1, it is known that three points A, B and C on the number axis represent rational numbers, which are 1 and-1 respectively, so it means ().

(a) the distance between points a and b (b) the distance between points a and c.

(c) Sum of distances from points A and B to the origin (d) Sum of distances from points A and C to the origin.

2. Wang Laobo bought five sheep in the market, with an average of RMB each, and later bought three sheep, with an average of RMB each. Later, he sold all the sheep at the price of each sheep and found himself losing money. The reason for the loss is ().

(a) (b) (c) and (d) have nothing to do with size.

3. The sum of two positive numbers is 60, and their least common multiple is 273, so their product is ().

273(B)8 19(C) 1 199(D) 19 1 1

4. A class of ***48 people went boating on the West Lake in Hangzhou in the spring, with 3 people per boat, and the rent was 16 yuan, with 5 people per big boat.

People, rent 24 yuan, then this class should at least spend rent ().

(A) 188 yuan (B) 192 yuan (C)232 yuan (D)240 yuan.

5. It is known that the circumference of a triangle is, one side is twice as long as the other, and the range of the smallest side of the triangle is ().

Between (a) and (b) and (c) and between (d) and.

6. Two identical bottles are filled with alcohol solution. The volume ratio of alcohol and water in one bottle is 1, and the volume ratio of alcohol and water in the other bottle is 1. Mix the two bottles together, and the volume ratio of alcohol to water in the mixed solution is ().

(A) (B)

(C) (D)

Second, fill in the blanks:

7, known,,, and > >, then =;

8, set a polynomial, when known = 0,; When,,

Then when =;

9. Arrange positive and even numbers into 5 columns according to the table below:

Column 1 column 2, column 3, column 4 and column 5

The first line 2 4 6 8

The second line16141210

Line 3 18 20 22 24

The fourth line 32 30 28 26

…… … … … …

According to the rules in the table, even numbers 2004 should be arranged in rows and columns;

10, Party A and Party B set off at the same time with their backs to point A on the 400m circular runway. Eight minutes later, they met for the fifth time. It is known that Party A walks 0. 1 meter more than Party B every second, so the shortest distance from the place where they met for the fifth time to point A along the runway is _ _ _ _ _ _ _ _ meters;

1 1. Someone asked Miss Li, "How many students are there in your class?" Teacher Li said: "Now half of the students in our class are taking part in the math contest, one quarter are taking part in the music interest group, one seventh are in the reading room, and three female students are watching TV." . So the number of students in teacher Li's class is;

12. As shown in the figure, B, C and D are three points on the line segment AE in turn. Given AE = 8.9 cm and BD = 3 cm, the sum of the lengths of all line segments at five points A, B, C, D and E in the figure is equal to.

13. An individual clothing dealer first buys a batch of children's clothes at the price of every three pieces 160 yuan, and then buys twice as many children's clothes at the price of every four pieces10 yuan. He wants to resell all these two batches of children's clothes at a profit of 20%, so he needs to sell them at the price of _ _ _ _ yuan for every three pieces.

14. If x and y are known to be satisfied, the value of the algebraic expression is _ _ _ _ _ _ _ _.

15,12+22+32+...+N2 =16n (n+1) (2n+1), then 22+42+62+...+.

Third, answer questions:

16, find the integer solution of inequality.

17. When the clock is at 12, the three hands overlap. How many minutes did it take the second hand to set the angle of the minute hand and the hour hand for the first time?

Acute angle) equally divided? (expressed in fractions)

18, Party A and Party B run at a constant speed along the circular runway, and start from both ends of the diameter AB in the opposite direction. When meeting for the first time, it is 0/00 meters away from point A/KLOC-,and when meeting for the second time, it is 60 meters away from point B. Find the total length of the circular runway.

19, five integers A, B, C, D, E, and their sums are 183, 186, 187, 190,19/kloc respectively. be called

(1) Find the values of a, b, c, d, e and x;

(2) If y= 10x+4, find the value of y.

