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
2026 Practice Test D English, question 40Passage Martial Arts for the Mind and Body
Martial Arts for the Mind and Body
(1) The martial arts blend a series of physical movements with strategic mental discipline so that practitioners can defend themselves, physically defeat an opponent, or both. (2) Historians are unsure of exactly when and where martial arts were first used. (3) Martial arts have been practiced by several different societies for many centuries. (4) Martial arts such as karate, kung fu, tae kwon do, and judo are still taught and practiced as methods of self-defense, but they offer students more than that. (5) The study of martial arts can provide students with a way to enhance their mental discipline as well as their physical fitness.
(6) Discipline, focus, and respect are important qualities for everyone to have. (7) However, for most people these qualities are not innate; they must be learned and practiced. (8) The study of martial arts can provide an opportunity to develop these skills. (9) Students are rewarded for their dedication by passing tests and advancing to higher ranks or levels. (10) For example, in a typical tae kwon do class, students learn discipline by diligently practicing moves, improve focus by listening carefully, and demonstrate respect by bowing to the instructor and following directions.
(11) For teenagers, martial arts classes provide a safe and structured environment for gaining physical skills, building confidence, and enjoying a sense of community. (12) A lot of teens go through hard situations as they try to do well in school and in life. (13) A martial arts class can provide teens with a physical outlet for stress while also challenging them mentally. (14) Participating in a martial arts program also helps children and teens focus on self-improvement rather than on competition. (15) Progressing through levels of achievement involves mastering more physically demanding techniques. (16) It requires students to take responsibility and be accountable for achieving set goals. (17) Students gain confidence and experience companionship with other students who are progressing through the ranks.
(18) Adults who practice martial arts can experience many of the same benefits that younger people do, but perhaps the greatest of these is health and fitness. (19) Adult martial arts students often see changes in their body within weeks of beginning a program.
(20) For people interested in studying a martial art, there are many ways to learn and practice. (21) In addition to private studios, community recreation centers often offer low-cost or free martial arts classes. (22) There are even online videos that introduce students to the basic concepts. (23) People should study martial arts.
Question
Which concluding sentence should replace sentence 23 to best support the topic presented in the passage?
- AWith so many ways to begin studying martial arts, people can easily discover how the skills needed to progress in rank may help them in life.
- BBy taking advantage of opportunities to practice martial arts, people can experience the satisfaction of achieving goals while also improving themselves.
- CBecause people are eager to reap the mental and physical benefits of studying martial arts, enrollment in martial arts courses has increased.
- DWhile taking martial arts classes can improve health for both young people and adults, the effects are clearly more immediate for adults.
Show the answer
Correct answer: B
The question asks for the concluding sentence that best replaces sentence 23 and supports the topic presented in the passage.
A. Incorrect. The phrase “the skills needed to progress in rank” is vague, and progressing in rank is not related to the overall topic of the passage, which is the benefits of studying martial arts. The topic of the passage is not the “many ways to begin studying martial arts” or how “people can easily discover” the benefits of martial arts.
B. CORRECT. This option is correct because it best supports the topic of the passage—the benefits of studying martial arts—by stating two reasons why people should study martial arts: to “experience the satisfaction of achieving goals while also improving themselves.”
C. Incorrect. Some readers may choose this option because it refers to the benefits of martial arts, but the word “because” and the detail that “enrollment in martial arts courses has increased” make this sentence unrelated to the overall topic of the passage, which is about the benefits of studying martial arts, not the number of people who participate.
D. Incorrect. Although the benefits of studying martial arts are described for both teens (in the third paragraph) and adults (in the fourth paragraph), the topic of the passage is the overall benefits of studying martial arts, which include mental discipline (discussed in the first, second, and third paragraphs) in addition to health benefits. Furthermore, the passage does not compare the health effects of studying martial arts across age groups.
Question analysis
This conclusion question asks which sentence should replace sentence 23, the bare closing line “People should study martial arts,” to best support the topic of the passage. Students must keep all five paragraphs in view, from mental discipline to fitness to ways of getting started, because every choice sounds like a reasonable final line when read on its own.
- NYS standards
- 7W2e concluding informative writing
- Grade level
- Grade 8 reading and task
- Compared with grade 7
- Above grade 7 Grade 7 writers choose conclusions that follow from a passage’s topic. This passage covers mental and physical benefits for different ages, and each long choice picks up a real thread, so judging the best fit takes more than typical grade 7 work.
- Estimated difficulty
- Hard: combines ideas, needs a plan, and has more than one tempting wrong answer.
- Thinking it demands
- Depth of knowledge 2, skills and concepts · mainly evaluate
- What makes it hard
- A very close wrong answer moderate
- Evidence in several places moderate
- A lot to read minor
- Evidence
- Answered from the whole text
- Reading level
- Passage: about grade 11, 402 words; question and choices: about grade 12, 106 words.
