Tüm alıştırma soruları

In right triangle $ABC$, the measure of angle $C$ is $90^\circ$. If $\cos(A) = 3\sin(A)$, what is the value of $\tan(B)$?

Which word completes the text with the most logical and precise word?

Deep-sea hydrothermal vent ecosystems are typically characterized by their reliance on chemosynthesis, where microbes convert chemical energy from vent fluids into organic matter. However, marine biologist Marcus Vance has identified several vent sites where photosynthetic microbes utilize geothermal radiation—the faint infrared glow emitted by superheated water��to perform a form of non-solar photosynthesis. This discovery challenges the long-held paradigm that photosynthesis is strictly dependent on sunlight reaching the photic zone. Consequently, Vance's research suggests that primary production in the deep ocean may be more diverse and widespread than previously assumed, requiring a revision of ecological models for aphotic environments.

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

In rectangle $ABCD$, the length of side $AB$ is $12$ and the length of side $BC$ is $9$. Point $P$ lies on the diagonal $AC$ such that $AP = \frac{1}{3} AC$. What is the area of triangle $BPD$?

While preparing a presentation on zoology, a student took the following notes:
* Ethology is the scientific study of animal behavior, particularly under natural conditions.
* It is considered a sub-discipline of zoology.
* The field was formalized by biologists Nikolaas Tinbergen and Konrad Lorenz.
* Ethologists study behaviors such as communication, mating rituals, and social interactions.
* A primary goal of ethology is understanding how behaviors adapt and evolve to assist in animal survival.

The student wants to introduce the field of ethology and define the term. Which choice best uses information from the notes to achieve this goal?

The table below shows several values of the function $f$.

The function $g$ is defined by $g(x) = \frac{1}{2}f(x + 4) + 3$. What is the value of $g(-5)$?

In the late fourth millennium BCE, administrative practices in Mesopotamian city-states underwent a critical transformation due to expanding trade networks. Initially, accounting relied on individual clay tokens of various shapes representing specific quantities of goods. As transactions grew more complex, administrators began impressing these tokens directly into clay envelopes, and eventually, drawing representations of the tokens on flat clay tablets instead. This transition marked the birth of proto-cuneiform writing, shifting human communication from three-dimensional object-based recordkeeping to two-dimensional symbolic notation. Consequently, this technological shift laid the foundation for the development of fully abstract writing systems capable of recording spoken language.

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

In right triangle $RST$, the measure of angle $T$ is $90^\circ$ and the length of the hypotenuse $RS$ is $10$. If $\tan(R) + \tan(S) = \frac{5}{2}$, what is the area of triangle $RST$?

In the field of sociolinguistics, researchers have documented that speakers frequently alter their speech patterns depending on their social environment, a phenomenon known as style-shifting. ________, a bilingual individual might utilize informal slang when conversing with peers but adopt formal grammar and vocabulary during a job interview.

Which choice completes the text with the most logical transition?

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

In right triangle $ABC$, the hypotenuse $AC$ has length $25$, and leg $AB$ has length $20$. What is the length of leg $BC$?

An angle has a measure of $72^\circ$. What is the measure of this angle in radians?

The graph of the polynomial function $f$ in the $xy$-plane is tangent to the $x$-axis at $(1, 0)$ and crosses the $x$-axis only at $(-2, 0)$ and $(4, 0)$. If the $y$-intercept of the graph of $f$ is $(0, 8)$, what is the value of $f(-1)$?

Scholars studying the evolution of Indo-European languages have traditionally relied on comparative reconstruction. Recently, researchers applied evolutionary biology models to vocabulary databases, treating words as traits that mutate over time. These models revealed that high-frequency basic vocabulary items, such as pronouns, mutate at a much slower rate than low-frequency terms, such as words for specific tools. Because high-frequency words are reinforced daily within a speech community, they remain highly resistant to replacement, whereas low-frequency words are more susceptible to borrowing during cultural contact. Thus, in an ancient language that experienced intense and prolonged contact with neighboring tongues, ______

Which choice most logically completes the text?

In a study of the history of technology and metallurgy, researchers analyzed copper artifacts from the Bronze Age in the Aegean region. It was previously assumed that smiths preferred copper sourced from nearby local mines due to transportation difficulties. However, chemical analysis of the isotopic signatures of trace lead impurities in these artifacts reveals that a substantial portion of the bronze objects found in coastal settlements matches copper deposits from distant western Mediterranean islands, whereas artifacts found in inland settlements match local mainland deposits. This pattern remained consistent even during periods of regional conflict that disrupted overland trade routes. Which choice most logically completes the text?

To create a specific shade of green paint, a painter mixes yellow paint and blue paint in a ratio of $3:5$ by volume. To create a specific shade of teal paint, the painter mixes yellow paint and blue paint in a ratio of $1:3$ by volume. If the painter mixes equal volumes of the green paint and the teal paint to create a new mixture, what is the ratio of yellow paint to blue paint in the new mixture?

The graph of the quadratic function $f$ in the $xy$-plane is defined by $f(x) = x^2 - 6x + 5$. If the graph of $f$ is translated $3$ units to the left and $2$ units down, which of the following equations defines the resulting function $g$?

In right triangle $ABC$, the measure of angle $C$ is $90^\circ$, $AC = 15$, and $BC = 20$. Altitude $CD$ is drawn to the hypotenuse $AB$. From point $D$, perpendicular line segments $DE$ and $DF$ are drawn to sides $AC$ and $BC$, respectively, where $E$ lies on $AC$ and $F$ lies on $BC$. What is the ratio of the area of triangle $CEF$ to the area of triangle $ABC$?