All practice questions

A fair game spinner is divided into $8$ equal sectors numbered $1$ through $8$. If Maya spins the spinner once, what is the probability that the spinner lands on a number strictly greater than $5$?

Read the following passage and consider the underlined portion:

Palynologists analyzing sediment cores from subarctic peat bogs can reconstruct ancient climate conditions. By cataloging fossilized pollen grains preserved in oxygen-poor soil layers, researchers map shifting forest boundaries over millennia, however, sudden temperature fluctuations often disrupt local plant migration patterns.

Which of the following alternatives to the underlined portion is grammatically correct?

In the standard $(x, y)$ coordinate plane, a line passing through the points $(-3, 5)$ and $(1, -3)$ has a slope of $-2$. Is this statement true or false?

A freight shipping company calculates the total fuel consumption, $C$ in gallons, for a cargo vessel using the equation $C = 45h$, where $h$ represents the number of hours the vessel operates at cruising speed. If the vessel consumed a total of $3,150$ gallons of fuel on a recent journey, for how many hours did the vessel operate at cruising speed?

A high school robotics team recorded their scores across 5 qualification matches: $90, 78, 86, 82,$ and $84$. In their 6th qualification match, the team earned a score of $x$, which increased their overall 6-match mean score by $3$ points compared to their 5-match mean score. What is the positive difference between the median and the mean of all 6 match scores?

A juice bar allows customers to create a custom smoothie by selecting exactly $1$ fruit base out of $4$ available options and $1$ liquid base out of $3$ available options. How many different custom smoothie combinations of $1$ fruit base and $1$ liquid base are possible?

In the sentence below, a portion of the text is underlined.

"To determine the chemical composition of the ancient metal alloy, metallurgical technicians analyzed the structural properties of the sample, measured its thermal conductivity, recorded its magnetic susceptibility; and verified the presence of rare trace elements."

Which choice for the underlined portion best maintains parallel structure and correct list punctuation in standard written English?

An artisan pottery workshop uses a total of $c$ kilograms of clay to make ceramic vases. If each vase requires $4$ kilograms of clay and the workshop produced $18$ vases in total, which of the following equations models this scenario, and what is the total amount of clay $c$ used?

Line $k$ in the coordinate plane is represented by the equation $4x - 6y = 15$. If Line $p$ is perpendicular to Line $k$, what is the slope of Line $p$?

A commercial printing press operates at a constant rate throughout the day. At 10:15 a.m., a total of 180 posters have been printed since the morning shift began. By 11:45 a.m. on the same morning, a total of 540 posters have been printed. What is the printing rate of the press, in posters per hour?

Atmospheric scientists conducted an experiment to evaluate how varying the ambient relative humidity ($\text{RH}$, measured as a percentage) influences the crystallization time (in seconds) of acoustically levitated ammonium sulfate ($(\text{NH}_4)_2\text{SO}_4$) microdroplets. Throughout all trials, the ambient temperature was held constant at $20.0^\circ\text{C}$ and the initial droplet radius was held constant at $5.0\,\mu\text{m}$.

Match each experimental component from the investigation to its corresponding variable classification.

Oceanographers measured the sound velocity in seawater at various depths under two different salinity levels ($34\text{ ppt}$ and $36\text{ ppt}$). The results are recorded in Table 1 below:

Statement: If the data in Table 1 were translated into a two-line graph plotting Sound Velocity (m/s) on the y-axis against Depth (m) on the x-axis, both curves would reach a minimum value at a depth of $1,000\text{ m}$, and the curve representing $36\text{ ppt}$ salinity would be positioned strictly above the curve representing $34\text{ ppt}$ salinity across all measured depths.

Read the following passage adapted from an essay on nineteenth-century American science:

In the autumn of 1847, the island of Nantucket was a bustling whaling port, but two miles off its cobblestone streets, on the roof of the Pacific National Bank, a quiet observation was about to reshape American astronomy. Maria Mitchell, a twenty-nine-year-old librarian at the Nantucket Atheneum, spent her evenings sweeping the skies with a modest two-inch Gregorian reflector telescope purchased by her father, William Mitchell, who served as the bank’s cashier. On the clear, chilly night of October 1, 1847, at approximately 10:30 p.m., Maria positioned her instrument toward the northern sky and noticed a faint, nebulous object near the North Star, lying just below the star Polaris in the constellation Ursa Minor.

Unlike recognized stars, which appeared as sharp points of light, this object possessed a soft, hazy glow and lacked any discernible tail. Suspecting she had located a previously unrecorded comet, Maria immediately called her father to the roof to confirm the sighting. William recorded the object’s coordinates in his ledger, noting its right ascension and declination. Over the next two nights, Maria returned to the telescope to monitor the object’s position. By observing that the fuzzy mark had shifted relative to the background field of fixed stars, she confirmed that it was moving—a definitive characteristic of a comet in orbit around the Sun.

