All practice questions

The following passage is adapted from an essay on twentieth-century linguistics and the decipherment of ancient Aegean scripts.

In the history of epigraphy, few intellectual achievements rival the decipherment of Linear B, the Bronze Age administrative script discovered at Knossos and mainland Mycenaean sites in the early 1900s. While history often accords primary fame to Michael Ventris—the British architect who announced the script's decipherment in 1952—modern scholars increasingly recognize the foundational groundwork laid by Dr. Alice Kober, a professor of classics at Brooklyn College. Working throughout the 1940s until her untimely death in 1950, Kober engaged in an extraordinarily rigorous, empirical investigation of the undeciphered tablets at a time when digital data processing was virtually nonexistent.

To manage the vast array of character combinations without pre-existing bilingual glosses (such as the Rosetta Stone), Kober constructed an intricate, physical database. Over more than a decade, she accumulated approximately 180,000 individual index cards, onto which she meticulously transcribed character groups, contextual occurrences, and grammatical inflections. Because paper was scarce and strictly rationed during the height of the Second World War, Kober could not purchase standard academic index cards in bulk. Instead, she salvaged discarded tobacco boxes, cereal cartons, and promotional book flyers, cutting them by hand using scissors into small, uniform slips. Her colleagues at the college frequently gathered paper scraps from campus waste receptacles to support her labor-intensive filing system.

Kober’s manual database allowed her to identify systematic patterns of inflectional endings without making speculative assumptions about the phonetic values of the symbols. By analyzing how symbol clusters shifted across different contextual positions, she established that Linear B was an inflected language featuring distinct grammatical cases and gender declensions. She organized these relationships into what she termed "triplets"—grids that grouped related root signs with varying suffix signs. Crucially, Kober developed this structural framework while maintaining strict neutrality regarding the underlying language spoken by the scribes, resisting the temptation of her contemporaries to force the script into a Hellenic, Etruscan, or Semitic paradigm.

Following Kober’s death, her extensive grid system and cardboard slip archive were preserved. When Ventris renewed his analysis in the early 1950s, he relied heavily on Kober’s published grids and her physical index cards, which provided the structural foundation that eventually enabled him to confirm that Linear B encoded an early form of Greek. Kober’s meticulous physical catalog remains a testament to empirical rigor, demonstrating how systematic manual analysis paved the way for one of the greatest linguistic breakthroughs of the modern era.

Based on the passage, from what source did Alice Kober primarily obtain the paper material used to construct her index card database?

The following passage is adapted from an essay on nineteenth-century geological science:

For much of the early nineteenth century, European geologists accounted for "erratics"—gigantic, isolated boulders deposited far from their parent rock formations—by appealing to catastrophic marine deluges. This prevailing deluge hypothesis offered a satisfying synthesis for scholars of the era: it reconciled traditional narratives with observable landscape features while requiring no radical reevaluation of Earth's climate history. Consequently, when Swiss naturalist Louis Agassiz presented his alternative theory of continental glaciation in 1837, proposing that massive ice sheets had once carpeted Europe, the initial reaction from the scientific establishment was sharp disdain. Dominant figures of the era argued that moving ice across hundreds of miles of flat terrain violated known physical laws, treating Agassiz's proposal as an eccentric detour from established principles.

In the 1840s, however, the discourse surrounding Agassiz's work underwent a marked shift. As Agassiz and his supporters amassed precise field measurements—cataloging parallel striations carved into granite bedrock and mapping the distinct arc-shaped moraines left by retreating glaciers—the scientific conversation moved away from ideological attacks on Agassiz's credibility. Scholars stopped arguing over whether continental ice was theoretically plausible and turned instead to investigating the precise mechanics of glacial motion and sediment deposition. Consequently, the debate evolved from a contentious dispute over competing origin narratives into a collaborative, empirical effort to map the extent of past glaciation.

Which of the following best describes the structural shift that occurs between the first paragraph and the second paragraph?

Based on the passage below, place the recorded milestones of Basil Brown's archaeological work at Sutton Hoo in the exact chronological order in which they occurred.

In May 1938, self-taught archaeologist Basil Brown arrived at the Sutton Hoo estate in Suffolk, England, commissioned by landowner Edith Pretty to investigate several mysterious earth mounds on her property. Brown initially focused his efforts on Mound 3, where he excavated damaged grave goods including an axe head and textile fragments. Satisfied with his preliminary survey there, he moved to Mound 2 in July 1938, where his trench work revealed scattered iron ship rivets and fragmented human remains, confirming the presence of disturbed early Anglo-Saxon burials.

Recognizing the potential significance of the site, formal support was arranged for a second digging season. On May 11, 1939, Brown returned to begin excavating the untried Mound 1. Within hours of opening the trench, he uncovered a row of corroded iron ship rivets still set in their original positions within the soil matrix. Realizing that the mound concealed an intact ship burial of exceptional size, Brown proceeded with meticulous care. By June 14, 1939, his careful removal of sand and earth fully exposed the eighty-nine-foot impression of a seventh-century wooden vessel, establishing Sutton Hoo as one of the most remarkable medieval archaeological discoveries in Europe.

Passage:
In the field of historical economics, scholars long asserted that the 18th-century Industrial Revolution in Britain was driven primarily by domestic technological innovations in steam power and textile production. Economic historian Dr. Aris Thorne, however, argues that global maritime trade networks and cheap colonial raw materials were the true indispensable catalysts. Critics of Thorne's perspective point out that Britain possessed abundant, low-cost domestic coal reserves, suggesting that internal resource availability—not external trade—was the primary driver of industrial mechanization. Thorne responds to this objection by demonstrating that domestic coal could only be extracted and transported cost-effectively after foreign-sourced timber secured mine shafts and colonial capital funded early transport infrastructure.

Based on the passage, which of the following best describes the function of the critics' argument regarding domestic coal reserves?

A delivery drone departs from a central launch pad and travels due north for $12$ miles, then turns and travels due east for $16$ miles to reach Drop Point P. A secondary relay station is located $18$ miles due south of the central launch pad. What is the straight-line distance, in miles, from Drop Point P to the secondary relay station?

Passage:
For decades, conservation biologists asserted that the primary driver of declining kelp forest ecosystems along the Pacific coast was elevated sea surface temperatures resulting from climate shifts. However, recent ecological studies have highlighted the profound impact of sea otter population dynamics on these marine environments. Proponents of the trophic cascade theory argue that sea otters, as keystone predators, regulate sea urchin populations, thereby preventing overgrazing of giant kelp. Skeptics of this ecological model point out that in certain northern coastal bays where otter populations remained robust, kelp beds still experienced severe seasonal die-offs, suggesting that thermal stress remains the decisive factor. Nevertheless, proponents clarify that these localized die-offs occurred exclusively during extreme marine heatwaves that temporarily inhibited kelp nutrient absorption regardless of urchin density. By addressing this apparent anomaly, researchers demonstrated that top-down predator control and bottom-up climatic factors interact rather than act as mutually exclusive forces.

Based on the passage, the author refers to the observation regarding kelp die-offs in bays with robust otter populations primarily in order to:

The following passage is adapted from an essay on the history of marine bioluminescence research.

In the early twentieth century, the biological mechanism behind coastal luminescent displays remained one of marine biology's most enigmatic puzzles. While ancient naturalists had documented the cold light emitted by sea organisms, formal biochemical investigation did not gain momentum until American physiologist E. Newton Harvey turned his focus to *Vargula hilgendorfii*, a small benthic ostracod abundant along the Japanese coastline.

In 1917, Harvey successfully extracted crude luciferin—the substrate responsible for light emission—from dried ostracod specimens that had been gathered in Japan and shipped to his Princeton laboratory. Working with these desiccated samples, Harvey demonstrated that the substrate retained its reactive capacity even after prolonged storage. However, determining the precise environmental parameters necessary for the reaction required subsequent experimentation. In 1928, by systematically eliminating atmospheric gases from his reaction chambers, Harvey proved conclusively that molecular oxygen was an indispensable catalyst when luciferin combined with its complementary enzyme, luciferase.

