Tüm alıştırma soruları

A local utility company is evaluating two different methods, Method A and Method B, to reduce electricity distribution losses. The table below shows the modeled annual electricity losses, in megawatt-hours (MWh), for each method over the first two years ($t = 0$ to $t = 2$), where $t$ is the number of years since the evaluation began.

One method is modeled by a linear function, and the other method is modeled by an exponential function. What is the difference, in MWh, between the modeled annual electricity losses for the two methods at $t = 3$ years?

For the polynomial $p(x) = 2x^3 - x^2 - kx + 6$, where $k$ is a constant, the remainder when $p(x)$ is divided by $2x - 3$ is $0$. What is the value of $k$?

A student is researching the Lycurgus Cup, an ancient Roman artifact. The student has taken the following notes:
- The Lycurgus Cup is a 4th-century CE glass cage cup.
- It is made of dichroic glass, which changes color depending on how light passes through it.
- When lit from the front, the cup appears green.
- When lit from behind, the cup glows red.
- This optical effect is caused by gold and silver nanoparticles embedded in the glass.
- The cup is currently housed in the British Museum in London.

The student wants to write a sentence that emphasizes how the Lycurgus Cup's appearance changes depending on the lighting. Which choice most effectively uses information from the given notes to accomplish this goal?

For decades, historians assumed that medieval European painters obtained ultramarine pigment, derived from lapis lazuli, exclusively through arduous trade routes terminating in Central Asia. However, a recent chemical analysis of a tenth-century monastic manuscript revealed trace impurities of cobalt and copper that are characteristic of mineral deposits in northern Europe. This finding suggests that regional monasteries may have engaged in local, small-scale mining operations rather than relying entirely on distant imports. Consequently, scholars are now re-evaluating the degree of economic self-sufficiency maintained by early medieval religious centers.

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

In the figure, lines $AB$ and $CD$ intersect at point $O$, and ray $OE$ is perpendicular to line $AB$. If the measure of $\angle EOC$ is $27^\circ$, what is the measure, in degrees, of $\angle BOD$?

In botany, the phenomenon of 'foliar water uptake' (FWU) allows plants in arid environments to absorb water directly from fog or dew through their leaves. While FWU is crucial during dry periods, researchers hypothesized that it might carry a hidden cost by facilitating the entry of foliar pathogens. To test this, botanists examined several species of desert shrubs, exposing some to simulated fog containing common bacterial pathogens and others to dry conditions. They found that shrubs subjected to high-humidity fog exhibited significantly higher rates of pathogen infection, but only when their stomata were fully open. Which choice most logically completes the text?

A food packaging company produces a trail mix containing almonds, cashews, and raisins. The ratio of the weight of almonds to the weight of cashews is $3:2$, and the ratio of the weight of cashews to the weight of raisins is $5:4$. If a batch of trail mix contains $360$ ounces of raisins, what is the total weight, in ounces, of the trail mix?

In triangle $ABC$, the measure of angle $ABC$ is $90^\circ$ and the measure of angle $BAC$ is $30^\circ$. Segment $BD$ is perpendicular to segment $AC$ such that $D$ lies on $AC$. Segment $DE$ is perpendicular to segment $BC$ such that $E$ lies on $BC$. If the length of segment $CE$ is $3$, what is the length of segment $AC$?

A student is preparing a presentation on the discovery of the Terracotta Army.

* In $1974$, local farmers were digging a water well near Xi'an, China.
* The farmers unearthed fragments of a clay figure, leading to the discovery of the Terracotta Army.
* The Terracotta Army is a collection of thousands of life-sized clay sculptures.
* The sculptures depict the armies of Qin Shi Huang, the first Emperor of China.
* The tomb complex and its sculptures date back to the late third century BCE.

Based on the notes provided, complete the sentence to emphasize the specific activity that led to the $1974$ discovery of the Terracotta Army.

At the beginning of 2015, Forest A had 4,000 trees and Forest B had 3,000 trees. The number of trees in Forest A increases by 150 trees each year. The number of trees in Forest B increases by 4% each year. If $A(t)$ and $B(t)$ represent the number of trees in Forest A and Forest B, respectively, $t$ years after the beginning of 2015, what is the value of $A(5) - B(5)$, rounded to the nearest whole number?

