Bristlecone pines in the White Mountains of California grow in thin, rocky soil where cold, wind, and drought limit how much wood they can add each year. That slow growth produces wood so dense and resinous that it resists rot and insects, and some living trees have ______ for more than 4,500 years, making them among the oldest known individual organisms on Earth.
Which choice completes the text with the most logical and precise word or phrase?
Correct choice: endured
The text explains that the trees’ dense, resinous wood resists rot and insects, which is why some living trees are more than 4,500 years old. Endured, meaning lasted or survived, describes trees that have remained alive for that long despite harsh conditions.
A: Trees are rooted in place; nothing in the text suggests that they have moved.
B: The text stresses that the trees grow slowly, so saying they have accelerated contradicts the passage.
D: The text describes the age of individual trees, not an increase in their number.
Watch for: Use the cause the text gives (wood that resists rot and insects) to predict what the trees have done for 4,500 years.
Reading and Writing · Module 1 · Question 2 of 27
The following text is from Joseph Conrad’s 1904 novel Nostromo. In the fictional South American province of Sulaco, a ceremony is being held to mark the start of construction on a railroad financed by foreign investors.
Everybody of note in Sulaco had been invited—the one or two foreign merchants, all the representatives of the old Spanish families then in town, the great owners of estates on the plain, grave, courteous, simple men, caballeros of pure descent, with small hands and feet, conservative, hospitable, and kind. The Occidental Province was their stronghold; their Blanco party had triumphed now; it was their President-Dictator, a Blanco of the Blancos, who sat smiling urbanely between the representatives of two friendly foreign powers. They had come with him from Sta. Marta to countenance by their presence the enterprise in which the capital of their countries was engaged.
As used in the text, what does the word “countenance” most nearly mean?
Correct choice: endorse
The two foreign representatives are described as “friendly,” and they have traveled with the President-Dictator to the ceremony for an enterprise financed by “the capital of their countries.” Their presence is meant to show official approval of that enterprise, so countenance means endorse.
B: In modern usage countenance often means put up with (“would not countenance such behavior”), but the representatives are friendly and have come on purpose to support a venture their own countries are investing in, not merely to accept it reluctantly.
C: The representatives do see the ceremony, and “by their presence” may suggest watching, but their presence is the means; the purpose stated is to lend support to the enterprise, not simply to observe it.
D:Countenance can mean face, but nothing in the text suggests that the representatives oppose or challenge the enterprise; they are described as friendly.
Watch for: When an older text uses a familiar word, ask what the people described are trying to accomplish; here the purpose (backing their countries’ investment) rules out the modern sense “tolerate.”
Reading and Writing · Module 1 · Question 3 of 27
In the 1930s and 1940s the forger Han van Meegeren sold several paintings as newly discovered works by the seventeenth-century Dutch painter Johannes Vermeer. To make his paint look centuries old, van Meegeren mixed it with a synthetic resin and baked the finished canvases until the surface hardened and cracked. Chemical analyses carried out after his arrest found traces of that resin, a substance first manufactured in the twentieth century, in the paint. The very material that van Meegeren relied on to make the works look old thus ______ their recent origin.
Which choice completes the text with the most logical and precise word or phrase?
Correct choice: betrays
Van Meegeren added the resin to make the paintings look old, yet chemical analysis of that resin exposed them as modern. Betrays, in its sense of reveals unintentionally or against someone’s purpose, captures this ironic self-exposure.
B: To confide is to reveal something privately to a trusted person, which adds an intention and intimacy that the text does not support.
C: To flaunt is to display something ostentatiously; the resin was hidden in the paint and was detected only by analysis.
D: To advertise is to call public attention to something deliberately; the resin revealed the paintings’ recent origin against the forger’s intention, and only under chemical analysis.
Watch for: When several choices all mean some kind of revealing, decide whether the text treats the revealing as deliberate or as working against someone’s purpose.
Reading and Writing · Module 1 · Question 4 of 27
Archaeologists long assumed that people began building large monuments only after they had adopted farming, since farming could produce the food surpluses needed to support many workers. At Göbekli Tepe in southeastern Turkey, however, people raised rings of massive carved limestone pillars more than 11,000 years ago, when communities in the region still appear to have lived mainly by hunting and gathering. Some researchers have proposed that the effort of feeding the crowds who gathered to build and use such structures may even have encouraged people to begin cultivating wild grains.
Which choice best states the main purpose of the text?
Correct choice: To present a discovery that challenges an assumed order of two developments, along with a proposal that reverses the assumed relationship between them
The text states an assumption (farming came first and made monuments possible), presents Göbekli Tepe as a site where monuments seem to have come first, and then reports a proposal that reverses the assumed causal link: building monuments may have encouraged farming. Its purpose is to present both the challenging discovery and the reversing proposal.
A: This restates the long-held assumption that the text challenges; the site is presented as evidence that monuments may have come before farming, not after it.
C: The text says nothing about the builders stopping construction; the proposal concerns how monument building may have encouraged cultivation.
D: The proposal is reported as something “some researchers have proposed”; the text cites no evidence of farming at the site that confirms it.
Watch for: When a text reports an assumption and then a discovery, check which way each choice runs the cause and effect; a choice that restates the assumption reverses the text’s point.
Reading and Writing · Module 1 · Question 5 of 27
The following text is Edward Thomas’s 1917 poem “The Owl.” The speaker has reached an inn after walking on a cold night.
Downhill I came, hungry, and yet not starved; Cold, yet had heat within me that was proof Against the North wind; tired, yet so that rest Had seemed the sweetest thing under a roof.
Then at the inn I had food, fire, and rest, Knowing how hungry, cold, and tired was I. All of the night was quite barred out except An owl’s cry, a most melancholy cry
Shaken out long and clear upon the hill, No merry note, nor cause of merriment, Underlined: But one telling me plain what I escaped End underlined. Underlined: And others could not, that night, as in I went. End underlined.
And salted was my food, and my repose, Salted and sobered, too, by the bird’s voice Speaking for all who lay under the stars, Soldiers and poor, unable to rejoice.
Which choice best describes the function of the underlined portion in the text as a whole?
Correct choice: It turns the owl’s cry into a reminder of people who remain exposed to the night, shifting the speaker’s attention from his own relief to others’ hardship.
Before the underlined lines, the speaker describes his own hardship and then his comfort at the inn, with the night “barred out.” The underlined lines make the owl’s cry tell him “what I escaped / And others could not”: his relief now points to those still outside. The final stanza develops this shift, saying his food and rest are “salted and sobered” by the thought of “soldiers and poor.”
A: The lines say the speaker has escaped the night’s hardship; the danger belongs to others, not to him.
B: The first stanza qualifies his hunger and cold (“not starved,” “heat within me”), but the underlined lines are about what he escaped and others did not, not about misjudging his own condition.
D: The lines do imply that the speaker is fortunate, but the final stanza does not celebrate his comfort; it says his food and rest were “salted and sobered” by thoughts of those still outside.
Watch for: A choice can describe the underlined lines accurately and still fail by misdescribing how the rest of the poem uses them; check the claim about the final stanza.
Reading and Writing · Module 1 · Question 6 of 27
Popular accounts often describe forests as communities in which trees use underground fungal networks to pass sugars to struggling neighbors and to send chemical warnings of insect attack. Field studies have shown that the root-colonizing fungi of some forests do link the roots of neighboring trees. Underlined: Whether substantial amounts of carbon or warning signals actually travel through those links in natural forests, rather than through the soil or by other routes, is far less clear. End underlined. A 2023 review of field research found that few studies had ruled out such alternative pathways and that some results had been cited more confidently than the studies themselves justified.
Which choice best describes the function of the underlined sentence in the text as a whole?
Correct choice: It distinguishes a further claim that the evidence has not yet established from a claim that the text treats as established.
The sentence before the underlined one accepts that fungi link neighboring trees. The underlined sentence then separates that established point from the further claim that substantial carbon or signals move through the links rather than by other routes, a claim it calls “far less clear.” The final sentence gives the review’s findings as support for that uncertainty.
B: The text accepts that fungal links exist (“Field studies have shown”); the underlined sentence questions what travels through them, not whether they exist.
C: The review is reported in the next sentence, and it concerned whether studies ruled out alternative pathways and how results were cited; the underlined sentence states an uncertainty that the review supports rather than summarizing the review.
D: The sentence treats carbon and signals together as equally uncertain; it does not rank one as more likely than the other.
Watch for: In hedged science texts, locate exactly where the author moves from what has been shown to what has only been claimed; that boundary is often the underlined sentence’s job.
Reading and Writing · Module 1 · Question 7 of 27
Text 1
Across the grasslands of the Namib Desert, millions of bare, roughly circular patches called fairy circles are ringed by taller grass. In a survey of hundreds of circles, one researcher found sand termites in nearly all of them and proposed that the termites create the circles: by eating the roots of grasses, they clear patches in which rainwater, no longer drawn up by plants, is stored in the soil and sustains their colonies.
Text 2
Some ecologists attribute fairy circles to the grasses themselves. Where water is scarce, grasses at the edge of a bare patch draw water from the surrounding soil, and computer models of this competition reproduce the circles’ remarkably even spacing. These ecologists note that termites could well be attracted to the moist soil that a bare patch provides; in their view, finding termites in a circle does not reveal how the circle began.
Based on the texts, how would the author of Text 2 most likely respond to the survey finding described in Text 1?
Correct choice: By granting that termites are common in the circles but denying that their presence shows that they formed them
Text 2 does not dispute that termites occur in the circles; it says termites “could well be attracted” to the moist soil of bare patches and that “finding termites in a circle does not reveal how the circle began.” So Text 2 would accept the survey’s observation but reject the causal conclusion drawn from it.
A: Text 2 does not say that termites keep the circles bare; it suggests only that termites may be attracted to the moist soil of patches that already exist.
B: This accurately reports Text 2’s own evidence for its explanation, but it does not respond to the survey finding, which concerns termites’ presence in the circles.
C: Text 2 does not concede that termites clear the patches, and it agrees that bare patches hold water (“the moist soil that a bare patch provides”).
Watch for: A choice can state something the second text says and still fail to answer the question asked, which here is how Text 2 would respond to one particular finding.
Reading and Writing · Module 1 · Question 8 of 27
The following text is from Nathaniel Hawthorne’s 1851 novel The House of the Seven Gables. Hepzibah Pyncheon, an elderly woman from a once-prominent family, has been forced by poverty to open a small shop.
A lady—who had fed herself from childhood with the shadowy food of aristocratic reminiscences, and whose religion it was that a lady’s hand soils itself irremediably by doing aught for bread,—this born lady, after sixty years of narrowing means, is fain to step down from her pedestal of imaginary rank. [...] In this republican country, amid the fluctuating waves of our social life, somebody is always at the drowning-point. The tragedy is enacted with as continual a repetition as that of a popular drama on a holiday, and, nevertheless, is felt as deeply, perhaps, as when an hereditary noble sinks below his order. More deeply; since, with us, rank is the grosser substance of wealth and a splendid establishment, and has no spiritual existence after the death of these, but dies hopelessly along with them.
Which choice best states the main idea of the text?
Correct choice: Hepzibah’s loss of status is a common American misfortune that may be felt even more painfully than a noble’s fall, because in America rank does not survive the wealth that sustains it.
The narrator places Hepzibah’s fall within a general observation: in America “somebody is always at the drowning-point,” and although such falls are common, they are felt as deeply as a noble’s fall, or “more deeply,” because American rank consists only of wealth and “dies hopelessly along with” it.
B: The narrator calls her rank “imaginary,” but the passage treats her fall as a “tragedy” to be felt deeply, not as a deserved punishment.
C: This reverses the text: despite the “continual … repetition,” the fall “is felt as deeply” as a noble’s, and perhaps more deeply.
D: The text says the opposite: in America rank “has no spiritual existence” once wealth is gone, whereas a noble’s rank might outlast it.
Watch for: Words such as “nevertheless” and “More deeply” mark the turn in the narrator’s generalization; a choice that treats frequency as lessening the pain misses that turn.
Reading and Writing · Module 1 · Question 9 of 27
In “Crossing Brooklyn Ferry,” a poem by Walt Whitman included in the 1891–92 edition of Leaves of Grass, the speaker addresses people who will ride the ferry between Brooklyn and Manhattan in future generations. Rather than merely predicting that they will see what he sees, the speaker asserts that the emotions they will feel on the crossing are ones he has already felt himself.
Which quotation from “Crossing Brooklyn Ferry” most effectively illustrates the claim?
Correct choice: “Just as you feel when you look on the river and sky, so I felt, / Just as any of you is one of a living crowd, I was one of a crowd,”
The claim has two parts: the speaker addresses future passengers, and he says their feelings are ones he has already had. In these lines he speaks to “you” and matches their feeling to his own past feeling (“Just as you feel … so I felt”).
B: These lines address the speaker’s present fellow passengers and express his curiosity about them, not a match between future passengers’ feelings and his own.
C: These lines predict what future passengers will do and see, which is exactly what the claim says the speaker goes beyond (“Rather than merely predicting”); they say nothing about his own feelings.
D: “I too” suggests a shared experience, but these lines list things the speaker saw on earlier crossings; they do not speak of anyone’s feelings or equate future passengers’ emotions with his.
Watch for: Test each quotation against every part of the claim; a quotation about the same subject can still fail because it concerns actions or sights rather than feelings.
Reading and Writing · Module 1 · Question 10 of 27
The scaly-foot snail has a shell with an outer layer containing iron sulfide, an organic middle layer, and a calcified inner layer. Researchers studying its mechanical properties argue that protection depends on the interaction of layers, not simply on having a hard outer surface. They investigated how the layered structure dissipates the energy of forces resembling a predator’s attack.
Which finding, if true, would most directly support the researchers’ claim about the shell’s protective mechanism?
Correct choice: Stiffening the shell’s middle layer increases transmitted force without changing the outer layer’s resistance to penetration.
The claim attributes protection to the layered system rather than just to a hard exterior. Changing the middle layer’s stiffness while leaving the outer layer’s penetration resistance unchanged isolates a contribution beyond exterior hardness: more force reaches inward when the middle layer is stiffened. The rivals all concern mechanical properties, but each can be established for an individual layer without demonstrating that interaction among layers contributes to the shell’s protection.
A: Ranking the layers by penetration resistance establishes different material properties, but does not show that their interaction improves protection.
C: A fracture threshold characterizes the inner layer under loading; it does not establish how another layer changes the force that reaches it.
D: The isolated-sample comparison concerns thickness within the outer material alone, so it cannot demonstrate the protective contribution of a layered arrangement.
Watch for: Prefer evidence that isolates the proposed interaction; measurements of individual components can be mechanically relevant without testing how the components work together.
Reading and Writing · Module 1 · Question 11 of 27
The table shows the approximate size of the world’s population at 25-year intervals from 1950 to 2025. A student claims that the world’s population grew by more people from 2000 to 2025 than from 1950 to 1975 but that its growth over the later period was smaller when expressed as a percentage.
World Population at 25-Year Intervals
Year
Population (billions)
1950
2.5
1975
4.1
2000
6.2
2025
8.2
Which choice most effectively uses data from the table to support the student’s claim?
Correct choice: The population grew by about 1.6 billion, or about 64%, from 1950 to 1975 and by about 2.0 billion, or about 32%, from 2000 to 2025.
The claim has two parts: the later increase was larger in number but smaller as a percentage. From 1950 to 1975 the population rose by about 1.6 billion (1.6 ÷ 2.5, about 64%); from 2000 to 2025 it rose by more, about 2.0 billion, but that is only about 32% of the 6.2 billion of 2000.
A: This is true, but the overall increase says nothing about how the two periods compare in number or in percentage.
B: This is true and supports the first part of the claim (the later increase was larger), but it gives no percentages, so it does not show that the later growth was smaller as a percentage.
C: This has the shape the claim needs, but its second percentage divides the increase by the 2025 population (2.0 ÷ 8.2, about 24%) instead of by the 2000 population (2.0 ÷ 6.2, about 32%).
Watch for: A percentage change is measured from the starting value of the period; dividing by the ending value is the most common way to misstate it.
Reading and Writing · Module 1 · Question 12 of 27
Ecosystems store carbon both in living vegetation and in soil. The graph shows estimates of the average amount of carbon stored per hectare in the vegetation and in the upper meter of soil of four types of ecosystems. A student claims that the ecosystem type that stores the most carbon in its vegetation is not the type that stores the most carbon overall.
Average Carbon Stored per Hectare in Four Ecosystem Types
Which choice most effectively uses data from the graph to support the student’s claim?
Correct choice: Tropical forests store the most carbon in vegetation, about 120 metric tons per hectare, but boreal forests store the most in vegetation and soil combined, about 408.
The claim needs two facts: which type stores the most carbon in vegetation, and which stores the most overall. Tropical forests lead in vegetation (about 120), but boreal forests have the largest total: 64 + 344 = 408, compared with 243 for tropical forests, 153 for temperate forests, and 243 for temperate grasslands.
A: This is true, but it compares only soil carbon; it does not identify which type leads in vegetation or show that a different type leads overall.
C: This has the shape of a supporting statement, but it misstates the graph: temperate grasslands store 7 + 236 = 243 metric tons per hectare in total, the same as tropical forests (120 + 123 = 243), not more.
D: This misstates the graph: tropical forests store about 120 metric tons per hectare in vegetation and about 123 in soil, so they store slightly more in soil.
Watch for: When a claim is about totals, add the two series for every category before accepting a choice that compares totals.
Reading and Writing · Module 1 · Question 13 of 27
In the early 1900s a horse named Clever Hans became famous in Berlin for tapping out correct answers to arithmetic questions with his hoof. In 1907 the psychologist Oskar Pfungst tested the horse under varied conditions. Hans usually answered correctly when his questioner knew the answer and stood where Hans could see him, but he rarely did so either when the questioner did not know the answer or when the questioner was hidden from view. These results suggest that ______
Which choice most logically completes the text?
Correct choice: Hans’s correct answers depended on cues that were available only from a questioner who knew the answer.
Hans succeeded only when two conditions held together: the questioner knew the answer, and Hans could see the questioner. The pattern suggests that Hans was picking up visible cues that only a questioner who knew the answer could supply.
B: The results show that Hans responded to something he saw, but they do not show that the cues were deliberate or meant to deceive.
C: If Hans had memorized the answers, the questioner’s knowledge would not matter, yet he failed when the questioner did not know the answer.
D: This fits the visibility condition but ignores the other one: Hans also failed when he could see a questioner who did not know the answer.
Watch for: Use every condition in the results; a choice that explains one condition but not the other is incomplete.
Reading and Writing · Module 1 · Question 14 of 27
The following text is from Katherine Mansfield’s short story “Miss Brill,” collected in her 1922 book The Garden Party and Other Stories. Miss Brill, an aging Englishwoman living in France, spends every Sunday afternoon in a public garden, watching the people there.
Miss Brill put up her hand and touched her fur. Dear little thing! It was nice to feel it again. She had taken it out of its box that afternoon, shaken out the moth-powder, given it a good brush, and rubbed the life back into the dim little eyes. [...] Other people sat on the benches and green chairs, but they were nearly always the same, Sunday after Sunday, and—Miss Brill had often noticed—there was something funny about nearly all of them. They were odd, silent, nearly all old, and from the way they stared they looked as though they’d just come from dark little rooms or even—even cupboards!
Based on the text, what can most reasonably be inferred about Miss Brill?
Correct choice: She does not recognize that details of her own life resemble what she finds odd in the garden’s other regular visitors.
Miss Brill herself comes to the garden every Sunday, and her fur has just come out of a box after being stored with moth-powder. Yet she judges the other regulars, who appear “Sunday after Sunday,” as odd people who look as if they had come “from dark little rooms or even—even cupboards!” The irony is that she does not see how closely her own habits match the oddness she notices in others.
B: The text shows her affection for the fur (“Dear little thing!”), not any wish to be noticed; it never says why she wears it.
C: The text does not say that she avoids the other visitors or that she thinks they judge her; it presents only her judgment of them.
D: She treats the fur tenderly and has brushed it and “rubbed the life back into” it; nothing suggests embarrassment or a plan to replace it.
Watch for: In literary irony, connect details the character reports about herself to what she criticizes in others; the inference often lies in a resemblance she fails to notice.
Reading and Writing · Module 1 · Question 15 of 27
Pando, a stand of quaking aspens in central Utah, looks like a forest of roughly 47,000 separate ______ genetic tests have shown that all of the stems are part of a single organism connected by one root system.
Which choice completes the text so that it conforms to the conventions of Standard English?
Correct choice: trees, but
The sentence joins two independent clauses (“Pando … looks like a forest …” and “genetic tests have shown …”). A comma followed by the coordinating conjunction but correctly joins them.
A: Without a comma before but, the two independent clauses run together.
C: The comma after but separates the conjunction from the clause it introduces, which is not standard.
D: This omits the needed comma before but and adds an unneeded one after it.
Watch for: When a conjunction such as but joins two complete sentences, place the comma before the conjunction, not after it.
Reading and Writing · Module 1 · Question 16 of 27
Goats, sheep, and many other grazing animals have horizontal, rectangular pupils, which researchers think widen the animals’ view of the ground around them and help them spot approaching predators. These pupils are shaped very differently from ______ of cats and other ambush predators, which are narrow vertical slits.
Which choice completes the text so that it conforms to the conventions of Standard English?
Correct choice: those
The blank stands for pupils, the plural noun being compared (“the pupils of cats”). The plural demonstrative pronoun those agrees with it.
A:It is singular and cannot stand for the plural pupils; “it of cats” is also not a standard construction.
B:This is singular, so it does not agree with the plural noun pupils that it replaces.
C:That is singular; it would fit a comparison with a singular noun (“the shape of … that of”), but here the compared noun is the plural pupils.
Watch for: In a comparison such as “different from ___ of cats,” the pronoun must match the number of the noun it replaces: that for a singular noun, those for a plural one.
Reading and Writing · Module 1 · Question 17 of 27
The Lycurgus Cup, a Roman glass vessel made in the fourth century CE, looks jade green when light shines on it from the front but glows red when light shines through it from behind. Researchers have traced this effect to tiny particles of gold and silver dispersed throughout the ______ and absorbing light differently depending on the direction from which the light arrives.
Which choice completes the text so that it conforms to the conventions of Standard English?
Correct choice: glass, scattering
The phrase “scattering and absorbing light differently …” is a participial phrase describing the particles, not an independent clause. A comma correctly attaches it to the end of the sentence.
A: A semicolon must separate two independent clauses, but the participial phrase has no subject or finite verb.
C: A period would leave “Scattering and absorbing light differently …” as a sentence fragment.
D: A colon introduces an explanation or list after a complete clause; here it would wrongly set the descriptive phrase apart as though it explained what came before.
Watch for: A phrase beginning with an -ing verb and lacking its own subject cannot stand after a semicolon or period; attach it with a comma.
Reading and Writing · Module 1 · Question 18 of 27
In April 1815 Mount Tambora in present-day Indonesia erupted with a force unmatched in recorded history, sending ash and sulfur high into the atmosphere. No one who witnessed the eruption could have known that its effects ______ crops half a world away the following year, when parts of New England and western Europe endured what came to be called the Year Without a Summer.
Which choice completes the text so that it conforms to the conventions of Standard English?
Correct choice: would ruin
The crop failures lay in the future from the point of view of 1815 witnesses, but the text narrates them in the past. Would ruin, the future seen from a past vantage point, fits this sequence.
A: The present tense ruin does not fit a sentence narrated in the past about events that followed the eruption.
B:Will ruin treats the crop failures as still in the future from today, but they happened in 1816.
