All practice questions

A group of materials engineers evaluated the power conversion efficiency of perovskite solar cells fabricated with different layer thicknesses of a titanium dioxide ($\text{TiO}_2$) electron-transport layer ($50\text{ nm}$, $100\text{ nm}$, $150\text{ nm}$, and $200\text{ nm}$). All solar cell samples were constructed using identical perovskite absorber layers, tested under a constant simulated solar light intensity of $1,000\text{ W/m}^2$, and maintained at a temperature of $25^\circ\text{C}$. Which of the following correctly identifies the independent variable and the dependent variable in this experiment?

A lighthouse beacon sweeps across a circular region of the ocean. The illuminated area forms a circular sector with a radius of $15$ nautical miles and an area of $75\pi$ square nautical miles. What is the total perimeter, in nautical miles, of this illuminated sector?

Read the excerpt below regarding early musicological field work. Fill in the blank with the most precise word that describes converting recorded audio into written musical notation while maintaining an academic register.

A group of neurobiologists investigated the impact of a novel fungal compound, Toxin-Z, on acetylcholinesterase ($\text{AChE}$) activity. Because Toxin-Z is hydrophobic, it was dissolved in a $1\%$ dimethyl sulfoxide ($\text{DMSO}$) solvent. Four reaction mixtures were prepared under constant temperature ($37^\circ\text{C}$) and $\text{pH}$ ($7.4$):

- Reaction 1: $\text{AChE}$ + substrate + buffer
- Reaction 2: $\text{AChE}$ + substrate + buffer + $1\%$ $\text{DMSO}$
- Reaction 3: $\text{AChE}$ + substrate + buffer + $1\%$ $\text{DMSO}$ + $10\ \mu\text{M}$ Toxin-Z
- Reaction 4: Substrate + buffer (no $\text{AChE}$)

Match each reaction mixture to its specific experimental role or control designation.

A commercial bakery mixes three types of flour—whole wheat, rye, and oat—to create a specialty bread blend. Initially, the ratio of whole wheat flour to rye flour to oat flour by weight is $5:3:2$. The baker then adds 12 pounds of oat flour and 6 pounds of rye flour to the batch while leaving the amount of whole wheat flour unchanged. As a result, the ratio of whole wheat flour to oat flour in the new mixture becomes $1:1$. What was the total weight, in pounds, of the initial flour mixture before any additional flour was added?

An environmental scientist measured the rate of enzymatic breakdown of microplastics ($\text{mg/L/hr}$) by a bacterial strain across five different incubation temperatures ($^\circ\text{C}$). The results are shown in the table below:

Which of the following descriptions best characterizes the line graph that accurately translates these experimental results?

A circular theater stage has a designated performance section shaped as a circular sector with a central angle measuring $\frac{2\pi}{5}$ radians. If the arc length along the outer edge of this sector is $8\pi$ feet, what is the area, in square feet, of the performance section?

Read the sentence below. Which choice provides the idiomatically correct preposition for the underlined portion?

In his monograph on modern typography, the design critic argued that minimalist aesthetics are not necessarily synonymous to functional design.

A local library recorded the number of books read by students participating in a summer reading program. The results are summarized in the frequency table below.

What is the mean number of books read per student for this group?

Glaciologists studying subglacial Lake Mercer in Antarctica deployed a customized hot-water drill to penetrate over one thousand meters of ice. They successfully recovered sediment cores containing ancient microbial forms, however, maintaining sterile conditions throughout the drilling process presented unprecedented technological challenges. Subsequent analysis revealed viable bacteria that had survived in extreme isolation for thousands of years.

Which choice produces a grammatically correct sentence that properly joins the two independent clauses?

A box contains $5$ red tickets, $7$ blue tickets, and $8$ green tickets. If one ticket is selected at random from the box, what is the probability that the selected ticket is NOT blue?

Researchers investigated the hydrothermal growth of zinc oxide ($\text{ZnO}$) nanorods for use in piezoelectric nanogenerators. In five separate experimental trials, the reaction vessel temperature was set to $90^\circ\text{C}$, $100^\circ\text{C}$, $110^\circ\text{C}$, $120^\circ\text{C}$, and $130^\circ\text{C}$, respectively. In all trials, the zinc nitrate precursor concentration was maintained at $0.05\text{ M}$, the reaction duration was held at $4\text{ hours}$, and the autoclave fill volume was kept at $100\text{ mL}$. After each trial, the average aspect ratio (length-to-diameter ratio) of the synthesized nanorods was determined using scanning electron microscopy. Match each experimental component to its correct variable classification.

A straight ramp is constructed for a skateboard park. The ramp rises to a vertical height of $5\sqrt{3}$ feet above flat horizontal ground, and the horizontal distance from the base of the ramp to the point directly beneath its highest point is $15$ feet. If $\theta$ represents the angle of inclination of the ramp with respect to the ground, what is the value of $\cos(\theta)$?

For any real number $x$ such that $0 < x < 3$, which of the following expressions is equivalent to $\sin\left(\arccos\left(\frac{x}{3}\right)\right)$?

A municipal water authority pumps water into a storage reservoir. During a drought conservation phase, the authority reduces its standard daily pumping volume by $35\%$. If the resulting reduced daily pumping volume is $W$ acre-feet, which of the following equations correctly expresses the standard daily pumping volume, $S$, in acre-feet, in terms of $W$?

Biologists conducted an experiment to investigate the effects of heavy metal contamination on the photosynthetic activity of the freshwater alga *Chlorella vulgaris*. Four identical culture flasks were prepared, each containing $100\text{ mL}$ of standard growth medium and an initial cell density of $1.0 \times 10^5\text{ cells/mL}$:

- Flask 1: Standard growth medium with no added heavy metal ions.
- Flask 2: Standard growth medium containing $5.0\text{ mg/L}$ of copper ions ($\text{Cu}^{2+}$).
- Flask 3: Standard growth medium containing $5.0\text{ mg/L}$ of lead ions ($\text{Pb}^{2+}$).
- Flask 4: Standard growth medium containing $5.0\text{ mg/L}$ of cadmium ions ($\text{Cd}^{2+}$).

All four flasks were kept at $25^\circ\text{C}$ under continuous illumination for 48 hours. Dissolved oxygen ($\text{DO}$) concentration was then measured to quantify photosynthetic output.

Which flask served as the control group in this experiment, and what was its primary purpose?

Biochemists measured the rate of glucose consumption (in $\text{mM/min}$) by a newly isolated bacterial strain across 3 temperature treatments ($25^\circ\text{C}$, $35^\circ\text{C}$, and $45^\circ\text{C}$). Each temperature condition was evaluated in 3 separate trials. The results are recorded in the table below:

Based on the data provided, what is the average rate of glucose consumption, in $\text{mM/min}$, for the $35^\circ\text{C}$ treatment across the 3 trials?

A community theater company uses a combination of red, yellow, and blue light filters to create a specific lighting effect on stage. The ratio of the number of red filters to yellow filters is $4:3$, and the ratio of the number of yellow filters to blue filters is $2:5$. If the lighting setup uses a total of $58$ filters across these three colors, how many blue filters are used in the setup?

In right triangle $PQR$, the right angle is located at vertex $Q$. The length of leg $PQ$ is $30$ centimeters. If $\sin(P) = \frac{8}{17}$, what is the length, in centimeters, of leg $QR$?

A biology class recorded the height, in centimeters, of $15$ plant seedlings after two weeks of growth. The frequency table below summarizes the recorded measurements:

What is the positive difference between the mean height and the median height, in centimeters, of these $15$ seedlings?