"Hope Cup" Mathematics Invitational Tournament Training Questions 1

Multiple choice questions (only one of the four options in each of the following questions is correct)

The absolute value of 1 -7 is ()

(A)-7(B)-7(C)- 1/7(D) 1/7

2. The value of1999-is equal to ()

(A)200 1(B) 1997(C)200 1(D) 1999

3. Here are four propositions:

There is only one positive integer (1), and its inverse is the same.

(2) There is only one rational number and its inverse is the same.

③ Only one positive integer has the same reciprocal.

(4) There is only one rational number with the same reciprocal.

The correct proposition is: ()

(A)① and ② (B)② and ③

(C)③ and ④ (D)④ and ①

4.4 The similar item of AB C is ()

(A)4bc a (B)4ca b (C) ac b (D) ac b

The output of a product produced by a factory in July decreased by 20% compared with that in June. If the products in August are to reach the output in June, the output in August will be higher than that in July ()

(A)20% (B)25% (C)80% (D)75%

6. Among the four numbers, the number with the smallest absolute value of the difference between the sum is ().

(A) (B) (C) (D)

7. If x =- and y = 0.5, then x-y-? The value of 2X is ()

(A)0 (B) (C) (D) ―

8.ax+b=0 and mx+n=0 have the same solution equation about the unknown X, then there is ().

(A)A+m & gt； 0.(B)mb≥an。

(C)mb≤an。 (D)mb=an。

9. The result of (-1)+(-1)-(-1) × (-1) ÷ ().

(A)- 1 (B)

10. In the following operations, the error is ().

(A)2X +3X =5X (B)2X -3X =- 1

(C)2X？ 3X =6X (D)2X ÷4X =

1 1. Known

(A) 2 (B) 1 (C) 0 (D) -2

12. The result of calculating (-1)+(-1) ÷|-1| is ().

(A)0 (B) 1 (C)- 1 (D)2

13. Among the following formulas, the correct one is ().

(1) Answer? a =a . (B)(x ) =x。

(C)3 =9。 (D)3b？ 3c= 9 BC.

The negative reciprocal of the reciprocal of 14. -|-3 | Yes ()

(A)- (B) (C)-3 (D)3

15. 10 month/day, Xiao Ming counted that the average age of everyone is just 38 years old. Grandpa said that these people also got together on October 1st two years ago, so when they got together two years ago, their average age was () years old.

38 (B)37 (C)36 (D)35

16. If a

1 1a(B)- 1 1a(C)-3a(D)3a

17. If the rational number x. y satisfies | 2x- 1 |+(y+2) = 0, the value of x. y is equal to ().

(A)- 1 (B) 1 (C)-2 (D)2

18. The corresponding points of rational numbers A, B and C on the number axis are shown as follows: Then the correct one in the following formula is ().

(A)c + b >; a+b .(C)AC & gt； abdominal muscle

(B)cb <。 ab。 (D)CB & gt； abdominal muscle

19. Inequality < 1 has () positive integer solutions.

2 (B)3 (C)4 (D)5

20. A computer system can only execute one task at a time, and the next task can only be executed after the task is completed. At present, the time of U, V and W is 10 second, 2 minutes and 15 minutes respectively. The relative waiting time of a task is the ratio of the time from submitting the task to completing the task to the time of executing the task by the computer system, so the following four execution sequences make the sum of the relative waiting time of the three tasks minimum.

(A)U，V，W. (B)V，W，U

(C)W，U，V. (D)U，W，V

2 1. As shown in the figure, the lengths of line segments AD, AB, BC and EF are 1, 8, 3, 2, 5, 2 respectively, and the area of closed polyline AEBCFD is S, then the correct one of the following four options is ().

(A) S=7.5 (B) S=5.4

(C)5.4 & lt； S & lt7.5(D)4 & lt； S & lt5.4.

22. The number of participants in the first Hope Cup is 1 10000, and the number of participants in the tenth Hope Cup is 1480000, so the value closest to the average growth rate of participants in the first Hope Cup is ().

2 1.8%。 33.5% (C)45% (D) 50%

23. it is known that x and YI satisfy 3x+4y = 2, x-y.

