits on. h is the height: the straight-up distance from the base to the top corner, at a right angle to the base. You take half because a triangle is half of a rectangle with the same base and height.
- Area of a square
- A is the area and s is the length of one side. All four sides of a square are equal, so the area is side times side.
- Surface area
- A face is one flat side of a solid shape. The surface area is the total area of the outside. Picture unfolding the solid into flat pieces. Then add up the area of every piece.
Sort out the question
Raquel’s pyramid has a square base. Each side is a triangle like the one in the figure. The triangle’s base is 10 in. Its two slanted sides are 13 in. Its height, the arrow beside it, is 12 in. You need the total surface area, including the square base, in square inches.
Picture the pyramid
Surface area is the total area of all the flat sides, called faces. Each triangle stands on one edge of the square. So each edge of the square is 10 inches, the same as the triangle’s base. A square has 4 edges, so the pyramid has 4 triangles.
Here that is 4 triangles plus 1 square. Watch out: counting only 3 triangles gives 280, choice A.
Find the area of one triangle
Each triangle is 60 square inches. Watch out: the height is 12 in., the straight-up arrow. It is not 13 in., the slanted side. Using 13 gives 65 for each triangle and 360 in all, choice D.
Find the area of the base
The base is a square with sides of 10 inches, the same as each triangle’s base.
The square base is 100 square inches.
Add all five faces
The four triangles and the square together cover 340 square inches.
So the answer is C, 340 square inches.
Check your answer
Each triangle is half of a 10 by 12 rectangle, which has an area of 120. So two triangles make 120, and four make 240. Add the base: . The units fit too: inches times inches gives square inches.
More questions like this
The original DOE question
Question 5 of 6
2018 Test B Math, question 8Question
Based on the statement above, which variable has the greatest value?
- A
- B
- C
- D
Show the answer
Correct answer: D
Break the equations apart to each equal :
Pick a number to substitute into the equations, and solve the equations to find the values of , , , , and .
Let . Since all the equations are equal to 2, substitute 2 to find each variable.
Variable has the greatest value.
Question analysis
This algebra question sets five expressions equal to one another and to a positive number, then asks which variable has the greatest value. It tests whether students can rewrite each variable in terms of one shared value and compare them. What makes it tricky is that there are no numbers to compute, so each variable's size has to be reasoned out.
- Grade level
- Grade 7 content, by NYS standard
- Compared with grade 7
- Above grade 7 Grade 7 students rewrite expressions to see how quantities relate, usually one equation at a time. This chain of five linked expressions, with no numbers to compute and a positivity condition to use, is a reasoning task beyond routine grade 7 work.
- Estimated difficulty
- Hard: combines ideas, needs a plan, and has more than one tempting wrong answer.
- Thinking it demands
- Depth of knowledge 3, strategic thinking · mainly analyze
- What makes it hard
- Variables instead of numbers major
- No obvious method moderate
- Much to keep track of minor
- Solution
- 3 steps
- Reading level
- Question and choices: about grade 10, 16 words.
- Students, last 30 days
- Not enough answers yet to show (it takes 10).
Why it is hard, traps and wrong answers (shows the answer)
Why it is hard
The question rewards a strategy, not a calculation: once the shared value is named, each variable follows in one line and R is clearly largest. Without that step, students judge by how the expressions look, and the look is backwards, since the 3 in 3N makes N small and the 7 under R makes R large. The positivity condition at the end is easy to skip but is what fixes the order.
Variables instead of numbers major Understanding the question
There are no numbers to compute: five variables are tied together in the one chain M = 3N = P/4 = Q + 5 = R/7, and each must be compared through the shared value. (Koedinger & Nathan, 2004; Enright, Morley & Sheehan, 2002)
No obvious method moderate Working it out
Nothing says how to compare; the efficient move is to name the common value, or pick one such as 12, and rewrite each variable, which students must think of themselves. (Schoenfeld, 1985)
Much to keep track of minor Working it out
Five relations and the condition > 0 must be held at once; the condition matters, since with a negative common value the order of M, N, P and R would reverse. (Sweller, 1988; Carpenter, Just & Shell, 1990)
Strategy: Call the shared value k, a positive number, and rewrite each variable as an expression in k; or substitute a convenient positive value such as 12 and compare the results.
Traps
- Equation written backwards: Writes a comparison the wrong way round, word for word: "six times as many students as professors" as 6S = P. The bigger quantity gets the bigger number.
The wrong answers, classified
A Equation written backwards (Clement, Lochhead & Monk, 1981)
Reads P/4 and R/7 as a quarter and a seventh of M, the reverse of the truth, so M looks largest of all.
B Equation written backwards (Clement, Lochhead & Monk, 1981)
Reads the 3 in 3N as making N three times as large, when 3N = M actually makes N one third of M.
C Stops one step early (King et al., 2004; Gierl et al., 2017)
Correctly sees that P is four times M but stops there without checking R, which at seven times M is larger.
Worked solution, step by step
Formulas used
- Undoing division
- a is the top of the fraction, b is the bottom, and c is the result. Multiplying undoes dividing. So if a divided by b is c, then a is b times c.
- Undoing multiplication
- b is the number multiplied by a, and c is the result. Dividing undoes multiplying. So to get a alone, divide c by b.
Understand the chain
The statement is a chain of equal signs. It says five expressions all have the same value. The last part says that value is greater than 0, so it is positive.
You need to find which letter has the largest value.
Pick a value to test
All five expressions are equal, so give them one shared value. Pick a positive number that 3 divides evenly. That way N will be a whole number.
Let the shared value be 12. Then , and each of the other four expressions also equals 12.
Solve for each letter
Undo each operation to find each letter. Divide to undo times. Multiply to undo divide. Subtract to undo plus.
