All practice questions

Read the following passage:

In 1928, biologist Alexander Fleming discovered penicillin in his London laboratory. Before leaving for a summer vacation in August, he stacked his staphylococcus culture plates on a bench in the corner of his room. Upon returning to the laboratory in September, he noticed that one of the culture plates was contaminated with mold. He subsequently spent the following years attempting to isolate the active substance, but it was not until 1940 that scientists Howard Florey and Ernst Chain successfully purified penicillin for medical application.

Based on the passage, which of the following events occurred first chronologically?

Passage A
Nineteenth-century cartography was driven by an Enlightenment ideal: the comprehensive cataloging of physical space. Explorers and surveyors aimed to produce definitive, static maps that would permanently archive terrain, coastlines, and topography. Mapmaking was viewed as a finite project with a clear endpoint—once a territory was measured and rendered on paper, its physical reality was considered fully captured and mastered for future generations.

Passage B
The advent of satellite geodesy and real-time geographic information systems (GIS) has fundamentally transformed the discipline of cartography. Modern spatial science no longer treats mapping as the creation of an enduring, complete portrait of a landscape. Instead, continuously updated digital layers reveal that coastlines erode, urban centers shift, and climate patterns alter terrain dynamically. Contemporary cartography views maps not as permanent records, but as fluid, evolving models of an ever-changing environment.

Which of the following best describes the overall relationship between the primary function of Passage A and the primary function of Passage B?

Read the following passage:

"Before beginning her pioneering work in industrial toxicology in 1910, Dr. Alice Hamilton completed her medical degree at the University of Michigan in 1893. Following her graduation, she spent two years studying bacteriology in Germany. Upon returning to the United States in 1897, Hamilton accepted a professorship at the Woman's Medical School of Northwestern University and moved into Hull House in Chicago. Years later, after completing her landmark study on lead poisoning for the state of Illinois, she was appointed as the first female faculty member at Harvard University in 1919."

Based on the passage, arrange the following events in chronological order from earliest to latest.

The following passage is adapted from an essay on twentieth-century paleontology:

In August 1909, while conducting geological fieldwork in the Canadian Rockies near Field, British Columbia, American paleontologist Charles Doolittle Walcott made a remarkable discovery on the slopes of Fossil Ridge. While traversing a trail between Mount Wapta and Mount Field, Walcott's pack horse stumbled on a slab of dark shale. Splitting the stone, Walcott uncovered exceptionally preserved fossils of soft-bodied organisms from the Middle Cambrian period, dating back roughly 508 million years. Unlike typical fossil sites, which preserve only hard mineralized structures such as shells and bones, the Burgess Shale retained delicate internal organs, appendages, and soft tissue outlines compressed between thin layers of sediment.

During subsequent field seasons between 1910 and 1924, Walcott returned repeatedly to the quarry that now bears his name. Assisted by his family, he extracted over 65,000 specimens, meticulously documenting each find in his field notebooks. Walcott categorized these ancient organisms—such as the bizarre five-eyed Opabinia and the spiny Hallucigenia—within existing modern taxonomic groups, classifying them primarily as early primitive ancestors of living marine annelids and crustaceans. Although later paleontologists in the 1970s, led by Harry Whittington, re-examined the specimens and argued that many represented entirely novel, extinct phyla unrelated to modern lineages, Walcott’s initial recovery and painstaking preservation of the quarry's fossils established the site as one of the most significant paleontological discoveries of the twentieth century.

According to the passage, Walcott first encountered the fossil-bearing slab of shale when which of the following occurred?

For an angle $\theta$ satisfying $\pi < \theta < \frac{3\pi}{2}$, if $\cos \theta = -\frac{12}{13}$, what is the value of $\frac{\sec \theta - \cos \theta}{\tan \theta}$?

The following passage is adapted from an essay on paleoclimatology and polar ice research:

In 1966, Danish geophysicist Willi Dansgaard conducted a landmark investigation using an ice core retrieved from Camp Century in northwestern Greenland by the U.S. Army Corps of Engineers. Dansgaard analyzed the ratios of stable oxygen isotopes ($^{18}\text{O}$ to $^{16}\text{O}$) across successive annual layers of ice, establishing that higher concentrations of heavy oxygen ($^{18}\text{O}$) correlated directly with warmer local atmospheric temperatures at the time precipitation fell. Through this isotope analysis, Dansgaard uncovered abrupt climatic oscillations—subsequently termed Dansgaard-Oeschger events—in which Greenland temperatures rose by up to 16 degrees Celsius within a few decades. Prior to this discovery, prevailing meteorological theories assumed that polar climates shifted exclusively over long orbital cycles spanning tens of thousands of years.

