3 English and 3 math
Here are 6 random questions to try. Takers earning below 75% are unlikely to receive an offer. You have 1 minute 48 seconds per question on the real exam.
Question 1 of 6
2024 Test B English, question 8Passage Find Time to Volunteer
Find Time to Volunteer
(1) Many people believe that they gain a greater sense of purpose by giving their time to serve others. (2) These are the people who spend their free time volunteering at various places within the community. (3) Those who are served benefit from the work of these volunteers. (4) However, research shows that those who volunteer also receive benefits.
(5) For many students, this proposition may sound impossible. (6) Schoolwork can require hours of study each week. (7) Volunteering at a retirement center or homeless shelter requires both time and energy. (8) Extracurricular activities fill up after-school time. (9) Family obligations and part-time jobs often have to be worked into the schedule, too. (10) However, if students can find time to volunteer, even for a few hours a month, they may find that the benefits outweigh the scheduling difficulties.
(11) To begin with, students who engage in volunteer activities acquire valuable skills and experience, which can help them focus on potential fields of study and career options. (12) Furthermore, when students list volunteer work on college applications, admissions counselors see applicants who care about making their community and college campus a better place.
(13) Volunteerism benefits more than students applying to college. (14) This type of experience is equally important for students moving directly into the workforce after high school. (15) Volunteering demonstrates initiative, dedication, and a strong work ethic, qualities that companies value in a potential employee. (16) In a CareerBuilder study, 60 percent of managers regarded volunteerism as a significant asset when considering applicants.
(17) Students who volunteer undoubtedly make a positive investment in their future, but they also affect their present quality of life. (18) Studies have shown that volunteering is good for both the mind and the body. (19) Volunteering can boost mood levels and reduce anxiety. (20) According to the Mayo Clinic,1 the feeling of doing something meaningful and the appreciation received from that action can reduce stress.
(21) Even the busiest of students can find a way to donate some time to a worthy cause. (22) Though managing different commitments may seem overwhelming at times, students are sure to feel a sense of fulfillment in volunteerism.
1Mayo Clinic: a nonprofit medical organization dedicated to treatment and research
Question
Which of these would best follow sentence 12 and support the ideas presented in the third paragraph (sentences 11–12)?
- AThese students show that they are likely to be responsible, reliable, and helpful young adults. Admissions counselors know that character traits like these will benefit the applicants as well as whomever they interact with.
- BVolunteering can help students meet new people who can provide references and advice to the students when they are applying to colleges. It can also be an invaluable opportunity for students to meet possible future employers.
- CThe counselors hope that young adults who demonstrate this behavior will go on to volunteer during their college years, working on campus in student government and leadership programs or serving in the community at hospitals, schools, and homeless shelters.
- DMany colleges are looking for students who are not just academically successful but who also work well with others and care about improving and serving surrounding communities.
Show the answer
Correct answer: D
The question asks which option would best follow sentence 12 to support the ideas presented in the third paragraph (sentences 11–12).
A. Incorrect. The subject of the main clause in sentence 12 is “admissions counselors.” Although the second sentence in the option mentions “admissions counselors,” it does not support the ideas in the paragraph, because the statement that “admissions counselors know that character traits like these will benefit the applicants” focuses on how students benefit, while sentence 12 focuses on how these traits benefit the community.
B. Incorrect. While sentence 11 discusses the potential academic and professional connections that can be made through volunteering, sentence 12 moves on to the topic of college admissions. Since the sentences in the option revert back to the topic of connections, they do not support and logically follow a sentence about how college admissions counselors view students with volunteering experience.
C. Incorrect. Although the sentence in the option continues on the subject of admissions counselors and follows the idea in sentence 12 that these counselors tend to favor students who “care about making their community and college campus a better place,” the sentence focuses on what students will do while in college rather than on how volunteering helps them get into college. Therefore, the sentence does not best follow sentence 12 and support the ideas presented in the third paragraph.
D. CORRECT. In sentence 12, the author states that college admissions counselors view students who list volunteer work on admissions applications as “applicants who care about making their community and college campus a better place.” The sentence in the option best follows sentence 12 and supports the ideas in the third paragraph because it provides additional details about why admissions counselors look beyond academics when considering students for admissions and the positive qualities assigned to those who have volunteering experience.
Question analysis
This supporting-details question asks which addition would best follow the volunteering essay’s sentence about how college admissions counselors view applicants who list volunteer work. Every option mentions college and sounds reasonable on its own, so students must decide which one develops the paragraph’s point rather than drifting to a related idea.
- NYS standards
- 7W1b supporting claims with evidence
- Grade level
- Grade 8 reading and task
- Compared with grade 7
- Above grade 7 Grade 7 students choose evidence that supports a claim. Here the options are one or two full sentences, all of them about college, and the right fit depends on the precise idea in sentence 12, a finer judgment than usual.
- Estimated difficulty
- Hard: combines ideas, needs a plan, and has more than one tempting wrong answer.
- Thinking it demands
- Depth of knowledge 2, skills and concepts · mainly evaluate
- What makes it hard
- A very close wrong answer major
- How sentences fit together moderate
- A lot to read minor
- Evidence
- Answered from one paragraph or stanza
- Reading level
- Passage: about grade 11, 354 words; question and choices: about grade 13, 153 words.
- Students, last 30 days
- Not enough answers yet to show (it takes 10).
Why it is hard, traps and wrong answers (shows the answer)
Why it is hard
Every option stays on the subject of college, so the work is matching sentence 12’s exact idea: counselors see applicants who care about making their community a better place. The near miss also explains what counselors value, but it swaps caring for the community for a new set of traits and ends on what those traits do for the applicants. Students who restate sentence 12 before reading the options can hear that the right one simply widens it, from community service to what colleges want beyond grades.
