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Every question, cut by skill
All 351 questions in the course in one place, filterable down to a single skill when you know what you’re bad at — and mixed by default, because the real test never tells you which type you’re looking at.
351 questions
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Snapshot the filter above into a fixed, timed, retakable test — shorter than a full adaptive exam, more structured than open-ended drilling, with its own score report at the end.
Before any teaching: "The committee's decision was ______; despite three separate appeals, not one term of the original ruling was altered." Which direction must the blank point?
Text 1: The gullies cut into the walls of Martian craters are young — some incise dunes only a few million years old. The planetary scientist Hana Osei notes that they also branch and taper exactly as terrestrial water channels do, and that hydrated salts have been detected in the debris at several gully mouths. Liquid brine, briefly stable under present-day Martian conditions, is in her view the most economical account of all three observations. Text 2: Blocks of carbon dioxide frost, sublimating as they slide, can excavate channels indistinguishable in plan view from those cut by water; laboratory flumes have reproduced the resemblance repeatedly. Morphology does not discriminate between the two processes, and a hypothesis resting on channel shape is resting on the one piece of evidence that cannot decide the question.
Based on the texts, how would Osei most likely respond to the argument advanced in Text 2?
Ceramic vessels recovered from a 3,000-year-old Baltic settlement carry a fine soot layer on their outer surfaces but almost none on their inner rims. Archaeologist Juno Halvorsen hypothesizes that the vessels were not used for cooking over open flame but for storing liquids, and were set near hearths only to keep their contents from freezing.
Which finding, if true, would most strongly support Halvorsen’s hypothesis?
Botanists call a plant an obligate outcrosser if it cannot produce viable seed from its own pollen. In a greenhouse trial, researchers hand-pollinated 240 flowers of the rare shrub Corvia stellata using pollen taken from the same plant; none of the 240 set seed. The researchers note that daytime temperatures in the greenhouse ran about six degrees above the range the shrub experiences in the field, and that in a companion trial pollen from these same plants fertilised flowers of neighbouring individuals only when temperatures were held near field levels. The greenhouse result therefore ______
Which choice most logically completes the text?
Before any teaching: "By the time the survey team reached the site in 1974, looters ______ nearly every accessible chamber." What decides which form of the verb belongs in the blank?
Early reviewers of Zora Neale Hurston’s Their Eyes Were Watching God, published in 1937, often treated its Black Southern speech as local colour — a decorative surface laid over a conventional romance. That judgement mistakes the novel’s method for its ornament. Hurston’s narration moves continually in and out of Janie’s idiom, so that the gap between what Janie can say aloud and what the narrator can say on her behalf becomes measurable from page to page. The dialect is not a flourish. ______, it is the instrument by which the book registers how much freedom its protagonist has at any given moment.
Which choice completes the text with the most logical transition?
Which expression is equivalent to 7 − 2(x − 4)?
The graphs of two linear equations in the xy-plane intersect at the point (4, −1) and nowhere else. What does that fact tell you?
For the system of equations x/3 + y/4 = 5 and x/6 − y/2 = −5, what is the value of x + y?
The equation x² + (k − 2)x + 9 = 0, where k is a constant, has exactly one real solution. What is the sum of all possible values of k?
A rectangular plot has an area of 2 square meters. Given that 1 meter = 100 centimeters, what is its area in square centimeters?
Data set P consists of the values 20, 20, 20, 50, 80, 80, 80. Data set Q consists of the values 20, 45, 50, 50, 50, 55, 80.
Which of the following correctly compares the standard deviations of P and Q?
Before any teaching. A random sample of 400 adults from a city reports a mean daily commute of 34.2 minutes, with a margin of error of 1.6 minutes at the 95% confidence level. Which statement does that support?
A random sample of 250 registered voters in a county found that 46% support a proposed measure, with an associated margin of error of 4 percentage points at the 95% confidence level. Which of the following conclusions is best supported by these results?
A closed cylindrical can has a radius of 3 centimeters and a height of 8 centimeters. What is the total surface area of the can, in square centimeters?
Before any teaching. The equation (x + 4)² + (y − 1)² = 20 defines a circle in the xy-plane. What are the circle's centre and radius?
Two candidate words both mean roughly "happy": content and euphoric. A sentence describes someone’s reaction to winning a lottery jackpot. Which is the more precise fit, and why?
Text 1: Great tits nesting beside major roads sing at a higher minimum frequency than great tits in quiet woodland a few kilometres away — a difference of several hundred hertz, and one that holds across dozens of European cities. Because traffic noise is concentrated at low frequencies, researchers have taken the pattern as evidence that road noise is driving the difference. Text 2: Playback experiments make the mechanism concrete. The low notes of a great tit's song are exactly the ones traffic noise covers: recordings of low-pitched song played beside a road draw answering calls from rival males far less often than the same recordings played in woodland, while high-pitched song is answered at the same rate in both settings. Nor is the pitch fixed at hatching. Males that settled beside a newly opened motorway raised the minimum frequency of their songs within a single breeding season.
Based on the texts, which choice best describes the relationship between them?
In a two-year study of a coastal city, researchers found that residential blocks where the city planted street trees in 2019 used 18 percent less electricity in the summer of 2021 than blocks where no trees were planted. The researchers concluded that shade from the new trees reduced households’ air-conditioning demand.
Which finding, if true, would most strongly undermine the researchers’ conclusion?
TABLE. "Mean tuber yield per plot, in kilograms, by seed treatment — 2023 field trial." Untreated control: 38.0. Fungicide dip: 61.5. Hot-water treatment: 84.6. Fungicide dip and hot water together: 96.2. TEXT. Seed-borne disease depresses potato yields across the region, and growers have generally relied on a fungicide dip to control it. Agronomist Femi Okoye argues that hot-water treatment on its own more than doubles yield relative to untreated seed: ______
Which choice most effectively uses data from the table to support Okoye's argument?
Before any teaching: a sentence opens "Trained for years to identify the calls of individual whales, ______". Without seeing any answer choices, what is already fixed about what comes next?
Economists have long modelled bank runs as a coordination failure: the bank is solvent, but a depositor who expects others to withdraw finds it rational to withdraw first, and the expectation makes itself true. Deposit insurance was designed to break that loop by removing the reason to run. The guarantee has an edge, though — in most countries it covers balances only up to a threshold, and large corporate deposits sit well above it. ______, the model predicts that a modern run should begin among uninsured depositors rather than among households, which is what the American bank failures of 2023 did.
Which choice completes the text with the most logical transition?
What value of x satisfies (3x + 1)/4 − (x − 3)/2 = 5?
For the system 5x + 3y = 17 and 3x + 5y = 15, what is the value of x + y?
In the xy-plane, line ℓ passes through the points (−2, 7) and (2, −1). Which of the following inequalities describes the set of all points (x, y) that lie below line ℓ?
Which of the following describes the solutions of the equation 1/(x − 3) + 1/(x + 3) = 6/(x² − 9)?
A taxi charges a $4 flat fee plus $2 for each mile driven, so a 5-mile ride costs $14. What does a 10-mile ride cost?
A box plot summarises the 64 recorded completion times, in minutes, for a task. The five-number summary is: minimum 4.2, Q1 7.5, median 9.1, Q3 15.8, maximum 28.0.
Which of the following statements is best supported by the box plot?
The same commute study is repeated with 1,600 randomly selected adults instead of 400 — same city, same method, same 95% confidence level. What happens to the margin of error, which was 1.6 minutes?
A scatterplot relates x, the number of years since 1990, to y, the mean number of hours per week that households in a region spent watching broadcast television. One point was recorded for each year from 1990 through 2015, and the line of best fit for the data is y = 21.4 − 0.35x.
According to this model, what is the first year in which the predicted mean falls below 10 hours per week?
A rectangular aquarium with a base measuring 30 inches by 18 inches contains water to a depth of 12 inches. Water is then added at a constant rate of 90 cubic inches per minute. How many minutes does it take for the depth of the water to reach 20 inches?
A circle has radius 12. A central angle of 150° cuts off an arc. What is the length of that arc?
Historians have long treated the merchant’s account books as a ______ source: useful for confirming dates and prices, but silent on the motives and rivalries that better explain why the trade routes shifted when they did.
Which choice completes the text with the most logical and precise word or phrase?
Recipes printed before the middle of the nineteenth century rarely give quantities and almost never give times. The modern reader takes this as imprecision, or as evidence of a kitchen indifferent to consistency. It is better read as evidence about who the books were for. A page that says a good piece of butter and cook until it is done is addressed to someone who has made the dish before, standing at a fire whose heat no number would have described anyway; the measurements were in the hands, not on the page. What the modern recipe added was not accuracy. It was the assumption that the reader had never cooked the thing before.
Which choice best states the main purpose of the text?
“The Cartographer’s Daughter” is a 2004 novel by Rasheed Okonjo. In the novel, Bem is convinced that his father’s survey maps contain deliberate errors, though the novel never confirms whether they do.
Which quotation from “The Cartographer’s Daughter” most effectively illustrates the claim?
Guidebooks to the Scottish islands routinely describe the drystone field walls there as a product of the eighteenth-century clearances, built by landlords enclosing ground for sheep. Excavation beneath three such walls on Lewis has complicated that dating. Under each, archaeologists found the footings of an earlier wall running along the same line, and radiocarbon dates from peat sealed beneath those footings fall between the eleventh and thirteenth centuries. On this evidence the clearance-era walls are not new boundaries but rebuildings of lines already several centuries old.
Which choice best states the main idea of the text?
A recent study of urban heat islands found that the temperature difference between a city's densest districts and the farmland surrounding it can exceed seven degrees Celsius on a summer night. The study's authors argue that the network of paved surfaces, dark rooftops, and heat-trapping canyons formed by tall buildings ______ far more of this difference than vehicle exhaust does.
Which choice completes the text so that it conforms to the conventions of Standard English?
Bees were long assumed to navigate home by dead reckoning alone — tracking the direction and distance of each leg of the outbound flight and summing them into a return vector. The account is at least incomplete: a bee carried to an unfamiliar site inside a dark box, its outbound path erased, still finds its hive. ______, the insects appear to consult a learned map of landmarks, orienting themselves much as a person does on climbing out of an unfamiliar underground station.
Which choice completes the text with the most logical transition?
In the equation 4(kx − 3) = 9x + 7 − x, k is a constant. For which value of k does the equation have no solution?
For the system y = 2x − 9 and 3x + 2y = 17, what is the value of x − y?
Two workers are spreading mulch on a site. One has already spread 18 bags and spreads 4 more bags each hour. The other has already spread 45 bags and spreads 1 more bag each hour. At the moment when the two have spread the same number of bags, how many bags will each have spread?
The solutions of the system y = x² − 4x + 7 and y = 2x − 1 are (x₁, y₁) and (x₂, y₂). What is the value of x₁ + x₂?
A bottling machine fills 12 bottles every 5 seconds. At this rate, how many bottles does the machine fill in 1.5 hours?
A histogram shows the sizes of 300 donations made to a charity. The tallest bars cover donations between $10 and $60, and the bars decrease steadily across the higher intervals, with a small number of donations spread thinly across intervals reaching as far as $5,000.
Which of the following best describes the shape of this distribution and the relationship between its mean and its median?