During the Paleocene-Eocene Thermal Maximum (PETM) approximately 56 million years ago, global temperatures rose rapidly. Many scientists hypothesized that this warming event led to an increase in insect herbivory due to elevated metabolic rates. To test this, paleontologist Elena Vance and her team examined fossilized leaves from the Bighorn Basin in Wyoming, meticulously documenting the frequency and variety of insect feeding damage. Vance's team found that leaves from the peak warming period exhibited significantly higher rates of diverse insect damage compared to leaves from pre-warming intervals. This finding suggests that ancient insect populations experienced rapid expansion and diversification in response to shifting climates, offering critical insights into how modern ecosystems might react to ongoing global warming.

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

An agricultural irrigation system uses two types of sprinklers, Type A and Type B. Water flows through $3$ Type A sprinklers at a combined rate of $15$ gallons per minute. Water flows through $5$ Type B sprinklers at a combined rate of $18$ gallons per minute. If a farmer runs $8$ Type A sprinklers and $10$ Type B sprinklers simultaneously, what is the total rate of water flow, in gallons per minute?

In 2009, NASA launched the Kepler space telescope to search for Earth-sized exoplanets. While computer algorithms successfully analyzed the vast majority of light curves—dips in starlight indicating a passing planet—certain complex orbital patterns proved difficult for automated systems to detect. To address this, astronomers established the Planet Hunters project, allowing citizen science volunteers to visually inspect the data. Although professional researchers initially doubted that amateurs could rival sophisticated software, the volunteers quickly identified several multi-planet systems that computers had overlooked. This success demonstrated that human visual pattern recognition remains an invaluable supplement to machine-learning algorithms in astronomical data analysis.

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

While the senator's initial response to the controversial bill was one of outright hostility, her subsequent statements offered a more _______ critique, acknowledging the validity of her opponents' concerns while still voicing reservations.

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

In the $xy$-plane, an angle $\theta$ in standard position has its terminal ray intersecting the unit circle at the point $\left(-\frac{\sqrt{2}}{2}, -\frac{\sqrt{2}}{2}\right)$. The angle is rotated counterclockwise by $15^\circ$, and then its measure is doubled. The final resulting angle is coterminal with an angle of $\frac{a\pi}{b}$ radians, where $0 \le \frac{a\pi}{b} < 2\pi$, and $a$ and $b$ are positive integers with no common factors. What is the value of $a + b$?

A student is preparing a presentation on the archaeological excavation of Thonis-Heracleion. The student has taken the following notes:
* Thonis-Heracleion was an ancient Egyptian port city that sank into the Mediterranean Sea in the $8\text{th}$ century CE.
* In $2000$, underwater archaeologist Franck Goddio discovered the city's ruins in Abu Qir Bay.
* Among the recovered artifacts was a statue of Hapy, the Egyptian god of the Nile flood.
* The statue is carved from black granite.
* The statue stands $17.7$ feet tall.

The student wants to emphasize the material and size of the Hapy statue. Which choice most effectively uses information from the given notes to accomplish this goal?

In historical sociolinguistics, researchers analyze how language variations spread across geographic boundaries. The rapid adoption of phonetic innovations among diverse, isolated communities _______ that early trade networks played a far more influential role in cultural transmission than scholars previously assumed. As a result, modern linguists are actively revising their existing models of regional dialect evolution.

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

In the $xy$-plane, the graph of the quadratic function $f$ has a vertex at $(h, k)$, where $h$ and $k$ are constants. The graph passes through the points $(1, 10)$ and $(7, 10)$. If the minimum value of the function $f$ is $1$, what is the value of $f(2)$?

A circle has a circumference of $16\pi$. An arc on this circle has a length of $2\pi$. What is the measure, in degrees, of the central angle that subtends this arc?

A marine biologist wants to estimate the number of blue crabs in a bay that are infected with a specific parasite. The biologist captures a random sample of $250$ blue crabs from the bay, finds that $15$ of the crabs are infected, and then releases them. Based on this sample, if there is a total population of $12,000$ blue crabs in the bay, what is the best estimate of the total number of blue crabs infected with the parasite?