News of the discovery traveled quickly from Nantucket to the Harvard College Observatory, where director William Cranch Bond verified Mitchell’s observations. However, establishing Maria’s priority as the first discoverer proved contentious. Years earlier, King Frederick VI of Denmark had established a prestigious gold medal to be awarded to any astronomer who discovered a telescopic comet—one invisible to the naked eye. The strict regulations of the Danish prize required the observer to notify the British Admiralty or the Danish government immediately by the next available mail post. Because Nantucket was isolated from the mainland and post ships were delayed by autumn gales, Maria’s official letter announcing the comet did not reach Europe for several weeks.

During the delay, European astronomers, including Father Francesco de Vico in Rome and W. Dawes in England, independently sighted the same comet. Initial reports from the Royal Astronomical Society credited de Vico with the discovery, assuming his notification had arrived first. William Mitchell, determined to secure his daughter’s rightful place in scientific history, initiated an extensive correspondence with American statesmen and scholars, including Edward Everett, then president of Harvard University. Everett petitioned the Danish Minister in Washington, presenting William’s dated observatory logbook entries from October 1 as indisputable physical evidence of Maria’s prior detection.

After a thorough review of the logbooks and postal transit delays, King Christian VIII of Denmark (who had succeeded Frederick VI) officially awarded the gold medal to Maria Mitchell in 1848. The recognition made her the first professional female astronomer in the United States and the first woman awarded a European scientific prize of this distinction. The comet was officially designated C/1847 T1, though in popular science it became known as "Miss Mitchell’s Comet."

According to the passage, Maria Mitchell used which of the following instruments to make her initial observation of the comet on October 1, 1847?

Read the passage below and answer the question that follows.

In August 1856, American scientist Eunice Newton Foote presented her groundbreaking findings on atmospheric gas absorption at the annual meeting of the American Association for the Advancement of Science in Albany, New York. Foote had constructed an experimental apparatus consisting of two glass cylinders, each fitted with a thermometer, into which she introduced different gases—including compressed air, rarefied air, hydrogen, and carbon dioxide. After placing the filled cylinders in direct sunlight, Foote recorded the resulting temperature changes over several hours. She observed that the cylinder filled with moist carbon dioxide trapped significantly more heat than the cylinder containing dry atmospheric air, and took much longer to cool down once removed from sunlight.

In her paper, titled 'Circumstances Affecting the Heat of the Sun's Rays,' Foote explicitly deduced that an atmosphere composed of carbon dioxide would impart to our Earth a higher temperature than it currently possessed. Although Foote was a member of the association, her paper was read aloud by Joseph Henry, the first secretary of the Smithsonian Institution, because women were not permitted to formally present research at the conference. Following the presentation, an abstract of Foote’s paper was published in November 1856 in the American Journal of Science and Arts. Despite this publication, her experimental proof of carbon dioxide's heat-trapping properties remained largely unacknowledged by mainstream European physicists for over a century.

Based on the passage, place the following events regarding Eunice Foote's experiment and its presentation in the correct chronological order in which they occurred, from earliest to latest.

Read the passage and consider the underlined portion.

Oceanographers monitoring deep convective currents in the Labrador Sea recently deployed an autonomous underwater glider equipped with acoustic Doppler sensors. Operating continuously for six months, the submersible glided through frigid water columns to capture salinity profile data, however, the gathered measurements revealed an unexpected sub-surface eddy carrying warm, highly saline water northward. This hydrographic anomaly challenges existing circulation models and provides critical insights into ocean overturning dynamics.

Which of the following choices best corrects the underlined portion of the passage?

If $\theta = \arctan\left(-\frac{4}{3}\right)$, what is the exact value of $\sin(2\theta)$?

A diagonal support beam is installed to stabilize a wooden wall frame. The beam extends from the top-left corner of the frame to the bottom-right corner, forming a right triangle with the top horizontal beam and the right vertical post. The vertical post has a height of $15$ feet. If the angle $\theta$ between the diagonal support beam and the top horizontal beam satisfies $\tan(\theta) = \frac{3}{4}$, what is the length, in feet, of the diagonal support beam?

A materials scientist investigated how the average pore diameter of polyurethane acoustic foam panels affects their sound absorption performance. Four foam panels of identical thickness ($50\text{ mm}$) were tested in a sound chamber at a constant ambient temperature ($22^\circ\text{C}$) and fixed incident sound frequency ($1,000\text{ Hz}$). The experimental conditions and measured outcomes are summarized in the table below:

Which of the following correctly identifies the independent variable and the dependent variable in this investigation?

A commercial printing press uses large rolls of paper for magazine production. During a morning shift, a technician uses $\frac{4}{9}$ of the total mass, $m$ (in kilograms), of a full paper roll. If the mass of paper used during the shift is $36$ kilograms, what is the total mass $m$, in kilograms, of the full paper roll?

A circular metal disk has a radius of $12$ centimeters. A wedge-shaped sector with a central angle of $75^\circ$ is cut out and removed from the disk. What is the perimeter, in centimeters, of the remaining portion of the disk?