Tüm alıştırma soruları

In the field of volcanology, continuous satellite monitoring of sulfur dioxide plumes emitted by active volcanoes ______ researchers to track shifts in magma movement. By measuring the concentration of these gases from orbit, scientists can detect impending eruptions days before they occur on the ground, thereby providing critical warnings to nearby communities.

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

While preparing a presentation on Anglo-Saxon warfare, a student took the following notes:
* The Sutton Hoo helmet is an Anglo-Saxon artifact excavated in 1939 in Suffolk, England.
* It was crushed when the burial chamber collapsed and was reconstructed from hundreds of iron fragments.
* The helmet is made primarily of iron and tinned bronze.
* It features decorative panels depicting warriors and mythical beasts.
* It is one of only four surviving Anglo-Saxon helmets known to archaeologists.

The student wants to emphasize the helmet's material composition and its rarity among archaeological finds. Which choice most effectively uses information from the given notes to accomplish this goal?

A logo design consists of a region bounded by an isosceles trapezoid and a semicircle. The semicircle is attached to the shorter parallel side of the trapezoid such that the diameter of the semicircle is equal to the length of that side, and the semicircle lies entirely outside the trapezoid. The trapezoid has a height of $8$ centimeters, a longer parallel side of $18$ centimeters, and a shorter parallel side of $10$ centimeters. What is the total area, in square centimeters, of the logo?

Data collected by the Cassini spacecraft during its flybys of Saturn's moon Enceladus revealed the presence of silica nanoparticles in the plumes of water vapor erupting from the subsurface ocean. Laboratory simulations indicate that such nanoparticles can only form at temperatures above $90^\circ\text{C}$ in alkaline water that is in direct contact with a rocky core containing specific minerals. Because the surface temperature of Enceladus is constantly below $-180^\circ\text{C}$, the detection of these nanoparticles in the plumes indicates that Enceladus's subsurface ocean ______.

Which choice most logically completes the text?

In triangle $ABC$, angle $C$ is a right angle. The length of side $AC$ is $15$ and the length of side $BC$ is $8$. Point $D$ lies on side $AC$ such that $CD = 6$. A line segment $DE$ is drawn perpendicular to side $AC$ such that point $E$ lies on side $AB$. What is the length of segment $BE$?

In astrobiology, researchers analyze distant worlds for environments capable of supporting organisms. The detection of potential biosignatures—specifically atmospheric methane and oxygen found in precise ratios on rocky exoplanets orbiting distant stars—______ that biological processes may be occurring elsewhere in the galaxy. However, astronomers must remain cautious, as abiotic geochemical reactions can also synthesize these atmospheric gases under specific conditions.

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

In the $xy$-plane, a circle with radius $r$, where $r > 1$, has its center in the first quadrant. The circle is tangent to the line $x = 1$ and tangent to the line $y = 2$. If the center of the circle lies on the line with equation $y = \frac{4}{3}x$, what is the value of $r$?

Points $A$, $B$, and $C$ lie on a circle. The measure of minor arc $AB$ is $110^\circ$ and the measure of minor arc $BC$ is $130^\circ$. What is the measure of the inscribed angle $\angle ABC$, in degrees?

While preparing a presentation on the ancient Maya city of Tikal, a student took the following notes:
* Tikal is an ancient Maya citadel located in the rainforests of Guatemala.
* It was one of the largest archaeological sites and urban centers of the pre-Columbian Maya civilization.
* Temple IV is the tallest pre-Columbian structure in the Americas, standing at 65 meters (213 feet) tall.
* Temple IV was built around 741 CE by the ruler Yik'in Chan K'awiil to commemorate his reign.
* Archaeologists estimate that Tikal was abandoned by the end of the 10th century CE.

The student wants to emphasize the height of Temple IV and the ruler who built it. Based on the notes, complete the sentence to meet this goal.

