All practice questions

A marine biologist set up four tanks to investigate how varying concentrations of dissolved sodium chloride ($\text{NaCl}$) affect the cellular respiration rate of a microalgae species. Each tank contained $500\text{ mL}$ of purified water and $10^6$ algal cells maintained at a constant temperature of $20^\circ\text{C}$.

After 4 hours, the biologist measured oxygen consumption in each tank. Which tank served as the control group in this experiment?

Match each transformed trigonometric function on the left with its set of defining graphical properties on the right.

Determine whether the following statement regarding quadrilateral properties is true or false: Any convex quadrilateral whose diagonals intersect at right angles must be a rhombus.

Passage A
In recent years, urban planners have increasingly turned to urban forestry to combat the "urban heat island" (UHI) effect, wherein built environments absorb and re-emit solar radiation, causing city temperatures to exceed surrounding rural baselines by 2 to 5 degrees Celsius. The primary mechanism driving the cooling efficacy of trees is evapotranspiration—the process by which trees draw soil moisture through their roots and release water vapor from stomata in their leaves. A 2022 study conducted in Atlanta monitored microclimate stations across thirty residential neighborhoods over three summer months. The data demonstrated that canopy coverage exceeding forty percent lowered local ambient daytime temperatures by up to 2.8��C compared to unshaded asphalt corridors. Crucially, the researchers noted that tree canopies act as dual-action buffers: while physical leaves block shortwave solar radiation from reaching heat-absorbing paved surfaces, the latent heat flux from evapotranspiration actively converts incoming thermal energy into liquid-to-vapor phase shifts rather than atmospheric sensible heat. Consequently, municipal initiatives targeting aggressive reforestation have gained widespread advocacy among urban climatologists who contend that living vegetation offers the most ecologically robust defense against urban heat distress.

Passage B
While urban forestry remains a popular strategy for microclimate moderation, civil engineers increasingly advocate for high-albedo materials as a more scalable and resource-efficient remedy for urban thermal loading. Conventional dark asphalt absorbs up to ninety-five percent of incoming solar energy, reradiating it as heat well into the night. In contrast, engineered "cool pavements"—which utilize reflective coatings, light-colored aggregates, or permeable resin matrices—elevate surface albedo from 0.10 to upwards of 0.45. A comprehensive 2023 thermal mapping project across Phoenix evaluated the performance of retrofitted reflective road coatings over two annual cycles. The findings revealed that although cool pavements do not alter latent heat fluxes through moisture release, their surface temperatures remained up to 12°C cooler at solar noon than adjacent standard asphalt, leading to an average net reduction of 1.5°C in canopy-level air temperature across entire municipal sectors. Proponents emphasize that unlike urban trees, which require decades to reach mature canopy density and demand substantial irrigation infrastructure in arid zones, high-albedo surface retrofits yield immediate thermal mitigation across dense infrastructure networks without placing additional stress on municipal water supplies.

Based on Passage A and Passage B, which statement best synthesizes how the evidence presented in both passages addresses the challenge of mitigating urban thermal loading?

Read the passage below:

In November 1958, sound archivist Arthur Pendelton published his definitive catalog of early acoustic wax cylinder recordings. However, the path to this milestone was far from direct. Pendelton had first encountered the deteriorating cylinders in 1949 when a flood damaged the Royal Conservatory's basement, prompting him to transfer the collection into climate-controlled storage. Although he secured an initial preservation grant from the Heritage Foundation in 1951, technical hurdles delayed progress. Following two years of failed attempts to build a mechanical playback stylus, Pendelton successfully digitized the rarest cylinders in 1953 using a modified optical pick-up. Shortly after releasing his published catalog in 1958, Pendelton donated the restored digital archive to the National Library.

Based on the passage, arrange the following events in chronological order from earliest (first) to latest (last).

In right triangle $XYZ$, $\angle Y = 90^\circ$ and $\angle X = 45^\circ$. The hypotenuse $XZ$ has a length of $12\sqrt{2}$ units. Point $W$ lies on leg $XY$ such that $XW = 7$ units. What is the length, in units, of segment $ZW$?