While Harvey illuminated the chemical prerequisites of the light-producing reaction, the cellular architecture supporting this chemical system in living organisms remained unmapped. That structural foundation was unveiled in 1948, when Japanese biologist Yata Haneda published detailed histological examinations of *Vargula hilgendorfii*. Haneda discovered that the ostracod possessed specialized submandibular glands containing anatomically separated cellular chambers, which prevented luciferin and luciferase from mixing prior to expulsion into seawater.

Building upon both Harvey's chemical foundation and Haneda's anatomical insights, organic chemist Osamu Shimomura sought to determine the exact molecular structure of the substrate. Previous attempts had been hindered by the extreme instability of purified luciferin when exposed to ambient light and air. In 1953, by developing a specialized low-temperature extraction protocol using organic solvents, Shimomura achieved the first successful crystallization of pure ostracod luciferin, finally allowing scientists to map its atomic composition.

Based on the explicit details provided in the passage, place the following scientific discoveries and milestones in the exact chronological order in which they occurred.

Passage:
In polar regions, glaciologists extract deep ice cores to reconstruct past atmospheric conditions. As snow accumulates and gradually compacts into glacial ice, tiny bubbles of atmospheric gas become trapped within the ice matrix. However, when drilling down past depths of roughly 600 meters, researchers encounter the brittle ice zone. At these depths, the immense hydrostatic pressure forces atmospheric gases to dissolve directly into the ice crystal structure, forming clathrate hydrates rather than distinct gas bubbles. Because these gas hydrates are stored under intense pressure, bringing ice cores to the surface causes the trapped gas to expand rapidly as external pressure drops. This rapid expansion creates micro-fractures in the core, making the ice extremely fragile and prone to shattering upon retrieval. To prevent core destruction, scientists must store freshly drilled brittle ice cores in relaxation chambers for up to a year, allowing the internal pressure within the crystal lattice to equalize before handling.

Based on the passage, what explicitly causes ice cores from the brittle ice zone to shatter upon retrieval at the surface?

A circular stained-glass window with a radius of $12\text{ inches}$ contains a sector, $OAB$, with a central angle measuring $120^\circ$. A straight piece of lead wire is placed along chord $\overline{AB}$, dividing sector $OAB$ into a triangular region $\triangle OAB$ and a circular segment bounded by chord $\overline{AB}$ and arc $\widehat{AB}$. What is the area, in square inches, of the circular segment?

If $\pi < \theta < \frac{3\pi}{2}$ and $\tan \theta = \frac{3}{4}$, what is the value of the expression $\frac{\sin^2 \theta}{1 + \cos \theta}$?

Read the following passage from a fictional memoir:

When I introduced the European predatory beetle to my apple orchards in 1928, I acted solely out of a noble desire to protect the valley’s agricultural heritage from the gypsy moth blight. While the county agricultural board urged restraint, claiming we ought to wait for official trial results, their bureaucratic delay threatened my seasonal yield. It is true that my immediate neighbors experienced a decline in their native ladybeetle populations shortly thereafter, but to attribute that to my beetles is mere coincidence; native insect populations naturally fluctuate. My orchard yielded a record harvest that autumn, proving the wisdom of my decisive intervention, even if a few overly cautious farmers remain bitter about their ruined honeybee hives.

Based on the passage above, match each excerpt from the narrator (left) with the underlying bias, motive, or evidence of unreliability it demonstrates (right).

If $\sin \theta - \cos \theta = 0.6$, what is the value of $\sin \theta \cos \theta$?

Read the passage below and match each paragraph (Left Items) with the primary structural focus or perspective shift it conveys (Right Items).

[Paragraph 1]
In the early decades of the twentieth century, sound archivists approached traditional folk music with a strictly preservationist ethos. Armed with bulky wax-cylinder recorders, researchers cataloged acoustic artifacts with the detached precision of museum curators arranging specimens behind glass. The music was treated as a static relic of a vanishing past, worthy of collection primarily because it was presumed to be on the verge of extinction.