A magazine emails a survey to its own subscribers, receives 5,000 replies, and reports that 71% support a policy, with a margin of error of 1.3 percentage points. A statistician objects that the result says nothing about the country's adults. Does the very small margin of error answer that objection?
Nine hundred adults were selected at random from all adults in a country. Each was randomly assigned to take either a new supplement or an identical-looking placebo daily for 12 weeks, and neither the participants nor the people scoring the tests knew which had been taken. At the end, mean improvement on a memory test was 0.4 points in the supplement group and 0.3 points in the placebo group. The difference was not statistically significant.
Which of the following is the most appropriate conclusion based on this study?
A straight section of metal pipe is 10 feet long. Its outer radius is 4 inches and the pipe wall has a uniform thickness of 1 inch. What is the volume of metal in this section of pipe, in cubic inches? (1 foot = 12 inches.)
Points A, B, and C lie on a circle with centre O, and C lies on the major arc AB. The central angle AOB measures 110°. What is the measure of angle ACB?
Even the harshest critics of the reform conceded that its architects had been ______ in anticipating objections, having drafted responses to nearly every criticism the proposal eventually received.
Which choice completes the text with the most logical and precise word or phrase?
The senator's praise for the bill was so ______ that colleagues on both sides wondered whether she supported it at all: two sentences of vague approval, offered without a single specific reason.
Which choice completes the text with the most logical and precise word or phrase?
Economic historians disagree about why the port of Kasimir declined after 1780. Talia Renn argues that the decline was driven chiefly by the silting of the harbor channel, which forced deep-hulled ships to unload at anchor. Piet Lundqvist counters that silting was a nuisance the port had managed for a century, and that the decline followed the opening of an inland canal that let goods bypass Kasimir entirely.
Which finding, if true, would most directly support Renn’s claim rather than Lundqvist’s?
"The Tin Ceiling" is a 1976 novel by Ottoline Baz. In the novel, Sabri keeps his failing bakery open not out of any attachment to the work but because closing it would mean telling his mother.
Which quotation from "The Tin Ceiling" most effectively illustrates the claim?
In 1927 the astronomer Lise Halvorsen published a catalogue of variable stars compiled over eleven years of observation at a mountain observatory. The catalogue was controversial from the moment it appeared. By the time it reached print, two rival observatories ______ measurements that contradicted nearly a third of her entries, and the dispute took another decade to settle.
Which choice completes the text so that it conforms to the conventions of Standard English?
Before any teaching. On a Rhetorical Synthesis question, all four choices are built from the student's notes and all four are accurate about them. What decides which one is credited?
The equation −2(3x − 7) + 5x = c − x, where c is a constant, has infinitely many solutions. What is the value of c?
For the system 5x + 7y = 34 and 7x + 5y = 26, what is the value of x + y?
The linear function f satisfies f(x + 3) = f(x) + 12 for every value of x. If f(5) = 7, what is the value of f(11)?
Before any teaching. The function f is defined by f(x) = (x − 3)(x + 7). In the xy-plane, what is the x-coordinate of the vertex of the graph of y = f(x)?
A protective coating is applied at a rate of 4 grams per square meter. Given that 1 gram = 1,000 milligrams and 1 meter = 100 centimeters, what is the application rate in milligrams per square centimeter?
A data set of 15 values has a mean of 62 and a median of 58. A sixteenth value, equal to 62, is added to the data set. Which of the following correctly describes the effect on the mean and on the standard deviation?
A quality-control team selects 120 bottles at random from a day's production run and measures each one. The sample has a mean fill volume of 7.35 fluid ounces, with an associated margin of error of 0.28 fluid ounces at the 95% confidence level. Which conclusion about the day's entire production run is best supported?
At a school, the number of students enrolled in Spanish is 40% greater than the number enrolled in French. The number enrolled in French is what percent less than the number enrolled in Spanish?
A concrete drainage channel is a solid right prism 9 centimeters long. Its cross section is a trapezoid whose parallel sides measure 5 centimeters and 11 centimeters and whose height — the perpendicular distance between those parallel sides — is 4 centimeters. What is the volume of the prism, in cubic centimeters?
The equation (x − 3)² + (y + 5)² = 49 defines a circle in the xy-plane. What is the length of the circle's diameter, and in which quadrant does its centre lie?
The photograph’s composition was so arresting that visitors, mid-conversation, would stop and stand before it in silence.
As used in the text, "arresting" most nearly means
Asked whether a language is dying, linguists usually answer by counting speakers, and by that measure the outlook for the indigenous languages of the Pacific Northwest is bleak. But counting speakers assumes that a language is the sum of the people currently fluent in it, and a language is also a documented record, a set of teaching materials, and a community's claim on all of it. Several of the region's languages now have more fluent speakers under thirty than they had in 1990, and nearly every one of those speakers learned the language in a classroom, from recordings made a century ago by people long dead. Whether that counts as survival, or as something else — reconstruction, perhaps — is not a question the speaker count was built to answer.
Which choice best describes the function of the sentence beginning "But counting speakers assumes that a language is the sum of the people currently fluent in it" in the text as a whole?
“Ledger of Small Weather” is a 2011 poetry collection by Hana Sørensen. A critic has observed that in the collection’s title sequence, the speaker’s grief is conveyed entirely through attention to ordinary objects, never through direct statement of feeling.
Which quotation from the title sequence most effectively illustrates the critic’s claim?
TABLE. "Mean bat carcasses recovered per turbine per night, by operating condition, late summer." Normal operation, towers lit: 1.92. Blades feathered below 5.0 m/s wind, towers lit: 0.61. Blades locked motionless, towers lit: 0.55. Blades locked motionless, towers unlit: 0.49. TEXT. Two explanations have been offered for bat deaths at wind farms: that bats are drawn in by the lights on the towers, and that the deaths are caused by the moving blades themselves. Ecologist Marta Weiss concludes that the blades, not the lights, account for nearly all of the mortality: ______
Which choice most effectively uses data from the table to support Weiss's conclusion?
Unlike most seabirds, which return to the same nesting ledge year after year, the Arctic tern is a habitual wanderer. A single bird, tracked by researchers using geolocators no heavier than a paper clip, may breed on three separate continents over the course of ______ life, following food supply rather than any loyalty to one colony.
Which choice completes the text so that it conforms to the conventions of Standard English?
A goal reads: "The student wants to emphasize that the new bridge design cut construction time." Two candidate sentences both contain that fact. (1) "The new modular design, which cut construction time in half, was chosen mainly for its performance under seismic loading." (2) "The new modular design cut construction time in half." Which emphasizes the fact, and why?
A theater sold 300 tickets to a performance. Adult tickets cost $12 each and student tickets cost $8 each, and ticket sales brought in $3,160 in total. How many student tickets were sold?
A theater sold only adult tickets and student tickets for one performance. Adult tickets cost $12 each and student tickets cost $8 each. The number of student tickets sold was 30 greater than the number of adult tickets sold, and the theater collected $1,000 in total. How much of the $1,000 came from student tickets?
At a bakery, 3 croissants and 2 muffins cost $16.50, and 5 croissants and 4 muffins cost $29.50. At these prices, what is the total cost of 2 croissants and 1 muffin?
A bacterial population is modeled by P(t) = 240(1.35)^t, where t is the number of hours since the culture was prepared. What is the best interpretation of 1.35 in this model?
A batch of mortar weighing 72 kilograms is made of sand and cement in a ratio of 5 to 3 by mass. How many kilograms of cement must be added to the batch so that the ratio of sand to cement becomes 5 to 4?
Before any teaching. A scatterplot relates x, the number of minutes a cup of coffee has been sitting on a table, to y, its temperature in degrees Celsius. The line of best fit is y = 78.6 − 1.4x. Which is the best interpretation of the number 1.4?
A report states only this: "Based on a random sample, it is plausible that the mean weekly grocery spend of households in the region is between $61.40 and $68.20." What were the sample mean and the margin of error?
A press prints 1,200 pages per minute while it is running, but after every 20 minutes of running it must pause for 45 seconds to cool before it can run again. The press starts cool and operates under this cycle for exactly 2 hours of elapsed time. How many pages does it print?
Before any teaching: two parallel lines are cut by a transversal, creating eight angles. One of them measures 62°. What can you say about the other seven?
The equation 2x² + 2y² − 12x + 20y − 6 = 0 defines a circle in the xy-plane. What is the radius of the circle?
Rather than settling the dispute, the court’s ruling proved ______: within a year, three lower courts had issued conflicting interpretations of it, and legal scholars were divided over what the decision even required.
Which choice completes the text with the most logical and precise word or phrase?
Text 1: Excavators at the settlement have argued for thirty years about whether the great timber hall at its centre was a temple or a chief's residence. The argument turns on the animal bone. The deposits are dominated by cattle skulls, which one side reads as the residue of sacrifice and the other as the remains of feasts held by a household of unusual size. Text 2: The question is put wrongly. In a society of this kind the obligation to feast one's dependants was itself a religious obligation, discharged before the same ancestors whose names the hall carried. A building in which a chief killed cattle for his followers was not a residence that occasionally hosted rites, and not a temple that happened to have a hearth. Sorting the bone into a sacrificial pile and a domestic one imports a boundary the builders never drew, and whichever pile is larger, the result will describe our categories rather than theirs.
Based on the texts, how would the author of Text 2 most likely respond to the disagreement described in Text 1?
Before any teaching. A text argues that new bus lanes increased ridership on the routes that received them. One choice reads: "Route 12, which did not receive a bus lane, carried more trips in 2023 than any other route." Assume that is an accurate reading of the graph. Can it be the credited answer?
Conservators call a pigment fugitive if it fades measurably under ordinary gallery lighting within a human lifetime. At one museum, conservators masked a narrow strip of each of eleven nineteenth-century watercolours and left the rest of each sheet under ordinary gallery lighting for four years. On nine of the eleven, the exposed area had lightened measurably relative to its masked strip. The conservators note that all eleven sheets were acquired from a single dealer's stock, and that the two unchanged works are painted on a paper the other nine do not share. The test therefore ______
Which choice most logically completes the text?
In 1911 two expeditions raced for the South Pole using sharply different methods: one relied on dogs and skis, the other on motor sledges and ponies. The ______ divergent outcomes are still taught in logistics courses more than a century later, less as a story about endurance than as a case study in equipment selection.
Which choice completes the text so that it conforms to the conventions of Standard English?
A goal reads: "The student wants to introduce the imaging technique to an audience already familiar with conventional ultrasound." What does the phrase "already familiar with conventional ultrasound" require of the credited answer?
In the equation a(x + 3) = 6x + b, a and b are constants. For which pair (a, b) does the equation have no solution?
In the system 2x + 5y = 8 and ax + 15y = b, where a and b are constants, the system has infinitely many solutions. What is the value of a + b?
In the equation (2/3)(9x − 6) = kx + m, k and m are constants and the equation is true for every value of x. What is the value of k − m?
The function f is defined by f(x) = −2(x + 4)² + 9. Which statement correctly describes the extreme value of f?
A 3-D printer extrudes filament at a constant 25 millimeters per second. Each meter of the filament has a mass of 4 grams, and the filament costs $25 per kilogram. What is the cost, in dollars, of the filament the printer uses during 45 minutes of continuous printing?
A line of best fit predicts a value of 61 for a certain data point. The value actually measured at that x is 68. What is the residual for this point, and where does the point sit relative to the line?
