Tüm alıştırma soruları

An acute angle $\theta$ in a right triangle satisfies the equation $\cos(\theta) = \frac{5}{13}$. What is the value of $\tan(90^\circ - \theta)$?

Analyses of skeletal remains from the transition to agriculture in the Fertile Crescent show a significant rise in dental caries (cavities) among early farmers compared to hunter-gatherers, a shift typically blamed on carbohydrate-rich grain diets. However, bioarchaeologist Clara Vance notes that dental health did not decline uniformly; some agricultural settlements maintained low, stable caries rates for centuries. Vance argues that diet alone cannot explain this variation, pointing out that these low-caries populations lived in regions where local groundwater contained exceptionally high levels of naturally occurring fluoride. Which choice most logically completes the text?

At a currency exchange booth, $4$ US dollars (USD) can be exchanged for $5$ local credits, and $6$ local credits can be exchanged for $15$ reward coupons. Based on these rates, what is the total number of reward coupons that can be obtained in exchange for $24$ USD?

Two connected gears, Gear A and Gear B, rotate together such that the belt connecting them does not slip. The radius of Gear A is $15$ centimeters and the radius of Gear B is $9$ centimeters. If Gear A rotates through a central angle of $\frac{4\pi}{15}$ radians, Gear B rotates through a central angle of $x$ degrees. What is the value of $x$?

The table below shows selected values of $x$ and the corresponding values of the polynomial function $p(x)$.

If $p(x) = a(x-2)(x-4)(x-k)$ for all real numbers $x$, where $a$ and $k$ are constants, what is the value of $k$?

In the late nineteenth century, historians studying the rapid growth of industrial cities in the American Midwest hypothesized that urban development was driven almost entirely by the expansion of the rail network. Sociologist Marcus Vance, however, argued that this explanation overlooks the crucial role of local municipal incentive programs. Vance analyzed demographic records from several mid-sized Illinois towns between 1870 and 1890. He found that towns offering tax exemptions to new factories grew at nearly twice the rate of neighboring towns with similar rail access. This finding suggests that regional transport infrastructure was a necessary, but not sufficient, factor in urban industrialization, highlighting the agency of local policymakers in shaping economic geography.

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

A student is researching Göbekli Tepe, an ancient archaeological site. The student has taken the following notes:

* Göbekli Tepe is an archaeological site located in southeastern Turkey.
* The site features massive T-shaped stone pillars dating to the $10\text{th}$ millennium BCE.
* It was first surveyed in $1963$ by researchers from Turkey and the United States.
* Detailed excavations at the site began in $1995$.
* These excavations were directed by German archaeologist Klaus Schmidt.
* Schmidt interpreted the site as a Neolithic sanctuary rather than a residential settlement.

The student wants to write a sentence that emphasizes when the detailed excavations at Göbekli Tepe began and who directed them. Based on the notes, what year and which archaeologist's name should be filled in the blanks to achieve this goal?

In historical sociolinguistics, researchers analyzing sixteenth-century European administrative texts have noted a rapid decline in regional orthographic variations following the introduction of the movable-type printing press. Traditionally, scholars attributed this standardization solely to the preference of printers for dominant metropolitan dialects. However, a recent study by Dr. Clara Vance reveals that early print shops frequently employed compositors from diverse regional backgrounds, who initially maintained their native spelling habits in printed books. Vance also found that official administrative centers began mandating standardized spelling systems for legal documents only after print-distribution networks had fully integrated regional markets. Which choice most logically completes the text?

In a science department, the ratio of the number of students enrolled in Chemistry to the number of students enrolled in Physics is $5$ to $3$. The ratio of the number of students enrolled in Physics to the number of students enrolled in Biology is $2$ to $7$. If no student is enrolled in more than one of these courses and there are $105$ students enrolled in Biology, what is the total number of students enrolled in these three courses?

A cubic polynomial function $f$ has $x$-intercepts at $(2, 0)$, $(5, 0)$, and $(c, 0)$, where $c$ is a positive constant. In the $xy$-plane, the graph of $y = f(x)$ has a $y$-intercept at $(0, 60)$. If $f(1) = 16$, what is the value of $c$?

An artist designs a logo consisting of a rectangle and an isosceles triangle. The rectangle has a length of $12$ centimeters and a width of $8$ centimeters. The base of the isosceles triangle is one of the $8$-centimeter sides of the rectangle, and the vertex of the triangle lies outside the rectangle. If the total area of the logo is $120$ square centimeters, what is the height, in centimeters, of the triangle?

A polynomial $f(x)$ has a remainder of $12$ when divided by $x - 4$. If $g(x) = (x - 2)f(x - 2) - 5$, what is the remainder when $g(x)$ is divided by $x - 6$?

While preparing a presentation on ancient civilizations in the Americas, a student took the following notes:
* The Sacred City of Caral-Supe is an archaeological site located in Peru.
* It is considered the oldest known civilization in the Americas, dating back to $3000$ BCE.
* In $2001$, archaeologist Ruth Shady published radiocarbon dating results that confirmed the site's age.
* The city features the Pirámide Mayor, a massive structure measuring $150$ meters long and $110$ meters wide.
* Shady's excavations revealed that builders used woven reed bags filled with stones, called shicras, to protect the buildings from earthquakes.

The student wants to emphasize the age of the Sacred City of Caral-Supe and the archaeologist who confirmed it. Which choice most effectively uses information from the given notes to accomplish this goal?

In a circle with center $O$, chord $AB$ has length $12\sqrt{3}$. A radius $OC$ is perpendicular to chord $AB$ and intersects $AB$ at point $D$. If $CD = 6$, what is the area of the sector of the circle bounded by radii $OA$, $OB$, and the minor arc $AB$?

In cognitive science, the 'spacing effect' describes the phenomenon where information is more easily recalled if learning sessions are spaced out over time rather than crammed into a single block. ______ studies have shown that students who review new vocabulary words over several days retain the definitions significantly longer than those who study them in one marathon session.

Which choice completes the passage with the most logical transition?

The measure of angle $A$ is $45^\circ$ greater than the measure of angle $B$. If the measure of angle $B$ is $\frac{5\pi}{12}$ radians, what is the measure of angle $A$, in degrees?

In mycology, the study of subterranean mycorrhizal networks has revealed complex interactions between tree species in temperate forests. A network of fungal threads, which extends through the soil to connect the root systems of different plants, ______ the sharing of vital nutrients and water. This cooperative exchange enhances the overall resilience of the entire forest ecosystem.

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

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

In a circle with center $O$, $AB$ is a diameter. Point $C$ lies on the circle such that the measure of arc $AC$ is $\frac{5\pi}{9}$ radians. Point $D$ lies on the circle such that chord $AC$ is parallel to segment $OD$, and points $C$ and $D$ lie on the same side of diameter $AB$. What is the measure, in radians, of angle $COD$?