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The Decipherment of the Rosetta Stone

In 1799, during Napoleon Bonaparte's Egyptian campaign, French soldiers uncovering the foundations of an addition to a fort near the port city of Rashid (Rosetta) unearthed a large, dark basalt slab. This slab, which would become known as the Rosetta Stone, bore inscriptions in three distinct scripts: Greek, Demotic (the everyday script of ancient Egypt), and hieroglyphs (the formal writing system used for sacred texts). Recognizing its potential historical value, the French scholars accompanying the military expedition documented the artifact. However, following the defeat of French forces in Egypt, the stone fell into British hands under the Treaty of Alexandria in 1801 and was subsequently shipped to the British Museum in London, where it has remained on public display since 1802.

The discovery of the stone sparked an intellectual race across Europe to decode the hieroglyphs, a language that had been dead for over a millennium. The Greek text on the stone, which was easily translated, revealed that the monument was a decree issued at Memphis in 196 BCE on behalf of King Ptolemy V Epiphanes. The decree established the divine cult of the young king and was written in three scripts so that priests, government officials, and common literate Egyptians alike could read it. Since the three inscriptions were assumed to share identical or nearly identical content, the Greek text served as the crucial key to unlocking the other two.

Early progress was made by the English polymath Thomas Young. In 1814, Young focused his attention on the Demotic script, identifying it as a cursive form of writing rather than a collection of purely symbolic drawings. He noticed that certain groups of Demotic characters closely resembled words in the Greek text. Young also turned his attention to the hieroglyphic text and made a vital breakthrough regarding cartouches—oval loops enclosing groups of hieroglyphs. He correctly deduced that these cartouches contained the phonetic spellings of royal names, such as Ptolemy. By matching the characters within the cartouches to the known Greek pronunciation of the king's name, Young identified several phonetic signs. However, he remained bound by the prevailing belief that hieroglyphs were primarily symbolic ideograms, using phonetic spelling only for foreign names that lacked direct symbolic representations in Egyptian culture.

It was the French scholar Jean-François Champollion who would ultimately fully decipher the system. Champollion, who had studied ancient languages since childhood and was fluent in Coptic—a descendant of the ancient Egyptian language written in the Greek alphabet—approached the task with a different hypothesis. In 1821, he began analyzing a newly discovered bilingual inscription on an obelisk from Philae, which featured cartouches for both Ptolemy and Cleopatra. By comparing the signs in these cartouches, Champollion identified shared characters representing the sounds for "p," "t," "o," and "l."

The decisive moment came in September 1822. Champollion received drawings of inscriptions from the temple of Abu Simbel, which predated the Greek and Roman periods of Egyptian history. Within these older cartouches, he recognized a glyph that represented the sun (which he knew from Coptic was pronounced "ra"). He followed this with a glyph that he recognized as "mes" (meaning "to give birth" in Coptic) and two instances of the letter "s" he had previously identified. Together, these spelled "Ramses," the name of a famous pharaoh from the nineteenth dynasty. Crucially, Ramses was a native Egyptian ruler, not a foreign Ptolemaic one. This proved that the phonetic system was not just an auxiliary tool used for spelling foreign names, but an intrinsic feature of the native Egyptian language itself. Champollion famously ran into his brother's office, shouted "Je tiens mon affaire!" ("I've got it!"), and collapsed from exhaustion.

Champollion’s breakthrough relied heavily on his mastery of Coptic. Unlike his contemporaries, who viewed Coptic as an unrelated tongue, Champollion understood that Coptic grammar and vocabulary preserved the phonetics and structure of the ancient Egyptian language. This linguistic bridge allowed him to read the ancient texts as spoken language, rather than treating them merely as visual cryptograms. By the time he published his landmark work, the Lettre à M. Dacier, in late 1822, Champollion had outlined a complete system of grammar and decipherment, demonstrating that Egyptian hieroglyphic writing was a complex mixture of figurative, symbolic, and phonetic signs all in the same text.

According to the passage, the British acquired possession of the Rosetta Stone as a direct result of which of the following?

In the standard $(x, y)$ coordinate plane, what is the $y$-intercept of the perpendicular bisector of the line segment with endpoints $(0, 1)$ and $(2, 5)$?

