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Six SHSAT Questions

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.

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Question 1 of 6

2024 Test A English, question 8
Passage 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.
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.

  1. 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)

  2. 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)

  3. 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

How the questions are analyzed, and the research behind it

Working it out, step by step

  1. 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.

  2. 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.

  3. 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.

  4. 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.

  5. 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
Question 8 as printed on page 40 of the DOE handbook.
As printed in the DOE’s NYC Guide to the Specialized High Schools Admissions Test (SHSAT) for 2025 Admissions, page 40, question 8. Open page 40 of the handbook (PDF) The handbook letters this question’s choices E–H; here they are A–D (E = A, F = B, G = C, H = D).
The passage “The Free College Debate” as printed (page 38)The passage “The Free College Debate” as printed on page 38 of the DOE handbook.

Question 2 of 6

2026 Practice Test D English, question 17
Passage Wolves of the Sea

Wolves of the Sea

The cool and misty landscape of the Great Bear Rainforest can be found along the coast of British Columbia, Canada, and its nearby islands, from Vancouver Island to the Alaskan border. Within this protected area, wolves roam the forests, islands, and beaches. When biologist Chris Darimont began to study these wolves, he wanted to confer with local First Nations groups, as aboriginal Canadians are known, in order to learn what they knew about these wolves. He spoke with Chester Starr, an elder of the Heiltsuk Nation that has occupied the Great Bear Rainforest for thousands of years. What Starr had to say about the wolves changed Darimont’s perception of the animals.

Starr asked Darimont which wolves he and his team were going to study—the timber wolves (mainland wolves) or the coastal wolves on the islands. The question took Darimont by surprise. Biologists had always believed that the wolves that are sometimes spotted swimming between islands and eating salmon are the same wolves that live on the mainland. Darimont was intrigued by Starr’s classification of the wolves as two different groups. At first, he was hesitant to accept the idea. The distances between the mainland and the islands are small, less than a mile. Why would the wolves on the islands be any different from the wolves on the mainland? To find out, Darimont and his research team studied the wolves on the islands and in the densely forested territory of the Great Bear Rainforest for ten years.

Throughout the study, Darimont recorded several significant, observable differences between the “sea wolves,” as they are nicknamed, and the mainland wolves. Compared with the mainland wolves, the sea wolves are smaller in size and are strong swimmers. In 1996 sea wolves were spotted on an island nearly eight miles from any other land formation. While mainland wolves almost exclusively eat meat, such as deer and elk, and teach their young to hunt for land animals, sea wolves get as much as 90 percent of their nutrition from the sea and teach their young to dig for clams and to catch fish. Sea wolves regularly swim between islands and have been known to sneak up on a seal sunning itself on a rock and make a leaping attack from the water. Some salmon-eating mainland wolves come and go from the islands with the fish-spawning season, but the sea wolves are full-time island residents. Darimont suspects that some sea wolves live their entire life on the islands.

The sea wolves displayed not only physical and behavioral differences but also genetic variations from the mainland wolves. After collecting and analyzing the DNA in 800 samples of gray fur and wolf waste, researchers could produce hard biological evidence that sea wolves had genetic markers that made them distinct from the mainland wolves. A genetic marker is a variation in a DNA sequence that can be used to identify individuals or a species because it is passed down to offspring. Darimont hypothesizes that a change in habitat led to the eventual genetic differences between sea wolves and mainland wolves. Many years ago, loss of habitat and food sources forced some mainland wolves out to the islands. They learned to eat everything from kelp and fish eggs to the remains of sea creatures that washed up on the beach. Wolves living on the islands and mainland wolves became more isolated and rarely mated with each other. Over time the two types of wolves became more distinct.

It turned out that Chester Starr was right all along. “It sounded totally bizarre at first,” admits Darimont, “that there could be two versions of the species.” But he now realizes that this skepticism “definitely reflected my ignorance of indigenous knowledge at the time.” Learning to trust the wisdom of the Heiltsuk people opened Darimont up to knowledge accumulated over millennia and positioned him so that he could gather new scientific evidence about one of British Columbia’s most elusive species, the sea wolf.

Question

Read this sentence from paragraph 4.