D: The present perfect have ruined describes past events connected to the present, not events that lay ahead of witnesses in 1815.
Watch for: When a past-tense sentence looks ahead to something that happened later, use would, not will.
Reading and Writing · Module 1 · Question 19 of 27
Examining by hand the long rolls of chart paper that a new radio telescope near Cambridge, England, produced every day in ______ graduate student Jocelyn Bell noticed a faint signal that pulsed with extraordinary regularity, about once every 1.34 seconds. The source proved to be the first known pulsar, a rapidly spinning neutron star.
Which choice completes the text so that it conforms to the conventions of Standard English?
Correct choice: 1967, the
The sentence opens with a long participial phrase (“Examining … in 1967”) that describes the subject, the graduate student Jocelyn Bell. A comma separates this introductory phrase from the main clause.
A: A semicolon must separate two independent clauses, but the introductory phrase cannot stand alone as a sentence.
B: A colon must follow an independent clause; the introductory phrase is not one.
C: Without a comma, the long introductory phrase runs into the subject, and the commas inside the phrase (“Cambridge, England,”) make the boundary even harder to see.
Watch for: Commas inside an introductory phrase do not replace the comma that ends it; find where the phrase stops and the subject begins.
Reading and Writing · Module 1 · Question 20 of 27
The Great Enclosure at Great Zimbabwe, built between the thirteenth and fifteenth centuries, is ringed by a massive outer wall of fitted granite blocks laid without mortar. The number of blocks in that wall, which rises as high as eleven meters in places, ______ estimated at about 900,000.
Which choice completes the text so that it conforms to the conventions of Standard English?
Correct choice: is
The subject is The number, which is singular; of blocks in that wall and the clause which rises as high as eleven meters in places only modify it. The singular present-tense verb is agrees with number and matches the present tense of the text.
A:Are agrees with blocks, but blocks is the object of the preposition of; the subject is The number.
B:Have been is plural and so does not agree with the singular subject number.
D:Were is plural and past tense; the subject is singular, and the estimate is presented as current.
Watch for:The number of takes a singular verb, while a number of takes a plural one; ignore the plural noun inside the prepositional phrase.
Reading and Writing · Module 1 · Question 21 of 27
The man whose body hikers found in the Ötztal Alps in 1991 lived about 5,300 years ago, and his well-preserved clothing and equipment have revealed much about daily life in his time. He carried a belt pouch holding flint ______ wore shoes stuffed with grass for warmth.
Which choice completes the text so that it conforms to the conventions of Standard English?
Correct choice: tools and
The last sentence has one subject, He, with two verbs: carried and wore. Because and wore … has no subject of its own, it is not an independent clause, so no punctuation separates the two parts of this compound predicate.
A: A comma before and would be appropriate if and began a second independent clause, but wore … shares the subject He with carried.
C: A semicolon must separate independent clauses, but and wore … has no subject of its own.
D: A colon must follow an independent clause and introduce an explanation or list; and wore … is neither.
Watch for: Before placing a comma before and, check whether what follows has its own subject; if it shares the earlier subject, it is part of a compound predicate.
Reading and Writing · Module 1 · Question 22 of 27
In 1847 Ignaz Semmelweis, a physician at Vienna General Hospital, noticed that far more new mothers died of fever in a ward staffed by doctors and medical students than in one staffed by midwives. He concluded that the doctors, who often came directly from performing autopsies, were carrying infectious material on their hands to patients. ______ he required the ward’s doctors to wash their hands in a chlorinated lime solution before examining patients, and deaths in the ward dropped sharply.
Which choice completes the text with the most logical transition?
Correct choice: Accordingly,
Semmelweis concluded that doctors were carrying infectious material on their hands; the handwashing rule is the action he took in response to that conclusion. Accordingly, meaning in a way that follows from what was just said, marks this logical consequence.
A:Nevertheless signals an action taken despite what came before, but the handwashing rule follows directly from his conclusion.
B: The handwashing rule is not an example of his conclusion; it is a response to it.
D:Similarly signals a parallel case, but the rule is not like the conclusion; it results from it.
Watch for: When the next sentence describes an action taken because of a conclusion, look for a transition of consequence.
Reading and Writing · Module 1 · Question 23 of 27
The explosion that flattened some 80 million trees near the Tunguska River in Siberia in 1908 left no impact crater, and expeditions found no large meteorite fragments. Most researchers therefore conclude that the object responsible, probably a small asteroid or comet, exploded in the air rather than striking the ground. The pattern of fallen trees supports this view: across more than 2,000 square kilometers, trunks lay pointing away from a central area. ______ trees at that central area were left standing but stripped of their branches, as would be expected directly beneath a blast from above.
Which choice completes the text with the most logical transition?
Correct choice: Moreover,
The standing but stripped trees are a second, different kind of evidence for the airburst view that the previous sentence has begun to support. Moreover adds this further support.
A:In other words introduces a restatement, but the standing trees are a new piece of evidence, not a rewording of the tree-fall pattern.
B:Similarly would signal that the central trees behaved like the others, but they were left standing, while the others fell; what the two observations share is only that both support the conclusion.
C:Instead signals that something replaces what came before, but the new evidence adds to the tree-fall pattern rather than replacing it.
Watch for:Moreover and Similarly both continue a line of thought; Similarly requires a likeness between the two things described, while Moreover only requires that the new point add to the same argument.
Reading and Writing · Module 1 · Question 24 of 27
The star-nosed mole, a small burrowing mammal of eastern North America, hunts in dark tunnels and wetlands, and it finds prey almost entirely by touch. ______ the 22 fleshy appendages that ring its nose carry roughly 25,000 touch-sensitive structures, allowing the mole to identify and swallow an insect in a fraction of a second.
Which choice completes the text with the most logical transition?
Correct choice: Specifically,
The previous sentence says that the mole finds prey by touch; the next sentence explains exactly how its nose makes this possible. Specifically introduces this more detailed account of the general point.
A: Nothing in the previous sentence is being contrasted; the next sentence explains the organ that makes hunting by touch possible.
C:Nonetheless signals something true despite a difficulty, but the next sentence explains the mole’s success rather than conceding a problem.
D:In addition introduces a separate further point, but the next sentence elaborates the same point, how the mole hunts by touch.
Watch for: If the next sentence tells how something just mentioned works, it is an elaboration.
Reading and Writing · Module 1 · Question 25 of 27
While researching a topic, a student has taken the following notes:
Most soils in the Amazon rainforest are acidic and low in nutrients.
Scattered across the Amazon basin are patches of unusually fertile dark soil known as terra preta (“black earth”).
Terra preta contains large amounts of charcoal, along with pottery fragments, bone, and other refuse.
Radiocarbon dating shows that much terra preta formed between about 2,500 and 500 years ago at sites of human settlement.
Researchers study terra preta because it suggests that the pre-Columbian population of the Amazon was larger and more settled than once believed.
Farmers today still dig terra preta to use and sell as potting soil.
The student wants to explain how terra preta differs from most Amazon soils and why researchers study it. Which choice most effectively uses relevant information from the notes to accomplish this goal?
Correct choice: Unlike most Amazon soils, which are acidic and low in nutrients, terra preta is unusually fertile; researchers study it because it suggests that the pre-Columbian Amazon was more populous and settled than once believed.
The goal has two parts: how terra preta differs from most Amazon soils (it is fertile where they are acidic and nutrient-poor) and why researchers study it (it points to a larger, more settled pre-Columbian population). Only this choice states both.
A: This states the difference and mentions the soil’s origin, but it does not say why researchers study terra preta.
B: This describes terra preta’s contents and origin but neither compares it with other Amazon soils nor explains why researchers study it.
D: This explains why researchers study terra preta but does not say how it differs from most Amazon soils.
Watch for: Check each choice against both parts of a two-part goal; a choice that fully meets one part still fails.
Reading and Writing · Module 1 · Question 26 of 27
While researching a topic, a student has taken the following notes:
On September 1, 1859, the astronomer Richard Carrington observed an intense flare of white light on the Sun.
About 17 hours later, a burst of charged particles from the Sun reached Earth and set off a powerful geomagnetic storm.
A geomagnetic storm is a disturbance of Earth’s magnetic field caused by charged particles from the Sun.
During the 1859 storm, auroras were seen as far south as the Caribbean, and telegraph systems failed or gave operators electric shocks.
Today, a storm of similar strength could damage satellites and electrical power grids.
The student wants to contrast the effects of the 1859 storm with the effects that a storm of similar strength could have today. Which choice most effectively uses relevant information from the notes to accomplish this goal?
Correct choice: In 1859 a geomagnetic storm disrupted telegraph systems and produced auroras as far south as the Caribbean; today a storm of similar strength could damage satellites and power grids.
The goal requires both the 1859 effects and the possible effects today, set against each other. This choice pairs the telegraph failures and auroras of 1859 with the threat to satellites and power grids now.
A: This describes the 1859 effects but says nothing about what a similar storm could do today.
B: This defines a geomagnetic storm and dates the 1859 event, but it describes no effects, then or now.
C: This mentions 1859 and gives the possible effects today, but it does not describe the effects of the 1859 storm, so no contrast is drawn.
Watch for: A choice that mentions both time periods is not necessarily a contrast; check that it states the effects in each period.
Reading and Writing · Module 1 · Question 27 of 27
While researching a topic, a student has taken the following notes:
Each fall, monarch butterflies from eastern North America migrate as far as about 4,000 kilometers to overwintering sites in central Mexico.
Monarchs use the Sun’s position in the sky to hold a southwest heading.
Because the Sun’s position changes during the day, the butterflies must adjust for the time of day to keep a constant heading.
Researchers have shown that clocks in the monarchs’ antennae supply the timing needed for this adjustment.
How the butterflies find their specific overwintering sites once they reach Mexico remains unknown.
The student wants to present a finding about how monarchs navigate while acknowledging a question that research has not yet answered. Which choice most effectively uses relevant information from the notes to accomplish this goal?
Correct choice: Clocks in their antennae let monarchs adjust their Sun-based heading for the time of day, but how the butterflies locate their specific overwintering sites in Mexico remains unknown.
The goal requires a navigation finding and an unanswered question. This choice states the finding (antenna clocks let monarchs adjust their Sun-based heading) and the open question (how they locate their specific sites in Mexico).
A: This presents the finding but acknowledges no unanswered question.
B: This acknowledges the open question but presents no finding about how monarchs navigate.
D: This mentions a question, but it is one that research has answered; the choice presents a finding without acknowledging anything still unknown.
Watch for: A choice that raises a question is not the same as one that acknowledges an unanswered question; check whether the question in each choice has already been resolved.
Reading and Writing · Module 2 · Question 1 of 27
In 2005 astronomers announced the discovery of Eris, an icy body orbiting beyond Neptune that is roughly the size of Pluto. If Pluto counted as a planet, it seemed, then Eris and perhaps many similar objects would have to be counted as planets too. The discovery ______ the International Astronomical Union to adopt a formal definition of planet in 2006, under which both Pluto and Eris were classified as dwarf planets.
Which choice completes the text with the most logical and precise word or phrase?
Correct choice: prompted
The text explains that Eris raised a problem: if Pluto was a planet, Eris and many similar objects would be too. The Union then adopted a formal definition. Prompted, meaning moved someone to act, captures how the discovery led to the new definition.
A: The discovery made a definition more necessary, not less; the Union did adopt one.
B: To exempt is to free someone from an obligation, which does not fit a discovery that led the Union to act.
D: The Union did adopt a definition in 2006, so the discovery did not forbid it.
Watch for: Look at what happened after the blank (a definition was adopted) and choose the word that links the discovery to that action.
Reading and Writing · Module 2 · Question 2 of 27
The following text is from Henry David Thoreau’s 1854 book Walden. Thoreau describes building a small house by Walden Pond in Massachusetts, where he lived for two years.