(A) (B) (C) (D)

24. The following four sentences are correct ()

A. the greatest common divisor of positive integers a and b is greater than or equal to a.

B. The least common multiple of positive integers A and B is greater than or equal to ab.

C. the greatest common divisor of positive integers a and b is less than or equal to a.

D. the common multiple of positive integers a and b is greater than or equal to ab.

25. Given that a≤2, B ≥-3, c≤5 and A-B+C = 10, the value of A+B+C is equal to ().

10 (B)8 (C)6 (D)4

"Hope Cup" Mathematics Invitational Tournament Training Topic 2

26. The absolute value of-6 divided by the reciprocal is _ _.

27. expressed by scientific notation: 890000 = _ _ _ _.

28. Use rounding method to approximate 1999.509 (accurate to one place), and the approximate number is _ _.

29. Two rational numbers-12.43 and-12.45 are known. Then, the difference obtained by reducing the number of large numbers is _ _.

30. Known and similar items, then = _ _.

The sum of the negative reciprocal of 3 1 The reciprocal of -| 4 | is equal to _ _.

32. The effective number of the approximate number 0, 1990 is _ _.

33. The sum of the four numbers A, B, C and D is equal to -90, A is -4, B is +4, C is a multiple of -4, and D is the divisibility of -4, so the largest of the four numbers is greater than the smallest.

34. Given the formula+□ =, the number to be filled in is _ _.

35.( ÷ )÷ ___。

36. It is known that the complementary angle of angle A is equal to 3.5 times of angle A, then angle A is equal to _ _ degrees.

37. Given the equation (1.9x-1.1)-() = 0.9 (3x-1)+0.1,the value of x is _.

38. Building A is 24.5 meters higher than building C, and building B is 15.6 meters higher than building C, so building B is _ _ _ meters lower than building A..

39. As shown in the figure, if the sum of four numbers in four small triangles is equal to zero, then the sum of the absolute values of these four numbers is equal to _ _.

40. Equations 3mx+7 = 0 and 2x+3n = 0 about X are homotopy equations, then

x-2y= 1999

The solution of the 4 1. equation is _ _.

2x-y=2000

42. Xiaoming rides a bike from place A to place B, going uphill first and then downhill. It takes 34 minutes to return to place A immediately after arriving at place B. Given that the uphill speed is 400 meters/minute and the downhill speed is 450 meters/minute, the distance from place A to place B is _ _ meters.

43. My father is 24 years older than Xiao Ming, and the age of 1998 is three times that of Xiao Ming in 2000, so Xiao Ming is _ _ years old 1999.

44. If the known sum is similar, then _ _.

45.and = rules

46. They are all two-person buildings. Given that their minimum common multiple is 385, their maximum value is _ _.

47.A bottle of salt water concentration is 8%, B bottle of salt water concentration is 12%, two bottles of salt water * * weight1000g, A and B bottles of salt water concentration is 10.08%, then a bottle of salt water weighs _ _ _ grams.

48. As shown in the figure, there are _ _ triangles in the five-pointed star.

49. Known = _ _ _ _.

50. It is known that the series is 1, 1, 2, 3, 5, 8, 13, ... As the third number, each number is equal to the sum of its two neighboring numbers, then the remainder obtained by dividing the1999th number in the series by 3 is _.

"Hope Cup" Mathematics Invitational Tournament Training Topic 3

5 1. Divide a rectangle with the same length and width into six identical small rectangles.

Then draw a shape similar to the letter m in the rectangle, and remember the letter m.

If the graphic area is s, then s = _ _.

52. In rational numbers -3, +8,-,0. 1, 0,-10.5, -0.4, all positive sums are filled in the zero of the following formula, all negative sums are filled in the □ of the formal formula, and the calculation results of the following formula are filled in the horizontal line on the left of the equal sign. 〇÷□=__。

53. Number-filling calculation: fill in the smallest natural number in zero, the smallest non-negative number in δ, the integer not less than -5 and less than 3 in□, and write the calculation result of the following formula on the horizontal line to the right of the equal sign. (〇+□)×△=__。

54. Take three different numbers from the set, fill in □ as the maximum product that can be obtained, and fill in □ as the minimum product that can be obtained. Write the results of the following formula on the horizontal line on the right side of the equal sign. -(-□)÷〇=__。

55. Calculation:

56. There is such a simple algorithm to measure whether the weight is normal or not. The standard weight of boys (in kilograms) is the height (in centimeters) minus 1 10. The normal weight is between the standard weight loss 10% and the standard weight increase 10. It is known that student A is tall 16 1 cm and weighs W. If his weight is normal, the range of W's kilograms is _ _ _ _.

