All practice questions

For centuries, luthiers have attempted to replicate the exquisite sound of violins crafted by Antonio Stradivari in the late seventeenth and early eighteenth centuries. Many researchers believe that the secret lies in the density of the wood, which grew during the Maunder Minimum—a period of abnormally cold European winters. Consequently, recent chemical analyses suggest that Stradivari treated his wood with complex mineral mixtures containing borax, chromium, and table salt to prevent insect infestation.

Which of the following options best replaces the underlined portion of the passage to establish the most logical transition between the two sentences?

For all real numbers $a$, $b$, and $c$, let the operation $\oplus$ be defined by $a \oplus b = ab + 1$. Which of the following statements must be true?

I. $a \oplus b = b \oplus a$
II. $a \oplus (b \oplus c) = (a \oplus b) \oplus c$
III. $a \oplus (b + c) = (a \oplus b) + (a \oplus c)$

Passage Excerpt:
In 1856, while attempting to synthesize quinine to treat malaria, eighteen-year-old chemist William Henry Perkin accidentally created mauveine, the world’s first synthetic organic dye. At the time, purple clothing was a status symbol affordable only by the extremely wealthy because natural purple dyes were harvested from rare sea snails. [1]

The writer wants to add a sentence at point [1] that contrasts the traditional difficulty of obtaining purple dye with the ease and affordability introduced by Perkin's synthetic alternative. Which choice best accomplishes this goal?

Recognized worldwide as a leading authority over volcanic seismology, Dr. Elena Rostova spent decades analyzing tremor patterns before major eruptions. Her research provided crucial warnings that saved thousands of lives.

Which choice best replaces the underlined portion of the sentence?

The passage below contains a blank indicating a missing punctuation mark. Read the passage and determine which punctuation mark correctly completes the sentence. In the blank provided, what punctuation mark should be placed to ensure the sentence is punctuated correctly?

The following paragraph contains numbered sentences.

[1] In the early nineteenth century, a Cherokee silversmith named Sequoyah became convinced that written communication was the key to the political and economic power of European settlers. [2] He spent years experimenting with pictographs, but he eventually abandoned this approach as too cumbersome. [3] Instead, he developed a system of 85 symbols, each representing a distinct syllable in the Cherokee language. [4] Within a few years, Cherokee literacy rates soared, even surpassing those of neighboring European settlers.

To make the paragraph most logical, the following sentence should be added:

"This breakthrough allowed speakers of the language to learn to read and write in a matter of weeks, rather than years."

Where is the most logical placement for this sentence?

In 1856, eighteen-year-old chemist William Henry Perkin was attempting to synthesize quinine, a drug used to treat malaria, in his home laboratory. Instead of quinine, he accidentally produced a dark sludge that, when diluted with alcohol, turned a beautiful shade of purple. Perkin had created mauveine, the first synthetic organic dye, which was an invention that would go on to completely revolutionize the entire global textile industry.

Which of the following options is the most concise and grammatically correct replacement for the underlined portion?

Evaluate the four mathematical expressions below and arrange them in order from least to greatest value.

A writer is editing a draft of an essay about the history of meteorology. Read the passage and answer the question that follows.

[1] In the mid-nineteenth century, meteorology was a fragmented field, relying on isolated observers who recorded local weather conditions without any coordination. [2] British polymath Francis Galton realized that understanding weather patterns required analyzing simultaneous observations across a wide geographical area. [3] In 1861, he distributed standardized recording kits to observers across Europe, asking them to document barometric pressure, wind direction, and temperature at three specific times each day. [4] Galton was also a cousin of Charles Darwin and made significant contributions to the field of statistics. [5] By plotting this synchronized data onto a map using custom-designed symbols, Galton created the first modern weather map, revealing previously invisible atmospheric systems like anticyclones.

The writer is considering deleting Sentence 4 from the passage. Should the sentence be kept or deleted?

When art restorers began working on the Sistine Chapel ceiling in 1980, they faced the daunting task of reversing centuries of soot accumulation. Over the years, candle smoke, dust, and animal-fat varnishes had obscured Michelangelo's brilliant frescoes under a thick, dark crust. Using a gentle solvent wash, the conservationists painstakingly lifted the grime layer by layer. Critics initially worried that the process would strip away the artist's original detailing. However, the restoration ultimately revealed that Michelangelo had employed a far more vibrant color palette than previously assumed. Rather than the somber, muted tones long associated with the High Renaissance, the frescoes actually boasted brilliant pastels, [1] which were super bright and totally popped in the restored light.

Given the context of the passage, which option most effectively maintains the established tone and style of the narrative?

As a seasoned wildlife tracker, Marcus was highly attuned with the subtle rustles and shifts in the forest undergrowth, often identifying approaching predators long before they came into view.

Which of the following is the most idiomatically correct choice to replace the underlined portion?

What is the value of the expression $15 - 3 \times 2^3 + 10$?

A writer is editing an essay about inventor Walter Hunt and has drafted the following paragraph:

In 1849, inventor Walter Hunt was twisting a piece of brass wire at his desk, trying to figure out a way to pay off a fifteen-dollar debt. Within three hours, he had designed the first modern safety pin, featuring a clasp that covered the sharp point and a circular loop at the bend to act as a spring. Hunt quickly patented his invention and sold the rights for four hundred dollars, which easily cleared his debt but left him with none of the subsequent millions the product would generate. Over his lifetime, Hunt also designed a sewing machine and a street-sweeping vehicle, though he rarely capitalized on his creations.

The writer is considering adding the following sentence to the paragraph:

'Brass wire was relatively cheap and easy to acquire in nineteenth-century New York.'

Should the writer make this addition?

Read the following passage and focus on the underlined portion:

Wild yeast and bacteria drive the fermentation of sourdough bread, a process that yields its signature tangy flavor. This natural fermentation is currently slow at this time; however, the long rise allows complex organic acids to develop.

Which of the following options is the most effective and grammatically correct replacement for the underlined portion?

Although now cultivated in gardens worldwide, the Ginkgo biloba tree is native of the Zhejiang province in eastern China, where wild stands still survive.

Which choice best replaces the underlined portion of the sentence?

What is the greatest common factor of $36$ and $54$?

Ada Lovelace, a nineteenth-century mathematician, is widely celebrated as the world's first computer programmer. Working alongside Charles Babbage, Lovelace wrote notes on his analytical engine that included what is recognized as the first algorithm. While Babbage focused primarily on the mechanical calculations of the machine, Lovelace envisioned its potential to compose music and create art. In her writings, she explained these complex ideas with remarkable clarity, demonstrating a mind that was super smart and totally ahead of its time.

Which choice best maintains the formal, academic tone of the passage?

Astronomers have long been fascinated by Saturn’s rings, which are composed of billions of individual ice and rock particles. While early observers believed the rings were solid bands, modern space probes have revealed a highly dynamic system shaped by gravitational interactions with nearby moons. These moons act as "shepherds," clearing gaps in the ring material and maintaining the rings' sharp boundaries. The delicate balance of these structures is super cool to look at, prompting ongoing research into how planetary systems evolve over time.

Which of the following choices best maintains the style and tone of the passage?

A red light flashes every 8 seconds, and a blue light flashes every 12 seconds. If they both flash at the same instant, how many seconds will pass before they next flash at the same instant?

For all non-zero real numbers $x$ and $y$, let the operation $\star$ be defined by $x \star y = \frac{x}{y} - \frac{y}{x}$. Which of the following equations must be true for all non-zero real numbers $a$, $b$, and $c$?