After collecting and analyzing the DNA in 800 samples of gray fur and wolf waste, researchers could produce hard biological evidence that sea wolves had genetic markers that made them distinct from the mainland wolves.

The phrase “hard biological evidence” conveys that the goal of the research team was to

  • Adevelop a procedure in order to ensure their study yielded plentiful data about the wolves.
  • Bseek definitive scientific proof of the number of wolf species present in the area of the study.
  • Cconduct a study to evaluate multiple theories about the diets of different wolf species.
  • Ddiscover if the new data would provide information different from that of previous studies.
Show the answer

Correct answer: B

The question asks what the phrase “hard biological evidence” in the sentence from paragraph 4 conveys about the goal of the research team.

A. Incorrect. Although the research team followed a labor-intensive procedure, the phrase “hard biological evidence” refers to the product of their scientific research (the genetic markers revealed within the DNA samples), not the process by which they collected it. Their goal was not to develop a procedure for data collection but to determine precisely how many species of wolf were present in the area.

B. CORRECT. The research team wanted to prove or disprove the theory that two separate groups of wolves were present in the area, an idea that was already supported by the observations of scientists and local indigenous people. The phrase “hard biological evidence” conveys that the scientists wanted to bolster their observations of the wolves with concrete scientific data about the wolves’ biological makeup. The goal of the researchers was to use the data to prove how many species of wolf were present in the area of the study.

C. Incorrect. The research team gathered extensive data during their study (“After collecting and analyzing the DNA in 800 samples of gray fur and wolf waste” [paragraph 4]), and their goal in doing so was to evaluate a single theory about the wolves: that the wolves had evolved into two separate and genetically distinct species. The research team did not conduct the study in order to evaluate multiple theories about the diets of the wolves.

D. Incorrect. The phrase “hard biological evidence” does not suggest that the research team was hoping to discover if the new data would provide information that was different from previous studies. In fact, the goal of the research team was to use the genetic data to supplement their initial sources of information about the wolves and their own observations from the field.

Question analysis

This word-in-context question quotes a sentence from paragraph 4 of “Wolves of the Sea” about DNA taken from 800 samples of gray fur and wolf waste, and asks what the phrase “hard biological evidence” shows about the research team’s goal. Students must work out what the phrase says about the evidence and then turn that into a statement of purpose, choosing among four plausible aims for a study.

NYS standards
  • 7R4 word meaning and choice
  • 7L4a context clues
Grade level
Grade 8 reading and task
Compared with grade 7
Above grade 7 Grade 7 students regularly interpret a phrase in context. Here the phrase must be turned into a claim about the team’s purpose, which the passage never states outright, and the four choices are abstract research goals that each sound reasonable.
Estimated difficulty
Hard: combines ideas, needs a plan, and has more than one tempting wrong answer.
What makes it hard
Evidence
Answered from several paragraphs or stanzas
Reading level
Passage: about grade 10, 662 words; question and choices: about grade 10, 114 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 asks for a purpose, but the phrase it quotes describes a result, so students have to reason from the kind of evidence produced to what the team wanted it for. Readers who take “hard” as difficult drift toward a goal about procedure, and those who remember that biologists had long thought the wolves were one group are drawn to a goal of overturning earlier studies. The key’s “number of wolf species” is looser than the passage’s “two versions of the species,” which can make careful readers hesitate.

  1. Reading between the lines moderate Working it out

    The passage never states the team’s goal, so students must work back from “hard biological evidence” to the question paragraph 2 set up: whether island and mainland wolves are really two groups. (Graesser, Singer & Trabasso, 1994; Kintsch, 1998)

  2. Hard words moderate Understanding the question

    “Hard” here means solid and conclusive, as in hard evidence, not difficult; students who know only the everyday sense connect it to the labor of analyzing 800 samples of fur and waste. (Perfetti, 2007; Freedle & Kostin, 1993)

  3. Evidence in several places minor Working it out

    The goal the phrase points to lies two paragraphs back, in Starr’s two-group question and Darimont’s ten-year study “to find out,” not in the sentence the stem quotes. (Kirsch & Mosenthal, 1990; Gorin & Embretson, 2006)

Strategy: Replace “hard” with a word that fits evidence produced by DNA analysis, then ask what the team wanted that kind of evidence for, recalling the question Darimont set out to answer.

Traps

The wrong answers, classified

How the questions are analyzed, and the research behind it

Working it out, step by step

  1. Figure out what the question asks

    This asks what a phrase shows about the team’s goal. A goal is what you are trying to get. The phrase names the kind of evidence the team got. Work back from that to what they wanted it for.

  2. Read the sentence with the phrase

    In paragraph 4, the team studied “800 samples of gray fur and wolf waste.” Then they “could produce hard biological evidence that sea wolves had genetic markers that made them distinct from the mainland wolves.” A genetic marker is a small difference in the DNA that parents pass to their young. Distinct means clearly different.

  3. Work out what “hard” means

    Here “hard” does not mean difficult. Hard evidence is solid proof that is tough to argue with. Biological means it comes from living things and their bodies. So the team wanted firm proof from the wolves’ own bodies.

  4. Connect the proof to the question

    What did they want to prove? Go back to paragraph 2. Starr said there were two groups of wolves. Darimont was unsure. “To find out,” his team studied the wolves. The DNA gave a firm answer: the sea wolves really are a separate group. So the goal was solid proof of how many groups of wolves live there.

  5. Check each choice

    • A is wrong. It reads “hard” as hard work. The phrase is about how firm the proof is, not about a procedure.
    • B is right. Definitive means final and settled. The team wanted settled proof of how many groups of wolves live there. B says “species,” which goes further than the passage. Darimont speaks only of “two versions of the species.”
    • C is wrong. Diets come up in paragraph 3. The DNA work tested whether there were two groups.
    • D is wrong. The phrase says nothing about earlier studies.

    Watch out: D is tempting because biologists “had always believed” the wolves were one group. But “hard” evidence is about firm proof, not about beating old studies.

  6. Choose the answer

    “Hard biological evidence” shows the team wanted firm, scientific proof. So the answer is B, “seek definitive scientific proof of the number of wolf species present in the area of the study.”

Why this answer and not the closest wrong one

D is the closest wrong answer. Biologists had thought the wolves were one group, so D can seem to fit. But the phrase “hard biological evidence” is about how firm the proof is. It says nothing about earlier studies. B matches that: the team wanted settled proof of how many groups there were.

More questions like this

The original DOE question
Question 17 as shown on the DOE’s digital test, page 27 of its printable version.
As printed in the DOE’s printable version of 2026 Practice Test D English, page 27, question 17.
The passage “Wolves of the Sea” as printed (pages 23–24)The passage “Wolves of the Sea” as printed on page 23 of the DOE handbook.The passage “Wolves of the Sea” as printed on page 24 of the DOE handbook.

Question 3 of 6

2026 Practice Test B English, question 45
Passage The End of an Era

The End of an Era

(1) In 2004, the National Aeronautics and Space Administration (NASA) landed a rover, or robotic vehicle, named Opportunity on the surface of Mars. (2) The rover’s mission was to search for evidence of water and life on the planet. (3) The rover was designed to gather data on Mars for about 90 days, but Opportunity’s assignment did not come to an end until nearly 15 years later in 2019.

(4) During the rover’s mission, a high-resolution camera on the rover’s robotic arm took magnified photographs of the surface of Mars. (5) The photographs revealed small round rocks scattered across the surface of the planet. (6) The scientists nicknamed these rocks “blueberries” based on the rocks’ resemblance to the fruit. (7) These rocks were important because their spherical shape suggested that liquid water may have flowed over them for a substantial amount of time.

(8) Opportunity continued to provide valuable data about craters and other surface features. (9) Throughout the mission, the rover traveled a total of 28.06 miles across Mars’ surface. (10) When Opportunity had traveled nearly the length of a marathon, scientists celebrated the accomplishment by naming the valley that the rover was in Marathon Valley. (11) However, in 2018, a dust storm spread all over the planet, putting the rover’s progress on hold.

(12) Prior to this planet-wide dust storm, minor dust storms had periodically deposited a layer of dust onto the solar panels of the rover. (13) These prevented it from charging its batteries. (14) Scientists then had to rely on the passing winds and dust devils to clean off the solar panels. (15) After the massive 2018 dust storm subsided, scientists expected to be able to reestablish communication with Opportunity. (16) They made repeated attempts but to no avail. (17) In 2019, NASA finally declared Opportunity’s mission complete.