A very close wrong answer major Choosing the answer
The right sentence and the two-sentence option about responsible, reliable, helpful students both explain why volunteers impress admissions; only the right one keeps sentence 12’s point, caring about improving communities. (Embretson & Wetzel, 1987; Gorin & Embretson, 2006; Ascalon et al., 2007)
How sentences fit together moderate Working it out
The new sentence must extend sentence 12’s specific idea, what admissions counselors see in volunteers, rather than return to sentence 11’s skills and careers or move on to college life. (Halliday & Hasan, 1976)
A lot to read minor Understanding the question
The options run 27 to 39 words, two of them two sentences long, and all four are about college, so topic alone rules none of them out. (Kintsch, 1998; Gorin & Embretson, 2006; Freedle & Kostin, 1993)
Strategy: Restate sentence 12 in your own words, then ask of each option whether it explains or extends that exact point about what admissions counselors value.
Traps
- Off the point: Adds or keeps something that does not support the paragraph's or the passage's focus, or an introduction or conclusion that misses the main point.
The wrong answers, classified
A Off the point (Halliday & Hasan, 1976)
Follows the admissions counselors from sentence 12 but replaces caring for the community with new traits, responsibility and reliability, and turns to how those traits help the applicants.
B Off the point (Halliday & Hasan, 1976)
Is drawn by “applying to colleges,” but networking for references and future employers is a new benefit that neither sentence 11 nor sentence 12 develops.
C Off the point (Halliday & Hasan, 1976)
Stays with the counselors and picks up “college campus” from sentence 12, but jumps ahead to what students might do in college instead of explaining admission decisions.
Working it out, step by step
Figure out what the question asks
You need the sentence that best follows sentence 12. A good next sentence adds to the same idea. It does not jump to a new point. Example: after Dogs make loyal pets, the sentence They stay by their owners’ side fits. Dogs come in many colors drifts away. So first put sentence 12 in your own words.
Restate sentence 12
Sentence 12 says that “when students list volunteer work on college applications, admissions counselors see applicants who care about making their community and college campus a better place.” Admissions counselors are the people who choose which students get into a college. So the idea is this: colleges like volunteers because volunteers care about their communities.
Check each choice
- D says colleges want students who are “not just academically successful.” That means more than good grades. They also want students who “care about improving and serving surrounding communities.” That explains sentence 12 and builds on it.
- A swaps in new traits: “responsible, reliable, and helpful.” Then it says those traits help the applicants and the people around them. It drops caring for the community.
- B brings in a new benefit: meeting people who can give advice or jobs. Neither sentence 11 nor sentence 12 talks about that.
- C jumps ahead to what students might do in college. It doesn’t explain how volunteering helps them get in.
Pick the answer
Watch out: A is the most tempting. It is about what counselors value, just like the right answer. But it changes the reason they value it. Only D keeps sentence 12’s idea of caring for the community. So the answer is D.
Why this answer and not the closest wrong one
A is the closest wrong answer. Like D, it explains why admissions counselors like volunteers. But A’s reasons are new ones, such as being responsible and reliable. D keeps sentence 12’s exact idea, caring about the community, and adds that colleges want more than good grades. So D supports the paragraph best.
More questions like this
The original DOE question
The passage “Find Time to Volunteer” as printed (page 163)
Question 2 of 6
2026 Practice Test B English, question 32Passage Using Fire to Keep a Prairie Healthy
Using Fire to Keep a Prairie Healthy
Inside the 40,000-acre Joseph H. Williams Tallgrass Prairie Preserve in northern Oklahoma, herds of bison roam on the scenic land that is home to hundreds of different species of plants and animals. While one of the greatest threats to the prairie is wildfire, the use of controlled fires is actually an effective way to protect this idyllic landscape.
Fires that are started by lightning or other natural circumstances are inevitable, and the results can be disastrous. However, hundreds of years ago the American Indian people who inhabited the Great Plains area between Minnesota and Texas realized that these fires could also be helpful. The bison in the area seemed to prefer grazing on tender new grass on the recently burned land rather than on grass in the unburned areas. The American Indian people began to deliberately burn areas of land for bison to graze on, which enticed the herds away from the people’s crops.
Today conservationists at the Tallgrass Prairie Preserve and farmers in the Great Plains continue to use controlled burns for land management. Intentionally burning a portion of land can dramatically improve the quality of the vegetation that regrows there. The fires burn away weedy undergrowth and help limit the overcrowding of shrubs and trees in the burn area, creating less competition for water and nutrients. Additionally, the process of burning excess plant matter adds nitrogen, an essential element for plant growth, to the soil.
One common target of controlled burns at the preserve and the surrounding area is the invasive red cedar tree. A single red cedar tree can consume up to 40 gallons of water per day, taking this vital resource away from other plant life. These tall trees also cast shade that prevents sunlight from reaching the plants beneath them. The fast-growing red cedar trees tend to crowd out prairie grasses, the primary food source for wild and domestic animals that make the prairie their home. An imbalance in one component of the prairie’s ecosystem affects the entire web of life. Controlled burns help maintain this ecosystem’s delicate balance.
Of course, these controlled fires are intended to burn only a portion of an area. A total burn, which is a risk with an uncontrolled wildfire, would destroy all wildlife as well as the crops farmers plant for income. The key to using controlled fires is knowing which areas of land to burn and when. Conservation experts at the preserve employ the “patch-burn” approach, meaning they rotate which portion of land is burned each year. They study the land to find out which areas would most benefit from being burned, and then they arrange about a dozen burns over one-third of the land. This patch burning contains the fire within a specific area and allows animals in the burn area to safely relocate. The following year, conservationists will burn a different section of the preserve, while the land burned the previous year regrows healthier than before.
Researchers have tracked and studied the variety of plant species and animals that live on the preserve, and their studies show that the patch-burn approach has restored biodiversity to the area by promoting the growth of species that were at risk of being crowded out. The patch-burn system is so successful that the conservationists at the preserve provide training to prairie farmers about conducting controlled burns on their own land. Burning land to make it healthy may seem counterintuitive, but strategic controlled fires have helped the prairie sustain life for hundreds of years and, with careful management, will continue to do so.
