Theo Bất đẳng thức Cauchy, trung bình cộng của 2 số thực không âm lớn hơn hoặc bằng trung bình nhân của chúngA. Cho hàm chỉnh hình f xác định trên một miền của mặt phẳng phức,.[r]
(1)Mid-term Test (Time alloted: 60ms) I Choose the best answer for each question below
1 If it is now June, what month will be 400 months from now?
A January B April C June D October E Another answer If 5/9 of the members of the school chorus are boys, what is the ratio of girls to boys in the chorus?
A 4/9 B 4/5 C 5/4 D 9/4 E It can not be determined from the information given
What is the volume of a cube whose total surface area is 54? A B 54 C 27 D 81 E 729
If the lengths of two of the sides of a triangle are and 10, which of the following could be the length of the third side?
A B 11 C 21 D 23 E 19
If x is a positive integer, which of the following cann’t be an integer? A √(x-1) B.√(x^2 -1) C 1/x D (x+2)/(x+1) E 7/(x+1) If p pencils cost c cents, how many pencils can be bought for d dollars (knowing that 1$= 100 cents)?
A cdp B 100cdp C dp/(100c) D 100cd/p E 100dp/c Which of the following expresses the area of a circle in terms of C, its circumference?
A C^2 /(4π) B C^2/(2π) C √C/(2π) D Cπ/4 E C/(4π) Because her test turned out to be more difficult than she intended it to be, a teacher decided to adjust the grades by reducing only half the munber of points a student missed For example, if a student missed 10 points, he received 95 instead of 90 Befors the grades were adjusted, the class average was A, what was the average after the adjustment?
A 50+A/2 B (100-A)/2 C 100- A/2 D (50+A)/2 E A+25
Which is the greatest common factor of 4n+1 and 6n+2?
A B C D -1 E Not determined 10 If a square and an equilateral triangle have equal perimeters what is the ratio of the area of the triangle to the area of the square?
(2)II Indentify one underlined word or phrase that must be changed in order for sentences below to be correct.
1 If we divide 120 balls in parts, then each part has 40 balls A B C D
2 If the height of a cyclinder is times its circumference, what is the volume of A B C
the cyclinder in terms of it circumference? D
3 Multyplying with and dividing by then adding 3, we get the desired A B C D number
4 A geometric series in power of q with |q|< converge A B C D
5 With the development of modern technologies, applied mathematic is now A B C
studied more than ever D
6 If a square and an equilateral triangle have equal perimeters, what is the ratio A B C
of the area of the triangle and the area of the square? D
7 Many branch of mathematics such as differential equation, probability… A B
examine and describe real phenonmina by equations C D
8 Let E be a Banach space of infinite dimension and f: E → E a compact A
operator which is one-to-one, then the converse of A, denoted by A^-1 must B C D
be unbounded
9 Put a = xy + yz +zx then the inequality above is rewritten in the form A B C
(3)
10 A continuous function f defines in a compact metric spcace with real values A B C
attains its maximum and minimum D
III. Translate the following sentences into English
1 Theo Bất đẳng thức Cauchy, trung bình cộng số thực không âm lớn trung bình nhân chúng Dấu xảy hai số
……… ……… ……… ……… Godel Cohen sử dụng ý tưởng logic trừu tượng để chứng minh giả thuyết continuum độc lập với tiên đề lý thuyết tập hợp
……… ……… ……… ………
3 Nghịch lý tiếng Zeno chứng sống động cho thấy nhà toán học cổ Hy Lạp cách đơn giản không hiểu khái niệm giới hạn
……… ……… ……… Cho hàm chỉnh hình f xác định miền mặt phẳng phức,
được kí hiệu Ω, tức tập mở liên thông Hơn giả sử f khác Ω Khi tồn hàm chỉnh hình g Ω cho f = e^g
(4)……… ……… Đối với hình chữ nhật có chu vi, chênh lệch
độ dài hai cạnh chúng nhỏ diện tích chúng lớn ……… ……… ………
IV. Solve problems below in English
1 There are popular music CDs and classical music CDs You choose CDs from them How many ways to perform this task in each of the following case?
a, Choose randomly
b, At least one in Cds is of popular music and so is classical music
In the figure below, Q is a point on the circlle whose center is O and whose radius is r, and OPQR is a rectangle What is the length of diagonal PR?
P Q