To estimate the mean number of hours per week that students at a university spend on paid work, a researcher randomly selected 150 students from among those who visited the campus library on a Tuesday afternoon and surveyed all of them. The sample mean was 9.4 hours, with a margin of error of 1.2 hours. Which of the following best describes the study's principal limitation?
A factory's entire daily output comes from two lines. Line 1 produces 3,000 units a day, of which 2% are defective; line 2 produces 2,000 units a day, of which 5% are defective. One unit is selected at random from a day's defective units. What is the probability that it came from line 2?
Triangle A and triangle B are similar, and every side of B is 3 times the corresponding side of A. Triangle A has an area of 5 square units. What is the area of triangle B?
In a circle of radius 6, a sector is bounded by two radii and an arc of length 5π/2. What is the area of the sector?
Before any teaching. A short text reports that a newly sequenced fungal genome contains genes for enzymes no other known fungus produces, and closes by noting that no one has yet observed the fungus using them. Which of the following states the text's PURPOSE, as opposed to its subject, its main idea, or a detail from it?
When the first rate-supported public libraries opened in Britain in the 1850s, the speeches at their openings promised working people access to improving literature: history, science, biography. The borrowing registers record something else. Through the rest of the century novels accounted for the large majority of loans at most municipal branches, and librarians spent decades arguing among themselves about whether to stock them at all. This is not evidence that the libraries failed. It is evidence that what they were actually supplying — warm, free, respectable access to fiction — was wanted more than what they had been promised for, and that the institution survived by supplying it.
Which choice best describes the overall structure of the text?
A text reads: "In the greenhouse, the two fertiliser treatments produced nearly identical yields. In the field, however, ______" What must the data in the credited choice do?
Across twenty-six countries, adults who report eating fermented foods daily score higher on a standard measure of digestive comfort than adults who report eating them rarely. A research team proposes that the live microorganisms in those foods are responsible for the difference, rather than the dietary fibre the same foods contain.
Which finding, if true, would most strongly support the team's proposal?
The 1507 Waldseemuller map is the first surviving document to apply the name "America" to the western continents, and only one copy is known to have survived. Its condition owes something to luck. Bound into a German prince's atlas and shelved unopened for nearly four hundred years, ______
Which choice completes the text so that it conforms to the conventions of Standard English?
NOTES. While researching a topic, a student has taken the following notes: • Dendrochronology dates wood by matching the pattern of its annual growth rings against a master sequence for the region. • Radiocarbon dating estimates age from the decay of carbon-14 in organic material. • Dendrochronology can place a sample in an exact year, but only where a regional master sequence has been built. • Radiocarbon dating works almost anywhere organic material survives, but returns a range of decades rather than a single year. • Both methods depend on a reference record assembled from samples whose ages were already known.
The student wants to emphasize a similarity between the two dating methods. Which choice most effectively uses relevant information from the notes to accomplish this goal?
If 5(x + 2) − 3(x − 4) = 40, what is the value of 2x − 3?
In the system 8y = 3x + 5 and 9x + ky = 20, where k is a constant, the system has no solution. What is the value of k?
The solution set of the inequality 6x + a > 4x + 9, where a is a constant, is x > 5. What is the value of a?
The function V(t) = 18,000(0.82)^t models the value, in dollars, of a machine t years after it was purchased. Which of the following is the best interpretation of the model?
A nursery waters its planting beds at a rate of m milliliters of water per square meter per day. It has b beds, each with an area of a square meters. Which expression gives the number of days the nursery can water all of its beds from a full tank holding L liters of water? (1 liter = 1,000 milliliters)
A table gives a quantity at times t = 0, 1, 2, and 3 as 500, 460, 423.2, and 389.344. Is the relationship better modeled by a linear or an exponential function, and on what evidence?
Two independent random samples were drawn from the students of the same university. Sample P (200 students) gave a mean of 14.2 study hours per week, margin of error 1.1 hours. Sample Q (800 students), drawn a year later, gave a mean of 15.0 hours, margin of error 0.6 hours. Both intervals are at the 95% confidence level. Which conclusion is best supported?
Data set M consists of the eleven values 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 70. Data set N consists of the eleven values 30, 34, 38, 42, 46, 50, 54, 58, 62, 66, 70.
Which of the following correctly compares the standard deviations of M and N?
Two sides of a triangle measure 7 and 11. Which statement describes every possible length x of the third side?
Points A, B, and C lie on a circle. Segment AB is a diameter of the circle, and the arc from B to C that does not contain A has measure 50°. What is the measure of angle ABC?
A paragraph makes a broad claim, and the next sentence begins: "In the Netherlands, however, the pattern reverses." Without seeing the rest of the paragraph, what is the most likely FUNCTION of that sentence?
Text 1: After the bleaching event of 1998, corals on the inner-lagoon reefs of the archipelago recovered within a decade; the outer-slope reefs, a few kilometres away, largely did not. Lagoon water is warmer than open-ocean water and swings several degrees between tides, and the marine biologists working the site argue that this routine thermal stress had toughened the lagoon colonies in advance. They note that fragments they moved from the lagoon to the outer slope in 2012 bleached less in the following summer than the outer-slope colonies growing around them. Text 2: The lagoon sites share something the temperature explanation leaves out: all of them lie within a few hundred metres of dense mangrove stands, which shade the water and buffer it against the clear-sky heating that drives bleaching. Across the archipelago's thirty monitored sites, recovery tracks mangrove cover more closely than it tracks any measure of thermal variability.
Based on the texts, how would the marine biologists cited in Text 1 most likely respond to the argument in Text 2?
A table reports that a district's literacy rate rose from 24 percent to 42 percent. Which statement describes that change accurately?
A widely reported finding holds that people who keep houseplants report less stress than people who do not. Nearly all the studies behind it recruit participants who already own plants, which leaves open whether the plants lower stress or whether people settled enough to keep plants were less stressed to begin with. One trial did assign plants to offices at random; it found an effect about a fifth the size of the correlational estimate, and that effect had faded by the sixth month.
Which choice best states the main idea of the text?
Advocates of congestion pricing argue that the policy works on two fronts at once. Charging drivers to enter a city center not only reduces the number of vehicles competing for road space but also ______, since buses and delivery vans move faster when the road ahead of them is clear.
Which choice completes the text so that it conforms to the conventions of Standard English?
NOTES. While researching a topic, a student has taken the following notes: • Conventional ultrasound imaging sends pulses of sound into tissue and records the echoes that return from structures inside the body. • Photoacoustic imaging has been developed over roughly the past two decades. • It illuminates tissue with a very short pulse of laser light. • The tissue absorbs the light, warms by a fraction of a degree, and expands. • That sudden expansion generates an ultrasound wave, picked up by the same kind of detector conventional ultrasound uses. • Photoacoustic images show which molecules are present — oxygenated versus deoxygenated haemoglobin, for instance — where ultrasound shows structure.
The student wants to introduce photoacoustic imaging to an audience already familiar with conventional ultrasound. Which choice most effectively uses relevant information from the notes to accomplish this goal?
A candle is 20 cm tall when lit and burns down at a constant rate of 0.5 cm per minute. In an equation for height h after m minutes, which number is the slope and which is the intercept?
In the system 6x + 15y = 24 and 10x + ky = 40, k is a constant. Which of the following statements is true?
Before any teaching: you need the minimum value of f(x) = 2x² − 12x + 23. Which single rewriting hands you that value with no further work?
The function f is defined by f(x) = 3x² + 30x + 68. What is the minimum value of f(x)?
One pump moves water at 0.75 cubic meters per minute. A second pump moves 250 liters per minute. Running at the same time, how many minutes will the two pumps take to fill an empty 30,000-liter tank? (1 cubic meter = 1,000 liters)
A scatterplot relates x, the number of years since 2000, to y, the total annual rainfall, in millimeters, recorded at a weather station. Rainfall was recorded each year from 2000 through 2018, and the line of best fit for the data is y = 812 − 6.4x.
Which of the following is the best interpretation of the number 6.4 in this context?
A polling firm surveys 900 randomly selected residents and reports a margin of error of 2.4 percentage points at the 95% confidence level. It now wants a margin of error of about 1.2 percentage points, keeping the same sampling method, the same population, and the same confidence level. Approximately how many residents must it survey?
A hospital offered two rehabilitation programmes to all 240 patients discharged in one month and let each patient choose which of the two to follow. Patients who chose programme A regained full mobility 9 days sooner on average than patients who chose programme B.
Which of the following is the strongest objection to concluding that programme A causes faster recovery?
Lines ℓ and m are parallel and are cut by transversal t. The two interior angles on the same side of t measure (5x + 8)° and (3x + 12)°. What is the measure, in degrees, of the smaller of those two angles?
The equation x² + y² − 6x + 8y = 56 defines a circle in the xy-plane. What is the length of the chord that the circle cuts from the y-axis?
A question asks what an underlined sentence does in the text as a whole. One of the four choices accurately paraphrases what that sentence says — in substance, word for word. Is that choice therefore correct?
The proposal's financing structure was, several bankers admitted, genuinely novel — no comparable deal had closed in the sector before.
As used in the text, "novel" most nearly means
FIGURE. Bar graph, "Annual ridership by route, City Transit Authority, 2019 and 2023." The vertical axis is labeled "thousands of trips." Route 4: 820 in 2019, 610 in 2023. Route 9: 540 in 2019, 705 in 2023. Route 12: 1,150 in 2019, 980 in 2023. Route 17: 305 in 2019, 640 in 2023. TEXT. In 2020 the authority converted a full traffic lane into a dedicated bus lane on Routes 9 and 17; Routes 4 and 12 were left unchanged. Reviewing all four routes, an analyst argued that the ridership figures are consistent with the new lanes having produced a recovery: ______
Which choice most effectively uses data from the figure to complete the text?
TABLE. "Percentage of survey respondents reporting a museum visit in the past year, by age group." Ages 18–29: 34 in 2013, 41 in 2023. Ages 30–44: 46 in 2013, 44 in 2023. Ages 45–64: 52 in 2013, 47 in 2023. Ages 65 and over: 39 in 2013, 43 in 2023. TEXT. Museum directors routinely describe their audiences as steadily ageing — younger visitors falling away as older ones take their place. Over the decade the survey covers, the figures do not describe that pattern: ______
Which choice most effectively uses data from the table to complete the text?
Bathymetric charts of the mid-century Atlantic were assembled from thousands of individual soundings, each one a single depth reading taken from a ship. In the early 1950s the geologist Marie Tharp plotted those readings into a continuous profile of the North Atlantic floor ______ and identified in it the deep rift valley that would become central evidence for seafloor spreading.
Which choice completes the text so that it conforms to the conventions of Standard English?
NOTES. While researching a topic, a student has taken the following notes: • Roman marine concrete in harbour structures has survived two thousand years of direct seawater exposure. • Modern Portland-cement concrete exposed to seawater typically begins to degrade within decades. • Roman builders mixed volcanic ash and lime with seawater. • Samples drilled from Roman harbour structures contain aluminous tobermorite, an interlocking mineral that reinforces the material around it. • The mineral was not present in the original mix; it grew over time as seawater percolated through the concrete. • In modern reinforced concrete, seawater penetration cracks the matrix and corrodes the steel inside it.
The student wants to explain why Roman marine concrete has proven so durable. Which choice most effectively uses relevant information from the notes to accomplish this goal?