At length, in the beginning of May, with the help of some of my acquaintances, rather to improve so good an occasion for neighborliness than from any necessity, I set up the frame of my house. No man was ever more honored in the character of his raisers than I. They are destined, I trust, to assist at the raising of loftier structures one day.
As used in the text, what does the word “improve” most nearly mean?
Correct choice: make use of
Thoreau says he accepted his acquaintances’ help not because he needed it (“rather … than from any necessity”) but to take advantage of the house-raising as a chance for neighborliness. In this older sense, to improve an occasion is to make use of it.
A:Enhance, the familiar modern sense of improve, would mean making the occasion better; Thoreau is explaining why he chose to use the occasion at all, not how he made it better.
B: The next sentence speaks of being “honored,” but that describes Thoreau’s pride in his helpers; improve concerns his reason for inviting help, which was to seize a chance for neighborliness.
D: Nothing suggests that Thoreau made the occasion last longer; the contrast is between using the occasion and needing the help.
Watch for: Older texts often use improve to mean take advantage of (as in “improve the time”); test the modern sense against the reason the sentence gives.
Reading and Writing · Module 2 · Question 3 of 27
Reports that hot water can sometimes freeze faster than cold water, a phenomenon now known as the Mpemba effect, go back at least to Aristotle. Because small differences in container shape, dissolved gases, evaporation, or the frost beneath a container could each explain why a hot sample occasionally froze first, many physicists were inclined to ______ such reports, even though few had shown that any of these factors accounted for a particular observation.
Which choice completes the text with the most logical and precise word or phrase?
Correct choice: discount
The physicists had possible explanations that would make the reports unreliable, but they had not shown that those explanations applied to any particular case. They were therefore inclined to give the reports little weight without disproving them. Discount, meaning regard as unreliable or unimportant, captures this attitude.
B: To refute is to prove false, but the text says few had shown that the suggested factors accounted for any observation, so the reports had not been refuted.
C: To disparage is to speak of something with contempt; the text describes a judgment about reliability, not scornful talk.
D: To overlook is to fail to notice, but the physicists had clearly noticed the reports; they had reasons to doubt them.
Watch for: When the choices share a general meaning (rejecting something), use the text’s qualification (“even though few had shown …”) to decide how strong and how deliberate the word should be.
Reading and Writing · Module 2 · Question 4 of 27
The following text is from Mark Twain’s 1883 memoir Life on the Mississippi. Twain, who trained as a steamboat pilot, compares the surface of the river to a book that only a trained pilot can read.
The passenger who could not read it was charmed with a peculiar sort of faint dimple on its surface (on the rare occasions when he did not overlook it altogether); but to the pilot that was an italicized passage; indeed, it was more than that, it was a legend of the largest capitals, with a string of shouting exclamation points at the end of it; for it meant that a wreck or a rock was buried there that could tear the life out of the strongest vessel that ever floated. Underlined: It is the faintest and simplest expression the water ever makes, and the most hideous to a pilot’s eye. End underlined.
Which choice best describes the function of the underlined sentence in the text as a whole?
Correct choice: It condenses the preceding contrast into a paradox: the feature least conspicuous to an untrained eye is the most alarming to a trained one.
The preceding sentence contrasts the passenger, who barely notices the dimple and finds it charming, with the pilot, for whom it is a warning in “the largest capitals.” The underlined sentence sums up that contrast in one pointed statement: the dimple is the “faintest and simplest” thing the water shows, yet the “most hideous” to a pilot.
A: The underlined sentence still concerns the same dimple (“It”), and it is the pilot, not the passenger, who notices its significance.
C: The text does not describe how a pilot learns to recognize the dimple; the sentence states the contrast rather than explaining a process.
D: The sentence calls the dimple faint, but it does not say pilots fail to see it; it says the dimple is “most hideous to a pilot’s eye.”
Watch for: A final sentence that restates a contrast in compressed, surprising form is often functioning as a summary or paradox, not introducing new information.
Reading and Writing · Module 2 · Question 5 of 27
The palm forests that once covered Rapa Nui (Easter Island) had almost entirely disappeared by the time Europeans arrived in 1722. A widely cited account attributes the loss to islanders who cleared trees for farmland and for moving the island’s great stone statues, and it presents the island as a warning about societies that exhaust their resources. Underlined: Yet many palm nuts recovered by archaeologists bear the gnaw marks of Polynesian rats, which arrived with the first settlers and may have kept the palms from regenerating. End underlined. Such evidence does not absolve human clearing, but it complicates any account that assigns the deforestation to a single cause.
Which choice best describes the function of the underlined sentence in the text as a whole?
Correct choice: It introduces evidence of an additional possible cause of the deforestation, one that the widely cited account does not include.
The underlined sentence introduces the gnawed nuts as evidence that rats may have prevented the palms from regenerating, a cause separate from the human clearing that the widely cited account emphasizes.
A: The final sentence says the evidence “does not absolve human clearing,” so the text does not treat it as showing that the widely cited account is mistaken.
C: Nothing suggests that the account overlooked the settlers’ arrival; the underlined sentence adds a separate factor, the rats that came with them.
D: The text gives no information about when the forests disappeared relative to the moving of the statues.
Watch for: Describe what the underlined sentence itself contributes (here, new evidence of a further cause), and use the following sentence to rule out choices that overstate that contribution.
Reading and Writing · Module 2 · Question 6 of 27
The following text is Charlotte Mew’s poem “Sea Love,” from the 1921 edition of her collection The Farmer’s Bride. The speaker uses a regional dialect in which “I mind” means “I remember” and “glim” means “gleam.”
Tide be runnin’ the great world over: T’was only last June month I mind that we Was thinkin’ the toss and the call in the breast of the lover So everlastin’ as the sea.
Heer’s the same little fishes that sputter and swim, Wi’ the moon’s old glim on the grey, wet sand; An’ him no more to me nor me to him Than the wind goin’ over my hand.
Which choice best describes the overall structure of the text?
Correct choice: The speaker recalls a belief that she and her lover once shared, then uses the unchanged seaside scene to show that the belief has proved false.
The first stanza recalls that only last June the speaker and her lover thought their passion “So everlastin’ as the sea.” The second stanza returns to the same seaside scene, the same fishes and the same moonlight on the sand, and states that the two now mean no more to each other “Than the wind goin’ over my hand.” The unchanged sea exposes the shared belief as mistaken.
B: The second stanza does not show that love has endured; it says the lovers now mean nothing to each other.
C: The poem contrasts the lasting sea with a love that has ended, not with human life in general, and the speaker expresses no resolve to find comfort.
D: The first stanza does compare the lovers’ passion to the sea, but the second stanza overturns that comparison rather than arguing that love lasts.
Watch for: A choice can describe the first half of a poem accurately and still fail on the second half; check what each stanza actually does.
Reading and Writing · Module 2 · Question 7 of 27
Text 1
The Norse settlements in Greenland, founded around 985 CE, were abandoned by about 1450. For much of the twentieth century, their end was blamed on a cooling climate. Recent studies of lake sediments suggest that the region became drier rather than much colder, but the researchers who conducted them still attribute the settlements’ end chiefly to environmental stress on the pastures and hayfields on which the settlers’ livestock depended.
Text 2
Other researchers emphasize trade. Walrus ivory, much of which the settlers exported to Europe, lost value in the 1300s as elephant ivory became more available there. As the colony’s chief export declined, these researchers argue, ships from Europe came less often, leaving the settlers less able to recover from poor harvests. In this view, it was isolation that turned the colony’s hard years into its end.
Based on the texts, both the researchers in Text 1 and the researchers in Text 2 would most likely agree with which statement?
Correct choice: The settlers at times had difficulty producing enough food from the land.
Text 1 attributes the settlements’ end to environmental stress on pastures and hayfields. Text 2 argues that trade was decisive, but its argument assumes the settlers faced “poor harvests” and “hard years.” Both texts therefore accept that the settlers sometimes struggled to produce food from the land, though they disagree about why the colony ended.
A: Neither text holds this view: Text 1 reports that the region became drier rather than much colder, and Text 2 emphasizes trade.
B: This is the view of Text 2 only; Text 1 attributes the end chiefly to environmental stress.
D: This combines ideas from both texts, but only Text 2 makes the claim; Text 1 says nothing about isolation or trade.
Watch for: Common ground between two texts is often an assumption one text takes for granted (here, poor harvests) rather than a claim it argues for; a choice that blends both texts’ ideas may still belong to only one of them.
Reading and Writing · Module 2 · Question 8 of 27
In most mammals, including most humans, production of lactase, the enzyme that digests the sugar in milk, declines sharply after infancy. In some human populations, however, many adults keep producing it. Genetic studies have found that this trait, called lactase persistence, is associated with different gene variants in northern European populations than in several East African herding populations, even though the variants have similar effects. Because the variants differ, researchers conclude that the trait arose separately in these populations, spreading in each as milk from herded animals became an important food.
Which choice best states the main idea of the text?
Correct choice: Lactase persistence appears to have evolved more than once, through different genetic changes, in separate populations that relied on milk.
The text builds to the researchers’ conclusion: because the gene variants linked to lactase persistence differ between European and East African herding populations, the trait arose separately in each, spreading as milk became important.
A: This contradicts the text, which says the trait arose separately in these populations rather than spreading from one to the other.
C: The text states that the variants “have similar effects”; it does not present this as unresolved.
D: This is a supporting detail from the first sentence, not the text’s main idea, which concerns how lactase persistence arose.
Watch for: An accurate detail from the opening sentence is not the main idea if the rest of the text builds toward a different conclusion.
Reading and Writing · Module 2 · Question 9 of 27
The following text is from Charlotte Brontë’s 1853 novel Villette. The narrator, Lucy Snowe, teaches at a school run by Madame Beck and has just secretly watched Madame search through Lucy’s belongings.
I will not deny that it was with a secret glee I watched her. Had I been a gentleman I believe Madame would have found favour in my eyes, she was so handy, neat, thorough in all she did [...] I could hardly get another employer whose yoke would be so light and so easy of carriage; and truly I liked Madame for her capital sense, whatever I might think of her principles: as to her system, it did me no harm; she might work me with it to her heart’s content: nothing would come of the operation. Loverless and inexpectant of love, I was as safe from spies in my heart-poverty, as the beggar from thieves in his destitution of purse.
Which choice best states the main idea of the text?
Correct choice: The narrator admires Madame’s skill and is untroubled by her spying because the narrator has nothing, such as a romantic attachment, that the search could uncover.
The narrator watches the search with “secret glee,” praises Madame as “handy, neat, thorough,” and says Madame’s system “did me no harm” because “nothing would come of the operation.” She explains why: “Loverless and inexpectant of love,” she has no secrets to find, just as a penniless beggar has nothing for thieves to take.
B: The narrator does call Madame’s yoke “light,” but she watches the search “with a secret glee” and likes Madame; the text shows amusement and admiration, not hidden resentment.
C: This reverses the text: the narrator likes Madame’s “capital sense” and finds her work “handy, neat, thorough,” while reserving judgment on her “principles.”
D: The text implies that a spy would look for signs of love, but it does not say what the narrator thinks prompted this particular search; the passage’s focus is her indifference to it.
Watch for: The closing comparison (the beggar and the thieves) explains the narrator’s calm; a main idea must account for both her admiration and her reason for feeling safe.
Reading and Writing · Module 2 · Question 10 of 27
After gray wolves were reintroduced to Yellowstone National Park in 1995 and 1996, willows began recovering along some streams where elk had long browsed them heavily. Some researchers attribute the recovery to a “landscape of fear”: elk, wary of wolves, avoided lingering in places such as narrow stream valleys where escape was difficult. The researchers claim that this change in elk behavior, rather than simply a decline in the number of elk, which also fell during this period because of wolves, hunting, and drought, explains where the willows recovered.
Which finding, if true, would most directly weaken the researchers’ claim?
Correct choice: Willows recovered wherever local elk numbers fell, whether or not the site was one where escape from wolves was difficult, and failed to recover wherever elk remained numerous.
