Tüm alıştırma soruları

If $\theta = \arcsin\left(\frac{3}{5}\right)$, where $0 \leq \theta \leq \frac{\pi}{2}$, what is the value of $\tan(\theta)$?

If $\theta$ is an angle in Quadrant IV such that $\cos\theta = \frac{4}{5}$, what is the value of $\frac{\tan\theta + \sec\theta}{\csc\theta}$?

The following passage is adapted from an essay on mid-twentieth-century oceanography and cartography.

In 1952, geologist Marie Tharp was tasked with analyzing soundings collected by research vessels across the North Atlantic Ocean. Because women were prohibited from aboard research ships at Columbia University's Lamont Geological Observatory, Tharp relied entirely on continuous depth profiles recorded by echo sounders and transcribed onto paper rolls by her colleague Bruce Heezen. While plotting six east-to-west profiles across the ocean floor, Tharp identified a distinct V-shaped notch that descended nearly 10,000 feet below sea level at the center of a continuous undersea mountain chain. She hypothesized that this central depression was a rift valley—a continuous rift where the ocean floor was pulling apart. When she presented her finding to Heezen, he initially dismissed the rift valley hypothesis as 'girl talk,' attributing the V-shaped notch to measurement errors in the echo sounding instruments. It was not until 1953, when Heezen correlated the location of earthquake epicenters mapped by seismologist Maurice Ewing with Tharp's profile coordinates, that he recognized the earthquake epicenter points aligned precisely within the V-shaped valley. This alignment provided independent confirmation of Tharp's rift hypothesis, leading to the publication of their first physiographic map of the North Atlantic in 1957.

Based on the passage, what did Bruce Heezen initially believe caused the V-shaped notch identified on the ocean floor profiles?

Passage A
For decades, deep-sea oceanography relied on tethered instruments and remote sensors, leaving the vast abyss largely abstract to human perception. The advent of crewed submersibles altered this paradigm by placing human observers directly inside the benthic environment. There is an irreplaceable cognitive advantage to direct human sight and real-time sensory processing. A researcher gazing through a pressure hull can perceive subtle shifts in bioluminescence, micro-topography, and organismal behavior that video feeds invariably flatten. Human presence allows for spontaneous decision-making—shifting a dive plan instantly when an unpredicted hydrothermal structure appears. While robotic probes have expanded data collection metrics, reducing ocean exploration to automated data points strips marine biology of the serendipitous discoveries that only an observant human mind, experiencing the deep environment firsthand, can achieve.

Passage B
The argument that deep-ocean science requires human presence inside submersibles is increasingly anachronistic and financially inefficient. Modern Autonomous Underwater Vehicles (AUVs) and remotely operated robotics can remain submerged for weeks, sampling environmental DNA, mapping bathymetry with high-resolution sonar, and collecting delicate biological specimens with sub-millimeter precision. Crewed dives, by contrast, consume exorbitant budgets, risk human lives, and restrict operational time to mere hours due to oxygen and power constraints. Furthermore, human sensory observation is inherently subjective and prone to observational bias, whereas calibrated sensors generate standardized, reproducible datasets essential for modern ecological modeling. Oceanography must transition away from romanticized human expeditions and allocate its limited funding toward scalable, long-duration robotic fleets that yield far greater empirical value.

Which statement best describes the difference in perspective between the author of Passage A and the author of Passage B regarding human presence in deep-sea exploration?

Passage
For decades, urban centers of the ancient Indus Valley, such as Harappa and Mohenjo-daro, were characterized as strictly regimented societies dependent entirely on centralized, large-scale granaries for food distribution. However, recent micro-botanical analyses of starch grains and phytoliths retrieved from domestic hearths challenge this monolithic narrative. Archaeobotanist Dr. Elena Rostova identified diverse residues of millets, pulses, and local wild flora within modest residential structures. These findings suggest that urban households engaged in decentralized, opportunistic cultivation and gathering alongside state-administered grain supplies. Furthermore, isotopic analysis of cattle teeth found near residential quarters revealed localized grazing patterns rather than long-distance transhumance. Together, these lines of evidence indicate that Indus urban food systems were far more resilient and flexible than previously thought, relying on a hybrid economy of centralized infrastructure and localized, household-level subsistence strategies.