(18) Opportunity was an important asset in scientists’ study of Mars; it returned valuable data about our neighbor planet and survived powerful dust storms. (19) NASA described the mission of Opportunity as “one of the most successful and enduring feats of interplanetary exploration.” (20) Even though this rover’s journey ended, other rovers still roam the surface of Mars.

Question

Which revision of sentence 11 best maintains the formal style established in the passage?

  • AHowever, in 2018, a dust storm covered the planet, bringing the rover’s progress to a standstill.
  • BHowever, in 2018, a dust storm shrouded the planet, impermanently halting the rover’s progress.
  • CHowever, in 2018, a dust storm enveloped the whole of the planet, arresting the rover’s progress for a time.
  • DHowever, in 2018, a dust storm covered up the whole planet, which quickly brought a stop to the progress of the rover.
Show the answer

Correct answer: A

The question asks for the revision of sentence 11 that best maintains the formal style established in the passage.

A. CORRECT. This sentence uses clear and formal writing throughout. The phrase “covered the planet” is accurate and formal without being overly poetic, and “standstill” is a precise word for putting something “on hold,” as expressed by the original sentence, while maintaining the formal style of the passage.

B. Incorrect. Although the sentence is formal in style, the word “shrouded” is overly poetic, and the phrase “impermanently halting” is too stilted and formal for the style and tone of the passage.

C. Incorrect. Although the sentence is formal in style, the words “enveloped” and “arresting” are overly poetic, especially when used in the same sentence, and the phrases “the whole of the planet” and “for a time” are needlessly wordy and imprecise, compared with the formal scientific language of the passage.

D. Incorrect. The phrases “covered up the whole planet” and “quickly brought a stop to the progress of the rover” are less formal and unnecessarily wordy, compared with the formal style established by the rest of the passage.

Question analysis

This style question asks which revision of sentence 11, about the 2018 dust storm that covered Mars and stopped the Opportunity rover, best maintains the formal style of the passage. All four versions say the same thing, so students must compare word choice and wordiness and decide which one reads like the rest of the passage.

NYS standards
  • 7W2f informative writing style
  • 7L3a precise and concise language
Grade level
Grade 8 reading and task
Compared with grade 7
Above grade 7 Keeping a formal style is grade 7 writing work, usually tested by spotting slang or casual wording. Here all four revisions keep the meaning and differ in register by degrees, so students must judge the passage's own style closely, more than typical.
Estimated difficulty
Hard: combines ideas, needs a plan, and has more than one tempting wrong answer.
Evidence
Answered from one sentence or line
Reading level
Passage: about grade 11, 337 words; question and choices: about grade 9, 80 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 turns on what “formal” means. Many students equate it with impressive words and choose the revision with “enveloped” and “arresting,” or the one with “shrouded,” missing that both are more poetic than a passage that reports dates and distances. The casual revision is easy to reject, so the real test is preferring the plainest formal sentence to the grandest one.

  1. Something you must already know moderate Working it out

    Students must know that a formal informational style is plain and precise, so words such as “shrouded,” “enveloped” and “arresting” are too ornate for a passage that reports miles and dates. (Anderson & Krathwohl, 2001)

  2. Every choice must be checked moderate Choosing the answer

    All four revisions keep the meaning of sentence 11 and differ only in register and length, so each must be heard against the passage’s voice rather than checked for errors. (Embretson & Wetzel, 1987)

  3. Hard words minor Understanding the question

    “Impermanently,” “shrouded” and “arresting,” in its sense of stopping, are uncommon words, and students must judge how they sound in the passage, not only what they mean. (Perfetti, 2007; Freedle & Kostin, 1993)

Strategy: Reread a few sentences around sentence 11 to hear the passage's voice, then check each revision for casual phrasing, needless words and words that would sound out of place in that voice.