- Corrected from the DOE handbook
- The DOE printed this question’s explanation after a different question; the site matches the question with its own explanation.
- 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 ending borrows something real from the passage: ways to begin, ranks, mental and physical benefits, or adults’ quick results. The work is deciding what the whole passage is about, the benefits of martial arts for mind and body, and then noticing which ending adds a new claim or shrinks the topic. The rank-based ending is hardest to reject because it is shaped like the key and promises help “in life,” but its focus is how easily people discover rank skills.
A very close wrong answer moderate Choosing the answer
The rank choice is built like the key, a phrase about ways or chances to train followed by what people gain; it differs in resting on the vague “skills needed to progress in rank.” (Embretson & Wetzel, 1987; Gorin & Embretson, 2006; Ascalon et al., 2007)
Evidence in several places moderate Working it out
The topic is pieced together from all five paragraphs, from the opening’s mind-and-body claim through teens, adults’ fitness and ways to learn, so a fitting ending must cover both kinds of benefit. (Kirsch & Mosenthal, 1990; Gorin & Embretson, 2006)
A lot to read minor Understanding the question
Each choice is a two-part sentence of 21 to 26 words, and each picks up a real thread of the passage, so all four must be held against the topic. (Kintsch, 1998; Gorin & Embretson, 2006; Freedle & Kostin, 1993)
Strategy: State the passage’s topic in a few words using all five paragraphs, then test each ending: does it sum up that topic, or does it narrow it or add a new claim?
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.
- Too narrow: A single detail offered as the central idea or a summary, or a summary that keeps minor details and leaves out an essential part.
The wrong answers, classified
A Too narrow (King et al., 2004)
Follows on from the last paragraph’s many ways to start, but rests the ending on vague “skills needed to progress in rank,” one thread of paragraphs 2 and 3, not the benefits overall.
C Off the point (Halliday & Hasan, 1976)
Names the passage’s “mental and physical benefits,” which fits, but ends on rising enrollment, a claim about numbers of students that the passage never discusses.
D Half right (King et al., 2004; Thissen, Steinberg & Fitzpatrick, 1989)
Rightly says training can improve health for young people and adults, but adds that adults clearly benefit sooner, a comparison the passage never makes, and drops the mental benefits.
What was corrected from the DOE handbook, and why
- Explanation: In the DOE’s explanations appendix, the explanation printed after this question belongs to question 39 (“the sentence that would best follow and support sentence 18”) and marks C correct, and this question’s explanation (“the concluding sentence that best replaces sentence 23 and supports the topic presented in the passage”) is printed after question 39, marking B correct. Read page by page, the appendix gives this question the answer C. The site gives the question the explanation that restates it, and the answer follows that explanation: B, because it sums up the passage’s topic, the benefits of studying martial arts.
Working it out, step by step
Figure out what the question asks
This asks for a better last sentence. A good concluding sentence sums up the topic of the whole passage. Sentence 23, “People should study martial arts,” is short and plain. It doesn’t remind the reader why.
Find the passage’s topic
Sentence 5 states the topic. Martial arts can help students “enhance their mental discipline as well as their physical fitness.” Enhance means improve. Paragraph 2 covers discipline, focus and respect. Paragraph 3 covers teens and goals. Paragraph 4 covers adults and fitness. Paragraph 5 lists ways to start. So the topic is how martial arts help both mind and body.
Name the rule
A conclusion should sum up the main point. It should not shrink the point or add a brand-new claim. For example, after a report on why sleep matters, a good ending is Getting enough sleep helps both your body and your mind. A poor one is More people buy pillows now.
Check each choice
- A is wrong. It rests on vague “skills needed to progress in rank,” one small part of the passage.
- B is right. “Opportunities to practice” follows paragraph 5. “Achieving goals” and “improving themselves” sum up the benefits.
- C is wrong. Enrollment is the number of people who sign up. The passage never says it has gone up.
- D is wrong. The passage never says adults see results sooner than young people. D also leaves out the benefits to the mind.
Watch out: A is built like B and promises help “in life.” But it shrinks the topic to rank skills.
Choose the answer
B sums up what the whole passage says martial arts offer. So the answer is B, “By taking advantage of opportunities to practice martial arts, people can experience the satisfaction of achieving goals while also improving themselves.”
Why this answer and not the closest wrong one
A is the closest wrong answer. Like B, it starts with ways to begin and ends with what people gain. But its gain is vague “skills needed to progress in rank.” That is only one thread of the passage. B sums up the whole topic: reaching goals and improving yourself.
