24th "Hope Cup" National Mathematics Invitational Tournament
The second exam of the second day of junior high school
20 13 April 15 8:30 am to 10:30 am.
First, multiple-choice questions (this big question * *10 small questions, 4 points for each small question, 40 points for food. Only one of the four options in each of the following questions is correct. Please write the English letters of the correct answers in brackets after each question.
1, the red ribbon is a symbol of international concern about AIDS prevention and treatment. Cut the red ribbon into small pieces with human glue, and tie the folded red ribbon tightly on the chest with a pin, as shown in figure 1. The pattern formed by overlapping red ribbons is ().
(a) Square (b) Rectangular (c) Diamond (d) Trapezoidal
2. Let a, b and c be nonzero real numbers, then the value of is ().
(A)3 species (B)4 species (C)5 species (D)6 species.
The side lengths of 3 and 3 are,, and are ()
(a) equilateral triangle (b) obtuse triangle (c) right triangle
acute triangle
4. The ancients recorded the order by heavenly stems and earthly branches, among which Tiangan had10; Underground branch12; Zi Chou Mao Yinchen applied for a memorial service at noon, and arranged Tiangan 10 and Dizhi 12 into the following two lines;
a，B，D，E，G，N，N，N，E，B，D，N，N，E，D ...
Mao Yinchen's third ugly son applied for Yin Mao ugly son at noon, and Tatsumi applied for ugly son at noon. ...
From left to right, the column 1 is Jiazi, the second column is Ugly B, and the third column is Bingyin ... That's how the calendar year in China is obtained. For example, 2007 is the year of dinghai in Gregorian calendar, so from now on, the year of Jiahai in Gregorian calendar is ().
(a) 20 19，(b) 203 1，(c) 2043，
(d) There is no corresponding year number.
5. Real numbers A, B, M and N satisfy A.
Then the relationship between m and n is ()
(A)M & gt； N(B)M = N(C)M & lt； N (D) cannot be determined.
6. Several squares and isosceles right triangles are spliced into the figure shown in Figure 2. If the side length of the largest square is 175px, then the sum of the areas of squares A, B, C and D is ().
(A) (B) (C) (D)
7. It is known that the inequality group about has exactly three integer solutions, so the range of a is ().
(A)≤≤B)≤≤C)