Traps

The wrong answers, classified

How the questions are analyzed, and the research behind it

Working it out, step by step

  1. Figure out what the question asks

    This question asks which version of sentence 11 keeps the passage’s formal style. Formal writing is serious and clear, like a textbook. It avoids slang and casual words. But formal doesn’t mean fancy. Formal writing about science uses plain, exact words. For example, The game got called off is casual. The contest was halted indefinitely is too fancy. The game was canceled is formal and plain.

  2. Hear the passage’s voice

    Sentence 9 says “the rover traveled a total of 28.06 miles across Mars’ surface.” Sentence 12 says minor storms “deposited a layer of dust onto the solar panels.” The words are exact and plain. The passage gives dates and numbers. It doesn’t paint poetic pictures.

  3. Check each revision

    • A is right. “Covered the planet” is plain and exact. A standstill is a complete stop, a clear way to say “on hold.”
    • B is wrong. “Shrouded” is poetic. A shroud is a cloth wrapped around a body. “Impermanently halting” sounds stiff and odd.
    • C is wrong. “Enveloped” and “arresting” are fancy words. Here arresting means stopping. “The whole of the planet” and “for a time” add extra words.
    • D is wrong. “Covered up” is casual. “Brought a stop to the progress of the rover” is wordy, or longer than it needs to be.

    Watch out: Many students think formal means big words, so they choose C. But a passage of dates and miles calls for plain words.

  4. Choose the answer

    Only A is both formal and plain, like the rest of the passage. So the answer is A: “However, in 2018, a dust storm covered the planet, bringing the rover’s progress to a standstill.”

Why this answer and not the closest wrong one

C is the closest wrong answer, because it has no slang and sounds serious. But “enveloped” and “arresting” are poetic, and “the whole of the planet” is wordy. The passage reports facts in plain words. A says the same thing in the plainest formal way.

More questions like this

The original DOE question
Question 45 as shown on the DOE’s digital test, page 63 of its printable version.
As printed in the DOE’s printable version of 2026 Practice Test B English, page 63, question 45.
The passage “The End of an Era” as printed (page 60)The passage “The End of an Era” as printed on page 60 of the DOE handbook.

Question 4 of 6

2024 Test A Math, question 39

Question

Triangle with its two slanted sides each labeled 13 in. and its base labeled 10 in. Beside it, a vertical arrow as tall as the triangle, from its base to its top vertex, is labeled 12 in.

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

10×10=10010 \times 10 = 100

Each triangular face has a base of 10 inches and a height of 12 inches, so the area of each face is

12×10×12=60\frac{1}{2} \times 10 \times 12 = 60

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.

(4×60)+100=240+100(4 \times 60) + 100 = 240 + 100

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.

NYS standards
  • 7.G.6 area, surface area, and volume
  • 6.G.4 nets and surface area
  • 6.G.1 area of polygons
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.
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.

  1. 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)

  2. 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)

  3. 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

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.”

How the questions are analyzed, and the research behind it

Worked solution, step by step

Formulas used

Area of a triangle
A=12×b×hA = \frac{1}{2} \times b \times h
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=s×sA = s \times s
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
surface area=sum of the areas of all the faces\text{surface area} = \text{sum of the areas of all the faces}
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.

  1. 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.

  2. 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.

    surface area=sum of the areas of all the faces\text{surface area} = \text{sum of the areas of all the faces}

    Here that is 4 triangles plus 1 square. Watch out: counting only 3 triangles gives 280, choice A.

  3. Find the area of one triangle

    A=12×b×hA = \frac{1}{2} \times b \times h

    A=12×10×12=60A = \frac{1}{2} \times 10 \times 12 = 60

    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.

  4. Find the area of the base

    The base is a square with sides of 10 inches, the same as each triangle’s base.

    A=s×sA = s \times s

    A=10×10=100A = 10 \times 10 = 100

    The square base is 100 square inches.

  5. Add all five faces

    surface area=4×60+100=240+100=340\text{surface area} = 4 \times 60 + 100 = 240 + 100 = 340

    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: 240+100=340240 + 100 = 340. The units fit too: inches times inches gives square inches.

More questions like this

The original DOE question
Question 96 as printed on page 86 of the DOE handbook.
As printed in the DOE’s NYC Guide to the Specialized High Schools Admissions Test (SHSAT) for 2025 Admissions, page 86, question 96. Open page 86 of the handbook (PDF) The handbook letters this question’s choices E–H; here they are A–D (E = A, F = B, G = C, H = D). This is the DOE’s version, before the corrections listed in the analysis.