Compare the values
The values are M = 12, N = 4, P = 48, Q = 7 and R = 84. R is the largest.
Watch out: 3N does not make N big. It means 3 times N equals M, so N is only one third of M. That trap points to choice B. Also, P is big, but R is bigger. Check every letter before you pick choice C.
So the answer is D, R.
Check your answer
Think without numbers. R divided by 7 is M, so R is 7 times M. P is only 4 times M. N is a third of M, and Q is 5 less than M. Since M is positive, 7 times M is the biggest.
More questions like this
The original DOE question
Question 6 of 6
2018 Test B Math, question 53Question
At North High School, a survey asked two questions, Question A and Question B. For each question, students could answer either “yes” or “no.” Of the 800 students who responded to the survey, 720 answered “yes” to Question A, and 640 answered “yes” to Question B. What is the least possible number of these students who could have answered “yes” to both questions?
- A80
- B160
- C560
- D640
Show the answer
Correct answer: C
None of the 80 students (800 − 720) who answered “no” to Question A could have answered “yes” to both questions.
Therefore, the least possible number of students who could have answered “yes” to both questions can be found by subtracting the 80 who answered “no” to Question A from the 640 who answered “yes” to Question B or 640 − 80 = 560.
Question analysis
In a survey of 800 students at North High School, 720 said yes to the first question and 640 said yes to the second. Students must find the smallest possible number who said yes to both. It tests reasoning about overlapping groups, and asking for the least possible overlap rather than an exact count makes it unusual.
- NYS standards
- Grade level
- Grade 7 content, by NYS standard
- Compared with grade 7
- Above grade 7 Grade 7 students work with Venn diagrams and two-way tables when all counts are given. Finding the smallest possible overlap requires reasoning about extremes rather than computing, which is rare in grade 7 and new to most students.
- Estimated difficulty
- Among the hardest on the SHSAT: a non-obvious approach, heavy reading, or a well-hidden trap.
- Thinking it demands
- Depth of knowledge 3, strategic thinking · mainly analyze
- What makes it hard
- No obvious method major
- Turning words into math moderate
- A very close wrong answer minor
- Solution
- 2 steps
- Reading level
- Question and choices: about grade 8, 60 words.
- Corrected from the DOE handbook
- A repeated phrase and a stray comma in the explanation were removed.
- 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 students have never been asked for a smallest overlap, so they fall back on a picture of nested groups and give the largest one. The key move is to push the two yes groups apart as far as possible: only the 80 students who said no to Question A can absorb some of Question B's yes answers. Once that is seen, the arithmetic is one subtraction, so the question rewards reasoning far more than computation.
No obvious method major Working it out
Nothing in the wording points to the method: the smallest overlap appears only when all 80 students who said no to Question A are imagined saying yes to Question B. (Schoenfeld, 1985)
Turning words into math moderate Understanding the question
"The least possible number of these students who could have answered “yes” to both questions" asks for an extreme case, which has to be turned into an arrangement of the 800 students. (Hegarty, Mayer & Monk, 1995; Koedinger & Nathan, 2004)
A very close wrong answer minor Choosing the answer
640 is only 80 above the right 560, so a rough sense of size cannot choose between them; only asking whether the overlap is the least or the greatest separates them. (Embretson & Wetzel, 1987; Gorin & Embretson, 2006; Ascalon et al., 2007)
Strategy: Add the two yes counts and compare the sum with the number of students; any amount above the total must come from students counted in both groups.
Traps
- NOT, LEAST or EXCEPT: The question asks for the exception, the least, or what is not true.
- 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 Stops one step early (King et al., 2004; Gierl et al., 2017)
Finds the 80 students who said no to Question A, 800 − 720, and stops before subtracting them from the 640 who said yes to Question B.
B Answers a different question (King et al., 2004; Hegarty, Mayer & Monk, 1995)
Finds the 160 students who said no to Question B, 800 − 640, which bears on the count but is not the overlap asked about.
D Answers a different question (King et al., 2004; Hegarty, Mayer & Monk, 1995)
Assumes everyone who said yes to Question B also said yes to Question A, giving the greatest possible overlap instead of the least.
What was corrected from the DOE handbook, and why
- Explanation: The handbook prints “(800 − 720)” twice in its first sentence, after “80 students” and again after “Question A,” and puts a comma between subject and verb in “the least possible number of students who could have answered “yes” to both questions, can be found.” The site keeps the first “(800 − 720)” and drops the comma.
Worked solution, step by step
Formulas used
- Least overlap of two groups
- a is the size of the first group and b is the size of the second. t is the total number of people. If a + b is more than t, some people must be in both groups. The extra amount is the smallest number that can be in both.
Sort out what you know
There were 800 students. Of them, 720 said yes to Question A and 640 said yes to Question B. You need the least number who could have said yes to both. The overlap is the group in both yes groups. You want the smallest overlap.
Find who said no to A
Students who said no to Question A cannot be in the overlap.
So 80 students said no to Question A.
Watch out: 80 is not the answer. It is only a step, and it is choice A.
Keep the overlap small
To make the overlap as small as you can, put as many B yes answers outside it as possible. The only students outside it are the 80 who said no to A. So pretend all 80 of them said yes to B.
Count the rest of the yes group
The other yes answers to B must come from students who also said yes to A.
So at least 560 students said yes to both.
Watch out: 640 is the most that could say yes to both, not the least. That is choice D.
Give the answer
The fewest students who could say yes to both questions is 560. So the answer is C, 560.
Check your answer
Use the overlap formula: . There are 1,360 yes answers but only 800 students, so 560 students must be counted twice. You can also check the groups. 560 said yes to both, 160 to A only and 80 to B only. That makes .
More questions like this
The original DOE question
