All practice questions

Four real estate agents reported the proportion of their home listings that sold above asking price last month as follows: Agent W reported $\frac{31}{50}$, Agent X reported $\frac{5}{8}$, Agent Y reported $63\%$, and Agent Z reported $0.64$. Place the four agents in order from the smallest proportion of listings sold above asking price to the largest proportion.

A custom bicycle workshop builds specialized cargo bikes. The total frame assembly weight, $W$ pounds, is determined by adding a fixed base frame weight of $f$ pounds to the weight of $n$ reinforced structural struts, where each strut weighs 2.4 pounds. For a cargo bike configured with 5 structural struts, the total frame assembly weight is 26.0 pounds. Which of the following one-step linear equations can be solved to find $f$, the weight in pounds of the fixed base frame?

An automated manufacturing line produces component X and component Y in a ratio of $4:7$. During a single production run, a total of $1,760$ components were produced. How many more component Y than component X were produced during this run?

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

Architects designed the museum's new wing using durable sustainable materials, but city officials delayed construction until environmental impact assessments were completed.

Consider the underlined portion in the sentence below:

To examine how urban green spaces influence localized humidity, environmental scientists measured moisture levels near asphalt parking lots, recorded ambient air temperatures across open lawns, and tracked vegetation density using drone photography.

Which choice provides the correct punctuation for the list of actions in the sentence?

A community garden allocates its total area among three crops: vegetables, herbs, and flowers. Exactly $\frac{3}{8}$ of the total area is dedicated to vegetables, and $40\%$ of the remaining area is planted with herbs. If the remaining flower section covers $270$ square feet, what is the total area, in square feet, of the community garden?

A surveyor standing at point $P$ on level ground measures the angle of elevation to the top of a cliff, point $T$, as $\theta$. The ground distance from point $P$ to the vertical base of the cliff, point $B$, is $120$ feet. If $\cos(\theta) = \frac{12}{13}$, what is the vertical height of the cliff, in feet?

During a deep-sea exploration mission near the Mariana Trench, oceanographers launched a durable high-tech probe, and transmitted real-time thermal data back to the research vessel.

Which choice produces a grammatically correct sentence that accurately uses commas?

A biochemist investigated how varying the pH of a reaction mixture affects the rate of hydrogen peroxide ($\text{H}_2\text{O}_2$) decomposition by the enzyme catalase. In each trial, the catalase concentration, total reaction volume, and incubation temperature ($25^\circ\text{C}$) were held constant, while the volume of oxygen gas ($\text{O}_2$) produced per minute was measured across solutions ranging from $\text{pH } 4.0$ to $\text{pH } 10.0$.

Match each experimental component from the study to its correct variable classification.

While studying the neural mechanisms of memory consolidation during sleep, neuroscientists recorded slow, rhythmic delta waves, monitored rapid eye movement, and mapped activity patterns in the hippocampus.

Which choice produces a grammatically correct sentence that accurately punctuates the list and coordinate adjectives?

Evaluate the algebraic expression for the given variable values.

In the standard $(x, y)$ coordinate plane, a circle is defined by the equation $x^2 + y^2 - 6x + 8y - 11 = 0$. What is the distance from the center of this circle to the origin $(0, 0)$?

A bookstore recorded the number of books purchased by a sample of $25$ customers. The frequency table below summarizes the purchases made by $20$ of these customers:

The remaining $5$ customers each purchased the exact same number of books, $n$. If the mean number of books purchased by all $25$ customers is $2.8$, what is the median number of books purchased by the entire group of $25$ customers?

A team of biomedical researchers investigated the inhibitory effect of a plant-derived polyphenol, compound CP, on bacterial biofilm formation by *Pseudomonas aeruginosa* on silicone catheter surfaces. The researchers prepared four different culture setups in microtiter plate wells and measured biofilm mass after incubation at $37^\circ\text{C}$ for 24 hours:

- Setup I: Silicone catheter disc + nutrient broth + *P. aeruginosa* + $0\text{ }\mu\text{g/mL}$ compound CP (vehicle solvent only)
- Setup II: Silicone catheter disc + nutrient broth + *P. aeruginosa* + $50\text{ }\mu\text{g/mL}$ compound CP
- Setup III: Silicone catheter disc + nutrient broth (no bacteria added) + $0\text{ }\mu\text{g/mL}$ compound CP
- Setup IV: Nutrient broth only (no catheter disc, no bacteria added)

Based on the experimental design, match each culture setup (Setups I–IV) to its specific experimental role or baseline function.

What is the exact decimal value of $\tan\left(\arcsin\left(\frac{12}{13}\right)\right)$?

Consider the following passage:

Satellite remote sensing has transformed space archaeology by revealing ancient silk trade outposts buried beneath sand dunes in the Taklamakan Desert. High-resolution synthetic aperture radar can penetrate hyper-arid soils to outline subterranean mud-brick foundations. These structural outlines provide crucial spatial data, however, field archaeologists must still conduct physical excavations to recover artifacts and confirm site dates. Consequently, ground-validation expeditions remain essential to verifying orbital discoveries.

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

"These structural outlines provide crucial spatial data, however, field archaeologists must still conduct physical excavations"

If $a = -4$ and $b = 3$, what is the value of the expression $3a^2 - 2ab$?

Biophysicists investigating avian navigation have identified cryptochrome proteins in the retinas of migratory songbirds. These specialized light-sensitive molecules undergo quantum entanglement when activated by blue <u style="text-decoration: underline;">light, consequently, the birds</u> can perceive subtle inclinations in Earth's magnetic field. This quantum compass allows night-migrating species to navigate accurately across thousands of miles.

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

A section of a circular garden is enclosed by two radii and an outer arc, forming a circular sector with a central angle of $60^\circ$. If the total perimeter of this sector is $12 + 2\pi$ meters, what is the area of the sector, in square meters?

A university professor teaches two sections of Introductory Statistics. Section 1 contains $30$ students and had a mean score of $82$ on the midterm exam. Section 2 contains $20$ students and had a mean score of $92$ on the same exam. What is the overall mean midterm exam score for all $50$ students combined?