57. If a is a rational number, the minimum value of is _ _.

Calculation:

.

59. The position of rational number on the number axis is simplified as shown in the figure.

60. If x is a rational number, the minimum value of is _ _ _ _.

6 1. As shown in the figure, C is the midpoint of the AB line and D is the AC line.

At the midpoint, it is known that the sum of the lengths of all the line segments in the graph is 23.

Then the length of line segment AC is _ _ _ _ _.

62. Let sum be a non-negative integer, and the least common multiple of sum is known as 36.

63. Party A and Party B are at the starting line of100m. Party A stays where it is, and Party B runs to the end of 100 meters at a speed of 7 meters per second. Five seconds later, Party A heard Party B's cry and saw Party B fall to the ground. As we all know, the speed of sound propagation is 340 meters per second. At this time, Party B has run _ _ _ _ _ _ _ meters (accurate to one place).

64. An existing algebraic expression.

When the value of a numeric expression is, the value of an algebraic expression is.

65. As shown in the picture, a square with an area of 50 square centimeters is connected with another square.

It would be nice if you put a small square side by side.

The area is _ _ square centimeters.

66. The six digits 25 52 are all numbers greater than 7, and these six digits can be divisible by 1 1, so there are four digits.

67. Today, there are 1, 2,5 coins * *15, and the value of * * * is 52 cents, so the product of the number of three coins is _ _.

68. If the number of boys in a math group accounts for more than 40% and less than 50% of the total number of the group, then the math group has at least _ _ _ members.

69. Three numbers 1 and three numbers 2 can form _ _ different four digits.

70. Among the three digits, one hundred digits are less than ten digits, and those with ten digits less than one digit have _ _ * digits.

7 1. 1900 natural numbers 100- 1999, there are _ _ * ten digits that are the same as single digits.

72. Pythagoras was asked how many students there were in his school. He replied, "Half of the students are studying math, a quarter are studying music, a seventh are resting, and there are three female students left." How many students are there in Pythagoras' school?

A: There are _ _ students in Pythagoras' school.

73. The epitaph on the monument of Diophantu (a Greek mathematician in the second century) records: "The philosopher Diophantu buried here lived a long life, one-sixth of which was childhood, one-twelfth was a teenager, and one-seventh married a bride after his life, and gave birth to a son five years later. Unfortunately, his son only lived half his father's life, and his late father died four years ago. How long did Diophantu live?

A: The life span of Diophantine is _ _ years.

74. A child was asked how many brothers and sisters he had, and he replied, "As many brothers as there are, there are several sisters." Asked his sister how many brothers and sisters she has, she replied, "My brother is twice as old as my sister." Ask how many brothers and sisters they have.

They have _ _ brothers and _ _ sisters.

75. A said to B, "When I was your age, your salary this year was half my age. When you reach my age, I will be twice your age this year and seven years younger. " How old are they now? A: A is _ _ years old and B is _ _ years old.

"Hope Cup" Mathematics Invitational Tournament Training Question 4

answer the question

76. A bus travels from the departure station to the terminal station (including the departure station and the terminal station) for 8 stops. It is known that there are 0/00 people getting on at the first six stops and 80 people getting off at the terminal. How many passengers got on at the last six stops and got off at the terminal?

77. Known algebra, when the value is 1-, 2, 2, and not equal to 0, find the value of the algebra?

78. As shown in the figure, three marbles move counterclockwise at the same time on a circular track. It is known that A catches up with B in 10 second, C catches up with B again in 30 seconds, A catches up with B again in 60 seconds and C catches up with B again in 70 seconds. How long did it take B to catch up with C?

79. Rational numbers are not 0. Try to find the value of algebraic expression 2000.

80. Known as an integer, if so, please prove: