A =/x-2001/ + /x-1/
Với x<1 ta có A = 2001 - x +1 -x =2002-2x. Khi đó A>2002
Với 1<= x <= 2001 ta có A = 2001-x +x-1 = 2000
Với x>2001ta có A=x-2001+x -1 = 2x -2000. Khi đó A> 2.2001 - 2000 =2002.
Vậy minA = 2000 khi 1<= x <= 2001.

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Cho tam giác cân ABC (AB = AC). Trên cạnh BC lấy điểm D, trên tia đối của tia CB lấy điểm E sao cho BD = CE. Các đường thẳng vuông góc với BC kẻ từ D và E cắt AB, AC lần lượt ở M, N. Chứng minh rằng:

a) DM = EN

Read the following passage and mark the letter A, B, C or D on your answer sheet to indicate the correct answer to each of the following questions.

         The economic expansion prompted by the Second World War triggered a spectacular population boom in the West. Of course, the region was no stranger to population booms. Throughout much of its history, western settlement had been characterized by spurts, rather than by a pattern of gradual and steady population growth, beginning with the gold and silver rushes of the 1850's and 1860's. The decade after the First World War - the 1920's - witnessed another major surge of people pouring into the West, particularly into urban areas. But the economic depression of the 1930's brought this expansion to a halt; some of the more sparsely settled parts of the region actually lost population as migrants sought work in more heavily industrialized areas. By 1941 when the United States entered the Second World War and began to mobilize, new job opportunities were created in the western part of the nation.

          If the expansion of industries, such as shipbuilding and aircraft manufacturing, was most striking on the pacific coast, it also affected interior cities like Denver, Phoenix, and Salt Lake City. Equally dramatic were the effects of the establishment of aluminum plants in Oregon and Washington and the burgeoning steel industry in Utah and California. The flow of people into these areas provided an enormous impetus to the expansion of the service industries - banks, health care services and schools. Although strained to the limit by the influx of newcomers, western communities welcomed the vast reservoir of new job opportunities. At the same time, the unprecedented expansion of government installations in the West, such as military bases, created thousands of new civilian openings. As land had served as a magnet for western migrants in the late nineteenth century, so wartime mobilization set in motion another major expansion of population. Indeed, it could be said that the entire western United States became a giant boomtown during the Second World War. This was especially true of California. Of the more than eight million people who moved into the West in the decade after 1940, almost one-half went to the Pacific coast. In fact, between 1940 and 1950, California's population surged by more than three million people.

The passage suggests that industrialization in the West led to all of the following EXCEPT  ______.

A. An increase in school construction.

B. Improved access to doctors.

C. An increase in the number of banks.

D. A reduction in the price of land.

A = 1+2+2²+2³+....+2¹⁰⁰

2A = 2+2²+2³+2⁴+...+2¹⁰¹

2A - A = 2¹⁰¹ - 1

=> A = 2¹⁰¹ - 1

=> A + 1 = 2¹⁰¹

=> 2⁵⁰.(A + 1) = 2⁵⁰.2¹⁰¹ = 2¹⁵¹

Mà 2⁵⁰.(A + 1) = 2^m

=> 2¹⁵¹ = 2^m

=> m = 151

Read the following passage and mark the letter A, B, C, or D on your answer sheet to indicate the correct answer to each of the questions.

Fish that live on the sea bottom benefit by being flat and hugging the contours. There are two very different types of flatfish and they have evolved in very separate ways. The skates and rays, relatives of the sharks have become flat in what might be called the obvious way. Their bodies have grown out sideways to form great “wings” They look as though they have been flattened but have remained symmetrical and “the right way up”. Conversely fish such as plaice, sole, and halibut have become flat in a different way. There are bony fish which have a marked tendency to be flattened in a vertical direction; they are much “taller” than they are wide. They use their whole vertically flattened bodies as swimming surfaces, which undulate through the water as they move. Therefore when * their ancestors migrated to the seabed, they lay on one side than on their bellies. However, this raises the problem that one eye was always looking down into the sand and was effectively useless - In evolution this problem was solved by the lower eye “moving” around the other side. We see this process of moving around enacted in the development of every young bony flatfish. It starts life swimming near the surface, and is symmetrical and vertically flattened, but then the skull starts to grow in a strange asymmetrical twisted fashion, so that one eye for instance the left, moves over the top of the head upwards, an old Picasso - like vision. Incidentally, some species of 20 flatfish settle on the right side, others on the left, and others on either side

According to the passage, the ability of a bony flatfish to move its eyes around is:

A. average

B. weak

C. excellent

D. variable