Question
Which sentence supports the idea that farmers and people who manage land may be concerned about using fire as a way to benefit the land?
- A“While one of the greatest threats to the prairie is wildfire, the use of controlled fires is actually an effective way to protect this idyllic landscape.” (paragraph 1)
- B“The American Indian people began to deliberately burn areas of land for bison to graze on, which enticed the herds away from the people’s crops.” (paragraph 2)
- C“This patch burning contains the fire within a specific area and allows animals in the burn area to safely relocate.” (paragraph 5)
- D“The following year, conservationists will burn a different section of the preserve, while the land burned the previous year regrows healthier than before.” (paragraph 5)
Show the answer
Correct answer: A
The question asks which sentence supports the idea that farmers and people who manage land may be concerned about using fire as a way to benefit the land.
A. CORRECT. The sentence from paragraph 1 supports the idea that farmers and people who manage land may be concerned about using fire as a way to benefit the land because it acknowledges that “one of the greatest threats to the prairie is wildfire.”
B. Incorrect. Although the sentence from paragraph 2 relates how American Indians “began to deliberately burn areas of land for bison to graze on” and to protect people’s crops, the sentence does not support the idea that farmers and people who manage land may be concerned about using fire as a way to benefit the land. Instead, it focuses on the cause-and-effect relationship between bison and newly burned areas.
C. Incorrect. The sentence from paragraph 5 provides details about how “patch burning contains the fire” and “allows animals in the burn area to safely relocate,” but it does not adequately support the idea that farmers and people who manage land may be concerned about using fire as a way to benefit the land, because it does not mention that wildfires can be a threat to the prairie.
D. Incorrect. While the sentence from paragraph 5 does explain how “conservationists will burn a different section of the preserve” in order to rotate the process year after year so that the burned land has time to regrow, the sentence does not support the idea that farmers and people who manage land may be concerned about using fire as a way to benefit the land because it does not mention the potential for total burns.
Question analysis
This evidence question asks which sentence from the article on controlled prairie burns supports the idea that farmers and others who manage land may be concerned about using fire to benefit it. The passage never states that concern directly, so students must infer it, and all four quoted sentences, taken from across the article, talk about burning land in some way.
- Grade level
- Grade 8 reading and task
- Compared with grade 7
- Above grade 7 Grade 7 evidence questions usually ask for support of an idea the text states. This idea, that people who manage land may worry about using fire, is never stated outright, so students must infer which sentence implies it, more than typical.
- Estimated difficulty
- Hard: combines ideas, needs a plan, and has more than one tempting wrong answer.
- Thinking it demands
- Depth of knowledge 3, strategic thinking · mainly evaluate
- What makes it hard
- Reading between the lines major
- A very close wrong answer moderate
- Every choice must be checked minor
- Evidence
- Answered from one sentence or line
- Reading level
- Passage: about grade 11, 598 words; question and choices: about grade 13, 123 words.
- Students, last 30 days
- Not enough answers yet to show (it takes 10).
Why it is hard, traps and wrong answers (shows the answer)
Why it is hard
The idea to support is about people’s feelings, yet none of the four sentences mentions farmers worrying, so students have to decide what would justify such worry. The opening sentence does it by naming wildfire as a great threat before praising controlled fire, a concession many students read past as background. The strongest pull is the sentence on containing the fire, which implies caution but presents patch burning as the answer, not the concern.
Reading between the lines major Working it out
No sentence mentions worry; students must see that calling wildfire “one of the greatest threats to the prairie” gives landowners a reason to fear fire, and that “actually” answers that fear. (Graesser, Singer & Trabasso, 1994; Kintsch, 1998)
A very close wrong answer moderate Choosing the answer
The patch-burn sentence about containing the fire “within a specific area” also hints at fire’s danger; it differs from the right one by describing the safeguard without ever naming a threat. (Embretson & Wetzel, 1987; Gorin & Embretson, 2006; Ascalon et al., 2007)
Every choice must be checked minor Choosing the answer
The four sentences come from paragraphs 1, 2 and 5, and each is about burning land, so each must be tested for a hint of risk rather than for its topic. (Embretson & Wetzel, 1987)
Strategy: Before rereading the choices, decide what a sentence would need to say to show that landowners have reason to be wary of fire, then test each quoted sentence for exactly that.
Traps
- Supports only part of the claim: In a question about evidence: a line that backs one half of the claim but not the other, or a related point rather than the claim itself.
- True but not the answer: A choice says something accurate about the text that does not answer this question.
The wrong answers, classified
B True but not the answer (King et al., 2004; Embretson & Wetzel, 1987)
Links “the people’s crops” to farmers, but the sentence tells how early burns drew bison away from the crops and shows no worry about fire itself.
C Supports only part of the claim (King et al., 2004; Thissen, Steinberg & Fitzpatrick, 1989)
Sees caution in containing the fire “within a specific area,” but the sentence explains how patch burning keeps animals safe and never says fire threatens the land.
D Supports only part of the claim (King et al., 2004; Thissen, Steinberg & Fitzpatrick, 1989)
Takes the yearly rotation as a careful precaution, but the sentence describes the schedule and land that “regrows healthier than before,” which backs the benefit, not the worry.
Working it out, step by step
Figure out what the question asks
This is an evidence question. Evidence is the words in a text that back up an idea. The idea here is that farmers might worry about using fire to help land. No sentence says farmers are worried. So look for a sentence that gives them a reason to fear fire.
Decide what the evidence needs
A sentence that supports this idea must show that fire can be dangerous. If fire can harm land, people have a reason to be careful with it. So test each sentence with one question: does it say fire is a threat?
Look closely at paragraph 1
Choice A quotes paragraph 1. Its first half says “one of the greatest threats to the prairie is wildfire.” That is a reason to fear fire. Its second half says controlled fires are “actually” helpful. The word “actually” pushes back against that fear. It means: you might expect fire to hurt the land, but here it helps.
Check each choice
- A is right. It names wildfire as a great threat. That gives farmers a reason to worry about fire.
- B is wrong. It tells how early burns drew bison away from crops. It shows no danger from fire.
- C is wrong. It tells how patch burning keeps the fire in one area. It describes a safety step but never names a threat.
- D is wrong. It describes burning a new section each year. It shows a benefit: land that “regrows healthier than before.”
Watch out: C hints that fire must be contained, or kept in, so it sounds careful. But it describes the solution, not the danger.
Choose the answer
Only one sentence names fire as a danger. So the answer is A, the sentence from paragraph 1: “While one of the greatest threats to the prairie is wildfire, the use of controlled fires is actually an effective way to protect this idyllic landscape.” Idyllic means peaceful and lovely.
Why this answer and not the closest wrong one
C is the closest wrong answer, because keeping fire “within a specific area” suggests caution. But C only explains how patch burning works. It never says fire can harm the prairie. A does, by calling wildfire one of the greatest threats.
More questions like this
The original DOE question
The passage “Using Fire to Keep a Prairie Healthy” as printed (page 41)
Question 3 of 6
2018 Test B English, question 31Passage Excerpt from “Niagara Falls”
Excerpt from “Niagara Falls”
by Rupert Brooke
The real secret of the beauty and terror of the Falls is not their height or width, but the feeling of colossal power and of unintelligible disaster caused by the plunge of that vast body of water. If that were taken away, there would be little visible change, but the heart would be gone.
The American Falls do not inspire this feeling in the same way as the Canadian. It is because they are less in volume, and because the water does not fall so much into one place. By comparison their beauty is almost delicate and fragile. They are extraordinarily level, one long curtain of lacework and woven foam. Seen from opposite, when the sun is on them, they are blindingly white, and the clouds of spray show dark against them. With both Falls the colour of the water is the ever-altering wonder. Greens and blues, purples and whites, melt into one another, fade, and come again, and change with the changing sun. Sometimes they are as richly diaphanous as a precious stone, and glow from within with a deep, inexplicable light. Sometimes the white intricacies of dropping foam become opaque and creamy. And always there are the rainbows. If you come suddenly upon the Falls from above, a great double rainbow, very vivid, spanning the extent of spray from top to bottom, is the first thing you see. If you wander along the cliff opposite, a bow springs into being in the American Falls, accompanies you courteously on your walk, dwindles and dies as the mist ends, and awakens again as you reach the Canadian tumult. And the bold traveller who attempts the trip under the American Falls sees, when he dare open his eyes to anything, tiny baby rainbows, some four or five yards in span, leaping from rock to rock among the foam, and gambolling beside him, barely out of hand’s reach, as he goes. One I saw in that place was a complete circle, such as I have never seen before, and so near that I could put my foot on it. It is a terrifying journey, beneath and behind the Falls. The senses are battered and bewildered by the thunder of the water and the assault of wind and spray; or rather, the sound is not of falling water, but merely of falling; a noise of unspecified ruin. So, if you are close behind the endless clamour, the sight cannot recognise liquid in the masses that hurl past. You are dimly and pitifully aware that sheets of light and darkness are falling in great curves in front of you. Dull omnipresent foam washes the face. Farther away, in the roar and hissing, clouds of spray seem literally to slide down some invisible plane of air.
Beyond the foot of the Falls the river is like a slipping floor of marble, green with veins of dirty white, made by the scum that was foam. It slides very quietly and slowly down for a mile or two, sullenly exhausted. Then it turns to a dull sage green, and hurries more swiftly, smooth and ominous. As the walls of the ravine close in, trouble stirs, and the waters boil and eddy. These are the lower rapids, a sight more terrifying than the Falls, because less intelligible. Close in its bands of rock the river surges tumultuously forward, writhing and leaping as if inspired by a demon. It is pressed by the straits into a visibly convex form. Great planes of water slide past. Sometimes it is thrown up into a pinnacle of foam higher than a house, or leaps with incredible speed from the crest of one vast wave to another, along the shining curve between, like the spring of a wild beast. Its motion continually suggests muscular action. The power manifest in these rapids moves one with a different sense of awe and terror from that of the Falls. Here the inhuman life and strength are spontaneous, active, almost resolute. . . . A place of fear.
One is drawn back, strangely, to a contemplation of the Falls, at every hour, and especially by night, when the cloud of spray becomes an immense visible ghost, straining and wavering high above the river, white and pathetic and translucent. The Victorian lies very close below the surface in every man. There one can sit and let great cloudy thoughts of destiny and the passage of empires drift through the mind; for such dreams are at home by Niagara. I could not get out of my mind the thought of a friend, who said that the rainbows over the Falls were like the arts and beauty and goodness, with regard to the stream of life—caused by it, thrown upon its spray, but unable to stay or direct or affect it, and ceasing when it ceased. In all comparisons that rise in the heart, the river, with its multitudinous waves and its single current, likens itself to a life, whether of an individual or of a community. A man’s life is of many flashing moments, and yet one stream; a nation’s flows through all its citizens, and yet is more than they. In such places, one is aware, with an almost insupportable and yet comforting certitude, that both men and nations are hurried onwards to their ruin or ending as inevitably as this dark flood. Some go down to it unreluctant, and meet it, like the river, not without nobility. And as incessant, as inevitable, and as unavailing as the spray that hangs over the Falls, is the white cloud of human crying. . . . With some such thoughts does the platitudinous heart win from the confusion and thunder of a Niagara peace that the quietest plains or most stable hills can never give.
