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16 "Hope Cup" The first day of the national mathematics invitational tournament 1 Questions and answers!
19th "Hope Cup" National Mathematics Invitational Tournament

(Exam 1, Grade One)

First, multiple-choice questions (40 points):

1、2008+2008-2008× ÷(-2008)=( )

A: In 2008; B, -2008; c、40 16; d、6024;

2. Among the four three-dimensional figures shown in the figure, one with a rectangular left view is ().

a、0; b、 1; c、2; d、3;

3. There are two conclusions as follows:

① There is at least one rational number between any rational number and its inverse number;

(2) If a rational number has a reciprocal, there is at least one rational number between this rational number and its reciprocal.

Then ()

A, ① and ② are all wrong; B, ① Yes, ② No; C, ① and ② are all fine; D, ① wrong, ② right;

4. There is a point A in the square, and the distance from each side is from small to large: 1, 2, 5, 6, then the area of the square is ().

a、33; b、36; c、48; d、49;

5. The number of digits of the product of 25 17×233 is ().

a、32; b、34; c、36; d、38;

(English-Chinese Dictionary: Numbers, Products)

6. The figure shows a semi-circular ADB with a diameter of AB and a sector with a central angle of 450.

ABC, then the ratio of the area of I to the area of II in the figure is ()

a、 1.6; b、 1.4; c、 1.2; d、 1;

7. Positive integers x and y satisfy (2x-5)(2y-5)=25, then the value of x+y is ().

a、 10; b、 18; c、26; D, 10 or18;

8. As shown in the figure, in the quadrilateral ABCD, AB=3, BC=4, CD=9, AD=a,

Then ()

a、a≥ 16; b、a < 2; c、2 < a < 16; d、a = 16;

9. There are 60 students in Class 7, Grade 1 (1), among whom 36 are in the math group. The number of people who participate in English group is 5 less than those who participate in math group, and the number of people who do not participate in two groups is 2 more than those who participate in two groups. Then the number of people participating in both groups at the same time is ().

a、 16; b、 12; c、 10; d、8;

The outer angles of the three inner angles A, B and C of 10 and △ABC are denoted as α, β and γ in turn. If β=2B and α-γ=400, the degrees of three internal angles A, B and C are () in turn.

a、600,600,600; b、300、600、900; c、400、600、800; d、500、600、700;

Two. Fill in the blanks in Group A (40 points):

1 1、( )÷[( )÷4-0.75]÷0.03 125= ;

12. It is estimated that the service export growth rate of the following six countries is as follows:

The United States, Germany, Britain, China, Japan and Italy.

-3.4% -0.9% -5.3% 2.8% -7.3% 7.3%

Then, according to the order of the growth rate of service exports of the above six countries from high to low, the third country is;

13, (x+5)2+ =0, then y2-=;

14, -2a+7 and are reciprocal, then a =;;

The elliptical orbits of 15 and "changmo-1" in orbit for the first time are shown in the figure, in which the black circle represents the earth with a radius of R=637 1km, a is perigee, 205km away from the earth, b is apogee, 50930km away from the earth (the known geocentric, perigee and apogee are in a straight line), and.

16. In Figure 5, MON is a vertical line. If angles α, β and γ satisfy β:α=2: 1, γ:β=3: 1, then the angle β =; (English-Chinese dictionary: straight line, straight line, angle, satisfaction)

17. After learning the algorithm of rational numbers, Xiao Ming compiled a program: when any rational number is input, the result on the display screen is always equal to the square of the input rational number minus 2. If he enters it for the first time and then enters the result, the result that appears on the display screen at this time is;

18. If the value of polynomial 2x2-x is equal to 1, the value of 4x4-4x3+3x2-x- 1 is equal to;

19. As shown in the figure, point m is the intersection of two bisectors at the inner corner of △ABC, and point n is the intersection of two bisectors at the outer corner of △ABC. If ∠ CMB: ∠ CNB = 3: 2, ∠CAB= degrees;

20. Two boxes of candy *** 176. Take 16 from the second box and put it in the first box. At this time, the number of sweets in the first box is 3 1 more than that in the second box (m is an integer greater than1), so there are at least sweets in the first box.

Three. Fill in the blanks in Group B (40 points):

2 1, a four-digit number with a decimal point becomes 2059.2 less than the original number, then this four-digit number is; Divided by 4, the remainder is;

22. It is known that positive integers A, B and C (where a≠ 1) satisfy abc=ab+30, then the minimum value of a+b+c is; The maximum value is;

23. The distance from the number axis to the origin is less than 5 and there are only two integers, and the sum of the corresponding numbers is;

24. Let A and B be the lengths of two sides of an isosceles triangle, respectively, and M be the perimeter of the triangle. If a, b and m satisfy the following equation:

The value of m is or;

25. Party A, Party B and Party C leave at the same time. Among them, Party C rode from Town B to Town A, while both Party A and Party B rode from Town A to Town B (Party A drove slowly at a speed of 24 kilometers per hour and Party B walked at a speed of 4 kilometers per hour). On the way, Party C and Party A met in Town D, rode back to Town B, and Party A turned around to meet Party B. Then when Party A received Party B, Party C had already returned to DB. After A receives B (B gets on A's car), he drives to B town at a speed of 88 kilometers per hour. As a result, three people arrived at B town at the same time, so the speed of C cycling was kilometers per hour.

Reference answer

First, multiple-choice questions (4 points for each small question)

The title is 1 23455 6789 10.

Answer D C A D B D D C B C c c

Second, group A multiple-choice questions (4 points for each small question)

1 1.2008; 12 Germany; 13.-94; 14. 1 1 15; 15.6.3877× 104;

16.40? ; 17.- 1 15 16; 18. 1; 19.36; 20. 13 1.

Three. Group B fills in the blanks (4 points for each question, 2 points for the first question, 2 1 two answers for each question)

2 1.2288 or 2080; 0; 22. 10; 53; 23.9; 0; 24. 163; 5; 25.57; Or eight.