Question 5 of 6

2026 Practice Test C Math, question 18

Question

I. s−ts - t
II. st2st^{2}
III. sts^{t}

If s is a positive integer and t is a negative integer, which of the above expressions must be a positive number?

  • AII only
  • BI and II only
  • CII and III only
  • DI, II, and III
Show the answer

Correct answer: D

Each of the three expressions must be considered:

Expression I: s−ts - t, where s is a positive integer and t is a negative integer:

Subtracting a negative integer is the equivalent of adding a positive integer, so s−ts - t is equivalent to finding the value of s+(−t)s + (-t), which must result in a positive number.

Expression II: st2st^{2}, where s is a positive integer and t is a negative integer:

Squaring a negative integer results in a positive integer, so s(−t)2s(-t)^{2} is equivalent to finding the value of st2st^{2}, which must result in a positive number.

Expression III: sts^{t}, where s is a positive integer and t is a negative integer:

A negative exponent results in the reciprocal of the same exponential expression, so sts^{t} is equivalent to finding the value of 1s(−t)\frac{1}{s^{(-t)}}, which must result in a positive number.

Therefore, Expressions I, II, and III must all result in a positive number.

Question analysis

Three expressions, s − t, s times t squared, and s to the power t, are listed, and students decide which must be positive when s is a positive integer and t is a negative integer. It tests sign rules for subtraction and multiplication and the meaning of a negative exponent. Each expression has to be judged for every possible pair, not just one example.

NYS standards
  • 8.EE.1 integer exponent properties
  • 7.NS.1c rational number subtraction
  • 7.NS.2a rational number multiplication
Grade level
Grade 8 content, by NYS standard
Compared with grade 7
Above grade 7 Grade 7 students learn sign rules for subtracting and multiplying signed numbers. Here they reason about letters rather than numbers, decide what must always hold, and handle a negative exponent, a grade 8 idea.
Estimated difficulty
Hard: combines ideas, needs a plan, and has more than one tempting wrong answer.
Solution
3 steps
Reading level
Question and choices: about grade 5, 42 words.
Corrected from the DOE handbook
  • Two steps of the explanation that treated t as a positive number were corrected.
  • A punctuation error 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

The three expressions test three different sign facts: subtracting a negative, squaring a negative, and raising to a negative power. The last is the trap, since a negative exponent seems to promise a negative result when it really gives a fraction, and that belief alone leads to a listed choice. Trying s = 2 and t = −3 gives 5, 18 and 1/8, all positive, and the rules show why no other pair can change that.

  1. Variables instead of numbers moderate Understanding the question

    No values are given for s and t, only their signs, and must means each expression has to be positive for every such pair, not just for one example. (Koedinger & Nathan, 2004; Enright, Morley & Sheehan, 2002)

  2. Something you must already know moderate Working it out

    Expression III needs the meaning of a negative exponent, s to the power t equals 1 over s to the power −t, a grade 8 rule the question does not state. (Anderson & Krathwohl, 2001)

  3. Every choice must be checked minor Choosing the answer

    Each of the three expressions is judged on its own and the choices combine the verdicts, so one wrong judgment anywhere points to a wrong combination. (Embretson & Wetzel, 1987)

Strategy: Try a pair such as s = 2 and t = −3 in each expression, then explain why its sign could or could not change for any other positive s and negative t.

Traps

  • 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.
  • 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.)

The wrong answers, classified

What was corrected from the DOE handbook, and why

  • Explanation: The question makes t the negative integer, but two steps of the DOE’s explanation write the negative integer as −t, as if t were positive. For Expression I it says “s − (−t) is equivalent to finding the value of s + t, which must result in a positive number”: s − (−t) is not Expression I, and with the question’s t, s + t need not be positive (s = 1 and t = −2 give −1). For Expression III it says “s^(−t) is equivalent to finding the value of 1/s^t”, about s^(−t) rather than Expression III. The site now says that s − t is equivalent to s + (−t), and that s^t is equivalent to 1/s^(−t). Since t is negative, −t is a positive integer, so s + (−t) is the sum of two positive integers and 1/s^(−t) is the reciprocal of a positive integer: both positive, and the answer, I, II and III, is unchanged. The step for Expression II, s(−t)² = st², is true for any t and is unchanged.
  • Explanation: The DOE’s explanation introduces Expression III as “s^t. where s is a positive integer and t is a negative integer”, with a period where Expressions I and II (and the 2022–23 guide, which first printed this explanation) have a comma. The site has the comma.