To perform measurements without compromising the structural integrity of fragile annual layers, Dansgaard designed a precise sampling protocol. In an underground trench maintained at a constant temperature of $-15^\circ\text{C}$ to prevent surface melting, technicians used a motorized diamond-bladed saw to bisect the 1,387-meter ice core longitudinally. One longitudinal half was immediately crushed and vaporized for mass spectrometry measurements in a surface laboratory, while the remaining half was sealed in polyethylene tubing and stored at $-25^\circ\text{C}$ in an excavated ice chamber to serve as a permanent physical archive.

According to the passage, what specific equipment was used inside the underground trench to divide the Camp Century ice core longitudinally?

Passage:
Early twentieth-century aviation saw the development of two distinct types of lighter-than-air craft: rigid airships and non-rigid airships. Rigid airships, commonly known as Zeppelins, relied on an internal structural framework—typically constructed from lightweight aluminum alloys—that maintained the vessel's shape regardless of the gas pressure inside. In contrast, non-rigid airships, or blimps, possessed no internal metal framework; their envelope maintained its aerodynamic shape entirely through the internal pressure of the lifting gas. Consequently, while rigid airships could be built significantly larger to carry heavy payloads, blimps were lighter, easier to deflate, and far simpler to store when not in service.

According to the passage, how did rigid airships explicitly differ from non-rigid airships in maintaining their shape?

Passage:
In urban planning literature, high-albedo reflective roofs have frequently been promoted as the single most effective municipal intervention for mitigating the urban heat island effect. Proponents highlight how increasing surface albedo significantly reduces thermal absorption at the roof level. However, microclimate researchers point out that while reflective roofs lower surface temperatures on rooftops, they reflect solar radiation downward into surrounding pedestrian corridors, potentially intensifying heat stress for individuals at ground level during peak afternoon hours. To resolve this trade-off, recent architectural frameworks advocate for a integrated approach combining reflective roofing with vertical green walls to absorb reflected light.

Based on the passage, what function does the reference to the downward reflection of solar radiation into pedestrian corridors serve in the overall argument?

In quadrilateral $ABCD$, diagonal $AC$ divides the figure into two triangles, $\triangle ABC$ and $\triangle ACD$. It is given that $AB = 6$, $BC = 10$, $\angle ABC = 120^\circ$, $\angle CAD = 45^\circ$, and $\angle ADC = 60^\circ$. What is the length of side $CD$?

Read the passage below and arrange the listed events in chronological order from earliest to latest based on the explicit statements in the text.

Passage:
In the summer of 2014, marine biologist Dr. Elena Rostova led a deep-sea expedition to the Mariana Trench. Before launching the remote submersible, the research team spent three weeks calibrating the high-pressure camera housing. Once the submersible reached a depth of 4,000 meters, it recorded the first clear footage of a giant bioluminescent siphonophore. Following this discovery, Dr. Rostova published her findings in the Oceanographic Journal of America in early 2016. Later that year, the International Marine Institute awarded the expedition team the Medal of Exploration Excellence.

In what sequence did these events occur?

In the standard $(x, y)$ coordinate plane, trapezoid $ABCD$ has vertices at $A(0, 0)$, $B(4, 8)$, $C(12, 8)$, and $D(16, 0)$. Point $P$ is the midpoint of diagonal $AC$, and point $Q$ is the midpoint of diagonal $BD$. What is the distance, in coordinate units, between point $P$ and point $Q$?

In a circle with center $O$, sector $AOB$ has an area of $18\pi$ square centimeters and an arc length along $\widehat{AB}$ of $3\pi$ centimeters. A straight line segment $AB$ is drawn to complete triangle $AOB$. What is the area, in square centimeters, of the circular segment bounded by line segment $AB$ and arc $\widehat{AB}$?

In right triangle $XYZ$, the right angle is at vertex $Y$, and line segment $YW$ is an altitude perpendicular to hypotenuse $XZ$ at point $W$. If the length of side $XY$ is $15$ units and $\cos(X) = \frac{4}{5}$, what is the length of line segment $ZW$?

Geothermal geologists analyzed fluid samples collected from 4 distinct wells (Well W, Well X, Well Y, and Well Z). Table 1 lists the measured reservoir temperature in degrees Celsius ($^\circ\text{C}$) and the dissolved silica ($SiO_2$) concentration in milligrams per liter ($\text{mg/L}$) for each well.

Figure 1 displays the fluid viscosity ($\eta$, in centipoise, $\text{cP}$) as a function of dissolved $SiO_2$ concentration at four different temperature curves:
- At $140^\circ\text{C}$: $\eta = 0.005 \times (\text{dissolved } SiO_2) + 0.10$
- At $170^\circ\text{C}$: $\eta = 0.003 \times (\text{dissolved } SiO_2) + 0.20$
- At $200^\circ\text{C}$: $\eta = 0.002 \times (\text{dissolved } SiO_2) + 0.40$
- At $230^\circ\text{C}$: $\eta = 0.001 \times (\text{dissolved } SiO_2) + 0.50$

Based on Table 1 and Figure 1, rank the geothermal wells in order from lowest fluid viscosity to highest fluid viscosity.

