Cho đường thẳng (d): (y=(2m+1)x-2) với m là tham số và (m\ne-\frac{1}{2}.) Khoảng cách từ (A(-2;1)) đến đường thẳng d được tính theo công thức:

[\sqrt{(-2-(2m+1)(-2))^2+(1-(2m+1)(-2))^2}]

[\sqrt{(16m^2+20m+4)^2+(24m+4)^2}]

[\sqrt{256m^4+640m^3+320m^2+576m^2+960m+16}]

[\sqrt{256m^4+1216m^3+1536m^2+960m+16}]

[\sqrt{16m^2(16m^2+79m+96)+4(16m^2+79m+96)}]

[\sqrt{(4m+7)^2(4m+16)}]

Theo đề bài, khoảng cách này bằng (\frac{1}{\sqrt{2}}.) Do đó, ta có phương trình:

[\sqrt{(4m+7)^2(4m+16)}=\frac{1}{\sqrt{2}}]

Từ đây, ta được phương trình bậc hai:

[(4m+7)^2(4m+16)=1 ]

Giải phương trình này, ta được hai nghiệm:

[m=-\frac{3}{2}\pm\frac{\sqrt{3}}{2} ]

Do (m\ne-\frac{1}{2},) ta có nghiệm duy nhất là:

[m=-\frac{3}{2}+\frac{\sqrt{3}}{2}=\frac{5}{7} ]

Vậy, tổng các giá trị của m thỏa mãn bài toán là [\frac{5}{7}.]

Part 1: Read the following passage and mark the letter A, B, C or D on your answer sheet to indicate the correct word or phrase that best fits each of the numbered blanks from 25 to 28. (1.0 pt).

            English is the (25)_________ important language in the world today. A very large number of people understand and use English in all parts of the world. Indeed, English is very useful language. If we know English, we can go to any place or country we like. We shall not find it hard to (26)_________ people understand what we wish to say.English also helps us to learn all kinds of subjects. Hundreds of books are written in English everyday in all countries to teach people many useful things. The English language has therefore helped to spread ideas and knowledge to all the corners of the world. There is no subject that cannot be learned in the English language.

            As English is used so much everywhere in the world, it has helped to make the countries of the world become more (27)_________ with one another. The leaders of the world use English to understand one another. The English language has therefore also helped to spread better understanding and friendship among countries of the world. Lastly, a person (28)_________ knows English is respected by people. It is for all these reasons that I want to learn English.

Question 25: A. most                         B. mostly                     C. chiefly                    D. best

Question 26: A. get                            B. let                           C. persuade                 D. make

Question 27: A. friend                       B. friendly                   C. friendship               D. friendliness

Question 28: A. what                         B. whom                     C. who                        D. whose