Tüm alıştırma soruları

A sequence of numbers begins with $t_1 = 4$. For all integers $n \geq 2$, each term is defined by $t_n = 3t_{n-1} - 2$. What is the value of $t_5$?

Which word best completes the blank in the passage below based on the structural contrast clue provided?

Which vocabulary choices best complete the passage below so that the blanks maintain logical coherence and inter-blank dependency?

At the beginning of a quarter, the cost of raw material for a manufacturing plant was $x$ dollars per ton. During the first month, the cost per ton increased by $15\%$. During the second month, the cost per ton decreased by $20\%$ relative to the first month's price. If the cost per ton at the end of the second month was $\$552$, what was the initial cost $x$, in dollars?

Read the passage below:

For decades, historical demographers treated nineteenth-century municipal censuses as remarkably (i)________ records, assuming that civic authorities recorded births and deaths with meticulous objectivity. Recent archival analysis, however, reveals that local magistrates frequently manipulated mortality figures to avoid public panic during epidemic outbreaks. Consequently, far from providing an unvarnished mirror of demographic reality, these registries offer a deeply (ii)________ account, requiring modern scholars to approach official statistics with unprecedented (iii)________.

Which of the following combinations of terms best completes the passage to preserve its logical and cross-sentence contextual coherence?

A plumbing service charges a flat diagnostic fee of $\$45$ plus $\$65$ for each hour of repair work. If the total bill for a repair job was $\$305$, how many hours of repair work were performed?

A contractor prepares a concrete mix using gravel and sand in a ratio of $4 : 7$ by weight. If the contractor uses $28$ tons of sand for a project, what is the total weight, in tons, of the concrete mix?

Read the following passage from an essay on architectural conservation:

'In mid-twentieth-century architectural conservation, practitioners frequently lauded concrete for its remarkable structural durability. Contemporary conservators, however, evaluate the material through a more dynamic lens, emphasizing instead its remarkably plastic nature—its capacity to deform under persistent loads and accommodate subtle seismic shifts over decades without catastrophic fracturing.'

In the context of the passage, which of the following words best captures the meaning of 'plastic' as it is used by contemporary conservators?

Read the passage below and select the word that logically completes the sentence.

Paradoxically, while early musicologists dismissed the traditional singers' performances as ________, recent acoustic re-examinations reveal that the musicians adhered to an astonishing degree of structural discipline and rhythmic precision.

Which of the following words best completes the blank?

Complete the passage by determining which terms best fill each corresponding blank to maintain cross-sentence contextual coherence.

On a real number line, point $A$ has coordinate $-5$ and point $B$ has coordinate $11$. Point $C$ has coordinate $x$ such that the distance between $C$ and the midpoint of line segment $AB$ is equal to $\frac{1}{3}$ of the distance between $C$ and point $B$. What is the maximum possible value of $x$?

For how many integer values of $x$ does the inequality $||2x - 7| - 5| \le 4$ hold true?

At a public university, the ratio of the number of undergraduate students to the number of graduate students at the beginning of an academic year was $4$ to $1$. By the end of the academic year, the number of undergraduate students had increased by $15\%$, and the total student population (undergraduate and graduate combined) had increased by $18\%$. By what percent did the number of graduate students increase?

Far from viewing the early naturalist's preliminary logs as (i)________ speculations lacking empirical rigor, contemporary historians of science maintain that these tentative observations were (ii)________ to the ultimate formulation of her unified theory; without these initial records, the overarching paradigm could never have been consolidated.

Which of the following combinations of words best completes the passage in a logically coherent manner?

In the $xy$-plane, line $L$ is given by the equation $4x + 3y = 24$. Line $M$ passes through the origin $(0,0)$ and is perpendicular to line $L$. Which of the following statements must be true? Select all that apply.

At a logistics company, fuel expenditure accounted for $40\%$ of total operational costs in Year 1, while maintenance expenditure accounted for the remaining $60\%$. In Year 2, fuel expenditure increased by $25\%$, and maintenance expenditure decreased by $15\%$. If there were no other operational costs in either year, by what percentage did the total operational cost change from Year 1 to Year 2?

An astronomical digital sensor captures $4.5 \times 10^7$ raw data packets during an observation run, where each packet has a size of $1.6 \times 10^{-4}$ megabytes. A compression algorithm reduces the total volume of these combined packets by $75\%$. What is the total volume, in megabytes, of the compressed data expressed in scientific notation?

At the beginning of Year 1, a commercial real estate portfolio consisted of two properties, Property A and Property B, where the value of Property A was $50\%$ greater than the value of Property B. During Year 1, the value of Property A increased by $20\%$ while the value of Property B decreased by $20\%$. During Year 2, the value of Property A decreased by $x\%$ while the value of Property B increased by $x\%$. If the combined value of the two properties at the end of Year 2 was equal to the combined value of the two properties at the beginning of Year 1, what is the value of $x$?

Three automated production lines—Line A, Line B, and Line C—run continuous maintenance cycles every $45$ minutes, $60$ minutes, and $75$ minutes, respectively. All three lines completed a maintenance cycle simultaneously at 8:00 a.m. on Monday. A supervisory inspection is triggered whenever at least two of the three lines complete a maintenance cycle at the exact same time. Between 8:01 a.m. on Monday and 8:00 a.m. on Tuesday, inclusive, how many supervisory inspections will be triggered?

On the real number line, $x$ is a real number such that its distance from $1$ is at most $6$, and its distance from $-2$ is at least $4$. Which of the following inequalities represents all possible values of $x$?