[Paragraph 2]
By the mid-1950s, however, the arrival of portable magnetic tape devices fundamentally altered this academic posture. Rather than observing music as an isolated artifact, fieldworkers began to record live community performances over extended periods. This technological shift forced scholars to acknowledge that traditional music was not a frozen historical remnant, but an adaptive, evolving cultural practice shaped continuously by living performers.

[Paragraph 3]
Ultimately, this methodological evolution reshaped how institutions defined the boundary between collector and subject. Today, ethnomusicologists increasingly engage in collaborative documentation, recognizing that the act of recording is itself a dynamic exchange rather than an objective extraction of data.

In rectangle $ABCD$, the length of side $AB$ is $16$ centimeters and the length of side $BC$ is $12$ centimeters. Point $P$ lies on diagonal $AC$ such that segment $DP$ is perpendicular to $AC$. What is the length, in centimeters, of segment $DP$?

The following passage is adapted from an article on seventeenth-century natural history and scientific illustration:

In June 1699, the German-born naturalist and scientific illustrator Maria Sibylla Merian set sail from Amsterdam bound for Suriname in South America. Accompanied by her youngest daughter, Dorothea Maria, the fifty-two-year-old Merian funded the voyage independently by selling her own paintings and specimens. At a time when scientific expeditions were almost exclusively state-sponsored and led by men, Merian’s journey was unprecedented. Her primary objective was to observe and document tropical insects in their natural habitats, specifically focusing on the stages of insect metamorphosis. Prior to her work, many scholars still adhered to the ancient belief that insects spontaneously generated from decaying matter. Over the course of two years in Suriname, Merian collected, raised, and drew hundreds of insect species, producing intricate folio illustrations that documented their complete life cycles alongside the specific host plants upon which they fed.

Based on the passage, how did Maria Sibylla Merian finance her 1699 expedition to Suriname?

Passage:
In agricultural science, soil structure plays a vital role in determining crop yields. During periods of heavy, continuous rainfall, non-compacted clay soils absorb excessive moisture, filling the microscopic pore spaces between soil particles. When these pore spaces become completely saturated with water, oxygen is effectively displaced from the root zone. Deprived of oxygen, plant roots are unable to perform cellular respiration, a crucial biological process necessary for absorbing essential nutrient ions like potassium and nitrogen from the surrounding dirt. Consequently, plants growing in waterlogged fields exhibit severe stunting and leaf yellowing, not because the soil lacks mineral nutrients, but because root cell damage directly prevents nutrient uptake. To mitigate this issue, farmers often cultivate cover crops such as deep-rooting radishes during the off-season. As these taproots penetrate dense clay layers and decay, they create stable macro-channels. These channels dramatically increase soil drainage and aeration, thereby ensuring that oxygen remains available to crop roots even during torrential rainstorms.

Based on the passage, what explicitly causes plants in waterlogged soil to stop absorbing essential mineral nutrients?

Passage A
Urban tree canopies are frequently celebrated for aesthetic reasons, but their primary value in modern municipal planning lies in their measurable ecological functionality. As cities face intensifying urban heat island effects and extreme precipitation events, trees must be understood as critical gray-green infrastructure. High-resolution LiDAR mapping and microclimate sensors demonstrate that a mature canopy can reduce localized surface temperatures by up to twelve degrees Fahrenheit and intercept thousands of gallons of stormwater runoff per tree annually. To maximize these biophysical benefits, municipal forestry departments must shift from reactive maintenance to data-driven planting strategies that prioritize high-transpiration species and optimal spatial distribution. Romanticizing urban trees as decorative landscape features diminishes their role in climate adaptation. Without systematic canopy targets, clear performance metrics, and targeted investment in vulnerable, low-canopy neighborhoods, cities forfeit one of their most cost-effective tools for environmental mitigation. Urban forestry is not an exercise in beautification; it is a discipline of municipal engineering.

