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题目内容
Two sides of a right triangle have lengths $$5$$ and $$12$$.

Quantity A

The length of the third side of the triangle

Quantity B

$$11$$


$$PQ$$ is a diameter of the circle, line $$l$$ is tangent to the circle at $$P$$, line $$m$$ is tangent to the circle at $$Q$$, line $$n$$ is tangent to the circle, and $$x \lt 90$$.

Quantity A

$$RS$$

Quantity B

$$PQ$$
A ball is dropped from a height of $$6$$ meters and bounces to no more than $$90$$ percent of its original height. It falls back down and then repeatedly bounces to no more than $$90$$ percent of its maximum height after the previous bounce. What is the maximum height, in meters, that the ball can reach after the $$5th$$ bounce?
A sequence of numbers $$P_1, P_2, P_3.......P_n........$$ is defined as follows: $$P_1=1, P_2=2, and P_n=4\frac{P_n-1}{P_n-2}$$ for each integer $$n$$ greater than $$2$$. What is the value of $$P_4$$


The figure above shows the xy-coordinate system with its quadrants labeled. Line $$l$$ (not shown) has the equation $$y=ax+b$$, where $$a$$ and $$b$$ are constants $$a < 0$$, and $$b < 0$$. Which quadrant or quadrants cannot contain any part of line $$l$$?
Triangles $$ABC$$ has sides of lengths $$6, 7$$, and $$j$$, where $$j$$ is an integer. Triangle $$DEF$$ has sides of lengths $$2, 13$$, and $$j$$. What is the value of $$j$$?


A certain experiment consists of making $$25$$ observations of the variable $$x$$, which can have integer values between $$-3$$ and $$3$$, inclusive. The experiment was performed twice, and Tables I and II represent the results. Which of the three statistics- mean, median, and mode were the same both times the experiment was performed?


The table summarizes the waiting times, in minutes, of $$500$$ patients at a certain doctor's office. Of the $$500$$ waiting times, a waiting time of $$15$$ minutes is at the $$25$$th percentile and a waiting time of $$25$$ minutes is at the $$k$$th percentile.

Quantity A

$$k$$

Quantity B

$$50$$
If $$2^{3x} -64=0$$, what is the value of $$2^x$$?
$$n$$ and $$k$$ are integers greater than $$1$$ for which $$\sqrt{n^k}=(n^{13})\sqrt{n}$$

Quantity A

$$k$$

Quantity B

$$14$$


The right circular cylindrical tank above has inner dimensions of radius $$4$$ feet and height $$10$$ feet. What is the greatest possible distance, in feet, between $$2$$ points inside the tank?
Which of the following, if true, would most seriously weaken the argument given?
The unification of China in the third century B.C. may have contributed to the rise of a nomadic empire only two decades later in Central Asia. [hl:2]Skilled in archery and horsemanship[/hl:2], nomads formed armies in which every adult male could participate. Political power derived primarily from success in battle against other tribes and in raids on the Chinese, with the successful war chief securing his followers' loyalty by distributing booty. Because the nomadic elite derived power from distributing goods taken from the Chinese, nomadic politics evolved in close association with China. China' s increasing power required that nomads field larger armies themselves, and the prosperity of a united China offered wealth they could extract as payments. This redistribution of wealth generated the political power of nomadic rulers.
Which statement about nomadic armies is supported by the passage?
In context, the highlighted phrase serves in part to
Only since the 1970s have American scholars regularly included mortuary remains in their research on Merovingian Gaul in the early medieval period. Prior to the 1970s, most American medievalists neglected archaeological evidence from burial sites, including skeletal fragments and artifacts, in favor of more familiar historical and documentary sources. This oversight was dismissed by many European scholars as popular distaste in the United States for studies linked to death. Of greater consequence, however, were the small number of American archaeologists occupied with the early medieval period and the inaccessibility to American scholars of locally published and unpublished excavation reports in Western Europe. Lack of attention to important studies of Merovingian mortuary rites was thus not altogether surprising.
The author suggests that American scholars' lack of attention to Merovingian mortuary remains prior to the 1970s was due in part to the
The passage suggests which of the following about pre- 1970s research on Merovingian mortuary rites?
Montesquieu' s influence on James Madison and other founders of the American republic, particularly evident in the theory of separation of powers that informs the United States Constitution, is well noted by scholars. Madison' s critique of elements of Montesquieu' s political philosophy, however, has been given scant attention. The crux of Madison' s criticism concerned Montesquieu' s praise for the British system of balanced government. According to Montesquieu, the institutional and corporate division of powers and checks and balances established in Britain provided for political moderation and made the English constitution the model of free government in the modern world. Most English politicians and writers agreed with the general assumptions underlying the theory of balanced government advocated by Montesquieu; [hl:3]their disagreement[/hl:3] essentially concerned whether the parts of their government were effectively separated and balanced and thus whether liberty was sufficiently protected. A number of French thinkers disagreed with Montesquieu' s assumptions, rejecting their countryman' s theory of balanced government as any real guarantee of stability or safeguard for liberty. [hl:2]Interestingly, when Madison publicly invoked the name of Montesquieu in his writings of the early 1790s, it was primarily to challenge rather than to celebrate the political wisdom of the French oracle[/hl:2]. Madison' s proposed alternative to Montesquieu' s vaunted British model was grounded in the recognition of public opinion as the ruling authority in republican government.
The primary purpose of the passage is to

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