More questions like this
The original DOE question
The passage “Martial Arts for the Mind and Body” as printed (page 52)
Question 2 of 6
2018 Test B English, question 52Passage Invention of the Telegraph
Samuel Morse, an American inventor, is credited with creating the electronic telegraph, a communication device that allows users to send messages using a system of short and long pulses that represent letters, numbers, and punctuation. In 1843 the United States Congress passed the Telegraph Bill, which provided Morse with the funds to build an electric telegraph system.
Invention of the Telegraph
Earlier Signal Systems
Long before Samuel F. B. Morse electrically transmitted his famous message “What hath God wrought?” from Washington to Baltimore on May 24, 1844, there were signaling systems that enabled people to communicate over distances. Most were visual or “semaphore” systems using flags or lights. In the eighteenth century, such systems used an observer who would decipher a signal from a high tower on a distant hill and then send it on to the next station. The young American republic wanted just such a system along its entire Atlantic coast and offered a prize of $30,000 for a workable proposal. The framers of this legislation had no way of knowing that when they used the word “telegraph” to refer to this visual semaphore system, they would be offered an entirely new and revolutionary means of communication—electricity.
The Growth of an Idea
The idea of using electricity to communicate over distance is said to have occurred to Morse during a conversation aboard ship when he was returning from Europe in 1832. Michael Faraday’s recently invented electromagnet was much discussed by the ship’s passengers, and when Morse came to understand how it worked, he speculated that it might be possible to send a coded message over a wire. While a student at Yale College years before, he had written his parents a letter about how interesting he found the lectures on electricity. Despite what he had learned at Yale, Morse found when he began to develop his idea that he had little real understanding of the nature of electricity, and after sporadic attempts to work with batteries, magnets, and wires, he finally turned for help to a colleague at the University of the City of New York, Leonard D. Gale.
Gale was a professor of chemistry and familiar with the electrical work of Princeton’s Joseph Henry, a true pioneer in the new field. Well before Morse had his shipboard idea about a telegraph, Henry rang a bell at a distance by opening and closing an electric circuit. In 1831, he had published an article, of which Morse was unaware, that contained details suggesting the idea of an electric telegraph. Gale’s help and his knowledge of this article proved crucial to Morse’s telegraph system because Gale not only pointed out flaws in the system but showed Morse how he could regularly boost the strength of a signal and overcome the distance problems he had encountered by using a relay system Henry had invented. Henry’s experiments, Gale’s assistance, and, soon after, hiring the young technician Alfred Vail were keys to Morse’s success.
Obstacles and Opportunities
By December 1837, Morse had enough confidence in his new system to apply for the federal government’s appropriation, and during the next year he conducted demonstrations of his telegraph both in New York and Washington.
However, when the economic disaster known as the Panic of 1837 took hold of the nation and caused a long depression, Morse was forced to wait for better times. It was during this period that Morse visited Europe again and tried not only to secure patent protection overseas but to examine competing telegraph systems in England. . . .
By 1843, the country was beginning to recover economically, and Morse again asked Congress for the $30,000 that would allow him to build a telegraph line from Washington to Baltimore, forty miles away. The House of Representatives eventually passed the bill containing the Morse appropriation, and the Senate approved it in the final hours of that Congress’s last session. With President Tyler’s signature, Morse received the cash he needed and began to carry out plans for an underground telegraph line.
Realizing a Great Invention
Morse had hired the ingenious construction engineer Ezra Cornell to lay the pipe carrying the wire, and although Cornell did his job superbly, one of Morse’s partners, Congressman F. O. J. Smith, had purchased wire with defective insulation. Too much time had been wasted laying bad wire, and with the project on a rigid deadline, something had to be done quickly. Cornell suggested that the fastest and cheapest way of connecting Washington and Baltimore was to string wires overhead on trees and poles. The desperate Morse gave the go-ahead, and the line was completed in time for the dramatic and spectacularly successful link between the Supreme Court chamber of the Capitol building and the railroad station in Baltimore.
Soon, as overhead wires connected cities up and down the Atlantic coast, the dots-and-dashes method that recorded messages on a long moving strip of paper was replaced by the operator’s ability to interpret the code in real time. . . . Telegraph lines soon extended westward, and within Morse’s own lifetime they connected the continents of Europe and America.
“Invention of the Telegraph”—Public Domain/Library of Congress
legislation: Telegraph Bill
dots-and-dashes method: the short and long pulses of Morse code that are sent and received by telegraph operators
The first transatlantic electric telegraph message was sent in 1858, and by 1902 the British All-Red Line connected most of the world.
Source: U.S. Bureau of the Census. Historical Statistics of the United States, Colonial Times to 1970, Bicentennial Edition, Part 2. Washington, D.C., 1975.
Question
The details of the section “The Growth of an Idea” convey a central idea of the passage by suggesting that
- Athe collaborative efforts of colleagues resulted in successful communication over a wire.