From LETTERS FROM AMERICA by Rupert Brooke—Public Domain
diaphanous: sheer, translucent
platitudinous: clichéd, common
Question
With which statement would the author of this excerpt most likely agree?
- AA sense of ease and assurance comes with accepting one’s fate.
- BNo matter where one’s path goes in life, one will always have regrets.
- CThe best way to overcome fear is to recognize it and then defy it.
- DReason will die out with humanity, but art will remain immortal.
Show the answer
Correct answer: A
The question asks for the statement the author would agree with most. In paragraph 4, the author states that the Falls make a person feel “with an almost insupportable and yet comforting certitude, that both men and nations are hurried onwards to their ruin or ending.” Later, the final sentence says, “With some such thoughts does the platitudinous heart win from the confusion and thunder of a Niagara peace.” This sentence supports the author’s belief that a person can find peace in accepting the certainty of his or her own ending, as expressed in Option A.
Option B is incorrect because the author does not discuss regrets in the excerpt.
Option C is incorrect because, while the excerpt discusses fear when looking at the power of the Falls, the excerpt does not support the idea that one should defy fear.
Option D is incorrect because the excerpt states in paragraph 4 that art and beauty are “caused by” the stream of life and end with it, “ceasing when it ceased.”
Question analysis
This question asks students to infer which statement about life the author of “Niagara Falls” would most likely agree with, based on the reflections that close his essay. It is hard because the evidence sits in long, abstract sentences of century-old prose and must be pieced together from more than one place in the final paragraph.
- Grade level
- Grade 9 reading and task
- Compared with grade 7
- Above grade 7 Grade 7 point-of-view questions usually rest on a clearly stated opinion. Here the author’s view must be pieced together from abstract reflection on lives, nations and the river, with words like “insupportable” and “platitudinous,” which is closer to high school reading.
- Estimated difficulty
- Among the hardest on the SHSAT: a non-obvious approach, heavy reading, or a well-hidden trap.
- Thinking it demands
- Depth of knowledge 3, strategic thinking · mainly analyze
- What makes it hard
- Reading between the lines major
- Complex sentences major
- The right answer is reworded moderate
- Hard words moderate
- Evidence
- Answered from one paragraph or stanza
- Reading level
- Passage: about grade 9, 987 words; question and choices: about grade 6, 61 words.
- Corrected from the DOE handbook
- A misreading of a word in the passage was corrected in the 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
This question asks for the author’s outlook, which he reaches only in the closing sentences of a long, abstract paragraph. The mood there is gloomy, with ruin, a dark flood and human crying, so students who read the mood but not the argument choose regret. The comfort and peace he finds in that certainty are easy to miss in the inverted final sentence, and they are exactly what the answer rests on.
Reading between the lines major Working it out
The author never states a belief; students must combine “comforting certitude,” people who meet their end “unreluctant” and “not without nobility,” and the closing “peace” into an attitude of accepting fate. (Graesser, Singer & Trabasso, 1994; Kintsch, 1998)
Complex sentences major Understanding the question
The last sentence inverts normal order, “With some such thoughts does the platitudinous heart win from the confusion and thunder of a Niagara peace,” so its subject and object are hard to find. (Abedi & Lord, 2001; Freedle & Kostin, 1993; Messick, 1989)
The right answer is reworded moderate Choosing the answer
The right statement uses none of the passage’s words, turning “certitude” into “assurance” and “peace” into “ease,” while wrong choices pick up “fear” and “art.” (Freedle & Kostin, 1993; Kirsch & Mosenthal, 1990)
Hard words moderate Understanding the question
“Certitude,” “unreluctant,” “unavailing” and “platitudinous” carry the author’s attitude, and the glossary defines only the last of them. (Perfetti, 2007; Freedle & Kostin, 1993)
Strategy: Reread the second half of paragraph 4 slowly, translating each long sentence into plain words, then choose the statement those lines support without adding ideas the author never mentions.
Traps
- Outside knowledge: A choice is plausible in the real world but not supported by this text.
- Reads too much in: A reasonable-sounding conclusion that goes further than the text allows.
The wrong answers, classified
B Reads too much in (Graesser, Singer & Trabasso, 1994)
Reads “the white cloud of human crying” and the dark flood as a claim about lifelong regret, though the author never mentions regret and finds comfort in the end.
C Outside knowledge (King et al., 2004; Recht & Leslie, 1988)
Falls back on familiar advice about facing fears, prompted by the excerpt’s talk of terror, but the author recommends accepting what is inevitable, not defying it.
D Twists what the text says (King et al., 2004)
Reverses the friend’s rainbow comparison: art and beauty are “caused by” the stream of life and end with it, “ceasing when it ceased,” so art is not immortal.
What was corrected from the DOE handbook, and why
- Explanation: The handbook rejects Option D because paragraph 4 says art is “unable to stay.” In the passage, art and beauty are “unable to stay or direct or affect” the stream of life: “stay” means to stop or hold back the stream, not to last. What shows that art is not immortal is that it is “caused by” the stream of life and ends with it, “ceasing when it ceased,” which the site now quotes.
Working it out, step by step
Figure out what the question asks
This asks which statement the author would most likely agree with. He never states his belief outright, so you must infer it from his words, especially at the end of paragraph 4.
Find what he says about endings
In paragraph 4, he says that at Niagara one feels “with an almost insupportable and yet comforting certitude” that people and nations reach an end. He adds: “Some go down to it unreluctant, and meet it, like the river, not without nobility.” His last sentence says the heart can “win from the confusion and thunder of a Niagara peace.”
Put his words in plain English
“Certitude” means being sure. “Insupportable” means too hard to bear. So knowing that everything ends is hard, yet it is also comforting. “Unreluctant” means willing. Some people meet their end willingly, with dignity. And the Falls give the heart peace. Put together: accepting what must happen brings calm.
Check each choice
- A is right. He finds comfort and peace in accepting fate. That is “ease and assurance.”