Is the statement that a convex quadrilateral with perpendicular and equal-length diagonals must be a square true or false?

An architect is designing a triangular roof truss, $\triangle ABC$, where side $AB$ is equal in length to side $AC$. The height of the truss, represented by the altitude from vertex $A$ to the base $BC$, is $12$ feet. If the measure of the base angle $\angle ABC$ is $30^\circ$, what is the length, in feet, of the base $BC$? (Round your answer to the nearest tenth.)

On a coordinate map of a state park, a straight hiking trail begins at a campsite located at $(2, -3)$ and ends at a lookout point. A hiker walks along the trail at a constant pace, and after $3$ hours, reaches a trail marker located at $(11, 9)$. What is the slope of the line on the coordinate map that represents this straight trail?

Passage

In $1964$, two radio astronomers, Arno Penzias and Robert Wilson, were conducting research at the Bell Telephone Laboratories in Holmdel, New Jersey. Their primary objective was to measure the intensity of radio waves emitted by the halo of our galaxy, the Milky Way. To accomplish this, they utilized a state-of-the-art instrument known as the Holmdel Horn Antenna. This massive, $20$-foot horn-shaped reflector had been constructed in $1959$ for NASA’s Project Echo, a satellite communication initiative, but it had recently become available for astronomical research. Because of its unique design, which shielded the receiver from thermal radiation emitted by the ground, it was exceptionally suited for detecting incredibly weak cosmic signals.

However, when Penzias and Wilson began calibrating the antenna, they encountered an unexpected obstacle. Regardless of where they pointed the horn, they detected a persistent, low-frequency static hum that was far stronger than expected. The noise was equivalent to a temperature of about $3.5$ Kelvin (approximately minus $270$ degrees Celsius). This background radiation did not change when they rotated the antenna, nor did it vary between day and night, or as the seasons shifted. The uniformity of the signal suggested that its source could not be localized within our galaxy, let alone within the solar system.

Determined to isolate the cause of this interference, the two scientists embarked on a rigorous process of elimination. They initially suspected that the noise was generated by human activity, specifically broadcasting from nearby New York City. However, pointing the antenna directly toward the metropolis yielded no increase in the static. They then investigated whether the signal was caused by radar systems, atmospheric testing, or even extraterrestrial broadcasts. Each of these hypotheses was systematically tested and rejected. They also examined the antenna's electrical components, checking for loose connections or faulty wiring, but found the system to be in perfect working order.

Upon closer physical inspection of the horn antenna, Penzias and Wilson discovered a more terrestrial source of potential interference: a pair of pigeons had taken up residence inside the narrow throat of the horn. The birds had built nests and coated the interior aluminum surfaces with a sticky layer of droppings, which Penzias later referred to as "white dielectric material." Believing that this debris was causing the unwanted electrical resistance, the scientists evicted the pigeons, captured them, and shipped them away. They then climbed inside the horn and meticulously scrubbed away the droppings. Despite these efforts, and the subsequent installation of a liquid-helium cooling system to reduce internal thermal noise, the mystery hum persisted, remaining just as strong and steady as before.

Unbeknownst to Penzias and Wilson, a team of theoretical physicists at nearby Princeton University, led by Robert Dicke, was searching for the very signal the Bell Labs astronomers were trying to eliminate. Dicke, along with his colleagues Jim Peebles and David Wilkinson, had hypothesized that if the universe had expanded from a hot, dense singularity—the Big Bang—there should be a faint, uniform leftover radiation permeating all of space. Over the course of nearly $14$ billion years, this radiation would have cooled and stretched into the microwave portion of the electromagnetic spectrum.

When Penzias contacted Dicke to discuss the anomalous hum, the connection was immediately made. Dicke famously turned to his colleagues and remarked, "Well, boys, we've been scooped." The Holmdel Horn Antenna had accidentally detected the cosmic microwave background (CMB) radiation, the ancient echo of the early universe. This landmark discovery, which occurred in $1964$ and was published in $1965$, provided the first concrete evidence supporting the Big Bang model over the competing Steady State theory. In recognition of their monumental contribution to astrophysics, Arno Penzias and Robert Wilson were awarded the Nobel Prize in Physics in $1978$.

