All practice questions

Experiment 1

Students investigated the rate of enzymatic hydrolysis of $o$-nitrophenyl-$\beta$-D-galactopyranoside ($ONPG$) catalyzed by the enzyme lactase. The reaction yields $o$-nitrophenol, a product that absorbs light strongly at a wavelength of $420\text{ nm}$. To accurately measure the rate of product formation using a spectrophotometer without error from background absorbance or premature reaction, which of the following represents the correct chronological sequence of procedural steps the students must perform?

In the standard $(x, y)$ coordinate plane, the equation of a circle is given by $3x^2 + 3y^2 - 12x + 24y - 15 = 0$. What is the radius of this circle?

A water desalination plant processes seawater using two filtration units, Unit P and Unit Q. Unit P can process $720$ gallons of water in $45$ minutes. Unit Q processes water at a rate that is $25\%$ faster than Unit P. If both units operate continuously at their respective rates, how many total gallons of water can Unit P and Unit Q process combined in $2.5$ hours?

During their research expedition in the Atacama Desert, radio astronomers calibrated the sensitive, optical telescope, collected high-resolution data and mapped the spatial distribution of distant star clusters. Which choice for the underlined portion best conforms to the conventions of standard written English?

If $x = -2$, $y = \frac{1}{2}$, and $z = -3$, what is the value of the algebraic expression $\frac{x^3 y^{-2} - 4z}{(x + 2y)^2 - z}$?

A commercial bakery uses an automated dough divider that cuts a large batch of dough of mass $m$ kilograms into $48$ identical portioned rolls. If each portioned roll has a mass of $0.125$ kilograms, what was the total mass $m$, in kilograms, of the original batch of dough?

A biochemist conducted an experiment to investigate how substrate availability influences cellular respiration rates in yeast. Five identical incubation flasks were prepared, each containing $50\text{ mL}$ of yeast suspension in a buffer solution maintained at a constant temperature of $30^\circ\text{C}$ and a $\text{pH}$ of $6.5$. Different masses of glucose—$0.5\text{ g}$, $1.0\text{ g}$, $1.5\text{ g}$, $2.0\text{ g}$, and $2.5\text{ g}$—were added to Flasks 1 through 5, respectively. The volume of carbon dioxide ($\text{CO}_2$) gas generated by each flask was measured after $10\text{ minutes}$.

Which of the following operational parameters represents the independent variable in this experiment?

A marine biologist conducted an experiment to investigate how varying water salinity affects the oxygen consumption rate of shore crabs (*Carcinus maenas*). Five identical tanks were prepared with water salinities of $10\text{ ppt}$, $15\text{ ppt}$, $20\text{ ppt}$, $25\text{ ppt}$, and $30\text{ ppt}$. All tanks were held at a constant water temperature of $18^\circ\text{C}$, and crabs of equal body mass were used in each trial.

Match each experimental component on the left with its corresponding variable classification on the right.

Read the passage below:

Before botanist Dr. Evelyn Reed published her breakthrough classification of Alpine mosses in 1988, her field research followed a detailed timeline over several years. In the summer of 1982, Reed secured initial grant funding from the Alpine Research Council, which allowed her to assemble her expedition team the following spring. After conducting preliminary soil sampling across the Bernese Alps throughout 1984, Reed spent the winter of 1985 cataloging collected specimens in her Geneva laboratory. Only after completing the laboratory analysis in mid-1986 did she commence writing the formal manuscript that was eventually submitted to the Botanical Society in late 1987.

Based on the passage, arrange the following events from Dr. Reed's research project in chronological order from earliest to latest.

To restore degraded coastal wetlands, environmental scientists planted native salt marsh grasses, installed wooden sediment fences, and monitored water salinity levels over a three-year period.

Which choice for the underlined portion best conforms to the conventions of standard written English?