- B is wrong. He never mentions regrets.
- C is wrong. He talks about accepting what must happen, not about fighting fear.
- D is wrong. Art and beauty are “caused by” life and end with it, “ceasing when it ceased.” So art does not last forever.
Watch out: “The white cloud of human crying” sounds sad, so B may tempt you. But sadness is not regret, and the author ends on peace.
Choose the answer
The author finds calm and comfort in accepting what must come. So the answer is A.
Why this answer and not the closest wrong one
B is the closest wrong answer, because paragraph 4 mentions human crying and ruin. But the author never talks about regret. He calls the certainty of an ending “comforting,” and the essay closes on the word “peace.” Feeling calm by accepting fate is what A says.
More questions like this
The original DOE question
The passage “Excerpt from “Niagara Falls”” as printed (pages 134–135)
Question 4 of 6
2024 Test A Math, question 39Question
Raquel is cutting out pieces of cardboard to make a pyramid. She will use a square piece for the base and identical triangular pieces for the sides. The figure above shows the dimensions of the triangle for each side. What will be the total surface area, in square inches, of the pyramid, including the square base?
- A280
- B295
- C340
- D360
Show the answer
Correct answer: C
Surface area is found by calculating the area of each side, including the base, and adding them all together.
The base of the pyramid measures 10 inches on each side, so the area of the base is
Each triangular face has a base of 10 inches and a height of 12 inches, so the area of each face is
There are 4 triangular faces (because the square base has 4 edges, each of which will have a triangular face). So the total surface area of the pyramid is the sum of the areas of 4 triangles and 1 square.
So the total surface area is 340 square inches.
Question analysis
This surface area word problem shows one triangular face, with sides of 13 inches, a base of 10 inches and a height of 12 inches, that Raquel will use to build a cardboard pyramid with a square base. Students find the total area of the base and all the triangular sides. Picturing the solid and choosing the right measurements from the figure are the tricky parts.
- Grade level
- Grade 7 content, by NYS standard
- Compared with grade 7
- Above grade 7 Grade 7 students find the surface area of a pyramid from a drawn net or solid. Here only one triangular face is shown, so students must picture the whole pyramid, count its faces, and choose which labeled length belongs in the area formula.
- Estimated difficulty
- Hard: combines ideas, needs a plan, and has more than one tempting wrong answer.
- Thinking it demands
- Depth of knowledge 2, skills and concepts · mainly apply
- What makes it hard
- Reading a figure, table or graph moderate
- Combines ideas moderate
- Something you must already know minor
- Solution
- 4 steps
- Reading level
- Question and choices: about grade 6, 56 words.
- Corrected from the DOE handbook
- A wrong unit in the explanation was corrected.
- Students, last 30 days
- Not enough answers yet to show (it takes 10).
Why it is hard, traps and wrong answers (shows the answer)
Why it is hard
Students have to build the pyramid in their heads from one flat triangle, then choose the right measurement from three labels. The 13-inch sides look like the natural height, and using them gives a listed total; picturing a pyramid with three sloping faces gives another. Sketching the square base with a triangle on each edge, and marking 12 as the height, settles both the face count and the formula.
Reading a figure, table or graph moderate Understanding the question
The figure gives one triangle with three length labels, 13, 13 and 10, and puts its height, 12, on a separate arrow beside it, where it is easy to overlook. (Lesh, Post & Behr, 1987; Kirsch & Mosenthal, 1990)
Combines ideas moderate Working it out
The solid is never drawn: students must see that the square's side equals the triangle's 10-inch base, count four triangles, and add triangle and square areas. (Embretson, 1998; Daniel & Embretson, 2010)
Something you must already know minor Working it out
A triangle's area uses its perpendicular height, not a slanted side, and a pyramid on a square base has four triangular faces; neither fact is given. (Anderson & Krathwohl, 2001)
Strategy: Sketch the pyramid: a square base whose side is the triangle's base, and one triangular face on each side of the square. Find each area with the matching formula, then add them all.
Traps
- Misreads the figure: Reads a value, label or tick spacing in a figure, table or graph wrongly.
- Information you don't need: The question gives numbers or facts that play no part in the answer.
- Misunderstands the concept: A wrong belief about a concept: that percents can be added, that area grows like length, that averages can be averaged, that a bigger denominator means a bigger fraction.
The wrong answers, classified
A Misunderstands the concept (Smith, diSessa & Roschelle, 1993; De Bock et al., 1998; Ni & Zhou, 2005)
Counts only three triangular faces, as if the pyramid had a triangular base, so 3 × 60 + 100 = 280.
B Misunderstands the concept (Smith, diSessa & Roschelle, 1993; De Bock et al., 1998; Ni & Zhou, 2005)
Counts three faces and also uses the 13-inch side as each triangle's height: 3 × 65 + 100 = 295.
D Misreads the figure (Lesh, Post & Behr, 1987; Kirsch & Mosenthal, 1990)
Takes the 13-inch slanted side as each triangle's height instead of the 12-inch arrow beside it, so 4 × 65 + 100 = 360.
What was corrected from the DOE handbook, and why
- Explanation: The handbook ends “So the total surface area is 340 square feet.” The triangle’s dimensions are in inches and the question asks for square inches, so the site now reads “340 square inches.”
Worked solution, step by step
Formulas used
- Area of a triangle
- A is the area. b is the base, the side the triangle sits on. h is the height: the straight-up distance from the base to the top corner, at a right angle to the base. You take half because a triangle is half of a rectangle with the same base and height.
- Area of a square
- A is the area and s is the length of one side. All four sides of a square are equal, so the area is side times side.
- Surface area
- A face is one flat side of a solid shape. The surface area is the total area of the outside. Picture unfolding the solid into flat pieces. Then add up the area of every piece.