- Ba great deal of interest and work was devoted to understanding how to use electricity to send signals.
- CFaraday’s invention of the electromagnet inspired the invention of the telegraph.
- Dcolleges like Yale played a great role in making new discoveries about electricity and its applications.
Show the answer
Correct answer: B
The question asks how a passage section helps convey a central idea of the passage. Paragraph 3 states that “Henry’s experiments, Gale’s assistance, and, soon after, hiring the young technician Alfred Vail were keys to Morse’s success.” The level of interest inspired Morse and others to work together to find a way to use electricity to send long-distance messages.
Option B is correct; the section helps convey a central idea because, overall, the section focuses on what fascinated Morse enough to begin his work and how others were just as interested and willing to work to achieve this goal.
Option A is incorrect because, although the word collaborative suggests that multiple people contributed to the telegraph’s success, the option does not clarify the research and effort needed in order to understand how to use electricity to send signals.
Option C is incorrect because when Morse came to understand how Faraday’s electromagnet worked, Morse wondered if it might be possible to send a coded message over a wire, but that thought later evolved into the telegraph only after more research and experimentation.
Option D is incorrect because the influence of what Morse learned at Yale was only a minor factor in his development of the telegraph.
Question analysis
This central idea question asks what the details in the section “The Growth of an Idea” suggest about the passage “Invention of the Telegraph.” The section covers Faraday’s electromagnet, Morse’s Yale lectures, and help from Gale, Henry and Vail, so students must judge which statement those details support as a group, and more than one choice sounds right.
- Grade level
- Grade 8 reading and task
- Compared with grade 7
- Above grade 7 Grade 7 central-idea questions usually have one clearly best summary. Here two paragraphs of names and events must be weighed, and several choices restate true details, so judging which fits the whole section is unusually demanding.
- 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 understand
- What makes it hard
- A very close wrong answer major
- Evidence in several places moderate
- The right answer is reworded moderate
- Evidence
- Answered from several paragraphs or stanzas
- Reading level
- Passage: about grade 11, 910 words; question and choices: about grade 12, 77 words.
- Students, last 30 days
- 67% right, of 21 answers
Why it is hard, traps and wrong answers (shows the answer)
Why it is hard
This is among the hardest questions in the set because the most tempting wrong choice reads like a paraphrase of the section’s final sentence. Rejecting it means noticing that the section never shows a message getting through and never shows Henry working with Morse, who had not even read his article. The right choice is vague by design, and only a summary of both paragraphs together shows that it fits better.
A very close wrong answer major Choosing the answer
The colleagues choice and the interest-and-work choice both describe effort spent on sending signals by wire; they part on one claim, that the effort “resulted in successful communication,” which the section never shows, the working line arriving in paragraph 7. (Embretson & Wetzel, 1987; Gorin & Embretson, 2006; Ascalon et al., 2007)
Evidence in several places moderate Working it out
The idea emerges only from details across two paragraphs, passengers discussing the electromagnet, Morse’s Yale letter, his failed attempts, Henry’s bell and article, Gale’s relay advice, taken together. (Kirsch & Mosenthal, 1990; Gorin & Embretson, 2006)
The right answer is reworded moderate Choosing the answer
The key names none of the section’s people, while the wrong choices echo its “colleague,” “over a wire,” Faraday’s electromagnet and Yale, and so look more firmly rooted in the text. (Freedle & Kostin, 1993; Kirsch & Mosenthal, 1990)
Strategy: Summarize paragraphs 2 and 3 together in one sentence of your own before reading the choices, then choose the statement closest to your summary, checking that every part of it is true of this section.
Traps
- Half right: One half of a two-part choice is right and the other is not.
- Too narrow: A single detail offered as the central idea or a summary, or a summary that keeps minor details and leaves out an essential part.
- Too broad or too strong: A choice overstates, generalizes, or uses absolute words the text does not support.
The wrong answers, classified
A Half right (King et al., 2004; Thissen, Steinberg & Fitzpatrick, 1989)
Rightly sees teamwork in the section’s close, but successful communication over Morse’s wire comes later, under “Realizing a Great Invention,” and the passage never shows Henry working with Morse.
C Too narrow (King et al., 2004)
Treats the spark as the whole story: Faraday’s electromagnet gave Morse the idea, but the section goes on to years of failed attempts and help from others.
D Too broad or too strong (King et al., 2004)
Inflates a passing mention: Morse’s Yale lectures appear once, and the section notes that despite them he had “little real understanding of the nature of electricity.”
How 21 answers split, last 30 days
- A19%
- B67%
- C14%
- D0%
Working it out, step by step
Figure out what the question asks
This asks what the section “The Growth of an Idea” says about a central idea, or main message. The section is paragraphs 2 and 3. Sum up both paragraphs together before you look at the choices.