You know a line's slope and exactly one point it passes through. Can you write its full equation without knowing a second point?
Before any teaching: which single step takes −2x < 6 to its correct solution?
Before any teaching: for x > 0, the expression (2x³)⁴ / (4x⁵) is equivalent to which of the following?
In the xy-plane, the graph of the quadratic function h intersects the x-axis at (−9, 0) and (3, 0) and passes through the point (1, −40). What is the y-coordinate of the vertex of the graph of h?
Before any teaching: a shirt's original price is $40. Store A's sign reads "80% of the original price." Store B's sign reads "80% off the original price." What does the shirt cost at each store?
In a greenhouse study, the mass of each plant, in grams, was recorded against the number of days since planting. The line of best fit for the data is y = 1.8x + 4.5, where x is the number of days since planting and y is the mass in grams. One plant measured 30 days after planting had a mass of 52.5 grams.
What is the residual for that plant's data point?
From one random sample of 500 households, an analyst computes two intervals for the mean monthly water use: 3,420 to 3,580 gallons, and 3,395 to 3,605 gallons. One is a 95% interval and the other is a 99% interval. Which statement is correct?
For a sample of used cars of one model, the line of best fit relating x, the car's age in years, to y, its resale value in thousands of dollars, is y = 23.6 − 1.9x. One 7-year-old car in the sample has a residual of −1.4.
What was that car's actual resale value?
In triangle ABC, point D lies on side AB and point E lies on side AC so that segment DE is parallel to side BC. If AD = 8, DB = 6 and DE = 12, what is the length of BC?
In the xy-plane, the graph of x² + y² − 10x + 2y + k = 0, where k is a constant, is a circle tangent to the x-axis. What is the value of k?
Sea otters were hunted nearly to extinction along the North Pacific coast in the nineteenth century, and the kelp forests there thinned dramatically in the decades that followed. Ecologists long attributed the loss of kelp to warming coastal waters. But otters eat sea urchins, and urchins eat kelp; where otter populations have since recovered, urchin numbers have fallen and kelp has returned, in some places even where water temperatures have continued to rise. The kelp forests were not, then, primarily a casualty of temperature. They were a casualty of a missing predator.
Which choice best states the main purpose of the text?
Before any teaching. On a "Which choice best states the main idea of the text?" item, you check all four choices against the passage and find that three of them state things the passage actually says. What does that tell you about how to choose?
TABLE. "Bacterial canker survey, four orchards, 2023." Columns: orchard; infected trees; trees surveyed. North: 96 infected of 4,800 surveyed. East: 150 of 3,000. South: 210 of 14,000. West: 44 of 1,100. TEXT. Treatment supplies were limited, so the regional agronomist recommended starting with the orchard where the disease was most prevalent — that is, where the largest share of surveyed trees was infected. The table identifies it: ______
Which choice most effectively uses data from the table to complete the text?
Sourdough bread rises without commercial yeast because the flour-and-water starter that leavens it hosts a stable community of wild yeasts and lactic acid bacteria. Bakers have long held that this community comes chiefly from the flour. A survey of starters maintained in eighteen bakeries found otherwise: starters made from a single sack of flour and then kept in different kitchens diverged within weeks, while starters kept in the same kitchen converged whatever flour they had been made from. The strongest single predictor of a starter's bacterial composition proved to be the hands of the baker who fed it.
According to the text, what did the survey find to be the strongest predictor of a starter's bacterial composition?
A garage in Ipswich kept a day book from the year it opened until the year it closed, and the historian who found the volume in a house clearance has been mining it ever since. In the first week of August 1974, according to the entries, the two ______ overhauled nine engines between them, rebuilt a gearbox, and still closed early on the Friday.
Which choice completes the text so that it conforms to the conventions of Standard English?
NOTES. While researching a topic, a student has taken the following notes: • Jan van Eyck's Ghent Altarpiece was completed in 1432. • A conservation campaign running from 2012 to 2019 examined its panels under the microscope. • Roughly 70 percent of the painted surface on the panels examined proved to be overpaint added in the sixteenth century. • The overpaint had been applied so skilfully that earlier conservators had taken it for van Eyck's own work. • With the overpaint removed, the altarpiece's central lamb was found to have a far more frontal, humanlike face. • Some art historians objected that stripping away four centuries of accumulated material destroys part of an object's history.
The student wants to emphasize the extent of the overpainting the campaign uncovered. Which choice most effectively uses relevant information from the notes to accomplish this goal?
A moving company charges a flat inspection fee plus an hourly labor rate. A 3-hour job costs $260, and a 5-hour job costs $380. Which equation gives the total cost C, in dollars, for a job lasting h hours?
A student begins graphing y ≥ 2x − 1 by drawing the line y = 2x − 1. What is left to decide, and how is it decided most reliably?
Before any teaching: exactly one of these is true for every value of x at which the left-hand side is defined. Which one?
A culture that begins with 5,000 cells triples in number every 8 hours. Which function gives the number of cells, n, present d days after the culture begins?
A price rises by 30%. Later, that new price falls by 30%. Compared with where it started, the price is now:
For a group of children whose ages ranged from 2 to 10 years, height was recorded against age. The line of best fit for the data is y = 6.1x + 84.2, where x is age in years and y is height in centimeters.
Using this model to predict the height of a 40-year-old gives what value, and is that prediction appropriate?
Before any teaching. Researchers randomly selected 900 adults from a city's residency records and recorded, for each, whether the adult belongs to a gym and his or her resting blood pressure. Gym members had lower resting blood pressure on average. Which conclusion does this study design support?
Two independent random samples are drawn from the same large population, using the same method and reported at the same 95% confidence level. Sample R has 500 members and sample S has 2,000 members. Which of the following must be true?
Two sides of a triangle have lengths 9 and 14. If the length of the third side is an integer, how many different values are possible for that length?
In triangle ABC, side BC is extended beyond C to a point D. Angle ACD measures 118°, angle A measures (2x + 10)°, and angle B measures (3x − 12)°. What is the measure, in degrees, of angle A?
Beginning in the 1970s, art historians working through nineteenth-century French exhibition catalogues found that women painters appeared in them far more often than the standard survey histories suggested. The point was not that these painters had been forgotten by accident. Museums acquire what dealers offer, dealers offer what collectors want, and collectors have generally wanted what museums display — a circuit that, once a painter is outside it, is hard to re-enter. The absence of women from the surveys was therefore not a neutral record of who had painted well; it was a record of what the market had kept in circulation.
Which choice best describes the function of the sentence "Museums acquire what dealers offer, dealers offer what collectors want, and collectors have generally wanted what museums display — a circuit that, once a painter is outside it, is hard to re-enter." in the text as a whole?
Manatees have poor eyesight and live in murky water, so biologists long assumed they navigated chiefly by touch. Recent work points elsewhere. The bristles covering a manatee's face are innervated far more densely than contact with objects would require, and in tank experiments the animals reliably detected pressure waves from a moving paddle they could neither see nor reach. On this evidence the bristles function less like fingertips than like a fish's lateral line.
Which choice best states the main idea of the text?
TABLE. "Microplastic concentration by depth, sediment core from Lake Reyner," in particles per kilogram of dry sediment. Deeper layers were deposited earlier. 0–5 cm: 910. 5–10 cm: 350. 10–15 cm: 130. 15–20 cm: 40. TEXT. If the amount of plastic reaching the lakebed had been climbing at a steady rate, each successive layer would hold roughly the same amount more than the layer beneath it. Ecologist Hana Voss argues that the climb has instead been accelerating: ______
Which choice most effectively uses data from the table to support Voss's argument?
A museum displays an object from its reserve collection only if the object has been conserved and its provenance has been documented to the standard set by the museum's 2018 policy. Conservation of the entire reserve collection was completed in 2021. Of the 340 objects in the reserve collection, provenance research has so far been completed for 96, and 71 reserve objects have been displayed since 2021. It follows that ______
Which choice most logically completes the text?
Ada Lovelace is often described as the first computer programmer, a label that flattens a more interesting story. She was one of a handful of nineteenth-century writers who ______ willing to describe Babbage's engine as something other than a calculating machine, and she was the only one of them who worked out in detail what operating on symbols would actually require.
Which choice completes the text so that it conforms to the conventions of Standard English?
NOTES. While researching a topic, a student has taken the following notes: • Researchers tested whether wild crows can recognise individual human faces. • At five sites, they captured and banded crows while wearing one distinctive mask. • Afterwards, volunteers walked the same sites wearing either that mask or a different one. • Crows scolded and mobbed the volunteers wearing the capture mask far more often than those wearing the other mask. • At some sites the response was still present more than five years after the original captures. • Birds that had never been captured also scolded the capture mask, suggesting the recognition spread socially.
The student wants to present the study's methodology to an audience unfamiliar with it. Which choice most effectively uses relevant information from the notes to accomplish this goal?
In the equation V = 1,200 − 45t, which models the resale value V, in dollars, of a piece of equipment t years after purchase, what does the number 45 represent?
A point (x, y) satisfies the first inequality of a two-inequality system but not the second. Is it a solution to the system?
Which expression is equivalent to (3x⁴y)³ / (9x⁵y⁻²), where x and y are positive?
The polynomial function p is defined by p(x) = −2(x − 4)²(x + 1)³. Which statement about the graph of y = p(x) in the xy-plane is true?
After a 25% discount, a coat costs $96. What was the price before the discount?
The table gives the value V, in dollars, of a piece of equipment at the end of each of four consecutive years: 2018, $24,000; 2019, $20,400; 2020, $17,340; 2021, $14,739.
Which function best models V, in dollars, as a function of t, the number of years after 2018?
Before any teaching. A researcher put up flyers at a community centre, and 180 people volunteered for a study on sleep. Each volunteer was randomly assigned to one of two evening routines and followed it for three weeks. The group using routine A fell asleep 14 minutes faster on average. Which conclusion does this design support?
A delivery van covers 120 kilometers of motorway at an average speed of 80 kilometers per hour and then 40 kilometers of city streets at an average speed of 40 kilometers per hour. What is its average speed for the whole 160-kilometer journey?
In right triangle PQR, angle Q is a right angle and angle R measures 30°. If PQ = 9, what is the perimeter of triangle PQR?
In right triangle ABC, the right angle is at C. The altitude drawn from C meets the hypotenuse AB at point D. If AD = 4 and DB = 9, what is the value of tan B, where B is the angle at vertex B?
A recent review of river-restoration projects reports that most are evaluated within three years of completion, and that projects judged successful at that point are frequently judged unsuccessful when revisited after a decade. The review's authors treat this as an argument for longer monitoring windows. They do not argue that the projects fail; they argue that three years is too short a period in which to know. Funding agencies, however, tend to set evaluation deadlines to match grant cycles rather than ecological ones, and the review does not address how that constraint might be changed.
Which choice best describes the function of the sentence "They do not argue that the projects fail; they argue that three years is too short a period in which to know." in the text as a whole?
"According to the text, what challenge did the researchers have to overcome?" and "Which choice best states the main idea of the text?" appear on the same skill. What actually differs in what they ask you to do?
TABLE. "Germination of Ceanothus seeds after simulated fire treatments," as the percentage of seeds germinating. Untreated control: 4. Heat only: 31. Smoke only: 9. Heat and smoke together: 34. TEXT. Chaparral shrubs germinate en masse in the season after a wildfire, and two cues have been proposed for it: the pulse of heat the fire drives into the soil, and the chemical compounds carried in its smoke. Botanist Ines Arrieta concludes that for Ceanothus the cue is heat: ______
Which choice most effectively uses data from the table to support Arrieta's conclusion?
Records of the rufous-sided towhee submitted to a network of citizen-science bird surveys have risen sharply in one region over the past decade. Reviewing the data, ornithologist Dele Fanaka argues that the network's expanding coverage, more than any change in the bird's numbers, explains the rise.
Which finding, if true, would most strongly support Fanaka's claim?
Only eleven whales remain in the resident pod that feeds year-round in the strait, and in March researchers fitted every one of them with a satellite tag. The results overturned an assumption that had stood for thirty years. The ______ within a hundred kilometres of the coast for the entire following year, and not one of them crossed to the open Pacific.
Which choice completes the text so that it conforms to the conventions of Standard English?
NOTES. While researching a topic, a student has taken the following notes: • Kevlar and spider dragline silk are both studied as models for high-performance fibres. • Kevlar has the higher tensile strength: it withstands more force before it breaks. • Dragline silk stretches much further than Kevlar before breaking. • Toughness measures the total energy a material absorbs before it fails, combining how much force it takes and how far it stretches. • By that measure dragline silk is roughly three times as tough as Kevlar. • Kevlar fibres are spun from a sulfuric acid solution at high temperature; spiders spin silk from water at ordinary temperature.
The student wants to explain why dragline silk absorbs more energy than Kevlar despite being the weaker fibre. Which choice most effectively uses relevant information from the notes to accomplish this goal?
The line 6x + 2y = k passes through the point (5, −3). What is the value of k?
Which of the following gives all values of x that satisfy 5(3 − 2x) ≤ 4x − 13?
The expression (x² − 2x − 35)/(x² − 49) is equivalent to which of the following for all values of x for which both expressions are defined?
The function f is defined by f(x) = x² − 6x + 5, and the function g is defined by g(x) = f(x − 2) + 7. In the xy-plane, the graph of y = g(x) has its minimum at the point (a, b). What is the value of a + b?
A company's monthly software revenue was $65,000 in 2019 and $52,000 in 2024. By what percent did the monthly revenue decrease from 2019 to 2024?
A scatterplot relates x, the number of years since 1995, to y, the number of registered vehicles in a county, in thousands. The line of best fit passes through the points (4, 63.5) and (16, 92.3).
According to the line of best fit, what is the predicted increase in the number of registered vehicles from 2001 to 2011?
Before any teaching. A survey is mailed to every one of the 20,000 households in a town. Three thousand households return it, and 68% of those returning it say they support a new library tax. Which statement about the 68% figure is best supported?
A store's sales come entirely from two departments. Last year department X took $120,000 and department Y took $280,000. This year department X's sales rose 30% and the store's total sales rose 2%. By what percent did department Y's sales change?
Triangle ABC is similar to triangle DEF. The perimeter of triangle ABC is 24 and the perimeter of triangle DEF is 36. If the area of triangle DEF is 162 square units, what is the area of triangle ABC?
A sphere is inscribed in a cube whose edges each measure 10 centimeters, so that the sphere touches all six faces of the cube. What is the volume, in cubic centimeters, of the region inside the cube but outside the sphere?
The standard account of the Moon's origin holds that a Mars-sized body struck the early Earth and that the Moon condensed out of the resulting debris. The account explains the Moon's unusually small iron core well. It also predicts that lunar material should be isotopically distinguishable from Earth's, since the impactor would have formed elsewhere in the solar system. It is not: in oxygen, titanium, and tungsten, the Apollo samples match Earth's mantle to within measurement error. Some researchers have since proposed a far more energetic collision, one that vaporised and thoroughly mixed both bodies. Whether an impact of that kind is dynamically plausible is not yet settled.
Which choice best describes the overall structure of the text?
In several firefly species, males flashing in a dense group fall into near-perfect unison, and the behavior has usually been explained as a mating adaptation: a synchronized signal, the reasoning goes, is easier for a female to locate than a scatter of competing flashes. Recent modeling work complicates that account. When researchers gave simulated males one local rule — flash shortly after you see a neighbor flash — group-wide synchrony emerged on its own, with no mating advantage written into the rule and no coordination among the insects. The simulations suggest that synchrony may be a consequence of crowding rather than a signal shaped by selection for it.
Which choice best states the main idea of the text?
TABLE. "Households with home internet access, four districts," in percent of households. District A: 41 in 2016, 62 in 2023. District B: 68 in 2016, 79 in 2023. District C: 22 in 2016, 51 in 2023. District D: 84 in 2016, 88 in 2023. TEXT. Reporting on the period, a regional authority stated that the distance between its least-connected district and its best-connected district had closed considerably. The figures bear this out: ______
Which choice most effectively uses data from the table to complete the text?
Before any teaching: which of these can stand alone as a complete sentence?
Removing a nineteenth-century overpaint from a fourteenth-century fresco is a problem of differential solubility: the solvent has to dissolve the upper layer faster than it dissolves the layer beneath. The conservators' first three formulations failed that test ______ the fourth lifted the overpaint cleanly and left the original surface untouched.
Which choice completes the text so that it conforms to the conventions of Standard English?
The Svalbard Global Seed Vault holds duplicate samples of crop seed sent from gene banks around the world, and it was cut a hundred metres or so into an Arctic mountainside partly so that the permafrost around it would keep the collection frozen even if the refrigeration and the power both failed. In the autumn of 2016 that permafrost thawed further than the design had allowed for: meltwater ran into the entrance tunnel, froze inside it, and staff arriving with new deposits found the corridor glazed shut. ______, the water reached no further than the tunnel; the storage chambers beyond it stayed dry, and no depositor was reported to have lost a sample.
Which choice completes the text with the most logical transition?
Before any teaching. The function f is defined by f(x) = 3x − 12. What is the value of f(−6)?
A field team has $1,480 budgeted for a season. A one-time research permit costs $250, and each day spent in the field costs $95 in supplies. What is the greatest number of whole days the team can spend in the field without exceeding the budget?
The function f is defined by f(x) = 3x² + 24x + 41. What is the minimum value of f(x)?
The function f is quadratic, and f(0) = 7, f(1) = 4, f(2) = 7, and f(3) = 16. What is the value of f(5)?
A stock opens a quarter at $48.00. During the first quarter its price increases by 25%, and during the second quarter the resulting price decreases by 16%. What is the price at the end of the second quarter?
A linear model was fitted to eight data points. Listed in order of increasing x, the residuals are 4.2, 1.8, −1.6, −2.8, −2.9, −1.5, 1.4, and 1.4.
Which conclusion about the model is best supported by these residuals?
A researcher selected 400 of the 6,200 employees at a large manufacturing firm at random and recorded, for each, the number of hours of sleep the employee reported getting on a typical night and the employee's score on a standard reaction-time test. Employees who reported more sleep tended to have faster reaction times.
Which of the following is the most appropriate conclusion based on this study?
TABLE. "Coffee and pastry purchases across 600 transactions at a café." Transactions that included coffee: 96 also included a pastry, 384 did not, row total 480. Transactions that did not include coffee: 24 included a pastry, 96 did not, row total 120. Column totals: 120 transactions included a pastry, 480 did not. Grand total 600.
Which of the following statements is best supported by the table?
In triangle ABC, AB = AC and angle BAC measures 110°. Point D lies on segment BC, between B and C, such that AD = BD. What is the measure, in degrees, of angle DAC?
A circle in the xy-plane has its center at (−2, 5) and is tangent to the line y = 1. Which equation defines this circle?
Every morning for eleven years Adaeze had unlocked the shop at six and set the kettle on before the lights. She knew which floorboard complained, which drawer stuck in August, the exact weight of the door in a crosswind. When the letter came saying the building had been sold, she read it twice, folded it into quarters, and put it in the drawer that stuck. Then she filled the kettle. At a quarter past six a customer asked whether she had heard anything about the sale, and she said that she had not.
Which choice best states the main purpose of the text?
To keep their eggs at a constant temperature, mound-building megapodes — birds of Australia and the Pacific — do not sit on them. Instead the male rakes together a heap of leaf litter and sand, buries the clutch inside, and then spends months tending the mound, adding material when the decomposing litter cools and opening vents when it grows too warm. He checks the temperature by pushing his bill deep into the heap.
According to the text, how does a male megapode determine whether his mound needs adjusting?
FIGURE. Bar graph, "Nesting pairs of piping plover at four monitored beaches, 2014 and 2024." The vertical axis is marked at intervals of 20 pairs, and no bar carries a printed value. Site 1: the 2014 bar rises just past the 120 mark, the 2024 bar stops just short of 60. Site 2: 2014 just past 40, 2024 just past 100. Site 3: the two bars stand level with each other, a little below 180. Site 4: 2014 just short of 100, 2024 just past 20. TEXT. Sites 1 and 4 were opened to off-road vehicle traffic in 2016; Sites 2 and 3 remained closed to it throughout. A monitoring biologist notes that the counts are consistent with — though on their own they cannot demonstrate — a harmful effect of vehicle access: ______
Which choice most effectively uses data from the figure to complete the text?
Both halves of the following are complete sentences on their own: "The vaccine trial met its primary endpoint" and "the results have not yet been published." Which joining is acceptable in Standard English?
The two vineyards sit less than forty kilometres apart, but one faces south and the other north, and the difference shows up in the harvest data every year without exception. The sugar concentration in the fruit picked on the south-facing slope routinely exceeds ______ by nearly two degrees Brix.
Which choice completes the text so that it conforms to the conventions of Standard English?
NOTES. While researching a topic, a student has taken the following notes: • Old Italian violins, and Stradivari's above all, have long been held to sound better than anything made since. • In a double-blind trial, ten professional soloists each played six old Italian violins, several of them by Stradivari, and six recently made instruments. • The players wore darkened goggles, and the instruments were prepared so that neither smell nor the look of the varnish could give an age away. • Each soloist played the instruments in a rehearsal room and again in a concert hall. • The violin chosen most often as a player's preferred instrument was one of the new ones; the violin chosen least often was old. • Asked after playing whether an instrument was old or new, the soloists were right about as often as chance would predict. • The researchers took the results to show that whatever advantage old Italian violins are believed to hold is not one players can detect when the instrument's age is hidden from them. • The trial measured what players preferred, not what an audience at a distance hears.
The student wants to state the conclusion the researchers drew from the trial. Which choice most effectively uses relevant information from the notes to accomplish this goal?
The function C(m) = 0.12m + 35 gives the monthly cost, in dollars, of a phone plan that includes m minutes of international calling. What is the best interpretation of 35 in this context?
Which of the following points (x, y) is a solution to the system of inequalities 2x + 3y ≤ 12 and y > 2x − 5?
(2x + 5)(3x − k) = 6x² − x − 40 for all values of x, where k is a constant. What is the value of k?
The expression (9 − x²)/(x² − x − 6) is equivalent to which of the following for all values of x for which both expressions are defined?
A store applies a 15% discount to a bicycle's list price, and a 6% sales tax is then charged on the discounted price. The customer pays $270.30. What was the list price?