How the questions are analyzed, and the research behind it

Worked solution, step by step

Formulas used

Subtracting a number
s−t=s+(−t)s - t = s + (-t)
s and t are integers, and −t is the opposite of t. Subtracting a number is the same as adding its opposite. When t is negative, −t is positive. So subtracting t adds a positive amount.
A negative exponent
st=1s−ts^{t} = \frac{1}{s^{-t}}
s is the base and t is the exponent. When t is negative, −t is positive. So a negative exponent means 1 over the base to a positive exponent. For example, 2 to the power −3 is 1 over 2³, which is 1/8.

  1. Sort out the question

    An integer is a whole number or its opposite, such as −2, 0 or 5. Here s is a positive integer, like 1, 2 or 3. And t is a negative integer, like −1, −2 or −3. Must means always. An expression counts only if it is positive for every such pair.

  2. Try one pair of numbers

    Try s = 2 and t = −3 in each expression:

    • I: 2−(−3)=2+3=52 - (-3) = 2 + 3 = 5
    • II: 2×(−3)2=2×9=182 \times (-3)^{2} = 2 \times 9 = 18
    • III: 2−3=123=182^{-3} = \frac{1}{2^{3}} = \frac{1}{8}

    All three are positive this time. Now see why that always happens.

  3. Explain expression I

    Use the rule for subtracting:

    s−t=s+(−t)s - t = s + (-t)

    t is negative, so its opposite, −t, is positive. So s − t is a positive plus a positive. That is always positive.

    Watch out: subtracting does not always make a number smaller. Subtracting a negative makes it bigger. Missing this leads to choice C.

  4. Explain expression II

    t2t^{2} means t × t. A negative times a negative is positive, so t2t^{2} is always positive. Then s×t2s \times t^{2} is a positive times a positive. That is always positive too.

  5. Explain expression III

    Use the rule for a negative exponent:

    st=1s−ts^{t} = \frac{1}{s^{-t}}

    −t is a positive integer, so s−ts^{-t} is a positive integer. So sts^{t} is 1 over a positive number. That is a positive fraction.

    Watch out: a negative exponent does not make the answer negative. It makes a fraction. Thinking it does leads to choice B, I and II only.

  6. Choose the answer

    Each of the three expressions is positive for every positive s and negative t. None of them can ever be zero or negative.

    So the answer is D, I, II, and III.

Check your answer

Try the values closest to 0: s = 1 and t = −1. I gives 1−(−1)=21 - (-1) = 2. II gives 1×(−1)2=11 \times (-1)^{2} = 1. III gives 1−1=11=11^{-1} = \frac{1}{1} = 1. All three are still positive.

More questions like this

The original DOE question
Question 18 as shown on the DOE’s digital test, page 91 of its printable version.
As printed in the DOE’s printable version of 2026 Practice Test C Math, page 91, question 18. This is the DOE’s version, before the corrections listed in the analysis.

Question 6 of 6

2024 Test B Math, question 17

Question

A bowl contains 12 green candies, 4 yellow candies, and some red candies. The probability of choosing a green candy at random is twice as great as the probability of choosing a red candy at random. What is the probability of choosing a yellow candy at random?

  • A211\frac{2}{11}
  • B29\frac{2}{9}
  • C14\frac{1}{4}
  • D311\frac{3}{11}
Show the answer

Correct answer: A

The probability of choosing a green candy is twice as great as the probability of choosing a red candy. There are 12 green candies. Let r = the number of red candies.

12=2r12=2r

r=6r=6

So there are 6 red candies. 12 green candies + 4 yellow candies + 6 red candies = 22 total candies.

