Tüm alıştırma soruları

While researching the Elfdalian language, a student takes the following notes:
* Elfdalian is a North Germanic language spoken in Älvdalen, Sweden, that evolved from Old Norse starting in the fourteenth century.
* Because of its geographical isolation, Elfdalian preserved many archaic grammatical features lost in modern Swedish.
* In a 2015 study, linguist Yair Sapir investigated Elfdalian's historical isolation and its retention of the runic alphabet.
* Sapir concluded that the language's geographical isolation served as a key preservation mechanism for these ancient linguistic traits.

The student wants to summarize the study and its findings. Which choice most effectively uses information from the given notes to accomplish this goal?

In the $xy$-plane, a square has vertices at $(0,0)$, $(10,0)$, $(10,10)$, and $(0,10)$. A line that passes through the points $(0,2)$ and $(8,10)$ divides the square into two regions. What is the area of the larger region?

The graph of a third-degree polynomial function $g$ has $x$-intercepts at $(-2, 0)$ and $(3, 0)$. At $x = -2$, the graph is tangent to the $x$-axis, and the graph passes through the point $(1, -12)$. What is the $y$-intercept of the graph of $g$?

The graph of the quadratic function $h$ has a vertex at $(2, -5)$ in the $xy$-plane. If the function $g$ is defined by $g(x) = h(x + 3) + 4$, what is the vertex of the graph of $g$?

During the late Renaissance in England, a playwright's professional success depended heavily on securing royal patronage. Because staging new productions in London's public theaters required expensive licensing fees and elaborate costumes, a theatre company without a wealthy ________ financial backing was unlikely to survive for more than a few seasons.

Which choice completes the text so that it conforms to the conventions of Standard English?

In right triangle $ABC$, the measure of angle $B$ is $90^\circ$. If the length of side $AB$ is 6 and the length of side $AC$ is 10, what is the length of side $BC$?

In the field of materials science, researchers have developed self-healing concrete containing bacterial spores that produce calcium carbonate to seal cracks when exposed to moisture. __________, scholars in building preservation have successfully utilized bacterial treatments to repair historical stone monuments suffering from environmental degradation.

Which transition word or phrase most logically completes the passage?

The number of active participants in an online educational forum has been growing exponentially since the forum was launched. At the launch of the forum ($t = 0$), there were $5,000$ active participants. Two months after the launch ($t = 2$), there were $7,200$ active participants. If the number of active participants continues to grow exponentially at this constant monthly percent rate, what is the number of active participants in the forum four months after the launch ($t = 4$)?

A scientist measures the concentration of a chemical solution across five different trials. The concentrations recorded for the first four trials are $12.1$ grams per liter ($\text{g/L}$), $12.2\text{ g/L}$, $12.4\text{ g/L}$, and $12.5\text{ g/L}$. The concentration for the fifth trial is $x\text{ g/L}$, where $x < 12.0$. If the mean of the concentrations from all five trials is equal to their median, what is the value of $x$?

Discovered in 1995 on the mouthparts of the Norway lobster (*Nephrops norvegicus*), the microscopic organism *Symbion pandora* belongs to the phylum Cycliophora. To anchor itself, the organism utilizes an adhesive disk located at its base, attaching to the lobster's sensory bristles, or setae. *Symbion pandora* does not prey on its host; instead, it consumes microscopic food debris generated when the lobster feeds. Intriguingly, its reproductive cycles are synchronized with the lobster's molting schedule. When the host sheds its exoskeleton, the organism initiates a sexual reproduction phase, producing free-swimming larvae that can quickly colonize the lobster's newly formed outer shell, thereby maintaining the association across generations.

Based on the text, what is true of *Symbion pandora*?

The function $f$ is defined by $f(x) = (x - 2)^2 - 5$. The graph of the function $g$ in the $xy$-plane is obtained by translating the graph of $f$ by $3$ units to the left and $4$ units up. If the vertex of the graph of $g$ is $(h, k)$, what is the value of $h + k$?

A right circular cylinder and a right circular cone have equal volumes. The radius of the cylinder's base is $3$ times the radius of the cone's base. If the height of the cone is $k$ times the height of the cylinder, what is the value of $k$?

The graph of the polynomial function $h$ in the $xy$-plane has $x$-intercepts only at $(-4, 0)$, $(1, 0)$, and $(3, 0)$. If the $y$-intercept of the graph of $h$ is $(0, -12)$ and the degree of $h$ is $3$, what is the value of $h(2)$?

Great Zimbabwe, a medieval city in the southeastern hills of Zimbabwe, is renowned for its monumental stone walls. Constructed between the 11th and 15th centuries by the ancestral Shona people, these walls are unique because they were built entirely using dry-stone masonry, meaning no mortar was used to bind the granite blocks together. The largest structure, the Great Enclosure, has walls reaching heights of over 30 feet. While early European investigators incorrectly hypothesized that the city was built by foreign civilizations, modern archaeological evidence confirms that the local Shona population designed and constructed the complex. The walls likely served as a symbol of royal authority and prestige rather than primary defensive fortifications, given their layout and lack of defensive features.

According to the text, which statement is true about the construction of the walls at Great Zimbabwe?

A landscape architect is designing two similar gardens. The smaller garden is in the shape of a regular hexagon and has an area of $24\sqrt{3}$ square meters. The larger garden is also a regular hexagon, and its perimeter is $3$ times the perimeter of the smaller garden. An inscribed circular fountain is to be placed in the center of the larger garden, touching all six sides. What is the area, in square meters, of the circular fountain?

Mangrove forests serve as critical coastal buffers, mitigating the impact of severe storms by absorbing wave energy. Specifically, the complex, interlaced prop roots of the red mangrove (*Rhizophora mangle*) create a dense physical barrier that disrupts the momentum of incoming tides. While some researchers argue that the level of protection varies significantly depending on coastal topography, others emphasize the uniform benefits these ecosystems provide in high-risk zones. Ultimately, understanding these local variations is essential for designing effective coastal conservation strategies.

Which choice best describes the function of the underlined sentence in the text as a whole?

A student is taking notes on epigraphy for a research project:

* Epigraphy is the scientific study of ancient inscriptions (epigraphs) engraved on durable materials.
* These materials include stone, clay, and metal.
* It is a primary branch of archaeology and historical linguistics.
* Deciphering these inscriptions helps researchers reconstruct historical events and cultural practices.
* The term "epigraphy" originates from the Greek words *epi* (meaning "upon") and *graphein* (meaning "to write").

The student wants to introduce the field of epigraphy to an audience unfamiliar with the term. Which choice most effectively uses information from the notes to accomplish this goal?

In restoration ecology, the introduction of non-native plant species is sometimes proposed as a rapid method to stabilize soil and prevent erosion in degraded landscapes. While this approach can yield immediate benefits, many researchers caution that it can also ______ unforeseen ecological disruptions. For instance, these introduced species may outcompete native flora for resources, ultimately destabilizing local food webs and reducing biodiversity.

Which choice completes the text with the most logical and precise word or phrase?

The polynomial function $p$ is defined by $p(x) = x^4 - 3x^3 + ax^2 - 7x + 10$, where $a$ is a constant. If $x - 2$ is a factor of $p(x)$, what is the value of $a$?

To show that the work belongs to the single artist mentioned in the passage, which form of the noun 'artist' should be used? Complete the passage by typing the correct form of the noun in the blank.