Passage A
Deep-sea organisms inhabit an environment devoid of solar light, leading to unique evolutionary adaptations. Among these, bioluminescence—the biological production and emission of light—serves predominantly as a defensive mechanism. Species such as the deep-sea shrimp (Acanthephyra purpurea) spew bioluminescent clouds to disorient predators, while others utilize counterillumination to match ambient downwelling light, obscuring their silhouettes from benthic hunters below. These adaptations demonstrate that light production in the bathypelagic zone evolved primarily to mitigate predation pressure where concealment is otherwise impossible.

Passage B
While early abyssal research framed marine bioluminescence strictly through the lens of predator evasion, recent visual ecology studies reveal a far more dynamic communicative function. Photophores in organisms like the lanternfish (Myctophidae) display species-specific and sexually dimorphic spatial patterns. These bioluminescent signatures facilitate conspecific recognition and mate selection in an expansive, structureless habitat. Rather than merely deterring threats, bioluminescent signaling functions as a vital social apparatus, enabling species cohesion and reproductive success in the open ocean.

Which of the following best describes the relationship between the primary functions attributed to bioluminescence in Passage A and Passage B?

Dr. Helen Vance published her seminal paper on cosmic microwave anomalies in the winter of 1948, validating a theoretical model she had constructed six years prior during her residency at the Cambridge Observatory. However, the path to this discovery was non-linear. Before arriving in Cambridge, Vance worked as a technician at a meteorological station in Aberystwyth, where she first observed unexplained signal distortions. It was not until 1944—two years after her arrival at Cambridge and immediately before her team secured high-altitude telemetry data—that she re-evaluated those early Aberystwyth logs. That re-evaluation prompted her to redesign the observatory's primary spectrograph, a task completed just months prior to her 1948 publication.

Based on the passage, which of the following events occurred chronologically AFTER Dr. Vance constructed her theoretical model at Cambridge, but BEFORE her team secured high-altitude telemetry data?

The following passage is adapted from an article on early atmospheric aviation.

On the morning of May 27, 1931, Swiss physicist Auguste Piccard and his assistant Paul Kipfer stepped inside a spherical, airtight aluminum gondola attached to a massive hydrogen-filled balloon named FNRS-1. Launching from Augsburg, Germany, their primary objective was to reach the stratosphere to measure cosmic rays.

Shortly after ascent, a critical mechanical failure occurred: a pressure valve malfunctioned, causing a sudden drop in cabin pressure. Working quickly in the cramped sphere, Kipfer sealed the leaking valve joint using a rudimentary compound of petroleum jelly and oakum fiber. Once the leak was secured, the balloon continued its climb into the upper atmosphere.

At 3:57 PM, the FNRS-1 reached a peak altitude of 15,781 meters (51,775 feet), making Piccard and Kipfer the first human beings to enter the stratosphere. However, a new crisis emerged within the cabin. The motorized mechanism designed to slowly rotate the gondola—intended to regulate internal temperature by turning the heat-reflecting silver side toward the Sun—failed completely. Suspended with the dark-painted side facing the Sun constantly, internal cabin temperatures soared past 106°F (41°C).

Desperately short of liquid oxygen and suffering from severe heat exhaustion, the two aeronauts spent several hours drifting across the Alps. Finally, as cold air aloft caused the hydrogen gas to contract, the balloon began a gradual descent. At 8:50 PM, the gondola touched down safely on the snowpacks of the Gurgler glacier near Obergurgl, Austria, concluding a historic seventeen-hour voyage.

Based on the passage, place the following explicitly stated events from Auguste Piccard's flight in the chronological order in which they occurred from first to last.

In kite $ABCD$, diagonals $AC$ and $BD$ intersect perpendicularly at point $P$. If $AP = 9$ centimeters, $PC = 16$ centimeters, and $BP = PD = 12$ centimeters, what is the perimeter, in centimeters, of kite $ABCD$?

In right triangle $ABC$, the right angle is located at vertex $C$. Point $M$ is the midpoint of leg $BC$. The length of leg $AC$ is $12$ units, and $\tan(\angle MAC) = \frac{1}{3}$. What is the value of $\sin(\angle BAC)$?

In isosceles trapezoid $ABCD$, side $AB$ is parallel to side $CD$. If the measure of $\angle A$ is $(3x + 10)^\circ$ and the measure of $\angle C$ is $(5x - 30)^\circ$, what is the measure of $\angle B$?