Sort out the question
Raquel’s pyramid has a square base. Each side is a triangle like the one in the figure. The triangle’s base is 10 in. Its two slanted sides are 13 in. Its height, the arrow beside it, is 12 in. You need the total surface area, including the square base, in square inches.
Picture the pyramid
Surface area is the total area of all the flat sides, called faces. Each triangle stands on one edge of the square. So each edge of the square is 10 inches, the same as the triangle’s base. A square has 4 edges, so the pyramid has 4 triangles.
Here that is 4 triangles plus 1 square. Watch out: counting only 3 triangles gives 280, choice A.
Find the area of one triangle
Each triangle is 60 square inches. Watch out: the height is 12 in., the straight-up arrow. It is not 13 in., the slanted side. Using 13 gives 65 for each triangle and 360 in all, choice D.
Find the area of the base
The base is a square with sides of 10 inches, the same as each triangle’s base.
The square base is 100 square inches.
Add all five faces
The four triangles and the square together cover 340 square inches.
So the answer is C, 340 square inches.
Check your answer
Each triangle is half of a 10 by 12 rectangle, which has an area of 120. So two triangles make 120, and four make 240. Add the base: . The units fit too: inches times inches gives square inches.
More questions like this
The original DOE question
Question 5 of 6
2018 Test A Math, question 5Question
The sum of two consecutive integers is −15. If 1 is added to the smaller integer and 2 is subtracted from the larger integer, what is the product of the two resulting integers?
Grid-in question: work out the answer and enter it as a number.
Show the answer
Correct answer: 63
If x is the smaller consecutive integer, then
is the larger consecutive integer. Use their sum (−15) to find x:
The two consecutive integers are −8 and −7. One is added to the smaller integer:
and 2 is subtracted from the larger integer:
Find the product:
Question analysis
A grid-in problem about two consecutive integers whose sum is −15. Students find the two integers, add 1 to the smaller and subtract 2 from the larger, then multiply the results. Deciding which negative integer is the smaller one, and keeping signs straight through every step, are what make it tricky.
- Grade level
- Grade 7 content, by NYS standard
- Compared with grade 7
- Above grade 7 A typical grade 7 task solves one two-step equation or multiplies signed numbers. This links both: set up a consecutive-integer equation, solve it with negatives, adjust each integer, and multiply, with no choices to check against.
- 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
- Error-prone arithmetic moderate
- Turning words into math moderate
- Many steps moderate
- Solution
- 4 steps
- Reading level
- Question and choices: about grade 9, 30 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 the question collects most of the ways students lose points with negatives. The crucial judgment is which of −8 and −7 is the smaller; a student who picks −7 still produces a tidy, wrong product. Gridding the product of the original pair, or giving a negative product, are the other usual losses. Writing each intermediate pair down, rather than holding them in mind, protects against all three.
Error-prone arithmetic moderate Working it out
Every number in play is negative: −8 and −7, then −7 and −9, and a product of two negatives that must come out positive. (Brown & Burton, 1978; Junker & Sijtsma, 2001)
Turning words into math moderate Understanding the question
"1 is added to the smaller integer and 2 is subtracted from the larger" depends on knowing that −8, not −7, is the smaller, since it lies farther below zero. (Hegarty, Mayer & Monk, 1995; Koedinger & Nathan, 2004)
Many steps moderate Working it out
Four linked steps: set up x + (x + 1) = −15, solve for x, adjust each integer, then multiply; an error early in the chain carries through to the product. (Daniel & Embretson, 2010; Enright, Morley & Sheehan, 2002)
Strategy: Halve the sum to see which two integers sit on either side of it, remember that the smaller negative is farther from zero, then adjust each and multiply.
Traps
- Negatives and direction: Arithmetic with negative numbers, the order of a subtraction, or direction on a number line. (Moving a term across the equals sign without changing its sign is a faulty procedure.)
- Misreads the question: Misses or misreads a condition or a word in the question: "at least", "each", "remaining", "not".
The wrong answers, classified
60 Negatives and direction (Brown & Burton, 1978)
Takes −7 as the smaller integer because 7 is less than 8, so adjusts to −7 + 1 = −6 and −8 − 2 = −10, and multiplies to 60.
56 Misreads the question (Hegarty, Mayer & Monk, 1995)
Finds −8 and −7 and multiplies them to get 56, skipping the sentence that adds 1 to one integer and subtracts 2 from the other.
-63 Negatives and direction (Brown & Burton, 1978)
Finds the adjusted integers −7 and −9 correctly but gives their product a negative sign, gridding −63.
Worked solution, step by step
Formulas used
- Consecutive integers
- Integers are whole numbers and their opposites, like −2, −1, 0, 1 and 2. Consecutive integers come one right after another. If n is the smaller one, the next one is n + 1, because each step up the number line adds 1.
- Multiplying two negative numbers
- a and b are positive numbers, so −a and −b are negative. When you multiply two negative numbers, the answer is positive. The two minus signs cancel out.
Sort out the question
Two consecutive integers add up to −15. Integers are whole numbers and their negatives. Consecutive means one comes right after the other, like 4 and 5. You need to do three things:
- Find the two integers.
- Add 1 to the smaller one. Subtract 2 from the larger one.
- Find the product of the two new numbers. The product is the answer when you multiply.
Find the two integers
Call the smaller integer n. Then the larger one is n + 1. Their sum is −15.
Subtract 1 from both sides. Then divide both sides by 2.
So the integers are −8 and −7.
Decide which one is smaller
On a number line, −8 is to the left of −7. Numbers to the left are smaller. So −8 is the smaller integer, and −7 is the larger one. Watch out: 8 is bigger than 7, but −8 is smaller than −7. Mixing them up gives −6 and −10, and the wrong answer 60.
Change each integer
Add 1 to the smaller integer.
Subtract 2 from the larger integer.
The two new numbers are −7 and −9.
Multiply the new numbers
Both numbers are negative, so their product is positive.