List the section’s details
On the ship, Faraday’s electromagnet “was much discussed by the ship’s passengers.” Morse had found the electricity lectures at Yale interesting. He made “sporadic attempts” on his own. In paragraph 3, Henry “rang a bell at a distance by opening and closing an electric circuit.” Gale showed Morse how to use Henry’s relay system.
Find what the details share
Look at what links these details. Passengers talked about electricity. Morse was curious and kept trying. Henry ran tests and wrote an article. Gale gave advice. All of it is people taking an interest in electricity and working to send signals with it. That is the section’s main point. A working telegraph line does not appear until paragraph 7.
Check each choice
- A is close but wrong. Morse’s telegraph does not send a message until paragraph 7. Also, Henry never worked with Morse. At first, Morse did not even know about Henry’s article.
- B fits. It covers the interest and the work in both paragraphs.
- C is wrong. The electromagnet gave Morse the idea, but that is only the start of the section.
- D is wrong. Yale is only a small part of paragraph 2. And “Despite what he had learned at Yale,” Morse still knew little.
Choose the answer
The section shows lots of interest and effort aimed at sending signals with electricity. So the answer is B, “a great deal of interest and work was devoted to understanding how to use electricity to send signals.”
Why this answer and not the closest wrong one
A sounds like a summary of the section’s last sentence, which is why it tempts. But it claims the teamwork “resulted in successful communication,” and that only happens in a later section. B claims less, so every detail in paragraphs 2 and 3 fits it.
More questions like this
The original DOE question
The passage “Invention of the Telegraph” as printed (pages 146–148)
Question 3 of 6
2026 Practice Test B English, question 45Passage 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.
- 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.
- Thinking it demands
- Depth of knowledge 2, skills and concepts · mainly evaluate
- What makes it hard
- Something you must already know moderate
- Every choice must be checked moderate
- Hard words minor
- 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
- 80% right, of 10 answers
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.
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)
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)
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
- Wordy, vague or informal: A revision is grammatical but wordy, imprecise or too casual for the passage.
The wrong answers, classified
B Wordy, vague or informal (Connors & Lunsford, 1988)
Equates formal with elevated, so “shrouded” and “impermanently halting” seem best, though both are stilted and poetic beside the passage’s plain reporting of facts.
C Wordy, vague or informal (Connors & Lunsford, 1988)
Avoids casual words, but “enveloped” and “arresting” are poetic, and “the whole of the planet” and “for a time” add words the plain version does without.
D Wordy, vague or informal (Connors & Lunsford, 1988)
Keeps the meaning, but the casual “covered up” and the roundabout “brought a stop to the progress of the rover” make it wordier and less formal.
How 10 answers split, last 30 days
- A80%
- B20%
- C0%
- D0%
Working it out, step by step
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.
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.
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.
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
The passage “The End of an Era” as printed (page 60)
Question 4 of 6
2018 Test A Math, question 1Question
In the figure above, PQRS is a parallelogram. What is the value of ?
Grid-in question: work out the answer and enter it as a number.
Show the answer
Correct answer: 162
First, find the measure of angle PQR. The measure of angle PQR is equal to the measure of angle PSR.
m∠PSR = 180 − 72 = 108.
So, the measure of angle PQR is also 108.
108 + 90 + x = 360
198 + x = 360
x = 162
Question analysis
A grid-in geometry question about angles around a parallelogram PQRS. A 72° angle sits outside corner S on the extended base, and at corner Q a right angle and the unknown angle x complete the turn around the point. Students chain three angle facts, and the angle asked for lies outside the shape, not inside it.
- NYS standards
- Grade level
- Grade 8 content, by NYS standard
- Compared with grade 7
- Above grade 7 Grade 7 angle work usually applies one or two facts, such as supplementary or vertical angles, to find an angle. This chains three, and needs the equal opposite angles of a parallelogram, which rest on grade 8 parallel-line facts.
- Estimated difficulty
- Hard: combines ideas, needs a plan, and has more than one tempting wrong answer.
- Thinking it demands
- Depth of knowledge 2, skills and concepts · mainly apply
- What makes it hard
- Reading a figure, table or graph major
- Combines ideas moderate
- An answer in an unexpected form minor
- Solution
- 3 steps
- Reading level
- Question and choices: about grade 7, 14 words.
- Students, last 30 days
- 60% right, of 30 answers
Why it is hard, traps and wrong answers (shows the answer)
Why it is hard
The arithmetic is two subtractions; the difficulty is seeing which angles the marks refer to. Students lose points by treating the 72° as the parallelogram's own angle at S, or by stopping at angle PQR, the most natural number to grid. The question rewards tracing a route from S to Q before computing anything, and checking at the end that x is the angle outside the shape that the arc marks.