According to the passage, the persistent hum that Penzias and Wilson detected disappeared completely after they cleaned the pigeon nests and droppings from the antenna.

The measures of the six interior angles of a convex hexagon are in the ratio $3:4:5:5:6:7$. What is the measure, in degrees, of the largest interior angle of this hexagon?

An isosceles trapezoid $ABCD$ has vertices $A(-4, -1)$, $B(6, -1)$, and $C(3, 3)$ in the standard $(x, y)$ coordinate plane. If the base $AB$ is parallel to the x-axis, which of the following represents the coordinates of vertex $D$?

The passage below is adapted from an essay on deep-sea exploration.

In the early months of 1977, a research expedition set out for the Galapagos Rift, an underwater volcanic ridge located in the eastern Pacific Ocean. Organized by Oregon State University, the Woods Hole Oceanographic Institution, and other research bodies, the expedition aimed to locate active hydrothermal activity. Geologists had hypothesized that seawater must circulate deep into the oceanic crust near mid-ocean ridges, where it would be heated by magma chambers below before venting back into the cold ocean depths. However, because no such vent had ever been directly observed, the expedition's primary goal was geological rather than biological. Indeed, none of the chief scientists on the expedition were biologists; they expected to find nothing more than warm water and bare rock.

Before deploying the three-person crewed submersible Alvin, scientists scanned the ocean floor using a heavily instrumented, unmanned sled named ANGUS (Acoustically Navigated Geological Undersea System). Towed by the surface research vessel Knorr, ANGUS was equipped with cameras and temperature sensors designed to detect the subtle thermal plumes expected from deep-sea hot springs. On February 15, 1977, ANGUS recorded a temperature anomaly of only 0.1 degrees Celsius above the ambient deep-sea temperature. Although tiny, this anomaly was accompanied by high-resolution photographs showing clusters of large, white clam shells littered across the basaltic rock, suggesting that something unusual was happening on the seafloor.

Two days later, on February 17, 1977, Alvin made its historic 713th dive. Inside the titanium pressure sphere were pilot Jack Donnelly and geologists John Corliss and John Edmond. Descending to a depth of 2,500 meters, they guided the submersible toward the coordinates flagged by ANGUS. When they reached the seafloor, they were astonished to find a vibrant oasis teeming with life, completely contrasting with the barren, desert-like expanse of the surrounding abyssal plains. Clustered around openings in the volcanic rock were dense populations of giant tube worms, crabs, and large white clams, some up to thirty centimeters in length.

Using Alvin’s mechanical arm, the scientists inserted a temperature probe directly into one of the fluid vents, which they named Clambake I. The probe registered a temperature of 17 degrees Celsius (approximately 63 degrees Fahrenheit). While this temperature seems modest, it was remarkably warm compared to the ambient bottom water, which hovered at a near-freezing 2 degrees Celsius.

Crucially, the venting water did not contain oxygen. Instead, it was highly enriched with toxic minerals, most notably hydrogen sulfide, a chemical compound that smells of rotten eggs. This chemical signature provided the key to solving the biological mystery of how such a dense community could survive in the absolute darkness of the deep ocean, where sunlight could not penetrate to fuel photosynthesis. Rather than relying on solar energy, these ecosystems were powered by chemosynthesis. Unseen, specialized bacteria oxidized the hydrogen sulfide to produce organic matter, establishing a food web independent of the Sun. Some of these bacteria lived symbiotically inside the tissues of the giant tube worms, which lacked both mouths and digestive tracts, relying entirely on their internal bacterial partners for nutrition.

The discovery at the Galapagos Rift fundamentally altered our understanding of life on Earth. It proved that complex ecological communities could thrive completely isolated from solar radiation, utilizing chemical energy from the planet's interior. This realization expanded the definition of habitable zones, not just on Earth, but potentially on icy moons and distant planets within our solar system and beyond.

Based on the passage, is the statement that the high-resolution photographs captured by the unmanned sled ANGUS on February 15, 1977, provided the first visual evidence of giant tube worms clustered on the seafloor true or false?

What is the period of the function $f(x) = \tan(3x)$?