Read the passage below:

In August 1942, inventor Hedy Lamarr and pianist-composer George Antheil were granted U.S. Patent No. 2,292,387 for a secret communication system. Developed to prevent enemy forces from jamming radio-controlled torpedoes, the system relied on frequency hopping across eighty-eight distinct channels—a number selected to match the keys of a standard piano keyboard. Antheil implemented this design using synchronized paper rolls identical to those found in player pianos. Although the U.S. Navy declined to adopt the technology during World War II due to its mechanical complexity, the fundamental concept of frequency hopping eventually served as an essential foundation for modern wireless technologies such as Bluetooth and Wi-Fi.

According to the passage, why did the frequency-hopping communication system utilize exactly eighty-eight frequency channels?

An engineer conducts an experiment to investigate how varying the thickness of synthetic rubber padding affects the peak impact force absorbed during a collision test. In each trial, a $2.0\text{ kg}$ steel sphere is dropped from a constant height of $1.5\text{ m}$ onto padding samples measuring $5\text{ mm}$, $10\text{ mm}$, or $15\text{ mm}$ in thickness while maintaining the laboratory temperature at $20^\circ\text{C}$. Match each experimental component on the left with its corresponding variable classification on the right.

In his small workshop along the harbor, master glassblower Eli Bennett conducted his craft with an unyielding patience that distinguished him from his more hurried contemporaries. While other artisans in the district prioritized speed to fulfill growing merchant orders, Eli spent hours fine-tuning the heat of his furnace, refusing to shape a piece until the molten glass reached the exact consistency he required. Visitors often noted how he would discard an entire morning's work if a single microscopic bubble remained in the glass stem. His apprentices occasionally grew frustrated by his deliberate pace, but Eli insisted that true glassblowing demanded absolute composure and quiet endurance. For Eli, the art was not merely a livelihood, but a discipline requiring steadfast, unwavering calm.

Based on the passage, Eli Bennett's approach to his craft is explicitly described as being characterized by which trait?

In rhombus $JKLM$, diagonals $JL$ and $KM$ intersect at point $P$. If $JP = 2x + 3$, $PL = 4x - 5$, and $m\angle JKL = 60^\circ$, what is the length of side $JK$?

In the standard $(x,y)$ coordinate plane, a cosine function of the form $y = a \cos(b(x - c)) + d$, where $a > 0$ and $b > 0$, has a local maximum at $(2, 9)$ and the very next local minimum at $(6, 1)$. What is the value of $b$?

The following passage is adapted from an essay on twentieth-century marine biology:

In December 1952, fourteen years after the first identified coelacanth was preserved in South Africa, a second specimen was caught off the island of Anjouan in the Comoros archipelago. Captain Eric Hunt, a schooner trader who had distributed leaflets offering a reward for the fish, recognized the unusual fins and immediately preserved the specimen in formalin. Hunt then sent an urgent telegram to South African ichthyologist J. L. B. Smith in Grahamstown. Upon receiving the message, Smith recognized that the fish needed to be inspected before decomposition ruined its internal organs. He appealed directly to South African Prime Minister D. F. Malan, requesting an official military aircraft to bypass commercial flight delays. Prime Minister Malan authorized a Dakota military transport plane for the urgent mission. Smith boarded the aircraft, flew to Anjouan, and personally verified that the specimen was indeed a coelacanth. Finally, Smith loaded the preserved fish onto the plane and returned to South Africa to conduct a detailed scientific dissection.

Based on the explicit details provided in the passage, arrange the following events in the exact chronological sequence in which they occurred.