Reading a figure, table or graph major Understanding the question
The 72° is marked outside the parallelogram, between side SR and the base extended past S, and x sits outside corner Q, between QP and a vertical ray that meets QR at a right-angle mark. (Lesh, Post & Behr, 1987; Kirsch & Mosenthal, 1990)
Combines ideas moderate Working it out
Three angle facts have to be chained: a straight line gives the angle inside S, opposite angles of a parallelogram carry it to Q, and the angles around Q make a full 360° turn. (Embretson, 1998; Daniel & Embretson, 2010)
An answer in an unexpected form minor Choosing the answer
As a grid-in there are no choices to check against, so a student who stops at angle PQR, inside the parallelogram, gets no signal that the job is unfinished. (Enright, Morley & Sheehan, 2002)
Strategy: Use the straight line at S to find the parallelogram's angle there, carry it to the opposite corner Q, then take that angle and the right angle away from 360.
Traps
- Stops one step early: A choice is a number from partway through the solution.
The wrong answers, classified
108 Stops one step early (King et al., 2004; Gierl et al., 2017)
Finds angle PSR = 180 − 72 = 108 and carries it to angle PQR, then grids that interior angle instead of the angle x outside it.
198 Misreads the figure (Lesh, Post & Behr, 1987; Kirsch & Mosenthal, 1990)
Reads the 72° as the parallelogram's interior angle at S, so takes angle PQR as 72 and grids 360 − 90 − 72 = 198.
252 Misreads the figure (Lesh, Post & Behr, 1987; Kirsch & Mosenthal, 1990)
Overlooks the right-angle mark at Q and subtracts only the 108° angle PQR from 360, giving 252.
How 30 answers split, last 30 days
- Right60%
- Wrong40%
Worked solution, step by step
Formulas used
- Angles on a straight line
- a and b are two angles side by side on a straight line. Together they make a half turn, so they always add up to 180 degrees. Use it when an angle you need shares a straight line with an angle you know.
- Opposite angles of a parallelogram
- The symbol ∠ means angle. ∠PQR is the angle at corner Q, between sides QP and QR. ∠PSR is the angle at the opposite corner, S. In a parallelogram, opposite corners always have equal angles, because the shape leans the same way at both.
- Angles around a point
- a, b and c are angles that fit around one point with no gaps and no overlaps. Going all the way around is a full turn, which is 360 degrees. So the angles add up to 360.
Sort out what the figure shows
PQRS is a parallelogram. That is a four-sided shape whose opposite sides are parallel, which means they never meet. You need the value of x, in degrees.
Look closely at the marks. The 72° angle is outside the shape, at S. It sits between side SR and the base line, which keeps going past S. At Q, a vertical line meets side QR. The small square means a right angle, 90°. The angle x is outside the shape too. It runs from that vertical line around to side QP.
Find the angle inside corner S
Angle PSR is the shape’s own angle at S. It sits right next to the 72° angle, on the same straight base line. So the two angles add up to 180°.
So angle PSR is 108°. Watch out: 72° is not the inside angle at S. Using 72 as the inside angle leads to the wrong answer 198.
Carry the angle over to Q
Corners Q and S are opposite each other. In a parallelogram, opposite angles are equal. So angle PQR matches angle PSR.
So angle PQR is 108°. Watch out: this is not x. Angle PQR is inside the shape, and x is outside it. Stopping here and gridding 108 is the most common mistake.
Add the angles around Q
Three angles fill the space all the way around point Q. They are the right angle (90°), angle PQR (108°) and x. Together they make a full turn.
Watch out: don’t skip the right angle at Q. Leaving out the 90 gives 252.
Solve for x
Subtract 198 from 360 to find what is left for x.
So x is 162°. So you would grid 162.
Check your answer
Add the three angles at Q: . That is a full turn. Also, the arc for x is wider than a right angle but not as wide as a straight line. So x should be between 90° and 180°, and 162° is.
More questions like this
The original DOE question
Question 5 of 6
2026 Practice Test C Math, question 35Question
If , what is the value of a in terms of b?
Enter your answer in the space provided. Enter only your answer.
On the test you build the answer on an on-screen keypad; here, type it. Use ^ for a power, sqrt( ) or √ for a root, pi for π, and <= or >= for ≤ and ≥.
Show the answer
Correct answer: a = 10b
To find the value of a in terms of b, solve for a. Begin by distributing 4 on the left side of the equation:
Then, get the a terms on one side and the b terms on the other:
Solve for the value of a in terms of b by combining like terms and then dividing each side by 2:
Question analysis
An algebra question gives an equation with a and b on both sides, one side written as 4 times a sum in parentheses, and students type a in terms of b after a printed "a =". It tests the distributive property and solving linear equations. The answer is typed, so a slip in distributing or moving terms is not caught by any choices.