Passage B
While municipal planners increasingly quantify urban forests through the narrow lens of environmental engineering, such metrics risk obscuring the profound social and cultural dimensions of neighborhood canopies. Trees are not merely biological instruments for stormwater retention or temperature reduction; they are living anchors of community identity and collective memory. A neighborhood’s mature oak or elm canopy often reflects decades of local stewardship, offering psychological refuge, social gathering spaces, and a tangible connection to local history. When city agencies treat urban forestry purely as an optimization problem—prioritizing fast-growing species for maximum carbon capture or heat reduction—they frequently overlook how residents actually interact with their immediate natural surroundings. Technocratic canopy management plans imposed without community involvement often result in low survival rates for newly planted trees, as residents feel disconnected from unconsulted municipal interventions. To truly flourish, urban forestry initiatives must honor the human relationships embedded within neighborhood landscapes rather than reducing nature to a utilitarian utility.

Which choice best describes the difference in perspective between the author of Passage A and the author of Passage B regarding urban trees?

This passage is adapted from an essay on plant ecology and forestry science.

For much of the twentieth century, forest ecology was dominated by a strictly competitive paradigm. Rooted in classical evolutionary biology, this framework viewed individual trees as autonomous economic actors vying for limited environmental resources. In dense stands, species competed in a zero-sum game for sunlight, soil moisture, and essential minerals such as nitrogen and phosphorus. Under this reductionist model, a forest was understood primarily as an assemblage of isolated organisms, where the success of one tree inevitably came at the direct expense of its neighbors. Silvicultural practices reflected this assumption: forest managers routinely thinned canopies and suppressed understory vegetation to minimize competition and maximize timber yield for favored timber species.

Early laboratory studies reinforced this competitive doctrine. Researchers placed individual seedlings into isolated pots, measuring biomass production and nutrient absorption under controlled light and soil conditions. These experiments demonstrated that when two seedlings of differing species occupied the same container, the faster-growing plant predictably depleted available soil resources, stunting the growth of its neighbor. Data from such trials formed the empirical bedrock of mid-century forestry manuals. By isolating plants from their natural soil matrices, scientists observed robust evidence of competitive exclusion, concluding that subterranean interactions were characterized exclusively by conflict and resource hoarding.

However, this fiercely competitive paradigm began to fracture in the late 1990s with the advent of field-based radioisotope tracing. By injecting labeled carbon isotopes into the foliage of paper birch trees in natural forest plots, researchers traced the movement of sugars through the soil. To their astonishment, the radioactive carbon did not remain confined to the donor trees, nor did it leach indiscriminately into the dirt. Instead, significant quantities of carbon moved directly into neighboring Douglas fir seedlings. Microscopic examination revealed that this subterranean transport was mediated by extensive networks of mycorrhizal fungi—hyphal threads that physically linked the root systems of distinct trees into a shared physiological web. Rather than acting purely as isolated rivals, trees were actively shuttling metabolic resources across species barriers, particularly when one tree was shaded and in physiological distress.

This discovery prompted a fundamental reassessment of forest architecture and ecosystem resilience. The recognition of fungal-mediated resource sharing shifted the scholarly focus from individual survival strategies to complex communal dynamics. Modern ecological research now investigates how these subterranean networks regulate forest succession, buffer stands against environmental stress, and facilitate inter-generational nutrient transfer from mature "mother trees" to regenerating saplings. What was once viewed as a battlefield of solitary competitors is increasingly understood as an integrated, cooperative superorganism.

Which of the following best describes the structural shift in focus that occurs between the second paragraph and the third paragraph?

A triangular region $PQR$ has side lengths $PQ = 8$ meters and $QR = 10$ meters, and the measure of angle $\angle PQR$ is $120^\circ$. A straight walkway $QM$ is constructed from vertex $Q$ to a point $M$ on side $PR$ such that $QM$ bisects $\angle PQR$. What is the length, in meters, of the walkway $QM$?

Determine whether the following statement is true or false: In any trapezoid, the line segment connecting the midpoints of the non-parallel sides (the midsegment) is parallel to the bases and has a length equal to half the difference of the lengths of the bases.