Tüm alıştırma soruları

A network router transmits data from two sources, Server $A$ and Server $B$, at a constant ratio of $5$ megabytes ($\text{MB}$) from Server $A$ for every $3\text{ MB}$ from Server $B$. In a single session, the router transmitted a combined total of $160\text{ MB}$ of data from both servers. During the next session, the router transmits data at the same ratio, but the amount of data transmitted from Server $A$ is $20\%$ greater than the amount of data transmitted from Server $A$ in the first session. How many megabytes of data are transmitted from Server $B$ in the second session?

In architectural conservation, specialists face the challenge of preserving structural elements without altering their original character. The restoration of historic limestone facades, a process that often requires delicate chemical treatments and specialized manual labor, _______ meticulous planning to ensure that the ancient masonry is not inadvertently damaged. Which choice completes the text so that it conforms to the conventions of Standard English?

In the $xy$-plane, the graph of $y = x^2 - 8x + 12$ represents the quadratic function $f$. If this graph is shifted $3$ units to the left and $5$ units up to create the graph of a new function $g$, what is the $y$-value of the vertex of the graph of $g$?

The polynomial $p(x)$ is defined by $p(x) = x^3 - 2x^2 - kx + 6$, where $k$ is a constant. If $x - 3$ is a factor of $p(x)$, which of the following is a factor of $p(x) - 2x + 8$?

In the mid-twentieth century, linguists studying the evolution of the Basque language noted its lack of demonstrable relatives, classifying it as a language isolate. To explain this isolation, some researchers hypothesized that Basque represents a sole surviving pre-Indo-European language that resisted replacement by migrating Indo-European speakers. However, recent computational analyses of Basque phonology and grammar compared against ancient Aquitanian inscriptions suggest a more complex timeline of regional linguistic contact rather than total isolation. Consequently, scholars are increasingly shifting their focus from tracing a singular prehistoric origin to mapping these historical networks of contact with neighboring Latin and Celtic dialects.

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

A student is preparing a presentation on ancient technology and has taken the following notes:

* The Antikythera mechanism is an ancient Greek hand-powered model of the solar system.
* It was recovered from a cargo shipwreck off the coast of a Greek island in 1901.
* It is considered the oldest known example of an analog computer.
* It was designed to predict astronomical positions and eclipses.
* The device is currently housed at the National Archaeological Museum in Athens.

The student wants to write a sentence that introduces the device by emphasizing the year of its recovery and its current location. How should the student complete the sentence to achieve this goal?

An agricultural researcher wants to evaluate the effectiveness of a new organic fertilizer. The researcher selects a random sample of $80$ tomato plants of a specific variety from a greenhouse containing $1,200$ tomato plants of this variety. The researcher randomly assigns $40$ of the selected plants to receive the organic fertilizer and the remaining $40$ plants to receive a standard chemical fertilizer. At the end of the study, the plants that received the organic fertilizer produced a significantly higher average yield of tomatoes than the plants that received the standard chemical fertilizer. Based on this information, which of the following is the most appropriate conclusion?

In the $xy$-plane, the graph of the equation $x^2 - 8x + y^2 = 0$ is a circle. What is the radius of the circle?

In right triangle $XYZ$, the measure of angle $Y$ is $90^\circ$. If $\cos(X) + \sin(Z) = 1.6$, what is the value of $\sin(X)$?

In the field of dendrochronology, researchers analyze the patterns of annual growth rings in trees to reconstruct past climate variations and date ancient wooden structures. The precise synchronization of tree-ring sequences from wood samples collected across different geographical regions ______ scientists to construct a continuous chronological record stretching back thousands of years.

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

Complete the text with the most logical and precise word.

Preserving digital artwork presents a unique challenge for conservators, as the software and hardware required to run these pieces can quickly become obsolete. Rather than trying to keep outdated machines functioning indefinitely, many museums have adopted a strategy of emulation—recreating the artwork’s original digital environment on modern computer systems. This approach ensures that the interactive elements of the art remain ________ even as the hardware for which they were designed ceases to function.

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

In the $xy$-plane, a particle moves along a circular path centered at the origin. The particle starts at the point $(3, 0)$ and travels counterclockwise along the circle. If the particle stops after traveling an arc length of $5\pi$ units, what is the measure of the central angle subtended by the particle's path, in degrees?

In the $xy$-plane, a circle with its center at the origin contains the point $P(6, -2\sqrt{3})$. Point $P$ is rotated counterclockwise about the origin by an angle of $\frac{5\pi}{6}$ radians to a new position $Q$. What are the coordinates of point $Q$?

A metallic plate is in the shape of a trapezoid. The parallel sides of the plate have lengths of $9$ centimeters and $30$ centimeters. The two non-parallel sides have lengths of $10$ centimeters and $17$ centimeters. What is the area, in square centimeters, of the metallic plate?

Ancient Maya cities, such as Tikal, relied on sophisticated reservoir systems to survive the region's intense seasonal droughts. Traditionally, archaeologists viewed these reservoirs purely as passive holding basins designed to store rainwater during the wet season. However, researcher Lisa Lucero and her colleagues have recently argued that the Maya actively maintained these reservoirs as self-cleaning aquatic ecosystems. By introducing aquatic plants like water lilies and cattails, the Maya could naturally filter out nitrogen and phosphorus, preventing harmful algal blooms. Consequently, these reservoirs functioned not just as simple cisterns, but as complex, biologically managed wetlands that secured clean water for thousands of urban inhabitants.

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

An older printing press can produce $420$ brochures every $15$ minutes. A newer printing press can produce brochures at a rate that is $1.5$ times the rate of the older press. If both presses run simultaneously at their respective constant rates, how many minutes will it take them to produce a total of $2,100$ brochures?

Although the physical structures of the ancient Silk Road trading posts have largely succumbed to erosion, the cultural exchanges they facilitated have proved remarkably _______. Many contemporary culinary, musical, and linguistic traditions in Central Asia can be traced directly back to the interactions between merchants and locals during the peak of the trade network's activity.

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

Ecologists studying urban wildlife have observed that many mammal species adapt their daily behaviors to minimize contact with human populations. __________, researchers monitoring coyote populations in heavily developed regions of Southern California documented a pronounced shift toward nocturnal activity, finding that these urban coyotes were active primarily during hours when human foot traffic was at its lowest.

Which choice completes the passage with the most logical transition?

In right triangle $ABC$, the measure of angle $C$ is $90^\circ$. Point $D$ lies on side $AC$ and point $E$ lies on hypotenuse $AB$ such that segment $DE$ is perpendicular to $AB$. The length of segment $AE$ is $x$, the length of segment $AD$ is $x + 1$, the length of segment $CD$ is $2$, and the length of segment $BE$ is $5$. What is the value of $x$?