Passage

In the shallow, murky waters of the Indo-Pacific, particularly off the coast of Sulawesi, Indonesia, lies a habitat that appears largely inhospitable and barren. The estuary floors are covered in dark, volcanic sand and silt, offering little to no structural cover such as coral reefs or rock formations. In this exposed environment, marine organisms are highly vulnerable to predators. It was here, in $1998$, that researchers first documented a creature that has since redefined our understanding of animal behavior and camouflage: *Thaumoctopus mimicus*, commonly known as the mimic octopus.

Unlike other cephalopods, which typically rely on static camouflage—matching the color, texture, and pattern of their immediate background to blend in—the mimic octopus employs a dynamic, active form of mimicry. It does not merely hide; it impersonates. Growing to a total length of approximately $60$ centimeters, including its long, slender arms, this small octopus is capable of mimicking the physical appearance and movement profiles of at least fifteen different local marine species.

Among its most frequent impersonations is that of the flatfish, specifically sole. To achieve this, the octopus draws all of its arms together, flattens its body into a leaf-like shape, and undulatingly glides just above the sandy bottom, replicating the precise swimming motion of the flatfish. This behavior is particularly effective because sole are toxic or unpalatable to many predators. Alternatively, when threatened by damselfish or other territorial reef fish, the mimic octopus will enter a crevice and expose only two of its arms. It flares these arms in opposite directions, displaying the alternating black and white bands along their length. To an observer, and crucial to the attacking fish, these arms bear an uncanny resemblance to the venomous banded sea snake, a primary predator of damselfish.

Another common disguise is the lionfish. The octopus achieves this by swimming near the surface or mid-water while splaying its arms in all directions. The arms mimic the long, venomous spines of the lionfish, warning potential predators to keep their distance. Researchers have also observed the mimic octopus imitating jellyfish, stingrays, mantis shrimp, and even sea anemones.

What elevates the mimic octopus's behavior from a simple mechanical reflex to a complex cognitive strategy is its selectivity. Observations indicate that the octopus does not choose its disguise at random. Instead, it tailors its mimicry to the specific threat it faces. For instance, when attacked by damselfish, it selectively adopts the guise of the banded sea snake, demonstrating a capacity to recognize predator-prey relationships and deploy the most effective deterrent.

The physiological mechanisms behind this mimicry are incredibly sophisticated. Like other cephalopods, the mimic octopus possesses chromatophores—pigment-filled sacs in its skin controlled by complex muscle contractions. By dilating or contracting these sacs, the octopus can rapidly alter its coloration and create intricate patterns in milliseconds. Additionally, specialized skin structures called papillae allow it to alter its skin texture from smooth to spiky, further enhancing the physical resemblance to its target model.

However, the physical transformations are only part of the equation. The mimic octopus’s nervous system, which is highly decentralized, plays a vital role. With three-fifths of its neurons located in its arms rather than its brain, each arm can operate with a high degree of autonomy. This allows the octopus to coordinate the complex, multi-limb movements required to simulate the distinct swimming styles of completely different classes of animals, such as vertebrates (fish and reptiles) and invertebrates (jellyfish).

While camouflage is a common survival strategy in the animal kingdom, the mimic octopus represents an evolutionary pinnacle of behavioral adaptation. In an environment devoid of physical shelter, it has transformed its very identity into a shield, proving that in the struggle for survival, deception can be as effective as armor.

Based on the passage, is the statement "The mimic octopus has the majority of its neurons located in its brain rather than its arms" true or false?

This passage is adapted from an article discussing the history of linguistic decipherment in Mesoamerica.

For centuries, the hieroglyphic writing carved into the limestone structures of Mesoamerica remained an inscrutable enigma. When the American explorer John Lloyd Stephens and English artist Frederick Catherwood published their illustrated accounts of ruined Maya cities in the early 1840s, they sparked a wave of intellectual curiosity, yet the script itself resisted explanation. Early Western scholars, influenced by prevailing theories of language development, assumed that the intricate glyphs were purely ideographic or pictographic—pictorial representations of ideas or objects rather than components of a phonetic writing system. This misconception was consolidated in the mid-twentieth century by the towering figure of Sir J. Eric S. Thompson, the preeminent Mayanist of his era. Thompson argued dogmatically that the glyphs were symbols of time, astronomy, and religious contemplation, devoid of phonetic syntax. Because of Thompson’s academic authority and his active hostility toward dissenting opinions, his view dominated the field for decades, effectively stalling progress in decipherment.

