Tüm alıştırma soruları

A straight ladder is leaning against a vertical wall. The base of the ladder is placed $9$ feet from the bottom of the wall. If the top of the ladder touches the wall at a height of $12$ feet above the ground, what is the length, in feet, of the ladder?

While researching bioacoustics, a student takes the following notes:
* Blue whales (*Balaenoptera musculus*) use low-frequency vocalizations to communicate across vast ocean distances.
* In a $2018$ study, researchers analyzed underwater audio recordings of blue whale songs collected from $1960$ to $2018$.
* The analysis revealed that the fundamental frequency of blue whale songs has decreased by approximately $30\%$ globally.
* Researchers hypothesize that this pitch reduction is an adaptation to cope with rising ambient ocean noise caused by commercial shipping.

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

Paleontologists studying the fossilization of soft-bodied organisms from the Burgess Shale have noted that specific chemical microenvironments are required to prevent decay before mineralization can occur. ______ extremely low oxygen levels in the sediment can inhibit the activity of aerobic decomposers, allowing delicate structures like gills and antennae to be preserved.

Which choice completes the text with the most logical transition?

In subglacial lakes beneath the Antarctic Ice Sheet, primary production cannot rely on photosynthesis due to the absolute absence of sunlight. Instead, chemosynthetic microbes oxidize inorganic compounds, such as iron or sulfur, to generate energy. In Lake Mercer, researchers discovered high concentrations of dissolved organic carbon (DOC) alongside these chemosynthetic communities. Because the ice sheet has isolated the lake from the atmosphere for thousands of years, this DOC cannot have originated from recent photosynthetic activity. However, analysis revealed that the DOC molecules are structurally similar to those produced by marine phytoplankton, which require sunlight. Which choice most logically completes the text?

Historically, geologists characterized the Earth’s mantle as a largely homogenous and static layer of solid rock. However, recent high-resolution seismic imaging has ________ this traditional model, revealing complex, localized convection currents and composition gradients that indicate a far more dynamic interior.

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

In marine ecology, the term "kleptoplasty" describes a symbiotic phenomenon where a host organism sequesters functional chloroplasts from digested algae and uses them to perform photosynthesis. ______ the sea slug *Elysia chlorotica* feeds on the alga *Vaucheria litorea* and is subsequently able to survive for months solely on the energy produced by these stolen organelles.

Which choice completes the passage with the most logical transition?

A small design firm employs $10$ people. The mean of their annual salaries is $\$50,000$, and the median is $\$48,000$. The employee with the highest salary of $\$95,000$ receives a $\$10,000$ raise, while the salaries of all other employees remain unchanged. What are the mean and the median of the salaries after the raise?

The function $g$ is defined by $g(x) = f(x - 3) - 2$. If the point $(5, 7)$ lies on the graph of $y = f(x)$ in the $xy$-plane, which of the following points must lie on the graph of $y = g(x)$?

The table below shows several values of $x$ and the corresponding values of the third-degree polynomial function $f$.

If $f(x) = a(x-r_1)(x-r_2)(x-r_3)$ for all real numbers $x$, where $a$, $r_1$, $r_2$, and $r_3$ are constants, what is the value of $a$?

In triangle $ABC$, point $D$ lies on side $BC$ such that the ratio of $BD$ to $DC$ is $1$ to $2$. Point $E$ lies on segment $AD$ such that the ratio of $AE$ to $ED$ is $3$ to $1$. A line passing through $E$ and parallel to $AC$ intersects side $AB$ at $F$ and side $BC$ at $G$. If the area of triangle $ABC$ is $128$, what is the area of triangle $BFG$?

An aerospace company designs two similar solar panels. The smaller panel is in the shape of a parallelogram and has an area of $80$ square centimeters. If the perimeter of the larger panel is $1.5$ times the perimeter of the smaller panel, what is the area, in square centimeters, of the larger panel?

During boreal forest fires, the combustion of organic matter produces pyrogenic carbon (charcoal), which is highly resistant to microbial decomposition. Some ecologists hypothesized that this carbon represents a long-term sink that helps offset carbon dioxide emissions from the fire. However, researcher Maya Lin and her team demonstrated that pyrogenic carbon particles adsorb dissolved organic compounds from the soil, concentrating easily degradable nutrients. This process stimulates local soil microbe activity, which in turn increases the decomposition rate of nearby unburned soil organic matter. Therefore, while pyrogenic carbon itself remains stable, its presence in the soil may ______

Which choice most logically completes the text?

An acute angle $\theta$ satisfies the equation $\sin(\theta) = 0.6$. What is the value of $\cos(\theta)$?

In the study of art history, researchers long believed that the vibrant blue pigment used in ancient Maya murals, known as Maya Blue, was highly susceptible to biodegradation over centuries due to its organic dye component, indigo. ________, recent chemical analysis has revealed that the encapsulation of indigo molecules within the crystalline channels of the clay palygorskite creates a highly stable organo-clay complex that is impervious to acids, alkalis, and microbial attack.

Which choice completes the passage with the most logical transition?

The Antarctic hair grass (*Deschampsia antarctica*) is one of only two flowering plant species native to Antarctica. To survive the region’s extreme cold and high ultraviolet (UV) radiation, the plant produces high concentrations of sucrose and specialized proteins, such as dehydrins. Sucrose acts as a natural cryoprotectant, preventing ice crystal formation within the plant's cells, while dehydrins stabilize cell membranes during sudden freezing events. Researchers have also observed that *D. antarctica* exhibits an unusually high rate of self-pollination, a reproductive strategy that minimizes its reliance on insect pollinators, which are extremely scarce in the harsh Antarctic environment.

Based on the text, what is true of the dehydrins produced by *Deschampsia antarctica*?

A right triangle in the $xy$-plane has vertices at the coordinates $(0, 0)$, $(15, 0)$, and $(15, 8)$. What is the perimeter of this triangle?

In the $xy$-plane, the graph of the quadratic function $f$, defined by $f(x) = -(x - 4)^2 + c$ where $c$ is a constant, intersects the $x$-axis at two points. If the distance between these two points is $10$, what is the value of $c$?

While researching the Cherokee writing system, a student takes the following notes:
* Sequoyah, a Cherokee silversmith, began developing a writing system for the Cherokee language in 1809.
* He completed the system, a syllabary of 85 characters representing spoken syllables, in 1821.
* Prior to Sequoyah's syllabary, the Cherokee language was purely oral.
* Within a decade of its introduction, the system enabled the Cherokee people to achieve literacy rates higher than those of neighboring European-American settlers.

The student wants to summarize the creation and impact of the Cherokee writing system. Which choice most effectively uses information from the given notes to accomplish this goal?

While preparing a presentation on branches of zoology, a student took the following notes:
* Myrmecology is the branch of entomology focused on the scientific study of ants.
* The name of the field is derived from the Greek words *myrmex* (meaning "ant") and *logos* (meaning "study").
* Myrmecologists research diverse topics, including ant social structures, chemical communication, and ecological roles.
* Key foundational research in the discipline was conducted in the early twentieth century by entomologist William Morton Wheeler.

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

Many cognitive scientists hypothesized that language acquisition in infants relies entirely on domain-general learning mechanisms, such as pattern recognition and statistical learning. A recent study by Dr. Clara Mendez showed that infants are highly sensitive to statistical regularities in speech. ________, Mendez's team observed that this sensitivity alone is insufficient for infants to grasp syntactic structure, which appears to require innate domain-specific constraints.

Which choice completes the passage with the most logical transition?