- NYS standards
- Grade level
- Grade 8 content, by NYS standard
- Compared with grade 7
- Above grade 7 Grade 7 students solve equations like 4(x + 2) = 28 with numbers. This one has letters on both sides, needs the distributive property and like terms, and asks for a in terms of b, which is grade 8 algebra.
- Estimated difficulty
- Hard: combines ideas, needs a plan, and has more than one tempting wrong answer.
- Thinking it demands
- Depth of knowledge 1, recall and reproduction · mainly apply
- What makes it hard
- Variables instead of numbers moderate
- Many steps moderate
- An answer in an unexpected form minor
- Solution
- 3 steps
- Reading level
- Question and choices: about grade 4, 23 words.
- Students, last 30 days
- Not enough answers yet to show (it takes 10).
Why it is hard, traps and wrong answers (shows the answer)
Why it is hard
Every step is routine, yet there are four of them, each with a classic slip, and the typed answer catches none. Multiplying the 4 into only the a, or carrying 8b across without changing its sign, gives another whole multiple of b that looks finished. Testing b = 1, where 4(a + 2) and 28 + 2a must come out equal, confirms an entry quickly.
Variables instead of numbers moderate Understanding the question
Both letters appear on both sides, and the answer must stay a multiple of b, so there is no number to check an entry against unless students invent one. (Koedinger & Nathan, 2004; Enright, Morley & Sheehan, 2002)
Many steps moderate Working it out
Four moves run in a chain, distributing the 4, gathering the a terms, gathering the b terms and dividing by 2, and an error at any one carries into the typed result. (Daniel & Embretson, 2010; Enright, Morley & Sheehan, 2002)
An answer in an unexpected form minor Choosing the answer
The answer is typed after a printed “a =”, with no choices, so 20b, the line before dividing by 2, can be entered without anything on screen questioning it. (Enright, Morley & Sheehan, 2002)
Strategy: Distribute the 4 to both terms in the parentheses, gather the a terms on one side and the b terms on the other, then divide by the coefficient of a.
Traps
- A faulty procedure: A systematic but wrong procedure: adding fractions straight across, applying an exponent to each term of a sum, dropping a sign when moving a term.
- Stops one step early: A choice is a number from partway through the solution.
The wrong answers, classified
13b A faulty procedure (Brown & Burton, 1978; Tatsuoka, 1983)
Multiplies only the a by 4, writing 4a + 2b = 28b + 2a, so 2a = 26b and a = 13b.
18b A faulty procedure (Brown & Burton, 1978; Tatsuoka, 1983)
Distributes correctly but moves 8b to the right without changing its sign, so 2a = 28b + 8b = 36b and a = 18b.
20b Stops one step early (King et al., 2004; Gierl et al., 2017)
Reaches 2a = 20b correctly and enters 20b, stopping before dividing both sides by 2 to get a alone.
Worked solution, step by step
Formulas used
- Distributive property
- k is the number outside the parentheses. x and y are the terms inside. The number outside multiplies every term inside, not just the first one. It works because 4 groups of (x + y) hold 4 x’s and 4 y’s.
- Doing the same thing to both sides
- A and B are the two equal sides of an equation. C is any amount. Taking the same amount from both sides, or dividing both by the same number, keeps them equal, like a balanced scale.
Sort out the question
The equation is . You need a in terms of b. That means a alone on one side, with only b and numbers on the other.
The answer box already shows a =, so you type only what comes after it.
Multiply out the parentheses
Use the distributive property. The 4 multiplies both terms inside:
Watch out: multiplying only the a by 4 gives 4a + 2b. That leads to the wrong answer 13b.
Gather the a terms
Like terms are terms with the same letter, such as 4a and 2a. Put the a terms on the left. Subtract 2a from both sides:
Gather the b terms
Now subtract 8b from both sides:
Watch out: moving 8b without changing its sign gives . That leads to 18b, which is wrong.
Divide both sides by 2
2a means 2 times a. Divide both sides by 2 to get a alone:
Watch out: 20b is equal to 2a, not a. Do not stop there.
Enter it after the printed a =
On the test, the box already shows a =. Press 1, then 0, then the b key. You do not need a times sign. Do not type a = again. On this site, type 10b in the box.
So you would enter 10b, which makes a = 10b.
Check your answer
Pick b = 1, so a = 10. The left side is . The right side is . The sides match, so 10b works.
More questions like this
The original DOE question
Question 6 of 6
2024 Test B Math, question 44Question
Which inequality is equivalent to ?