Read the passage below:

When horologist Mateo Silva patented his revolutionary dual-balance escapement mechanism in 1928, scholars assumed it was the culmination of his Madrid period. However, Silva had actually sketched the preliminary designs for the escapement four years prior, while convalescing from fever in Toledo. Before establishing his Madrid laboratory in 1924, he completed a rigorous three-year apprenticeship under master clockmaker Alonzo Perez, during which he restored the municipal tower clock. Immediately following his move to Madrid, Silva initiated a series of systematic friction experiments on brass gears. These experiments formed the core of a treatise he published in 1926, two years before obtaining his patent and five years prior to securing commercial manufacturing backing in 1931.

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

A weather researcher recorded the daily high temperatures, in degrees Fahrenheit, for $5$ consecutive days in a mountain town: $68^\circ\text{F}$, $74^\circ\text{F}$, $71^\circ\text{F}$, $65^\circ\text{F}$, and $72^\circ\text{F}$. If the daily high temperature on the 6th day is $x^\circ\text{F}$, and the mean high temperature for all $6$ days is $72^\circ\text{F}$, what is the value of $x$?

A middle school librarian recorded the number of books checked out by $15$ students during a reading program, as summarized in the table below:

What is the positive difference between the median and the mean of the number of books checked out per student?

A high school athletic department set a total fundraising goal of $\$2,400$ for new equipment. During the first week, the department raised $\frac{3}{8}$ of the total goal. During the second week, they raised $35\%$ of the total goal. During the third week, they raised $0.15$ of the total goal. How much money must the department raise in the fourth week to meet its total goal exactly?

An electric vehicle charging station delivers energy at a constant rate of $k$ kilowatt-hours (kWh) per hour. If a vehicle receives a total of $48\text{ kWh}$ of energy after charging for $1.5$ hours, which of the following equations can be solved to find $k$?

At a community theater performance, the ratio of adult tickets sold to student tickets sold was $5 : 3$. After $12$ additional student tickets were sold and no additional adult tickets were sold, the ratio of adult tickets to student tickets became $4 : 3$. How many total tickets (adult and student combined) were sold originally?

Read the passage below:

Before glaciologist Dr. Lars Lindqvist deployed the deep-ice thermal probe at the Maud Rise station in 2014, his team completed two seasons of radar mapping to identify stable subglacial channels. That mapping effort had been delayed for a year when severe blizzards forced an emergency evacuation of their base camp in 2011. Lindqvist's initial field surveys, conducted in 2009, had established the baseline ice-thickness measurements that justified the original grant proposal. Following the successful probe deployment, the team published their preliminary melt-rate analysis in 2016, confirming their subglacial water flow models.

Based on the passage, what is the correct chronological sequence of events in Dr. Lindqvist's research program, from earliest to latest?

A group of biochemical researchers measured the enzymatic breakdown rate of cellulose (in $\text{mg/L}\cdot\text{min}$) by three bacterial strains (Strain X, Strain Y, and Strain Z) across three different pH environments ($5.0$, $6.0$, and $7.0$) at a constant temperature of $37^\circ\text{C}$. The results are recorded in the table below:

True or False: The average enzymatic breakdown rate across all three pH environments for Strain Y is $5\text{ mg/L}\cdot\text{min}$ greater than the average breakdown rate for Strain X.

A nursery technician prepares a liquid fertilizer mixture using nitrogen, phosphorus, and potassium in a volume ratio of $4 : 2 : 1$, respectively. A storage tank currently holds $35\text{ liters}$ of this mixture. If the technician adds $6\text{ liters}$ of pure nitrogen to the tank, what is the ratio of nitrogen to phosphorus in the resulting mixture?

A technology firm allocated its annual equipment budget among three divisions. The engineering division received $\frac{3}{8}$ of the total budget, and the operations division received $30\%$ of the total budget. The remaining $\$52,000$ was allocated to the design division. What was the total equipment budget, in dollars, for the technology firm?