Which of the following details from the passage provides the most direct evidence supporting the claim that Indus urban food systems relied in part on localized, household-level subsistence strategies?

Passage A
The primary duty of the archaeologist and architectural conservator is the preservation of physical truth. When we encounter ancient ruins—whether a collapsed Roman amphitheater or a crumbling Maya temple—our intervention must be strictly limited to structural stabilization. The urge to rebuild, to fill in missing colonnades with reconstituted stone or to repaint faded frescoes, is fundamentally misleading. Every act of physical restoration introduces contemporary bias and aesthetic preference into an ancient artifact, permanently obscuring the distinction between original craftsmanship and modern conjecture. A ruin in its eroded state speaks honestly of the passage of time and the fragility of human endeavors. To reconstruct it fully is to commit an act of historical forgery, reducing an authentic witness of the past to a mere theme-park attraction designed for superficial consumption by casual tourists. Conservators must resist commercial pressure and honor the quiet integrity of historical decay.

Passage B
Standing before a scattered pile of weathered stones, few visitors possess the architectural training required to mentally visualize the magnificent proportions of an ancient civic space. While academic purists advocate for leaving ruins in romantic decay, this passive approach neglects the broader educational responsibility of archaeology. Modern preservation should not function merely as a museum of decay; it ought to serve as an act of vivid historical translation. By utilizing reversible assembly techniques, discreet steel scaffolding, and selective stone integration, conservationists can safely rebuild key architectural elements without harming original artifacts. Reconstruction renders abstract history tangible, allowing the public to experience the true scale, function, and cultural ambition of ancient societies. Far from desecrating history, responsible physical restoration bridges the cognitive gap between past and present, transforming static ruins into dynamic educational spaces.

Based on the passages, which statement best contrasts the perspective and tone of the author of Passage A with that of the author of Passage B regarding the restoration of ancient ruins?

The following passage is adapted from an article on desert ecology and bio-inspired engineering:

In the hyper-arid Namib Desert along the southwestern coast of Africa, annual rainfall is exceedingly rare. Yet, the Namib Desert beetle (*Stenocara gracilipes*) thrives by extracting moisture directly from morning ocean fogs. The key to this remarkable survival strategy lies in the micro-structure of the beetle's hardened forewings, or elytra.

The surface of the elytra features a microscopic array of smooth, hydrophilic (water-attracting) bumps interspersed throughout a wax-coated, hydrophobic (water-repelling) trough region. When fog rolls across the dunes, the beetle tilts its body upward into the wind—a behavior known as fog-basking. Droplets of airborne water accumulate on the hydrophilic peaks of the bumps. Because the surrounding troughs repel water, the droplets remain anchored to the peaks, growing progressively larger as more fog condenses. Once a droplet reaches a critical diameter of approximately five millimeters, its weight overcomes the electrostatic forces holding it to the peak. The droplet detaches and rolls down the hydrophobic trough directly into the beetle’s mouthparts.

Based on the passage, arrange the steps of the Namib Desert beetle's water-collection process in the exact chronological order in which they explicitly occur, from first to last.

The following passage is adapted from an essay on the history of architectural acoustics and auditorium design.

