All practice questions

Origin of Earth's Water

Liquid water covers approximately $71\%$ of Earth's surface, yet the origin of this water remains a subject of scientific debate. Scientists have proposed two main models to explain how Earth acquired its water.

*Model 1*
Earth's water was delivered during the late stage of planetary accretion by carbonaceous chondrites (meteorites originating from the outer asteroid belt). Carbonaceous chondrites are rich in water and organic compounds. The deuterium-to-hydrogen ($D/H$) ratio of these meteorites is approximately $1.4 \times 10^{-4}$, which closely matches the $D/H$ ratio of Earth’s modern oceans ($1.56 \times 10^{-4}$). Proponents of Model 1 argue that because asteroids formed closer to the Sun, they were more likely to intersect Earth's orbit during its final formation phases.

*Model 2*
Earth's water was delivered during the Late Heavy Bombardment, roughly $3.9$ billion years ago, by icy comets originating from the outer solar system. Comets contain up to $80\%$ water ice. Proponents of Model 2 argue that the extreme gravitational perturbations caused by the migration of giant planets scattered comets inward, resulting in frequent impacts on Earth. Although many comets have $D/H$ ratios of approximately $3.0 \times 10^{-4}$ (twice that of Earth's oceans), proponents argue that a subset of comets from the Kuiper Belt has $D/H$ ratios matching Earth's oceans and that comet impacts delivered the vast majority of Earth's volatile elements.

Based on the provided models, is the following statement true or false?

According to Model 2, gravitational perturbations caused by the migration of giant planets scattered comets inward, leading to frequent impacts that delivered Earth's water.

The following passage is adapted from an essay on the history of industrial chemistry and pigments:

In 1824, the French Société d'Encouragement pour l'Industrie Nationale announced a lucrative prize of six thousand francs to any chemist who could synthesize a commercially viable alternative to natural ultramarine. At the time, ultramarine was extracted solely from rare lapis lazuli stone, making it more expensive than its weight in gold. The competition sparked intense research across Europe.

In 1826, French chemist Jean-Baptiste Guimet successfully formulated a vibrant synthetic ultramarine in his laboratory in Toulouse by heating kaolin clay, sodium sulfate, sodium carbonate, and charcoal in a sealed crucible. Shortly thereafter, in 1828, German chemist Christian Gmelin independently published his own sulfur-based synthesis technique, sparking a prolonged dispute regarding priority of discovery. However, because Guimet had confidentially submitted samples to the French society prior to Gmelin's publication, the official prize was formally awarded to Guimet in 1830. Industrial scale manufacturing began at Guimet’s factory in Bouchet-du-Rhône in 1831, permanently transforming textile printing and fine art production.

Based on the explicit details in the passage, place the following events in chronological order from earliest to latest.

Passage:
In eighteenth-century glassmaking, artisans relied primarily on two methods to produce flat window glass: the crown glass method and the cylinder glass method. The crown glass technique involved blowing a globe of molten glass, flattening it, and spinning it rapidly to form a large, thin disk with a thick central bullseye. In contrast, the cylinder glass method required blowing a long glass cylinder, cutting it lengthwise, and flattening it on a hot iron plate. While crown glass boasted a remarkably smooth and brilliant surface because it was never touched by flattening tools, cylinder glass allowed glassmakers to manufacture significantly larger rectangular panes despite having a slightly rougher surface texture.

According to the passage, how did crown glass explicitly differ from cylinder glass regarding its physical quality?

Passage:
For decades, comparative psychologists maintained that tool innovation in corvids was driven exclusively by social learning and observational tradition within avian flocks. Proponents of this view argued that young crows acquired complex foraging techniques solely by mimicking adult behavior, pointing to regional variations in tool shape as definitive evidence of cultural transmission. However, recent experimental trials with isolated, lab-raised New Caledonian crows have challenged this strict cultural consensus. Juveniles raised without exposure to adult tutors or pre-fabricated tools nevertheless constructed functional leaf-stripping implements when presented with raw materials. While these findings demonstrate that basic tool manufacturing possesses an innate genetic component, they do not completely negate the role of social interaction. Rather, the innate cognitive blueprint provides a structural foundation upon which social refinement can subsequently occur.

Based on the passage, what is the primary rhetorical purpose of citing the experiment involving lab-raised New Caledonian crows?

The sentence below describes the final steps of preparing a report. What verb form correctly completes the sentence to maintain parallel structure with the other actions in the list?

What is the value of the expression $\frac{-2^4 - 6 \times |2 - 2 \times 3|}{2 - (-2)^3}$ ?

If the product of the complex numbers $4 - 2i$ and $k + 6i$ is a real number, where $k$ is a real constant and $i = \sqrt{-1}$, what is the value of $k$?