- A
- B
- C
- D
Show the answer
Correct answer: D
Distribute the coefficient −2 on the right-hand side:
Subtract from both sides:
Add 10 to both sides:
Divide both sides by 5:
This is equivalent to
Question analysis
Students choose the simplest equivalent form of a linear inequality that has x on both sides and a negative number multiplied into parentheses. It tests distributing, combining like terms and solving inequalities. Sign errors in the distribution, and reading the direction of the final inequality, are where most mistakes happen.
- NYS standards
- Grade level
- Grade 8 content, by NYS standard
- Compared with grade 7
- Above grade 7 Grade 7 inequalities have the form px + q < r. This one has x on both sides and a negative factor to distribute across a subtraction, steps that belong to grade 8 equation work, so it is harder than typical grade 7 practice.
- Estimated difficulty
- Hard: combines ideas, needs a plan, and has more than one tempting wrong answer.
- Thinking it demands
- Depth of knowledge 1, recall and reproduction · mainly apply
- What makes it hard
- Error-prone arithmetic moderate
- A very close wrong answer moderate
- Many steps minor
- Solution
- 4 steps
- Reading level
- Question and choices: about grade 16+, 10 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 move is standard algebra, but the inequality is built so that small slips change the answer completely. The −2 has to reach both terms in the parentheses, and once the boundary −2 is found its direction still has to be read correctly, since the variable ends up on the right as −2 < x. Rewriting that as x > −2, or substituting x = 0 into the original, catches the trap.
Error-prone arithmetic moderate Working it out
Distributing −2 over (5 − 3x) gives −10 + 6x, two sign decisions in one move, and the x terms then sit on both sides of the inequality. (Brown & Burton, 1978; Junker & Sijtsma, 2001)
A very close wrong answer moderate Choosing the answer
x < −2 and x > −2 share the boundary and differ only in direction, which depends on reading −2 < x correctly or flipping the sign when dividing by a negative. (Embretson & Wetzel, 1987; Gorin & Embretson, 2006; Ascalon et al., 2007)
Many steps minor Working it out
Four moves follow one another, distributing, collecting 5x + 6x, moving the x terms and dividing by 5, and a slip at any of them changes the result. (Daniel & Embretson, 2010; Enright, Morley & Sheehan, 2002)
Strategy: Distribute the −2 to both terms in the parentheses, combine the x terms on the right, then gather the x terms on the side that keeps their coefficient positive.
Traps
- Order of operations: Working left to right, or distributing a minus sign wrongly, gives a choice.
- 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.)
- A faulty procedure: A systematic but wrong procedure: adding fractions straight across, applying an exponent to each term of a sum, dropping a sign when moving a term.
The wrong answers, classified
A A faulty procedure (Brown & Burton, 1978; Tatsuoka, 1983)
Treats 5 − 3x as 2, combining a number with an x term, so the right side becomes 5x − 4 and the solution x < 16.
B Order of operations (Brown & Burton, 1978)
Multiplies the −2 by the 5 but not by the −3x, writing 5x − 10 − 3x, which leads to 4x < 10 and x < 5/2.
C Negatives and direction (Brown & Burton, 1978)
Finds the boundary −2 but points the inequality the wrong way, by misreading −2 < x or by not flipping the sign after dividing by −5.
Worked solution, step by step
Formulas used
- Distributive property
- a is the number outside the parentheses. b and c are the terms inside. Multiply a by each one. A minus sign inside counts as a negative term, so 5 − 3x is 5 + (−3x). A negative times a negative is positive.
- Keeping an inequality true
- a and b are the two sides, and c is any number. Adding or subtracting the same number on both sides keeps the inequality true. Dividing both sides by a positive number also keeps it true. Only multiplying or dividing by a negative number flips the sign.
Sort out the question
An inequality compares two sides with a sign like <, which means is less than. To solve it, you get x alone on one side.
You need the short inequality that has the same answers as the long one.
Distribute the −2
Multiply −2 by both terms inside the parentheses, 5 and −3x.
A negative times a negative is positive, so the second part is +6x. Watch out: If the −2 multiplies only the 5, you end up with , choice B.
Combine the x terms
The right side is now 5x − 10 + 6x. Put the x terms together: 5x + 6x = 11x.
Gather the x terms on one side
Subtract 6x from both sides. That leaves the x terms on the right, where they stay positive.
Get x by itself
Add 10 to both sides. Then divide both sides by 5.
You divided by a positive 5, so the sign does not flip.
Read it with x first
says −2 is less than x. That is the same as saying x is greater than −2, just as 3 < 5 means 5 > 3.
Watch out: , choice C, has the same number but points the wrong way.
So the answer is D, .
Check your answer
Test x = 0, which is greater than −2. The left side is . The right side is . And −20 < −10 is true. Now test x = −3. The left side is −38 and the right side is −43. That is false, as it should be.
More questions like this
The original DOE question