TABLE. "Commuting method by age, 200 employees at one firm." Employees who drive: 45 are under 40, 105 are 40 or older, row total 150. Employees who take public transit: 30 are under 40, 20 are 40 or older, row total 50. Column totals: 75 employees are under 40, 125 are 40 or older. Grand total: 200.
Before any teaching. One of the 200 employees is selected at random from those who take public transit. What is the probability that the selected employee is under 40?
A university researcher recruited 250 participants from among students who responded to a poster advertising a study on memory. Each participant was randomly assigned either to a group that studied a word list in 20-minute blocks spread over four days or to a group that studied the same list for 80 minutes in a single session. On a test administered one week later, the group that studied in spread-out blocks recalled significantly more words on average.
Which of the following is the most appropriate conclusion based on this study?
The seven recorded values 12, 14, 15, 15, 16, 18, 60 include one entry, 60, that is later found to be a data-entry error and is deleted. Which of the following describes the effect of the deletion on the mean, the median, and the standard deviation of the data set?
Before any teaching: triangle A and triangle B are both right triangles, and each contains an angle measuring 35°. Every side of triangle B is exactly four times the length of the corresponding side of triangle A. How do the two values of sin(35°) compare?
In triangle ABC, AB = AC and angle BAC measures 40°. The bisector of angle ABC intersects side AC at point D. What is the measure, in degrees, of angle BDC?
A frequently cited study reported that shoppers bought more fresh produce when a supermarket played slower background music, and the result was absorbed quickly into popular writing about ambient influence on behaviour. A later analysis raised a structural objection: in the stores studied, the slower playlists ran mainly on weekday mornings, when the customers present skewed older and were shopping for groceries rather than browsing. Once time of day is modelled, much of the original difference shrinks. The study's authors have granted the scheduling point while maintaining that a residual effect survives it. What is genuinely in dispute, then, is not whether tempo matters at all, but how much of the difference is left once the artefact is removed.
Which choice best describes the function of the sentence "The study's authors have granted the scheduling point while maintaining that a residual effect survives it." in the text as a whole?
Roman harbor concrete has survived two millennia of seawater, and materials scientists have offered several explanations for its durability. One long-standing account credits the volcanic ash in the Roman mix, which reacts with seawater to form interlocking mineral crystals. A more recent analysis focuses instead on the small white lumps of lime scattered through the material, long dismissed as evidence of careless mixing. Because these lumps dissolve when water reaches them, they can flood a fresh crack with calcium and seal it. On this account the lumps are not a defect but the mechanism by which Roman concrete repairs itself.
According to the text, what function do the white lime lumps serve in Roman concrete?
In a recent overwintering trial, every hive that was fed the experimental supplement survived the winter. Hive 12, one of the hives in the trial, did not survive the winter.
Before any teaching: which statement must be true if both sentences are true?
A colon is being used to introduce a list. What has to be true of the words that come BEFORE the colon?
The 1996 core is still the most cited in the field and also the one nobody can check: the drill site was lost to a surface collapse the following winter. Researchers who have spent years reconciling its anomalies against later cores now mostly agree that if the meltwater layer ______ logged correctly at the time, the two decades of argument that followed would have been unnecessary.
Which choice completes the text so that it conforms to the conventions of Standard English?
NOTES. While researching a topic, a student has taken the following notes: • A tide gauge measures the height of the sea against a benchmark fixed to the coast, so what it records is sea level relative to the land the gauge is bolted to. • A handful of European ports hold continuous tide-gauge records beginning in the early nineteenth century. • Satellite altimeters have flown since 1992; they measure the height of the sea surface relative to the centre of the Earth. • Altimeter coverage stops short of the highest latitudes, roughly beyond 66 degrees north and south. • Land itself rises and falls — rebounding where ice sheets have gone, subsiding where groundwater is pumped out — so a gauge's record has to be corrected using satellite positioning of the gauge itself. • Altimeters drift as their instruments age, and their measurements are checked against the network of tide gauges.
The student wants to contrast what each instrument measures sea level relative to and to note that each one depends on the other kind of measurement. Which choice most effectively uses relevant information from the notes to accomplish this goal?
A drone begins a flight at an altitude of 120 meters and descends at a constant rate of 15 meters every 30 seconds. Which function gives the drone's altitude a, in meters, t minutes after the descent begins?
A caterer buys small trays, which cost $18 each and serve 8 people, and large trays, which cost $30 each and serve 15 people. The caterer must serve at least 120 people and can spend no more than $260 in total. If s is the number of small trays and t is the number of large trays, which system of inequalities represents these constraints?
The expression (6x² + 5x − 1)/(2x − 1) is equivalent to 3x + 4 + A/(2x − 1) for all x ≠ 1/2, where A is a constant. What is the value of A?
What is the sum of all solutions to the equation x − 7√x + 10 = 0?
In a laboratory, the mass of sample B is 60% less than the mass of sample A. The mass of sample B is 480 grams. What is the mass, in grams, of sample A?
Which wording in a probability question tells you the denominator is one row or one column of the table rather than the grand total?
To estimate the proportion of the 40,000 residents of a city who support a proposed transit levy, a newspaper posted the question on its website and invited readers to respond. Of the 9,400 people who responded, 71% expressed support. An analyst argued that because the sample was so large — nearly a quarter of the city's population — the result can be treated as a reliable estimate of city-wide support.
Which of the following best identifies the flaw, if any, in the analyst's reasoning?
Two reservoirs each hold 4,000 megaliters of water at the start of a drought, at time t = 0, where t is measured in years. A model predicts that reservoir P loses 12% of its remaining volume each year, while reservoir Q loses 400 megaliters each year.
According to these models, what is the smallest whole-number value of t at which reservoir P holds more water than reservoir Q?
Let x° be the measure of one acute angle of a right triangle. Which statement is true for every such x?
A conical paper cup is held with its point downward. Filled to the brim, it holds 240 milliliters. Water is poured in until the depth of the water is exactly half the height of the cup. How many milliliters of water are in the cup?
Before any teaching. A question asks how the author of Text 2 would most likely respond to a claim made in Text 1. Which constraint must the credited answer satisfy?
The following text is from a Meridian-original short story set in 1890s Massachusetts, in which Ellen, a schoolteacher, has been left a house by an aunt she scarcely knew. "Ellen had expected to feel something at the door — grief, perhaps, or the small greed of ownership — and felt instead only the draught coming under it. She went through the rooms opening shutters. In the back parlor she found the aunt's account books, forty years of them, ruled in a hand so even it might have been printed, and she stood turning the pages for an hour without once thinking of the house, or the money, or what she would do with either. Somewhere in the third volume she stopped noticing that the woman in the columns was a stranger."
Which choice best states the main idea of the text?
A passage reports a research finding and then stops mid-sentence: "However, ______". Two choices are left standing, and both are consistent with the passage: (i) a sweeping claim that the finding overturns the field's long-standing consensus, and (ii) a narrow claim that the finding does not by itself identify the mechanism involved. Which is more likely to be the keyed answer, and on what grounds?
Coral reefs cover well under one percent of the ocean floor ______ provide habitat for roughly a quarter of all known marine species.
Which choice completes the text so that it conforms to the conventions of Standard English?
The 1815 eruption of Tambora put enough sulphate aerosol into the stratosphere to depress mean global temperature measurably for the next three years ______ producing the failed harvests that made 1816 the year without a summer across much of the northern hemisphere.
Which choice completes the text so that it conforms to the conventions of Standard English?
A wall of stone or rammed earth takes hours to warm through and hours more to give the heat back, and where the air swings widely between afternoon and dawn that lag is worth building for: the wall soaks up the day's heat before it can reach the room, then releases it after dark, when the outside air has turned cold and the room wants it. ______, in a climate whose nights stay nearly as warm as its days, the same lag is a liability, since the wall never meets air cool enough to discharge into and hands its stored heat back to a room that has no relief coming.
Which choice completes the text with the most logical transition?
The function f is linear. It is known that f(1) = 9, f(4) = 21, and f(7) = 33. What is the value of f(0)?
The inequality 4x − 2y > 10 is graphed in the xy-plane. Which statement correctly describes that graph?
Which expression is equivalent to (a⁻²b³)⁻³ / (a⁴b⁻²)², where a and b are positive?
The function f is defined by f(x) = −2x² + 20x − 42. Which of the following equivalent forms of f displays the maximum value of f as a constant or coefficient?
Of the 250 people who responded to a survey, 40% were students and the rest were not. Of the students, 65% reported using public transit daily; of the non-students, 30% reported using public transit daily. What percent of all 250 respondents reported using public transit daily?
At a school, 90% of the students who play a varsity sport also take a music course. Does it follow that 90% of the students who take a music course also play a varsity sport?
A county health office wants to estimate the proportion of adults living in the county who have received a particular vaccine. It selects 500 names at random from the county's list of registered voters and successfully contacts all 500. Of those contacted, 62% report having received the vaccine.
Which of the following is the most appropriate conclusion based on this study?
A firm has 8,000 employees. Five hundred of them were selected at random, and each of those 500 was randomly assigned to one of two schedules for eight weeks: a workday containing two 15-minute walking breaks, or a workday with no scheduled breaks. Employees on the walking-break schedule reported significantly lower stress scores at the end of the study. The firm's newsletter reported: "Walking breaks reduce stress — and four 15-minute breaks a day would reduce it twice as much."
Which of the following best evaluates the newsletter's report?
In right triangle ABC, the right angle is at C, the length of AB is 25, and the length of BC is 7. What is the value of cos A?
In the xy-plane, a circle is defined by (x − 6)² + (y + 8)² = 25. A line through the origin is tangent to this circle at point T. What is the distance from the origin to T?
Text 1 reports that patients' symptoms improved during a trial of a new drug and concludes that the drug works. Text 2 says, in full: "The improvement is real. But the trial had no placebo group, and patients who expect relief reliably report it." What is Text 2 doing to Text 1?
Although self-report surveys remain the standard instrument for measuring how much people sleep, they disagree systematically with wrist-worn accelerometers: across large samples, adults report roughly forty minutes more sleep per night than the devices record. The gap is not evenly distributed. It is widest among short sleepers, who overreport most, and narrows among those who sleep long hours. Because much of the epidemiological literature linking short sleep to poor health rests on self-report, an error concentrated precisely among short sleepers is not a minor measurement problem — it may inflate the apparent size of the very association that literature is built on.
Which choice best states the main idea of the text?
Between 2005 and 2020, the proportion of the city's commuters who cycled to work rose from 4 percent to 11 percent. Over the same period, the city's population fell by roughly a third.
Which statement is guaranteed by the text?
By the end of the two-year survey, the three species the team had confirmed still breeding in the valley were ______ the Iberian lynx, the black stork, and the Spanish imperial eagle.
Which choice completes the text so that it conforms to the conventions of Standard English?
Before any teaching. Consider this pair: “Solar panels installed in desert regions generate more power per unit area than those in temperate ones. ______, dust settling on their surfaces can cut output by a quarter within weeks, and washing them consumes water the region does not have.” Before you see a single word choice — what relationship does the blank have to name?