The researchers claim that where willows recovered is explained by elk avoiding risky places, not merely by fewer elk. If recovery tracked local elk numbers regardless of how risky a site was, then elk numbers, not fear-driven behavior, would explain the pattern, directly weakening the claim.
A: Greater recovery where wolves were often present, even with similar elk numbers, is what the “landscape of fear” explanation predicts, so it supports rather than weakens the claim.
B: The text already grants that elk numbers fell; a decline alone does not show whether behavior or numbers explains where willows recovered.
D: Elk avoiding risky valleys is the behavior the researchers describe, so this finding supports their claim.
Watch for: When a claim credits one cause “rather than” another, the finding that weakens it shows the effect following the rival cause even where the favored cause is absent.
Reading and Writing · Module 2 · Question 11 of 27
Sound travels at different speeds through different materials. The table shows the approximate density and the approximate speed of sound for four materials at room temperature. A student claims that although sound generally travels faster in denser materials, density alone does not determine the speed of sound.
Density and Speed of Sound in Four Materials
Material
Density (kilograms per cubic meter)
Speed of sound (meters per second)
Air
1.2
343
Water
1,000
1,480
Aluminum
2,700
6,420
Steel
7,850
5,960
Which choice most effectively uses data from the table to support the student’s claim?
Correct choice: Aluminum is less dense than steel, yet sound travels faster in aluminum, about 6,420 meters per second, than in steel, about 5,960 meters per second.
The claim needs a case in which a less dense material nonetheless carries sound faster. Aluminum (about 2,700 kilograms per cubic meter) is less dense than steel (about 7,850), yet sound travels faster in aluminum, so density alone cannot determine the speed.
A: This is true, but it fits the general pattern of faster sound in denser materials; it does not show that density alone fails to determine speed.
C: This has the shape of the needed exception, but it misstates the table: sound travels about 1,480 meters per second in water and about 6,420 in aluminum.
D: This misstates the table: sound travels faster in aluminum than in steel. Even if true, it would fit the general pattern rather than show an exception.
Watch for: A claim that a factor “alone does not determine” an outcome is supported by an exception to the pattern, not by more examples of it.
Reading and Writing · Module 2 · Question 12 of 27
The number of hours of daylight a place receives changes over the year, and the size of that change depends on the place’s latitude. The graph shows the approximate hours of daylight on four dates at the equator and at two latitudes in the Northern Hemisphere. A student claims that the farther a place is from the equator, the greater the difference between the number of daylight hours on its longest and shortest days.
Hours of Daylight on Four Dates at Three Latitudes
Which choice most effectively uses data from the graph to support the student’s claim?
Correct choice: The difference between the longest and shortest days shown is about 0 hours at the equator, about 5.7 hours at 40°N, and about 13.0 hours at 60°N.
The claim concerns the difference between the longest and shortest days at each latitude. From the graph: the equator has about 12.1 hours on every date shown (a difference of about 0), 40°N ranges from 9.3 to 15.0 hours (about 5.7), and 60°N ranges from 5.9 to 18.9 hours (about 13.0). The difference grows with distance from the equator.
B: This is true, but it reports only the shortest days; a shorter shortest day does not by itself show a larger difference between the longest and shortest days.
C: This has the shape the claim needs but misstates the graph: 9.3 and 5.9 are the shortest days at those latitudes, not the differences, and the actual difference is larger at 60°N.
D: This is true, but it describes the equinoxes, when the latitudes hardly differ; the claim concerns the difference between each latitude’s longest and shortest days.
Watch for: Compute the quantity the claim names (here, longest minus shortest) for every group before comparing; single values or one series can look relevant without being the evidence.
Reading and Writing · Module 2 · Question 13 of 27
A thin layer of clay marking the end of the Cretaceous period, about 66 million years ago, contains unusually high levels of iridium at sites around the world. Iridium is rare in Earth’s crust but more abundant in many meteorites, so the layer has been cited as evidence that a large asteroid struck Earth at that time. Iridium can also reach the surface from Earth’s mantle in massive volcanic eruptions, however, and such eruptions were occurring in India during the same period. Grains of shocked quartz, which bear microscopic deformation features known to form under the extreme pressures of an impact but not in volcanic eruptions, have also been found in the layer. The shocked quartz is therefore significant because ______
Which choice most logically completes the text?
Correct choice: it points to an impact in a way that the iridium alone cannot, since volcanic eruptions could account for the iridium but not for the shocked quartz.
The text sets up a problem: iridium fits both an impact and volcanic eruptions, so it cannot decide between them. Shocked quartz forms in impacts but not in eruptions, so its presence favors an impact in a way the iridium could not.
A: The text says shocked quartz does not form in volcanic eruptions, so it cannot show anything about the eruptions’ power.
B: The quartz points to an impact, but the text gives no way to tell where the iridium itself came from; both an impact and the eruptions could have contributed it.
D: The text never discusses extinctions or their cause, and evidence of an impact would not by itself prove what caused them.
Watch for: When two explanations both fit one piece of evidence, the significant new evidence is the kind that only one explanation can produce.
Reading and Writing · Module 2 · Question 14 of 27
The following text is from James Weldon Johnson’s 1912 novel The Autobiography of an Ex-Colored Man. The narrator, a man of mixed racial ancestry who once hoped to become a composer, has lived for years as a white man. He reflects on a group of Black leaders who are publicly working for the advancement of their race.
Beside them I feel small and selfish. I am an ordinarily successful white man who has made a little money. They are men who are making history and a race. I, too, might have taken part in a work so glorious. My love for my children makes me glad that I am what I am and keeps me from desiring to be otherwise; and yet, when I sometimes open a little box in which I still keep my fast yellowing manuscripts, the only tangible remnants of a vanished dream, a dead ambition, a sacrificed talent, I cannot repress the thought that, after all, I have chosen the lesser part, that I have sold my birthright for a mess of pottage.
Based on the text, what can most reasonably be inferred about how the narrator views his choice?
Correct choice: He values what his choice has given his family, yet he suspects that it has cost him a more meaningful life.
The narrator holds two feelings at once. His love for his children makes him “glad that I am what I am,” yet his old manuscripts, “the only tangible remnants of a vanished dream,” make him suspect he has “chosen the lesser part” compared with the leaders “making history.” He values his choice for his family’s sake while fearing it has cost him something greater.
B: He describes himself as “ordinarily successful” and says he has “made a little money”; his regret concerns meaning, not money.
C: He calls his ambition “a sacrificed talent” and fears he chose “the lesser part,” so he does not regard giving it up as clearly right.
D: His love for his children makes him glad of his choice, but the text says nothing about sparing them hardships he endured, and “only” overstates his reasoning, since he also doubts the choice.
Watch for: When a narrator says “and yet,” keep both sides of the tension; choices that reduce the feeling to one side, or give it the wrong cause, fail.
Reading and Writing · Module 2 · Question 15 of 27
In 1705 the German-born naturalist Maria Sibylla Merian published Metamorphosis insectorum Surinamensium, a book of engravings showing insects from Suriname at each stage of their lives alongside the plants on which they fed. Ever since its publication, the book ______ naturalists and artists alike, who continue to admire its accuracy and its striking compositions.
Which choice completes the text so that it conforms to the conventions of Standard English?
Correct choice: has influenced
The phrase “Ever since its publication” describes a span that began in 1705 and continues to the present, so the present perfect is needed, and its singular form has influenced agrees with the singular subject the book.
A:Have influenced is in the right tense, but it is plural and does not agree with the singular subject the book.
B: The past perfect had influenced places the influence before some other past moment, but the span described runs to the present.
C:Will have influenced refers to a span ending in the future, but the text describes influence from 1705 to now.
Watch for: A span that runs up to the present (“ever since …”) calls for the present perfect; then check that the helping verb agrees with the subject.
Reading and Writing · Module 2 · Question 16 of 27
Because light bends as it passes between air and water, an insect on an overhanging leaf appears to an underwater observer to be somewhere other than where it actually is. Yet the archerfish knocks such insects off their leaves with precisely aimed jets of ______ aim adjusted for the bending of light at the water’s surface.
Which choice completes the text so that it conforms to the conventions of Standard English?
Correct choice: water, its
“Its aim adjusted for the bending of light at the water’s surface” has no finite verb (adjusted is a participle), so it is an absolute phrase, not an independent clause. A comma attaches it to the main clause.
B: A semicolon must separate two independent clauses, but “its aim adjusted …” has no finite verb.
C: A period would leave “Its aim adjusted for the bending of light …” as a sentence fragment.
D: Without a comma, the absolute phrase runs into the main clause and reads as though water its aim were a single phrase.
Watch for: A noun followed by a participle (“its aim adjusted”) can look like a clause; check for a finite verb before choosing a semicolon or period.
Reading and Writing · Module 2 · Question 17 of 27
Cuttlefish can blend into sand, gravel, and even artificial checkerboards within seconds, yet laboratory tests indicate that they cannot distinguish colors. Tracking the body patterns of individual cuttlefish as researchers moved them across dozens of different backgrounds ______ shown that the animals match brightness, contrast, and texture rather than color.
Which choice completes the text so that it conforms to the conventions of Standard English?
Correct choice: has
The subject of the second sentence is the gerund phrase Tracking the body patterns of individual cuttlefish …, which names a single activity and takes a singular verb. Has shown agrees with it.
A:Have agrees with a plural noun such as patterns, cuttlefish, or backgrounds, but those nouns sit inside the subject; the subject itself is the singular gerund phrase.
C:Are is plural and does not combine with shown to form a standard verb here.
D:Having is not a finite verb, so the sentence would have no main verb.
Watch for: A subject that begins with an -ing word (a gerund phrase) is singular, however many plural nouns it contains.
Reading and Writing · Module 2 · Question 18 of 27
Maya blue, a pigment used on murals and pottery in Mesoamerica for centuries, combines indigo dye with palygorskite, a fibrous clay. Heating the mixture traps the dye molecules in tiny channels within the ______ the color has survived hundreds of years of tropical heat and humidity with little fading.
Which choice completes the text so that it conforms to the conventions of Standard English?
Correct choice: clay. Thus,
“Heating the mixture traps the dye molecules in tiny channels within the clay” and “the color has survived hundreds of years …” are independent clauses. Thus is a conjunctive adverb, not a conjunction, so it cannot join them; a period ends the first clause, and Thus followed by a comma begins the next sentence.
A: Commas cannot join two independent clauses, even with thus between them; this is a comma splice.
C: This is also a comma splice, and it omits the comma after the introductory thus.
D: With no punctuation before thus, the two independent clauses run together.
Watch for: Words like thus, therefore, and however do not join clauses; when one begins a new independent clause, put a period or semicolon before it.
Reading and Writing · Module 2 · Question 19 of 27
Between the 1950s and the 1980s, the folklorists Iona and Peter Opie collected thousands of rhymes, chants, and games from schoolchildren across Britain. Their books showed that many of the ______ rhymes had been passed from child to child, with little help from adults, for generations.
Which choice completes the text so that it conforms to the conventions of Standard English?
Correct choice: children’s
The rhymes belong to the children, so a possessive is needed. Children is already plural, so its possessive is formed by adding an apostrophe and s: children’s.
A:Childrens is not a standard word and shows no possession.
B:Childrens’ treats childrens as a plural form, but children is already the plural of child.
D:Children is plural but not possessive; the sentence needs the rhymes to belong to the children.
Watch for: For a plural that does not end in s (children, people, women), form the possessive by adding ’s.
Reading and Writing · Module 2 · Question 20 of 27
The paintings in Chauvet Cave in southern France, made more than 30,000 years ago, are unusual among Ice Age cave art for the animals they emphasize. Among the hundreds of animals depicted on the cave’s ______ lions, rhinoceroses, and bears, species that appear far less often in other painted caves of the period.
Which choice completes the text so that it conforms to the conventions of Standard English?
Correct choice: walls are
The second sentence is inverted: the introductory prepositional phrase is followed by the verb are and then the subject lions, rhinoceroses, and bears. No punctuation belongs between the phrase and the verb, or between the verb and its subject.
A: A colon must follow an independent clause; “Among the hundreds of animals depicted on the cave’s walls are” is not complete, and the colon separates the verb from its subject.
B: A comma between the introductory phrase and the verb that immediately follows it breaks the inverted clause apart.
C: A dash, like the colon, separates the verb from its own subject.
Watch for: In an inverted sentence (phrase, then verb, then subject), a list after the verb is its subject; do not introduce it with a colon or dash.
Reading and Writing · Module 2 · Question 21 of 27
In 1887 Albert Michelson and Edward Morley compared the speed of light traveling in perpendicular directions, expecting Earth’s motion through a supposed “ether” to make one beam slightly slower than the other. In their instrument, a half-silvered glass plate, which split a single beam of light in two, and a massive stone slab, which floated on a pool of mercury to damp vibrations, ______ perhaps the most important components.
Which choice completes the text so that it conforms to the conventions of Standard English?
Correct choice: were
The subject is compound: “a half-silvered glass plate … and a massive stone slab.” Two singular nouns joined by and form a plural subject, so the plural verb were is required; each nonessential which clause only describes one part of the subject.
A:Was is singular; it may seem to agree with the nearby singular nouns slab or mercury, but the subject joins two nouns with and.
B:Being is not a finite verb, so the sentence would have no main verb.
C:Is is singular and in the present tense, while the subject is plural and the text describes a past experiment.
Watch for: When each part of a compound subject carries its own descriptive clause, strip the clauses away and count the nouns joined by and.
Reading and Writing · Module 2 · Question 22 of 27
When a mantis shrimp strikes prey with its clublike appendages, the blow is so fast that it creates cavitation bubbles, tiny pockets of vapor that collapse with a burst of energy and deliver a second impact. ______ the pistol shrimp snaps one of its claws shut so quickly that it shoots out a jet of water, forming a cavitation bubble whose collapse can stun small fish.
Which choice completes the text with the most logical transition?
Correct choice: Similarly,
Both sentences describe a crustacean whose extremely fast movement creates a collapsing cavitation bubble that strikes prey. Similarly signals that the pistol shrimp’s method parallels the mantis shrimp’s.
A: The pistol shrimp’s method resembles the mantis shrimp’s, so a transition of contrast is illogical.
B: The pistol shrimp is not an example of the mantis shrimp; it is a second, parallel case.
D: The pistol shrimp’s behavior does not result from the mantis shrimp’s; the two are independent cases.
Watch for: Two parallel cases call for a transition of similarity; For example requires the second sentence to illustrate a general claim made in the first.
Reading and Writing · Module 2 · Question 23 of 27
Most adult amphibians lose much of their ability to regenerate damaged tissue as they mature, and a frog that loses a leg as an adult generally cannot grow a new one. ______ the axolotl, a salamander native to lakes near Mexico City, can regrow entire limbs, parts of its heart, and even sections of its spinal cord throughout its life.
Which choice completes the text with the most logical transition?
Correct choice: However,
The first sentence describes what most adult amphibians cannot do; the next describes an amphibian that can. However signals this contrast between the general pattern and the exception.
B:Instead signals that one thing takes the place of another, as after a negation about the same subject; the axolotl does not replace the frog, but contrasts with it.
C: The axolotl is not an example of the pattern described; it is an exception to it.
D:Similarly signals likeness, but the axolotl differs sharply from most adult amphibians.
Watch for:However and Instead both signal contrast; Instead requires that the second sentence replace something ruled out in the first, while However marks a contrast between two different cases.
Reading and Writing · Module 2 · Question 24 of 27
In 1986 Lake Nyos in Cameroon suddenly released a cloud of carbon dioxide that suffocated about 1,700 people in nearby villages. Carbon dioxide seeping from volcanic rock beneath the lake had built up in its deep water for years because the lake is stratified. ______ its layers of water do not mix with the seasons as those of many lakes do, so gas dissolved near the bottom stays trapped there until something disturbs the layers.
Which choice completes the text with the most logical transition?
Correct choice: That is,
The previous sentence uses the technical term stratified; the next sentence explains what that term means (the layers do not mix). That is introduces a restatement or clarification of what was just said.
A: The next sentence does not give an example of stratified lakes or of anything else; it explains what stratified means for this lake.
B: The next sentence does not contrast with the claim that the lake is stratified; it clarifies it.
C:In addition introduces a new point, but the next sentence restates the same point in plainer terms.
Watch for: When a sentence explains the term used just before it, the transition is one of restatement (That is, In other words), not an example or addition.
Reading and Writing · Module 2 · Question 25 of 27
While researching a topic, a student has taken the following notes:
Naked mole-rats are small burrowing rodents that live in underground colonies in East Africa.
They can live more than 30 years, far longer than other rodents of similar size.
Cancer has been observed only rarely in naked mole-rats.
Their tissues contain an unusually large form of hyaluronan, a substance found in the spaces between cells.
In laboratory studies, reducing this form of hyaluronan made naked mole-rat cells more likely to form tumors.
The student wants to explain to an audience unfamiliar with naked mole-rats a possible reason for the animals’ resistance to cancer. Which choice most effectively uses relevant information from the notes to accomplish this goal?
Correct choice: Naked mole-rats, small burrowing rodents of East Africa, rarely develop cancer, possibly because their tissues contain an unusually large form of hyaluronan, a substance found between cells.
The goal has two parts: introduce naked mole-rats to an unfamiliar audience, and give a possible reason for their resistance to cancer. This choice identifies the animals and links their rarity of cancer to the unusual form of hyaluronan, explaining that substance as well.
A: This introduces the animals and mentions their resistance to cancer, but their long lives are not a reason for that resistance, so no reason is given.
C: This gives evidence relevant to a reason, but it does not tell an unfamiliar audience what naked mole-rats are or what hyaluronan is.
D: This introduces the animals and explains hyaluronan, but it never mentions cancer, so it does not present hyaluronan as a reason for anything.
Watch for: Placing two facts side by side is not the same as presenting one as a reason for the other; look for a choice that states the link the goal asks for.
Reading and Writing · Module 2 · Question 26 of 27
While researching a topic, a student has taken the following notes:
The Inca Empire, which controlled much of western South America in the fifteenth and early sixteenth centuries, had no writing system based on marks on a surface.
Inca officials instead recorded information on khipus, arrangements of knotted cords.
On many khipus, the type and position of knots on a cord represent numbers in a base-ten system.
Spanish colonial accounts report that khipus also recorded histories and other narratives.
Researchers have deciphered the numerical system but have not determined how, or whether, khipus encoded language.
The student wants to contrast how khipus recorded information with how writing systems do and to explain how khipus represented numbers. Which choice most effectively uses relevant information from the notes to accomplish this goal?
Correct choice: Unlike writing systems, which use marks on a surface, khipus recorded information in knotted cords, with the type and position of knots representing numbers in a base-ten system.
The goal has two parts: a contrast with writing systems (knotted cords rather than marks on a surface) and an explanation of how khipus represented numbers (knot type and position in a base-ten system). Only this choice does both.
A: This draws the contrast with writing systems, but it reports narrative content from Spanish accounts rather than explaining how khipus represented numbers.
B: This explains how khipus represented numbers but draws no contrast with writing systems.
C: This describes the state of research on khipus but neither contrasts them with writing systems nor explains how their knots represented numbers.
Watch for: A choice that states that researchers understand something is not the same as one that explains it; check that the choice says how the numbers were represented.
Reading and Writing · Module 2 · Question 27 of 27
While researching a topic, a student has taken the following notes:
Pacific salmon hatch in freshwater streams, grow at sea, and return to the streams to spawn and die.
Nitrogen from the ocean contains a higher proportion of the isotope nitrogen-15 than nitrogen from most land sources.
Researchers in Alaska found that the leaves of trees along salmon streams contained more nitrogen-15 than the leaves of trees along streams without salmon.
They concluded that nitrogen from salmon carcasses, spread by bears and other animals and by flooding, fertilizes streamside forests.
The isotope measurements could not show how much this added nitrogen affects the trees’ growth.
The student wants to explain how the isotope measurements support the researchers’ conclusion while noting a limitation of the data the researchers collected. Which choice most effectively uses relevant information from the notes to accomplish this goal?
Correct choice: Because ocean nitrogen is richer in nitrogen-15 than most land nitrogen, the extra nitrogen-15 in leaves along salmon streams indicates that salmon nitrogen reaches streamside trees, though the measurements cannot show how much it affects their growth.
The goal has two parts: explain how the measurements support the conclusion (ocean nitrogen is rich in nitrogen-15, so extra nitrogen-15 in streamside leaves shows that salmon nitrogen reaches the trees), and note a limitation (the measurements cannot show the effect on growth). Only this choice does both.
A: This states the conclusion and the limitation but does not explain how the measurements support the conclusion.
B: This explains how the measurements support the conclusion but notes no limitation.
C: This reports the measurements and their limitation but omits the fact that makes them relevant (ocean nitrogen is richer in nitrogen-15), so it does not explain how they support the conclusion.
Watch for: Check each choice for both parts of the goal; a choice that fully explains the evidence can still fail by leaving out the limitation.
Math · Module 1 · Question 1 of 22
In the -plane, a line has an -intercept at and a -intercept at . Which equation defines this line?
The line passes through its -intercept, , and its -intercept, .
The slope is the change in divided by the change in :
The point on the -axis has -coordinate , so is in the form .
Filling in the slope and the intercept:
Math · Module 1 · Question 2 of 22
The function is defined by for and by for . What is the value of ?
The input is less than , so the first rule applies.
The input is greater than , so the second rule applies.
Adding the two outputs:
Math · Module 1 · Question 3 of 22
A pallet weighs pounds when empty, and each crate loaded onto it weighs pounds. A courier charges one flat rate for any loaded pallet weighing at least pounds and at most pounds. Which inequality gives all numbers of crates for which the flat rate applies?
Each crate adds pounds, so crates weigh pounds.
The empty pallet adds another pounds, so the loaded pallet weighs pounds.
The flat rate applies when that weight is at least pounds and at most pounds, which is written as
Math · Module 1 · Question 4 of 22
The height of a ball above the ground, in feet, seconds after it is thrown is modeled by . Based on this model, how many seconds after it is thrown does the ball reach the ground?
The ball is on the ground when its height is .
A product is only when one of its factors is . The factor is never , and the factor is positive at every time after the throw.
So the height is when
Adding to both sides:
The ball reaches the ground seconds after it is thrown.
Math · Module 1 · Question 5 of 22
If , what is the value of ?
Answer: C.
Multiply both sides by :
Subtracting from both sides and adding gives . Therefore .
Check: With , the left side is and the right side is .
A: This comes from multiplying only the left side by : gives , and .
B: This comes from doubling but not the on the right side: gives , and .
D: This is the value of , not the value of .
Watch for: When clearing a denominator, multiply every term on the other side, and answer the question asked (), not .
Math · Module 1 · Question 6 of 22
If , which expression gives in terms of and ?
Multiplying both sides by gives . Adding gives , so . Subtracting instead of adding it gives . Forgetting to multiply by at all gives . And multiplying the whole right side by after adding , rather than before, gives .
Math · Module 1 · Question 7 of 22
The table shows three values of each of the linear functions and . For what value of is ?
Values of and
Answer: C.
From the table, increases by for every units of , so . The function decreases by for every units of , so .
Solve :, so .
Check: and , and .
A: This solves , adding to the wrong side.
B: This solves and ignores the .
D: This uses , misreading the direction of change in the column.
Watch for: Build each rule from the table before combining them, and keep the on the side of .
Math · Module 1 · Question 8 of 22
Which expression is equivalent to , where ?
Split the radicand into a perfect square times whatever is left. The largest perfect square factor of is , and holds the perfect square with one left over.
The square root of is , so the expression becomes
Math · Module 1 · Question 9 of 22
A water utility serves homes. Researchers selected of these homes at random and then randomly assigned of the selected homes to have a low-flow showerhead installed; the other selected homes kept their existing showerheads. Over the next year, the homes with the low-flow showerhead used an average of fewer gallons of water per month than the other selected homes. Based on the study, which of the following is the best estimate of how many fewer gallons of water per month the homes would use in total if all of them had a low-flow showerhead than if none of them did?
Answer: D.
The homes were selected at random from all homes the utility serves, so the results can be generalized to those homes. The showerheads were then randomly assigned, so the difference in water use can be attributed to the showerheads.
So each home is estimated to use about fewer gallons per month with a low-flow showerhead, and for all homes the decrease is about gallons per month.
Check: Random selection supports applying the result to all homes, and random assignment supports a causal effect of gallons per home per month; .
A: is , the decrease for only the homes that received the showerhead in the study.
B: is , the decrease if only the selected homes had the showerhead installed.
C: is , which applies the effect to only half of the homes, as if the study’s even split carried over to the whole utility.
Watch for: Random selection lets the result be applied to all homes, and random assignment lets the difference be attributed to the showerheads; multiply the per-home effect by all homes.
Math · Module 1 · Question 10 of 22
Right triangle
has right angle
,,
and perimeter 90. What is its area?
Enter an integer, decimal, or fraction. Up to 5 characters, or 6 including a leading minus. No units or mixed numbers.
Answer: 270
The legs have ratio
,
so the hypotenuse has ratio 13 by the Pythagorean theorem. Write the
sides as
.
Then
,
so
.
The area is
.
Check: The side lengths 15, 36, and 39 sum to 90 and satisfy
.
Watch for: A trigonometric ratio supplies a shape, not the triangle’s scale.
Math · Module 1 · Question 11 of 22
An ultrasonic rail-joint scanner covers the first 40% of a route at 3
meters per minute and the rest at 6 meters per minute. The total
scanning time is 28 minutes. How long is the route, in meters?
Enter an integer, decimal, or fraction. Up to 5 characters, or 6 including a leading minus. No units or mixed numbers.
Answer: 120
Let D be the route length. The time equation is
.
The coefficient is
,
so
and D = 120.
Check: The two distances are 48 and 72 meters, taking 16 and 12 minutes,
respectively.
Watch for: Add times, not speeds; the percentages describe distances, not equal
time intervals.
Math · Module 1 · Question 12 of 22
Which expression is equivalent to , where ?
Dividing by a fraction is the same as multiplying by its reciprocal.
The numerator is a difference of two squares:
Cancel the shared factor , and reduce to :
Math · Module 1 · Question 13 of 22
During a drought, the volume of water in a pond fell by . By what percent must the volume then rise to return to what it was before the drought?
Let the original volume be . A fall of leaves of it, so the volume after the drought is .
To return to , the volume must grow by the amount it lost:
A percent rise is measured against the current amount, which is now , not against the original:
A rise equal to times the current volume is a rise of .
Math · Module 1 · Question 14 of 22
In the figure, points ,, and lie on the circle with center . If the measure of central angle is , what is the value of ?
An inscribed angle is half the central angle that opens onto the same arc. Angle and angle both open onto arc , so . Halving a second time gives . Taking the angle to equal the central angle gives . Subtracting from , as though the inscribed angle were the complement of the answer, gives .
Math · Module 1 · Question 15 of 22
For what value of does the equation have no solution for ?
Answer: C. 3 The coefficient of x is zero when or . At , the equation is , so it has no solution. At , it is , so every real x works. For all other a, the coefficient is nonzero and there is one solution.
Watch for: Check the right side at each value that makes the variable coefficient zero.
Math · Module 1 · Question 16 of 22
A fountain-sheet model gives height
,
in meters, at horizontal distance
.
The sheet is 3 meters high at
and 15 meters high at
.
What is the greatest height predicted by the model?
Answer: D.
The conditions give
and
.
Subtracting yields
,
so
.
Then
.
Since a is negative, the vertex height b is the maximum.
Check: The vertex is at x = 6; the fitted rule gives 3 and 15 at the
specified inputs.
A: This is the modeled height at zero.
B: This is the horizontal vertex coordinate.
C: This is a given height away from the vertex.
Watch for: A vertex-form model does not give a maximum unless its squared-term
coefficient is negative.
Math · Module 1 · Question 17 of 22
The graph shows
.
If the only zeros of
are
and
,
which pair gives all solutions of
?
Answer: A.
Whenever g(x) = 0,
.
Therefore the required original inputs are u = x - 3. From x = -1 and 5,
obtain u = -4 and 2.
C: This leaves the horizontal input shift unapplied.
D: This uses the vertical shift as a horizontal shift.
Watch for: Translate from the new input to the old one using the inside
expression, not the visual shift direction alone.
Math · Module 1 · Question 18 of 22
In the inequality , is a constant. The solution set of the inequality is . What is the value of ?
Answer: C.
Rearrange: . The solution set has its inequality reversed, which happens only when both sides are divided by a negative number. So , and the solution is . Setting gives , so .
Check: With :, so and .
A: is the boundary value of , not the value of .
B: is the value of , not of .
D: With , the inequality becomes , whose solution set is , not .
Watch for: A solution set of the form from a “” inequality signals division by a negative number.
Math · Module 1 · Question 19 of 22
For a positive constant , the equations and have exactly one solution in common. What is the sum of all possible values of ?
Enter an integer, decimal, or fraction. Up to 5 characters, or 6 including a leading minus. No units or mixed numbers.
Answer: 8
The solutions of are and . The solutions of are and . A common solution matches one from each list:
gives .
gives .
gives , and gives ; neither is positive.
For , the solutions are and , so is the only common solution. For , they are and , so is the only common solution. The sum of the possible values of is .
Check: For : and . For : and .
Watch for: The most common wrong value is , which matches only the two “plus” solutions; the solution of the first equation can also match .
Math · Module 1 · Question 20 of 22
A data set consists of the five numbers ,,,, and . The mean of the data set is greater than the median of the data set. What is the sum of all possible values of ?
Enter an integer, decimal, or fraction. Up to 5 characters, or 6 including a leading minus. No units or mixed numbers.
Answer: 16.25
The mean is , and the median depends on where falls in the ordered list.
If , the median is , so the mean is : and , which satisfies .
If , the median is , so : and , which satisfies .
If , the median is , so the mean is : and , which satisfies .
All three values work, and their sum is .
Check: For : median , mean . For : median , mean . For : median , mean .
Watch for: The most common wrong value is , which assumes the median is and misses the cases in which itself is the median or is below it.
Math · Module 1 · Question 21 of 22
Right triangle , shown in the figure, has its right angle at , with and . Point lies on so that is perpendicular to , and point lies on so that is perpendicular to . What is the length of ?
Enter an integer, decimal, or fraction. Up to 5 characters, or 6 including a leading minus. No units or mixed numbers.
Answer: 5.76
By the Pythagorean theorem, .
Triangles and are similar: each has a right angle, and they share angle . So , which gives .
Triangles and are also similar: each has a right angle, and they share angle . So , which gives
Check: With at , at , and at , line is , and the foot of the perpendicular from the origin is . Point is directly below on the -axis, so .
Watch for: The most common wrong values are , the length of , and , the length of ; is a second perpendicular, inside triangle .
Math · Module 1 · Question 22 of 22
The function is defined by , where is a constant. In the -plane, the vertex of the graph of lies in quadrant IV. Which of the following describes all possible values of ?
Answer: A.
Complete the square: , so the vertex is .
In quadrant IV, the -coordinate is positive, so , and the -coordinate is negative:
which is , so . Together with , this gives .
Check: For the vertex is , in quadrant IV. For it is , in quadrant III, and for it is , in quadrant I.
B: This uses only the condition that the vertex is below the -axis; for the vertex is not to the right of the -axis.
C: This reverses the inequality, which gives or , and then keeps only the positive values; for the vertex is above the -axis.
D: This reverses the inequality and ignores the condition on the -coordinate.
Watch for: A point in quadrant IV needs a positive -coordinate and a negative -coordinate; use both conditions.
Math · Module 2 · Question 1 of 22
The system
and
has infinitely many solutions. What is
?
Enter an integer, decimal, or fraction. Up to 5 characters, or 6 including a leading minus. No units or mixed numbers.
Answer: -6
The second equation must be twice the first. Doubling the coefficient
of y gives
.
Check: With b = -6, all three terms of the second equation are exactly
doubled.
Watch for: For infinitely many solutions, the constants must share the same
multiplier as both variable coefficients.
Math · Module 2 · Question 2 of 22
The table gives a linear model for the number of visible stitches
after a machine has advanced a backing strip by
centimeters. What does the model predict when
?
Backing-strip advance and visible stitches
Advance d (cm)
Visible stitches
6
38
12
62
Answer: B.
The increase is
stitches over 6 centimeters, so the rate is 4 stitches per centimeter.
From the first row, the intercept is
.
Check: The rule
reproduces both rows.
A: Thirty-eight is the output after six centimeters.
C: Four is the rate per centimeter.
D: Twenty-four is the difference between the two rows.
Watch for: An inferred intercept is the model’s baseline, not its change per
input unit.
Math · Module 2 · Question 3 of 22
What is the greater of the two solutions to ?
The quadratic formula gives . Since , both terms divide by , leaving . The greater solution is . Taking the lesser root gives . Dividing only the by and leaving the radical untouched gives the two options containing , of which the greater is .
Math · Module 2 · Question 4 of 22
A closed rectangular box has interior edges of length inches, inches, and inches. What is the length, in inches, of the longest straight rod that can fit inside the box?
The longest segment inside a rectangular box joins two opposite corners. It is the hypotenuse of a right triangle whose legs are one edge and the diagonal of the face the other two edges span.
The diagonal of the by face:
That diagonal and the -inch edge meet at a right angle, so the corner-to-corner segment is
A rod inches long fits along that segment, and no longer rod fits.
Math · Module 2 · Question 5 of 22
The dot plot shows a data set of values. Some values of are to be added to the data set. What is the least number of values of that must be added so that the median of the new data set is ?
Answer: B.
In order, the data have values of or less (positions through ) and then four s (positions through ). With added values of , there are values.
With added value there are values, and the median is the average of the th and th values, . With added values there are values, and the median is the th value, . So the least number is .
Check: Adding more s moves the middle position later, but the median stays for anywhere from through added values, so is the least number.
A: One added value gives values, and the median averages and to get .
C: Three added values also give a median of , but is fewer.
D: Four added values give values with median the th value, , but fewer values suffice.
Watch for: With an even number of values, the median is the average of the two middle values, which can land between data values.
Math · Module 2 · Question 6 of 22
A solar tracker is correctly aligned when its measured tilt angle , in degrees, satisfies . Its controller does not report directly; it reports the value . Which inequality gives all values of that correspond to a correctly aligned tracker?
Answer: D.
The condition means . Multiplying through by 2 gives , and subtracting 11 gives . That interval has center 57 and radius 3, so it is written .
Check: Test the endpoints directly: gives and gives , and both are exactly 3 away from 57.
A: 23 is , so the doubling in was left out of the center.
B: The center 57 is correct, but the tolerance was not doubled along with the angle.
C: 68 is , so the subtraction of 11 was left out of the center.
Watch for: Under a rule , the center of an interval moves by the whole rule but the radius is scaled by only.
Math · Module 2 · Question 7 of 22
The function is defined by . For how many integer values of is ?
Answer: A.
The factor is positive for every except , where it is .
The product is negative exactly when .
So exactly when and . The integers that qualify are ,,, and , which is values.
Check: and are negative, while ,, and are not.
B: counts ,,,, and , but , which is not less than .
C: solves as , which contains integers, and then removes only the double root ; the zeros and make the product , not negative.
D: counts every integer from through , which solves .