For all non-zero real numbers $a$ and $b$, the expression $(a^2 b^k)^3$ is equivalent to $a^6 b^{15}$. What is the value of the integer $k$?

What is the value of $x$ that satisfies the equation $\frac{3}{4}(x - 8) = \frac{1}{2}x + 2$?

If the expression $\frac{(p^3 q^{-2})^{-1}}{(p^{-1} q^2)^3}$ is simplified to the form $p^x q^y$ for all non-zero real numbers $p$ and $q$, what is the value of $2x - y$?

[1]
For decades, the clay tablets unearthed at the ancient palace of Knossos on Crete remained an inscrutable enigma. Discovered by archaeologist Arthur Evans in 1900, the script—dubbed "Linear B"—defied translation. Evans believed that the tablets recorded a non-Greek Minoan language, and his towering authority in the field led most scholars to follow his lead, searching in vain for connections to ancient languages of the Near East.

[2]
Enter Michael Ventris, an English architect who had been obsessed with the mystery since hearing Evans speak about it during his schooldays. Unlike academic linguists who worked within rigid paradigms, Ventris approached the script as a cryptanalyst. He began by meticulously constructing grids that mapped the relationships between different signs, noting which symbols appeared together and how word endings changed depending on context.

[3]
In 1952, Ventris made a breakthrough. By analyzing place names on the tablets, he realized that the phonetic values of the symbols aligned perfectly with archaic Greek nouns and verbs. Working alongside classical scholar John Chadwick, Ventris proved that Linear B was not a foreign tongue at all, but rather the earliest written form of Greek, dating back some five centuries before Homer.

[4]
The decipherment revolutionized our understanding of the Bronze Age Aegean. It revealed that the Mycenaeans, not the Minoans, ruled Knossos in its final phase and showed that their society was highly bureaucratic, keeping detailed inventories of sheep, oil, and bronze. Ventris’s outsider status and grid-based methodology had unlocked a civilization's voice.

Suppose the writer’s goal had been to write an essay that demonstrates how Michael Ventris’s cryptanalytic methodology successfully challenged Arthur Evans’s theory about the linguistic origin of the Knossos tablets. Is the statement that the essay successfully achieves this goal True or False?

______ In 1943, marine engineer Richard James was working in a shipyard, trying to develop springs that could support and stabilize sensitive marine instruments. After accidentally knocking one of the steel springs from a shelf, he watched in amazement as it did not merely fall, but rather "stepped" down from a stack of books, to a tabletop, and then to the floor, where it coiled itself back up. James immediately saw the toy's potential, and his wife, Elizabeth, named it the "Slinky" after searching the dictionary for a word that described the spring's sleek, fluid movement.

Which choice most effectively introduces the paragraph?

What is the sum of the squares of the two real solutions to the quadratic equation $\frac{1}{2}x^2 - 3x + 2 = 0$?

The sentence below contains a dangling modifier because the introductory participial phrase does not logically modify the subject of the clause that follows:

'Determining that the fossilized tracks belonged to a juvenile theropod, the footprints were carefully cast by the paleontologists in plaster.'

To correct this error, complete the sentence by typing a grammatically correct clause in the blank that begins with the subject 'the paleontologists' and includes the verb 'cast', the adverb 'carefully', and the direct object 'the footprints'.

The botanist spent several months studying the rare orchid in the cloud forest. Because she wanted to document its unique pollination process.

Which of the following choices best replaces the underlined portion of the sentence?

[1] In 1912, geophysicist Alfred Wegener proposed the theory of continental drift, claiming that Earth's continents were once united as a single supercontinent. [2] To support this claim, Wegener pointed to matching geological formations and fossil records on opposite sides of the Atlantic Ocean. [3] For instance, fossils of the freshwater reptile Mesosaurus are found only in southern Africa and eastern South America. [4] The writer wants to add a sentence after sentence 3 to provide specific, concrete geological evidence that supports the claim that these two continents were once physically connected.

Which of the following sentences best achieves this goal?

To complete the architectural project on time, the team spent the weekend drafting the blueprints, revising the budget, and [they conducted site inspections].

Which choice best maintains parallel structure in the sentence?

The following sentences, when ordered correctly, form a cohesive paragraph that supports a claim about Sequoyah's writing system. Arrange the sentences in the most logical order to construct a paragraph where supporting evidence and details logically follow the claim.

To prepare for the chemistry lab, students must put on their safety goggles, tie back long hair, and they should wash their hands thoroughly.

Which of the following options completes the sentence with the correct parallel structure?

The oceanographers spent several weeks tracking the migration of blue whales in the Pacific Ocean. Hoping to understand how changing water temperatures affect their travel routes.

Which of the following choices best corrects the underlined portion to ensure the sentence is grammatically complete?