When the Washington Monument was capped in 1884, the little pyramid set at its point was cast in aluminium — a metal then dear enough that putting it where almost nobody could see it was itself the boast. The metal was never scarce; aluminium makes up something like a twelfth of the Earth's crust by weight. What had kept it expensive was not the supply of ore but one step in the chemistry, the separation of the metal from the oxide it is locked into, and that step changed within a decade of the monument's completion. ______, an electrolytic process worked out independently in France and the United States in 1886 displaced the chemical reduction methods that had preceded it and took the price of aluminium down by more than an order of magnitude, from a jeweller's material to the stuff of saucepans.
Which choice completes the text with the most logical transition?
A tank holds 4,500 liters of water. A pump removes water at a constant rate of 90 liters every 4 minutes. Which function gives the number of liters, w, remaining in the tank h hours after the pump starts, for values of h during which the tank still contains water?
In the xy-plane, the solution set of the system y ≤ −x + 9 and y ≤ 3x + 1 is a shaded region. Which of the following is the point of that region with the greatest y-coordinate?
Before any teaching: in the quadratic equation kx² + 12x + 9 = 0, where k is a nonzero constant, the equation has exactly one real solution. What is the value of k?
The equation 2x² + 12x + k = 0, where k is a constant, has no real solutions. Which of the following describes all possible values of k?
A city reports that 24% of its household waste was recycled in 2015 and that 30% was recycled in 2023. Which of the following correctly describes the change in the city's recycling rate from 2015 to 2023?
TABLE. "Fitness class attendance in one week, 400 community centre members." Members under 30: 72 attended, 48 did not, row total 120. Members 30 or over: 108 attended, 172 did not, row total 280. Column totals: 180 attended, 220 did not. Grand total 400.
Given that a randomly selected member is under 30, what is the probability that the member attended a fitness class that week?
A nutritionist wants to determine whether a new meal-replacement drink lowers resting heart rate in adults aged 40 to 60, and wants the result to apply to all adults aged 40 to 60 in her region. Which of the following study designs would allow both a cause-and-effect conclusion and a conclusion about that entire age group in the region?
A city contains 84,000 households. In a random sample of 600 of them, 27% own at least one bicycle, with an associated margin of error of 3 percentage points at the 95% confidence level. Which of the following best estimates the number of households in the city that own at least one bicycle, together with a plausible range for that number?
In right triangle ABC, the right angle is at C. If sin A = 0.6, what is the value of cos B?
A vertical flagpole stands on level ground. From a point on the ground the angle of elevation to the top of the pole is 60°. From a second point 20 feet farther from the base, on the same straight line, the angle of elevation to the top is 30°. What is the height of the flagpole, in feet?
A question asks what both authors would most likely agree about. Text 1 argues that a city's sharp drop in burglaries was caused by expanded street lighting. Text 2 argues the drop was caused by a simultaneous change in police deployment, and never mentions lighting at all. Which statement can be credited as shared?
For most of the twentieth century, the thousands of small clay tablets excavated from Bronze Age Aegean sites were treated as a disappointment. Deciphered in 1952, the script turned out to record not poetry or law but inventories: sheep counts, allocations of grain, lists of chariot wheels awaiting repair. Historians of literature moved on. Economic historians did not. Because the tablets were baked, and so preserved, only when the palaces holding them burned, each archive is a snapshot of a single administrative year — and read together, those snapshots have yielded a picture of centralized Bronze Age redistribution that no literary text could have supplied.
Which choice best states the main idea of the text?
Ferns reproduce by releasing spores, which must land somewhere moist in order to develop. Because spores are extremely light, wind can carry them hundreds of kilometres, and botanists have documented fern species establishing themselves on newly formed volcanic islands within a few decades of the islands' emergence. Seed plants, whose seeds are heavier and generally travel shorter distances from the parent plant, typically arrive later. Therefore, on a newly formed volcanic island, ______
Which choice most logically completes the text?
Hedy Lamarr ______ better known in her lifetime as a film actor than as an inventor ______ co-patented a frequency-hopping signalling system that anticipated later work on spread-spectrum radio.
Which choice completes the text so that it conforms to the conventions of Standard English?
Before any teaching. A passage states, in this order: (1) a city converted its bus fleet to electric power; (2) the city’s transit emissions fell by a third. Which connective correctly opens the second sentence, and on what grounds?
NOTES. While researching a topic, a student has taken the following notes: • A pilot project in Iceland injected carbon dioxide into basalt bedrock, dissolved in water rather than pumped down as a gas. • Basalt is rich in calcium, magnesium and iron; carbonated water reacting with it forms solid carbonate minerals. • Monitoring of the pilot reported that more than 95 percent of the injected carbon had turned to carbonate mineral within two years. • Earlier estimates for the mineralisation of injected carbon dioxide in other rock types had been measured in centuries. • Dissolving the gas first took roughly twenty-five tonnes of water for every tonne of carbon dioxide injected. • Basalt of a suitable kind is common on ocean floors and in a few volcanic regions, but does not lie under most of the places that emit carbon dioxide.
The student wants to emphasize how quickly the injected carbon dioxide turned to rock, while acknowledging the constraint that limits where the method can be used. Which choice most effectively uses relevant information from the notes to accomplish this goal?
The function P(t) = 1,850 − 27t models the number of nesting pairs of a seabird on an island t years after 1990, where 0 ≤ t ≤ 25. Which statement is the best interpretation of P(15) = 1,445 in this context?
The linear function g satisfies g(−2) = 17 and g(4) = −1. For what value of x does g(x) = 26?
Solving √(x + 7) = x − 5 by squaring both sides gives x + 7 = x² − 10x + 25, then x² − 11x + 18 = 0, then (x − 2)(x − 9) = 0, so x = 2 or x = 9. Which of these actually solves the original equation?
The function V(t) = 3,000(1.44)^t gives the value, in dollars, of an investment t years after it was made. Which of the following expressions is equivalent to 3,000(1.44)^t and displays, as its base, the factor by which the value grows every 6 months?
Before any teaching: the data set 4, 6, 7, 8, 9 is changed so that the 9 becomes 900. Every other value stays as it is. What happens to the mean and to the median?
TABLE. "Housing status by year of study, 900 university students." First-year students: 252 live on campus, 36 live off campus, 72 live with family, row total 360. Upper-year students: 216 live on campus, 252 live off campus, 72 live with family, row total 540. Column totals: 468 on campus, 288 off campus, 144 with family. Grand total 900.
One student is selected at random from those who do not live on campus. What is the probability that the selected student is a first-year student?
A researcher randomly selected 1,200 of the 45,000 undergraduates enrolled at a state university and randomly assigned each of them to one of two versions of the same online course: one version included a short quiz every week, and the other did not. All 1,200 completed the course and sat the same final examination, on which students in the weekly-quiz version scored 6 points higher on average.
Which of the following is the most appropriate conclusion based on this study?
Before any teaching. A right circular cylinder is enlarged so that its radius and its height are both 3 times as large as the original's. The volume of the enlarged cylinder is how many times the volume of the original?
In the equation sin(2x°) = cos((3x + 10)°), both 2x° and (3x + 10)° are the measures of acute angles. What is the value of x?
In triangle ABC, point D lies on side AB and point E lies on side AC so that segment DE is parallel to side BC. If AD : DB = 2 : 3, the area of quadrilateral DBCE is what fraction of the area of triangle ABC?
Text 1: In a widely cited study, the biologist Ana Reyes recorded New Caledonian crows bending lengths of wire into hooks to extract food from narrow tubes. Because none of the birds had ever watched another crow perform the behaviour, Reyes concluded that hook-making in this species is innate: the birds arrive with the design already specified, and experience merely supplies the occasion to express it. Text 2: Reyes's birds were not naive. All had spent months in enclosures furnished with pliable twigs, and juvenile crows in such settings handle flexible material constantly. A bird that has spent a season discovering what a twig does when it is bent has been trained — not by another crow, but by the material. What Reyes documented may well be a genuine capacity, but the absence of a demonstrator does not establish the absence of learning.
Based on the texts, how would the author of Text 2 most likely respond to Reyes's conclusion as it is described in Text 1?
Before any teaching. A novel is described this way: “The narrator’s fascination with the harbor comes not from its beauty but from its constant motion.”
Which quotation from the novel would most effectively illustrate that claim?
A first-century Roman agricultural manual advises farmers to plant vines on north-facing slopes, and historians of climate have sometimes cited the advice as evidence that first-century Italy was warmer than Italy is today: north-facing slopes receive less direct sun, which would be an advantage in a hotter climate. The same manual, however, recommends north-facing slopes for orchards in provinces whose climates it elsewhere describes as cooler than Italy's. The manual's siting advice therefore ______
Which choice most logically completes the text?
The long-standing claim that the eruption of Thera destroyed the Minoan palaces outright ______ has been steadily undercut by excavations showing undisturbed occupation layers above the ash.
Which choice completes the text so that it conforms to the conventions of Standard English?
Before any teaching. A sentence makes a general claim. The next sentence goes further in the same direction — a stronger version of the same claim, not a case drawn from it. Which connective is right, and why?
Shade is the cheapest cooling a city can buy. A street under a closed canopy runs a few degrees cooler on a summer afternoon than the same street stripped of its trees, and unlike an air conditioner, which cools a room by pushing its heat out into the street, a tree lowers the temperature on both sides of the wall. ______, the cooling arrives late: a sapling planted this year will shade almost nobody until the 2040s, and the heat that kills people is arriving now. But the objection cuts the other way too, since a city that declines to plant on those grounds will reach the 2040s with exactly the canopy it has today.
Which choice completes the text with the most logical transition?
The function E(t) = 15,400 + 260t models the enrollment at a university t years after 2010. According to this model, by how much does enrollment increase over any 5-year period?
Which of the following gives all values of x for which −3 ≤ 4 − 2x < 9?
In the xy-plane, the system y = x² + 4x + 7 and y = 2x + c has exactly one solution. What is the value of c?
For x > 0, the expression (√(x³) · ∛(x²)) / x is equivalent to which of the following?
Two classes of 20 students each sat the same test, and both classes had a mean score of 74. In class A nearly every score fell between 70 and 78. In class B many scores were near 50 and many were near 98. Which class has the larger standard deviation, and what is standard deviation actually measuring?
At a conference with 500 attendees, 60% are researchers and the rest are industry practitioners. Of the researchers, 40% attended the opening keynote; of the practitioners, 65% attended it. An attendee is selected at random from those who attended the keynote. What is the probability that the selected attendee is a researcher?
A data centre's backup generator burns diesel at a constant 8.4 liters per hour for every 100 kilowatts of load it is carrying. The generator is to run continuously at a load of 250 kilowatts for 3 days. Diesel is delivered only in sealed barrels holding 160 liters each. What is the smallest number of barrels that will hold enough diesel for the whole 3 days?
The Digital SAT gives you a reference sheet at the start of every Math module. Which of the following formulas is NOT printed on it, and therefore has to be known from memory?
In right triangle ABC, the right angle is at B, AB = 5, and BC = 12. Triangle DEF is similar to triangle ABC, where D, E, and F correspond to A, B, and C respectively. If DF = 39, what is the value of tan F?
A sector of a circle of radius 9 has a central angle of 2π/3 radians. What is the perimeter of the sector?
Text 1: The economist Marcus Delaney's analysis of 240 municipal transit expansions found that ridership rose an average of 18 percent in the three years after a new rail line opened. Delaney argues that a pattern this consistent supports a general rule: cities seeking to raise transit use should build rail. Text 2: Delaney's average conceals its own explanation. Of the 240 expansions, 61 occurred in cities that simultaneously raised downtown parking prices, and those 61 account for nearly all of the aggregate gain; across the remaining cities, ridership was essentially flat. Rail may still be worth building, but the evidence assembled here supports a considerably narrower claim than the one Delaney draws from it.
