Điểm P nằm giữa hai điểm M và N thì:

A. PN + MN = PN     

B. MP + MN = PN

C. MP + PN = MN     

D. MP - PN = MN

Cho các số thực x, y, z  thay đổi và thỏa mãn điều kiện x 2 + y 2 + z 2 = 1 . Giá trị nhỏ nhất của biểu thức P = x y + y z + 2 x z 2 − 8 x + y + z 2 − x y − y z + 2  

A.  min P = − 5  

B.  min P = 5  

C.  min P = 3  

D.  min P = − 3

Cho hàm số y = x 3 + 3 x  có đồ thị là C ,     M 1  là điểm trên C  có hoành độ bằng 1. Tiếp tuyến tại điểm M 1  cắt  C  tại điểm M 2  khác M 1  Tiếp tuyến tại điểm  M 2  cắt  C  tại điểm M 3  khác  M 2 . Tiếp tuyến tại điểm M n - 1  cắt  C tại điểm M n  khác M n - 1 n ≥ 4 , n ∈ ?  Tìm số tự nhiên n thỏa mãn điều kiện y n - 3 x n + 2 21 = 0  

A. 7

B. 8

C. 22

D. 21

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 from 38 to 45.

A rather surprisingly geographical feature of Antarctica is that a huge freshwater lake, one of the world's largest and deepest, lies hidden there under four kilometers of ice. Now known as Lake Vostok, this huge body of water is located under the ice block that comprises Antarctica. The lake is able to exist in its unfrozen state beneath this block of ice because its waters are warmed by geothermal heat from the earth's core. The thick glacier above Lake Vostok actually insulates it from the frigid temperature (the lowest ever recorded on Earth) on the surface.

The lake was first discovered in the 1970s while a research team was conducting an aerial survey of the area. Radio waves from the survey equipment penetrated the ice and revealed a body of water of indeterminate size. It was not until much more recently that data collected by satellite made scientist aware of the tremendous size of the lake; satellite -borne radar detected an extremely flat region where the ice remains level because it is floating on the water of the lake.

The discovery of such a huge freshwater lake trapped under Antarctic is of interest to the scientific community because of potential that the lake contains ancient microbes that have survived for thousands upon thousands of years, unaffected by factors such as nuclear fallout and elevated ultraviolet light that have affected organisms in more exposed areas. The downside of the discovery, however, lies in the difficulty of conducting research on the lake in such a harsh climate and in the problems associated with obtaining uncontaminated samples from the lake without actually exposing the lake to contamination. Scientists are looking for possible ways to accomplish this.

The passage mentions which of the following as a reason for the importance of Lake Vostok?

A. It may contain uncontaminated microbes

B. It can be studied using radio waves

C. It has already been contaminated.

D. It may have elevated levels of ultraviolet light.