In 1895, Harvard University requested that physics assistant professor Wallace Clement Sabine address the dismal acoustic performance of the main lecture hall inside the newly constructed Fogg Art Museum. Sabine approached the issue empirically by measuring reverberation time—the time required for sound intensity to decay by sixty decibels from its initial level. Utilizing a set of organ pipes and a precise stopwatch, Sabine discovered that the hall’s long reverberation time was primarily caused by its hard, non-porous plaster walls and cushionless wooden seating, which absorbed less than three percent of incident sound energy. To quantify sound absorption, Sabine established a standard unit of acoustic absorption equivalent to one square meter of open window, later named the 'sabin.' He systematically brought varying lengths of cushions from the nearby Sanders Theatre into the Fogg lecture hall, discovering a linear relationship between total cushion length and the reduction of reverberation time.

When major architectural firm McKim, Mead & White was commissioned to design Boston Symphony Hall in 1899, they consulted Sabine to ensure superior acoustic properties before construction commenced. Rather than mimicking the traditional horseshoe shape of European opera houses, Sabine recommended a rectangular 'shoebox' layout modeled after the Gewandhaus in Leipzig. To further control sound reflection, Sabine specified that the side balconies be kept shallow to prevent acoustic shadows beneath the overhangs and directed that the walls be lined with heavy plaster rather than hollow wood paneling. Crucially, Sabine insisted on installing statues within niche recesses along the upper walls, asserting that these irregular surfaces would scatter high-frequency sound waves evenly throughout the hall without producing harsh echoes. When Boston Symphony Hall opened on October 15, 1900, acoustic testing confirmed a reverberation time of 1.9 seconds when fully occupied, matching Sabine's initial theoretical calculation within two-tenths of a second.

Based on the passage, evaluate the truth of the following statement:

Sabine recommended shallow side balconies for Boston Symphony Hall specifically to scatter high-frequency sound waves evenly throughout the hall without producing harsh echoes.

Read the following excerpt adapted from an essay on the development of architectural acoustics:

[Paragraph 1] For centuries, master masons constructed cathedral halls relying solely on traditional intuition, accepting long echoes and muddy reverberation as inevitable attributes of sacred grandeur. Builders prioritized visual majesty over sonic clarity, regarding sound as an ethereal phenomenon largely beyond physical measurement.

[Paragraph 2] In 1895, young physics professor Wallace Sabine was tasked with rectifying the notoriously muffled acoustics of Harvard University's newly constructed Fogg Lecture Hall. Approaching the room not as a static monument but as a dynamic laboratory, Sabine systematically moved seat cushions into the hall, measuring how incremental surface absorption reduced sound decay time.

[Paragraph 3] Through hundreds of late-night trials, Sabine derived a definitive formula linking room volume and material absorption to reverberation time, establishing architectural acoustics as a rigorous branch of applied physics. Nevertheless, contemporary designers note that strictly optimizing acoustic metrics can sometimes produce acoustically dry spaces that lack musical intimacy.

Based on the excerpt, match each structural transition in the text to the description of the shift in tone, focus, or perspective it represents.

The following passage is adapted from an essay on polar paleoclimatology and tephrochronology.

In the ice sheets of Antarctica and Greenland, layers of accumulated snow preserve an uninterrupted physical archive of Earth's atmospheric history spanning hundreds of thousands of years. While paleoclimatologists frequently measure stable isotope ratios of oxygen and hydrogen to reconstruct ancient temperatures, another subdiscipline—tephrochronology—focuses on microscopic layers of volcanic ash, known as tephra, embedded within the ice core strata. When a volcano erupts with sufficient explosive intensity, fine volcanic glass particles and ash are injected high into the stratosphere. Winds distribute these microscopic shards globally or regionally before they settle onto the ice sheet surface, becoming sealed beneath subsequent snowfalls.

In 1998, a research team analyzing the Siple Dome ice core in West Antarctica uncovered a distinct 0.5-millimeter tephra horizon situated at a depth of 620 meters. Initial visual inspection under optical microscopes identified glassy shards with a refractive index characteristic of highly silicic magma. To pinpoint the precise volcanic source, geochemists subjected individual glass shards to electron microprobe analysis, measuring concentrations of major elements including silicon, aluminum, iron, and sodium. The resulting chemical signature matched precisely with the eruptive products of Mount Tethys, a remote submarine volcanic complex in the South Sandwich Arc.