There are 4 yellow candies out of a total of 22 candies. So the probability of choosing a yellow candy is

422=211\frac{4}{22}=\frac{2}{11}.

Question analysis

A probability question about a bowl of 12 green candies, 4 yellow candies and an unknown number of red ones. A green candy is twice as likely to be picked as a red one, and students find the chance of picking a yellow candy. The missing red count has to be worked out before any probability can be found.

NYS standards
Grade level
Grade 6 content, by NYS standard
Compared with grade 7
Above grade 7 Simple probability is grade 6 content in New York, and grade 7 problems usually give every count. Working backward from a comparison of two probabilities to a missing count, then forward to a third probability, is more than typical grade 7 work.
Estimated difficulty
Hard: combines ideas, needs a plan, and has more than one tempting wrong answer.
What makes it hard
Solution
3 steps
Reading level
Question and choices: about grade 7, 49 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 withholds the red count, and everything depends on recovering it from the comparison of probabilities. Students who cannot make that step tend to leave red out altogether, while those who find 6 red candies can still slip at the end by using the wrong total or the wrong color. Writing all three counts and the total of 22 before forming any fraction prevents both endings.

  1. Turning words into math moderate Understanding the question

    “Twice as great as the probability of choosing a red candy” must become 12 = 2 × the red count, which works only because both probabilities share one total. (Hegarty, Mayer & Monk, 1995; Koedinger & Nathan, 2004)

  2. Combines ideas moderate Working it out

    An unknown count has to be found from a ratio before any probability can be written, joining proportional reasoning with probability as a part over the total. (Embretson, 1998; Daniel & Embretson, 2010)

Strategy: Turn twice as likely into a statement about numbers of candies to find the red count, add all three colors for the total, then put the yellow count over that total and simplify.

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.
  • 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

How the questions are analyzed, and the research behind it

Worked solution, step by step

Formulas used

Probability
P=number of the kind you wanttotal numberP = \frac{\text{number of the kind you want}}{\text{total number}}
P is the probability, the chance that something happens. The top is how many candies are the kind you want. The bottom is how many candies there are in all. Each candy is just as likely to be picked, so this fraction gives the chance.

  1. Sort out what you know

    The bowl has 12 green candies, 4 yellow candies and some red candies. You are not told how many are red. Let r be the number of red candies.

    The chance of picking green is twice the chance of picking red. You need the probability (the chance) of picking yellow.

  2. Compare green and red

    Write each chance with the probability formula.

    P=number of the kind you wanttotal numberP = \frac{\text{number of the kind you want}}{\text{total number}}

    Green and red have the same bottom number, the total number of candies. So if the chance of green is twice the chance of red, there are twice as many green candies as red ones.

    12=2×r12 = 2 \times r

  3. Find the red candies and the total

    r=12÷2=6r = 12 \div 2 = 6

    There are 6 red candies. Now add up all the candies.

    12+4+6=2212 + 4 + 6 = 22

    There are 22 candies in all. Watch out: do not leave out the red candies just because their number was not given. Using 16 as the total gives 1/4, choice C.

  4. Find the chance of yellow

    There are 4 yellow candies out of 22.

    P=422=211P = \frac{4}{22} = \frac{2}{11}

    Divide the top and the bottom by 2 to simplify. Watch out: the question asks for yellow, not red. 6/22 = 3/11 is the chance of red, choice D. The bottom must be all 22 candies. Using 18 gives 2/9, choice B.

    So the answer is A, 211\frac{2}{11}.

Check your answer

Check the clue. The chance of green is 1222\frac{12}{22}, and the chance of red is 622\frac{6}{22}. Twelve is twice 6, so green is twice as likely. Also, the three chances add up to 1: 1222+422+622=2222=1\frac{12}{22} + \frac{4}{22} + \frac{6}{22} = \frac{22}{22} = 1.

More questions like this

The original DOE question
Question 74 as printed on page 203 of the DOE handbook.
As printed in the DOE’s NYC Guide to the Specialized High Schools Admissions Test (SHSAT) for 2025 Admissions, page 203, question 74. Open page 203 of the handbook (PDF) The handbook letters this question’s choices E–H; here they are A–D (E = A, F = B, G = C, H = D).

Sample #653014