Watch for: A squared factor does not change sign, but it makes the function at its zero, so that -value must be excluded from a strict inequality.
Math · Module 2 · Question 8 of 22
In the figure, is a regular hexagon. Diagonals and intersect at point . What is the measure, in degrees, of ?
Answer: B.
Each interior angle of a regular hexagon measures .
Triangle is isosceles with and , so each base angle is degrees. Thus .
Similarly, in isosceles triangle ,, so .
In triangle ,.
Check: In triangle , and , so . Angles and form a straight angle, and .
A: is the measure of (and of ), one of the base angles, not the angle at .
C: is the measure of , the angle of triangle at .
D: is an interior angle of the hexagon, and also , the angle next to .
Watch for: Break the hexagon into isosceles triangles and find the angles at the vertices before finding the angle at the intersection.
Math · Module 2 · Question 9 of 22
Last month, folders and markers cost a total of $14.50. This month, the price of each folder is greater than it was last month, the price of each marker is less than it was last month, and folders and markers cost a total of $14.60. What is this month’s price of one marker?
Answer: A.
Let and be last month’s prices, in dollars, of a folder and a marker. Then
The second equation is . Multiplying the first equation by gives . Subtracting, , so . Then , so .
This month’s price of a marker is dollars.
Check: This month a folder costs dollars, and dollars.
B: $1.50 is last month’s price of a marker; the question asks for this month’s price.
C: $1.80 increases last month’s marker price by instead of decreasing it.
D: $2.75 is this month’s price of a folder.
Watch for: Solve for last month’s prices first, and then apply the decrease to the marker price.
Math · Module 2 · Question 10 of 22
Which expression is equivalent to for ?
Answer: D.
Combine the first two fractions:
Then subtract the third fraction over the common denominator :
Check: At :, and .
A: This reverses the order of subtraction in the last step, computing .
B: This gets the sign of the first combination wrong, , and then subtracts .
C: This adds the third fraction instead of subtracting it: .
Watch for: Combine in stages and keep track of which numerator is subtracted; the terms cancel only when both subtractions are done correctly.
Math · Module 2 · Question 11 of 22
When a person walks up a moving escalator, the person reaches the top in seconds. When the person stands still on the same moving escalator, the person reaches the top in seconds. The person walks at a constant rate, and the escalator moves at a constant rate. How many seconds would the person take to walk up the escalator if it were not moving?
Enter an integer, decimal, or fraction. Up to 5 characters, or 6 including a leading minus. No units or mixed numbers.
Answer: 60
Measure rates in escalators per second. Walking on the moving escalator, the combined rate is . The escalator alone moves at . The person’s walking rate is the difference:
so walking up the escalator when it is not moving takes seconds.
Check: With a walking rate of and an escalator rate of , the combined rate is , which gives seconds.
Watch for: The walking rate is the combined rate minus the escalator’s rate: . The most common wrong values are , from subtracting the times, and , from combining the times as if the rates added: .
Math · Module 2 · Question 12 of 22
A rescue-drill coordinator can load at most 156 kilograms of training
equipment. A marker buoy weighs 6 kilograms and a locator case weighs 9
kilograms. At least 20 items must be loaded. What is the greatest
possible number of locator cases?
Answer: B.
Let b and c be the counts. To allow the most heavier cases while
meeting the count requirement, use the minimum total of 20 items, so b =
20 - c. Then
,
giving
and
.
Check: Twelve cases and eight buoys weigh
kilograms. Thirteen cases require at least seven buoys, weighing 159
kilograms.
A: This is the buoy count at the optimum.
C: This ignores the minimum total number of items.
D: This exceeds the weight limit.
Watch for: A lower bound on total count can force lighter items into a
weight-limited load.
Math · Module 2 · Question 13 of 22
The quadratic function is defined by , where ,, and are constants. If and , what is the value of ?
Enter an integer, decimal, or fraction. Up to 5 characters, or 6 including a leading minus. No units or mixed numbers.
Answer: 4 Expand the given outputs: , while . Subtracting eliminates b and c, leaving . Therefore .
Watch for: Two aggregate conditions can determine a particular coefficient even though they do not determine the whole function.
Math · Module 2 · Question 14 of 22
The histogram represents ten integer measurements. Each interval includes its left endpoint but not its right endpoint. What is the greatest possible mean of the ten measurements?
Answer: C. 39 The three bins contain 3, 4, and 3 measurements. To maximize the mean, place every measurement at the largest integer in its bin: 29, 39, or 49. The greatest possible sum is 3(29) + 4(39) + 3(49) = 390, so the greatest mean is 39.
Watch for: The right endpoints 30, 40, and 50 belong to the next intervals and cannot be used as values in these bins.
Math · Module 2 · Question 15 of 22
The function is defined by , and the function is defined by , where is a positive constant. In the -plane, the graphs of and intersect at a point whose -coordinate is . What is the value of ?
Answer: D.
Completing the square, , so . At an intersection point,
Since , the two quantities being squared are opposites: , so . The graphs cross halfway between their axes of symmetry.
The -coordinate there is . Setting this equal to gives , so and .
Check: With ,. At , and .
A: is an -value where (the other is ); it is not the shift .
B: uses instead of for the horizontal distance from the crossing point to the axis of :.
C: leaves out the , solving .
Watch for: A horizontal shift of moves the axis of symmetry by , and the two parabolas cross halfway between their axes, from each.
Math · Module 2 · Question 16 of 22
In the -plane, the graph of is a circle, and is the origin. Point lies on the circle so that is a diameter of the circle. Line is tangent to the circle at . What is the -coordinate of the point where line intersects the -axis?
Answer: A.
Complete the square:
so the circle has center and radius . The origin satisfies the original equation, so it is on the circle, and the center is the midpoint of diameter :. The radius to has slope , and a tangent is perpendicular to the radius, so line has slope :
At ,.
Check: Point is on line :. The slope of times the slope of the radius is , so is perpendicular to the radius at .
B: This uses the slope of the diameter, , instead of the perpendicular slope; that line through is line itself.
C: This uses the slope , making a sign error in the negative reciprocal.
D: This takes the center to be , copying the signs of the coefficients, so it works with the point instead of .
Watch for: Find the center by completing the square, use it as the midpoint of the diameter, and make the tangent perpendicular to the radius at .
Math · Module 2 · Question 17 of 22
In the -plane, line has slope and passes through the point . Line does not pass through any point with and . Which of the following describes all possible values of ?
Answer: A.
The line is . If , then stays positive, or grows, as decreases through negative values, so the line enters the region ,. If , then for the values of are all less than the -intercept . They are all at most exactly when , that is, when .
Check: At the line passes through the origin, and every point with has . At the -intercept is , so points just left of the -axis have .
B: This excludes , but that line passes through the origin, which does not have , so it still avoids the region.
C: For the -intercept is positive, so points just left of the -axis lie in the region.
D: Slopes make positive for every negative ; the inequality points the wrong way.
Watch for: Test the boundary value directly: a line through the origin touches the corner of a quadrant but not the quadrant itself.
Math · Module 2 · Question 18 of 22
The box plot summarizes a data set of values. What is the least possible number of values in the data set that are greater than ?
Enter an integer, decimal, or fraction. Up to 5 characters, or 6 including a leading minus. No units or mixed numbers.
Answer: 1
The third quartile of the data set is . List the values in increasing order as . The third quartile is the median of the upper values, so . This allows , and then through can all equal , which is not greater than .
The only value that must be greater than is the maximum, . So the least possible number is .
Check: Example: through all equal and . The third quartile is still , the box plot is unchanged, and only is greater than .
Watch for: The most common wrong value is , from reading “at least a quarter of the values are at or above the third quartile” as “greater than” it. Values equal to are not greater than .
Math · Module 2 · Question 19 of 22
The functions and are defined by and . In the -plane, points and are the two points where the graph of meets the graph of . Point is the vertex of the parabola , and point is the vertex of the parabola . What is the area of quadrilateral ?
Answer: C.
Since ,. So and .
At an intersection point,
so , and or . Both points have , so and are and .
The diagonal is horizontal with length , and the diagonal is vertical with length . The diagonals are perpendicular, so the area is .
Check: splits the quadrilateral into triangles and . Each has base and height ( and ), so each has area , for a total of .
A: is the area of only one of the two triangles, or , into which divides the quadrilateral.
B: places at , as if the vertex of were units above the -axis; negating first moves the vertex to , so .
D: is the product of the diagonals, , without the factor .
Watch for: Negating moves the vertex from to before the shift up . The diagonals and are perpendicular, so the area is half their product.
Math · Module 2 · Question 20 of 22
An isosceles trapezoid has parallel sides of lengths and , and its diagonals are perpendicular to each other. What is the area of the trapezoid?
Answer: C.
Let the diagonals meet at point . Because the trapezoid is isosceles, the diagonals are equal and are cut into equal pieces on each base, so the triangle formed by and the base of length is an isosceles right triangle, and so is the triangle formed by and the base of length .
The height of an isosceles right triangle drawn to its hypotenuse is half the hypotenuse, so is units from the longer base and units from the shorter base. The height of the trapezoid is , and its area is
Check: Place the longer base from to and the shorter base from to . The diagonal from to has slope , and the diagonal from to has slope , so they are perpendicular.
A: uses a height of , the distance from to the longer base only.
B: uses a height of , the difference of the bases.
D: leaves out the factor in the trapezoid area formula.
Watch for: The height is the sum of the distances from to the two bases, .
Math · Module 2 · Question 21 of 22
An exponential function has the form , with and . The values of satisfy and . What is the value of ?
Enter an integer, decimal, or fraction. Up to 5 characters, or 6 including a leading minus. No units or mixed numbers.
Answer: 81
The conditions are and . Divide the second equation by the first:
So , or , which factors as . Because ,. Then
Check: With , gives . Then ,,, and ;.
Watch for: The most common wrong values are , from treating as a linear function, , from assuming , and , from multiplying by instead of .
Math · Module 2 · Question 22 of 22
In the -plane, the line , where and are constants, intersects the graph of at two points. The midpoint of the segment joining these two points is . What is the value of ?
Enter an integer, decimal, or fraction. Up to 5 characters, or 6 including a leading minus. No units or mixed numbers.
Answer: -5
Let the intersection points be and , where . Both points are on the line, so its slope is
The midpoint’s -coordinate is , so and .
The midpoint of two points on a line is also on the line, so satisfies :
and .
Check: With , the equation becomes , so the points are and . Their midpoint is .
Watch for: The midpoint’s -coordinate, , is half of , not itself. Taking gives the common wrong value . The midpoint is on the line but not on the parabola, because , not .
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Read the mathematical conditions. Use real numbers and the real domain of each expression unless stated otherwise. Geometry sketches are schematic unless a scale is specified; rely on stated lengths and relationships. Coordinate graphs and data displays use their labeled scales.
Work at your own pace. Browse has no timer. Use the module buttons and question grid to move freely between questions.
Check when ready. Use Show solution for one question or Check all attempted questions for the current module. Checked answers are locked until you reset them. Unanswered questions stay unrevealed when you check the module.
Try again. Reset this question clears that answer and hides its solution. Reset this module asks for confirmation before clearing its answers, solutions, flags and annotations. Other modules are kept. Your Browse progress saves separately from timed attempts.
Reference sheet
AVAILABLE DURING BOTH MODULES
Formula reference
The relationships below match the standard SAT-provided Math reference. This is a newly typeset reference, not a reproduction of the official sheet. [4]
Area and circumference
Circle A = πr2,C = 2πr
Rectangle A = lw
Triangle A = bh
Right triangles
Pythagorean theorem a2 + b2= c2, where c is the hypotenuse.
45°–45°–90° Side lengths s, s, s, in increasing order.
A full circle has 360° or 2π radians. The interior angles of a triangle sum to 180°.
Symbols: r is radius; l is length; w is width; b is base length; h is perpendicular height; A is area; C is circumference; V is volume. Source: official reference linked in the directions, [4].
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