All practice questions

At the start of $2018$, City A and City B each recycled $12,000$ tons of plastic. For the next several years, the annual amount of plastic recycled in City A increased by $800$ tons each year. During the same period, the annual amount of plastic recycled in City B increased by $5\%$ each year. Which of the following is closest to the difference, in tons, between the annual amount of plastic recycled in City B and the annual amount of plastic recycled in City A at the start of $2023$?

Biologists studying deep-sea ecosystems have long observed the phenomenon of abyssal gigantism, in which certain marine species grow to sizes far exceeding those of their shallow-water relatives. _______, the giant isopod (*Bathynomus giganteus*) can reach a length of up to 30 centimeters, whereas its coastal counterparts typically measure no more than a few centimeters. This stark size difference is hypothesized to be an adaptation to the extreme pressure and scarce food resources characteristic of the deep ocean.

Which choice completes the text with the most logical transition?

While preparing a presentation on environmental biotechnology, a student took the following notes:
* Phytoremediation is a method that uses plants to remove, transfer, or stabilize contaminants in soil and water.
* The term was coined in 1991 by plant biologist Ilya Raskin.
* It is a type of bioremediation, which uses living organisms to clean up polluted environments.
* Certain plants, like Indian mustard, are used because they accumulate high levels of toxic metals.
* Traditional cleanup techniques, like landfilling or soil excavation, are often much more expensive.

The student wants to provide a definition of phytoremediation. Which choice most effectively uses information from the given notes to accomplish this goal?

In a right triangle, one of the acute angles is $\theta$. If $\tan(\theta) = \frac{x}{y}$, where $x$ and $y$ are positive constants, what is the value of $\cos\left(\frac{\pi}{2} - \theta\right)$ in terms of $x$ and $y$?

In the $xy$-plane, the vertex of the parabola defined by $y = a(x - 2)(x - 8)$ has a $y$-coordinate of $-18$, where $a$ is a positive constant. What is the value of $a$?

In paleoclimatology, the ratio of oxygen isotopes ($\delta^{18}\text{O}$) in stalagmites is used to reconstruct historical rainfall, as wetter periods typically result in lower $\delta^{18}\text{O}$ values in the precipitated calcium carbonate. However, researchers analyzing a stalagmite from Spain’s system of caves noticed that during a documented multi-decade drought in the thirteenth century, the stalagmite’s $\delta^{18}\text{O}$ values remained persistently low. They hypothesized that the cave's drip water during this dry spell was fed by a massive, deep aquifer that takes decades to filter water downward, rather than by immediate precipitation. If this hypothesis is correct, it suggests that the Spanish stalagmite ______

Which choice most logically completes the text?

For decades, paleontologists debated whether dinosaurs were endothermic (warm-blooded) or ectothermic (cold-blooded), with many assuming that their massive size would make active metabolic heating unsustainable. Recent isotopic analysis of fossilized eggshells, which provides a direct record of female body temperatures during ovulation, has revealed internal temperatures comparable to those of modern birds. __________, some researchers argue that these high temperatures might simply reflect passive heat retention from warm environments rather than true endothermy.

Which choice completes the text with the most logical transition?

In the figure, triangle $RST$ is a right triangle with the right angle at vertex $S$. If the length of side $RS$ is $8$ and the length of side $ST$ is $15$, what is the length of the hypotenuse $RT$?

In the $xy$-plane, the graph of the polynomial function $f$ has $x$-intercepts at $(-3, 0)$, $(1, 0)$, and $(k, 0)$, where $k$ is a constant greater than $1$. The function is defined by $f(x) = -2(x + 3)(x - 1)(x - k)$. If the graph of $f$ passes through the point $(2, 20)$, what is the value of $k$?

In his 1858 study of the *Iliad* and the *Odyssey*, British statesman William Gladstone observed that Homer's color vocabulary was remarkably sparse, often using the same word to describe objects of vastly different hues. To account for this eccentricity, Gladstone hypothesized that the ancient Greeks possessed a less developed physiological capacity for color perception than modern humans. This evolutionary hypothesis was quickly rejected by subsequent researchers, who argued instead that Homeric color descriptors were metaphoric or centered on light intensity rather than hue. Nonetheless, Gladstone’s work is widely credited with initiating the modern field of linguistic relativity, prompting scholars to investigate how language structures sensory experience.

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

A wheel rotates through a central angle of $\frac{11\pi}{18}$ radians. What is the measure of this angle in degrees?

An environmental science class recorded the daily PM2.5 air quality index (AQI) values for a city over a 7-day period. The recorded values for 6 of the days were $38$, $42$, $45$, $49$, $52$, and $58$. The AQI value for the 7th day, $x$, is unknown. If the mean AQI value for the 7 days is $48$, what is the median AQI value for the 7 days?

A scientist is tracking the growth of a cell culture. The cell culture's area, in square millimeters, can be modeled by either a linear function or an exponential function. The table below shows the area of the cell culture at the end of Day 1 and Day 2.

If the area of the cell culture grows exponentially, the area on Day 4 would be $E$ square millimeters. If the area grows linearly, the area on Day 4 would be $L$ square millimeters. What is the value of $E - L$?

In triangle $ABC$, the angle at vertex $B$ is a right angle. The lengths of sides $AB$ and $BC$ are $12$ and $16$, respectively. A point $D$ is chosen on the hypotenuse $AC$ such that $AD = 5$. A line drawn through $D$ perpendicular to $AC$ intersects the line passing through $B$ and $C$ at point $G$, such that $B$ lies between $G$ and $C$. What is the length of segment $GD$?

An agricultural drone sprays liquid fertilizer at a constant rate. The drone covers $3$ acres of cropland every $20$ minutes. If the drone operates continuously at this rate, how many hours will it take the drone to spray $54$ acres of cropland?

In the dry grasslands of the American Southwest, the resilient seed pods of the desert lupine (*Lupinus sparsiflorus*) can remain dormant in the soil for several years during prolonged periods of drought. The germination of these seeds, which occurs only after a sequence of uncommonly heavy winter rains fully saturates the parched ground, _______ a rapid, vibrant bloom that temporarily transforms the landscape.

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

In urban environments, some species of leafcutter bees (*Megachile*) have adapted to using synthetic materials for nest construction. Researchers J. MacIvor and A. Moore documented that *Megachile rotundata* collected pieces of polyurethane plastics, such as shopping bags, to build their brood cells. While traditional nests made of leaves allow moisture to escape, the non-porous plastic cells trapped moisture inside. This trapped moisture led to increased mold growth within the nests, which consequently reduced the survival rate of the offspring. However, the plastic-constructed nests also demonstrated a notable benefit: they experienced significantly fewer infestations by parasitic wasps compared to nests constructed from natural leaves.

Based on the text, what is true of the *Megachile rotundata* nests made from polyurethane plastics?

If the measure of an angle is $\frac{5\pi}{4}$ radians, what is its measure in degrees?

The graph of the quadratic function $f$ in the $xy$-plane has its vertex at $(3, 2)$. If the graph passes through the point $(5, -6)$, what is the $y$-intercept of the graph of $f$?

In materials science, the degradation rate of biodegradable polymers, which varies depending on exposure to environmental factors such as humidity and temperature, _______ the structural lifespan of medical implants. Because these temporary devices must support healing tissues before safely dissolving in the body, researchers must carefully control the rate at which the material breaks down. Which choice completes the text so that it conforms to the conventions of Standard English?