The breakthrough came from an unexpected quarter: a quiet office in Leningrad, where a Soviet linguist named Yuri Valentinovich Knorozov approached the problem from a distance. Knorozov had never visited Mesoamerica, but he possessed a facsimile of the three surviving Maya codices—the Dresden, Madrid, and Paris codices—as well as a copy of Diego de Landa’s sixteenth-century manuscript, *Relación de las cosas de Yucatán*. Landa, a Spanish bishop infamous for burning countless Maya books in an auto-da-fé in 1562, had ironically recorded what he believed to be a Maya "alphabet." For centuries, scholars had attempted to apply Landa's alphabet directly to the codices to read them phonetically, but because the resulting sequences yielded gibberish, they concluded that Landa's guide was either a colonial fabrication or a collection of random sketches drawn by a confused scribe.

Knorozov’s genius lay in recognizing that the failure of previous scholars stemmed from a fundamental misunderstanding of Landa's elicitation process. Knorozov realized that when Landa asked his Maya informant for the glyph corresponding to the letter *b*, he was not asking for a single phoneme, which does not exist in isolation in spoken Maya. Instead, Landa pronounced the name of the Spanish letter *b* (which sounds like "beh"). The Maya scribe, attempting to cooperate, drew the glyph that corresponded to the syllable *beh*, which in Maya means "road" or "path." Similarly, when asked for *c* (pronounced "seh"), the scribe drew the glyph for the syllable *ze*. Knorozov hypothesized that the Maya writing system was not alphabetic, but logosyllabic, consisting of both logograms (signs representing whole words) and phonetic syllabic signs (typically representing consonant-vowel combinations).

To test this theory, Knorozov analyzed the glyphs accompanying illustrations of animals in the codices. He examined a glyph associated with the drawing of a turkey, a bird known in Yucatec Maya as *kutz*. The glyph consisted of two signs. Under Knorozov's hypothesis, the first sign represented the syllable *ku*. He knew from Landa’s manuscript that a particular glyph corresponded to the sound of the Spanish letter *u* (pronounced "oo"). Since the Maya word for turkey ends in a consonant (*tz*), Knorozov reasoned that the scribe had written the syllables *ku-tzu*, with the final vowel dropped in pronunciation—a principle Knorozov termed synharmony. To confirm this, Knorozov cross-referenced the second sign, *tzu*, with a glyph associated with a dog (*tzul* in Maya). The dog glyph was written with the sign *tzu* followed by a sign that Knorozov correctly identified as *lu*. The spelling *tzu-lu* yielded *tzul* (dog), verifying that the sign *tzu* functioned consistently across different words.

Despite the mathematical elegance of Knorozov’s methodology, his discoveries met with fierce resistance, particularly from Thompson. Operating within the heightened tensions of the Cold War, Thompson dismissed Knorozov’s work as Marxist-Leninist propaganda, arguing that the Soviet scholar was merely trying to impose dialectical materialism on ancient writing. Thompson’s denunciations kept the Western archaeological establishment aligned against Knorozov for nearly a quarter of a century. It was not until the late 1950s and 1960s, as Western scholars like Tatiana Proskouriakoff began identifying historical, rather than purely calendrical, information in Maya inscriptions, that the utility of Knorozov’s phonetic approach became undeniable. By the 1970s, Knorozov's syllabic key was widely accepted, transforming the Maya from an abstract, silent civilization into a people with a written history as detailed and personal as those of ancient Egypt or Mesopotamia.

According to the passage, for what reason did scholars prior to Yuri Knorozov's work dismiss Diego de Landa's written Maya "alphabet"?

In the standard $(x, y)$ coordinate plane, an isosceles trapezoid $ABCD$ has vertices at $A(0, 0)$, $B(8, 0)$, $C(6, 4)$, and $D(2, 4)$. The diagonals $AC$ and $BD$ intersect at point $P$. What is the area of triangle $APB$?

A $10$-foot ladder leans against a vertical wall. The base of the ladder is $6$ feet away from the bottom of the wall, and the top of the ladder reaches a height of $8$ feet up the wall. If $\theta$ is the angle formed between the ladder and the ground, what is the value of $\cos(\theta)$?