A team of biochemists investigated the activity of the enzyme *lactase* under varying pH conditions. Four test tubes were prepared, each containing $5.0\text{ mL}$ of a $2\%$ lactose substrate solution and $1.0\text{ mL}$ of standardized lactase solution. Buffer solutions were added to adjust the pH in the test tubes to 3.0, 5.0, 7.0, and 9.0, respectively. All test tubes were placed in a water bath maintained at a constant temperature of $37.0^\circ\text{C}$ for 15 minutes. The final concentration of glucose produced (measured in $\text{mg/dL}$) was determined for each test tube to quantify enzymatic activity.

Match each experimental component to its correct variable classification.

Biochemists investigated the catalytic activity of the enzyme carbonic anhydrase under various environmental conditions across three distinct experimental setups, as summarized in the table below.

Based on the experimental design shown for Trial 3, which of the following correctly identifies the independent variable, the dependent variable, and a key controlled variable, respectively?

In the standard $(x,y)$ coordinate plane, a sinusoidal function $f(x) = A \sin(Bx - C) + D$ reaches a maximum value of $9$ at $x = 1$ and its immediate next minimum value of $-1$ at $x = 4$. What is the period of $f(x)$?

In right triangle $PQR$, the measure of $\angle PQR$ is $90^\circ$. Segment $QS$ is an altitude drawn perpendicular to hypotenuse $PR$ with point $S$ lying on $PR$. If $PQ = 15$ centimeters and $PS = 9$ centimeters, what is the length, in centimeters, of hypotenuse $PR$?

Read the following passage carefully:

Before securing the official permit to excavate the subterranean granary at Alaca Höyük in 1988, Dr. Aris Thorne had spent two years analyzing satellite imagery at his university lab. It was during that initial imaging analysis, conducted in 1986, that he first identified the anomalous soil density patterns indicating buried structures. However, his actual field research did not begin until three months after receiving the permit, when his team cleared the outer trench. Prior to clearing the trench, Thorne had secured emergency funding from the Antiquities Board, a step he was forced to take only after his initial university grant was abruptly revoked just weeks following the permit approval. It was only after the outer trench was completely excavated that the team uncovered the bronze storage jars.

According to the passage, which of the following events occurred FIRST chronologically?

Atmospheric researchers conducted an experiment inside a sealed environmental chamber maintained at a constant ambient temperature of $20.0^\circ\text{C}$ and a constant airflow velocity of $0.5\text{ m/s}$. The researchers adjusted the relative humidity ($RH$) across four distinct test runs ($40\%$, $50\%$, $60\%$, and $70\%$) while keeping the surface area and material of the condensing plate identical. After $60\text{ minutes}$ for each run, the total mass of condensed water on the plate surface was recorded.

Based on this experimental setup, which of the following correctly identifies the independent variable, the dependent variable, and one controlled variable in this investigation?

An atmospheric scientist conducts an experiment in a temperature-controlled environmental chamber to investigate the photolysis kinetics of nitryl chloride ($ClNO_2$) under varying moisture conditions. During the experiment, the scientist adjusts the initial atmospheric water vapor concentration ($H_2O$ mole fraction in ppmv) across five distinct trials while maintaining the total chamber pressure at $760\text{ Torr}$, ambient temperature at $298\text{ K}$, and UV actinic flux intensity at $1.5 \times 10^{16}\text{ photons}\cdot\text{cm}^{-2}\cdot\text{s}^{-1}$. For each trial, the scientist uses cavity ring-down spectroscopy to quantify the first-order photolysis rate constant ($k_{\text{phot}}$ in $\text{s}^{-1}$). Unintended background desorption of trace volatile organic compounds (VOCs) from the chamber walls occurs unpredictably between trials.

Match each experimental component described below to its correct variable classification.

A marine biology student designs an experiment to measure the rate of oxygen production in *Chlorella* algae. Four identical glass flasks are filled with equal volumes of an algal suspension of the same cell density. Each flask is exposed to a light source of a different wavelength (red, blue, green, and yellow) while keeping the light intensity fixed at $500\text{ lux}$ and the temperature constant at $22^\circ\text{C}$. The volume of dissolved oxygen produced by each culture is measured after $3\text{ hours}$.

Match each experimental element from this investigation to its corresponding variable type.