Based on the texts, how would the author of Text 2 most likely characterise Delaney's "general rule"?
A question asks: “Which finding, if true, would most strongly support the researchers’ hypothesis?” One of the four findings describes a result you think is unlikely to occur in the real world. What should be done with it?
In a recent survey of 1,200 households in a metropolitan area, 68 percent reported owning at least one motorcycle, up from 41 percent in a comparable survey conducted a decade earlier, which sampled 3,000 households. The researchers note that the earlier survey drew its sample from the entire metropolitan area, whereas the recent survey was restricted to households within five kilometres of a major arterial road. The comparison therefore ______
Which choice most logically completes the text?
The residency's inaugural cohort included Nadia Ferrante, a printmaker from Trieste ______ Owen Mbeki, a sculptor and muralist ______ and Halina Duda, a poet who later founded the city's first bilingual theatre.
Which choice completes the text so that it conforms to the conventions of Standard English?
Venice rests on millions of wooden piles driven into the soft mud of a lagoon. Through the middle of the twentieth century, factories on the nearby mainland pumped groundwater out of the aquifer beneath that mud, and as the water was withdrawn the sediment above it compacted. ______, the city sank by roughly twelve centimetres between 1930 and 1970 — a drop that, added to rising seas, put its lowest squares under water at ordinary high tides.
Which choice completes the text with the most logical transition?
NOTES. While researching a topic, a student has taken the following notes: • In 1989 researchers ploughed a patch of the deep seafloor in the southeast Pacific to imitate the disturbance that mining polymetallic nodules would cause. • The site was revisited several times, most recently in 2015. • The plough tracks were still sharply visible in 2015. • Animals that live fixed to the nodules — sponges, corals and the like — had not returned to the ploughed lanes, whose nodules had been buried or shifted aside. • Some mobile animals, certain sea cucumbers among them, were found inside the tracks in numbers not far below those outside them. • The nodules themselves accumulate at rates measured in millimetres per million years. • The experiment disturbed a single site in one ocean basin.
The student wants to make a generalization about the pace of recovery that the notes support. Which choice most effectively uses relevant information from the notes to accomplish this goal?
The function f is linear, f(−3) = 14, and f(5) = −10. What is the value of f(2)?
The system of equations 4x + 3y = 21 and −8x + ky = 12, where k is a constant, has a solution (x, y) in which y = 3. What is the value of k?
If (2x − 5)² = 49 and x < 0, what is the value of x?
The temperature of a cup of coffee, in degrees Fahrenheit, t minutes after it is poured is modeled by C(t) = 118(0.93)^t + 72. Which of the following is the best interpretation of 72 in this model?
A distribution of household incomes has a dense cluster between $30,000 and $70,000 and a thin tail stretching out to $3,000,000. Which measure of centre is larger, and why?
TABLE, partially filled. "Streaming subscription and broadband access, 800 households." Households that subscribe to a streaming service: 440 have broadband, the number without broadband is not shown, and the row total is not shown. Households that do not subscribe: the number with broadband is not shown, 90 do not have broadband, and the row total is not shown. Column totals: 600 households have broadband, the no-broadband total is not shown. Grand total: 800.
One household is selected at random from those that do not have broadband. What is the probability that the selected household subscribes to a streaming service?
TABLE OF RELATIVE FREQUENCIES. "Device used and whether a purchase was completed, across 2,500 sessions on a retail website. Each entry is the proportion of all 2,500 sessions." Mobile: purchase completed 0.18, no purchase 0.42. Desktop: purchase completed 0.16, no purchase 0.24. The four entries sum to 1.00.
One of the 2,500 sessions is selected at random from those in which a purchase was completed. What is the probability that the selected session was on a desktop?
A shipping container has a volume of 2 cubic feet. What is its volume in cubic inches? (1 foot = 12 inches.)
For an acute angle x, cos x = k and sin x = 3k, where k is a positive constant. What is the value of sin x?
In a right triangle, θ is an acute angle with tan θ = 5/12. What is the value of sin θ + cos θ?
Text 1: Critics have long read Charlotte Mew's late poems as records of private grief, taking the recurring image of the shuttered house as a figure for the poet's own withdrawal. On this account the poems' formal severity — the clipped lines, the endings that refuse to resolve — is symptomatic: the form registers a mind under pressure. Text 2: To treat Mew's shuttered house as autobiography is to mistake a device for a confession. The image appears first in poems written years before the losses it is said to encode, and it is given to speakers Mew takes evident pains to distinguish from herself. The clipped lines are worked, not involuntary; the manuscripts show the severity arriving late, in revision.
Based on the texts, both authors would most likely agree with which statement about Mew's late poems?
Researchers conclude that a desert shrub survives drought because its roots reach deeper water than its neighbors’ roots do. Which finding, if true, would most strongly undermine that conclusion?
Scholars of the Nahuatl-language annals of colonial Mexico have generally assumed that the annalists wrote for readers in their own communities, since the texts take detailed local knowledge for granted and rarely explain it. The historian Ana Delgado has proposed a further consequence: because the annalists expected their audience to know the events already, the details they chose to record indicate what those communities considered worth preserving rather than what a reader would need in order to follow the story. If Delgado's reasoning is sound, a passage in an annal that dwells at unusual length on a minor local official ______
Which choice most logically completes the text?
Formal peer review, as historians of science have documented ______ was not universal practice at the major journals until well into the twentieth century ______ editors had for decades relied largely on their own judgment and that of a few trusted correspondents.
Which choice completes the text so that it conforms to the conventions of Standard English?
When astronomers aimed the Hubble Space Telescope at an apparently empty patch of sky in 1995 and held the exposure for ten days, they expected a mostly dark frame. The image contained several thousand galaxies. ______, the field proved so crowded that what looked like gaps between those galaxies have, in deeper exposures since, turned out to hold galaxies of their own.
Which choice completes the text with the most logical transition?
Before any teaching. How many values of x satisfy 5(2x + 3) = 10x + 12?
The function f is defined by f(x) = 3x + 7, and the function g is defined by g(x) = f(x + 4). The graph of y = g(x) in the xy-plane has a y-intercept at (0, k). What is the value of k?
In the equation 3(2x − k) = 5x + 12, k is a constant. If the solution to the equation is x = −3, what is the value of k?
In the equation (x − 5)(x + 2) = 8, what is the positive solution for x?
What is the solution set of the equation x/(x − 3) + 2/(x + 1) = 12/(x² − 2x − 3)?
A school recorded the number of absences for each of 20 students over one term. The results: 0 absences, 4 students; 1 absence, 7 students; 2 absences, 5 students; 3 absences, 2 students; 4 absences, 1 student; 9 absences, 1 student.
What is the median number of absences for these 20 students?
TABLE. "Regional science fair results, 250 projects." Biology: 28 won an award, 62 did not, row total 90. Chemistry: 22 won an award, 38 did not, row total 60. Physics: 30 won an award, 70 did not, row total 100. Column totals: 80 projects won an award, 170 did not. Grand total 250.
One project is selected at random. What is the probability that the selected project is a biology project or won an award?
Between 2010 and 2024 the population of a region increased by 15% and the number of registered vehicles in the region increased by 38%. By what percent did the number of registered vehicles per person change over that period?
A right circular cylinder has a volume of 245π cubic inches and a height of 5 inches. What is the diameter of the cylinder's base, in inches?
In right triangle ABC, the right angle is at C, and sin A = cos A. If the length of AB is 8√2, what is the area of triangle ABC?
A rectangular box has a square base with an area of 36 square inches and a volume of 252 cubic inches. What is the length, in inches, of the longest straight rod that fits entirely inside the box?
Text 1: Between roughly 1300 and 1450, hundreds of villages across northern England were abandoned. The conventional explanation is plague: a settlement that lost half its inhabitants within a decade, the argument runs, fell below the number of households required to work the open fields, and the survivors had no choice but to leave. Text 2: Plague mortality by itself cannot have emptied a village, since abandonment frequently followed an outbreak by two full generations. What the outbreaks did was raise wages. With labour suddenly scarce, a tenant who stayed could bargain — and a tenant who left could bargain better still, in a town or on richer soil. The villages did not die of plague; they were dissolved by the opportunities plague created.
Based on the texts, how would the author of Text 2 most likely respond to "the conventional explanation" described in Text 1?
“The Long Field” is a 1958 novel by Adela Marchetti. In the novel, Ines returns to the farm where she grew up, now run by her brother, and finds that her detailed knowledge of the land makes her feel like a trespasser rather than an owner.
Which quotation from “The Long Field” most effectively illustrates the claim?
Between 1998 and 2018 the number of peer-reviewed papers retracted each year rose roughly tenfold, a trend often cited as evidence that research misconduct is worsening. Over the same two decades, however, the number of papers published annually also rose substantially, and the share of journals with a formal retraction policy went from under 10 percent to more than 60 percent. A researcher who wanted to argue from these figures that misconduct itself has become more common would therefore need to show that ______
Which choice most logically completes the text?
Before any teaching: "The collection of rare seventeenth-century maps donated by the historian ______ housed in the library's east wing." Which single word decides whether the missing verb is singular or plural?
The 1972 Anti-Ballistic Missile Treaty is often described as a disarmament agreement, though it removed no weapons from either arsenal. What it limited was defence: each signatory agreed to leave most of its own territory unprotected against the other’s missiles. Its architects reasoned that a state confident of surviving a nuclear exchange would be likelier to begin one, so that mutual vulnerability was the more stable arrangement. ______, they argued that any defensive system would simply provoke the other side into building more warheads, since saturating a shield costs far less than building one.
Which choice completes the text with the most logical transition?
For which value of a does the equation ax + 9 = 6x + 9 have no solution?
Before any teaching. How many ordered pairs (x, y) satisfy both equations of this system at once? 3x + 6y = 12 and x + 2y = 9
The function f is linear. If f(4) = 3·f(0) and f(2) = 20, what is the value of f(0)?
What is the complete solution set of the equation √(x + 11) = x − 1?
Before any teaching. A pipeline carries 3,600 gallons per hour, and you want that figure in gallons per minute. You are going to multiply by a fraction built from "1 hour = 60 minutes." Which fraction, and why?
Each of the 30 values in a data set is increased by exactly 4. Which of the following statistics has the same value after the change as it had before?
A bookstore recorded 720 customer visits in one week. The probability that a randomly selected visit involved a loyalty card is 5/12. Given that a visit involved a loyalty card, the probability that a discounted title was bought is 3/5. Among the visits that did not involve a loyalty card, 84 included the purchase of a discounted title. How many of the 720 visits included the purchase of a discounted title?
Class A has 12 students and their mean score on a test is 92. Class B has 18 students. When the two classes are combined, the mean score of all 30 students is 86. What is the mean score of class B?
A cube-shaped shipping crate is redesigned so that each edge is 20% longer than the corresponding edge of the original crate. The volume of the redesigned crate is what percent greater than the volume of the original crate?
An observation deck sits 120 feet above sea level. From the deck, the angle of depression to a boat on the water is 30°. What is the horizontal distance, in feet, from the base of the deck to the boat?