Passage

The introduction of the potato (Solanum tuberosum) to continental Europe was met with profound suspicion. In eighteenth-century France, the tuber was widely regarded as unfit for human consumption, believed to cause leprosy and deplete the soil of vital nutrients. The Parlement of Paris went so far as to officially ban its cultivation in 1748. It was not until the tireless efforts of Antoine-Augustin Parmentier, an apothecary who served in the French army during the Seven Years’ War, that the French public began to reconsider this prejudice.

During his military service, Parmentier was captured five times by Prussian forces. During these periods of confinement, most notably in a prison camp in Hamburg, he was forced to subsist on a diet consisting almost exclusively of potatoes. Surprised by his own survival and continued health, he resolved to rehabilitate the vegetable's reputation upon his return to France. Parmentier’s campaign began in earnest when he won a prestigious essay contest hosted by the Academy of Besançon in 1773, which sought solutions to the frequent famines plaguing the nation. His winning paper argued that the potato was the ideal crop to alleviate public hunger.

Despite his academic success, Parmentier faced steep resistance from the established medical and political authorities. Seeking to dismantle their objections, he initiated a series of chemical analyses to prove the potato's nutritional value. In 1772, largely due to his persistent lobbying and scientific demonstrations, the Paris Faculty of Medicine formally declared the potato edible. Yet, declaring the crop safe was only half the battle; Parmentier still had to convince a highly skeptical agrarian population to grow it and a suspicious public to eat it.

To accomplish this, Parmentier utilized a series of ingenious public relations strategies designed to generate interest and prestige around the humble root. In 1785, he secured the patronage of King Louis XVI, who granted him fifty arpents (approximately forty-two acres) of sandy, historically infertile land at Les Sablons, just west of Paris. Parmentier cultivated potatoes on this land and employed a clever psychological trick: he hired royal guards to watch over the fields in their distinctive uniforms. The presence of armed guards suggested that the crop was of immense value, meant only for the nobility. Critically, Parmentier instructed the guards to accept any bribes offered by curious locals and to intentionally look the other way if peasants attempted to pilfer the plants under the cover of darkness. The plan worked precisely as intended. Believing they were stealing a royal delicacy, local farmers quickly acquired the seeds, and potato cultivation spread throughout the region.

In addition to this agricultural subterfuge, Parmentier sought to elevate the potato's culinary status among the elite. He hosted lavish dinners in Paris where every course, from the soup to the liqueurs, featured the potato in some form. These banquets were attended by prominent figures of the day, including the American envoy Benjamin Franklin and the pioneering chemist Antoine Lavoisier. At one public gathering, Parmentier presented a bouquet of potato blossoms to King Louis XVI, who placed one in his buttonhole, while Queen Marie Antoinette wore them in her hair, briefly making the pale purple flowers a fashion trend among the aristocracy.

While these theatrical gestures captured the attention of the upper classes, it was the harsh reality of the crop's resilience that ultimately secured its place in French agriculture. During the devastating famine of 1785 and the subsequent agricultural disruptions of the French Revolution, the potato proved to be a reliable lifesaver when grain crops failed. By the time of Parmentier's death in 1813, the potato had transitioned from a feared vector of disease to a staple of the French diet, a transformation catalyzed by scientific advocacy and theatrical showmanship.

According to the passage, the presence of armed guards at the Les Sablons estate was intended to achieve which of the following results?

In the standard $(x, y)$ coordinate plane, if a line $L$ is perpendicular to the line passing through the points $(2, 5)$ and $(2, -3)$, then the slope of line $L$ is $0$.

An angle $\theta$ lies in the third quadrant, where $\pi < \theta < \frac{3\pi}{2}$. If $\sin\theta - \cos\theta = -\frac{1}{5}$, what is the value of the expression $125(\sin^3\theta + \cos^3\theta)$?

The graph of the function $f(x) = a \cos(b(x - c)) + d$ is shown below for constants $a > 0$, $b > 0$, $c \in [0, \pi]$, and $d$. The graph has a local maximum at $(\frac{\pi}{3}, 5)$ and the nearest local minimum to its right is at $(\frac{5\pi}{6}, -1)$. What is the y-intercept of the graph of $f(x)$?