Watch out: the answer is not −63, because two negatives make a positive. Also, don’t multiply the first pair, −8 and −7. That gives 56 and skips the changes. So you would grid 63.
Check your answer
Check the pair: , and they are one apart. Half of −15 is −7.5, and −8 and −7 sit on either side of it. Then , and the sign is positive.
More questions like this
The original DOE question
Question 6 of 6
2024 Test B Math, question 25Question
Which number line represents the values of x that satisfy the inequality ?
- A
- B
- C
- D
Show the answer
Correct answer: B
Split the compound inequality into two inequalities.
and
For each inequality, subtract 1 from each side.
and
For each inequality, divide both sides by −3. Note that dividing each side of an inequality by a negative number changes the direction of the inequality.
and
Combining the pieces gives the compound inequality .
The solution is that x is greater than or equal to −1 and less than or equal to 2, so choose the number line with filled circles at −1 and 2, with the filled segment between the circles.
Question analysis
An inequality question: choose the number line that shows the solutions of the compound inequality −5 ≤ 1 − 3x ≤ 4. Students solve an inequality whose x term has a negative coefficient, then match the endpoints, open or closed circles, and shading to one of four graphs.
- Grade level
- Grade 7 content, by NYS standard
- Compared with grade 7
- Above grade 7 Grade 7 students solve and graph two-step inequalities one at a time. This compound inequality needs two solved together and a division by a negative number, which reverses the signs, a step many grade 7 classes only touch on.
- Estimated difficulty
- Hard: combines ideas, needs a plan, and has more than one tempting wrong answer.
- Thinking it demands
- Depth of knowledge 1, recall and reproduction · mainly apply
- What makes it hard
- Error-prone arithmetic moderate
- A very close wrong answer moderate
- Reading a figure, table or graph minor
- Solution
- 4 steps
- Reading level
- Question and choices: about grade 12, 13 words.
- Students, last 30 days
- Not enough answers yet to show (it takes 10).
Why it is hard, traps and wrong answers (shows the answer)
Why it is hard
The question stacks two classic traps: reversing the inequality signs when dividing by −3, and matching filled or open circles to ≤. All four graphs use the endpoints −1 and 2, so finding those numbers proves little; the choice turns on the circles and the direction of the shading. Testing x = 0, x = 3 and the endpoint x = 2 in the original inequality checks both decisions in under a minute.
Error-prone arithmetic moderate Working it out
Dividing all three parts of −6 ≤ −3x ≤ 3 by −3 reverses both signs and the order, giving 2 ≥ x ≥ −1, which must be rewritten as −1 ≤ x ≤ 2. (Brown & Burton, 1978; Junker & Sijtsma, 2001)
A very close wrong answer moderate Choosing the answer
Two graphs share the endpoints −1 and 2 and the shading between them; only the circles, filled for ≤ and open for <, separate them. (Embretson & Wetzel, 1987; Gorin & Embretson, 2006; Ascalon et al., 2007)
Reading a figure, table or graph minor Understanding the question
Each graph must be read for three things at once: the endpoints, the fill of each circle, and whether the shading runs between them or outward. (Lesh, Post & Behr, 1987; Kirsch & Mosenthal, 1990)
Strategy: Subtract 1 from all three parts, divide all three by −3 while reversing both inequality signs, then rewrite the result from smallest to largest before matching circles and shading.
Traps
- Negatives and direction: Arithmetic with negative numbers, the order of a subtraction, or direction on a number line. (Moving a term across the equals sign without changing its sign is a faulty procedure.)
- Counting the ends: Inclusive or exclusive ends, fence posts, consecutive numbers: an answer that is one too many or too few, or an endpoint drawn open where it belongs closed (or the reverse).
The wrong answers, classified
A Counting the ends (Brown & Burton, 1978)
Solves for the right endpoints and shading but draws open circles, as if ≤ excluded −1 and 2 instead of including them.
C Negatives and direction (Brown & Burton, 1978)
Divides by −3 without reversing the signs, so the solutions seem to lie outside −1 and 2; with open circles, this graph shows exactly the values that fail.
D Negatives and direction (Brown & Burton, 1978)
Shades outward as if the signs had not reversed, but mixes the circles, filled at −1 and open at 2, which no single reading of ≤ gives.
Worked solution, step by step
Formulas used
- Subtracting from every part
- a and b are the two sides of an inequality, and c is any number. Subtracting the same number from every part keeps the inequality true. The sign does not change.
- Dividing by a negative number
- a and b are numbers, and c is a positive number, so −c is negative. When you divide both sides by a negative number, the inequality sign flips. For example, 2 is less than 3, but −2 is greater than −3.
Sort out the question
The inequality says that is between −5 and 4. The sign ≤ means less than or equal to. So −5 and 4 themselves are allowed. You need the number line that shows every x that works. To find them, get x alone in the middle.
Subtract 1 from every part
First take away the 1 in the middle. Subtract 1 from all three parts.
Divide by −3 and flip
Now x is multiplied by −3. Divide all three parts by −3. Dividing by a negative number flips each sign.
Watch out: if you forget to flip, x seems to lie outside −1 and 2. That leads to choices C and D, which are shaded outward.Read the result
Turn it around so the smaller number is on the left. It means the same thing.
So x can be any number from −1 to 2. The ends, −1 and 2, are included, because the signs are ≤.
Pick the number line
On a number line, a closed (filled-in) circle means the end number is included. An open circle means it is not. So you need closed circles at −1 and 2, with the part between them shaded. Watch out: choice A has the right shading but open circles, which leave out −1 and 2.
So the answer is B.
Check your answer
Test a few numbers in . For x = 0 you get 1, which is between −5 and 4, and 0 is shaded. For x = 2 you get −5, which is allowed, so the circle at 2 is filled in. For x = 3 you get −8, which is too small, so 3 is not shaded.
More questions like this
The original DOE question