The identification of Mount Tethys tephra in the Siple Dome core served two critical functions for ice core chronology. First, because the eruption of Mount Tethys had previously been dated using argon-argon ($^{40}\text{Ar}/^{39}\text{Ar}$) radiometric techniques on terrestrial lava flows to $24,500 \pm 300$ years before present, the Siple Dome tephra horizon provided a definitive absolute chronological marker, known as an isochron. Prior to this discovery, glaciologists had relied primarily on annual layer counting, which becomes increasingly subject to cumulative uncertainty at depths exceeding 500 meters due to severe ice compaction and thinning.

Second, the geochemical profile revealed that despite being separated by over 2,200 kilometers of open ocean and ice sheet, atmospheric transport had conveyed the tephra plume south-southwest across the Ross Ice Shelf within a window estimated at less than seventy-two hours. This rapid atmospheric transport was deduced from the unblemished, angular geometry of the glass shards, which exhibited virtually no physical abrasion or micro-fracturing—features that would inevitably have developed had the particles undergone extended re-entrainment or saltation near the surface.

Based on the passage, evaluate the following statement:
Glaciologists found annual layer counting to be increasingly subject to cumulative uncertainty at ice core depths exceeding 500 meters because of severe ice compaction and thinning.

In any parallelogram $ABCD$, if consecutive angles $\angle A$ and $\angle B$ are supplementary, then quadrilateral $ABCD$ must be a rectangle.

In rectangle $ABCD$, the length of side $AD$ is $12$ units and the length of side $CD$ is $17$ units. Point $E$ lies on side $CD$ such that $\triangle ADE$ is an isosceles right triangle with the right angle at vertex $D$. What is the length, in units, of segment $BE$?

Match each transformed trigonometric function listed on the left with the correct description of its key graphical features listed on the right.

A decorative emblem is shaped as the region bounded by two concentric circular sectors sharing the same central angle of $\theta$ radians. The outer sector has radius $R\text{ cm}$, and the inner sector has radius $r\text{ cm}$, where the difference between the two radii is $R - r = 4\text{ cm}$. If the area of the emblem is $15\pi\text{ cm}^2$ and the length of the outer arc is $5\pi\text{ cm}$, what is the value of $\theta$, in radians?

In right triangle $PQR$, the right angle is at vertex $Q$. Point $S$ lies on side $QR$ such that line segment $PS$ bisects $\angle QPR$. If the length of $PQ$ is $14$ units and $\tan(\angle QPS) = \frac{3}{4}$, what is the length, in units, of side $PR$?

In rhombus $ABCD$, the measure of interior angle $\angle DAB$ is $120^\circ$, and the length of diagonal $AC$ is $12$ inches. What is the perimeter, in inches, of rhombus $ABCD$?

The following passage is adapted from an essay on deep-sea piezobiology and organismal adaptations.

In 2009, a deep-sea research expedition to the Mariana Trench's Challenger Deep retrieved specimens of the supergiant amphipod *Hirondellea gigas* from depths exceeding $10,000\text{ meters}$. Researchers analyzed the organism's exoskeletal armor and digestive physiology to understand how it survives under hydrostatic pressures exceeding $100\text{ megapascals}$.

Unlike shallower crustaceans whose exoskeletons rely predominantly on calcium carbonate—a compound that readily dissolves under extreme pressure and low temperature—*H. gigas* utilizes an extraordinary biomineralization strategy. Chemical analysis revealed that the amphipod's carapace contains an outer layer composed of amorphous aluminum hydroxide. The amphipods synthesize this protective coating by processing sediment-derived metal ions through an acidic gut environment, where ingested sediment containing aluminum debris reacts with endogenous organic acids before being secreted onto the epicuticle as a stabilizing gel.