Triangle $ABC$ is similar to triangle $DEF$, where the ratio of the length of side $AB$ to the length of side $DE$ is $3$ to $5$. If the area of triangle $ABC$ is $18$, what is the area of triangle $DEF$?

While preparing a presentation on ancient Greek technology, a student took the following notes:

* The Antikythera mechanism is an ancient Greek hand-powered model of the solar system.
* It is widely considered the world's oldest known analog computer.
* The device was constructed around 150 BCE.
* It contains at least thirty meshing gears made of bronze.
* It was recovered from a shipwreck off the coast of Greece in 1901.

The student wants to write a single sentence that emphasizes the construction date and the material composition of the Antikythera mechanism. Complete the sentence by filling in the blanks.

In a circle with center $O$, segment $PT$ is tangent to the circle at point $T$. The distance from point $P$ to the center of the circle is $25$. If the radius of the circle is $7$, what is the length of segment $PT$?

In a circle, chords $WY$ and $XZ$ intersect at point $P$. The measure of minor arc $WX$ is $55^\circ$ and the measure of minor arc $YZ$ is $105^\circ$. What is the measure, in degrees, of angle $WPX$?

Urban heat islands (UHIs) are areas where city infrastructure absorbs and retains heat, making them warmer than surrounding rural areas. To combat this, urban planners have widely introduced vegetative roofs, which utilize evapotranspiration to cool buildings and lower ambient air temperatures. However, sociologist Dr. Clara Vance notes that vegetated roof initiatives are disproportionately implemented on commercial high-rises and luxury residential developments in high-income neighborhoods. Because lower-income areas typically have higher baseline temperatures and fewer green spaces, she argues that unless cities alter their current distribution policies for vegetated infrastructure, these sustainability initiatives will likely Which choice most logically completes the text?

A designer has a rectangular piece of fabric that measures $12$ inches by $18$ inches. The designer cuts out two identical right triangular pieces from the corners along one of the $12$-inch sides. Each right triangular piece has a leg of length $4$ inches along the $12$-inch side and a leg of length $x$ inches along the $18$-inch side. If the area of the remaining piece of fabric is $180$ square inches, what is the value of $x$?

In a circle with center $O$, chord $AB$ has a length of $12$. The perpendicular distance from center $O$ to chord $AB$ is $8$. If the area of the circle is $k\pi$, what is the value of $k$?

A circle with center $O$ has a radius of $8$. Points $A$ and $B$ lie on the circle such that the length of the minor arc $AB$ is $5\pi$. What is the area of the major sector $AOB$?

While preparing a presentation on the discovery of Tutankhamun's tomb, a student took the following notes:

* The tomb of Tutankhamun was discovered in the Valley of the Kings in November 1922.
* The excavation was led by British archaeologist Howard Carter.
* The extensive search was funded by the wealthy aristocrat Lord Carnarvon.
* The tomb contained thousands of intact artifacts, including a solid gold coffin.

The student wants to write a sentence that emphasizes who provided the financial backing for the excavation. Complete the sentence by filling in the blank with the appropriate detail from the notes.

While preparing a presentation on the Voyager 1 space probe, a student took the following notes:
* Voyager 1 is a NASA space probe launched in September 1977 to study the outer Solar System.
* In August 2012, it crossed the heliopause to become the first human-made object to enter interstellar space.
* At the moment of this crossing, Voyager 1 was located approximately 121 astronomical units (AU) from the Sun.
* The spacecraft carries a Golden Record containing sounds and images selected to portray life on Earth.

The student wants to emphasize the distance from the Sun at which Voyager 1 entered interstellar space. Which choice most effectively uses information from the given notes to accomplish this goal?

A property line is in the shape of a trapezoid with parallel sides of length $20$ meters and $30$ meters, and a height of $12$ meters. A second property is geometrically similar to the first, where each linear dimension of the second property is $1.5$ times the corresponding dimension of the first property. What is the area, in square meters, of the second property?