All practice questions

A security system requires a 4-digit passcode created using the digits $1, 2, 3, 4, 5, 6,$ and $7$. No digit may be repeated in a passcode. If the first digit and the last digit must both be odd numbers, how many different passcodes can be formed?

If $x = -3$, $y = -\frac{1}{3}$, and $z = 16$, what is the value of the algebraic expression $\frac{x^3 y^{-2} + 3 z^{1/2}}{(xy + 2)^3 - \frac{3}{2} z^{1/2}}$?

An electric commuter train consumes energy at a constant rate of $450\text{ kilowatt-hours (kWh)}$ for every $120\text{ miles}$ it travels. Electricity costs $\$0.14$ per $\text{kWh}$. What is the total cost of the electricity consumed by the train during a $320\text{ mile}$ trip?

If $p = -3$, $q = -\frac{1}{2}$, and $r = 8$, what is the value of the algebraic expression below?

To reconstruct atmospheric conditions from the last glacial period, glaciologists extracted deep core samples from Greenland's ice sheet, analyzed the trapped, ancient gas bubbles, and recorded precise methane levels.

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

While investigating the acoustic properties of ancient amphitheaters, acoustics engineers measured sound decay across the spacious, stone theater, and they documented how subtle architectural details enhanced vocal clarity.

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

At a university, three sections of an introductory chemistry course took the same midterm examination. Section 1 has $15$ students with a mean score of $80$ points, Section 2 has $25$ students with a mean score of $88$ points, and Section 3 has $10$ students with a mean score of $74$ points. What is the overall mean score for all $50$ students combined?

A botanical garden conservatory uses a specialized organic fertilizer mixture containing $f$ pounds of nutrient concentrate. The concentrate is divided equally into $14$ separate watering reservoirs. If each reservoir receives exactly $2.5$ pounds of concentrate, which of the following equations correctly models this situation?

If $r = -3$, $s = 2$, and $t = -\frac{1}{2}$, what is the value of the algebraic expression $\frac{r^2 s - t^{-2}}{r + s t}$?

A team of acoustic engineers conducted an experiment to evaluate how the sound dampening efficiency of polyurethane foam panels is impacted by the concentration of embedded micro-perforated ceramic beads. Five panels of identical dimensions ($50\text{ cm} \times 50\text{ cm} \times 5\text{ cm}$) were manufactured with varying concentrations of ceramic beads ($0\%$, $5\%$, $10\%$, $15\%$, and $20\%$ by mass). Each panel was placed between a sound generator emitting a constant $1\text{-kHz}$ sine wave tone at $90\text{ dB}$ and a decibel sensor positioned $1.0\text{ m}$ away in an anechoic chamber held at $20^\circ\text{C}$. The decibel sensor measured the acoustic absorption coefficient ($\alpha$) of each panel. In this experiment, which factor served as the independent variable?

Read the following passage carefully:

Before Dr. Miriam Vance began structural stabilization on Vienna’s historic St. Jude Opera House in 2021, her archival research had already yielded crucial insights. In 2018, while searching municipal records, she located architect Leopold Weber’s original 1782 floor plans. However, these blueprints omitted the hydraulic stage lift uncovered by her crew behind plaster walls that had been applied during a 1910 renovation. Historical records later confirmed that this hydraulic system had been installed in 1845 to replace timber rigging destroyed in a backstage fire earlier that year. Following years of conservation after the 2021 discovery, Vance’s team successfully tested the restored hydraulic mechanism in 2023.

According to the passage, which of the following events occurred chronologically BEFORE the 1910 renovation?

A long-distance runner is training for an upcoming race. On Monday, she completed $\frac{2}{5}$ of her total weekly distance goal. On Tuesday, she completed $0.35$ of her total weekly distance goal. If she has $12$ miles left to complete her weekly goal, what is her total weekly goal distance, in miles?

A craft workshop instructor purchases a large spool of decorative ribbon of length $L$ meters. She cuts the entire spool into $15$ equal-length pieces to make banners for an art project. If each piece measures $2.4$ meters, which of the following equations can be solved to find the total length $L$, in meters, of the spool of ribbon?

An environmental engineer conducted an experiment to evaluate wastewater purification efficiency. She prepared three identical filtration columns containing different concentrations of activated charcoal ($5\text{ g/L}$, $10\text{ g/L}$, and $15\text{ g/L}$). For all trials, she maintained a fluid temperature of $22^\circ\text{C}$, a flow rate of $10\text{ mL/min}$, and an initial methylene blue dye concentration of $50\text{ mg/L}$. She recorded the time required to achieve $99\%$ decolorization of the solution in each column.

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

Read the passage below:

Before paleoclimatologist Dr. Soren Kjaer extracted the 400-meter speleothem sample from the submerged coastal cave in 2018, his team spent three years designing a custom pressure-sealed core drill. In 2012, prior to securing research funding, Kjaer had mapped the cave's underwater topography using acoustic sonar. Following the 2018 extraction, the team subjected the mineral layers to high-precision uranium-series dating, which revealed a significant growth hiatus. It was not until 2022 that Kjaer published the complete isotopic analysis in a paleontology journal.

Based on the passage, arrange the events in chronological order from earliest to latest.

Based on the passage below, arrange the events in chronological order from earliest to latest.

Before sound archivist Elena Rostova cataloged the rare wax cylinder recordings of Baltic folk songs in 2018, her investigation required reconstructing their origin. In 1935, ethnomusicologist Karlis Ozols had recorded the villagers of Kuldīga on-site. However, prior to Ozols's field expedition, local teacher Marta Liepiņa had compiled handwritten song transcripts in 1928, which later guided Ozols’s travel itinerary. Decades after the recording sessions, in 1972, the wax cylinders were transferred to a regional museum vault to prevent degradation during structural renovations. Only after Rostova unearthed these cylinders from the vault did she cross-reference them with Liepiņa’s initial transcripts.

An artisan bakery prepared a total batch of dough weighing $60$ pounds. In the morning, the baker used $\frac{2}{5}$ of the total dough to make loaves of bread. In the afternoon, the baker used $35\%$ of the remaining dough to make pastries. How many pounds of dough from the initial batch were left unused at the end of the day?

Experiment 1
Students constructed a Soxhlet extraction apparatus to isolate lipids from an algal biomass sample using an organic solvent. The apparatus consists of a boiling flask on a heating mantle, a thimble chamber containing the solid algal sample, an outer vapor tube, a side-arm siphon tube, and a water-cooled reflux condenser mounted at the top.

During operation, solvent boiled in the flask rises as vapor, condenses, and continuously washes over the solid sample inside the extraction chamber until a siphon cycle is triggered.

Match each apparatus component below with its primary procedural function in the extraction process.