Furthermore, enzymatic assays performed on the midgut secretions of *H. gigas* uncovered remarkable digestive versatility. To process detrital matter falling from the photic zone, the amphipod secretes high concentrations of cellobiase, amylase, and a specialized pressure-tolerant cellulase enzyme designated as Hg-Cel1. Crucially, laboratory assays demonstrated that Hg-Cel1 exhibits its maximum catalytic rate under a hydrostatic pressure of $80\text{ megapascals}$ at a baseline temperature of $2^\circ\text{C}$, making it one of the few known obligate piezophilic cellulases.

Osmolytes within the muscle tissue of *H. gigas* also showed distinct structural adaptations. While shallow marine invertebrates maintain intracellular osmotic balance using glycine and betaine, *H. gigas* exhibits elevated cellular concentrations of trimethylamine N-oxide (TMAO) alongside a secondary piezolyte, scyllo-inositol. Cellular assays indicated that scyllo-inositol acts synergistically with TMAO to stabilize lactate dehydrogenase against pressure-induced denaturation, preserving metabolic flux during rapid vertical locomotion along trench slopes.

Based on the passage, the specialized cellulase enzyme Hg-Cel1 achieves its maximum catalytic rate under which of the following specific conditions?

The vertical displacement, $d(t)$ in centimeters, of a particle executing simple harmonic motion is modeled by the trigonometric function $d(t) = A \sin(B(t - C)) + D$, where $A > 0$, $B > 0$, and $C$ represents the smallest non-negative phase shift in seconds. The graph of $d(t)$ completes one full cycle every $\frac{2\pi}{3}$ seconds, has a maximum value of $7\text{ cm}$ at $t = \frac{5\pi}{18}\text{ seconds}$, and has a minimum value of $-3\text{ cm}$. What is the value of $C$?

Read the passage excerpt below regarding the evolution of speleology:

[Paragraph 1] For decades in the mid-twentieth century, subterranean exploration was largely classified as a thrill-seeking outdoor pastime rather than a structured field of earth science. While early speleologists cataloged cavern topography with painstaking detail, academic institutions generally regarded cave mapping as a hobbyist endeavor lacking theoretical rigor or broader ecological application.

[Paragraph 2] This perception shifted radically in the late 1970s with the introduction of high-precision mass spectrometry to geological research. Geochemists realized that mineral layers within stalagmites preserved precise ratios of oxygen isotopes, effectively recording regional precipitation and temperature fluctuations over millennia. The underground environment was suddenly re-envisioned not as an empty void to be charted, but as an undisturbed vault of paleoclimate data.

[Paragraph 3] Present-day speleothem research now provides some of the most reliable continental climate records available to science, bridging critical temporal gaps left by ice cores and marine sediments. By correlating cave isotope data with global climate models, researchers can reconstruct historic droughts with unprecedented annual accuracy.

Match each paragraph block with the primary structural focus or perspective shift it conveys.

Read the following passage:

When I organized the private papers of the early twentieth-century botanical illustrator Dr. Evelyn Vance, I sought only to restore her rightful place in scientific history. Her contemporary, Dr. Arthur Sterling, had long been credited with identifying the rare *Sarracenia aurea* during the 1912 Rio Negro expedition. However, Dr. Vance's personal field journal contains detailed sketches dated three weeks prior to Sterling's published findings. Critics have noted that Dr. Vance's journal entries from that month were recorded on loose-leaf sheets rather than her bound ledger, suggesting they may have been inserted retroactively. Moreover, as Dr. Vance’s grand-nephew, I have studied her meticulous hand for decades and can attest to the authenticity of the ink and paper. Sterling’s supporters rely entirely on his published expedition log, convenient in its official stamp yet suspiciously silent regarding Dr. Vance’s presence on the trail. My archive presents the indisputable truth of her priority.

Which of the following details from the passage most directly indicates potential narrator bias regarding Dr. Vance's claim of priority?